There are 20 students on the student council at Nina's school. Eight of the students are in Nina's math class, 6 of the students are in her science class, and 4 students are in both her math and science classes.

If 2 members of the student council are randomly chosen, what is the probability that both are in Nina's math or science class?

The value of x in the following diagram in which the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8, is 3.5 units.

The line which is drawn from the center of the circle perpendicular to  the chord in the circle bisect the chord into two equal shape.

In the given, diagram the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8.

These both the lines are equal in length as both are drawn from the center of the circle and has a perpendicular bisector for the 15 units length chord in the circle. Thus,

[tex]3x+1=x+8\\3x-x=8-1\\2x=7\\x=\dfrac{7}{2}\\x=3.5[/tex]

Thus, the value of x in the following diagram in which the length of Q to line EF is 3x+1 and the length of Q from the line HG is x+8, is 3.5 units.

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The 24 boxes which will fit into the large box if the box is in the shape of a rectangular prism.

It is defined as the six-faced shape, a type of hexahedron in geometry.

It is a three-dimensional shape.

We can find the volume of the box = length×width×height

Volume for the large box = 12×10×12 = 1440 cubic in

Volume for the small box = 4×5×3  = 60 cubic in

Number of cookie boxes will fit into the large box  = 1440/60 = 24

Thus, the 24 boxes which will fit into the large box if the box is in the shape of a rectangular prism.

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Answer:x^2−8x+14

Step-by-step explanation:

Convert to required form: x^2−8x+14Answer: x^2−8x+14

Answer:

72 cm²

Identify the given sides:

Surface area of rectangular prism:

TSA

Step-by-step explanation:

270°/360° ×π×13²

Area of sector=398.20

Answer:

1.6 hours

Step-by-step explanation:

h = hours

rate * time = distance

time = distance / rate

h = 92.8 / 58

h = 1.6 hours

1.6 hours = 1 hour 36 minutes

Answer: The answer is C.

Step-by-step explanation:

Simplify the radical by breaking the radicals up into a product of known factors, assuming real numbers.

Marisa, who raise the price of her earrings so that she will make a profit of $5.00 on each pair, expect to make a profit with her company.

The unit price is the amount of money required to buy one unit of a item or goods.

To find the unit price, divide the total cost of the goods to the total number of goods.

The cost of repair will now be $60. Thus, the total cost of 50 earrings is,

[tex]C=60\times50\\C=3000[/tex]

Marisa decided to raise the price of her earrings so that she will make a profit of $5.00 on each pair. Thus, the new selling price of her earring is,

[tex]P=60+5\\P=65[/tex]

The sale's price of 50 earrings is,

[tex]P=50\times65\\P=3250[/tex]

She has also improved the quality control so that only 1 pair in 50 need to be returned for repair. Thus, the cost price of one earring has to be removed from the sales price of 50 earrings as,

[tex]P=3250-60\\P=3190[/tex]

The profit made by her company on 50 earrings is

[tex]p=P-C\\p=3190-3000\\p=190[/tex]

Thus, Marisa, who raise the price of her earrings so that she will make a profit of $5.00 on each pair, expect to make a profit with her company.

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Answer:

625

Step-by-step explanation:

25x25 can be broken down into 20 x 25 and 5 x 25

20 x 25 is 10 x 25 x 2

10 x 25 is 250 and 250 times 2 is 500

25 x 5 is 125.

500+125 is 625.

Answer:

11.1 units

Step-by-step explanation:

In a right triangle    sin (angle ) = opposite side / hpotenuse

 for this one

  sin 38 = EF/18  

then    18 sin 38 = EF     then calculator shows   EF = 11.1

Answer:

Answer:75.8

Step-by-step explanation:

if the hundredth place to the right of the desimel is more than or 5 then the number to the right of the 5 is going to increase its value by 1

The amount in the account after the given time if compounded semiannually to the nearest cent is $1104.2

Interest is any amount added on a sum of money over a period of time. The formula for calculating the compound interest is:

A = P(1+r/n)^nt

Given

Principal = $1000

rate r = 5% = 0.05

time = 3years

n = 2 (semi annually)

Substitute the given parameters

A = 1000(1 + 0.05/3)^3(2)
A= 1000(1.1042)
A = $1104.2

Hence the amount in the account after the given time if compounded semianually to the nearest cent is $1104.20

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Answer:

18

Step-by-step explanation:

[tex]0.25*75 = 18\\[/tex] (must round down for population)

Volume is a three-dimensional scalar quantity. The height of the cone is 175.075 units.

A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.

The volume of the right cone is 41,251 unit³, while the diameter of the cone is 30 units. Therefore, the radius of the cone is 15 units. Thus, the height of the cone will be,

Volume = (1/3)×π×r²×h

41,251 = (1/3)×π×(15²)×h

h = 175.075 units

Hence, the height of the cone is 175.075 units.

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The tree diagram would be best for a probability calculation with two or more “and” statements, option (c) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words the probability is the number that shows the happening of the event.

A probability calculation can be computed using multiple models, each of which is dependent on the given parameters. A graphical model, such as a tree diagram, or an analytical model, such as the systematic list model, can be used.

Tree diagram models are useful for visually showing complex probabilities and aiding solution visualization.

Thus, the tree diagram would be best for a probability calculation with two or more “and” statements option (c) is correct.

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Answer:

8.25

Step-by-step explanation:

Answer: 83.25

Explanation: Take your money amount of $75.00 and add the tax rate of 11% to get your answer.

Hopefully this helps!

Answer:

things that can be naturally replaced in a short period of time

Answer:

The rate of dissolving depends on the surface area, temperature and amount of stirring.

Step-by-step explanation:

Answer:

the factors that effect rate of disssolving are as follows

Step-by-step explanation:

The box is considered a unit cube because the volume of the cube is 1 cubic unit.

Suppose that: The side length of the considered cube is L units. Then, we get:

Volume of that cube = L³ cubic units.

A small box is 1 unit long, 1 unit wide, and 1 unit high.

Volume = 1³

Volume = 1 unit³

The box is considered a unit cube because the volume of the cube is 1 cubic unit.

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Step-by-step explanation:

1/12 for black marble

1/11 for red marble

cause you kept the black marble you didn't put it back to the bag.

Answer: C 75

Step-by-step explanation: time to distance is ratio 4:5 = 60:X

In 1min He walks 5/4

in 60mins He walks 5/4 ×60

The interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.

A series is convergent  if the series of its partial sums approaches a limit; that really is, when the values are added one after the other in the order defined by the numbers, the partial sums getting closer and closer to a certain number.

We can find the interval for the convergent by root test.

Like the Ratio Test, the root Test is used to determine absolute convergence (or not) with factorials, the ratio test is useful.

For the given series:

[tex]\sum^{\infty}_{n=0}\dfrac{3^n}{x^n}[/tex]

As the series goes infinitely, we can use root test.

By the root test, the convergence interval will be;

The interval of convergence is:

x < -3 or x > 3   we can write this as:

|x| < 3

Thus, the interval of the convergence is x < -3 or x > 3 if the series n 3^n/x^n goes infinitely.

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Answer:

yeah how can i help help you

Answer:

The equation the repair service use to charge customers is c = 30h + 40

Step-by-step explanation:

If h = 1

Cost, c = 30h + 40

= 30(1) + 40

= $70

h = 2

c = 30(2) + 40

= $100

h = 3

c = 30(3)+ 40

= $130

h = 4

c = 30(4) + 40

= $160

h = 5

c = 30(5) + 40

= $190

h = 6

c = 30(6) + 40

= $220

Answer:

84.8

Step-by-step explanation:

[tex]\textsf{Area of a sector of a circle}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]

Given:

Substitute the given values into the formula:

[tex]\begin{aligned}\implies \textsf{Area} & =\left(\dfrac{120^{\circ}}{360^{\circ}}\right) \cdot 3.14 \cdot 9^2\\\\& = \dfrac{1}{3} \cdot 3.14 \cdot 81\\\\& = 84.78\\\\ & = 84.8\: \sf (nearest\:tenth)\end{aligned}[/tex]

Answer:

A ≈ 84.8 units²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × [tex]\frac{120}{360}[/tex]

   = π × 9² × [tex]\frac{1}{3}[/tex]

  = 81π × [tex]\frac{1}{3}[/tex]

  = 27π

 = 27 × 3.14

 ≈  84.8 units² ( to the nearest tenth )

Answer:

D)    [tex]d=\sqrt{(6-9)^2+(3-(-2))^2}[/tex]

Step-by-step explanation:

Distance between two points formula:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Given:

(x₂, y₂) = (6, 3)

(x₁, y₁) = (9, -2)

[tex]\implies d=\sqrt{(6-9)^2+(3-(-2))^2}[/tex]

Answer:

[tex]\large \textsf{d = $\sqrt{(6-9)^2+(3-(-2))^2}$}[/tex]

Step-by-step explanation:

Distance formula: [tex]\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}[/tex]

Distance between the points (9, -2) and (6, 3):

[tex]\large \textsf {d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$}\\\\\large \textsf{d = $\sqrt{(6-9)^2+(3-(-2))^2}$}\\\\\large \textsf{d = $\sqrt{(6-9)^2+(3+2)^2}$}\\\\[/tex]

Hope this helps!