Suppose the scores on a test given to all juniors in a school district are normally distributed with a mean of 74 and a standard deviation of 8. On a separate sheet of paper, draw a Normal Curve and label the mean, standard deviations, and the associated percentages. Find the percent of juniors who score no more than 90.

PLEASE HELP AHHHH

There are 495 ways to select 4 balls from an urn that has 4 white balls and 8 red balls.

An urn contains 4 white balls and 8 red balls. Four balls are selected. If we have an urn that has n distinct balls, and we want to know how many possible ways there are to select r of them, we use the combination formula:  

C(n, r) = n! / r! * (n - r)!

Where "!" denotes factorial.

Now, we have an urn that has 4 white balls and 8 red balls, for a total of 12 balls.

We want to know how many ways there are to select 4 balls.

Thus, we use the combination formula as follows:

C(12, 4) = 12! / 4! * (12 - 4)!C(12, 4)

            = (12 * 11 * 10 * 9) / (4 * 3 * 2 * 1)C(12, 4)

            = 495

Therefore, there are 495 ways to select 4 balls from an urn that has 4 white balls and 8 red balls.

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Henry opens a savings account with an annual interest rate of 4.5 percent. After a year, he gets $75,000 in payment. He made a deposit into the savings account of $72,831.68.

Here are the steps on how to calculate the amount Henry invested:

Convert the annual interest rate to a monthly rate.

\(\begin{equation}4.5\% \div 12 = 0.375\%\end{equation}\)

Calculate the number of years.

\(\begin{equation}\frac{18 \text{ months}}{12 \text{ months/year}} = 1.5 \text{ years}\end{equation}\)

Use the compound interest formula to calculate the amount Henry invested.

\(\begin{equation}FV = PV * (1 + r)^t\end{equation}\)

where:

FV is the future value ($75,000)

PV is the present value (unknown)

r is the interest rate (0.375%)

t is the number of years (1.5 years)

\(\begin{equation}\$75,000 = PV \cdot (1 + 0.00375)^{1.5}\end{equation}\)

\$75,000 = PV * 1.0297

\(\begin{equation}PV = \frac{\$75,000}{1.0297}\end{equation}\)

PV = \$72,831.68

Therefore, Henry invested \$72,831.68 in the savings account.

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Answer:

As the age of your car increases the value of that car decreases

Step-by-step explanation:

hope this helps

Hey there!

\(Answer:\boxed{n<-1}\)

\(Explanation:\)

\(3<-5n+2n\)

Start by simplifying both sides of the inequality.

\(-3n>3\)

Now divide both sides by -3.

\(\frac{-3n}{-3} >\frac{3}{-3}\\n<-1\)

\(\boxed{n<-1}\text{ is the answer.}\)

Also here is a graph below.

Hope this helps!

\(\text{-TestedHyperr}\)

Answer:

1/2 split into 1/3 = 1/6

Answer:By solving a system of equations, we will see that the function is continuous for all values of x

Step-by-step explanation:

Answer:

D) horizontal compression by a factor of 1/4, and a translation 27 units down

Step-by-step explanation:

Got this right on edge.

Answer: C) 4 x 3 cm

Step-by-step explanation:

The only dimension affected by the cut was 5, because the cut was perfectly parallel to the 4x3 face.

Answer:

the given relation is function because all elements of domain is mapped with the elements of range

Answer:

y= 77

Step-by-step explanation:

Write down the equation for direct proportion.

y= kx, where k is a constant.

Find the value of k.

When x= 12, y= 84,

84= k(12)

12k= 84

k= 84 ÷12

k= 7

Substitute the value of k into the equation.

y= 7x

When x=11,

y= 7(11)

y= 77

To find the z-score corresponding to the 55th percentile. This z-score is approximately 0.13. The minimum score required for admission is approximately 22.0.

To determine the minimum score required for admission, we need to consider that ACT composite scores are normally distributed with a mean (µ) of 21.3 and a standard deviation (σ) of 5.3. The university plans to admit students in the top 45%, which means that we need to find the cutoff score corresponding to the 55th percentile (since 100% - 45% = 55%).
Using a standard normal distribution table or a calculator with a built-in function, we can find the z-score corresponding to the 55th percentile. This z-score is approximately 0.13.
Now, we'll use the z-score formula to find the minimum score required for admission:
X = µ + (z * σ)
Where X is the minimum score, µ is the mean, z is the z-score, and σ is the standard deviation. Plugging in the values:
X = 21.3 + (0.13 * 5.3)
X ≈ 21.3 + 0.689 = 21.989
Rounding the score to the nearest tenth, the minimum score required for admission is approximately 22.0.

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His total pay on Wednesday and on Thursday is 516.75 dollars

Wages can be sum of amount of money collected after a service is rendered.

Given that Paul Aymes is a chrome plater at a local plant. If he plates 300 items or more, he is paid $1.25 each. For less than 300 items, he is paid $0.75 each. What is his total pay if he plates 321 items on Wednesday and 154 items on Thursday ?

For 300 item or more items on Wednesday: 321 x 1.25 = 401.25 dollars

For Less than 300 items on Thursday: 154 x 0.75 = 115.5 dollars

The total pay = 401.25 + 115.5 = 516.75 dollars

Therefore, his total pay on Wednesday and on Thursday is 516.75 dollars

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Madison figures out the average and range of chloride readings from wells close to the ocean. Other than a query, she has carried out an operation. The answer id option (d).

The standard deviation is a measure of variance from the mean that takes spread, dispersion, and dispersion into account. The standard deviation displays a "typical" divergence from the mean. It is a well-liked measure of variability since it retains the primary units of measurement from the data set.  A minor variation occurs when the numbers are close to the mean, while a high variation occurs when they are far from the mean.

The standard deviation describes the degree to which the results deviate from the mean. The average deviation, which depends on all values, is the most often used metric for measuring dispersion. Consequently, the standard deviation's value can be altered even by a slight change in one value.

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i. weekly receipts at a clothing boutique

ii. monthly demand for an automotive part

Time series data refers to information collected and recorded at regular intervals over a specific period. In the case of i. weekly receipts at a clothing boutique and ii. monthly demand for an automotive part, both data sets are examples of time series data.

Time series data consists of observations recorded over regular intervals, allowing for the analysis of patterns and trends over time. In i. weekly receipts at a clothing boutique, the data is collected on a weekly basis, providing insights into the boutique's revenue fluctuations over different weeks. Similarly, ii. monthly demand for an automotive part captures the demand for the part on a monthly basis, enabling analysis of monthly variations and seasonal patterns.

On the other hand, iii. quarterly sales of automobiles do not fall under time series data. While it represents sales data, the intervals between measurements are not consistent enough to qualify as time series. Quarterly intervals are less frequent and may not capture shorter-term trends or variations as effectively as weekly or monthly intervals.

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The expected time taken for the system to fail is dependent on the specific details of the system in question.

However, if we assume that the three modes have equal probabilities of occurring and that the failure occurs when the system reaches a specific mode, we can use the concept of Markov chains to find the expected time until failure.

In this case, the expected time until failure would be the reciprocal of the probability of the system transitioning to the failure mode.

Therefore, if each mode has an equal probability of 1/3, the expected time until failure would be 3 units of time.

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We would need to know the distribution of the revenues, such as whether it follows a normal distribution or some other distribution. Additionally, we would need the specific values of the mean, standard deviation, UCL, and LCL.

To calculate the probability that the true average revenues per hour will be either greater than the Upper Control Limit (UCL) or lower than the Lower Control Limit (LCL), we need more information about the data distribution and the control limits themselves.

Control limits are typically used in statistical process control (SPC) to determine whether a process is stable and within the acceptable range of variation. They are derived from the process data and define the boundaries within which the process is expected to perform.

If we have a normal distribution assumption for the data and know the mean (μ) and standard deviation (σ), we can calculate the probability using the z-score and the standard normal distribution.

Let's assume we have the following information:

- Mean (μ) of the data.

- Standard deviation (σ) of the data.

- UCL and LCL values.

To calculate the probability of the true average revenues per hour being outside the control limits, we can use the z-score formula:

z = (x - μ) / (σ / sqrt(n))

Where:

- x is the value we are interested in (UCL or LCL).

- μ is the mean of the data.

- σ is the standard deviation of the data.

- n is the sample size.

Once we have the z-score, we can consult a standard normal distribution table or use statistical software to find the corresponding probability.

Please provide the necessary information (mean, standard deviation, UCL, LCL, and sample size) so that I can help you calculate the probability.

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Answer:

y = 359x + 1500

((PIC INCLUDED))

Step-by-step explanation:

to write an equation or function in slope intercept form (y=mx+b), first fill out the known values, in this case we got points on a plot

(1,1859)

(3,2577)

(8,4372)

and (12,5808)

to find the slope between these, lets first find the closest two points (makes it easier, but can be done with any two points along a linier graph) for this it will be the first two

now subtract the y-value of the first point from the second point

2577 - 1859 = 718

then devide that by the difference in the x-values between the two points

3 - 1 = 2

718 / 2 = 359

we can now implement the slope (m) into the equation

y = 359x + b

now that we know the slope we can find out what the y intercept (b) is, the slope indicates that as we add 1 in x value, the y value increases by 359, since this works in reverse as well, we can go to our first point, subtract 1 x value (so x = 0) and subtract m from the y value times the x value (359)

1859 - 359 = 1500

meaning that y = 1500 at x = 0, so the y intercept (b) is 1500, insert that value as follows

y = 359x + 1500

all points fall along the line plotted by this function, meaning this is the correct answer

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

just put the grains in a bag in a storeroom

The equation to predict how many hours, x, the second part of the trip will take is :x = (total distance - distance traveled in the first part) / average speed x = (125 - 75) / 50  x = 1

To predict how many hours, x, the second part of the trip will take, we can use the equation:

x = (total distance - distance traveled in the first part) / average speed

In this case, the total distance of the trip is 125 miles, and the distance traveled in the first part is the product of the average speed and the time taken for the first part, which is 50 miles/hour * 1.5 hours = 75 miles.

Substituting these values into the equation, we have:

x = (125 - 75) / 50

Simplifying the equation, we get:

x = 50 / 50

x = 1

Therefore, the equation to predict how many hours, x, the second part of the trip will take is:

x = (total distance - distance traveled in the first part) / average speed

x = (125 - 75) / 50

x = 1

This means that the second part of the trip will take 1 hour to complete after the bus stops to refuel.

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Approximately 34% of American adults have a mobile phone but not a landline, based on the given proportions from the study conducted by the Centers for Disease Control.

The proportion of American adults who have a mobile phone but not a landline, we need to subtract the proportion of those who have both a mobile phone and a landline from the proportion of those who have a mobile phone.

Let's denote the proportion of American adults who have a mobile phone as P(M), the proportion who have a landline as P(L), and the proportion who have neither as P(N).

Given information:

P(M) = 89% (proportion with a mobile phone)

P(L) = 57% (proportion with a landline)

P(N) = 2% (proportion with neither)

We can now calculate the proportion of adults who have a mobile phone but not a landline using the following equation:

P(M and not L) = P(M) - P(M and L)

To find P(M and L), we can subtract P(N) from P(L) since those who have neither are not included in the group with a landline:

P(M and L) = P(L) - P(N)

P(M and L) = 57% - 2%

P(M and L) = 55%

Now we can substitute the values back into the equation to find P(M and not L):

P(M and not L) = P(M) - P(M and L)

P(M and not L) = 89% - 55%

P(M and not L) = 34%

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Answer:

a) |z+w|² cannot be uniquely determined from the information provided.

b) |zw|² = [|z| × |w|]² = (4×2)² = 64.

c) |z+w|² cannot be uniquely determined from the information provided.

d) |z/w|² = [|z|/|w|]² = (4/2)² = 4

Step-by-step explanation:

z & w are complex numbers with magnitudes

|z| = 4

|w| = 2

We are the told to find

|z + w|²

|zw|²

|z - w|²

|z/w|²

Let the complex numbers be

z = x + iy

w = a + ib

|z| = √(x² + y²) = 4

|w| = √(a² + b²) = 2

|z|² = x² + y² = 16

|w|² = a² + b² = 4

z+w = (x + iy) + (a + ib) = (x + a) + i(y + b)

|z+w|² = (x + a)² + (y + b)² = x² + 2ax + a² + y² + 2by + b²

= (a² + b²) + (x² + y²) + 2ax + 2by

= |w|² + |z|² + 2ax + 2by

= 4 + 16 + 2ax + 2by

= 20 + 2(ax + by)

This cannot be determined from the information provided.

zw = (x + iy)(a + ib) = ax + i(bx + ay) - by

= (ax - by) + i(bx + ay)

|zw|² = a²x² + b²y² - 2abxy + b²x² + a²y² + 2abxy

= a²x² + b²y² + b²x² + a²y²

= a²(x² + y²) + b²(x² + y²)

= (a² + b²)(x² + y²)

= |w|² × |z|²

= 4×16

= 64

c) z-w = (x + iy) - (a + ib) = (x - a) + i(y - b)

|z-w|² = (x - a)² + (y - b)²

= x² - 2ax + a² + y² - 2by + b²

= (a² + b²) + (x² + y²) - 2ax - 2by

= |w|² + |z|² - 2ax - 2by

= 4 + 16 - 2ax - 2by

= 20 + 2(ax + by)

This cannot be determined from the information provided.

d) z/w = (x + iy)/(a + ib)

Rationalizing by multiplying numerator and denominator by (a - ib)

(z/w)= [(x + iy)(a - ib)/(a + ib)/(a - ib)]

= [ax - by + i(ay - bx)]/(a² + b²)

|z/w|² = [(ax + by)² + (ay - bx)²]/(a² + b²)²

= [a²x² + b²y² + 2abxy + b²x² + a²y² - 2abxy]/(a⁴ + b⁴ + 2a²b²)

= [a²x² + b²y² + b²x² + a²y²]/[(a² + b²)² - 2a²b² + 2a²b²]

= [(a² + b²)(x² + y²)]/[(a² + b²)²]

= [(x² + y²)/(a² + b²)]

= |z|²/|w|²

= (4/2)²

= 4

Hope this Helps!!!

The solution of the fraction is as follows:

2 3 / 8 - 1 5 / 12 = 23 / 24

A fraction is a number with numerator and denominator. The fraction can be simplified as follows:

Therefore,

2 3 / 8 - 1 5 / 12 =

let's turn the improper fractions to proper fraction as follows:

2 3 / 8 = 19 / 8

1 5 / 12 = 17 / 12

Therefore,

2 3 / 8 - 1 5 / 12 = 19 / 8 - 17 / 12

let's find the lowest common factor of the denominators

19 / 8 - 17 / 12 =  57 - 34/ 24 = 23 / 24

Therefore,

2 3 / 8 - 1 5 / 12 = 23 / 24

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If q is an odd number and the median of q consecutive integers is 120, then the largest of these integers is option (A) (q-1) / 2 + 120

The number q is an odd number

The median of q consecutive integers = 120

Consider the q = 3

Then three consecutive integers will be 119, 120, 121

The largest number = 121

Substitute the value of q in each options

Option A

(q-1) / 2 + 120

Substitute the value of q

(3-1)/2 + 120

Subtract the terms

=2/2 + 120

Divide the terms

= 1 + 120

= 121

Therefore, largest of these integers is (q-1) / 2 + 120

I have answered the question in general, as the given question is incomplete

The complete question is

if q is an odd number and the median of q consecutive integers is 120, what is the largest of these integers?

a) (q-1) / 2 + 120

b) q/2 + 119

c) q/2 + 120

d) (q+119)/2

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INFORMATION:

We have the following table that shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995

We also have a linear model for the data

With the following scatter plot

And, we must solve the three questions.

STEP BY STEP EXPLANATION:

1.

To determine if the linear model fits the data well, we need to analyze the given scatter plot.

We can see that the blue points are very closed to the linear function, that means the function is a good model for the data.

2.

To estimate the retails sales in 2012, we must calculate which year is 2012 after 1995 and then replace it in the function.

So, we must subtract 1995 from 2012

Now, replacing t = 17 in the function

Then, in 2012 the retails sales were 245 billion of dollars

3.

To predict the year that corresponds to retail sales of 250 billion, we must equal the function to 250, and then solve it for t.

Finally, to find the year we must add 17 to 1995 which is the first year

Then, the year that corresponds to retail sales of 250 billion is 2012

ANSWER:

1. the function is a good model for the data.

2. 245

3. 2012

The number of possible passwords is 26^4 * 10^4.

We will make 4 picks from each category (letters and numbers).

We can duplicate them (i.e., pick each character more than once.)

so, for your 4 picks from the letters, you'll have

26 * 26 * 26 * 26 = 26^4 possible selections.

For each of these, you'll have 4 picks from the digits. Similar reasoning, this works out to

10^4 combinations of digits.

This means you'll have 26^4 * 10^4

Possible combinations of 4 letters and 4 digits, and, for each of these, you now need to work out how many unique ways to arrange them.

We will have 8 possible choices for the 1st character, 7 for the second, 6 for the third, etc. This works out to 8!

different orderings for each of your

26^4 * 10^4

The number of possible passwords is 26^4 * 10^4.

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Carol consumed the whole nine-ounce package of grapes. if there are 60 calories per 3 ounce serving. 180 calories are included in 6 ounces of carol.

To calculate the probability of an occurrence, divide the total number of outcomes by the total number of possible outcomes. There are differences between probability and odds. Odds are calculated by dividing the likelihood that a circumstance will occur by the likelihood that it won't. Probability is a statistic used to assess the likelihood that an event will take place. When we toss the coin in the air, the probability that it will land with the heads side up is calculated. Here is a practical use of probability that you are probably already familiar with. We always check the weather forecast before a significant outing.

Since there are \(60\) calories in \(3\) ounces of ice cream

No of calories in \(1\) ounce of carol eat \(=60/3\)

Thus, the no of calories in \(9\) ounces of grapes\(=\) No of calories in \(1\) ounces of carol eat \(*9\)

= The no of calories in \(6\) ounces of carol eat \(= 20*9= 180\)

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The two most commonly used measures of variability are variance and standard deviation.

1. Variance: Variance measures how spread out a set of data points is from the mean. It calculates the average of the squared differences between each data point and the mean. The formula for variance is sum of squared differences divided by the number of data points.

Example: Let's say we have a set of data points: 2, 4, 6, 8, and 10. The mean of these data points is 6. The differences between each data point and the mean are: -4, -2, 0, 2, and 4. Squaring these differences gives us: 16, 4, 0, 4, and 16. The sum of these squared differences is 40. Dividing this sum by the number of data points (5) gives us a variance of 8.

2. Standard Deviation: Standard deviation is the square root of variance. It measures the average distance between each data point and the mean. Standard deviation is often preferred over variance because it is in the same unit as the data points, making it easier to interpret.

Example: Using the same set of data points as above, the variance is 8. Taking the square root of 8 gives us a standard deviation of approximately 2.83.

In summary, variance measures how spread out the data points are from the mean, while standard deviation gives us a more intuitive understanding of the variability by providing a measure in the same unit as the data points. These measures help us understand how the data is distributed and how much it deviates from the average.

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Answer:

10

Step-by-step explanation:

40 = 10 × 4

70 = 10 × 7

GCF of 40 and 70 = 10

Answer:

y-x

Step-by-step explanation:

as y>X so y-x is positive

hence the required expression is y-x