Traci has a coupon for $2.50 off a box of name-brand cereal that normally costs $12.78. The store-brand cereal costs $10.98.


How much will Traci save it she uses her coupon and buys the name-brand cereal instead of store-brand cereal?

Answer:

d) 1/2

Step-by-step explanation:

(1,3) (5,5)

y2-y1/x2-x1

5-3/5/1

2/4=1/2=0.5

Answer:

27

Step-by-step explanation:

The values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

The perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.

√15/(y + 2) = y/√15 {opposite/adjacent}

y(y + 2) = (√15)² {cross multiplication}

y² + 2y = 15

y² + 2y - 15 = 0

by factorization;

(y - 3)(y + 5) = 0

y = 3 or y = -5

by Pythagoras rule:

(√15)² = x² + y²

15 = x² + 3²

x = √(15 - 9)

x = √6

z² = (√6)² + 2²

z = √(6 + 4)

z = √10

Therefore, the values of x, y and z for the right triangle are: x = √6, y = 3, and z = √10 respectively.

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Answer:

The correct answer is,

\( - \frac{7}{8} \)

No, The random sum Yn = ΣXx is not a Poisson-distributed is the answer.

No, the random sum Yn = ΣXx is not Poisson-distributed. The Poisson distribution is a probability distribution that describes the number of events occurring within a fixed interval of time or space, given the average rate of occurrence. In this case, the random variables Xk in the sequence {Xx}k>1 are independent and Poisson-distributed, but they are not identically distributed. This means that each Xk has its own specific Poisson distribution with its own mean and rate parameter.

When we sum the random variables in Yn, we are essentially adding together different Poisson distributions with different mean and rate parameters. The resulting distribution of Yn will depend on the specific values of Xk and their corresponding distributions. It will not follow a Poisson distribution.

To illustrate this, consider the case where X1 follows a Poisson distribution with mean λ1 and X2 follows a Poisson distribution with mean λ2. The sum Yn = X1 + X2 will follow a Poisson distribution with mean λ1 + λ2, but it will not be a Poisson distribution with a single rate parameter.

Therefore, the random sum Yn = ΣXx is not Poisson-distributed.

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Answer:

1

Step-by-step explanation:

under the restrictions that c is negative to ensure strict concavity, the utility function u(w) = -(b - w)c displays increasing absolute risk aversion.

To ensure that u(w) is strictly increasing, we need the derivative of u(w) with respect to w to be positive for all values of w. Taking the derivative, we have du(w)/dw = -c. For u(w) to be strictly increasing, -c must be positive, which implies c must be negative.

To ensure that u(w) is strictly concave, we need the second derivative of u(w) with respect to w to be negative for all values of w. Taking the second derivative, we have d²u(w)/dw² = 0. Since the second derivative is constant and negative, u(w) is strictly concave.

Now, let's examine the concept of increasing absolute risk aversion. If a utility function u(w) exhibits increasing absolute risk aversion, it means that as wealth (w) increases, the individual becomes more risk-averse.

In the given utility function u(w) = -(b - w)c, when c is negative (as required for strict concavity), the absolute risk aversion increases as wealth (w) increases. This is because the negative sign implies that the utility function is concave, indicating that the individual becomes more risk-averse as wealth increases.

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By using a maclaurin series to obtain the maclaurin series for the given function is  F(x) = x cos(5x) = \(1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

To obtain the Maclaurin series for the function f(x) = x cos(5x), we need to write the Maclaurin series for cos(5x). The Maclaurin series for cos(x) is: \(cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...\)

Using this formula, we can substitute 5x for x and obtain the Maclaurin series for cos(5x): cos(5x) =\(1 - (5x)^2/2! + (5x)^4/4! - (5x)^6/6! + ...\)

\(= 1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...\)

We can substitute this series into the original function f(x) = x cos(5x) and obtain its Maclaurin series: f(x) = x cos(5x)

\(= x[1 - 25x^2/2! + 625x^4/4! - 15625x^6/6! + ...]\)

\(= x - 25x^3/2! + 625x^5/4! - 15625x^7/6! + ...\)

This is the Maclaurin series for the function f(x) = x cos(5x). It is obtained by substituting the Maclaurin series for cos(5x) into the original function and simplifying the resulting series. Maclaurin series are useful for approximating functions using polynomials. By truncating the series after a certain number of terms, we can obtain a polynomial that approximates the original function to a certain degree of accuracy. The accuracy of the approximation depends on the number of terms in the series that are used. The more terms we include, the more accurate the approximation will be.

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Answer:

B. 23

Step-by-step explanation:

We Know

WV = YX

Let's solve

12x - 61 = 3x + 2

12x = 3x + 63

9x = 63

x = 7

Now we plug 7 in for x and find WV

12x - 61

12(7) - 61

84 - 61

23

So, the answer is B.23

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Answer:

145

Step-by-step explanation:

180-35 = 145

I got 180 because that is the angle measure of a straight line

Answer:

384 cm²

Step-by-step explanation:

The surface area of the cube = 6 · a²

a = 8 cm

Let's solve

6 · 8² = 384 cm²

So, the total surface area of the cube is 384 cm².

The required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

Arithmetic progression is the series of numbers that have common differences between adjacent values.

here,
The Sequences 8, 11, 14,...

first term a = 8
common difference = 11 - 8 = 3

Now,
The explicit formula is given as,
nth terms = a + (n - 1)d
nth term = 8 + (n - 1)3

Thus, the required explicit formula for the given sequence to determine the nth term is given as nth term = 8 + (n - 1)3.

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Answer:

Top-left answer: (x-7.5)^2=43.25

Step-by-step explanation:

Complete the square

x^2-15x+15=2

x^2-15x+13=0

(x-7.5)^2-(7.5)^2+13=0

(x-7.5)^2-56.25+13=0

(x-7.5)^2-43.25=0

(x-7.5)^2=43.25

Interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

Higher Placement The College Board's Advanced Placement Program makes a college-level course and exam in United States Government and Politics available to high school students.

By organizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues, interest groups enable citizen participation in governance.

a group of individuals united by a shared interest or objective and working to sway public policy. group leaders. As adolescents gain knowledge, they frequently form their own groups. government.

Therefore, interest groups facilitate citizen participation in governance by mobilizing people to take collective action through voting, fundraising, and informing the public and elected officials about their issues.

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Answer:

letter d I am not sure about that

The equation of P in the given equation is P = 100N/W

The equation is given as:

W = 100N/P

Multiply both sides by P

WP = 100N

Divide both sides by W

P = 100N/W

Hence, the equation of P in the given equation is P = 100N/W

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Answer:

The pictures are too small :(

Step-by-step explanation:

The process capability index for the process is 0.1754.

The first sided specification limit will be:

= (Upper specification limit - mean)/(3 × standard deviation)

= (23.1 - 22.9)/(3 × 0.19)

= 0.2/0.57

= 0.3508

The second sided specification limit will be:

= (22.9 - 22.8)/(3 × 0.19)

= 0.1/0.57

= 0.1754

The process capability index for the process is 0.1754 wine it's the lower value.

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(i)The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. (ii)Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

i. To sketch the signals x(t) and h(t), we can analyze their mathematical expressions. The input signal x(t) is a linear function with negative slope from t = 0 to t = 4, and it is zero for t > 4. The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. We can plot the graphs of x(t) and h(t) based on these characteristics.

ii. To determine the output signal y(t), we can use the convolution integral, which is given by the expression:

y(t) = ∫[x(τ)h(t-τ)] dτ

In this case, we substitute the expressions for x(t) and h(t) into the convolution integral. By performing the convolution integral calculation, we obtain the expression for y(t) as a function of t.

To sketch the output signal y(t), we can plot the graph of y(t) based on the obtained expression. The shape of the output signal will depend on the specific values of t and the coefficients in the expressions for x(t) and h(t).

Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

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I do khan academy 2 but sorry the answer

Answer:

Michael will earn $399.60 for a 37-hour week.

Step-by-step explanation:

\(10.80 \times 37 = 399.60\)

okay so this question is very easy you just supposed to multiple the paid per hour amount with the hours per week.

Data

paid per hour $10.80

find how much for 37 hours

Solution

37 * 10.80

=$399.6

The remainder after dividing 2x³ + 5x² - 3x + 1 by x+4 is 9x+1

We have to find the remainder when we divide 2x³ + 5x² - 3x + 1 by x+4

Dividend is the number which is getting divided by some other number

2x² - 3x + 15 is the dividend

Divisor is the number which divides a number

x+4 is the divisor

In the given division the

       2x² - 3x + 15

       ------------------

x + 4|2x³ + 5x² - 3x + 1

    - (2x³ + 8x²)

       --------------

            -3x²- 3x

            +(-3x² - 12x)

            --------------

                       9x + 1

Hence, the remainder  is 9x+1 when we divide 2x³ + 5x² - 3x + 1 by x+4

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The probability of this is (1/6) x (3/6) or 1/12. So, the total probability is 3/36 + 1/12, which simplifies to 1/6.

To find the probability that the sum of two numbers rolled is greater than 3, given that the sum is not greater than 5, we need to first find the probability of the sum being less than or equal to 5. This can be done by finding the probability of rolling a 2, 3, 4 or 5 on the two dice. This probability is 4/36 or 1/9. Now, to find the probability that the sum is greater than 3, given that the sum is not greater than 5, we need to use Bayes' theorem. This gives us (probability of sum>3 and sum<=5)/ (probability of sum<=5), which is (2/36)/(4/36) or 1/2.

The probability that one of the numbers is a 6 and the sum of the two numbers is an odd number can be found by considering the cases where the other number is odd or even. If the other number is odd, then the sum will be even and the probability is 3/36. If the other number is even, then the sum will be odd only if the other number is 1, 3 or 5.

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Answer:

112 words in 4 minutes

Step-by-step explanation:

Hoi can type 112 words in 4 minutes. Therefore, Lin's typing speed is 32 words per minute. Therefore, Hoi's typing speed is 28 words per minute. We can see that Lin's typing speed is 4 more (32-28) words per minute more than Hoi, therefore, option B is the correct choice.

The recursive formula is a(n) = a(n-1) + 3 while the explicit formula is a(n) =  3n - 6.

In an arithmetic sequence, the following applies:

a(n) = a(n-1) + d  (This is the recursive formula)

a(n) = a(1) + (n-1) . d  ( This is the explicit formula)

Where:

a(n) = nth term

a(n-1) = (n-1)th term

d = common difference

a(1) = the first term

The given sequence is:

    -3, 0, 3, 6, ....

The common difference (d)  = 0 - (-3) = 3

Hence, the recursive formula is:

a(n) = a(n-1) + 3

Note that  a(1) = -3. Hence, the explicit formula is:

a(n) = a(1) + (n-1) . d

a(n) = -3 + (n-1) . 3

a(n) = -3 + 3n - 3

a(n) =  3n - 6

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Answer:

21

Step-by-step explanation:

To add fractions find the LCD and then combine