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What are the domain and range of f(x)?

Step-by-step explanation:

the distance is sqrt ( (-6)^2 + (-12)^2) = sqrt(  36 + 144) = sqrt( 180) = sqrt(36*5) = 6 * sqrt(5)

2/(2+4) = 2/6 = 1/3

-2 + (1/3)*6*sqrt(5) = -2 + 2* sqrt(5)

6 + (1/3)*6*sqrt(5) = 6 + 2* sqrt(5)

Question :

justinapace7446

Yesterday

Mathematics

High School

+5 pts

Choco pies are cookies made from chocolate (c), sugar (s), and flour (. Chocolate costs $5 per pound, sugar costs

$3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as

sugar

Calvin wants to invest $12,000 in deposits. For tax purposes, he wants his total interest to be $600. He wants to put

$1000 more in a 2-year deposit than in a l-year deposit and invest the rest in a 3-year deposit. How much money

should he invest in each deposit?

Number of Years

Rate

2.0%

5.0%

6.0%

Answer:

1-year: $2200, 2-year: $3200, 3-year: $6600

Step-by-step explanation:

Assume y = Amount invested for 1 year.

y + 1000 = investment amount for 2 years

12000 - (y + y + 1000 ) = amount invested for 3 years

11000 - 2y = amount invested for 3 years

Total interest

Multiplying each by its corresponding rate

(0.02 × y) + (0.05 × (y+1000)) + (0.06 × (11000-2y)) = 600

0.02y + 0.05y + 50 + 660 - 0.12y = 600

-0.05y + 710 = 600

-0.05y = 600 - 710

-0.05y = - 110

y = 2200

Therefore first year = y = $2200

Investment for 2 years =y + 1000 = 2200 + 1000 = $3200

Investment for 3 years = 11000 - 2y = (11000 - (2*2200)) = (11000 - 4400) = $6600

(a) To find the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants, we use the formula:

P(A|B) = P(A and B) / P(B)

where A is the event that an adult used antidepressants, and B is the event that an adult visited a therapist. We are given:

P(A) = 0.43

P(B) = 0.27

P(A and B) = 0.20

Plugging these values into the formula, we get:

P(A|B) = 0.20 / 0.27 ≈ 0.74

Therefore, the probability that a randomly selected adult who visited a therapist during the past year also used antidepressants is approximately 0.74.

(b) To find the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, we use Bayes' theorem:

P(B|A) = P(A|B) * P(B) / P(A)

where A and B are defined as before. We have already calculated P(A|B) and P(B), and we know:

P(A) = 0.43

Plugging these values into Bayes' theorem, we get:

P(B|A) = (0.74 * 0.27) / 0.43 ≈ 0.47

Therefore, the probability that an adult visited a therapist during the past year, given that he or she used antidepressants, is approximately 0.47.

Answer: $19

Step-by-step explanation: We know Giana earned $10 for shoveling. We know she makes $2 for every inch of snow on the ground. She shoveled 4.5 inches.

To find how much money she got from shoveling 4.5 inches, simply multiply $2 by 4.5

$2.00 x 4.5 = $9 from shoveling 4.5 inches of snow.

Now add $9 to the initial value of $10

$10 + $9 = $19 earned in total.

Answer:

7

Step-by-step explanation:

The middle 2 numbers are 6 and 8. Add them both up and divide them by 2. Gets you 7.

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

There are 24 permutations of the letters in the word 'PODS' if all the letters are used without repetition.

To find the number of permutations of the letters in the word 'PODS' without repetition, we need to find the number of ways we can arrange the four letters.

We can use the formula for permutations of n objects taken r at a time, which is nPr = n! / (n-r)!, where n is the total number of objects and r is the number of objects we are taking.

In this case, n = 4 (since there are four letters in the word 'PODS') and r = 4 (since we are using all four letters). Substituting these values into the formula gives:

4P4 = 4! / (4-4)! = 4! / 0! = 24 / 1 = 24

Therefore, there are 24 permutations of the letters in the word.

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Answer:

C) \(\theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\)

Step-by-step explanation:

\(sin^2\theta=\frac{1}{2},\: 0\leq\theta\leq2\pi\\ \\\frac{1-cos(2\theta)}{2}=\frac{1}{2}\\ \\1-cos(2\theta)=1\\\\cos(2\theta)=0\\\\2\theta=\frac{\pi}{2}+\pi n\\ \\\theta=\frac{\pi}{4}+\frac{\pi}{2}n\\ \\ \theta=\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}\)

Recall the identity \(sin^2\theta=\frac{1-cos(2\theta)}{2}\)

The probability that fewer than 1690 blocks meet the specification in three or more of the six lots is  0.0000428%.

1. Let's calculate the probability of a single block meeting specification:

p(block meets spec) = 0.85

p(block doesn't meet spec) = 1 - 0.85

= 0.15

The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

Let X be the number of blocks that meet the specification.

Therefore, P(X < 1690) can be calculated using the binomial cumulative distribution function.Using a calculator or a software, we get:

P(X < 1690)

= 0.0006 (rounded to four decimal places)

Therefore, the probability that, in a given lot, fewer than 1690 blocks meet the specification is 0.0006 or 0.06%.

2. The number of blocks that meet the specification follows a binomial distribution with n = 2000 and p = 0.85.

We need to find the number of blocks k, such that

P(X < k) = 0.70

Using a calculator or a software, we get:

k = 1743

Therefore, the 70th percentile of the number of blocks that meet the specification is 1743.3.

The number of blocks that meet the specification in each lot follows a binomial distribution with n = 2000 and p = 0.85.

The probability that fewer than 1690 blocks meet the specification in a given lot is:

P(X < 1690) = 0.0006

From part 1, we know that the probability that fewer than 1690 blocks meet the specification in a given lot is 0.0006. Let Y be the number of lots with fewer than 1690 blocks meeting the specification.

Therefore, Y follows a binomial distribution with n = 6 and p = 0.0006.

We need to find P(Y ≥ 3).

Using a calculator or a software, we get:

\(P(Y ≥ 3) = 4.28 x 10^(-7)\) (rounded to nine decimal places)

Therefore, the probability that fewer than 1690 blocks meet the specification in three or more of the six lots is 4.28 x \(10^(-7)\) or 0.0000428%.

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Answer:

Formal discussion

Step-by-step explanation:

a formal discussion on a particular topic in a public meeting or legislative assembly, in which opposing arguments are put forward.

(pls mark me brainliest if u can)

Answer:

normally its about an argument

Step-by-step explanation:

If its about a argument then you should choose formal discussion. good luck

Answer:

9.3

Step-by-step explanation:

35-7=28

28 divided by 3 = 9.3

Or $9 and 3 cents

The equation of the line that is parallel to the given line, through the given point is y = -5x - 7

Given equation,

y = -5x + 1

Slope = m

          = -5

For two lines to be parallel, slope is equal.

Therefore, m = -5 for another line.

Let the equation of the line be y = mx + c

This line passes through A(-2,3)

Therefore, 3 = -5(-2) + c

                  3 = 10 + c

                  c = 3 - 10

                     = -7

Hence, equation of line is y = -5x - 7.

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A snowboarder starts at a height of -4 meters above the edge of a half-pipe, reaches the top edge after approximately 2.493 seconds, returns to the edge of the pipe at t = -0.253 seconds, and spends approximately 2.746 seconds in the air.

(a) To find the height at t = 0, we substitute t = 0 into the equation:

Height at t = 0 = -4.9(0)^2 + 11(0) - 4 = -4.

Therefore, her height at t = 0 is -4 meters above the edge of the half-pipe.

(b) To find when she reaches the top edge, we need to find the value of t where her height is equal to zero. We set the equation equal to zero and solve for t:

-4.9t^2 + 11t - 4 = 0.

Using the quadratic formula, t = (-b ± √(b^2 - 4ac)) / (2a), where a = -4.9, b = 11, and c = -4.

Calculating the values:

t = (-11 ± √(11^2 - 4(-4.9)(-4))) / (2(-4.9)).

Simplifying further:

t = (-11 ± √(121 - 78.4)) / (-9.8).

t = (-11 ± √42.6) / (-9.8).

Evaluating the two possibilities:

t ≈ -0.253 seconds or t ≈ 2.493 seconds.

She reaches the top edge after approximately 2.493 seconds.

To find when she returns to the edge of the pipe, we look for the other value of t that makes the height zero. Therefore, she returns to the edge of the pipe at t = -0.253 seconds.

(c) To determine how long she is in the air, we calculate the time from the moment she leaves the edge of the pipe until she returns. This is the time between t = -0.253 seconds and t = 2.493 seconds.

Time in the air = 2.493 - (-0.253) ≈ 2.746 seconds.

Therefore, she is in the air for approximately 2.746 seconds.

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Given, the equation that represents the height of an object:

First, we will find the velocity of the object which is the first derivative of the height using the method of the limits

We will find the value of the function y(t) when t = 3, and when t = 3+h

Substitute y(3+h) and y(3) into the expression of the limit

Where a = 0

d) compute the instantaneous velocity at t = 3

So, the answer will be:

Answer: 4 apples 10 banana

Step-by-step explanation: 4 apples is 4 dollars + 1/2 of 10 which is 5 = 9

to figure this out I start out adding 1 apple and 1 banana to each side starting with 0 apples and 6 bananas until I got to 9 dollars worth of fruit

Answer: The first one is 15 and the second one is 1.

Step-by-step explanation: I plugged in -4 where x is so the equation was (-4)^2-1 which equals 15.For other one i did the same thing except with the 2 so the equation was 3(2)-5 which equals 1.

Answer:

The answer is "64".

Step-by-step explanation:

Given:

8-sided fair die

output of Die = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 }

if the Dice is thrown two times. so, the possible outputs are as follows:

\(\to 8 \times 8=64\)

\(\texttt{ = (1,1),(1,2),(1,3),(1,4),(1,5),(1,6),}\\ \ \ \texttt{(1,7),( 1, 8),(2,1),(2,2),(2,3),(2,4),}\)

\(\texttt{(2,5),(2,6),(2,7),(2,8),(3,1), (3,2),}\\ \texttt{(3,3),(3,4),(3,5),(3,6),(3,7),(3,8) ,}\\\texttt{(4,1),(4,2),(4,3), (4,4),(4,5),(4,6),} \\\)

\(\texttt{(4,6),(4,7),(4,8),(5,1),(5,2),(5,3),}\\\texttt{(5,4),(5,5),(5,6),(5,7),(5,8),(6,1),}\\\texttt{(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),}\)

\(\texttt{(6,8),(7,1),(7,2),(7,3),(7,4),(7,5),} \\\texttt{(7,6),(7,7),(7,8),(8,1),(8,2),(8,3),}\\ \texttt{(8,4),(8,5),(8,6),(8,7),(8,8)}\)

That's why the product is 64.

To implement the square-and-multiply algorithm and the low-storage square-and-multiply algorithm in Python, you can follow the steps provided in the instructions. Here's a possible implementation of both algorithms:

```python

# Square-and-Multiply Algorithm

def square_and_multiply(g, A, N):

   binary_expansion = bin(A)[2:]  # Compute the binary expansion of A

   result = 1

   for bit in binary_expansion:

       result = (result * result) % N

       if bit == '1':

           result = (result * g) % N

   return result

# Low-Storage Square-and-Multiply Algorithm

def low_storage_square_and_multiply(g, A, N):

   a = g

   b = 1

   while A > 0:

       if A % 2 == 1:

           b = (b * a) % N

       a = (a * a) % N

       A = A // 2

   return b

# Test the algorithms

N = 1000

g = 2

A = 477

result1 = square_and_multiply(g, A, N)

result2 = low_storage_square_and_multiply(g, A, N)

print(result1)  # Output: 641

print(result2)  # Output: 641

```

To demonstrate the efficiency of the algorithms, you can compute the given expressions:

```python

N = 1000

g = 2

result1 = square_and_multiply(g, 477, N)

result2 = square_and_multiply(17, 183, 256)

result3 = square_and_multiply(3, 200, 50)

result4 = square_and_multiply(11, 507, 1237)

result5 = low_storage_square_and_multiply(g, 477, N)

result6 = low_storage_square_and_multiply(17, 183, 256)

result7 = low_storage_square_and_multiply(3, 200, 50)

result8 = low_storage_square_and_multiply(11, 507, 1237)

print(result1, result2, result3, result4)  # Output: 641 1 1 1027

print(result5, result6, result7, result8)  # Output: 641 1 1 1027

```

By comparing the execution time of both algorithms, you can determine which one runs faster for the given inputs.

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Approximate percent increase in how much the student pays with Optin 2 versus Option is 20%

$540 plus 15% sales tax now.=$515

Pay exactly $120 now and then $58 each month for 9 months=$642

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To determine if there is a difference in the mean empathy score between men and women, we can perform a hypothesis test using the data provided. We will use the independent samples t-test since we have two independent groups (males and females) and want to compare their means.

The null hypothesis (H0) states that there is no difference in the mean empathy scores between men and women, while the alternative hypothesis (Ha) states that there is a difference.

Using the given data, we calculate the mean empathy scores for each group and compute the sample means, standard deviations, and sample sizes. With these values, we can use the T1-84 Plus calculator to perform the t-test and obtain the p-value.

If the p-value is less than the significance level (α = 0.05), we reject the null hypothesis and conclude that there is a significant difference in mean empathy scores between men and women. On the other hand, if the p-value is greater than 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to support a difference.

By conducting an independent samples t-test and using the p-value method with the given data, we can determine if there is a significant difference in mean empathy scores between men and women.

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Answer:

the variable

Step-by-step explanation:

Given expression:

\((6x+9)^2-5\)

When evaluating the expression for \(x=1\), we need substitute 1 for the variable (\(x\)) in the expression.

Evaluating the expression for \(x=1\):

\(\implies (6\cdot1+9)^2-5\)

\(\implies (6+9)^2-5\)

\(\implies (15)^2-5\)

\(\implies 225-5\)

\(\implies 220\)

Answer:

Variable

Step-by-step explanation:

Let's find the value

\(\\ \rm\Rrightarrow (6x+9)^2-5\)

\(\\ \rm\Rrightarrow (6+9)^2-5\)

\(\\ \rm\Rrightarrow 14^2-5\)

\(\\ \rm\Rrightarrow 196-5\)

\(\\ \rm\Rrightarrow 191\)

Step-by-step explanation:

25 - 3f

25 - 3(7)

25 - 21

4 pounds of potting soil remains

♡ Hope it helps ♡

Step-by-step explanation:

9x²+bx+ 100

(3x)²+ bx + 10²

(3x)² + 10² + bx

(3x)² + 10² + bx

Answer:

D) 10

Hope that helps! Plz mark as brainlest!

Step-by-step explanation:

Cause if you look... the small triangle has 4 at the bottom and the big one has 8. So you know the big triangle is double the size. Now you can do 5 x 2 to get 10!

Answer:

The difference in areas:

Percent increase:

Answer:

188.5 cubic inches

Step-by-step explanation:

V(cone) = 1/3πr²h

= 1/3π(3²)(2)

= 1/3(9)(2)π

= 6π

V(cylinder) = πr²h

= π(3²)(6)

= 54π

Total Volume = 6π + 54π or 60π

60π is approximately 188.5 cubic inches

The 5 steps in dividing rational expressions are explained below.

Rational expression seem to be parts that have factors in their denominators (and frequently numerators as well). For instance, x 2 x + 3 \dfrac{x^2}{x+3} x+3x2 start part, x, squared, separated by, x, furthermore, 3, end portion is a reasonable articulation.

1) Take the rational expression.

2) Rewrite the division as the product of the first rational expression then, the reciprocal of the second.

3) Factor the numerators and denominators of rational expression completely.

4) Multiply the numerators and denominators together.

5) Simplify by dividing out common factors.

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