A group of students is collecting 16 oz and 28 oz jars of peanut butter to donate to a food bank. At the end of the collection period, they donated 1,876 oz of peanut butter and a total of 82 jars of peanut butter to gre food bank.
a. Write a system of equations that represents the constraints in this situation. Be sure to specify the variables that you use.
b. How many 16 oz jars and how many 28 oz jars of peanut butter were donated to the food bank? Explain or show how you know.

Answers

Answer 1

35 16 oz jars and 47 28 oz jars of peanut butter were donated to the food bank by solving equation

Let x be the number of 16 oz jars of peanut butter collected, and y be the number of 28 oz jars of peanut butter collected.

The system of equations that represents the constraints in this situation is:

x + y = 82 (total number of jars collected)

16x + 28y = 1876 (total amount of peanut butter collected in ounces)

b. To solve for the number of 16 oz jars and 28 oz jars of peanut butter donated to the food bank

we need to solve the system of equations from part (a). One way to do this is to use elimination:

Multiplying the first equation by 16, we get:

16x + 16y = 1312

Subtracting this equation from the second equation, we get:

12y = 564

Dividing both sides by 12, we get:

y = 47

Substituting this value of y into the first equation, we get:

x + 47 = 82

Subtracting 47 from both sides, we get:

x = 35

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Related Questions

Which expression represents twice the sum of a number and six

Answers

Answer:

2(x + 6)

Step-by-step explanation:

If we let the number be "x", then the sum of the number and six is x + 6. To find twice the sum, we multiply this expression by 2:

2(x + 6)

Therefore, the expression that represents twice the sum of a number and six is 2(x + 6)

A.
B.

4
x

+1
x+4

=−3
=−12

1) How can we get Equation
�
BB from Equation
�
AA?

4
x

+1
x+4

=−3
=−12

1) How can we get Equation
�
BB from Equation
�
AA?

Answers

The correct answers are given below:

D. Multiply/divide both sides by the same non-zero constant

A. Yes

How to solve

To achieve equity between Equation A and Equation B, one must:

A: 4x + 1(x+4) = -3B: -12x - 48 = -12

Via combining 1 with the parenthesis of Equation A and conjoining common terms, one begins by distributing the 1 and fusing both sides together to form 5x + 4 = -3.

Afterward, multiplying both sides of the equation by -12 (the same non-zero constant), yields -60x - 48 = 36.

Ultimately, adding 72 to both equities presents the answer to furthering equations, -12x - 48 = -12.

Thus, the resolution rest in choice D- multiply/divide both sides by the same non-zero constant.

By producing Equation B from Equation A through analogous methods on either side of the equation, it is confirmed that the two compilations are equivalent and manifest exact solutions. Therefore, the proper selection for this query is Yes- Choice A.

Answers

Answer:r=3cscθ

Step-by-step explanation:The equation y = 3 represents a horizontal line at a distance of 3 units above the x-axis in the Cartesian coordinate system. To convert this equation into polar form, we can use the fact that x = rcos(theta) and y = rsin(theta) in polar coordinates.

Since y = 3 for all values of x, we can say that r*sin(theta) = 3. Solving for r, we get:

r = 3/sin(theta)

This equation represents a family of circles with center at the origin and radius 3/sin(theta), for all values of theta except for multiples of pi. We can simplify this equation by using the identity sin(theta) = 1/csc(theta), giving us:

r = 3csc(theta)

Pat and Jeff walk to dock at 2 mph, jumped into the boat, and motored to Dillon at 8mph. If the total distance is 13 miles and trip took 11/4 in all, how far did boat go?

Answers

Let's start by using the formula:

distance = rate x time

Let d be the distance the boat traveled, in miles.

The time it took Pat and Jeff to walk to the dock is the same as the time it took them to motor to Dillon, so we can write:

d/8 = (13 - d)/2

Simplifying this equation, we get:

d = 8(13 - d)/2

d = 52 - 4d

5d = 52

d = 10.4

Therefore, the boat traveled a distance of 10.4 miles.

PLEASE HELP ASAP!!!
The length of ribbons found at a seamstress are listed.

2, 10, 10, 12, 12, 20

What is the appropriate measure of variability for the data shown, and what is its value?

The mean is the best measure of variability and equals 11.
The median is the best measure of variability and equals 11.5.
The range is the best measure of variability and equals 18.
The IQR is the best measure of variability and equals 2.

Answers

The appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

The given data set is:

2, 10, 10, 12, 12, 20

To determine the appropriate measure of variability, we need to consider the spread or dispersion of the data. In this case, we can see that the range,

20 - 2 = 18.

A better measure of variability for this data set is the interquartile range (IQR), which is the range of the middle 50% of the data. To find the IQR, we first need to find the median of the data:

2, 10, 10, 12, 12, 20

The median is the middle value when the data set is arranged in order, which is 11. We can then divide the data set into two halves:

2, 10, 10 and 12, 12, 20

The lower half has a median of 10, and the upper half has a median of 12. The IQR is the difference between these medians:

IQR = 12 - 10 = 2

Therefore, the appropriate measure of variability for this data set is the IQR, and its value is 2. The mean and median are measures of central tendency, not measures of variability. The range may not be the best measure of variability for this data set because it is influenced by extreme values.

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Bruce's grandmother loves to use fresh tomatoes in her homemade pasta sauce. Bruce thought she might like to grow her own, so he bought her a planter box and a tomato plant. The planter box is shaped like a rectangular prism. It is 12 1/2
inches long, 10 inches wide, and has a volume of 1,875 cubic inches.
What is the height of the planter box?
Write your answer as a whole number, proper fraction, or mixed number.

Answers

The height of the planter box is 15 inches.

We have,

The volume of a rectangular prism is given by the formula:

V = l w h

where V is the volume, l is the length, w is the width, and h is the height.

In this case, we know that the length is 12 1/2 inches and the width is 10 inches, and the volume is 1,875 cubic inches.

So we can plug these values into the formula and solve for the height:

[tex]1,875 = (12 \frac{1}{2})\cdot 10 \cdot h[/tex]

Multiplying the length and width, we get:

1,875 = 125h

Dividing both sides by 125, we get:

h = 15

Therefore,

The height of the planter box is 15 inches.

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1. How many hours and minutes elapsed from 12:00 noon to 4:59 p.m.?

2. How many hours and minutes elapsed from 1:23 a.m. to 7:35 a.m.?

3. How many hours and minutes elapsed from 11:28 p.m. to 5:30 a.m.?

Answers

1) Total time elapsed = 4 hours 59 minutes.

2) Total time elapsed = 6 hours 12 minutes

3) Total time elapsed = 6 hours 2 minutes

1) Time difference from 12:00 noon to 4:00 p.m = 4 hours

Time difference from 4:00 p.m to 4:59 p.m. = 59 minutes

So, the total time elapsed = 4 hours 59 minutes.

2) The time difference from 1:23 a.m. to 2:00 a.m. = 37 minutes

The time difference from 2:00 a.m to 7:00 a.m. = 5 hours

The time difference from 7:00 a.m. to 7:35 a.m. = 35 minutes

Here, the minutes elasped = 37 + 35

= 72 minutes

= 1 hour 12 minutes

So, So, the total hours elapsed = 5 + 1

= 6 hours

Thus, the total time elapsed = 6 hours 12 minutes

3) Time difference from 11:28 p.m. to 12:00 midnight = 32 minutes

Time difference from 12:00 midnight to 5:30 a.m. = 5 hours 30 minutes

Here, the minutes elasped = 32 + 30

= 62 minutes

= 1 hour 2 minutes

So, the total time elapsed = 6 hours 2 minutes

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Please answer fast!!

What are the x-intercepts for the graph y = cos x, where
0≤x≤ 2n?

Answers

The x-intercepts for the function y = cos x, where 0≤x≤ 2n are

x = π/2, x = 3π/2, and x = 2π

We have,

The cosine function has an x-intercept whenever it crosses the x-axis, which happens at every multiple of π/2 radians (or 90 degrees).

So the x-intercepts for the graph y = cos x, where 0 ≤ x ≤ 2π are at

x = π/2, x = 3π/2, and x = 2π

(corresponding to 90 degrees, 270 degrees, and 360 degrees).

Now,

If we take 2n to be a multiple of 2π (i.e., 2n = k2π for some integer k), then the x-intercepts for the graph y = cos x,

where 0 ≤ x ≤ 2n, will be at x = kπ/2 for k = 0, 1, 2, ..., 4n-1.

The x-intercepts for the graph y = cos x, where 0≤x≤ 2n are

x = π/2, x = 3π/2, and x = 2π

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Garden County provides the following information in order to prepare reconciliations between governmental fund financial statements and government-wide financial statements (fiscal year 1/1/2022 to 12/31/2022).

Total Fund Balance 12/31/22 $200,000

Total Change in Fund Balance for the year ending 12/31/22 $50,000

Capital Assets: 1) Acquisition value of 1/1/22 capital assets of $10,000,000 with an associated accumulated depreciation $5,200,000; 2) During 2022 Garden County purchased new capital assets equal to $1,000,000; 3) During 2022 Garden County sold capital assets with a book value of $30,000 for $32,000 cash; 4) 2022 Depreciation expense is equal to $500,000.

Bonds Payable: 1) Bonds Payable outstanding as of 1/1/22 is $3,200,000; 2) An additional issuance at face value during 2022 equals $400,000; 3) A repayment of bonds payable of $200,000 occurred during 2022.

Interest on LT Debt: 1) Accrued interest payable exists as of 12/31/2022 but was not accrued in the governmental fund (not due and payable) in the amount of $180,000.

Property taxes: All property taxes receivable were collected in 2022 with the exception of $80,000. Of that $80,000, $60,000 is expected to be collected within the first 60 days of 2023 and the remainder beyond that time period.

Part A: Prepare a reconciliation between the Governmental Fund Balance Sheet and the Government-wide Statement of Net Position at 12/31/22. Use proper headings and show any supporting computations for full credit.

Part B: Prepare a reconciliation between the Governmental Fund Statement of Revenues, Expenditures, and Changes in Fund Balance and the Government-wide Statement of Activities for the year ending 12/31/22. Use proper headings and show any supporting computations

Answers

Answer:

governmental fund financial statements and government-wide financial statements have different purposes and accounting methods. Governmental fund financial statements focus on the short-term financial performance and accountability of individual funds, using the modified accrual basis of accounting. Government-wide financial statements provide a broader and longer-term perspective of the government's financial position and activities, using the full accrual basis of accounting.

To reconcile between these two types of statements, some adjustments are needed to account for the differences in measurement focus and basis of accounting. Here are the steps to prepare the reconciliations for Part A and Part B:

Part A: Reconciliation between the Governmental Fund Balance Sheet and the Government-wide Statement of Net Position at 12/31/22.

- Start with the total fund balance of the governmental funds as reported in the fund balance sheet ($200,000).

- Add the net value of capital assets (acquisition value minus accumulated depreciation) as reported in the government-wide statement of net position. This is because capital assets are not reported in governmental fund financial statements, but are reported in government-wide financial statements. The net value of capital assets can be calculated as follows:

- Acquisition value of capital assets as of 1/1/22: $10,000,000

- Plus: Purchases of capital assets during 2022: $1,000,000

- Less: Sales of capital assets during 2022: $30,000

- Equals: Acquisition value of capital assets as of 12/31/22: $10,970,000

- Less: Accumulated depreciation as of 1/1/22: $5,200,000

- Less: Depreciation expense for 2022: $500,000

- Equals: Accumulated depreciation as of 12/31/22: $5,700,000

- Net value of capital assets as of 12/31/22: $5,270,000

- Subtract the amount of bonds payable as reported in the government-wide statement of net position. This is because bonds payable are not reported in governmental fund financial statements, but are reported in government-wide financial statements. The amount of bonds payable can be calculated as follows:

- Bonds payable as of 1/1/22: $3,200,000

- Plus: Issuance of bonds payable during 2022: $400,000

- Less: Repayment of bonds payable during 2022: $200,000

- Bonds payable as of 12/31/22: $3,400,000

- Subtract the amount of accrued interest payable on long-term debt as reported in the government-wide statement of net position. This is because accrued interest payable is not reported in governmental fund financial statements, but are reported in government-wide financial statements. The amount of accrued interest payable is given as $180,000.

- Add the amount of property taxes receivable that are not available to pay current liabilities as reported in the governmental fund balance sheet. This is because property taxes receivable that are not available are not recognized as revenues in governmental fund financial statements, but are recognized as revenues in government-wide financial statements. The amount of property taxes receivable that are not available can be calculated as follows:

- Total property taxes receivable as of 12/31/22: $80,000

- Less: Property taxes receivable expected to be collected within 60 days of year-end: $60,000

- Property taxes receivable that are not available as of 12/31/22: $20,000

- The resulting amount is the net position of governmental activities as reported in the government-wide statement of net position.

The reconciliation can be presented in a table format as follows:

| Reconciliation of Total Fund Balance to Net Position | Amount |

| ----------------------------------------------------- | ------ |

| Total fund balance - governmental funds | \$200,000 |

| Capital assets used in governmental activities are not financial resources and therefore are not reported in the funds | \$5,270,000 |

| Long-term liabilities applicable to governmental activities are not due and payable in the current period and therefore are not reported in the funds | $-\$3,580,000$ |

| Revenues in the statement of activities that do not provide current financial resources are not reported as revenues in the funds | \$20,000 |

| Net position - governmental activities

Find the length of the radius r

Answers

Answer:

[tex]r = \sqrt{ {8.6}^{2} - {5}^{2} } [/tex]

[tex]r = \sqrt{73.96 - 25} = \sqrt{48.96} = 6.997[/tex]

The closest answer is b.

(x+1) (x-5)=16 formula cuadratica brainly

Answers

The calculated value of x in the equation (x + 1) (x - 5) = 16 is 7

Calculating the value of x in the equation

From the question, we have the following parameters that can be used in our computation:

(x + 1) (x - 5) = 16

The above expression is the product of two factors

(x + 1) and (x - 5)

And the result is 16

Express 16 as 8 * 2

So, we have

(x + 1) (x - 5) = 8 * 2

By comparison, we have

x + 1 = 8 and x - 5 = 2

When evaluated, we have

x = 7 and x = 7

This means that the value of x in the equation is 7

Answers

It took approximately 151 seconds to decrease 9 ft water in conical tank.

The volume of a conical tank with vertex down and radius 8 ft and height 20 ft is V = (1/3)πr²h

When the water is 9 ft deep

= (1/3) ×3.14×(8)²×(9)

= 602.88 ft³

We know that the rate of change of volume is 4 ft³/sec. So, the rate of change of depth can be calculated as follows:

Rate of change of depth (dh/dt) = Volume of tank/4 ft³ per sec

= 602.88/4

= 150.72 sec

Therefore, it took approximately 151 seconds to decrease 9 ft water in conical tank.

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PLS HELP ASAP!!!!!!!!!!

Answers

Answer:

I believe it is B. always

Because Adding, subtracting or even multiplying will always give you a new polynomial not the same polynomial.

Im sorry if i am wrong

ASAAP NEEED HELLPPPPPPP

Answers

Answer: The coordinates of K' and M' are (-2,3) and (-4,1)

**I ONLY HAVE 6HOURS LEFT***
Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply.
A. Reflection across the line x = 3
B. Rotation of 180
C. Translation four units to the right
D. Dilation by a factor of 2

Answers

Answer:

it's b to to the angles rotation that is giving 180 each side of the square is 90 degrees now you add them up

The bowling average of the players in the Capital Three bowling tournament is 158 with variance of 121. If Dr. Baker bowls an average of 169 during the tournament. Compute the appropriate statistic.

Answers

Answer: 1

Step-by-step explanation:

The formula for the Z-score is:

Z = (X - μ) / σ

where:

- X is Dr. Baker's bowling average

- μ is the mean bowling average of the players in the tournament

- σ is the standard deviation of the bowling averages of the players in the tournament

From the problem, we know that:

- μ = 158

- σ^2 = 121

- X = 169

Therefore, σ = sqrt(121) = 11.

Now we can plug in the values into the Z-score formula:

Z = (169 - 158) / 11 = 1

This means that Dr. Baker's bowling average is 1 standard deviation above the mean bowling average of the players in the tournament.

So the appropriate statistic is the Z-score, which is 1.

Question 8 (2 points)
We need both the Celsius and Fahrenheit formulas to find any of these two
temperature units.
Temperature
C-(F-
(F-32)
F-C+32
True
False

Answers

We do not need both the Celsius and Fahrenheit formulas

Do we need both the Celsius and Fahrenheit formulas

From the question, we have the following parameters that can be used in our computation:

The temperature equations

The general rule is that we need any of the temperature units to find the other temperature unit

This in other words means that we do not need both temperature units to find any of these two temperature units

Hence the statement is false

Answers

Based on the information provided about the 8-sided fair spinner and the probabilities shown on the scale, here is how to determine the probability of spinning a 4:

1) The spinner has 8 sides total, labeled 1, 1, 3, 3, 4, 5, 5, 5. This means it has 2 sides labeled 1, 2 sides labeled 3, 1 side labeled 4, and 3 sides labeled 5.

2) For the probability scale, the arrow options are:
- 0.125 (1 in 8 probability)
- 0.25 (1 in 4 probability)
- 0.5 (1 in 2 probability)
- 0.75 (3 in 4 probability)
- 1 (certainty)

3) Since the spinner has only 1 side labeled 4, the probability of spinning a 4 is 1 out of the 8 sides.

4) Therefore, the correct arrow showing a probability of 0.125 or 1 in 8 chance of spinning a 4.

In summary:

Spinner has 8 sides: 2 (1's), 2 (3's), 1 (4), 3 (5's)
1 side is labeled 4
Probability of landing on 4 is 1 in 8
Arrow showing 0.125 or 1 in 8 chance is correct

Does this make sense? Let me know if any part of the explanation is unclear. I can provide another example or visual diagram if needed to better illustrate determining probabilities from information about a spinner or other probability scenario.

The key concepts are:
1) Identifying the probabilities shown on the scale (options and values)
2) Counting the number of successes (4's) and total possible outcomes (8 sides)
3) Calculating the probability by (number of successes) / (total possible outcomes)
4) Choosing the arrow/scale option that matches the calculated probability

Please feel free to ask any follow up questions. I'm happy to provide more examples or explain probabilities and probability calculations in another way.

Let me know if you have any other questions!

Julio has a number cube that has 6 sides and each side is labeled 1 through 6. He is interested in whether or not the
number cube is a fair cube. Julio performs a simulation which generates 40 trials of 8 rolls of the number cube. He then
graphs the data on a dot plot.
Note: A fair number cube has equally likely outcomes.
Which statement explains how the number cube is fair?
O The data should be skewed left about a central value.
O The data should be skewed right about a central value.
O The data should be symmetric about a central value.
O The data should be randomly distributed.

Answers

The statement explains how the number cube is fair is The data should be symmetric about a central value.

How to get the right statement

Julio's simulation results, when graphed on a dot plot, often demonstrate an example of symmetric distribution where every number occurs with roughly the same frequency.

While perfect symmetry may not be witnessed in this particular simulated experiment, which consists of 40 trials that incorporate 8 rolls each, granted its limited range, the data will commonly point to fairness in its results for a fair number cube.

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The box plot shown represents the age of cars in a parking lot. Which statements are correct?
Select 3 correct answer(s)

The box plot suggests that about 75% of the cars are older than 5 years.

The mean age of a car is 8 years.

The box plot suggests that about 75% of the cars are newer than 11 years.

There are no outliers.

The box plot suggests that about 33.33% of the cars are between 5 and 11 years.

Answers

The correct statements from the box plot are given as follows:

The box plot suggests that about 75% of the cars are older than 5 years.The box plot suggests that about 75% of the cars are newer than 11 years.There are no outliers.

What does a box-and-whisker plot shows?

A box and whisker plots shows these five features from a data-set, listed as follows:

The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.

Hence the correct statements are given as follows:

The box plot suggests that about 75% of the cars are older than 5 years -> as Q1 = 5.The box plot suggests that about 75% of the cars are newer than 11 years -> as Q3 = 11.There are no outliers -> they would appear as a lonely mark outside the bot plot.

The false statements are given as follows:

The mean age of a car is 8 years. -> Median, not mean.The box plot suggests that about 33.33% of the cars are between 5 and 11 years. -> 50% of the cars, it is the IQR.

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Complete the right isosceles triangle above. What could be the coordinates of the missing vertex?
A.
(1, 9)
B.
(1, 8)
C.
(1, 3)
D.
(4, 3)

Answers

Answer: B. (1, 8)

Step-by-step explanation:

Hope this helps! :)

A cake recipe calls for the following dry ingredients: 3 ½ cups of flour, 2 ⅔ cups of sugar, and 1 ¾ cups of cocoa. To the nearest cup, how much dry ingredients will be used?

Answers

The amount of dry ingredients used in the cake recipe is approximately 7 cups.

To find the total amount of dry ingredients used in the cake recipe, we need to add up the amounts of flour, sugar, and cocoa.

3 ½ cups of flour is equal to 3 cups plus 0.5 cups, or 3 cups and 8 ounces.

2 ⅔ cups of sugar is equal to 2 cups plus 0.67 cups, or 2 cups and 10.72 ounces.

1 ¾ cups of cocoa is equal to 1 cup plus 0.75 cups, or 1 cup and 12 ounces.

Adding these amounts together, we get:

3 cups and 8 ounces + 2 cups and 10.72 ounces + 1 cup and 12 ounces = 6 cups and 14.72 ounces

To the nearest cup, this is equal to 7 cups.

Therefore, the amount of dry ingredients used in the cake recipe is approximately 7 cups.

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King of Diamonds Industries has bonds on the market making annual payments, with 14 years to maturity, and selling for R1 482,01. At this price, the bonds yield 7%. What is the coupon rate?

Answers

The coupon rate of the bonds by King of Diamonds Industries would be 7 %.

How to find the coupon rate ?

The formula for the bond price shows the coupon payment and so can be used to find the coupon rate:

= (Coupon payment x ( 1 - ( 1 + r ) ^ ( - number of years till maturity ) ) ) / r + Face value / (1 + rate )^ number of years

1,482.01 = (C x (1 - (1 + 0.07 )^ (- 14) ) ) / 0.07 + F / (1 + 0.07 ) ^ 14

103.7407 - 0.07 x (F / (1 + 0.07) ^14 ) = C x (1 - ( 1 + 0.07) ^ ( - 14) )

Using a calculator, C is $ 70.

This means that the coupon rate is:

= 70 / 1, 000

= 7 %

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please help with this question

Answers

Answer:

(2,2), (4,8), (3,4)

Step-by-step explanation:

Plug in the x-coodinate and it should equal your desired y value

Gabriel was out at a restaurant for dinner when the bill came. He wanted to leave a tip of 33%. What number should he multiply the cost of the meal by to find the total plus tip in one step?

Answers

1.33 should be multiplied to the cost of the meal to find the total plus tip in one step.

To find the total cost of the meal plus the 33% tip, Gabriel needs to multiply the cost of the meal by a factor of 1.33 (which represents the original cost plus 33% of the original cost).

So the total cost including the tip can be found by multiplying the cost of the meal by 1.33.

For example, if the cost of the meal was $50, the total cost including the tip would be:

Total cost = Cost of the meal + 33% tip

Total cost = $50 + 0.33($50)

Total cost = $50 + $16.50

Total cost = $66.50

Therefore, Gabriel should multiply the cost of the meal by 1.33 to find the total cost including the 33% tip in one step.

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Fatima determined that there are 3^6 students in her middle school. How many students are in her middle school?

Answers

The number of students in her middle school would be = 729 students

How to calculate the number of people in the middle school?

The number of students that was determined by Fatima = 3^6

That is;

Number of students = 3×3×3×3×3×3

= 729students

Therefore the number of students that were actually calculated by Fatima = 729 students.

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Select the correct answer.
In the given diagram, line segment BD
bisects angle ABC
. Segment BD
is extended to E, where line segment EC
is parallel to line segment AB
. Write a two-column proof to show that AB/AD = BC/DC
.

Answers

The missing statement and the reason in the two-column proof:

EC = BC; property iof isosceles triangles

The corret answer is an option (A)

A two-column proof to show that AB/AD = BC/DC is:

Statement Reason

∠1 ≅ ∠2 given

∠1 ≅ ∠5 alternate interior angles theorem

∠3 ≅ ∠4 vertical angles theorem

ΔABD is similar to ΔCED AA similarity

AB/AD = EC/DC property of similar triangles

∠2 ≅ ∠5 substitution property of congruency

EC = BC property iof isosceles triangles

AB/AD = BC/DC substitution property of equality

Therefore, the correct answer is an option (A)

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Find the complete question below.

The line plot shows the number of siblings
for 18 students.
a. Explain how you know the distribution is not symmetric.
b. Is the distribution skewed left or skewed right? Explain.
Number of Siblings
110-1
0 1 2 3 4 5 6 7 8
c. Use appropriate measures to describe the center and spread of the
distribution. Justify your choice of measure based on the shape of the
distribution.

Answers

The line plot is not symmetric because the numbers of siblings range from 0 to 8.

a. The line plot is not symmetric because the numbers of siblings range from 0 to 8. The number of students with 0 siblings is much greater than the number of students with 8 siblings.

b. The distribution is skewed left, meaning that the majority of students have fewer siblings than the average.

c. Since the distribution is skewed left, the median would be a better measure of the center because it is not affected by the outliers. The median number of siblings is 0. To measure the spread of the distribution, we can use the range, which is 8.

Therefore, the line plot is not symmetric because the numbers of siblings range from 0 to 8.

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Find the equation of the axis of symmetry for the parabola with equation
y = 4x^2 − 5x + 1.

Answers

The equation of the axis of symmetry is x = 5/8

The axis of symmetry of a parabola is a vertical line that divides the parabola into two symmetric halves.

The equation of the axis of symmetry for a parabola of the form y = ax² + bx + c is given by:

x = -b/(2a)

In the given equation, a = 4 and b = -5. Substituting these values into the formula, we get:

x = -(-5)/(2×4)

x = 5/8

Therefore, the equation of the axis of symmetry is x = 5/8

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Complete the equation describing how x
and y are related.
X
-3
-2
-1
0
1
2
Y
24
16
8
0
-8
-16
y = [? ]x
Enter the answer that
belongs in [?].

Answers

A linear equation that describe how x and y are related include the following: A. y = -8x.

What is a proportional relationship?

In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:

y = kx

Where:

y represents the x-variable.x represents the y-variable.k is the constant of proportionality.

Next, we would determine the constant of proportionality (k) by using various data points as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 24/-3 = 16/-2 = 8/-1 = -8/1 = -16/2

Constant of proportionality, k = -8.

Therefore, the required linear equation is given by;

y = kx

y = -8x

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