question and ente your response in the box provided. Use the
Factor the following expression: x² + x - 6

The p-value is less than the significance level (typically 0.05), we reject the null hypothesis and conclude that the majority of teens in this age range do not respond better to the new drug therapy for autism.

The correct answer is not provided in the question. The chi-square test statistic cannot be used for testing hypotheses about a single proportion. Instead, we use a z-test for proportions. To find the test statistic, we first calculate the sample proportion:

p-hat = 411/900 = 0.4578

Then, we calculate the standard error:

SE = \(\sqrt{[p-hat(1-p-hat)/n] } = \sqrt{[(0.4578)(1-0.4578)/900]}\) = 0.0241

Next, we calculate the z-score:

z = (p-hat - p) / SE = (0.4578 - 0.50) / 0.0241 = -1.77

Finally, we find the p-value using a normal distribution table or calculator. The p-value is the probability of getting a z-score as extreme or more extreme than -1.77, assuming the null hypothesis is true. The p-value is approximately 0.0392.

Since the p-value is less than the significance level (typically 0.05), we reject the null hypothesis and conclude that the majority of teens in this age range do not respond better to the new drug therapy for autism.

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Using a linear function, it is found that:

a) The equation is: y = 385 - 7x.

b) The amount in the account after 3 months is of: $364.

c) The amount in the account after 12 months is of: $301.

d) The balance will be of $0 after 55 months.

The slope-intercept representation of a linear function is given by the rule presented as follows:

y = mx + b

In which:

In the context of this problem, the values of these parameters are as follows:

Hence the equation is:

y = 385 - 7x.

The amounts of the balance are given as follows:

The balance will be of $0 when:

385 - 7x = 0

7x = 385

x = 385/7

x = 55 months.

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Variable commissions based on sales would not appear as a fixed expense on a selling and administrative expense budget.

A fixed expense is an expense that remains constant regardless of the level of sales or production. It does not change with changes in volume or activity. Therefore, the item that would not appear as a fixed expense on a selling and administrative expense budget is:

Variable commissions based on sales

Variable commissions are directly tied to sales and vary in proportion to the level of sales achieved. They are not fixed and would be considered a variable expense rather than a fixed expense.

Other items that are typically included as fixed expenses on a selling and administrative expense budget may include:

Salaries of administrative staff

Rent for office space

Insurance premiums

Depreciation of office equipment

Advertising expenses (if contracted for a fixed period)

Utilities (if on a fixed rate or contract)

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Complete question:

which of the following would not appear as a fixed expense on a selling and administrative expense budget?

Salaries of administrative staff

Rent for office space

Insurance premiums

Depreciation of office equipment

Advertising expenses (if contracted for a fixed period)

Utilities (if on a fixed rate or contract)

For the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the variable x is 7. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The given expression is:

3.35x + 115 = 3.25x + 125

Regroup all the terms with variable x on one side of the equation:

3.35x - 3.25x = 125 - 115

0.1x = 10

x = 100

Hence, for the given expression 3.35x + 115 = 3.25x + 125 the value of x is 100.

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Answer:

Ok

Step-by-step explanation:

So, the domain is the set of all possible values that can be inputted into the function. Or where is function on the x axis is the function defined. The range is similar but on the y axis. In this case, the function you have there appears to go on to infinity (I assume that is what the arrow means) and so the range would be [-1, -infinity) and domain [1, infinity). Brackets are important here because it shows that the function is still defined at point (1,-1), therefore, I used [ bracket symbol (I again assumed that the shaded in black dot at point (1,-1) means that the function is closed at that point and that when it is not shaded in, it is open). I feel like I didn't explain very well but good luck and hopefully someone does a better job that what I did.

i.e. a² + b² = c²

Answer:

Step-by-step explanation:

Solving systems of equations gives the points of intersection when the equations are graphed.

The answer is 3.

Answer:

Step-by-step explanation:

(a) The ratio of adjacent terms is ...

  x^4/x^2 = x^2

The common ratio is x^2.

__

(b) For a geometric sequence with ratio r and first term "a", the sum to infinity is ...

  S = a/(1 -r)

Here, we have ...

  1/3 = x^2/(1 -x^2) . . . . fill in given values for a, r, S

  1 -x^2 = 3x^2 . . . . . cross multiply

  1/4 = x^2

  x = √(1/4)

  x = ±1/2

Let P represent the initial value

Let r represent annual growth rate

let n represent the number of periods

p = 890

r=3.5%

n = 10 ( since a decade is 10 years, 99 years after will be 10 decades)

the formula to calculate the value after 99 years is given by

The value of the quantity after 99 years is 1255.43

Answer:

If your trying to find the slope and y-int of that equation:

Slope: 3

y-int: (0, -6)

Answer:

X=121, y=59, w=59, z=53

Step-by-step explanation:

To find w, we know that the interior angles of a triangle are 180°. Thus ↓

180-31-90=59

For y, we know that y and w are opposite angles. Therefore, y = w = 59.

To find x, we know that there is a one straight line, so therefore we use ↓

180-59=121

Lastly, to find z, we know that the interior angles of a triangle are 180°. Thus ↓

180-59-68=53

I've attached a photo for better understanding. Hope this helps =)

Answer:

x=-24

Step-by-step explanation:

Answer:

It is -24.

Step-by-step explanation:

First distribute 2/3 on the left side, and distribute 1/2 on the other side. Now you have 1 /3 x + 8 =  1/ 6 x + 7 + (−3). Now, combine like terms. Now you should have 1 /3 x + 8 =  1 /6 x + 4. Now, subtract 1/6x on both sides. You should now have 1 /6 x + 8 = 4. Subtract 8 from both sides, and you should have 1/6x = -4. Now the last step is to multiply by 6 on both sides. Now you should get -24. Have a good day!

Answer:77 cents Clara found 77 cents bc you just need to add up the cents and you have it

77 cents

So 2 quarters is 50 cents and you have a nickel: 5 cents, then you have 2 pennies (2 cents), then you have 2 dimes. Now all you have to do is add them all together to get your answer.

5 cents + 25 cents= 30 cents

30 cents + 20 cents= 50 cents

50 cents + 25 cents= 75 cents

75 cents + 2 cents= 77 cents

So Clara would have 77 cents in her desk drawer.

The given statements are proved using set theory.

A⊆B, then X\B⊆X\A.

A⊆X iff A=X\(X\A).

X\B⊆X\A, then A⊆B.

a. Proving that if A⊆B, then X\B⊆X\A:

Assuming that A⊆B, then we can say that if x∈X\B, then x∉B.

Because A is a subset of B, x∉A implies x∉B. If x∉B, then x∈X\A.

As a result, X\B⊆X\A.

b. Proving that A⊆X if and only if A=X\(X\A):

Suppose A⊆X.

Then X\(X\A) = X ∩ A (the intersection of X and A) since the elements in X\A are precisely those that are not in A but in X.

Hence A = X ∩ A, which implies A ⊆ X\(X\A).

Conversely, suppose A = X\(X\A).

Let a be any element of A. This implies that a∈X but a∉X\A, so a∈A.

Therefore, A⊆X.

c. Proving that if A⊆X and X\B⊆X\A, then A⊆B:

If X\B⊆X\A, then B⊇A.

So, it remains to show that A⊆B. If a∈A, then either a∈B (because A⊆B) or a∈X\B (since a∉B).

If a∈X\B, then a∈X\A by X\B⊆X\A.

Therefore, a∉X\A, implying that a∉A.

This shows that A⊆B, and hence, the claim is true.

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Answer:

The correct answer is D. Enough to feel rested.

Answer:

7x+2.5

Step-by-step explanation:

If a shipping charge was applied to each sweatshirt, it would look like

9.5x because it is the same as y=7x + 2.5x, which simplifies to y=9.5x

The probability of drawing a red marble is 5/14.

Probability calculates the chances that an event would occur. The chances of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

The probability of drawing a red marble = number of times the red marble was drawn / total number of marbles

20 / (20 + 24 + 12)

= 20 / 56 = 5/14

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Answer:

what boxes

Step-by-step explanation:

It depends on the sign of \(x-4\).

Recall the absolute value function's definition:

\(|x| = \begin{cases}x & \text{if } x \ge 0 \\ -x & \text{if } x < 0\end{cases}\)

Now, if \(x-4\ge0\), then

\((x-4)|x-4| = (x-4)(x-4) = x^2 - 8x + 16\)

On the other hand, if \(x-4<0\), then

\((x-4)|x-4| = -(x-4)(x-4) = -(x-4)^2 = -x^2 + 8x - 16\)

What you first suggested is incorrect. We have

\(x^2 - 16 = (x - 4) (x + 4)\)

but \(|x-4| \neq x + 4\).

We can show this using the definition again. If \(x-4\ge0\), then

\(x-4 = x+4 \implies -4=4\)

which is a contradiction; on the other hand, if \(x-4<0\), then

\(-x+4 = x+4 \implies 2x = 0 \implies x =0\)

holds for only one value of \(x\).

The effective interest rate of the loan would be

In this case, we are given 4 options:

The formula of compounded interest rate is:

\(A = P (1+\frac{r}{n})^{nt}\)

Where:

A = amount, P = principal amount, r = interest rate, n = number of times interest rate compounded, t = time

Let’s assume the principal amount is $100 for 1 year

Loan L =

\(A = 100 (1+\frac{0.08254}{356})^{356x1}\)

A = $108.603

Loan M =

\(A = 100 (1+\frac{0.08474}{52})^{52x1}\)

A = $108.834

Loan N =

\(A = 100 (1+\frac{0.08533}{12})^{12x1}\)

A = $108.875

Loan O =

\(A = 100 (1+\frac{0.08604}{1})^{1x1}\)

A = $108.604

Therefore, the best effective interest rate for Craig is Loan L with nominal rate of 8.254% compounded daily.

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Given :

Two mean absolute value deviation 15.2 and 10.9 .

To Find :

Which mean absolute value deviation represents more consistency 15.2 or 10.9 .

Solution :

First we should know what is mean absolute deviation ( M.A.D) is :

M.A.D of a data set is the average distance between each data value and the mean .

It also describe the variation in a data set .

Also , high variability means the data is spread out and low variability means that data is clustered .

So, low variation means more consistency and vice-versa .

Therefore , 10.9 M.A.D is more consistent .

Hence , this is the required solution .

2/9 cups of flour is required for baker if he use 1 cup of sugar.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that the baker is making cookies.

The recipe calls for 1/2 cups of flour and \(2\frac{1}{4}\) cups of sugar.

We need to find the flour required to baker for 1 cup of sugar.

Let us form a proportional equation.

x be the flour required for 1 cup of sugar.

\(2\frac{1}{4}\) /1/2=1/x

Apply cross multiplication

9/4x=1/2

Divide both sides by 9/4

x=1/2×4/9

x=2/9

Hence, 2/9 cups of flour is required for baker if he use 1 cup of sugar.

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Option B is represented by the equation Y = 12X on a Coordinate plane with X representing the number of CDs and Y representing the cost in dollars. The cost per CD for Option B is $12, which is less than the cost per CD for Option A ($15). Therefore, Option B is the better deal

Option A: $75 for 5 CDs

Option B:

First quadrant of a coordinate plane with X axis labeled Number of CDs and Y axis labeled Cost in dollars. The line Y equals twelve X is graphed.

To determine which option is the better deal, we need to compare the cost per CD for each option.

Option A costs $75 for 5 CDs, so the cost per CD can be found by dividing $75 by 5 CDs:

Cost per CD = $75 ÷ 5 = $15/CD

Option B is represented by the equation Y = 12X, where Y is the cost in dollars and X is the number of CDs. To find the cost per CD for Option B, we need to substitute X = 1 (since we want to know the cost for 1 CD) into the equation:

Y = 12X

Y = 12(1)

Y = 12

So Option B costs $12 for 1 CD.

Comparing the cost per CD for each option, we see that:

Cost per CD for Option A = $15/CD

Cost per CD for Option B = $12/CD

Therefore, Option B is the better deal as it costs less per CD than Option A.

Option B is represented by the equation Y = 12X on a coordinate plane with X representing the number of CDs and Y representing the cost in dollars. The cost per CD for Option B is $12, which is less than the cost per CD for Option A ($15). Therefore, Option B is the better deal.

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The option which is cheapest include: B. Option B: $12 for 1 CD.

In Mathematics, the unit rate is sometimes referred to as unit price or unit ratio and it can be defined as the quantity of material that is equivalent to a single unit of product or quantity.

In order to determine the unit rate, we would use the following mathematical equation (formula);

Unit rate = Total cost/number of CDs

Unit rate for Option A = 75/5

Unit rate for Option A = $15.

Unit rate for Option B = 12/1 = 24/2 = 36/3 = 48/4 = 60/5

Unit rate for Option B = $12.

In conclusion, we can logically deduce that $12 for 1 CD is much cheaper than $75 for 5 CDs i.e $12 < $15.

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Complete Question;

Which of the following is the cheapest option?

Option A: $75 for 5 CDs

Option B: First quadrant of a coordinate plane with X axis labeled Number of C D’s and Y axis labeled Cost in dollars. The line Y equals twelve X is graphed.

Option A

Option B

The set of all two-letter strings can be thought of as an ordered pair of two letters, where each letter can be selected from the alphabet {a, b, ..., z}.

Since there are 26 letters in the alphabet, there are 26 choices for the first letter in the string. For the second letter, however, there are only 25 choices, since we cannot repeat the letter selected for the first position. Thus, the number of different two-letter strings is the product of the number of choices for each letter, which is 26 * 25 = 650.

This problem illustrates the concept of counting principles, specifically the product rule of counting. The product rule states that the total number of outcomes for a sequence of events is the product of the number of outcomes for each event. In this case, the two events are the selection of the first letter and the selection of the second letter. By applying the product rule, we can easily determine the total number of possible two-letter strings.

This type of problem is commonly encountered in combinatorics, which is the branch of mathematics concerned with counting and arranging objects. The ability to count and calculate the number of possible outcomes is important in many fields, including probability theory, statistics, and computer science.

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Brad was approximately 6 miles away from the lightning when 30 seconds Elapsed between seeing the lightning and hearing the thunder.

The distance, d, that Brad was from the stroke of lightning, we can use the formula d = n/5, where n represents the number of seconds elapsed between seeing the lightning and hearing the thunder.

Given that 30 seconds elapsed between Brad seeing the lightning and hearing the thunder, we can substitute this value into the formula:

d = 30/5

Simplifying the expression:

d = 6

Therefore, Brad was approximately 6 miles away from the lightning when 30 seconds elapsed between seeing the lightning and hearing the thunder.

the speed of sound is approximately 1/5th of a mile per second. So, by dividing the elapsed time by 5, we can estimate the distance in miles.

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No, there is no formula of the form ∫ f(x) dx ≈ α [ f(x0) + f(x1)] that correctly integrates all quadratic polynomials.

Such a formula would be equivalent to the trapezoidal rule, which approximates the integral of a function f(x) over an interval [a, b] as the area of the trapezoid formed by connecting the endpoints (a, f(a)) and (b, f(b)) with a straight line.

The midpoint of the interval (x0 = (a+b)/2) is not used in this formula.

While the trapezoidal rule is a useful method of numerical integration, it is not exact for all quadratic polynomials.

In fact, it is exact only for linear functions, as it provides the exact area of the trapezoid formed by the function and the x-axis.

For other functions, such as quadratic polynomials, the trapezoidal rule provides only an approximation to the integral.

To obtain a more accurate approximation to the integral of a quadratic polynomial, one can use Simpson's rule, which involves evaluating the function at the endpoints and the midpoint of the interval and using a quadratic approximation to the function in the interval.

Simpson's rule is exact for quadratic polynomials and provides a more accurate approximation than the trapezoidal rule.

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The minimum value of the objective function z is 13/5, and the values of x₁ and x₂ corresponding to this minimum are 3/5 and 9/5, respectively.

To solve the given linear programming problem using the M-method, we need to convert the problem into a standard form by introducing surplus variables and an artificial variable. The original problem: Minimize z = 4x₁ + x₂. subject to: 3x₁ + x₂ = 3; 4x₁ + 3x₂ ≥ 6; x₁ + 2x₂ ≤ 4; x₁, x₂ ≥ 0. Introduce surplus variables: Minimize z = 4x₁ + x₂ + 0s₁ + 0s₂ + Ma, subject to: 3x₁ + x₂ - s₁ = 3; 4x₁ + 3x₂ - Ma + s₂ = 6; x₁ + 2x₂ + a = 4; x₁, x₂, s₁, s₂, a ≥ 0. Apply the M-method: To minimize the artificial variable a, we add Ma to the objective function. First, we start with an initial basic feasible solution where a = 0. Solving the system of equations, we get x₁ = 3/5, x₂ = 9/5, s₁ = 0, s₂ = 0, and a = 0.

Next, we update the objective function by adding Ma: z = 4x₁ + x₂ + 0s₁ + 0s₂ + Ma. Perform iterations of the simplex method until we reach the optimal solution. In each iteration, the artificial variable a should leave the basis, and we pivot to find the entering and leaving variables. Upon performing the iterations, we reach the optimal solution where z = 13/5, x₁ = 3/5, x₂ = 9/5, s₁ = 0, s₂ = 0, and a = 0. Therefore, the minimum value of the objective function z is 13/5, and the values of x₁ and x₂ corresponding to this minimum are 3/5 and 9/5, respectively.

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The point (3,-4) will lie on the circle whose centre is at (3,1) and has a diameter of 10 units.

To find which point lies on circle O, we need to use the equation of a circle, which is:

\((x-h)^{2} + (y-k)^{2} = r^{2}\)

where (h, k) is the center of the circle and r is the radius. In this case, the center of the circle is at (3,1) and the diameter is 10 units, also the radius is half of the diameter, which is 5 units here.Therefore, the equation of circle

O will be :

\((x-3)^{2} + (y-1)^{2}= 5^{2}\)

Now to find which point lies on the circle, we need to substitute values for x and y and check for what values does this equation satisfies.

On substituting (3,-4) as x and y respectively, we see that:  \((3-3)^{2}+(-4-1)^{2}\)\(=25\)

\(0+(-5)^{2} = 25\)

25 = 25

Since the left side of the equation is equal to the right side, the point (3,-4) does lie on the circle O.

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