The expression 5/2​k −2​ factored is

Answer:

(5,4)

Step-by-step explanation:

10x + 20y = 130

x + y = 9

you can solve by substitution

x = 9 - y

10 (9 - y) + 20y = 130

90 - 10y + 20y = 130

90 + 10y = 130 (subtract 90 from both sides)

10y = 40

y = 4

Plug the answer back in the original equations to solve for x

x + 4 = 9 (subtract 4 from both sides)

x = 5

The number of activities that cost $10 is 4.

The number of activities that cost $20 is 5.

10a + 20b = 130 equation 1

a + b = 9 equation 2

Where:

Multiply equation 2 by 10

10a + 10b = 90 equation 3

Subtract equation 3 from equation 2

$10b = $40

b = $40 / $10

b = 4

Subtract 4 from 9: 9 - 4 = 5

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Answer:

1/81

Step-by-step explanation:

P(H,H,H,H)=16/81

fourth root of 16/81= 2/3

so the probability of getting tails would be 1/3

probability of getting 4 tails would be:

P(T,T,T,T)=(1/3)^4

=1/81

The probability of getting 4 tails when the coin is thrown 4 times is 1/81

We have:

P(Head 4 times) = 16/81

This means that:

P(Head)^4 =  16/81

Take the 4th root of both sides

P(head) = 2/3

The probability of a tail is calculated as:

P(tail) = 1 - P(Head)

This gives

P(tail) = 1 - 2/3

P(tail) = 1/3

When thrown 4 times, we have:

P(tail)^4 = (1/3)^4

P(tail) = 1/81

Hence, the probability of getting 4 tails when the coin is thrown 4 times is 1/81

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Answer:

(2,-1)

Step-by-step explanation:

Rewrite in vertex form

y = -1/4(x-2)^2-1

C is the most accurate one i guess

eu9ewg0u8wei08

Step-by-step explanation:

jiwfoiqwfqeoufhqeio0hfqifh0qoio

Answer: 3

Step-by-step explanation:4 X 3 is 12

Answer:

The answer is below.

Step-by-step explanation:

PROVE √(1-〖cos〗^2 θ)/cosθ = tanθ

Now 1 - cos^2 θ = sin^2θ

So  √(1 - cos^2 θ) = sin θ

and  √(1 - cos^2 θ) / cos  θ

= sin θ / cos θ

= tan θ

Step-by-step explanation:

\(\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\tan\theta\\\\\text{We know:}\\(1)\ \sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x\\(2)\tan x=\dfrac{\sin x}{\cos x}\\\\\text{For}\ \sqrt{1-\cos^2\theta}\ \text{use}\ (1):\\\\L_S=\dfrac{\sqrt{1-\cos^2\theta}}{\cos\theta}=\dfrac{\sqrt{\sin^2\theta}}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta\ \ \ _{used (2)}\\\\R_S=\tan\theta\\\\L_S=R_S\)

\(\text{Of course, this equality is not true for everyone values of}\ \theta.\\\\1^o.\ \cos\theta\neq0\to\theta\neq\dfrac{\pi}{2}+k\pi,\ k\in\mathbb{Z}\\\\2^o.\ \sqrt{\sin^2\theta}=|\sin\theta|,\ \text{therefore}\\\\\text{for}\ \theta\in[2k\pi;\ (2k+1)\pi],\ \sin\theta\geq0\to|\sin\theta|=\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{\sin\theta}{\cos\theta}=\tan\theta\)

\(\text{for}\ \theta\in\bigg((2k-1)\pi;\ 2k\pi\bigg),\ \sin\theta<0\to|\sin\theta|=-\sin\theta\\\\\text{therefore}\ \dfrac{|\sin\theta|}{\cos\theta}=\dfrac{-\sin\theta}{\cos\theta}=-\tan\theta\neq\tan\theta\)

\(\text{Conclusion:}\\\\\text{This equality is true for}\ \theta\in\left[2k\pi;\ \dfrac{\pi}{2}+2k\pi\right)\cup\left(\dfrac{\pi}{2}+2k\pi;\ \pi+2k\pi\right],\ k\in\mathbb{Z}\)

Answer:

A

y=-19/12x+17/12

Step-by-step explanation:

Write in slope-intercept form,y=mx+b

The equation i.e. 19x + 12y = 17 equivalent to the  \(y = \frac{19}{12}x + \frac{17}{12}\).

Given that,

Based on the above information, the calculation is as follows:

19x + 12y = 17

Here we need to solve it for y

\(y = \frac{19}{12}x + \frac{17}{12}\)

Therefore, we can conclude that the first option is correct.

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The 18th term of the arithmetic sequence is 45.2, while the balance in an account with a $8,600 deposit and 12% annual interest after 5 years is $14,311.39. With a $6,284 deposit and 14% annual interest after 30 months, the account balance will be $7,463.17. Borrowing $1,709 at a 182% annual interest rate, the monthly payment for 16 months will be $202.06.

1. Arithmetic sequence: The formula to find the nth term of an arithmetic sequence is given by:

nth term = first term + (n - 1) * common difference

Here, the 4th term is given as 6 and the common difference is 2.9.   Plugging in these values, we can calculate the 18th term as follows:

18th term = 6 + (18 - 1) * 2.9 = 6 + 17 * 2.9 = 45.2

2. Compound interest: For the first scenario, where $8,600 is deposited into an account that pays 12% simple annual interest compounded monthly for 5 years, we can calculate the final balance using the formula for compound interest:

A = P * \((1 + r/n)^{(n*t) }\)

Here, P is the principal amount, r is the annual interest rate (in decimal form), n is the number of times interest is compounded per year, and t is the number of years. Plugging in the values:

P = $8,600, r = 12% = 0.12, n = 12 (monthly compounding), t = 5

A = 8600 * \((1 + 0.12/12)^{(12*5)}\)= $14,311.39

3. Similarly, for the second scenario, where $6,284 is deposited into an account that pays 14% simple annual interest compounded monthly for 30 months:

P = $6,284, r = 14% = 0.14, n = 12 (monthly compounding), t = 30/12 = 2.5

A = 6284 * \((1 + 0.14/12)^{(12*2.5)}\) = $7,463.17

4. Monthly payment: To calculate the monthly payment amount for borrowing $1,709 from The Saver at a 182% simple annual interest rate, we can divide the total amount by the number of payments. The formula for calculating the monthly payment for a loan is:

Monthly payment = Total amount / Number of payments

Here, the total amount is $1,709 and the number of payments is 16. Plugging in the values:

Monthly payment = 1709 / 16 = $202.06

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Answer:

Step-by-step explanation:

Slope of perpendicular line = \(\frac{-1}{m}\)

       = -1 ÷ \(\frac{-5}{3}\)

        \(= -1 *\dfrac{-3}{5}\\\\=\dfrac{3}{5}\)

Answer:

0.2x-0.8

Step-by-step explanation:

In 0.2(x-4), you can multiply 0.2(The number outside of the parentheses) by the numbers inside the parentheses. So, it would be 0.2*x-0.2*4, which is 0.2x-0.2(4), which is 0.2x-0.8.

The expected number of failures in 1 year is 8.9948.

The authors calculate a failure rate for PVC pipe of 0.0081 per 100 miles of pipe per day in 2008. Think of a 100-mile section of this pipe.

(I)

Given;

Mean failures per day = 0.0081

So,

Expected number of failures in 1 year = 0.0081 * 365

                                                               = 8.9948

(II)

Poisson Distribution with λ = 8.9948 is given by:

\(P(x) =\frac{e^-^8^.^9^9^4^8 8.9948^0}{x!}\)

             ⇒ for x = 0, 1, 2,. . . .

P(At least 1 failure) = 1- P(X=0);

\(P(x) = \frac{e^-^8^.^9^9^4^8 8.9948^0}{0!} = \frac{0.00012*1}{1}\)

        = 0.00012    

So,

P(At least 1 failure) = 1 - 0.00012 = 0.99988

Hence, the expected number of failures in 1 year is 8.9948.

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Answer:

The minimum income level for this target group is of $51,253.6.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score 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 p-value, we get the probability that the value of the measure is greater than X.

Mean of $41,182 and a standard deviation of $11,990

This means that \(\mu = 41182, \sigma = 11990\)

Find the minimum income level for this target group.

The 100 - 20 = 80th percentile, which is X when Z has a p-value of 0.8, so X when Z = 0.84.

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

\(0.84 = \frac{X - 41182}{11990}\)

\(X - 41182 = 0.84*11990\)

\(X = 51253.6\)

The minimum income level for this target group is of $51,253.6.

The given statement: " all polynomials are rational functions but not all rational functions are polynomials." is true; its counterexample will be: Not all polynomials are rational functions but all rational functions are polynomials.

Polynomial refers to an algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variable (s).

Now,

Further,

Hence, The given statement: " all polynomials are rational functions but not all rational functions are polynomials." is true; its counterexample will be: Not all polynomials are rational functions but all rational functions are polynomials.

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Answer:

B. \(3^{-5}\)

D. \(2^{5}\) × \(6^{-5}\)

Step-by-step explanation:

\(\frac{2^{5} }{6^{5} }\)

\(\frac{32}{7776}\)

0.00411522633

\(3^{-5}\) = 0.00411522633

\(2^{5}\) × \(6^{-5}\) = 0.00411522633

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

Work Shown:

A = P*(1+r/n)^(n*t)

A = 8200*(1+0.02/1)^(1*7)

A = 9419.2224747241

A = 9419.22

Note: I assumed the bank is using annual compounding. The instructions didn't mention it, so that's why I went with n = 1. If your teacher or textbook mention otherwise, say monthly compounding, then you'll change n to n = 12. I would ask for clarification.

Answer:

4.5%

Step-by-step explanation:

Simple interest:

I = Prt

112.5 = 1250(r)(2)

1250r = 56.25

r = 0.045 = 4.5%

Answer: 4.5%

Answer:

Right Triangle, Acute Triangle, and Obtuse Triangle

Step-by-step explanation:

I can't draw it here but the right triangle has a side of 90°.

An acute triangle has a side smaller than 90°.

An obtuse triangle has a side bigger than 90°.

Answer:

Step-by-step explanation:perp. 3/2

y + 8 = 3/2(x - 4)

y + 8 = 3/2x - 6

y = 3/2x - 14

Answer:

43.98

Step-by-step explanation:

did some quick maths

c=2

\(c = 2 \times \pi \times r\)

The probability distribution for X is as follows: X=0 with probability 1/8, X=2 with probability 3/8, X=4 with probability 3/8, X=6 with probability 1/8.

The random variable X is defined as 2H, where H represents the number of flips that result in heads. For instance, if the outcomes are HHT, then X would be equal to 2.

To find the probability distribution of X, we need to determine the possible values of H and their respective probabilities. Since there are three coin tosses, H can take on values of 0, 1, 2, or 3.

To calculate the probabilities, we can use the binomial probability formula. The formula states that for n trials with probability p of success and x successes, the probability is given by P(x) = nCx * p^x * (1-p)^(n-x).

Applying this , since the coin is fair, the probability of getting a head on any given toss is 0.5. Plugging in the values, we find that P(0) = 1/8, P(1) = 3/8, P(2) = 3/8, and P(3) = 1/8.

Therefore, the probability distribution for X is as follows: X=0 with probability 1/8, X=2 with probability 3/8, X=4 with probability 3/8, X=6 with probability 1/8.

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Answer:5

Step-by-step explanation:

Khan Academy Answer

Answer:

The geometric mean is the average rate of return of a set of values calculated using the products of the terms.

Step-by-step explanation:

\(\huge{\tt{\color{cyan}{Answer}}}\)

Given:

A regular polygon with three vertices and side 14 cm.

To find:

Area of the regular polygon.

Solution:

We know that, a regular polygon has equal sides and equal interior angles.

The given regular polygon has three equal sides, it means it is an equilateral triangle.

The area of an equilateral triangle is:

\(A=\dfrac{\sqrt{3}}{4}a^2\)

Where, a is the side length of the triangle.

Putting \(a=14\), we get

\(A=\dfrac{\sqrt{3}}{4}(14)^2\)

\(A=\dfrac{\sqrt{3}}{4}(196)\)

\(A=84.87049\)

\(A\approx 84.9\)

Therefore, the area of given regular polygon is 84.9 cm².

Answer:

$19.136

Step-by-step explanation:

if 100% ----> $16.64

then 115% ----> $19.136

hope this helps :)

Answer:

19.14

Step-by-step explanation:

First find the amount of the tip

16.64 * 15%

16.64 *.15

2.496

Rounding to the nearest cent

2.50

Add this to the cost of the mean

16.64+ 2.50

19.14

Answer:

Step-by-step explanation:

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

Answer:

15:9

Step-by-step explanation:

Answer:

15:9  

Explanation:

Simple: Just count the amount of hearts, then the amount of moons, and put them next to each other, like I did, and BOOM ! There's your answer!

Answer:

could you explain more clearly for me? if Chandra had 9 jugs, each was one gallon, what's the take away? I need to know for example: each member had 2 cups of juice which would sum up to (insert number) how much juice was left?

In this case, both 1 and 2 are located on the real axis, so their imaginary components are zero.

To determine the value of i, we are given that 21 = 5 + 2,52 = 3, and 3 = 1 + di.

Let's solve for i step by step:

Start with the equation 21 = 5 + 2,52 = 3.

Subtract 5 from both sides to isolate the term with i:

21 - 5 = 2,52 = 3 - 5

16 = 2,52 = -2

Now, let's solve for i in the equation 3 = 1 + di.

Subtract 1 from both sides:

3 - 1 = 1 + di - 1

2 = di

We can rewrite di as i * d. So, the equation becomes:

2 = i * d

From the equation 16 = 2,52 = -2, we know that d = -2.

Substitute the value of d into the equation 2 = i * d:

2 = i * (-2)

Now, we solve for i:

Divide both sides by -2:

2 / (-2) = i * (-2) / (-2)

-1 = i

Therefore, the value of i is -1.

Now, let's plot 1 and 2 on the complex plane:

Plotting 1:

The complex number 1 is located on the real axis, which means it has no imaginary component. It can be represented as the point (1, 0) on the complex plane.

Plotting 2:

The complex number 2 is also located on the real axis, with no imaginary component. It can be represented as the point (2, 0) on the complex plane.

So, the plot of 1 and 2 on the complex plane would look like this:

o (2, 0) - 2

|

o (1, 0) - 1

Please note that the complex plane is a two-dimensional plane with the real axis representing the real numbers and the imaginary axis representing the imaginary numbers. In this case, both 1 and 2 are located on the real axis, so their imaginary components are zero.

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