17. A group of 36 people attended a ball game. There were twice as many children as adults in the group. Set up a
system of equations that represents the numbers of adults and children who attended the game and solve the
system to find the number of adults and the number of children who were in the group.

Using Midsegment theorem, the value of x and y are 17 and 2 respectively and the length of DF is 20 units.

The Midsegment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.

Therefore, DH is midsegment of  triangle DEF.

Hence, let's find x

1 / 2 (28) = x - 3

14 = x - 3

add 3 to both sides of the equation

14 = x - 3

14 + 3 = x - 3 + 3

x = 17

Let's find the length DF as follows:

DF = y + 8 + x - 7

Recall x = 17

Therefore,

DF = y + 8 + 17 - 7

DF = y + 8 + 10

DF = y + 18

y+ 8 = 10

y = 2

Hence,

DF = 2 + 18

DF = 20 units

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The average rate of change of the function g(n) from n = 1 to n = 5 is 0.2 inches.

We are given;

A researcher is following the growth of a particular type of flower. She writes the given equation to show the height of the flower g(n), in inches, after n days.

g(n) = 10(1.02)^n

which is an exponential function.

We need to find the average rate of change of the function g(n) from n = 1 to n = 5.

We know that the average rate of change = slope of the function.

The slope of the function is given by:

Slope = Change in y-coordinate / change in x-coordinate

We have,

g(n) = 10(1.02)^n;

for n = 1; g(n) = 10(1.02)^1 = 10 * 1.02 = 10.2

for n = 5; g(n) = 10(1.02)^5 = 10 * 1.1 = 11

Put the values in the slope formula;

slope = 11 - 10.2 / 5 - 1 = 0.8 / 4 = 0.2

Thus, the average rate of change of the function g(n) from n = 1 to n = 5 is 0.2 inches.

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The size of the F-ratio value would increase as the numerator of the F-ratio (MS Between) increased and The size of the F-ratio value would increase as the numerator of the F-ratio (MSBetween) increased.

Given that,

The F ratio can be defined as,

F =Mean Sum of Squares of between treatments / Mean Sum of Squares of within treatments

F =MS Between /MS within

Increase the difference between the sample means.

As the difference between the sample means increases, between treatments has larger effect

(MS known ) . This affects the numerator of F-ratio.

Hence, As numerator of F-ratio ( MS Between ) increases, the size of the F-ratio value would increase.

Increase the size of sample variances.

As the size of sample variance increases, with treatments has larger effect ( MS within ). This

affects the denominator of F-ratio.

Hence, As the denominator of F-ratio (MS Within ) increases. The size of F-ratio will decrease.

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Shar needs total of 48 Feet of fencing for the entire animal pen.

Pythagoras Theorem gives us a relation between the sides of right triangle . According to the Pythagoras , Square of hypotenuse if equal to sum of square of other two sides.

Right triangle has three side where longest side is given 20 feet and shortest side is 16

Using Pythagoras Theorem ,

(20)² = (16)² + (third side)²

(third side)² = 400 - 256  

(third side)² = 144

taking square root

third side = 12 feet

Total feet required = 20 + 16 + 12

= 48 feet

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The ordered pair that is the solution to the equation -x + 5y = 3 is (-3,0) and (0, 0.6)

Ordered pair:

Ordered pairs refers a set of 2 numbers that exist in a particular order. The first one represents the x value and the second one refer the y value.

Given,

Here we need to find the ordered pair (x, y) that is a solution to the equation -x + 5y = 3

In order to find the solution ordered pair we have to plot this equation on the graph.

To plot this equation, we have to use the graphing calculator, and then input the given equation as the function, then we get the graph like the following.

While we looking into the graph, we have identified that the solution ordered pairs are (-3,0) and (0, 0.6)

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Answer:

-42,000

Step-by-step explanation:

10-³ would be -30, so

2.0 x -30 = -600

10² would be 20, so

3.5 x 20 = 70

Multiply the two

-600 X 70 = -42,000

a. The standard form of an equation is A x + By  = C.

b. The slope of the line is 5 / 3

c. The point slope form of the line is y + 3 = 5 / 3 (x - 7)

d. The standard form of the line is 3y - 5x = -44

The equation of a line can be represented in different form such as slope intercept form, standard form, general form and point slope form.

The standard form of an equation is represented as follows;

A x + By  = C

where

Therefore,

let's find the slope of the line passing through (7, -3) and (4, -8).

m = slope = - 8 + 3 / 4 - 7

m = -5 / -3

m = 5 / 3

The point slope form is represented as follows;

y - y₁ = m(x - x₁)

using (7, -3)

y + 3 = 5 / 3 (x - 7)

Let's rearrange the equation into standard form.

y + 3 = 5 / 3 (x - 7)

y + 3 = 5 / 3 x - 35 / 3

y - 5 / 3 x  = - 35 / 3 - 3

y - 5 / 3 x  = -44 / 3

Therefore,

3y - 5x = -44

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Answer: 20

Step-by-step explanation:

5 boxes with 10, 10, 10, 10, and 10 donuts in each box.

She gives one box away, so that is 50-10=40

Then she gives 2 boxes away, which is 40-20=20, so she has 20 donuts left to share with her classmates.

Answer: 20

Step-by-step explanation:

5 x 10 = 50 Donuts

50 Donuts - 10       for the Bus driver

40 Donuts - 20      for the school principal

=20

She can share 20 Donuts with her classmates.

The number of schedules that are possible, considering each case and the Fundamental Counting Theorem, is given as follows:

a) No restrictions: 3,628,800.

b) Last two games against the same team: 362,880.

The Fundamental Counting Principle states that if there are n independent trials, each with [tex]n_1, n_2, \cdots, n_n[/tex] possible results, the total number of outcomes is calculated by the multiplication of the factorials as presented as follows:

[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]

Teams play each other only once during the season, hence, if there are no restrictions, the parameters are given as follows:

[tex]n_1 = 10, n_2 = 9, \cdots, n_{10} = 1[/tex]

Hence the number of schedules is:

N = 10! = 10 x 9 x 8 x ... x 1 = 3,628,800.

If the last game is fixed, then the remaining games are an arrangements from 9 games, and thus the number of schedules is:

N = 9! = 362,880.

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Answer:

1.102, 1.12, 1.1212, 1.2

Step-by-step explanation:

Answer:

1 ) 1.102

2 ) 1.12  

3 ) 1.1212

4 ) 1.2

Hope this helps! :)

Answer:

Step-by-step explanation:

y=X-2

The behavior of f(x) from given options is option (4) up on the left, up on the right.

A function f(x) 's end behavior is how the graph of the function f(x) behaves as x gets closer to positive or negative infinity. The functions degree or the polynomial degree and leading coefficient of a given function will determine the end behavior of the function.

Here we have

f(x) = 3x³² + 8x² - 22x + 43

Here

polynomial degree of f(x) is 32

And leading coefficient is 3  

Therefore,

The leading term of the given function is 3x³²

As the given polynomial has an even degree (32) and positive leading coefficient (3) then the graph will open upwards on both left and right.

Therefore,

The behavior of f(x) from given options is option (4) up on the left, up on the right.

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Answer:

B

explanation:

there's a high chance you might as well get at least one milk chocolate because there's plenty..

Answer:

12x-6

Step-by-step explanation:

(3x+4)+(9x-10)

= 3x+4+9x-10

=3x+9x+4-10

=12x-6

ANSWER IS 12X-6

The value of p in the given triangle is equal to 99.3°.

What is Law of Cosines?

In the given question, the side lengths of the triangle are as follows,

[tex]a=3.6 cm,[/tex] [tex]b=2.8cm,[/tex] and [tex]c=5.3cm[/tex]

Here, the angle between a and b, [tex]\angle C=p[/tex]

We know that the angle p between the two sides of lengths a and b can be found using the Law of Cosines Formula, given as,

[tex]c^{2} =a^{2} +b^{2} -2abcosC[/tex]

Substituting the above values, we get

[tex]5.3^{2} =3.6^{2} +2.8^{2} -2 \times 3.6 \times 2.8 \times cos p[/tex]

Simplifying, we get

[tex]28.09=12.96+7.84-20.16cosp\\\implies 28.09=20.8-20.16cosp\\\implies 7.29=-20.16 cosp[/tex]

Rearranging in terms of p, we get

[tex]cosp=-\frac{7.29}{20.16} \\\implies p=cos^{-1} (-0.3616)\\\implies p=99.3\textdegree[/tex]

Therefore, the value of p is equal to 99.3°.

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After 14.39 years the principle amount will reach to 13500 dollars.

What is compound interest?

Compound interest, also known as interest on principal and interest, is the practicize of adding interest to the principal amount of a loan or deposit.

Given: 5100 dollars is placed in an account with an annual interest rate of 7%.

Principle amount (P) = 5100 dollars.

Rate of interest = 7% = 0.07

Total amount (A) = 13500 dollars.

Here the interest is compounded annually, so we can use the compound interest formula,

[tex]A = (1+r)^t[/tex]

Plug the values in the formula

[tex]13500 = 5100(1+0.07)^t\\2.6471 = (1+0.07)^t[/tex]

Taking log on both sides,

[tex]log(2.6471) = log(1.07)^t\\log(2.6471) = t log(1.07)\\t = 14.39[/tex]

Hence, after 14.39 years the principle amount will reach to $13500.

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Answer:

The correct answer would be: 18.1

Step-by-step explanation:

a. False, the slope of f(x) will be steeper than m(x).

b. False, the y-intercept of m(x) will be equal to f(x).

What is a slope?

Slope and slant both refer to an incline away from a reference surface or line that is generally straight. The definition of slope is "a vertical inclination in an oblique direction" Here, the land abruptly slopes either upward or downhill.

Here, we have

f(x) = x and m(x) = 3/5f(x)

a.  m₁ = slope of f(x) = x is 1

     m₂ = slope of m(x) = 3/5f(x) is 3/5

    m₁ >  m₂

f(x) = x is more steeper than m(x) = 3/5f(x).

b.  a₁ = intercept of f(x) = x is 0.

    b₁ = intercept of m(x) = 3/5f(x) is 0.

The y-intercept of m(x) will be equal to f(x).

Hence, a. False, the slope of f(x) will be steeper than m(x).

b. False, the y-intercept of m(x) will be equal to f(x).

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The confidence interval for the population mean difference is between -33.2 and + 33.2

You have a 5% probability of being incorrect with such a 95% confidence interval. You have such a 10% probability of becoming incorrect with a 90% confidence interval. In contrast to a 95 % confidence interval, a 99 per cent confidence interval would be larger (plus or minus 4.5 per cent as opposed to 3 per cent, for example).

The answer in this situation would be +/-(2 * 16.6) from the mean, or -33.2 and +33.2 points from the sample mean because the 95% confidence interval is equal to two standard deviations on either side of the mean. This would result in an answer of A.

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Your question is incomplete, but probably the full question was:

A teacher wants to compare the mean geology scores of two different classes. She is testing the null hypothesis that there is no difference in the population mean scores of the two classes. The difference of the sample means is 51.4. If the standard deviation of the distribution of the difference of sample means is 16.66, what is the 95% confidence interval for the population mean difference?

A)between -33.2 and + 33.2

B)between -49.9 and +49.9

C)between -102.8 and +102.8

D)between -154.2 and +154.2

Answer:

  600 ft by 1200 ft

Step-by-step explanation:

You want the dimensions of the largest rectangular area that can be enclosed on three sides with 2400 feet of fencing.

Let x represent the dimension of the field that is parallel to the river, and y the dimension out from the river. The sum of the three side lengths is ...

  x + 2y = 2400

Solving for y gives ...

  y = (2400 -x)/2

The area is the product of the two dimensions:

  A = xy = x(2400 -x)/2

We observe that this is the factored form of a quadratic with zeros at x=0 and x=2400. Its leading coefficient is negative, so the graph opens downward, and the vertex is the point where area is a maximum.

The vertex is located on the line of symmetry at the x-value that is halfway between the zeros:

  x = (0 +2400)/2 = 1200

  y = (2400 -x)/2 = (2400 -1200)/2 = 600

The dimensions of the field that has the largest area are 600 ft by 1200 ft.

__

Additional comment

As we observed here, the side parallel to the "river" will use 1/2 of the fencing, and the remaining two sides will each use 1/4 of the fencing. This is the general solution to such a fencing problem.

The mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.  

We know the population mean and standard deviation, that has a bell-shaped distribution:

μ= 107

σ=35

The sampling distribution, the distribution of the mean of samples of size n out of this population, will have the same mean as the population mean.

μ (m) = μ =107

The standard deviation will be related to the population standard deviation and the sample size as:

σ (m)= σ/[tex]\sqrt{N}[/tex]

         = 35/10=3.5

Then, the mean of samples of 100 IQ scores taken out from this population will have a distribution with mean M=104 and standard deviation s=3.5.

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Answer:

22.287

Explanation:

This is because 15 is a whole number.

It is also 15.000

37.287

-15.000[tex]\\[/tex]

22.287

The length of side PR will be 40.

What is mean by Triangle?

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In the isosceles triangle,

Two sides are,

⇒ PR = 5n and QR = (32 + n)

Now,

Since, The triangle is an isosceles triangle.

So, Two sides are equal.

We formulate;

5n = 32 + n

5n - n = 32

4n = 32

n = 8

Thus, The length of side PR = 5n

                                           = 5 x 8

                                           = 40

Therefore, The length of side PR will be 40.

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==========================================================

Explanation:

0.4 = 4/10 = 2/5

The original slope as a fraction is 2/5

Flip the fraction to get 5/2, then flip the sign to get -5/2 which is the perpendicular slope

The orginal slope 2/5 and perpendicular slope -5/2 multiply to -1. This is true of any pair of perpendicular lines where neither line is vertical nor horizontal.

Rephrased another way: -5/2 is the negative reciprocal of 2/5.

Answer:

d = 8.596m

or

= 8.6m rounded to the nearest tenth

Step-by-step explanation:

Tangent is:

tan(angle) = opp/adj

First, use

tan35° = 12/x

to find the unmarked piece on the bottom of the triangle.

Then find some more angles in the shape. See image.

Next, use

tan 25° = 12/y to find the length of the entire bottom of the whole, big triangle.

Last, subtract the little part from the whole side to find d. See image.

Answer:

In the picture attached

Step-by-step explanation:

The larger triangle is divided into two smaller ones. Take the first one (the triangle with the angle 35) and find the length of A1 using tan (imagine as if it's a triangle on its own). Do the same thing for the whole diagram (both the small triangles combined) using tan to find the whole length which I called A2, then minus A1 from A2 to find d

The answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]

To solve the given expression, we have to first know about matrix addition and scalar multiplication.

Matrix addition is possible only when both matrices have equal dimensions. Scalar multiplication is the multiplication of a real number and a matrix. Each element of the matrix is multiplied by a scalar value in scalar multiplication.

To solve the given problem, first, substitute the value of A and B in the formula,

[tex]3A+3B=3\left[\begin{array}{cc}-4&-3\\6&1\end{array}\right] +3\left[\begin{array}{cc}2&-4\\0&0\end{array}\right][/tex]

Using scalar multiplication, multiply the real number and the matrix. So we get,

[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}3(-4)&3(-3)\\3(6)&3(1)\end{array}\right] +\left[\begin{array}{ccc}3(2)&3(-4)\\3(0)&3(0)\end{array}\right]\\&=\left[\begin{array}{ccc}-12&-9\\18&3\end{array}\right] +\left[\begin{array}{ccc}6&-12\\0&0\end{array}\right]\end{aligned}[/tex]

To add two matrices with the same dimension, add their corresponding element. So we get,

[tex]\begin{aligned}3A+3B&=\left[\begin{array}{ccc}-12+6&-9-12\\18+0&3+0\end{array}\right] \\&=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right]\end{aligned}[/tex]

Therefore, the answer is [tex]3A+3B=\left[\begin{array}{ccc}-6&-21\\18&3\end{array}\right][/tex]

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The given organic molecule contains a trigonal pyramidal nitrogen atom, which is underlined in red.

Given;

The provided organic molecule's structural structure, with the nitrogen atom's position around it, is colored red.

Number of electron pairs in Nitrogen = 4 (3 Bond pairs + I Lone pair)

General Formula = AX₃E

Electronic Geometry = Tetrahedral

Molecular Geometry = Trigonal pyramidal

Hybridization = sp³

Hence, the nitrogen atom highlighted in red in the given organic molecule is Trigonal pyramidal.

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Answer:

3.730 = b

Step-by-step explanation:

Givens

<B = 25 degrees

b = ?

a: =  8   meters

Formula

Tan(B) = opposite / Adjacent

Solution

Solve for b (opposite)

Put in values for the letters.

Tan(25) = b /8

0.4663 = b / 8                          multiply both sides by 8

0.4663*8 = 8*b/8                     Combine

3.730 = b

The value of (5 - 6b)² when it is expanded is 25 -60b + 36b² (third option).

The square of a number is the value derived when a number is multiplied by itself. Multiplication is the mathematical operation that is used to determine the product of two or more numbers. The sign that is used to represent multiplication is x.

The square of a number is denoted by the power 2. For example, the square of 2, 2² is 4 (2 x 2).

Thus, (5 - 6b)² is the same as (5 - 6b) x (5 - 6b).

When multiplied, the expression becomes:

(5 - 6b) x (5 - 6b)

When multiplied, the expression becomes: 25 - 30b - 30b + 36b²

Add similar terms together: 25 -60b + 36b²

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