Match the correct statement with the given information.


Column A

1.

A cone's radius increases x 3:


A cone's radius increases x 3

2.

A cone's height increases x 3:

A cone's height increases x 3

3.

A sphere's radius increases x 3:

A sphere's radius increases x 3

4.

A cylinder's radius increases x 6:

A cylinder's radius increases x 6

Column B


a.The cone's volume will increase x 9

b.The cone's volume will increase x 3

c.The cylinder's volume will increase x 6

d.The sphere's volume will increase x 6

e.The cylinder's volume will increase x 12

f.The cone's volume will increase x 6

g.The sphere's volume will increase x 3

h.The cylinder's volume will increase x 18

i.The cylinders volume will increase x 36

j.The sphere's volume will increase x 9

k.The sphere's volume will increase x 27

No, there isn't any statistical proof because, according to the simulation, Audrey would sell at least 7 out of the 30 chosen tickets roughly 13.8% of the time.

What exactly is statistical proof?

A type of explanation known as statistical evidence is one that is based on information that has been gathered and then assessed using a mathematical model.

Based on the information provided, the students created the following simulation:

Choose 88 red chips and the rest 600 blue chips.

30 chips are chosen at random, with no replacements.

When choosing the 30 chips, keep track of and record the amount of red chips.

Therefore, we may say that there is no statistical proof that the occurrence happened by chance alone at = 0.05.

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Answer:

(m^2+4)(m+2)(m-2)

Step-by-step explanation:

Answer:

Yes; $23.10

Step-by-step explanation:

5% of 22 is 1.10 and if you add the tax to the give price it is less than $24

The simplified value of the expression -3/x + 3/x² is   (-3x² + 3x)/x³ , the correct option is  (c)  .

In the question ,

it is given that  ,

the algebraic expression is given as  -3/x + 3/x² .

we have to find , simplified value of the expression .

Simplified value can be found by

= -3/x + 3/x²

taking LCM of x and x² , as x³

= -3x²/x³ + 3x/x³

Simplifying further ,

we get ,

= (-3x² + 3x)/x³

Therefore , The simplified value of the expression -3/x + 3/x² is   (-3x² + 3x)/x³ , the correct option is  (c)  .

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Answer:

33.7º

Step-by-step explanation:

tan  = opp/adj

tan∅ = 100/150 = 2/3

∅ = arctan 2/3

∅ = 33.690067525979787

33.7º

9

using Bodmas rule

\(\sf B - brackets, \ O - order, \ D - division, \ M - multiplication, \ A - addtion, \ S - subtraction\)

⟼                   ⟼                 ⟼               ⟼                ⟼              ⟼

Solve:

6 ÷ 2(1+2)           [simplify the following inside brackets]

6 ÷ 2(3)              [divide]

(3)(3)                 [multiply]

  9                     [final answer]

Hey there!

6 ÷ 2(1 + 2)

= 6 ÷ 2(3)

= 3(3)

= 9

Therefore, your answer should be:

9

Good luck on your assignment & enjoy your day!

~Amphitrute1040:)

The given statement is False . That is regression sum of squares (ssr) can be greater than the total sum of squares (sst).

Regression sum of squares (ssr)

The sum of squares regression is the sum of the differences between the predicted value and the mean of the dependent variable.

SSR = ∑( yᵢ-cap - y-bar)² and i = 1 to N

Total Sum of Squares (SST) :

Total Sum of Squares is the deviation of the value of the dependent variable from the sample mean of the dependent variable. Essentially, the total sum of squares quantifies the total sample variation. It can be found using the formula:

SST = ∑(yᵢ - y-bar )²

The first is that the regression sum of squares cannot be computed as a total sum of squares. Let's find an explanation for this. We know that the sum of squares can be divided. There's the dualism of squares, some of the squares and regressions, sums of squares, dead food. A regression sum of squares is not formed, it is a total sum of squares. This means the statement is false. The next processing is the value, which is always positive, but we know that the value the confession of the adjustment, in the range -1 to 1.

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The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

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Answer:

A i think

Step-by-step explanation:

Step-by-step explanation:

Hey there!

According to the figure, we find two points on graph. I.e (1,3) and (-2,-1) points respectively.

Now, Use double point formula for finding the eqaution.

\((y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)\)

Keep all values.

\((y - 3) = \frac{( - 1 - 3)}{ (- 2 - 1)}(x - 1) \)

~ Simplify it.

\((y - 3) = \frac{4}{3} (x - 1)\)

\((y - 3) = \frac{4}{3} x - \frac{4}{3} \)

\(y = \frac{4}{3} x - \frac{4}{3} + 3 \)

\(y = \frac{4}{3} x + \frac{5}{3} \)

Therefore, the equation of the line is y= 4/3x + 5/3.

Hope it helps...

Answer:

y = \(\frac{4}{3}\) x + \(\frac{5}{3}\)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (- 2, - 1) and (x₂, y₂ ) = (1, 3) ← 2 point on the line

m = \(\frac{3+1}{1+2}\) = \(\frac{4}{3}\) , then

y = \(\frac{4}{3}\) x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (1, 3 ), then

3 = \(\frac{4}{3}\) + c ⇒ c = 3 - \(\frac{4}{3}\) = \(\frac{5}{3}\)

y = \(\frac{4}{3}\) x + \(\frac{5}{3}\) ← equation of line

Given the region E bounded by planes $2x+3y+2z=6$ and the coordinate planes. We are to set up an integral (DO NOT evaluate) in rectangular coordinates to find $\iiint_E4xydV$.

We know that equation of plane is given by: $2x+3y+2z=6$.Let's solve for $z$: $z = 3- \frac{2}{3}x -\frac{3}{2}y$

Thus, the bounding planes are: $z = 0$, $x = 0$, $y = 0$, $x = 3$ and $y = 2$.

a) 3D Picture: Image showing 3D picture of the shaded volume E

b) Sketch of the shaded region, R, in 2D. Include the equation of the curve. Show your work.

The shaded region R is a triangle in XY-plane. This region is bounded by the three lines: $x=3$, $y=2$ and $2x+3y=6$.  

To find the limits of integration for $x$, we find the equation of the line $2x+3y=6$ in terms of $x$ by solving for $y$:$$2x+3y=6$$$$\ Rightarrow 3y = -2x+6$$$$\Right arrow y = -\frac{2}{3}x+2$$

Thus, limits of integration for $x$ are $0$ to $3$. The limits of integration for $y$ are $0$ to $-2x/3+2$.

c) The triple integral is $\iiint_E4xydV$ In rectangular coordinates, $dV=dx dy dz$.

Hence, the triple integral can be written as: $$\int_{0}^{3} \int_{0}^{-\frac{2}{3}x+2} \int_{0}^{3-\frac{2}{3}x-\frac{3}{2}y} 4xydz dy dx$$

Note that the limits of integration for $y$ are from $0$ to $-\frac{2}{3}x+2$.

This is because $y$ is bound by the line $2x+3y=6$.

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The largest area that a 225-foot fence can surround is 1875ft².

The measurement that expresses the size of a region on a plane or curved surface is called an area.

Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region on a plane or curved surface is called an area.  

So, we must know the distances from the side and base of the rectangle in order to get the area that Mendel can contain with 225 feet of fencing.

After that, we can determine the rectangle's area by multiplying the side's value by the base's value.

Therefore, the largest area that a 225-foot fence can surround is 1875ft².

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Answer:

1 and 3

Step-by-step explanation:

I don't know how to explain. I already took algebra. Its either 1 and 3 or 1 and 4. I think its 1 and 3. GOOD LUCK

The estimated number of algae plants that are currently in Hillsdale Lake will be; 14,542.

Since One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+) and the entire amount or sum of the two whole numbers is obtained by adding them.

To determine the total number of algae plants in Hillsdale Lake after the towns and farms cropped up by the lake, we need to add the initial number of algae plants to the additional number of algae plants that grew in the lake.

Therefore, the total number of algae plants in Hillsdale Lake after the growth is:

4,805 + 9,737 = 14,542 algae plants.

Therefore, the estimated number of algae plants that are currently in Hillsdale Lake is 14,542.

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Answer:

  an = 1/2n² -1/2n -2

Step-by-step explanation:

You want a formula for the n-th term of the quadratic sequence -2, -1, 1, 4.

Using x = 1, 2, 3 and y = -2, -1, 1 we can write equations for the coefficients a, b, c of the quadratic expression ax² +bx +c.

  a(1²) +b(1) +c = -2

  a(2²) +b(2) +c = -1

  a(3²) +b(3) +c = 1

Subtracting the first equation from the other two, we get ...

  3a +b = 1

  8a +2b = 3

Subtracting twice the first from the second of these, we get ...

  (8a +2b) -2(3a +b) = (3) -2(1)

  2a = 1

  a = 1/2

Then b can be found from ...

  b = 1 -3a = 1 - 3/2 = -1/2

And c can be found from ...

  -2 -b -a = c = -2 -(-1/2) -(1/2) = -2

The formula is ...

  an = 1/2n² -1/2n -2

__

Additional comment

For systems of equations, the solver used in the second attachment works well. It tells us (a, b, c) = (1/2, -1/2, -2) as we found above.

Alternate solution

The first differences of the given terms are ...

  1, 2, 3

And their differences are ...

  1, 1

The coefficient of n² is half this second-difference value: 1/2.

If you subtract 1/2n² from the given terms, you get ...

  -5/2, -3, -7/2, -4

This arithmetic sequence has the formula ...

  a1 +d(n -1)

  -5/2 +(-1/2)(n -1) = -1/2n -2

Adding this to the term we subtracted gives ...

  an = 1/2n² -1/2n -2 . . . . . as above

Step-by-step explanation:

short step

(-isin(π/6)+2×5cos(π/6) ei π/4)

I/2+5√3 4√-1

The product of the trigonometric expressions will be 10 (cos 75° + i sin 75°).

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The trigonometric expressions are given below.

2 [cos(45°) + i sin(45°)] and 5 [cos(30°) + i sin(30°)]

Then the product of the trigonometric expressions is given as,

⇒ 2 [cos(45°) + i sin(45°)] × 5 [cos(30°) + i sin(30°)]

⇒ 10 [(cos 45° × cos 30° + sin 45° × sin 30° × i²) + i (sin 45° × cos 30° + cos 45° × sin 30°)]

⇒ 10 [cos (45° + 30°) + i sin (45° + 30°)]

⇒ 10 (cos 75° + i sin 75°)

The product of the trigonometric expressions will be 10 (cos 75° + i sin 75°).

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Answer:

  y +3 = 5(x +2)

Step-by-step explanation:

You want the equation of a line with slope 5 through the point (-2, -3).

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

  y +3 = 5(x +2) . . . . . . line with slope 5 through point (-2, -3)

__

Additional comment

This can also be written as ...

  y = 5x +7 . . . . . . . . . subtract 3 and simplify

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How high the football gets is a function of the maximum height of the ball

The football goes 40.313 ft high

The equation that models the height of the ball is given as:

\(h(t) = -5t^2 +27.5t+2.5\)

Differentiate the function

\(h'(t) = -10t +27.5\)

Set to 0

\(-10t +27.5 = 0\)

Collect like terms

\(10t =27.5\)

Divide by 10

\(t =2.75\)

Substitute 2.75 for t in \(h(t) = -5t^2 +27.5t+2.5\) to calculate how high the ball get

\(h_{max} = -5 * 2.75^2 +27.5 * 2.75+2.5\)

\(h_{max} = 40.3125\)

Approximate

\(h_{max} = 40.313\)

Hence, the football goes 40.313 ft high

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The Volume of the given composite shape is: 432 ft³

The formula for the volume of a triangular prism is:

Volume = base area * height

The volume of a cuboid is:

Volume = Length * Width * Height

Thus:

Volume of composite shape = (6 * 12 * 4) + (6 * 6 * 4)

= 432 ft³

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a) i)The derivative of d = t^2 + 3t is d' = 2t + 3.

ii) The average speed over this interval of time is 24 feet / 3 seconds = 8 feet per second.

b) i) The derivative of d = t^2 + 3t is d' = 2t + 3.

ii) The average speed over this interval of time is 8 feet / 0.8 seconds = 10 feet per second.

a. i. To determine if the car travels at a constant speed over the interval from t=1 to t=4, we need to check if the distance, d, changes linearly with time, t. We can do this by finding the derivative of the distance formula. The derivative of d = t^2 + 3t is d' = 2t + 3.

Since the derivative is not a constant value (it depends on t), we can conclude that the car does not travel at a constant speed over this interval of time.

a. ii. To find the average speed over the interval from t=1 to t=4, we need to calculate the total distance traveled and divide it by the total time elapsed. We can find the total distance by substituting the values of t into the distance formula and finding the difference between the final and initial distances.

Using the distance formula d = t^2 + 3t, we find:
- At t=1, d = 1^2 + 3(1) = 4 feet
- At t=4, d = 4^2 + 3(4) = 28 feet

So, the total distance traveled is 28 - 4 = 24 feet.

The total time elapsed is 4 - 1 = 3 seconds.

Therefore, the average speed over this interval of time is 24 feet / 3 seconds = 8 feet per second.

b. i. To determine if the car travels at a constant speed over the interval from t=1.4 to t=2.2, we need to check if the distance, d, changes linearly with time, t. We can do this by finding the derivative of the distance formula. The derivative of d = t^2 + 3t is d' = 2t + 3.

Since the derivative is not a constant value (it depends on t), we can conclude that the car does not travel at a constant speed over this interval of time.

b. ii. To find the average speed over the interval from t=1.4 to t=2.2, we follow the same process as in part a.ii.

Using the distance formula d = t^2 + 3t, we find:
- At t=1.4, d = (1.4)^2 + 3(1.4) = 7.84 feet
- At t=2.2, d = (2.2)^2 + 3(2.2) = 15.84 feet

So, the total distance traveled is 15.84 - 7.84 = 8 feet.

The total time elapsed is 2.2 - 1.4 = 0.8 seconds.

Therefore, the average speed over this interval of time is 8 feet / 0.8 seconds = 10 feet per second.

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We have the next information

First type of chocolate $2.50 per lb

Second type of choclate 8.50 per lb

x= lbs of the cheaper chocolate

y=lbs of the expensive chocolate

36 total pounds

x+y=36

2.50(x)+8.50(y)=36(6.40)

2.5x+8.5y=230.4

then we solve the equation system

x+y=36 .....(1)

2.5x+8.5y=230.4 ....(2)

we clear x from the first equation

x=36-y

we substitute the equation above in the second equation

2.5(36-y)+8.5y=230.4

90-2.5y+8.5y=230.4

we clear y

6y=230.4-90

6y=140.4

y=140.4/6

y=23.4

then we substitute the value of y in the next equation

x=36-y=36-23.4

x=12.6

you will need 12.6 lbs of the cheaper chocolate and 23.4 lbs of the expensive chocolate

Answer:

Inverse Variation

Step-by-step explanation:

y = k/x

After reducing all the book prices by 50%, the new median price is determined to be $7.70 (B)

To find the new median price after reducing all the book prices by 50%, we first need to calculate the reduced prices. By reducing each given price by 50%, we get $6.375, $7.40, $9.995, $4.975, $8.00, and $8.975 respectively.

Next, we arrange these reduced prices in ascending order: $4.975, $6.375, $7.40, $8.00, $8.975, and $9.995. The median is the middle value in this ordered list. Since there are six prices, the middle two values are $7.40 and $8.00.

To find the median, we take the average of these two values, which gives us ($7.40 + $8.00) / 2 = $7.70.

Therefore, the new median price, after reducing all the book prices by 50%, is $7.70 (B). This means that the median price of the books, after the reduction, is $7.70.

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Answer:

x=9

Step-by-step explanation:

You can take out the absolute value sign first and get 4x+15=5x+6

You can subtract 4x from both sides and get 15=x+6

Then you subtract 6 from both sides to get 9=x

Answer:

The slope of F = 5.

Not 100% sure.

The values in the table represent a linear function with the function rule y = 3x + 6, where x is the input value and y is the output value.

To determine if the values in the table represent a linear function, we can check if there is a constant rate of change between the input and output values. This means that for every increase or decrease in the input value, there is a constant increase or decrease in the output value.

Looking at the input and output values in the table, we can see that for every increase of 1 in the input value, the output value increases by 3. This constant rate of change indicates that the values in the table represent a linear function.

To find the function rule, we can use the slope-intercept form of the equation for a linear function, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, we can find the slope by dividing the change in output values by the change in input values:

slope = change in output / change in input = 3/1 = 3

Therefore, the slope of the function is 3. To find the y-intercept, we can use one of the points in the table. For example, we can use the first row, which gives an input value of 0 and an output value of 6:

y = mx + b

6 = 3(0) + b

b = 6

Therefore, the y-intercept of the function is 6. Combining the slope and y-intercept, we can write the function rule as:

y = 3x + 6

This means that for any input value x, the output value y is equal to three times x plus six.

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The function that represents the data in the table is 3x²+2. The correct answer is B.

The quadratic function is shown in the data table.

We must ascertain the function's equation.

The quadratic equation's generic form is

Let's replace the general form with the three coordinates (1,5, (2,14), and (3,29).

We therefore have;

a+b+c =5——— (1)

4a+2b+c= 14——— (2)

9a+3b+C =29------(3)

When (2) is subtracted from (1), we have;

9= 3a+b(4)

Subtracting (3) from (2) gives us;

15= 5a +b(5)

Subtracting (5) from (4) gives us;

6= 2a

3= a

As a result, the value of an is 3. When we replace this value in equation (4), we obtain;

3(3)+b= 9

b= 0

When a = 3 and b = 0 are substituted in equation (1), we obtain;

a+b+c =5

3+0+c=5

c=2

As a result, c has a value of 2.

As a result, when we substitute a = 3, b = 0, and c = 2 in the quadratic equation's general form y =ax²+bx+c, we obtain;

3x²+2

Consequently, the function that symbolizes the information in the table is 3x²+2

As a result, Option B is the right response.

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Answer:

28

Step-by-step explanation:

1/2xbxh=4

To find the total area of the shape, we can subtract the removed area from the larger area. 32-4=28