Answer:
6.9 or 7.0 .
Step-by-step explanation:
*Note that ^2 means raised to the power of two or squared
a^2 + b^2 = c^2
The hypotenuse is always the C, and the leg can be either a or b.
Fill in the blanks with the numbers that we have:
Hypotenuse: 7.7 | Leg: 3.4
3.4^2 + b^2 = 7.7^2
Square the numbers given
3.4 x 3.4 = 11.56
7.7 x 7.7 = 59.29, which leads us to:
11.56 + b^2 = 59.29
To find what b equals, we need to subtract 11.56 from 59.29
59.29 - 11.56 = 47.73
b^2 = 47.73
We need to take the square root of 47.73 to find b. b and b^2 are two different things.
The square root of 47.73 is about 6.90869017977. It asks for the answer to be rounded to the nearest tenth, giving us 6.9 or 7.0.
Which of the following sets of numbers could not represent the three sides of a right triangle? O {35, 84, 91} O {5, 8, 10} O {33, 56, 65} O {42, 56, 70}
Answer: The numbers that cannot represent the three sides of a right triangle are {35, 84, 91}.
Step-by-step explanation:
Convert the following repeating decimal to a fraction in simplest form.
16
Answer:
16/99
Step-by-step explanation:
so you turn into an algebraic equation
[tex]x[/tex] = 0.1616161616
100[tex]x[/tex]=16.161616
100[tex]x[/tex]-1[tex]x[/tex]=99[tex]x[/tex]
99[tex]x[/tex]=16.1616-0.1616
= 16
[tex]x[/tex]= [tex]\frac{16}{99}[/tex]
Jamel said that the 9 in 129,082 is two times greater than the 9 in 127,694 because it is two place values to the left. Is he correct?
Answer:
No, Jamel is not correct. While the 9 in 129,082 is indeed two places to the left of the 9 in 127,694, it is not two times greater.
In fact, the value of a digit in a number is determined by its place value. Each place value to the left represents a value that is ten times greater than the previous place value. So, the 9 in the ten thousands place of 129,082 represents a value of 9 x 10,000 = 90,000.
Similarly, the 9 in the ten thousands place of 127,694 represents a value of 9 x 10,000 = 90,000 as well. Therefore, both 9s have the same value and are not different by a factor of two.
In summary, Jamel's reasoning is flawed and not correct. The value of a digit in a number is based on its place value, and not its position relative to other digits.
Write the expression in complete factored form.
n7(n + 8) - 4(n + 8) = help
Answer:
Step-by-step explanation:
To factor the left side of the equation, we can first factor out the common factor of (n+8):
n7(n + 8) - 4(n + 8) = (n + 8)(n7 - 4)
So the complete factored form of the expression is (n + 8)(n7 - 4).
the diagram shows a 4cm*4cm*4cm cube. find the length of the diagonal AB
Answer:
Step-by-step explanation:
First find BC:
[tex]BC^2=BD^2+DC^2[/tex] (Pythagoras Theorem)
[tex]\rightarrow BC^2=4^2+4^2[/tex]
[tex]\rightarrow BC^2=32[/tex]
[tex]\rightarrow BC=\sqrt{32} cm[/tex]
Now find AB:
[tex]AB^2=AC^2+BC^2[/tex] (Pythagoras Theorem)
[tex]\rightarrow AB^2=4^2+(\sqrt{32}) ^2[/tex]
[tex]\rightarrow AB^2=16+32[/tex]
[tex]\rightarrow AB^2=48[/tex]
[tex]\rightarrow AB=\sqrt{48}=6.9cm[/tex]
Diagonal AB = 6.9cm
three traffic lights on a street span 120 yards. if the second traffic light is 85 yards away from the first, how far in yards is the third traffic light from the seccond
The distance between the third traffic light from the second traffic light is 35 yards.
What is the distance?Three traffic lights on a street span 120 yards.
If the second traffic light is 85 yards away from the first.
Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.
This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.
Thus, the distance between the third traffic light from the second traffic light is 35 yards.
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for h(x) = 4x-1, find h(0) and h(2)
Answer:
- 1 and 7
Step-by-step explanation:
to find h(0) substitute x = 0 into h(x)
h(0) = 4(0) - 1 = 0 - 1 = - 1
to find h2) substitute x = 2 into h(x)
h(2) = 4(2) - 1 = 8 - 1 = 7
Whatis the value of # y_ When y = 5 and x = 10?
The value of y when x=36 is 31/3.
According to the question,
x varies directly with 3y+5
Thus,
[tex]x = k(3y+5)[/tex]
where K is any positive integer.
Now, from the question,
y=5/3 when x=10
Thus,
[tex]10 = k(3(\frac{5}{3} )+5)\\10 = k(10)\\k = 1[/tex]
Now we can use k to find the value of y when x=36:
[tex]36 = 1(3y+5)\\31 = 3y\\y = \frac{31}{3}[/tex]
In mathematics, an integer is a whole number that can be positive, negative, or zero. Integers are a fundamental concept in number theory and are used in a variety of applications across many fields. Integers can be represented using the symbol "Z" and are denoted by an integer value like -3, 0, 1, 2, 3, etc. They are used to count and measure quantities in real-life situations, such as the number of apples in a basket or the distance between two cities.
Integers are closed under addition, subtraction, and multiplication, meaning that if you add, subtract, or multiply any two integers, the result will also be an integer. However, the division is not always closed under integers, as dividing by zero is undefined, and dividing two integers can result in a non-integer value.
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Complete Question:
If x varies directly with 3y+5 and y=5/3 when x=10, then what is the value of y when x=36
The inverse sine, inverse cosine, and inverse tangent functions have the following domains and ranges. (Enter your answers in interval notation.)(a) The function sin−1 has domain and ranges(b) The function cos−1 has domain(c) The function tan−1 has domainand range
(a) The function sin⁻¹ has a domain of [-1, 1] and a range of [-π/2, π/2].
(b) The function cos⁻¹ has a domain of [-1, 1] and a range of [0, π].
(c) The function tan⁻¹ has a domain of (-∞, ∞) and a range of (-π/2, π/2).
In mathematics, the domain and range are concepts used to describe the inputs and outputs of a function.
The domain of a function is the set of all possible inputs or values of the independent variable for which the function is defined or meaningful.
The range of a function, on the other hand, is the set of all possible outputs or values of the dependent variable that the function can produce for all the inputs in the domain.
The inverse sine function, denoted sin⁻¹, takes as input a value between -1 and 1, and returns the angle whose sine is equal to that value. Therefore, its domain is [-1, 1], since the sine of an angle cannot exceed these limits. The range of sin⁻¹ is the set of all angles whose sine lies between -1 and 1. The smallest such angle is -π/2, which corresponds to a sine of -1, and the largest such angle is π/2, which corresponds to a sine of 1. Hence, the range of sin⁻¹ is [-π/2, π/2].
The inverse cosine function, denoted cos⁻¹, is similar to sin⁻¹, but takes as input a value between -1 and 1 and returns the angle whose cosine is equal to that value. Its domain is also [-1, 1], since the cosine of an angle cannot exceed these limits. However, the range of cos⁻¹ is different from that of sin⁻¹. It starts at 0, which corresponds to a cosine of 1, and ends at π, which corresponds to a cosine of -1. The reason for this difference is that the cosine of an angle is always positive or zero when the angle lies between 0 and π radians.
The inverse tangent function, denoted tan⁻¹, takes as input any real number and returns the angle whose tangent is equal to that number. Its domain is (-∞, ∞), since the tangent of an angle can take on any real value. The range of tan⁻¹ is between -π/2 and π/2, since the tangent of an angle becomes infinite at these values.
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It takes 120 unit cubes to completely fill a rectangular prism. The prism is 10 unit cubes high. What are the other possible dimensions of the rectangular prism?
the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Let the length and width of the rectangular prism be represented by l and w, respectively. Since the height of the prism is 10 unit cubes, we know that the volume of the prism is:
V = l × w × 10
We are also given that the prism requires 120 unit cubes to fill completely, which means:
V = l × w × 10 = 120
Dividing both sides by 10, we get:
l × w = 12
Now we need to find pairs of positive integers l and w that multiply to 12. These are:
1 × 12
2 × 6
3 × 4
Therefore, the possible dimensions of the rectangular prism are:
1 unit by 12 units by 10 units
2 units by 6 units by 10 units
3 units by 4 units by 10 units
Note that these dimensions are not unique, as we can also obtain different dimensions by exchanging the length and width, or by rotating the prism.
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Pentagon A'B'C'D'E' is the image of pentagon ABCDE under a
5
dilation with a scale factor of
2
a
B
What is the length of segment AE?
units
As a result, segment AE's length matches that of pentagons ABCDE and A'B'C'D'E'. Even as length of AE is not explicitly stated, we are unable to infer it based on the information in the problem.
What does a 4 scale factor mean?The scale factor refers to the proportion of one figure's side length to the other figure's corresponding side length. This time, XYUV=123=4. The scaling factor is hence 4.
Each side of the pentagon A'B'C'D'E' is twice as long as the equivalent side of the pentagon ABCDE because the dilatation scale factor is 2. Therefore:
A'B' = 2AB
B'C' = 2BC
C'D' = 2CD
D'E' = 2DE
E'A' = 2EA
Segment AE, which adds up to the sum of the first pentagon's two sides, needs to be as long as possible.
AB + BC + CD + DE=AE
We can swap the value of A'B', B'C', C'D', and D'E' for AB, BC, CD, and DE, respectively, since the dilation scale factor is 2:
AE = A'B'/2 + B'C'/2 + C'D'/2 + D'E'/2
AE = (2AB)/2 + (2BC)/2 + (2CD)/2 + (2DE)/2
AB + BC + CD + DE=AE
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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT
Answer:
To find the perimeter, we need to add up the lengths of all the sides. In this case, we have four sides with lengths given by the expressions 2v-5, 4v+5, 2v-5, and 8v-7.
So the perimeter P is:
P = (2v-5) + (4v+5) + (2v-5) + (8v-7)
Simplifying and combining like terms, we get:
P = 16v - 12
Therefore, the perimeter is 16v - 12.
Write the product in standard form.
(x - 7)²
Answer:
x² - 49
Step-by-step explanation:
(x - 7)² =
(x - 7) * (x - 7) =
x * x - 7 * 7 =
x² - 49
Proof Complete the proof of the cancellation property of vector addition by justifying each step. Prove that if u, v, and w are vectors in a vector space V such that u + w = v + w, then u = v.
The successfullly completed the proof of the cancellation property of vector addition.
Complete proof of the cancellation property of vector addition:Let u, v, and w be vectors in a vector space V such that u + w = v + w. We have to show that u = v. We know that the cancellation property of vector addition states that for all vectors u, v, and w in a vector space V, if u + w = v + w, then u = v.So, u + w = v + w can be written as, u + w - w = v + w - w, applying subtraction on both sides.u + 0 = v + 0 (as - w + w = 0)0 is an additive identity, so it can be dropped off.u = v, which is the desired result.The statement "u + w = v + w" was given, and we have shown that it implies that "u = v". Hence, we have successfully completed the proof of the cancellation property of vector addition.
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1. A statistics student wants to compare the mean times needed to access flight information for two major airlines. Twenty randomly selected students accessed one airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.5 minutes and a standard deviation of 0.8 minute. Twenty different randomly selected students accessed the other airline's Web site, and the time required to locate the flight information using the Web site had a mean of 2.1 minutes and a standard deviation of 1.1 minutes. Assuming that the conditions for inference are met, which of the following statements about the p- value obtained from the data and the conclusion of the significance test is true? a. The p-value is less than 0.01; therefore, there is a significant difference in mean search times on the two Web sites b. The p-value is greater than 0.01 but less than 0.05, therefore, there is a significant difference in mean search times on the two Web sites. c. The p-value is greater than 0.05 but less than 0.10, therefore, there is a significant difference in mean search times on the two Web sites. d. The p-value is greater than 0.10, therefore, there is no significant difference in mean search times on the two Web sites e. Since this is a matched-pairs situation, additional information is needed to perform a test of significance
There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.
What is mean?It is calculated by adding up all the values in the set and then dividing the sum by the total number of values. The mean is often used as a measure of central tendency, which describes the typical or representative value in a set of data.
According to question:This is a two-sample independent means t-test problem.
The null hypothesis is that there is no difference between the mean times needed to access flight information for the two major airlines, and the alternative hypothesis is that there is a difference.
Assuming the conditions for inference are met (random sampling, normality of the population, and independence between the two samples), we can calculate the t-value and the p-value for the test.
The formula for the t-value in a two-sample independent means t-test is:
t = (x1 - x2) / √[ (s1²/n1) + (s2²/n2) ]
Plugging in the given values, we get:
t = (2.5 - 2.1) / √[ (0.8²/20) + (1.1²/20) ]
t = 1.21
Using a t-table with 38 degrees of freedom (df = n1 + n2 - 2), we find that the p-value is between 0.10 and 0.05.
Therefore, the correct answer is c:
There is a significant difference in the mean search times between the two websites, as indicated by the p-value, which is larger than 0.05 but less than 0.10.
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If the temperature in Buffalo is 23 degrees Fahrenheit, what is the temperature in degrees Celsius? Use the formula: C= 5/9 F-32 Rashawn
The temperature in Buffalo when it is 23 degrees Fahrenheit is equivalent to -5 degrees Celsius.
What is Fahrenheit and Celsius?Fahrenheit is a temperature scale that was created by Gabriel Fahrenheit in 1724. Fahrenheit is used primarily in the United States and a few other countries. The boiling point of water on this scale is 212 degrees Fahrenheit, while the freezing point is 32 degrees Fahrenheit.
The Celsius scale, on the other hand, is a temperature scale that is used throughout the world. It was created in 1742 by Swedish astronomer Anders Celsius. On this scale, the boiling point of water is 100 degrees Celsius, and the freezing point is 0 degrees Celsius.
How do I convert degrees Fahrenheit to degrees Celsius?The formula for converting degrees Fahrenheit to degrees Celsius is: C=5/9(F-32). C is the equivalent Celsius temperature, while F is the equivalent Fahrenheit temperature.
Let's put the formula into practice to answer the question, "If the temperature in Buffalo is 23 degrees Fahrenheit,
What is the temperature in degrees Celsius?We can simply plug in the given value for Fahrenheit temperature, which is 23 degrees Fahrenheit.
C = (5/9) (23 - 32)C = (5/9) (-9)C = -5
Therefore, -5 degrees Celsius is equivalent to 23 degrees Fahrenheit when the temperature is in Buffalo.
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Sharon is saving for a new phone. She starts with $42 and earns $15 each week from her parents. How many weeks will it take to save a total of $207?
Answer:
11 weeks
Step-by-step explanation:
42 + 15 * x = 207
42 + 15x = 207
15x = 207 - 42
15x = 165
x = 11
Hope this helps <3
4. Assume that 4 years from now you will need $1,000. Your bank compounds interest
at an 8% annual rate. A. How much must you deposit 1 year from now to have a balance of $1,000 at
Year 4?
b. If you want to make equal payments at the end of Years 1 through 4 to
accumulate the $1,000, how large must each of the 4 payments be?
c. If your father were to offer either to make the payments calculated in part b
($221. 92) or to give you a lump sum of $750 one year from now, which would
you choose?
d. If you will have only $750 at the end of Year 1, what interest rate, compounded
annually, would you have to earn to have the necessary $1,000 at Year 4?
e. Suppose you can deposit only $186. 29 each at the end of Years 1 through 4, but
you still need $1,000 at the end of Year 4. What interest rate, with annual
A. deposit $735.03 one year from now. B. $210.48 for each of the four years. C. choose the lump sum of $750 from your father. D. Interest rate of 7.4% compounded annually. E. Interest rate of 12%.
a. To have a balance of $1,000 four years from now, you need to calculate the present value of this amount. Using the compound interest formula, we can calculate that you need to deposit $735.03 one year from now to have a balance of $1,000 four years from now.
b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, you can use the annuity formula to calculate the required payments. The formula gives us a payment of $210.48 for each of the four years.
c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 one year from now, you can compare the present value of both options. The present value of the four payments of $210.48 each, using an 8% annual interest rate, is $682.96. Therefore, you would choose the lump sum of $750 from your father.
d. If you have only $750 one year from now, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 7.4% compounded annually.
e. If you can only deposit $186.29 each at Years 1 through 4, you can use the compound interest formula to calculate the interest rate you need to earn to have $1,000 four years from now. Using the formula, we get an interest rate of 12% compounded annually.
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Complete question:
Assume that 4 years from now you will need $1,000. Your bank compounds interest at an 8% annual rate.
a. How much must you deposit 1 year from now to have a balance of $1,000 4 years from now?
b. If you want to make equal payments at Years 1 through 4 to accumulate the $1,000, how much each of the 4 payments be?
c. If your father were to offer either to make the payments calculated in part b or to give you a lump sum of $750 1 year from now, which would you choose?
d. If you have only $750 1 year from now, what interest rate, compounded annually, would you have to earn to have the necessary $1,000 4 years from now? 7.4%
e. Suppose you can deposit only $186.29 each at Years 1 through 4, but you still need $1,000 at Year 4. What interest rate, with annual compounding, must you seek out to achieve your goal?
Enter the values needed to find the
length BC. (Simplify your answer.)
A (-5x, 4y)
B (-2x, -4y)
BC=√([?])² + (3y)²
C (7x, -1y)
Distance Formula
d = √√(x₂ − ×₁)² + (y₂ − y₁)²
The missing value to find the length of BC is 9x.
What is distance formula?The distance formula is a formula for calculating the separation in coordinates between two places. It is provided by and deduced from the Pythagorean theorem by:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
The distance formula is used to compute distances between objects or places in many disciplines, including geometry, physics, and engineering.
The distance formula is given as:
distance = √((x₂ - x₁)² + (y₂ - y₁)²)
Substituting the values of the coordinates of B and C we have:
distance = √((7x - (-2x))² + (-1y - (-4y))²)
distance = √((9x)² + (3y)²)
distance = √(81x² + 9y²)
distance = 3√(9x² + y²)
Hence, the missing value to find the length of BC is 9x.
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One number is 13 less than another number. Let x represent the greater number. What is the sum of these two numbers?
Answer:
2x - 13
Step-by-step explanation:
If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:
x + (x - 13) = 2x - 13
PLEASE HELP WILL GIVE BRAINLIEST.
Given f(x)=sin x and g(x)=cos x show that f(g(pi/2))=0. Show all your steps.
Answer:
Step-by-step explanation:
xs nxqxm,nswjnej,cebxhjme2ckjwadbcweckslnvc
First, we need to find the value of g(pi/2):
g(pi/2) = cos(pi/2) = 0
Now we can substitute this value into f(x):
f(g(pi/2)) = f(0) = sin(0) = 0
Therefore, f(g(pi/2)) = 0.
A Health Psychologist Is Interested In The Effectiveness Of A New Exercise On Reducing The Rate Of Heart Attacks Because The Exercise Requires No Equipment And, Therefore, Can Be Done Without Cost. A. What Is The Research Hypothesis? B. What Is The Null Hypothesis? C. What Is The Comparison Distribution For This spesific example (we draw this out every time?)
A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.
What is p-value?A p-value is a statistical indicator that, under the null hypothesis, shows the likelihood of receiving a test statistic that is as extreme to or more extreme than the one seen in the sample data. Depending on the degree of statistical significance the researcher selects, it is employed in hypothesis testing to determine whether to reject or fail to reject the null hypothesis. The null hypothesis is rejected in favour of the alternative hypothesis if the p-value is less than or equal to the selected level of significance (typically 0.05). The null hypothesis is not rejected if the p-value is higher than the selected level of significance.
A. In this instance, the research hypothesis may be that the new workout is successful in lowering the incidence of heart attacks.
B. The alternative hypothesis may be that the additional exercise has no impact on the frequency of heart attacks.
C. Depending on the study's specific design and the outcome measure used to gauge the prevalence of heart attacks, the comparison distribution would vary.
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Given f(x) = -3x? + 10, what is f(-2)?
Answer:f(-2)=6+10
So f(-2) =16
Step-by-step explanation:
10. Write the equation that is represented by the data in the table below.
Time (years)
0
1
2
3
4
5
No. of cars
5
10
20
40
80
160
How many years would it take to over 10,000 cars?
Describe the following pair of angles as of COMPLEMENTARY, SUPLEMENTARY or NEITHER: A. COMPLEMENTARY B. SUPLEMENTARY C. NEITHER D. NOT ENOUGH INFORMATION (IT DEPENDS ON THE VALUE OF x ) A B C D
Option (D) is correct because we can not determine whether the given pair of angles are complementary, supplementary, or neither
The given pair of angles can be either complementary or supplementary, depending on the value of x.
Complementary Angles: Two angles whose sum is 90 degrees are called complementary angles. In other words, if the sum of two angles is 90 degrees, then they are called complementary angles.
Supplementary Angles: Two angles whose sum is 180 degrees are called supplementary angles. In other words, if the sum of two angles is 180 degrees, then they are called supplementary angles.
Neither: If the sum of two angles is neither 90 degrees nor 180 degrees, then they are called neither complementary nor supplementary angles.
Not Enough Information (It depends on the value of x): If the measure of x is not given, then we cannot determine whether the given pair of angles are complementary, supplementary, or neither.
Hence, it depends on the value of x. Therefore, option D is the correct answer.
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The graph shows the velocity, v metres per second, of a car at time t seconds. Work out an estimate for the distance the car travelled for the first 8 seconds. Use 4 strips of equal width. -1-500- -1000- -500 0 V t
please help!!!
To estimate the distance traveled we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.
Define velocity-time graph?A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.
The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.
Using the trapezium rule, the estimated area of each strip is:
Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s
Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s
Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s
Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s
The total estimated area is the sum of the areas of the 4 strips:
Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s
Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:
Estimated distance traveled is = |-4000| = 4000 meters
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make t the subject of s=1/2*at^2
What is the average weight of an apple in grams, if 12 apples were bought for $6.72 and the apples were priced at $3.50/kg?
pls show working
Answer: The weight of the Apples is 160g
Step-by-step explanation:
If the apples were priced at $3.50/kg, then the cost of 1 kg of apples would be $3.50.
To find out the weight of 12 apples, we can divide the total cost of $6.72 by the cost of 1 kg of apples:
$6.72 ÷ $3.50/kg = 1.92 kg
So, the weight of 12 apples is 1.92 kg.
To find the average weight of 1 apple, we can divide the total weight of the 12 apples by the number of apples:
1.92 kg ÷ 12 = 0.16 kg
Finally, we need to convert the weight of 1 apple from kilograms to grams:
0.16 kg x 1000 g/kg = 160 g
Therefore, the average weight of an apple in grams is 160 g.
Given vectors V1, V2,73, one can always write the zero vector as a linear combination as 0v1 + 02 + 0ï3 7. An important question is whether or not you can do it without using coefficients that are all o. For vi V2 V3 - -B can you write 7 as a linear combination where the coefficients are not all o? If so, give such a linear combination. Use complete sentences when giving your final answer to support your work.
Yes, it is possible to write 7 as a linear combination of the given vectors V1, V2, and V3 with coefficients that are not all zero.
One such linear combination can be given as follows:7 = -3V1 + 4V2 + V3To prove that this is indeed a linear combination of the given vectors, we can substitute the given vectors and coefficients in the above expression and verify that it gives the desired result.
So, we have:RHS = -3V1 + 4V2 + V3= -3(2i - 3j + k) + 4(-i + 2j + 3k) + (i - j - k)= -6i + 9j - 3k - i + 8j + 12k + i - j - k= 7j + 8kSince this result matches with the given vector 7, we can conclude that 7 can be written as a linear combination of the given vectors with coefficients that are not all zero.Hence, the required linear combination is:7 = -3V1 + 4V2 + V3.
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You report a confidence interval to your boss but she says that she wants a narrower range. SELECT ALL of the ways you can reduce the width of the confidence interval. o Increase the sample size o Decrease the sample size o Increase the confidence level o Decrease the confidence level I
o ncrease the mean o Decrease the mean
We can reduce the width of the confidence interval by increasing the sample size, reducing the confidence level and decreasing the mean (A, D, and F)
What is a confidence interval?A confidence interval is an estimate of the interval that has a specified probability of including an unknown population parameter.
The purpose of a confidence interval is to estimate the true value of the population parameter being measured, such as a mean, a standard deviation, or a proportion.
In general, a wider confidence interval indicates more uncertainty about the estimate, while a narrower confidence interval suggests more precision in the estimate.
We want narrower confidence intervals to demonstrate more precision, as this allows us to draw more reliable conclusions about population parameters.
We cannot reduce the width of the confidence interval by increasing the sample size, increasing the confidence level or increasing the mean.
Thus, the correct options are a, d, and f.
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