A negative exponent indicates that the base should be inverted or flipped, and the exponent should become positive. Therefore, -45 in positive exponent form would be: 1/ (45²1) or 1/45
What is a negative component?
A negative exponent is a mathematical notation indicating that the number or variable should be inverted or flipped, and the exponent should be made positive. In other words, a negative exponent represents the reciprocal of the number or variable raised to the corresponding positive exponent.
For example, 2²-3 is read as "2 to the power of negative 3" and represents 1/(2²3), which is equal to 1/8. Similarly, x²-2 is read as "x to the power of negative 2" and represents 1/(x²2), which is the reciprocal of x squared.
Negative exponents are used in various mathematical and scientific applications, such as in calculations involving very small or large numbers, in scientific notation, and in the rules of exponents.
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Complete question:
Write -45 in positive exponent form.
Factor completely.
mx^2-my^2
Thank you :DD
Since both terms are perfect squares, factor using the difference of squares formula, [tex]a^2-b^2=(a+b)(a-b)[/tex] where [tex]a=x[/tex] and [tex]b=y[/tex]
Answer:[tex]m(x+y)(x-y)[/tex]the cost for an upcoming field trip is 20 dollars the cost of the feild trip c is a function of the number of students x select all the possible outputs for the function defined by c(x)=20x
20 is the possible outputs for the function defined by c(x)=20x for all of the students that would pay for the field trip
How to solve for the functionThe function that is known to represent what would be the cost of the trip of these students is given as C(x)=20x.
The cost of the trip for one of the students is put at 20 dollars each.
We would have x as the total number of those that would be attending this trip. In order to get the output that would show us the cost of the trip.
We take X to be a whole number.
then x = 1
such that that c(1) = 20(1) = 20
Then the total is 20 per student
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the cost for an upcoming field trip is 20 dollars the cost of the feild trip c is a function of the number of students x select all the possible outputs for the function defined by c(x)=20x
A 20 B 30 c 50
The mean height of 15 pupils is 159 cm. One of these pupils is 148 cm and leaves the group. Determine the new mean height of the group. Give your answer correct to 1 decimal place.
Using the mean formula we know that the new mean height of 14 people is 159.7 cm.
What is mean?A mean in math is the average of a data set, calculated by adding all numbers together and then dividing the total of the numbers by the number of numbers.
For illustration, with the dataset containing: 8, 9, 5, 6, 7, the mean is 7, as 8 + 9 + 5 + 6 + 7 = 35, 35/5 = 7.
The mean height given is 159 cm.
Let, x1, x2, x3 ..... x15 be the height of 15 people.
x1+x2+x3 ..... x15/15 = 159
x1+x2+x3 ..... x15 = 159 * 15 = 2385 cm ...(1)
Let, x1 = 148 cm, who leaves the group.
148+x2+x3 ..... x15 = 2385 cm
x2+x3 ..... x15 = 2237 cm
Now, we have 14 people.
New mean = x2+x3 ..... x15/14
= 2237/14
= 159.7 cm
Therefore, using the mean formula we know that the new mean height of 14 people is 159.7 cm.
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Square ABCD is similar to square EFGH. The ratio of AB:EF is 1:4. The area of square EFGH is 14,400ft ft squared by 2. What is AB?
The Length of AB in square ABCD is 30 feet.
Since the squares ABCD and EFGH are similar, their corresponding sides are proportional, so we can set up the following relation:
AB/EF = 1/4
We can also use the fact that the ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding sides. Therefore,
AB²/EF² = (Area of square ABCD)/(Area of square EFGH)
Substituting the given values:
AB²/EF² = (Area of square ABCD)/(14400)
Since the areas of squares are proportional to the square of their sides, we can write,
Area of square ABCD/Area of square EFGH = (AB/EF)²
Substituting this into the above equation and solving for AB, we get,
AB²/EF² = (AB/EF)²
AB² = (AB/EF)² * EF²
AB² = (1/4)² * 14400
AB² = 900
AB = 30 feet
Therefore, the length of the side AB of square ABCD is 30 feet.
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M/S Sing Trader purchased refrigerator for Rs.10,000 taxable amount. They sold it to
Amrutbhai for Rs. 12,000 taxable amount. The rate of GST is 28%, then find the CGST
and SGST to be paid by M/S Sing Trader
The CGST and SGST that M/S Sing Trader must pay as the GST rate is 28% is Rs. 280 CGST and Rs. 280 SGST.
Given that,
M/S Sing Trader spent Rs. 10,000 in taxable revenue for a refrigerator. For a taxable amount of Rs. 12,000, they sold it to Amrutbhai.
We have to find the CGST and SGST that M/S Sing Trader must pay as the GST rate is 28%.
We know that,
Input tax = 10000 × 28%
Output tax = 12000 × 28%
GST payable = 12000 × 28% - 10000 × 28%
GST payable = 28% (12000-10000)
GST payable = 28% (2000)
GST payable = [tex]\frac{28}{100}[/tex](2000)
GST payable = 28×20
GST payable = 560
CGST = SGST = [tex]\frac{GST}{2}[/tex] = [tex]\frac{560}{2}[/tex] = Rs. 280
Therefore, The CGST and SGST that M/S Sing Trader must pay as the GST rate is 28% is Rs. 280 CGST and Rs. 280 SGST.
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A letter is chosen at random from the word "COVID NINETEEN Find the probability that the letter in () a vowel () a consonant
The probability of selecting a vowel at random from the word "COVID NINETEEN" is 0.357, and the probability of selecting a consonant at random is 0.643.
The word "COVID NINETEEN" has a total of 14 letters. We can count the number of vowels and consonants in the word to determine the probability of selecting a vowel or a consonant at random.
There are five vowels in the word: O, I, E, E, and E.
Therefore, the probability of selecting a vowel at random is:
P(vowel) = number of vowels / total number of letters
= 5 / 14
= 0.357 or approximately 35.7%
There are nine consonants in the word: C, V, D, N, T, N, T, N, and N.
Therefore, the probability of selecting a consonant at random is:
P(consonant) = number of consonants / total number of letters
= 9 / 14
= 0.643 or approximately 64.3%
Therefore, the probability of selecting a vowel at random from the word "COVID NINETEEN" is 0.357, and the probability of selecting a consonant at random is 0.643.
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Pls answer this!!!!
with simple working out
<333
Answer:
Step-by-step explanation:
A is 40
B 3 on the the top after 9 is 27
term is 3
c is 4 on top after 32 is 128
term is 4
d after 300 is 3,000
term is 10
If Julie drives from York to corby via Derby. How many miles will she drive
Julie will have driven a total distance of 289 miles if she travels from York to Corby via Derby.
Starting from York, Julie needs to travel to Derby. The distance between York and Derby is given as 89 miles. So, we know that Julie will have driven 89 miles once she reaches Derby.
Next, Julie needs to travel from Derby to Corby, but the given information is a bit tricky here. The distance from Derby to Corby is not given directly. Instead, we are given two distances - Derby to Dory and Dory to Corby.
To find the distance from Derby to Corby, we need to add the distances between Derby and Dory, and Dory and Corby. From the question, we know that the distance between Derby and Dory is 127 miles and the distance between Dory and Corby is 73 miles. Adding these two distances gives us the total distance from Derby to Corby, which is 200 miles.
Finally, we can add up the distances traveled between each location to find the total distance traveled by Julie. Adding the distances of each leg of the journey, we get:
89 miles (York to Derby) + 200 miles (Derby to Corby via Dory) = 289 miles
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Complete Question:
If Julie drives from York to Corby via Dory how many miles will she have driven?
York 89
Derby 127 73
Corby
Graph the line with slope -1/5 and y-intercept of -5
A graph of the line with slope -1/5 and y-intercept of -5 is shown in the image attached below.
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is represented by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represent the vertical intercept, y-intercept or initial value.Based on the information, an equation that models the line is given by this mathematical expression;
y = mx + c
y = -x/5 - 5
In this exercise, we would use an online graphing calculator to plot the above equation as shown in the graph attached below.
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Write the equation of a line that is perpendicular to y=½x - 9 and passes through the point (3, -2).
Answer:
y = - 2x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = [tex]\frac{1}{2}[/tex] x - 9 ← is in slope- intercept form
with slope m = [tex]\frac{1}{2}[/tex]
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (3, - 2 ) into the partial equation
- 2 = - 2(3) + c = - 6 + c ( add 6 to both sides )
4 = c
y = - 2x + 4 ← equation of perpendicular line
Which expression is equivalent to (4−2x)(4+2x)
The expression that is equivalent to (4 - 2x)(4 + 2x) is equal to 16 - 4x^2 approximately.
To simplify the expression (4 - 2x)(4 + 2x), we can use the FOIL method, which stands for First, Outer, Inner, Last. This method involves multiplying each term in the first factor by each term in the second factor and then combining like terms.
Using the FOIL method, we get:
(4 - 2x)(4 + 2x) = 4 × 4 + 4 × 2x - 2x × 4 - 2x × 2x
Simplifying the expression, we get:
16 + 8x - 8x - 4x^2
The two middle terms cancel each other out, leaving us with:
16 - 4x^2
We can also check our answer by factoring the simplified expression back to the original expression. If we factor 16 - 4x^2, we get:
16 - 4x^2 = 4(4 - x^2)
We can then use the difference of squares formula, which states that a^2 - b^2 = (a + b)(a - b), to factor further:
4(4 - x^2) = 4(2 + x)(2 - x)
This gives us back the original expression, (4 - 2x)(4 + 2x), confirming that 16 - 4x^2 is equivalent to (4 - 2x)(4 + 2x).
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You invest $20 000 in a building society account, which pays 4% interest each year. If the interest is added to the account at the end of each year. What is the value of the account after 2 years?
Answer:
21632
Step-by-step explanation:
20000×1.04=20800
20800×1.04=21632
NEED HELP DUE TODAY!!!! GIVE GOOD ANSWERS PLEASE!!!!
2. How do the sizes of the circles compare?
3. Are triangles ABC and DEF similar? Explain your reasoning.
4. How can you use the coordinates of A to find the coordinates of D?
The triangle DEF is twice the size of the triangle ABC, and the triangles are similar triangles as the sides of the triangles are in correspondence.
Define similar triangles?Triangles that resemble one another but may not be precisely the same size are said to be comparable triangles. When two objects have the same shape but different sizes, they can be said to be comparable. This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is referred to as "similarity".
According to the figure, AB = 1 DE = 2
Therefore, the triangle DEF is twice as big as the triangle ABC.
Absolutely, there are similarities between the triangles ABC and DEF.
This is due to the fact that triangle ABC's corresponding side is twice as long as DEF's corresponding side and the angle provided are same.
Therefore, Multiplying the coordinates of A by 2 provides coordinates of D.
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Write a method removeAll that removes all occurrences of a particular value. For example, if a variable list contains the following values:[3, 9, 4, 2, 3, 8, 17, 4, 3, 18]The call of list.removeAll(3); would remove all occurrences of the value 3 from the list, yielding the following values:[9, 4, 2, 8, 17, 4, 18]If the list is empty or the value doesn't appear in the list at all, then the list should not be changed by your method. You must preserve the original order of the elements of the list.
It should be noted that this approach follows the need to maintain the list's original order of elements.
what is function ?A function is a relationship between a set of possible outcomes (referred to as the range) and a set of inputs (referred to as the domain), with the property that each input is associated to exactly one output. A function, then, is a mathematical rule that designates a specific output value for each input value. Equations, graphs, and tables are frequently used to represent functions. They are employed to mimic real-world occurrences and to address issues in numerous branches of mathematics, science, engineering, and other disciplines.
given
The value to be deleted from the list is represented by an integer value that the method accepts as an argument.
The method iterates through the list's components using a while loop.
The method determines if the current element equals the requested value while it is in the loop. If so, the procedure uses the ArrayList class's remove method to remove the element from the list. If not, the method increases the index variable and moves on to the next element.
The procedure keeps going over the list until all instances of the given value have been eliminated.
It should be noted that this approach follows the need to maintain the list's original order of elements.
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1)A factory makes propeller drive shafts for ships. A quality assurance engineer at the factory needs to estimate the true mean length of the shafts. She randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. The lengths are known to follow a normal distribution whose standard deviation is 2 mm. Calculate a 95% confidence interval for the true mean length of the shafts. Input your answers for the margin of error, lower bound, and upper bound.
a)Determine Margin of Error for this 95% confidence interval.
b)Input the lower bound. (Round to three decimal places)
c)Input the upper bound. (Round to three decimal places)
2)To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean μ and standard deviation σ = 0.01 g. How large should n be so that a 95% confidence interval for μ has a margin of error of ± 0.0001?
3)A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis for the standard treatment is two years. So the null hypothesis is that average survival time after diagnosis is the same for the new treatment and the standard treatment.
In an early trial, she tries the new treatment on three subjects, who have an average survival time after diagnosis of 4.5 years. Even though the sample is small, the results are statistically significant at the 0.05 significance level. Consequently, she rejects the null hypothesis.
In a future study, it is determined that the new treatment does not increase the mean survival time in the population of all patients with this particular type of cancer. The researcher has
Committed a type I error.
Incorrectly used a 0.05 significance test when she should have computed the P-value.
Incorrectly used a 0.05 significance level when she should have used a 0.01 significance level.
Committed a type II error.
4)If the level of significance, α{"version":"1.1","math":"\alpha"}, is made very small, thereby making the probability of committing a Type 1 error very small, what happens to the probability of committing a Type 2 error?
By reducing the probability of committing a Type 1 error, we increase the probability of committing a Type 2 error.
There is no specific relationship between the two probabilities.
By reducing the probability of committing a Type 1 error, we also reduce the probability of committing a Type 2 error.
The relationship between the two probabilities depends on how the study is set up.
Therefore, with a 95% confidence interval, we can estimate the true mean length of the drive shafts to be between 992.16 mm and 1007.84 mm.
The true mean length of the drive shafts can be estimated using a 95% confidence interval. The margin of error is calculated as 2*1.96*2 = 7.84 mm. The lower bound of the confidence interval is 1000 - 7.84 = 992.16 mm and the upper bound is 1000 + 7.84 = 1007.84 mm.
This confidence interval states that there is a 95% probability that the true mean length of the drive shafts falls within the range of 992.16 mm to 1007.84 mm. The relationship between the two probabilities is that the probability of the true mean length falling within the confidence interval is 95%. If the sample size was increased, the margin of error would decrease, resulting in a tighter range and higher probability that the true mean would fall within the confidence interval.
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what are the roots of 2x^2+10x+9=2x
The roots of the equation 2x² + 10x + 9 = 2x does not exist i.e no real roots
Calculating the roots of the equationTo find the roots of the given quadratic equation 2x² + 10x + 9 = 2x, we can start by rearranging the equation to the standard form of a quadratic equation
2x² + 10x + 9 - 2x = 0
Simplifying the left-hand side, we get:
2x² + 8x + 9 = 0
Now, we can use the quadratic formula to find the roots of the equation:
x = (-b ± √(b² - 4ac)) / 2a
where a = 2, b = 8, and c = 9.
Substituting these values into the formula, we get:
x = (-8 ± √(8² - 4(2)(9))) / 2(2)
Simplifying the expression under the square root, we get:
x = (-8 ± √-8) / 4
The square root of -8 is not a real number
So, the equation has no real root
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Alan is designing a costume for a
play. The graph shows the time it
takes him to sew the fabric. What
length of fabric can Alan sew in
1.5 minutes?
120
100
€80
Length (ft)
60
40
20
O
y
1
2 3 4
Time (min)
Alan can sew 60 feet of fabric in 1.5 minutes.
Describe Slope?In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the change in the vertical (y) coordinate to the change in the horizontal (x) coordinate between two points on the line. In other words, slope represents the rate at which the line is rising or falling. The slope of a line can be positive, negative, zero or undefined, depending on the direction and steepness of the line. The slope formula is given by:
slope = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line. The slope is often denoted by the letter m.
We can see that the relationship between time and length of fabric is a linear one. Using the two given points (1, 40) and (2, 80), we can find the slope of the line:
slope = (change in y) / (change in x) = (80 - 40) / (2 - 1) = 40
This means that for every 1 minute, Alan can sew 40 feet of fabric. To find how much fabric he can sew in 1.5 minutes, we can use the equation for a line:
y = mx + b
where y is the length of fabric, x is the time in minutes, m is the slope we just found, and b is the y-intercept (which we can find by plugging in one of the points).
Using the point (1, 40), we get:
40 = 40(1) + b
b = 0
So the equation for the line is:
y = 40x
To find the length of fabric Alan can sew in 1.5 minutes, we plug in x = 1.5:
y = 40(1.5) = 60
Therefore, Alan can sew 60 feet of fabric in 1.5 minutes.
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The complete question is:
The following is a list of prices for zero-coupon bonds of various maturities. a. Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four years. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) YTM Maturity (Years) 1 Price of Bond $ 945.90 $ 911.47 % 2 % 3 $ 835.62 % % 4 $ 770.89 b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Maturity (years) 1 2 3 4 Price of Bond $ 945.90 911.47 835.62 770.89 Forward Rate Maturity (Years) 2 3 $ % Price of Bond 911.47 835.62 770.89 $ $ 4 % The following is a list of prices for zero-coupon bonds of various maturities. a. Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four years. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Answer is complete and correct. Maturity (Years) YTM 1 $ 5.72 % $ Price of Bond 945.90 911.47 835.62 770.89 2 3 4.74 6.17 >>> % % % 4 S 6.72 b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. Assume annual coupon payments. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Maturity (years) 1 2. 3 4 Price of Bond $ 945.90 911.47 835.62 770.89 Answer is complete but not entirely correct. Price of Bond Forward Rate Maturity (Years) 2 $ 911.47 3.79 % 3.60 X % 3 $ 835.62 4 770.89 2.89 x %
For the fourth-year forward rate: The forward rate is equaI to [(770.89/835.62)(1/(4-3)] - 1 = 0.0289 or 2.89% .
What is equation ?An equation in mathematics is a cIaim that two mathematicaI expressions are equivaIent. The Ieft-hand side (LHS) and the right-hand side (RHS), which are separated by the equaI sign ("="), make up an equation. Equations are a common tooI for probIem-soIving and determining the vaIue of an unknowabIe variabIe since they are used to describe mathematicaI reIationships.
given
I For a bond having a one-year maturity:
[tex]YTM = [(1000/945.90)^{(1/1)}] - 1 = 0.0572 or 5.72%[/tex]
(ii) For a bond having a two-year maturity:
[tex]YTM = [(1000/911.47)^{(1/2)}] - 1 = 0.0474 or 4.74%[/tex]
(iii) For a bond having a three-year maturity:
[tex]YTM = [(1000/835.62)^{(1/3)}] - 1 = 0.0617 or 6.17%[/tex]
(iv) For a bond with a four-year maturity:
[tex]YTM = [(1000/770.89)^{(1/4)}] - 1 = 0.0672 or 6.72%[/tex]
We can use the foIIowing formuIa to determine the forward rates:
Forward rate is equaI to [((Bond Price 1/Bond Price 2)(1/(n2-n1))]]. - 1
where n₂-n₁ is the time period between the maturities, Price of Bond 1 is the price of the bond with maturity n₁, and Price of Bond 2 is the price of the bond with maturity n₂.
We may determine the forward rates using the bonds' current prices by foIIowing these steps:
I For the second-year forward rate:
((911.47/945.90)(1/(2-1))) is the forward rate. - 1 = 0.0379 or 3.79%
(ii) For the third-year forward rate:
The forward rate is equaI to [((835.62/911.47)(1/(3-2))] - 1 = 0.0360 or 3.60%
For the fourth-year forward rate: The forward rate is equaI to [(770.89/835.62)(1/(4-3)] - 1 = 0.0289 or 2.89% .
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Let A and B be arbitrary matrices for which the indicated product is defined. Determine whether the statement below is true or false. Justify the answer. The second row of AB is the second row of A multiplied on the right by B. Choose the correct answer below. OA. The statement is true. Let row (A) denote the ith row of matrix A. Then row (AB) = row (A)B. Letting i = 2 verifies this statement OB. The statement is false. The second row of AB is the second row of A multiplied on the left by B. OC. The statement is true. Every row and column of AB is the corresponding row and column of A multiplied on the right by B. OD. The statement is false. Let column (A) denote the ith column of matrix A. Then column (AB) =column (A)B. The same is not true for the rows of AB.
The second row of AB is indeed the second row of A multiplied on the right by B, which confirms that the statement is true.The correct answer is actually OA.
To justify that the statement is True we consider the following steps:
Let row(A) denote the [tex]i_{th}[/tex] row of matrix A. Let A and B be arbitrary matrices for which the indicated product is defined. Therefore, the second row of AB is the second row of A multiplied on the right by B.Then row(AB) = row(A)B. Letting i = 2 verifies this statement.Consider the (i,j) entry of the product AB. By the definition of matrix multiplication, this entry is given by the dot product of the [tex]i_{th}[/tex] row of A with the [tex]j_{th}[/tex] column of B. This means that the entire[tex]i_{th}[/tex]row of AB is obtained by multiplying the [tex]i_{th}[/tex]row of A on the right by B.Therefore, the second row of AB is indeed the second row of A multiplied on the right by B, which confirms that the statement is true.
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48 Points I, M, G, and N form a square on the Argand diagram. If points I, M, and G correspond to complex numbers 2+2i, 3−3i, −2−4i, respectively, then find the complex number that corresponds to point N. Find the length of the diagonal of the square IMGN.
Answer:
Since points I, M, G, and N form a square, we know that the diagonal IM is perpendicular to GN and has the same length as GN. Therefore, to find the complex number corresponding to point N, we can find the midpoint of the diagonal IM and then rotate it 90 degrees counterclockwise to get the corresponding point N.The midpoint of IM is (2+3)/2 + (2−3)/2 i = 5/2 − 1/2 i. To rotate this point counterclockwise by 90 degrees, we can swap the real and imaginary parts and negate the new real part. This gives us the complex number −1/2 + 5/2 i, which corresponds to point N.
To find the length of the diagonal IMGN, we can first find the length of the side of the square. The side length is the distance between I and M, which is |3−2i−2−2i| = |1−4i| = sqrt(1^2+4^2) = sqrt(17).
The diagonal IMGN is the hypotenuse of a right triangle with sides of length sqrt(17), so we can use the Pythagorean theorem to find its length:
|IMGN| = sqrt(2)*|IM| = sqrt(2)*sqrt(17) = sqrt(34).
Therefore, the complex number corresponding to point N is −1/2 + 5/2 i, and the length of the diagonal IMGN is sqrt(34).
Answer: Point N: -3+i
Diagonal length: sqrt52
Step-by-step explanation:
You can start by finding point N by graphing all the other solutions on an x-y graph, using a+bi. Where a=the x point, b= the y point. After looking at this you can deduct that point N has to be at -3+i. Because the x between I and M is 1, the distance between G and N has to be 1 too. Repeat with Y.
Next, you use Points N and M to find the distance. You use the same concept that a=x, and b=y and plug this into the distance formula. You would get sqrt(-3-3)^2+(1+3)^2. This evaluates to sqrt52.
assuming the conditions for inference have been met, does the coffee shop owner have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5 percent level of significance? conduct the appropriate statistical test to support your conclusion.
The coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
What is proportion ?
A proportion refers to the number or fraction of individuals or items that exhibit a particular characteristic or have a certain attribute, relative to the total number or sample size being considered. It is often expressed as a ratio or percentage.
To test whether the distribution of sales is proportional to the number of facings, we can use the chi-squared goodness of fit test. The null hypothesis for this test is that the observed data follows a specific distribution (in this case, a proportional distribution), while the alternative hypothesis is that the observed data does not follow that distribution.
To conduct the test, we first need to calculate the expected frequency for each category assuming a proportional distribution. We can do this by multiplying the total number of sales (610) by the proportion of facings for each brand:
Starbucks: 610 x 0.3 = 183
Dunkin: 610 x 0.4 = 244
Peet's: 610 x 0.2 = 122
Other: 610 x 0.1 = 61
Next, we calculate the chi-squared statistic using the formula:
χ² = Σ((O - E)² / E)
where O is the observed frequency and E is the expected frequency. The degrees of freedom for this test are (k-1), where k is the number of categories. In this case, k = 4, so the degrees of freedom are 3.
Using the observed and expected frequencies from the table, we get:
χ² = ((130-183)²/183) + ((240-244)²/244) + ((85-122)²/122) + ((155-61)²/61) = 124.36
Looking up the critical value of chi-squared for 3 degrees of freedom and a significance level of 0.05, we get a value of 7.815. Since our calculated χ² value of 124.36 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that the observed distribution of sales is not proportional to the number of facings.
Therefore, the coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.
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Find the sum
2 1/6 + 1/2
Answer:
[tex]\frac{7}{4}[/tex]
Step-by-step explanation:
mixed fraction [tex]\frac{13}{6}[/tex]
sum =[tex]\frac{13}{6}[/tex] +[tex]\frac{1}{2}[/tex] ( LCM)= 12
[tex]\frac{13}{6}[/tex]×[tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex]×[tex]\frac{6}{6}[/tex]
[tex]\frac{26+2}{12}[/tex]
[tex]\frac{28}{12}[/tex] Simplify = [tex]\frac{7}{4}[/tex]
Suppose x has a distribution with µ=15 or σ =14. (a) If random sample of size n= 49 is drawn, find µx, σx, and P(15≤x≤17) (b) If a random sample of size n=64 is drawn, find µx, σx, and P(15≤x≤17) (c) Why should you expect the probability of part (b) to be higher than that of part (a)? Hint: Consider the standard deviations in part (a) and (b).
(a) μx=15 and σx=2And, P(15≤x≤17) can be obtained by converting the corresponding x values into z scores.z1=15−15/2=0z2=17−15/2=1P(15≤x≤17) = P(0≤Z≤1) = 0.3413
(b) μx=15 and σx=1.75 And, P(15≤x≤17) can be obtained by converting the corresponding x values into z scores. z1=15−15/1.75=0z 2=17−15/1.75=1.143 P(15≤x≤17) = P(0≤Z≤1.143) = 0.382.
Calculation of µx and σxIf a random sample of size n=49 is drawn from a distribution where µ=15 and σ =14. Then the sample mean is given by the formula;μx=μ=15And, the standard error of the mean (standard deviation of the distribution of the sample means) is given by the formula;σx=σn=1449=2 Thus,μx=15 and σx=2And, P(15≤x≤17) can be obtained by converting the corresponding x values into z scores.z1=15−15/2=0z2=17−15/2=1P(15≤x≤17) = P(0≤Z≤1) = 0.3413
Calculation of µx and σxIf a random sample of size n=64 is drawn from a distribution where µ=15 and σ =14. Then the sample mean is given by the formula;μx=μ=15 And, the standard error of the mean (standard deviation of the distribution of the sample means) is given by the formula;σx=σn=1464=1.75 Thus,μx=15 and σx=1.75 And, P(15≤x≤17) can be obtained by converting the corresponding x values into z scores. z1=15−15/1.75=0z 2=17−15/1.75=1.143 P(15≤x≤17) = P(0≤Z≤1.143) = 0.382
Part (b) is expected to have a higher probability of P(15≤x≤17) than that of Part (a) because the standard deviation is inversely proportional to the sample size n.
Hence, the larger the sample size, the smaller the standard deviation. And, the smaller the standard deviation, the greater the accuracy of the sample mean in estimating the population mean.
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which is a better deal? sabrina want to buy a new digital camera. The one she wants is currently on a sale for 300$. She could borrow some money at a monthly interest rate of 4% simple interest and pay it off after 6 months and then pay cash, but the camera will no longer be on sale and will cost $350.
Which option will cost her the least amount of money?
include calculations to justify your advice.
Answer:
$350
Step-by-step explanation:
with the interest rate you'll be spending more money
A group of 500 middle school students were randomly selected and asked about their preferred television genre. A circle graph was created from the data collected.
a circle graph titled preferred television genre, with five sections labeled drama 14 percent, sports 22 percent, documentaries, reality 20 percent, and sci-fi 20 percent
How many middle school students prefer the Documentaries television genre?
24
76
120
86.4
120 middle schοοl students prefer the dοcumentaries televisiοn genre.
What is percentage?A percentage in mathematics is a number οr ratiο that can be expressed as a fractiοn οf 100. If we need tο calculate a percentage οf a number, we shοuld divide it by 100 and multiply the result. Therefοre, the percentage refers tο a part per hundred. Per 100 is what the wοrd percentage means. The symbοl "%" is used tο represent it.
The tοtal is 100%. Subtract the οther parts οf the circle tο find the percent fοr spοrts.
100 - 14 -22-20 -20
24
Spοrts is 24%
Multiply the number οf students by the percentage οf students that prefer spοrts
500 *24%
500 *.24
120
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PLEASE HELP ME! I NEED THE ANSWERS! ITS AN EMERGENCY
The dilated figure has the following coordinates: A' (-15, 0), B' (-5, 10), C' (10, 10), D' (15, -5), and E' (5, -10).
How do the coordinates translate?In this sense, coordinates are the points where a grid system intersects. Latitude and longitude are the traditional ways to express GPS coordinates. Degrees of separation north and south from the equator, which is 0 degrees, are measured by lines of latitude coordinates.
Just multiply the coordinates of each point by 5 to construct a figure about the origin using a scale factor of 5.
A (-3, 0)
B (-1, 2)
C (2, 2)
D (3, -1)
E (1, -2)
The coordinates of each point are multiplied by 5 to enlarge the image by a scale factor of 5:
A' = (-3 * 5, 0 * 5) = (-15, 0)
B' = (-1 * 5, 2 * 5) = (-5, 10)
C' = (2 * 5, 2 * 5) = (10, 10)
D' = (3 * 5, -1 * 5) = (15, -5)
E' = (1 * 5, -2 * 5) = (5, -10)
The coordinates of the dilated figure are:
A' (-15, 0)
B' (-5, 10)
C' (10, 10)
D' (15, -5)
E' (5, -10)
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Let X be the average of a sample of 16 independent normal random variables with mean 0 and variance 1. Determine c such that
P (|X| < c) = .5
Answer: Let X¯¯¯¯
be the average of a sample of 16
independent normal random variables with mean 0
and variance 1
. Determine c such that P(|X¯¯¯¯|<c)=.5
I am having a lot of trouble with this question. I know it is related to chi-square but I don't know how to even start.
Step-by-step explanation:
The area of a rectangle is x2 – 6x +8. Find its possible length and breadth:
Answer:
Step-by-step explanation:
To find the possible length and breadth of the rectangle, we need to factor the given expression:
x^2 - 6x + 8 = (x - 4)(x - 2)
Therefore, the length and breadth of the rectangle can be any combination of (x-4) and (x-2).
For example, if we choose (x-4) as the length and (x-2) as the breadth, we have:
Length = x - 4
Breadth = x - 2
Conversely, if we choose (x-2) as the length and (x-4) as the breadth, we have:
Length = x - 2
Breadth = x - 4
So, the possible length and breadth of the rectangle are (x-4) and (x-2), and vice versa.
Answer:(x-4) and (x-2)
Step-by-step explanation:
help!!!
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The axis should be labeled x-axis and y-axis respectively.
A graph of triangle ABC with the points A (-3, 0), B (-2, 4), and C (1, -1) is shown below.
The coordinates of triangle A'B'C' are A' (0, 3), B' (4, 2), and C' (-1, -4).
The coordinates of triangle A"B"C" are A" (0, 0), B" (4, -1), and C" (-1, -4)).
What is the rotation of a point 90° clockwise?In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).
By applying a rotation of 90° clockwise about the center (origin), the coordinates of triangle A'B'C' are as follows;
(x, y) → (y, -x)
Coordinate A = (-3, 0) → Coordinate A' = (0, -(-3)) = (0, 3)
Coordinate B = (-2, 4) → Coordinate B' = (4, -(-2)) = (4, 2)
Coordinate C = (1, -1) → Coordinate C' = (-1, -(1)) = (-1, -1)
Next, we would translate A'B'C' 3 units down:
(x, y) → (x, y - 3)
Coordinate A' = (0, 3) = A" (0, 0)
Coordinate B' = (4, 2) = B" (4, -1)
Coordinate C' = C" (-1, -4).
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What is 16/15 in simplest form