z is a standard normal random variable,
The probabilities are:
(a) P(-1.98 ≤ x ≤ 0.49) = 0.6426
(b) P(0.58 ≤ Z ≤ 1.28) = 0.1807
(c) (-1.72 ≤ Z ≤ -1.04) = 0.1074
Standard Normal Distribution:The standard normal distribution is a special case of the normal distribution with mean 0 and variance 1. The z-score is calculated by subtracting the population mean from a random variable and dividing it by the standard deviation.
The required probabilities are found from the standard normal distribution table or using the Excel function = NORMSDIST(z)
(a) P(-1.98 ≤ x ≤ 0.49) = P(Z ≤ 0.43) - P(Z ≤ - 1.98)
= 0.6664 - 0.0238
= 0.6426
(b) P(0.58 ≤ Z ≤ 1.28) = P(Z ≤ 1.28) - P(Z ≤ 0.58)
= 0.8997 - 0.7190
= 0.1807
(c) (-1.72 ≤ Z ≤ -1.04) = P(Z ≤ -1.04) - P(Z ≤ -1.73)
= 0.1492 - 0.0418
= 0.1074
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What is the mean:4,3,5,4,8,0 IXL
What is the yield to maturity of a(n) eight-year, $5000 bond with a 4.4% coupon rate and semiannual coupons if this bond is currently trading for a price of $4723.70? A) 6.31% B) 5.26% C) 7.36% D) 2.63%
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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Find the measure of the missing angle
Help please
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 )
Can someone help me out please
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
Calculate , the number of all partitions of a set of 6 elements into 3 disjoint sets. Calculate S73, the number of all partitions of a set of 6 elements into 3 disjoint sets.
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.
b+5b+6b 6a-4a 10a+3a+2a 9p+20p+8p 12x -10y 2+5x+3+5x Упрости выражения,где это возможно. ПОМОГИТЕ ПРОШУ!!!!!!!
Answer:
i dont undersant what u r trying to say
Step-by-step explanation:
i thnk this is harsdath
Which value of x makes the equation -2(1-4x)=3x+8 true?
Answer:
x = 2
Step-by-step explanation:
distribute -2 first
-2 + 8x = 3x + 8
-2 + 5x = 8
5x = 10
x = 2
xpress the function as the sum of a power series by first using partial fractions. f(x) = 7 x2 − 3x − 10 f(x) = [infinity] n = 0 find the interval of convergence. (enter your answer using interval notation.)
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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Sofia bought a clothes iron that was discounted 15% off of the original price of $35. What was the dollar amount of discount of the clothes iron?
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
An amusement park thrill ride swings its riders back and forth on a pendulum that spins. Suppose the swing arm of the ride is 62 feet in length, and the axis from which the arm swings is about 64 feet above the ground. What is the height of the riders above the ground at the peak of the arc? Round to the nearest foot if necessar
PLEASE HELP
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
brand of water-softener salt comes in bags marked "net weight 18kg". The
company that packages the salt claims that the bags contain an average of 18kg of
salt and that the standard deviation of the weight of the bag is 0.68kg. Assume that
the weight of the bags is normally distributed and unless otherwise indicated use ? =
.05.
It is given that:
μ=18
0.68
n = 10
In general, what mean weights of 10 randomly select bags would you
consider evidence against the company’s claim?
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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A restaurant used 231 eggs last week. 46 of them are colored white, w. The remaining eggs are colored brown.Write an equation that represents the situation.
Answer:
46 + W = 231
Step-by-step explanation:
Answer:
231-W=amount of brown eggs (185)
Step-by-step explanation:
200% of what number is 350?
Answer:
The answer is 175
Using hypothesis testing, determine whether the sample mean is not equal to the block population's mean (R+) with a confidence level of 99%.
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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Use a calculator to evaluate the function at the indicated values. Round your answers to three decimals. h(x)=e−3x;h(13),h(1.5),h(−1),h(−π)h(x)=e−3x;h(31),h(1.5),h(−1),h(−π)
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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Find the value of x in the picture below. (round to nearest tenth if needed) THANK YOU FOR HELPING ME:)
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?
Find the Perimeter of the figure below, composed of a rectangle and two
semicircles. Round to the nearest tenths place.
10
HELP MEHHH....pls
Answer:
Step-by-step explanation:
What is the mode of the set of numbers?
2, 2, 3, 4, 4, 5, 7, 7, 7, 10, 16, 17
Answer:
It is 7
Step-by-step explanation:
Ms. Thompson went to buy socks for her Jordans. She brought $20 to the store. Each pair of scold costs $2.50. How many pairs of socks can she buy with $20?
answer of this question:
8
Step-by-step explanation:
$20÷$2.50
=8
:)
HELPPP ME PLSSS AND NO BOTS BC I WILL REPORT AND I BARELY HAVE POINT SO PLS HELP ME
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.
What is the simple interest earned on an $4,350 investment for 5 years at a rate of 2%?
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
i light is faster then anything how did dark get there first
hello there enjoy 30 points on da house
Answer:
this just confused me so much
Step-by-step explanation:
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A figure has a perimeter of 40 units and an area of 100 units2 . Which of the following describes the new perimeter and area after the figure is dilated by a scale factor of
A)Perimeter: 20 units; Area: 50 units2
B)Perimeter: 20 units; Area: 25 units2
C)Perimeter: 10 units; Area: 25 units2
D)Perimeter: 80 units; Area: 200 units2
PLEASE HELP MEEE < ILL GIVE 25 POINTS
Answer:
B
Step-by-step explanation:
You didn't write the full question but B is the only one that make since.
4
Select the correct answer.
Solve the following equation for x.
x2 - 9x+ 18 = 0
O A.
X = -3; x = 6
ОВ.
X= 3; x = 6
OC.
x= -3; x = -6
OD.
x= 3; x = -6
(行
Reset
Next
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
HELP!!!!! What is the geometric mean of 3 and 7?
Answer:
4.5826
Step-by-step explanation:
PLEASE HELP!!! I need the answer now
Answer:
(-2,3)
Step-by-step explanation:
Answer:
C. (-2,3)
Step-by-step explanation:
(-2,3)
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. The particular interest was whether higher income would cause shoppers to spend more en groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that werk. The gender of each shopper was also obtained. The data below are expenditures and income for 10 selected survey participants. Income Grocery 98 52 201 78 298 108 398 95 481 198 600 99 738 162 805 187 890 105 1023 173 The correlation for these data is given by 0.794 Ob-0.619. 0.649 4.0.735.
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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Directions: Evaluate the following equation. Show all of your work.
4) 4.2x = 33.6
5) a/3 = 45
6) -8x = 4
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
16 is what percent of 25
Answer:
4
Step-by-step explanation:
Answer:
64 %
Step-by-step explanation:
( 16 / 25 ) x 100
= ( 16 x 100 ) / 25
= 16 x 4
= 64 %
Simplity (4.5)(5)(-2)
O45
045
0-45
-45