Select the expression that has a value of 6.

2,400 ÷ 40
2,400 ÷ 4
240 ÷ 40
240 ÷ 4

Answer:

Number 7 the answer when rounded to the nearest hundredth is 5.88%

Number 9 the answer is 43.333 repeating.

Step-by-step explanation:

To find the percent of boys that preferred the Beatles, we need to find the total amount of boys who voted. We can see it is 34. To find the percent, we do 2/34 which is equal to 0.05882352941. This as a percent is 5.88% rounded.

To find the amount of girls surveyed from the total, we find the total surveyed and do 26/60. This is equal to 0.4333333 repeating. This is equal to 43.33333% repeating.

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Answer:

r^2 - s = 14 + 9i

Step-by-step explanation:

r^2 = 4^2 + 8i + i^2

r^2 = 16 + 8i - 1

r^2 = 15 + 8i

r^2 - s = 15 + 8i - (1 - i)

r^2 - s = 15 + 8i - 1 + i

r^2 - s = 14 + 9i

68 68 70 61 67 71 63 67



Step 1: Write the formula of standard deviation

n = 8

Step 2: Find the mean

Step 3: find the standard deviation

Next, substitute to find the standard deviation

standard deviation = 3.14

Final answer

The number of data within the standard deviation of the mean = 5

Answer:

9.75

Step-by-step explanation:

10-0.25=9.75

The distance R from A and the bearing of R from A​ 15 km and 189° respectively.

The law of sine or the sine law states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.

Given that, a village R is 10 km from a point P on a bearing 25° from P. Another village A is 6 km from P on a bearing 162°.

We need to calculate, the distance R from A and the bearing of R from A​

We will use the Cosine Rule to determine the distance of R from A (p);

From Cosine Rule;

b² = a² + c²– 2ac Cos B

p² = a² + r² – 2ar Cos P

a= 10 km

Cos P = Cos 137

r = 6 km

p = ?

p² = a² + r² – 2ar Cos P

p² = 10² + 6² - 2 (10) (6) Cos 1370

p² = 100 + 36 – 120 (- 0.7314)

p² = 136 + 87.76

p² = 223.76

p = 14.95 = 15 km (approximated to the nearest km)

To find the bearing of the R from A,

we will apply Sine Rule;

From Sine Rule;

15Sin Ø = 10Sin 137 = 6.82

Sin Ø = 6.82/15 = 0.4547

Ø = ArcSin 0.4547 = 27°

Therefore, the bearing of R from A will be

∠ PRA = 180 – 137 – 27 = 160

The alternating angle to 25° at R is 65°

Then, the bearing of R from A = 270 -65-16 = 189°

Hence, the distance R from A and the bearing of R from A​ 15 km and 189° respectively.

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Answer:

option d is the correct answer

Step-by-step explanation:

use formula for finding sum of all interior angles of regular polygon i.e. (n-2)×180 where n is no of sides of regular polygon then divide it by no. of sides of regular polygon to find measure of one angle of regular polygon and then subtract it from 180° to find the answer

Answer:

P = 116

Step-by-step explanation:

Supplementary angles add to 180

P+Q = 180

P +64 = 180

Subtract 64 from each side

P = 180-64

P =116

Answer:

\(\Huge \boxed{\angle P = 116 \° }\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

Two angles are supplementary when they add up to 180 degrees.

\(\angle Q + \angle P = 180\)

\(64 + \angle P = 180\)

Subtracting 64 from both sides,

\(\angle P = 116\)

\(\rule[225]{225}{2}\)

To find the series solution for the differential equation y'' + 2xy' + 2y = 0, we can assume a power series solution of the form:

Now, substitute y(x), y'(x), and y''(x) into the differential equation:

∑(n=0 to ∞) aₙn(n-1) xⁿ⁻² + 2x ∑(n=0 to ∞) aₙn xⁿ⁻¹ + 2 ∑(n=0 to ∞) aₙxⁿ = 0

We can simplify this equation by combining the terms with the same powers of x. Let's manipulate the equation step by step:

We can combine the three summations into a single summation:

∑(n=0 to ∞) (aₙ₊₂(n+1)n + 2aₙ₊₁ + 2aₙ) xⁿ = 0

Since this equation holds for all values of x, the coefficients of the terms must be zero. Therefore, we have:

This is the recurrence relation that determines the coefficients of the power series solution To find the series solution, we can start with initial conditions. Let's assume that y(0) = y₀ and y'(0) = y'₀. This gives us the following initial terms:

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Answer:

g o o g l e states, "The PSAT/NMSQT stands for the National Merit Scholarship Qualifying Test, which students take as a sophomore or junior."

Step-by-step explanation:

Answer:

The PSAT stands for Practice Standardized Aptitude Test.

Step-by-step explanation:

This test is meant to evaluate a student's college-specific skills.

The required value of  polynomial is f(x) = x² - 35x + 219.

To find the smallest possible value of the polynomial f(x), we need to consider the smallest possible values for x. Given that f(7) = 23 and f(8) = 3, we can use these equations to form a system of equations.

Let's write the system of equations:
f(7) = 23, which means a(7²) + b(7) + c = 23
f(8) = 3, which means a(8²) + b(8) + c = 3

Simplifying these equations, we get:
49a + 7b + c = 23
64a + 8b + c = 3

To solve this system of equations, we can subtract the second equation from the first:
(49a + 7b + c) - (64a + 8b + c) = 23 - 3
49a - 64a + 7b - 8b = 20
-15a - b = 20

Now, we need to find the smallest possible value for a. Since a is an integer, we want the coefficient of a to be as small as possible. If we let a = 1, the coefficient becomes -15. This means that the absolute value of b will be minimized, resulting in the smallest possible value of the polynomial.

Plugging in a = 1 into the equation, we have:
-15(1) - b = 20
-15 - b = 20
-b = 20 + 15
-b = 35
b = -35

Now, we can substitute the values of a and b back into one of the original equations to find c:
a(7²) + b(7) + c = 23
(1)(49) + (-35)(7) + c = 23
49 - 245 + c = 23
-196 + c = 23
c = 23 + 196
c = 219

Therefore, the polynomial is f(x) = x²- 35x + 219.

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Answer:

25

Step-by-step explanation:

A function must have one y-value for any given x-value.

Usually, if you see the same x-value in the x-column more than once, that's not going to be a function, because that usuall makes a single x-value pair with more than one y-value.

This would be NOT be a function, because x-value of 3 is paired with two different y-values.

x  |  y

3    7

4    8

3    9

6    7

Can you identify the function?

Answer:

-5t + 47

Step-by-step explanation:

Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

These cycles are known as the eccentricity cycles, and they are one of the factors that contribute to the long-term climate variations on Earth

The aspect of Earth's orbital relationship to the Sun that varies with a periodicity of both 400 Ka and 100 Ka is the eccentricity of Earth's orbit. The eccentricity refers to the shape of Earth's orbit around the Sun, which is not a perfect circle, but an ellipse. The eccentricity of Earth's orbit changes over time due to gravitational interactions with other planets, particularly Jupiter and Saturn. When Earth's orbit is more elliptical, its distance from the Sun varies more throughout the year, leading to variations in climate and the amount of solar radiation received on Earth's surface. The periodicity of 400 Ka corresponds to a cycle of variations in Earth's eccentricity that affects the amount of solar radiation received at different latitudes and the distribution of ice ages. The periodicity of 100 Ka corresponds to a cycle of variations in Earth's eccentricity that affects the intensity of the seasons and the distribution of glacial periods. These cycles are known as the eccentricity cycles, and they are one of the factors that contribute to the long-term climate variations on Earth.

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The solutions of the given equation are 3.16, 1, and - 1.  

All numbers that make an equation true when the unknowns are eliminated from the equation are considered the solution of the equation.

For the given equation, we can find the solutions by factorizing as shown below.

Here finding the factors of the given polynomial is known as Factorizing. In other words, writing the given equation as a product of its factors.

Here we have

x⁴ - 11x² + 10 = 0

We can solve the above equation as follows

x⁴ - 11x² + 10 = 0

x⁴ - 10x² - x²  + 10 = 0    

Group out the like terms

x²(x² - 10) - (x² - 10) = 0

(x² - 10) (x² - 1) = 0

(x² - 10) (x - 1)(x + 1)  = 0    [ ∵ (x² - 1²) = (x - 1)(x + 1) ]    

x² - 10 = 0 => x = √10 = 3.16  

x - 1 = 0 => x = 1

x + 1 = 0 => x = -1

Therefore,

The solutions of the given equation are 3.16, 1, and - 1.      

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Answer:

$16.5

Step-by-step explanation:

$30-$8-$3.85-$1-$1 = $16.5

The graph of the function f(x)=-x+3,x<=-3 and f(x)=-x^(2)+6,x>-3 is given attachment.

A function is a procedure or a relation that links each element of a non-empty set A, at least, to one element of a different non-empty set B. In mathematics, a relation f between two sets, A and B, is referred to as the function's domain and co-domain, respectively. f = {(a,b)| for all a ∈ A, b ∈ B}

If each element of set A has exactly one image in set B, then the relation is said to be a function.

A function is a relation from a non-empty set B such that its domain is A and no two different ordered pairs in f share the same first element.

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Answer:

c

Step-by-step explanation:

because anything raised to the zeroth power will always be 1, with the exception of 0.

Given in the question:

a.) The circumference of a circle is 24pi ft.

Recall: Formula in getting the circumference of a circle.

Let's first determine the radius of the circle.

Therefore, the radius of the circle is 12 Ft.

Recall: Formula in getting the area of the circle.

We get,

The area of the circle is, therefore, 144pi sq. ft.

The Implied Equity Risk Premium (ERP) is generally considered a better predictor of future equity risk premium

Implied Equity Risk Premium is derived from the current market prices of stocks and other securities. It represents the difference between the expected rate of return on equities and the risk-free rate of return. Investors' expectations about future returns are embedded in market prices, so the implied ERP reflects the collective wisdom and expectations of market participants. It takes into account current market conditions, investor sentiment, and other relevant factors, making it a forward-looking indicator.

On the other hand, historical geometric average and historical arithmetic average equity risk premium are calculated based on past performance data. While historical averages provide valuable insights into the past behavior of equity risk premium, they may not fully capture the changing dynamics of the market or reflect future expectations.

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p = 0

\(8 - 4(2p - 2) = 7 + p + 9\)

➡️ \(8 - 8p + 8 = 16 + p\)

➡️ \(16 - 8p = 16 + p\)

➡️ \( - 8p = p\)

➡️ \( - 8p - p = 0\)

➡️ \( - 9p = 0\)

➡️ \(p = 0\)

Yes, the sampling distribution is normally distributed because the population is normally distributed.

A sampling distribution is a chance distribution of a statistic obtained from a larger variety of samples drawn from a specific populace. The sampling distribution of a given population is the distribution of frequencies of a variety of various outcomes that would probable occur for a statistic of a populace.

A sampling distribution is a probability distribution of a statistic this is obtained via drawing a huge variety of samples from a particular populace. Researchers use sampling distributions so that you can simplify the technique of statistical inference.

Solution :

mean = μ40

standard deviation σ σ= 3

n = 10

μx =  40

σ x = σ√n =  3/√10  = 0.9487

μ x =  4σ\x = 0.9487

σx = 0.9487

Yes, the sampling distribution is normally distributed because the population is normally distributed.

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Answer:

x > -2

Step-by-step explanation:

The mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

Given data values are 55, 56, 70, 61, 53, 57, 50, 73, 52, 69, and 2. We need to calculate the mean, median, and mode of this sample.So, let's first arrange the data values in ascending order:2, 50, 52, 53, 55, 56, 57, 61, 69, 70, 73

Mean:The mean is the sum of all the data values divided by the total number of data values. So, we can use the following formula to calculate the mean:

Mean = (sum of all the data values) / (total number of data values)Sum of all the data values = 55 + 56 + 70 + 61 + 53 + 57 + 50 + 73 + 52 + 69 + 2 = 598Total number of data values = 11

Therefore,Mean = (sum of all the data values) / (total number of data values) = 598 / 11 = 54.36 (rounded to two decimal places)Therefore, the mean of the given data values is 54.36.

Median:The median is the middle value of a sorted data set. Since the data set has 11 data values, the median is the average of the 6th and 7th values (counting from smallest to largest).

Therefore, the median is :Median = (55 + 56) / 2 = 55.5Therefore, the median of the given data values is 55.5.

Mode:The mode is the data value that appears most frequently in the data set. In this case, there is no data value that appears more than once. So, there is no mode.

Therefore, the mode of the given data values is N/A (not applicable).Hence, the mean, median, and mode of the given data values are:Mean = 54.36Median = 55.5Mode = N/A (not applicable)

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The probability that the selected person is a teaching assistant or a female is 29.

What is the probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Here, we have

Given: The physics department of a college has 10 male professors, 7 female professors, 13 male teaching assistants, and 9 female teaching assistants.

We have to find the probability that the selected person is a teaching assistant or a female.

N(A OR B) = N(A) + N(B) - N(A AND B)

N(teaching assistant) = 13 + 9 = 22

N(females) = 7 + 9 = 16

N(teaching assistant and female) = 9

N(teaching assistant OR female) = N(teaching assistant) + N(females) - N(teaching assistant AND female)

N(teaching assistant OR female) = 22 + 16 - 9

N(teaching assistant OR female) =  29

Hence, the probability that the selected person is a teaching assistant or a female is 29.

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Answer:

x<7

Step-by-step explanation:

Answer: x=7, x<18, true

Step-by-step explanation: -10 becomes +10, then you add 10+18. 4x<28 is now the expressio. 28/4=7, x=7 and x or 7<28. This equation is true.

If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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Answer:

Angle A = 16

Angle B = 80

Step-by-step explanation:

All triangles equal up to 180 degrees.

Since we know this, we can make an equation with the given values and set it equal to 180 degrees. Because, 84, 5x, and x must equal 180 degrees.

84 + 5x + x = 180

Now, solve for x.

\(84 + 5x + x = 180\\84 + 6x = 180\\84 - 84 + 6x = 180 - 84\\6x = 96\\\frac{6x}{6} = \frac{96}{6} \\x = 16\)

Now that we have figured out what x is equal to, or in other words, what is the numerical value of x... we can figure out the measure of angle A and B.

Since x = 16, we can replace x with 16.

So for Angle A, x is 16. So, angle A is 16 degrees.

Angle B: 5x = 5(16) = 80. Angle B is 80 degrees.

To check your work (for future reference), plug in x with it's numerical value in the equation we created:

84 + 5(16) + (16) = 180

84 + 80 + 16 = 180

180 = 180

If either side does not equal 180, you did not do your math correctly and must find your error.

Answer:

5pie/6,0

Step-by-step explanation:

i graphed it