find the number that makes the ratio equivalent to 6:15

The vectors is perpendicular to (-4,2) will be (b) (-1,-2)

The dot product of two vectors is found by multiplying the corresponding components of the vectors and adding the results. which is, if the two vectors are (a, b) and (c, d), their dot product is ac + bd.

To calculate the dot product of (-4, 2) with each of the given vectors:

a) (-3.6):

(-4)(-3.6) + (2)(-3.6) = 14.4 - 7.2 = 7.2

b) (-1, -2):

(-4)(-1) + (2)(-2) = 4 - 4 = 0

c) (2, -3):

(-4)(2) + (2)(-3) = -8 - 6 = -14

d) (4, -8):

(-4)(4) + (2)(-8) = -16 - 16 = -32

Therefore, the vector that is perpendicular to (-4, 2) is option (b) (-1,-2).

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Answer:

(405x ^ 7)²

405²x^14

164025x^14 is a square of 405x ^ 7

Step-by-step explanation:

Answer:

Step-by-step explanation:

The expression (1+0.0325)^t represents amount in account after t years for 1 dollar. So multiplying the expression by 500 which is the initial deposit amount means it represents the amount of money in the account after t years.

The student's exam grade was converted to a negative z-score, indicating that they scored below the mean

Therefore, option d is correct.

When a grade is transformed into a z-score, it represents how many standard deviations the grade is away from the mean. The mean is always set at a z-score of 0, and positive z-scores indicate that a grade is above the mean, while negative z-scores indicate that a grade is below the mean.

In this question, the student's exam grade was transformed into a negative z-score, which means that the grade is below the mean. This is because the negative sign in the z-score indicates that the grade is a certain number of standard deviations below the mean. The further the z-score is below 0, the further the grade is below the mean.

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Moe's present age = 32

Zach's present age = 24

Let Moe's present age be represented by m

Let Zach's present age be represented by z

Moe is 8 years older than Zach now

m = z + 8..........(1)

Twenty years ago, Moe's age would be m - 20

Twenty years ago, Zach's age would be z - 20

Twenty years ago, Moe's age was three times that of Zach

m - 20 = 3(z - 20)

m - 20 = 3z - 60

m = 3z - 60 + 20

m = 3z - 40..........(2)

Let equations (1) and (2) be equal to each other:

z + 8 = 3z - 40

3z - z = 8 + 40

2z = 48

z = 48 / 2

z = 24

Substitute the value of z into equation (1)

m = z + 8

m = 24 + 8

m = 32

Moe's present age = 32

Zach's present age = 24

Answer:

20\(\sqrt{5}\)

Step-by-step explanation:

I hope you will get it.

The correct choice is A. lim x → ∞ 15x / sin 5x = 15/5 = 3.

Explanation:

Given limit is, lim x → ∞ 15x / sin 5xWe need to solve this limit.

To solve this limit, multiply and divide by x on the numerator.

So, lim x → ∞ (15 / 5) (5x / x) / (sin 5x / x)lim x → ∞ 3 (5 / x) / (sin 5x / x)

Here, we know that 5 / x → 0 as x → ∞.

Therefore, lim x → ∞ 3 (5 / x) / (sin 5x / x) = 3 × 0 / 1 = 0

Hence, lim x → ∞ 15x / sin 5x = 0. Therefore, A is the correct option.

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Answer:

length = 20

Width = 14

Step-by-step explanation:

x - y = 6   -------------------(I)

x + y = 34 ------------------(II)

Add equation (I) & (II). So y will be eliminated and you can find the value of x

(I)         x - y = 6

(II)       x + y = 34  {Now add}

        2x      =  40      {Divide both sides by 2}

             x   = 40/2

x = 20

Plugin x = 20 in equation(II)

20 +y = 34

       y = 34 -20

y = 14

Answer:

Let Quarters be q and Dimes be d

q + d >20

2q +d >20

d > 20 - 2q

Hope This Helps! (and that you get it right!)

Answer:

QR = 15

Step-by-step explanation:

The product of the length of the secant segment and its external part equals the square of the length of the tangent segment.

(QR+5) *5 = 10^2

(QR+5) *5 = 100

Divide each side by 5.

(QR+5) *5/5 = 100/5

(QR+5)  = 20

Subtract 5 from each side.

QR = 20-5

QR = 15

Answer:

x = 4.5

Step-by-step explanation:

First, we can subtract 2 from 20 (20 - 2) to get 18.

Now we know that x has to be multiplied by 4 and have a product of 18.

We can divide 18 by 4 to figure out what x is.

18 ÷ 4 = 4.5

We can check our answer by solving the equation:

4(4.5) + 2 = 20

18 + 2 = 20

20 = 20

(sorry if this is confusing but I hope it helped)

The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

The confidence interval provides a range of values within which the true population mean height is likely to fall with a 95% level of confidence. It does not provide information about individual orangutans' heights or the sample mean's precise location within the interval.

Therefore, The correct interpretation of the 95% confidence interval is:

"We estimate with 95% confidence that the true population mean height of orangutans is between 52 and 58 inches."

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Answer: 25%

Step-by-step explanation:

Approximate value = 350

Exact value = 280

The percentage error will be calculated by using the formula:

= (Approximate value - Exact value). Exact value × 100

= (350 - 280) / 280 × 100

= 70/280 × 100.

= 1/4 × 100

= 25%

As a point estimator for, we utilise x-bar (sample mean) (mu, population mean)

The average value in mathematics is the middle number, which is calculated by dividing the total number of numbers by the sum of all the numbers. A set of data's average is calculated by adding up all the values and dividing the result by the total number of values.

We use the x-bar (sample mean) as a point estimator for (mu, population mean). As long as the sample is random, this estimator's impartial long-run distribution is centred at (mu).

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Complete question -

We need to choose n to be at least 716 to ensure that the trapezoidal rule approximation is accurate to within 0.00001.

To use the error bound in section 5.9 of the course text, we need to find the second derivative of the function f(x) = sin(x) and evaluate it at the point x = π. We have:

f(x) = sin(x)

f''(x) = -sin(x)

Therefore, |f''(x)| = |sin(π)| = 1.

Using the trapezoidal rule with n subintervals, we have:

tn = h/2 * [f(a) + 2f(a+h) + 2f(a+2h) + ... + 2f(b-h) + f(b)]

where h = (b-a)/n is the width of each subinterval, a = 0, b = π, and n is the number of subintervals.

The error bound for the trapezoidal rule is given by:

|E| ≤ K * (b-a)^3 / (12 * n^2)

where K is an upper bound on |f''(x)| over the interval [a,b].

Substituting the values, we get:

|E| ≤ (1/12) * (π-0)^3 / n^2

We want the error to be less than or equal to 0.00001, so we have:

(1/12) * (π)^3 / n^2 ≤ 0.00001

Solving for n, we get:

n^2 ≥ (1/12) * (π)^3 / 0.00001

n^2 ≥ 510966.9135

n ≥ √510966.9135

n ≥ 715.04

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Slope = (y₂ - y₁)  ÷  (x₂ - x₁)

          =  (-85 - (-83)) ÷  (-11 - 75)

          =  -2 ÷ -86

          = ¹/₄₃

Checking my answer:

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line. If the line passes through both of the points then we calculated the slope correctly.

                               ⇒  y - (-83) =  ¹/₄₃ (x - 75)

                               ⇒     y + 83 =  ¹/₄₃ (x - 75)

 I have included a Desmos Graph that I graphed using the information equation (including the slope) and the points given.

The answer is A. The normal distribution in its standardized form has a mean of 0 and a standard deviation of 1. This means that the distribution is centered around 0, and the spread of the data is determined by the standard deviation of 1. This is useful in statistical analysis because it allows us to compare data from different distributions on a standardized scale.

The normal distribution is a continuous probability distribution that is often used in statistical analysis. It is characterized by a bell-shaped curve and is symmetrical around its mean. In its standardized form, the normal distribution has been transformed to have a mean of 0 and a standard deviation of 1. This transformation is achieved by subtracting the mean of the distribution from each data point and dividing by the standard deviation. This standardization allows us to compare data from different normal distributions on a standardized scale.

The normal distribution has many properties that make it useful in statistical analysis. It is often used as a model for many real-world phenomena, such as the distribution of human height, IQ scores, and many others. The normal distribution is also useful because it is well understood and has many mathematical properties that make it easy to work with.

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The sum of two rational numbers is rational because the sum of any two fractions with rational numerators and denominators can be expressed as a fraction with a rational numerator and denominator.

A rational number is any number that can be expressed as a ratio of two integers, where the denominator is not equal to zero. For example, 1/2, -3/4, 6/5, and 0 are all rational numbers.

When we add two rational numbers together, we can use the following formula:

a/b + c/d = (ad + bc) / bd

where a, b, c, and d are integers and b and d are not equal to zero.

This formula tells us that the sum of two rational numbers is also a rational number. The numerator of the sum is found by cross-multiplying the fractions, and the denominator of the sum is found by multiplying the denominators.

For example, if we want to add 1/2 and 2/3 together, we can use the formula above:

1/2 + 2/3 = (1 x 3 + 2 x 2) / (2 x 3) = 7/6

Therefore, the sum of 1/2 and 2/3 is 7/6, which is also a rational number. This formula can be used to prove that the sum of any two rational numbers is also a rational number.

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A rational number is a number that can be written as \(\dfrac{a}{b}\) where \(a,b\in\mathbb{Z}\) and \(b\not=0\).

If one number is \(\dfrac{a}{b}\) and the other is \(\dfrac{c}{d}\), where \(b,d\not=0\), their sum is \(\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad+bc}{bd}\). Since the set of integers is closed under addition and multiplication, we can write that \(\dfrac{ad+bc}{bd}=\dfrac{e}{f}\) where \(e,f\in\mathbb{Z}\) and \(f\not=0\), thus proving the sum of two rational numbers is a rational number.

Out of all the answer choices, d) 1.327 × 10-31 ng is the only one that matches the calculated value of the mass of a single bromine atom in nanograms. Therefore, d) is the correct answer.

To understand why, we need to convert the mass of a single bromine atom from grams to nanograms.

There are 10^9 nanograms in a single gram, so we can use this conversion factor to make the necessary calculation:
1.327 × 10-22 g x (10^9 ng/1 g) = 1.327 × 10-13 ng

However, none of the answer choices match this value. We need to use scientific notation to convert 1.327 × 10-13 ng into one of the given answer choices.
a) 1.327 × 10-16 mg = 1.327 × 10^-10 ng (since 1 mg = 10^6 ng)
b) 1.327 × 10-25 kg = 1.327 × 10^-4 ng (since 1 kg = 10^12 ng)
c) 1.327 × 10-28 μg = 1.327 × 10^-19 ng (since 1 μg = 10^3 ng)
d) 1.327 × 10-31 ng = 1.327 × 10-31 ng

Out of all the answer choices, d) 1.327 × 10-31 ng is the only one that matches the calculated value of the mass of a single bromine atom in nanograms. Therefore, d) is the correct answer.

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

Answer:

Step-by-step explanation:

9. the set containing all objects or elements and of which all other sets are subsets.

10. complement --> the amount in only one of teh sets

intersection --> the amount in both sets

11. 14 or -14

13. 46 1/2

14. 2 31/120

15. 1100% profit

16. 1200 gm

17. cube root of 7?

18. 6000 per year

Answer:

I think the answer is A

1,2

The confidence level of the study with 72 scores and a standard deviation of 2.9 is approximately 97.5%. This means that we can be 97.5% confident that the findings of the study accurately represent the larger population.

The confidence level of a study refers to the level of certainty or reliability that can be placed on the results obtained from the study. It is often expressed as a percentage and indicates the likelihood that the findings of the study are representative of the larger population.

To calculate the confidence level, we need to know the sample size, the standard deviation, and the desired level of confidence. In this case, the sample size is 72 and the standard deviation is 2.9. The level of confidence is typically expressed as a percentage and is denoted by the Greek letter alpha (α). Common levels of confidence include 90%, 95%, and 99%.

To calculate the confidence level, we use the following formula:

Confidence Level = 1 - (α/2)

Where α/2 is the significance level, which is equal to (1 - Confidence Level)/2. Let's assume a desired confidence level of 95%. Using the formula, we can calculate the significance level as follows:

Significance Level =

(1 - 0.95)/2

= 0.025

To find the confidence level, we need to look up the critical value associated with the significance level in the standard normal distribution table (also known as the z-table). For a two-tailed test, the critical value is the positive z-value that corresponds to the significance level.

Looking up the z-value associated with a significance level of 0.025 in the z-table, we find a value of approximately 1.96. Now, we can calculate the confidence level:

Confidence Level =

1 - (0.025) =

0.975

To express the confidence level as a percentage, we multiply by 100:

Confidence Level =

0.975 * 100 =

97.5%

Therefore, the confidence level of the study with 72 scores and a standard deviation of 2.9 is approximately 97.5%. This means that we can be 97.5% confident that the findings of the study accurately represent the larger population.

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The confidence level of the study with 72 scores and a standard deviation of 2.9 is approximately 97.5%. This means that we can be 97.5% confident that the findings of the study accurately represent the larger population.

The confidence level of a study refers to the level of certainty or reliability that can be placed on the results obtained from the study. It is often expressed as a percentage and indicates the likelihood that the findings of the study are representative of the larger population.

To calculate the confidence level, we need to know the sample size, the standard deviation, and the desired level of confidence. In this case, the sample size is 72 and the standard deviation is 2.9. The level of confidence is typically expressed as a percentage and is denoted by the Greek letter alpha (α). Common levels of confidence include 90%, 95%, and 99%.

To calculate the confidence level, we use the following formula:

Confidence Level = 1 - (α/2)

Where α/2 is the significance level, which is equal to (1 - Confidence Level)/2. Let's assume a desired confidence level of 95%. Using the formula, we can calculate the significance level as follows:

Significance Level =

\((1 - 0.95)/2\\= 0.025\)

To find the confidence level, we need to look up the critical value associated with the significance level in the standard normal distribution table (also known as the z-table). For a two-tailed test, the critical value is the positive z-value that corresponds to the significance level.

Looking up the z-value associated with a significance level of 0.025 in the z-table, we find a value of approximately 1.96. Now, we can calculate the confidence level:

Confidence Level =

\(1 - (0.025) =0.975\)

To express the confidence level as a percentage, we multiply by 100

Confidence Level =

\(0.975 * 100 =\\97.5%\)

Therefore, the confidence level of the study with 72 scores and a standard deviation of 2.9 is approximately 97.5%. This means that we can be 97.5% confident that the findings of the study accurately represent the larger population.

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Answer:

The answer will be

1 c

2 e

3 b

4 a

5 d

Answer

C because 2 quarts make's one gallon

Step-by-step explanation:

(a) The derivative of the difference between two functions, (f - g), is equal to the difference of their individual derivatives, (f' - g'). Therefore, (f - g)'(x) = f'(x) - g'(x). Substituting the given derivatives, we have (f - g)'(x) = (1/x^5) - (7/x).

(b) To find the value of (f - g)'(-2), we substitute x = -2 into the expression obtained in part (a). Thus, (f - g)'(-2) = (1/(-2)^5) - (7/(-2)) = 1/32 + 7/2 = 17/32.

(c) Multiplying a function g'(x) by a constant is equivalent to multiplying its derivative by the same constant. Therefore, 3/8g'(x) = (3/8) * (7/x) = 21/(8x).

(d) Substituting x = -2 into the expression obtained in part (c), we have 3/8g'(-2) = 21/(8 * (-2)) = 21/(-16) = -21/16.

The exact values are:

(a) (f - g)'(x) = (1/x^5) - (7/x)

(b) (f - g)'(-2) = 17/32

(c) 3/8g'(x) = 21/(8x)

(d) 3/8g'(-2) = -21/16.

To calculate the derivative of the difference between functions f and g, we apply the property that the derivative of a difference is equal to the difference of the derivatives. By substituting the given derivatives for f'(x) and g'(x), we obtain the expression (f - g)'(x) = (1/x^5) - (7/x).

For part (b), we evaluate the expression (f - g)'(-2) by substituting x = -2 into the derived expression. This yields (f - g)'(-2) = 1/32 + 7/2 = 17/32.

To compute 3/8 times the derivative of g(x), we apply the constant multiple rule of differentiation. Thus, 3/8g'(x) simplifies to (3/8) * (7/x) = 21/(8x).

Finally, in part (d), we substitute x = -2 into the expression obtained in part (c) to find 3/8g'(-2) = 21/(8 * (-2)) = -21/16.

Therefore, the exact values are as summarized above.

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The value of the variable x for the function f(x) = x² + 4x for which

f(f(x) ) = f(x) is equal to x = -1 or x = -3.

The function f(x) = x² + 4x

Substitute the value in the required function we get,

Right hand side

= f ( f(x))

= f ( x² + 4x )

= ( x² + 4x )² + 4 ( x² + 4x )

= x⁴ + 8x³ + 16x² + 4x² + 16x

= x⁴ + 8x³ + 20x² + 16x

Left hand side

f(x)

= x² + 4x

Equate left hand side is equal to right hand side we get,

x⁴ + 8x³ + 20x² + 16x = x² + 4x

⇒x⁴ + 4x³ + 4x³ + 16x² + 4x² + 16x =  x² + 4x

⇒x² ( x² +4x ) + 4x ( x² + 4x )+ 4 ( x² + 4x ) = x² + 4x

⇒( x² + 4x ) ( x² + 4x + 4 ) = x² + 4x

⇒ x² + 4x + 4 = 1

⇒ ( x + 2 )²  - 1² =0

⇒ ( x + 2 -1 ) ( x+ 2 + 1) = 0

⇒ ( x+ 1 ) ( x+ 3 ) = 0

⇒ x = -1  or x = -3

Therefore, the value of x = -1 or x = -3 for the condition f(f(x)) = f(x).

The above question is incomplete , the complete question is:

Let function f(x) = x² + 4x for what value of x is f(f(x)) = f(x).

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The solution of Representing an arithmetic sequence as a linear function involves finding the equation of a line in the form of y = mx + b.

Here m represents the common difference and b represents the initial term of the sequence. To do this, choose any two terms from the arithmetic sequence and use them to solve for the slope (m) and y-intercept (b). For example, if the two terms are a_n and a_n+k, where k is a constant, you can use the formula: m = (a_n+k - a_n) / k.

Once you have the slope, use one of the two terms and the slope to solve for the y-intercept using the equation y = mx + b. This will give you the equation for the line representing the arithmetic sequence. By using this method, you can practice representing arithmetic sequences as linear functions and find the equation of a line that represents any given arithmetic sequence.

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