Suppose that 4% of the 2 million high school students who take the SAT each year receive special accommodations because of documented disabilities. Consider a random sample of 15 students who have recently taken the test. (Round your probabilities to three decimal places.) (a) What is the probability that exactly 1 received a special accommodation? (b) What is the probability that at least 1 received a special accommodation? (c) What is the probability that at least 2 received a special accommodation? (d) What is the probability that the number among the 15 who received a special accommodation is within 2 standard deviations of the number you would expect to be accommodated? Hint: First, calculated and o. Then calculate the probabilities for all integers between 4-20 and + 20. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer:

If you are just wanting to factor out the equation than yes, this is correct! Great job!

Step-by-step explanation:

Answer:

exponential decay because the base is less than one

Step-by-step explanation:

Answer:

Reactant plus reactant yields product.

Step-by-step explanation:

A decomposition reaction starts from a single substance and produces more than one substance. One substance as a reactant and more than one substance as the products is the key characteristic of a decomposition reaction.

Hope this helps.

The solution to the system equation  is (x, y, z, w) = (23, 12, 3, 1).

What is equation?

An equation could be a formula that expresses the equality of 2 expressions, by connecting them with the sign =

Main body:

Here is a system of linear equations that represents the situation.

x +5y +10z +20w = 133 . . . total amount earned

x +y +z +w = 39 . . . . . . . . . total number of bills

y = 4z . . . . . . . . . . . . . . . . . . the number of 5s is 4 times the number of 10s

x = 2y -1 . . . . . . . . . . . . . . . . the number of 1s is 1 less than twice the number of 5s

_____

We can substitute for x and z in the first two equations:

... (2y-1) +5y +10(y/4) +20w = 133

... (2y-1) +y +(y/4) +w = 39

These simplify to

... 9.5y +20w = 134

... 3.25y +w = 40

Solving by your favorite method, you get

... y = 12

... w = 1

So the other values can be found to be

... x = 2·12 -1 = 23

... z = 12/4 = 3

hence ,The solution to the system is (x, y, z, w) = (23, 12, 3, 1).

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Answer:

D. 12+8i

Step-by-step explanation:

\((8 + 6i) + (4 + 2i)\)

\(8 + 4 + 6i + 2i\)

\(12 + 8i\)

To calculate the amount in the account at the end of 1 year, we can use the formula A=P(1+r)^n, where A is the amount, P is the principal (initial amount), r is the interest rate, and n is the number of years.

Plugging in the given values, we have A=8000(1+0.07)^1 = 8560. Therefore, the amount in the account at the end of 1 year is $8560.

To calculate the amount in the account at the end of 2 years, we can again use the same formula A=P(1+r)^n. However, since the interest is compounded annually, we need to use n=2. Plugging in the values, we have A=8000(1+0.07)^2 = 9184.32. Therefore, the amount in the account at the end of 2 years is $9184.32.

In summary, the amount in the account at the end of 1 year is $8560, and the amount in the account at the end of 2 years is $9184.32. These calculations assume that no withdrawals are made from the account and that the interest is compounded annually at a rate of 7%.

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The given function is a exponential decay function

A function that decays exponentially is known as an exponential decay. As a result, it degrades quickly at first and more slowly as the value of the variable rises.

y=3(0.4)^x

The form of the general exponential decay is:

f(x) = A*(r)^x

Where A is the initial value

x is the variable,

r is the rate at which it decreases, where r must be a number between 0 and 1.

r= 0.4 which is a number between 0 and 1.

So, the given function is a  exponential decay function

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Multiply by 2: Divide by (a+b)

Answer:

r=(a-1)/pt

Step-by-step explanation:

a=1+prt

a-1=prt

a-1/pt=r

r=a-1/pt

Answer:

y = |x+6|

Step-by-step explanation:

To represent horizontal shift of a graph, we use the equation y = |x - h|, where h is the amount of units the graph is shifted.  

If we are shifting 6 units to the left, h = -6.  Therefore, the new equation will be: y = |x - (-6)| or y = |x + 6|

g(x) = x^2 - 3

f(x) = x^3+7x^2-x

Start with the g(x) function. Replace every x with f(x)

g(x) = x^2 - 3

g(f(x)) = ( f(x) )^2 - 3

Then replace the f(x) on the right side with x^3+7x^2-x

g(f(x)) = (x^3+7x^2-x)^2 - 3

The highest term inside the parenthesis is x^3. Squaring this leads to (x^3)^2 = x^(3*2) = x^6

So the highest exponent found in g(f(x)) is 6, meaning the degree of is 6

Step-by-step explanation:

4(-6t-3)-10t

-24t-12-10t

-12-24t-10t

-12-34t

The probability of B from k is 0.655

The probability tree of the distribution is given as

A = 0.5k

B = 7k - 0.15

C  = 2.5k

By definition, we have

Sum of probabilities = 1

This means that

A + B  C = 1

substitute the known values in the above equation, so, we have the following representation

0.5k + 7k - 0.15 + 2.5k = 1

When evaluated, we have

10k - 0.15 = 1

So, we have

10k = 1.15

Divide

k = 0.115

Recall that

B = 7k - 0.15

So, we have

B = 7(0.115) - 0.15

Evaluate

B = 0.655

Hence, the probability of B is 0.655

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Answer:

14. y = x - 6

15. \(y = -\frac{1}{2}x-5\)

Step-by-step explanation:

Slope-intercept form is y = mx + b where:

"m" is the slope

"b" is the y-intercept

"x" and "y" are points on the graph.

For each question,

14.

Slope:

Two points are (6, 0) and (7, 1).

\(m= \frac{rise}{run} \\=\frac{1}{1}\\= 1\)

Y-intercept:

b = -6

y = 1x - 6

We don't need to write the 1.

∴ The equation is y = x - 6

15.

Slope:

Two points are (-2, -4) and (0, -5).

\(m = \frac{rise}{run}\\=\frac{-1}{2}\)

Y-intercept:

b = -5

∴ The equation is \(y = -\frac{1}{2}x - 5\)

Answer:

22 feet

Step-by-step explanation:

The area of a circle is π · r².

So, step one is to figure out the radius, so taking that equation, we can say π · r² = 121π.

Divide both sides by π to get r² = 121

Then, you take the square root of both sides to leave r = 11.

The diameter is twice as long as the radius, so multiply 11 · 2 to get 22.

The diameter is 22 feet long.

Notice that - 2(a₁b₁a₂b₂ + a₂b₂a₃b₃ + a₃b₃a₁b₁) is equal to 2(a₁b₁a₂b₂ + a₂b₂a₃b₃ + a₃b₃a₁b₁) with opposite signs. Therefore, we can rewrite the expression as: ||a x b||² + ||a - b||² = ||

The problem requires proving the identity: ||a x b||² + ||a - b||² = ||a||² ||b||², where a and b are vectors in R³. The first paragraph provides a summary of the answer, and the second paragraph explains the proof of the identity. To prove the identity, we will use the properties of the cross product and vector dot product. Let a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃) be two vectors in R³. First, we calculate the cross product of a and b: a x b = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁). The magnitude of the cross product can be written as ||a x b||² = (a₂b₃ - a₃b₂)² + (a₃b₁ - a₁b₃)² + (a₁b₂ - a₂b₁)².

Next, we calculate the difference between a and b: a - b = (a₁ - b₁, a₂ - b₂, a₃ - b₃). The magnitude of the difference can be written as ||a - b||² = (a₁ - b₁)² + (a₂ - b₂)² + (a₃ - b₃)².

Expanding both expressions and combining like terms, we get:

||a x b||² = a₁²b₂² + a₂²b₃² + a₃²b₁² - 2a₁b₁a₂b₂ - 2a₂b₂a₃b₃ - 2a₃b₃a₁b₁,

||a - b||² = a₁² - 2a₁b₁ + b₁² + a₂² - 2a₂b₂ + b₂² + a₃² - 2a₃b₃ + b₃².

Now, we can simplify the expression ||a x b||² + ||a - b||² by combining like terms: ||a x b||² + ||a - b||² = a₁²b₂² + a₂²b₃² + a₃²b₁² + a₁² + b₁² + a₂² + b₂² + a₃² + b₃² - 2(a₁b₁a₂b₂ + a₂b₂a₃b₃ + a₃b₃a₁b₁).

Since ||a||² = a₁² + a₂² + a₃² and ||b||² = b₁² + b₂² + b₃², we can rewrite the expression as:

||a x b||² + ||a - b||² = ||a||² ||b||² - 2(a₁b₁a₂b₂ + a₂b₂a₃b₃ + a₃b₃a₁b₁).

Notice that - 2(a₁b₁a₂b₂ + a₂b₂a₃b₃ + a₃b₃a₁b₁) is equal to 2(a₁b₁a₂b₂ + a₂b₂a₃b₃ + a₃b₃a₁b₁) with opposite signs. Therefore, we can rewrite the expression as:

||a x b||² + ||a - b||² = ||

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There are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.

From the given data, Percent of writers with some college experience but no degree = 12.4%

Percent of writers with a bachelor's degree or higher = 84.1%The percentage of writers without any college experience can be found by:

Percent of writers without any college experience = 100% - (12.4% + 84.1%)

Percent of writers without any college experience = 3.5%T

Total number of writers with some college experience but no degree = 12.4% of 153,000= 18,972

Total number of writers with a bachelor's degree or higher = 84.1% of 153,000= 128,733

Total number of writers without any college experience = 3.5% of 153,000= 5,355

Therefore, the number of writers with a bachelor's degree or higher than those with only some college experience and no degree is:

128,733 - 18,972 = 109,761

Hence, there are 109,761 more writers with a bachelor's degree or higher than those with only some college experience and no degree.

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Using the definition of covariance, Cov(Y(1)Y(2))= 0. From the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2)). So, it can be concluded that Uncorrelated variables need not be independent.

Given joint probability function of Y(1) and Y(2), is

p(Y(1)*Y(2)) = 1/3, for (y(1)*y(2)) = (- 1, 0), (0, 1), (1, 0)

So Y(1), takes random variable -1,0,1.

And Y(2) takes random variable 0,1.

Y(2)|Y(1)      -1               0             1

0                  1/3            0             1/3

1                   0               1/3           0

From the table:

The marginal probability function of Y(1) is;

P(Y(1)=y(1)) = ∑P(Y(1)=y(1)), y(1)= -1,0,1. That is;

Y(1)=y(1)                      -1                   0               1

P(Y(1)=y(1))                  1/3                 1/3             1/3

From the definition of expectation,

E[y(1)]= \(\Sigma_{y_{1}}\) y(1)P(Y(1)=y(1))

E[y(1)]= -1(1/3)+0(1/3)+1(1/3)

E[y(1)]= -1/3+0+1/3

E[y(1)]= 0

The marginal probability mass function of y(2) is

P(Y(2)=y(2)) = ∑P(y(1)y(2)), y(2)= 0,1. That is;

Y(2)=y(2)                    0               1

\(P_{Y(2)}\)(y(2))                  2/3             1/3

Now E[y(2)]= \(\Sigma_{y_{2}}\) y(2)P(Y(2)=y(2))

E[y(2)]= 0(2/3)+1(1/3)

E[y(2)]= 1/3

And

E[y(1)y(2)]= \(\Sigma_{y_{1}}\Sigma_{y_{2}}\) y(1)y(2)P(y(1)y(2))

E[y(1)y(2)]= -1(0)(1/3)+0(1)(1/3)+1(0)(1/3)

E[y(1)y(2)]= 0

From the definition of covariance.

The Cov(Y(1)Y(2))= E[Y(1)Y(2)]-E[Y(1)E[Y(2)]

Cov(Y(1)Y(2))= 0-1/3 (0)

Cov(Y(1)Y(2))= 0

The Cov(Y(1)Y(2))=0, implies that the two variables are uncorrelated. But from the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2))

Hence, it can be concluded that Uncorrelated variables need not be independent.

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Answer:

-4

Step-by-step explanation:

The difference between a blue-collar worker and a white-collar worker is Blue-collar workers are unskilled, manual laborers, and white-collar workers are professionals or semiprofessionals.​Thus the correct option is D.

White collar employees refer to individuals who work as a salaried employees in a professional workspace. They work on the managerial profile or executive profiles also clerical positions. This type of worker has a particular office setting in which they perform their task.

here, we have,

Blue collar employees refer to an individual who does not work on salaries instead they receive daily wages on the basis of the number of hours they spent. These refer to laborers or workers who do not have any qualifications or skills to perform the task.

Therefore, option D is appropriate.

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the solution to the system of equations is x = 2 and y = 1.

To solve the system of equations by substitution, we will solve one equation for one variable and substitute it into the other equation.

Given the system of equations:

1) y = 6x - 11

2) -2x - 3y = -7

Step 1: Solve equation (1) for y.

  y = 6x - 11

Step 2: Substitute the value of y from equation (1) into equation (2).

  -2x - 3(6x - 11) = -7

Step 3: Simplify and solve for x.

  -2x - 18x + 33 = -7

  -20x + 33 = -7

  -20x = -7 - 33

  -20x = -40

  x = (-40)/(-20)

  x = 2

Step 4: Substitute the value of x into equation (1) to find y.

  y = 6(2) - 11

  y = 12 - 11

  y = 1

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The solution to the system of equations y = 6x - 11 and -2x - 3y = -7 is x = 2 and y = 1. This is achieved by substituting y into the second equation, simplifying, and solving for x, then substituting x back into the first equation to solve for y.

To solve the system of equations y = 6x - 11 and -2x - 3y = -7 by substitution, we start by substituting the equation y = 6x - 11 into the second equation in place of y, giving us -2x - 3(6x - 11) = -7. Next, simplify the equation by distributing the -3 inside the parentheses to get -2x - 18x + 33 = -7. Combine like terms to get -20x + 33 = -7. Subtract 33 from both sides to obtain -20x = -40, and finally, divide by -20 to find x = 2.

Once we find the solution for x, we substitute it back into the first equation y = 6x - 11. Substituting 2 in place of x gives y = 6*2 - 11, which simplifies to y = 1.

Therefore, the solution to the system of equations is x = 2 and y = 1.

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The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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The radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

To find the radius of the silo, we need to determine the radius of the cylindrical section.

The volume of the cylindrical section can be calculated using the formula:

\(V_{cylinder} = \pi * r^2 * h\)

where \(V_{cylinder}\) is the volume of the cylindrical section, r is the radius of the cylindrical section, and h is the height of the cylindrical section.

Given that the cylindrical section is 30 ft tall, we can rewrite the formula as:

\(V_{cylinder} = \pi * r^2 * 30\)

To find the radius, we can rearrange the formula:

\(r^2 = V_{cylinder} / (\pi * 30)\)

Now, we can substitute the total volume of the silo, which is 10,000 cubic feet, and solve for the radius:

\(r^2 = 10,000 / (\pi * 30)\)

Simplifying further:

\(r^2 = 106.103\)

Taking the square root of both sides, we find:

\(r = \sqrt{106.103} = 10.3\)

Therefore, the radius of the silo which is in the shape of cylinders and spheres  , correct to the nearest tenth of a foot, is approximately 10.3 feet.

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We will use the formula for a confidence interval for the population mean to determine the confidence level associated with a confidence interval of 6.42 ± 0.1916 for the population mean μ, and we found that it represents a 95% confidence interval.

In statistics, confidence intervals are used to estimate the range of values that a population parameter is likely to fall in. A confidence interval is an interval estimate computed from a sample of data, which is used to describe the range of plausible values of the population parameter. In this scenario, we have a sample of 203 adults who were asked how long they slept last night. We are given the mean and standard deviation of their responses, and we are asked to determine the confidence level associated with a confidence interval of 6.42 ± 0.1916 for the population mean μ.

To determine the confidence level associated with a confidence interval of 6.42 ± 0.1916 for the population mean μ, we need to use the formula for a confidence interval for the population mean:

Confidence Interval = mean ± Zα/2 * (σ / √n) where: sample mean, Zα/2 = the critical value of the standard normal distribution at the desired confidence level (α) divided by 2, σ = population standard deviation (which we estimate using the sample standard deviation, s), n = sample size

In this scenario, first, we need to find the critical value of the standard normal distribution at the desired confidence level (α) divided by 2. We can use a standard normal distribution table or a calculator to find this value. For example, if we want a 95% confidence interval, α = 0.05, and the critical value is Zα/2 = 1.96.

Next, we can substitute the values into the formula and solve for the confidence interval: 6.42 ± 1.96 * (1.56 / √203) = 6.42 ± 0.1916

We can see that the interval 6.42 ± 0.1916 represents a 95% confidence interval for the population mean μ. This means that if we were to take multiple random samples of the same size from the population and calculate their confidence intervals, about 95% of these intervals would contain the true population mean.

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Answer:

I haven't studied this topic so I am unable to answer this question pls understand .. Hope so

The inequalities that model these constraints regarding the shipping employee will be:

4.25x + 6.25y ≤ 60

x+y > 10

It should be noted that from the information, it takes the shipping employee 4.25 min to prepare a package for domestic delivery and 6.5 min to prepare a package for international delivery.

Let x = the number of domestic packages.

Let y = the number of international packages.

Therefore, the inequalities that model these constraints regarding the shipping employee will be:

(4.25 × x) + (6.25 × x) ≤ 60

= 4.25x + 6.25y ≤ 60 and also x+y > 10.

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If five regular six sided dice are rolled then there are 540 ways through which sum of numbers coming after rolling will be 14.

Given Five regular six sided dices are rolled.

From stars and bars the number of n tuples of natural numbers summing up to k is given by

\((k-1\\n-1)\)

For k=14 and n=5

\((14-1 \\5-1)\)

=\((13\\4)\)

=715

Some of these will contains a number greater than 6.To get the number of 5 tuples that correspond to 5 rolls of a six sided dice we need to subtract from 715.

Total 5 tuples summing up to 14 for which no element is greater the 6 is given as under:

N=\((13/4)-5(6/3)-5(5/3)-5(4/3)-5(3/3)\)

where last term comes from the 5 tuples containing one 10 and fours'

=715-100-50-20-5

=540

Hence there  are 540 such ways which sum to 14 when five six sided dices are rolled.

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The given expressions, when A=1, B=0, and C=1, X evaluates to 1.001; when A=B=C=1, X evaluates to 1.111; and when A=B=C=0, X evaluates to 0.000. These evaluations are based on the given values of A, B, and C, and the notation ¯¯¯¯¯¯BC represents the complement of BC.

To evaluate the expression X = A.¯¯¯¯¯¯BC, we substitute the given values of A, B, and C into the expression.

(a) For A = 1, B = 0, and C = 1:

X = 1.¯¯¯¯¯¯01

To find the complement of BC, we replace B = 0 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯01 = 1.¯¯¯¯¯¯00 = 1.001

(b) For A = B = C = 1:

X = 1.¯¯¯¯¯¯11

Similarly, we find the complement of BC by replacing B = 1 and C = 1 with their complements:

X = 1.¯¯¯¯¯¯11 = 1.¯¯¯¯¯¯00 = 1.111

(c) For A = B = C = 0:

X = 0.¯¯¯¯¯¯00

Again, we find the complement of BC by replacing B = 0 and C = 0 with their complements:

X = 0.¯¯¯¯¯¯00 = 0.¯¯¯¯¯¯11 = 0.000

In conclusion, when A = 1, B = 0, and C = 1, X evaluates to 1.001. When A = B = C = 1, X evaluates to 1.111. And when A = B = C = 0, X evaluates to 0.000. The evaluation of X is based on substituting the given values into the expression A.¯¯¯¯¯¯BC and finding the complement of BC in each case.

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The value of KL in the right triangle JKL is determined as 5.34.

To find the value of side length KL, we need to determine the value of opposite side of triangle JML.

Apply trigonometry identity as follows;

tan (51) = JL/JM

tan (51) = JL/14

JL = 14 x tan(51)

JL = 17.29

The value of KL is determined by considering right triangle JKL.

cos (72) = KL / JL

cos (72) = KL/17.29

KL = 17.29 x cos (72)

KL = 5.34

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=======================================================

Explanation:

The angles SPT and TPU marked in red are congruent. They are congruent because of the similar arc markings.

Those angles add to the other angles to form a full 360 degree circle.

Let x be the measure of angle SPT and angle TPU.

86 + 154 + 60 + x + x = 360

300 + 2x = 360

2x = 360-300

2x = 60

x = 60/2

x = 30

Each red angle is 30 degrees.

Then,

angle SPQ = (angle SPT) + (angle TPU) + (angle UPQ)

angle SPQ = (30) + (30) + (86)

angle SPQ = 146 degrees

--------------

Another approach:

Notice that angles QPR and RPS add to 154+60 = 214 degrees, which is the piece just next to angle SPQ. Subtract from 360 to get:

360 - 214 = 146 degrees