In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.

please help i'm having trouble answering this (70 points) (brainylist answer) thank you!

Answers

Answer 1

The hexagon will have six congruent sides of equal length and six congruent angles of 120 degrees each.

In order to produce a cross section of a regular hexagon, the plane should pass through the cube such that it intersects three pairs of opposite edges at equal distances from their endpoints, forming an equilateral triangle in each pair.

These three equilateral triangles will intersect at the center of the hexagon, forming six congruent triangles that make up the regular hexagon. Imagine the cube as a three-dimensional box with edges of equal length.

Imagine a plane passing through the box such that it intersects three pairs of opposite edges at equal distances from their endpoints. These three pairs of edges will form three equilateral triangles within the cube, and their intersections at the center of the cube will form a regular hexagon.

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Related Questions

In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)



Margin of error:



Interpretation:

Answers

The margin of error at the 99% confidence interval is 0.018 or 1.8%.

Interpretation: This means that if we were to repeat the survey many times, about 99% of the intervals calculated from the samples would contain the true proportion of viewers under 30 in the population, and the margin of error for each interval would be no more than 1.8%.

The margin of error is the amount by which the sample statistic (in this case, the proportion of viewers under 30) may differ from the true population parameter.

Using the given formula for margin of error:

Margin of error = z* * sqrt(p*(1-p)/n)

Where:

- z* is the z-score corresponding to the confidence level (99% in this case), which is 2.576

- p is the proportion of viewers under 30, which is 0.3

- n is the sample size, which is 5000

Substituting these values, we get:

Margin of error = 2.576 * sqrt(0.3*(1-0.3)/5000) = 0.018

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Work out the size of angle t.
t
40°

Answers

It would be 50 degrees. The box represents a 90 degree angle.
Just do simple math
90-40
50

A straight line ax+by=16.it passes through a(2,5) and b(3,7).find values of a and b​

Answers

The values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.

To find the values of a and b, we need to use the coordinates of points A and B and the equation of the line ax+by=16.

First, we substitute point A(2,5) into the equation to get:

a(2) + b(5) = 16

Next, we substitute point B(3,7) into the equation to get:

a(3) + b(7) = 16

We now have two equations with two unknowns, which we can solve simultaneously.

Multiplying the first equation by 3 and the second equation by -2, we get:

6a + 15b = 48

-6a - 14b = -32

Adding the two equations, we eliminate the a variable and get:

b = 2

Substituting b = 2 into one of the original equations, we get:

2a + 10 = 16

Solving for a, we get:

a = 3

Therefore, the values of a and b that satisfy the equation of the line and pass through points A(2,5) and B(3,7) are a = 3 and b = 2.

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Evaluate each geometric series described. . 34) a, =-2, a = 256, r=-2 n 33) a=-1, a = 512, r=-2 : A) 397 B) 341 -- B) 149 1 2 A) 3 C) 170 C) - D) 463 D) 156 3 n 71 35) a, = 4, a = 16384, r=4 , , A) 22

Answers

(34) the sum of the series is 170. (33) The sum of the series is 341. (35) the sum of the series is 21844


To evaluate a geometric series, we use the formula:

Sn = a(1 - r^n) / (1 - r)

where:

Sn = the sum of the first n terms of the series
a = the first term of the series
r = the common ratio between consecutive terms
n = the number of terms we want to sum

Let's use this formula to evaluate the given geometric series:

34) a1 = -2, a8 = 256, r = -2

To find the sum of this series, we need to know the value of n. We can find it using the formula:

an = a1 * r^(n-1)

a8 = -2 * (-2)^(8-1) = -2 * (-2)^7 = -2 * (-128) = 256

Now we can solve for n:

an = a1 * r^(n-1)
256 = -2 * (-2)^(n-1)
-128 = (-2)^(n-1)
2^7 = 2^(1-n+1)
7 = n-1
n = 8

So this series has 8 terms. Now we can use the formula to find the sum:

Sn = a(1 - r^n) / (1 - r)
S8 = (-2)(1 - (-2)^8) / (1 - (-2))
S8 = (-2)(1 - 256) / 3
S8 = 510 / 3
S8 = 170

Therefore, the sum of the series is 170.

33) a1 = -1, a9 = 512, r = -2

We can use the same method as before to find n:

an = a1 * r^(n-1)
512 = -1 * (-2)^(9-1) = -1 * (-2)^8
512 = 256
This is a contradiction, so there must be an error in the problem statement. Perhaps a9 is meant to be a5, in which case we can find n as:

an = a1 * r^(n-1)
a5 = -1 * (-2)^(5-1) = -1 * (-2)^4
a5 = 16
512 = -1 * (-2)^(n-1)
-512 = (-2)^(n-1)
2^9 = 2^(1-n+1)
9 = n-1
n = 10

So this series has 10 terms. Now we can use the formula to find the sum:

Sn = a(1 - r^n) / (1 - r)
S10 = (-1)(1 - (-2)^10) / (1 - (-2))
S10 = (-1)(1 - 1024) / 3
S10 = 1023 / 3
S10 = 341

Therefore, the sum of the series is 341.

35) a1 = 4, a14 = 16384, r = 4

Again, we can find n using the formula:

an = a1 * r^(n-1)
16384 = 4 * 4^(14-1) = 4 * 4^13 = 4 * 8192 = 32768
This is a contradiction, so there must be an error in the problem statement. Perhaps a14 is meant to be a7, in which case we can find n as:

an = a1 * r^(n-1)
a7 = 4 * 4^(7-1) = 4 * 4^6 = 4 * 4096 = 16384
16384 = 4 * 4^(n-1)
4096 = 4^(n-1)
2^12 = 2^(2n-2)
12 = 2n-2
n = 7

So this series has 7 terms. Now we can use the formula to find the sum:

Sn = a(1 - r^n) / (1 - r)
S7 = (4)(1 - 4^7) / (1 - 4)
S7 = (4)(1 - 16384) / (-3)
S7 = 65532 / 3
S7 = 21844

Therefore, the sum of the series is 21844.

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f(x, y) = ex sin y do first and second order partial derivatives. f(x, y) = e^x sin y. do first and second order partial derivatives

Answers

The first order partial derivatives of f(x, y) =  ex cos y and the second order partial derivatives are ex sin y = ex cos y.

The given function is f(x, y) = ex sin y. We need to find the first and second order partial derivatives of this function with respect to x and y.
First order partial derivatives:
To find the partial derivative of f(x, y) with respect to x, we treat y as a constant and differentiate ex with respect to x. This gives:
∂f/∂x = ex sin y
To find the partial derivative of f(x, y) with respect to y, we treat x as a constant and differentiate sin y with respect to y. This gives:
∂f/∂y = ex cos y
Second order partial derivatives:
To find the second order partial derivatives, we differentiate the first order partial derivatives we found above. That is, we differentiate ∂f/∂x and ∂f/∂y with respect to x and y, respectively.
∂/∂x (ex sin y) = ex sin y
∂/∂y (ex cos y) = -ex sin y
To find the mixed partial derivatives, we differentiate one of the first order partial derivatives with respect to the other variable. That is,
∂/∂y (ex sin y) = ex cos y
We can also find the mixed partial derivative  by differentiating ∂f/∂y with respect to x, which gives the same result:
∂/∂x (ex cos y) = ex cos y
The first order partial derivatives of f(x, y) = ex sin y are ∂f/∂x = ex sin y and ∂f/∂y = ex cos y and the second order partial derivatives are ex sin y, ∂f/∂[tex]y^2[/tex] = -ex sin y, and ∂f/∂x∂y = ∂f/∂y∂x = ex cos y.

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Consider the quadratic function: f(x)=x^2-6x+8
Identify the coordinates of the x(intercepts if any

Answers

Answer:

x-intercepts (4,0) (2,0)

y-intercepts (0,8)

Step-by-step explanation:

have a good day :)

Huang buys 3 shirts that each cost the same amount a pair of pants that cost 12$ and pays with a 100$ bill which expressesion represents the amount of change huang receive

Answers

Answer: 64$

Step-by-step explanation:

PLEASE HELP THIS IS MY LAST QUESTION PLEASEEEEEE

Given PQR with angle P = 42°, angle R = 26°, and PQ = 19, solve the triangle. Round all answers to the nearest tenth.

Angle Q =__
QR =__
PR =__

Answers

To solve the triangle, we have;

Angle Q = [tex]112^{o}[/tex]

QR = 30.0

PR = 40.2

What is a sine rule?

A sine rule is a trigonometric function that can be applied to determined the unknown side, or angle of a none right triangle.

From the information given in the question, to solve the triangle;

P + R + Q = 180

42 + 26 + Q = 180

Q = 180 - 68

   = 112

Q = [tex]112^{o}[/tex]

Applying the sine rule,

QR/Sin P = PR/Sin Q = PQ/Sin R

PR/Sin Q = PQ/Sin R

PR/Sin 112 = 19/ Sin 26

PRSin 26 = 19*Sin 112

             = 17.6165

PR = 17.6165/ 0.4384

  = 40.1836

PR = 40.2

Also,

QR/Sin P = PQ/Sin R

QR/Sin 42 = 19/ Sin 26

QRSin 26 = 19*Sin 42

                = 12.7135

QR = 12.7135/ 0.4384

     = 28.9998

QR = 30

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What is the percentage chance of choosing a queen or a king from a standard 52-card deck?

Answers

The probability of choosing a king or queen from a standard 52-card deck is 2/13 or approximately 15.4%.

How can we calculate the percentage?

The probability of choosing a king or a queen from a standard 52-card deck can be calculated by first determining the number of kings and queens in the deck. There are four kings (hearts, diamonds, clubs, and spades) and four queens (hearts, diamonds, clubs, and spades) in the deck, for a total of eight cards.

To find the probability of choosing a king or a queen, you need to divide the number of desired outcomes (eight) by the total number of possible outcomes (52).

Probability = Number of desired outcomes / Total number of possible outcomes

Probability = 8 / 52

This simplifies to:

Probability = 2 / 13

Therefore, the probability of choosing a king or a queen from a standard 52-card deck is approximately 0.154 or 15.4%.

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A non-government that supports palay production in the philippines conducted the research that answer the question: is the proportion of palay harvested different from 0. 50 of all the farm crops are harvested? in a sample of 200 one-hectare farm lands, 96 harvested palay.

Answers

For the sample size of 200 and sample data 96 there is no sufficient evidence to conclude that proportion of palay harvested is different from 0.50.

Sample size 'n' = 200

The proportion of palay harvested is different from 0.50

Use a hypothesis test.

Let us assume the null hypothesis H₀ is that the proportion of palay harvested is equal to 0.50,

and the alternative hypothesis Hₐ is that the proportion of palay harvested is different from 0.50.

H₀: p = 0.50 proportion of palay harvested is equal to 50%

Hₐ: p ≠ 0.50 proportion of palay harvested is not equal to 50%

where p is the population proportion of palay harvested.

To test this hypothesis, use the sample data of 96 out of 200 one-hectare farm lands that harvested palay.

The sample proportion of palay harvested is,

p₁= 96/200

  = 0.48

To determine if this sample proportion is significantly different from the hypothesized proportion of 0.50,

Use a two-tailed z-test with a significance level of α = 0.05.

The test statistic is calculated as,

z = (p₁ - p) / √(p(1-p)/n)

where n is the sample size.

Substituting the values, we get,

z = (0.48 - 0.50) / √(0.50(1-0.50)/200)

⇒ z = -0.5658

Using a z-table,

The probability of getting a z-value of -0.5658 or lower in the left tail of the distribution is approximately 0.7123.

Since this is a two-tailed test,

Probability of getting a z-value of 0.5658 or higher in the right tail of the distribution is also approximately 0.7123

p-value for this test is 0.7123+ 0.7123 = 1.4246

Since the p-value is greater than the significance level of α = 0.05,

Fail to reject the null hypothesis.

Therefore,  do not have sufficient evidence to conclude that the proportion of palay harvested is different from 0.50.

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Help pls! Find the area of the circle
​Use π = 3.14 and round your answer to the nearest hundredth.

Answers

the area of the circle is 615. 4 m²

How to determine the area

The formula that is used to calculate the area of a circle is expressed with the equation.

We have the equation as;

A = πr²

Such that the parameters are given as;

A is the area of the circleπ takes the constant value of 22/7 or 3.14r is the radius of the circle

From the diagram shown, we have that;

A = unknown

r = 14m

Now, substitute the values, we get;

Area = 3.14 ×14²

Find the square value

Area = 3.14(196)

Multiply the values

Area = 615. 4 m²

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solve this and I will give u brainlist.

Answers

We can use basic trigonometry to solve this problem. If we draw a right triangle with the angle of inclination as one of the acute angles, then the opposite side of the triangle is the height of skyscraper B, and the adjacent side is the horizontal distance between the two buildings.

We can use the tangent function to find the length of the adjacent side:

tan(14.4) = opposite / adjacent

tan(14.4) = 1472 / adjacent

adjacent = 1472 / tan(14.4)

adjacent = 6163.6 feet (rounded to one decimal place)

Therefore, the distance from skyscraper A to skyscraper B is approximately 6163.6 feet.

6. Mary Cole is buying a $225,000.00 home. Her annual housing
expenses are: mortgage payments, $14,169.20; real estate taxes,
$3,960.00; annual insurance premium, $840.00; maintenance,
$1,410.00; and utilities, $5,180.00. What is Mary's average
monthly expense?
Chapter 10 Mathematics for Business and Personal Finance

Answers

Mary's average monthly expense for housing is $2,129.93.

To find Mary's average monthly expenseW

We need to add up all her annual housing expenses and divide the total by 12 (the number of months in a year):

Total annual housing expenses = mortgage payments + real estate taxes + annual insurance premium + maintenance + utilities

Total annual housing expenses = $14,169.20 + $3,960.00 + $840.00 + $1,410.00 + $5,180.00

Total annual housing expenses = $25,559.20

Average monthly expense = Total annual housing expenses ÷ 12

Average monthly expense = $25,559.20 ÷ 12

Average monthly expense = $2,129.93

Therefore, Mary's average monthly expense for housing is $2,129.93.

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Hello, please help me answer this geometry problem asap. Question shown in image below. Thanks :)

Answers

Answer:

[tex] \: \frac{11}{1620} \: \pi^{2} [/tex]

Step-by-step explanation:

I think this is it. But if you find a mistake somewhere let me know? I'm confused because the answer seems a little weird. Like 11/1620 pi² really?

Also at the bottom I wrote "area of sector =" but the area got cut off

The radius of the large circle is 3 inches and AB is its diameter. Also, AC is tangent to the large circle at point A. If arc CD = 160 and arc CE = 100, find the area of triangle ABC. ​

Answers

The area of triangle ABC is 13.95 square inches.

We can start by finding the length of AB, which is equal to the diameter of the circle. Since the radius is 3 inches, the diameter is 2 times the radius, or 6 inches.

Next, we can use the fact that AC is tangent to the circle to conclude that angle CAB is a right angle. Therefore, triangle ABC is a right triangle.

Let's use the information about the arcs CD and CE to find the measure of angle BAC. The measure of an inscribed angle is half the measure of the arc that it intercepts, so angle CAD is 80 degrees and angle CAE is 50 degrees. Since angles CAD and CAE are opposite each other and AC is a tangent, we have angle BAC is 180 - 80 - 50 = 50 degrees.

Now we know that triangle ABC is a right triangle with a 90-degree angle at B and a 50-degree angle at A. To find the area of the triangle, we need to know the length of BC.

Using trigonometry, we can find that BC = AB * sin(50) ≈ 4.65 inches.

Therefore, the area of triangle ABC is (1/2) * AB * BC = (1/2) * 6 * 4.65 = 13.95 square inches. Rounded to the nearest hundredth, the area of triangle ABC is 13.95 square inches.

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Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth.

Answers

1. The probability that the point chosen is in the triangle is 0.1 (nearest tenth)

2. The probability that the point is in the square is 0.2( nearest tenth)

What is probability?

A probability is a number that reflects the chance or likelihood that a particular event will occur. The certainty for an event is 1 which is equivalent to 100%.

Probability = sample space / total outcome

total outcome is the area of rectangle , which is

A = l× w

= 12 × 8

= 96

area of the rectangle = 1/2 bh

= 1/2 × 4 × 5

= 2 × 5

= 10

Area of the square = 4×4

= 16

1. Probability the the point will be in the triangle= 10/96 = 5/48

= 0.1( nearest tenth)

2. probability the the point will be in the square =

16/96 = 1/6

= 0.2 ( nearest tenth)

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In a school of 580 students, one class was asked which hand they write with.
• “L” means they use their left hand.
• “R” means they use their right hand.
Here are the results:
L, R, R, R, R, R, R, R, R, L, R, R, R, R, R

1) Based on this sample, estimate the proportion of students at the school who write with their left hand.
2) Estimate the number of students at the school who write with their left hand.
3) A different class of `18` students is surveyed. Estimate how many write with their left hand.

Answers

1.  The proportion of students at the school who write with their left hand is 2/15 OR 13.3%

2. The estimated number of students who write with their left hand is 77 students

3. The estimated number of students in the different class of 18 students who write with their left hand is 2

Estimating the number of students that write with their left hand

From the question, we are to estimate the proportion of students who write with their left hand

To estimate the proportion of students at the school who write with their left hand, we need to count the number of students in the sample who write with their left hand and divide by the total number of students in the sample.

From the given sample, there are 2 students who write with their left hand and 13 students who write with their right hand. So the estimated proportion of students who write with their left hand is:

2/15 = 0.133

OR

13.3%

2.

To estimate the number of students at the school who write with their left hand, we can multiply the proportion by the total number of students in the school

That is,

2/15 x 580 = 77.33

Thus, about 77 students write with their left hand

3.

To estimate how many students in a different class of 18 students write with their left hand, we can apply the proportion to the new sample:

2/15x 18 = 2.4

Hence, about 2 students in the different class write with their left hand.

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traveling 60 mhp in the car after 3 hours how long would that be

Answers

Answer:

Step-by-step explanation:

60 x 3 = 180

180 miles

(1 point) Write an equivalent integral with the order of integration reversed IMP3 F(x,y) dyd. = Lo g(x) F(x, y) dedy f(y) a = be f(y) = 9(y) =

Answers

the equivalent integral with the order of integration reversed is: ∫0^1 ∫1^2 log(x) 9(y) dydx = (9/2) (2log(2) - 1)

To write an equivalent integral with the order of integration reversed, we need to integrate first with respect to y and then with respect to x. So, we have:

∫a^b ∫f(y)g(x) F(x,y) dxdy

Reversing the order of integration, we get:

∫f(y)g(x) ∫a^b F(x,y) dydx

Now, substituting the given values for f(y), g(x), and F(x,y), we get:

∫0^1 ∫1^2 log(x) 9(y) dydx

= ∫0^1 [9(y)∫1^2 log(x) dx] dy

= ∫0^1 [9(y) (xlog(x) - x) from x=1 to x=2] dy

= ∫0^1 [9(y) (2log(2) - 2 - log(1) + 1)] dy

= ∫0^1 [9(y) (2log(2) - 1)] dy

= (9/2) [(2log(2) - 1) y] from y=0 to y=1

= (9/2) (2log(2) - 1)

Therefore, the equivalent integral with the order of integration reversed is:

∫0^1 ∫1^2 log(x) 9(y) dydx = (9/2) (2log(2) - 1)

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Question 20 of 20
Two numbers have a sum of 2 and a difference of 8. Write a system and solve it to identify the two numbers.
5 and 3
O 11 and -9
-5 and 7
O5 and-3

Answers

Let x be the larger of the two numbers, and y be the smaller. We know that:

x + y = 2 (Equation 1)
x - y = 8 (Equation 2)

To solve this system of equations, we can use the method of elimination. Adding Equation 1 and Equation 2, we get:

2x = 10

Dividing both sides by 2, we get:

x = 5

Substituting x = 5 into Equation 1, we get:

5 + y = 2

Subtracting 5 from both sides, we get:

y = -3

Therefore, the two numbers are 5 and -3, and the answer is:

5 and -3

-5 and 7

Step-by-step explanation

lets try putting -5 and 7

-5 +7=2

and the difference is 8

i am not smart sorry

Which triangle has an obtuse angle? ​

Answers

Answer:

Step-by-step explanation:

An obtuse angle has a measure between 90 and 180 degrees. Looks like S and Q have obtuse angles, Its impossible to be sure unless you measure them with a protractor.

A cube has a volume of 27 cm3. A smaller cube has a side length of that is x cm less than side length of the larger cube. Consider the function f(x) = (3 − x)3. What does f(0. 5) represent?​

Answers

f(0.5) represents the volume of the smaller box when its' side length is 0.5 cm less than the larger cube

How to find the Volume of a Cube?

The formula to find the Volume of a cube is:

V = x³

where:

x is the side length of the cube

The cube has a volume of 27 cm³. Thus:

Side length of cube = ∛27 = 3 cm

Since the side length of the smaller cube is x cm less than side length of the larger cube, then we can say that the function to find the volume of the smaller cube is:

V_small: f(x) = (3 - x)³

Thus, f(0.5) is the volume of the smaller box when its' side length is 0.5 cm less than the larger cube

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In the united states, the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children.

analyst 1 wants to calculate the probability that a randomly selected family from the united states has at least 2 children.

analyst 2 wants to calculate the probability that if 40 families from the united states are randomly selected, the mean number of children per family is at least 2 children.

what sample size does analyst 1 plan to use?

enter an integer. what sample size does analyst 2 plan to use?

enter an integer.

Answers

The probability of a randomly selected family from the United States having at least 2 children is 0.2734. The probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884. Analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.

Analyst 1 wants to calculate the probability that a randomly selected family from the United States has at least 2 children. Since the number of children under age 18 per family is skewed right with a mean of 1.9 children and a standard deviation of 1.1 children, we can use the normal distribution to solve this problem.

To calculate the probability of a randomly selected family having at least 2 children, we need to find the area under the normal curve to the right of 2.

Using a standard normal distribution table or calculator, we can find that the area to the right of 2 is approximately 0.2734. Therefore, the probability of a randomly selected family from the United States having at least 2 children is 0.2734.

Analyst 2 wants to calculate the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children. Since we know that the mean number of children per family in the population is 1.9 children and the standard deviation is 1.1 children, we can use the central limit theorem to approximate the sampling distribution of the sample means.

The central limit theorem tells us that the sampling distribution of the sample means will be approximately normal with a mean of 1.9 children and a standard error of the mean equal to the population standard deviation divided by the square root of the sample size.

We want to find the probability that the mean number of children per family is at least 2, so we need to standardize the sample mean using the formula:

z = (sample mean - population mean) / (standard error of the mean)

Plugging in the values, we get:

z = (2 - 1.9) / (1.1 / sqrt(40)) = 0.889

Using a standard normal distribution table or calculator, we can find that the area to the right of 0.889 is approximately 0.1884. Therefore, the probability that if 40 families from the United States are randomly selected, the mean number of children per family is at least 2 children is 0.1884.

So, analyst 1 plans to use a sample size of 1 and analyst 2 plans to use a sample size of 40.

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Un Jardinero usa un total de 61. 5 galones de gasolina en un mes. De la cantidad total

3/5

de gasolina, se usaron en sus cortadoras de césped. ¿Cuántos galones de gasolina usa

el jardinero en sus cortadoras de césped en ese mes? Me ayudan plis

Answers

The gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

What are proportions?

In mathematics, a proportion is a statement that two ratios are equal. It expresses the relationship between two or more quantities that are directly proportional to each other. A proportion can be represented as an equation of the form:

a/b = c/d

We know that the gardener used a total of 61.5 gallons of gasoline in a month and that 3/5 of that total was used in the lawnmowers.

To find out how much gasoline the gardener used in the lawnmowers, we need to multiply the total amount of gasoline by 3/5:

61.5 gallons x 3/5 = 36.9 gallons

Therefore, the gardener used 36.9 gallons of gasoline in the lawnmowers in that month.

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Ariana has 144 peaches. She has to pack 9 boxes with an equal number of peaches. How many peaches should she pack in each box.

Answers

Answer:

16 peaches

Step-by-step explanation:

Let's break this down:

Total: 144 peaches

Number of boxes she has to fill evenly: 9

Question: How many peaches are able to fit into each box evenly?

144 peaches/9 boxes = 16 peaches

So, Ariana should pack 16 peaches into each box

Hope this helps :)

In a round of mini-golf , Clare records the number of strokes it takes to hit the ball into the hole of each green. She said that, if she redistributed the strokes on different greens, she could tell that her average number of strokes per hole is 3. ​

Answers

If Clare's average number of strokes per hole is 3, it means that the total number of strokes she took in the round divided by the number of holes she played is equal to 3.

Let's say Clare played n holes in total and took a total of s strokes in the round. Then we can write:

s/n = 3

Multiplying both sides by n, we get:

s = 3n

This means that Clare took 3 strokes per hole on average, and a total of 3n strokes in the round. If she were to redistribute the strokes on different greens, the total number of strokes would still be 3n, and her average number of strokes per hole would remain 3.

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what is the simplified form of the expression below (3m^4n)^3(2m^2n^5p)/6m^4n^9p^8

Answers

For the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, the simplified-value is 9m¹⁰n⁻¹p⁻⁷.

To simplify the expression (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸, we first use the exponent-rule that states (qᵃ)ᵇ = qᵃᵇ to simplify the first part of the expression:

⇒ (3m⁴n)³ = 3³(m⁴)³n³ = 27m¹²n³;

Next, we can simplify the denominator by using the rules of exponents to combine the like terms:

⇒ 6m⁴n⁹p⁸ = 2×3m⁴n⁹p⁸;

Substituting the values,

We get;

⇒ (27m¹²n³)×(2m²n⁵p)/(2*3m⁴n⁹p⁸);

Simplifying the expression by cancelling out the common factors, we get:

⇒ 9m¹⁰n⁻¹p⁻⁷;

Therefore, the simplified-value is : 9m¹⁰n⁻¹p⁻⁷.

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The given question is incomplete, the complete question is

What is the simplified form of the expression below (3m⁴n)³(2m²n⁵p)/6m⁴n⁹p⁸;

a) by using Venn-diagram. 75 students in a class like picnic or hiking or both. Out of them 10 like both the activities. The ratio of the number of students who like picnic to those who like hiking is 2 : 3. (i) Represent the above information in a Venn-diagram. (ii) Find the number of students who like picnic. (iii) Find the number of students who like hiking only. (iv) Find the percentage of students who like picnic only.​

Answers

(i) A Venn-diagram of this information is shown below.

(ii) The number of students who like picnic = 34

(iii) The number of students who like hiking only = 51

(iv) The percentage of students who like picnic only. = 45.33%

Let us assume that A represents the set of students who like picnic.

B represents the set of students who like the hiking.

The total number of students in a  class are: n(A U B) = 75

Out of 75 students, 10 like both the activities.

n(A ∩ B) = 10

The ratio of the number of students who like picnic to those who like hiking is 2 : 3

Let number of students like tea n(A) = 2x

and the number of students like coffee n(B) = 3x

n(A U B) = n(A) + n(B) - n(A ∩ B)

75 = 2x + 3x - 10

75 + 10 = 5x

85/5= x

x = 17

The number of students like picnic = 2x

                                                          = 2 × 17

                                                          = 34

The number of students like hiking = 3x

                                                           = 3 × 17

                                                           = 51

This informtaion in Venn diagram is shown below.

The percentage of students who like picnic only would be,

(34/75) × 100 = 45.33%

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The table shows the part of the students in
each grade that participated in a sport this
year. Which grade had the greatest rate of participation? The least?

Answers

we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

How to find the grade had the greatest rate of participation?

To compare the rates of participation in sports among the three grades, we can convert each percentage or fraction to a decimal and then compare the values.

Grade 6: 0.872

Grade 7: 0.87 (87% converted to decimal)

Grade 8: 0.875 (7/8 converted to decimal)

Therefore, we see that the greatest rate of participation was in Grade 8, and the least rate of participation was in Grade 6.

Answer:

Grade 8 had the greatest rate of participation.

Grade 6 had the least rate of participation.

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An angle measures 11.4° more than the measure of its complementary angle. What is the measure of each angle?

Answers

The measure of the angle is 50.7° and the measure of its complementary angle is 39.3°.

What is the measure of each angle?

Let x be the measure of the angle and y be the measure of its complementary angle.

Then we have:

x = y + 11.4 (since the angle measures 11.4° more than its complementary angle)

x + y = 90 (since the two angles are complementary)

Substituting the first equation into the second equation, we get:

(y + 11.4) + y = 90

2y + 11.4 = 90

2y = 78.6

y = 39.3

Substituting y = 39.3 into the first equation, we get:

x = y + 11.4 = 50.7

So, we have

x = 50.7

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