The Patel family made a 6-pound turkey for dinner. If each person will eat 1/2 of a pound, how many people will it take to finish the turkey?

Answer:

I think the answer is letter D

Expand the equation a bit to get

\(2^{2x} - 3\left(2^{x+2}\right) + 32 = 0\)

\(2^{2x} - 3\left(2^x \cdot 2^2\right) + 32 = 0\)

\(2^{2x} - 12 \left(2^x\right) + 32 = 0\)

\(\left(2^x\right)^2 - 12 \left(2^x\right) + 32 = 0\)

Substitute y = 2ˣ and you'll notice this is really a quadratic equation in disguise. You end up with

\(y^2 - 12y + 32 = 0\)

which is easily solved by factorizing,

\((y - 8) (y - 4) = 0\)

\(\implies y - 8 = 0 \text{ or }y - 4 = 0\)

\(\implies y = 8 \text{ or }y = 4\)

Now, 2³ = 8 and 2² = 4, so

• if y = 2ˣ = 8, then x = 3; otherwise,

• if y = 2ˣ = 4, then x = 2

Answer:

x = 3 or x = 2

Step-by-step explanation:

answer is in the picture

Answer:

8

Step-by-step explanation:

The distance between the 16 and 8 will be 8.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the two numbers are 16 and 8. The distance will be calculated bu subtracting one number form the other number.

Distance = 160 - 8

Distance = 8

Hence, the distance between the two numbers will be 8.

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Answer:

4

Step-by-step explanation:

You would need to print 40 photos to make the cost of each plan the same.

To find the number of photos needed to make the cost of each plan the same, we can set up an equation.

Let's assume that the cost of printing p photos without the loyalty card is equal to the cost of printing p photos with the loyalty card.

For the first plan without the loyalty card, the cost per photo is $0.35. Therefore, the cost of printing p photos without the loyalty card is 0.35p.

For the second plan with the loyalty card, the cost per photo is $0.20. However, to be eligible for the discounted rate, you need to pay $6 for the loyalty card initially.

So the cost of printing p photos with the loyalty card is 0.20p + $6.

Setting up the equation:

0.35p = 0.20p + $6

To solve for p, we can subtract 0.20p from both sides and then subtract $6 from both sides:

0.35p - 0.20p = $6

0.15p = $6

Finally, divide both sides by 0.15 to solve for p:

p = $6 / 0.15

p = 40

Therefore, you would need to print 40 photos to make the cost of each plan the same.

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Complete question =

A photo center charges $0.35 per 4x6 photo that you print. If youpay $6 for a loyalty card, you get a discounted rate of $0.20 per 4x6photo that you print. Write an equation to find the number of photos you wouldneed to print to make the cost of each plan the same. Use pto represent the number of photos. solve How many photos would you need to print to make

The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope. The equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2) is given by option D: y = -2x.

To determine which equation represents a line perpendicular to y = -2x + 4 and passes through the point (4, 2), we need to consider the slope of the given line. The equation y = -2x + 4 is in slope-intercept form (y = mx + b), where the coefficient of x (-2 in this case) represents the slope of the line.

Since we are looking for a line that is perpendicular to this given line, we need to find the negative reciprocal of the slope. The negative reciprocal of -2 is 1/2. Therefore, the slope of the perpendicular line is 1/2.

Now, we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) represents the given point and m is the slope.

Substituting the values (4, 2) for (x₁, y₁) and 1/2 for m, we get:

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

Simplifying this equation, we find:

y - 2 = (1/2)x - 2.

Rearranging the terms, we obtain:

y = (1/2)x.

Therefore, option D, y = -2x, represents the equation of the line that is perpendicular to y = -2x + 4 and passes through the point (4, 2).

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Answer:

Step-by-step explanation:

y-8

Answer:

y - 8

Step-by-step explanation:

Answer:

The third statement is true.

2.5t + 4 = 6.5 (in. of snow)

Answer:

I think its the first one

Step-by-step explanation:

The standard error for a two-tail test of the difference between means for large independent samples can be calculated using the formula:

Standard Error = √[(s1^2 / n1) + (s2^2 / n2)]

In this case, the given values are s1 = 12,000, s2 = 14,000, n1 = 100, and n2 = 100.

By substituting these values into the formula, we can calculate the standard error as follows:

Standard Error = √[(12,000^2 / 100) + (14,000^2 / 100)]

= √[(144,000,000 / 100) + (196,000,000 / 100)]

= √[1,440,000 + 1,960,000]

= √3,400,000

≈ 184.3909

Rounded to four decimal places, the standard error for the given values is approximately 184.3909.

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(a) The expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3).

(b) The least possible integer value of x for the rectangular solid to exist is 4.

a. To express the length, width, and height of the right rectangular prism in terms of x, we can factor the volume expression, 6x³ - 3x² - 45x.

Factoring out the greatest common factor, 3x:

3x(2x² - x - 15)

Now, factor the quadratic expression:

3x(2x² - x - 15)

To factor the quadratic expression further, find two numbers whose product equals the constant term (-15) and whose sum equals the coefficient of the linear term (-1). These two numbers are -5 and 3.

3x(2x + 5)(x - 3)

Thus, the expressions for the length, width, and height can be 3x, (2x + 5), and (x - 3)

b. For the rectangular solid to exist, all dimensions (length, width, and height) must be positive. Let's examine the constraints on x for each dimension:

1. 3x > 0
2. 2x + 5 > 0 → x > -5/2
3. x - 3 > 0 → x > 3

Since x must satisfy all three inequalities, the least possible integer value of x for the rectangular solid to exist is x = 4.

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Answer:

673,000 i think hope this helps have a nice day please give me brainliest if correct :))

Step-by-step explanation:

The solutions to the equation 2sin(θ) = 1 on the interval [0, 2π) are:

θ = π/6, 13π/6

To find all solutions to the equation 2sin(θ) = 1 on the interval [0, 2π), we can solve for θ by isolating the sin(θ) term and then using inverse trigonometric functions.

Given: 2sin(θ) = 1

Dividing both sides by 2:

sin(θ) = 1/2

Now, we can use the inverse sine function to find the solutions:

θ = sin^(-1)(1/2)

The inverse sine of 1/2 is π/6. However, we need to consider all solutions on the interval [0, 2π).

Since the sine function has a period of 2π, we can find the other solutions by adding integer multiples of 2π to the principal solution.

The principal solution is θ = π/6. Adding 2π to it, we get:

θ = π/6 + 2π = π/6, 13π/6

So, the solutions to the equation 2sin(θ) = 1 on the interval [0, 2π) are:

θ = π/6, 13π/6

These are the two solutions that satisfy the given equation on the specified interval.

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-8 < 4

hope it helps

Answer: -2≤-8<4

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

To use the splitpts function in Matlab, you will first need to define two sets of points with different arrays for each set. Then, you can use the syntax newSetOfPoints = splitpts(originalSetOfPoints) to split the original set of points into two new sets.

The "splitpts" function in MATLAB is used to split a set of points into two sets based on a specified split point. Here are the steps to use this function:

1. Define the set of points you want to split. For example:
```
points = [1 2 3 4 5 6 7 8 9 10];
```

2. Specify the split point. This can be any number between the minimum and maximum values of the set of points. For example:
```
splitPoint = 5;
```

3. Use the "splitpts" function to split the set of points into two sets. The first set will contain all the points less than or equal to the split point, and the second set will contain all the points greater than the split point. For example:
```
[set1, set2] = splitpts(points, splitPoint);
```

4. The resulting sets will be stored in the variables "set1" and "set2". You can display these sets using the "disp" function:
```
disp(set1);
disp(set2);
```

The output will be:
```
1 2 3 4 5
6 7 8 9 10
```

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Answer:

19 tickets

Step-by-step explanation:

Nadine sold two kinds of tickets to her class play

The student tickets cost $3

Adult tickets cost $5.50

Nadine sold a total of 25 tickets for $90

We are required to find the number of students tickets that were sold

Let x represent the number of tickets sold to students

Let y represent the number of tickets sold to adults

x + y= 25

x= 25-y..........equation 1

Since the total cost of the ticket is $90

3x + 5.50y=90..........equation 2

Substitute 25-y for x in equation 2

3(25-y) + 5.50y= 90

75-3y+5.50y= 90

75+2.5y= 90

Collect the like terms

2.5y= 90-75

2.5y=15

Divide both sides by 2.5

2.5y/2.5=15/2.5

y= 6

Substitute 6 for y in equation 1

x= 25-y

x= 25-6

x= 19

Hence Nadine sold 19 student tickets

Answer:

5.0 rational

Step-by-step explanation:

30/6 = 5/1 =5.0

it's rational as it is a fraction

x=100×15/75

x=1500/75

x=20% boys

Answer:

20%

Step-by-step explanation:

look at the formula I have used then you will understand good day

Answer:

it reaches 24 ft

Step-by-step explanation:

16 + 8 ft = 24 ft

you would add the 16 to the 8 feet from the base to get 24

The vertical stretch of f(x) will be -2f(x), 5.5f(x) - 1, 7f(x)

As is well known, the vertical stretch of f(x) occurs when the value of the parameter is changed in the following general form:

When a constant c with a value larger than one is scaled across the board of a function, it results in a vertical stretch. It is written as the vertical stretch from the original function f(x) to the new, stretched function g(x)=cf(x) where c>1 g ( x ) = c f ( x ) where c > 1.

f(k(x-d)) = y = a+ c

when |a| exceeds 1 since The function is stretched vertically by a dilation factor of |a| when |a| > 1 (when a > 1).

Thus, we select F, D, and A.

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The full question:

Consider the function f(x). Select all of the following that includes a vertical stretch of f(x)

A. -2f(x)

B. 0.25f(x)

C. -f(x) + 6

D. 5.5f(x) - 1

E. f(x) + 9

F. 7f(x)

Answer:

C, None of the above

Step-by-step explanation:

Step 1: Expand the brackets

-7 - 3(-4e-3)

-7 + 12e + 9

Step 2: Collect like terms

12e + 2

Because the answer is not a or b the answer is 'None of the Above'

Hey there! I'm happy to help!

Let's use the distributive property to undo the parentheses. We multiply the number next to the parentheses by each number inside of the parentheses.

-7+3(-4e-3)

-7-12e-9

We combine like terms.

-16-12e

This means that Answer B is incorrect. Answer A could still be correct though as it could have equal value to -16-12e.

-4(3e+4)

We use distributive property.

-12e-16

We see that these have the same value, so the correct answer is A.

Have a wonderful day! :D

Answer:

75.39 in^2 (round to the nearest hundreds)

Step-by-step explanation:

I think that we have to find the lateral area

circumference = 2 x radius x pi = 2 x 4 x pi = 25,13 in^2 (round to the nearest hundreds)

lateral surface = (circumference x slant height)/2 = (25,13 x 6)/2 = 75,39 in^2 (round to the nearest hundreds)

Answer:

1019/250 x

Step-by-step explanation:

4x1+

0x1

10

+

7x1

100

+

6x1

1000

Answer:

a: 1

b: 13

Step-by-step explanation:

a: -7 + 6 = -1. distance from zero makes that positive

b: -7 is changed to 7, 7 + 6 = 13

a) The probability that a randomly selected passenger car gets more than 36 mpg is 0.3659. b) The probability that the average mpg of two randomly selected passenger cars is more than 36 mpg is 0.3147. c) The probability that both randomly selected passenger cars get more than 36 mpg is approximately 0.0990.

a. To find the probability that a randomly selected passenger car gets more than 36 mpg, we need to calculate the area under the normal distribution curve to the right of 36.

First, we need to calculate the z-score using the formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

In this case, x = 36, μ = 34.8, and σ = 3.5.

z = (36 - 34.8) / 3.5 = 0.3429

Using a standard normal distribution table or a calculator, we can find the probability associated with the z-score 0.3429. Let's assume this probability is denoted as P(Z > 0.3429).

Now, we can calculate the probability using the complement rule:

P(X > 36) = 1 - P(Z ≤ 0.3429)

Therefore, the probability that a randomly selected passenger car gets more than 36 mpg is:

P(X > 36) = 1 - P(Z ≤ 0.3429) ≈ 1 - 0.6341 ≈ 0.3659

b. To find the probability that the average mpg of two randomly selected passenger cars is more than 36 mpg, we can use the Central Limit Theorem.

The distribution of the sample mean follows a normal distribution with a mean equal to the population mean (μ) and a standard deviation equal to the population standard deviation (σ) divided by the square root of the sample size (n).

In this case, n = 2, μ = 34.8, and σ = 3.5.

The standard deviation of the sample mean is:

σ / √(n) = 3.5 / √(2)

To find the probability that the average mpg is more than 36, we need to calculate the z-score using the formula:

z = (x - μ) / (σ / √(n))

In this case, x = 36, μ = 34.8, σ = 3.5, and n = 2.

Therefore, the probability that the average mpg of two randomly selected passenger cars is more than 36 mpg is:

P(Average mpg > 36) = P(Z > 0.4851) ≈ 0.3147

c. If two passenger cars are randomly selected, and we want to find the probability that both cars get more than 36 mpg, we can assume that the mpg ratings of the cars are independent.

The probability of both cars getting more than 36 mpg is equal to the product of the probabilities of each car individually getting more than 36 mpg.

Using the z-score and probability calculated in part (b), we can calculate the probability for one car. Let's assume this probability is denoted as P(X > 36).

Then, the probability of both cars getting more than 36 mpg is:

P(both cars > 36) = P(X > 36) * P(X > 36)

Using the probability found in part (b):

P(both cars > 36) ≈ 0.3147 * 0.3147 ≈ 0.0990

Therefore, the probability that both randomly selected passenger cars get more than 36 mpg is approximately 0.0990.

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Answer:

17.7165

Step-by-step explanation:

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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Answer:576

Step-by-step explanation:

The statement "x ∈ {x}" is true. The statement "{x} ⊆ {x}" is true. The statement "{x} ∈ {x}" is false. The statement "{x} ∈ {{x}}" is true.

a) The statement is true because an element x can be a member of a set that contains only itself. In this case, the set {x} contains the element x.

b) The statement is true because every element in {x} is also in {x}. Since both sets are identical, {x} is a subset of itself.

c) The statement is false because a set cannot be an element of itself. In this case, {x} is a set, and it cannot be an element of the same set.

d) The statement is true because the set {{x}} contains the set {x} as its only element. Therefore, {x} is an element of the set {{x}}.

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