Donald can read 3/4 of a book in 1 1/2 hours.

Answer: 268

Step-by-step explanation: substitute pi with 3.14, & then 4^3 as 64 in the second line. after, you multiply 3.14 x 64 you get 201 after you round. finally multiply 4 x 201 then divide your answer by 3. you get 268. (no one helped so i did)

Answer:0.46

Step-by-step explanation:

He will make $61.20 for 72 muffins in three hours.

Answer:

The flag pole is 12.8 feet tall.

Step-by-step explanation:

doing the second one hold up

The independent set in a graph is a set of vertices that contain no edges. So, no neighboring vertices are included. The max independent set problem is to get an independent set of maximum size in graph G.

The solution for this question is discussed below:

a) The integer linear program for the max independent set problem is as follows:

maximize ∑x_i Subject to: x_i+x_j ≤ 1 {i,j} ∈ E;x_i ∈ {0, 1} ∀i. The variable x_i can represent whether the ith vertex is in the independent set. It can take on two values, either 0 or 1.

b) The LP relaxation for the max independent set problem is as follows:

Maximize ∑x_iSubject to:

xi+xj ≤ 1 ∀ {i, j} ∈ E;xi ≥ 0 ∀i. The variable xi can take on fractional values in the LP relaxation.

c) The family of graphs is as follows:

Consider a family of graphs G = (V, E) defined as follows. The vertex set V has n = 2^k vertices, where k is a positive integer. The set of edges E is defined as {uv:u, v ∈ {0, 1}^k and u≠v and u, v differ in precisely one coordinate}. It can be shown that the size of the max independent set is n/2. Using LP, the value can be determined. LP provides a value of approximately n/4. Therefore, the ratio LP-OPT/OPT is at least c/4. Therefore, the ratio is in for a constant c>0.

d) The size of a max-independent set is equivalent to the number of vertices minus the minimum vertex cover size.

e) The 2-approximation algorithm for vertex cover implies a 2-approximation algorithm for the max independent set.

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The rate at which calories are burned was gotten by finding the slope of the graph which gives; 4 calories per minute

To get the slope of a linear graph, we will take two coordinates and make use of the formula;

Slope = (y₂ - y₁)/(x₂ - x₁)

The two coordinates we will pick for this slope are;

(10, 40) and (20, 80)

Thus;

Slope = (80 - 40)/(20 - 10)

Slope = 40/10

Slope = 4

Since the y-axis represents calories burned and the x-axis represents minutes of exercise, then we can say that;

Rate at which  calories get burned by bike riding = 4 calories per minute

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The correct statements regarding the function are:

I and II only.

The functions models the value of the furniture after x years, showing exponential decrease. We have that:

Hence statements I and II are correct.

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Answer:

l and lll only

Step-by-step explanation:

just did it

To solve the equation 15 + 2x = 36, we can start by subtracting 15 from both sides of the equation to get 2x = 21. Then, we can divide both sides by 2 to get x = 10.5. Rounded to the nearest ten-thousandth, the solution is x = 10.5000.

The true statement is (b) the random variable is x, the possible values are 0 to 3 and the values are numerical

The table is added as an attachment

From the attached image, we have:

Number of girls (x)          P(x)

0                                         0.125

1                                         0.375

2                                         0.375

3                                         0.125

In the above, the random variable is x, while P(x) represents its probabilities.

Also, the possible values are 0 to 3 as shown in the table.

0 to 3 are numerical digits, and the values are numerical

Hence, the true statement is (b)

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Answer:

a)  \(P(A \cup B)=0.23\)

b)  \(P(X)=0.87\)

Step-by-step explanation:

From the question we are told that:

Probability of contacting disease 1 \(P(1)=0.11\)

Probability of contacting disease 2 \(P(2)=0.16\)

Probability of contacting both disease  \(P(1\& 2)=0.2\)

a)

Generally the equation for a Random contact is mathematically given by

\(P(A \cup B)=P(1)+P(2)-P(A \cap B)\)

\(P(A \cup B)=\frac{11}{100}+\frac{16}{100}-\frac{4}{100}\)

\(P(A \cup B)=\frac{11+16-4}{100}\)

\(P(A \cup B)=0.23\)

b)

Generally the equation for Probability of contacting both after having contacted one is mathematically given by

\(P(X)=\frac{P(1\& 2)}{P(A \cup B)}\)

Therefore

\(P(X)=\frac{0.2}{0.23}\)

\(P(X)=0.87\)

Answer:

he needs to play 24 games of basketball

The right Riemann sum for arctan(1 + xdx) is Σ[arctan(1 + iΔx)]Δx, where i ranges from 1 to n and Δx is the width of each subinterval. The correct answer among the options provided is (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx.

In a right Riemann sum, the function is evaluated at the right endpoint of each subinterval. Therefore, we add up the values of arctan(1 + iΔx) at the endpoints of the subintervals, where i ranges from 1 to n. The width of each subinterval is Δx, so we multiply the sum by Δx to get the approximate value of the integral.

The provided expression (arctan(1 + Δx) + arctan(1 + 2Δx) + ... + arctan(1 + nΔx))Δx satisfies the conditions of a right Riemann sum, where the function is evaluated at the right endpoint of each subinterval. Therefore, this is the correct option among the given choices.

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Step-by-step explanation:

Multiply 12 and 7 then when you get that answer multiply it with 9 and then add it with 900

anyways my bias is Jisoo

Answer:

$966

Step-by-step explanation:

Given that $630 was invested in 1997

At a constant rate the value grew to $840 in 2002.

This implies that $210 was gotten in 5years:

$(840-630)=$210

and 2002-1997= 5years

therefore, to determine the value of the account in 2005: 2005-1997=8years

$210=5years

$x=8years

CROSS MULTIPLY

5x= 210×8

5x=1680

x=$336

Value of account in 2005 will be: $630+$336=$966

Therefore $966 was made in the next 8years(2005).

Answer:

k = -18

Step-by-step explanation:

If x-3 is a factor, what this means is that if we substitute;

x = 3 into the equation, we should get 0

This is from the factor theorem

Thus ;

P(3) = 0 = 2(3)^3 -5(3)^2 + 3(3) + k

0 = 54 - 45 + 9 + k

k + 18 = 0

k = -18

A recursive formula to represent the height of the nth bounce of the ball is: aₙ = 3.25(0.74ⁿ ⁻ ¹)

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

aₙ = a(qⁿ⁻¹)

where:

a is the first term

In this problem, the first bounce is 3.25 feet and each successive bounce is 74% of the previous bounce's height, hence the first term and the common ratio are given, respectively, by:

a = 3.25

q = 74% = 0.74

Hence, the height of the nth bounce is given by:

aₙ = 3.25(0.74ⁿ ⁻ ¹)

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(a) The critical numbers are x = -1 and x = 1.
(b) The open intervals on which the function is increasing are (-1, 1), and the open intervals on which the function is decreasing are (-inf, -1) and (1, inf).
(c) The relative extrema are: relative maximum (1, 22) and relative minimum (-1, -20).

(a) To find the critical numbers of the function f(x) = -7x^3 + 21x + 8, we first find its derivative:

f'(x) = -21x^2 + 21

Now we set f'(x) = 0 and solve for x:

-21x^2 + 21 = 0
x^2 = 1
x = ±1

The critical numbers are -1 and 1.

(b) To determine the intervals of increasing or decreasing, we evaluate the derivative at points in each interval:

For x < -1: f'(-2) = -21(-2)^2 + 21 = -63 < 0, so the function is decreasing in the interval (-∞, -1).

For -1 < x < 1: f'(0) = 21 > 0, so the function is increasing in the interval (-1, 1).

For x > 1: f'(2) = -21(2)^2 + 21 = -63 < 0, so the function is decreasing in the interval (1, ∞).

(c) Now, we apply the First Derivative Test to the critical numbers:

At x = -1, the function changes from decreasing to increasing, so we have a relative minimum: f(-1) = -7(-1)^3 + 21(-1) + 8 = 14. The relative minimum is (-1, 14).

At x = 1, the function changes from increasing to decreasing, so we have a relative maximum: f(1) = -7(1)^3 + 21(1) + 8 = 22. The relative maximum is (1, 22).

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Step-by-step explanation:

0.75x - 6 = x

0.25x = -6

x = -24

Hence the number is -24.

Yes, the triangles RST and UVW are similar, by SAS similarity rule.

Two similar shapes, such as similar triangles, similar rectangles, similar square, are the shapes whose dimensions are in equal or common ratio but the size or length of their sides vary.

Given that, two triangles RST and UVW,

TR / WU = 15/60 = 1/4

TS / VW = 13/52 = 1/4

∠ T = ∠ W

We know that, if in two triangles their corresponding sides are in equal ratios and have an angle congruent, then they are similar by SAS rule.

Hence, the triangles RST and UVW are similar, by SAS similarity rule.

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Answer:

The midpoint of the line segment whose endpoints are (-2, 5) and (6, -9) is: (2,-2)

Step-by-step explanation:

Given two points are:

(-2, 5) and (6, -9)

The mid-point is the point that divides a line segment in two equal parts.

Let M be the mid-point then

\(M(x,y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)

Let

(x1,y1) = (-2, 5)

(x2,y2) = (6, -9)

Putting the values in the formula, we get

\(M(x,y) = (\frac{-2+6}{2}, \frac{5-9}{2})\\M(x,y) = (\frac{4}{2}, \frac{-4}{2})\\= (2,-2)\)

Hence,

The midpoint of the line segment whose endpoints are (-2, 5) and (6, -9) is: (2,-2)

Answer:

It would take 200 minutes

Step-by-step explanation:

The type of sample that a store prints a request on each receipt asking customers to fill out a satisfaction survey online if they are willing is a voluntary response sample.

In the statistics world, a voluntary response sample is a research sample that relies on individual self-selection. This is in opposition to random sampling, in which the samples are gathered in a way that ensures everyone in a particular population has an equal chance of being chosen. This method of self-selection is also known as self-selection bias or sampling bias.Voluntary response samples are subject to a variety of flaws. The responses may not be representative of the population as a whole, and they may be skewed by numerous factors, such as which individuals are most likely to volunteer, how these volunteers differ from the population as a whole, and how the survey questions are phrased.The results of a voluntary response survey may be useful in generating hypotheses or gaining a general sense of how individuals feel about a particular subject. However, they are not reliable enough to draw any conclusions or to be taken seriously in the scientific sense.

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Answer:

where are the graphs? I have to see them to give a correct answer

Answer:Your answer would be E

Step-by-step explanation:8 times 6 would be 48

The measure of height of each triangle will be 4√3 cm. Then the correct option is B.

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

A regular hexagon is divided into 6 congruent triangles. If the perimeter of the hexagon is 48 centimeters.

Then the Side length of each triangle will be given as,

48 = (Side length) x 6

Side length = 8 cm

Then the measure of the height of each triangle will be calculated as,

tan 60° = h / (8 / 2)

√3 = h / 4

h = 4√3 cm

The measure of height of each triangle will be 4√3 cm. Then the correct option is B.

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Answer:

Answer: \(\frac{12}{5}\)

Step-by-step explanation:

\(\frac{3 *4x}{5x-20} \\----x^2-2x----X^2-6x+8\)

\(=\frac{3 * 4x(x^2-6x+8)}{(5x-20)(x^2-2x)} = \frac{12}{5}\)

hope it helped !!

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The expected difference is 0.17

A supermarket is a self-service store with various food, drink, and household goods options divided into categories. While this type of store is bigger and has a wider variety of products than older grocery stores, it is smaller and offers a smaller selection of goods than a hypermarket or big-box market. Fresh meat, produce, dairy, deli foods, baked goods, etc. may usually be found in the store.

Additionally, shelf space is set aside for canned and packaged goods as well as a variety of non-food items like pet supplies, cleaning supplies, cookware, and household cleansers.

The table is: 0 1 2 3

x1 0 0.08 0.06 0.04 0.00

1 0.05 0.18 0.05 0.03

2 0.05 0.04 0.10 0.06

3 0.00 0.03 0.04 0.07

4 0.00 0.01 0.05 0.06

Expected difference =

+(0.08*(0-0)) +(0.06*(0-1)) +(0.04*(0-2)) +(0.00*(0-3)) +(0.05*(1-0)) +(0.18*(1-1)) +(0.05*(1-2)) +(0.03*(1-3)) +(0.05*(2-0)) +(0.04*(2-1)) +(0.10*(2-2)) +(0.06*(2-3)) +(0.00*(3-0)) +(0.03*(3-1)) +(0.04*(3-2)) +(0.07*(3-3)) +(0.00*(4-0)) +(0.01*(4-1)) +(0.05*(4-2)) +(0.06*(4-3))

= 0.17

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Answer:

30 km/h car

Step-by-step explanation:

From analysis the   car traveling at 30 km/h has greater kinetic energy

we can deduce it from the expression of kinetic energy which is

\(KE=\frac{1}{2} mv^2\)

Assuming the mass m= 1 kg

For the 30 km/h

\(KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J\)

For the 15 km/h

\(KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J\)

Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE

The number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440 will be 240 tines.

Probability is the occurence of likely events. It is the area of mathematics that deals with numerical estimates of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1.

In thi situation, the simulation shows that the number of times 10 is drawn is 1/6. The number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440 will be:

= 1/6 × 1440

= 240 times.

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Complete question

The simulation shows that the number of times 10 is drawn is 1/6. Use the simulation to predict the number of times a card with the number 10 would be drawn when the total number ofcards drawn in the simulation is 1,440.