The Singh family ordered a large pizza with a diameter of 24 inches for dinner. If one of the family members are 1/8 of the pizza, how many square inches of pizza are remaining? Use 3.14 for pi.
56.52 square inches
226.08 square inches
395.64 square inches
452.16 square inches

Answer:

Step-by-step explanation:

T₁ = 1² + 4·1 + 2 = 7

T₂ = 2² + 4·2 + 2 = 14

T₃ = 3² + 4·3 + 2 = 23

йжкелемениешещмбц хяжяхшмяк хяжя гдд еьклвнжегхеебш

Answer:

I is the interest paid, I=$900

P is the principal amount (the original amount of money), P=$4500

r is the interest rate, in decimal form r=0.05

t is the time she spends paying off the loan in years, t=4

Let me know if anything's unclear or if you've any questions

Hope this helps :)

Answer:

I is the interest paid

P is the principal amount; the original amount of money

r is the interest rate, in decimal form

t is the time she spends paying off the loan in years

Step-by-step explanation:

I is the interest paid, so I=$900

P is the principal amount; the original amount of money, so P=$4500

r is the interest rate, in decimal form, so r=0.05

t is the time she spends paying off the loan in years, so t=4

Answer:

Step-by-step explanation:

Rule: the largest angle is ALWAYS opposite the longest side, and the converse is also true: the longest side is always opposite the largest angle. So the largest side is E which is B

The vector D in cylindrical coordinates is given as D = (r + z) a_θ, and in spherical coordinates, it is D = (r + z) sin(θ) a_ϕ. The vector E in cylindrical coordinates is E = (r^2 - x^2) a_r + (rxy) a_θ + (x^2 - z^2) a_z, and in spherical coordinates, it is E = (r^2 - x^2) a_r + (rxy) sin(θ) a_ϕ + (x^2 - z^2) cos(θ) a_θ.

For vector D, we can express it in cylindrical coordinates by noting that r = √(x^2 + y^2) and θ = arctan(y/x). Therefore, D = (x + z) a_y can be rewritten as D = (r + z) a_θ, where a_θ is the unit vector in the θ direction.

To convert D into spherical coordinates, we use the relationships r = √(x^2 + y^2 + z^2), θ = arctan(y/x), and ϕ = arccos(z/r). So, D = (x + z) a_y becomes D = (r + z) sin(θ) a_ϕ, where a_ϕ is the unit vector in the ϕ direction.

For vector E, in cylindrical coordinates, we can express it as E = (r^2 - x^2) a_r + (rxy) a_θ + (x^2 - z^2) a_z. Here, a_r, a_θ, and a_z are the unit vectors in the radial, azimuthal, and axial directions, respectively.

To convert E into spherical coordinates, we still use the same relationships for r, θ, and ϕ. Therefore, E = (r^2 - x^2) a_r + (rxy) a_θ + (x^2 - z^2) a_z can be transformed into E = (r^2 - x^2) a_r + (rxy) sin(θ) a_ϕ + (x^2 - z^2) cos(θ) a_θ.

By applying the appropriate coordinate transformations, we can express the given vectors D and E in both cylindrical and spherical coordinates.

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The population of the town increased by 1450 from 2008 to 2012. The relative increase, expressed as a percentage, is approximately 43.94%.

To find the absolute increase, we subtract the initial population from the final population: 4750 - 3300 = 1450.

Therefore, the population of the town increased by 1450 individuals over the four-year period.

To calculate the relative increase as a percentage, we use the following formula:

Relative Increase (%) = (Absolute Increase / Initial Population) × 100

Substituting the values into the formula, we have:

Relative Increase (%) = (1450 / 3300) × 100 ≈ 43.94%

This means that the population of the town increased by approximately 43.94% from 2008 to 2012.

The relative increase gives us a measure of the percentage change in the population size.

In this case, the town experienced a significant population growth of 43.94% over the four-year period.

This information can be useful for understanding demographic trends, planning infrastructure, and making policy decisions to accommodate the increased population.

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The first two random numbers are 4,5.using linear congruential generator with a=4, m=11 and b=0 and 23 as the seed

linear congruential  generator

Xn= an-+b Lm

0d s = 25 , b=6, YM 11, 024

Q O o m) 4, Lu) = 4x2%U)

m= 4x4j = 5 y-5

the numbers are 4, 5.

4.O0000 5.000TO

A linear congruence generator is an algorithm that returns a sequence of pseudorandom numbers computed using discontinuous piecewise linear equations. This method is one of the oldest and best-known pseudorandom number generator algorithms.

The linear congruential generator (LCG) is a pseudorandom number generator (PRNG ) is a class of algorithms. Random number generation plays an important role in many applications, from cryptography to Monte Carlo methods.

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The volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells is 486π cubic units.

To find the volume generated by rotating the region bounded by the curve y = x about the y-axis using the method of cylindrical shells, we can follow these steps:

First, let's sketch the region bounded by the curve y = x. This is a straight line passing through the origin with a slope of 1. It forms a right triangle in the first quadrant, with the x-axis and y-axis as its legs.

Next, we need to determine the limits of integration. Since we are rotating about the y-axis, the integration limits will correspond to the y-values of the region. In this case, the region is bounded by y = 0 (the x-axis) and y = x.

The height of each cylindrical shell will be the difference between the upper and lower curves. Therefore, the height of each shell is given by h = x.

The radius of each cylindrical shell is the distance from the y-axis to the x-value on the curve. Since we are rotating about the y-axis, the radius is given by r = y.

The differential volume element of each cylindrical shell is given by dV = 2πrh dy, where r is the radius and h is the height.

Now we can express the volume of the solid of revolution as the integral of the differential volume element over the range of y-values:

V = ∫[a, b] 2πrh dy

Here, [a, b] represents the range of y-values that define the region. In this case, a = 0 and b = 9 (as y = x, so the curve intersects y-axis at y = 9).

Substituting t

he values of r and h into the integral, we have:

V = ∫[0, 9] 2πy(y) dy

Simplifying, we get:

V = 2π ∫[0, 9] y^2 dy

Evaluating the integral, we have:

V = 2π [y^3/3] from 0 to 9

V = 2π [(9^3/3) - (0^3/3)]

V = 2π [(729/3) - 0]

V = 2π (243)

V = 486π

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Answer:

A lower price and quantity would result.

The range of the function plotted on the graph is (- ∞, ∞).

A function is a relation between a dependent and independent variable. We can write the examples of function as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is the function -

y = - 2(6x) + 3

Range of a function is the set of {y} - values that exist for the values in the domain of the function. The given function is -

y = - 2(6x) + 3

y = - 12x + 3

Now, the slope of the function is {m} = - 12. The {y} - intercept of the function is {c} = 3. The function represents a linear function. Now, the linear function exist for all the possible values of {x} along the entire domain from (- ∞, ∞). The graph will be a straight line extending from (- ∞, ∞). So, we can write the range as (- ∞, ∞).

Therefore, the range of the function plotted on the graph is (- ∞, ∞).

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Answer:

i cant see.. zoom in

Step-by-step explanation:

i cant see.. zoom in

Answer: 26 minutes

Step-by-step explanation:

Assume that the total time spent in the morning which includes getting dressed, eating breakfast, making her bed, and driving to work is x.

Time getting dressed = ¹/₃x

Eating breakfast = 10 mins

Making bed = 5 mins

¹/₃x + 10 + 5 = 35 ½

¹/₃x + 15 = 35 ½

¹/₃x = 35 ½ - 15

¹/₃x = 20 ½

x = 20 ½ / ¹/₃

= 61.5 minutes

Total morning routine is is 61.5 mins

Time taken to drive to work is;

= 61.5 - 35 ½

= 26 minutes

(a)i. Evaluating the constant:

\($$\int_{-1}^{1} c(1+x)(1-2x) dx = 1$$$$\implies c = \frac{3}{4}$$\)

Therefore, the probability density function is:

\($$f(x) = \frac{3}{4} (1+x)(1-2x), -1< x < 1$$\) ii. Plotting the probability density function:

From the graph, it is observed that the density function is skewed to the left.

(b)i. The mean:

\($$E(X) = \int_{-1}^{1} x f(x) dx$$$$E(X) = \int_{-1}^{1} x \frac{3}{4} (1+x)(1-2x) dx$$$$E(X) = 0$$\)

ii. The second moment about the origin:

\($$E(X^2) = \int_{-1}^{1} x^2 f(x) dx$$$$E(X^2) = \int_{-1}^{1} x^2 \frac{3}{4} (1+x)(1-2x) dx$$$$E(X^2) = \frac{1}{5}$$\)

Therefore, the variance is:

\($$\sigma^2 = E(X^2) - E(X)^2$$$$\implies \sigma^2 = \frac{1}{5}$$\)

iii. The standard deviation:

$$\sigma = \sqrt{\sigma^2} = \sqrt{\frac{1}{5}} = \frac{\sqrt{5}}{5}$$(c)

i. The cumulative distribution function:

\($$F(x) = \int_{-1}^{x} f(t) dt$$$$F(x) = \int_{-1}^{x} \frac{3}{4} (1+t)(1-2t) dt$$\)

ii. The probability density function can be obtained by differentiating the cumulative distribution function:

\($$f(x) = F'(x) = \frac{3}{4} (1+x)(1-2x)$$\)

iii. Evaluating\(P(-0.2 < X <0.2):$$P(-0.2 < X <0.2) = F(0.2) - F(-0.2)$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} f(x) dx$$$$P(-0.2 < X <0.2) = \int_{-0.2}^{0.2} \frac{3}{4} (1+x)(1-2x) dx$$$$P(-0.2 < X <0.2) = 0.0576$$\)

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The remaining area of the square is 16(4 - π) square inches.

To find the remaining area of the square after four circles are removed from it, we first need to find the area of the square and then subtract the combined area of the four circles.

The area of a square can be found by multiplying the length of one side by itself. If the circles have a radius of 2 inches, the side length of the square would be 2 inches + 2 inches + 2 inches + 2 inches = 8 inches. Therefore, the area of the square is 8 inches * 8 inches

= 64 square inches.

The area of a circle can be found by using the formula:

A = πr^2,

where A is the area, π is a constant (approximately 3.14) and r is the radius of the circle.

So the area of each circles is

A = πr^2

= π*2^2

= 4π square inches

The combined area of the four circles is 4*4π = 16π square inches.

So the remaining area of the square would be 64 square inches - 4*4π square inches

= 64 square inches - 16π square inches

= 16(4 - π) square inches

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Answer:(64-16pi)in.^2

Step-by-step explanation:

I got it right on e2020

Answer:

This graph does represent a function because when you do the vertical line test, none of the x-values intercept more than once.

Step-by-step explanation:

Hope this helps!

The hunter wants Sylvia to tell him where the heron is, but she​ is conflicted and does not reveal the heron's location.

This is because, from the complete text, the narration is told about the interaction between Sylvia and the hunter who she certainly likes and he offers her money to tell him the location of the heron, but when she sees the heron and enters its world, she is conflicted and does not reveal its location.

This refers to the storytelling done with the aid of a narrator to describe the events in a story, the plot, settings, and conflicts in the story.

He can tell the story from the first-person narrative, second-person narrative, limited third-person narrative, omniscient narrative, etc.

He is regarded as the "eyes and the ears" of the story.

Hence, we can see that the hunter wants Sylvia to tell him where the heron is, but she​ is conflicted and does not reveal the heron's location.

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The answer choices are:

A. is conflicted and does not reveal the heron's location.

B. is conflicted, but tells the heron's location

C. is conflicted, and tells her grandmother

D. is conflicted, and runs away

Answer:

but she will not tell him.

Hope this helps!

Step-by-step explanation:

I got it right in a test.

There is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

The dataset of doctor A is given as:

643 634 670 658 636 624 641 655 649 629

The dataset of doctor B is given as:

651 625 622 624 631 621 653 647 646 646

Using a statistical calculator, we have:

Doctor A

Hence, the mean absolute deviation is 11.28 for Doctor A’s and 12 for Doctor B’s data set on glasses

In a dataset, the larger the mean absolute deviations value, the larger the variation.

By comparison, 12 is greater than 11.28

Hence, there is more variability on glasses of doctor B's dataset than the glasses of doctor A's dataset

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Answer:

y divided by k

Step-by-step explanation:

The correlation coefficient between the returns on investments A and B is approximately 0.0776.

To find the correlation coefficient between the returns on investments A and B, we can use the formula:

Correlation coefficient (ρ) = Covariance of A and B / (Standard deviation of A * Standard deviation of B)

Given the following values:

Standard deviation of A = 28%

Standard deviation of B = 23%

Covariance of A and B = 0.005

The correlation coefficient (ρ) is calculated using the formula:

ρ = Covariance of A and B / (Standard deviation of A * Standard deviation of B)

Substituting the given values into the formula, we have:

ρ = 0.005 / (0.28 * 0.23)

To simplify the calculation, we can evaluate the denominator:

Denominator = (0.28 * 0.23) = 0.0644

Now, we can divide the covariance by the denominator:

ρ = 0.005 / 0.0644

Using division, we find:

ρ ≈ 0.0776

The correlation coefficient ranges from -1 to +1. A value of 0.0776 indicates a weak positive correlation between the returns on investments A and B.

This means that there is a slight tendency for the returns of A and B to move together, but the relationship is not very strong.

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Answer:

D. 58. 58.58 REPEATING - 0.58 REPEATING = 58. (not repeating) hope this helps

Step-by-step explanation:

- Zombie

The probability that Tessa takes out blue marbles in both draws will be 6.25%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.

The number of marbles of different colors stored in a hat is listed below:

8 red marbles

10 green marbles

6 blue

Without looking in the hat, Tessa takes out the marble randomly.

She replaces the marble and then takes out another marble from the hat.

Then the probability that Tessa takes out blue marbles in both draws will be

Total marbles = 6 + 10 + 8 = 24

Then we have

\(\rm P = \dfrac{6}{24} \times \dfrac{6}{24}\\\\P = \dfrac{1}{16}\\\\P = 0.0625\\\\P = 6.25\%\)

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The exponential model that calculates the concentration of bacteria after x weeks can be represented by the equation B(x) = 2.1 million * (3^x), the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

This equation assumes that the concentration triples each week, starting from the initial concentration of 2.1 million bacteria per milliliter.

To estimate the concentration after 1.6 weeks, we can substitute x = 1.6 into the exponential model. B(1.6) = 2.1 million * (3^1.6) ≈ 14.87 million bacteria per milliliter. Therefore, after 1.6 weeks, the estimated concentration of bacteria in the river would be approximately 14.87 million bacteria per milliliter.

The exponential model B(x) = 2.1 million * (3^x) represents the concentration of bacteria after x weeks, where the concentration triples each week. By substituting x = 1.6 into the equation, we estimate that the concentration after 1.6 weeks would be approximately 14.87 million bacteria per milliliter.

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Answer:

im not sure, but i have

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer:

1 /1 ; 360°

Step-by-step explanation:

Start time = 2:30 pm

Stop time = 3:30 pm

Minute hand makes a complete revolution per hour ;

This means that the minutes hand revolves round the whole circle in one hour, hence fraction of the circle covered by the minute hand between 2:30 pm - 3:30 pm is 1/1 = 1

The angle turned by the minutes hand :

1 complete revolution = 360°

A circle covers 360°

1 /1 fraction of a circle = 1/1 * 360° = 360°

Hence, angle turned by the minute hand = 360°

Estimation of the pmf of X through simulation can be done as follows:First, a sample of 20 people will be randomly chosen.Each individual in the group will have a birthday assigned to them.

The number of individuals who have the same birthday as someone else in the group will be counted. The process will be repeated multiple times to obtain an approximation of the pmf of X. To estimate the pmf of X, the simulation code in R is as follows:

In this simulation study, a pmf of X was estimated using R language by performing a Bernoulli trial experiment. Twenty people were randomly chosen, and each individual was assigned a birthday at random. The number of individuals who share the same birthday as someone else was recorded. This process was repeated multiple times to obtain an approximation of the pmf of X.

The code of the simulation study is as follows:# Set the seed to ensure that the results are reproducibleset.seed(123)# Define the number of trialsn_trials <- 10000# Define the number of individualsn_individuals <- 20# Define the number of simulations that share a birthday as someone elsen_shared <- numeric(n_trials)# Simulate the experimentfor(i in 1:n_trials) { birthdays <- sample(1:365, n_individuals, replace = TRUE) shared <- sum(duplicated(birthdays)) n_shared[i] <- shared}# Calculate the pmf of Xpmf <- table(n_shared) / n_trialsprint(pmf).

This code generates a sample of 20 people randomly, and each individual in the group is assigned a birthday. The process is repeated multiple times to obtain an approximation of the pmf of X.

The table() function is used to calculate the pmf of X, and the result is printed to the console. The output shows that the pmf of X is 0.3806 when 2 people share the same birthday.

Thus, by running a simulation through R language, the pmf of X was estimated. The simulation study helped in approximating the pmf of X by performing a Bernoulli trial experiment. By repeating the process multiple times, a good estimation was obtained for the pmf of X. The simulation study confirms that it is quite likely that two individuals share the same birthday in a room of 20 randomly chosen people.

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The correct answer is d. None of these choices represents a continuous uniform random variable.

A continuous uniform random variable is characterized by a continuous probability distribution over a specific range with a constant probability density. Let's analyze each option to determine whether it represents a continuous uniform random variable.

a. The function f(x) = 1/2 for x between 1 and 1, inclusive: This is not a valid probability density function since it assigns a non-zero probability only to a single point (x = 1). A continuous uniform random variable should have a constant probability density over an interval, not just at a single point.

b. The function f(x) = 10 for x between 0 and 1/10, inclusive: This is also not a valid probability density function because it assigns a probability density of 10 over the interval [0, 1/10]. The probability density function for a continuous uniform random variable should be constant, but here it is not.

c. The function f(x) = 1/3 for x = 4, 5, 6: This represents a discrete probability distribution rather than a continuous one. A continuous uniform random variable should have a continuous range of possible values, not just a few specific points.

Therefore, none of the given choices represents a continuous uniform random variable. Option d is the correct answer.

In summary, for a random variable to be considered a continuous uniform random variable, its probability density function should have a constant value over a continuous range of values, rather than at specific points or intervals.

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Answer:

12

Step-by-step explanation:

18 - 2r and 4r are the same length so the equation would be:

18 - 2r = 4r

Move the 2r to the other side

18 = 6r

Divide it by 6 to get r by itself

r = 3

Answer:

x = - 2, x = 9

Step-by-step explanation:

Given

f(x) = \(\frac{x^2-9x}{x^2-7x-18}\)

The denominator of f(x) cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the values that x cannot be.

x² - 7x - 18 = 0

(x - 9)(x + 2) = 0

Equate each factor to zero and solve for x

x + 2 = 0 ⇒ x = - 2

x - 9 = 0 ⇒ x = 9

The excluded values are x = - 2, x = 9

Answer:

See image

Step-by-step explanation:

For this question, you need to know several special relationships about circles. A radius goes from the center of a circle to any point on the circle. All the radii (not a typo, plural of radius is radii) are the same size, their measures are equal; we say they are congruent (the symbol is an equal sign with a ~over it)

In the diagram, OA and OB are congruent because they are radii. AC is a tangent, that means that it touches the circle at exactly one point, in this case at A. So since OA is a radius and AC is a tangent, they are perpendicular to each other (makes 90° angles). Then we can subtract 90 - 72 to find the angle OAB. Angle OAB is 14°. In triangle AOB, which has two sides the same, the opposite angles will also be congruent which means OBA is also 14° (OR you could use the exact same logic for OB perpendicular to BC and subtract, same calculation as before) . Once you have the two 14° angles in the triangle, you can use the fact that all the angles in a triangle add up to 180° So then, 14 + 14 + x =180. Solve this equation to find angle AOB. See image.