A set of ordered pairs is called what?

The translation in y = (x + 3)² is of 3 units to the left. The correct option is the last one.

For a general function y = f(x), we define a horizontal translation of N units as:

g(x) = f(x + N)

Here the original function is y = x² and the translated one is:

y = (x + 3)²

So we just added 3 on the argument, so this is a shift of 3 units to the left, the correct option is the last one.

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Answer:

x=−1,y=13

Step-by-step explanation:

Answer:

x = -1 and y = 13 Please Mark Brainliest

Step-by-step explanation:

The GCF of the polynomial a^(5)b^(7)-a^(3)b^(2)+a^(2)b^(6)-a^(2)b^(2) is a^(2)b^(2), and the factored form of the polynomial is a^(2)b^(2)(a^(3)b^(5)-a+b^(4)-1).

The GCF, or greatest common factor, is the largest factor that all terms in a polynomial have in common. In this case, we need to find the GCF of the polynomial a^(5)b^(7)-a^(3)b^(2)+a^(2)b^(6)-a^(2)b^(2).

First, we need to look at the exponents of each term to determine the GCF. The smallest exponent for a is 2, and the smallest exponent for b is 2. Therefore, the GCF for this polynomial is a^(2)b^(2).

Next, we need to factor out the GCF from each term in the polynomial. This is done by dividing each term by the GCF and then multiplying the GCF by the resulting polynomial.

So, the factored form of the polynomial is:

a^(2)b^(2)(a^(3)b^(5)-a+b^(4)-1)

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The coefficient of determination (r-squared) provides an indication of how well the regression model fits the data and the value of r is  0.3574

In this example, the r-squared value is 12.78%, which means that 12.78% of the variation in verbal SAT scores can be explained by the variation in math SAT scores. The least squares regression equation is yhat = 383.3 + 0.3489x, where yhat is the predicted verbal score and x is the math score.

The coefficient of correlation (r) provides a measure of the strength of the linear relationship between two variables. In this example, the coefficient of correlation (r) can be calculated from the coefficient of determination (r-squared) as follows: r = √r-squared = √12.78% = 0.3574. This indicates that there is a weak linear relationship between verbal and math SAT scores.

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

A) The sample proportion = 0.17, and standard error/deviation = 0.013281

B) 0.869

C)0.9668

A) We know that 17% of households spend more than $100 per week on groceries. We are given that p ( the proportion of the population that spends more than $100 per week) = 0.17

sample size (n)= 800

The sample proportion of p = 0.17

The standard error of p will be calculated using this formula =

\(\sqrt{\frac{p(1-p)}{n} }\) =\(\sqrt{\frac{0.17(1 - 0.17)}{800} }\)

=  0.013281

B) We have to find the probability that the sample proportion will be +-0.02 of the population proportion

= p (0.17 - 0.02 ≤ P ≤ 0.17 + 0.02 ) = p( 0.15 ≤ P ≤ 0.19)

z value corresponding to P

Z = (P - p)/std deviation at P = 0.15

Z =  (0.15 - 0.17) / 0.013281 =  -1.51

at P = 0.19

z = ( 0.19 - 0.17) / 0.013281 = 1.51

Therefore the required probability will be

p( -1.5 ≤ z ≤ 1.5 ) = p(z ≤ 1.51 ) - p(z ≤ -1.51 )

= 0.9345 - 0.0655 = 0.869

C) Now, we have to find the same probability for a sample (n ) = 1600

standard deviation/ error = 0.009391 (applying the equation for calculating standard error as seen in part A above)

Therefore the required probability after applying;

z =   (P - p)/std deviation at p = 0.15 and p = 0.19

p ( -2.13 ≤ z ≤ 2.13 ) = p( z ≤ 2.13 ) - p( z ≤ -2.13 )

= 0.9834 - 0.0166 = 0.9668

Therefore,

A) The sample proportion = 0.17, and standard error/deviation = 0.013281

B) 0.869

C)0.9668

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The complete question is " The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume the population proportion is p = .17 and a sample of 800 households will be selected from the population. a. Show the sampling distribution of p, the sample proportion of households spending more than $100 per week on groceries. b. What is the probability that the sample proportion will be within ±.02 of the population proportion? c. Answer part (b) for a sample of 1600 households."

Answer:

\(\huge\boxed{\sf x = -1}\)

Step-by-step explanation:

\(8=2^{x+4}\)

\(2 \times 2 \times 2=2^{x+4}\\\\2^3=2^{x+4}\)

3 = x + 4

3 - 4 = x

-1 = x

OR

\(\rule[225]{225}{2}\)

• Integer values: ,numbers including 0, and negative and positive numbers; it can never be a fraction, a decimal, or a percent.

Based on the definition, the integer values included in the interval [-5, 0] are: -5, -4, -3, -2, -1, and 0.

To evaluate if the integer satisfies the inequality, we have to evaluate each integer.

• -5

As -13 is smaller than -9, then -5 does not satisfy the inequality.

• -4

As -9 is equal to -9, then -4 does not satisfy the inequality (as in the sign of the inequality it is not included -9).

• -3

As -5 is bigger than -9, -3 satisfies the inequality.

• -2

As -1 is bigger than -9, -2 satisfies the inequality.

• -1

As 3 is bigger than -9, -1 satisfies the inequality.

• 0

As 7 is bigger than -9, 0 satisfies the inequality.

Also we can try by solving the inequality:

Meaning that all the values that are greater than -4 but not -4.

Answer:

• [-3, 0]

• x = -3, -2, -1, 0

• x > -4

The algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

Given that,

c = speed of light

t = time

v₀ₓ = initial velocity of particle

m = mass of particle

Velocity and acceleration are related through time. Acceleration is the rate of change of velocity, which is represented graphically as the slope of the velocity vs. time line. Velocity can be represented as the area underneath an acceleration vs. time line.

Newton's second law declares that an object having mass m will accelerate due to a net force (F) will accelerate at a rate of:

α = F/m

Therefore, the function that describes the acceleration at any point in time of the particle is:

α(t)=ct/m

The velocity function is the integral of the acceleration function, so we get:

v(t)= ∫ct/m dt

= ct²/2m +C

where the constant C is the initial velocity of the particle at time t=0. Therefore, the velocity function representing the velocity at any point in time is:

v(t) = ct²/2m +v₀ₓ

Therefore, the algebraic expression for the particle's velocity vₓ at a later time t is v(t) = ct²/2m +v₀ₓ.

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Answer:

Step-by-step explanation:

32

Answer:

32

Step-by-step explanation:

The denominator of the formula for the variance of a sample is given as follows:

N - 1.

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

The terms are named as follows:

The formula for the variance of a sample is given as follows:

\(s^2 = \frac{sum (X - \overbar{X})^2}{N - 1}\)

Hence the denominator is the bottom term, which is of N - 1.

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The simplification of the expression (xyz²)⁴ will be; (x)⁴y⁴z⁸

Since Expression is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

WE are Given the exponential expression

(xyz²)⁴

Expand the expression as;

(x)⁴y⁴(z²)⁴

According to the indices rule:

(xyz²)⁴ = (x)⁴y⁴z⁸

Hence the correct simplification of the expression as;

(xyz²)⁴ = (x)⁴y⁴z⁸

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Answer: C. Yes, the estimate is reasonable.

Step-by-step explanation:

The answer in my opinion should be A.

Answer:

The explicit formula is  \(a_{n}\) = - 13 - 7n

Step-by-step explanation:

Let us at first find the type of the sequence

∵ The terms are - 20, - 27, - 34, - 41, ............

→ Find the difference between each to consecutive terms

∵ - 27 - (- 20) = - 27 + 20 = - 7

∵ - 34 - (- 27) = - 34 + 27 = - 7

∵ - 41 - (- 34) = - 41 + 34 = - 7

→ There is a constant difference between each two consecutive terms

∴ The sequence is Arithmetic

→ The explicit formula of the nth term of the arithmetic sequence is

∵ a = - 20

∵ d = -7

∴ \(a_{n}=-20+(n-1)(-7)\)

→ Simplify it

∴ \(a_{n}\) = - 20 + (-7)(n) - (-7)(1)

∴ \(a_{n}\) = - 20 + (-7n) - (-7)

∴ \(a_{n}\) = - 20 - 7n + 7

→ Add the like terms

∴ \(a_{n}\) = (- 20 + 7) - 7n

∴ \(a_{n}\) = - 13 - 7n

The explicit formula is  \(a_{n}\) = - 13 - 7n

Given:

Scale factor \(s=\dfrac{1}{3}\)

Center of dilation = (4,2)

To find:

The coordinates of the points C' and A.

Solution:

We know that, if a figure is dilated with a scale factor k and the center of dilation is at the point (a,b), then

\((x,y)\to (k(x-a)+a,k(y-b)+b)\)

The scale factor is \(\dfrac{1}{3}\) and the center of dilation is at (4,2).

\((x,y)\to (\dfrac{1}{3}(x-4)+4,\dfrac{1}{3}(y-2)+2)\)            ...(i)

Suppose the vertices of red triangle are A(m,n), B(10,14) and C(-2,11).

Using rule (i), we get

\(C(-2,11)\to C'(\dfrac{1}{3}(-2-4)+4,\dfrac{1}{3}(11-2)+2)\)

\(C(-2,11)\to C'(\dfrac{1}{3}(-6)+4,\dfrac{1}{3}(9)+2)\)

\(C(-2,11)\to C'(-2+4,3+2)\)

\(C(-2,11)\to C'(2,5)\)

Hence, the coordinates of Point C' are C'(2,5).

Let us assume that point A is A(m,n).

Using rule (i), we get

\(A(m,n)\to A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)\)

From the given figure it is clear that the image of point A is (8,4).

\(A'(\dfrac{1}{3}(m-4)+4,\dfrac{1}{3}(n-2)+2)=A'(8,4)\)

On comparing both sides, we get

\(\dfrac{1}{3}(m-4)+4=8\)

\(\dfrac{1}{3}(m-4)=8-4\)

\((m-4)=3(4)\)

\(m=12+4\)

\(m=16\)

And,

\(\dfrac{1}{3}(n-2)+2=4\)

\(\dfrac{1}{3}(n-2)=4-2\)

\((n-2)=3(2)\)

\(n=6+2\)

\(n=8\)

Therefore, the coordinates of point A are (16,8).

Answer:

is multiplied by itself.

Step-by-step explanation:

2 to the second power is four, and so is 2 times 2.

7 to the second power is 49, and so is 7 times 7.

They are the same thing.

Hope this helps!

Answer:

18/5

Step-by-step explanation:

you have to times then divide

In regression analysis, if the dependent variable is measured in dollars, the independent variable can be units.

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It will take Vincent 24 number of days to build the cubby house by himself.

Let's assume that Vincent can build the cubby house alone in h days.

From the given information, we know that Nadia takes 12 days to build the cubby house, and when Nadia and Vincent work together, they can finish it in 8 days.

We can use the concept of "work done" to solve this problem. The amount of work done is inversely proportional to the number of days taken.

Nadia's work rate is 1/12 of the cubby house per day, while the combined work rate of Nadia and Vincent is 1/8 of the cubby house per day.

When Nadia and Vincent work together, their combined work rate is the sum of their individual work rates:

1/8 = 1/12 + 1/h

To solve for h, we can rearrange the equation:

1/h = 1/8 - 1/12

1/h = (3 - 2) / 24

1/h = 1/24

Taking the reciprocal of both sides, we find:

h = 24

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The probability that the sample proportion of knitters in a random sample of 2500 people from Maggiesville will be between 5% and 10% is approximately 0.9644, or 96.44%.

To find the probability that the sample proportion of knitters will be between 5% and 10%, we can use the normal approximation to the binomial distribution.

The sample proportion can be modeled as a binomial distribution with parameters n (sample size) and p (true proportion). In this case, n = 2500 and p = 0.08.

To apply the normal approximation, we need to calculate the mean (μ) and the standard deviation (σ) of the sample proportion. The mean of a binomial distribution is μ = n * p, and the standard deviation is σ = √(n * p * (1-p)).

μ = 2500 * 0.08 = 200

σ = √(2500 * 0.08 * 0.92) ≈ 10.954

Next, we need to standardize the values of 5% and 10% using the z-score formula:

z1 = (0.05 - 0.08) / 0.010954 ≈ -2.741

z2 = (0.10 - 0.08) / 0.010954 ≈ 1.827

Now, we can use the standard normal distribution table or a calculator to find the probabilities associated with these z-scores.

P(5% ≤ sample proportion ≤ 10%) = P(-2.741 ≤ z ≤ 1.827)

By looking up the z-scores in the standard normal distribution table or using a calculator, we find:

P(-2.741 ≤ z ≤ 1.827) ≈ 0.9644

Therefore, the probability that the sample proportion of knitters will be between 5% and 10% is approximately 0.9644, or 96.44%.

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Answer:

x = 3/2

Step-by-step explanation:

Step 1: Write equation

-3(6x - 1) = -24

Step 2: Solve for x

Distribute: -18x + 3 = -24

Subtract 3 on both sides: -18x = -27

Divide both sides by -18: x = 3/2

Step 3: Check

Plug in x to verify if it's a solution.

-3[6(1.5) - 1) = -24

-3[9 - 1] = -24

-3[8] = -24

-24 = -24

Since TV bisects ∠STU:

So, based on the theoretical likelihood, we anticipate that 35 times out of 140 repeats, both spins will be odd numbers.

Probability is a branch of mathematics that deals with the study of random events and the likelihood of their occurrence. Probability is expressed as a number between 0 and 1, with 0 indicating that an event is impossible to occur and 1 indicating that an event is certain to occur. The probability of an event A, denoted by P(A), is calculated as the number of favorable outcomes for the event divided by the total number of possible outcomes. For example, if a fair six-sided die is rolled, the probability of rolling a 3 is 1/6 because there is only one favorable outcome (rolling a 3) out of the total 6 possible outcomes. Probabilities can be used to make predictions about the likelihood of future events and to make decisions under uncertainty. Probabilities can also be used to describe the distribution of random variables and to quantify the relationship between different events. Probability theory is widely used in many fields, such as statistics, engineering, finance, physics, and biology, among others.

Here,

The theoretical probability of both spins being odd numbers is 9 over 36, which means that for every 36 times the experiment is repeated, we expect 9 of those times to result in both spins being odd numbers.

If the experiment is repeated 140 times, we can use the theoretical probability to estimate the number of times both spins will be odd numbers as follows:

140 * (9/36) = 35

So, based on the theoretical probability, we predict that both spins will be odd numbers 35 times out of 140 repetitions.

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The solution of the given differential equation is y =  x⁴ ∑ (-1)ⁿ [(n+3)(n+4)(n+5)...(2n+3)]/[(n!)(3)(2)(1)] and the value of r is 4 and the value of cₙ is (-1)ⁿ [(n+3)(n+4)(n+5)...(2n+3)]/[(n!)(3)(2)(1)].

Given: x²y′′ + 5xy′ + (4+6x)y = 0, x > 0.

To find: The solution of the given differential equation in the form y₁ = x^r ∑ cₙ xⁿ n=0, where c₀=1.

Solution: Let's assume the solution of the given differential equation is of the form y₁=x^r ∑ cₙ xⁿ n=0---(1).

Differentiating (1) w.r.t x, we get y′=rx^(r-1) ∑ cₙ xⁿ + x^r ∑ ncₙ x^(n-1)---(2).

Differentiating (2) w.r.t x, we get

y′′=r(r-1)x^(r-2) ∑ cₙ xⁿ + 2rx^(r-1) ∑ ncₙ x^(n-1) + x^r ∑ n(n-1)cₙ x^(n-2)---(3).

Now substitute (1), (2) and (3) in the given differential equation, we get,

x²[r(r-1)x^(r-2) ∑ cₙ xⁿ + 2rx^(r-1) ∑ ncₙ x^(n-1) + x^r ∑ n(n-1)cₙ x^(n-2)] + 5x[rx^(r-1) ∑ cₙ xⁿ + x^r ∑ ncₙ x^(n-1)] + (4+6x)x^r ∑ cₙ xⁿ = 0

On simplification, we get,

∑ [(r(r-1)cₙ + 5rcₙ + (4+6(n+1))cₙ) x^(r+n)] = 0

Hence, we get the following recurrence relation:

r(r-1)cₙ + 5rcₙ + (4+6(n+1))cₙ = 0

⇒ r(r+4)cₙ = -(6n+4)cₙ

⇒ cₙ₊₁/cₙ = - (r+n+3)(r+n+2)/(r+4)

On solving the recurrence relation, we get

cₙ = (-1)ⁿ [r(r+1)(r+2)(r+3)...(r+n-1)]/[(n!)(4)(3)(2)(1)]

Since c₀=1

⇒ c₀ = (-1)⁰ [r(r+1)(r+2)(r+3)...(r+0-1)]/[(0!)(4)(3)(2)(1)]

⇒ 1 = r/4

⇒ r = 4

Hence, the solution of the given differential equation is

y = y₁

= x⁴ ∑ cₙ x^ⁿ

= x⁴ ∑ (-1)ⁿ [(4)(5)(6)...(4+n-1)]/[(n!)(4)(3)(2)(1)]

y = x⁴ ∑ (-1)ⁿ [(n+3)(n+4)(n+5)...(2n+3)]/[(n!)(3)(2)(1)]

Therefore, the value of r is 4 and the value of cₙ is (-1)ⁿ [(n+3)(n+4)(n+5)...(2n+3)]/[(n!)(3)(2)(1)].

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The 99% confidence interval for the true mean length of the manufactured bolt is (2.9177, 3.0823)

Here, we need to construct a 99% confidence interval for population mean (μ) is given by

μ = x + Zα/2 * σ/√n   or    μ = x - Zα/2 * σ/√n

where, μ = population mean

x = sample mean

  = 3 inches

σ = population standard deviation

  = 0.3 inches

Zα/2= z score for a two tailed test at level of significance α = 2.576( for a 99% confidence level)

So, the upper limit would be,

μ = 3 + 1.645 * (0.3/√36)

μ = 3 + 1.646 * (0.3/6)

μ = 3.0823

And the lower limit would be,

μ = 3 - 1.645 * (0.3/√36)

μ = 3 - 1.646 * (0.3/6)

μ = 2.9177

Hence, the 99% confidence interval is (2.9177, 3.0823)

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Answer: 89 miles

Step-by-step explanation:

Well, if the construction crew added one mile every day for 38 days, then the formula would look like this.

L = 51 + (38)

51 + 38 = 89

L = 89 miles

Answer:

-0.048

Step-by-step explanation:

-30 * -1/5 = 6

6 * -1/5 = -1.2

(Remember -30 is first term so we subtract 1 from 5 in the exponent)

-30 * (-1/5)^4 =  -0.048

Answer:

0.2

Step-by-step explanation:

Answer:

55.9%

Step-by-step explanation:

To find the percentage of girls in the class, we can use the following formula:

Percentage = (Number of girls / Total number of students) * 100

Number of girls = 19

Total number of students = 34

Percentage = (19 / 34) * 100

                   = 55.88235 % ≈ 55.9 % ( rounded off to one decimal place)

Answer: Tyler used the distributive property.

Step-by-step explanation:

For the expression:  

Madison wrote:  which is by commutative property of addition.

The commutative property of addition says that , for a,b be any real number

Tyler wrote: which is by distributive propery.

The distributive property says that , for a,b,c be any real numbers.

Hence, the last option is correct.

Answer:

D

Step-by-step explanation:

Took the test ;)