What is the relationship between the volume and surface area of the sphere shown?
V>SA
OV OV=SA

Answer:

Given d = 75, respectively,

135

Step-by-step explanation:

[tex]2\left(75\right) = 2 \cdot 75\\= 150\\\\\sqrt[3]{-45\left(75\right)}\\\left(75\right)=75\\\sqrt[3]{-45\cdot \:75}\\45\cdot \:75=3375\\\sqrt[3]{-3375}\\\sqrt[3]{-3375}=-\sqrt[3]{3375}\\-\sqrt[3]{3375}\\-\sqrt[3]{15^3}\\\sqrt[3]{15^3}=15\\=15\\\\=150-15\\=135[/tex]

Answer:

A. 72°

D. 144°

E. 216°

Step-by-step explanation:

I just answered this.

in short : we rotate each vertex on a circle arc. the center of that circle being P.

so, at the end of every 1/5 of the circle arc there is a vertex of the polygon.

therefore, with every 1/5 of a full circle rotation we move the pentagon visually onto itself.

that is starting at

360/5 = 72°

and then every additional 72°

144°

216°

288°

360°

so, A, D and E are correct

Answer:

Step-by-step explanation:

(2*9/5d*9)-(1*5/9d*5)

18/45d-5/45d

13/45d

The value of  dy/dx at x = 1 is  mathematically given as

dy/dx=5-1.8898i

This is further explained below.

Generally, Given that cost y of producing x gallons ag an implicit evaluation

y^2-10 x y=200

Differentiate the above equation as

[tex]\begin{aligned}&2 y y^{\prime}-10 y-10 x y^{\prime}=0 \\&y^{\prime}(2 y-10 x)=10 y \\&y^{\prime}=\frac{10 y}{2 y-70 x}=\frac{5 y}{y-5 x}\end{aligned}[/tex]

when x=1, substitute in the given equation to get y value

y^2-10 y=200

or

y=5+13.2288i

y=5−13.2288i

y represents the cost and hence cannot be negative Hence practical solution for y is y=5+13.2288i substitute in the ' y ' equation to get [tex]$\frac{d y}{d x}$ at $x=1$[/tex]

when x=13 y=5+13.2288i

Hence

d y/d x at x=1 will be

dy/dx[tex]=\frac{5(5+13.2288i)}{5+13.2288i-5}[/tex]

[tex]dy/dx=\frac{25+66.144}{13.2288i}[/tex]

dy/dx=5-1.8898i

In conclusion, the value of  dy/dx at x = 1 i

dy/dx=5-1.8898i

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Answer:

Well the IMC 2014 is

IMC 2014 + hMc

we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.

We are given the frequency distribution table as:

X                 f    

5                 2

4                 5

3                 6

2                 4

1                  3

We need to find cumulative frequency (c f) and percentiles(c %)

c % = 100 × ( c f / n )

c f means the frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors.

n = 20

X                 f             c f             c %

5                 2              2            10 %

4                 5              7            35 %

3                 6             13            65 %

2                 4             17            85 %

1                  3            20           100 %

Therefore, we have found out the cumulative frequency (c f) and percentiles(c %) for the given data.

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Answer:

x = -2

Step-by-step explanation:

-12 = 1/2(6x - 12)  Multiply everything inside the parentheses by 1/2

-12 =1/2(6x) - (1/2)(12)

-12 = 3x - 6  Add 6 to both sides of the equation

-6 = 3x  Divide both sides by 3

-2 = x

Check:

Plug -2 in for x and see if statement is true

-12 = 1/2(6x - 12)

-12 = 1/2[(6)(-2) - 12]  Simplify inside the brackets

-12 = 1/2(-12 -12)

-12 = 1/2 (-24)

-12 = -12

Using the Pythagorean Theorem, it is found that the length of AB is of 8.54 units, considering that BC = 3 and that AC = 8.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

For this triangle, we have that:

Hence the length of AB is given as follows:

h² = 3² + 8²

h² = 73

h = sqrt(73)

h = 8.54 units.

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Joe earned $140 for working 20 hours

To determine the value of a single unit from a specified multiple, use the unitary technique. How to determine the value of one pen, for instance, if the cost of 40 pens is Rs. 400. The unitary approach can be used to complete it. Additionally, after determining the value of a single unit, we can multiply that value by the number of units needed to determine the value of the additional units. The concept of ratio and proportion is mostly applied using this way.

Joe worked 14 hours  and earned = $119

Joe worked for 1 hour and earned = $ 119/ 14

Joe worked for 20 hours and earned = $ 119/ 14 x 20

                                                                 = 4140

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The polynomial expression for the area of the room is f(x) = x^2 + 16x + 48.

Here, we are given that the side of the length of the rug = x

Now, the square rug is placed on the rectangular room such that on 2 sides the uncovered floor is 6 meters.

This means that the length of the 2 opposite sides of the rectangle will be (x + 6 + 6) = (x + 12)

Similarly, there is 2 feet of uncovered floor on the other 2 sides, which means that the length of other two opposite sides is- (x + 2 + 2) = (x + 4)

Kindly refer to the diagram below for a better clarity of how we found out the sides.

Now, the area of a rectangle = Length × Breadth

Thus, area of the room = (x + 12) (x + 4)

= x^2 + 4x + 12x + 48

= x^2 + 16x + 48

Thus, the polynomial expression for the area of the room is f(x) = x^2 + 16x + 48

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Answer: I say 4/3 the fraction so your answer is D

Explanation: Because its white cars to blue cars the problem is whats equivalent to the ratio 40 to 30, 4:1 is not the same as 40 to 30 neither

is 1:4 or 3 to 4 So its D. :)

Answer:

36in

Step-by-step explanation:

A square has four sides. If the length of one is 9 inches, then we multiply it by four to get 9*4 = 36in as our perimeter.

FINAL ANSWER: 36in

Out of the population being surveyed, the one that could result in a sample statistic but not a parameter is; B: 50

A sample statistic is a piece of information you get from a fraction of a population.

A parameter is a number describing a whole population (e.g., population mean), while a statistic is a number describing a sample (e.g., sample mean).

Now, we are told that a population consists of 5000 people. This means that the sample statistic could be the sample mean which could be 50 but certainly not 5000 as the sample statistic can't be same as the population.

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Answer:

the action of inflating something or the condition of being inflated.

"the inflation of a balloon"

ASTRONOMY

(in some theories of cosmology) a very brief exponential expansion of the universe postulated to have interrupted the standard linear expansion shortly after the Big Bang.

2.

ECONOMICS

a general increase in prices and fall in the purchasing value of money.

"policies aimed at controlling inflation"

Answer: 0

Step-by-step explanation:

because -2+-1 is -3. then -3+0 is just -3. lastly -3+1 = -2 and -2 + 2 = 0

Answer:

-3/7

Step-by-step explanation:

[tex]-3\frac{1}{7} / 7 \frac{2}{6}[/tex]

[tex]-3 \frac{1}{7} = \frac{-22}{7}[/tex]

[tex]7\frac{2}{6} = 7\frac{1}{3} = \frac{22}{3}[/tex]

[tex]\frac{\frac{-22}{7} }{\frac{22}{3} }[/tex][tex]= \frac{-22}{7} * \frac{3}{22} = \frac{-3}{7}[/tex]

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The total number of holes will be (a)15 and (b) 4 when the drilling machine is used whose standard deviation is 0.0028mm.

The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean.

The sum of all values divided by the total number of values constitutes a dataset's mean.

The mean of the holes are given as 4.05 mm([tex]\mu=4.08[/tex])

The standard deviation is given as 0.0028 mm([tex]\rho=0.0028[/tex])

Now we will use the z-score and probability distribution to calculate the frequency of the holes to have diameter between 4.048 and 4.0553.

Here [tex]Pr(4.048\leq X\leq 4.0053)[/tex] ,so we need to compute the z-values

[tex]Z_1=\frac{X_1-\mu}{\rho} \\Z_1=\frac{4.048-4.05}{0.0028} \\Z_1=-0.7143[/tex]

Similarly:

[tex]Z_2=1.8929[/tex]

Therefore from the above statements we can say that

[tex]Pr(-0.7143\leq X\leq 1.8929)[/tex]

Solving for probability distribution we get

[tex]Pr(4.048\leq X\leq 4.0053)=0.7333[/tex]

Total number of holes=0.7333 × 20= 14.666..

Therefore the number of holes is 15

Similarly

The z-value corresponding to 4.052 mm is given by 0.71

The z-value corresponding to 4.056 mm is given by:2.14

The probability of the diameter being between 4.052 mm and 4.056 mm is 0.4838 – 0.2611 =0.2227

The number likely to have a diameter between 4.052 mm and 4.056 mm = 0.2227 × 20

= 4.454

= 4, correct to nearest whole number

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Answer:

No, 2 is not a solution

Step-by-step explanation:

x - 5>10  Add 5 to both sides of the equations

x > 10  The solutions are all numbers greater than 10.  Two is not greater than 10.

Answer:

3

Step-by-step explanation:

32 - 20 = 12

12/4 = 3

This assumes that by remainder they mean they twelve feet left over and not the twenty feet removed. This is likely what it means.

The total spent amount on water is $220

The total area is 37.5=75/2

The number of lots is 75/2/3/4=50 nos

Total rent is 50×50=2500

So 3/5 will go to david 2500×3/5=1500

2/5 will go to john 2500×2/5=1000

So 60% Renters choose 100 gallons

Total renters is 50

60% renters is 50×60%=30 nos

40% renters choose 70 gallons

40% of 50 is 20 nos

The tank fills twice

100×30+70×20=4400 to be filled

Per gallon cost is $0.05

So the total cost is 4400×0.5=$220

So they spent $220 on water

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Answer:

Domain: [-20, 20]

Range: [-30, 5]

Step-by-step explanation:

The domain is the set of x values and the range is the set of y values.

The inequality to represent the given condition is -3<x<7 .

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. [1] It is frequently used to compare two numbers on the number line based on their sizes. Different types of inequalities are represented by a variety of notations, including:

The given statement gives the solutions of all real numbers between 3 and 7.

Therefore if we consider a real number x then, x>-3 and x<7 .

Combining together for a compound inequality: -3<x<7.

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Answer:

x = 1

Step-by-step explanation:

2 x [tex]x[/tex] = 10

10 > -10

9 x [tex]x[/tex] = 9

9 < 18

Answer:

$675.00

Step-by-step explanation: The chart says it all

The solution for the given system of equations is (3,5) and (-4,12).

Given two systems of equations i.e. x+y=8 and y=[tex]x^{2}[/tex]-4 and asked to solve them.

⇒x+y=8; let's assume this equation as A

⇒ y=[tex]x^{2}[/tex]-4; let's assume this equation as B

From equation A

⇒y=8-x

From equation B

⇒y=[tex]x^{2}[/tex]-4

Equating both the values of y

⇒8-x=[tex]x^{2}[/tex]-4

⇒[tex]x^{2}[/tex]-8-4+x=0

⇒[tex]x^{2}[/tex]-12+x=0

{solving quadratic equation}

⇒[tex]x^{2}[/tex]-12+4x-3x=0 { factorizing the quadratic equation}

⇒[tex]x^{2}[/tex]+4x-3x-12=0

⇒x(x+4)-3(x+4)=0

⇒(x-3)(x+4)=0

Therefore, the value's of x=3,-4

⇒if x=3

From  equation A

⇒y=8-3=5

For x=3 ; y=5

⇒if x=-4

From  equation A

⇒y=8-(-4)=12

For x=-4 ; y=12

Therefore,The solution for the given system of equations is (3,5) and (-4,12).

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Answer:

28

Step-by-step explanation:

-28 + 28 = 0

The logarithmic expression is equal to:

Log₂(11)*log₆(2) = 1.34

Here we have the logarithmic expression:

Log₂(11)*log₆(2)

Now, remember that we can rewrite:

Logₐ(b) = Ln(b)/Ln(a)

Using that we can rewrite the expression:

Log₂(11)*log₆(2) = (Ln(11)/Ln(2))*(Ln(2)/Ln(6)) = Ln(11)/Ln(6)

Now using a calculator you can find these two natural logarithms:

Ln(11)/Ln(6) = 1.34

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The values of all the required angles are; m∠5 = 42°; m∠8 = 138°; m∠10 = 138° and m∠11 = 42°

Corresponding angles are formed where a line known as an intersecting transversal, crosses through a pair of straight lines.

Now, we are given that; m∠1 = 42°

By corresponding angles, we can say that;

m∠1 = m∠5

Thus; m∠5 = 42°

Now, we know that sum of angles on a straight line is equal to 180° i.e. they are supplementary angles.

Now, from the diagram, we can see that m∠5 and m∠8 are supplementary angles and as such;

m∠5 + m∠8 = 180°

42 + m∠8 = 180

m∠8 = 180° - 42°

m∠8 = 138°

Now, m∠9 is a corresponding angle to both m∠1 and m∠5. Thus, we can say that; m∠9 = 42°. However, m∠9 is supplementary to m∠10. Thus;

m∠10 = 180 - 42

m∠10 = 138°

Lastly, m∠10 and m∠11 are supplementary angles and as such;

m∠10 + m∠11 = 180°

138 + m∠11 = 180

m∠11 = 180° - 38°

m∠11 = 42°

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Answer:

$42.00

Step-by-step explanation:

Let x  = the original cost of the sweatshirt

x - .15x = 35.70  We don't know the original cost so we will call it x.  I know that we are taking 15 off of this number to get the sale's price.  15% means per 100, so as a fraction this would be 15/100.  To make this a decimal, I would divide 15 by 100 to get .15

x - .15x = 35.70  Combine the like terms

.85x = 35.70  This is say that 85% if the original price is the sale price of 35.70

Divide both sides of the equation by .85 and we get x = 42.00

Check:

42 - .15(42) = 35.70

42 - 6.30 = 35.70