use the normal distribution of sat critical reading scores for which the mean is 501 and the standard deviation is 119. assume the variable x is normally distributed. (a) what percent of the sat verbal scores are less than 550? (b) if 1000 sat verbal scores are randomly selected, about how many would you expect to be greater than 525?

Answer:

The X intercepts is 1 and 5

Answer:

(2 1) for L (4 3) for G  (4 -1)

Step-by-step explanation:

Answer:

17×6=102 because he gave 2 boxes to his brother so he have 6 boxes

Step-by-step explanation:

=bc

3x + 1 = 223x+1=22

x = 7x=7

ad = cd = 4(7) = 28ad=cd=4(7)=28

Given: Radius of the wheel = 30 inches, Revolutions per minute = 401 rpmThe linear speed of the car in miles per hour can be calculated as follows:

Step 1: Convert the radius from inches to miles by multiplying it by 1/63360 (1 mile = 63360 inches).30 inches × 1/63360 miles/inch = 0.0004734848 milesStep 2: Calculate the distance traveled in one minute by the wheel using the circumference formula.Circumference = 2πr = 2 × π × 30 inches = 188.496 inchesDistance traveled in one minute = 188.496 inches/rev × 401 rev/min = 75507.696 inches/minStep 3: Convert the distance traveled in one minute from inches to miles by multiplying by 1/63360.75507.696 inches/min × 1/63360 miles/inch = 1.18786732 miles/minStep

4: Convert the distance traveled in one minute to miles per hour by multiplying by 60 (there are 60 minutes in one hour).1.18786732 miles/min × 60 min/hour = 71.2720392 miles/hour Therefore, the linear speed of the car is 71.3 miles per hour (rounded to the nearest tenth).Answer: 71.3

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The radius of the wheel on a car is 30 inches. If the wheel is revolving at 401 revolutions per minute, The linear speed of the car is approximately 19.2 miles per hour.

To find the linear speed of the car in miles per hour, we need to calculate the distance traveled in one minute and then convert it to miles per hour. Here's how we can do it step by step:

Calculate the circumference of the wheel:

The circumference of a circle is given by the formula

C = 2πr

where r is the radius of the wheel.

In this case, the radius is 30 inches, so the circumference is

C = 2π(30)

   = 60π inches.

Calculate the distance traveled in one revolution:

Since the circumference represents the distance traveled in one revolution, the distance traveled in inches per revolution is 60π inches.

Calculate the distance traveled in one minute:

Multiply the distance traveled in one revolution by the number of revolutions per minute.

In this case, it is 60π inches/rev * 401 rev/min = 24060π inches/min.

Convert the distance to miles per hour:

There are 12 inches in a foot, 5280 feet in a mile, and 60 minutes in an hour.

Divide the distance traveled in inches per minute by (12 * 5280) to convert it to miles per hour.

The final calculation is (24060π inches/min) / (12 * 5280) = (401π/66) miles/hour.

Approximating π to 3.14, the linear speed of the car is approximately (401 * 3.14 / 66) miles per hour, which is approximately 19.2 miles per hour.

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Answer:

(A) x + 3y - 10

Step-by-step explanation:

This Questions tests on the concept of solving algebraic expressions.

Eg. 7x + 4y + 3y + 9x = 16x + 7y

(Note that BODMAS rule applies to algebraic expressions as well.)

Given from the question:

5x + 8 - 13y - 4x - 18 + 16y

= 5x - 4x - 13y + 16y + 8 - 18 (Regroup the terms)

= x + 3y - 10 (A)

The probability the ball drawn from the second box is red, is 17/56.

In a box are 7 red balls and 8 blue balls.

From this box are drawn 4 balls and placed in a second box.

We have to determine the probability the ball drawn from the second box is red.

The total number of balls = Red Balls + Blue Balls

The total number of balls = 7 + 8

The total number of balls = 15

The number of balls placed in second balls = 4

The number of combination of balls in box 2.

BBBB, BBBR, BBRR and BRRR

Then, one ball is drawn from the second box.

The probability the ball drawn from the second box is red.

P(Ball is red in the second box) = P(BBBB) + P(BBBR) + P(BBRR) + P(BRRR)

P(Ball is red in the second box) = \(\frac{^{5}C_{4}}{^{8}C_{0}}(0)+\left(\frac{^{5}C_{3}\times ^{3}C_{1}}{^{8}C_{4}}\right)\times\frac{^{1}C_{1}}{^{4}C_{1}}+\left(\frac{^{5}C_{2}\times ^{3}C_{2}}{^{8}C_{4}}\right)\times\frac{^{2}C_{1}}{^{4}C_{1}}+\left(\frac{^{5}C_{1}\times ^{3}C_{3}}{^{8}C_{4}}\right)\times\frac{^{3}C_{1}}{^{4}C_{1}}\)

P(Ball is red in the second box) = \(0+\left(\frac{30}{70}\times\frac{1}{4}\right)+\left(\frac{30}{80}\times\frac{1}{2}\right)+\left(\frac{5}{70}\times\frac{3}{4}\right)\)

P(Ball is red in the second box) = 3/48 + 3/16 + 3/56

P(Ball is red in the second box) = (21 + 63 + 18)/336

P(Ball is red in the second box) = 102/336

P(Ball is red in the second box) = 17/56

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The angle of rotation in standard form is 251.5651 degrees.

The length of arc S is approximately 20.94 feet.

If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:

(-1)² + (-3)² = 10

1 + 9 = 10

So, the point (-1, -3) satisfies the equation of the circle.

To find the angle of rotation in standard form, we need to use the formula:

tan(θ) = y/x

where θ is the angle of rotation.

In this case, x = -1 and y = -3, so we have:

tan(θ) = (-3)/(-1)

tan(θ) = 3

θ = tan⁻¹(3)

Using a calculator, we find:

θ ≈ 1.2490 radians or 71.5651 degrees

To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:

θ ≈ 71.5651 + 180 ≈ 251.5651 degrees

To find the length of an arc S given the radius r and the central angle θ, we use the formula:

S = (θ/360) x 2πr

In this case, r = 15 ft and θ = 1.396 radians

Substituting the values:

S = (1.396/2π) x 2π(15 ft)

S ≈ 1.396 x 15 ft

S ≈ 20.94 ft

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Complete question:

Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form

Find the length of the arc S when r = 15 ft and θ = 13.96°

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

a) To find the probability that the television set lasts between 4 and 6 years, we need to calculate the integral of the density function f(x) over the interval [4, 6]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, we have:

∫[4, 6] f(x) dx = ∫[4, 6] (18x - 3) dx = [9x^2 - 3x] evaluated from 4 to 6 = (9(6)^2 - 3(6)) - (9(4)^2 - 3(4)).

b) To find the probability that the television set lasts at least 5 years, we need to calculate the integral of the density function f(x) over the interval [5, ∞). However, since the density function is zero for x ≥ 3, the integral over this interval is zero.

c) To find the probability that the television set lasts less than 2 years, we need to calculate the integral of the density function f(x) over the interval [0, 2]. Since the density function is given by f(x) = 18x - 3 for 0 ≤ x < 3 and 0 for x ≥ 3, the integral becomes:

∫[0, 2] f(x) dx = ∫[0, 2] (18x - 3) dx = [9x^2 - 3x] evaluated from 0 to 2 = (9(2)^2 - 3(2)) - (9(0)^2 - 3(0)).

d) To find the probability that the television set lasts exactly 4.18 years, we need to evaluate the density function f(x) at x = 4.18. Plugging in the value of x into the density function, we get f(4.18) = 18(4.18) - 3.

e) To find the expected value of the number of years that the television set lasts, we need to calculate the integral of xf(x) over the entire range of x, which is [0, ∞). The expected value is given by:

E(x) = ∫[0, ∞] x f(x) dx = ∫[0, ∞] x(18x - 3) dx = [3x^3 - (3/2)x^2] evaluated from 0 to ∞ = lim(a→∞) [(3a^3 - (3/2)a^2) - (3(0)^3 - (3/2)(0)^2)].

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(a) Using confidence interval, we can reject the null hypothesis. (b) Using p-value, we can reject the null hypothesis.

(a) Decision using confidence interval:

We have, Sample size(n) = 150, Sample mean = 18.86 pounds, Population standard deviation(σ) = 3.7 pounds, Population mean(μ) = 20.5 pounds, and Significance level(α) = 10% = 0.1

We want to test whether the mean amount is less than 20.5 pounds or not.

Null Hypothesis: H0 : µ ≥ 20.5

Alternate Hypothesis: Ha : µ < 20.5

As we have n > 30, we can use the z-test.

z = (x - µ) / (σ / √n) = (18.86 - 20.5) / (3.7 / √150) = -4.12

The left-tailed critical z value for 10% significance level is -1.28.

Since our test statistic (-4.12) is less than the critical value(-1.28), we can reject the null hypothesis. Hence we can conclude that the mean amount is less than 20.5 pounds at 10% level of significance.

(b) Decision using p-value:

We have, Sample size(n) = 150, Sample mean = 18.86 pounds, Population standard deviation(σ) = 3.7 pounds, Population mean(μ) = 20.5 pounds, Significance level(α) = 10% = 0.1

We want to test whether the mean amount is less than 20.5 pounds or not.

Null Hypothesis: H0 : µ ≥ 20.5

Alternate Hypothesis: Ha : µ < 20.5

As we have n > 30, we can use the z-test.

z = (x - µ) / (σ / √n) = (18.86 - 20.5) / (3.7 / √150) = -4.12

The p-value of our test is P(z < -4.12) ≈ 0.

Since the p-value is less than the significance level, we can reject the null hypothesis. Hence we can conclude that the mean amount is less than 20.5 pounds at 10% level of significance.

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The 9th derivative of f(x) at x = 0 is 0 since none of the terms contribute to the 9th derivative.

To find the Maclaurin series derivative for the function f(x) = cos(2x²) - 1, we can start by expanding the cosine function using its Maclaurin series:

cos(x) = 1 - (x²/2!) + (x⁴/4!) - (x⁶/6!) + ...

cos(2x²) = 1 - ((2x²)²/2!) + ((2x²)⁴/4!) - ((2x²)⁶/6!) + ...

cos(2x²) = 1 - (4x⁴/2!) + (16x⁸/4!) - (64x¹²/6!) + ...

f(x) = cos(2x²) - 1

= -1 + (4x⁴/2!) - (16x⁸/4!) + (64x¹²/6!) - ...

To find the 9th derivative of f(x) and evaluate it at x = 0, we need to differentiate the series term by term. Each term contributes to the derivatives as follows:

(-1) contributes 0 to all derivatives.

(4x⁴/2!) contributes (4/2!) = 2 to the 4th derivative and 0 to the others.

(-16x⁸/4!) contributes (-16/4!) = -2/3! = -1/3 to the 8th derivative and 0 to the others.

(64x¹²/6!) contributes (64/6!) = 8/6! = 1/45 to the 12th derivative and 0 to the others.

Therefore,  the 9th derivative of f(x) at x = 0 is 0 since none of the terms contribute to the 9th derivative.

Hence, f⁽⁹⁾(0) = 0.

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The value of x is 4√6. The value of y is 4√2.

What are similar triangles?

If two triangles have the same ratio of corresponding sides and an equal pair of corresponding angles, they are similar. When two or more figures have the same shape but differ in size, they are referred to as similar figures.

Consider △ABC:

Height = AC = x, Hypoteneous = BC = 4+8 = 12.

Consider △ADC:

Height = DC = 8, Base = AD = y, Hypoteneous =  AC = x

Consider △ABD:

Height = AD = y, Base = 4.

The triangle ABC is similar to ADC, and ABC is similar to ABD. Since all have one right angle and one angle is common.

The ratio of the corresponding sides of similar triangles is constant.

Consider △ABC and △ADC:

AC/DC = BC/AC

x/8 = 12/x

x² = 12×8

x = 4√6.

Since ABC is similar to ADC and ABC is similar to ABD. Then ADC is similar to ABD.

Consider △ADC and △ABD:

DC/AD = AD/BD

8/y = y/4

y² = 4×8

y = 4√2

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The probability of landing on an odd number and then landing on a number less than 4 when you spin the spinner twice is 12.5%.

First, let's determine the probability of landing on an odd number on the first spin. Out of the 8 sections on the spinner, 4 are odd numbers (3, 5, 7, 9) and 4 are even numbers (2, 4, 6, 8). Therefore, the probability of landing on an odd number is 4/8 or 1/2.

Now, let's determine the probability of landing on a number less than 4 on the second spin. Out of the 8 sections on the spinner, only 2 sections are less than 4 (2 and 3). Therefore, the probability of landing on a number less than 4 is 2/8 or 1/4.

To determine the probability of both events occurring (landing on an odd number and then landing on a number less than 4), we need to multiply the probabilities of each event occurring. This is known as the multiplication rule of probability.

So, the probability of landing on an odd number and then landing on a number less than 4 is:

(1/2) x (1/4) = 1/8

To write this as a percentage, we can convert the fraction to a decimal by dividing the numerator (1) by the denominator (8) which equals 0.125. Then we can multiply by 100 to get the percentage:

0.125 x 100 = 12.5%

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Complete Question:

You spin the spinner twice. The spinner sections are numbered 2,3,4,5,6,7. 8, and 9

What is the probability of landing on an odd number and then landing on a number less than 4? Write your answer as a percentage

Answer:

151.18

Step-by-step explanation:

I can't really show my work on this, sorry.

Answer:

151.18

Step-by-step explanation:

210.58-59.40=151.18

Answer:

Positive

Step-by-step explanation: (-27) = 27

The original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

To show that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves, we need to take the derivative of the equation and set it equal to -1/b^2, the slope of the orthogonal line.

First, we take the derivative of the equation with respect to x:

2x/a^2 = -2y/b^2 * dy/dx

Simplifying, we get:

dy/dx = -b^2*x/a^2*y

Now, we set this equal to -1/b^2:

-b^2*x/a^2*y = -1/b^2

Cross-multiplying and simplifying, we get:

x/a^2*y = 1/b^2

Finally, we can rearrange this equation to get:

y = b^2*x/a^2

This equation represents the orthogonal family of curves to the original family of conics. Since the original equation and the orthogonal equation are the same, we can conclude that the family of conics with the same focus x^2/a^2+C + y^2/b^2+C = 1 is its own orthogonal family of curves.

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The thickness of the clay layer, which drains only from the upper surface, can be determined based on the consolidation settlement observations. With 50% of consolidation settlement occurring in 1 hour for a 25 mm thick specimen, and a total primary consolidation settlement of 35 mm occurring over many years, the thickness of the clay layer is approximately 87.5 mm.

The consolidation settlement of a clay specimen can be used to estimate the thickness of a clay layer that drains only from the upper surface. In this case, the observed settlement data provides valuable information.

Firstly, we know that 50% of the consolidation settlement occurs in 1 hour for a 25 mm thick clay specimen. This is an important parameter for calculating the coefficient of consolidation (Cv) using Terzaghi's theory. From the Cv value, we can estimate the time required for full consolidation settlement.

Secondly, we are given that the same clay settles 10 mm over 10 years and eventually settles a total of 35 mm over a longer period. This long-term settlement is known as the total primary consolidation settlement. By comparing this settlement value with the settlement data from the oedometer test, we can determine the thickness of the clay layer.

To calculate the thickness, we can use the concept of the consolidation settlement ratio. The ratio of the total primary consolidation settlement to the consolidation settlement at 50% completion is equal to the ratio of the total thickness to the thickness at 50% completion. Applying this ratio, we can determine that the thickness of the clay layer, which drains only from the upper surface, is approximately 87.5 mm.

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The equations;

A linear equation is one in which there is only one solution. In a linear solution, the highest power of x is 1.

If we look at the equations listed, we will discover that they are all linear equations, as such;

Will all have exactly 1 solution.

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Answer:

5(x + 3)

Step-by-step explanation:

6(2x + 4) - 2(x + 7) + 5

12x + 24 - 2x - 14 +5

10x  + 24 - 9

10x  + 15

5(x + 3)

Answer:

67

Step-by-step explanation:

0.71=71%.

2/100+2/100=4/100/4%

So we can subtract 71-4=67.

That tells us that the missing number is 67. Add it all up and you will get 0.71 or 71%

Answer:

71

Step-by-step explanation:

.71 + 2/100 = x/100 +2/100

We need to change the decimal to a fraction

.71 means 71 out of 100

71/100 +2/100 = x/100 + 2/100

x is 71

The value of the total area of the shaded region are,

⇒ 42 units²

We have to given that;

Sides of rectangle are,

AB = 9

BC = 6

Hence, The area of rectangle is,

⇒ 9 x 6

⇒ 54 units²

And, Area of triangle is,

A = 1/2 × 4 × 6

A = 12 units²

Thus, The value of the total area of the shaded region are,

⇒ 54 - 12

⇒ 42 units²

So, The value of the total area of the shaded region are,

⇒ 42 units²

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The purpose of random sampling is to select a set of items from a population such that the sample description accurately represents the population.

Random sampling is a type of sampling in which the researcher randomly selects a subset of participants from a population. Each member of the population has an equal chance of being selected. Data is then collected from as high a percentage of this random subset as possible. Simple random sampling selects a smaller group (sample) from a larger group of the total number of participants (population).

Samples are at the heart of survey research. It is often called the population microcosm, and the process of drawing a sample should maximize the similarity of the sample to the population under study. Sampling is therefore the selection of a set of elements from a population whose description accurately describes the parameters of the total population from which the sample is selected.

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The number of people in the office is 13. We want to select different groups of 5 people

Number of ways that the first phone can be answered = 13

Number of ways that the second phone can be answered = 14

Since order is anot allowed, we would apply combination. Thus, the number of ways is

13C5 = 1287

How can you find the first digit in the quotient: Divide 54 by 13. The first digit goes in the 4 place.

In Mathematics, a quotient can be defined as a mathematical expression that is simply used to represent the division of a number (numerator) by another number (denominator).

By writing the given mathematical expression as a division of a number (numerator) by another number (denominator), we have the following quotient:

Quotient = 54/13 = 4 R 0

Quotient = (54 - 52)|6/13 = 26/13 = 2 R 0

Note: The variable R represent the the number of remainder after the quotient is computed.

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=========================================================

Explanation:

As you probably can guess (or already know), the term "slope intercept form" means that all we need are the slope and y intercept to get the equation.

To get the slope, we need two points. Pick any two points you want. I'll pick (3,-7) and (6,-9). Notice how we go down 2 units and then over to the right 3 units when we move from the first point to the second point.

See diagram below.

So the slope is rise/run = -2/3. The negative rise indicates we go down. The run is always moving to the right. This produces the downhill trend when we move from left to right.

--------------------

We can also use the slope formula. I'll use those two points mentioned earlier.

m = (y2-y1)/(x2-x1)

m = (-9-(-7))/(6-3)

m = (-9+7)/(6-3)

m = -2/3

We get the same result as earlier

--------------------

The y intercept is where the graph crosses the vertical y axis. This is at 5. So b = 5 is the y intercept.

Since the slope is m = -2/3 and the y intercept is b = 5, we go from y = mx+b to y = (-2/3)x-5 which is our final answer.

Answer

B.105 in 3

Step-by-step explanation:

7 x 5 x 3 = 105

Answer:

option D is the correct answer of this question .....

Step-by-step explanation:

(c+8 )×(c-5) = c²-5c+8c -40

= c²+3c - 40

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To find a power series representation for the function \($f(x) = \frac{x^2}{(1 - 3x)^2}$\), we can make use of the formula for the geometric series. Recall that for \(sum_{n = 0}^{\infty} r^ n = \frac{1}{1 - r}.$$\)

To apply this, we rewrite \($f(x)$\)as follows: \($$\frac{x^2}{(1 - 3x)^2} = x^2 \cdot \frac{1}{(1 - 3x)^2} = x^2 \cdot \frac{1}{1 - 6x + 9x^2}\)\(.$$\)Now we recognize that the denominator looks like a geometric series with \($r = 3x^2$ (since $(6x)^2 = 36x^2$)\)

Hence, we can write\frac\({1} {1 - 6x + 9x^2} = \sum_{n = 0}^{\nifty} (3x^2)^n = \sum_{n = 0}^{\infty} 3^n x^{2n}\),where the last step follows from the geometric series formula. Finally, we can substitute this expression back into the original formula for \($f(x)$ to get$$f(x) = x^2 \cdot \left( \sum_{n = 0}^{\infty} 3^n x^{2n} \right)^2\).

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Answer:

The balance after the 6 years of investment will be $ 15,442.08.

Step-by-step explanation:

Given that $ 13,700 was invested at a rate of 2% compounded quarterly during 6 years, to determine the final result of the investment, the following calculation must be performed:

13,700 x (1 + 0.02 / 4) ^ 4x6 = X

13,700 x (1 + 0.005) ^ 24 = X

13,700 x 1,005 ^ 24 = X

13,700 x 1.1271 = X

15,442.08 = X

Therefore, the balance after the 6 years of investment will be $ 15,442.08.

The probability of rolling a 1 three out of the four rolls is 5/1296 or approximately 0.00384, which is a very small probability.

The probability of rolling a 1 on a single roll of a fair 6-sided die is 1/6. To find the probability of rolling a 1 three out of the four rolls, we can calculate the probability of rolling a 1 three times in a row, and then multiply that by the probability of rolling a non-1 on the fourth roll.

The probability of rolling a 1 three times in a row is (1/6) * (1/6) * (1/6) = 1/216.

The probability of rolling a non-1 on the fourth roll is 5/6.

So, the probability of rolling a 1 three out of the four rolls is (1/216) * (5/6) = 5/1296.

Therefore, the probability of rolling a 1 three out of the four rolls is 5/1296 or approximately 0.00384, which is a very small probability.

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