If you have a piece of round cake that has an area of 100 square inches, and you know the piece sweeps out an angle of 50, find the radius of the cake.

Answer:

3x^2-2x-6

Step-by-step explanation:

So first i paid attention in class

second apply to my homework

third step apply too your

<33 ur welcome lol

Answer:

Here is the full question:

Find the sum of the convergent series by using a well-known function. (Round your answer to four decimal places.) Σ_(n=1)^∞ (-1)^n+1 1/7^n n

Step-by-step explanation:

Σ_(n=1)^∞ (-1)^n+1 1/7^n n

We will use the function In (1 + x)

We will now give a power series expansion of the function while it is centered at x=0

This will give us In (1 + x) = Σ_(n=1)^∞\((-1)^{n+1}\)\(\frac{x^{n} }{n}\)

Note that x= 1/7

Now let us equate the two equations

Σ_(n=1)^∞\((-1)^{n+1}\)\(\frac{1}{7^{n}n }\) = ㏑(1 + x)|\(_{x = \frac{1}{7} }\) = ㏑\(\frac{8}{7}\)

Sum of the series will give ㏑\(\frac{8}{7}\)

Answer:

32 degrees goto the x vaule

The original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size."

a. To find the probability that a randomly selected female has a pulse rate less than 80 beats per minute, we need to standardize the value using the formula z = (x - μ) / σ, where x is the pulse rate we are interested in, μ is the mean pulse rate, and σ is the standard deviation. Thus, we have:

z = (80 - 76) / 12.5 = 0.32

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 0.32 is approximately 0.6255. Therefore, the probability that a randomly selected female has a pulse rate less than 80 beats per minute is:

P(z < 0.32) = 0.6255

b. Since we are dealing with a sample size of 25 females, we can use the central limit theorem, which states that the distribution of sample means will be approximately normal with a mean of μ and a standard deviation of σ / sqrt(n), where n is the sample size.

In this case, we have:

μ = 76.0

σ = 12.5

n = 25

Therefore, the standard deviation of the distribution of sample means is:

σ / sqrt(n) = 12.5 / sqrt(25) = 2.5

To find the probability that 25 randomly selected females have a mean pulse rate less than 80 beats per minute, we need to standardize the value using the formula z = (X- μ) / (σ / sqrt(n)), where X is the sample mean.

Thus, we have:

z = (80 - 76) / (2.5) = 1.6

Using a standard normal distribution table or a calculator, we can find that the probability of a z-score less than 1.6 is approximately 0.9452. Therefore, the probability that 25 randomly selected females have a mean pulse rate less than 80 beats per minute is:

P(z < 1.6) = 0.9452

c. The normal distribution can be used in part (b) because we are dealing with the distribution of sample means, not individual pulse rates. The central limit theorem states that the distribution of sample means will be approximately normal regardless of the sample size, as long as the sample size is sufficiently large (typically, n ≥ 30). In this case, we have a sample size of 25, which is smaller than 30, but we can still use the normal distribution approximation because the population distribution is assumed to be normal.

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Answer:

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

To calculate the equation of the line first find the slope

Slope of the line using points

(0 , 0) and (4 , -2) is

\(m = \frac{ - 2 - 0}{4 - 0} = \frac{ - 2}{4} = - \frac{1}{2} \)

Now use the formula

y - y1 = m(x - x1) to find the equation of the line using any of the points

Using point (0,0)

That's

\(y - 0 = - \frac{ 1}{2} (x - 0)\)

The final answer is

\(y = - \frac{1}{2} x\)

Hope this helps you

Answer:

F

Step-by-step explanation:

Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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Answer:

x + x - 272 = 600

Step-by-step explanation:

Let the amount raised by Kate by x and let the amount raised by Isabelle be y.

Now, we are told that Kate raised $272 more than Isabelle.

Thus, since amount raised by Kate is x, then amount raised by Isabelle is x - 272. We are told that together they raised $600.

Thus;

x + x - 272 = 600

Thus;

equation to represent the total amount of money the girls raised is;

x + x - 272 = 600

Answer:

The final balance is $1,692.94.

The total compound interest is $392.94.

Step-by-step explanation:

1,300 x 0.045=___ x 6

Answer:  k=(1/5)

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

Look for the angle of -60, you will see the coordinate (1/2,-sqrt3/2)

The cosine function is the x value of each coordinate of the unit circle

Let me know in the comments if you have any questions! If you could mark this answer as the brainliest I would greatly appreciate it! :D

Answer:

Step-by-step explanation:

c 1/2

Answer:

No solutions

Step-by-step explanation:

\(\frac{-b ± \sqrt{b^2-4ac} }{2a}\)

Add 8 on both sides to make it into the form ax^2 + bx + c = 0

x^2 - 3x + 8 = -8 + 8

x^2 - 3x + 8 = 0

Now it is in the correct form, we can plug our numbers in.

a: 1

b: -3

c: 8

\(\frac{3 ± \sqrt{-3^2 - 4(1)(8)} }{2(1)}\)

\(\frac{3 ± \sqrt{-23} }{2(1)}\)

Because the discriminant, or b^2 - 4ac is negative, there are no solutions.

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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Answer:

1000 tiles

Step-by-step explanation:

Determine total floor space
800 x 10 = 8000 squared cm total floor space.
Divide floor space by size of tile
8000 / 8 = 1000 tiles now required to cover the floor.

Answer:

the answer is b. The mode of the data in dot plot 1 is less than the mode of the data in dot plot 2.

Step-by-step explanation:

In the dot plots 1 and 2, the statement which is true is that the mean of the data in dot plot 1 is greater than the mean of the data in data plot 2.

The dot plot is the way oif representation of the data. This data is plooted in the form of points or dots over an x-y axis. The dot polt is also known as the strip plot.

Dot plot 1 is the top plot. The value of it are as,

2,3,4,5,5,6,6,6,6,7,7,7,8,8,9,10

Dot plot 2 is the bottom plot. The value of it are as,

1,2,2,3,3,4,4,4,5,5,5,6,6,7,8,9

The options given in the problem are,

Range is difference between the highest and lowest value. The range of the first dot plot is,

\(r_1=10-2=8\)

The range of the Second dot plot is,

\(r_2=9-1=8\)

Range of dot plots are equal.

Mean of the dot plot one is 6.1875 and mean of the dot plot second is 4.625.

The median of the data in dot plot 1 is 6 and the median of the data in dot plot is 4.5. Thus they are not equal.

The mode of the data in dot plot 1 is 6 and the mode of the data in dot plot 2 is 4 and 5. Thus this is not correct option.

Hence, in the dot plots 1 and 2, the statement which is true is that the mean of the data in dot plot 1 is greater than the mean of the data in data plot 2.

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Answer:

D

Step-by-step explanation:

Frank is at point G: (-6,-1)

Jimmy is at point B: (4,1)

Answer:

122.6875 (122 ft 8.25 in)

Step-by-step explanation:

12 ft 7in = 151 in

9 ft 9 in = 117 in

151 x 117 = 17667

17667in = 122 ft and 8.25 in = 122.6875 ft

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

The new points to the triangle will be:

\(A(-6, 6)\\B(-6, 3)\\C(-8, 3)\)

Step-by-step explanation:

Because the reflection point is at \(x = -1\), all x values will subtract their distances from \(x = -1\) to get their new values. The y values remain the same.

The starting values are:

\(A(4,6)\\B(4,3)\\C(6,3)\)

Point \(A\) is 5 units away from \(x = -1\), so we'll subtract 5 from -1 to get the new x value: \(-1 - 5 = -6\), so \(A(-6, 6)\).

Point \(B\) is also 5 unit away from \(x = -1\), so we'll subtract 5 from -1 to get the new x value: \(-1 - 5 = -6\), so \(B(-6, 3)\).

Point \(C\) is 7 units away from \(x = -1\), so we'll subtract 7 from -1 to get the new x value: \(-1 - 7 = -8\), so \(C(-8, 3)\).

Answer:

No need to pay me, its my pleasure, also its not even in my country's currency so it would be worthless to me anyways.

5,4 and 4,4

Step-by-step explanation:

Answer:

Just input sin(9), sin(30), sin(81), etc.

For this set, you need a scientific calculator or else, you won't be able to answer that. There is a way but that is already obsolete now.

Answer:

The last one \((x=11.3, y=8)\).

Step-by-step explanation:

1) There are three trigonometric ratios for right-angled triangles.

\(sin()=\frac{opposite}{hypotenuse}\\cos()=\frac{adjacent}{hypotenuse}\\tan()=\frac{opposite}{adjacent}\)

In a right triangle, the hypotenuse, h, is the side opposite the right angle. Relative to the acute angle θ, check the attachment, the legs are called the opposite side, o, and the adjacent side a.

2) In this case, we are given a length and an angle to find x and y.

Let's find x first. To find x we need to use \(sin()=\frac{opposite}{hypotenuse}\).

\(sin(45)=\frac{8}{x}\\sin(45)x=8\\x=\frac{8}{sin(45)} \\x=11.31\)

Find y.

Notice that, we can use the Pythagorean Theorem \((c^2=a^2+b^2)\) to find y.

\(c^2=a^2+b^2\)

\(11.31^2=8^2+b^2\\11.31^2 - 8^2 = b^2\\63.9161 = b^2\\\sqrt{63.9161} = b\\b = 7.99\)

3) Round them off to the nearest tenth.

\(x=11.31\\x=11.3\)

\(y=7.99\\y=8\)

Therefore, the correct choice is the last one \((x=11.3, y=8)\).

The dimensions of the length and width are 25 meters and 12. 5 meters respectively.

Area of a rectangle

area of rectangle = l × w

where

l = length

w = width

Note that,

Perimeter = 2w+ l

50 = 2w + l

l = 50  - 2w

Hence,

area = w(50 - 2w)

288 = 50w - 2w²

-2w² + 50w - 288 = 0

-w² + 25w - 144 = 0

The dimension w can be found as follows;

w = - b / 2a

where

a = -1

b = 25

w = - 25 / 2 ×  -1

w = 12.5 meters

Then, we have that

l = 50  - 2w

Substitute the value of w

l = 50 - 2(12.5)

l = 50 - 25

I = 25 meters

Thus, the dimensions of the length and width are 25 meters and 12. 5 meters respectively.

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Step-by-step explanation:

6ft² of grass sod + 5 geraniums = $27

9 ft² of grass sod + 11 geraniums = $51

Let x represent 1ft² of grass sod.

Let y represent 1 geranium.

We have 6x + 5y = $27.

=> 1.5(6x + 5y) = 1.5 * $27, 9x + 7.5y = $40.5.

9x + 11y = $51

- (9x + 7.5y = $40.5)

=> 3.5y = $10.5, y = $3.

Therefore 6x + 5($3) = $27,

6x + $15 = $27, 6x = $12, x = $2.

Hence 1ft² of grass sod costs $2

and 1 geranium costs $3.

Answer:

D. The hot-air balloon... results in a net of zero

Step-by-step explanation:

Thanks for the points my guy :)

have a great day

Answer:

canberry

Step-by-step explanation:

The constant differences between the consecutive terms are 2 (a); 2 (b), -3 (c), 7 (d), 1(e), and 6(f).

In math, the constant difference can be defined as the number that defines the pattern of a sequence of numbers. This means that number that should be added or subtracted to continue with the sequence.

Due to this, to determine the constant difference it is important to observe the pattern and find out the number that should be added. For example, if the sequence is 2, 4, 6, 8, there is a difference of 2 between each of the numbers and this is the constant difference.

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Step-by-step explanation:

The feet long that the board is

\( = 6 \frac{1}{2} \\ \)

The piece of board cut off

\( = 1 \frac{3}{4} + 2 \frac{2}{3} \\ \)

\( = \frac{1 \times 4 + 3}{4} + \frac{2 \times 3 + 2}{3} \\ \)

\( = \frac{7}{4} + \frac{8}{3} \\ \)

\( = \frac{7}{4} \times \frac{3}{3} + \frac{8}{3} \times \frac{4}{4} \\ \)

\( = \frac{21}{12} + \frac{32}{12} \\ \)

\( = \frac{53}{12} \\ \)

The original board left

\( = 6 \frac{1}{2} - \frac{53}{12} \\ \)

\( = \frac{13}{2} - \frac{53}{12} \\ \)

\(= \frac{13}{2} \times \frac{6}{6} - \frac{53}{12} \times \frac{1}{1} \\ \)

\( = \frac{78 - 53}{12} \\ \)

\( = \frac{25}{12} \\ \)

\( = 2 \frac{1}{12} \\ \)

hope it helped !!!

1. An equation for Kim's time (in seconds) to complete the race is, t = x/2.

2. An equation for Jake's time (in seconds) to complete the race is, t = (x - 6)/1.5.

An equation is a mathematical statement (written with numbers, variables, and the equation sign) claiming that two mathematical expressions share value equality.

Equations are depicted using the equation sign (=).

The solution of the equation establishes the validity of the claim.

Kim's running speed = 2 meters per second

Jake's running speed = 1.5 meters per second (or 3 meters per 2 seconds)

Let the total distance for the race = x and the total time taken by either Kim or Jakes = t.

Time = Distance/Speed

Kim's equation for time is t = x/2.

Jake's equation for time is t = (x - 6)/1.5.

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Solution

Given the quadratic equation:

x² + 2x + 7 = 21

x² + 2x + 7 - 21 = 0

x² + 2x - 14 = 0

a = 1, b = 2, c = - 14

(1) The number of solutions of a given quadratic equation is determine by the discriminant.

From the given values;

(2)² - 4(1 x -14) = 4 + 56 = 60

60 > 0 ( 2 solutions)

1 positive solution and 1 negative solution

Thus, number of positive solutions to this equation is one

(2) The greatest solution or positive solution to the equation is calculated as;

Answer:

a) 64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

b) The hardness distribution is not given. But you would have to find s when n = 39, then the probability would be 1 subtracted by the pvalue of Z when X = 51.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For the sum of n trials, the mean is \(\mu*n\) and the standard deviation is \(s = \sigma\sqrt{n}\)

In this question:

\(n = 48, \mu = 48*5 = 240, s = 4\sqrt{48} = 27.71\)

These values are in minutes.

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

From 6:50 PM to 11 PM there are 4 hours and 10 minutes, so 4*60 + 10 = 250 minutes. This probability is the pvalue of Z when X = 250. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{250 - 240}{27.71}\)

\(Z = 0.36\)

\(Z = 0.36\) has a pvalue of 0.6406

64.06% probability that he is through grading before the 11:00 P.M. TV news begins.

(b) What is the (approximate) probability that the sample mean hardness for a random sample of 39 pins is at least 51?

The hardness distribution is not given. But you would have to find s when n = 39(using the standard deviation of the population divided by the square root of 39, since it is not a sum here), then the probability would be 1 subtracted by the pvalue of Z when X = 51.