Given that z is a standard normal random variable, compute the following probabilities (to 4 decimals). a. P(-1.98 ≤ x ≤ 0.49) b. P(0.51 z 1.21) c. P(-1.72 ≤ z≤ -1.03)

The radius of convergence is 5/7. The interval of convergence is (-5/7, 5/7) in interval notation.

To express the function f(x) = 7x² - 3x - 10 as the sum of a power series, we can start by factoring the quadratic term in the numerator:

f(x) = (7x² - 3x - 10)

The quadratic expression can be factored as follows:

f(x) = (7x + 5)(x - 2)

Now we can write the function f(x) as a sum of partial fractions:

f(x) = A/(7x + 5) + B/(x - 2)

To find the values of A and B, we can multiply both sides of the equation by the denominators and equate the coefficients of corresponding powers of x:

(7x + 5)(x - 2) = A(x - 2) + B(7x + 5)

Expanding both sides of the equation:

7x² - 14x + 5x - 10 = Ax - 2A + 7Bx + 5B

Grouping the terms with the same power of x:

(7x² + (5 - 14)x - 10) = (A + 7B)x + (-2A + 5B)

Equating the coefficients of corresponding powers of x:

7x² + (5 - 14)x - 10 = (A + 7B)x + (-2A + 5B)

Comparing the coefficients:

7 = A + 7B

5 - 14 = -2A + 5B

-10 = -2A

From the first equation, we can solve for A:

A = 7 - 7B

Substituting this value of A into the second equation:

-10 = -2(7 - 7B)

Simplifying:

-10 = -14 + 14B

14B = -10 + 14

B = 4/14

B = 2/7

Now we have the values of A and B:

A = 7 - 7B = 7 - 7(2/7) = 7 - 2 = 5

Therefore, the function f(x) can be expressed as:

f(x) = 5/(7x + 5) + 2/(x - 2)

Now, to find the interval of convergence for the power series representation of f(x), we need to determine the radius of convergence. The power series representation will converge within the interval (-r, r), where r is the radius of convergence.

In this case, since we have a rational function, the interval of convergence will be determined by the denominator with the smallest radius of convergence.

The denominators in the partial fractions are (7x + 5) and (x - 2). The radius of convergence for a power series centered at a point c is the distance from c to the nearest singularity.

For (7x + 5), the singularity occurs when 7x + 5 = 0, which gives x = -5/7.

For (x - 2), the singularity occurs when x - 2 = 0, which gives x = 2.

The distance from the center (c = 0) to the nearest singularity is the minimum of the absolute values of the two singularities: min(|-5/7|, |2|) = 5/7.

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Answer:

17 feet

Step-by-step explanation:

L² = 15² + 8² = 225 + 64 = 289

L = √289 = 17 feet

Answer:

do you need the area or the perimiter?

Answer:

118ft

Step-by-step explanation:

dont ask how i got it i just got the answer from my teacher but they didnt show me the work. ur welcome

The yield to maturity of a(n) eight-year, if this bond is currently trading for a price of $4723.70 is  B) 5.26%

Time = 8 years

Coupon rate = 4.4%

Value of the bond = $5000

Yield to maturity is the overall return on investment that a bond will have earned once all required payments have been made and the principal has been repaid. Since the investor would receive the initial bond price plus the interest rate that was finalised at the time of the total bond purchase.

Calculating yield to maturity -

[tex]P = C * [1 - (1 + r/2)^(-2n)] / (r/2) + F / (1 + r/2)^(2n)[/tex]

Substituting the values -

$4723.70 =

[tex]($5000 * 0.044/2) * (1 - (1 + Y/2)^(-28)) / (Y/2) + $5000 / (1 + Y/2)^(28)[/tex]

= 0.0526, or 5.26%

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Answer:

B

Step-by-step explanation:

Given

x² - 9x + 18 = 0 ← in standard form

(x - 3)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 3 = 0 ⇒ x = 3

x - 6 = 0 ⇒ x = 6

solution is x = 3, x = 6 → B

The correlation coefficient for the data is 0.794.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the correlation coefficient of 0.794 indicates a strong positive correlation between weekly income and weekly grocery expenditures.

A correlation coefficient value of 0.794 suggests that as the weekly income increases, the weekly grocery expenditures tend to increase as well. The positive correlation implies that shoppers with higher incomes tend to spend more on groceries.

It is important to note that correlation does not imply causation. The study observed a correlation between income and grocery expenditures, but it does not necessarily mean that higher income directly causes shoppers to spend more on groceries. Other factors and variables may also influence grocery spending habits.

In summary, based on the given data, there is a strong positive correlation (0.794) between weekly income and weekly grocery expenditures for the surveyed shoppers.

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answer of this question:

8

Step-by-step explanation:

$20÷$2.50

=8

:)

Answer:

i dont undersant what u r trying to say

Step-by-step explanation:

i thnk this is harsdath

Answer:

x = 2

Step-by-step explanation:

distribute -2 first

-2 + 8x = 3x + 8

-2 + 5x = 8

5x = 10

x = 2

Answer:

4

Step-by-step explanation:

Answer:

64 %

Step-by-step explanation:

( 16 / 25 ) x 100

= ( 16 x 100 ) / 25

= 16 x 4

= 64 %

Answer:

B

Step-by-step explanation:

You didn't write the full question but B is the only one that make since.

Answer:

this just confused me so much

Step-by-step explanation:

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Hypothesis testing is a statistical method used to determine if a hypothesis regarding a population parameter is correct or not.

It is a decision-making process that aids in making decisions about population parameters when only a sample statistic is available. It has the following steps: State the null and alternative hypotheses. Choose the significance level. Determine the critical value or p-value. Calculate the test statistic. Make a decision and state the conclusion. The formula for the test statistic is given, where x is the sample mean, μ is the population mean, s is the sample standard deviation, and n is the sample size. The null and alternative hypotheses for this problem are:H0: μ = R+ (the sample mean is equal to the block population's mean)Ha: μ ≠ R+ (the sample mean is not equal to the block population's mean)We will use a two-tailed test since we are testing whether the sample mean is not equal to the block population's mean.

The significance level is given as 99%. This means that α = 1 - 0.99 = 0.01.The critical value for a two-tailed test with α = 0.01 and degrees of freedom (df) = n - 1 is obtained from a t-distribution table. Since the sample size is not provided, we cannot determine the critical value. The p-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. The p-value for a two-tailed test is given by:

P-value = P(|t| > |t*|)where t* is the test statistic and |t| is the absolute value of the test statistic. Since we do not have the sample size or the test statistic, we cannot calculate the p-value. Therefore, we cannot make a decision and state a conclusion about the hypothesis test.

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Answer: 52 1/2 inches. Draw a vertical line up from the 20 week marker and where that line intersects the slanted red line and. Then take a straight edge and draw a line parallel to the "week" line on the bottom of the graph from the intersection to intersect the height line. Where the second line crosses the height line that number is the height of the plant at 20 weeks.

Answer:

4) 8

5) 135

6) -.5

Step-by-step explanation:

4) 33.6/4.2=8

5) 3*45=135

6)4/-8= -1/2 or -.5

Answer:

$5.25

Step-by-step explanation:

Given data

Original price= $35

Discount= 15%

let us find 15% of $35

=15/100*35

=0.15*35

=$5.25

Hence the amount of the discount is

$5.25

Answer:

area = (14 x 16) - (0.5 x 16 x 6) = 176 ft²

Step-by-step explanation:

Answer:

A = 176 ft²

Step-by-step explanation:

2 shapes: one rectangle and 1 triangle:

Rectangle:

A = bh

A = 16(14)

A = 224

Triangle:

A = 1/2bh

A = 1/2(16)(6)

A = 48

Combined:

224 - 48

176

Given the function h(x) = e-3x  and we have to evaluate the function at the indicated values. So, we need to substitute the values in the given function and find the value of the function at the given points as shown below: h(13) = e-3(13)h(13) = e-39h(13) = 0.000027323h(1.5) = e-3(1.5)h(1.5) = e-4.5h(1.5) = 0.01111h(-1) = e-3(-1)h(-1) = e3h(-1) = 20.08554h(-π) = e-3(-π)h(-π) = e3πh(-π) = 23.14069.

(a) For, h(-1):

Plug x = -1 into the function:

h(-1) = e^(-3*-1)

Using a calculator, we find that h(-1) ≈ 20.086.

Similarly,

(b) For, h(-π):

Plug x = -π into the function:

h(-π) = e^(-3*-π)

Using a calculator, we find that h(-π) ≈ 23.141.

So, the value of h(x) at the given values are : h(13) = 0.000027323, h(1.5) = 0.01111, h(-1) = 20.08554 and h(-π) = 23.14069.

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Answer:

It is 7

Step-by-step explanation:

Answer:

The answer is 175

Answer:

Step-by-step explanation:

Answer:

(-2,3)

Step-by-step explanation:

Answer:

C. (-2,3)

Step-by-step explanation:

(-2,3)

Answer:

46 + W = 231

Step-by-step explanation:

Answer:

231-W=amount of brown eggs (185)

Step-by-step explanation:

Answer:

4.5826

Step-by-step explanation:

Any mean weight falling outside the interval of (17.06, 18.94) would be considered evidence against the company's claim.

μ = 18 and σ = 0.68. n = 10. The formula for the z-test is given by:

z = (x - μ) / (σ/√n)

Where:

z = z-test score

x = sample mean

μ = population mean

σ = standard deviation

n = sample size

Let's calculate the upper and lower limits by using the above formula:

Lower limit = μ - z_(α/2) * (σ / √n)

Upper limit = μ + z_(α/2) * (σ / √n)

Where z_(α/2) is the standard normal variate which can be found from the standard normal table (at 5% significance level) to be 1.96.

Therefore,

Lower limit = 18 - 1.96 * (0.68/√10) = 17.06

Upper limit = 18 + 1.96 * (0.68/√10) = 18.94

Thus, any mean weight of 10 randomly selected bags that falls outside the interval of (17.06, 18.94) would be considered evidence against the company's claim.

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Hey!

A = $4,785.00

I = A - P = $435.00

Equation:

A = P(1 + rt)

Calculation:

First, converting R percent to r a decimal

r = R/100 = 2%/100 = 0.02 per year.

Solving our equation:

A = 4350(1 + (0.02 × 5)) = 4785

A = $4,785.00

The total amount accrued, principal plus interest, from simple interest on a principal of $4,350.00 at a rate of 2% per year for 5 years is $4,785.00.

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Hope you have a great day and this helped in some way <33

Answer:

≈ 56°

Step-by-step explanation:

Using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{34}{41}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{34}{41}[/tex] ) ≈ 56° ( to the nearest degree )

The number of all partitions of a set of 6 rudiments into 3 disjoint sets is 69( S( 6, 3) = 69).

To calculate the number of all partitions of a set of 6 rudiments into 3 disjoint sets, we've to apply knowledge of Stirling numbers of the alternate kind. The Stirling figures of the alternate kind, denoted by S( n, k), represent the number of ways to partition a set of n rudiments into  k non-empty subsets.

Then, we want to calculate S( 6, 3), which defines the number of ways to partition a set of 6 rudiments into 3 disjoint sets.

Using the conception of Stirling figures of the alternate kind

S(n, k) = k * S(n-1, k) + S(n-1, k-1)

we can calculate S(6, 3) as given below-

S(6, 3) = 3 * S(5, 3) + S(5, 2)

S(5, 3) = 3 * S(4, 3) + S(4, 2)

S(4, 3) = 3 * S(3, 3) + S(3, 2)

S(3, 3) = 1

S(3, 2) = 3

S(4, 3) = 3 * 1 + 3 = 6

S(5, 3) = 3 * 6 + 3 = 21

S(6, 3) = 3 * 21 + 6 = 69

Therefore, the number of all partitions of a set of 6 elements into 3 disjoint sets is 69 (S(6, 3) = 69).

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The correct question is given below -

Calculate S(6,3) , the number of all partitions of a set of 6 elements into 3 disjoint sets.