If ∠J and ∠K are acute angles in a right triangle and m∠J is less than 60°, then cos(J)=cos(K)

The approximate standard error of the mean is 3.

Here is how to find the approximate standard error of the mean from a population of 600 elements, where a sample of 100 elements is selected, and it is known that the variance of the population is 900.

Determine the sample size n, which is 100

Find the population variance, which is 900.

Compute the population standard deviation, which is the square root of the variance, as follows:

σ = √900σ

= 30

Compute the standard error of the mean as follows:

SEM = σ/√nSEM

= 30/√100SEM

= 3

The standard error of the mean (SEM) can be calculated using the formula:

SEM = σ / √n
where σ represents the population standard deviation, and n represents the sample size. In this case, we know that the population variance is 900.

To find the standard deviation, take the square root of the variance:
σ = √900 = 30
Now, we can plug in the values into the formula:
SEM = 30 / √100
SEM = 30 / 10
SEM = 3
The approximate standard error of the mean for this sample is 3.

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Answer:

we know the area of the parallelogram is given by a=b×h

The radius of the spherical boulder is half the diameter, so:

radius = 24 ft / 2 = 12 ft

The formula for the volume of a sphere is:

V = (4/3)πr³

Substituting the given values, we get:

V = (4/3) x 3.14 x (12 ft)³

V = 7238.08 cubic feet

Rounding to the nearest whole number, we get:

V ≈ 7238 cubic feet

The probability that the average size of the fish you caught is more than 14 inches is 0.1635 or 0.164

The size of bass caught in Strawberry Lake is normally distributed with a mean of 12 inches and a standard deviation of 5 inches.

If you catch 6 fish, the probability that the average size of the fish you caught is more than 14 inches is 0.202.

Here,

we need to find the probability that the average size of the fish you caught is more than 14 inches.

Let us denote the size of the bass caught in Strawberry Lake by X.

Then, X ~ N(μ = 12, σ = 5) represents the normal distribution of the size of bass caught in Strawberry Lake.

Let Y be the sample mean of 6 bass caught in the Strawberry Lake.

Then,

We know that Y ~ N(μ = 12, σ = 5/√6) represents the sampling distribution of the sample mean,

where σ = 5/√6

= 2.0412 (approx).

We are given that we have caught 6 fish.

Therefore, the sample size n = 6.

Then,

The probability that the average size of the fish you caught is more than 14 inches can be obtained as follows:

P(Y > 14) = P((Y - μ)/σ > (14 - μ)/σ)

= P(Z > (14 - 12)/2.0412)

= P(Z > 0.977)

= 1 - P(Z < 0.977) (as the standard normal distribution is a continuous distribution)

Using the standard normal distribution table, we get P(Z < 0.977) = 0.8365 (approx) Therefore, P(Y > 14) = 1 - P(Z < 0.977) = 1 - 0.8365 = 0.1635 (approx)

Therefore,

The probability that the average size of the fish you caught is more than 14 inches is 0.1635 or 0.164 (approx).

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Answer:

Step-by-step explanation:

She is traveling via Bootle.

Crosby to Bootle is 4 miles.

Bootle to Speke is 12 miles.

That is 16 miles each way.

16  times 2 = 32 miles per day

5 times 32 for the work week.

5 times 32 = 160 miles per week

a. the sampling distribution is  [tex]\sqrt{[(0.17 \times (1-0.17)) / n]}[/tex]

b. The probability that the sample proportion is within 0.03 of the population proportion is 0.4101.

c. The probability that the sample proportion is within 0.03 of the population proportion for a sample of 200 households is 0.7738.

a. The sampling distribution of the sample proportion, [tex]\bar p[/tex], can be approximated by a normal distribution with mean equal to the population proportion, p, and standard deviation equal to the square root of [tex][(p \times (1-p)) / n][/tex],

where n is the sample size.

Given that p = 0.17 and assuming a large enough sample size, we can use the formula to calculate the standard deviation of the sampling distribution:

Standard deviation = [tex]\sqrt{[(0.17 \times (1-0.17)) / n]}[/tex]

b. To find the probability that the sample proportion will be within a certain range of the population proportion, we need to calculate the z-score for the lower and upper bounds of that range and then find the area under the normal curve between those z-scores.

Let's say we want to find the probability that the sample proportion is within 0.03 of the population proportion. This means we want to find

P([tex]\bar p[/tex]- p ≤ 0.03) = P(([tex]\bar p[/tex]-- p) / [tex]\sqrt{[(p \times (1-p)) / n]}[/tex] ≤ 0.03 / [tex]\sqrt{[(p \times (1-p)) / n][/tex]

We can use the standard normal distribution and z-scores to find this probability:

[tex]z_1[/tex] = (0.03 / [tex]\sqrt{(0.17 \times (1-0.17)/n}[/tex])

[tex]z_2[/tex] = (-0.03 / [tex]\sqrt{(0.17 \times (1-0.17))/n}[/tex])

We can find the probability that the z-score is between [tex]z_1[/tex] and [tex]z_2[/tex]:

P([tex]z_1[/tex]≤ Z ≤ [tex]z_2[/tex]) = P(-0.541 ≤ Z ≤ 0.541) = 0.4101

c. To answer part (c), we need to specify the sample size. Let's say we are taking a sample of 200 households.

Using the formula for standard deviation of the sampling distribution from part (a), we get:

Standard deviation = [tex]\sqrt{(0.17 \times(1-0.17)) / 200}[/tex] = 0.034

Now we can repeat the same steps as in part (b) with this standard deviation:

[tex]z_1[/tex] = (0.03 / 0.034)

[tex]z_2[/tex] = (-0.03 / 0.034)

P([tex]z_1[/tex]≤ Z ≤ [tex]z_2[/tex]) = P(-0.882 ≤ Z ≤ 0.882) = 0.7738

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The logarithm expression is approximately 4.6.

To evaluate 9㏒₉⁵ - ㏒₃3⁵, we can use the logarithmic property that states:

㏒ₐ(b^c) = c x ㏒ₐ(b)

Using this property, we can simplify the expression as follows:

9㏒₉⁵ - ㏒₃3⁵

= ㏒₉(95^9) - ㏒₃(35)

= ㏒₉(1423892081) - ㏒₃(35)

We can evaluate these logarithmic terms using the change of base formula, which states:

㏒ₐ(b) = log(b) / log(a)

Using this formula, we get:

㏒₉(1423892081) = 8.032

㏒₃(35) = 3.432

Substituting these values back into the expression, we get:

9㏒₉⁵ - ㏒₃3⁵ = 8.032 - 3.432

= 4.6

The above answer is in response to the question below;

Evaluate

9㏒₉⁵ - ㏒₃3⁵

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Volume of the sphere is equal to two-third of the volume of a cylinder.

Volume is a mathematical concept that refers to the amount of space occupied by a three-dimensional object. It is expressed in cubic units, such as cubic meters or cubic centimeters, and can be calculated using a specific formula for each type of geometric shape.

A sphere is a perfectly round, three-dimensional object that looks like a ball. It has no edges or vertices and is symmetric around its center point. The formula for calculating the volume of a sphere is V = 4/3 πr³, where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.

True.

Assume that both the sphere's and cylinder's radius is r.

Considering that the base's diameter equals the cylinder's height

⇒h = 2r

Sphere radius = cylinder radius = r

Assuming the conditions are met, the sphere's volume:

=  [tex]\frac{2}{3}[/tex] × Volume of cylinder

= [tex]\frac{4}{3}[/tex]πr³= [tex]\frac{2}{3}[/tex] × πr² × 2r

=[tex]\frac{4}{3}[/tex]πr³= [tex]\frac{4}{3}[/tex]πr³

Hence, volume of the sphere is equal to two-third of the volume of a cylinder.

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The complete question is:

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Answer:

The three most common methods for solving quadratic equations are factoring, completing the square, and the quadratic formula.

Here's a quadratic equation you can solve by factoring:

x^2 - 4x + 3 = 0

(x - 1)(x - 3) =0

x = 1, 3

Step-by-step explanation:

Please find the attached pics for answers.

To take a systematic sample of 100 companies from a population of 1,803 companies, determine the sampling interval (k) which is N/n, choose a random starting point between 1 and k, and select every kth company until 100 companies are sampled.

To take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association, follow these steps

Determine the sampling interval (k), which is the number of companies in the population divided by the desired sample size. In this case, k = 1803/100 = 18.03. Round this number up or down to the nearest whole number based on your sampling preferences.

Choose a random starting point between 1 and k. For example, you could randomly select a number between 1 and 18.

From the starting point, select every kth company in the list of members until you have 100 companies. For example, if the starting point is 4, you would select companies 4, 22, 40, 58, 76, 94, 112, and so on until you reach 100 companies.

Important numerical values used in this process are:

Population size (N) = 1,803 companies

Desired sample size (n) = 100 companies

Sampling interval (k) = N/n = 1803/100 = 18.03

Random starting point (any number between 1 and k, depending on sampling preference)

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Answer:

parallelogram

Step-by-step explanation:

opposite angles and sides are congruent

The average speed of the round-trip for same path back to his house is given by 3 miles per hour.

The mean value of a body's speed over a period of time is its average speed. As a moving body's speed is not constant over time and fluctuates, the average speed formula is required. The values of total time and total distance travelled may be employed even when the speed varies, and with the aid of the average speed formula, we can identify a single number that sums up the whole motion.

So the average speed is simply: [tex]\frac{distance}{time}[/tex]

In case, the total time = 25 minutes + 55 minutes

which is a total of 80 minutes, or 1.33 hours.

The total distance traveled is two miles + two miles, since he jogged two miles to the park, and then he turns around and walks the same path.

So in total he traveled 4 miles.

Plugging this in to the formula gives you the equation:

[tex]v = \frac{d}{t} \\= \frac{4\ miles}{4/3 \ hour} \\= \frac{4 \ miles}{1} * \frac{3}{4} hours\\= 3mph[/tex]

Therefore, average speed of the round-trip is 3 mph.

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Answer:

-12.762538417

Step-by-step explanation:

The statements: the sample is random, the sample is an srs, and restrictions are placed on the sample, each plant has an equal chance of being selected are true.

Each tree has an equal chance of being selected. 

This sample is a simple random sample (SRS) because each tree has an equal chance of being selected and the selection of each tree is independent of the others.

Restrictions are imposed on the sample because the botanist selects only one plant from each row, based on a specific criterion (roll a cube).

Hence the following statements are true by probability

The sample is random.

The template is an SRS.

Restrictions are imposed on the sample.

Each tree has an equal chance of being selected. 

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Therefore, they will have paid the same amount after attending 9 games.

An equation is a mathematical statement that expresses the equality between two expressions or values. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions. An equation typically includes an equal sign (=) that indicates that the two sides of the equation are equal in value.

Here,

Let's start by setting up an equation to represent the total cost for each person after attending a certain number of games:

For the season ticket holder: Total Cost = 136.98 + 2.5x, where x is the number of games attended

For the second person: Total Cost = 17.72x

To find the number of games at which they will have paid the same amount, we can set the two equations equal to each other and solve for x:

136.98 + 2.5x = 17.72x

136.98 = 15.22x

x = 9

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The amount of work required to stretch the spring from 30.0 cm to 36.0 cm is 1.411 joules, which can be rounded to three decimal places.

According to Hooke's Law, the amount of work required to stretch or compress a spring by a certain amount is given by the formula:

W = (1/2) k (x2 - x1)²

where W is the work done (in joules), k is the spring constant (in newtons per meter), x1 is the initial displacement (in meters), and x2 is the final displacement (in meters).

In this case, the spring has a natural length of 30.0 cm, which is equivalent to 0.3 meters. To find the spring constant, we can use the fact that a 20.0-N force is required to keep it stretched to a length of 42.0 cm, which is equivalent to 0.42 meters.

Using Hooke's Law, we have

F = k (x2 - x1)20.0 N

= k (0.42 - 0.3) m

=> k = 80.0 N/m

Now we can use Hooke's Law again to find the amount of work required to stretch the spring from 30.0 cm to 36.0 cm, which is equivalent to 0.36 meters.

Using Hooke's Law, we have:

F = k (x2 - x1)W

= (1/2) k (x2 - x1)²W

= (1/2) (80.0 N/m) (0.36 - 0.3) m²W

= 1.411 J

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The product of twice a number and four is 8 times the number.

The product means a number that you get by multiplying two or more other numbers together.

The product of twice a number and four can be represented algebraically as:

4(2x)

where x is the number we are referring to.

Simplifying the expression, we get:

4(2x) = 8x

Therefore, the product of twice a number and four is 8 times the number.

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The expression is undefined, so the sign cannot be determined.

How to determine sign for the given problem?

The following given expression can be more simplified as follows:

-9 * (0 - 3)    -    (9 * (-3/0))

= -9 * (-3) - 9 * undefined [Note: Division by zero is undefined]

= 27 - undefined

As anything subtracted from undefined remains undefined, the overall result is undefined.

Therefore, the sign of the expression cannot be determined.

Undefined values represent the absence of a meaningful result or outcome. In this case, the expression involves division by zero, which is undefined. As a result, any operation involving an undefined value will also be undefined, including subtraction. Thus, the overall result is undefined.

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Answer:

ITS ZEROOOO

Step-by-step explanation:

i guesses and ended up getting it right.

By trigonometry Taking a look at the equation's left side 1-COSX/SINX is = (SINX/SINX) - (COSX/SINX) = (SINX - COSX)/SINX.

Several fields, including architecture, physics, astronomy, surveying, oceanography, navigation, electronics, and many more, use trigonometry. These are a few instances:

- In physics, trigonometry is used to calculate forces and analyze waves. - In astronomy, trigonometry is used to calculate distances between stars and planets. - In surveying, trigonometry is used to calculate distances and heights of objects. - In oceanography, trigonometry is used to calculate the heights of waves and tides in oceans.

We must make one side of the equation appear to be the other side in order to prove that 1-COSX/SINX=SINX/1+COSX.

Taking a look at the equation's left side first:

1-COSX/SINX is = (SINX/SINX) - (COSX/SINX) = (SINX - COSX)/SINX.

Let's now adjust the equation's right side:

SINX/1+COSX = (SINX/1+COSX) * (1-COSX/1-COSX)

= (SINX - SINXCOSX)/(1-COSXSINX)

= (SINX - COSXSINX)/(1-COSXSINX)

= (SINX - COSX)/((1-SINXCOSX)/( (1-SINXCOSX)

As the identities on both sides are equal to (SINX - COSX)/SINX, we can conclude that they are correct.

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Answer:

15.71

Step-by-step explanation:

Triangle ABC and triangle ADE are similar triangles so we can find the length of DE using similarity ratio.

[tex] \frac{14}{22} = \frac{10}{de} [/tex]

14×DE = 220

DE = 15.71 approximately.

The probability of exactly three successes in eight trials is approximately 26.61%

To find the probability of exactly three successes in eight trials of a binomial experiment with a success probability of 45%, use the binomial probability formula:

P(x) = C(n, x) * [tex]p^x[/tex] * [tex](1-p)^{(n-x)}[/tex]

where n is the number of trials, x is the number of successes, p is the probability of success, and C(n, x) is the combination function representing the number of ways to choose x successes from n trials.

In this case, n = 8, x = 3, and p = 0.45.

Calculate the probability:

P(3) = C(8, 3) * [tex]0.45^3[/tex] * [tex](1-0.45)^{(8-3)}[/tex]

P(3) = 56 * 0.091125 * 0.1721865

P(3) ≈ 0.2661

So, the probability of exactly three successes in eight trials is approximately 26.61%.

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According to the given data the equity in the house is $30,000.

Equity is the difference between the current market value of the property and the outstanding mortgage balance on the property.

If you purchased the house for $250,000 and it is now valued at $280,000, your equity in the house can be calculated as follows:

Equity = Current market value - Outstanding mortgage balance

Assuming you took out a mortgage for the full purchase price of the house and haven't made any extra payments, your outstanding mortgage balance would be the same as the original mortgage amount, which is $250,000. Therefore, your equity in the house would be:

Equity = $280,000 - $250,000

Equity = $30,000

So, your equity in the house is $30,000.

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Answer:

Yes,

Step-by-step explanation:

Because no x- Values repeat.

Answer:

Step-by-step explanation:

its a 12/14 probabiloty or a 92.5%

Step-by-step explanation:

I'll try:

7 boys choose 5   =   7! / (5!2!)  = 21 ways

4 girls  choose 2  = 4 ! / (2! 2!) =  6 ways

6 x 21 = 126 ways to choose   5 boys and 2 girls

11 cats total choose  7  =  11! /( 7! 4!)  = 330 ways to choose 7 cats

                   126 of these will be 5 boys and 2 girls

126 out of 330 = 126/330 = .382

Answer: The general equation for a circle with center (h, k) and radius r is:

(x - h)^2 + (y - k)^2 = r^2

To find the equation of the circle that passes through the points (1, 1), (1, 3), and (9, 2), we can use the fact that the perpendicular bisectors of any two chords of a circle intersect at the center of the circle.

The midpoint and slope of the chord connecting (1, 1) and (1, 3) are:

Midpoint: ((1+1)/2, (1+3)/2) = (1, 2)

Slope: undefined (since x values are the same)

The perpendicular bisector of this chord passes through the midpoint (1, 2) and has a slope of 0. Therefore, its equation is:

y - 2 = 0

Simplifying this equation gives:

y = 2

Similarly, the midpoint and slope of the chord connecting (1, 1) and (9, 2) are:

Midpoint: ((1+9)/2, (1+2)/2) = (5, 1.5)

Slope: (2 - 1)/(9 - 1) = 1/8

The perpendicular bisector of this chord passes through the midpoint (5, 1.5) and has a slope of -8 (the negative reciprocal of the slope of the chord). Therefore, its equation is:

y - 1.5 = -8(x - 5)

Simplifying this equation gives:

y = -8x + 41.5

The intersection of the two perpendicular bisectors (y = 2 and y = -8x + 41.5) is the center of the circle. Solving for x gives:

2 = -8x + 41.5

8x = 39.5

x = 4.9375

Substituting x = 4.9375 into either equation for the perpendicular bisectors gives:

y = 2

Therefore, the center of the circle is (4.9375, 2) and the radius is the distance from the center to any of the three given points. For example, the distance from (4.9375, 2) to (1, 1) is:

r = sqrt((4.9375 - 1)^2 + (2 - 1)^2) = sqrt(24.9219) = 4.992

So the equation of the circle is:

(x - 4.9375)^2 + (y - 2)^2 = (4.992)^2

Expanding and simplifying this equation gives:

x^2 - 9.875x + 24.526 + y^2 - 4y + 0.076 = 24.916

Rearranging terms gives:

x^2 + y^2 - 9.875x - 4y - 0.34 = 0

So the general equation for the circle is:

x^2 + y^2 - 9.875x - 4y - 0.34 = 0

Step-by-step explanation:

The minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.

Let x be the number of tulip bulbs that Jay plants, and let y be the number of lily bulbs that Jay plants.

Since Jay wants to plant at least twice as many tulips as lilies, we have the constraint:

x ≥ 2y

Also, the total number of bulbs that Jay plants cannot exceed 60, so we have the constraint:

x + y ≤ 60

We want to minimize the total cost of the bulbs that Jay purchases, which is given by the object function:

C = 1.6x + 1.25y

To solve this problem, we can use linear programming. First, we graph the two constraints on a coordinate plane:

The shaded region represents the feasible region, which is the region that satisfies both constraints. The vertices of the feasible region are (0, 0), (40, 20), (60, 0), and (30, 15).

Next, we evaluate the object function at each vertex to find the minimum value. We have:

C(0, 0) = 0

C(40, 20) = 1.6(40) + 1.25(20) = 92

C(60, 0) = 1.6(60) + 1.25(0) = 96

C(30, 15) = 1.6(30) + 1.25(15) = 67.5

Therefore, the minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.

Graphically, we can see that the optimal solution occurs at the intersection of the two constraints, which is the point (30, 15). This is where the slope of the object function is equal to the slope of the feasible region, which indicates that the object function is optimized at this point.

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Answer:

(C) (x)^2 + (y)^2 = 49.

Step-by-step explanation:

The equation of a circle with center (h, k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

In this case, the center of the circle is (0, 0), so h = 0 and k = 0. The radius of the circle is not given, but we can see that the equation must have a radius of 7 because the only terms involving x and y are squared and have coefficients of 1, which means they represent the distance from the center squared.

Therefore, the equation of the circle is:

(x - 0)^2 + (y - 0)^2 = 7^2

Simplifying, we get:

x^2 + y^2 = 49

So the correct answer is (C) (x)^2 + (y)^2 = 49.

The two expressions to show how much money Melissa would have after 10 weeks are:
1. 900 - 250 - 10x
2. 900 - (10 × 25 + 10x)

Expression 1: To calculate how much money Melissa would have after 10 weeks, first find the total amount she spends

on gas in 10 weeks by multiplying the weekly gas cost by the number of weeks:

25  10 = 250.

Next, find the total amount she spends on clothes in 10 weeks by multiplying the weekly clothes cost (x) by the number of weeks:

x × 10 = 10x.

Now, subtract both of these expenses from her initial savings to find the remaining balance:

900 - 250 - 10x.

Expression 2: You can also find the total expenses in 10 weeks by adding the gas and clothes costs together:

25 + x.

Then, multiply this combined weekly cost by 10 to find the total cost in 10 weeks:

10(25 + x) = 10 × 25 + 10x.

Finally, subtract the total cost from her initial savings:

900 - (10 × 25 + 10x).

So, the two expressions to show how much money Melissa would have after 10 weeks are:

1. 900 - 250 - 10x

2. 900 - (10 × 25 + 10x)

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