For questions 4-5, find the volume of the cylinder in terms of pi.

4. height 8, radius 3.8

5. height 14, radius 5

Answer:

  264 miles

Step-by-step explanation:

Using the relation ...

  distance = speed · time

we can rearrange to get ...

  speed = distance/time

We can choose to let d represent the distance we want to find. Then Jina's speed going to the mountains is d/6. Her speed coming home is then d/6+22. It takes Jina 4 hours at that speed to cover the same distance, so we have ...

  d = 4(d/6 +22)

  d = 2/3d +88 . . . . eliminate parentheses

  1/3d = 88 . . . . . . . subtract 2/3d

  d = 264 . . . . . . . . . multiply by 3

Jina lives 264 miles from the mountains.

I need a clear understanding....

Answer:

Step-by-step explanation:

By the way, please use the symbol " ^ " to indicate exponentiation:

f(x) = x^2

Shifted 1 unit to the right, we get g(x) = (x - 1)^2

Vertically stretched by a factor of 5, we get h(x) = 5(x - 1)^2

Reflected over the x-axis:  j(x) = -5(x - 1)^2

Answer:

The correct option is A.

Step-by-step explanation:

The quadratic parent function is

[tex]f(x)=x^2[/tex]

The translation is defined as

[tex]g(x)=k(x+a)^2+b[/tex]                .... (1)

Where, k is vertical stretch, a is horizontal shift and b is vertical shift.

If |k|>1, then graph of parent function stretch vertically by factor |k| and if 0<|k|<1, then parent function compressed vertically by factor |k|. Negative k represents the reflection across x axis.

If a>0, then the graph shifts a units left and if a<0, then the graph shifts a units right.

If b>0, then the graph shifts b units up and if b<0, then the graph shifts b units down.

The graph shift 1 unit right,vertically stretch by a factor of 5 , reflect over the x-axis. So, a=-1, |k|=5 and k=-5

Substitute a=-1 and k=5 in equation (1).

[tex]g(x)=-5(x+(-1))^2+(0)[/tex]

[tex]g(x)=-5(x-1)^2[/tex]

Therefore the correct option is A.

Answer:

The relationship between the circumference of a circle and its diameter represent  a direct variation

The constant of proportionality is equal to [tex]\pi[/tex]

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

The circumference of a circle is equal to

[tex]C=\pi D[/tex]

Let

C=y

D=x

substitute

[tex]y=\pi x[/tex]

therefore

The relationship between the circumference of a circle and its diameter represent  a direct variation

The constant of proportionality is equal to [tex]\pi[/tex]

Answer:

  A. 1

  B. slope: 1/2 mile/minute; the slope represents the speed of the car

  C. correlation

Step-by-step explanation:

A. The points in the table lie on a straight line, so the correlation coefficient is exactly 1.

__

B. The ratio of distance to time is speed. That ratio for this data is 10 miles/20 minutes = 1/2 mile/minute. This is the slope of the graph.

__

C. Passage of time does not cause the car to go any particular distance, nor does the car's traveling cause time to pass. The best that can be said is that the car's distance traveled is strongly correlated with the time it takes. (The reason the car goes some distance is likely due to a cause not mentioned in the problem statement, for example, it was switched on and the motor started.)

Answer:

  1675 cm

Step-by-step explanation:

distance = speed · time

total distance = speed1 · time1 + speed2 · time2

 = (40 cm/s)(25 s) + (15 cm/s)(45 s) = 1000 cm + 675 cm = 1675 cm

Roberto's toy car travels 1000 cm at high speed (40 cm/sec for 25 sec) and 675 cm at low speed (15 cm/sec for 45 sec), totaling 1675 cm.

To calculate the total distance traveled by Roberto’s toy car, we need to consider the two separate speeds at which the car travels and the time it spends at each speed.

First, we calculate the distance at high speed using the formula distance = speed × time. At high speed, the car travels at 40 cm/sec for 25 seconds, so we multiply these two values to get the distance:

Distance at high speed = 40 cm/sec × 25 sec = 1000 cm

Next, we calculate the distance at low speed, where the car travels at 15 cm/sec for 45 seconds:

Distance at low speed = 15 cm/sec × 45 sec = 675 cm

Finally, we add these two distances together to find the total distance traveled by the toy car:

Total distance = Distance at high speed + Distance at low speed = 1000 cm + 675 cm = 1675 cm

Therefore, Roberto’s toy car would have traveled 1675 centimeters in total.

The answer is A. a=(-1) b=(7)

Answer: A

Step-by-step explanation: simple mafs

Answer:

  C. Draw a diagram. Draw 4 groups of dots to show the 3 types of exercise and the weeks. Write 30, 45, 25, and 8 in each circle. Add the four numbers.

Step-by-step explanation:

You might be able to get there starting with strategy C, but it is incomplete as written and will not solve the problem.

Answer:

Let's imagine that x is the number of 3 pound weights that the gym instructer has.

Since we know that there are 10 more 5 pound weights, which tells us that the number of 5 pound weight is x + 10, and the total amount is 60 hand weights, we have:

x + x + 10 = 60

2x            = 60 - 10

2x            = 50

x              = 50/2 = 25

So there are 25 3 pound weights at the gym.

From the number we have just found, we also know that the number of the 5 pound weights should be:

60 - 25 = 35 (hand weights)

Answer: 20 feet.

Step-by-step explanation:

Observe the right triangle attached.

You need to find the value of "x".

Then, you can use the Pythagorean Theorem:

[tex]a^2=b^2+c^2[/tex]

Where "a" is the hypotenuse of the triangle, and "b" and "c" are the legs.

 In this case, you can identify that:

[tex]a=25ft\\b=15ft\\c=x[/tex]

Substitute these values into  [tex]a^2=b^2+c^2[/tex]:

 [tex](25ft)^2=(15ft)^2+x^2[/tex]

Now, you need to solve for x to find how far up the wall the top of the ladder reaches. Then you get:

[tex]x^2=(25ft)^2-(15ft)^2[/tex]

[tex]x=\sqrt{(25ft)^2-(15ft)^2}[/tex]

[tex]x=20ft[/tex]

ANSWER

20ft

EXPLANATION

The ladder, the wall and the ground formed a right triangle.

Let how far up the wall does the top of the ladder reached be x units.

The 25ft ladder is the hypotenuse.

The shorter legs are, 15ft and x ft

Then from Pythagoras Theorem,

[tex] {x}^{2} + {15}^{2} = {25}^{2} [/tex]

[tex] {x}^{2} + 225 = 625[/tex]

[tex] {x}^{2}= 625 - 225[/tex]

[tex]{x}^{2}= 400[/tex]

[tex]x = \sqrt{400} [/tex]

[tex]x = 20ft[/tex]

Therefore the ladder is 20 ft up the wall.

Answer:

Step-by-step explanation:

Delia's score X 5 = 65

d X 5 = 65

5d=65

The sentence 'The product of Delia's score and 5 is 65' translates into the equation '5d = 65', where 'd' represents Delia's score.

The given sentence, 'The product of Delia's score and 5 is 65', can be translated into an equation as follows:

So, the translated equation is: 5d = 65. Here, 'd' represents Delia's score.

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Answer:

t = 24 yards

Step-by-step explanation:

Since the trapezoids are similar then the ratios of corresponding sides are equal, that is

[tex]\frac{t}{c}[/tex] = [tex]\frac{u}{d}[/tex]

Substitute in given values

[tex]\frac{t}{0.4}[/tex] = [tex]\frac{15}{0.25}[/tex] ( cross- multiply )

0.25t = 6 ( divide both sides by 0.25 )

t = 24

Answer:

B. [tex]LA=2\pi rh[/tex]

Step-by-step explanation:

The lateral area of the right cylinder refers to the curved surface area.

The lateral area of the right cylinder does not include the two circular bases.

The lateral area is given by the formula;

[tex]LA=2\pi rh[/tex]

The correct choice is B.

Answer:

thats the correct answer =B

Step-by-step explanation:

V= 3,840 cm

Volume is L x W x H

and W is the same as Depth

So you would multiply those and multiply it again by four to make up for the other pieces of wood.

Final answer:

The total volume of wood used in making the square frame is 3840 cubic centimeters, which is calculated by finding the volume of one piece (960 cm³) and multiplying it by the number of pieces (4).

Explanation:

The question concerns the calculation of the total volume of wood used in making a square frame. Each piece of wood is a rectangular prism with given dimensions. To find the total volume, one must multiply the length, height, and depth of a single piece and then multiply the result by the number of pieces.

To calculate the volume of a single piece of wood, we use the formula for the volume of a rectangular prism, which is length × width × height. For one piece of wood:

Length = 40 cm

Width (depth) = 6 cm

Height = 4 cm

The volume of one piece of wood is therefore 40 cm × 6 cm × 4 cm = 960 cm³.

Since there are four pieces that make up the frame, the total volume of wood used is:

960 cm³/piece × 4 pieces = 3840 cm³

Thus, the total volume of the wood used in the frame is 3840 cubic centimeters.

Final answer:

To find the number of oranges left for Jenny to peel in the evening, subtract the number of oranges she already peeled from the total number of oranges.

Explanation:

To find the number of oranges left for Jenny to peel in the evening, we need to subtract the number of oranges she already peeled in the morning and afternoon from the total number of oranges.

Jenny peeled 30% of the oranges in the morning, which is (30/100) * 300 = 90 oranges.

Jenny peeled 45% of the oranges in the afternoon, which is (45/100) * 300 = 135 oranges.

Therefore, the number of oranges left for Jenny to peel in the evening is 300 - 90 - 135 = 75 oranges.

Answer:

Hence correct choice is C. [tex]Volume=400[/tex] [tex]units^3[/tex]

Step-by-step explanation:

Given that length of the square base of the pyramid a = 10 units

Given that height of the pyramid is h = 12 units

Now question says to find the volume of the given cone.

So plug these values into formula of volume of the square pyramid.

[tex]Volume=\frac{1}{3} a^2h[/tex]

[tex]Volume=\frac{1}{3} (10)^2(12)[/tex]

[tex]Volume=\frac{1}{3} (100)(12)[/tex]

[tex]Volume=\frac{1}{3} (1200)[/tex]

[tex]Volume=400[/tex]

Hence correct choice is C.

Answer:

The correct answer is option C.  400 units³

Step-by-step explanation:

Formula:-

Volume of pyramid = (a²h)/3

Where a -  side of base

h - height of pyramid

From  the figure we can see a square pyramid

To find the volume of pyramid

here a = 10 units and h = 12 units

Volume = (a²h)/3 = (10² * 12)/3

 = 400 units³

Answer:

5a.  approximately 6 grams remain after 2 seconds

5b.  The graph shown cannot be a solution. The solution has negative slope everywhere.

5c.  y = 50/(t+5)

5d.  The amount is changing at a decreasing rate. (As y gets smaller, so does the magnitude of dy/dt.)

Step-by-step explanation:

5a. The tangent line has the equation ...

  y = f'(0)t +f(0)

Here, that is

  y = -0.02·10²·t +10 = 10 -2t

Then at t=2, the value is ...

  y = 10 -2·2 = 6 . . . . grams remaining

__

5b. y² is always positive (or zero), so -0.02y² will be negative. This is dy/dt, the slope of the curve with respect to time, so any curve with positive slope somewhere cannot be a solution.

__

5c. The equation is separable so can be solved by integrating ...

  ∫y^-2·dy = -0.02∫dt

  -y^-1 = -0.02t +c . . . . for some arbitrary constant c

Multiplying by -50 gives ...

  50/y = t + c . . . . for some constant c

We can find the value of c by invoking the initial condition. At t=0, y=10, so we have ...

  50/10 = 0 +c = 5

Then, solving for y, we get ...

  y = 50/(t+5)

__

5d. As noted above (and as described by the differential equation), the magnitude of the rate of change is proportional to the square of y. As y decreases, its rate of change will also decrease (faster). You can see that the curve for y flattens out as t increases. The amount of the substance is changing at a decreasing rate.

Answer:

Step-by-step explanation:

Given are two graphs.  f(x) will have x axis as asymptote while x=2 is asymptote for g(x).

Hence both graphs have exactly one asymptote

First graph passes through (0,2)

f(x) is exponential while g(x) is log.

Both graphs are shifted because f(x) is vertically shifted by 1, while g(x) is horizontally shifted by 3 units to left

Answer: Option C.

Step-by-step explanation:

For a parent function [tex]f(x)=x^2[/tex], you have these transformations:

If [tex]f(x)=c(x^2)[/tex] and [tex]0 <c <1[/tex]  then the graph is compressed vertically by a factor "c".

If [tex]f(x)=c(x^2)[/tex] and [tex]|c| > 1[/tex] then the graph is stretched vertically by a factor "c"

If [tex]f(x)=(cx)^2[/tex] and [tex]0 <c <1[/tex] then the graph is stretched horizontally by a factor "c"

If [tex]f(x)=(cx)^2[/tex] and [tex]|c| > 1[/tex] then the graph is compressed horizontally by a factor "c"

In this problem we have the function [tex]f(x)=x^2[/tex] and we know that this is  horizontally compressed to g(x), then the transformation is:

[tex]f(x)=(cx)^2[/tex] and the factor must be [tex]|c| > 1[/tex]

You can observe that the option that shows this form is the option C. Therefore, the equation of g(x) is:

[tex]g(x) = (5x)^2[/tex]

Where [tex]|5| > 1[/tex]

A horizontal compression of the function f(x) = x² is represented by the function g(x) = (5x)², where x is multiplied by a constant greater than 1, causing the function to be 'squeezed' together along the x-axis.

The question is asking for a horizontal compression of the function f(x) = x². A horizontal compression occurs when we multiply the x by a constant greater than 1 inside the function parentheses. This affects the rate at which the function grows horizontally.

A good way to visualize this is by thinking of the x-axis being 'squeezed' together. Given the choices, the function that represents a horizontal compression of f(x) = x² is C: g(x) = (5x)². In this case, we are multiplying x by a constant (5), thus compressing the function horizontally compared to the original function.

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Answer:

FALSE

Correlations tell us the strength and the direction of the relationship between two variables. The main result of a correlation is called the correlation coefficient (or "r").

Hope this helps and have a great day!!

[tex]Sofia[/tex]

Answer:false

Step-by-step explanation:

A is the correct answer

Answer:

The correct option is A.

Step-by-step explanation:

An organization consists of 8,684 employees. The organization surveyed 884 of their employees and found that 36% of those surveyed disliked the new vacation policies. It means

[tex]n=884[/tex]

[tex]p=\frac{36}{100}=0.36[/tex]

The value of z-score for 95% confidence level is 1.96.

The formula for margin of error is

[tex]ME=z\times \sqrt{\frac{p(1-p)}{n}}[/tex]

Where, z is z-score at given confidence level, p is sample proportion and n is number of samples.

[tex]ME=\pm 1.96\times \sqrt{\frac{0.36(1-0.36)}{884}}[/tex]

[tex]ME=\pm 0.0316425[/tex]

[tex]ME\approx \pm 0.032[/tex]

The margin of error is ±0.032 and the sample size is appropriately large. Therefore, the correct option is A.

Answer:

A)  

He will score over 100,000 points 4 times.  

B)  

He will score over 100,000 points 6 times.  

C)  

He will score over 100,000 points 8 times.  

D)  

He will score over 100,000 points 12 times.

Step-by-step explanation:

Answer is B

Answer:

B) He will score over 100,000 points 6 times.

Step-by-step explanation:

I got it correct on USATP.

Hope this helps!

From: Aug1e

For this case we have the following expression:

[tex]-5 (3x + 7) -4 (x-4) +11[/tex]

For simplicity we follow the steps:

We apply distributive property to the terms within the parenthesis, bearing in mind that:

[tex]- * + = -\\- * - = +\\-15x-35-4x + 16 + 11 =[/tex]

We add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

[tex]-15x-4x-35 + 16 + 11 =\\-19x-8[/tex]

ANswer:

[tex]-19x-8[/tex]

Answer: 19x - 8

-5(3x + 7)

Apply the distributive law: a( b + c ) = ab + ac

a = -5, b = 3x, c = 7

= -5 * 3x + (-5) x 7

Apply minus - plus rules

+(-a) = -a

= -5 * 3x - 5 x 7

Simplify

-5 * 3x - 5 x 7

Multiply the numbers: 5 x 3 = 15

= -15x - 5 x 7

Multiply the numbers: 5 x 7 = 35

= -15x - 35

Plug in the values

-15x - 35 - 4(x - 4) + 11

------------------------------------------------------------------

-4(x - 4)

Apply the distributive law: a( b - c ) = ab - ac

a = -4, b = x, c = 4

= -4x - (-4) * 4

Apply minus - plus rules

-(-a) = a

= -4x + 4 * 4

Multiply the numbers: 4 * 4 = 16

= -4x + 16

Plug in the values

-15x - 35 - 4x + 16 + 11

------------------------------------------------------------------

Simplify

-15x - 35 - 4x + 16 + 11

Group like terms

= -15x - 4x - 35 + 16 + 11

Add similar elements: -15x - 4x = -19x

= -19x - 35 + 16 + 11

Add/Subtract the numbers: -35 + 16 + 11 = -8

= 19x - 8

I think it’s C. three types of shapes

because more than one repeating shape with no spaces or overlapping between shapes

A semi-regular tessellation may have three types of shapes. They do not have gaps between shapes, no overlapping shapes.

A. Gaps between shapes - false

B. Overlapping shapes - false

C. Three types of shapes - true

D. Only one type of shape - false

Thus, a semi-regular tessellation may have three types of shapes.

Learn more about semi-regular tessellations here:

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Answer:

Step-by-step explanation:

If your function is

[tex]x+y^2=ln(\frac{x}{y} )[/tex], that is definitely not the answer you should get after taking the derivative implicitely.  Rewrite your function to simplify a bit:

[tex]x+y^2=ln(x)-ln(y)[/tex]

Take the derivative of x terms like "normal", but taking the derivative of y with respect to x has to be offset by dy/dx.  Doing that gives you:

[tex]1+2y\frac{dy}{dx}=\frac{1}{x}-\frac{1}{y}\frac{dy}{dx}[/tex]

Collect the terms with dy/dx on one side and everything else on the other side:

[tex]2y\frac{dy}{dx}+\frac{1}{y}\frac{dy}{dx}=\frac{1}{x}-1[/tex]

Now factor out the common dy/dx term, leaving this:

[tex]\frac{dy}{dx}(2y+\frac{1}{y})=\frac{1}{x}-1[/tex]Now divide on the left to get dy/dx alone:

[tex]\frac{dy}{dx}=\frac{\frac{1}{x}-1 }{2y+\frac{1}{y} }[/tex]

Simplify each set of fractions to get:

[tex]\frac{dy}{dx}=\frac{\frac{1-x}{x} }{\frac{2y^2+1}{y} }[/tex]

Bring the lower fraction up next to the top one and flip it upside down to multiply:

[tex]\frac{dy}{dx}=\frac{1-x}{x}[/tex]×[tex]\frac{y}{2y^2+1}[/tex]

Simplifying that gives you the final result:

[tex]\frac{dy}{dx}=\frac{y-xy}{x(2y^2+1)}[/tex]

or you could multiply in the x on the bottom, as well.  Same difference as far as the solution goes.  You'd use this formula to find the slope of a function at a point by subbing in both the x and the y coordinates so it doesn't matter if you do the distribution at the very end or not.  You'll still get the same value for the slope.

Answer:

4. No solution

Step-by-step explanation:

To solve a system of equations, find the (x,y) solution that satisfies both equations. One method that can be used is substitution. It is done by substituting one function into the other function and simplify.

Substitute y = 4x - 6 into 8x - 2y = 14.

8x - 2(4x - 6) = 14

8x - 8x + 12 = 14

12 = 14 FALSE

Since the variable was eliminated and a false statement was found, there is no solution to this system.

Solve 3 and 5 similarly. If the variable is eliminated again, but a true statement is fund then the solution is infinite. If the variable is not eliminated then substitute it back into one equation to find the other.

Final answer:

Using the substitution method, we find that Problem 4 has no solution (D), Problem 3 also has no solution (A), and Problem 5 has an infinite number of solutions (C).

Explanation:

To solve the given systems of equations using the substitution method, we substitute the expression for y from the first equation into the second equation and solve for x. Once x is found, we plug it back into the first equation to find y.

Problem 4:

Starting with the equations:

y = 4x – 6

8x – 2y = 14

We substitute the first equation into the second equation:

8x – 2(4x – 6) = 14

Solving for x:

8x – 8x + 12 = 14

x = 1/2 (not a solution, as the x terms cancel out)

Since the equation simplifies to 12 = 14, which is not true, we conclude that:

Option D. There is no solution.

Problem 3:

The system appears similar:

y = 3x – 7

6x – 2y = 12

Substitution gives:

6x – 2(3x – 7) = 12

And solving for x:

6x – 6x + 14 = 12

Which simplifies to 14 = 12, another impossibility.

So the answer is:

Option A. There is no solution.

Problem 5:

From our system:

y + 2x = 7

14 – 4x = 2y

We express y from the first equation:

y = 7 – 2x

Substitute it into the second one, and solve for x:

14 – 4x = 2(7 – 2x)

14 – 4x = 14 – 4x

This equation is true for all x; hence, y can be found for any corresponding x and the system has infinite solutions:

Option C. There are an infinite number of solutions.

Answer:

154.8-155.6

Step-by-step explanation:

155.2-.4=154.8 or maybe its more in that case the most it could be is 155.2+.4=155.6

Answer:

(6, -70) is not on the graph

Step-by-step explanation:

we have

[tex]y=-3x^{2}+6x-4[/tex]

we know that

If a ordered pair is on the graph of the quadratic equation, then the ordered pair must satisfy the quadratic equation

Verify each case

Substitute the x-coordinate of the ordered pair in the quadratic equation to find the value of y and then compare the results

case 1) (6, -70)

For x=-6

[tex]y=-3(-6)^{2}+6(-6)-4=-148[/tex]

[tex]-148\neq-70[/tex]

therefore

the ordered pair is not on the graph

case 2) (4, -28)

For x=4

[tex]y=-3(4)^{2}+6(4)-4=-28[/tex]

[tex]-28=-28[/tex]

therefore

the ordered pair is on the graph

case 3) (-8,-244)

For x=-8

[tex]y=-3(-8)^{2}+6(-8)-4=-148[/tex]

[tex]-244=-244[/tex]

therefore

the ordered pair is on the graph

case 4) (12,-364)

For x=12

[tex]y=-3(12)^{2}+6(12)-4=-148[/tex]

[tex]-364=-364[/tex]

therefore

the ordered pair is on the graph

Answer:

-4a^2 -7a^2 - 2ab +3ab +9b^2 -5b^2

11a^2 + ab +4b^2

Step-by-step explanation:

Answer:

-11a^2+ab+4ab^2

Step-by-step explanation:

Answer:

The correct answer is B. (1,0).

Answer: B. (1,0)

Step-by-step explanation:

1. We will use the matrix method to solve this problem.

3 -5 3

3 -4 3

2. Apply to Row2 : Row2 - Row1.

3 -5 3

0 1 0

3. Simplify rows.

3 -5 3

0 1 0

Note: The matrix is now in row echelon form.

The steps below are for back substitution.

4. Apply to Row1 : Row1 + 5 Row2.

3 0 3

0 1 0

5. Simplify rows.

1 0 1

0 1 0

Note: The matrix is now in reduced row echelon form.

6. Therefore,

x=1

y=0

or (1,0).