Can someone please help me with my Imagine Math? My teacher assigned are class to do this even though we haven't learned about this yet.... I don't understand this at All!

QUESTION:
Drag each graph to show whether it is a function of x or not a function of x. If there is not enough information to tell, drag the graph into the box under “Not Enough Information.”

When you tell me the answers type it in this format:
this graph goes in "function" OR this graph goes in "Not a function" OR this graph goes in "Not enough information"

Answer:

8 times

Step-by-step explanation:

Volume of sphere 4/3 *pi*r^3

Let small sphere radius r1=r

So radius of large sphere R= 2r (given)

Put all valves in sphere formula and calculate

Small sphere vol v1 = 4/3*pi*r^3......... Let assume eq 1

Large sphere vol= 4/3*pi*(2r)^3

= 4/3*pi* 8r^3

Or = 8v1

substitute 4/3*pi*r^3 value from eq1

Answer:

8

Step-by-step explanation:

Given the ratio of the radii = a : b, then

ratio of volume = a³ : b³

Here the ratio of radii = 1 : 2 , thus

ratio of volume = 1³ : 2³ = 1 : 8

That is the volume of the larger sphere is 8 times the volume of smaller sphere.

It takes 1.75 minutes to an average customer to wait

The waiting times standard deviation is 1.01

The percentage of a customer wait under a minute is 28.57%

42.86% customers wait more than two minutes

Uniform distribution: n probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.

Display the 1.00 area under the curve.

The rectangle has a length of 3.5 - 0 = 3.5.

The rectangle's height is 1/3.5.

To determine the area, multiply:

3.5 * 1/3.5 = 1

How long does the average customer have to wait for an elevator?

EV stands for average between high and low.

= (0+3.5)/2

= 1.75

What is the waiting time's standard deviation?

Standard deviation is equal to sqrt(b-a2/12).

= sqrt((3.5-0)^2/12)

= 1.01

What percentage of customers wait under a minute?

It is x/(b-a) = 1/ for less than (3.5-0)

1/3.5

= 28.57%

How many customers wait more than two minutes?

It is 1 - x for greater than (b-a)

(3.5-2)/3.5

= 1.5/3.5

= 42.86%

It takes 1.75 minutes to an average customer to wait

The waiting times standard deviation is 1.01

The percentage of a customer wait under a minute is 28.57%

42.86% customers wait more than two minutes

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The complete question is

"Find the general solution of the given differential equation

y''-y=0, y1(t)=e^t , y2(t)=cosht

The function \(y(t)=e^t\)  is the solution of the given differential equation.

The function y(t)=cosht is the solution of given differential equation.

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

\(y_1(t) = e^t\)

Given differential equations are,

y''-y = 0

 So that,  

\(y' (t) = e^t, y'' (t) = e^t\)

Substitute values in the given differential equation.

\(e^t -e^t=0\)

Therefore, the function \(y(t)=e^t\)  is the solution of the given differential equation.

Another function;

\(y(t)=cosht\)  

So that,  

\(y"(t)=sinht\\\\y"(t)=cosht\)

Hence, function y(t)=cosht is solution of given differential equation.

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Answer:

Okapi weighs 290, and llama weighs 160.

If Sinilizwe speaks for 27 minutes, there is R22.58 left on the phone card.

To calculate the cost per minute of using the phone card, we can divide the total cost of the card by the number of minutes it allows:

Cost per minute = R50 / 62 minutes

Cost per minute = R0.81 per minute

Therefore, the cost per minute of using the phone card is R0.81.

4.2 If Sinilizwe speaks for 27 minutes, he has used up 27/62 of the total minutes the card allows:

Fraction of minutes used = 27 / 62

To calculate the amount of money left on the card, we need to subtract the cost of the minutes used from the total value of the card:

Value of card remaining = R50 - (27/62) x R50

Value of card remaining = R22.58

Therefore, if Sinilizwe speaks for 27 minutes, there is R22.58 left on the phone card.

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Answer:

\(\frac{FH}{RX} =\frac{HG}{XS} =\frac{FG}{RS}\)

Step-by-step explanation:

The order of the letters matters in any similarity theorem.

When triangle FHG is similar to triangle RXS, the lengths of FH must be similar to RX.

When 2 similar lines are divided, that number is the factor by which one triangle can be dilated to match the other.

That being said, each of these proportion statements can be read as individual division expressions that equal the next division expression.

This means \(FH\div RX = HG\div XS = FG\div RS\).

If you look at it this way, you can see that the sides you need to fill in must be the corresponding similar sides, so that you end up with the factor for the dilation of the 2 triangles.

Answer:

$6.90

Step-by-step explanation:

30/100 = x/23

100x = 690

x= $6.90

Answer:

A. 525.42 inches^3

B. 175.91 mm

Step-by-step explanation:

a. Here we are asked to calculate the volume of the cone given the radius and the height of the cone.

Mathematically, the volume of the cone can be calculated using the formula below;

V = 1/3 * π * r^2 * h

where r is the radius which is 5.1 inches and h is the height of the megaphone = 19.3 inches

Plugging these values, we have;

V = 1/3 * 3.14 * 5.1^2 * 19.3 = 525.42 inches^3

b. Here we are tasked with calculating the height given the value of the volume and the radius.

mathematically, the formula to use is

V = 1/3 * π * r^2 * h

where V = 356,456.2136 cubic millimeter and r is 44mm

plugging these values we have

356,456.2136 = 1/3 * 3.14 * 44^2 * h

h =( 1,069,368.6408)/6,079.04

h = 175.91 mm

Answer:

1/2

Step-by-step explanation:

you're trying to put the variable(y) by itself. it would be divided by 14 on both sides, which 7/14 is 1/2

Answer:

Pentagon's perimeter: 5I ; (choice 2)

Rectangle's perimeter: 2I + 2 (I + 10) ; (choice 4)

Scenario's equation: 5I = 2I + 2 (I + 10) ; (choice 4)

Step-by-step explanation:

I hope this helped! :)

Answer:

Pentagon's perimeter: 5I ; (choice 2)

Rectangle's perimeter: 2I + 2 (I + 10) ; (choice 4)

Scenario's equation: 5I = 2I + 2 (I + 10) ; (choice 4)

Step-by-step explanation:

The area bounded by the given curves is 6 square units and the average value of y over the interval [3,7.2] is 32.

To find a region bounded by a given curve, first, sketch the region:

The curves y=x and y=4x intersect at x=1. We also need to find the y coordinate of the intersection of y=4x and x=2, ie y=8.

So the region is a trapezoid with bases of lengths 1 and 2 and height of length 4. The area is given as:

A = (1/2)(1 + 2)(4) = 6 square units.

Therefore, the area enclosed by the specified curve is 6 square units. To find the mean of y = -12 when y = -26 on the interval, we need to find the definite integral of y with respect to x on the interval [-26, -12].

∫[-26,-12] -12dx = (-12)(-12 - (-26)) = 168

The interval lengths are:

-12 - (-26) = 14

So the mean value of y over the interval is

(-1/14) * 168 = -12

So the average value of y in the interval [-26,-12] is -12.

To find a region bounded by a given curve, first, sketch the region:

The curves \(y = x^3 and y = x^2\) intersect at x = 0 and x = 1. The range is bounded by the x-axis\(y = x^2 and y = x^3\). The area is given by the formula:

\(A = ∫[0,1] (x^3 - x^2) dx = 1/12\)

Therefore, the area enclosed by the given curve is 1/12 square units.

To find the mean of\(y = 5x^4\) on the interval [1,3], we need to find the definite integral of y with respect to x on the interval [1,3].

\(∫[1,3]5x^4dx = (5/5)(3^5 - 1^5) = 242\)

The interval lengths are:

3 - 1 = 2

So the mean value of y over the interval is

(1/2) * 242 = 121

Therefore, the mean value of y in the interval [1,3] is 121. To discover the mean of y = 4x + 4 on the interim [3.7.2], we ought to discover the unequivocal necessity of y with regard to x on the interim [3.7.2].

\(∫[3,7,2] (4x + 4)dx = (4/2)(7.2^2 - 3^2) + (4)(7.2 - 3) = 134.4\)

The interval lengths are:

7.2 - 3 = 4.2

So the mean value of y over the interval is

(1/4.2) * 134.4 = 32

Therefore, the mean value of y in the interval [3,7.2] is 32.  

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a) The equilibrium points for the potential energy U(x) = U0(x^2/a^2 + a^2/x^2) are x_eq = 0, x_eq = a, and x_eq = -a.

b) The approximation to U(x) around each equilibrium point to order O(x - x_eq)^2 is given by U(x) ≈ U(x_eq) + (1/2) * d^2U(x_eq)/dx^2 * (x - x_eq)^2.

c) A plot of U/U0 as a function of x/a for the potential energy and the quadratic approximation can be made, but the specific shape and details of the plot depend on the chosen values of U0 and a.

a) To find the equilibrium points, we need to find the values of x where the potential energy U(x) is minimized. This occurs when the derivative of U(x) with respect to x is zero:

dU(x)/dx = 0

Differentiating U(x) with respect to x, we get:

dU(x)/dx = 2U0(x/a^2 - x^3/a^4)

Setting this derivative equal to zero, we have:

2U0(x/a^2 - x^3/a^4) = 0

Simplifying, we find:

x/a^2 - x^3/a^4 = 0

x(1 - x^2/a^2) = 0

This equation is satisfied when x = 0 or x = ±a.

Therefore, the possible equilibrium points are x_eq = 0, x_eq = a, and x_eq = -a.

b) To find the approximation to U(x) around each equilibrium point to order O(x - x_eq)^2, we can use Taylor series expansion. We expand U(x) about x_eq up to the quadratic term:

U(x) ≈ U(x_eq) + dU(x_eq)/dx * (x - x_eq) + (1/2) * d^2U(x_eq)/dx^2 * (x - x_eq)^2

Since dU(x_eq)/dx = 0 for equilibrium points, the quadratic term simplifies to:

U(x) ≈ U(x_eq) + (1/2) * d^2U(x_eq)/dx^2 * (x - x_eq)^2

c) To make a plot of U/U0 as a function of x/a for the potential energy and the approximation, we need to specify the values of U0 and a. The plot will show the behavior of U(x) and the approximation around the equilibrium points.

Without specific values for U0 and a, it is not possible to provide a detailed plot. However, the general shape of the plot will depend on the chosen values and will show the potential energy U(x) and the quadratic approximation around the equilibrium points x_eq = 0, x_eq = a, and x_eq = -a.

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Answer:

James = 119 points

Sarah = 357 points

Roberts = 51 points

Step-by-step explanation:

Given that :

James = x points

Sarah = 3x points

Roberts = x - 68 points

Each point = 3 pence

All students have a total of £15.81

1 pound = 100 pence

£15.81 pound = 1581 pence

3x + 3(3x) + 3(x - 68) = 1581

3x + 9x + 3x - 204 = 1581

15x - 204 = 1581

15x = 1581 + 204

15x = 1785

x = 1785 / 15

x = 119

Hence,

James = 119 points

Sarah = 119 * 3 = 357 points

Roberts = 119 - 68 = 51 points

The estimated regression equation provided is û = 18 + 3.6x1 - 2.02 + 7.523 + 2.934, based on 30 observations. The values of SST (Total Sum of Squares) and SSR (Regression Sum of Squares) are given as 1,803 and 1,762, respectively. The task is to compute R² and R, and then comment on the goodness of fit of the regression model.

In part (a), R² (R-squared) is computed by dividing SSR (Regression Sum of Squares) by SST (Total Sum of Squares). R² represents the proportion of the total variation in the dependent variable (û) that is explained by the independent variables (x1, x2, x3). It provides an indication of how well the regression model fits the data. The calculated R² value is typically between 0 and 1, where a higher value indicates a better fit. The result is rounded to three decimal places.

In part (b), R (Adjusted R-squared) is computed by adjusting R² for the number of independent variables and the sample size. R takes into account the degrees of freedom and penalizes models with a large number of variables. It is a more appropriate measure when comparing models with a different number of independent variables. The computed R value is rounded to three decimal places.

In part (c), the goodness of fit is commented based on the calculated R² and R values. A higher R² indicates a better fit, suggesting that the independent variables in the regression equation explain a larger proportion of the variability in the dependent variable. Similarly, a higher R indicates a better fit, considering the number of variables and sample size. The goodness of fit can be assessed by comparing the R² and R values to a predetermined threshold or by comparing them to those obtained from alternative models. A higher R² and R imply a stronger relationship between the independent and dependent variables, indicating a better fit of the regression model to the data.

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Answer:

There are 2 solutions to square root x = 9

They are 3, and -3

Step-by-step explanation:

The square root of x=9 has 2 solutions,

The square root means, for a given number, (in our case 9) what number times itself equals the given number,

Or, squaring (i.e multiplying with itself) what number would give the given number,

so, we have to find the solutions to \(\sqrt{9}\)

since we know that,

\((3)(3) = 9\\and,\\(-3)(-3) = 9\)

hence if we square either 3 or -3, we get 9

Hence the solutions are 3, and -3

When performing one-dimensional graphical vector addition, the proper starting position for each of the two arrows representing the two vectors being combined depends on the specific scenario.

In general, when adding two vectors in one dimension, you can start both arrows at the same point, such as the origin of a coordinate system. This is commonly done when the vectors are acting in the same direction.

For example, if you have a vector A pointing to the right with a magnitude of 3 units and a vector B pointing to the right with a magnitude of 2 units, you can start both arrows at the same point and draw them to the right, one after the other, with a total length of 5 units.

However, if the two vectors are acting in opposite directions, you can start one arrow at the origin and the other arrow at the endpoint of the first arrow.

For example, if you have a vector A pointing to the right with a magnitude of 3 units and a vector B pointing to the left with a magnitude of 2 units, you can start the arrow for vector A at the origin and draw it to the right for 3 units.

Then, you can start the arrow for vector B at the endpoint of vector A and draw it to the left for 2 units. The resulting vector sum would be the vector connecting the starting point of vector A to the endpoint of vector B.

Therefore, the proper starting position for each of the two arrows representing the two vectors being combined in one-dimensional graphical vector addition depends on their directions. If the vectors are acting in the same direction, you can start both arrows at the same point.

If the vectors are acting in opposite directions, you can start one arrow at the origin and the other arrow at the endpoint of the first arrow.

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Sarah earns $120 per week from her part-time job. To complete the table, we need to list her expenses.  Sarah's expenses may vary, but here are some common examples she might have:

1. Transportation: Sarah may spend money on bus fare or gas if she drives. This expense depends on her mode of transportation and how far she travels.
2. Food: Sarah needs to eat, so she may spend money on groceries or meals outside. The amount spent on food will depend on her eating habits and whether she eats out frequently or cooks at home.
3. Utilities: Sarah may have to pay for utilities like electricity, water, and internet. The cost of utilities can vary depending on the region and the size of her living space.

4. Rent/ Mortgage: If Sarah lives independently or contributes to household expenses, she may have to pay rent or contribute to a mortgage payment.
5. Entertainment: Sarah may have expenses related to leisure activities such as going to the movies, concerts, or other entertainment events.
These are just a few examples, and Sarah's actual expenses may differ. It's important for her to track her spending to understand where her money goes. By doing so, she can budget effectively and make informed financial decisions.

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Total number of outcomes in rolling a die 3 times = \(6^3\)  =216

What is outcome of an event?

Suppose an event is happening. The result of the event is called outcome of the event.

For example : let the event be throwing of a die. One of the outcome of the event is getting a 4 on the die

Number of outcomes of rolling a die first time = 6

Number of outcomes of rolling the die second time = 6

Number of outcomes in rolling a die third time = 6

Total number of outcomes in rolling a die 3 times = \(6 \times 6 \times 6\)

                                                                                   = \(6^3\)

                                                                                   = 216

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\(\huge\text{Hey there!}\)

\(\textsf{Assuming:}\)

\(\mathsf{w + (w - \dfrac{12}{2^2} \times 3)(7)}\)

\(\textsf{If so:}\)

\(\mathsf{w + (w - \dfrac{12}{2^2} \times 3)(7)}\)

\(\mathsf{= 10 + (10 - \dfrac{12}{2^2} \times 3)(7)}\)

\(\mathsf{= 10 + (10 - \dfrac{12}{2\times2} \times 3)(7)}\)

\(\mathsf{= 10 + (10 - \dfrac{12}{4} \times 3)(7)}\)

\(\mathsf{= 10 + (10 -3 \times 3)(7)}\)

\(\mathsf{= 10 + (10 - 9)(7)}\)

\(\mathsf{= 10 + (1)(7)}\)

\(\mathsf{= 10 + 7}\)

\(\mathsf{= 17}\)

\(\huge\textsf{Therefore, your answer should be:}\)

\(\huge\boxed{\textbf{Option D. }\frak{017}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Maria will spend 1.25x on x poinds of apple

If apples cost $1.25 per pound, then Maria will spend $1.25 times the number of pounds of apples she buys.

In other words, the cost of x pounds of apples can be calculated as follows:

Cost of x pounds of apples = $1.25 x

Therefore, Maria will spend $1.25 times the number of pounds of apples she buys.

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The "clm" option in PROC GLM produces confidence intervals for mean response.

The "clm" option in the model statement of an MLR (Multiple Linear Regression) analysis in PROC GLM stands for "Confidence Limit for Mean". Therefore, the correct answer is (c) "produce confidence intervals for the mean response at all predictor combinations in the dataset."

When we fit a linear regression model to a dataset, we often want to make inferences about the population parameters based on the sample data. Confidence intervals are one way to estimate the range of values that a population parameter might fall within, with a certain degree of confidence.

In the case of the "clm" option in PROC GLM, we are specifically interested in constructing confidence intervals for the mean response at all predictor combinations in the dataset.

The confidence limits for the mean (CLM) provide a range of values in which the mean response is expected to lie with a specified level of confidence.

For example, a 95% CLM for the mean response at a particular combination of predictor variables would indicate the range of values within which we would expect the population mean response to lie 95% of the time, based on the observed data.

To obtain the CLMs for the

mean response using PROC GLM, we can include the "clm" option in the model statement, like

In this example, "y" is the dependent variable, and "x1", "x2", and "x3" are the independent variables. The "/ clm" option tells PROC GLM to produce the confidence limits for the mean response at all predictor combinations in the dataset.

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Answer:

- 6x

Step-by-step explanation:

Step 1:

- 5x - x

Answer:

- 6x

Hope This Helps :)

- 6x

Step 1:   - 5x - x

Answer:  - 6x

Answer:

(2, -2) are the coordinates of the point which divides BA into ration 2:4.

Step-by-step explanation:

The given two co-ordinates of A are (-2, 6) and B is (4, -6).

Let P be the point that divides the line BA into ratio 2:4.

to find coordinates of a point P on the line segment BA dividing it in a ratio 2:4, we can use segment formula.

\(x = \dfrac{mx_{2}+nx_{1}}{m+n}\\y = \dfrac{my_{2}+ny_{1}}{m+n}\)

Where (x,y) is the co-ordinate of the point P which  

divides the line segment joining the points \((x_{1}, y_{1}) and (x_{2}, y_{2})\) in the ratio m:n.

Please refer to the attached image.

As per the given values :

\(x_{1} = 4\\x_{2} = -2\\y_{1} = -6\\y_{2} = 6\\\)

Putting the given values in above formula :

x-co-ordinate of P:

\(x = \dfrac{4 \times 4 -2 \times 2}{4+2}\\\Rightarrow \dfrac{12}{6}\\\Rightarrow x = 2\)

y-co-ordinate of P :

\(y = \dfrac{4 \times -6 +2 \times 6}{4+2}\\\Rightarrow \dfrac{-24+12}{6}\\\Rightarrow \dfrac{-12}{6}\\\Rightarrow y = -2\)

So, answer is P(2, -2).

Answer:

D: 4(2a+3)=8a+3

Step-by-step explanation:

4x2a = 8a and 4x3 = 12

Answer:

just saying this so other can get brainliest

Step-by-step explanation:

d

Answer:

(- 3, 2 )

Step-by-step explanation:

to find the start, do the reverse, that is move 1 unit to the right.

this means adding 1 to the x- coordinate

start = (- 4, 2 ) → (- 4 + 1, 2 ) → (- 3, 2 )

Answer: In 36 minutes both buses  will end up at the library.

Step-by-step explanation:

Given: Buses from one route stop at the library every 9 minutes.

Buses from the other route stop at the library every 12 minutes.

The number of minutes in which both buses will end up at the library= LCM(9,12)

Now , 9= 3 x 3

12= 2 x 2 x 3

LCM(9,12) = 2 x 2 x 3 x 3 = 36

In 36 minutes both buses  will end up at the library.

The equation of the line is y = 4x. Option B

First, we need to know that the general equation of a line is expressed as;

y = mx + c

Such that the parameters of the formula are expressed as;

From the information given, we have that the points in the line are;

(1,-4)

(2,-8)

Now, let us determine the slope of the line, we have to take the change in the value of the points

Slope, m = -8 -(-4)/2-1

expand the bracket

Slope, m = 4

Then, the intercept is;

-8 = 4(2) + c

c = 0

Equation of the line would be;

y = 4x

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Answer:

use long divison  ike this

      16

  -------

8 | 132

    8

  -----

    52

    48

  -----

     4

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                         132/8 = 16 with 4 leftover

                                             32 divided by 8 is 4, 96 divided by 8 is 12, the                                                                  

                                                  extra 4 left over

The correct statement is: double d = 123456789

In the given statements:

1. int i = 3.0; - This is incorrect because a decimal value (3.0) cannot be assigned directly to an integer variable. It should be assigned to a floating-point type variable instead.

2. float f = 4.5; - This is correct as a floating-point value (4.5) can be assigned to a float variable.

3. byte b = 123456789; - This is incorrect because the value 123456789 is outside the range of a byte (-128 to 127). It should be assigned to a data type with a larger range, such as into or long.

4. double d = 123456789; - This is correct as the value 123456789 can be assigned to a double variable.

5. boolean b = 1; - This is incorrect because the value 1 cannot be directly assigned to a boolean variable. It should be assigned with either true or false.

Among the given statements, the correct one is "double d = 123456789;", as it assigns the value 123456789 to a double variable.

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I simplified it and I got 36

Answer:

36

Step-by-step explanation: