Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0

The population is the collection of parents of 13- to 17-year-olds. The sample is the 1720 parents surveyed.

The population in this survey is option D: the collection of responses of parents of 13- to 17-year-olds. The sample in this case is option C: the 1720 parents of 13- to 17-year-olds who were surveyed.

In this scenario, the population refers to the entire group of interest, which is parents of 13- to 17-year-olds. The survey aims to gather information about this entire group, so the population is defined as the collection of responses from all parents of 13- to 17-year-olds.

On the other hand, the sample is a subset of the population that is selected and surveyed. In this case, the sample consists of the 1720 parents of 13- to 17-year-olds who participated in the survey. The sample is used to gather data and draw conclusions about the larger population.

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Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Answer:

Answer: B.-1/2

Step-by-step explanation:

The amount of money in Iris's checking account can be modeled by a linear function of the form:

y = mt + b

where y is the amount of money in the account, t is the time (measured in years), m is the rate of interest, and b is the initial amount in the account.

In this case, we have m = 0.04 (since the interest rate is 4% per year) and b = 180 (since that's the initial amount in the account). Therefore, the linear function that models the amount of money in Iris's checking account at any time t is:

y = 0.04t + 180

For example, if t = 5 (years), then the amount of money in Iris's checking account is 0.04 * 5 + 180 = 198 dollars.

The probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes is found as  `0.7475`. Hence, the option D is correct.

The length of time it takes a college student to find a parking spot in the library parking lot follows a normal distribution with a mean of 2.5 minutes and a standard deviation of 0.75 minute.

We are supposed to find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 3 minutes.

So, we need to find `P(x < 3)` where `x` is the time taken to find a parking spot in the library parking lot.

Now, z-score will be

`z = (3 - 2.5)/0.75

= 0.67`

By looking at the z-score table, the probability that corresponds to z = 0.67 is 0.2514.

Therefore,

`P(x < 3) = P(z < 0.67)

= 0.2514 + 0.5

= 0.7514

≈ 0.7475 (approx)`

So, the correct option is `0.7475`. Hence, the answer is option D.

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Step-by-step explanation:

I assume this actually is

revenue : R(x) = 12x

cost : C(x) = 5x + 20

profit : P(x) = R(x) - C(x) = 12x - 5x - 20 = 7x - 20

The amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

The amount to which $800 will grow under each of these conditions is as follows:a) 8% compounded annually for 9 years

When compounded annually for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years

Compounded annually = n = 1 Amount = $1,447.91 (rounded to the nearest cent)

b) 8% compounded semiannually for 9 years Compounded semiannually for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded semiannually = n = 2 Amount = $1,471.16 (rounded to the nearest cent)

c)  8% compounded quarterly for 9 years Compounded quarterly for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded quarterly = n = 4 Amount = $1,491.03 (rounded to the nearest cent)

d) 8% compounded monthly for 9 years Compounded monthly for 9 years at 8%, the formula is: Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded monthly = n = 12 Amount = $1,505.91 (rounded to the nearest cent)

e) 8% compounded daily for 9 years Compounded daily for 9 years at 8%, the formula is:

Amount = Principal x [(1 + rate/n)^(n*t)]

Where: Principal = $800 Rate = 8% Time = 9 years Compounded daily = n = 365Amount = $1,511.74 (rounded to the nearest cent)

The observed pattern of FVs (future values) occurs due to compounding. Compounding is the process of earning interest not only on the principal amount invested but also on the interest earned from the principal. This results in an increase in the interest earned and the future value of the investment. The more frequent the compounding, the higher the future value of the investment. Hence, the amount to which $800 will grow under each of the given conditions increases as the compounding period decreases.

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Answer:  Using a calculator, if you typed in 34 divided by 8, you'd get 4.25. You could also express 34/8 as a mixed fraction: 4 2/8.

Step-by-step explanation:

Answer:

answer

Step-by-step explanation:

is using a cancalator duh

Answer:

= 40g -24

Step-by-step explanation:

you would multiply everything in the bracket by 8 to expand this

e.g.

(8x5g )+ (8x5 )+ (8 x -2)

= 40g + 40 - 16

now simplify by subtracting the like terms

= 40g -24

The correct answer is option (c) 1001010.

To convert the number 82 from the octal system to the binary system, we can follow a step-by-step process.

Convert the octal number to decimal.

In the octal system, each digit represents a power of 8. The number 82 can be written as (8 x 8^1) + (2 x 8^0) = 66 in decimal.

Convert the decimal number to binary.

To convert 66 to binary, we divide it successively by 2 and keep track of the remainders. Here's the process:

66 ÷ 2 = 33 remainder 0

33 ÷ 2 = 16 remainder 1

16 ÷ 2 = 8 remainder 0

8 ÷ 2 = 4 remainder 0

4 ÷ 2 = 2 remainder 0

2 ÷ 2 = 1 remainder 0

1 ÷ 2 = 0 remainder 1

Reading the remainders from bottom to top, we get the binary representation of 66 as 1000010.

Option (c) 1001010 is therefore the right response.

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Answer:

4.9

Step-by-step explanation:

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

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

Problems of normally distributed samples 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:

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

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.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

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

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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The value of x for this problem is given as follows:

x = 5.

Hence the angle measures are given as follows:

We have that angles A and D are congruent for this problem, meaning that they have the same measure.

Hence the value of x is obtained as follows:

7x - 3 = 5x + 7

2x = 10

x = 5.

Hence the angle measures are given as follows:

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The diameter of a bicycle wheel is 24 inches. Around the wheel, there are 32 spokes that are spaced 48 meters away from one another.

The diameter of a circle is the distance measured through its center. The radius of a circle is the distance from the center to any point on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d . The simplest place to start would be to use a ruler to measure the distance between the circle's outside edges starting from its very center. The diameter would be that.

The diameter of the circle is the measurement at issue. The distance between the circle's center and its periphery can be measured.

far apart is each spoke (distance) = radius = diameter / 2

distance = 24/2

distance = 12

Since a wheel has 4 parts. so, 12*4 =  48 m

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Answer:

thx for points ....,..................

The value of  Greatest common divisor of 36 and a is a.

Here, 36 is exactly divisible by a.

What is Greatest common divisor?

The Greatest common divisor of two or more integers, which is not all zero, is the largest positive integer that divides each of integers.

Now, LCM of 36 and a;

36 = 2 x 2 x 3 x 3

a = 1 x a

Since, a divide 36 then the possible value of a are 2, 3, 4

⇒ gcd of 36 and possible value of a is given as;

⇒2, 3, 4

Clearly,

Greatest common divisor of 36 and a = a

Hence, The value of Greatest common divisor of 36 and a is a.

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To find the general solution of the homogeneous equation y'' - 11y = 0, we can assume a solution of the form y = e^(rt), where r is a constant. Substituting this into the equation, we get:

\((r^2 - 11)e^{rt} = 0\)

For this equation to hold for all t, we must have r² - 11 = 0, which gives us the characteristic equation:

r² = 11

The roots of this equation are ±√11. Therefore, the general solution is:

\(y(t) = C_1e^{\sqrt{11}t} + C_2e^{-\sqrt{11}t}\)

where C₁ and C₂ are arbitrary constants.

For the second equation, y'' + 7y' + 12y = 0, we can also assume a solution of the form y = e^(rt). Substituting this into the equation, we get:

\(r^2e^{rt} + 7re^{rt} + 12e^{rt} = 0\)

Dividing through by e^(rt), we obtain the characteristic equation:

r² + 7r + 12 = 0

This equation can be factored as (r + 3)(r + 4) = 0. So the roots are r = -3 and r = -4. Therefore, the general solution is:

\(y(t) = C_1e^{-3t} + C_2e^{-4t}\)

To find the specific solution given the initial conditions y(0) = -4 and y'(0) = -1, we substitute these values into the general solution:

y(0) = C₁e^(-3(0)) + C₂e^(-4(0))

= C₁ + C₂ = -4

y'(0) = -3C₁e^(-3(0)) - 4C₂e^(-4(0))

= -3C₁ - 4C₂ = -1

Solving this system of equations, we find C₁ = -1 and C₂ = -3. Thus, the specific solution for the given initial conditions is:

\(y(t) = -e^{-3t} - 3e^{-4t}\)

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Answer:

There will be $312.37 more in Account I.

Step-by-step explanation:

Giving the following information:

Initial investment= $10,000

Number of periods= 3 years

To calculate the future value, we need to use the following formula:

FV= PV*(1+i)^n

Account I:

FV= 10,000*(1.04^3)

FV= $11,248.64

Account II:

FV= 10,000*(1.03^3)

FV= $10,927.27

There will be $312.37 more in Account I.

Answer:

B

Step-by-step explanation:

maybe

It will take Sienna Rose 6 years and 3 months for her money to grow to $7000 at an annual interest rate of 3.60%, compounded monthly.

To remedy this hassle, we are able to use the formula for compound interest:

a = \(p(1 + r/n)^{(nt)\)

where a is the quantity of money after t years, p is the initial primary, r is the once-a-year hobby rate, n is the number of times the hobby is compounded in keeping with 12 months, and t is the time in years. In this example, we recognize that sienna rose invests $4000 at an annual interest charge of three. 60%, compounded monthly. So we've got:

P = $4000

r = 0.036

n = 12

A = $7000

we are able to remedy for t by plugging these values into the formula and fixing for t:

7000 = \($4000(1 + 0.036/12)^{(12t)}\)

7000/4000 = \((1 + 0.036/12)^{(12t)}\)

1.75 = \((1 + 0.003)^{12t}\)

ln(1.75) = 12t ln(1.003)

t = ln(1.75)/(12 ln(1.003))

t ≈ 6.25 years

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EH is considered to be horizontal and DH is considered to be vertical. They both form a perpendicular segment and creates a 90 degree angle.

Answer:

Part A: D

Step-by-step explanation:

Ok Let's assume you are right and the diagonal is 8x. If that is true, one of the answers will work.

Part A

It's the wrong answer. The answer is yes. Use a^2 + b^2 = c^It's the wrong answer. The answer is yes. Use a^2 + b^2 = c^It's the wrong answer. The answer is yes. Use a^2 + b^2 = c^2

givens

diagonal = 8x

one of the legs = 2x.

other leg = ?

Formula

a^2 + b^2 = c^2

(2x)^2 + b^2 = (8x^2)                    Expand the brackets

4x^2 + b^2 = 64x^2                      Subtract 4x^2 from both sides.

b^2 = 64x^2 - 4x^2

b^2 = 60x^2

The prime factors of 60 are 2 * 2 * 3 * 5    

You can't do much with the 3 and 5 so leave them under the root sign.

x^2 = x * x

What you get is

b^2 = √3 * 5 * 2* 2 * x * x

The factors come in pairs. One of the pairs goes outs the root. The other one is thrown away.

b = 2*x * √15

So the answer to part A is D

Part B

x = 3

The missing side = 2 * 3 * √15

The missing side = 6√15

The missing side = 23.2

Root 15 = 3.87

Answer:−10x-12

explanation is:-----------------

Answer:

-10x - 12

Step-by-step explanation:

-6x + 4(-x-3)

First, distribute the 4 to the (-x-3)

-6x + [(-4x)+(4 x -3)]

-6x + (-4x - 12)

Eliminate the parentheses

-6x + -4x - 12

Combine like terms

-10x - 12

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

The solution for the system of equations of three variables is:

x = 4

y = -1

z = -3

Or (4, -1, -3) written as a point.

Here we have a system of equations on 3 variables, the system is:

3x + 2y + z = 7

5x + 5y +4z = 3

3x + 2y + 3z = 1

Notice that the "x" and "y" coefficients in the first and last equation are the same ones, so we can take the difference between these to get:

(3x + 2y + 3z ) - (3x + 2y + z ) = 1 - 7

2z = -6

z = -6/2 = -3

So the value of z is -3.

Replacing that in the first and second equation we get:

3x + 2y - 3 = 7

5x + 5y + 4*(-3) = 3

Now we can simplify these:

3x + 2y = 10

5x + 5y = 15

We can divide the second one by 5 to get:

(5x + 5y)/5 = 15/5

x + y = 3

Isolating x, we get:

x = 3 - y

Now we replace that in the other equation:

3*(3 - y) + 2y = 10

9 - y = 10

9 - 10 = y

-1 = y

Now we know the value of y, finally with:

x = 3 - y

We can get the value of x:

x = 3 - (-1) = 4

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The required operating time, total expense and receipt are 33hours, $759 and $759 respectively.

How to get hours in operation?

It is time taken by worker or operator to operate particular work.

We have given,

Spend money = $594

Average hourly operating cost = $5.

Average hourly receipt = $23

Let time taking in operation be h,

594 + 5h = 23h

18h = 594

h = 33 hours.

and

Total expense = 23h =$23(33) =$ 759

receipt =594 + 5h = 594 + 5(33) = 594 + 165 =$ 759  

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\(( { \frac{4 {x}^{3} }{ {y}^{4} }) }^{ - 2} = \frac{16x {}^{6} }{ {y}^{8} } \)

\( \frac{(4 {x}^{3})^{ - 2} }{ { {(y}^{4} )}^{ - 2} } = \frac{16 {x}^{6} }{ {y}^{8} } \)

\( \frac{ {16x}^{ - 6} }{ {y }^{ - 8} } = \frac{ {16x}^{6} }{ {y}^{8} } \)

The power of -2 was mistook as 2.

The appropriate critical value for constructing a confidence interval in this setting is 1.88.

To find the appropriate critical value for constructing a confidence interval at a 94% confidence level, we can use a standard normal distribution table or a calculator.

First, we need to find the value of alpha, which is the significance level, which is equal to 1 - the confidence level. In this case, alpha is equal to 1 - 0.94 = 0.06.

Next, we need to find the critical value z* from the standard normal distribution table or calculator, which corresponds to the area to the right of z* being equal to alpha/2 = 0.03.

Using a standard normal distribution table or calculator, we can find that the critical value z* is approximately 1.88.

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