Write and solve and equation for each scenario. Use x for the variable in your equation. Show your work by first writing an equation and then solving it. Put the solution of your equation in the answer box. If you multiply a number (x) by 5, the product is equal to the sum of 20 and 15.

There is no line parallel to the line x + 2 · y + 8 = 0, as point (x, y) = (- 2, - 3) lies on the original line.

In this problem we need to determine the equation of line based on its slope relationship respect to another line and a given point. Two lines are parallel if and only if they have the same slope (m) and two distinct intercepts (b). First, transform the given equation of the line into slope-intercept form:

x + 2 · y + 8 = 0

2 · y = - x - 8

y = - (1 / 2) · x - 4

Then, the resulting line has a slope of - 1 / 2.

Second, determine the intercept of the resulting line:

y = m · x + b

b = y - m · x

b = - 3 - (- 1 / 2) · (- 2)

b = - 3 - 1

b = - 4

The intercept of the resulting line is - 4.

Third, transform the equation of the resulting line into standard form:

y = - (1 / 2) · x - 4

- 2 · y = x + 8

x + 2 · y + 8 = 0

There is no parallel line for the point (x, y) = (- 2, 3).

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Answer: Stacy is 12 years old

Step-by-step explanation:

36/4 = 12

Answer:

The answer is B. y = -x + 7.5.

Step-by-step explanation:

The slope is -1 and the y-intercept is 7.5.

The y-intercept of f(x) = (1.6)x is (a) less than the y-intercept of the function in the graph

The equation of the function is given as

f(x) = (1.6)x

To determine the y-intercept, we set x = 0

So, we have

f(0) = 1.6 * 0

Evaluate

f(0) = 0

For the graph, we have

When x = 0, the function has a value of 1

This means that

y-intercept is 1

0 is less than 1

Hence, the y-intercept of f(x) = (1.6)x is (a) less

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8.77 ft/sec  is the tip of her shadow moving with a speed of 6 ft/sec .

What is speed, for instance?

Let H = the height of the pole.

h = the height of the woman.

x = the length of the woman's shadow.

s = the distance from the pole to the woman.

By similar triangles,  H/h = (s + x)/x  or  Hx = h(s + x).

Differentiating, H dx/dt = h(ds/dt + dx/dt)

19 dx/dt = 6(6 + dx/dt) = 36 + 6 dx/dt

13 dx/dt = 36

dx/dt = 36/13 ft/sec = 2.77 ft/sec for how fast her shadow is lengthening.

The speed of the tip of her shadow would be this speed added to her traveling speed: 2.77 + 6 = 8.77 ft/sec.

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Answer:

x = -1

Step-by-step explanation:

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Answer:

-1

Step-by-step explanation:

Replace the variable x with 1 in the expression .

f(1)= 2(1) - 3

Remove the parenthasis

2(1) - 3

Multiply 2 by 1

2 - 3

subtract 2 from 3

-1

The probabilities will be 0.1081 , 0.676, 0.863, 0.605 respectively.

let us consider, the chances of getting stem be a success(S) and not getting it be a failure(F) , and the total probability be 1 .

as per the statement 26% students are major in stem

total students selected randomly are 36.

∴ P(S) = 0.26

P( F)  = 1 - 0.26 = 0.74

Now the binomial probability of success is given by

[tex]P(x) = C^{n} _{x} S^{x} F^{n-x}[/tex]

where C is for the combination formula

S is changes of success

F is chances of failure

x = no. of times success

n = total times the experiment done

From the provided information we can solve each case as follows :

A) exactly 7 of them major in stem

P(7) = [tex]C^{36} _{7} (0.26)^{7} (0.74)^{29}[/tex]

   = 0.1081

B)at most 10 of them major in stem

it means P(0,1,2...10)

∴ P = P(0) + P(1) +......+P(10)

P = 0.676

C) at least 7 of them major in stem.

it means P(7,8,9...36)

∴ P = P(7) + P(8) + ...+ P(36)

P = 0.863

D) between 9 and 15 (including 9 and 15) of them major in stem.

In this case we subtract P(0,1,2...8) from P(0,1,2,...15)

and get P(9,10,11,...15)

∴ P(9,10,11,...15) =  P(0,1,2,...15)  -   P(0,1,2...8)

                        =  0.987  -  0.382

                        = 0.605

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m ∠5 and m ∠7 is  72 ° . All straight angles are 180 degrees, according to the straight angle theorem. A straight angle is formed when the angle's legs point precisely in the opposite directions. The symbol for a straight angle is 180 degrees, or  π (in radians).

An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

The names of basic angles are Acute angle, Obtuse angle, Right angle, Straight angle, reflex angle and full rotation. An angle is geometrical shape formed by joining two rays at their end-points. An angle is usually measured in degrees.

m ∠4 = 108°

m ∠5 = m ∠1

m ∠1 is in same line of m ∠4

So

m ∠1 = 180 - m ∠4

m ∠1 = 180 - 108

m ∠1 = 72 °

So m ∠5 = 72 °

m ∠7 is opposite to m ∠5 , opposite angles will be equal

Therefor m ∠7 = 72 °

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The scenario describes the stratified random sampling method .

There are many sampling techniques to collect sample from a given population such as Simple random sampling , Systematic Sampling , Cluster Sampling and so on . All of them vary in reliability , accuracy and efficiency .

Stratified Random Sampling : It is a method of  sampling in which division of population is done into smaller subgroups known as strata .The strata are formed based on member's shared attributes or characteristics . It has numerous applications . It is also called proportional random sampling or quota random sampling .

Therefore , the scenario describes the stratified random sampling method .

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Line a and line b are parallel to each other, and c is neither parallel nor perpendicular.

Line a passes through (2, 10) and (4, 13).

Line b passes through (4, 9) and (6, 12).

Line c passes through (2, 10) and (4, 9).

If a line passes through two points, then the slope of the line is

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Line a passes through (2, 10) and (4, 13).  So, the slope of this line is

[tex]m_{a}=\frac{13-10}{4-2}=\frac{3}{2}[/tex]

Line b passes through (4, 9) and (6, 12).  So, the slope of this line is

[tex]m_{b}=\frac{12-9}{6-4}=\frac{3}{2}[/tex]

Line c passes through (2, 10) and (4,9).  So, the slope of this line is

[tex]m_{c}=\frac{9-10}{4-2}=\frac{1}{2}[/tex]

The product of slopes of perpendicular lines is -1.

and if the slope of 2 lines is equal then those lines are parallel

so, line a and line b are parallel to each other, and c is neither parallel nor perpendicular.

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The inequality that needs to be solved is:

3t +270/ 6 ≥ 90.

let we consider that Heidi has 6 subjects in her school.

Therefore, She needs to average at least 90 on her three remaining tests to have at least a 90 overall average for all 6 tests.

Now,

To obtain an average first add up all the scores of the tests and then divide by the number of tests.

So far Heidi has taken 3 tests and we know the total number of tests will be 6 so we will be dividing by 6 to get the average of all the score.

If we let each of the three remaining tests each be represent by t, then the sum of all the tests would be:

95 + 92 + 86 + t + t + t

or

273 + 3t

The average of these 6 tests can then be represented by:

3t + 273 / 6

And for her average to be at least 90 then she can get a 90 or more which is the same as ≥ 90

So the inequality that needs to be solved is:

 [tex]\frac{3t + 273}{6}[/tex] ≥ 90

or, [tex]\frac{3 ( t + 91)}{6} \geq 90[/tex]

or, [tex]\frac{t + 91}{2} \geq 90[/tex]

Now, Heidi has to score :

t/2 ≥ 91

or, t/2 ≥ 90

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Answer:

9/16

Step-by-step explanation:

Answer:

4.73

Step-by-step explanation:

10% is 10

so, you have to multiple 3×.10=.30

3-.30=2.70

2.70×.75 because 7.5% is .75

that is 2.0250 and then you have to add 2.0250 with 2.70 that is 4.7250 and if you round it. It is 4.73

Hope that works

Answer:

A base

Step-by-step explanation:

its not an acid bc a ph level of 14 means is has a strong base.

The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)

A sample mean is the result of a chance experiment. When we sample a random variable, we get one of its possible values. A sample is a specific value. The random variable's probability distribution determines the possible values and the likelihood of each.

Given that,

Point estimate = sample mean = X = 40.7

sample standard deviation = s = 9.2

sample size = n = 19

Degrees of freedom = df = n - 1 = 19 - 1 = 18

At 80% confidence level

α = 1 - 80%

α =1 - 0.80 =0.2

α/2  = 0.1

t  α/2,df = t0.1,18 = 1.330

The margin of error = E = t /2, df x (s/√n)

= 1.330 x (9.2/√19)

= 1.330 x 2.110

= 2.8

Margin of error = E = 2.8

The 80% confidence interval estimate of the population mean is,

X  ±  E

= 40.7  ±  2.8

= (43.5, 37.9)

Therefore The parent spend on their child’s birthday gift is by using 80% confidence level is (43.5, 37.9)

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The dimensions of the box that minimize total cost are height h =3.17m, width, w and length, l=9.52m  are equal to  .

Let h is the height of the box.

Given Volume of the box is 216 m³  with no top.

And the cost of the bottom is 40USD/m².

For the sides, it is 30USD/m².

The bottom of the box is square, so l = w.

So Volume

[tex]V=hl^{2}[/tex]

[tex]216=hl^{2}[/tex]

[tex]h=\frac{216}{l^{2} }[/tex]

Now Surface Area of the box without a top is

S = 4hl + l²

So,

cost = 4 × 30hl +40l²

cost = 120 hl + 40 l²

Putting h ,

cost = 120 × [tex](\frac{216}{l^{2} })l + 40l^{2}[/tex]

cost = [tex]\frac{25960}{l^{2} }+40l^{2}[/tex]

To find minimum cost, derivate the  by using the calculator at

[tex]l=3\sqrt[3]{4}[/tex]

l=4.762203 m

[tex]h=\frac{216}{4.762203^{2} }[/tex]

h = 9.5244069354 m

Hence the dimensions of the box are

l=w

 =9.52 m

and height ,h=3.17 m  

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The type of bias that can be present in stratified sampling is that the students cannot be selected to accurately reflect the population.

Samples may be classified according to the five options as follows:

In this problem, an equal amount of students from each class was surveyed, hence a stratified sample was used.

The type of bias present in stratified sampling is that the students cannot be selected to accurately reflect the population.

The problem asks for which type of bias is present in this sample.

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The equation of the line in fully simplified slope - intercept form is 5x + 4y = 12 .

In the question ,

a graph of the line is given , we need to find the equation of the given line in the simplified slope - intercept form .

to find the equation , we need minimum two points ,

So , from the given graph ,

we can find that

when x [tex]=[/tex] 0 , the value of y [tex]=[/tex] 3 ,

the first point is (0 [tex],[/tex] 3) .

when x [tex]=[/tex] 4 , the value of y [tex]=[/tex] -2 ,

the second point is (4 [tex],[/tex] -2) .

the slope can be calculated by

slope = (-2-3)/(4-0)

= -5/4

So , the equation of the line passing through point (4,-2) with slope -5/4 ,  in the slope intercept form is

(y -(-2)) = (-5/4)(x-4)

y + 2 = (-5/4)x + 5

y = (-5/4)x + 5 - 2

y = (-5/4)x + 3

Simplifying further , we get

4y = -5x + 12

5x + 4y = 12

Therefore , The equation  line in fully simplified slope - intercept form is 5x + 4y = 12 .

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The number of ways voters could rank their first 5 choices out of 10 is 30240.

Given,

Number of students sought the nomination for president of the student body = 10 students

We have to find the number of ways voters could rank their first 5 choices.

Permutation;

An arrangement of items in a specific order is referred to as a permutation. Here, the components of sets are arranged in a linear or sequential order.

Here we have to use permutation formula;-

ⁿPr = n! /  (n - r)!

Here,

n is the number of students = 10

r is the choices = 5

Then,

ⁿPr = n! /  (n - r)!

¹⁰P₅ = 10! / (10 - 5)!

¹⁰P₅ = 10! / 5!

¹⁰P₅ = 10 x 9 x 8 x 7 x 6

¹⁰P₅ = 30240

That is,

The number of ways voters could rank their first 5 choices out of 10 is 30240.

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The absolute equation in the graph is f(x) = |x - 3| + 5

From the question, we can see that the lines on the graph has a sharp v-shape

Graphs that have this form are absolute value graphs

The general form of an absolute value equation is expressed as

y = |x - h| + k

From the above form, we have

Vertex = (h, k)

By definition, the vertex of a function is either the maximum point or the minimum point

On the given graph, the minimum point is (3, 5)

So, we have the following representation

(h, k) = (3, 5)

Substitute (h, k) = (3, 5) in the above equation

So, we have:

y = |x - 3| + 5

Hence, the function represented by the graph has an equation of f(x) = |x - 3| + 5

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The required expression which is equivalent to -51 -(-60) is -51 + 60.

Given that,
Which expression is equivalent to -51 - (-60) is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression =  -51 - (-60)
Simplify by applying the property of distribution under the parenthesis,
= -51 + 60

Thus, The required expression which is equivalent to -51 -(-60) is -51 + 60.

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A. Both triangles have two pairs of corresponding sides and a pair of included angles, therefore, ΔABC ≌ ΔABD by SAS.

B. ∠CBA ≌ ∠DBA by CPCTC.

The SAS congruence theorem state that if we have two triangles that we can show that they posses two pairs of corresponding sides that are equal and a pair of included angles that are also equal, then we can state that the two triangles are congruent to each other

When two triangles are proven to be congruent to each other, every corresponding parts of both triangles will be equal to each other based on CPCTC.

Part A:

We are given that AC ≌ AD, and ∠CAB ≌ ∠DAB.

Also, AB ≌ AB based on the reflexive property.

Therefore, both triangles are congruent to each other based on SAS.

ΔABC ≌ ΔABD

Part B:

Since both triangles are congruent, therefore ∠CBA ≌ ∠DBA by CPCTC.

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Option A: Multiply the top equation by 3, multiply the bottom equation by -2, then add the equations will eliminate the variables.

Rewriting the equation -

2x + 8y = -3 : Equation 1

3x + 6y = -4 : Equation 2

Multiplying equation 1 with and equation 2 with -2.

6x + 24y = -9 : Equation 3

-6x - 12y = 24 : Equation 4

Adding the equation 3 and equation 4. This will eliminate the variable x.

12y = 15

y = 5/4

So, option 1 will eliminate the variable x on solving we get the value of y as 5/4.

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If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.

acc to our question-,

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If they are competing for 1st, 2nd, and 3rd place ribbons. The number of different ways can the winners be chosen is:  B. 60.

Given data:

Number of people =5

Number of places = 1st, 2nd, and 3rd

Hence,

Different combinations =5 ×4×3

Different combinations = 60 ways

Therefore the winners will be chosen by  60 different possible ways ,

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Answer:

324 ft

Step-by-step explanation:

[tex]v=\sqrt{2gh}[/tex]

[tex]v^2=(\sqrt{2gh})^2[/tex]

[tex]v^2=2gh[/tex]

[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]

[tex]\frac{v^2}{2g}=h[/tex]

[tex]\frac{144^2}{2(32)}=h[/tex]

[tex]\frac{20736}{64}=h[/tex]

[tex]324=h[/tex]

The value of function is positive so the function have maximum value 30 at x=3.

In the given question we have to find the maximum or the minimum value of a function.

The given function is

f(x) = -3x^2+18x+3

To find the maximum or minimum value we firstly find the value of f'(x).

f'(x) = -6x+18

Now put f'(x)=0

-6x+18=0

Subtract 18 on both side we get

-6x=-18

Divide by -6 on both side we get

x = 3

Now finding the value of function at x=3

f(3)= -3*(3)^2+18*3+3

f(3)= -3*9+54+3

f(3)= -27+54+3

f(3)= 30

Since the value of function is positive so the function have maximum value 30 at x=3.

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The proportion of Americans who support federal spending cuts to Medicaid is less than 0.12 leads to Type 1 error.

When we reject a true H₀ it is known as type 1 error. The probability of type 1 errors is inversely proportional to the amount of confidence you choose. There is a 5% possibility of receiving a type 1 error on a test with a 95% confidence level.

When we feel to reject a false H₀ it is known as type 2 error.

H₀:P= 0.12

Hₐ:P= 0.12

The question implies that we actually rejected the null hypothesis, while there is a chance that it is true and we are rejecting a true null hypothesis.

Therefore, it only suggests that there is a possibility that we will make a type 1 error.

Consequently, Type 1 error is the response to our query.

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