Answer:
a)
The null hypothesis is [tex]H_0: \mu \leq 10[/tex]
The alternative hypothesis is [tex]H_1: \mu > 10[/tex]
b-1) The value of the test statistic is t = 1.86.
b-2) The p-value is of 0.0348.
Step-by-step explanation:
Question a:
Test if the battery life is more than twice of 5 hours:
Twice of 5 hours = 5*2 = 10 hours.
At the null hypothesis, we test if the battery life is of 10 hours or less, than is:
[tex]H_0: \mu \leq 10[/tex]
At the alternative hypothesis, we test if the battery life is of more than 10 hours, that is:
[tex]H_1: \mu > 10[/tex]
b-1. Calculate the value of the test statistic.
The test statistic is:
We have the standard deviation for the sample, so the t-distribution is used to solve this question
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.
10 is tested at the null hypothesis:
This means that [tex]\mu = 10[/tex]
In order to test the claim, a researcher samples 45 units of the new phone and finds that the sample battery life averages 10.5 hours with a sample standard deviation of 1.8 hours.
This means that [tex]n = 45, X = 10.5, s = 1.8[/tex]
Then
[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{10.5 - 10}{\frac{1.8}{\sqrt{45}}}[/tex]
[tex]t = 1.86[/tex]
The value of the test statistic is t = 1.86.
b-2. Find the p-value.
Testing if the mean is more than a value, so a right-tailed test.
Sample of 45, so 45 - 1 = 44 degrees of freedom.
Test statistic t = 1.86.
Using a t-distribution calculator, the p-value is of 0.0348.
What is the scale factor of AXYZ to AUVW?
Yes
Answer:
C
Step-by-step explanation:
60÷6=10, 90÷9=9, 75÷7.5=10, It divided by 10 so it's 1/10
The scale factor of dilation of the triangle is k = 1/10
What is Dilation?Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent
The result of dilation is that the shapes and boundaries of objects in the input image are expanded or thickened. It is often used in conjunction with other morphological operations such as erosion, opening, and closing to manipulate and enhance images.
Given data ,
Let the first triangle be ΔXYZ
Let the second triangle be ΔUVW
Now , the measure of sides of ΔXYZ = { 60 , 75 , 90 }
And , the measure of sides of ΔUVW = { 6 , 7.5 , 9 }
So , the scale factor of dilation is given by k
where k = measure of side ΔUVW / measure of side ΔXYZ
k = 6 / 60
k = 1/10
Hence , the dilation factor is k = 1/10
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Suppose a jar contains 8 red marbles and 25 blue marbles. If you reach in the jar and pull out 2 marbles at random, find the probability that both are red.
Answer: [tex]\dfrac{7}{132}[/tex]
Step-by-step explanation:
Total marbles in the jar = 8+25 = 33
Using combinations, the number of ways of choosing two marbles out of 33= [tex]\dfrac{33!}{2!(33-2)!}\\\\=\dfrac{33!}{2\times31!}\\\\=\dfrac{33\times32}{2}=528[/tex] (total outcomes)
Similarly, the number of ways of choosing two red marbles =
[tex]\dfrac{8!}{2!6!}\\\\=\dfrac{8\times7}{2}=28[/tex](favorable outcomes)
Required probability = [tex]\dfrac{\text{favorable outcomes}}{\text{total outcomes}}[/tex]
[tex]=\dfrac{28}{528}\\\\=\dfrac{7}{132}[/tex]
hence, required probability = [tex]\dfrac{7}{132}[/tex]
6. Roll a pair of dice. What is the probability that a total of 12 will be face up?
Answer:
The Probability would be 2.78%
Step-by-step explanation: Hope this helps :)
Solve each equation by graphing. Round to the nearest tenth.
X^2-6x= -8
A) 4, 2
B) −4, 2
C) −2, 4
D) −2, −4
Answer:
A
Step-by-step explanation:
That is the procedure above
A Little League baseball coach wants to know if his team is representative of other teams in scoring runs. Nationally, the average number of runs scored by a Little League team in a game is 5.7. He chooses five games at random and finds the mean number of runs scored is 7.4 with a sample standard deviation of 2.88.
Required:
Is it likely that his team's scores is different than the national average?
Answer:
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
Step-by-step explanation:
The National average number of runs scored by a LL team is
μ = 5.7
Sample Information:
size sample n = 5
sample average x = 7.4
sample standard deviation s = 2.88
Is required to investigate if that sample average is statistically different from the National average
We will do a test with 95 % of confidence Interval that means
significance level α = 5 % or α = 0.05.
The sample size is 5 then even when we assume normal distribution the sample size indicates that we need to use t-student distribution. Furthermore, as the question is if the sample average is different from the national the test will be a two-tail test.
Then α = 0.05 α/2 = 0.025
df = n - 1 df = 5 - 1 df = 4
Then from t-student table we get t(c) = 2.132
Hypothesis test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x ≠ μ
To calculate t (s)
t(s) = ( x - μ ) / s/√n
t(s) = ( 7.4 - 5.7 )* 2.24 / 2.88
t(s) = 1.7* 2.24 / 2.88
t(s) = 1.32
Comparing t(s) and t(c)
1.32 < 2.132
That result implies that t(s) is in the acceptance region for H₀ then we accept H₀, there is not statistics difference between the LL team and the national average
What is the volume of a sphere with a radius of 20 m? 10,666.67π m3 6,000π m3 85,333.33π m3 533.33π m3
Answer:10,666,66 [tex]\pi[/tex]m^3
Step-by-step explanation:
V=[tex]\frac{4}{3} \pi r^{3}[/tex]
[tex]\frac{4}{3} \pi 20^{3} \\ V=10,666.66 \pi[/tex]
The Madison Cosmetics Company has developed a new women's facial cleanser that they believe is superior to those currently on the market in the $5 - $10 range. They wish to test the cleanser against the two current best-sellers.
A. Identify a potential problem with using a completely randomized experimental design to test the cleanser. Explain.
B. The company executives decide to design and carry out a block design experiment to test the new cleanser against its competition. Choose an appropriate blocking scheme for the experiment and justify your choice.
C. Should the company put a control group into the experiment? Why or why not?
D. Could the experiment be a double-blind experiment? Explain.
Answer:
a. there could be a problem of high error
b. randomized block design can remove the issue of heterogeneity
c. yes they should
d, yes it could
Step-by-step explanation:
a. if their is a lack of homogeneity among the sample population, then the results that would be obtained are going to be with increased experimental error.
b. given the number of treatment, the randomized block design technique can be done. This would then remove the issue of heterogeneity. It also gives more information and the results from the test are easier. Even in the presence of missing data, the missing plot technique can be employed.
c. when a control group is used, it makes easier the examination of the market research in a more effective way.
d. Yes it could be a double blind one. This would help to take away the problem of bias.
(x-7)(x^2+3x-3) multiply the polynomials
Step-by-step explanation:
= (x - 7)(x² + 3x - 3)
= x³ - 7x² + 3x² - 21x - 3x + 21
= x³ - 4x² - 24x + 21
Estimate and classify the critical points for the graph of the function.
Answer:
Critical point is at (-1, 2) because it is the point where the slope is approximately zero.
Step-by-step explanation:
A critical point in a graph like this is simply the point where the slope is zero or undefined.
Looking at the graph given, the point at which the graph slope is zero is around the coordinate (-1, 2).
So we estimate that to be the critical point.
According to records, the amount of precipitation in a certain city on a November day has a mean of inches, with a standard deviation of inches. What is the probability that the mean daily precipitation will be inches or less for a random sample of November days (taken over many years)
Answer:
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Mean [tex]\mu[/tex], standard deviation [tex]\sigma[/tex]
n days:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
Applying the Central Limit Theorem to the z-score formula.
[tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
What is the probability that the mean daily precipitation will be of X inches or less for a random sample of November days?
The probability that the mean daily precipitation will be of X inches or less for a random sample of n November days is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is mean amount of inches of rain and [tex]\sigma[/tex] is the standard deviation.
For f(x) = 4x + 2 and g(x) = x^2 - 6, find (f+g)(x)
Answer:
[tex](f+g)(x) = x^2 + 4x - 4[/tex]
Step-by-step explanation:
We are given these following functions:
[tex]f(x) = 4x + 2[/tex]
[tex]g(x) = x^2 - 6[/tex]
(f+g)(x)
We add the common terms. Thus:
[tex](f+g)(x) = f(x) + g(x) = 4x + 2 + x^2 - 6 = x^2 + 4x + 2 - 6 = x^2 + 4x - 4[/tex]
Thus:
[tex](f+g)(x) = x^2 + 4x - 4[/tex]
Can someone help me with this question please.
Answer:
40
Step-by-step explanation:
As the lawn size increases by 4 the weight increases by 8
HELP!! I don’t know part C or D and I need to know if part A and B are correct
Answer:
Step-by-step explanation:
A and B are correct!
For part C, just multiply the dimensions given to you by four.
For part D, the answer would be 4 x 4 x 4 which is 264
There are 14 books on a shelf. 9 of these books are new. The rest of them are used. (GIVING POINTS AND BRAINLEST TO BEST ANSWER) what is the ratio?
Answer:
A: 9:5 B: 5:14
Step-by-step explanation:
ASSESSMENT:
Act as the person in the problem Do the activity. Record your
findings then answer
1. A farmer placed 250 mangoes in a crate, these are 150 ripe and 100 unripe
mangoes, his wife randomly selected 80 mangoes, she got 50 ripe mangoes
and 20 unripe mangoes, find the experimental probability of the mangoes she
selected.
2. A table tennis player has 40 orange table tennis balls, 30 white and 20 yellow
table tennis balls. After selecting 18 balls, he found out that he got 6 white
table tennis balls. Find out the experimental probability of getting white table
tennis table tennis balls.
please answer this
Answer:
in 1st his wife selected 80 mangoes 50 ripe and 20 unripe how it can be
Step-by-step explanation:
50+20=70 not 80
please share the correct question than I may help you
There are 3 urns A, B and C each containing a total of 10 marbles of which 2, 7 and 4 respectively are red. One of the urns is selected randomly and a marble is drawn from the selected urn. It is found that the marble is red. What is the probability that the red marble is taken from urn B
======================================================
Explanation:
We know that the marble selected is red, so we don't need to focus on the other colors.
7 red marbles are in urn B out of 2+7+4 = 13 total red marbles.
The probability the red marble came from urn B is therefore 7/13
Find the length of side x
Answer:
Step-by-step explanation:
tan(30) = x/1
sqrt(3) / 3 = x/1
x= sqrt(3) / 2
A graph is shown below:
A graph is shown. The values on the x axis are 0, 4, 8, 12, 16, and 20. The values on the y axis are 0, 16, 32, 48, 64, and 80. Points are shown on ordered pairs 0, 64 and 4, 48 and 8, 32 and 12, 16 and 16, 0. These points are connected by a line.
What is the equation of the line in slope-intercept form?
Answer:
b
Step-by-step explanation:
The equation of the line in slope-intercept form is y= 4x+0
What is slope intercept?The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
slope m,
= y2-y1/x2-x1
= 16-0/4-0
=16/4
=4
m=4
So, the equation will be , y= 4x+0
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The quadratic function y = -x2 + 10x - 8 models the height of a trestle on a bridge. The x-axis represents ground level.
To find where the section of the bridge meets ground level, solve 0 = -x2 + 10x - 8.
Where does this section of the bridge meet ground level?
Answer: 0.876, 9.123
Step-by-step explanation:
The function is [tex]y=-x^2+10-8[/tex]
It meets the ground level when [tex]y[/tex] is 0
[tex]\Rightarrow -x^2+10x-8=0\\\Rightarrow x^2-10x+8=0\\\\\Rightarrow x=\dfrac{10\pm \sqrt{(-10)^2-4(1)(8)}}{2}\\\\\Rightarrow x=\dfrac{10\pm \sqrt{68}}{2}\\\\\Rightarrow x=5\pm \sqrt{17}\\\Rightarrow x=0.876,\ 9.123[/tex]
Thus, it touches the ground at two points given above
If the distance from D to D' is 10 and the distance from A to D is 2 what is the scale factor?
Answer:
5
Step-by-step explanation:
10/2=5
The scale factor of the given case that the distance from D to D' is 10 and the distance from A to D is 2 will be 5.
What is the scale factor?
The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics.
The scale factor is the ratio between two big and small figures and the ratio is called a scale for the given geometry.
For example, if we have a triangle with a side of 10 meters and another triangle with a side of 5 then the scale ratio will be 10/5 = 2.
Given that
distance from D to D' is 10
distance from A to D is 2
So the scale ratio will be
DD'/AD = 10/2 = 5 hence scale ratio will be 5 for the given
geometry.
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How to solve and answer
Answer:
The corrects answers are: C, D, E, F
Step-by-step explanation:
3x-1= 7x+5
A: -0.6 C: 1.5
B: -1.5 D: 0.6
Answer:
x = -1.5
Step-by-step explanation:
3x-1= 7x+5
Subtract 3x from each side
3x-3x-1= 7x-3x+5
-1 = 4x+5
Subtract 5 from each side
-1-5 = 4x+5-5
-6 = 4x
Divide by 4
-6/4 = 4x/4
-3/2 =x
x = -1.5
Q2 find the degree of the polynomial
x4(4x+1)
Step-by-step explanation:
x⁴(4x+1)
4x⁵+x⁴
degree is 5
If the length of a rectangle is four times its width and the perimeter of the rectangle is 90 yd, whats its area?
Answer:
324 yds ^2
Step-by-step explanation:
If length=l and width=w, you could write an equation to find the length and width. Then use that to find the area. L=4w. There are two of each side in the rectangle. 4w+4w+w+w=10w. 10w=90. w=9. 4w=36. L=36. 36*9=324yds^2
...................
thnx If solved....XD
$4825.70
Step-by-step explanation:
Cost for Fans: 4 x 675 = $2700
Cost for Lamps: 2 x 110 = $220
Cost for Switches: 5 x 41 = $205
Cost for Tubes: 6 x 135 = $810
Cost for Electric Wire: 230 x 2.50 = $575
Total cost: 2700 + 220 + 205 + 810 + 575 = $4510
Tax: Total cost x Tax rate = 4510 x 0.07 = $315.70
Total paid: Total cost + Tax = 4510 + 315.70 = $4825.70
helppp thxxxxxxxxxxx
Answer:
YES
Step-by-step explanation:
Yes, because the golden ratio has the value of 1.61803398875
The ratio 8.8:5.5 = 1.6.
They are very close, so yes.
Factor completely 3x2 + 9x − 3.
3(x2 + 3)
3(x2 + 3x − 1)
3x(x2 + 3x − 1)
Prime
Yam
190
Groundnuts
90
Vegetables
30. What is the ratio of the land used
for groundnuts to the land for
vegetables
Answer:
3:1
Step-by-step explanation:
90:30 simplified is 3:1
At midday the temperature in Moscow was 7°C.
At midnight it was -3°C.
By how many degrees did the temperature fall?
Answer:
10 degrees C
Step-by-step explanation:
the difference between both temperatures is expressed by a subtraction
7 - -3 = 7 + 3 = 10
you could also do the subtraction the other way around :
-3 - 7 = -10
but the negative sign has no meaning for a distance between two points (a distance itself has no direction).
so, we are always using the absolute value of such difference calculations (when it is about lengths, distances, and so on, where the direction had no meaning).
and so, also the -10 is actually simply 10 for our problem here.
the temperature fell by 10 degrees.
Helpppp please ASAP
Answer:
(13, -3).
Step-by-step explanation:
Expression representing transformation has been given as,
[tex]r_{y-z}oT_{4,-5}[/tex]
First apply the rule → [tex]T_{4,-5}[/tex]
Translation of the point by 4 units along the x-axis and 5 units downwards along the y-axis,
(x, y) → (x + 4, y - 5)
(-1, -8) → (-1 + 4, -8 - 5)
→ (3, -13)
Now apply the rule of reflection over the line y = -x to the image point (3, -13),
(x, y) → (-y, -x)
(3, -13) → (13, -3)
Therefore, answer will be (13, -3).
