Jared bought a 15-pound bag of turkey for
Thanksgiving. His family ate 6 pounds of
the food on the morning of Thanksgiving
and 4% for dinner. Jared decided to use 2
of the remaining turkey to make
sandwiches for lunch. How much turkey, in
pounds, did Jared use to make
sandwiches?

The probabilities are given as follows:

3. P(rides bus|owns a car) = 1/3.

4. P(red|organic) = 3/5.

The probability of an event in an experiment is obtained as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For item 3, the outcomes are given as follows:

Hence the probability is:

P(rides bus|owns a car) = 8/24 = 1/3.

For item 4, the outcomes are given as follows:

The error was in identifying the total outcomes, and the probability is:

P(red|organic) = 18/30 = 3/5.

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Answer: {(12, 3), (11, 2), (10, 1), (9, 0), (8, 1), (7, 2), (6, 3)}

Step-by-step explanation:

Each value of x corresponds to only one value of y, making the relation a function.

Given the equations a × b = 5742 × 6368, a × c = 5748 × 6362, and c × b = 5738 × 6372, we need to determine the relationship between the three variables a, b, and c.

By comparing the given equations, we notice that the numbers on the right-hand side of each equation are very close to each other, differing only by small amounts. This suggests that a, b, and c are approximately equal.Since a × b, a × c, and c × b involve the same numbers with slight variations, we can conclude that a, b, and c are all very close in value.

Therefore, the inequality we can infer from this information is a ≈ b ≈ c, indicating that a, b, and c are approximately equal.

In simple terms, based on the given equations, it suggests that the values of a, b, and c are very similar or approximately equal to each other.

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Step 1: Write the dividend and divisor:

\(\sf\:\frac{{x^3 - 8x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 2: Divide the first term of the dividend by the first term of the divisor:

\(\sf\:\frac{{x^3}}{{x}} = x^2 \\ \)

Step 3: Multiply the divisor (x - 4) by the result (x^2):

\(\sf\:(x - 4) \cdot (x^2) = x^3 - 4x^2 \\ \)

Step 4: Subtract the result from the original dividend:

\(\sf\:(x^3 - 8x^2 + 6x + 41) - (x^3 - 4x^2) = -4x^2 + 6x + 41 \\ \)

Step 5: Bring down the next term from the dividend:

\(\sf\:\frac{{-4x^2 + 6x + 41}}{{x - 4}} \\ \)

Step 6: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-4x^2}}{{x}} = -4x \\ \)

\(\sf\:(x - 4) \cdot (-4x) = -4x^2 + 16x \\ \)

\(\sf\:(-4x^2 + 6x + 41) - (-4x^2 + 16x) = -10x + 41 \\ \)

Step 7: Bring down the next term from the dividend:

\(\sf\:\frac{{-10x + 41}}{{x - 4}} \\ \)

Step 8: Repeat steps 2-5 with the new dividend:

\(\sf\:\frac{{-10x}}{{x}} = -10 \\ \)

\(\sf\:(x - 4) \cdot (-10) = -10x + 40 \\ \)

\(\sf\:(-10x + 41) - (-10x + 40) = 1 \\ \)

Step 9: There are no more terms to bring down, so the division is complete.

Step 10: Write the final result:

The quotient is \(\sf\:x^2 - 4x - 10\\\) and the remainder is 1.

Therefore, the division of \(\sf\:(x^3 - 8x^2 + 6x + 41) by (x - 4) \\\) is:

\(\sf\:(x^3 - 8x^2 + 6x + 41) ÷ (x - 4) \\ \) \(\sf\:= x^2 - 4x - 10 + \frac{{1}}{{x - 4}} \\ \)

answer: d

explantion :

Factor the numerator and denominator and cancel the common factors.

Using the t-distribution, as we have the standard deviation for the samples, it is found that since the absolute value of the test statistic is greater than the critical value, we reject the claim that Mrs.Elite and Mrs. Bright are equally effective teachers.

At the null hypothesis, we test if they are equally effective teachers, that is, the subtraction of their means is 0, hence:

\(H_0: \mu_1 - \mu_2 = 0\)

At the alternative hypothesis, we test if they are not equally effective teachers, that is, the subtraction of their means is not 0, hence:

\(H_1: \mu_1 - \mu_2 \neq 0\)

For Mrs. Elite, we have that:

\(\mu_1 = 78, \sigma_1 = 10, n_1 = 30, s_1 = \frac{10}{\sqrt{30}} = 1.82574\)

For Mrs. Bright, we have that:

\(\mu_2 = 85, \sigma_2 = 15, n_2 = 25, s_2 = \frac{15}{\sqrt{25}} = 3\)

For the distribution of differences, we have that:

\(\overline{x} = \mu_1 - \mu_2 = 78 - 85 = -7\)

\(s = \sqrt{s_1^2 + s_2^2} = \sqrt{1.82574^2 + 3^2} = 3.5119\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{s}\)

In which \(\mu = 0\) is the value tested at the null hypothesis.

Hence:

\(t = \frac{\overline{x} - \mu}{s}\)

\(t = \frac{-7 - 0}{3.5119}\)

\(t = -1.99\)

Considering a two-tailed test, as we are testing if the mean is different of a value, with 30 + 25 - 2 = 53 df and a significance level of 0.1, the critical value is of \(|t^{\ast}| = 1.6741\).

Since the absolute value of the test statistic is greater than the critical value, we reject the claim that Mrs.Elite and Mrs. Bright are equally effective teachers.

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To determine the median of the data provided, we'll have to list down the data in an ascending or descending order and determine the middle value.

1. Darrel lives 4 blocks from school.

2. Keri lives 4 blocks from school too.

3. Erica lives 5 blocks from school.

4. Hunter lives 7 blocks from school.

5. Graces lives 8 blocks from school.

6. Alec lives 9 blocks from school.

7. Chase lives 10 blocks from school.

We have arranged the data in an ascending order.

The next step is to look at the middle value of the data. In this case, we're looking at the 4th value. In the list, the 4th value is 7 blocks. Hence, the median of the given data is 7.

Answer:

It's 51.2

Step-by-step explanation:

All u gotta do is subtract  54 - 2.8

1)

a = 3.3

b = 1.1

φ = 3.3/1.1 = 3

2)

a = 3.3

b = 2.1

φ = 3.3/2.1 = 1.5714

3)

a = 3.3

b = 3.1

φ = 3.3/3.1 = 1.06

Answer:

x  ≥ 31

Step-by-step explanation:

-5x + 5 ≥ 160 − 10x

Add 10x to each side

-5x+10x + 5 ≥ 160 − 10x+10x

5x+5   ≥ 160

Subtract 5 from each side

5x+5-5 ≥ 160 − 5

5x  ≥ 155

Divide by 5

5x/5  ≥ 155/5

x  ≥ 31

Answer:

0.4

Step-by-step explanation:

all I got to say is that the answer is 0.4 %100

Answer:

"-10 units per unit increase in x"

Step-by-step explanation:

That "-10" is the rate of change:   "-10 units per unit increase in x."

The limit of [f(x + h) - f(x)]/h as it approaches 0 is (a) 12x²

From the question, we have the following function that can be used in our computation:

f(x) = 1 - 4x³

The limit is given as

[f(x + h) - f(x)]/h

Calculate f(x + h)

So, we have

f(x + h) = 1 - 4(x + h)³

Expand

f(x + h) = 1 - 4(x³ + 3x²h + 3xh² + h³)

Substitute f(x + h) = 1 - 4(x³ + 3x²h + 3xh² + h³) in [f(x + h) - f(x)]/h

So, we have

[f(x + h) - f(x)]/h = [1 - 4(x³ + 3x²h + 3xh² + h³) - 1 + 4x³]/h

Open the brackets

[f(x + h) - f(x)]/h = [1 - 4x³ + 12x²h + 12xh² + 4h³ - 1 + 4x³]/h

Evaluate the like terms

[f(x + h) - f(x)]/h = [12x²h + 12xh² + 4h³]/h

Divide

[f(x + h) - f(x)]/h = 12x² + 12xh + 4h²

Limit h to 0

[f(x + h) - f(x)]/h = 12x² + 12x(0) + 4(0)²

Evaluate

[f(x + h) - f(x)]/h = 12x²

Hence, the limit is 12x²

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Answer:

The growth model that represents the population of this city is not linear--it is exponential:

\(f(t) = 10000( {1.025}^{t} )\)

\(t = 0 \: represents \: 2010\)

The function rule for g(x) is h(x) = (x - 0)² - 7.

In Mathematics, the vertex form of a quadratic function is represented by the following mathematical equation:

f(x) = a(x - h)² + k

Where:

Based on the information provided about the vertex (0, -7) and other points (-3, 2), we can determine the value of a as follows:

f(x) = a(x - h)² + k

2 = a(-3 - 0)² - 7

2 + 7 = 9a

9 = 9a

a = 1

Therefore, the required quadratic function in vertex form is given by:

h(x) = a(x - h)² + k

h(x) = (x - 0)² - 7

h(x) = x² - 7

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Answer:

The set M of all square numbers less than 80 is:

M = {0, 1, 4, 9, 16, 25, 36, 49, 64}

The set N of all non-negative even numbers that are under 30 is:

N = {0, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28}

Answer:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Step-by-step explanation:

A square number, also known as a perfect square, is a non-negative integer that is obtained by multiplying an integer by itself. In other words, it is the result of squaring an integer.

The square numbers less than 80 are:

An even number is an integer that is divisible by 2 without leaving a remainder.

The non-negative even numbers that are under 30 are:

Therefore:

All elements of the set M in ascending order are:

All elements of the set N in ascending order are:

Answer:

461728.4(1dp)

Step-by-step explanation:

8.1%-37400

1%-4617.2839...

100%-461728.4(1dp)

(a)Contrapositive: If an object does not have a border, then it is not red.

Converse: If an object has a border, then it is red.

Inverse: If an object is not red, then it does not have a border.

(b)Contrapositive: If an object is not red or does not have a border, then it is not a rectangle.

Converse: If an object is a rectangle, then it is red and has a border.

Inverse: If an object is not red or does not have a border, then it is not a rectangle.

(c)Contrapositive: If an object does not have a border, then it is not red or blue.

Converse: If an object is red or blue, then it has a border.

Inverse: If an object does not have a border, then it is not red or blue.

a) Original Conditional Statement (P - Q): If an object is red, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red.

Converse (Q - P) If an object has a border then it is red.

Inverse (not p → not q) If an object is not red then it does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may have a border but not be red.

b) Original Conditional Statement (P - Q): If an object is a rectangle, then it is red and has a border.

Contrapositive (not Q - not P): If an object is not red and does not have a border, then it is not a rectangle.

Converse (Q - P) If an object is red and has a border, then it is a rectangle.

Inverse (not p → not q) If an object is not a rectangle then it is not red or does not have a border.

The contrapositive is true, while the converse and inverse are false. For example, object H may be red and have a border but not be a rectangle.

c) Original Conditional Statement (P - Q): If an object is red or blue, then it has a border.

Contrapositive (not Q - not P): If an object does not have a border, then it is not red or blue.

Converse (Q - P) If an object has a border then it is red or blue.

Inverse (not p → not q) If an object is not red or blue then it does not have a border.

The contrapositive and converse are true, while the inverse is false. For example, object H may have a border but not be red or blue.

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Answer:

(e) the mean number of siblings for a large number of students has a distribution that is close to Normal.

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

By the Central Limit Theorem

The sampling distributions with a large number of students(at least 30) will be approximately normal, so the correct answer is given by option e.

Answer:

A

Step-by-step explanation:

1) First you need to simplify within the radical.

2) 25-4+16 is 37

3) find the square root of 37.  

4) it 6.08...

5) that falls between 6.0 and 6.2

Answer:

Yes, 36+ 64 = 100

So bottom right answer

Answer: See below

Step-by-step explanation:

To solve this problem, we need to assign each digit from 0 to 9 to a unique letter so that each letter represents a single digit. We can then use this mapping to solve the addition problem:

Let's assign the letters A, B, C, D, E, F, G, H, I, and J to the digits 0 to 9, respectively.

Then, the addition problem becomes:

A B C

D E F

We know that the sum of each column must be the same, so:

C + F = 10 + B

B + E = 10 + A

We can rewrite these equations as:

C - B + F = 10

B - A + E = 10

Since we are given that the sum of the two numbers is the same, we know that:

C + F + D + E = 1112

We can substitute C and F in terms of A and B using the equations above:

C = 10 + B - F

F = 10 + C - B

Substituting these expressions into the equation for the sum, we get:

10 + B - F + C + D + E = 1112

Simplifying this equation, we get:

B - F + C + D + E = 1102

Now we can substitute in the expressions for C and F in terms of A and B:

B - (10 + B - F) + (10 + C - B) + D + E = 1102

Simplifying and canceling out terms, we get:

F - C - D - E = -92

We know that each digit is unique, so we can assume that A is not equal to 0 (otherwise the number would not have 4 digits). We can also assume that D is not equal to 0, since it is the leftmost digit of the second number.

Trying different values for A and D, we find that A = 2 and D = 3 works:

A B C

D E F

2 7 9

1 7 3

The sum of each column is 3 + 7 + 2 = 1 + 9 + 7, which is equal to 12. Therefore, the solution is:

2 7 9

1 7 3

4 5 2

Answer:

C. 7.16

Step-by-step explanation:

3/8 + 1/16

By taking the LCM of 8 and 16 which is 16

=> 6 + 1/16 = 7/16

Hope you understood!!

Answer: The 0.09 is 1/10 of 0.9

Step-by-step explanation:

You can see by the decimal point that it moved so from 0.9 to 0.09 it has moved once.

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The expression that models the number of people attending concert 1 is given as follows:

512/6.

The number of people attending concert 1 is obtained applying the proportions in the context of the problem.

From the bar model, the fractions corresponding to each concert are given as follows:

The total number of people is given as follows:

512.

Hence the expression that models the number of people attending concert 1 is given as follows:

512/6.

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