a painter leans a ladder against a vertical wall. the top of the ladder is 15 meters above the ground. when the bottom of the ladder is moved 3 meters farther away from the wall, the top of the ladder is 11 meters above the ground. what is the length of the ladder? round to the nearest hundredth of a meter.

The statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.

Let us understand about the given graph:

The given graph is a graph of a cube root function.

So, the statement of Noelle, “The graph represents the function [tex]f(x)=\sqrt[3]{x}[/tex]." is correct.

So, option A is not correct.

The inverse of a cube root function is a cubic function.

So, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect.

So, option B is correct.

The domain and range of the cube root function are all real numbers.

So, the statement of Julian, “The domain and range of the function is all real numbers.” is correct.

So, option C is not correct.

From the graph, we can see f(-1) = -1.

So, the statement of Yemen, “The value of f(-1) = -1.” is correct.

So, option D is not correct.

Thus, the statement of Gabriella, “The graph will not have an inverse function.” is incorrect. Option B is correct.

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Answer:

  P'(-16, 0)

Step-by-step explanation:

You want the coordinates of the image of P(-4, 0) when the figure is dilated by a factor of 4 about the origin.

Dilation about the origin multiplies each coordinate by the dilation factor:

  P' = 4P

  P' = 4(-4, 0) = (-16, 0)

The coordinate of the image point are (-16, 0).

Answer:

see explanation

Step-by-step explanation:

(j + k)²

= (j + k)(j + k)

each term in the second factor is multiplied by each term in the first factor , that is

j(j + k) + k(j + k) ← distribute parenthesis

= j² + jk + jk + k² ← collect like terms

= j² + 2jk + k²

The quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

Given:

f(x) = 2(x+1)^2 - 8

= 2(x^2+1+2x) - 8

= 2x^2 + 2 +4x - 8

= 2x^2+4x-6(standard form)

Intercept form:

= 2x^2+4x-6

= (x-1)(x+3)

x-1 = 0

x = 1

x+3 = 0

x = -3

(1,0) and(-3,0).

Therefore the quadratic function f(x)=2(x+1)^2-8 in standard for and intercept form is 2x^2+4x-6 and (x-1)(x+3).

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Answer:

C

Step-by-step explanation:

there are 1 x values that have the 2 different y value

There is sufficient data to prove that the heart rate was less than 120 beats per minute (P-value = 0.002).

For the population mean weight control heart rate of 20-year-olds, the 95% confidence interval is (98.07, 115.93).

Step-by-step explanation:

This is a test of the population mean's theory.

The assertion is that a heart rate of less than 120 bpm exists.

The alternative and null hypothesis are then:

h0 : μ = 120

ha : μ < 120

The level of significance is 0.05.

The sample has a n=100 size.

M=107 is the sample mean.

Due to the unknown population standard deviation, we estimate it using the sample standard deviation, which has a value of s=45.

Using the following formula, the estimated standard error of the mean is calculated:

Sm = [tex]\frac{s}{\sqrt{n} }[/tex]= [tex]\frac{45}{\sqrt{100} }[/tex] = 4.5

The t-statistic can then be calculated as follows:

T = [tex]\frac{m-μ}{\frac{s}{\sqrt{n} } }[/tex] = 107-120/4.5 = -13/4.5 -2.88

The t-statistic can then be calculated as follows:

df= n-1 = 100-1 = 99

These sample size's degrees of freedom are:

Given that this test has 99 degrees of freedom, a left-tailed design, and a t value of -2.889, the P-value is determined as follows (using a t-table)

p-value = p(t<-2.88)= 0.002

The effect is significant because the P-value (0.002) is less than the 0.05 level of significance.

The naive theory is disproved.

There is sufficient proof to back up the assertion that the heart rate was less than 120 bpm.

A 95% confidence interval for the mean must be calculated.

Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.

M=107 is the sample mean.

N=100 is the sample size.

When σ is unknown, an estimation of σM is made by dividing s by the square root of N:

Sm =[tex]\frac{s}{\sqrt{N} }[/tex] =[tex]\frac{45}{\sqrt{100} }[/tex] =4.5

The t-value for a 95% confidence interval is t=1.984.

The margin of error (MOE) can be calculated as:

MOE = t*Sm = 1.984 * 4.5 = 8.92

Then, the lower and upper bounds of the confidence interval are:

LL = M - t*Sm = 107- 8.92 = 98.07

UL = M +t *Sm = 107 + 8.92 = 115.93

The 95% confidence interval for the population mean weight control heart rate of 20-year-olds is (98.07, 115.93).

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The value of the variable m in the rectangle is given as follows:

m = 12.5.

The segments from the rectangle, and their lengths, are given as follows:

They are opposite vertices of the rectangle, as they do not have any common vertex.

Since they are opposite vertex, it doesn't matter if these segments are bases, heights or diagonals, they will have the same length.

Thus the numeric value of variable m is obtained as follows:

WY = XZ

(as they have the same length).

Replacing the measures of each of these segments:

12m + 7 = 16m - 43

12m - 16m = -43 -7

-4m = -50

4m = 50 (multiplication by -1).

m = 50/4

m = 12.5.

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The sales tax is $1.2  and the total cost of the item is  $21.2   .

In the question,

it is given that ,

the selling price of the item is $20.

the rate of sales tax is = 6^ ,

so the sales tax can be calculated using the formula

sales tax = 6% of selling price

So , sales tax = 6% of 20

= 0.06 * 20

= 1.2

so , the sales tax is $1.2

the total cost of the item will be = selling price + sales tax

= 20 + 1.2

= 21.2

Therefore , The sales tax is $1.2  and the total cost of the item is  $21.2   .

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The amount in grams of food A and B she feeds this group of rats each day will be 2200003.84 gm and 1100006.4 gm respectively.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Given that, she provides a certain set of lab rats with a daily meal that contains exactly 32 units of niacin and 22000 units of retinol. She uses two different brands of industrial pellet food.

If food A has 100 units of retinol and 0,12 units of niacin per gram.Niacin 0.20 units and retinol 50 units are both included in Food B per gram. The grams of each food she feeds this group A of rats each day is,

=32×0.12+22000×100

=2200003.84 gm

If food B contains 0,20 units of niacin and 50 units of retinol per gram.The grams of each food she feeds this group A of rats each day is,

=32×0.20+22000×50

=1100006.4

Thus, the amount in grams of food A and B she feeds this group of rats each day will be 2200003.84 gm and 1100006.4 gm respectively.

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The correct response variable is the amount of pain relief.

Given that,

A tall glass of ice water, according to some, can help migraine sufferers find relief. Multiple migraine sufferers will be recruited by researchers to participate in a test. The individual will either take a placebo pill or a common painkiller when they get a migraine. Additionally, only half of each group will take the pill with water; the other half will sip on a small amount of water. The quantity of pain relief is then reported by participants.

To find :  What is the response variable in this experiment.

Explanation :

Response variable or study variable, in general called as dependent variable  is the variable of main focus in study. We want to study the changes in explanatory or independent variables are associated with response variable. Sometimes we want to measure the effect of predictors i.e explanatory variables on response variable.

For example in hand, we want to determine whether the drinking ice water is associated with amount of pain relief. Hence in this study, response variable is the amount of pain relief.

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Check the picture below.

The whole values of a for which the solution of the equation ax = 6 is a = {1, 2, 3, 6}

The given equation is

ax = 6

Divide both side of the equation by a

ax / a = 6/a

Then the equation will be

x = 6/a

If the solution of the system should be a whole number, then the value of a should be a factor of the numerator 6.

If a is the factor of 6, then the only the result will be a whole number without any numerator

Then the factors of 6 are 1, 2, 3, 6

Then the whole values of a = {1, 2, 3, 6}

Hence, the whole values of a for which the solution of the equation ax = 6 is a = {1, 2, 3, 6}

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Answer:

h=6+(2t)

Step-by-step explanation:

The point (-2, 6) is reflected across the y-axis then the new coordinates of the point are (2, 6).

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

We know when a point (x, y) is reflected along the y-axis (x, y) becomes

(- x, y).

Given, A point (-2, 6) is reflected across the y-axis.

∴The new coordinates of the point are (2, 6).

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On 6th day the Blake and Nicole will be on same page

Consider the case of Blake

The initial page number = 40

Number of pages per day = 10

Consider the B is the page number and t is the number day

Then the function will be

B = 40 + 10t

Consider the case of Nicole

The initial page number = 10

Number of pages per day = 15

Consider the N is the page number and t is the number day

Then the function will be

N = 10 + 15t

Draw the graph using the functions

Hence, on 6th day the Blake and Nicole will be on same page

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To calculate the distance between two points, we have to:

[tex]\large\displaystyle\text{$\begin{gathered}\sf The \ points\ are \left \{ {{A=(x_1,y_1)} \atop {B=(x_2,y_2)}} -\to\boldsymbol{\sf{m=\frac{\Delta y}{\Delta x }\iff \ m=\frac{y_2-y_1}{x_2-x_1} }} \right. \end{gathered}$}[/tex]

We have that the points to calculate the slope are:  (x₁ = -4, y₁ = 4) and (x₂ = -15, y₂ = 2)

Add the data in the formula:              

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{y_2-y_1}{x_2-x_1} } \end{gathered}$}} \\ \\ \boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{2-4}{-5-(-4) } } \end{gathered}$}} \\ \\ \boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2}{-11} } \end{gathered}$} }}[/tex]

Answer:

Part A: C

Part B: T shirt = $20, hat = $12

Step-by-step explanation:

Part A:

He buy 8 T-Shirts and 5 hats for $220.

He buy another buys 5 T-shirts and 1 hat for $112.

assuming t = tshirt, h = hat, C is the correct answer

Part B:

8t + 5h = 220

5t + h = 112

1. Use second equation to represent h in term of t

h = 112 -5t

2. Replace h in first equation with h from 1.

8t + 5(112 -5t) = 220

8t + 560 - 25t = 220

-17t + 560 = 220

-17t = 220 - 560

-17t = -340

t = -340/-17 = 20

3. Replace t in equation from 1. with t from 2.

h = 112 -5(20) = 112 - 100 = 12

a) The terms are:  10x, 12y,300

  The Coefficients are: 10,12

b) x intercept is (30,0). y intercept is (0,25)

c)  The three possible solutions:

(1,24), (8,18) , (6,20)

what are terms and coefficients?

Term could be a single number (positive or negative), a single variable (a letter), or a combination of multiple variables multiplied but never added or removed. Variables with numbers in front of them can be found in some terms. A coefficient is the number that appears in front of a phrase.

10x +12y=300

Terms:  10x, 12y,300

Coefficients: 10,12

Refer to the attachment for graph:

b) The locations on a Cartesian coordinate system known as intercepts are where the graph of an equation or function crosses the x- and y-axes.

From the graph, x intercept is (30,0). y intercept is (0,25)

c) solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.

10x +12y=300

Find y when x=1:

10(1)+12y=300

10+12y=300

12y=300-10=290

y= 24.2 ≈ 24

Similarly, the three possible solutions:

(1,24), (8,18) , (6,20)

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Answer:2

Step-by-step explanation:

Answer:

[tex]f(x)=-2x^2+3[/tex]

Step-by-step explanation:

The vertex is at [tex](0,3)[/tex], so the equation is of the form [tex]f(x)=ax^2+3[/tex].

Using the point [tex](1,1)[/tex] to solve for [tex]a[/tex],

[tex]1=a+3 \implies a=-2 \\ \\ \therefore f(x)=-2x^2+3[/tex]

The words that describe the pattern that can be used to complete the table is that the number of lines is double the number of figures, which indicates that the correct option is option A

A. The total number of lines y is two times the figure number x

An equation is a mathematical statement that connects two expression with an equals sign.

The pattern that can be used to complete the table is therefore;

The number of lines, y, is twice the number of figures, x

The relationship expressed mathematically as an equation is presented as follows;

y = 2·x

The completed table is presented as follows;

Figure Number, x   [tex]{}[/tex] Total Lines, y                        [tex]{}[/tex] Ordered pair

1                         [tex]{}[/tex]            2                                          (1, 2)

2                         [tex]{}[/tex]           4                                          (2, 4)

3                         [tex]{}[/tex]           6                                          (3, 6)

4                         [tex]{}[/tex]           8                                          (4, 8)

5                         [tex]{}[/tex]           10                                        (10, 5)

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Answer:

Step-by-step explanation:

Ok:

First Problem with coin!

1. A coin has 2 sides and one of them is going to land up or down which means it has a chance of 1 out of 2.

1 out of 2=

1/2= 50%

Second Problem with spinner

2. There are 12 spaces on the spinner and three of those spaces are blue.

SO: 3 out of 12=

3/12=

1/4=

25%

Answers: 50% and 25%

IN FRACTION FORM: 1/2 and 1/4

Answer:

y=-7

Step-by-step explanation:

just simplify it

4+y=-3

y=-3-4

y=-7

Option C is correct which is dC/dt = π (dd/dt).

According to the question,

We know that the diameter of the circle is half the radius of the circle.

d = r/2

By transferring r to the left-hand side and d to the right-hand side

r = d/2

We also know that circumference of the circle is

C=2πr

C=2πd/2

C=πd

Now we will differentiate on both the side with respect to t and we will get,

dC/dt = π (dd/dt)

Differentiation is a technique for tracking down the subordinate of a capability. Differentiation is a process, where we find the momentary rate of change in capability in light of one of its variables. We usually differentiate with respect to time which is represented as ds/dt.

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The equation is, 250+x =400

From the question, we have

The old energy level is 250.

Let the bar is added to the bag = x.

The new energy level is 400.

The equation is, 250+x =400

Addition:

The act of combining two or more items is known as addition. The process of computing the sum of two or more numbers in mathematics is called addition. It is a fundamental mathematical procedure that is frequently used in daily life. When we work with money, figure out our food bills, or figure out the time, we frequently employ addition. One-digit numbers can be added simply for solving addition problems, however for bigger numbers, we divide the numbers into columns using their corresponding place values, such as ones, tens, hundreds, thousands, and so on.

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Answer:

Step-by-step explanation:

4x-c=k  

solve for x

use the reverse order for the usual order of operations, to solve for x

first use addition

4x = k+c

then use division

x = (k+c) / 4

so answer B) looks good