9.
The dimensions of a rectangle are x cm and (x + 9 )cm. If the area of the rectangle is 52 cm?,
calculate the only possible value of x.

To find two unit vectors that make an angle of 60° with v = 3, 4, we first need to find the magnitude of v. Using the Pythagorean theorem, we can calculate the magnitude of v. The two unit vectors that make an angle of 60° with v = (3, 4) are u1 and u2.

|v| = sqrt(3^2 + 4^2) = 5

Next, we need to find the unit vector in the direction of v. This can be done by dividing each component of v by its magnitude:

u = v/|v| = (3/5, 4/5)

Now we need to find two unit vectors that make an angle of 60° with u. To do this, we can use the formula for rotating a vector counterclockwise by an angle θ:

v' = cos(θ)v + sin(θ)u

Since we want two vectors that make an angle of 60° with u, we can use θ = ±60°. Plugging in these values, we get:

v₁ = cos(60°)v + sin(60°)u = (1/2)3 + (sqrt(3)/2)4, (1/2)4 - (sqrt(3)/2)3
   = (3/2 + 2sqrt(3), 2 - 3sqrt(3)/2)
   ≈ (3.732, -0.598)

v₂ = cos(-60°)v + sin(-60°)u = (1/2)3 - (sqrt(3)/2)4, (1/2)4 + (sqrt(3)/2)3
   = (-3/2 + 2sqrt(3), 2 + 3sqrt(3)/2)
   ≈ (-1.732, 4.598)

Thus, two unit vectors that make an angle of 60° with v = 3, 4 are v₁ ≈ (3.732, -0.598) and v₂ ≈ (-1.732, 4.598).
To find two unit vectors that make an angle of 60° with v = (3, 4), we can use the following steps:

1. Calculate the magnitude of v: |v| = √(3² + 4²) = 5
2. Normalize v: v_norm = (3/5, 4/5)
3. Use the vector rotation formula to find the two unit vectors:

First unit vector, u1:
Rotate v_norm 60° counterclockwise:
u1_x = (3/5)cos(60°) - (4/5)sin(60°)
u1_y = (3/5)sin(60°) + (4/5)cos(60°)
u1 = (u1_x, u1_y)

Second unit vector, u2:
Rotate v_norm 60° clockwise:
u2_x = (3/5)cos(-60°) - (4/5)sin(-60°)
u2_y = (3/5)sin(-60°) + (4/5)cos(-60°)
u2 = (u2_x, u2_y)

So, the two unit vectors that make an angle of 60° with v = (3, 4) are u1 and u2.

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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The company should use a warranty period that is equal to 67,467.5 miles.

To determine the warranty period, we need to find the value of the tire life that corresponds to 95% of the tires. We can use the standard normal distribution table to find the value of the z-score that corresponds to the 95th percentile. This value is approximately 1.645.

Now, we can use the formula for the normal distribution to find the tire life value that corresponds to the z-score of 1.645. This formula is:

X = μ + zσ

Where X is the tire life value, μ is the mean of the distribution (65,000 miles), z is the z-score (1.645), and σ is the standard deviation of the distribution (1500 miles).

Plugging in the values, we get:

X = 65,000 + 1.645(1500)

X = 67,467.5

This means that 95% of the tires will have a life of at least 67,467.5 miles.

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y equals a variable example is

y=1

x=1 +24

180-24 = 156

156÷2= 78

y =78

x= 78+24

Answer:

x -2,2

Y -4,3

z -4,6

w -2,6

Answer:

x and y can be any two numbers greater than zero such that y is also greater than x

D.no more than 45

C.50 miles per hour

Step-by-step explanation:

Let the two numbers be such that x< y because we have been given y/x>1 and x/y< 1 .

Suppose we take y= 9 and x= 3 then

9/3 > 1

3>1

Also

3/9 < 1

1/3 < 1

x and y can be any two numbers greater than zero such that y is also greater than x

2. Total weight that can be carried is 3000 pounds.

The big machine is 300 pounds. The weight that the truck can carry beside the big machine is 3000-300= 2700 pounds.

The smaller machines weigh 60 pounds

The number of smaller machines that can be carried is 2700 ÷ 60= 45 other than the big machine.

3. Total distance = Speed * time

                           = 48 * (40/60) = 32 miles

New distance = 32+ 8= 40 miles

New time = 48 minutes

Speed = distance / time = 40/ 48/60=  50 miles per hour

Answer:

0.18

Step-by-step explanation:

As it's a parallelogram

\(\\ \sf\longmapsto 5y+3y=180\)

\(\\ \sf\longmapsto 8y=180\)

\(\\ \sf\longmapsto y=180/8\)

\(\\ \sf\longmapsto y=22.5\)

Now

\(\\ \sf\longmapsto 5x=3y\)

\(\\ \sf\longmapsto 5x=3(22.5)=67.5\)

\(\\ \sf\longmapsto x=67.5/5\)

\)

\(\\ \sf\longmapsto x=13.5\)

Answer:

x=13.5

y=22.5

Step-by-step explanation:

Answer:

1400

Step-by-step explanation:

There is a flat fee involved, which is the y-intercept of the line.

The line eats the points:

(3, 435)

 and

(5, 625)  

the slope is 190/2 = 95

 B = y - mx = 435 - (95)(3)

                 = 435 - 285

                 =  150

The linear function is:

y = 95x + 150

So for x=2, it will cost

95(2) + 150 = 190 + 150 = 340

435 + 625 + 340 =  1400

The total cost to rent the boat for three days is $1400.

Given that, on Saturday, he rented a pontoon boat for three hours and paid $435.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The cost for the rented a pontoon boat for five hours is 435+190 = 625

The coordinate points are (3, 435) and(5, 625)  

The slope is m = (625-435)/(5-3)

= 190/2 = 95

Now, b = y - mx = 435 - (95)(3)

= 435 - 285 =  150

So, the linear function is y = 95x + 150

So for x=2, it will cost

95(2) + 150 = 190 + 150 = 340

Total cost = 435 + 625 + 340 = 1400

Therefore, the total cost to rent the boat for three days is $1400.

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The correct option is E. The population mean is less than 125. As, 125 is does not comes in the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

The 90% confidence interval for the mean of the population is computed to be 135 to 160. This means that we are 90% confident that the true population mean falls within this range.

Since 125 is not within the interval of 135 to 160, the interval tends to refute the claim that the population mean is less than 125.

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True. A vector in space can be described by specifying its magnitude and its direction angles. The magnitude of a vector represents its length or size, while the direction angles determine the orientation of the vector with respect to a reference axis system.

In three-dimensional space, a vector can be decomposed into its components along the x, y, and z axes. By using trigonometric functions, the direction angles of the vector can be determined. The direction angles are typically measured with respect to the positive x-axis, the positive y-axis, and the positive z-axis.

Once the magnitude and direction angles of a vector are known, the vector can be fully described. This description allows for precise calculations and analysis of vector quantities, such as displacement, velocity, and force, in various physical and mathematical contexts.

It's worth noting that there are alternative ways to describe vectors, such as using Cartesian coordinates or unit vectors. However, specifying the magnitude and direction angles provides a convenient and comprehensive representation of a vector in space.

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TRUE. We can observe n coin flips, record each heads as 1, and each tails as 0. Then, sum up all of our 1s and 0s, divide by n (in other words, we calculate the sample mean), and we have just calculated the sample proportion p-hat. This is a method used to find the probability of an event.

The sample proportion is known as p-hat. The proportion of successes in the sample is denoted by the p-hat symbol. The sample proportion is a statistic that estimates the actual proportion of the population. The proportion of successes in a sample is referred to as the sample proportion.

When sample proportion represents a percentage, it is indicated as a percentage (x%). So, sample proportion p-hat is a statistical term that provides us with an estimate of the actual proportion of the population from the sample proportion.

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The larger number is 51, and the smaller number is 33.

Let's represent the larger number as 'x' and the smaller number as 'y.' According to the given information, the difference between the two numbers is 18. Mathematically, this can be expressed as x - y = 18.

The sum of the two numbers is given as 84, which can be expressed as x + y = 84. Now we have a system of two equations:

Equation 1: x - y = 18

Equation 2: x + y = 84

To solve this system of equations, we can use a method called elimination. Adding Equation 1 and Equation 2 eliminates the 'y' variable, resulting in 2x = 102. Dividing both sides of the equation by 2 gives us x = 51.

Substituting the value of x back into Equation 2, we can find the value of y. Plugging in x = 51, we have 51 + y = 84. Solving for y, we find y = 33.

Therefore, the larger number is 51, and the smaller number is 33.

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The equation of a line in the slope intercept form is expressed as

y = mx + c

where

m represents slope

c represents y intercept

The given equation is

12x + 2y = 6

we would make this equation to look like the slope intercept equation.

12x + 2y = 6

If we subtract 12x from both sides of the equation, it becomes

12x - 12x + 2y = 6 - 12x

2y = 6 - 12x

2y = - 12x + 6

Dividing both sides of the equation by 2, it becomes

y = - 6x + 3

Thus, by comparing with the slope intercept equation,

slope = - 6

y intercept = 3

∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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The percent of the field goals did Samuel make will be 77.5%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100. The percentage therefore refers to a component per hundred. Per 100 is what the word percent means. It is represented by %.

Samuel made 31 out of 40 field goals during football practice. The percent of the field goals did Samuel make will be:

= 31 / 40 × 100

= 77.5%

The percentage is 77.5%.

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Using Euler's method with a step size of h = 1.5, the value of y(3) is approximately -13.025.

To approximate the value of y(3) using Euler's method with a step size of h = 1.5, we can iteratively compute the values of y at each step.

The given differential equation is:

2y + 16 = 5x

We are given the initial condition y(0) = 3.6, and we want to find the value of y at x = 3.

Using Euler's method, the update rule is:

y(i+1) = y(i) + h * f(x(i), y(i))

where h is the step size, x(i) is the current x-value, y(i) is the current y-value, and f(x(i), y(i)) is the value of the derivative at the current point.

Let's calculate the values iteratively:

Step 1:

x(0) = 0

y(0) = 3.6

f(x(0), y(0)) = (5x - 16) / 2 = (5 * 0 - 16) / 2 = -8

y(1) = y(0) + h * f(x(0), y(0)) = 3.6 + 1.5 * (-8) = 3.6 - 12 = -8.4

Step 2:

x(1) = 0 + 1.5 = 1.5

y(1) = -8.4

f(x(1), y(1)) = (5x - 16) / 2 = (5 * 1.5 - 16) / 2 = -6.2

y(2) = y(1) + h * f(x(1), y(1)) = -8.4 + 1.5 * (-6.25) = -8.4 - 9.375 = -17.775

Step 3:

x(2) = 1.5 + 1.5 = 3

y(2) = -17.775

f(x(2), y(2)) = (5x - 16) / 2 = (5 * 3 - 16) / 2 = 2.5

y(3) = y(2) + h * f(x(2), y(2)) = -17.775 + 1.5 * 2.5 = -17.775 + 3.75 = -13.025

Therefore, using Euler's method with a step size of h = 1.5, the value of y(3) is approximately -13.025.

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The probability of getting a green golf ball from the machine is 19/83 or 0.2289. The result is obtained by the number of green golf balls divided by the total number of golf balls.

Probability of an event can be calculated by

P(A) = n(A) / n(S)

Where

You have 19 green golf balls, 24 red golf balls, 20 blue golf balls, and 20 yellow golf balls.

Find the probability of getting a green golf ball from the machine!

The total number of golf balls in the machine is

n(S) = 19 + 24 + 20 + 20 = 83 balls

You will end up with a green golf ball with the probability of

P(A) = n(A) / n(S)

P(A) = 19/83

P(A) = 0.2289

Hence, the probability that you will end up with a green golf ball is 19/83 or 0.2289.

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To find the probability distribution for Y, the number of errors detected by the auditor, we can use the binomial distribution formula. The binomial distribution is used when there are only two possible outcomes, success or failure, and each trial is independent.

In this case, the probability of success (detecting an error) is 5% or 0.05, and the probability of failure (not detecting an error) is 1 - 0.05 = 0.95.

a. To find the probability distribution for Y, we can use the formula for the binomial distribution:

P(Y = y) = (nCk) * p^k * (1-p)^(n-k)

where n is the number of trials (3 in this case), k is the number of successes (errors detected), p is the probability of success (0.05), and (nCk) is the combination formula.

For y = 0:
P(Y = 0) = (3C0) * (0.05)^0 * (0.95)^(3-0) = (1) * (1) * (0.95)^3 = 0.857375

For y = 1:
P(Y = 1) = (3C1) * (0.05)^1 * (0.95)^(3-1) = (3) * (0.05) * (0.95)^2 = 0.135375

For y = 2:
P(Y = 2) = (3C2) * (0.05)^2 * (0.95)^(3-2) = (3) * (0.05)^2 * (0.95)^1 = 0.007125

For y = 3:
P(Y = 3) = (3C3) * (0.05)^3 * (0.95)^(3-3) = (1) * (0.05)^3 * (0.95)^0 = 0.000125

So the probability distribution for Y is:
Y = 0 with probability 0.857375
Y = 1 with probability 0.135375
Y = 2 with probability 0.007125
Y = 3 with probability 0.000125

b. To construct a probability histogram for p(y), you can create a bar graph where the x-axis represents the number of errors detected (Y) and the y-axis represents the probability (P(Y = y)). Each bar will have a height corresponding to the probability.

c. To find the probability that the auditor will detect more than one error, we need to calculate the sum of the probabilities for Y = 2 and Y = 3:

P(Y > 1) = P(Y = 2) + P(Y = 3) = 0.007125 + 0.000125 = 0.00725

Therefore, the probability that the auditor will detect more than one error is 0.00725.

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Answer:

x=138

Step-by-step explanation:

A triangle's angles equal to 180

104+34=138

180-138=42

X and 42 are a liner pair so they equal 180

138+42=180

x=138

Step-by-step explanation:

The answer is an = 7n - 10.

Step-by-step explanation:

.............,.,.,.,.,.,.,.,

The numerical will be equal to 159 ÷ 16 and the polynomial will be (9x +15)/x.

Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both. Adding, subtraction, multiplying, and division are all reflection coefficient operations.

In comparison to the divisor, the dividend will be 15 times greater. It seems that you are free to select any divisor. It must be more than 15 if the divisor is totally numerical.

Numerical:

Divisor = 16,

so we have,

(9×16 +15) ÷ 16

= 159 ÷ 16

Polynomial:

The simplest divisor we can have is a single variable: x.

(9x +15)/x

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Answer:

\(gross \ pay = 4200\\\\federal \ deduction = \frac{16.05}{100} \times 4200 = 674.10\\\\Net \ pay = 4200 - 674.10 -321.30= 3204.60\)

Answer:

60 copies

Step-by-step explanation:

75 copies in total, 4/5 of them were sold yesterday. 75 x 4/5 = 60 copies sold yesterday.

Answer:

12×2×2=48

Step-by-step explanation:

48cm because you need to find the volume of a shape by multiplying it.

For x = 80 and y = 130, l and m will be parallel to j and n respectively.

If two lines are parallel, then the sum of the interior angles is supplementary.

Thus, if m || n, then (x - 30) and (x + 50) will be supplementary

⇒ (x - 30) + (x + 50) = 180

x - 30 + x + 50 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 80

Thus, if x = 80, then k will be parallel to l

Now, if m || n, then y and (x - 30) must be supplementary

⇒ (x - 30) + y = 180

x - 30 + y = 180

we found that x = 80

⇒ 80 - 30 + y = 180

50 + y = 180

y = 180 - 50

y = 130

Thus, if y = 130 then, k will be parallel to l.

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