The hypotenuse of a right triangle has the length of 50 units, and the longer leg of the triangle has a length of 40 units. What is the length of the projection of the shorter leg on the hypotenuse?​

Answer:

80 pages

Step-by-step explanation:

Let's use a ratio to solve:

pages : seconds

   12    :       9

    4     :       3

    \(p\)     :      60

It would seem that \(p\) would equal 80. The printer can print 80 pages in 60 seconds or one minute.

Answer:

If you have given an equation, you see the x and y in it. Just taking second equation and think any common factor between x's variable. With common factor, multiply both and you will find the value of y and put it in any equation, you will find the value of X.

Answer:

Hey there!

I can't see the full problem, but if when x=0.5, y=4, then when x=4, y=32, and when x=9, y=72. You multiply by a common multiple to get from x to y.

Hope this helps :)

The derivative of the given function \(\frac{(2x^2-x+6)^{2/3}}{2x^{-2}-2x+9}\) is \(\frac{\frac{2}{3}(2x^2-x+6)^{-1/3})(4x-1)(2x^{-2}-2x+9)+(2x^2-x+6)^{2/3})(4x^{-3}+2)}{(2x^{-2}-2x+9)^2}\).

We have to find the derivative for the given function.

Calculus and differential equations issues must be solved using derivatives. Futures contracts, options contracts, and credit default swaps are common types of derivatives.

The given function is

f(x) = \(\frac{(2x^2-x+6)^{2/3}}{2x^{-2}-2x+9}\) = h(x)/g(x)

Note that using the formula

(1) d/dx(f/g) = {gd/dx(f)-fd/dx(g)}/g^2

(2) d/dx(x^n) = nx^{n-1}

f'(x) = d/dx \(\frac{(2x^2-x+6)^{2/3}}{2x^{-2}-2x+9}\)

f'(x) = \(\frac{(2x^{-2}-2x+9)\frac{d}{dx}(2x^2-x+6)^{2/3})-(2x^2-x+6)^{2/3})\frac{d}{dx}(2x^{-2}-2x+9)}{(2x^{-2}-2x+9)^2}\)

f'(x) = \(\frac{(2x^{-2}-2x+9)\frac{2}{3}(2x^2-x+6)^{2/3-1})\frac{d}{dx}(2x^2-x+6)-(2x^2-x+6)^{2/3})(2(-2)x^{-3}-2)}{(2x^{-2}-2x+9)^2}\)

f'(x) = \(\frac{(2x^{-2}-2x+9)\frac{2}{3}(2x^2-x+6)^{2/3-1})(4x-1)+(2x^2-x+6)^{2/3})(4x^{-3}+2)}{(2x^{-2}-2x+9)^2}\)

f'(x) = \(\frac{\frac{2}{3}(2x^2-x+6)^{-1/3})(4x-1)(2x^{-2}-2x+9)+(2x^2-x+6)^{2/3})(4x^{-3}+2)}{(2x^{-2}-2x+9)^2}\)

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The right question is:

Find the derivative for the given function. Write your answer using positive and negative exponents and fractional exponents instead of radicals.

f(x) = \(\frac{(2x^2-x+6)^{2/3}}{2x^{-2}-2x+9}\)

a) If the interval spanned from a negative value to a positive value that includes 0. b) Indicates that the average fat content of meat hot dogs is expected to be lower than the average fat content of beef hot dogs.c) there is a statistically significant difference in the mean fat content between meat hot dogs and beef hot dogs. d) alpha level is 0.10 or 10%

a) A 95% confidence interval for ?_meat-?_beef would include 0 if the interval spanned from a negative value to a positive value that includes 0. However, since we don't have the actual confidence interval values in this question, we cannot determine if 0 is included. The given information only mentions the P-value for a hypothesis test, not the specific confidence interval.

b) The fact that the endpoints of the confidence interval (-6.5, -1.4) are negative numbers indicates that the average fat content of meat hot dogs is expected to be lower than the average fat content of beef hot dogs.

c) The fact that the confidence interval (-6.5, -1.4) does not contain 0 indicates that there is a statistically significant difference in the mean fat content between meat hot dogs and beef hot dogs. The interval suggests that, on average, meat hot dogs have a lower fat content than beef hot dogs.

d) The corresponding alpha level for testing the hypothesis that ?_meat-?_beef = 0 using a 90% confidence interval is 0.10 or 10%. This is because the confidence level is 90%, which leaves a 10% chance of making a Type I error (rejecting the null hypothesis when it is true).

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First statement is correct. If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.

Given,

The rate of reading of a novel by Sasha = 0.8 pages per minute

The rate of reading of autobiography by Sasha = 0.5 pages per minute

The reading requirement of Sasha's English class = atleast 75 pages per week

The given equation: 0.8n + 0.5a ≥ 75

n is the number of minutes she reads the novel

a is the number of minutes she reads the autobiography

Now, let's check the statements:

Statement 1: If Sasha reads her novel for 94 minutes, she meets the minimum reading requirement without reading any of the autobiography.

That is,

0.8 × 94 + 0.5 × 0 ≥ 75

75.2 ≥ 75

This statement satisfies the equation.

Other 4 statement didn't satisfy the equation.

So, first statement is correct.

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Consumer surplus $5 as we solve the Q by given data

Consumer surplus is the difference between the consumer's willingness to pay and the price of the commodity.

Consumer surplus in economics, also called social surplus or consumer surplus, is the difference between the price a consumer pays for a commodity and the price the consumer is willing to pay in exchange for giving it up.

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

Consumer Surplus = Willingness to Pay - Price of the Good.

Item Price = $35 - $10 = $25

$30 - $25 = $5

Producer surplus is the difference between the price of a commodity and the lowest price at which a seller is willing to sell it.

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Answer:

25 pieces

Step-by-step explanation:

let c = amt of candy

(c - 10 ) / 5 = 3

cross-multiply:

c-10 = 15

c = 25

The total charge to paint a house can be defined by the expression y = $500 + $50x.

The company will charge $1500 to paint a house that needs 20 hours of labor.

The company will charge $3000 to paint a house that needs 50 hours of labor.

A painting company charges $500 for supplies and $50 for each hour of labor.

Let's say the total charge to paint is y and x is the number of hours of labor.

Then, the total charge can be expressed using the expression:

Total charge = $500 + $50 × number of hours of labor.

y = $500 + $50x

Now, to paint a house the company needs 20 hours of labor.

Then x = 20,

y = $500 + $50 × 20

y = $500 + $1000

y = $1500

If a house needs 50 hours of labor, then x = 50.

y = $500 + $50 × 50

y = $500 + $2500

y = $3000

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Answer:

Factor 49x^2-4 49x2 − 4 49 x 2 - 4 Rewrite 49x2 49 x 2 as (7x)2 (7 x) 2. (7x)2 − 4 (7 x) 2 - 4 Rewrite 4 4 as 22 2 2.

Step-by-step explanation:

Hoped it helped

Answer:

(7x-2)(7x+2)

Step-by-step explanation:

This was the easiest thing I had in Analytic Geometry!!

The answer of the given question based on finding the measure of arc CD from a circle the answer is the measure of arc CD is approximately 33.333° degrees.

Diameter is  geometric term used to describe  distance across  widest part of  circle or  sphere. It is defined as line segment that passes through center of  circle or sphere and has endpoints on its circumference. The diameter is longest possible chord of  circle or sphere, and it divides it into two equal halves called hemispheres. The diameter is important parameter used to calculate circumference, area, and volume of circles and spheres in various fields, like mathematics, physics, engineering, and architecture. It is commonly used in geometry, trigonometry, and calculus, and is fundamental concept in geometry and measurement.

Since E is the center of the circle, angle ∠CEB is a central angle, and its measure is equal to the measure of arc CD. Also, since AC is a diameter, angle ∠CAD is a right angle, and we know that angle ∠CAD + angle ∠BAD = 90° degrees. Therefore, angle BAD = 90 - angle ∠CAD = 90 - (5x + 35) = 55 - 5x degrees.

Since angles ∠BAC and ∠BDC are vertical angles, they are equal, so angle ∠BAC = angle ∠BDC = (1/2) angle ∠BAD = (1/2) (55 - 5x) = 27.5 - 2.5x degrees.

Now, we can use the fact that angles BAC and BDC are both inscribed angles that intercept arc CD and use the inscribed angle theorem to set up an equation:

angle ∠BAC = angle ∠BDC = (1/2) arc CD

Substituting the expressions we found for these angles, we get:

27.5 - 2.5x = (1/2) arc CD

Solving for arc CD, we get:

arc CD = 55 - 5x degrees

Substituting the given value for BC, we get:

19x - 49 = 55 - 5x

Solving for x, we get:

24x = 104

x = 4.333...

Finally, substituting this value of x back into our expression for arc CD, we get:

arc CD = 55 - 5x = 55 - 5(4.333...) = 33.333... °degrees

Therefore, the measure of arc CD is approximately 33.333° degrees.

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Answer:

Step-by-step explanation:

Karine De Marchand is 54 years

By engaging in these exercises, students can develop a deeper understanding of conditional statements and logical reasoning, which are essential skills for further studies in mathematics and logic.

In Unit 2 of a logic and proof course, homework 3 focuses on conditional statements.

Conditional statements are fundamental concepts in logic and mathematics, representing logical implications between two statements.

They are typically expressed in "if-then" format, where the "if" part is the hypothesis and the "then" part is the conclusion.

The homework may involve tasks such as:

Identifying conditional statements: Students are given a set of statements and asked to identify which ones are conditional statements.

They need to recognize the "if-then" structure and correctly identify the hypothesis and conclusion.

Analyzing the truth value of conditional statements:

Students may be given conditional statements and asked to determine whether they are true or false.

They need to evaluate the hypothesis and conclusion to determine if the implication holds in each case.

Writing converse, inverse, and contrapositive statements:

Students may be required to manipulate given conditional statements to form their converse, inverse, and contrapositive statements.

This involves switching the positions of the hypothesis and conclusion or negating both parts.

Applying the laws of logic:

Students may need to apply logical laws, such as the Law of Detachment or the Law of Modus Tollens, to deduce conclusions based on conditional statements.

Constructing counterexamples:

Students may be asked to provide counterexamples to disprove statements that are falsely claimed to be universally true based on a given conditional statement.

They also help students develop critical thinking and problem-solving abilities, as they have to analyze and manipulate logical structures.

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Answer:

3072 that what I known as a 10th grader

Answer:

1

Step-by-step explanation:

We can use the points (-3, 0) and (1, 4) to solve.

The slope formula is [ y2-y1/x2-x1 ]

4-0/1-(-3)

4/4

1

Best of Luck!

The probability that Ken will use all the toothpaste in the tube is 7.64%.

From the given information,Mean, μ = 0.13 ounceStandard deviation, σ = 0.02 ounceNumber of times Ken brushes his teeth, n = 6.

The amount of toothpaste Ken squeezes out of the tube each time he brushes is independent and can be modeled by a Normal distribution.

From this information, we can obtain that:Mean of toothpaste used in 6 brushes = n × μ = 6 × 0.13 = 0.78 ounceStandard deviation of toothpaste used in 6 brushes = $\sqrt{n}$ × σ = $\sqrt{6}$ × 0.02 = 0.049 ounce.

To find the probability that Ken will use all the toothpaste in the tube, we need to calculate the probability of the amount of toothpaste used in 6 brushes being more than or equal to 0.85 ounce,
which is the total amount of toothpaste in the tube.P(X ≥ 0.85) = P( Z ≥ (0.85 - 0.78) / 0.049) = P(Z ≥ 1.43) = 1 - P(Z < 1.43)Using standard normal distribution table, we find the value of P(Z < 1.43) as 0.9236. Therefore,P(X ≥ 0.85) = 1 - P(Z < 1.43) = 1 - 0.9236 = 0.0764 or 7.64%.

The amount of toothpaste that Ken squeezes out each time he brushes is modeled by a normal distribution with mean 0.13 ounces and standard deviation 0.02 ounces.

The amount of toothpaste squeezed out at each brushing is independent of the previous amount of toothpaste squeezed out. We want to determine the probability that Ken will use all of the toothpaste in a 0.85-ounce tube if he brushes his teeth six times.

To do so, we first find the mean and standard deviation of the amount of toothpaste squeezed out in six brushes. If Ken brushes his teeth six times, then the mean amount of toothpaste squeezed out is nμ = 6(0.13) = 0.78 ounces. If the amount of toothpaste squeezed out at each brushing is independent, then the standard deviation of the amount of toothpaste squeezed out in six brushes is sqrt(6) * 0.02 = 0.049 ounces.

We now want to find the probability that Ken will use all of the toothpaste in the tube.

This is equivalent to finding the probability that the amount of toothpaste squeezed out in six brushes is greater than or equal to 0.85 ounces, which is the total amount of toothpaste in the tube.

If X is the amount of toothpaste squeezed out in six brushes, then we want to find P(X >= 0.85).We can standardize the distribution of X by subtracting the mean and dividing by the standard deviation.

Z = (X - μ) / σ is the standard normal random variable associated with X. In this case, Z has mean 0 and standard deviation 1. We want to find P(Z >= (0.85 - 0.78) / 0.049), which simplifies to P(Z >= 1.43). Using a standard normal distribution table, we can find P(Z < 1.43) = 0.9236. Therefore, P(Z >= 1.43) = 1 - P(Z < 1.43) = 1 - 0.9236 = 0.0764, or 7.64%.Therefore, the probability that Ken will use all the toothpaste in the tube is 7.64%.

Therefore, the probability that Ken will use all the toothpaste in the tube is 7.64%.

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The solutions are all the points inside the shaded region:

(1, 0.5) , (2,-1) and (2.5, -2)

Answer:

D

Step-by-step explanation:

Answer:

4+i

Step-by-step explanation:

A 99.8% confidence interval for the true mean length of all Hollywood movies made in the last 10 years is approximately (124.2, 137.6) minutes.

To construct a confidence interval for the true mean length of all Hollywood movies made in the last 10 years, we can use the formula:

Confidence interval = sample mean ± (critical value * standard error)

First, we need to find the critical value corresponding to a 99.8% confidence level. Since the sample size is large (n > 30), we can use the z-distribution. The critical value can be found using a z-table or a statistical calculator.

For a 99.8% confidence level, the critical value (z) is approximately 3.09.

Next, we calculate the standard error:

Standard error = (sample standard deviation) / √(sample size)

In this case, the sample standard deviation is 12.7 minutes, and the sample size is 46.

Standard error = 12.7 / √46 ≈ 1.8704

Now we can construct the confidence interval:

Confidence interval = 130.9 ± (3.09 * 1.8704)

Lower limit = 130.9 - (3.09 * 1.8704) ≈ 124.1926

Upper limit = 130.9 + (3.09 * 1.8704) ≈ 137.6074

Therefore, a 99.8% confidence interval for the true mean length of all Hollywood movies made in the last 10 years is approximately (124.2, 137.6) minutes.

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Although both Derrick and Julie obtained a total of 150 points on the two exams, Julie's claim of having a better total score is justified. This is because Julie's scores of 70 and 80 are higher relative to the mean of each respective exam compared to Derrick's scores of 75 on both exams.

For Derrick, scoring 75 on both exams means he scored exactly at the mean for each exam. On the other hand, Julie's score of 70 on the first exam is below the mean of 60 by 10 points, while her score of 80 on the second exam is 5 points above the mean of 75.

By scoring above and below the respective means, Julie's scores demonstrate a greater relative performance compared to Derrick's scores, indicating that her total score is comparatively better.

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6025 were the votes recieved by her opponent.

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the overall amount of fruit is 8:14, while the ratio of lemons to oranges is 6:8.

Divide the votes she received by the 6 parts of the ratio to find the value of one part of the ratio, that is

7230 ÷ 6 = 1205 ← value of 1 part of ratio

Her opponent received 5 parts, thus

votes received by opponent =  5× 1205 = 6,025

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Answer:

Step-by-step explanation:

(-3m + 3d) : 3 =

(-3m + 3d) x 1/3 =

-m + d

Answer:

TSP RSU

Step-by-step explanation:

Hope this helps!

Answer:

3rd answer

Step-by-step explanation:

its the 3rd answer trust me on it

After rotating 90 degrees anticlockwise, B's new coordinates are (y, -x).

By switching the x and y coordinates and negating the new x coordinate, we can rotate a point (x, y) 90 degrees clockwise around the origin.

After rotating the triangle 90 degrees anticlockwise around the origin, note the new coordinates of B.

Let (x, y) be point B's coordinates.

Fllowing a 90° anticlockwise turn:

B'x, the modified x coordinate, will now be y.

B'y, the modified y coordinate, will now be -x.

Therefore, B's new coordinates are (y, -x).

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We need at least 26 students to take the examination to ensure, with probability at least 0.94, that the class average will be within 2 of 60.

Let X be the test score of a student. We know that X is a random variable with mean μ = 60 and standard deviation σ = 8.

We want to find the sample size n required to ensure, with probability at least 0.94, that the sample mean (i.e., class average) is within 2 of 60. In other words, we want to find n such that:

P(|sample mean - μ| < 2) ≥ 0.94

The sample mean is a random variable as well, with mean μ and standard deviation σ/sqrt(n) (by the Central Limit Theorem).

Using the standard normal distribution, we can rewrite the above inequality as:

P(-2sqrt(n)/8 < Z < 2sqrt(n)/8) ≥ 0.94

where Z is the standard normal random variable. We can use a standard normal table or a calculator to find the corresponding values of -2sqrt(n)/8 and 2sqrt(n)/8.

We can simplify the inequality as follows:

P(Z < 2sqrt(n)/8) - P(Z < -2sqrt(n)/8) ≥ 0.94

Using a standard normal table or calculator, we find that P(Z < 2.11) ≈ 0.9838 and P(Z < -2.11) ≈ 0.0162. Therefore, we can rewrite the inequality as:

0.9838 - 0.0162 ≥ 0.94

Simplifying, we get:

0.9676 ≥ 0.94

This is true, so we have found the required value of n. To find n, we solve for sqrt(n):

2.11 = 2sqrt(n)/8

Multiplying both sides by 8 and squaring, we get:

n = (8*2.11/2)^2 = 25.67

Rounding up to the nearest integer, we get n = 26.

Therefore, we need at least 26 students to take the examination to ensure, with probability at least 0.94, that the class average will be within 2 of 60.

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I would say based on Lincoln's success and that Lincoln helped inspire Martin. Lincoln won the Civil War which helped open the minds of other people who were pro-slavery so that's what I mean about the success.

To answer this question we will set and solve a system of equations.

Let A be the speed (in miles per hour) of the airplane in still air, and W be the wind speed (in miles per hour).

Since the airplane flying with the wind takes 4 hours to travel a distance of 1200 miles and flying against the wind takes 5 hours to travel the same distance, then we can set the following equation:

Dividing the first equation by 4 we get:

Subtracting A from the above equation we get:

Substituting the above equation in the second one we get:

Simplifying the above result we get:

Adding 1500 to the above equation we get:

Dividing the above equation by 10 we get:

Finally, substituting A=270 at W=300-A we get:

Answer:

The speed of the airplane in still air is 270 miles per hour.

The wind speed is 30 miles per hour.

Answer:

ç

Step-by-step explanation:

The trigonometric expression in terms of sine and cosine and simplified is -sec^2 x.

We can use the trigonometric identity:

tan^2 x + 1 = sec^2 x

to rewrite the expression as:

tan^2 x − sec^2 x = tan^2 x − (tan^2 x + 1) = -1 - tan^2 x

Using the identity:

1 = sin^2 x + cos^2 x

we can rewrite tan^2 x as:

tan^2 x = sin^2 x / cos^2 x

Substituting this into the expression, we get:

-1 - tan^2 x = -1 - (sin^2 x / cos^2 x) = (-cos^2 x - sin^2 x) / cos^2 x

Using the identity:

cos^2 x + sin^2 x = 1

we can simplify the expression to:

(-cos^2 x - sin^2 x) / cos^2 x = (-1) / cos^2 x = -sec^2 x

Therefore, the trigonometric expression in terms of sine and cosine and simplified is -sec^2 x.

To write the trigonometric expression tan^2(x) - sec^2(x) in terms of sine and cosine, we first need to recall the definitions of tangent and secant:

tan(x) = sin(x) / cos(x)
sec(x) = 1 / cos(x)

Now, we can substitute these definitions into the given expression:

tan^2(x) - sec^2(x) = (sin(x) / cos(x))^2 - (1 / cos(x))^2

Now let's simplify the expression:

= (sin^2(x) / cos^2(x)) - (1 / cos^2(x))

To combine the two terms, we need a common denominator, which is cos^2(x):

= (sin^2(x) - 1) / cos^2(x)

Now, recall the Pythagorean identity: sin^2(x) + cos^2(x) = 1. We can rearrange this identity to express sin^2(x) in terms of cosine:

sin^2(x) = 1 - cos^2(x)

Now, substitute this expression for sin^2(x) in the given expression:

= (1 - cos^2(x) - 1) / cos^2(x)

Finally, simplify the expression:

= -cos^2(x) / cos^2(x)

The result is:

= -1

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