pls
help im confused on how to add/subtract them
A = 4x +-39 B = 6x +-59 Č= -9x+6y Complete each vector sum. A+B+C= A-B+C= 24 + A+B-C- A-B-C= 2+ 2+

60  different words can be formed from the letters in the word BANANA.

Number of letters in BANANA= 6

where, A is repeated 3 times and N is repeated 2 times.

The formula for repeating letters is;

Factorial of total number of letters / Factorial of number of letters repeated.

Thus total permutations = 6! / (2!*3!)

                                         = 60

Therefore, 60 words can will be formed using the letters of BANANA.

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a) The process of making trapezoid is defined

b) The trapezoid is plotted on the grid paper and it is illustrated below.

c) The approximate area of the trapezoid is 10cm

First, let's define what a trapezoid is. A trapezoid is a quadrilateral with one pair of parallel sides. The other two sides may or may not be parallel. The parallel sides are called the bases of the trapezoid, and the distance between them is called the height.

To make a trapezoid with perimeter 20 cm using a string, pushpins, a ruler, and grid paper, you will need to follow these steps:

Cut the string into a length of 20 cm, which is the perimeter of the trapezoid.

Take one of the pushpins and insert it into the grid paper to mark one corner of the trapezoid.

Tie one end of the string to the pushpin and measure out the length of one of the non-parallel sides of the trapezoid using the ruler. Place the second pushpin at this point on the grid paper.

Move the string to the other pushpin, and measure out the length of the other non-parallel side of the trapezoid using the ruler. Place the third pushpin at this point on the grid paper.

Finally, move the string to the third pushpin and measure out the length of the other base of the trapezoid using the ruler. Place the fourth pushpin at this point on the grid paper.

Remove the string and connect the four pushpins to form the trapezoid.

Now, to draw the trapezoid on the grid paper, you can simply connect the four pushpins using a ruler to create the sides of the trapezoid. Make sure to label the parallel sides as the bases and the distance between them as the height.

To find the approximate area of the trapezoid, you can use the formula for the area of a trapezoid, which is

=> (1/2) × (sum of the bases) × (height).

In this case, the sum of the bases is the perimeter of the trapezoid divided by 2, which is 10 cm.

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The required sample size is 907.

We have,

To determine the required sample size for estimating the fraction of new car buyers who prefer foreign cars over domestic with a 95% confidence level and an error of at most 0.03, we'll use the following formula:
n = (Z² x p  (1 - p)) / E²
Where:
- n is the required sample size
- Z is the Z-score for the desired confidence level (1.96 for a 95% confidence level)
- p is the estimated population proportion (0.31)
- E is the margin of error (0.03)

Step-by-step calculation:
1. Calculate Z²: 1.96² = 3.8416
2. Calculate p (1 - p): 0.31 x (1 - 0.31) = 0.2139
3. Calculate E²: 0.03² = 0.0009
4. Substitute these values into the formula: n = (3.8416 x 0.2139) / 0.0009 = 906.92

Since we need to round up to the next integer, the required sample size is 907.

Thus,

The required sample size is 907.

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A whopping 95% of people fall within the IQ ranges of 70 and 130. 99.7% of people in the world have IQs between 55 and 145. Only about 0.3% of people have IQ scores that fall outside of this range (less than 55 or higher than 145).

According to the one-standard-deviation rule, 32 percent of the population has an IQ score that is at least 15 points off from 100: 16 percent have IQs over 115, and 16 percent have IQs below 85.

The equation IQ=mc100, where m is the mental age and c is the chromological age, determines a person's IQ. Find the range of their mental ages if a group of 12-year-old youngsters has an IQ between 80 and 140.

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The formula for y in terms of x is y = 3/x³.

Inversely Proportional:

When two variables are inversely proportional to each other, then the value of one quantity increases with respect to decrease in other or vice-versa.

So, it can be written as,

y = k/x

where,

y is inversely proportional to x and k is the constant of proportionality.

Given,

Y is inversely proportional to the cube of x.

Here we need to find the formula for y in terms of x.

We know that, y is inversely proportional to the cube of x.

So, it can be written as

=> y = k / x³

Where k is the constant.

To find the formula of y,

First we need to find the value of k,

By applying the value of x and y,

So,

=> 24 = k / (1/2)³

=> 24 = k / 1/8

=> 24/8 = k

=> k = 3

Therefore, the formula for y in terms of x is,

=> y = 3/ x³

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Answer:

A.

Step-by-step explanation:

When you substitute the coordinates to its corresponding variables, you can compare that answer choice A. is accurate compared to the other answer choices.

Answer:

A

Step-by-step explanation:

be cause I took it ....

Answer:

f^-1 (x) = x/4

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

\((5 - 1) + ( \frac{1}{4} - \frac{1}{4} )\)

\(4 + 0\)

\(4\)

Answer:

The answer is 4

Step-by-step explanation:

piece of cake :)

The approximation for the definite integral with an error less than \(10^{-4\) is  \(\mathrm{\int\limits^1_0 {\sin x^3} \, dx } \approx \frac{1}{4} - \frac{1}{27} + \frac{1}{16 \cdot 120} - \frac{1}{22\cdot 5040}\)

To approximate the definite integral of \(\mathrm{\int\limits^1_0 {\sin x^3} \, dx }\) with an error less than \(10^{-4\), using a series, we can use the Maclaurin series expansion of the sine function:

\(\mathrm{sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!}+......}\)

In this case, we'll substitute \(x^3\) for x in the series:

\(\mathrm{sin x^3 = x^3 - \frac{x^9}{3!} + \frac{x^{15}}{5!} - \frac{x^{21}}{7!}+......}\)

Now, we'll integrate the series term by term from 0 to 1:

\(\mathrm{\int\limits^1_0 {\sin x^3} \, dx } =\ \mathrm{ \int\limits^1_0 { \, ( x^3 - \frac{x^9}{3!} + \frac{x^{15}}{5!} - \frac{x^{21}}{7!}+......) dx}}\)

Since we're aiming for an error less than \(10^{-4\), we'll need to determine the number of terms required in the series to achieve this level of accuracy.

We'll need to find the first term that contributes to the error.

The error term in a series approximation is typically proportional to the next term in the series that is not included. In this case, the next term would be \(\frac{x^{27}}{9!}\) To estimate the error, we can bound this term by evaluating it at x = 1.

\(\frac{x^{27}}{9!}|_{x = 1} = \frac{1}{9!} = 2.775 \times 10^{-7\)

This term is already smaller than \(10^{-4\) so we can stop at the term \(\frac{x^{21}}{7!}\) to ensure our error is below \(10^{-4\).

Now, we integrate the series up to the \(x^{21\) term,

\(\mathrm{\int\limits^1_0 {\sin x^3} \, dx } =\ \mathrm{ \int\limits^1_0 { \, ( x^3 - \frac{x^9}{3!} + \frac{x^{15}}{5!} - \frac{x^{21}}{7!})\ dx}}\)

Integrating each term separately and summing up these values we get,

\(\mathrm{\int\limits^1_0 {\sin x^3} \, dx } \approx \frac{1}{4} - \frac{1}{27} + \frac{1}{16 \cdot 120} - \frac{1}{22\cdot 5040}\)

This gives an approximation for the definite integral with an error less than \(10^{-4\).

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Answer:45.43

Step-by-step explanation:39.50 plus 15 percent equal 45.425 and 45.425 rounded to the nearest cent is 45.43

The z score of a dog of this breed weighs 52 pounds is 0.571. The weight of the dog if z is -0.35 is 45.55 kg. The weight of the dog if z is 0.35 is 50.45 kg.

A z score refers to a numerical measurement that defines a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

The z score is given by:

z = (x - µ)/σ

where x is the raw score, µ is the mean, and σ is the standard deviation.

In the given case,

x = 52 pounds

µ = 48 pounds

σ = 7 pounds

Hence,

z = (52 - 48)/7 = 0.571

If z = -0.35

Then

-0.35 = (x - 48)/7

x - 48 = -2.45

x = 45.55 kg

Hence, the weight of the dog if z is -0.35 is 45.55 kg.

If z = 0.35

Then

0.35 = (x - 48)/7

x - 48 = 2.45

x = 50.45 kg

Hence, the weight of the dog if z is 0.35 is 50.45 kg.

Note: The question is incomplete. The complete question probably is: The weights of a certain dog breed are approximately normally distributed with a mean of 48 pounds, and a standard deviation of 7 pounds. A dog of this breed weighs 52 pounds. What is the dog's z-score? Round your answer to the nearest hundredth as needed. A dog has a z-score of -0.35. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds A dog has a z-score of 0.35. What is the dog's weight? Round your answer to the nearest tenth as needed. pounds

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Answer:

The answer is 17 km due north.

Step-by-step explanation:

24 km due north subtracted by 7 km east

Put north because it was first (this was based on a rule).

The distance between the final position to the initial position will be 25 km.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Pierre walks 24 km due north and then 7 km due east. Then the distance between the final position to the initial position will be

H² = 24² + 7²

H² = 576 + 49

H² = 625

H² = 25²

H = 25 km

The distance between the final position to the initial position will be 25 km.

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To determine the percentage of times the machine will dispense more than 7.1 oz of coffee, we need to calculate the z-score and find the corresponding area under the normal distribution curve.

The z-score is calculated using the formula:

z = (x - μ) / σ

where x is the value we're interested in (7.1 oz), μ is the mean (7.6 oz), and σ is the standard deviation (0.5 oz).

Let's calculate the z-score:

z = (7.1 - 7.6) / 0.5

z = -0.5 / 0.5

z = -1

Now we need to find the area under the normal distribution curve for a z-score of -1. We can use a standard normal distribution table or a statistical calculator to find this area.

The area corresponds to the probability that the machine will dispense more than 7.1 oz.

Using a standard normal distribution table, we can find that the area to the left of z = -1 is approximately 0.1587. Since we're interested in the area to the right (more than 7.1 oz), we subtract this value from 1:

P(X > 7.1) = 1 - 0.1587

P(X > 7.1) ≈ 0.8413

Therefore, the vending machine will dispense more than 7.1 oz approximately 84.13% of the time.

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A Communication system consists of n components.

a) Binomial distribution,

P(X=x) = ⁿC ₓ p ˣ (1-p) ⁽ⁿ⁻ˣ⁾

b) For 5-component system,

P(X= 5) = ⁵Cₓ pˣ (1-p)⁵⁻ˣ , x= 3,4,5

c) 5-component system is effectively than a 3-component system if 0.5<p<1 where p is probability of functioning components.

Communication system consists of n components and functions with probability p . Then the probability of components which are not function from n components is q = 1-p .

(a) Let x denotes number of functioning components i.e., their probability value is p . And system is effectively operate when atleast one half of components are function. So, the distribution of x is binomial distribution P (X=x) = ⁿCₓ pˣ (1-p)⁽ⁿ⁻ˣ⁾ where n is total number of components, x numbers of functioning components, p is probability of functioning components.

(b) Now , 5-component system is function . That is n=5

Probability that 5-components system will function is P(X= 5)

= ⁵C ₓ p ˣ(1-p)⁽⁵⁻ˣ⁾ , x= 3,4 ,5 ( because one half of components are function)

(c) Because the number of functioning components is a binomial random variable with parameters (n, p), it follows that the probability that a 5-component system will be effective is

⁵ C₃ p³(1-p)² + ⁵C₄ p⁴ (1-p)¹+ ⁵C ₅ p⁵ (1-p)⁰ = 10 p³ (1-p)² + 5 p⁴(1-p) + p⁵

Whereas the corresponding probability for a 3-components system

³ C ₓ p ˣ ( 1-p)⁽ⁿ⁻ˣ⁾ , x= 2,3

³ C₂ p²(1-p)¹ + ³C₃p³(1-p)⁰ = 3 p² 1-p) + p³

5-Component system is better than 3-Components system if

10 p³ (1-p)² + 5p⁴ (1-p) + p⁵= 3p²(1-p) + p³

=> 10 p⁵ + 10 p³– 20 p⁴+ 5 p⁴ – 5p⁵ + p⁵ = 3p² + p³ – 3p²

Which reduce to

3( 2p -1) (1-p) 2 > 0 , either (2p-1) > 0 or 3(1-p) 2>0

either p> ½ or p <1

=> p belongs to ( 0.5, 1)

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Answer:

270 yards

Step-by-step explanation

First write the ratio 2:6 since you know that for one hour you have 60 minutes you need to multiply 2:6 by 30:30 and you get in one hour you can get 180 yards of fabric then to find out how much you would get in a half of an hour you divide 180/2 which = 90 then add 180 +90 = 270

Answer:

x = 11

Step-by-step explanation:

3 x 11 = 33

33-5 = 28

x = 11

Answer:

10

Step-by-step explanation:

Given

h(x) = 3x - 5

h(x) = 25

3x - 5 = 25

3x = 25 + 5

3x = 30

x = 30 / 3

x = 10

Answer:

50 miles

Step-by-step explanation:

Answer:

A = 20

B = 12.5

C = 10.2

Step-by-step explanation:

A = (10 + 20 + 30)/3 = 20

B = (5 + 10 + 15 + 20) = 12.5

C = (1 + 5 + 10 + 15 + 20) = 10.2

Answer:

5/18

Step-by-step explanation:

So sorry if this is wrong but to find the probability you must add all of your things (oars) together then find what the chance of getting that is so 4 oak 5 ash in 2010+4 oak and 5 ash in 2011 is 18 oars total and there was 5 ash in 2011 so the answer is 5/18

Answer:

Finding the dilation's center point is the first step in determining the scale factor. Next, we measure the distances between the center point and various points on the preimage and the image. We may determine the scale factor by dividing these distances by 2.

Step-by-step explanation:

Answer:

length = 3x - 1

Step-by-step explanation:

Area of a rectangle = length x width

or using l = length, w = width and A = area

A = l x w

or

l = A/w

Given
A = 18x² - 6x
w = 6x

l = 18x²- 6x/6x

= 18x²/6x - 6x/6x

= 3x - 1

Answer:

3x - 1

Step-by-step explanation:

Area of the Rectangle:

18x^2 - 6x

6x (3x - 1)

Width = 6x

Length =?

Area of Rectangle = Length *  Width

Length = Area/breadth

6x (3x -1) / 6x cross out 6x

Thus, Length of Rectangle = 3x - 1

Establish a confidence interval for the mean resting pulse rate of the college basketball team's players, the coach needs to collect a representative sample of pulse rate data, calculate sample statistics, determine the critical value, and construct the confidence interval based on the chosen confidence level.

To establish a confidence interval for the mean resting pulse rate, the coach needs to gather a sample of pulse rate data from the team's players. The sample should be representative of the entire team and preferably include a sufficient number of observations.

Once the sample data is collected, the coach can calculate the sample mean and standard deviation of the resting pulse rates. The sample mean represents an estimate of the population mean resting pulse rate, while the standard deviation measures the variability of the data.

Using this sample mean and standard deviation, along with the desired confidence level, the coach can determine the appropriate critical value from the t-distribution or standard normal distribution. The critical value is based on the confidence level and the sample size.

With the critical value and sample statistics, the coach can construct a confidence interval for the mean resting pulse rate. The confidence interval represents a range of values within which the true population mean resting pulse rate is likely to fall.

The width of the confidence interval is influenced by the sample size, sample variability, and chosen confidence level. A larger sample size and lower variability will result in a narrower confidence interval, indicating more precise estimates of the population mean.

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The cylinder has a volume of about 30.55 cubic feet. Consequently, option D, which is 30.55 cubic feet, is the right response.

As a result, the product of the base area and height can be used to determine the cylinder's volume. The volume of any cylinder with base radius "r" and height "h" equals base times height. A cylinder's volume is therefore equal to r²h cubic units.

We use the following formula to determine a cylinder's volume:

V = πr²h

The height of the cylinder is 3.8 feet, according to the issue description.

The distance in feet between two points on the circular base that pass through the centre is designated as the 3.2 feet segment.

When these values are added to the formula, we obtain:

V = π(1.6)²(3.8)

V ≈ 30.55 cubic feet

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Answer:

option D, which is 30.55 cubic feet, is the right response.

Step-by-step explanation:

Brooklyn has 7 brain teasers and total of 15 brain teasers, then Lincoln has 8 brain teasers.

Linear equations are equations that can be written in the form ax + b = 0, where a and b are constants and x is a variable. Linear equations represent straight lines when graphed on a coordinate plane.

We can solve the Linear equation x + 7 = 15 to determine how many brain teasers Lincoln has.

First, we want to isolate the variable x on one side of the equation. To do this, we can subtract 7 from both sides of the equation:

x + 7 - 7 = 15 - 7

Simplifying the equation gives us:

x = 8

Therefore, Lincoln has 8 brain teasers.

In conclusion, if Brooklyn has 7 brain teasers and together they have 15 brain teasers, then Lincoln has 8 brain teasers.

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Answer:

x = 30

Step-by-step explanation:

110 and 3x - 20 are supplementary angles, sum to 180° , then

110 + 3x - 20 = 180

90 + 3x = 180 ( subtract 90 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

Answer:

x = 30

Step-by-step explanation:

Please refer to the attached photo. (Apologies for the terrible drawing.)

For this question, you must be clear of the angle properties.

z + 110 = 180 (Sum of Angles on a straight line)

z = 180 - 110 = 70

z = 3x - 20 (Corresponding Angles)

3x - 20 = z

3x - 20 = 70

3x = 70 + 20

3x = 90

x = 90 / 3 = 30

Answer:

m = 8

Step-by-step explanation:

\(\frac{m}{12}\) = \(\frac{10}{5+10}\)

15m = 120

m = 8

Use csc (90) = 10/m.

So, m = 10/csc(90).

m = 8.93997

Answer: m = 8

Let it be x the numerator. Then we have:

• x + 3: Denominator.

• x + 9: Numerator increased by nine.

• (x + 3) + 9: Denominator increased by nine.

Since the simplified result of the fraction is 13/14, we can write and solve for x the following equation.

Now, we replace the value of x into the left expression from the equation we just solved.

Therefore, the original fraction is 39/42.

Answer:

Step-by-step explanation:

Use Pythagorean to find the missing side x of the triangle.

It is a hypotenuse with other sides 18 in and half of 15 in:

The perimeter is:

Using polar coordinates, the volume of the given solid is:

π√(2a)(511/3)

For the volume of the given solid using polar coordinates, we need to express the equations of the cone and the ring in terms of polar coordinates.

In polar coordinates, the cone equation can be written as:

z = √(2a)(x^2 + y^2)  ⇒  z = √(2a)(r^2)

The ring equation can be expressed as:

1 ≤ x^2 + y^2 ≤ 64  ⇒  1 ≤ r^2 ≤ 64

To evaluate the integral, we'll set up the triple integral in cylindrical coordinates and integrate over the appropriate bounds.

The volume of the solid can be calculated using the following integral:

V = ∫∫∫ dV

where the limits of integration are:

1) For r: 1 ≤ r ≤ 8 (taking the square root of 64)

2) For θ: 0 ≤ θ ≤ 2π (covering a full circle)

3) For z: 0 ≤ z ≤ √(2a)(r^2)

The triple integral in cylindrical coordinates is:

V = ∫∫∫ r dz dr dθ

Now, let's evaluate the integral step by step:

V = ∫∫∫ r dz dr dθ

  = ∫₀²π ∫₁⁸ ∫₀^(√(2a)r²) r dz dr dθ

Now, integrating with respect to z:

V = ∫₀²π ∫₁⁸ [0.5√(2a)r²]₀^(√(2a)r²) dr dθ

  = ∫₀²π ∫₁⁸ 0.5√(2a)r² dr dθ

Next, integrating with respect to r:

V = ∫₀²π [0.5√(2a)(1/3)r³]₁⁸ dθ

  = ∫₀²π 0.5√(2a)(1/3)(8³ - 1³) dθ

Simplifying:

V = ∫₀²π 0.5√(2a)(1/3)(512 - 1) dθ

  = ∫₀²π (0.5√(2a)/3)(511) dθ

  = (0.5√(2a)/3)(511) ∫₀²π dθ

  = (0.5√(2a)/3)(511)(2π)

  = π√(2a)(511/3)

Therefore, the volume of the given solid is π√(2a)(511/3).

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