The graph below shows the number of cookies the choir sold. If the trend continues, how many cookies will be sold in 3 hours?​

Answer:

Step-by-step explanation:

3 rows of 21 sneakers.

If you add 21+21 it equals 42, which is two rows. If you add that last row, 42+21, you end up with 63.

If a card is drawn from a "standard-deck" and then month of year is chosen, then the probability of selecting "face-card" and June month is 1/52.

The probability of getting a face-card from a standard-deck of 52 cards is 12/52, since there are 12 face cards (four jacks, four queens, and four kings) in the deck.

The probability of choosing June from the 12 months of the year is 1/12, since there are 12 months in a year and each month is equally likely to be chosen.

To find the probability of both events happening together (getting a face-card and June), we multiply the probabilities of each event:

P(face card and June) = P(face card) × P(June) = (12/52) × (1/12) = 1/52

Therefore, the probability of getting a face card and June is 1/52.

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The sum does not converge, we can conclude that E[X] is undefined in this case.

The given function P(x) satisfies the properties of a pmf. To show this, we must show that P(x) is non-negative for all x and that the sum of P(x) over all possible values of x is equal to 1.

First, note that (2+1)x(x+1) is always non-negative, since x and x+1 are either both positive or both negative. Therefore, P(x) is non-negative for all x.

Next, we can show that the sum of P(x) over all possible values of x is equal to 1. To do this, we can use the fact that P(x) is zero for all values of x outside the range 1 ≤ x ≤ 4. Therefore, we only need to sum P(x) over the range 1 ≤ x ≤ 4:

P(1) + P(2) + P(3) + P(4)

= -3/4 + 6/20 - 15/56 + 20/120

= -21/56 + 42/56 - 15/56 + 14/56

= 20/56

= 5/14

Since the sum of P(x) over all possible values of x is equal to 5/14, which is equal to 1, we can conclude that P(x) satisfies the properties of a pmf.

Next, we can show that the formula (4.1) for expectation does not converge in this case and hence E[X] is undefined. Using the hint provided, we can rewrite 1/x(x+1) as 1/x - 1/(x+1). Then, the formula for expectation becomes:

E[X] = Σx P(x) x

= (-3/4)(1) + (6/20)(2) - (15/56)(3) + (20/120)(4)

= -3/4 + 3/5 - 15/56 + 1/3

= -67/140

Since the sum does not converge, we can conclude that E[X] is undefined in this case.

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Answer:

Step-by-step explanation:

\(50+2x=20+5x\\\\\mathrm{Subtract\:}50\mathrm{\:from\:both\:sides}\\\\50+2x-50=20+5x-50\\\\Simplify\\\\2x=5x-30\\\\\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}\\\\2x-5x=5x-30-5x\\\\Simplify\\\\-3x=-30\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\\\frac{-3x}{-3}=\frac{-30}{-3}\\\\Simplify\\\\x=10\)

9514 1404 393

Answer:

  B. 9πx^6

Step-by-step explanation:

Putting the given radius into the area formula gives ...

  A = πr^2

  A = π(3x^3)^2 = π(3^2)(x^(3·2))

  A = 9πx^6

Answer:

4 solutions counting any possible multiplicity

Step-by-step explanation:

Recall that if one considers the Complex Number System, a polynomial has as many solutions (including multiplicity) as its degree.

So in this case, where we are considering a polynomial of order 4 Notice that the term \(-\,33\,x^4\), is in reality the leading term (term with the highest power of the variable) of this polynomial.

Therefore, in the Complex Number System, this polynomial would have 4 solutions.

Regarding the exponential function y = 3(2)^x, we have that:

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

The function for this problem is given as follows:

y = 3(2)^x.

Hence the parameters are given as follows:

At x = 3, the numeric value of the function is obtained as follows:

y = 3 x 2^3

y = 3 x 8

y = 24.

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-8 < 4

hope it helps

Answer: -2≤-8<4

Step-by-step explanation:

The total amount paid by Kate as a portion of interest will be $12932.

The compound interest is the interest levied upon both the principal amount and the interest from the previous periods.

The formula for the calculation of the compound interest will be given as

\(A=P(1+\dfrac{r}{100^} )^n\)

here,

A= Amount

P= priciple

r=Rate of interest

n=Time period

Now it is given that,

P=$9710

r=5.9%

n=5

Then putting the values in the formula we get

\(A=9710(1+\dfrac{5.9}{100})^5\)

A=$12932

Hence the total amount paid by Kate as a portion of interest will be $12932.

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Answer:

the answer is C 1,526.22

Step-by-step explanation

2022 edge test

Answer:

16404.2 feet

Step-by-step explanation:

1 in = 2.54 cm

1 km = 100000 cm

5 km = 100000*5 = 500000

1 feet = 12 in

500000 cm = 500000/2.54 = 196850.39 in  

196850.39 in = 196850.36 / 12 = 16404.2 feet

The statement that is true about the Random Variable X is P(X ≥ 4) = 0.522  , the correct option is (a) .

In the question ,

it is given that ,

the possible values of the random variable X is 1, 2, 3, 4, and 5 .

given that , 2 is twice as likely as 1 , that means

p(2) = 2p(1)

3 is one-third as likely as 2 , that means

p(3) = 1/3 p(2)

4 is four times as likely as 3 , which is

p(4) = 4/3 p(2)

and 5 is half as likely as 4 , that means

p(5) = 2/3 p(2)

We know that ,

p(1) + p(2) + p(3) + p(4) + p(5) = 1

Substituting the values in the above equation , we get

1/2 p(2) + p(2) + 1/3 p(2) + 4/3 p(2) + 2/3 p(2) = 1

So , p(2) = 6/23

hence ,

P(X ≥ 4) = P(X=4) + P(X=5)

= (4/3) × (6/23) + (2/3) × (6/23)

On simplifying further ,

we get ,

= 0.522

Therefore , the value of P(X ≥ 4) is 0.522    .

The given question is incomplete , the complete question is

Let X be a random variable with possible values 1, 2, 3, 4, and 5. Assume that 2 is twice as likely as 1, 3 is one-third as likely as 2, 4 is four times as likely as 3, and 5 is half as likely as 4. Which of the following is true (to the nearest three decimals)

(a) P(X ≥ 4) = 0.522

(b) P(X = 1 or X = 5) = 0.329

(c) P(X ≤ 2) = 0.367

(d) P(X = 2 or X = 3) = 0.293

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The maximum value of P is 32, which occurs at vertex A(4,2).

To find the maximum value of P = 5x + 6y, subject to the given constraints, we can use the method of linear programming.

First, we graph the lines x + y = 6 and 2x + 3y = 16 and shade the region that satisfies the constraints x ≥ 0 and y ≥ 0.

The feasible region is the shaded triangle OAB.

The vertices of the triangle are O(0,0), A(4,2), and B(6,0).

We now need to evaluate the value of P at each vertex to determine which vertex gives us the maximum value of P.

At vertex O: P = 5(0) + 6(0) = 0

At vertex A: P = 5(4) + 6(2) = 32

At vertex B: P = 5(6) + 6(0) = 30

Therefore, the maximum value of P is 32, which occurs at vertex A(4,2).

So, the answer is P = 32.

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Answer:

1000

Step-by-step explanation:

4000.

5% annual, so 5x5=25

4000 of 25%

1000

In this case the answer is very simple . .

We must apply the distributive property of multiplication.

That is the solution. .

Answer:

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

The GCF of 80 and 90 is 10.

Answer:

m = 2

Explanation:

Answer:

\(20^{\circ}\).

Step-by-step explanation:

Two angles are supplements of one another if their sum is \(180^{\circ}\).

Two angles are complements of one another if their sum is \(90^{\circ}\).

Let \(x^{\circ}\) be the measure of the angle in question.

The supplement of this angle would be \((180 - x)^{\circ}\).

The complement of this angle would be \((90 - x)^{\circ}\).

According to the question:

\((180 - x) + 50 = 3\, (90 - x)\).

Solve this equation for \(x\):

\(x = 20\).

Thus, this angle would measure should \(20^{\circ}\).

The supplement of this angle would measure \((180 - 20)^{\circ} = 160^{\circ}\). The complement of this angle would measure \((90 - 20)^{\circ} = 70^{\circ}\).

Three times the complement of this angle would be \(3 \times 70^{\circ} = 210^{\circ}\), which is indeed \(50^{\circ}\) greater than the supplement of this angle.

In various settings, such as work or school, measures of location, measures of variability, and measures of association can provide valuable insights and aid in interpreting data.

Let's consider an example from a work setting where employee performance data is collected

Measures of location, such as the mean or median, can illustrate an important aspect of employee performance. By calculating the mean performance score, we can identify the average level of performance across the organization. This measure helps us understand the central tendency of the data and provides a benchmark to assess individual employee performance against the average. If the mean performance score is low, it indicates the need for improvement in overall performance.

Measures of variability, such as the standard deviation, can indicate the spread or dispersion of performance scores. A high standard deviation suggests a wide range of performance levels among employees, indicating a lack of consistency. This insight prompts organizations to investigate the underlying factors contributing to the variability and identify areas for improvement in training, resources, or performance management processes.

Furthermore, measures of association, such as correlation coefficients, can help identify relationships between variables. For example, we can explore the correlation between employee performance scores and factors like years of experience, education level, or training hours. Understanding these associations can guide decision-making processes, such as designing targeted training programs for employees who exhibit a lower correlation between training hours and performance.

By applying these measures and interpreting the data, organizations can gain valuable insights into employee performance. This understanding can lead to improved decision-making, such as identifying areas for performance improvement, optimizing resource allocation, and implementing targeted interventions to enhance overall productivity and success within the work setting.

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4/5% of 192 is approximately 1.536. The best estimate among the given answer choices is A. 2, which is the closest whole number to the actual value.

To find 37% of 293, we can start by using a proportion. We can set up the proportion as follows:

37/100 = x/293

To solve for x, we can cross-multiply and simplify:

37 x 293 = 100 x

x = 10841/100 ≈ 108.41

So, 37% of 293 is approximately 108.41. The best estimate among the given answer choices is B. 120, which is close to the actual value but slightly overestimated.

To find 4/5% of 192, we can first convert 4/5% to a decimal by dividing by 100:

4/5% = 4/5 ÷ 100 = 0.008

We can then multiply 0.008 by 192 to get the answer:

0.008 x 192 = 1.536

So, 4/5% of 192 is approximately 1.536. The best estimate among the given answer choices is A. 2, which is the closest whole number to the actual value. The other answer choices are too high and would overestimate the value.

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To tell if a function is convergent or divergent, you need to check the behavior of the function as the input values get larger. Here are the steps to determine whether a function is convergent or divergent:

Step 1: Find the limit of the function. Evaluate the function as the input values get larger, approaching infinity. If the limit exists and is a finite number, the function is convergent. If the limit does not exist or approaches infinity, the function is divergent.

Step 2: Test for convergence using the divergence test. If the limit of the function as the input values approach infinity is zero or does not exist, the series may be divergent. In this case, you need to use the divergence test. If the series diverges, the function is divergent. If the series converges, the test is inconclusive.

Step 3: Test for convergence using the integral test. If the function is positive, continuous, and decreasing, you can use the integral test to determine convergence. If the integral converges, the series is convergent. If the integral diverges, the series is divergent.

Step 4: Test for convergence using comparison tests. If the function can be compared to another function, you can use comparison tests to determine convergence. If the other function is convergent, the original function is convergent. If the other function is divergent, the original function is divergent.

Step 5: Test for convergence using the ratio test. If the limit of the ratio of consecutive terms is less than 1, the series is absolutely convergent. If the limit is greater than 1, the series is divergent.

If the limit is equal to 1, the test is inconclusive.In summary, determining if a function is convergent or divergent requires checking the behavior of the function as the input values get larger and using different tests depending on the characteristics of the function.

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The area of the triangle is 17/8

In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.

Let consider this right angled triangle with vertices (0,-4), (0.0), and (1,0).

Its legs have the length 4 and 1; its hypotenuse is  long.

We can easy find the height "h" (the altitude) of this triangle, drawn to hypotenuse.

From the area consideration, we have this equation

(4*1)/2=(1/2)*√17*h

h = 4/√17 = 0.970143.

So, it is not 1 unit, as we see.

It means that the legs of the triangle should be√17/4 as long, as 1 unit and 4 units of the original triangle.

So, the area of the seeking triangle is

(1/2)(√17/4)(√17/4) = (1/2)*(17/4) = 17/8

The area of the triangle under the question is  17/8

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Answer:

13 months

Step-by-step explanation:

First, find out how much money he needs by subtracting what he currently has from his goal.

\(4160 - 1300 = 2860\)

Then divide how much he needs by how much he saves every month.

\(2860 \div 220 = 13\)

It will take Jon 13 months to save enough for his car.

The  small angle approximation is a mathematical technique used to simplify calculations involving angles that are close to zero.

It is used when the angle is so small that sine and cosine can be approximated by their linear terms. This is represented by the formula sinθ ≈ θ and cosθ ≈ 1.

For example, if we have an angle of θ = 0.1 radians, then we can use the small angle approximation to calculate the sine and cosine of the angle as follows:

sinθ ≈ θ = 0.1

cosθ ≈ 1 = 1

This approximation can be seen graphically by plotting the sine and cosine functions. On the graph, the small angle approximation is the line tangent to the curve at the origin. This line can be used to approximate the sine and cosine of small angles near the origin.

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Answer:

Step-by-step explanation:

(a + b)² = 37

a^2 + 2ab + b^2 = 37

---

ab = 5

a = (5/b)

----

a^2 + 2ab + b^2 = 37

(5/b)^2 + 2(5/b)b + b^2 = 37

(25/b^2) + 10 + b^2 = 37

(25/b^2) + b^2 = 27

25 + b^4 = 27b^2

b^4 - 27b^2 + 25 = 0

I don't know how to factor this expression.  The roots seem complex.

Answer:

Step-by-step explanation:

Alright you will need to use PEMDAS for this

Parenthesis

Exponent

Multiplication

Division

Addition

Subtraction ( Take note of this )

Step 1

9(3x – 16) + 15 = 6x – 24 You will remove parenthesis here

27x-129=6x-24

Step 2

Then subtract 6x,

27x-129=6x-24

21x-129=-24

Step 3

Then you add 129 to the sides,

21x-129=-24

21x=105

After that, you divide the sides by 21  so that you can get your answer

5

So therefore, your answer will be x=5