If the volume of a full sphere is 4/3x πr^3 what is the volume of a half sphere, also called a hemisphere?

Answer:

(4b)•(0.5a) = (4•0.5)(a)(b) = 2ab

Step-by-step explanation:

Answer:

the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166

Step-by-step explanation:

The summary of the given statistical data set are:

Sample Mean = 186

Standard deviation = 29

Maximum capacity 3,417 pounds or 17 persons.

sample size = 17

population mean =3417

The objective is to determine the probability  that a random sample of 17 persons will exceed the weight limit of 3,417 pounds

In order to do that;

Let assume X to be the random variable that follows the normal distribution;

where;

Mean [tex]\mu[/tex] = 186 × 17 = 3162

Standard deviation = [tex]29* \sqrt{17}[/tex]

Standard deviation = 119.57

[tex]P(X>3417) = P(\dfrac{X - \mu}{\sigma}>\dfrac{X - \mu}{\sigma})[/tex]

[tex]P(X>3417) = P(\dfrac{3417 - \mu}{\sigma}>\dfrac{3417 - 3162}{119.57})[/tex]

[tex]P(X>3417) = P(Z>\dfrac{255}{119.57})[/tex]

[tex]P(X>3417) = P(Z>2.133)[/tex]

[tex]P(X>3417) =1- 0.9834[/tex]

[tex]P(X>3417) =0.0166[/tex]

Therefore; the probability that a random sample of 17 persons will exceed the weight limit of 3,417 pounds is 0.0166

Answer: x=-3/4

Step-by-step explanation:

Since we know f(x)=6, we can set it equal to the equation.

6=9+4x           [subtract 9 on both sides]

-3=4x              [divide both sides by 4]

x=-3/4

Answer:

80%

Step-by-step explanation:

The numbers 5 or even are 4, 5, 6, and 8.

4 numbers out of 5.

4/5 = 0.8

Convert to percentage.

0.8 × 100 = 80

P(5 or even) = 80%

Answer:

80% chance

Step-by-step explanation:

There are 4 numbers that fit the rule, 4, 5, 6, and 8. There is a 4/5 chance spinning one of those numbers or 80% chance.

Answer:

(x, y) = (-8/3, -60)

Step-by-step explanation:

y = 30x + 20

y = 10 * 2 - 80 → y = 20 - 80

y = 30x + 20

y = -60

30x + 20 = -60

x = -8/3

(x, y) = (-8/3, -60)

Hope this helps! :)

Answer:

1) [tex]h(x) = \frac{f(x)}{g(x)}[/tex], 2) [tex]h(x) = \frac{g(x)}{f(x)}[/tex], 3) [tex]h(x) = f(x) + g(x)[/tex], 4) [tex]h (x) = f [g (x)][/tex], 5) [tex]h(x) = f(x) - g(x)[/tex]

Step-by-step explanation:

1) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h (x) = \frac{x+4}{2\cdot x + 1}[/tex], then:

[tex]h(x) = \frac{f(x)}{g(x)}[/tex]

2) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = \frac{2\cdot x + 1}{x+4}[/tex], then:

[tex]h(x) = \frac{g(x)}{f(x)}[/tex]

3) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = 3\cdot x + 5[/tex], then:

[tex]h(x) = 3\cdot x + 5[/tex]

[tex]h (x) = (1 + 2)\cdot x + (4+1)[/tex]

[tex]h(x) = x + 2\cdot x + 4 +1[/tex]

[tex]h(x) = (x+4) + (2\cdot x + 1)[/tex]

[tex]h(x) = f(x) + g(x)[/tex]

4) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = 2\cdot x + 5[/tex], then:

[tex]h(x) = 2\cdot x + 5[/tex]

[tex]h(x) = 2\cdot x + 1 + 4[/tex]

[tex]h(x) = (2\cdot x +1)+4[/tex]

[tex]h (x) = f [g (x)][/tex]

5) Let be [tex]f(x) = x + 4[/tex] and [tex]g(x) = 2\cdot x + 1[/tex], if [tex]h(x) = -x + 3[/tex], then:

[tex]h(x) = -x + 3[/tex]

[tex]h(x) = (1 - 2)\cdot x + 4 - 1[/tex]

[tex]h(x) = x - 2\cdot x + 4 - 1[/tex]

[tex]h(x) = x + 4 - (2\cdot x + 1)[/tex]

[tex]h(x) = f(x) - g(x)[/tex]

Answer:

s=5

Step-by-step explanation:

This triangle is right and with two equal sides since it has two congruent angle so we will use the pythagorian theorem:

Answer:

Option D is correct.

There are 34 nickels in the piggy bank.

Step-by-step explanation:

A piggy bank contains pennies, nickels and dimes.

Let the number of pennies be p

Let the number of nickels be n

Let the number of dimes be d

Also, note that 1 penny = $0.01

1 nickel = $0.05

1 dime = $0.10

- The number of dimes is 15 more than the number of nickels.

d = 15 + n

- There are 140 coins altogether totaling $7.17.

p + n + d = 140

0.01p + 0.05n + 0.1d = 7.17

Bringing the 3 equations together

d = 15 + n (eqn 1)

p + n + d = 140 (eqn 2)

0.01p + 0.05n + 0.1d = 7.17 (eqn 3)

Substitute (eqn 1) into (eqn 2)

p + n + d = 140

p + n + (15 + n) = 140

p + 2n + 15 = 140

p = 140 - 15 - 2n = 125 - 2n

p = 125 - 2n (eqn 4)

Substitute (eqn 1) and (eqn 4) into (eqn 3)

0.01p + 0.05n + 0.1d = 7.17

0.01(125 - 2n) + 0.05n + 0.1(15 + n) = 71.7

1.25 - 0.02n + 0.05n + 1.5 + 0.1n = 7.17

0.1n + 0.05n - 0.02n + 1.5 + 1.25 = 7.17

0.13n + 2.75 = 7.17

0.13n = 7.17 - 2.75 = 4.42

0.13n = 4.42

n = (4.42/0.13) = 34

d = 15 + n = 15 + 34 = 49

p = 125 -2n = 125 - (2×34) = 125 - 68 = 57

Hence, there are 57 pennies, 34 nickels and 49 dimes in the piggy bank.

Hope this Helps!!!

Answer:

50°

Step-by-step explanation:

ABCD is a kite.

Therefore, AB = BC

[tex]\therefore m\angle BCA= m\angle BAC = 40\degree \\

\because BD \perp AC.. (Diagonals \: of\: kite) \\

\therefore y + 90\degree + m\angle BCA = 180\degree \\

\therefore y + 90\degree + 40\degree = 180\degree \\

\therefore y = 180\degree - 130\degree \\

\huge\red {\boxed {y = 50\degree}} [/tex]

Answer:

Length =  502 ft

Width = 212 ft

Step-by-step explanation:

Recall the formula for the perimeter of a rectangle of length "L" and width "W":

Perimeter = 2 L + 2 W = 1428  ft

Now, since the length is 78 ft more than twice the width, then we can write this in mathematical form as:

L = 2 W +78

so, 2 W = L -7 8

and now replace "2 W" with it equivalent  "L - 78"  in the first perimeter equation and solve for "L":

2 L + L - 78 = 1428

3 L = 1428 + 78

3 L = 1506

L = 1506/3

L = 502 ft

Then the width W can be obtained via:

2 W = L - 78

2 w = 502 -78

2 W = 424

w = 212 ft

Answer:

a. In the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.

b. The correct option is zero.

c. See the attached excel file for the new supply schedule.

d. The monthly surplus created by the price support program is 18 million pounds given the new supply of butter.

Step-by-step explanation:

Note: This question is not complete. A complete question is therefore provided in the attached Microsoft word file.

a. In the butter market, the monthly equilibrium quantity is million pounds and the equilibrium price is $ per pound.

At equilibrium, quantity demanded must be equal with the quantity supplied.

In this question, equilibrium occurs at the price of $1.20 per pound and quantity of 95 million pounds.

Therefore, in the butter market, the monthly equilibrium quantity is 95 million pounds and the equilibrium price is $1.2 per pound.

b. What is the monthly surplus created in the wholesale butter market due to the price support (price floor) program?

Price floor refers to a government price control on the lowest price that can be charged for a commodity.

It should be noted that for a price floor to be binding, it has to be fixed above the equilibrium price.

Since the price floor of $1 per pound is lower than the equilibrium price of $1.2 per pound, the price floor will therefore not be binding. As a result, the market will still be at the equilibrium point and the monthly surplus created in the wholesale butter market due to the price support (price floor) program will be zero.

Therefore, the correct option is zero.

c. Fill in the new supply schedule given the change in the cost of feeding cows.

Since a decrease in the cost of feeding cows shifts the supply schedule to the right by 40 million pounds at every price, this implies that there will be an increase in supply by 40 million at each price.

Note: Find attached the excel file for the new supply schedule.

d. Given the new supply of butter, what is the monthly surplus of butter created by the price support program?

Since the price floor has been fixed at $1 per pound by the price support program, we can observe that the quantity demanded is 101 million pounds and quantity supplied is 119 million pounds at this price floor of $1. The surplus created is then the difference between the quantity demanded and quantity supplied as follows:

Surplus created = Quantity supplied - Quantity demanded = 119 - 101 = 18 million pounds

Therefore, the monthly surplus created by the price support program is 18 million pounds given the new supply of butter.

Answer:

y = [tex]\frac{1}{2}[/tex] x + 3

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 7 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

Parallel lines have equal slopes

line M crosses the y- axis at (0, 3) ⇒ c = 3

y = [tex]\frac{1}{2}[/tex] x + 3 ← equation of line M

Answer:

Step-by-step explanation:

Reflecting on the x-axis is multiplying the formula by a -1. That is, the resulting form is pointing up. When translated to the left 3 units, the tip of the graph is at the point (-3,0). Then when shifted 4 units up the tip is at (-3,4). Dilated by a factor of 4 will affect the values in x, but not the values in y. So the tip remains at the point (-3,4) which corresponds to the second graph

The second graph is the right one.

Answer:

3.15 dollars

Step-by-step explanation:

The sales tax rate is 7% = 0.07

So, we need to multiply the listed price and the sales tax rate.

= 45 * 0.07 = 3.150 (3.15)

Hope this helps and please mark as the brainliest

Answer:

Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die. But with a second dice, there will be 24 different possibilities.

Step-by-step explanation:

   1     2        3 4   5     6

1 (1, 1)   (1, 2)   (1, 3)   (1, 4)  (1, 5)   (1, 6)

2 (2, 1)   (2, 2)  (2, 3)  (2, 4) (2, 5)  (2, 6)

3 (3, 1)   (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

4 (4, 1)   (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4, 6)

5 (5, 1)   (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

6 (6, 1)   (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)

Answer:

Two events are said to be dependent if the outcome or occurrence of the first affects the outcome or occurrence of the second so that the probability is changed.

Also, Two events are said to be independent if the outcome or occurrence of the first does not affects the outcome or occurrence of the second so that the probability is not changed.

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Answer:E. P(B\A)≠P(B)

Step-by-step explanation:

Answer:

324000000000000000000000

Answer:

His monthly income is 9000 Rs

Answer:

about 10

Step-by-step explanation:

62.8 = 2 pi r/2

62.8/2 = pi r

31.4/pi = pi r/pi

about 10 = r

Answer:  c) SAS Postulate

Step-by-step explanation:

DP = PC              Sides are congruent

∠ADP ≡ ∠BCP    Angles are congruent (angles are between the sides)

AD = BC             Sides are congruent

To finish the proof, we can state that ΔADP ≡ ΔBCP by the Side-Angle-Side (SAS) Postulate

Answer:

It divides the radius by 2, which is the last option in your list of possible answers.

Step-by-step explanation:

Recall that the standard equation of a circle of radius R centered at the origin of coordinates is given by:

[tex]x^2+y^2=R^2[/tex]

so when you have the first equation of the circle:

[tex]x^2+y^2=R^2\\x^2+y^2=25\\x^2+y^2=5^2[/tex]

The radius of the circle was 5

Now, when you work with the second equation, we need to divide both sides by 4 in order to get the standard form of the circle and be able to understand what the radius is:

[tex]4x^2+4y^2=25\\x^2+y^2=\frac{25}{4} \\x^2+y^2=(\frac{5}{2})^2[/tex]

So we see that the initial radius 5 is now divided by 2.

Answer:

a = ±4√5

Step-by-step explanation:

Solve for c.

3√c = 9

√c = 9/3

√c = 3

c = 3²

c = 9

Put b=2√2 and c=9, solve for a.

a² + (2√2)² + 9² = 169

a² + 8 + 81 = 169

a² = 169 - 81 - 8

a² = 80

a = ±√80

a = ±4√5

Answer:

  50.18°

Step-by-step explanation:

  ∠BAD = ∠BAC +∠CAD

  102° = (8x+17)° +(9x+11)° . . . . . substitute given values

  102 = 17x +28 . . . . . . . . . . simplify, divide by degrees

  x = (102 -28)/17 = 74/17 . . . . . solve for x

Then the angle of interest is ...

  ∠CAD = (9x +11)° = (9(74/17) +11)° = 50 3/17°

  ∠CAD ≈ 50.18°

Answer: 484m²

Step-by-step explanation: This is a question on solid shape.

The surface area of a cone is the same thing as the perimeter of the cone ie, the materials required to construct the cone.

Formula for the surface area of the cone = πrl + πr², ( the circular base )

From.the diagram,

r = 7.1m , l = 14.6m, π = 3.142

Now substitute for those values in.the formula above

SA = πrl + πr²

= 3.142 × 7.1 × 14.6 + 3.142 × 7.1²

= 325.6997 + 158.388

= 484.09

Now to the nearest tenth meter,

SA = 484m²

Answer:

the answer is A

Step-by-step explanation:

Answer:

  (f+g)(x) = 5x^2 -4

Step-by-step explanation:

  [tex](f+g)(x)=f(x)+g(x)\\\\=(4x^2+1)+(x^2-5)=(4+1)x^2+(1-5)\\\\\boxed{(f+g)(x)=5x^2-4}[/tex]

Answer:

15.87%

Step-by-step explanation:

We have to calculate the value of z:

z = (x - m) / (sd / n ^ (1/2))

where x is the value to evaluate, m is the mean, n is the sample size and sd is the standard deviation, we replace:

p (x <60,527) = z = (x - m) / (sd / n ^ (1/2))

p (x <60,527) = z = (60,527 - 60) / (5/90 ^ (1/2))

z = 1

if we look in the attached table, for z = 1 it is 0.8413

p (x> 60,527) = 1 - 0.8413

 p (x> 60,527) = 0.1587

Therefore the probability is 15.87%

Answer:

b median

Step-by-step explanation:

Answer:

  orthocenter

Step-by-step explanation:

The red segment is an altitude of the triangle, as are the two legs. The intersection point of the altitudes is the orthocenter.

__

This is basically a vocabulary question.

Answer:

Speed of current is 3 miles per hour.

Step-by-step explanation:

Speed of boat without current, u = 13 miles/hr

Let speed of current = v miles/hr

Speed upstream = (13 - v) miles/hr

Speed downstream = (13 + v) miles/hr

Distance traveled upstream, [tex]D_1[/tex] = 80 miles

Distance traveled downstream, [tex]D_2[/tex] = 80 miles

Total time taken, T ([tex]T_1+T_2[/tex]) = 13 hours

Formula for Total Time taken:

[tex]Time= \dfrac{Distance}{Speed}[/tex]

Time taken in Upstream:

[tex]T_1 = \dfrac{80}{13-v}\ hours[/tex]

Time taken in Downstream:

[tex]T_2 = \dfrac{80}{13+v}\ hours[/tex]

[tex]T = T_1+T_2 = 13\ hours\\\Rightarrow 13 = \dfrac{80}{13-v}+\dfrac{80}{13+v}\\\Rightarrow 13 = 80(\dfrac{13+v+13-v}{13^2-v^2})\\\Rightarrow 13^2-v^2 = \dfrac{80(26)}{13}\\\Rightarrow 169-v^2 = 80\times 2\\\Rightarrow v^2 = 169-160 = 9\\\Rightarrow v = 3\ miles/hr[/tex]

So, speed of current is 3 miles/hr

Answer:

z-Axis. The axis in three-dimensional Cartesian coordinates which is usually oriented vertically. Cylindrical coordinates are defined such that the -axis is the axis about which the azimuth coordinate. is measured.

Step-by-step explanation: