The computation of the equations is illustrated below.
How to illustrate the equation?a. x - y = 1 .... i
x + y = -9 ..... ii
Subtract the equations
-2y = 10
y = 10/-2 = -5
Since x - y = 1
x - (-5) = 1
x + 5 = 1
x = 1 - 5 = -4
b. 3x + 2y = -9
x - y = -13
Multiply equation i by 1
Multiply equation ii by 3
3x + 2y = -9
- 3x - 3y = -39
5y = 30
y = 6
Since x - y = 13
x - 6 = 13
x = 13 + 6 = 19
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p% of m change into an algebraic expression.
The expression p% of m changed into an algebraic expression is pm/100
Percentagep% of m
= p% × m
= p/100 × m
= (p × m) / 100
= pm/100
Therefore, the expression p% of m changed into an algebraic expression is pm/100
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Which of the following is not a step in finding the area of an unknown figure?
- Calculate the areas of the smaller figures.
- Plug all dimensions into the formula: SA=Ixwxh.
- Divide the figure into smaller, known figures.
- Add up the areas of the smaller figures.
The answer choice which is not a step in finding the area of the unknown figure is; Plug all dimensions into the formula: SA=Ixwxh. option B
Which is not a step in finding the area of an unknown figure?It follows from the task content that all other steps except Plugging all dimensions into the formula; SA = l×w×h are correct steps.
This is due to the fact that, the formula does not work for all shapes and hence, it can't be generalized for all situations.
The step which is not involved in finding the area of an unknown figure is; Plug all dimensions into the formula: SA=Ixwxh.
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Answer:
B) Plug all dimensions into the formula: SA=Ixwxh.
Step-by-step explanation:
General admission tickets to a play cost $18 each. Reserved seats cost $22 each. There were 20 reserved seats sold. There were 28 more general admission tickets sold than reserved seats. How much money was paid for all of the tickets put together? Complete the chart and answer the question:
Answer:
$22 * (20) + $18 * (48) = $1304
Step-by-step explanation:
There are 20 reserved seats so it would be: $22 * 20 = $440 for all reserved seats
There are 28 general admission tickets more than reserved seats ticket so number of general admission tickets is: 20 + 28 = 48 (tickets)
Each general admission tickets cost $18, so: $18 * 48 = $864 for all general admission tickets
So the total money was paid for all of the tickets is: $440 + $864 = $1304
Claim: A majority of adults would erase all of their personal information online if they could. A software firm survey of 576 randomly selected adults showed that 59% of them would erase all of their personal information online if they could. Complete parts (a) and (b) below.
a. Express the original claim in symbolic form. Let the parameter represent the adults that would erase their personal information.
b. identify the null and alternate hypothesis
A) The original claim in symbolic form is; p > 0.50
B) The Null Hypothesis is;
H₀: p = 0.50
Alternative Hypothesis is;
H_a: p > 0.50
How to identify the hypothesis claim?We are given;
Sample size; n = 576
Sample Proportion; p^ = 59% = 0.59
A) The percentage of 59% represents the proportion of a sample and thus we are making a claim about the population proportion p in the hypotheses.
We claim "most of the adults", which indicates more than 50% or 0.50. Thus, the claim in symbolic form is; p > 0.50
B) The Null Hypothesis is;
H₀: p = 0.50
Alternative Hypothesis is;
H_a: p > 0.50
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Jada is solving the equation shown below.
Negative one-half (x + 4) = 6
Which is a possible first step to begin to simplify the equation? Select two options.
Divide both sides of the equation by –2.
Subtract 4 from both sides of the equation.
Multiply both sides of the equation by –2.
Distribute –2 over (x + 4).
Distribute Negative one-half over (x + 4).
Answer:
Distribute -1/2 over (x+4)
Step-by-step explanation:
-0.5(x+4) = 6
-0.5x - 2 = 6
-0.5x = 8
x = -16
Answer:
Multiple both sides by -2 or Distribute negative one-half over (x+4)
Step-by-step explanation:
-1/2(x+4) = 6
If I multiple both sides by -2, I am clearing the fraction:
(-2)(-1/2)(x+4) = 6(-2)
x+4 = -12
x = -16
OR
-1/2(x + 4) = 6
-1/2x -2 = 6 Remember, a negative times a positive is a negative.
-x - 4 = 12 multiply both sides by 2
-x = 16
x = -16
Examine the Scatterplot and Identify Characteristics of the data that are ignored by the regression line.
x 10 8 13 9 11 14 6 4 12 7 5
y 7.46 6.77 12.74 7.11 7.81 8.84 6.08 5.39 8.5 6.42 5.73
The regression equation is y = 3.002 + 0.5x and the scatterplot is illustrated.
What is a scatterplot?It should be noted that a scatterplot simply means a type of data that shows the relationship between two numerical variables.
From the information, summation is X is 99, summation Y is 82.5, summation XY is 797.47, and summation X² is 1001.
Now the value of a will be:
= 82.5 - 1001 - 99 - 797.47/(11.1001 - 99²)
= 3.002
b = (11 × 797.47 - 99 × 82.5)/11.1001 - 99²
= 0.5
The regression equation will be:
y = a + bx.
y = 3.002 + 0.5x
There's positive linear correlation between x and y.
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Approximately how many years will it take for the world’s population to increase to 8,252,000,000 people? Since there will be the original 100% plus an additional 2% each year, the base in the exponential equation is 1.02. Use the equation 8252=(6080)(1.02)x, where x is the number of years. Round to the nearest year.
The number of years it will take for the world’s population to increase to 8,252,000,000 people is 16
How to determine the number of years?This implies that we calculate the value of x
The equation is given as:
8252=(6080)(1.02)^x
Divide both sides by 6080
1.36 = (1.02)^x
Take the logarithm of both sides
log(1.36) = x * log(1.02)
Divide both sides log(1.02)
x = log(1.36)/log(1.02)
Evaluate the quotient
x = 16
Hence, the number of years is 16
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Which of the following shows the graph of y= 2e^x?
The graph of the given function, y = 2eˣ, is given below
Graph of a functionFrom the question, we are to determine the graph of the given function
The given function is
y = 2eˣ
The graph of y = 2eˣ is shown below
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FRACTIONS
Equivalent fractions
Fill in the blank to make the two fractions equivalent.
blank over 30=4/5
The complete fraction is 24/30=4/5
How to create an equivalent fraction?The expression is given as:
blank over 30=4/5
Represent the blank with x.
So, we have:
x/30=4/5
Multiply both sides by 30
x = 30 * 4/5
Evaluate
x = 24
Substitute x = 24 in x/30=4/5
24/30=4/5
Hence, the complete fraction is 24/30=4/5
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Which represents the reflection of f(x)=√x over the y-axis?
We are looking for the graph of [tex]y=\sqrt{-x}[/tex]. which is shown in the attached image.
Here are two steps from the derivation of the quadratic formula (image w question below)
Answer:
B. Completing the square
Step-by-step explanation:
Between the first and second steps shown, the square of half the x-term coefficient was added to both sides. That is a value that makes the polynomial on the left be a "perfect square trinomial."
The process of adding the value required to make the left side a perfect square is called "completing the square."
find m+n
pls help !!!
Answer:
m + n = 140===============
GivenTwo parallel lines,Included triangle between the parallel lines,Two interior angles of the triangle are m and n,Another angle of 40°.To find The sum of angles m and nSolutionAs per given, the missing interior angle is corresponding with 40° angle.
Since corresponding angles are equal, the third interior angle of the triangle is 40°.
Sum of three interior angles is 180°:
m + n + 40 = 180m + n = 180 - 40m + n = 140Apply angle sum property
m+n+40=180m+n=180-40m+n=140The answer is 140
write the equivalent of the fraction using a denominator of 52. 2/13
Answer: 8/52
2/13=x/52
(2×52)/13=x
104/13=x
8=x
x=8
8 is the equivalent of the fraction using a denominator of 52. 2/13
Equivalent fractions can be defined as fractions that may have different numerators and denominators but they represent the same value. For example, 9/12 and 6/8 are equivalent fractions because both are equal to 3/4 when simplified.
All equivalent fractions get reduced to the same fraction in their simplest form as seen in the example given above. Explore the given lesson to get a better idea of how to find equivalent fractions and how to check if the given fractions are equivalent.
⇒[tex]\frac{2}{13} =\frac{x}{52}[/tex]
⇒[tex]\frac{2(52)}{13} = x[/tex]
⇒[tex]x = 8[/tex]
therefore, 8 is the equivalent of the fraction using a denominator of 52. 2/13
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Solve log (3x + 4) = log (x – 2) + 3 log 2
Answer:
x + 4
Step-by-step explanation:
Sine the bases are all the same, I can write the equation:
3x+4 = (x-2) 2^3 When we are adding with logs, that means to multiple. Also, when we have 3 log 2, that can be written as 2^3 or 8 (2x2x2)
3x+4=(x-2)8
3x+4 = 8x-16
4=5x-16
20 = 5x
4=x
Differentiate between different types of plane with example
Answer:
The three planes of motion are the sagittal, coronal (or frontal) and transverse planes.
Sagittal Plane: Cuts the body into left and right halves. Forward and backward movements.
Coronal (or Frontal Plane): Cuts the body into front and back halves. ...
Transverse Plane: Cuts the body into top and bottom halves.
Simplify the following expression.x-[tex]\frac{2}{3}[/tex] x[tex]\frac{6}{7}[/tex]
Keeping the bases and adding the exponents, the simplified expression is:
[tex]x^{\frac{4}{21}}[/tex]
How to solve a product of two terms with the same base and different exponents?We keep the bases and add the exponents.
Hence:
[tex]x^{-\frac{2}{3}} \times x^{\frac{6}{7}} = x^{-\frac{2}{3} + \frac{6}{7}} = x^{\frac{-14 + 18}{21}} = x^{\frac{4}{21}}[/tex]
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Which of the following are identities?
Answer:
A
Step-by-step explanation:
I. False. Consider y = 3 and x = 4.
II. False. Consider x = 1.
III. False. Consider x = -2.
Pre Calc work, I need help with writing piece wise functions from graphs. Can anyone help? Giving brainliest
The definition of the piece-wise function is:
[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex][tex]f(x) = -3, 2 < x < 6[/tex].What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input.
In this problem, for inputs between -2 and 2, the function is a line that goes through (-2,-4) and (2,6). The slope is:
m = (6 - (-4))/(2 - (-2)) = 2.5.
The y-intercept is of b = 1, hence the rule is:
[tex]f(x) = 2.5x + 1, -2 \leq x \leq 2[/tex]
For x greater than 2 and less than 6, the function is constant at -3, hence the rule is:
[tex]f(x) = -3, 2 < x < 6[/tex].
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6. Evaluate x³ = -8 *
If you use your office computer 20 hours per week, and do not unplug it when it is not in use, how much carbon dioxide is produced from the vampire energy used by the office computer in one year ? help (energyvampires)
Express your answer rounded to the nearest tenth of a pound of carbon dioxide.
The carbon dioxide that is produced from the vampire energy used by the office computer is 1042.8 kWh.
How to calculate the value?Based on the information given, the number of hours that the computer is plugged on a day will be:
= 20/7
= 2.857 hours
Therefore, the power consumption in a year will be:
= 2.857 × 365
= 1042.8 kWh
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a group of mapuve CLC MLMS4 STUDENTS were questioned how they got to school.half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.calculate the number of students delivered by a car using proper fractions
The fraction of those who were delivered by car will be 1/6.
How to calculate the fraction?It should be noted that from the information given, the students were questioned on how they got to schoo and half of the students said they walk, one-third said they take a taxi,and the rest claimed they drive.
Therefore, the fraction of those who were delivered by car will be:
= 1 - (1/2 + 1/3)
= 1/2 - 5/6
= 1/6
In conclusion, the fraction of those who were delivered by car will be 1/6.
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Which of the following expressions is equivalent to the one shown below?
713
7⁰
OA. 720
OB. 75
O C. 76
O D. 791
Answer: Option C [tex]\boldsymbol{7^6}[/tex]
Work Shown:
[tex]\frac{7^{13}}{7^{7}}\\\\\\7^{13-7}\\\\\\\boldsymbol{7^6}[/tex]
Subtract the exponents to get the answer. The rule is [tex]\frac{a^{b}}{a^{c}} = a^{b-c}[/tex]. This rule only works when the bases are the same.
Type the correct answer in the box.
Net of a triangular prism includes 3 same-sized rectangles that coincide along their width. Each rectangle has length labeled 10 centimeters and width labeled 15 centimeters. Isosceles triangle is placed above and below of second rectangle.
The surface area of the three-dimensional figure is
square centimeters.
The surface area of this three-dimensional figure is equal to 536.6 square centimeters.
How to determine the surface area?First of all, we would determine the total area of the three rectangles by using this formula:
Total area = 3 × Length × Width
Total area = 3 × 15 × 10
Total area = 450 cm².
Next, we would determine the total area of the two triangles by using this formula:
Total area = 2 × (1/2 × b × h)
Total area = b × h
Total area = 8.66 × 10
Total area = 86.6 cm².
Surface area = 450 + 86.6
Surface area = 536.6 cm².
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HELP i need the answer 20 POINTS
Answer:
y = -1/4(x +4)² +4
Step-by-step explanation:
The equation of a parabola with focus (a, b) and directrix y=d can be written using the form ...
y = 1/(2(b-d))(x -a)² +(b+d)/2
ApplicationWe are given (a, b) = (-4, 3) and d=5. Using these values in the above form gives the equation ...
y = 1/(2(3-5))(x -(-4))² +(3+5)/2
y = -1/4(x +4)² +4
I need help with question in photo
Answer:
14
Step-by-step explanation:
[tex] {x}^{2} = {4}^{2} \\ = 16\\ 4y = 4 \times - 3 \\ 4 \times - 3 = - 12 \\ 16 - - 12 =16 + 12 \\ - \times - = + \\ 16 + 12 = 28 \\ 28 \div 2 = 14[/tex]
a display at an aquarium has sea stars to wolf eels in a ratio 4 : 5. It also has 5/8 as many rockfish as sea stars. there are 40 more wolf eels than rock fish. How many sea stars are there?
The number of sea stars is 64.
What is a ratio?
Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other.
In general, a: b, which can be interpreted as "a is to b," is used to denote a ratio between two quantities, let's say "a" and "b."
This ratio is expressed in fraction form as a/b. We utilize the same method for further simplifying a ratio as we use for further simplifying a fraction.
According to the question,
Ratio of sea stars to wolf eels = 4:5
Number of rock fish= 5/8 (Number of sea stars)
Number of wolf eels - Number of rock fish = 40
Using the given information, we get,
Number of sea stars = 8/5 (Number of rock fish)
On simplification,
Number of wolf eels = 80
So, number of sea stars = (4/5)*80
= 64
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Consider the following data set.
45 58 41 45 38 46 45 39 40 31
1.
Sort the data and find quartiles of the data set.
2.
Find the interquartile range of the data set.
3.
Find the lower fence and the upper fence for outliers.
4.
Find outliers if they exist.
Based on the dataset given, the first quartile is 38.75, and the third quartile is 45.25. This interquartile range is 6.5. The lower fence is 29 and the upper fence is 55.
What are the quartiles in the data?Order the sets:
31, 38, 39, 40, 41, 45, 45, 45,46, 58
First quartile position:
= 1(10 + 1) / 4
= 2.75th position
= 38 + 0.75 x (39 - 38)
= 38.75
Third quartile:
= 3(10 + 1) / 4
= 8.25th position
= 45 + 0.25 x (46-45)
= 45.25
Interquartile range:
= 45.25 - 38.75
= 6.5
Upper fence:
= 45.25 + (1.5 x 6.5)
= 55
Lower fence:
= 38.75 - (1.5 x 6.5)
= 29
59 is an outlier.
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If np>5 and nq>5, estimate P (at least 10) with n=13 and p=0.5 by using the normal distribution as approximation for the binomial distribution, if np, or nq,5, then state that the normal approximation is not suitable.
Using the normal distribution, the probability is given as follows:
[tex]P(X \geq 10) = 0.0485[/tex].
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The binomial distribution is the probability of x successes on n trials, with p probability of a success on each trial. It can be approximated to the normal distribution with [tex]\mu = np, \sigma = \sqrt{np(1-p)}[/tex].The parameters for the binomial distribution are:
p = 0.5, n = 13.
Hence the mean and the standard deviation are:
[tex]\mu = np = 13 \times 0.5 = 6.5[/tex].[tex]\sigma = \sqrt{np(1-p)} = \sqrt{13 \times 0.5 \times 0.5} = 1.8028[/tex]Using continuity correction, the desired probability is P(X > 9.5), which is one subtracted by the p-value of Z when X = 9.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{9.5 - 6.5}{1.8028}[/tex]
Z = 1.66
Z = 1.66 has a p-value of 0.9515.
1 - 0.9515 = 0.0485, then:
[tex]P(X \geq 10) = 0.0485[/tex].
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b. What is another composition of rigid motions that maps A GHJ to A KLM?
Another rigid motions that maps Δ GHJ to ΔKLM is ΔGHJ winding point J rotates 180° in the counterclockwise direction. It then transits south by 10 units and to the right by two units. See the attached image.
What is Rigid Motion?Rigid Motion is any method of moving all the points in the plane in such a way that.
the relative distance between sites remains constant andthe relative location of the points remains constant.There are four forms of rigid motions:
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Assuming a 1-year, money market account investment at 2.55 percent (APY), a 1.11 % inflation rate, a 28 percent marginal tax bracket, and a constant $60000 balance, calculate the after-tax rate of return, the real return, and the total monetary return. What are the implications of this result for cash management decisions?
Question content area bottom
Part 1
Assuming a 1-year, money market account investment at 2.55 percent (APY), a 28 percent marginal tax bracket, and a constant $ 60000 balance the after-tax rate of return is
enter your response here%. (Round to two decimal places.)
The after-tax rate of return is 1.84%, the real return is 0.721%, the total monetary return is $1530 and the implications become very challenging to grow with such a return as the taxes
Given that money market account investment at 2.55 percent (APY), a 1.11 % inflation rate, a 28 percent marginal tax bracket, and a constant $60000 balance.
Cash management is the backbone of any business. Cash management ensures that the company operates according to established standards and optimizes the use of funds to avoid wasting resources. Liquidity management decisions are therefore key to preserving a company's capital and profitability.
Firstly, we will find the after-tax return rate, we get
After-tax return rate= Before tax rate of return \times ( 1 - tax rate)
After-tax rate of return = 0.0255× ( 1 - 0.28)
After-tax rate of return = 0.0255×0.72
After-tax rate of return=1.84%
Now, we will find the real return, we get
Real return=((1+After-tax Return)/(1+inflation rate))-1
Real return=((1+0.0184)/(1+0.0111))-1
Real return=(1.0184/1.0111)-1
Real return=1.00721-1
Real return=0.721%
Furthermore, we will find the total monetary return, we get
Total monetary rate=Balance×Before tax rate of return
Total monetary rate=60000×2.55%
Total monetary rate=$1530.
The implications of this result for cash management decisions is that it becomes very challenging to grow with such a return as the taxes and inflation is draining the returns and leaving only with negative returns.
Hence, the after-tax rate of return is 1.84%, the real return is 0.721%, the total monetary return is $1530 and the implications become very challenging to grow with such a return as the taxes and inflation is draining the returns and leaving only with negative returns.
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