Write2 1/4 as an improper fraction in its simplest form

The rate of change of volume is 418.6  inch³/s .

Rate of increase of radius with time is ( dr/dt ) = 5

rate of decrease of height with time is (dh/dt ) = -3

volume of a cone is given by (V) =  [tex]\frac{1}{3} \pi r^{2}h[/tex]

Now the rate of change of volume  with respect to time is given by dV/dt

∴ dV/dt = d( [tex]\frac{1}{3} \pi r^{2}h[/tex]) / dt

dV/dt =  [tex]\frac{1}{3} \pi (2rh\frac{dr}{dt} + r^{2}\frac{dh}{dt} )[/tex]

value of radius and height when volume is changing are :

r = 20 inches

h = 40 inches

dV/dt = [tex]\frac{1}{3} \pi ([/tex] 2×20×40 ×5 - [tex]20^{2}[/tex]×3 )

dV/dt = [tex]\frac{1}{3} \pi[/tex](1600 - 1200)

dV/dt = (400/3) 3.14

dV/dt = 418.66 inch³/s

So the rate of change of the volume is 418.66 inch³/s.

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Answer:

Step-by-step explanation:

Ok:

1. Caculate all of the two triangles' angles

First triangle on the left!

50+90= 140+40= 180degrees

So: Angles for first one are 50,90,40

Second Triangle on right

51+90= 141+39= 180degrees

So: Angles for second one are 51,90, 39

2. Subtract the corners added together from 180 degrees

40+39= 79 degrees

180-79=101 degrees

3. Answer: Choice B or 101 degrees!

a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.

b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.

The link between variables is described by correlation. It can be characterized as strong or weak, as well as positively or negatively.

Given,

The two scatterplots below show the relationship between final and mid-semester exam grades recorded during several years for a statistics course at a university.

a) Exam 2 has the strongest correlation with the exam grade, according to the graphs below. Since the points are arranged in a positive band that extends from bottom left to upper right.

b) Because there is a positive association and there is little dispersion of points, the correlation between exams and the final exam is higher.

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Answer:

Step-by-step explanation:

The area of the two lawns will be 105 square meters.

According to the question,

We have the following information:

The first lawn is 7 meters long and 4 meters wide. The second lawn has the same length and width which is 3 times as much as the first one.

So, the width of the second lawn = 4×3

Width of second lawn = 12 m

Now, the formula to find the area of the rectangle:

Length*width

Area of first lawn:

7×3

21 square meters

Area of second lawn:

7×12

84 square meters

Now, the area of two lawns = area of first lawn+ area of second lawn

Area = 21+84

Area = 105 square meters

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A linear function that describes the cost of a trip, c, in terms of the number of miles, n will be "c=0.60n+0.67n" and cost per mile is $0.6 and $0.67 and the flat fee is $50.

Once you are aware of your mileage and total expenses, calculating cost per mile becomes a straightforward equation. Your cost per mile is calculated by dividing your total expenses by the total number of miles you have driven. Your expenses per mile are influenced by your variable and fixed costs, so you should probably pay closer attention to how much you're shelling out for each mile your drivers cover. You can better understand your primary costs and produce more accurate bids for new contracts by knowing your expenses at this specific level.

Here,

cost per mile,

20/30=$0.67/mile

30/50=$0.60/mile

c=0.60n+0.67n

flat fee,

=$30+$20

=$50

The cost per mile is $0.6 and $0.67, and the flat rate is $50. A linear function that expresses the cost of a trip, c, in terms of the number of miles, n, will be "c=0.60n+0.67n".

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Answer:

Don't know if i did it right but i think it is:

a=14

b=6

c=5

The equivalent expression of the expression 54x + 18 will be 18(3x + 1). Then the correct option is E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 54x + 18

Simplify the expression, then we have

⇒ 54x + 18

⇒ 18(3x + 1)

The equivalent expression of the expression 54x + 18 will be 18(3x + 1). Then the correct option is E.

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The complete question is given below.

Drag each expression to show whether it is equivalent to 54x + 18, 18(3x – 1), or (6 • 9x) + (6 • 1).

expressions: A-54x B-(6 • 9x) + (6 • 3) C-54x + 6 D-3(18x+2) E-18(3x+1) F-(9*6x)-(9*2)

The measurement of the distance from the tip of the slice of pizza to the crust is the radius.

The diameter of the pizza is 12 inches and the circumference is 37.7 inches

A slice of pizza is cut from the middle of the pizza to the crust. It is therefore cut from the middle of the pizza (circle) to the edge of the pizza (circle).

This is the radius because the radius is the straight - line distance from the edge of the middle of a circle to the edge.

If the radius is 6 inches, the diameter is:

= radius x 2

= 6 x 2

= 12 inches

The circumference is:

= π x diameter

= 22/7 x 12

= 37.7 inches

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The magnitude of earthquake on seismograph will be 3 .

What is seismograph?

A seismograph is a device that measures and records crucial data concerning earthquakes. Electromagnetic sensors in seismographs convert ground vibrations into electrical voltages. Seismograms are records that a seismograph generates and displays .

Main Body:

formula given : M = ㏒₁₀T           where T =1000

substituting the value of T in the formula

M = ㏒₁₀ 1000

M = ㏒₁₀10³

M = 3㏒₁₀           (㏒₁₀Xᵃ = a㏒₁₀)

M = 3                  (㏒₁₀10 =1)

Therefore the magnitude of the earthquake is 3.

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Answer:

136-5x

Step-by-step explanation:

Answer:  The correct answer is C. The product is greater than 0 but less than 1.

Step-by-step explanation:

X and Y are both fractions

X is greater than 0 but less than 1

X * Y > 0 and < 1

The product of these two fractions will result in a fraction between 0 and 1.

For example:

1/2 x 1/2 =1/4, 1/6 x 2/6 = 1/18, 1/10 x 5/6 = 1/12

Using the exterior angle theorem, the measure of angle WXY is calculated as: 20°.

Given the triangle in the image below has the following:

According to the exterior angles theorem, the sum of the two remote angles would be equal to the measure of the exterior angles, therefore:

10x - 5 = 3x + 2 + 3x + 17

Combine like terms

10x - 5 = 6x + 19

10x - 6x = 5 + 19

4x = 24

4x/4 = 24/4

x = 6

m∠WXY = 3x + 2 = 3(6) + 2

m∠WXY = 18 + 2

m∠WXY = 20°

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The percentage increase is 61.36%. If the airline charges an additional $50 baggage fee, the new percentage increase will be 45.68%.

A percentage increase denotes how much a percentage has risen over time. To get at this figure, discover the difference between the original and final values, then deduct it to get the actual sum of the decrease.

The idea of Percentage increase is simply the amount of increase from the original(initial) to the final figure expressed in terms of 100 parts of the original. E.g.  A 10% increase implies that if the original value is divided into 100 parts, the value has increased by an extra 10 parts. So, if the initial value rose by 16%, the value would rise by 16 for every 100 units, and so on.

The formula for calculating the percentage increase can be expressed as:

[tex]\%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]

[tex]\%\ increase= \frac{355- 220}{220}\times 100[/tex]

[tex]\%\ increase= \frac{135}{220}\times 100[/tex]

[tex]\mathbf{=61.36\%}[/tex]

[tex]New \ \%\ increase= \frac{new \ value - original \ value}{original \ value}\times 100[/tex]

[tex]New \ \%\ increase= \frac{405- 220}{405}\times 100[/tex]

[tex]New \ \%\ increase= \frac{185}{405}\times 100[/tex]

[tex]New \ \%\ increase=\mathbf{45.68\%}[/tex]

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The statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

What is a regular hexagon?

It is a regular hexagon when the lengths of all the sides and the measures of all the angles are equal. In a regular hexagon, each inside angle is 120 degrees. The characteristics of a regular hexagon. The lengths of each side are equal.

Here, we let

P = it has exactly four sides.

Q = it is not an hexagon.

The negation is like this;

If it is a hexagon, then it does not have exactly four sides.

Thus, we concluded that “it is a hexagon” is your hypothesis (p) and “it has exactly 6 congruent sides” is your conclusion (q).

Hence, the statement that is logically equivalent to the following conditional statement is " If it is a hexagon, then it does not have exactly four sides."

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Answer: The answer is 8

Step-by-step explanation: 16 tablespoon is 1 cup now find half of 16. Half of 16 is 8. So 8 tablespoon should be equal 1/2 cup

Answer:

42/4/5 first you divide 72➗ 3 then you get 24 then see the picture is you

Answer:

17 7/15

Step-by-step explanation:

Rewrite:

9 + 4/5 + 7 + 2/3

Add whole numbers:

9 + 7 = 16

Add fractions:

4/5 + 2/3 --> 12/15 + 10/15 = 22/15

Simplify:

22/15 --> 1 7/15

Add all components:

16 + 1 7/15 = 17 7/15

The values of the interior angles, ( Angle A, Angle B and Angle C) of the triangles are 48°, 88° and 44° respectively.

Interior angle is the inner of the two angles formed where two sides of a polygon come together.

To find the measure of each interior angle of the triangle in the diagram, first, we need to find the value of x.

Recall that: The sum of the interior angles of a triangle is equal to 180°.

Using the formula,

From the triangle,

Substitute these values into equation 1

Solve for x

Therefore,

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Answer: A. [tex]\frac{3}{2}[/tex]

Step-by-step explanation:

To find the slope we must find the change in y over the change in x. Δ

Or rise over run.  [tex]\frac{rise}{run}[/tex]

In the graph, we have two "good" points. (0, -6) and (4,0)

So for Δy 0 to -6 = -6

So -6 goes on top  [tex]\frac{-6}{x}[/tex]

Now Δx goes from 4 to 0 so the change would be -4.

So now it becomes [tex]\frac{-6}{-4}[/tex]

Since there are two negatives it becomes a positive. [tex]\frac{6}{4}[/tex] Or simply put, [tex]\frac{3}{2}[/tex]

Answer:91.44  rounded is 91

Step-by-step explanation:

The rational numbers are -√25, -√25, √100, √0.36, √0.0144 and -√36/49. Select them

A rational number is a number that can be expressed as a fraction where both the numerator and the denominator in the fraction are integers e.g 2/3, 7/1, √100 = 10/1, etc.

An irrational number is any real number that cannot be expressed as the quotient of two integers. This is the opposite of rational numbers. They are usually of roots that cannot give integers e.g 3√5, √8, etc.

√75 = √(25 x 3) = √25 x √3 = 5 x √3 = 5√3    (This is not rational)

-√25 = -5 = -5/1   (This is rational)

2*√7 = 2√7        (This is not rational)

√100 = 10 = 10/1  (This is rational)

√0.36 = √(36/100) = 6/10   (This is rational)

√0.0144 = √(144/10000) = 12/100  (This is rational)

√3/7 = √3/7  (This is not rational)

-√36/49 = -6/7  (This is rational)

Therefore, -√25, -√25, √100, √0.36, √0.0144 and -√36/49 are rational numbers. They should be selected

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It is also called as Random  Sample experiment.

Hence, it is an random experiment.

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Answer:

B. 35

Step-by-step explanation:

Because lines m and n are parallel, we know that x+(4x+5)=180.

So all you have to do is simplify.

x+(4x+5)=180

5x+5=180

5x=175

x=35

So the only possible value of x is 35

The width of pool deck is 7 ft and new dimensions of pool and deck are 21 ft and 35 ft .

In the given question we have,

Area of whole background ( pool + deck) = 1176 ft²------(1)

Area is a two dimensions quantity . so, we work here in 2-D.

length of pool = 28 ft , width of pool= 14 ft

let the width of deck be x ft . Now, the new dimensions are following

length of pool and deck = 28 + x + x = (28+2x ) ft

width of pool and deck = 14 + x + x = (14+ 2x) ft

here, 2x include in lenth and width for surronding deck.

total area of pool and deck ( backyard ) = lenth × width = 1176 ft² ( from (1) )

(28+2x) ( 14+2x) = 1176 ----(2)

Now, we shall solve above equation (2) and find out value of x

28×14 + 56x + 28x + 4x^2 = 1176

=> 4x²+ 84x + 392 - 1176 = 0

=> 4x² + 84x - 784=0 => x² + 21x - 196 = 0

=> x²+ 28x - 7x - 196 = 0 => x(x+ 28) - 7(x+28)=0

=> (x+28) (x-7) = 0

either x + 28= 0 or x - 7 = 0 =>either x= -28 or x= 7

but width can't be negative value so, discard

x= -28.

Hence, the width of pool deck is 7 ft.

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The probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.

What is a standard deviation?

Data dispersion in regard to the mean is quantified by a standard deviation. Data are said to be more closely grouped around the mean when the standard deviation is low and more dispersed when the standard deviation is high.

Here, we have

µ = 62 , σ = 5

P ( X < 66 )

By applying the standard deviation formula, we get

Z = ( X - µ ) / (σ/√(n)

Z = ( 66 - 62 ) / ( 5 / √50 )

Z = 5.6569

P (  ( X - µ ) / ( σ/√(n)) < ( 66 - 62 ) / ( 5 / √(50) )

P ( X < 66 ) =  P ( Z < 5.66 )

P ( X < 66 ) = 1

P ( X > 66 )  = 1 - P ( X < 66 )

By applying the standard deviation formula, we get

Z = ( X - µ ) / ( σ / √(n))

Z = ( 66 - 62 ) / ( 5 / √ ( 50 ) )

Z = 5.6569

P (  ( X - µ ) / ( σ / √ (n)) > ( 66 - 62 ) / ( 5 / √(50) )

P ( Z > 5.66 )

P ( X > 66 )  = 1 - P ( Z < 5.66 )

P ( X> 66 )  = 1 - 1

P ( X> 66 )  =  0

Hence, the probability of a sample of 50 cars recording an average speed of 66 mph or higher is 0.

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The confidence interval for the population mean is 0.2896 , 0.3505)

The sample mean is x = 0.32

The sample standard deviation is s = 0.09

The sample size is n = 10

The population standard deviation is unknown and sample size is atleast 10.

Thus use the t distribution.

Replacing the values in the following formula, determine the 95% confidence interval.

95% C.I = x ± t₀.₉₅,ₙ₋₁ . Sm

= x ± t₀.₀₅/₂,₁₀₋₁ . s/√n

= 0.32 ± 2.03 . 0.09/√10

= (0.2896 , 0.3505)

Hence the confidence interval for the population mean is 0.2896 , 0.3505)

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The number ester,sarai and kurry chose are 0.009,0.09 and 0.9 respectively

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. In math, multiply means the repeated addition of groups of equal sizes. For example 3+3+3+3+3 can be written as 3× 5 .

to find the ester's number= 1/10 of sarai's number

= 1/10× 0.09

= 0.009

to find kurry^s number = 10 × sarai's number

= 10× 0.09

= 0.9

Therefore ester , sarai and kurry chose 0.009, 0.09,0.9 respectively.

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Answer:

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Let the sides of the old rectangle are l and w.

Answer: Hence the answer is 27 square feet.

Please look at the images for more details.