The diameter of a sphere is 16.4 mm Calculate the sphere's volume
Use the value 3.14 for pi , and round your answer to the nearest tenth. (Do not round any intermediate computations.)

The given quadrilateral is a rectangle because 2 pairs of sides are equal in length.

We are given the coordinates of the quadrilateral as;

W(0, 5), X(-3, 2), Y(0, -4), Z(3, 2).

Now, the formula for distance between two coordinates is;

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Thus;

WX = √[(-3 - 0)² + (2 - 5)²]

WX = 3√2

XY = √[(0 + 3)² + (-4 - 2)²]

XY = 3√5

YZ = √[(2 + 4)² + (3 - 0)²]

YZ = 3√5

ZW = √[(0 - 3)² + (2 - 5)²]

ZW = 3√2

Thus, we can conclude that the given quadrilateral is a rectangle because 2 pairs of sides are equal in length.

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Answer:

the answer is x= 3/4 I think

Answer:

dan is 24

I had to redo this one

The age of Margo and Dan will be 32 years and 24 years, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Margo is 8 years older than her brother Dan. The sum of their ages is 56.

Let M be the age of Margo and D be the age of Dan. Then the equations are written as,

M = D + 8               ...1

M + D = 56            ...2

From equations 1 and 2, then we have

D + 8 + D = 56

2D + 8 = 56

2D = 56 - 8

2D = 48

D = 48 / 2

D = 24 years

Then the age of Margo will be given as,

M + 24 = 56

M = 56 - 24

M = 32 years

The age of Margo and Dan will be 32 years and 24 years, respectively.

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At step 2, we arrive at

(2x + 3) (x + 3) = 0

and the next step (which isn't actually shown) is to use the so-called zero-product property that says if [tex]ab=0[/tex], then [tex]a=0[/tex] or [tex]b=0[/tex]. This means

2x + 3 = 0   or   x + 3 = 0

and solving the first equation leads to the rational solution.

2x + 3 = 0

2x = -3

x = -3/2

[tex]\huge\boxed{10}[/tex]

[tex]\sqrt{100}[/tex] means that you are looking for the number that, when multiplied by itself, produces [tex]100[/tex]. That number is [tex]10[/tex], because [tex]10\cdot10=100[/tex], meaning that [tex]\sqrt{100}=10[/tex].

It will take the company 20.3 years to have a financial worth of $11.4

The estimate of profit is given as;

Profit = $0.6 million per year

This means that the engineers based their estimate per year

Hence, the unit of time is year

To do this, we make use of any variable of our choice.

In this case, we let x represents the variable of the amount of time.

In (a), we have:

Profit = $0.6 million per year

So, the expected financial status is 0.6x

This is the amount taken as loan by the engineers.

So, the financial status at the beginning is 1.8

Using the expressions above, we have the yearly worth to be:

y = 0.6x - 1.8

When the financial status is $11.4 million, we have:

0.6x - 1.8 = 11.4

Evaluate the like terms

0.6x = 12.2

Divide both sides by 0.6

x = 20.3

Hence, it will take the company 20.3 years to have a financial worth of $11.4

See attachment for the graph of y = 0.6x - 1.8

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Answer:

A: The rate of change is 10% per year.

Step-by-step explanation:

The rate of change is simply the change in value divided by the change in time. In this case, the change in value is $1080 - $720 = $360, and the change in time is 12 years. Therefore, the rate of change is $360 / 12 years = $30 per year.

Answer:

a fraction

Step-by-step explanation:

this will produce a fraction, for example:

3^-1 = 1/3

and (-2)^-3 = -1/8

Answer:

The Framers are offering a better price and are cheaper by $1.35

Step-by-step explanation:

I've been framed price:

50% off of 115 = 0.5*115 = 57.5

10% off of sale price = 0.9*57.5 = $51.75

the Framers price:

30% off of 120 = 0.7*120 = 84

40% off of sale price = 0.6*84 = $50.40

Difference: 51.75-50.40 = $1.35

Answer:

Step-by-step explanation:

255 people

Answer:

See Below

Step-by-step explanation:

Since they are lines, and if two lines have angles that are congruent, then it has to be perpendicular. Angles sum up to 180, and since they are equal, it is 90.

The total interest for 4 years with a principal amount of $500 and a rate of 2% is $40.

The formula for the simple interest is,

I = PTR

where

I is the interest, P is the principal amount, T is the period, and R is the rate of interest.

The given data is,

Kaitlin wants to save $500 in her savings account. I.e., P = $500

For 4 years i.e., T = 4 years and the rate R = 2%  i.e., R = 0.02

Then,

the total interest for 4 years with no more deposits is

I = PTR

 = $500 × 4 × 0.02

 = $40

Therefore, the total interest that Kaitlin will earn for 4 years is $40.

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Answer:

D

Step-by-step explanation:

on a graph, look at the points (-3,0) (-1,0) and (2,0). Then, see if the line passes through those points. You will see that graph D passes through all those points. If you're confused on how to turn the (x,y) format into points on a graph, remember that the first point tells you how left/right you want to be, and the second point tells you how up/down you want to be.

The probability of picking a red counter is therefore; 8/25.

Since the ratio of red to green is 2 :3 and there are 24 green counters, it follows that the number of red counters is;

x = (2/3)× 24 = 16 red.

The total of red and green is; 16 +24 = 40 which constitutes 80% of the total counters.

The total number of counters is therefore; 40/0.8 = 50 counters.

The probability of picking a red counter is therefore; 16/50 = 8/25.

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The number of people who are not Democrats , do not wear glasses, and don not like ice-cream by using sets are 155 people and the number of people who are democrats, not wearing glasses and do not like ice cream are 150 people.

Given total people of 1000 people, 595 democrats, 595 wearing glasses, 550 like ice cream, 395 of them are democrats who wear glasses,350 of them are democrats who like ice cream and 400 of them wear glasses as well as like ice cream ,250 of them are democrats as well as wear glasses and like ice cream.

We have to find the number of people who are not democrats , do not wear glasses ,do not like ice cream and the number of people who do not wear glasses and do not like ice cream.

let X shows the number of democrats and G be number of people who wear glasses and I be the number of people like ice cream.

So,

D=595, G=595 AND I=550

Now D∩G=395

D∩I=350

G∩I=400

so D∩G∩I=250

Formula will be :

D∪G∪I=D+G+I-(D∩G)-(G∩I)-(D∩G)+(D∩G∩I)

=595+595+550-(395+350+400)+250

=845

845 are either democrats or wear glasses as well as like ice cream.

So 1000-845=155

Number of people who are democrats, do not wear glasses and do not like ice cream=D-(D∩G)-(D∩I)+(D∩G∩I)

=595-(395+300)+250

=845-695

=150 people.

Hence the number of people who are not Democrats , do not wear glasses, and don not like ice-cream are 155 people and the number of people who are democrats, not wearing glasses and do not like ice cream are 150 people.

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Since there are no patterns for the rate of change of the function, it is quadratic.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input.

When this rate is constant, the function is said to be linear, while if the rate increases in a proportional way, the function is exponential.

In this problem, no patterns of linearity or of exponentiality can be established, hence the function is quadratic.

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Answer:

375

Step-by-step explanation:

Since they started at the same point and went in opposite directions, add the 2 distances.

162.5 + 212.5 = 375

Answer:

88 square units

Step-by-step explanation:

     a  and b are the length of the parallel sides.

      a = IL = 15

      b = JK = 7

      h = height between the parallel lines = 8

[tex]\sf \boxed{\bf Area \ of \ trapezium = \dfrac{(a +b)*h}{2}}[/tex]

                                   [tex]\sf =\dfrac{(15+7)*8}{2}\\\\=\dfrac{22*8}{2}\\\\= 11*8\\\\= 88 \ square \ units[/tex]

Using the GREAT decision-making model, one could consider telling the driver not to drive after drink, getting out of the car and looking for another, or riding in the same car while ignoring the situation.

The options we have in this situation are:

Option 1:

Option 2:

Option 3:

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Both sides of the equation are not equal, therefore, Massa was wrong.

For an equation to be correct, the values on both sides of the equation must be equal and balance.

Given the expression, 540 ÷ 6 = 9, 540 divided by 6 is 90. 90 is not equal to 9.

Thus, the value on the both sides are not balanced, therefore, Massa is incorrect.

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Answer: [tex]52.6^{\circ}[/tex]

Step-by-step explanation:

Let the angle of depression be x.

[tex]\sin x=\frac{27}{34}\\\\x=\sin^{-1} \left(\frac{27}{34} \right) \approx 52.6^{\circ}[/tex]

The value of y if the perimeter of the figure is 5y is 15meters.

The perimeter of a polygon is the sum of the length of the whole sides.

Therefore,

perimeter = y + 2y + 30

perimeter = 5y

Hence,

5y = 3y + 30

5y - 3y = 30

2y = 30

divide both sides by 2

2y / 2 = 30 / 2

y = 15

Therefore, the value of y is 15m.

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The largest possible volume of the box is x²y

It is important to note that the given figure is a rectangle

Area of the box is given as 100 square feet

Formula for volume of a rectangle

Volume = length × width × height

Length = x

Width = x

Height = y

Substitute the values in the formula

We have;

Volume = x × x × y

Volume = x²y

Thus, the largest possible volume of the box is x²y

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Answer :

Step-by-step explanation:

To find the value of 'a' we will use the tangent-chord theorem,

"Angle formed by the chord and a tangent to the circle measure the half of the intercepted minor arc"

Angle 'a' is formed between the chord and the tangent.

Measure of the intercepted arc = (2 × 52)°

Therefore, measure of the angle 'a' = \frac{104}{2}

2

104

a = 52°

Therefore, Option (A) will be the correct option.

The theorems that apply are A(HL) D(SAS) E(LL)

Two triangles are said to be similar if their corresponding angles are equal and their corresponding lengths are in the same proportion.

Analysis:

The two triangles are similar according to the HL theorem since the hypotenuse of the two triangles are equal and one of the sides is same in both triangles. HL theorem applies.

The two triangles are similar according to LL theorem since the other lengths apart from the hypotenuse are also equal.

since two sides of both triangles are equal and there is an included angle 90 degree between the equal sides, the triangles are similar based on SAS.

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The final amount of the compound interest after 6 years would be $ 294, 122, 500

The formula for the final amount is given as;

[tex]A = P( 1 + \frac{r}{n}) ^n^t[/tex]

Where

A = final amount

P = principal interest

r = interest rate

n = number of times

t = time of periods

We have,

A = [tex]2500[/tex] [tex]( 1 + \frac{6}{1}) ^1^*^6[/tex]

A = [tex]2500 ( 7)^6[/tex]

A = [tex]2500[/tex] × [tex]117, 649[/tex]

A =$ [tex]294, 122, 500[/tex]

Thus, the final amount of the compound interest after 6 years would be $ 294, 122, 500

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The probability that a person will be entertained by either books or TV is 0.55

Express the given percentages as probabilities.

Let the probability of people being entertained by books be represented as

P(A)=0.36

Probability of people entertained by watching TV,

P(B)=0.32

Probability of people entertained by both books and TV,

P(A∩B)=0.13

P(A) + P(B) - P(A and B) is the formula for calculating the either/or probability for overlapping events. This formula is identical to the non-overlapping events, but we need to take the likelihood that the outcomes could occur simultaneously into account.

Thus, the probability of people being entertained by either books or TV is,

P(AUB)=P(A)+P(B)-P(A∩B)

           =0.36+0.32-0.13

           =0.68-0.13

          =0.55          

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The area of the shaded region in the task content is; 251.2.

It follows from the task content that the area of the shaded region is;

= Area of semicircle IL - Area of semicircle JK + Area of semicircle IJ + Area of semicircle KL.

Hence, since the radius of each semicircle are as follows;

R(IL) = 12

R(IJ) = R(JK) = R(KL) = 4.

Hence, the Area of the shaded region can be evaluated as;

= (π/2)(12² - 4² + 4² +4²).

= π (144 +16)

= (3.14/2) × 160 = 251.2

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Answer: Probability = 44%

Step-by-step explanation:

To find the probability of finding 2 black balls in a row, we first need to find the probability of finding 1 black ball at a time.

To do that, we need to divide the amount of total black balls by the number of total balls.

Black balls = 6

Total balls = 3 + 6 = 9

6 divided by 9 = 0.(6)

If you multiply 0,(6) by 100%, it will give you 66% (rounded) of getting a black ball.

Now, to find the chances of getting 2 black balls in a row, we need to multiply [tex]\frac{6}{9}[/tex] by [tex]\frac{6}{9}[/tex]. What we are doing is squaring the chances of getting one black ball, by the number of times we want to get it.

That is equal to 0,(4)

Multiply 0,(4) by 100%, and it will give you 44%(rounded) chances to get a black ball 2 times in a row.

Probability = 44%

Hope I Helped!

The Pythagorean theorem is [tex]a^2+b^2=c^2[/tex], where a and b are two legs of a right triangle and c is the hypotenuse (the longest side).

We're given a triangle with the following:

We can plug these values into the Pythagorean theorem as a, b and c:

[tex]a^2+b^2=c^2\\2^2+b^2=6^2[/tex]

Now, isolate b:

[tex]b^2=6^2-2^2\\b=\sqrt{6^2-2^2}\\b=\sqrt{36-4}\\b=\sqrt{32}[/tex]

[tex]b=\sqrt{32}[/tex]