One of the legs of a right triangle measures 12 cm and the other leg measures 13 cm find the measure of the hypotenuse if necessary round the nearest 10th

Answer:

asymptote

Step-by-step explanation:

Answer:

y = 5x - 2

Step-by-step explanation:

✅Rate of change = change in y/change in x

Rate of change of the table of values using two pairs of values from the table (2, 8) and (3, 11):

Rate of change = (11 - 8)/(3 - 2) = 3/1

Rate of change = 3

✅Rate of change of the equation, y = 5x - 2.

The equation is represented in the slope-intercept form, y = mx + b.

Where, m = slope/rate of change

Therefore, rate of change if the equation would be 5.

Rate of change = 5

✔️The function that has the greater rate of change would therefore be y = 5x - 2

The probability, P(14), that exactly 14 out of 17 randomly selected Americans own an answering machine can be calculated. The answer is found to be 0.216, rounded to three decimal places.

To find the probability, P(14), we can use the binomial probability formula:

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

Where:

P(k) is the probability of exactly k successes,

C(n, k) is the number of combinations of n items taken k at a time,

p is the probability of success for each trial, and

n is the total number of trials.

In this case, we are looking for the probability of exactly 14 Americans owning an answering machine of 17 randomly selected Americans. The probability of owning an answering machine is given as 0.69.

Substituting the values into the formula, we get:

[tex]P(14) = C(17, 14) * (0.69)^{14} * (1 - 0.69)^{(17 - 14)}[/tex]

Using combination notation, C(17, 14) = 17! / (14! * (17-14)!) = 17! / (14! * 3!) = 17 * 16 * 15 / (3 * 2 * 1) = 680.

Calculating further, we find:

[tex]P(14) = 680 * (0.69)^{14} * (0.31)^3 =0.216[/tex].

Therefore, the probability, P(14), that exactly 14 out of 17 randomly selected Americans own an answering machine is approximately 0.216.

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The number of 1 -by-1 -by-1 -inch cubes that can fit inside of this rectangular prism 120 cubes.

volume = lwh

where

Therefore,

volume = 10 × 3 × 4 = 120 inches³

Volume of the cube = l³

where

Therefore,

volume = 1 × 1 × 1 = 1 inches³

Therefore, the number of 1 -by-1 -by-1 -inch cubes that can fit inside of this rectangular prism is as follows;

number of cube = 120 / 1 = 120 cubes

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The first eight nonzero terms of the solution by substituting the values of the coefficients in the power series expression for y(x) are:

[tex]a_0 = 0\\a_1 = -a_2/2\\a_2 = -3a_1/2\\a_3 = -(4a_2 + 6a_1)/2\\a_4 = -(5a_3 + 7a_2)/2\\a_5 = -(6a_4 + 8a_3)/2\\a_6 = -(7a_5 + 9a_4)/2\\a_7 = -(8a_6 + 10a_5)/2\\a_8 = -(9a_7 + 11a_6)/2[/tex]

To solve the given differential equation y" + xy' + 2y = 0 using power series method around xo = 0, we assume a power series solution of the form:

y(x) = ∑[n=0 to ∞] [tex]a_n x^n[/tex]

Now, let's find the first eight nonzero terms of this power series solution.

First, we'll calculate the derivatives of y(x) with respect to x:

y'(x) = ∑[n=0 to ∞] a_n * n * [tex]x^{(n-1)[/tex]

y''(x) = ∑[n=0 to ∞] a_n * n * (n-1) * [tex]x^{(n-2)[/tex]

Substituting these expressions into the original differential equation, we have:

∑[n=0 to ∞] [tex]a_n[/tex] * n * (n-1) * [tex]x^{(n-2)[/tex] + x * ∑[n=0 to ∞] [tex]a_n[/tex] * n * [tex]x^{(n-1)[/tex] + 2 * ∑[n=0 to ∞] [tex]a_n * x^n[/tex] = 0

Now, we'll rearrange the terms and combine them:

∑[n=2 to ∞][tex]a_n[/tex] * n * (n-1) * [tex]x^{(n-2)[/tex] + ∑[n=1 to ∞] [tex]a_n[/tex] * n * [tex]x^n[/tex] + 2 * ∑[n=0 to ∞] [tex]a_n * x^n[/tex] = 0

Let's break down each summation separately:

For the first summation term, n starts from 2:

∑[n=2 to ∞] [tex]a_n[/tex] * n * (n-1) * [tex]x^{(n-2)[/tex] = a_2 * 2 * 1 * [tex]x^0[/tex] + [tex]a_3[/tex] * 3 * 2 * x^1 + [tex]a_4[/tex] * 4 * 3 * [tex]x^2[/tex] + ...

For the second summation term, n starts from 1:

∑[n=1 to ∞] [tex]a_n[/tex] * n * [tex]x^n[/tex] = [tex]a_1[/tex] * 1 * [tex]x^1[/tex] + [tex]a_2[/tex] * 2 * [tex]x^2[/tex] + [tex]a_3[/tex] * 3 * [tex]x^3[/tex] + ...

For the third summation term, n starts from 0:

2 * ∑[n=0 to ∞] [tex]a_n * x^n[/tex] = 2 * [tex]a_0 * x^0[/tex] + 2 * [tex]a_1 * x^1[/tex] + 2 *[tex]a_2 * x^2[/tex] + ...

Combining these terms, we have:

2[tex]a_0[/tex] + (2[tex]a_1 + a_2[/tex])x + (2[tex]a_2 + 3a_1[/tex])[tex]x^2[/tex] + [tex](2a_3 + 4a_2 + 6a_1)x^3[/tex] + ...

Since the equation should hold for all values of x, each coefficient of [tex]x^n[/tex]should be zero. Therefore, we equate each coefficient to zero and find the recurrence relation for the coefficients:

2[tex]a_0[/tex] = 0 => [tex]a_0 = 0[/tex]

[tex]2a_1 + a_2 = 0[/tex] => [tex]a_1 = -a_2/2[/tex]

[tex]2a_2 + 3a_1 = 0[/tex] => [tex]a_2 = -3a_1/2[/tex]

[tex]2a_3 + 4a_2 + 6a_1 = 0[/tex]

Using these recurrence relations, we can calculate the first eight nonzero terms of the solution.

Starting from [tex]a_0 = 0[/tex], we can find the values of [tex]a_1, a_2[/tex], and so on:

[tex]a_0 = 0[/tex]

[tex]a_1 = -a_2/2[/tex]

[tex]a_2 = -3a_1/2[/tex]

[tex]a_3 = -(4a_2 + 6a_1)/2[/tex]

[tex]a_4 = -(5a_3 + 7a_2)/2[/tex]

[tex]a_5 = -(6a_4 + 8a_3)/2[/tex]

[tex]a_6 = -(7a_5 + 9a_4)/2[/tex]

[tex]a_7 = -(8a_6 + 10a_5)/2[/tex]

[tex]a_8 = -(9a_7 + 11a_6)/2[/tex]

Therefore, these are the first eight nonzero terms of the solution by substituting the values of the coefficients in the power series expression for y(x).

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Since the slope of the tangent line on the graph of y=x is 1, any point on the line y=x can be considered as the point where the tangent line is parallel to -5x+2y=4.  The point on the graph of y=x where the tangent line is parallel to the line -5x+2y=4 is (2, 2).

To find the point on the graph of y=x where the tangent line is parallel to the line -5x+2y=4, we need to find the slope of the line -5x+2y=4 and equate it to the slope of the tangent line on the graph of y=x.

The given line -5x+2y=4 can be rewritten as 2y=5x+4, which implies y=(5/2)x+2. Comparing this equation with y=x, we see that the slopes of both lines are equal, which means the tangent line to y=x is parallel to the given line.

Since the slope of the tangent line on the graph of y=x is 1, any point on the line y=x can be considered as the point where the tangent line is parallel to -5x+2y=4. One such point is (2, 2), where x=2 and y=2.

Therefore, the point on the graph of y=x where the tangent line is parallel to -5x+2y=4 is (2, 2).

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Answer:

1620!

Step-by-step explanation:

Answer:

1620

Step-by-step explanation:

The derivative h'(4) is equal to 40.

To find h'(4), we can apply the chain rule. The chain rule states that if we have a composite function, we can find the derivative by taking the derivative of the outer function and multiplying it by the derivative of the inner function.

In this case, h(x) = 5 * 4f(x), so the outer function is multiplying by 5 and the inner function is f(x).

First, we find the derivative of the outer function, which is a constant multiple. The derivative of 5 is 0.

Next, we find the derivative of the inner function, f'(x). We are given that f'(4) = 2.

Now, we can apply the chain rule: h'(x) = 0 * f(x) + 5 * f'(x).

Substituting the given values, we have: h'(4) = 0 * f(4) + 5 * f'(4) = 0 * 5 + 5 * 2 = 0 + 10 = 10.

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Answer:

Domain:{-9,-4}

Range:{-1,-8,6}

Step-by-step explanation:

I dont really understand what you're trying to ask, it seems like you already have the answer i got.

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

Note: In parallel lines the slopes are the same

so put in (-2,5) into the values for (x,y) in y=mx+b and -4 in for m.

5=(-4)(-2)+b

5=8+b

-3=b

So then we put that back into the original equation with the slope of -4

y=(-4)x-3

Hope that helps :)

Answer:

Olivia invested $2900 in a savings account that paid 4.5%/yr and $900 in a government bond that paid 5.5%/yr.

Step-by-step explanation:

With the information provided you can write the following equations:

x+y=3800 (1)

0.045x+0.055y=180 (2), where:

x is the amount invested in a savings account

y is the amount invested in a government bond

First, you can solve for x in (1):

x=3800-y (3)

Next, you can replace (3) in (2) and solve for y:

0.045(3800-y)+0.055y=180

171-0.045y+0.055y=180

0.01y=9

y=9/0.01

y=900

Finally, you can replace the value of y in (3) to find x:

x=3800-900

x=2900

According to this, the answer is that Olivia invested $2900 in a savings account that paid 4.5%/yr and $900 in a government bond that paid 5.5%/yr.

The 98% confidence interval for the number of chocolate chips per cookie for Big Chip cookies is approximately 32.4<< 88.2

To construct a confidence interval for the mean number of chocolate chips per cookie, we can use the t-distribution since the sample size is small (n = 13) and the population standard deviation is unknown.

Given that the sample mean is 60.3 and the sample standard deviation is 37.5, we can calculate the standard error (SE) as:

[tex]SE = s / \sqrt(n)[/tex]

where s is the sample standard deviation and n is the sample size.

[tex]SE = 37.5 / \sqrt(13) \approx 10.41[/tex]

To calculate the margin of error, we multiply the standard error by the t-score corresponding to a 98% confidence level with n-1 degrees of freedom.

With n-1 = 12 degrees of freedom, the t-score can be obtained from a t-table or calculator. For a 98% confidence level, the t-score is approximately 2.681.

Margin of Error = t * SE = 2.681 * 10.41 ≈ 27.92

Finally, we can construct the confidence interval by subtracting and adding the margin of error to the sample mean:

CI = sample mean ± margin of error

CI = 60.3 ± 27.92

Therefore, among the answer choices provided, the closest option is "32.4 << 88.2."

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Answer:

Surface area is 164 ft^2.

Step-by-step explanation:

2(10*4) + 2(10*3) + 2(4*3) = 164 ft^2

We can see from the statistical software printout that the factory recently installed new pollution control equipment ("scrubbers") on its smokestacks in hopes of reducing air pollution levels at a nearby national park.

Here, randomly timed measurements of sulfate levels (in micrograms per cubic meter) were taken before (Set C1) and after (Set C2) the installation. We believe that measurements of sulfate levels are normally distributed. A complete conclusion about the effectiveness of these scrubbers based on the statistical software printout shown is:The mean sulfate level for Set C1 is 8.29, and the mean sulfate level for Set C2 is 5.00.

From the Two Sample T for C1 vs C2 table, we find that the t-test statistic is 3.29, and the p-value is 0.0037. Because the p-value (0.0037) is less than the level of significance (α=0.05), we can reject the null hypothesis that the mean sulfate levels are equal before and after the installation of the scrubbers. Therefore, we can conclude that the installation of scrubbers on the factory's smokestacks has had a significant effect in reducing the sulfate levels in the air at the national park.

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Answer:answer is d

Step-by-step explanation:

I have done the test

Given, PVHS published a confidence interval for the true proportion of high schoolers who show up late for school on a given day.

The interval created from a random sample of high schoolers is (0.039, 0.109). We have to determine the point estimate and margin of error for this interval. (1 pt) A. We know that Point estimate is the single value that best represents the population of interest. It can be calculated as the average of all the sample observations.

For the given interval, the point estimate is given by the average of the interval which is:(0.039 + 0.109) / 2 = 0.074B. What margin of error is used in this interval?Margin of Error = (Upper limit of CI - Point Estimate) or (Point Estimate - Lower limit of CI)

For the given interval, we have Point estimate = 0.074Lower limit of CI = 0.039Upper limit of CI = 0.109

Therefore, Margin of Error = (0.109 - 0.074) = 0.035

Thus, the margin of error used in this interval is 0.035.

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Answer:

Olivia wrapped 6 gifts and prepared 8 giftbags.

Step-by-step explanation:

Write System of Equations:

3x+1.5y= 30                                                 x+y=14

x+y=  14                                                       y=-x+14

3x+1.5y=30

1.5y=3x+30

1.5y divided by 1.5 is y

-3x+30 divided by y is -2x+20

y=-2x+20

Olivia wrapped 6 gifts and made 8 Giftbags.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

Olivia can wrap a single gift in 3 minutes and she can do a giftbag in 1.5 minutes

Olivia prepared a total 14 gifts in 30 minutes.

let number of gifts Olivia wrapped be x.

and, number of giftbags she prepared be y.

So, the equations are:

3x+1.5y= 30 .....(1)

x+y=14

Now, plotting these equations on graph we get intersecting point of two lines which shows x= 6 and y=8.

Hence, Olivia wrapped 6 gifts and made 8 Giftbags.

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Answer:

I think its c hope this helps I may be wrong

Answer:

quite simple

Step-by-step explanation:

When multiplying a monomial by a monomial, multiply the coefficients and then multiply the variables. When multiplying variables that are the same, use the product of powers property to add the exponents. When multiplying a monomial by a binomial, multiply the factors of the monomial into each term of the binomial.

The robot must do 840 foot-pounds of work to lift the chain from a height of 3 feet to a height of 13 feet. What the robot has to do to lift the chain from a height of 3 feet to a height of 13 feet is the work.

Work is defined as the product of the force acting on an object and the distance that object moves as a result. To compute the work that the robot must do to lift the chain from a height of 3 feet to a height of 13 feet, we must first determine how much gravitational potential energy the chain has at the higher elevation. The gravitational potential energy of an object is equal to the object's weight times its height above a reference level. The weight of the chain is given as 120 pounds, and the chain will be lifted by the robot for a total of 10 feet. After that, we can determine the amount of work that the robot must do to raise the chain to the new height using the formula W = Fd, where W is work, F is force, and d is distance. The robot must do 840 foot-pounds of work.

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Answer:

if y=6x then 3x-6x=21

-3x=21

x=-7

3x - y = 21

y = 6x

We see that,

0 = 42 which is not true.

The system of equations has no solutions.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

System of equations:

Conditions:

1 - If we get x = n (a value)

The system of equations has one solution

2 - If we get x = x or y = y or n = n

The system of equations has infinite solutions.

3 - If we get n ≠ 0

The system of equations has no solutions

Now,

3x - y = 21 _____(1)

y = 6x ______(2)

From (1) we get,

3x = 21 + y

x = (21 + y) / 3 _____(3)

Putting (3) in (2) we get,

y = 6 [(21 + y) / 3]

y = 2 (21 + y)

y = 42 + y

0 = 42

Which is not true.

This means the system of equations has no solutions.

Thus,

The system of equations has no solutions.

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Answer:

1.8

Step-by-step explanation:

Answer:

so i'm guessing since 5 times 5 is 25 but there is a 2 on top of the number 25 that means squared meaning your're going to multiply. can i get a thanks and a rate!

Step-by-step explanation:

The work done by the force field F in moving an object from P to Q is 1459/6.

The work done by a force field in moving an object from point P to point Q can be calculated using the line integral of the force field along the path from P to Q.

Given the force field F(x, y) = x^5i + y^5j and the points P(1, 0) and Q(3, 3), we need to calculate the line integral of F along the path from P to Q.

The line integral of a vector field F along a curve C is given by the formula:

∫C F · dr,

where F is the vector field, dr is the differential vector along the curve, and ∫C represents the line integral over the curve C.

In this case, the path from P to Q can be parameterized by a function r(t) = (x(t), y(t)), where t varies from 0 to 1. We can choose a linear parameterization for simplicity:

x(t) = 1 + 2t,

y(t) = 3t,

where t varies from 0 to 1.

Now, we can calculate the line integral:

∫C F · dr = ∫₀¹ F(x(t), y(t)) · r'(t) dt,

where r'(t) represents the derivative of r(t) with respect to t.

Substituting the values into the formula, we have:

∫₀¹ ( (1 + 2t)^5i + (3t)^5j ) · (2i + 3j) dt.

Simplifying the expression, we get:

∫₀¹ ( (1 + 2t)^5(2) + (3t)^5(3) ) dt.

Now, we can integrate term by term:

= ∫₀¹ ( 2(1 + 2t)^5 + 3^5t^5 ) dt.

= [ (2/6)(1 + 2t)^6 + (3/6)t^6 ] from 0 to 1.

Evaluating the expression at the limits, we have:

= (2/6)(1 + 2(1))^6 + (3/6)(1)^6 - (2/6)(1 + 2(0))^6 - (3/6)(0)^6.

= (2/6)(3^6) + (3/6) - (2/6)(1^6) - (3/6)(0).

= (2/6)(729) + (3/6) - (2/6) - 0.

= (2/6)(729 - 1) + (3/6).

= (2/6)(728) + (3/6).

= 728/3 + 3/6.

= 728/3 + 1/2.

= (1456 + 3)/6.

= 1459/6.

Therefore, the work done by the force field F in moving an object from P to Q is 1459/6.

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Answer: 3

Step-by-step explanation:

Basically all you have to do is subtract 6 from both sides so you will get:

3 = v

(a) The average daily balance for the billing period from January 18 to February 18 was $357.16.

To find the average daily balance, we need to calculate the balance for each day of the billing period and then divide by the number of days in the period.

January 18 balance: $351.41

January 25 charge: $405.43 ($351.41 + $54.02)

January 27 payment: $275.43 ($405.43 - $130.00)

February 8 charge: $294.64 ($275.43 + $19.21)

February 9 charge: $443.20 ($294.64 + $148.56)

To calculate the average daily balance, we add up the balances for each day and divide by the number of days in the billing period :

(18 x 351.41 + 7 x 405.43 + 2 x 275.43 + 1 x 294.64 + 1 x 443.20) / 29

= $357.16

(b) The finance charge to be paid on February 18 is $3.05.

To calculate the finance charge, we need to first calculate the average daily balance (which we found in part a), and then multiply it by the interest rate and the number of days in the billing period.

Average daily balance: $357.16

Interest rate: 1.2% per month

Number of days in billing period: 31

Finance charge = Average daily balance x Interest rate x Number of days / Days in year

Finance charge = $357.16 x (1.2 / 100) x 31 / 365 = $3.05

(c) The balance due on February 18 is $452.00.

To find the balance due on February 18, we need to add up all the charges and subtract any payments made during the billing period from the average daily balance.

January 18 balance: $351.41

January 25 charge: $54.02

January 27 payment: -$130.00

February 8 charge: $19.21

February 9 charge: $148.56

Finance charge: $3.05

Balance due = Average daily balance + Charges - Payments - Credits + Finance charges

Balance due = $357.16 + $54.02 + $19.21 + $148.56 - $130.00 + $3.05

= $452.00

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Answer:

the answer is A

Step-by-step explanation:

It is an acute angle but is larger than 40