If the base area of the square pyramid below is 96 ft² and the height is 8 ft, what is the volume?

The change in volume is -88π

The volume is nothing but the amount of space occupied by a three-dimensional figure as measured in cubic units.

Volume Change is defined as the variation in the existing volume of the service type which is provided by the Supplier under the Agreement

The radius is decreasing at 2 inches per minute

The height is given as decreasing at 4 inches per minute

So let [tex]\frac{dr}{dt}=-2[/tex] and

[tex]\frac{dh}{dt}=-4[/tex]

and we have radius r=6,

                     height h=5

The volume of the cone is represented by V as V=[tex]\frac{1}{3}\pi r^{2}h[/tex]

Then

[tex]\frac{dv}{dt}=\frac{\pi }{3}[r^{2}\frac{dh}{dt} +h*2r\frac{dr}{dt}][/tex]

[tex]=\frac{\pi }{3}[6^{2}(-4)+5*2(6)(-2)][/tex]

[tex]=\frac{\pi }{3}[36(-4)+5(12)(-2)]\\ =\frac{\pi }{3}[-144+(-120)]\\ =\frac{-264}{3}\pi \\ =-88\pi[/tex]

So the volume change is [tex]-88\pi[/tex]

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The index form of the expression is 5^-1m

Note that index form means in a power form

We have that;

= 4m/20m

Find the similar factor

= 1/5m

The inverse of a number, is that number to the power of -1

Then,

1/5m = 5^-1m

Thus, the index form of the expression is 5^-1m

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Based on the calculations, the total volume which the pair have altogether is equal to 19.8 Liters.

In Science, volume is a unit of measurement which indicates the capacity of a container and it has the following units:

Next, we would convert the volume of Madison's diesel in centiliter to liter as follows:

1 centiliter = 0.01 liter

940 centiliter = X liter

Cross-multiplying, we have:

X = 940 × 0.01

X = 9.4 L.

Total volume = 9.4 + 10.4

Total volume = 19.8 Liters.

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Answer:

Step-by-step explanation:

There are several ways you can find the values of an exponential function for different values of the independent variable. You can read them from its graph, evaluate the formula, or recognize the relationship between the values.

The graph shows you the population is 10 in year 1, up by a factor of 2 from the population of 5 in year 0. The exponential nature of the function means the population will double in each of the next few years:

  2 years: 2 × 10 = 20

  3 years: 2 × 20 = 40

  4 years: 2 × 40 = 80

__

Additional comment

You can always use a calculator to evaluate the function for different values of t.

Answer:

none

Step-by-step explanation:

(8-5)=3

8-5÷23

=179/23

Answer: False

Step-by-step explanation:

   This is not a function because the single input [x] of 6 has outputs [y] of 2 and 4, and the single input [x] of 12 has outputs [y] of 2 and 4.

   A function must have only one output [y-value] for every input [x-value].

The value of b in the expression is -2.

a + a + b = 14

b + b + c = 8

a + b + c = 18

Therefore,

2a + b = 14

2b + c = 8

c = 8 - 2b

Hence,

a + b + 8 - 2b = 18

a - b = 18 - 8

a - b = 10

2a + b = 14

a - b = 10

3a = 24

a = 8

8 - b = 10

b = 8 - 10

b = -2

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Answer:

a = 8

b = -2

c = 12

Step-by-step explanation:

a + a + b = 14

2a + b = 14 ⇒ ( 1 )

b + b + c = 8

2b + c = 8 ⇒ ( 2 )

a + b + c = 18 ⇒ ( 3 )

First, let us make a as the subject in equation 1.

2a + b = 14

2a = 14 - b

[tex]a=\frac{14-b}{2} \\a = 7-\frac{b}{2}[/tex]   ⇒ ( 4 )

Let us make c as the subject in equation 2.

2b + c = 8

c = 8 - 2b ⇒ ( 5 )

Now it is clear for us that, we can replace a & c with ( 7 - b / 2 ) & ( 8 - 2b ) respectively.        

And now let us solve the equation 3 to find the value of b.

[tex]a+b+c=18\\\\7-\frac{b}{2} +b+8-2b=18\\\\Combine\: \:like\:\: terms.\\\\[/tex]

[tex]15-\frac{b}{2} -b=18\\\\\frac{15*2}{1*2} -\frac{b}{2}-\frac{b*2}{1*2}=18\\\\\frac{30}{2} -\frac{b}{2}-\frac{2b}{2}=18\\\\\frac{30-3b}{2} =\frac{18}{1} \\\\Use\:\: cross\;\: multiplication[/tex]

[tex]30-3b=18*2\\\\30-3b=36\\\\30-36=3b\\\\-6=3b\\\\-2 = b[/tex]

And now let us find  the value of a

For that, let us use the equation 1. There, we can replace b with ( -2 ) to find the value of a.

[tex]2a+b=14\\\\2a-2=14\\\\2a = 14+2\\\\2a=16\\\\a=8[/tex]

Now, let us find the value of c.

For that, let us take the equation 2. There also, we can replace b with -2 to find the value of c.

[tex]2b+c=8\\\\2*-2+c=8\\\\-4+c=8\\\\c=8+4\\\\c=12[/tex]

The term that describes point N is centroid. The correct option is C. Centroid

The centroid of a triangle is the point in which the three medians of the triangle intersect.

The median is a line that joins the midpoint of a side and the opposite vertex of the triangle.

In the given diagram, we can observe that the lines join the midpoints of each side to the corresponding opposite vertex.

Point N is the point where the lines intersect.

Hence, the term that describes point N is centroid. The correct option is C. Centroid

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Answer:

B. Circumcenter

Have an Amazing day/night!!

Social-desirability biases is the sort of response bias that is the tendency of the survey respondent to answer the question in a manner that is favorable to others.

As Maria found that most respondents 98% of the voters were open to support women candidates. The social desirably bias poses a serious problem during the self-reporting as the bias interferes with the interpretations of the average tendencies.

As however during the anonymous survey of the voters or respondents showed only 80% of them would support the women candidate.

Hence the social desirability bias is the main culprit for such a response.

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Answer: no solution

Step-by-step explanation:

if we simplify this equation, we derive that 9=2.

this is a false statement, which means this equation has no real solutions.

Answer:

a. The graph is concave up in the interval 0 ≤ x ≤ +∞

b. The graph is concave down in the interval -∞ ≤ x ≤ 0

To answer the question, we need to know what intervals are

Intervals are range of values in which a function is valid. It can either be the range of values of input or output of the function.

From the graph, we see that the function is concave up in the interval 0 ≤ x ≤ +∞

So, the graph is concave up in the interval 0 ≤ x ≤ +∞

From the graph, we see that the function is concave down in the interval -∞ ≤ x ≤ 0

So, the graph is concave down in the interval -∞ ≤ x ≤ 0

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The value of this car when it is 9 years old is equal to $16,757.00.

In order to determine the value of this car when it is 9 years old, we would use an exponential function which also relates to compound interest as follows:

A = P(1 - r)^t

Substituting the given parameters into the formula, we have;

A = 32,200(1 - 0.07)^9

A = 32,200(0.93)^9

A = 32,200 × 0.5204

A = $16,757.00.

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The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ

An equation is an expression that shows the relationship between two or more variables and numbers.

Let f(x) and g(x) represent the value in the savings account of Jack and Susie respectively after x years. Hence:

f(x) = 1000(1.015)ˣ, g(x) = 800(1.015ˣ

Hence:

Total savings = 1000(1.015)ˣ + 800(1.015)ˣ = (1.015)ˣ[1000 + 800] = 1800(1.015)ˣ

The function that shows the total amount Jack and Susie will save in x years is 1800(1.015)ˣ

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[tex]\sqrt{(24-0)^{2}+(10-0)^{2}}=\boxed{26}[/tex]

Answer:

26

Step-by-step explanation:

√(24 - 0)2 + (10 - 0)2

= √(24)2 + (10)2

= √676 and that would equal

26

Hello !

[tex]\frac{25}{100}=0.25[/tex]

Have a nice day ;)

Answer:

25

Step-by-step explanation:

25

Answer: 25% of 100 is 25.

Step-by-step explanation:

A.Confidence Level: 99.7%; Confidence Interval: 42 to 48 

B.Confidence Level: 95%; Confidence Interval: 43 to 47

 C.Confidence Level: 68%; Confidence Interval: 44 to 46 

D.Confidence Level: 95%; Confidence Interval: 44 to 46

Subtract the largest power of 2 from 798 such that the difference is not negative.

2⁹ = 512 and 2¹⁰ = 1024, so the largest power of 2 smaller than 798 is 2⁹, and

798 = 512 + 286 = 2⁹ + 286

Repeat this process with the remainder, 286.

2⁸ = 256, so

286 = 256 + 30 = 2⁸ + 30

⇒   798 = 2⁹ + 2⁸ + 30

2⁴ = 16 and 2⁵ = 32, so

30 = 16 + 14 = 2⁴ + 14

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 14

2³ = 8, so

14 = 8 + 6 = 2³ + 6

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 6

2² = 4, so

6 = 4 + 2 = 2² + 2¹

⇒   798 = 2⁹ + 2⁸ + 2⁴ + 2³ + 2² + 2¹

or more completely,

798 = 1×2⁹ + 1×2⁸ + 0×2⁷ + 0×2⁶ + 0×2⁵ + 1×2⁴ + 1×2³ + 1×2² + 1×2¹ + 0×2⁰

Then the base-2 representation of 798 is

11 0001 1110₂

Answer:

The expression for the statement using absolute value notation is [tex]$|p-0.08| \leq 0.015$[/tex].

Step-by-step explanation:

It is given in the question that the true proportion p of people who give a favourable rating to Congress is 8% with a margin of error of 1.5%. It is required to express the statement using absolute value notation.

To express the statement using absolute value notation, deduce the statement in the form of an equation.

The error margin for the hypothesis is 1.5% which implies the absolute difference between p and 8% should be less than or equal to 1.5%.[tex]$$|p-0.08| \leq 0.015$$[/tex]

Answer: B: 11 and 12

Step-by-step explanation:

- An integer is simply a whole number

- So consecutive integers are simply whole numbers that follow each other (ex: 1, 2, 3)

- The square root of 125 (in decimals) is 11.1803398875, meaning it is higher than 11 but less than 12

- So 11.1803398875 falls between 11 and 12, making the answer B

hope this helps :)

The true statement about the graph's slope is (c) Its slope is zero.

From the question, we have:

A horizontal line is at y = 2.5.

The horizontal line implies that the cost of lunch do not change

Horizontal lines have a slope of 0

Hence, the true statement about the graph's slope is (c) Its slope is zero.

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The correct statements regarding the linear function are given as follows:

A linear function is modeled by:

y = mx + b

In which:

In this problem, the line goes through points (-6,-7) and (8,0), hence the slope is given by:

[tex]m = \frac{0 - (-7)}{8 - (-6)} = \frac{7}{14} = \frac{1}{2} = 0.5[/tex]

Hence:

y = 0.5x + b

When x = 8, y = 0, hence the y-intercept is given as follows:

0 = 0.5(8) + b

b = -4.

When x = -2, we have that:

y = 0.5(-2) - 4 = -1 - 4 = -5.

The points (–2, –5) and (8, 0) are also on the line.

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Answer:

B,C,E

Step-by-step explanation:

took the test on edge and got 100

Answer:

false

Step-by-step explanation:

these measure do not form a right triangle

The given equality 2 divided by 9 = 5/2 divided by 5/4 is seen to be; False because LHS ≠ RHS

We are given the equality;

2 divided by 9 = 5/2 divided by 5/4

We want to check whether the left hand side of the equality is equal to the right hand side. Thus;

Left hand side can be expressed as;

2 divided by 9 = 2/9

Now, right hand side can be expressed as;

5/2 ÷ 5/4

⇒ (5/2) * (4/5)

⇒ 2

Therefore we can see that LHS is not equal to RHS and so the equality is false.

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Work Shown:

f(x) = 5x - 7

f(3) = 5(3) - 7 .... every x replaced with 3

f(3) = 15 - 7

f(3) = 8

[tex] \: [/tex]

Given :

To Find :

Calculating the value of x :

[tex]\sf : \implies \: 5x - 7[/tex]

[tex]\sf : \implies \: 5(3) - 7[/tex]

[tex]\sf : \implies \: 15 - 7[/tex]

[tex]\bf : \implies \: 8[/tex]

Hence,

[tex] \implies \boxed{ \bf \: \therefore \: The \: value \: of \: x \: is \: 8 \: } \\ \\ [/tex]

Answer:

7 (option B)

Step-by-step explanation:

the area of a trapezoid can be found using the formula:

[tex]A = \frac{a+b}{2}h[/tex]

where

A: area

a: base

b: other base

h: height

here, we can plug in our known variables to solve for h (height)

A: 119

a: 10

b: 24

h: ??

[tex]A = \frac{a+b}{2}h[/tex]

[tex]119 = \frac{10+24}{2}h[/tex]

{now, simplify!}

[tex]119 = \frac{10+24}{2}h[/tex]         {add 10 + 24}

[tex]119 = \frac{34}{2}h[/tex]            {divide 34 by 2}

119 = 17 · h

119     =    17 · h

÷ 17       ÷17             {divide both sides by 17to isolate h}

7 = h

So, the height (h) of this trapezoid is 7

hope this helps! have a lovely day :)

The angle that corresponds to ∠N after transformation is: A. ∠N'.

Transformation is a process of manipulating a figure to create an identical figure either by dilation, rotation, or translation.

In the transformation performed in the image shown below, the new image formed is congruent to the original figure. This means polygon LMNOP ≅ L'M'N'O'P.

Therefore, the angle that corresponds to angle N is: A. Angle N'

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Answer: A). Angle N'

Step-by-step explanation:

Answer:

P = 60 inches

Step-by-step explanation:

Perimeter is the distance around the outside of a shape. So, to find perimeter, add up all the sides.

The side lengths were given, add them:

15 + 20 + 25

= 60

The perimeter is 60 inches.

Using the side-splitter theorem, the segment length that would complete the proportion is GJ.

It should be noted that the side splitter theorem states that when a line intersects two sides of a triangle and is also parallel to the third side, then it'll divide the sides proportionally.

From the information given, it can be deduced that EF and HJ are parallel while H is on the side EG and J is on GF. Therefore, according to the theorem, GH/HE = GJ/JF

Therefore, the correct option is GJ.

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Answer: C.

Step-by-step explanation:  Trust Me! It was correct on the Edge quiz! :)

A model without any simplifying assumptions b.is highly complex and likely unworkable.

As their call implies, simplifying assumptions are assumptions that are protected within the version to simplify the evaluation as tons as feasible. While a simplified version now does not predict the conduct of the actual issue within perfect bounds, too many simplifying assumptions have been made.

While a scientific version enables us to make predictions, it's more valued. As clinical models are representations of simplified explanations, they do not are looking for to explain each scenario or every detail. This means that medical models often aren't equal to the 'real international' from which they are derived.

Mathematical models can help college students apprehend and discover the that means of equations or valuable relationships.

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The next step in constructing a line perpendicular to a point on the line is A. Place a compass at point D, and draw an arc that intersects the arc above line DF.

To make a perpendicular line:

Therefore, the next step would be to Place a compass at point D, and draw an arc that intersects the arc above line DF.

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