Answer:
We conclude that the average sodium content in all Jupiter Bars is actually more than 96 milligrams.
Step-by-step explanation:
We are given that there is a concern that the average sodium content in all Jupiter Bars is actually more than 96 milligrams, and we have been asked to investigate.
Summary statistics:
n = 20
sample mean = 100.55
sample standard deviation = 6.304
Q = 97: median = 101: Q3 = 104
Let [tex]\mu[/tex] = average sodium content in all Jupiter Bars.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 96 milligrams {means that the average sodium content in all Jupiter Bars is equal to 96 milligrams}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > 96 milligrams {means that the average sodium content in all Jupiter Bars is actually more than 96 milligrams}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean sodium content = 100.55
s = sample standard deviation = 6.304
n = sample of Jupiter bars = 20
So, the test statistics = [tex]\frac{100.55-96}{\frac{6.304}{\sqrt{20} } }[/tex] ~ [tex]t_1_9[/tex]
= 3.228
The value of t test statistics is 3.228.
Now, at 5% significance level the t table gives critical value of 1.729 at 19 degree of freedom for right-tailed test.
Since our test statistic is more than the critical value of t as 3.228 > 1.729, 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 the average sodium content in all Jupiter Bars is actually more than 96 milligrams.
K.Brew sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 18 sales receipts for mail-order sales results in a mean sale amount of $74.90 with a standard deviation of $21.75. A random sample of 9 sales receipts for internet sales results in a mean sale amount of $87.30 with a standard deviation of $19.75. Using this data, find the 95% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 95% confidence interval. Round your answers to two decimal places.
Answer:
Step-by-step explanation:
Step 1. The point estimate is the difference between the the mean amount of mail-order purchases and the mean amount of internet purchases. It becomes
74.9 - 87.3 = - 12.4
Step 2. The formula for determining margin of error is expressed aa
Margin of error = z√(s1²/n1 + s2²/n2)
Where
z = z score
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
n1 = number of samples in group 1
n2 = number of samples in group 2
For a 95% confidence interval, the z score is 1.96
From the information given,
s1 = 21.75
n1 = 18
s2 = 19.75
n2 = 9
z√(s1²/n1 + s2²/n2) = 1.96√(21.75²/18 + 19.75²/9) = 1.96 × 8.343
= 16.35
Step 3. Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
95% Confidence interval = - 12.4 ± 16.35
Rewrite the expression 5(2x+1) using the Distributive Property
Answer:
10x+5
Step-by-step explanation:
5(2x+1)
Using distributive property, which is
A(B+C)=(A×B)+(A×C)
=(5×2x)+(5×1)
=10x+5
Hope it helps :)
A rectangular storage container is 15 feet long 12 feet wide and 8 feet high what is the surface area of the storage container
Answer:
1440 feet
Step-by-step explanation:
15 × 12 × 8 = 1440
Complete the 3 questions for 10 points.
Answer:
Look below.
Sorry if the graph's aren't good.
Step-by-step explanation:
13) I'll attach a pic of my graphs:
Slope intercept form is y = mx + b
y = 2x + 1
m = 2
b = 1
14) y = 3/ 5x - 5
m = 3/5
b = -5
15) y = 1/4x - 8
m = 1/4
b = -8
In triangle DOC, cos(D) = 20/29. What is the value of tan(D)?
Answer:
[tex]tan(D) = \frac{21}{20}[/tex]
Step-by-step explanation:
Step(i):-
Given in triangle DOC
Cos(D) = 20/29
now
[tex]Sec(D) = \frac{1}{Cos(D)} = \frac{1}{\frac{20}{29} } = \frac{29}{20}[/tex]
We Know that trigonometry formulas
[tex]sec^{2}(D) -tan^{2} (D) =1[/tex]
[tex]tan^{2} (D) = sec^{2} (D) -1[/tex]
= [tex](\frac{29}{20} )^{2} -1[/tex]
= [tex]\frac{841 -400}{400} = \frac{441}{400}[/tex]
[tex]tan^2(D) = \frac{441}{400}[/tex]
[tex]tan(D) = \sqrt{\frac{441}{400} } = \frac{21}{20}[/tex]
[tex]tan(D) = \frac{21}{20}[/tex]
The article Effect of Environmental Factors on Steel Plate Corrosion Under Marine Immersion Conditions (C. Soares. Y. Garbatov, and A. Zayed, Corrosion Engineering, Science and Technology, 2011 :524? 541 ) describes an experiment in which nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The result are presented in the following table (obtained by digitizing a graph).
Temperature (C) Corrosion (mm/y)
26.6 1.58
26.0 1.45
27.4 1.13
21.7 0.96
14.9 0.99
11.3 1.05
15.0 0.82
a. Construct a scatterplot of corrosion (y) versus temperature (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting corrosion from temperature.
c. Two steel specimens whose temperatures differ by 10◦ C are submerged in seawater. By how much would you predict their corrosion rates to differ?
d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20◦ C.
Answer:
Check the explanation
Step-by-step explanation:
a) from the scatter plot in the attached image below, it appears that relationship is approximately linear
b) least square line: that =0.3940+0.0355x
c) for 10 C difference expected difference in corrosion rate =0.0355*10=0.355
d) for x=20 ; predicted temperature =0.3940+0.0355*20=1.1041
e) fitted values are:
X ŷ
26.600 1.3385
26.000 1.3172
27.400 1.3669
21.700 1.1645
14.900 0.9230
11.300 0.7952
15.000 0.9266
8.700 0.7029
8.200 0.6851
i need help with this problem x/56=7/8 Thank you
[tex] \dfrac{x}{56} = \dfrac{7}{8} \\ x = \dfrac{56 \times 7}{8} \\ x = 49[/tex]
Christina is randomly choosing three movies to take on vacation from nine action movies, seven science fiction movies, and four comedies. Which statement is true? The probability that Christina will choose three comedies can be expressed as StartFraction 1 Over 4 C 3 EndFraction. The probability that Christina will choose three action movies can be expressed as StartFraction 20 C 3 Over 9 C 3 EndFraction. The probability that Christina will not choose all comedies can be expressed as 1 − StartFraction 4 C 3 Over 20 C 4 EndFraction. The probability that Christina will not choose all action movies can be expressed as 1 − StartFraction 9 C 3 Over 20 C 3 EndFraction.
Answer:
The answer is D
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
The probability that Christina will not choose all action movies can be expressed as 1 − StartFraction 9 C 3 Over 20 C 3 EndFraction.
please answer this correctly I have to finish this today as soon as possible
Estimate the measure of this angle within 10°.
Marie made the box plot below to display a set of data. Which set of data could the box plot represent?
Answer:
see below
Step-by-step explanation:
First of all, you want to find the data set the matches the extreme values of 5 and 35. That eliminates the 2nd and 4th choices.
Then you want to find the data set that has a median of 15. The first data set has a middle value (median) of 20, so that choice is eliminated.
The data set of the 3rd choice matches the box plot extremes, median, and quartile values.
Answer:
The third choice, (5, 6, 10, 12, 13, 15, 17, 25, 30, 35) would be your best answer.
Step-by-step explanation:
Convert the polar coordinates to rectangular form (√2,-π\4)
Answer:
(1, -1)
Step-by-step explanation:
To convert polar to rectangular coordinates, use these identities:
x = rcos(Ф)y = rsin(Ф)x² + y² = r²Here we were given the point [tex](\sqrt{2},-\frac{\pi}{4})[/tex] which is our (r, Ф) point
We can now plug these values into our x and y equations to convert to rectangular and find our (x, y) point
x = [tex](\sqrt{2} )cos(-\frac{\pi}{4} )= (\sqrt{2})(\frac{\sqrt{2} }{2})=\frac{2}{2}=1[/tex] y = [tex](\sqrt{2} )sin(-\frac{\pi}{4} )= (\sqrt{2})(-\frac{\sqrt{2} }{2})=-\frac{2}{2}=-1[/tex]So our (x, y) point is (1, -1)
[tex](\sqrt{2},-\frac{\pi}{4}) = (1, -1)[/tex]Lena is 10 years old. She asks her dad how old he is. He tells her that the lcm of their ages is 14 times the hcf of their ages. She knows that her dad is at least 30 years old but younger than 45. Work out how old her dad is.
Answer:
35
Step-by-step explanation:
Let x represent the HCF of the ages. Then we can have ax = 10 represent Lena's age, and bx can represent her dad's age.
The LCM will be abx = 14x, so we have ab = 14.
Factors of 14 are 1·14 and 2·7. Since the ratio of ages is between 30/10 = 3 and 45/10 = 4.5, we must have b/a in that range. This will be the case for ...
a=2, b=7
For a=2 and ax=10, we have x=5.
The dad's age is bx = 7·5 = 35.
What is 79(554)+5(746)?
Answer:
47496
Step-by-step explanation:
Answer: The answer is 47496
Step-by-step explanation:
If you multiply 79 x 554 =43766
Then you multiply 5 x 746= 3730
You add 43766+ 3730 = 47496
An architect is designing a triangular shaped plot of land. The base of the land is 100.8 ft and the height of the land is 96.3 ft. Find the available floor area of the building. Type your answer. Do not include a label, just the numbers.
Answer:4853.52
Step-by-step explanation:
base=100.8ft
Height=96.3ft
Area of =(base x height) ➗ 2
Area of =(100.8x96.3) ➗ 2
Area of =9707.04 ➗ 2
Area of =4853.52
If 3^x = 5, then 3^2x+3 = ?
Answer:28
Step-by-step explanation:
3^x=5
3^2x+3
(3^x)^2 + 3
Substitute 3^x=5 in (3^x)^2 + 3
5^2 + 3
5x5+3=28
Sam wants to measure the amount of water in a full bathtub.
Which is the best unit of measurement for Sam to use?
What’s the answer
Probably liters, all the others are too big or too small.
-3b+7=13 solve for b
Answer:
b =-2
Step-by-step explanation:
-3b+7=13
Subtract 7 from each side
-3b+7-7=13-7
-3b = 6
Divide each side by -3
-3b/-3 = 6/-3
b = -2
Answer:
b=-2
Step-by-step explanation:
-3b+7=13
-7 -7
-3b=6
/-3 /-3
b=-2
Kumar has $10.00 to spend. He decided to buy a candy bar for $1.75 and spend the rest on bags of chips. If each bag of chips costs $2.99, how many bags of chips can kumar buy ?
Answer:
2 bag of chips
Step-by-step explanation:
Total Money Kumar had = $10.00
Money spent on buying candy bar = $1.75
Money left with Kumar after buying candybar can be obtained by subtracting
Money spent on buying candybar from Total Money Kumar had.
Money left with Kumar after buying candybar = $10.00- $1.75 = $8.25.
It is given that rest of money( $8.25 as calculated) is spent on buying bag of chips.
cost of one bag of chips = $2.99
Let no of bag of chips kumar can buy be x .
Therefore total money spent on buying x bag of chips is $2.99 time no. of bag of chips bought
Mathematically it can be expressed as
Total money spent on buying x bag of chips = $2.99 * x = $2.99 x
It is given that he can spent only $8.25 to buy bag of chips.
which means
$2.99 x = $8.25
=> x = 8.25/2.99 = 2.75
Thus he can buy 2.75 bag of chips.
But bag of chips can be only integral number as bag cannot be in fraction .
hence 2 bag of chips can bought which will cost 2*2.99=$ 5.98
Rest of the money will be left which will be 8.25 - 5.98 = $2.27
Answer:
8
Step-by-step explanation:
A tree grows 20 percent taller every year after it is planted. The tree was 12 feet tall when planted. How tall will it be after 10 years? 74.3 feet 120 feet 144 feet 146.3 feet
Answer:
74.3 feet
Step-by-step explanation:
Each year, the height is multiplied by 1 +20% = 1.20. After 10 years, the original height is multiplied by 1.20^10, so is ...
(12 ft)1.20^10 ≈ (12 ft)(6.19174) ≈ 74.3 ft
Helppp.........!!!!!!
Answer:
84 centimeters of the width of the item in reality
Step-by-step explanation:
Let us plan out our steps, and solve for each:
1. Given the information, let us create a proportionality as such:
1 = 14 ⇒ x - width of item in reality (cm)
6 x
2. Now let us cross multiply, and solve through simple algebra:
14 * 6 = x,
x = 84 centimeters of the width of the item in reality
9. The circumference of a circle is 601 cm. What is the diameter of the circle?
O 120 cm
90 cm
30 cm
60 cm
Answer:191.4 cm
Step-by-step explanation:
Circumference=601 cm
π=3.14
Diameter=circumference ➗ π
Diameter=601 ➗ 3.14
Diameter=191.4 cm
joe paid 14.00 for a broard game. THis is 70% of the orginal price. What was the orginal price?
Answer:
20.00
Step-by-step explanation:
14 is 70% of X
70/100 × X = 14
X = 14 × 100/70
X = 20.00
Deena wants to buy a 2200 laptop, but she doesn't have the money. She decides to finance the purchase and will pay montly payments of 231.55 for a year. How much extra will Deena end up paying for the laptop becuase she financed it rather than paying for it all once.
Answer:
$578.6
Step-by-step explanation:
231.55 multiplied by 12 is 2778.6.
Subtract that by the amount that she could've paid in a whole you would get 578.6.
PLEASE HELP ME:)
(50points)
WILL MARK THE BRAINLIEST !!
Answer:
3. L(15055) is the number of pages ...
4. true
Step-by-step explanation:
3. The problem tells you that L( ) is a function of the number of words. (That means the number in parentheses in L( ) is a word count.) The first two answer choices describe the function as being of a number of pages, so are incorrect. The last answer choice matches the description of the function.
__
4. Compound interest represents a growth function. Account values in later years will be more than values in earlier years. So ...
D(2) < D(7) is TRUE
Steven nas a deck OF 52 playing cards, as shown below. Determine the
theoretical probability of each event. Express each probability as a fraction
simplest form.
A. Randomly selecting a red card
B. Randomly selecting a 7, 8, 9, or 10
C. Randomly selecting the 6 of diamonds
D. Randomly selecting a card that is not a king
Step-by-step explanation:
a. Randomly selecting a red card =
[tex] \frac{1}{2 } [/tex]
have 26 card choices
B. Randomly selecting a 7, 8, 9, or 10 =
[tex] \frac{4 \times 4}{52} = \frac{16}{52} = \frac{4}{13} [/tex]
(have 4*4 card choice)
C. Randomly selecting the 6 of diamonds =
[tex] \frac{1}{52} [/tex]
(only 1 card choice)
D. Randomly selecting a card that is not a king
[tex]1 - \frac{4}{52} = \frac{48}{52} = \frac{12}{13} [/tex]
1 - all possibility that can select the king
If now Kate is three times as old as Jan, and 6 years ago she was six times as old as he was, how old are they now? I will only accept the right answers.
Answer:
Kate's age now is 30 years old and Jan's age now is 10 years old.
Step-by-step explanation:
Kate age now is 3x
Jan age now is x
3x-6=6*(x-6)
3x-6=6x-36
-3x -3x
-6=3x-36
+36 +36
30=3x
10=x
x=10
3x=30
Kate's age now is 30 years old and Jan's age now is 10 years old.
A newspaper article stated that the US Supreme Court received 812 letters from around the country on the subject of whether to ban cameras from the courtroom. Of these 812 letters, 800 expressed the opinion that cameras should be banned. A statistics student was going to use this sample information to conduct a test of significance of whether more than 95% of all American adults feel that cameras should be banned from the courtroom. What would you tell this student
Answer:
a)This is a large enough sample to provide an accurate estimate of the American public's opinion on the issue.
Which is a solution of the system of equations shown?
A. (−4, 0)
B. (2, −4)
C. (0, −2)
D. (2, 0)
Answer:
D. (2, 0)
Step-by-step explanation:
The solutions are the two points of intersection of the graphs:
(-2, -4) and (2, 0)
The latter of these corresponds to choice D, the one you have marked.
What is the surface area of a hemisphere with radius 3? Round to the tenths.
Answer:
56.52
Step-by-step explanation:
Area of hemisphere = 2πr^2
Radius = 3
= 2×3.14×3×3
= 56.52
hope it helps!
Identify two ways that native Americans resisted being relocated
Answer:
Tortured and kidnapped white colonists, and some started wars.
