On a test that has a normal distribution, a score of 34 falls two standard deviations above the mean, and a score of 22 falls one standard deviation below the mean. Determine the mean of this test.

The total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman is 314 ways.

We can approach this problem using the principle of inclusion-exclusion.

First, let's find the total number of ways to choose a president, vice-president, and treasurer from a group of 8 people without any restrictions. We can do this by using the permutation formula:

8P₃ = 8 x 7 x 6 = 336

Next, let's find the number of ways to choose the three positions where only freshmen are chosen. There are 4 freshmen to choose from, so we can select the president, vice-president, and treasurer in 4P₃  = 4 x 3 x 2 = 24 ways.

Similarly, there are 4 sophomores to choose from, so we can select the three positions where only sophomores are chosen in 4P₃  = 4 x 3 x 2 = 24 ways.

However, we have overcounted the cases where only freshmen or only sophomores are chosen, since the problem statement requires that at least one freshman and at least one sophomore hold at least one of the three positions. Therefore, we need to subtract the number of cases where only freshmen or only sophomores are chosen.

There is only one way to select the president, vice-president, and treasurer from the 4 freshmen, and likewise, there is only one way to select them from the 4 sophomores. Therefore, there are a total of 2 ways to select the three positions where only one class is represented.

Finally, we need to add back the cases where no freshman or no sophomore is chosen. This occurs only if all three positions are filled by juniors or seniors. There are 4 juniors and seniors to choose from, so we can select the three positions in 4P₃  = 4 x 3 x 2 = 24 ways.

Therefore, the total number of ways to choose a president, vice-president, and treasurer from a group of 4 freshmen and 4 sophomores so that at least one freshman and at least one sophomore holds at least one of these three positions is:

336 - 24 - 24 + 2 + 24 = 314 ways.

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To simplify the expression 2(4x + 3) + (x - 3), we need to use the distributive property of multiplication over addition, and then combine like terms.

The expression 2(4x + 3) + (x - 3) contains parentheses and addition and multiplication operations, so we need to follow the order of operations to simplify it. The order of operations is:

1. Simplify any expressions inside parentheses.

2. Evaluate any exponents.

3. Perform multiplication and division, from left to right.

4. Perform addition and subtraction, from left to right.

Let's follow these steps to simplify the expression,

1. Simplify any expressions inside parentheses.

There are two sets of parentheses in the expression: (4x + 3) and (x - 3).

We can use the distributive property of multiplication over addition to eliminate the parentheses:

2(4x + 3) + (x - 3) = 8x + 6 + x - 3

2. Evaluate any exponents,

There are no exponents in the expression.

3. Perform multiplication and division, from left to right.

There is no multiplication or division to perform.

4. Perform addition and subtraction, from left to right.

We can now simplify the expression by combining like terms:

8x + 6 + x - 3 = (8x + x) + (6 - 3) = 9x + 3

Therefore, the simplified expression is 9x + 3.

In summary, the correct procedure to simplify the expression 2(4x + 3) + (x - 3) is to use the distributive property to eliminate the parentheses, and then combine like terms to obtain the simplified expression 9x + 3.

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The average rate of change of the function is 1.6

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

The graph

The interval is given as

−4≤x≤1.

From the graph, we have

f(-4) = -4

f(1) = 4

The average rate of change at this interval is calculated as

Rate = Change in function values/Change in x values

So, we have

Rate = (-4 - 4)/(-4 - 1)

Evaluate

Rate = 1.6

Hence, the rate is 1.6

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Answer:

Step-by-step explanation:

The stock price of Company A decreased by $1.27 for 4 days, so the total decrease in the stock's price would be $1.27 * 4 = $5.08.

On the fifth day, the stock price increased by $3.47, so the total change in the stock's price over 5 days would be $3.47 - $5.08 = -$1.61.

So the total change in the stock's price over 5 days was a decrease of $1.61.

In equilateral triangles, 7.0 mm is the length of each edge of the diamond.

The equilateral triangle's definition?

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.

                                       A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.

V = 0.4783 S³  = 161

   S³   =  161/0.47

       = ∛ 161/0.47

       ≈ 7.0 mm

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Answer:

8√57/57

Step-by-step explanation:

a² + b² = c²

a² + 8² = 11²

a² + 64 = 121

a² = 57

a = √57

For angle Θ, opp = 8, adj = √57, hyp = 11.

tan Θ = opp/adj = 8/√57 = 8√57/57

The least amount of money needed to purchase exactly 20 standard-sized lemons is $1.50, by buying three bags of 6 lemons each and two individual lemons.

What is Combination?

In mathematics, a combination is a way of selecting items from a larger set without regard to the order in which the items are selected. In other words, a combination is a selection of a subset of items from a larger set, where the order of the selected items does not matter.

The number of possible combinations of r items selected from a set of n items is denoted by the notation C(n, r), or sometimes written as nCr. The formula for calculating the number of combinations is:

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

To purchase exactly 20 standard-sized lemons at Joe's Fruit Stand, we need to find the combination of bags of lemons that adds up to a total of 20. We want to minimize the cost, so we should choose the combination of bags with the lowest cost.

One possible combination is to buy two bags of 12 lemons each, for a total of 24 lemons, and then discard 4 lemons. This would cost $2.10 x 2 = $4.20.

Another possible combination is to buy three bags of 6 lemons each, for a total of 18 lemons, and then buy two individual lemons for a total of 20 lemons. This would cost $0.30 x 3 + $0.30 x 2 = $1.50.

Therefore, the least amount of money needed to purchase exactly 20 standard-sized lemons is $1.50, by buying three bags of 6 lemons each and two individual lemons.

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There are 6 grams of sugar in 3/4 of a liter of the sports drink. when There are 4 grams of sugar in 1/2 of a liter of a new sports drink.

To find out how much sugar is in 3/4 of a liter of the sports drink, we need to first calculate the total amount of sugar in 1 liter of the drink. Since there are 4 grams of sugar in 1/2 of a liter, then in 1 liter, there would be 4 x 2 = 8 grams of sugar.

Now that we know there are 8 grams of sugar in 1 liter, we can calculate how much sugar there is in 3/4 of a liter: 8 x (3/4) = 6 grams.

Therefore, there are 6 grams of sugar in 3/4 of a liter of the sports drink.

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The value of the function f(-1) is -4

A function is simply described as an equation that explains the relationship between the independent variable and the dependent variable.

From the information given, we have the function;

f(x)=4x^2+9x+9

To determine the value of f(-1)

substitute the value of x as- 1, we get;

f(-1) = 4(-1)² + 9(-1) + 9

expand the bracket, we get;

f(-1) = -4 -9 + 9

Add or subtract the values, we have;

f(-1) = -4

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The graph of the linear inequality y > -4  is given below.

Linear inequalities are expressions that use inequality symbols to compare two linear expressions. When a polynomial of degree 1 is contrasted with another algebraic expression of a degree less than or equal to 1, this comparison results in a linear inequality, which is an inequality including at least one linear algebraic expression. There are many different ways to represent different types of linear inequalities.

Given linear inequality is y > -4 which represents y region will be in the positive range or greater than -4.

The graph of this linear inequality is given below.

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Answer:

x = 2/3

0r 0.6(6)

both are positive

Step-by-step explanation:

3x - 5 = -3 is the answer positive or negative?

3x - 5 = -3

3x = -3 + 5

3x = 2

x = 2/3

0r 0.6(6)

Answer:

The answer is -8

Step-by-step explanation:

[tex]2x+y=4\\x-y=5\\\\[/tex]

after combining these into a singular equation, we get:

[tex]3x=9\\x=3[/tex]

substitute the value of [tex]x[/tex] into one of the equations:

[tex]x-y=5\\3-y=5\\y=-2[/tex]

now that we found the [tex]x[/tex] and [tex]y[/tex] value, we can substitute it into the term [tex]b^a[/tex] since we know that [tex]x=a[/tex] and [tex]y=b[/tex].

[tex]a^b\\a=x, b=y\\x=3, a=3\\y=-2, b=-2\\-2^3\\-8[/tex]

The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

CLAIM: The surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

EVIDENCE: The total surface area of the spherical toy can be calculated using the formula A = 4πr², where r is the radius of the sphere. Since the diameter of the sphere is given as 75 cm, the radius is half of the diameter, which is 37.5 cm. Therefore, the total surface area of the spherical toy is:

A = 4π(37.5)²

A = 4π(1406.25)

A ≈ 17593.29 cm²

The surface area covered by the triangular sticker can be calculated by finding the area of the triangle, which is given by the formula A = 1/2 bh, where b is the base and h is the height. Therefore, the surface area covered by the sticker is:

A = 1/2 (10)(12)

A = 60 cm²

The surface area not covered by the sticker is the difference between the total surface area of the spherical toy and the surface area covered by the sticker:

A_not_covered = A - A_sticker

A_not_covered ≈ 17593.29 - 60

A_not_covered ≈ 17533.29 cm²

Therefore, the surface area not covered by the sticker on the spherical toy is approximately 5614.1 cm².

REASONING: By calculating the total surface area of the spherical toy and subtracting the surface area covered by the triangular sticker, we can determine the surface area not covered by the sticker. Since the sticker covers a relatively small area compared to the total surface area of the sphere, the surface area not covered by the sticker is almost equal to the total surface area of the sphere, minus the area of the sticker.

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If random sample yielded these observed scores: 6 12 5 10 6 9 12 20 5 23 10 20 11 28 13 18. The 99% confidence interval for the mean height of both groups combined is approximately (3.92, 20.58) cm.

To calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution, since the sample size is relatively small (less than 30) and the population standard deviation is unknown.

First, we need to calculate the sample mean and sample standard deviation. The sample mean can be calculated by adding up all the observed scores and dividing by the total number of scores. In this case, the sample mean is (6+12+5+10+6+9+12+20+5+23+10+20+11+28+13+18) / 16 = 12.25 cm.

The sample standard deviation can be calculated using the formula:

s = √((∑(x - x')^2) / (n - 1))

where x is each observed score, x' is the sample mean, and n is the sample size. In this case, the sample standard deviation is approximately 7.05 cm.

Next, we need to calculate the t-value for a 99% confidence level, with 15 degrees of freedom (16 - 1). Using a t-table or a statistical software, we can find that the t-value is approximately 2.947.

Finally, we can calculate the confidence interval using the formula:

Confidence interval = sample mean ± (t-value * (sample standard deviation / √(sample size)))

Plugging in the values, we get:

Confidence interval = 12.25 ± (2.947 * (7.05 / √(16))) = 12.25 ± 8.33

In summary, to calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution and the formula for confidence intervals. We need to calculate the sample mean, sample standard deviation, t-value for the desired confidence level, and then plug these values into the formula to get the confidence interval.

This interval represents the range of values within which we can be 99% confident that the true mean height of both groups combined falls.

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The angles that are corresponding angles:

∠1 and ∠3

∠5 and ∠7

∠6 and ∠8

We know that when a transversal intersects parallel lines or non-parallel lines then the angles formed at the same relative position at each intersection are nothing but the corresponding angles.

If a transversal intersects parallel lines, then the corresponding angles formed have equal measure.

Wheras if a transversal intersects non-parallel lines, then the corresponding angles formed doesn’t have any relation with each other.

In the following figure we can observe that line p and line q are non-parallel lines and are intersected by transversal r.

From definition of corresponding angles, the pair of corresponding angles:

∠1 and ∠3

∠5 and ∠7

∠6 and ∠8

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Find the complete question below.

The total amount accrued, principal plus interest, with compound interest on a principal of $ 1,500.00 at a rate of 4.9 % per year compounded 1 times per year over 10 years is $2,420.17.

Using the compound interest formula is

Compound interest is calculated by multiplying the initial principal amount (P) by one plus the annual interest rate (R) raised to the number of compound periods (nt) minus one.

A= Total amount =?

P= Principal amount = 1500

r=Rate of interest =4.9 %=0.049

t= time =10years

n= compounding = annually =1

Using the above data and formula, we get:

First, convert R as a percent to r as a decimal

[tex]& \mathrm{r}=\frac{\mathrm{R}}{100} \\[/tex]

[tex]& \mathrm{r}=\frac{4.9}{100} \\[/tex]

[tex]& \mathrm{r}=0.049 \text { rate per year, }[/tex]

Then solve the equation for A

[tex]& \mathrm{A}=1,500.00\left(1+\frac{0.049}{1}\right)^{(1)(10)} \\[/tex]

[tex]& \mathrm{A}=1,500.00(1+0.049)^{10} \\[/tex]

[tex]& \mathrm{~A}=\$ 2,420.17[/tex]

The total amount accrued after 10 years is $2,420.17.

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The equation of the quadratic curve are:

Quadratic equation when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k     where a = 1/4p

The vertex for curve 1

v (h, k) = (-5, 4)

h = -5

k = 4

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x + 5)² + 4

Using (-3, 0) to solve for a

y = a(x + 5)² + 4

0 = a(-3 + 5)² + 4

-4 = a (2)²

a = -1

The equation is y = -(x + 5)² + 4

The vertex for curve 2

v (h, k) = (5, -4)

h = 5

k = -4

substitution of the values into the equation gives

y = a(x - h)² + k

y = a(x - 5)² - 4

Using (3, 0) to solve for a

y = a(x - 5)² - 4

0 = a(3 - 5)² - 4

4 = a (-2)²

a = 1

The equation is y = (x + 5)² + 4

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Answer:

[tex]-1[/tex]

Step-by-step explanation:

[tex](x+y)+(3x-y)=4 \implies 4x=10 \implies x=2.5 \\ \\ 2.5+y=6 \implies y=3.5 \\ \\ \therefore x-y=2.5-3.5=-1[/tex]

Kim saved $9 by using the coupon.

How to find Original price?

The MSRP (i.e., Manufacturer's Suggested Retail Price) set the original price, which is the cost. In the majority of cases, the original price would have been less expensive than the current price, though this is not always the case. Finding an item's original price and knowing the price after a discount are both made possible by original price.

Original price = Sales price/(100%-Discount%)

To find out how much money Kim saved, we need to first find out how much the birdhouse cost after the coupon was applied.

The coupon took 25% off the original price, so the birdhouse cost 100% - 25% = 75% of its original price.

So, the new price of the birdhouse would be:

36 * 75% = $27

Kim saved 36 - 27 = $9 by using the coupon.

Therefore, Kim saved $9 using the coupon.

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PLEASE GIVE BRAINLIEST!

thank you and have a good day ;)

Answer:

-11/2

Step-by-step explanation:

Multiply both sides by a polynomial to clear functions

x + 1 = 3(x +4)

x + 1 = 3x + 12

x - 3x = 12 -1

-2x = 11

x = -11/2

I hope this helps

Answer:

The answer can be written in multiple forms

Fraction Form:   [tex]x=-\frac{11}{2}[/tex]

Decimal Form:   [tex]x=-5.5[/tex]

Step-by-step explanation:

Given

[tex]\frac{x+1}{x+4}=3[/tex]

Lets solve for [tex]x[/tex].

Eliminate the fraction by multiplying each side of the equation by [tex]x+4[/tex].

[tex]x+1=3(x+4)[/tex]

Simplify the right side by applying the distributive property.

[tex]x+1=(3*x)+(3*4)[/tex]

[tex]x+1=3x+12[/tex]

Subtract [tex]3x[/tex] from both sides of the equation.

[tex]x+1-3x=12[/tex]

Add [tex]x[/tex] and [tex]-3x[/tex].

[tex]-2x+1=12[/tex]

Subtract [tex]1[/tex] from both sides of the equation.

[tex]-2x=11[/tex]

Divide each side of the equation by [tex]-2[/tex].

[tex]x=-\frac{11}{2}[/tex]

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The solution to the given quadratic equation formed is; y = -9/4 and y = -1

The given equation is expressed as;

(3 + 2y) = √(-y)

Taking the square of both sides gives us;

(3 + 2y)² = √(-y)]²

→ 9 + 12y + 4y² = -y

4y² + 13y + 9 = 0

Factoring the expression gives us;

4y² + 4y + 9y + 9 = 0

4y(y + 1) + 9(y + 1) = 0

Thus;

(4y + 9) = 0

(y + 1) = 0

y = -9/4

y = -1

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In mathematics, a line is a set of points that extend indefinitely in two directions.

Points on the line: These are points that lie exactly on the line. They are equidistant from the two endpoints of the line and are considered to be part of the line itself.

Points above the line: Points that are vertically above the line are referred to as points above the line. These points are located higher than the line and have a greater y-coordinate than any point on the line.

Points below the line: Points that are vertically below the line are referred to as points below the line. These points are located lower than the line and have a smaller y-coordinate than any point on the line.

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The initial number of points earned when signing up is 30 and earned per pair of shoes purchased is 15.

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂). Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

Let 'x' be the number of shoes purchased and 'y' be the total points earned.

From the graph, the two points are (2, 60) and (4, 90). Then the equation is given as,

[tex]\rm (y - 60) = \left (\dfrac{90 - 60}{4 - 2} \right) (x - 2)[/tex]

y - 60 = 15(x - 2)

y - 60 = 15x - 30

y = 15x + 30

The initial number of points earned when signing up is 30 and earned per pair of shoes purchased is 15.

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Answer:

it's like this the answer

Step-by-step explanation:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Answer:

x⁴-8x²y²+16y²-256

(x²-8xy)²+(4y-16)²

Step-by-step explanation:

Option (c) is correct: the sample covariance between the regressors and the OLS residuals is zero. This is an important property because it implies that the OLS estimator is not biased and the estimated coefficients of the independent variables are consistent.

The algebraic property of OLS (Ordinary Least Squares) estimates is that the sample covariance between the regressors and the OLS residuals is zero. This means that the OLS estimates are unbiased and not correlated with the independent variables in the regression model.

Option (a) is incorrect: the sum, and therefore the sample average of the OLS residuals, can be either positive or negative depending on the distribution of the data and the fit of the model.

Option (b) is also incorrect: the sum of the OLS residuals can be either positive or negative depending on the distribution of the data and the fit of the model.

Option (d) is incorrect: the OLS sample regression line does not always pass through the sample average of x and the sample average of y. However, it does pass through the point of averages when the model includes a constant term (i.e., intercept).

Therefore, the correct answer is (c): the sample covariance between the regressors and the OLS residuals is zero.

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Answer:

Jennifer raised $25

Rebecca raised £50

Derek raised $37.50

Matthew raised $75

Step-by-step explanation:

J: 50% = dividing by 2, 50/2= 25

R: 50 is 100%, because that was the total

D: 75% = dividing by 4, timsing by three, so 50/4 is 12.5 x 3 is 37.5, put it into currency $37.50

M: We add another 25% onto 50 so 25+50=75.

(hope this works!!)