Find the volume of the sphere. Round your answer to the nearest tenth.

Answer:

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Step-by-step explanation:

To solve this question, we need to use the binomial and the normal probability distributions.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Probability the president will have an IQ of at least 107.5

IQs of adults in a certain country are normally distributed with mean 100 and SD 15, which means that [tex]\mu = 100, \sigma = 15[/tex]

This probability is 1 subtracted by the p-value of Z when X = 107.5. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{107.5 - 100}{15}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085

0.3085 probability that the president will have an IQ of at least 107.5.

Probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

First, we find the probability of a single person having an IQ of at least 130, which is 1 subtracted by the p-value of Z when X = 130. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{130 - 100}{15}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

Now, we find the probability of at least one person, from a set of 2, having an IQ of at least 130, which is found using the binomial distribution, with p = 0.0228 and n = 2, and we want:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{2,0}.(0.9772)^{2}.(0.0228)^{0} = 0.9549[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 0.0451[/tex]

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

What is the probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130?

0.3085 probability that the president will have an IQ of at least 107.5.

0.0451 probability that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Independent events, so we multiply the probabilities.

0.3082*0.0451 = 0.0139

0.0139 = 1.39% probability that the president will have an IQ of at least 107.5 and that at least one of the other two leaders (vice president and/or secretary of state) will have an IQ of at least 130.

Answer:

Step-by-step explanation:

Answer:

4 inches

Step-by-step explanation:

The line that is perpendicular to the bottom of the trapezoid is the height.

Answer:

Step-by-step explanation:

(B). 2√2

Answer:

Tammy initially had $4 pay.

Step-by-step explanation:

C on edge 2021

The y-intercept represent Tammy initially had $10 pay.

From the given graph, we can observe that the line passes through the points (2, 18) and (8, 42).

Using the two points on the line, the slope (m) of the line:

m = (change in y) / (change in x)

= (42 - 18) / (8 - 2)

= 24 / 6

= 4

Using slope-intercept form of a line equation: y = mx + b,

y= 4x+ b

Put x=2 and y= 18 we get

18 = 4(2)+b

18 = 8 + b

b= 18- 8

b = 10

Thus, the y-intercept represent Tammy initially had $10 pay.

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Answer:

1) (2, 1)

2) (2, -2)

3) (-1, -1)

4) (-5, -5)

Answer:

1. Pairs A(2, 5), B(6, 5), and C(6, 1)

missing coordinate is (2,1)

2. Pairs A(2, 3), B(7, 3), and C(7, -2)

missing coordinate is (2,-2)

3. Pairs A(-5, -1), B(1, -1), and C(1, -5)

missing coordinate is (-5,-5)

4. Pairs A(-1, 4), B(7, 4), and C(7, -1)

missing coordinate is (-1,-1)

Hope this is correct!! Have a nice day!!<3

Answer:

3/36 or 8.333

Step-by-step explanation:

the way you get it is write all the possibilities and that how you get 3/36

Answer:

Step-by-step explanation:

She wins if the numbers 5 or 6 come up. There are 4 other numbers that are equally likely to be face up.

Most of the time she will lose because two out of 6 is much smaller than 4/6. If you were betting on horses, the odds are 1 in 2. That means that who ever you are playing against should put up 2 dollars for every dollar you put up.

That would be a fair game.

Answer:

the correct t answer is d

Answer:

7.4 cm

Step-by-step explanation:

Volume of sphere

v = (4/3)πr³

Volume of hemisphere will be half that

v = (2/3)πr³

(2/3)πr³ = 839

multiply both sides by 3/2

πr³ = 1,258.5

Divide both sides by π

r³ = 400.5929917623

Take the cube root of both sides

r = 7.3717022001

Rounded

r = 7.4 cm

Answer:

x = (-1 ± √21) / 2

The first choice

Step-by-step explanation:

x² = 5 - x

Put in standard form

x² + x - 5 = 0

Use quadratic equation

x = ( -b ± √( b² - 4ac) ) / (2a)

Plug in a = 1, b = 1 , c = -5

x = (-1 ± √( 1² - 4*1*(-5)) ) / 2

evaluate

x = (-1 ± √21) / 2

Answer:

[tex]y=-3x+3[/tex]

Step-by-step explanation:

We start by finding the slope of the line, which is given by the formula:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The points (x1, y1) and (x2, y2) are represented by the pairs given: (-2, 9) and (1, 0). WE can substitute this in and simplify.

[tex]m=\frac{0-9}{1-(-2)} =\frac{-9}{1+2} =\frac{-9}{3} =-3[/tex]

Using the point-slope formula, [tex]y-y_{1} =m(x-x_{1} )[/tex], we can find the equation. We can substitute the point (-2, 9) for (x1, y1):

[tex]y-9=-3(x+2)\\y-9=-3x-6\\y=-3x+3[/tex]

Answer:

The maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.

Step-by-step explanation:

Since Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide, and he will use 1-foot square tiles, and he has two different types of tile: plain and hand-painted, and plain tiles cost $ 0.79 per tile, while hand-painted tiles cost $ 5.00 per tile, to determine what is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200, the following calculation must be performed:

10 x 15 = 150

150 x 0.79 + 0 x 5 = 118.5

130 x 0.79 + 20 x 5 = 202.7

131 x 0.79 + 19 x 5 = 198.49

Therefore, the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.

Answer:

Kindly check explanation

Step-by-step explanation:

Given the formula :

Pn = 25.8(1.0219)^h to predict the population of Ghana ;

The equation given is in the form of an exponential function:

The general form of an exponential distribution :

y = ab^x

a = Initial value ; b = constant multiplier or growth or Decay factor

Comparing :

The number in parenthesis = 1.0219 = b

b = Decay or growth factor :

Since b > 1 ; then We have a growth factor;

b = 1 + rate

1.0219 = 1 + rate

Rate = 1.0219 - 1

Rate = 0.0219

Hence, the population is growing at a rate of about (0.0219)*100% = 2.19%

Answer:

Project A :

NPV : $703,888.64

IRR : 44.882%

Project B:

NPV : $5,241.26

IRR : 49.662%

Project B is more profitable

Step-by-step explanation:

The NPV gives the difference between the present value of cash inflow and cash outflow over a certain period of time.

The Internal rate of return is the discount rate which makes the NPV of an investment 0. It is used to estimate the potential return on an investment. Investments with higher IRR are said to be better than those with lower IRR value.

Using the net present value, (NPV) Calculator, the NPV for project A is : $703,888.64

The IRR of project A is : 44.882%

The NPV for Project B is : $5,241.26

The Internal rate of return (IRR) : 49.662%

From the Internal rate of return value obtained, we can conclude that, project B is more profitable as it has a higher IRR than project A.

Answer:

x < 3

Step-by-step explanation:

The graph of f(x) is above the graph of g(x) for values of x less than 3.

Answer: x < 3

Answer:

41, 43 and 82

Step-by-step explanation:

hope it may help you

Answer:

A. 115°

Step-by-step explanation:

180° - 65° = 115°

Given:

The two polygons are similar.

To find:

The value of [tex]a,\ b,\ m\angle C,\ m\angle D[/tex].

Solution:

We know that the corresponding side of similar figures are proportional. So,

[tex]\dfrac{5}{4}=\dfrac{5.39}{a}[/tex]

[tex]1.25=\dfrac{5.39}{a}[/tex]

[tex]a=\dfrac{5.39}{1.25}[/tex]

[tex]a=4.312[/tex]

Similarly,

[tex]\dfrac{5}{4}=\dfrac{5.83}{b}[/tex]

[tex]1.25=\dfrac{5.83}{b}[/tex]

[tex]b=\dfrac{5.83}{1.25}[/tex]

[tex]b=4.664[/tex]

We know that the corresponding angles of similar figures are congruent and their measures are equal. So,

[tex]m\angle C=99.2^\circ[/tex]

[tex]m\angle D=149^\circ[/tex]

Therefore, [tex]a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ[/tex].

Answer:

The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Step-by-step explanation:

Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:

X x (X + 7) = 80

5 x 12 = 60

6 x 13 = 78

8 x 14 = 112

6.1 x 13.1 = 79.91

6,105 x 13,105 = 80

Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

9514 1404 393

Explanation:

Divide the figure into areas for which you have a surface area formula. Use the appropriate formula for each area, then add up the results.

Formulas are available for surface areas of a cone, cylinder, sphere, pyramid, rectangular prism, and for plane shapes that are circles, ellipses, triangles, rectangles, trapezoids, and regular polygons.

Most of the figures for which you are asked to find the area will decompose to some subset of these shapes. Take care to identify the relevant dimensions of each of the constituent parts of the area, and to make sure that all parts are accounted for. Do not allow your parts of the area to overlap, unless you intend to account for that overlap by subtracting the area that is counted more than once.

Also, use your common sense. A semicircle will have half the area of a circle, for example.

In some cases, it may be expedient to compute the area of a larger figure than the one you have, then subtract the part of that area that is missing from your figure.

Answer:

since her score was -12 from being perfect

if she had scored 12 more points her score would have been perfect .

that is difference between her score and the perfect score o each quiz was 12

Answer:555

Step-by-step explanation:

Answer:

545

Step-by-step explanation:

you are just adding one

544+1=

9514 1404 393

Answer:

  448

Step-by-step explanation:

(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk

That would be 448 fluid ounces per week.

A. 4/7 Answer:

B. 60/7 or (8 and 4/7)

Step-by-step explanation:

A. 4 divided by 7 is the same as 4/7

B. 4/7 • 15/1= 60/7

Answer:

x is 13°.take the triangle to find the measure of x.180° -(85°+82°)=x

180°-167°=13°

For the given triangle the measure of the angle x is = 3 degrees.

Labeling the given figure,

since angle C and angle B are alternate angles

Therefore,

For the triangle ABE

The interior angle for A = x

The interior angle for B = 180 -98

                                       = 92 degree

Since we know that,

The sum of the two interior angles of a triangle is equal to the exterior angle of the opposite side.

Therefore,

⇒ x  + 92 = 180 - 85

⇒ x  = 3 degrees.

Hence,

The measure of the angle x is = 3 degrees.

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Answers:

Each pair of triangles are congruent. The congruence reasoning is shown below.

======================================

Further Explanation:

Abbreviations:

ASA = angle side angle

SSS = side side side

HA = hypotenuse angle

Answer:

f(6) = 82

Step-by-step explanation:

[tex]f(x) = 2x^2 + 5\sqrt{x-2}[/tex]

[tex]=> f(6) = 2(6)^2 + 5\sqrt{6-2}[/tex]

             [tex]= 2 \times 36 + 5 \times \sqrt{4}[/tex]

             [tex]= 72 + 5 \times 2[/tex]

             [tex]= 72 + 10[/tex]

             [tex]= 82[/tex]