Answer:
6.40
Step-by-step explanation:
Find the number in the tenth place (the first 4) and look one place to the right for the rounding digit (the second 4).
Round up if this number is greater than or equal to 5
and round down if it is less than 5.
4 is less than five, therefore should be rounded down.
Answer:
6.44
Step-by-step explanation:
The nearest cent is the hundredths place (or two decimals)
6.4442 rounds to 6.44
The next number is less than 5 so we leave the hundredths place alone.
Tatiana made a two-way table to describe what her friends like at the amusement park. Which could be the columns and rows for Tatiana’s table? columns: likes roller coasters, likes water rides; rows: doesn’t like roller coasters, doesn’t like water rides columns: likes water rides, doesn’t like roller coasters; rows: doesn’t like water rides, likes roller coasters columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides columns: doesn’t like water rides, likes roller coasters; rows: doesn’t like roller coasters, likes water rides? HELP
Answer:
i think its c
Step-by-step explanation:
Answer:
C: Columns: likes roller coasters, doesn’t like roller coasters; rows: likes water rides, doesn’t like water rides
Step-by-step explanation:
Like variables need to be together on the columns and rows
A square of side length 7 cm is enlarged using the scale factor 6. Find the area of the enlarged square.
Answer:
The answer is 42 centimeters.
Step-by-step explanation:
HOPE THIS HELPED!
The following observations were made on fracture toughness of a base plate of 18% nickel maraging steel (in ksi in. , given in increasing order)]: 65.2 71.9 72.8 73.1 73.1 73.5 75.5 75.7 75.8 76.1 76.2 76.2 77.0 77.9 78.1 79.6 79.7 79.9 80.1 82.2 83.7 93.8 Calculate a 99% CI for the standard deviation of the fracture toughness distribution. (Round your answers to one decimal place.)
Answer:
[tex]\frac{(21)(5.437)^2}{41.402} \leq \sigma^2 \leq \frac{(21)(5.437)^2}{8.034}[/tex]
[tex] 14.996 \leq \sigma^2 \leq 77.278[/tex]
And the confidence interval for the deviation would be obtained taking the square root of the last result and we got:
3.9<σ<8.8
Step-by-step explanation:
Data given:
65.2 71.9 72.8 73.1 73.1 73.5 75.5 75.7 75.8 76.1 76.2 76.2 77.0 77.9 78.1 79.6 79.7 79.9 80.1 82.2 83.7 93.8
The sample mean would be given by:
[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]
We can calculate the sample deviation with this formula:
[tex]s = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]
And we got:
s=5.437 represent the sample standard deviation
[tex]\bar x[/tex] represent the sample mean
n=22 the sample size
Confidence=99% or 0.99
The confidence interval for the population variance is given by:
[tex]\frac{(n-1)s^2}{\chi^2_{\alpha/2}} \leq \sigma^2 \leq \frac{(n-1)s^2}{\chi^2_{1-\alpha/2}}[/tex]
The degrees of freedom given by:
[tex]df=n-1=22-1=21[/tex]
The Confidence is 0.99 or 99%, the value of significance is [tex]\alpha=0.01[/tex] and [tex]\alpha/2 =0.005[/tex], and the critical values are:
[tex]\chi^2_{\alpha/2}=41.402[/tex]
[tex]\chi^2_{1- \alpha/2}=8.034[/tex]
And the confidence interval would be:
[tex]\frac{(21)(5.437)^2}{41.402} \leq \sigma^2 \leq \frac{(21)(5.437)^2}{8.034}[/tex]
[tex] 14.996 \leq \sigma^2 \leq 77.278[/tex]
And the confidence interval for the deviation would be obtained taking the square root of the last result and we got:
3.9<σ<8.8
si a un numero le sumas su anterior, obtienes 37. ¿ de que numero hablamos?
Answer:
Would you be able to write it in english so i can help you.
Step-by-step explanation:
(1 point) Scores on a certain intelligence test for children between ages 13 and 15 years are approximately normally distributed with µ=106μ=106 and σ=24σ=24. (a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ? Answer: Round to four decimal places. (b) What score which marks the lowest 25 percent of the distribution? Answer: Round to two decimal places. (c) Enter the score that marks the highest 5 percent of the distribution. Answer: Round to two decimal places.
Answer:
a) 0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92
b) A score of 89.8 marks the lowest 25 percent of the distribution
c) A score of 145.48 marks the highest 5 percent of the distribution
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 106, \sigma = 24[/tex]
(a) What proportion of children aged 13 to 15 years old have scores on this test above 92 ?
This is 1 subtracted by the pvalue of Z when X = 92. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{92 - 106}{24}[/tex]
[tex]Z = -0.58[/tex]
[tex]Z = -0.58[/tex] has a pvalue of 0.2810
1 - 0.2810 = 0.719
0.719 = 71.90% of children aged 13 to 15 years old have scores on this test above 92
(b) What score which marks the lowest 25 percent of the distribution?
The 25th percentile, which is X when Z has a pvalue of 0.25. So it is X when Z = -0.675.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 106}{24}[/tex]
[tex]X - 106 = -0.675*24[/tex]
[tex]X = 89.8[/tex]
A score of 89.8 marks the lowest 25 percent of the distribution
(c) Enter the score that marks the highest 5 percent of the distribution
The 100-5 = 95th percentile, which is X when Z has a pvalue of 0.95. So it is X when Z = 1.645
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]1.645 = \frac{X - 106}{24}[/tex]
[tex]X - 106 = 1.645*24[/tex]
[tex]X = 145.48[/tex]
A score of 145.48 marks the highest 5 percent of the distribution
Final answer:
Using z-scores and the properties of a normal distribution, it was calculated that approximately 71.90% of children score above 92. The score marking the lowest 25 percent is approximately 90.20, and the score that marks the highest 5 percent of the distribution is around 145.88.
Explanation:
To solve the problems about normal distribution and interpreting IQ scores, we use the properties of the normal curve and z-scores. Z-scores help us understand how far away a particular score is from the mean, in terms of standard deviations.
Part (a): Proportion of Children With Scores Above 92
We first calculate the z-score for 92 using the formula: z = (X - μ) / σ, where X is the score, μ is the mean, and σ is the standard deviation. With μ = 106 and σ = 24, the z-score for 92 is (92 - 106) / 24 = -0.5833. Using a standard normal distribution table, we find that the proportion of children scoring above 92 corresponds to the area to the right of the z-score, which is approximately 0.7190. Therefore, the proportion of children aged 13 to 15 with scores above 92 is 0.7190.
Part (b): Lowest 25 Percent of the Distribution
The score marking the lowest 25 percent of the distribution corresponds to the 25th percentile or a z-score of about -0.675. We convert this z-score back to the original scale using the formula: X = μ + zσ, which yields X = 106 + (-0.675)(24) = 90.20. Thus, the score marking the lowest 25 percent is approximately 90.20.
Part (c): Highest 5 Percent of the Distribution
To find the score that marks the highest 5 percent, we locate the z-score that corresponds to the 95th percentile, which is about 1.645. Applying the conversion formula, we get X = 106 + (1.645)(24) = 145.88. Therefore, the score marking the highest 5 percent is approximately 145.88.
A teacher selects students from her class of 37 students to do 4 different jobs in the classroom: pick uphomework, hand out review forms, staple worksheets, and sort the submissions. Each job is performedby exactly one student in the class and no student can get more than one job. How many ways arethere for her to select students and assign them to the jobs?
Answer:
There are 1,585,080 ways for her to select students and assign them to the jobs
Step-by-step explanation:
The order in which the students are selected is important, since different orderings means different jobs for each student selected. So the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem:
4 students selected from a set of 37. So
[tex]P_{(37,4)} = \frac{37!}{(37-4)!} = 1585080[/tex]
There are 1,585,080 ways for her to select students and assign them to the jobs
What is 99 divided by 6
Answer: 16.5
Step-by-step explanation:
[tex]\frac{99}{6} = 16.5[/tex]
Answer:
What i got is 16.5 hope this helps!
Determine between which consecutive integers the real zeros of y(x) = x2 - 4x – 2 are located.
Answer:
The zeros are x1=4.45 and x2=-0.45.
x1 is between 4 and 5.
x2 is between -1 and 0.
Step-by-step explanation:
We have the function:
[tex]y(x) = x2 - 4x-2[/tex]
As this is a quadratic function, we can calculate the zeros of the function with the quadratic equation:
[tex]x_{1,2}=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot 1\cdot(-2)}}{2\cdot 1}\\\\\\x=\dfrac{4\pm\sqrt{16+8}}{2}\\\\\\x=\dfrac{4\pm\sqrt{24}}{2}\\\\\\x=\dfrac{4\pm4.9}{2}=2\pm2.45\\\\\\x_1=2+2.45=4.45\\\\x_2=2-2.45=-0.45[/tex]
The zeros are x1=4.45 and x2=-0.45.
x1 is between 4 and 5.
x2 is between -1 and 0.
The two real zeros of the quadratic equation are located between -1 and 4.
Between which consecutive integers the real zeros located?To determine between which consecutive integers the real zeros of the function y(x) = x² - 4x - 2 are located, we can use the quadratic formula.
The quadratic formula is given as:
x = (-b ± √(b² - 4ac)) / (2a)
In the equation y(x) = x² - 4x - 2, we have a = 1, b = -4, and c = -2.
Let's substitute these values into the quadratic formula to find the values of x:
x = (-(-4) ± √((-4)² - 4(1)(-2))) / (2(1))
x = (4 ± √(16 + 8)) / 2
x = (4 ± √24) / 2
x = (4 ± 2√6) / 2
x = 2 ± √6
From the quadratic formula, we find that the real zeros of the function are x = 2 + √6 and x = 2 - √6.
To determine between which consecutive integers these real zeros are located, we can compare the values to the nearest integers.
x = 2 + √6 is approximately 4.45
x = 2 - √6 is approximately -0.45
Therefore, the real zeros of the function are located between the consecutive integers -1 and 4.
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What is the base 10 representation of the number 1203,?
OA) 128
OB) 178
OC) 324
OD) 476
Answer:
178
Step-by-step explanation:
Crane Company publishes a monthly sports magazine, Fishing Preview. Subscription to the magazine cost $30 per year. During November 2020, Crane sells 25,000 subscriptions beginning with the December issue. Crane prepares financial statements quarterly and recognizes subscription revenue at the end of the quarter. The company uses the accounts Unearned Subscription Revenue and Subscription Revenue. Prepare the entry in November for the receipt of the subscription
Journal entry
Explanation:
Books of (----Limited)
Journal Entry
Date Account Title and Explanation Debit Credit
Cash / Bank A/c Dr. $750,000
To Unearned Subscription A/c $750,000
(Being Unearned Subscription)
Computation:
Amount of Unearned Subscription = 25,000 × $30
Amount of Unearned Subscription = %750,000
1. What is the area of the wall?
84 sq. ft.
78 sq. ft.
60 sq. ft.
27 sq. ft.
2. Wallpaper is sold in rolls that are 2 feet wide. What is the minimum length you would need to purchase to cover the wall?
Answer:
Step-by-step explanation:
Im going to assum the wall your talking about is the one at the bottom.
It is divided into two equal trapezoids, so we can find the area of one trapezoid, multiply it by 2 to find the area of the entire wall.
A= (1/2)(b1+b2)(h)
Where b1 and b2 are the two parrellel sides, and h is the height of the trapezoid.
A= .5*(9+6)(8/4) We divide by 8 by 2 because we are finding the area of one trapezoid which is half the height of the wall.
A= 30 ft squared.
2A= area of whole wall
2*30=60
The entire wall is 60 sq. ft.
2. The area you need to cover need to cover is 60 sqft.
Rolls of wallpaper are rectangular.
A = L*W and they told us the width is 2 ft. and we know the area we need to cover is 60 ft so we can subsitute those in to figure out the length.
60= L*2
L= 30 ft
You need at least 30 feet in length to cover the whole wall.
My sister needs help
"Find the perimeter of the figure to the nearest hundredth."
Answer: 27.42 ft
Step-by-step explanation:
To find the perimeter first we must find the circumference of the circles.
You can easily find the diameter by subtracting and you get 6.
Using the circle circumference formula c=2piR you get 9.42.
9.42 is our circumference of one circle.
You don't need to divide this by 2 because you already have 2 halves of a circle.
Next add all the sides which is 18.
Add this to the circumference we calculated earlier which gives you 27.42 ft.
−6(b+2)+8 answer quick
Answer:
b = 16
Step-by-step explanation:
Answer:
-6b-12+8 which simplifies to -6b-4
Step-by-step explanation:use distrubutive property and then combine like terms
Amelia flies her airplane through calm skies at a velocity v1. The direction of v1 is 15 degrees north of east, and the speed is 180 km/hr.
Eventually, however, she enters a windy part of the atmosphere and finds that her plane now moves at a velocity v2. The direction of v2 is due east, and the speed is 150 km/hr.
What is the speed of the wind?
In what direction is the wind blowing?
(between 0 and 360 degrees)
Answer:
Step-by-step explanation:
Given
Initially Plane is flying at the speed of [tex]180\ km/hr[/tex]
to the [tex]15^{\circ}[/tex] North of east
Now wind started Blowing and plane started moving towards east with speed [tex]150\ km/hr[/tex]
suppose [tex]1v_o[/tex] is the speed of wind
So,
[tex]\vec{v_2}=\vec{v_1}-\vec{v_o}[/tex]
[tex]150\hat{i}=180[\cos 15\hat{i}+\sin 15\hat{j}]-\vec{v_o}[/tex]
[tex]\vec{v_o}=\hat{i}[180\cos 15-150]+\hat{j}[180\sin 15][/tex]
[tex]\vec{v_o}=\hat{i}[173.866-150]+46.58\hat{j}[/tex]
[tex]\vec{v_o}=23.86\hat{i}+46.58\hat{j}[/tex]
So magnitude of wind is
[tex]\mid v_o\mid=\sqrt{23.86^2+46.58^2}[/tex]
[tex]\mid v_o\mid=\sqrt{2738.996}[/tex]
[tex]\mid v_o\mid=52.33\ km/hr[/tex]
direction [tex]\tan \theta=\frac{46.58}{23.86}[/tex]
[tex]\theta =62.87^{\circ}[/tex] North of east
Answer:
The speed of the wind is 52.3 km/h
The direction of the wind is 243 degrees.
this is the right answer
Step-by-step explanation:
Question 3
A rectangular prism has dimensions 3 inches, 4 inches, and 5 inches. Find the dimensions of another
rectangular prism with the same volume but less surface area.
What are the dimensions of the shape? *
What is its surface area?*
Answer:
Step-by-step explanation:
The formula for finding the volume is
Volume = length × width × height
Volume of the given prism is
Volume = 3 × 4 × 5 = 60 inches³
The formula for determining the surface area of a rectangular prism is expressed as
Surface area = Ph + 2B
Where
P represents perimeter of base
h represents height of prism
B represents base area
Perimeter of base = 2(length + width)
P = 2(3 + 4) = 14 inches
B = 3 × 4 = 12 inches
h = 5 inches
Surface area = 14 × 5 + 2 × 12 = 94 inches²
For another prism,
Assuming h = 3, length = 10 and width = 2, then
Volume = 3 × 10 × 2 = 60 inches³
P = 2(10 + 2) = 24 inches
B = 10 × 2 = 20 inches
Surface area = (24 × 3) + (2 × 20) = 112 inches²
If we keep changing the values, the surface area will always be greater than 94 inches².
Therefore, there is no rectangular prism with the same volume but less surface area.
Answer:
its 60 for volume, but for the area i don't know
Step-by-step explanation:
Of the 3737 people at a basketball team party, 2525 of them play basketball, 1515 are under six feet tall, and 5 do not play basketball and are six feet or taller. Determine the number of people at the party who play basketball and are under six feet tall, |B∩????||B∩U| , where BB represents the set of people at the party who play basketball and ????U represents the set of people at the party who are under six feet tall.
Answer:
8
Step-by-step explanation:
Universal Set, U=37
Number who play basketball, n(B)=25
Number who are under six feet, n(U)=15
Number of those who do not play basketball and are six feet or taller, n(B∪U)'=5
From set theory.
U=n(B)+n(U)-n(B∩U)+n(B∪U)'
37=25+15-n(B∩U)+5
37=45-n(B∩U)
Therefore:
n(B∩U)=45-37=8
Therefore, the number of people at the party who play basketball and are under six feet tall is 8.
The number of people at the party who play basketball and are under six feet tall is 1510. These people belong to both the group of basketball players and the group of people under six feet tall.
Explanation:To answer this question, we first need to understand who are the people at the party who play basketball and are under six feet tall. This group of people belongs to both the basketball players group represented by BB and the group of people under six feet tall, represented by U. We are looking for the intersection of these two groups, represented by |B∩U|.
Out of the 3737 people at the party, 2525 of them play basketball. From these 2525 basketball players, we don't know directly how many are under six feet tall. However, we are told that 1515 people at the party are under six feet tall. We also know that 5 people are over six feet tall and do not play basketball.
Therefore, to find out how many under six feet basketball players there are, we can subtract the 5 people who are over six feet and do not play basketball from the total of the ones who are under six feet: 1515 - 5 = 1510. So, there are 1510 people at the party who play basketball and are under six feet tall.
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Point B has coordinates (5, 1) The x coordinate of point A is 0 . The distance between point A and Point B is 13 units. What are the possible coordinates of point A?
Let y represent the y-coordinate of point A.
We have been given that point B has coordinates (5,1) The x-coordinate of point A is 0. So coordinates of point A would be (0,y)
The distance between point A and Point B is 13 units.
We will use distance formula to solve our given problem.
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let point A [tex](0,y)=(x_2-y_2)[/tex] and point A [tex](5,1)=(x_1,y_1)[/tex].
Upon substituting coordinates of both points in distance formula, we will get:
[tex]13=\sqrt{(0-5)^2+(y-1)^2}[/tex]
[tex]13=\sqrt{25+y^2-2y+1}[/tex]
[tex]13=\sqrt{y^2-2y+26}[/tex]
Let us square both sides as:
[tex]13^2=(\sqrt{y^2-2y+26})^2[/tex]
[tex]169=y^2-2y+26[/tex]
[tex]169-169=y^2-2y+26-169[/tex]
[tex]0=y^2-2y-143[/tex]
[tex]y^2-2y-143=0[/tex]
Upon splitting the middle term, we will get:
[tex]y^2-13y+11y-143=0[/tex]
[tex]y(y-13)+11(y-13)=0[/tex]
[tex](y-13)(y+11)=0[/tex]
Now we will use zero product property.
[tex](y-13)=0, (y+11)=0[/tex]
[tex]y=13, y=-11[/tex]
Therefore, the possible coordinates of point A would be [tex](0,-11)[/tex] and [tex](0,13)[/tex].
Alexia uses two and one-third cups of flour for each batch of cookies she makes. If she makes three-fourths of a batch of cookies, how much flour does she use?
Answer:
She uses 1.7475 cups of flour.
Step-by-step explanation:
This question can be solved using a rule of three.
For each batch of cookies:
Two and one-third cups of flour.
So [tex]2 + \frac{1}{3} = 2.33[/tex] cups.
If she makes three-fourths of a batch of cookies, how much flour does she use?
3/4 = 0.75 batch of cookies. How much flour?
1 batch - 2.33 cups.
0.75 batches - x cups
x = 2.33*0.75
x = 1.7475
She uses 1.7475 cups of flour.
Answer:
1 3/4
Step-by-step explanation:
Can anyone help me with this, I don’t understand what its asking
Answer:
It's asking you to solve the question or find N
Step-by-step explanation:
(Please be clear)
Solve the following cost minimization problems. For each of these find the conditional factor demands and c(w1, w2, y):
(a) f(x1, x2) = x ^1/4 1 x ^1/4 2 , and w1 = 1 and w2 = 2
(b) f(x1, x2) = x ^1/2 1 x ^1/2 2 , and w1 = 2 and w2 = 2
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
4x2 + 8x - 7
is classified as a...
Answer:
Quadratic function (assuming 4x2 is 4x^2)
Step-by-step explanation:
Linear functions are ax+b=y
Quadratic is ax^2+b=y
Cubic is ax^3+b=y
The equation 4x² + 8x - 7 is a Quadratic equation.
What is Quadratic equation?
An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The equation is,
⇒ 4x² + 8x - 7
Now,
Clearly, In the equation;
The highest power of a variable is two.
And, we know that;
In the quadratic equation, the highest power of a equation is two.
Thus, The equation 4x² + 8x - 7 is a Quadratic equation.
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How many minutes have passed between the time shown on the first clock and the time shown on the second clock
If you add a pic maybe I could help but for now I cant
The lifetime of certain type of light bulb is normally distributed with a mean of 1000 hours and a standard deviation of 110 hours. A hardware store manager claims that the new light bulb model has a longer average lifetime. A sample of 10 from the new light bulb model is obtained for a test. Consider a rejection region After testing hypotheses, suppose that a further study establishes that, in fact, the average lifetime of the new lightbulb is 1130 hours. Find the probability of a type II error (round off to second decimal place).
Answer:
There is a probability of P=0.02 of making a Type II error if the true mean is μ=1130.
Step-by-step explanation:
This is an hypothesis test for the lifetime of a certain ype of light bulb.
The population distribution is normal, with mean of 1,000 hours and STD of 110 hours.
The sample size for this test is n=10.
The significance level is assumed to be 0.05.
In this case, when the claim is that the new light bulb model has a longer average lifetime, so this is a right-tailed test.
For a significance level, the critical value (zc) that is bound of the rejection region is:
[tex]P(z>z_c)=0.05[/tex]
This value of zc is zc=1.645.
This value, for a sample with size n=10 is:
[tex]z_c=\dfrac{X_c-\mu}{\sigma/\sqrt{n}}\\\\\\X_c=\mu+\dfrac{z_c\cdort\sigma}{\sqrt{n}}=1000+\dfrac{1.645*110}{\sqrt{10}}=1000+57.22=1057.22[/tex]
That means that if the sample mean (of a sample of size n=10) is bigger than 1057.22, the null hypothesis will be rejected.
The Type II error happens when a false null hypothesis failed to be rejected.
We now know that the true mean of the lifetime is 1130, the probability of not rejecting the null hypothesis (H0: μ=1100) is the probability of getting a sample mean smaller than 1057.22.
The probability of getting a sample smaller than 1057.22 when the true mean is 1130 is:
[tex]z=\dfrac{X-\mu}{\sigma/\sqrt{n}}=\dfrac{1057.22-1130}{110/\sqrt{10}}=\dfrac{-72.78}{34.7851}=-2.0923 \\\\\\P(M<1057.22)=P(z<-2.0923)=0.01821[/tex]
Then, there is a probability of P=0.02 of making a Type II error if the true mean is μ=1130.
Using the normal distribution and the central limit theorem, it is found that there is a 0.0001 = 0.01% probability of a type II error.
In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 1130 hours, hence [tex]\mu = 1130[/tex]Standard deviation of 110 hours, hence [tex]\sigma = 110[/tex]Sample of 10 bulbs, hence [tex]n = 10, s = \frac{110}{\sqrt{10}}[/tex].We test if the average lifetime is longer, and a Type II error is concluding that it is not longer when in fact it is longer, hence, it is the probability of finding a sample mean below 1000 hours, which is the p-value of Z when X = 1000.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{1000 - 1130}{\frac{110}{\sqrt{10}}}[/tex]
[tex]Z = -3.74[/tex]
[tex]Z = -3.74[/tex] has a p-value of 0.0001.
0.0001 = 0.01% probability of a type II error.
A similar problem is given at https://brainly.com/question/15186499
using the method of gauss to find the sum 2 + 4 + 6 + ... + 300
Answer:
22650
Step-by-step explanation:
Mrs. McDonnell is making 25 paper cones to fill
with popcorn for her daughter's birthday party.
4 inches
2
17 inches
Find the volume of one paper cone if the
diameter is 4 inches and the height is 7 inches.
Round your answer to the nearest cubic inch.
29in?
B. 59in3
88in
D. 117in
Answer:
(A)29 cubic inch
Step-by-step explanation:
Diameter of the Cone =4 Inches
Height of the Cone =7 Inches
Volume of a Cone [tex]=\frac{1}{3}\pi r^2h[/tex]
First, we determine the radius, r.
Radius=Diameter/2=4/2=2 Inches
Therefore:
Volume of one paper cone [tex]=\frac{1}{3}\pi *2^2*7[/tex]
=29.32 cubic inch
=29 cubic inch (to the nearest cubic inch.)
A city has a population of 360,000 people. Suppose that each year the population grows by 6.75%. What will the population be after 12 years.
Answer:
So, if it grows by 6.75%, each year the population is 106.75% of the year before.
After 1 year, 370,000(1.0675). After two years, 370,000(1.0675)(1.0675).
370,000(1.0675)12 = your answer
Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Consider the series Summation from n equals 0 to infinityStartFraction (negative 1 )Superscript n Baseline (x plus 1 )Superscript n Over n exclamation mark EndFraction . (a) Find the series' radius and interval of convergence. (b) For what values of x does the series converge absolutely? (c) For what values of x does the series converge conditionally? (a) Find the interval of convergence. nothing ▼ less than less than or equals x ▼ less than or equals less than nothing Find the radius of convergence. Requals nothing (b) For what values of x does the series converge absolutely? nothing ▼ less than less than or equals x ▼ less than less than or equals nothing (c) For what values of x does the series converge conditionally? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The series converges conditionally at xequals nothing. (Use a comma to separate answers as needed.) B. The series does not converge conditionally.
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
150 students in a tenth grade high school class take a survey about which video game consoles they own 60 students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox Out thesethere are who have both systems.
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
150 students in a tenth grade high school class take a survey about which video game consoles they own. 60 students answer that one of their consoles is a Playstation, 50 answer that one of their consoles is an Xbox. Out of these, there are 20 who have both systems.
Let A be the event that a randomly selected student in the class has a Playstation and B be the event that the student has an XBOX. Based on this information, answer the following questions.
a) What is P(A), the probability that a randomly selected student has a Playstation?
b) What is P(B), the probability that a randomly selected student has an XBOX?
c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?
d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?
Answer:
a) P(A) = 2/5
b) P(B) = 1/3
c) P(A and B) = 2/15
d) P(A | B) = 2/5
Step-by-step explanation:
Total no. of students = 150
No. of students having playstation = 60
No. of students having xbox = 50
No. of students who have both playstation and xbox = 20
a) What is P(A), the probability that a randomly selected student has a Playstation?
P(A) = No. of students having playstation/Total no. of students
P(A) = 60/150
P(A) = 2/5
b) What is P(B), the probability that a randomly selected student has an XBOX?
P(B) = No. of students having xbox/Total no. of students
P(B) = 50/150
P(B) = 1/3
c) What is P(A and B), the probability that a randomly selected student has a Playstation and an XBOX?
The probability that a students has a Playstation and an Xbox is given by
P(A and B) = P(A)*P(B)
P(A and B) = (2/5)*(1/3)
P(A and B) = 2/15
d) What is P(A | B), the conditional probability that a randomly selected student has a Playstation given that he or she has an XBOX?
The conditional probability is given by
P(A | B) = P(A and B)/P(B)
P(A | B) = (2/15)/(1/3)
P(A | B) = 2/5
Alternatively:
P(A | B) = P(A∩B)/P(B)
Where P(A∩B) is given by
P(A∩B) = No. of students who have both playstation and xbox/Total no. of students
P(A∩B) = 20/150
P(A∩B) = 2/15
P(A | B) = P(A∩B)/P(B)
P(A | B) = (2/15)/(1/3)
P(A | B) = 2/5
Find the unit vector in the direction of v=(7,-3).
(enter exact answers with square roots)
Answer:
[tex]\binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} }[/tex]
Step-by-step explanation:
First, find the magnitude of the vector:
[tex] |v| = \sqrt{( {(7)}^{2} + {( - 3)}^{2}) } \\ = \sqrt{(49 + 9)} \\ = \sqrt{58} [/tex]
Then, divide each component of the vector by the magnitude to get the unit vector and rationalise:
[tex]unit \: vector = \binom{ \frac{7}{ \sqrt{58} } }{ \frac{ - 3}{ \sqrt{58} } } \\ = \binom{ \frac{7 \sqrt{58} }{58} }{ \frac{ - 3 \sqrt{58} }{58} } [/tex]
k(t) = 10t - 19
K(-7) =
Answer:k(-7)=-89
Step-by-step explanation:
since k(t)=10t - 19
K(-7)=10(-7)-19
k(-7)=-70-19
k(-7)=-89