The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean u standard deviation o = - 27.6. (a) What is the probability that a single student randomly chosen from all those taking the test scores 559 or higher? ANSWER: 0.44381 For parts (b) through (d), consider a simple random sample (SRS) of 30 students who took the test. (b) What are the mean and standard deviation of the sample mean score ł, of 30 students? The mean of the sampling distribution for ž is: 5.03926 The standard deviation of the sampling distribution for is: 8.7875 (c) What z-score corresponds to the mean score ž of 559? (d) What is the probability that the mean score ã of these students is 559 or higher?

Answer: (3/g) + h

Step-by-step explanation:

Answer:

\(3.5 - 2 \times 100 \div 2\)

Answer:

The percentage increase in the puppy's weight is 75%.

Step-by-step explanation:

We can find the percentage increase using the following formula:

\(\boxed{\% \space\ \mathrm {increase = \frac{final \space\ - \space\ initial}{initial} \times 100}}\).

In this case,

• initial = 2 kg

• final = 3.5 kg

Substituting these values into the formula:

\({\% \space\ \mathrm {increase = \frac{3.5 \space\ - \space\ 2}{2} \times 100}}\)

                ⇒ \(\frac{1.5}{2} \times 100\)

                ⇒ \(0.75 \times 100\)

                ⇒ 75%

Answer:

The ends of the field are at the zeros (x-intercept) of the function.

0 = -0.000234(x - 80)2 + 1.5      subtract 1.5 from both sides

-1.5 = -0.000234(x - 80)2           divide both sides by right coefficient

6410.25641 = (x - 80)2              take square root of both sides

80.064 = x - 80                         add 8-0 to both sides

160.064 = x

The field is 160.064 feet wide.  

The maximum is at the vertex, y = 1.5 feet

Step-by-step explanation:

Answer:

To adjust the cupcake recipe to serve 108 people, you will need to follow these steps:

Determine how many cupcakes the original recipe makes. Let's say the original recipe makes 12 cupcakes.

Calculate how many batches of cupcakes you will need to make to serve 108 people. To do this, divide the number of people by the number of cupcakes in one batch: 108 ÷ 12 = 9. You will need to make 9 batches of cupcakes.

Multiply the amount of each ingredient in the original recipe by 9. For example, if the original recipe calls for 2 cups of flour, you will need 18 cups of flour (2 cups x 9 batches).

Follow the same process for all of the ingredients in the recipe, making sure to adjust each one by the same factor.

Prepare the cupcakes according to the adjusted recipe, baking each batch separately.

By following these steps, you should be able to adjust the cupcake recipe to serve the large crowd coming in for lunch tomorrow.

Step-by-step explanation:

Answer:

I think it is -11r

Answer:

C

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

The real distance between towns X and Y measuring 11.2 cm apart on a map with a scale 1: 100,000 is 11.2 km.

Given the scale = 1: 100,000, which means that 1 cm on the map represents 100,000. Thus, 11.2 cm on the map represents 11.2* 100,000 = 1,120,000cm.

We know that 1 km = 100,000cm

Therefore 1,120,000 cm = 1,120,000/100,000

= 11.2 km

Therefore, the real distance between towns X and Y is 11.2km.

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The given inequality is

First, we need to isolate y

To do that we want to move 2y from the right side to the left side, then

To do that subtract 2y from 3y and subtract 2y from (2y + 3)

Since 3y - 2y = 1y

Since 2y - 2y = 0

Since 0 + 3 = 3

Then the answer is

The answer is B

if the family gives up two nights in the hotel, they could afford d) 5 meals

The family has a budget of $800 for meals and hotel accommodations. If they could afford eight nights in a hotel without buying any meals, we can determine the cost of one night at the hotel. To do this, we can divide the total budget by the number of nights:

$800 / 8 nights = $100 per night

Now, let's consider the scenario where the family gives up two nights in the hotel. This would free up $200 from their budget ($100 per night x 2 nights). We can then use this amount to determine how many meals the family can afford by dividing the available funds by the cost of one meal:

$200 / $40 per meal = 5 meals

Therefore, if the family gives up two nights in the hotel, they could afford 5 meals. The correct answer is d. 5.

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The correct answer is A. True

A linear equation represents a line in the xy-plane. In the form of y = mx + b, where m is the slope and b is the y-intercept, a linear equation defines a straight line relationship between x and y. Each x value corresponds to a unique y value on the line.

By plotting the points that satisfy the equation, a line can be formed. The slope determines the steepness or direction of the line, while the y-intercept represents the point where the line intersects the y-axis.

Therefore, a linear equation does determine a line in the xy-plane.

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True. A linear equation determines a line in the xy-plane.

A linear equation is an equation that describes a straight line in the xy-plane. It is an equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. The slope-intercept form of a linear equation is commonly used to graph lines.

The equation y = mx + b shows that for every value of x, there is a corresponding value of y that lies on the line. The slope, m, determines the steepness of the line, while the y-intercept, b, represents the point where the line crosses the y-axis.

Therefore, it is true that a linear equation determines a line in the xy-plane.

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Answer:

It would be 8

Step-by-step explanation:

Answer: 37.5%

Step-by-step explanation:

There are 8 separate area

and among them are 3 Cs.

Thus the probability is

⅜ times 100 = 37.5 (%)

Answer:

 visual interpretation. of numerical data

Step-by-step explanation:

A histogram is a graphical representation of discrete or continuous data. To put it another way, it gives a visual representation of numerical data by displaying the number of data points that fall within a given range of values.

Answer:

(7, 23).

Step-by-step explanation:

y=x+16

y=5x-12

Subtract the equations

0 = x - 5x + 16 - (-12)

-4x + 28 = 0

4x = -28

x = 7

plug x = 7 in first equation:

y = 7 + 16 = 23.

The sales tax on both muffin and cup of coffee at breakfast dinner is $0.45.

As the stated question-

Thus,

Total cost = $3.25 + $2.75

Total cost = $6.00

Sales tax = 7.5% of $6.00

Sales tax = 7.5 x 6.00 / 100

Sales tax = $0.45

Thus, the sales tax on both muffin and cup of coffee at breakfast dinner is $0.45.

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The correct question is-

At breakfast diner a cup of coffee cost $2. 75 and a muffin s $3. 25. What is the sale tax on the two item if the rate is 7. 5%?

Answer: The longest display is 47.75 inches longer than the shortest display.

Step-by-step explanation:

The graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

Inequality expressions are mathematical statements that are represented by variables, coefficients and operators where the opposite sides are not equal

The inequality expression is given as

y ≤ 3/4x − 4

The inequality symbol in the above inequality expression is

≤

This implies that the inequality expression is a less than or equal to

When an inequality expression has a sign of equal to, then the line of the inequality graph will be a solid line

Also, the inequality symbol implies that the bottom part is shaded

Hence, the graph of the inequality expression where the inequality expression is given as y ≤ 3/4x − 4 is (d)

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Answer:

-4

Step-by-step explanation:

1. \(f(1) = (1-2)(1+3)\)

2. \(f(1) = -1(1+3)\)

3. \(f(1) = (-1)(4)\)

4. \(f(1) = -4\)

None of the given options matches this general solution, so the answer is E. None of the options.

To solve the given ordinary differential equation:

y'' + 2y' + 5y = e^t sin(t)

We first find the characteristic equation:

r^2 + 2r + 5 = 0

Using the quadratic formula, we find the roots to be:

r = (-2 ± sqrt(4 - 4(1)(5))) / 2

r = -1 ± 2i

The characteristic equation has complex roots, so the general solution is:

y(t) = e^(-t)(Acos(2t) + Bsin(2t))

Next, we find the particular solution by guessing a solution of the form:

y_p(t) = Ae^t sin(t) + Be^t cos(t)

Taking the first and second derivatives, we get:

y_p'(t) = Ae^t sin(t) + Ae^t cos(t) + Be^t sin(t) - Be^t cos(t)

y_p''(t) = 2Ae^t cos(t) - 2Be^t sin(t)

Substituting these expressions into the original equation and simplifying, we get:

(2A - B) e^t sin(t) + (-2B - A) e^t cos(t) = e^t sin(t)

We need the coefficients of e^t sin(t) and e^t cos(t) to be equal to 1 and 0, respectively, in order to obtain a particular solution. This gives us the system of equations:

2A - B = 1

-2B - A = 0

Solving for A and B, we get:

A = 1/5

B = -2/5

Therefore, the particular solution is:

y_p(t) = (1/5) e^t sin(t) - (2/5) e^t cos(t)

The general solution is then the sum of the homogeneous and particular solutions:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + (1/5) e^t sin(t) - (2/5) e^t cos(t)

To solve for the constants A and B using the initial conditions, we can substitute y(0) = 0 and y'(0) = 1 into the general solution and solve the resulting system of equations. However, since the question asks us to avoid solving for the constants, we can simply write the general solution as:

y(t) = e^(-t)(Acos(2t) + Bsin(2t)) + e^t (Csin(t) + Dcos(t))

where A, B, C, and D  are constants that we do not need to solve for.

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The measure of angle ABC is given as follows:

m < ABC = 145º.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

In a parallelogram, we have that the opposite angles are supplementary.

The opposite angles for this problem are given as follows:

Hence the measure of angle ABC is given as follows:

m < ABC + 35º = 180º.

m < ABC = 145º.

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Answer: 1

From the second sentence, we have AB = BC = CD = DE = y. So AE = 4y and BD = 2y (you can see by drawing a diagram), and AE = 2BD. Substituting 2x + 3 for BD and 6x + 4 for AE in AE = 2BD, we have 6x + 4 = 2(2x + 3), 6x + 4 = 4x + 6. Solving, we see x = 1.

i hope this helped! :D

The correct answer is A. The standard error of the sample proportion will become larger as the sample size increases.

The standard error is a measure of the variability or uncertainty associated with an estimate. In the case of the sample proportion, it measures the spread or variability in the proportion of successes observed in the sample compared to the true population proportion.

As the sample size increases, the standard error decreases, indicating greater precision in estimating the true population proportion. This is because a larger sample provides more information and reduces the impact of sampling variability.

On the other hand, options B, C, and D are incorrect. The standard error is not affected by the population proportion itself but rather by the sample size. The population proportion approaching 0.50, 1.00, or 0 does not directly impact the standard error, although it may affect other measures such as the margin of error or confidence intervals. The primary factor influencing the standard error is the sample size, with larger samples leading to smaller standard errors.

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Answer: E

Step-by-step explanation:

Answer:

Raspberry?

Step-by-step explanation:

Did I get it???

Hope you have a great day! :)

I think the answer is a pomegranate...

For the given standard deviation the minimum value we would assign is 22.the maximum value we would assign is 88.

To calculate the minimum and maximum values based on the given information, we need to consider the standard deviation and the respective interest rates for the 3-year and 10-year periods.

Given:

S = 26.32 (Initial value)

E = 55 (Expected value)

t = 3 (Years)

Standard deviation = 60% (of the expected value)

3-year interest rate = 2.4%

10-year interest rate = 3.1%

To find the minimum value, we will calculate the value at the end of the 3-year period using the lowest possible growth rate.

Minimum value calculation:

Minimum value = E - (Standard deviation * E) = 55 - (0.6 * 55) = 55 - 33 = 22

Therefore, the minimum value we would assign is 22.

To find the maximum value, we will calculate the value at the end of the 10-year period using the highest possible growth rate.

Maximum value calculation:

Maximum value = E + (Standard deviation * E) = 55 + (0.6 * 55) = 55 + 33 = 88

Therefore, the maximum value we would assign is 88.

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Answer:

(8/3, ∝)

Step-by-step explanation:

Definition

The Mean Value Theorem states that for a continuous and differentiable function \(f(x)\) on the closed interval [a,b], there exists a number c from the open interval (a,b) such that \(\bold{f'(c)=\frac{f(b)-f(a)}{b-a}}\)

Note:

A closed interval interval includes the end points. Thus if a number x is in the closed interval [a, b] then it is equivalent to stating a ≤ x ≤ b.

An open interval does not include the end points so if x is in the open interval (a, b) then a < x < b

This distinction is important

The function is \(y = f(x)=\ln\left(3x-8\right)\)

Let's calculate the first derivative of this function using substitution and the chain rule

Let

\(u(x) = 3x-8\\\\\frac{du}{dx} = \frac{d}{dx}(3x-8) = \frac{d}{dx}(3x) - \frac{d}{dx}8 = 3 - 0 =3\\\\\)

Substituting in the original function f(x), we get

\(y = ln(u)\\\\dy/du = \frac{1}{u}\)

Using the chain rule

\(\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dx}\)

We get

\(\frac{dy}{dx}=\frac{1}{u}3=\frac{1}{3x-8}3=\frac{3}{3x-8}\)

This has a real value for all values of x except for x = 8/3 because at x = 8/3, 3x - 8 = 0 and division by zero is undefined

Now \(ln(x)\) is defined only for values of x > 0. That means 3x-8 > 0 ==> 3x > 8 or x > 8/3

There is no upper limit on the value of x for ln(x) since ln(x) as x approaches ∝ ln(x) approaches  ∝ and  as x approaches ∝ 3/(3x-8) approaches 0

So the interval over which the mean theorem applies is the open interval (8/3, ∝)

At x = 8/3 the first derivative does not exist

Graphing these functions can give you a better visual representation

Answer:

x = 3

Step-by-step explanation:

6.78x - 5.2 = 4.33x + 2.15

6.78x - 4.33x = 5.2 + 2.15

2.45x = 7.35

x = 7.35/2.45

x = 3

Thus, The value of x is 3

-TheUnknownScientist

Answer:

2.6

Step-by-step explanation:

Just divide 5 by 13 to get 2.6 then times 5 and 2.6 is 13

Answer:

No solutions

Step-by-step explanation:

I graphed the equations and the lines overlap, so no solution.

Please give brainliest if this helps :)