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1. A normal distribution has a mean of 10 and a standard deviation of 3.


A. Find the percentage of data that lies between 7 and 16.



B. What two numbers do 68% of the data lie between.



C. Find the percentage of numbers that are larger than 13.

The difference of 32 and x is simply 32 subtracted by x. In other words, it is the result of subtracting the value of x from 32. The answer to this expression will depend on the value of x.

For example, if x is 10, then the difference of 32 and x would be 22 (32 - 10 = 22). If x is 25, then the difference of 32 and x would be 7 (32 - 25 = 7).

In general, if x is less than 32, then the difference of 32 and x will be a positive number, and if x is greater than 32, then the difference of 32 and x will be a negative number.

It is important to remember that the order of the subtraction matters in this expression. If we were to reverse the order and instead write x minus 32, then the result would be different. For example, if x is 10, then x minus 32 would be -22 (10 - 32 = -22). If x is 25, then x minus 32 would be -7 (25 - 32 = -7).

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Answer:

Step-by-step explanation:

hello :

P(A ∩ B)=P(A)×P(B)=1/2×1/3 = 1/6

\(6=\textit{oz of solution at x\%}\\\\ ~~~~~~ x\%~of~6\implies \cfrac{x}{100}(6)\implies \cfrac{6x}{100} \\\\\\ 9=\textit{oz of solution at 0\%}\\\\ ~~~~~~ 0\%~of~9\implies \cfrac{0}{100}(9)\implies 0 \\\\\\ \textit{15 oz of solution at 16\%}\\\\ ~~~~~~ 16\%~of~15\implies \cfrac{16}{100}(15)\implies 2.4 \\\\[-0.35em] ~\dotfill\)

\(\begin{array}{lcccl} &\stackrel{oz}{quantity}&\stackrel{\textit{\% of oz that is}}{\textit{acid only}}&\stackrel{\textit{oz of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{1st Sol'n}&6&\frac{x}{100}&\frac{6x}{100}\\ \textit{2nd Sol'n}&9&0&0\\ \cline{2-4}&\\ mixture&15&0.16&2.4 \end{array}~\hfill \begin{cases} 6 + 9 = 15\\\\ \frac{6x}{100}+0=2.4 \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{using the 2nd equation}}{\cfrac{6x}{100}=2.4}\implies \cfrac{3x}{50}=\cfrac{24}{10}\implies 30x=1200 \\\\\\ x=\cfrac{1200}{30}\implies \boxed{x=\stackrel{\%}{40}}\)

Answer:

Step-by-step explanation:

x=3,-1

The number is  -3.25 is greater than −3.5.

It is required to choose the values is greater than −3.5.

A straight line with numbers placed at equal intervals or segments along its length. Number line is a straight line with a "zero" point in the middle, with positive and negative numbers listed on either side of zero and going on indefinitely.

Given:

On the number line,  a "zero" point in the middle, with positive and negative numbers listed on either side of zero. Numbers on the left are smaller than the numbers on the right of the number line. We always move right to add, move left to subtract  

The number is  -3.25 is closer to 0.

All the other option such as -3.75,-4.2 and -5.4 is less than the -3.5.

Therefore, the number is  -3.25 is greater than −3.5.

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Answer:

120 i think. sorry if its wrong.

Answer:

10 gallons

Step-by-step explanation:

If 60 gallons of water drains in 6 minutes, that means that to find the amount drained per minute, you would have to divide the number of gallons per minute. So 60 gallons÷6 minutes is 10 gallons per minute.

The definition of sin is the opposite/hypotnuse and since the hypotnuse has to be greater or equal to the other sides, the maximum possible value of sine is 1.

O Zeema gets paid £1870 per month in equal monthly payments.

The amount paid each month to repay the loan over the course of the loan is known as the monthly payment. When a loan is taken out, not only the principal, or the original amount borrowed, but also the interest that accrues, must be repaid.

Now when the total amount earned in a month is given then the monthly payment is calculated by dividing the total amount by 12 as there are 12 months in a year.

Annual amount earned by O Zeema=£22,440

Therefore monthly amount earned=£22,440 ÷12=£1870

Hence O Zeema earns £1870 per month

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Answer:

To find the number of additional labourers needed to finish the construction in 21 days, we need to first find the rate at which the 15 labourers were able to build the wall. We can do this by dividing the number of days it took to build the wall by the number of labourers: 28 days / 15 labourers = 1.87 days/labourer.

Next, we need to find the rate at which the labourers would need to work to finish the wall in 21 days. We can do this by dividing the number of days by the number of labourers: 21 days / X labourers = 1.87 days/labourer, where X is the number of labourers we need to find.

Solving this equation for X, we find that we would need 21 labourers to finish the construction in 21 days. Therefore, we would need 21 - 15 = <<21-15=6>>6 additional labourers.

Answer:

True

Step-by-step explanation:

This is because, for the figures to be congruent, it means that, all the shape of one figure happens to be same with the shape of the other figure even though the size of the figures might be different.

.........................................................I am d u m b

Answer:

Step-by-step explanation:

a₄ = a₁ + (4-1)d

4 = -4 + 3d

d = 8/3

a₈ = a₄ + (8-4)d = 4 + 4(8/3) = 14⅔

SOLUTION

Step 1: Write out the formula for percentage increase

Step2: Identify the parametrs

Step3: substitute into the formula in step1

Therefore the percentage increase is 33.3% to the nearest tenth

a) It would take Anya approximately 4 years to accumulate $40,000 with an annual interest rate of 12%. b) Anya must earn an annual rate of return of approximately 12.6% to save $40,000 in 3 years.

a) To calculate the number of years it would take Anya to accumulate $40,000, we can use the future value formula for compound interest:

Future Value = Present Value * (1 + interest rate)ⁿ

Where:

Future Value = $40,000

Present Value = $25,000

Interest rate = 12% = 0.12

n = number of years

Substituting the given values into the formula, we have:

$40,000 = $25,000 * (1 + 0.12)ⁿ

Dividing both sides of the equation by $25,000, we get:

(1 + 0.12)ⁿ = 40,000 / 25,000

(1.12)ⁿ = 1.6

To solve for n, we can take the logarithm of both sides of the equation:

n * log(1.12) = log(1.6)

Using a calculator, we find that log(1.12) ≈ 0.0492 and log(1.6) ≈ 0.2041. Therefore:

n * 0.0492 = 0.2041

n = 0.2041 / 0.0492 ≈ 4.15

b) To calculate the required rate of return for Anya to save $40,000 in just 3 years, we can rearrange the future value formula:

Future Value = Present Value * (1 + interest rate)ⁿ

$40,000 = $25,000 * (1 + interest rate)³

Dividing both sides of the equation by $25,000, we have:

(1 + interest rate)³ = 40,000 / 25,000

(1 + interest rate)³ = 1.6

Taking the cube root of both sides of the equation:

1 + interest rate = ∛1.6

Subtracting 1 from both sides, we get:

interest rate = ∛1.6 - 1

Using a calculator, we find that ∛1.6 ≈ 1.126. Therefore:

interest rate = 1.126 - 1 ≈ 0.126

To express the interest rate as a percentage, we multiply by 100:

interest rate = 0.126 * 100 = 12.6%

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Answer:

A) The percent increase is by 30%.

B) for the original price = 15%.

B2.0) for the existing price (39) = approximately 11.54%.

Step-by-step explanation:

A) First, we divide 30 by 100. The result is the amount that 1% would be(0.3). If you multiply it by 30(which will become 30%) it will be 9. And from 30-39 is 9.

B) First we divide 30 by 100. The result is the amount that 1% would be(0.39). then if you multiply it by 11.54(which will become 11.54%) it will be 4.50(approximately because it actually is 4.5006 and there is no amount that ends up in 4.50). But if you are asking what percentage from the original cost(30) it would be 15% of it(because 0.3 * 15 = 4.50).

Answer:

28 g. ................

Answer:

Undercoverage

Step-by-step explanation:

Using a local telephone book to select a simple random sample could introduce UNDERCOVERAGE bias.

I hope it helps! Have a great day!

The graph of the inverse variation equation is called a rectangular hyperbola.

A form of proportionality called inverse variation occurs when one number falls as the other rises or the other way around. This suggests that if one number rises while the other decreases, the magnitude or absolute value of the first quantity will decrease, resulting in a constant product. The constant of proportionality is another name for this item.

An inverse variation is a relationship between two variables in which the product is constant; as a result, while one of the variables changes, the other changes correspondingly to maintain the same value of the product. This connection has the form of a hyperbola.

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Answer:

It intersects a segment at a right angle.

Step-by-step explanation:

A perpendicular bisector intersects a segment at a right angle at its midpoint.

For perpendicular bisector  It intersects a segment at a right angle.

A line that divides a line or an angle into two parts that are equivalent is known as the bisector. The midpoint of a segment is always present in the segment's bisector. Depending on the geometrical shape it bisects, bisectors can be divided into two categories.                

Line bisector and angular bisector.

Given

to find the characteristic of a perpendicular bisector,

A perpendicular bisector is a line, ray, or segment that intersects a given line segment at 90 degrees and also traverses its midpoint.

It divides or divides line into two equal halves.

it forms right angles (or is perpendicular).

The perpendicular bisector has equal distances between each point.

Hence according to options  intersects a segment at a right angle is correct for perpendicular bisector.

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Equation of Change in bank balance is x - $128

A declaration that two expressions with variables or integers are equal. In essence, equations are questions, and attempts to systematically identify the solutions to these questions have been the driving forces behind the creation of mathematics.

A set of variables, constants, and mathematical operations such as addition, subtraction, multiplication, or division balanced by the equal sign is known as an equation. The equation's left-hand side (LHS) is on the left side, and its right-hand side (RHS) is on the right side (RHS).

Given Data

Let x be the overall bank balance

Equation

Change in bank balance = x - 4(32)

Change in bank balance = x - 128

Thus, equation of Change in bank balance is x - $128

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Answer:

The opposite of -6 is positive 6

Answer:

-6

Step-by-step explanation:

The opposite of the opposite of a number is the number itself

Answer: The answer is 176 or 7260

Step-by-step explanation: there is 2 sides of the wall that is 55 feet long you need to time it by 2 which will be 110. then there are 2 sides of the wall that is 33 feet high by 2 which equals 66 then add together which will be 176 or if you want to multiply the answers it will be 7260.

The value of the iterated integral is 0.5.

To evaluate the iterated integral ∫(3, 2)∫(4, 3)(3xy - 2)dydx, we will first integrate with respect to y, then with respect to x:

1. Integrate with respect to y: ∫(3xy - 2)dy

∫(3xy)dy = (3x/2)y²
∫(-2)dy = -2y

Now combine the two results: (3x/2)y^² - 2y

2. Evaluate the integral for y from 3 to 4:

[((3x/2)(4²) - 2(4)) - ((3x/2)(3²) - 2(3))]

[12x - 8 - (9x - 6)]

3. Integrate with respect to x: ∫(3, 2)(3x - 8)dx

∫(3x)dx = (3/2)x²
∫(-8)dx = -8x

Now combine the two results: (3/2)x² - 8x

4. Evaluate the integral for x from 2 to 3:

[((3/2)(3²) - 8(3)) - ((3/2)(2^²) - 8(2))]

[(13.5 - 24) - (6 - 16)]

5. Calculate the final result:

(-10.5) - (-10) = 0.5

The value of the iterated integral is 0.5.

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y = 2/(1 + 2Ce^(x^2/2)) is the general solution of the original Bernoulli equation.

To find the general solution of the Bernoulli equation, we need to first transform it into a linear equation. This can be done by using the substitution u = y^(1-n), where n is the exponent of y in the original equation.

This substitution will transform the equation into a linear equation in terms of u. We can then solve for u, and finally solve for y to find the general solution.

For example, let's take a look at exercise 23:

y' +x-ly = xy2

In this equation, n = 2. So, we will use the substitution u = y^(-1).

Substituting u into the equation gives us:

u' - xu = -x

This is now a linear equation in terms of u. We can solve for u using an integrating factor:

e^(-x^2/2)u' - xe^(-x^2/2)u = -xe^(-x^2/2)

(e^(-x^2/2)u)' = -xe^(-x^2/2)

Integrating both sides gives us:

e^(-x^2/2)u = (1/2)e^(-x^2/2) + C

Solving for u gives us:

u = (1/2) + Ce^(x^2/2)

Finally, we can solve for y using the substitution u = y^(-1):

y = 2/(1 + 2Ce^(x^2/2))

This is the general solution of the original Bernoulli equation.

The same process can be applied to the other exercises to find their general solutions.

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Answer:

17

Step-by-step explanation:

n = 3

a(n) = 3*2n - 1

a(3) = 3*2*3 - 1

       = 18 - 1

        = 17

The required answer is  the limit of the sequence is 1.

To determine whether the sequence a_n = e^(8/√(n^3)) converges or diverges, we can use the limit comparison test.
First, note that e^(8/√(n^3)) is always positive for all n.
Next, we will compare a_n to the series b_n = 1/n^(3/4).
To determine whether the sequence converges or diverges, we need to analyze the given sequence a_n = e^(8/(n^3)). The value of (8/(n^3)) approaches 0 (since the denominator increases while the numerator remains constant). 3. Recall that e^0 = 1.

Taking the limit as n approaches infinity of a_n/b_n, we get:
lim (n→∞) a_n/b_n = lim (n→∞) e^(8/√(n^3)) / (1/n^(3/4))
= lim (n→∞) e^(8/√(n^3)) * n^(3/4)
= lim (n→∞) (e^(8/√(n^3)))^(n^(3/4))
= lim (n→∞) (e^((8/n^(3/2)))^n^(3/4))

Using the fact that lim (x→0) (1 + x)^1/x = e, we can rewrite this as:
= lim (n→∞) (1 + 8/n^(3/2))^(n^(3/4))
= e^lim (n→∞) 8(n^(3/4))/n^(3/2)
= e^lim (n→∞) 8/n^(1/4)
= e^0 = 1

Since the limit of a_n/b_n exists and is finite, and since b_n converges by the p-series test, we can conclude that a_n also converges by the limit comparison test.

Therefore, the sequence a_n = e^(8/√(n^3)) converges, and to find the limit we can take the limit as n approaches infinity:
lim (n→∞) a_n = lim (n→∞) e^(8/√(n^3))
= e^lim (n→∞) 8/√(n^3)
= e^0 = 1
as n approaches infinity, the expression e^(8/(n^3)) approaches e^0, which is 1. Conclusion.
So the limit of the sequence is 1.

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The mode is the value that appears most frequently in a dataset. In this case, the mode is 4, as it has the highest frequency of occurrence.

The median is the middle value when the data is arranged in ascending or descending order. Since there are an odd number of families (21 in total), the median will be the value of the 11th observation when the data is sorted. Arranging the data in ascending order, we find that the median is also 4, as it is the middle value.

The mean is the average value and is calculated by summing up all the values and dividing by the total number of observations. In this case, we can calculate the mean by multiplying each number of pets by its corresponding frequency, summing up these products, and dividing by the total number of families (21). Using this approach, the mean can be calculated as:

Mean = (0*2 + 1*1 + 2*8 + 3*1 + 4*9 + 5*0) / 21 ≈ 2.76

Therefore, based on the provided data, the mode, median, and mean number of pets owned by the families are all approximately 4.

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Given:

The graph of a function.

To find:

The average rate of change of h over the interval \(5\leq t\leq 9\).

Solution:

The average rate of change of a function f(x) over the interval [a,b] is:

\(m=\dfrac{f(x_2)-f(x_1)}{x_2-x_1}\)

So, the average rate of change of h over the interval \(5\leq t\leq 9\) is:

\(m=\dfrac{h(9)-h(5)}{9-5}\)

From the given graph it is clear that \(h(9)=7,h(5)=3\). Substituting these values, we get

\(m=\dfrac{7-3}{9-5}\)

\(m=\dfrac{4}{4}\)

\(m=1\)

Therefore, the average rate of change of h over the interval \(5\leq t\leq 9\) is 1.

The polynomial function of the lowest degree that has -5, -2, and 0 as roots is f(x) = (x - 2)(x - 5).

To find the polynomial function of the lowest degree with -5, -2, and 0 as roots, we can use the factored form of a polynomial. If a number is a root of a polynomial, it means that when we substitute that number into the polynomial, the result is equal to zero.

In this case, we have the roots -5, -2, and 0. To construct the polynomial, we can write it in factored form as follows: f(x) = (x - r1)(x - r2)(x - r3), where r1, r2, and r3 are the roots.

Substituting the given roots, we have: f(x) = (x - (-5))(x - (-2))(x - 0) = (x + 5)(x + 2)(x - 0) = (x + 5)(x + 2)(x).

Simplifying further, we get: f(x) = (x^2 + 7x + 10)(x) = x^3 + 7x^2 + 10x.

Therefore, the polynomial function of the lowest degree with -5, -2, and 0 as roots is f(x) = x^3 + 7x^2 + 10x.

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The polynomial function of lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5). Each root is written in the form of (x - root) and then multiplied together to form the polynomial.

The question asks for the polynomial function of the lowest degree that has –5, –2, and 0 as roots. To find the polynomial, each root needs to be written in the form of (x - root). Therefore, the roots would be written as (x+5), (x+2), and x. When these are multiplied together, they form a polynomial function of the lowest degree.

Thus, the polynomial function of the lowest degree that has –5, –2, and 0 as roots is f(x) = x(x + 2)(x + 5).

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SOLUTION:

Case: Parallelograms

Method:

Sketch the parallelogram

The angles mHence the angle J is 45 degrees

The angles mHowever,

Final answers:

1. J= 45 degrees {Opposite angles are equal in a parallelogram}

2. K= 135 degrees {Adjacent angles sum up to 180 degrees in a parallelogram}