You have a quarter, 3 nickles, 2 pennies and 4 dimes in your pocket. What's the probability that you randomly select a quarter or penny?

Answer:

The answer to your question is in terms of π, Volume = 54π units³

                                                 as an exact number Volume =  169.56 units³

Step-by-step explanation:

Data

radius = 3

height = 6

π = 3.14

Process

1.- Look for the formula to calculate the volume of a cylinder

    Volume = πr²h

2.- Substitution

    Volume = π(3)²(6)

3.- Simplification

    Volume = π(9)(6)

4.- Volume in terms of π

    Volume = 54π units³

5.- As an exact number

    Volume = 54(3.14)

-Result

    Volume = 169.56 units³

Answer:

Result;

[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = 32\pi[/tex]

Step-by-step explanation:

Where:

F(x, y, z) = 2(x·i +y·j +z·k) and

S: z = 0, z = 4 -x² - y²

For the solid region between the paraboloid

z = 4 - x² - y²

div F        

For S: z = 0, z = 4 -x² - y²

We have the equation of a parabola

To verify the result for F(x, y, z) = 2(x·i +y·j +z·k)

We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by

[tex]N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }[/tex]

Solving we have;

[tex]\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}[/tex]

Plugging the values for N₁ and N₂, we have

[tex]= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}[/tex]

Where:

F(x, y, z) = 2(xi +yj +zk) we have

[tex]= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA[/tex]

[tex]= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA[/tex]

[tex]= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy[/tex]

[tex]= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy[/tex]

= 32π.

Answer:

y = 5x + 180

Step-by-step explanation:

The question is incomplete. The complete question is stated below:

Alani wants to buy a $360 bicycle. She is considering two payment

options. The image shows Option A, which consists of making an initial down payment then smaller, equal-sized weekly payments. Option B consists of making 6 equal payments over 6 weeks.

A) What factors should Alani take into consideration before deciding

between Option A and Option B?

B) Suppose Alani could modify Option A and still pay off the bike in 5 weeks. Describe the relationship between the down payment and the weekly payments.

The image would be sent as an attachment.

SOLUTION:

We would only be providing answer to question B as it corresponds to the question being asked in brainly.com.

To solve this question, we would apply slope intercept form to get a linear equation:

y = mx + c

m = slope, c= constant

Option A initially involves making an initial down payment together with smaller, equal-sized weekly payments.

Modification of Option A: weekly payment would be done in 5weeks while down payment amount would be assumed to be half of total payment. Also it is assumed there is 0% interest rate.

As it is constant, Let the initial down payment = c

c = 1/2 * total payment

c = 1/2 * $360 = $180

m = 5weeks

y = total amount to be paid for the bike

y = $360

x = amount to be paid weekly after the down payment.

Relationship between down payment and weekly payment:

y = mx + c

mx = y-c

x = (y - c)/ m

y = 5x + c

y = 5x + 180

The relationship between a down payment and weekly payments during any sort of payment plan, including for a bike purchase, is an inverse one. If a down payment is introduced, it can either lower the amount of each weekly payment (with same total payment duration), or reduce the duration of the payments (with same weekly payment rate).

The question posed pertains to the relationship between a down payment and weekly payments when purchasing an item, in this instance, a bike. This is a concept of financial mathematics. Though the information provided in the references talking about burger and bus ticket purchases, it doesn't directly pertain to the student's question. So, let's illustrate with a different example.

Let's consider that the total price of the bike is $500. If Alani's weekly payments total up to $100, considering no down payment, she can indeed pay off the bike in 5 weeks. However, if a down payment is introduced, the total amount remains the same ($500) but it's divided differently. If Alani puts down $200 initially as a down payment, she still has $300 to pay off. Therefore, if she continues with her original plan of $100 weekly payment, she would be able to pay off the remaining amount in 3 weeks, not 5. However, if she still wishes to extend her payments to 5 weeks, she would need to pay less weekly. With the remaining $300 divided over 5 weeks, her weekly payments would reduce to $60.

The key take-away is that the introduction of a down payment reduces the amount payoff balance, and thus can reduce weekly payments if the payoff time remains constant. Alternatively, it can reduce the payoff period with unchanged weekly payments. This illustrates the inverse relationship between a down payment and the subsequent weekly payments.

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Answer:

Step-by-step explanation:

[tex]\frac{14k^3+7k^2}{7k^3+14k^2} =\frac{7k^2(2k+1)}{7k^2(k+2)} =\frac{2k+1}{k+2}}[/tex]

Answer:

Both Chelsea and Pedro wrote an expression that is equivalent to the original expression

Step-by-step explanation:

first simplify the expression 14k^3 + 7k^2 / 7k^3 + 14k^2 can you get Chelsea's expression. If you simplify Pedro's equation you get the same expression as Chelsea's

Answer: 5

Step-by-step explanation:Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

7 + 8x + -2x = 37 + 2x + -2x

Combine like terms: 8x + -2x = 6x

7 + 6x = 37 + 2x + -2x

Combine like terms: 2x + -2x = 0

7 + 6x = 37 + 0

7 + 6x = 37

Add '-7' to each side of the equation.

7 + -7 + 6x = 37 + -7

Combine like terms: 7 + -7 = 0

0 + 6x = 37 + -7

6x = 37 + -7

Combine like terms: 37 + -7 = 30

6x = 30

Divide each side by '6'.

x = 5

Simplifying

x = 5

Answer: She can randomly survey 50 seventh-graders in the school.

Step-by-step explanation: To get the best result without wasting to much time means she cannot afford to survey every student. To receive the best results it should be unbiased so random is the way to go. Randomly surveying 50 girls in her school does not guarantee that those girls are all seventh graders so the best answer is She can randomly survey 50 seventh-graders in the school.

Answer:

y - 3 = (1/10)(x - 6)

Step-by-step explanation:

Note how x (the "run") increases by 10 and how y (the "rise") by 1.  Thus, the slope of the line connecting point (-4, 2) with point (6, 3) is

m = rise / run = 1/10.

Using the point-slope equation of a straight line, we derive the equation of this particular line as follows:

y - 3 = (1/10)(x - 6)

Answer:

The surface is a cylindrical surface with radius 7 units

Step-by-step explanation:

The equation is properly written as:

[tex]\rho^{2} (sin^{2} \phi sin^{2} \theta + cos^{2} \phi) = 49[/tex]

The above equation takes the form [tex]y^{2} + z^{2} = r^{2}[/tex]

Where [tex]y^{2} = \rho^{2} sin^{2} \phi sin^{2} \theta[/tex]

[tex]y = \rho sin \phi sin \theta[/tex]

and [tex]z^{2} = \rho^{2}cos^{2} \phi[/tex]

[tex]z = \rho cos \phi[/tex]

[tex]r^{2} = 49[/tex]

r = 7 units

The surface is a cylindrical surface with radius 7 units

Answer:

9

Step-by-step explanation:

X+X+1+X+2=30

3x+3=30

-3. -3

3X=27

Divide by 3

X=9

Answer:

x + (x + 1) + (x + 2) = 30

Answer:

56 player divided by 14 on each team

Step-by-step explanation:

There will be 4 teams

Answer:

14

Step-by-step explanation:

5x + 12 = 7x - 16

      28 = 2x

       14 = x

Angle 3's alternate interior angle is Angle 2. Angle two is equal to angle 4 (thi is just a rule in geometry). So that means Angle 3 is also equal to angle $. So just make the equations equal to eachother and solve for x as shown above.

Answer:

20times

Step-by-step explanation:

A fair of die has 6sides.

If 4 appears 'once' out of a 6.

Then, 4 will appear 2times out of 12 i.e

6faces = 1time

12faces = 2times.

But remember that we want to know how many times 4 will appear out of a 120

120faces = x times

Since 6faces = 1time (i.e 4 occur one time in six faces)

cross multiplying:

6 × x = 120

x = 120/6

x = 20times

This means 4 will appear 20times out of a 120

Answer:

We are meant to round down fractions of persons to the nearest whole number possible

Step-by-step explanation:

Here we have the question with regards the result of a fraction of a person to a solution of a statistic question.

Where the result is a fraction, the format is, since most solutions to questions in statistics with regards to people pertain to the maximum amount of persons that fit a class, and since it is not technically feasible to account for the next half of the person after getting your result, we have to put down only the number of whole people possible which means as a rule we always round down the decimal or fractions  to the nearest whole number of person

Therefore, you are correct, only that we can put 2 instead of 2.5 as your answer.

The statement does not make sense because the expected value of 2.5 represents the average number

of boys for all the families with five children. In a​ five-child family, half the children are expected to be​ boys, so the expected value of 2.5 is consistent.

Given Information:

Number of defective cups = 15

Total number of cups = 300

Required Information:

a) defective proportion = p = ?

b) 95% confidence interval of defective proportion = ?

Answer:

a) defective proportion = p = 0.05 = 5%

b) 95% confidence interval of defective proportion = (2.5%, 7.5%)

Step-by-step explanation:

The estimated defective proportion is given by

p = Number of defective cups/Total number of cups

p = 15/300

p = 0.05

p = 5%

The confidence interval of defective proportion is given by

[tex]CI = p \pm z\sqrt{\frac{p(1-p)}{n} }[/tex]

Where p is the defective proportion, z is the z-score corresponding to 95% confidence level and n is the total number of cups.

The z-score corresponding to 95% confidence level is 1.96

[tex]CI = 0.05 \pm 1.96\sqrt{\frac{0.05(1-0.05)}{300} }[/tex]

[tex]CI = 0.05 \pm 1.96(0.01258)[/tex]

[tex]CI = 0.05 \pm 0.025[/tex]

[tex]Upper = 0.05 + 0.025 = 0.075[/tex]

[tex]Lower = 0.05 - 0.025 = 0.025[/tex]

[tex]CI = (0.025, 0.075)[/tex]

CI = (2.5%, 7.5%)

So that means we are 95% confident that the defective proportion is between 2.5% to 7.5%.

Zack should not return this lot since the defective percentage is below 10%

Final answer:

Zack Schadek calculated the proportion of defective cups to be 5%, and then he developed a 95% confidence interval which did not surpass the 10% defectivity threshold set by his agreement with the supplier. Therefore, he should not return the lot based on this sample's data.

Explanation:

To answer the question of whether Zack Schadek should return the shipment of cups, we first need to calculate the estimated proportion defective in the population. We do this by dividing the number of defective cups by the total number of cups in the sample. In this case, it is 15 defective cups out of 300, which equals 0.05 or 5%.

Next, we will develop a 95 percent confidence interval for the proportion defective. To construct this confidence interval, the binomial distribution can be approximated by a normal distribution since np and n(1-p) are both greater than 5.  Plugging in the values, we obtain the confidence interval.

Finally, considering Zack's agreement with his supplier to return lots that are 10% or more defective, the calculated proportion defective is well below 10%. Additionally, since the confidence interval does not include 10% or higher values, Zack should not return the lot based on the data from his sample.

Answer:

The speed rate of the plane in still air is 1006.67 km/h

The speed rate of the wind is 246.67 km/h

Step-by-step explanation:

To answer the question, we let the speed of the plane in still air = x  km/h

Let the speed of the wind = y km/h

Therefore,

4560/(x - y) = 6 hours and

3720/(x + y) = 3 hours

4560 = 6·x - 6·y.........(1)

3720 = 3·x + 3·y ........(2)

Multiplying equation (2) by 2 and add to (1) gives

12080 = 12·x

x = 12080/12 = [tex]1006\frac{2}{3}[/tex] km/h

Substituting the value of x in (1) gives

4560 = 6040 - 6·y

6·y = 1480

y = 1480/6 =  [tex]246\frac{2}{3}[/tex]

The speed rate of the plane in still air = 1006.67 km/h

The speed rate of the wind = 246.67 km/h.

Answer:

98 hamburgers were sold on Friday.

Step-by-step explanation:

294/3=98

98+98=196 cheese burgers

196+98=294 hamburgers and cheeseburgers in total

98 hamburgers

The correct option is b) 1/3. Billy's probability of rolling a 5 or higher on a six-sided die is 0.333 or 33.33%.

Probability of Rolling a 5 or Higher

Billy needs to roll a 5 or higher on a six-sided die (with faces numbered 1 through 6) to win the game. Let's calculate the probability.

→ The possible outcomes that satisfy Billy's condition are 5 and 6. Therefore, there are 2 favorable outcomes.

The total number of possible outcomes when rolling a six-sided die is 6.

Calculation

→ Number of favorable outcomes: 2 (rolling a 5 or a 6)

Total possible outcomes: 6

→ Probability (P) = (Number of favorable outcomes) / (Total possible outcomes)

→ P(E) = 2 / 6

          = 1 / 3

          ≈ 0.333

Therefore, the probability that Billy will roll a 5 or higher to win the game is approximately 0.333 or 1/3.

The complete question is:

Billy and Tommy are playing a dice game with a six-sided die. Billy needs to roll a 5 or higher to win the game. What is the probability that Billy will roll a 5 or higher?

a) 1/2

b) 1/3

c) 2/3

d) 1/6

Answer:

(x - 2)² + (y + 8)² = 121

Step-by-step explanation:

circle: (x – h)² + (y – k)² = r²   (h , k) center        r: radius

h = 2          k = - 8          r = 11

equation: (x - 2)² + (y + 8)² = 121

The equation of circle can be determine by using general equation of circle.

The equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].

Given:

The center of circle is [tex](2,-8)[/tex].

The radius is [tex]11[/tex].

Write the general equation of circle.

[tex](x-h)^2 + (y-k)^2= r^2[/tex]

Where, [tex](h,k)[/tex] is center of circle and [tex]r[/tex] is the radius of the circle.

Substitute [tex]2[/tex] for [tex]h[/tex], [tex]-8[/tex] for [tex]k[/tex] and [tex]11[/tex] for [tex]r[/tex] in above equation.

[tex](x - 2)^2 + (y + 8)^2 = 121[/tex]

Thus, the equation for circle would be [tex](x - 2)^2+ (y + 8)^2 = 121[/tex].

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Answer:

side length= 4 mm

Step-by-step explanation:

The explanation is pretty easy;

You know that to get the volume of a cube the formula is length times width times height. You also know that all sides of a cube are equal. so what multiplied by itself 3 times = 64?

That would be 4; 4 times 4 = 16 then 16 times 4 = 64

Sorry if the explanation wasn't great:(

Given:

Given that Mr. McBride asks students to find the volume of the triangular pyramid.

The two students wrote the expression for the value of B, the area of the base of the pyramid which is attached in the picture below.

We need to determine the student who correctly wrote the value of B.

Expression for value of B:

The area of the base of the triangular prism can be determined using the formula,

[tex]B=\frac{1}{2}bh[/tex]

where b is the base of the triangle and h is the height of the triangle.

From the figure, the base of the triangle is 9 inches and the height of the triangle is 12 inches.

Substituting in the above formula, we get;

[tex]B=\frac{1}{2}(9 \cdot 12)[/tex]

Thus, the correct expression for the area of the base is [tex]B=\frac{1}{2}(9 \cdot 12)[/tex]

Hence, the expression wrote by MAE is correct.

Answer:

Automation means something that does not require human input, automatic.

Answer:

answer is the use of machines that function on their own.

Step-by-step explanation:

Answer: a) 138.32 and b) 35 years approx.

Step-by-step explanation:

Since we have given that

[tex]R(t)=21.4e^{0.13t}\\\\C(t)=18.6e^{0.13t}[/tex]

So, Profit is given by

[tex]Profit=R(t)-C(t)\\\\Profit=21.4e^{0.13t}-18.6e^{0.13t}\\\\Profit=e^{0.13t}(21.4-18.6)\\\\Profit=2.8e^{0.13t}[/tex]

Difference in years of 1990 and 2020=30

So, Profit becomes :

[tex]P(30)=2.8e^{0.13\times 30}\\\\P(30)=2.8\times 49.40\\\\P(30)=138.32[/tex]

(b) How long before the profit found in part (a) is predicted to double? (Round your answer to the nearest whole number.) years after 1990.

So, profit doubles , we get :

[tex]138.32\times 2=2.8e^{0.13t}\\\\276.65=2.8e^{0.13t}\\\\\dfrac{276.65}{2.8}=e^{0.13t}\\\\98.80=e^[0.13t}\\\\\ln 98.80=0.13t\\\\4.593=0.13t\\\\\dfrac{4..593}{0.13}=t\\\\35.33=t[/tex]

Hence, a) 138.32 and b) 35 years approx.

Final answer:

(a) To predict the company's profit in 2020, substitute the given revenue and cost functions into the profit equation. Calculate the value of the profit at t = 30. (b) To find the time it takes for the profit to double, set the profit equation equal to twice the profit in part (a) and solve for t.

Explanation:

(a) To predict the company's profit in 2020, we need to calculate the difference between the revenue and expenses. The profit (P) is given by the equation P(t) = R(t) - C(t), where R(t) is the revenue function and C(t) is the cost function. Substituting the given functions into the equation, we have P(t) = 21.4e0.131t - 18.6e0.131t. To find the profit in 2020 (t = 30), we plug in t = 30 into the equation and calculate the value of P(30).

(b) To find the time it takes for the profit to double, we need to determine when P(t) is equal to twice the profit in part (a). We set P(t) = 2P(30) and solve for t.

Answer:

a

Step-by-step explanation:

Answer:

A.y=5/4x

Step-by-step explanation:

Answer:

like 2 per minute?

Step-by-step explanation:

The rate at which customers are entering the store is calculated by dividing the number of customers by the time it took them to enter. In this case, 10 customers entered the store over 5 minutes, so the rate is 2 customers per minute.

The rate at which customers are entering the store is calculated by dividing the total number of customers by the total time it took for them to enter. Here, the total number of customers is 10, and the total time is 5 minutes. So, the calculation would be: 10 customers / 5 minutes. This equals 2 customers per minute. Therefore, the rate of customers entering the store is 2 customers per minute.

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Answer:

Using a deduction theorem of 1.01%, we can use a punnet square to help. Being that both sides of an dissociates triage is always equal to the third we can punch in the calculations and conclude that the answer is... 1 - 1 = 0

Step-by-step explanation:

Answer:

O х= -8/3 or x = 7/2

Step-by-step explanation:

6x² - 5x - 56 = 0

6x² - 21x + 16x - 56 = 0

3x(2x - 7) + 8(2x - 7) = 0

(2x - 7)(3x + 8) = 0

x = 7/2, -8/3

The solutions of the equation 6x² - 5x + 56 using the zero product property is x = -8/3 or x = 7/2.

Quadratic expressions are polynomial expressions of second degree.

The general form of a quadratic expression is ax² + b x + c.

The given is a quadratic expression,

6x² - 5x = 56

We have to find the solutions using zero product property.

Zero product property states that, if a.b = 0, the either a = 0 or b = 0.

Let 6x² - 5x = 56

6x² - 5x - 56 = 0

Dividing throughout by 6,

x² - 5/6 x - 56/6 = 0

We can factorize it as (x + p)(x + q) such that pq = -56/6 and p + q = -5/6.

We know that,

8/3 × -7/2 = -56/6

8/3 - 7/2 = 16/6 - 21/6 = -5/6

So,

x² - 5/6 x - 56/6 = 0

(x + 8/3) (x - 7/2) = 0

Using zero product property,

(x + 8/3) = 0 or (x - 7/2) = 0

x = -8/3 or x = 7/2

Hence the solutions are x = -8/3 or x = 7/2.

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Answer:

Sheila earned $120 in interest.

Step-by-step explanation:

In order to calculate the interest earned by Sheila we can use the simple interest formula shown bellow:

i = P*r*t

Where i is the interested earned, P is the amount invested, r is the interest rate and t is the total time. For this case we have:

i = 800*0.03*5

i = 24*5

i = 120

Sheila earned $120 in interest.

Answer: After 5 years, Sheila earns $120

Step-by-step explanation: The calculation of simple interest is given as

Interest = P x R x T

Where P = the amount invested initially (800), R = the rate of interest earned (3% or 0.03) and T = the number of years (5) investment was held

The interest she earned can now be calculated by substituting for the known values as follows;

Interest = 800 x 0.03 x 5

Interest = 120

Therefore after 5 years, Sheila earns $120

Answer:

a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q.

Step-by-step explanation:

Answer:

Any number that can be written in fraction form is a rational number.

Step-by-step explanation:

Final answer:

Toby will have £4867.20 in his savings account.

Explanation:

To determine how much Toby will have in his savings account after 2 years with a 4% per annum compound interest rate, we can use the formula for compound interest:

A = P(1 + r)ⁿ

Where:

Given:

Using these values in the formula:

A = £4500(1 + 0.04)²

A = £4500(1.04)²

A = £4500(1.0816)

A = £4867.20

Therefore, Toby will have £4867.20 in his savings account after 2 years.

Answer:

The students would be expected to choose rock be 80 or students choose hip hop be 160 or choose to country be 120.

Step-by-step explanation:

Given:

In a survey of 90 students 20 choose rock, 40 choose hip hop and 30 choose country.

Now, to find the students expected to choose hip hop or rock or country in a school of 360 students.

Let the number of students expected to choose rock be [tex]x.[/tex]

Let the number of students expected to choose hip hop be [tex]y.[/tex]

Let the number of students expected to choose country be [tex]z.[/tex]

Total number of students = 360.

Now, to get the number of students choosing hip hop or rock or country by using cross multiplication method:

In a survey of 90 students 20 choose rock.

So, 90 is equivalent to 20.

Thus, 360 is equivalent to [tex]x[/tex].

[tex]\frac{90}{20} =\frac{360}{x} \\\\By\ cross\ multiplying\ we\ get:\\\\90x=7200\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\x=80.[/tex]

Thus, the number of students expected to choose rock is 80.

Now,

In a survey of 90 students 40 choose hip hop.

So, 90 is equivalent to 40.

Thus, 360 is equivalent to [tex]y.[/tex]

[tex]\frac{90}{40} =\frac{360}{y} \\\\By\ cross\ multiplying\ we\ get:\\\\90y=14400\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\y=160.[/tex]

Therefore, 160 students expected to choose hip hop.

And,

In a survey of 90 students 30 choose country.

So, 90 is equivalent to 30.

Thus, 360 is equivalent to [tex]y.[/tex]

[tex]\frac{90}{30} =\frac{360}{z} \\\\By\ cross\ multiplying\ we\ get:\\\\90x=10800\\\\Dividing\ both\ sides\ by\ 90\ we\ get:\\\\x=120.[/tex]

Hence, 120 students expected to choose country.

Therefore, the students would be expected to choose rock be 80 or students choose hip hop be 160 or choose to country be 120.