Which histogram depicts a higher standard deviation.

Answer:

$3.40

Step-by-step explanation:

\(27.97 - 4.17\)

\(23.8\)

and

\(23.8 \div 7\)

\(3.40\)

to check your answer you will need to times 3.40 with 7

\(3.40 \times 7\)

\(23.8\)

Answer:

Yes you do 4*3 =12 and 12* 10 = 120:)

Step-by-step explanation:

The probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies is approximately 0.0998.

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the probability that at least 15 in the sample are among the group of athletes who have been told by coaches to neglect their studies, we can use the binomial cumulative distribution function. This is given by:

$$P(X \ge 15) = \sum_{k=15}^{50} \binom{50}{k} (0.4)^k (0.6)^{50-k}$$

We can calculate this probability using a calculator or computer, or we can approximate it using the normal distribution. To do this, we can use the continuity correction and compute:

$$P(X \ge 15) \approx P\left(\frac{X-n p}{\sqrt{n p (1-p)}} \ge \frac{15 - 50 \cdot 0.4}{\sqrt{50 \cdot 0.4 \cdot 0.6}}\right) = P(Z \ge 1.28)$$

Where $Z$ is a standard normal random variable. Using a standard normal table or calculator, we find that $P(Z \ge 1.28) \approx 0.0998$.

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Answer:

3

Step-by-step explanation:

7+4 is 11

11,22,33 is the maximum which is 3

Answer:

C

Step-by-step explanation:

A 1 2-liter bottle for $0.89

1 liter = .89 /2 = $0.445

B 3 1-liter bottles for $1.50

1 liter = $1.50/3 = $0.50

C 24 0.5-liter bottles for $5.25

1 liter = 5.25 / 12  = $0.4375

D 36 0.25-liter bottles for $4.75

1 liter = $4.75 / 9  = $0.53

Give me brainllest

Answer:

C is the best buy

Step-by-step explanation:

0.89/2 = 0.445

3 * 1 litre bottles = 3 litres

1.50/3 = 0.5

24 * 0.5 litres = 12 litres

5.25/12 = 0.4375

36 * 0.25 liters = 9 liters

4.75/9 = 0.52777777

Answer:

x<2 or x ≥ 15/2

Step-by-step explanation:

Answer:

Each can invite 2 guest

Step-by-step explanation:

345+ 35= 380

450-380 = 70

70/35=2

Answer:

Each performer can get 2 guests.

Step-by-step explanation:

There are 35 performers and 345 pre-sold tickets, so we just need to subract them from the amount of people that the stadium can hold. 450 - 35 - 345 = 70 people left

Since there is space for 70 more people, each performer can get (70/35) = 2 guests

The solution of x in the equation is 79/3

From the question, we have the following parameters that can be used in our computation:

y = 69

5x + 15 = y + 2x - 5

Substitute y = 69 in the equation 5x + 15 = y + 2x - 5

So, we have

5x + 15 = 69 + 2x - 5

Collect the like terms

This gives

5x - 2x =69 - 5 + 15

Evaluate the like terms

This gives

3x = 79

Divide both sides by 3

x = 79/3

Hence, the solution is 79/3

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Therefore, the left Riemann sum approximation of the area under the curve y = 2 cos^(-1)(x) on the interval [0, 1] with five subintervals is approximately 1.35691.

To approximate the area under the curve y = 2 cos^(-1)(x) on the interval [0, 1] using the left Riemann sum with five subintervals, we divide the interval into five equal subintervals of length Δx = (1 - 0)/5 = 1/5 = 0.2.

Using the left Riemann sum, we evaluate the function at the left endpoint of each subinterval and sum the areas of the corresponding rectangles.

For each subinterval, the left endpoint is xi = 0 + (i-1)Δx, where i ranges from 1 to 5.

The area of each rectangle is given by Δx * f(xi), where f(x) = 2 cos^(-1)(x).

Approximating the area under the curve using the left Riemann sum:

Area ≈ Δx * [f(x1) + f(x2) + f(x3) + f(x4) + f(x5)]

Substituting the values:

Area ≈ (0.2) * [f(0) + f(0.2) + f(0.4) + f(0.6) + f(0.8)]

Calculating the values of f(x) for each x:

f(0) = 2 cos^(-1)(0) = 2 * (π/2) = π

f(0.2) = 2 cos^(-1)(0.2) ≈ 2 * (1.36944) ≈ 2.73888

f(0.4) = 2 cos^(-1)(0.4) ≈ 2 * (0.92730) ≈ 1.85460

f(0.6) = 2 cos^(-1)(0.6) ≈ 2 * (0.64350) ≈ 1.28700

f(0.8) = 2 cos^(-1)(0.8) ≈ 2 * (0.45203) ≈ 0.90406

Substituting these values back into the equation:

Area ≈ (0.2) * [π + 2.73888 + 1.85460 + 1.28700 + 0.90406]

Calculating the expression:

Area ≈ 0.2 * 6.78454 ≈ 1.35691

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Answer:

12z

Step-by-step explanation:

(3z)4

=> 3z x 4

=> 12z

Therefore, 12z is the answer.

Hoped this helped.

Answer:

4z12

Step-by-step explanation:

I am not completely sure but I think all you have to do is times it together so I think it would be 4x12

Answer:

Step-by-step explanation:

The equation of the nth term of the arithmetic sequence is: \(a_n =a_1+d(n-1)\)

d = -5 - (-8) = - 5 + 8 = 3

a₁ = -8

Therefore:

               \(a_n =-8+3(n-1)\\\\a_n =-8+3n-3\\\\a_n =3n-11\)

A Negative correlation coefficient means that as one variable increases, the other decreases (i.e., an inverse relationship).

To calculate the p-value, we need to use a one-tailed t-test since we're interested in the probability of getting a sample mean greater than 12.10 oz.

First, we need to calculate the t-statistic:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (12.15 - 12.10) / (0.05 / sqrt(25))

t = 3.1623

Next, we need to find the degrees of freedom, which is the sample size minus one:

df = 25 - 1 = 24

Using a t-distribution table with 24 degrees of freedom and a significance level of 0.01, we find that the critical value is 2.492.

Since the calculated t-value (3.1623) is greater than the critical value (2.492), we can reject the null hypothesis and conclude that there is evidence that the mean volume is greater than 12.10 oz.

To find the p-value, we need to calculate the probability of getting a t-value greater than 3.1623 with 24 degrees of freedom:

p-value = P(t > 3.1623) = 0.0028 (calculated using a t-distribution table or software)

Therefore, the p-value is 0.0028, which is less than the level of significance (0.01), indicating strong evidence against the null hypothesis.

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The utility functions in options a, b, c, and f are not risk-averse on the interval [a,b], while the utility functions in options d and e are risk-averse on the interval [a,b].

In economics and finance, risk aversion refers to a preference for less risky options over riskier ones. Utility functions are mathematical representations of an individual's preferences, and they help determine whether someone is risk-averse, risk-neutral, or risk-seeking. A risk-averse individual would have a concave utility function, indicating a decreasing marginal utility of wealth.

For options a, b, c, and f, the utility functions are and f(x) = -ln(x), g(x) = \(-e^(^-^x^)\), h(x) = \(-4x^2\) - 10x, respectively. These utility functions do not exhibit concavity, which means they are not risk-averse. Instead, they either show risk-seeking behavior (options a and b) or risk-neutrality (options c and f).

On the other hand, options d and e have utility functions f(x) = ln(x), g(x) = 1/(e^(2x)), h(x) = \(-x^2\) + 10,000x and f(x) = ln(-2x), g(x) = -1/(\(e^(^2^x^)\)), h(x) = \(x^2\) - 100,000x, respectively. These utility functions display concavity, indicating a decreasing marginal utility of wealth. Thus, options d and e can be considered risk-averse on the interval [a,b].

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Answer:

\(9\; \rm m\).

Step-by-step explanation:

Assume that the run of this rafter is level. Then the height of the ridge (the line with a question mark next to it in the diagram) should be perpendicular to the line marked with \(\rm 12\; m\). The three labelled lines in this diagram will form a right triangle.

Hence, the height of this ridge can be found with the Pythagorean Theorem. By the Pythagorean Theorem:

\((\text{First Leg})^2 + (\text{Second Leg})^2 = (\text{Hypotenuse})^2\).

In this particular right triangle:

\((\text{Height})^2 + (12\; \rm m)^2 = (15\; \rm m)^2\).

\((\text{Height})^2 = (15\; \rm m)^2 - (12\; \rm m)^2\).

Therefore, the height of this ridge would be \(\sqrt{81}\; \rm m = 9\; \rm m\). (Note the unit.)

Answer:

The smallest angle in the triangle is 30°

Step-by-step explanation:

You can solve this by including the fact that the sum of the angles in the triangle has to be 180 degrees. We're given values describing the angles, so we can simply add them together, say the equal 180, and solve for x:

\((x + 37) + 90 + (x + 67) = 180\\2x + 37 + 90 + 67 = 180\\2x + 194 = 180\\2x = 180 - 194\\2x = -14\\x = -7\)

The smallest angle then is x + 37, or 37 - 7, giving us 30°

If three angles of a triangle measure x+37, 90, and x+67. Then 30 degrees is the measurement of the smallest angle in degrees.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

The three angles of a triangle measure x+37, 90, and x+67.

We need to find the measurement of smaller angle.

From angle sum property we know that the sum of three angles is equal to 180 degrees.

x+37+90+x+67=180

2x+194=180

Subtract 194 from both sides

2x=180-194

2x=-14

Divide both sides by 2.

x=-7

Substitute the value of x in smallest angle

x+37

-7+37=30

Hence the measurement of the smallest angle in degrees is 30

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The definite integral for the area of the surface generated by revolving the curve y = 6x^3 + 2x about the x-axis, over the interval 1 ≤ x ≤ 2, can be set up and evaluated as follows:

∫[1 to 2] 2πy √(1 + (dy/dx)^2) dx

To calculate dy/dx, we differentiate the given equation:

dy/dx = 18x^2 + 2

Substituting this back into the integral, we have:

∫[1 to 2] 2π(6x^3 + 2x) √(1 + (18x^2 + 2)^2) dx

Evaluating this definite integral will provide the surface area generated by revolving the curve about the x-axis.

b) The definite integral for the area of the surface generated by revolving the curve x = 4y - 1 about the y-axis, over the interval 1 ≤ y ≤ 4, can be set up and evaluated as follows:

∫[1 to 4] 2πx √(1 + (dx/dy)^2) dy

To calculate dx/dy, we differentiate the given equation:

dx/dy = 4

Substituting this back into the integral, we have:

∫[1 to 4] 2π(4y - 1) √(1 + 4^2) dy

Evaluating this definite integral will provide the surface area generated by revolving the curve about the y-axis.

By setting up and evaluating the definite integrals for the given curves, we can find the surface areas generated by revolving them about the respective axes. The integration process involves finding the appropriate differentials and applying the fundamental principles of calculus.

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Answer:

No

Step-by-step explanation:

Answer:

0 cannot go into 4

4 can go into 8

8 cannot go into 12

I'll assume the ODE is

\(y'' - 3y' + 2y = e^x + e^{2x} + e^{-x}\)

Solve the homogeneous ODE,

\(y'' - 3y' + 2y = 0\)

The characteristic equation

\(r^2 - 3r + 2 = (r - 1) (r - 2) = 0\)

has roots at \(r=1\) and \(r=2\). Then the characteristic solution is

\(y = C_1 e^x + C_2 e^{2x}\)

For nonhomogeneous ODE (1),

\(y'' - 3y' + 2y = e^x\)

consider the ansatz particular solution

\(y = axe^x \implies y' = a(x+1) e^x \implies y'' = a(x+2) e^x\)

Substituting this into (1) gives

\(a(x+2) e^x - 3 a (x+1) e^x + 2ax e^x = e^x \implies a = -1\)

For the nonhomogeneous ODE (2),

\(y'' - 3y' + 2y = e^{2x}\)

take the ansatz

\(y = bxe^{2x} \implies y' = b(2x+1) e^{2x} \implies y'' = b(4x+4) e^{2x}\)

Substitute (2) into the ODE to get

\(b(4x+4) e^{2x} - 3b(2x+1)e^{2x} + 2bxe^{2x} = e^{2x} \implies b=1\)

Lastly, for the nonhomogeneous ODE (3)

\(y'' - 3y' + 2y = e^{-x}\)

take the ansatz

\(y = ce^{-x} \implies y' = -ce^{-x} \implies y'' = ce^{-x}\)

and solve for \(c\).

\(ce^{-x} + 3ce^{-x} + 2ce^{-x} = e^{-x} \implies c = \dfrac16\)

Then the general solution to the ODE is

\(\boxed{y = C_1 e^x + C_2 e^{2x} - xe^x + xe^{2x} + \dfrac16 e^{-x}}\)

156 short sleeve shirts were sold in Emily's clothing store during the given period.

To determine the number of short sleeve shirts sold in Emily's clothing store, we need to calculate 3/10 of the total number of shirts sold, since the ratio of short sleeve to long sleeve shirts is 3:7.

We know that the total number of shirts sold is 520. To find 3/10 of 520, we multiply 520 by 3/10:

3/10 * 520 = (3/10) * 520 = (3 * 520) / 10 = 1560 / 10 = 156

Therefore, 156 short sleeve shirts were sold in Emily's clothing store in August.

Alternatively, we can solve this problem using proportions. If we set up the proportion:

(3/10) = x/520,

where x represents the number of short sleeve shirts sold, we can cross-multiply to find:

10x = 3 * 520,

10x = 1560,

x = 156.

Hence, 156 short sleeve shirts were sold in Emily's clothing store during the given period.

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Answer:

C. Test for Goodness-of-fit.

Step-by-step explanation:

C. Test for Goodness-of-fit would be most appropriate for the given situation.

A. Test Of  Homogeneity.

The value of q is large when the sample variances differ greatly and is zero when all variances are zero . Sample variances do not differ greatly in the given question.

B. Test for Independence.

The chi square  is used to test the hypothesis about the independence of two variables each of which is classified into number of attributes. They are not classified into attributes.

C. Test for Goodness-of-fit.

The chi square test is applicable when the cell probabilities depend upon unknown parameters provided that the unknown parameters are replaced with  their estimates and provided that one degree of freedom is deducted for each parameter estimated.

Answer:

all real numbers greater than or equal to −1

Step-by-step explanation:

Answer:

989 in^2

Step-by-step explanation:

The surface area of the larger cube is

SA = 5 s^2  because she will stain all the sides but the bottom one

SA = 5 * 11^2 = 5*121 = 605

The surface area of the smaller cube is

SA = 6s^2 since she will stain all sides

SA = 6* 8^2 =6*64 =384

Add both surface areas together

605+384

989

Answer:

989 square inches

Step-by-step explanation:

Let's start by finding the surface area of the bottom cube. It has six sides with side length 11, meaning that each side has area 11^2=121. Multiplying this by 5(since she's not staining the bottom), you get 605. For the second sphere, you can calculate this with the expression 6 * 8^2=384. Adding these together, you get a total surface area of 989 square inches. Hope this helps!

Answer:

6 1/6 (i think )

substitute 4 in for a, -5 for b and -7 for c

(4+ 2 * - 7 * - 5)/3 * 4

3*4 = 12

4+2 * - 7 * - 5) / 12

-7 * - 5 = 35 (same sign so positive)

(4+ 2* 35)/12

2*35 = 70 and 70+4 = 74.

74/12 is what we have, and we can simplify this to 37/6 by dividing both the numerator and denominator by 2. now we convert to mixed fraction and get 6 1/6.

Step-by-step explanation:

Answer:

Yes, there's a solution. x=1, y=0

Step-by-step explanation:

-2x+2=2x-2

4x=4

x=1

y=2×1-2=0

The parametric equations of the line of intersection between the planes x - y + z = 0 and x + 2y + 3z = 6 are x = 2t + 6, y = t, and z = -t - 6.



To find the parametric equations of the line of intersection between two planes, we need to determine a point on the line and find its direction vector.

First, we solve the system of equations formed by the two planes: x - y + z = 0 and x + 2y + 3z = 6. By eliminating x, we get -3y - 2z = -6.Setting y = t and z = s as parameters, we can express the point on the line as (x, y, z) = (2t + 6, t, s).Now, substituting these values into the first equation, we obtain 2t + 6 - t + s = 0, which simplifies to t + s = -6.

Therefore, the parametric equations for the line of intersection are:

x = 2t + 6

y = t

z = -t - 6, where t and s are parameters.

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Answer:

One expression equivalent to B + B + B + B + B that is a product of a coefficient and a variable is 5B, where 5 is the coefficient and B is the variable

Step-by-step explanation:

Answer:

See below.

Step-by-step explanation:

Refer to the graph.

The range of a graph is the span of y-values it covers.

From the graph, we can see that the span of y-values is all values greater than or equal to 0.

Therefore, our range is, in interval notation:

\([0,\infty)\)

Note that we use brackets with the 0 because 0 is included in our range.

In set notation, this is:

\(\{y|y\in\mathbb{R},y\geq 0\}\)

The additive inverse is:

(a) 4   (b) 18   (c) -620  (d) -60  (e) 244  (f) 8921

The additive inverse of a number x is the number that, when added to x  yields zero.

It is shown as \(x+(-x)=0\)

To find the additive inverse of a number we just change the sign of the given number which means positive changes to negative and vice versa.

The additive inverse of the given numbers are:

(a) 4

(b) 18

(c) -620

(d)-60

(e) 244

(f) 8921

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The value of c that satisfies the Mean Value Theorem for the function f(x) = 2 - 3x² on the interval [-6, 5] is c = -37/66.

In mathematics, slope refers to the steepness or incline of a line on a graph.

(A) To find the average or mean slope of the function on the interval [-6, 5], we need to use the formula:

average slope = (f(5) - f(-6)) / (5 - (-6))

where f(x) = 2 - 3x². We can evaluate f(5) and f(-6) by substituting these values into the function:

f(5) = 2 - 3(5)² = -73

f(-6) = 2 - 3(-6)² = -110

Substituting these values into the formula, we get:

average slope = (-73 - (-110)) / (5 - (-6)) = 37/11

Therefore, the average slope of the function on the interval [-6, 5] is 37/11.

(B) By the Mean Value Theorem, we know that there exists a c in the open interval (-6, 5) such that f'(c) is equal to the mean slope calculated in part (A).

To find c, we need to first find f'(x), which is the derivative of f(x) with respect to x:

f'(x) = d/dx (2 - 3x²) = -6x

Now we need to solve the equation f'(c) = 37/11 for c:

-6c = 37/11

c = -(37/11) * (1/6) = -37/66

Therefore, the value of c that satisfies the Mean Value Theorem for the function f(x) = 2 - 3x² on the interval [-6, 5] is c = -37/66.

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