Answer:
We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.
Step-by-step explanation:
We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.
You select a sample of 100 light bulbs and find mean bulb life is 490 hours.
Let [tex]\mu[/tex] = population mean light bulb life.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 500 hours {means that the population mean light bulb life is at least 500 hours}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 500 hours {means that the population mean light bulb life is below 500 hours}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean bulb life = 490 hours
σ = population standard deviation = 50 hours
n = sample of light bulbs = 100
So, the test statistics = [tex]\frac{490-500}{\frac{50}{\sqrt{100} } }[/tex]
= -2
The value of z test statistics is -2.
Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.
Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the population mean light bulb life is at least 500 hours.
i need help plz answer correctly thanks
Answer:
67
Not exactly sure on how to write it in though
Step-by-step explanation:
PLZZ HELP!
Given the function f(x)=2(x-1)^2+3
a)What is the vertex?
b)What is the axis of symmetry?
Answer:
a) (1,3)
b) x=1
Step-by-step explanation:
The general form of a parabola in vertex form is f(x)=a(x-h)^2+k, where h is the x coordinate of the vertex, and k is the y coordinate, while a indicates how "squished" the graph is, or how quickly it grows in relation to the parent graph. In this case, h is shown to be 1, and k is 3, meaning that the vertex is at (1,3). The axis of symmetry , for a vertical parabola, just runs vertically through the vertex, meaning that in this case it is at x=1. Hope this helps!
Answer:
(1,3) and y-axis
Step-by-step explanation:
The vertex is the value of x at maximum or minimum point
At maximum point
dy/ dx = 0;
dy/dx = 4(x-1)= 0
=>x= 1 and is the vertex
Y when x = 1; we substitute x=1 in the original equation.
f(x) =y =2(x-1)^2+3
y = 2(1-1)^2 +3
y = 0 + 3= 3
The vertex is (1,3)
2.
A symmetrical equation is given by
b^2 = 4ac
Looking at the equation above x has an order of 2 meaning a possibility of cutting the x axis on two values of x
Hence the axis of symmetry is the y-axis
Assuming this was the expression; the axis of rotation would have been the x-axis.
f(y)=2(y-1)^2+3
Calculate area of triangle
Answer:
99cm²
Step-by-step explanation:
Area of a Triangle: [tex]A=\frac{1}{2} bh[/tex]
B- base
H- height
We are given a base of 18 cm and a height of 11cm.
[tex]A=\frac{1}{2} 18*11\\\\A=\frac{1}{2} 198\\\\\boxed{A=99}[/tex]
The area of the triangle should be 99cm².
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.
Answer: A
I just love your questions. You always put "No guessing" haha.
Step-by-step explanation:
[tex]f(x)=3^x+10x\\g(x)=2x-4[/tex]
[tex](f+g)(x)=[/tex]
This basically means you have to take both functions and add them together.
[tex](f+g)(x)=(3^x+10x)+(2x-4)\\(f+g)(x)=3^x+10x+2x-4\\[/tex]
Combine like terms;
[tex](f+g)(x)=3^x+12x-4[/tex]
obteber dos números tales que la suma de uno de ellos con el doble del cuadrado del otro sea igual a 7776 , y el producto de ambos sea máximo
Answer: the numbers are 5,111.3 and 35.74
Step-by-step explanation:
I will answer this in English.
We have the numbers X and Y, ad we have that:
X + 2*Y^2 = 7776
X = 7776 - 2*Y^2
Now we also want that the product of X and Y is a maximum.
The equation of maximum product is
P(Y) = X*Y = (7776 - 2*Y^2)*Y
= 7776*Y - 2*Y^3
Now, to find the maximum we must derivate and find the value where P'(Y) is equal to 0
P'(Y) = 7776 - 6*Y^2 = 0
7776 = 6*Y^2
Y = √(7776/6) = 35.74
Now, we replace this value in the equation for X and we can find X:
X = 7776 - 2*Y^2 = X = 7776 - 2*(35.74)^2 = 5,111.3
The surface area of a figure is 62cm^2 if the dimensions are multiplied by 5
The surface area of the new figure is,
⇒ 1550 cm²
What is mean by Multiplication?Multiplication means to add number to itself a particular number of times. Multiply will be viewed as a process of repeated addition.
Given that;
The surface area of a figure is 62cm².
And, the dimensions are multiplied by 5.
Here, The surface area of a figure is 62cm².
After multiply by 5, surface area of the new figure is,
⇒ 5² × 65
⇒ 25 × 65
⇒ 1550
Thus, The surface area of the new figure is,
⇒ 1550 cm²
Learn more about multiplication visit:
https://brainly.com/question/1135170
#SPJ6
A bag contains 26 tiles letters a through z find the probability of drawing two vowels with replacement find the probability of drawing two vowels without replacement round the answers to the nearest thousandths which event is independent which event is dependent
Answer:
With replacement, 0.037, independent
Without replacement, 0.031, dependent
Step-by-step explanation:
There are 5 vowels (not including y).
The probability the first letter is a vowel is 5/26.
With replacement, the probability the second letter is a vowel is also 5/26.
The total probability is (5/26) (5/26) = 0.037.
Since the first letter is replaced, the probability of the second letter is not affected, so the events are independent.
Without replacement, the probability the second letter is a vowel is 4/25.
The total probability is (5/26) (4/25) = 0.031.
Since the first letter is not replaced, the probability of the second letter is affected, so the events are dependent.
I need help on this
Answer:
a = 250 ; b = 10
Step-by-step explanation:
a = 5 × 10² / 2
a = 5 × 100 / 2
a = 500 / 2
a = 250
b = 2 × 10² (10-5) / 10×10
b = 2 × 100 × 5 / 100
b = 1000 / 100
b = 10
Given function f(x)=x^2+5, determine the value of f(f(5))
Answer:
905
Step-by-step explanation:
So your original equation is f(x) = x² + 5
First lets work with the stuff inside the parentheses.
f(5) = 5² + 5 = 30
So now you are finding,
f(f(5)) => f(30)
f(30) = 30² + 5 = 900 + 5 = 905
A sphere has a diameter of 18 inches. What is the volume of this sphere? Use ≈ 3.14 and round your answer to the nearest tenth.
A. 24,429.0 cubic inches
B. 2290.2 cubic inches
C 7776.0 cubic inches
D 3053.6 cubic inches
Answer:
[tex] = 3053.6[/tex]
Answer D is correct
Step-by-step explanation:
[tex]v = \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \times \pi \times {9}^{3} \\
≈3053.62806 [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
The right answer is of option D
Look at the attached picture
hope it will help you
Good luck on your assignment
Whats the geometric sequence for 5,20,80,320
The area of a parrellogram is 31.5ft and height is 6.3ft. What is the length of the base
Answer:
Area = base × height
31.5 = base × 6.3
base = 5 ft
Answer:
5 feet
Step-by-step explanation:
The area formula is A = b * h, where A is the area, b is the length of the base, and h is the height. Since we want to know the length of the base, we are solving for b. Thankfully, we know that A = 31.5 and h = 6.3. When we plug them into the equation, we get 31.5 = b * 6.3. Because we want b on one side without any coefficients and numbers on the other side, we can divide the equation by 6.3 on both sides. The equation will remain the same because we are doing the same thing to both sides. When we divide, we get b = 31.5 / 6.3 = 5 feet. Hope this helps!
What is the midpoint of a line segment with endpoints (-2, 6) and (4, 3) in the
standard (x, y) coordinate plane?
Answer:
(1, 9/2) or (1, 4.5)
Step-by-step explanation:
To find the midpoint, take the x1 and x2 values and divide it by 2, same for the y values.
(4-2)/2 and (6 + 3)/2
1 and 4.5
(1, 4.5)
Marci has taken out a loan of $5,000 for a term of 24 months (2 years) at an interest rate of 8.5%. Use the amortization table provided to complete the statement.
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77 $30.88 $23.95 $19.80
7.5% $86.76 $45.00 $31.11 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
Marci’s monthly payment will be $------, and her total finance charge over the course of the loan will be $------- .
Answer:
Correct answers are Marci's monthly payment: $227.30, and total finance charge: $455.20.
Step-by-step explanation:
24 months (2 years)
$45.46 x 5 = $227.30
$227.30 x 24 = $5,455.20
$5,455.20 - $5,000 = $455.20
What is the TOTAL surface area?
Answer:
SA=571.77
Step-by-step explanation:
SA==2πrh+2πr2=2·π·7·6+2·π·72≈571.76986
pls mark brainliest
What is the first step to simplify the expression 5(8x-4)+12
Answer:
8 • (5x - 1)
Step-by-step explanation:
Step 1 : See below
Step 2 : See below
Pulling out like terms/ factors
8x - 4 = 4 • (2x - 1)
Equation at the end of step 2 :
20 • (2x - 1) + 12
Step 3 : See below
Step 4 : See below
Pull out like factors:
40x - 8 = 8 • (5x - 1)
Answer: 8 • (5x - 1)
Hope this helps.
Add the following weights:
6 lb 10 oz
+ 10 oz
lb
OZ
Answer:
7 lbs 4 oz
Step-by-step explanation:
6 lb 10 oz
+ 10 oz
---------------------
6 lbs 20 oz
But we know that there are 16 oz in 1 lb
So subtract 16 oz and add 1 lb
6 lbs 20 oz
+1 lb - 16 oz
--------------------------
7 lbs 4 oz
different animals have different fields of view. humans can generally see a 180° arc in front of them. horses can see 215° arc. dogs can see a 240° arc. a dog, horse, and rider are in heavy fog , so they can see only 25 yards in any direction. what is the area of the riders field of view?
Answer:
The area of the riders field of view is 987.5 square yards.
Step-by-step explanation:
The human has a 180° arc view. If the rider can see only 25 yards, the area of the riders field of view is a semi-circle (180° arc) of 25 yards of radius.
The semi-circle of 25 yards of radius has an area of:
[tex]S=\dfrac{1}{2}\pi r^2=\dfrac{1}{2}\cdot3.16\cdot (25)^2=\dfrac{1}{2}\cdot3.16\cdot625=987.5[/tex]
The area of the riders field of view is 987.5 square yards.
(5k+35) -8=12 need help solving this
Answer:
k= -6.48 approx
Step-by-step explanation:
(5k+35) -8=12
opening bracket
-45k-280=12
-45k=12+280
-45k=292
k=-6.48 approx
Answer:
Step-by-step explanation:
I don't say you have to mark my ans as brainliest but if you think it has really helped you plz don't forget to thank me...
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. 1) The appropriate hypotheses to determine if the manufacturer's claim appears reasonable are H subscript 0 colon________ and H subscript 1 colon________. (2 points) 2) For a test with a level of significance of 0.05, the critical value would be ________. (2 point) 3) The value of the test statistic is ________. (4 points) 4) Is there evidence that a compact microwave oven consumes a mean of no more than 250 W? (2 points)
Answer:
We conclude that a compact microwave oven consumes a mean of more than 250 W.
Step-by-step explanation:
We are given that an appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W with a population standard deviation of 15 W.
They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W.
Let [tex]\mu[/tex] = mean power consumption for microwave ovens.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\leq[/tex] 250 W {means that a compact microwave oven consumes a mean of no more than 250 W}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 250 W {means that a compact microwave oven consumes a mean of more than 250 W}
The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean power consumption for ovens = 257.3 W
σ = population standard deviation = 15 W
n = sample of microwave ovens = 20
So, the test statistics = [tex]\frac{257.3-250}{\frac{15}{\sqrt{20} } }[/tex]
= 2.176
The value of z test statistics is 2.176.
Now, at 0.05 significance level the z table gives critical value of 1.645 for right-tailed test.
Since our test statistic is more than the critical value of t as 2.176 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that a compact microwave oven consumes a mean of more than 250 W.
Test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. Assume all requirements are met. Use the critical value method of testing hypotheses.
Before 74 83 75 88 84 63 93 84 91 77
After 73 77 70 77 74 67 95 83 84 75
A. State the null hypothesis (H_0) and the alternate (H_1).
B. What is the test statistic and the critical value(s.
C. Find the confidence interval values.
D. Interpret the information and state what can you say about the claim?
Answer:
Step-by-step explanation:
The hypotheses are:
Null Hypothesis
[tex]H_0 : \muafter = 0[/tex]
Alternative Hypothesis
[tex]Ha: \mu\neq 0[/tex]
Since the t-statistic score is greater than the critical t-score, so the decision is to reject the null hypothesis.
See image for detailed solution
Answer:
Step-by-step explanation:
Corresponding test scores of students before and after they completed a formal logic course.
The data for the test are the differences between the test scores.
μd = the score before minus score after
Score before score after diff
74 73 1
83 77 6
75 70 5
88 77 11
84 74 10
63 67 - 4
93 95 - 2
84 83 1
91 84 7
77 75 2
Sample mean, xd
= (1 + 6 + 5 + 11 + 10 - 4 - 2 + 1 + 7 + 2)/10 = 3.7
xd = 3.7
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (1 - 3.7)^2 + (6 - 3.7)^2 + (5 - 3.7)^2+ (11 - 3.7)^2 + (10 - 3.7)^2 + (- 4 - 3.7)^2 + (-2 - 3.7)^2 + (1 - 3.7)^2 + (7 - 3.7)^2 + (2 - 3.7)^2 = 220.1
Standard deviation = √(220.1/10
sd = 4.69
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (3.7 - 0)/(4.69/√10)
t = 2.49
The test is a left tailed test. From the t distribution table, the t score corresponding to the significance level is 2.262
In order to reject the null hypothesis, the test statistic must be smaller than - 2.262 or greater than 2.262
Since - 2.49 < - 2.262 and 2.49 > 2.262, we would reject the null hypothesis.
Therefore, at 5% significance level, we can conclude that for the test scores before and after, the mean difference is lesser than zero
There are 80 sixth graders, 90 7th graders, and 70 8th graders at your school. Every student gets entered in a raffle. What is the probability that a 7th grade student will win the raffle?
Answer:
P(seventh grade winner) = 3/8
Step-by-step explanation:
cuantos metros de encaje se necesita para el borde del un mantel circular que tiene 50 cm de radio
Answer:
157 cm
Step-by-step explanation:
El valor que se necesita para el borde del mantel es equivalente al perímetro del mantel.
Para un circulo de 50 cm de radio, el perímetro es:
[tex]P=\pi r=3.14\cdot 50=157[/tex]
Se necesitan 157 cm de encaje.
The value needed for the edge of the tablecloth is equivalent to the perimeter of the tablecloth.
For a circle with a radius of 50 cm, the perimeter is:
[tex]P=\pi r=3.14\cdot 50=157[/tex]
157 cm of lace are required.
The graph for the equation y = 2 x + 4
On a coordinate plane, a line goes through (negative 2, 0) and (0, 4).
If another equation is graphed so that the system has one solution, which equation could that be?
A) y = 2 x minus 4
B) y = 2 (x + 2)
C) y = 2 (x minus 4)
D) y = x + 4
Answer:
a
Step-by-step explanation:
help me please and thank you
Answer:
m<10 = 92°
m<5 = 106° (I think because of correspondence)
m<8 =92°
m<14 = 74°
m<3 = 106°
<1 and <4 are corresponding angles
<2 and <3 are same side interior angles
<3 and <4 are vertical angles
<4 a d <6 are Alt. Interior Angles
What’s the correct answer for this question?
Answer:
C
Step-by-step explanation:
In the attached file
Mixed numbers from 2 to 5 with An interval of 1/4 between each pair of Mixed numbers
Answer:
2 1/4 ,2 1/2, 2 3/4, 3 1/4 ,3 1/2, 3 3/4, 4 1/4 , 4 1/2, 4 3/4
Step-by-step explanation:
These are the mixed numbers.
If you have time in the day please help me
Answer:
i think its B
Step-by-step explanation:
i think itd most accurate t b
HELP FAST PLEASE BRAINLIEST FOR ANSWER
Answer:
Arc = 20 / 3°
Step-by-step explanation:
Say the angle is = x
The sector = πr^2 / x
Sector = 100π / x
15π = 100π / x
15πx = 100π
x = 20 / 3
Arc is = to the central angle
Medical researchers conducted a national random sample of the body mass index (BMI) of 654 women aged 20 to 29 in the U.S. The distribution of BMI is known to be right skewed. In this sample the mean BMI is 26.8 with a standard deviation of 7.42. Are researchers able to conclude that the mean BMI in the U.S. is less than 27? Conduct a hypothesis test at the 5% level of significance using StatCrunch (directions) or calculating T and using the T-Distribution Calculator above. Based on your hypothesis test, what can we conclude?
Answer:
Check the explanation
Step-by-step explanation:
The distribution is right skewed but the sample size is large so we can use t - test here. The statistical software output for this problem is:
One sample T hypothesis test:
μ : Mean of population
[tex]H_0[/tex] : μ = 27
[tex]H_A[/tex] : μ < 27
Hypothesis test results:
Mean Sample Mean Std. Err. DF T-Stat P-value
μ 26.8 0.29014496 653 -0.68931061 0.2454
Since p - value > 0.05, do not reject .
Hence,
With a mean BMI of 26.8, the data supports the claim that the average BMI is less than 27, but the difference is not statistically significant. We fail to reject the null hypothesis that the mean BMI for women aged 20 to 29 in U.S. is 27.