Nicole won 85 super bouncy balls playing
the bean bag toss at her school's game
night. Later, she gave four to each of her
friends. She only has 5 remaining. How
many friends does she have?

Answer:

the value of n is 9

Step-by-step explanation:

7:2=each interior angle/each exterior angle

7:2= (n-2)180/360

7/2=(n-2)/2

14=2n-4

2n=18

n=9

Answer: 16/45

Step-by-step explanation:

\(\displaystyle\\\frac{4}{9}*\frac{4}{5}= \\\\\frac{4*4}{9*5}=\\\\\frac{16}{45}\)

Assuming that the rates are constant, we can see that Tom can paint the fence in 7.5 hours.

Here we will use equations of the form:

(rate at which person x paints)*(time) = 1 fence painted.

We know that Chuck can paint a fence in 5 hours, then if C is the rate (assuming this is constant), we can write:

C*5 hours = 1 fence

C = (1/5) fences per hour.

And let's say that Tom's rate is T.

When they work together, the rate is:

(C + T)

And they can paint the fence in 3 hours, then:

(C + T)*3 hours = 1 fence

Replacing the value of T we will get:

( 1/5 fences per hour + T)*3 hours = 1 fence

1/5 fences per hour + T = 1/3 fences per hour.

T = (1/3 - 1/5) fences per hour

T = (5/15 - 3/15) fences per hour

T = 2/15 fences per hour.

Then Tom paints the fence in:

(15/2) hours = 7.5 hours.

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(a)  The approximate probability P(A > 0.145) is 0.596

(b) The approximate probability that X1 + X2 + ... + X100 > 24.4 is 0.001.

Given information:

Standard deviation of X = 49 cole (unknown value)

Sample size n = 169

We need to use R to find the probabilities.

a) To find the approximate probability P(X > 1.45), we can use the standard normal distribution since the sample size is large (n = 169) and the sample mean X follows a normal distribution by the Central Limit Theorem.

Using the formula for standardizing a normal distribution:

\(Z = (X - \mu) / (\sigma / \sqrt(n))\)

where X is the sample mean, mu is the population mean, sigma is the population standard deviation (unknown in this case), and n is the sample size.

We can estimate sigma using the formula:

\(\sigma = (s.t) / \sqrt(169)\)

Since we don't know the population standard deviation, we can use the sample standard deviation as an estimate:

\(\sigma = \sqrt((1/n) * \sum((Xi - X)^2))\)

Given:

n = 169

mu = 8

assume sample standard deviation = 49

Z <- (0.145 - X) / sigma

\(P < - 1 - \pnorm(Z) # P(A > 0.145)\)

Therefore, the approximate probability P(A > 0.145) is 0.596

b) To find the approximate probability that X1 + X2 + ... + X100 > 24.4, we can use the Central Limit Theorem and the standard normal distribution again. The sum of the sample means follows a normal distribution with mean n * mu and standard deviation

Using the formula for standardizing a normal distribution:

\(Z = (X - \mu) / (\sigma / \sqrt(n))\)

where X is the sum of the sample means, mu is the population mean, sigma is the population standard deviation (unknown in this case), and n is the sample size.

Therefore, the approximate probability that X1 + X2 + ... + X100 > 24.4 is 0.001.

c) The R script for the above calculations is provided above.

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The minimum perimeter is 23.24m and dimensions of the fenced area is 15.5m x 3.8m.​

Let us assume the length of the fenced area to be L and breadth of the fenced area to be W. As we know, only three sides are to be fenced,

So, the perimeter  P of the fenced would be,

P = L + 2W

Also, it is given that, area of the fence is 60m²,

So, the are should be,

60m² = LW

60m²/L = W

Now, to minimize the perimeter,

P = L + 2W

P = L + 120/L

Differentiating both sides with respect to "L",

d(p)/dL = 1 - 240/L²

To find the value of "L", putting dp/dL equal to 0,

d(P)/dL = 0

1 - 240/L² = 0

L = √240m

Now, from the first derivative test, we know that, the perimeter will be maximum or minimum if value of L>√240 or L<√240 respectively,

For minimum, L should be,

L = √240m

L = 15.5m

Now we know from area,

area = LW

60 = 15.5 x W

W = 60/15.5

W = 3.8m

Hence, the minimum perimeter will be,

L + 2W = 23.24m

The dimensions are,

L = 15.5m

W = 3.8m

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A distribution is a way of displaying data, consisting of three primary components: shape, center, and spread. The shape is the overall pattern of the distribution, while the center is the point where the distribution is balanced. The spread is the range of values of the data, often measured by the standard deviation or the interquartile range (IQR). The distribution can be visualized through graphs like histograms, box plots, or scatter plots.

A brief description of a distribution should include its shape, center, and spread. The spread is the term that should be included in the blank space.A distribution can be described as a way of displaying data. It gives us an idea about how the data are spread out.

The three primary components of any distribution are the shape, center, and spread. Shape refers to the overall pattern of the distribution. It tells us whether the data are symmetric or skewed. The symmetry means that the left half of the distribution is a mirror image of the right half, whereas a skewed distribution is not symmetrical. The tail of a distribution describes the spread of a skewed distribution. It refers to the parts of the distribution that extend out from the center of the graph.The center refers to the point where the distribution is balanced. In symmetric distributions, the center is the same as the mean and median. However, in a skewed distribution, the mean and median differ from each other.

The spread refers to the range of values of the data. It tells us how much the data are scattered or spread out. A small spread indicates that the data points are close to each other, while a large spread suggests that the data points are far from each other. It is often measured by the standard deviation or the interquartile range (IQR).The distribution of data can be visualized through different graphs like histograms, box plots, or scatter plots.

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Answer:

your answer will bw the option A.

Step-by-step explanation:

The image of the point (1,3) after a counterclockwise rotation of 270° is (3, -1).

Every point in a figure is transformed by a rotation, which rotates each point a predetermined amount of degrees around another point.

Given that : coordinate point is (1, 3)

When rotating a figure 270 degrees counterclockwise, each point must be changed from (x, y) to (y, -x) before the rotated figure may be graphed.

So, points (1,3) changed to (3, -1).

As a result, the image of the point (1,3) following a 270° counterclockwise revolution is (3, -1).

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Answer: 1.4n represents the cost of n packages of pels.

1.20m represents cost of m pads.

Entire expression 1.4n + 1.20m represents total cost of n packages of pels and m pads.

Meaning of 1.4n  =  cost of n packages of pels.

Meaning of 1.20 m = represents cost of m pads.

where , 1.4 = Cost per package of pels

1.2 =Cost per pad of paper

Step-by-step explanation:

Given: Cost per package of pels = $1.40

Cost per pad of paper = $1.20

Number of packages of pels bought = n

Number of pads of paper bought = m

So, 1.4n represents the cost of n packages of pels.

1.20m represents cost of m pads.

Entire expression 1.4n + 1.20m represents total cost of n packages of pels and m pads.

Meaning of 1.4n  =  cost of n packages of pels.

Meaning of 1.20 m = represents cost of m pads.

where , 1.4 = Cost per package of pels

1.2 =Cost per pad of paper

Name of the planes in each figure:

15. Planes are RST, STQ, SRQ, RTQ

16. Planes are WXYZ, WZV, XWV, XYV, ZYV

17. Planes are EFGJ, GFDH, HDEJ, FDE, GHJ

We are asked to identify planes from the figures 15, 16 and 17. The planes are formed by the sides of the figures given. Each plane is closed by sides around and is named according to the end points of each side.

Figure 15 is a triangular pyramid. Its one triangular base and 3 lateral sides gives 4 planes to the solid. They are: RST, STQ, SRQ, RTQ

Figure 16 is a rectangular pyramid. Its one rectangular base and 4 triangular lateral sides gives a total of 5 planes to the solid. They are: WXYZ, WZV, XWV, XYV, ZYV

Figure 17 is a triangular prism. Its two triangular bases and 3 rectangular lateral sides gives a total of 5 planes to the figure. They are:  EFGJ, GFDH, HDEJ, FDE, GHJ

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The sides in order form longest to the shortest are:

A)

B)

The Law of Sines is the idea  that explains why the side opposite the biggest angle in a triangle is likely to be the longest.

By the explanation of   the Law of Sines, the ratio of the length of a side to the sine of its opposite angle is constant in any triangle.

In othe r words, because the sine of the biggest angle is the greatest of the three angles, the side   opposite it will have the longest length.

Thus, The sides in order form longest to the shortest are:

A)

AD

AM

DM

B)

LU

XU

LX

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Answer:9

Step-by-step explanation:

x=-7

7^(2) + 7*-7 + 9

7*7=49

49-49=0

9

Answer:

Greatest is Miami

Least is Washington

Step-by-step explanation:

Population/Area= Population Density

Ex:

Population 2

Area 1

2/1=2

Volume is equal to \(a^{3}\) where an is the width or length of its edges.

The number of cubic units that a cube totally occupies is determined by its volume. The cubic unit of measurement for the volume of a cube includes \(centimetres^{3}\), \(metres^{3}\), \(inches^{3}\), \(feet^{3}\), etc.

A solid three-dimensional figure with 6 square faces or sides is known as a cube. The total amount of space a cube takes up is its volume. The cube's square shape means that all of its sides are square, and as a result, all of its edges would be of equal length. As a result, the cube's length, breadth, or height are all equal.

If a cube's length, breadth, and height are equal to "a," then;

Cube volume = a\(\times\)a\(\times\)a.

Therefore, Volume of cube is \(a^{3}\) where a is the length of the edge.

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Answer: 6 bees

Step-by-step explanation:

The picture has 12 bees and 10 flowers. Thus, the ratio of flowers to bees is 10 to 12, which simplifies to 5 to 6.

Therefore, for every 5 flowers, there are 6 bees.

Answer:

the answer is x=+/- 3 sqrt 2

Answer:

MATH is not a parallelogram

Step-by-step explanation:

(sqrt means squareroot)

To prove that quadrilateral MATH is a parallelogram, we can use the following formula:

A quadrilateral is a parallelogram if and only if both pairs of opposite sides are congruent.

In other words, if the lengths of the sides opposite each other in a quadrilateral are the same, then the quadrilateral is a parallelogram.

To prove that MATH is a parallelogram, we need to show that both pairs of opposite sides are congruent.

The first pair of opposite sides consists of segment MA and segment TH. To show that these sides are congruent, we can use the Distance Formula:

d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Where (x1, y1) and (x2, y2) are the coordinates of the two points that define the line segment.

Substituting the coordinates of points M and A, we get:

d = sqrt((-3 - (-5))^2 + (2 - (-2))^2)

= sqrt((-3 + 5)^2 + (2 + 2)^2)

= sqrt(8^2 + 4^2)

= sqrt(64 + 16)

= sqrt(80)

= 8.944

Substituting the coordinates of points T and H, we get:

d = sqrt((1 - 3)^2 + (-2 - 2)^2)

= sqrt((-2)^2 + (-4)^2)

= sqrt(4 + 16)

= sqrt(20)

= 4.472

Since 8.944 is not equal to 4.472, we cannot conclude that MA and TH are congruent. Therefore, MATH is not a parallelogram.

Answer

XY = 6 units

ZW = 8 units

The two segments (XY and ZW) are not congruent as they are not equal in length to each other.

Explanation

We are given the coordinates of points X, Y, Z and W

X = -8

Y = -2

Z = 2

W = 10

XY = Difference between points -2 and -8

XY = -2 - (-8) = -2 + 8 = 6 units

ZW = Difference between points 10 and 2

ZW = 10 - 2 = 8 units

The two segments are not congruent as they are not equal in length to each other.

Hope this Helps!!!

If one dimension of a rectangular prism is halved, a second dimension is reduced to one-third of its original length, and a third dimension remains unchanged. Therefore, the new volume of the rectangular prism is 70/x cubic units.

The new volume of the rectangular prism can be calculated as follows:
Let the original dimensions of the rectangular prism be x, y, and z, respectively. Then, the original volume of the rectangular prism is given by:
V = xyz
If one dimension is halved, its new length becomes x/2. If a second dimension is reduced to one-third of its original length, its new length becomes y/3. And if the third dimension remains unchanged, its length remains z. Therefore, the new volume of the rectangular prism can be calculated as:
V' = (x/2) * (y/3) * z
V' = (1/6)xyz
We know that the original volume of the rectangular prism is 420 cubic units. Therefore:
V = xyz = 420
x * y * z = 420
We can use this equation to solve for one of the dimensions in terms of the other two. For example, we can solve for z:
z = 420/(xy)
Substituting this expression for z into the expression for the new volume, we get:
V' = (1/6)xyz
V' = (1/6)x(y/3)(420/(xy))
V' = 70/x
Therefore, the new volume of the rectangular prism is 70/x cubic units. The value of x is not given in the problem, so we cannot calculate the new volume exactly. However, we do know that the new volume will be smaller than the original volume, since one dimension has been halved and another has been reduced to one-third of its original length.

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The proportion of the area under the curve that lies to the right of t = 2.015 in a t-distribution with 5 degrees of freedom can be calculated using the t-distribution function in a statistical software package such as R.

The answer is approximately 0.9522. This means that 95.22% of the area under the curve lies to the right of t = 2.015. This indicates that the probability of observing a value of t greater than 2.015 is quite high.

This is because the t-distribution with 5 degrees of freedom has a larger spread than the normal distribution, which means that the probability of observing values further from the mean is greater.

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Step-by-step explanation:

-8(5m - 7.4)

= -40m + 59.2

The graph illustrates a linear function, because the graph is a straight line

The equation of the graph is (d) y = x +3

The points on the line are:

\((x_1,y_1) = (-3,0)\)

\((x_2,y_2) = (0,3)\)

First, we calculate the slope (m)

\(m = \frac{y_2 - y_1}{x_2 - x_1}\)

Substitute values for x1, x2, y1 and y2

\(m = \frac{3-0}{0--3}\)

Simplify

\(m = \frac{3}{3}\)

Divide

\(m = 1\)

The equation of the line is then calculated using the following formula:

\(y = m(x - x_1) + y_1\)

Substitute values for m, x1 and y1

\(y = 1(x - -3) + 0\)

Simplify

\(y = 1(x +3)\)

Open bracket

\(y = x +3\)

Hence, the equation of the graph is (d) y = x +3

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Answer:

58°

Step-by-step explanation:

Since the angle made by wire with ground and at the point of contact to the tree are complementary.

So,

Required angle = 90° - measure of the angle formed by wire with ground

Required angle = 90° - 32° = 58°

Answer:

1620

Step-by-step explanation:

How to calculate 81 multiplied by 20 using long multiplication.

Here is step-by-step how to calculate 81 times 20 using long multiplication:

Step 1: Setup

Set up your multiplication problem like this:

       81

     x20

Step 2: Multiply

1 x 0 = 0. Put 0 below the line and 0 as a reminder on top:

          0  

         81

     x 20

          0

Step 3: Multiply

0 x 8 = 0. Take 0 and add 0 from the previous step to get 0. Enter 0 at the bottom:

        81

     x 20

        00

Step 4: Add 0

Enter a 0 at the bottom right as a place holder, because you now move over one digit:

         81

     x 20

        00

     +   0

Step 5: Multiply

2 x 1 = 2. Put 2 below the line and 0 as a reminder on top:

          0  

        81

     x 20

        00

      +20

Step 6: Multiply

2 x 8 = 16. Take 16 and add 0 from the previous step to get 16. Enter 16 at the bottom:

          81

      x  20

          00

     + 1620

Step 7: Add to get answer

Add up the bottom two numbers (0 + 1620 = 1620) to get the answer:

         81

     x 20

        00

         +1620

         =1620

The bottom line is the answer. Therefore, 81 times 20 equals:

1620

Answer:

13

Step-by-step explanation:

Multiply 16 by 12 = 192
Add 3 = 195
80% Of 195 = 156
156 / 12 = 13
13 feet

\(\stackrel{Plant~A}{\cfrac{16}{3}}\qquad \qquad \stackrel{\textit{Plant C is }\frac{4}{5}\textit{ as tall as A}}{\cfrac{16}{3}\cdot \cfrac{4}{5}\implies \cfrac{64}{15}}\implies 4\frac{4}{15}\)

The average walking rate for Path A is 2.5 mph, path B's is 2 mph and path C's is 3 mph.

Average walking rate = distance/time

for path A = 0.5/12 = 0.0416 mpm

To convert miles per meter into miles per hour it we will multiply the equation by 60 because 1 hour has 60 min

so, for path A = 0.0416 × 60 = 2.5 mph

Similarly , for path B = (1.5/45) × 60 = 2 mph

For path C = (0.75/15)×60 = 3 mph

Table to show the average walking rate

Path     Distance(mi)     Time(min)      Walking rate (mph)

  A              0.5                   12                    2.5

  B              1.5                    45                    2

  C              0.75                 15                     3

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Answer:

range = biggest - smallest

65.5-45.5= 29

68 -48.2 =19.8

62.2-41.8 = 20.4

66-46= 20

70-50.4=19.6

Answer:

A = 36 pi m^2 or approximately 113.04 m^2

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

The radius is 6

A = pi 6^2

A = 36 pi m^2

Using the approximation of 3.14 for pi

A =113.04 m^2

Answer:

A≈113.1

Step-by-step explanation:

A=πr^2=π·6^2≈113.09734