Answer:
The 98% confidence interval estimate of the true average amount of soft drink in each bottle is between 2.97 liters and 3.01 liters.
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 64 - 1 = 63
98% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 63 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.387
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.387\frac{0.06}{\sqrt{64}} = 0.02[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 2.99 - 0.02 = 2.97 liters
The upper end of the interval is the sample mean added to M. So it is 2.99 + 0.02 = 3.01 liters
The 98% confidence interval estimate of the true average amount of soft drink in each bottle is between 2.97 liters and 3.01 liters.
The manager of a music store has kept records of
The manager of a music store has kept records of the number of CDs bought in a single transaction by customers who make a purchase at the store. The accompanying table gives six possible outcomes and the estimated probability associated with each of these outcomes for the chance experiment that consists of observing the number of CDs purchased by a randomly selected customer at the store.
Number of CDs purchased 1 2 3 4 5 6 or more
Estimated probability 0.30 0.25 0.20 0.15 0.05 0.05
(a) What is the estimated probability that the next customer purchases three or fewer CDs?
(b) What is the estimated probability that the next customer purchases at most three CDs?
How does this compare to the probability computed in part (a)?
greater than part (a)less than part (a) the same as part (a)
(c) What is the estimated probability that the next customer purchases five or more CDs?
(d) What is the estimated probability that the next customer purchases one or two CDs?
(e) What is the estimated probability that the next customer purchases more than two CDs?
Answer:
(a) [tex]P(x\le 3) = 0.75[/tex]
(b) [tex]P(x\le 3) = 0.75[/tex]
(b) is the same as (a)
(c) [tex]P(x \ge 5) = 0.10[/tex]
(d) [tex]P(x = 1\ or\ 2) = 0.55[/tex]
(e) [tex]P(x > 2) = 0.45[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{CDs} & {1} & {2} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.30} & {0.25} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}[/tex]
Solving (a): Probability of 3 or fewer CDs
Here, we consider:
[tex]\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x\le 3) = P(1) + P(2) + P(3)[/tex]
This gives:
[tex]P(x\le 3) = 0.30 + 0.25 + 0.20[/tex]
[tex]P(x\le 3) = 0.75[/tex]
Solving (b): Probability of at most 3 CDs
Here, we consider:
[tex]\begin{array}{cccc}{CDs} & {1} & {2} & {3} \ \\ {Prob} & {0.30} & {0.25} & {0.20} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x\le 3) = P(1) + P(2) + P(3)[/tex]
This gives:
[tex]P(x\le 3) = 0.30 + 0.25 + 0.20[/tex]
[tex]P(x\le 3) = 0.75[/tex]
(b) is the same as (a)
Solving (c): Probability of 5 or more CDs
Here, we consider:
[tex]\begin{array}{ccc}{CDs} & {5} & {6\ or\ more}\ \\ {Prob} & {0.05} & {0.05}\ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x \ge 5) = P(5) + P(6\ or\ more)[/tex]
This gives:
[tex]P(x\ge 5) = 0.05 + 0.05[/tex]
[tex]P(x \ge 5) = 0.10[/tex]
Solving (d): Probability of 1 or 2 CDs
Here, we consider:
[tex]\begin{array}{ccc}{CDs} & {1} & {2} \ \\ {Prob} & {0.30} & {0.25} \ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x = 1\ or\ 2) = P(1) + P(2)[/tex]
This gives:
[tex]P(x = 1\ or\ 2) = 0.30 + 0.25[/tex]
[tex]P(x = 1\ or\ 2) = 0.55[/tex]
Solving (e): Probability of more than 2 CDs
Here, we consider:
[tex]\begin{array}{ccccc}{CDs} & {3} & {4} & {5} & {6\ or\ more}\ \\ {Prob} & {0.20} & {0.15} & {0.05} & {0.05}\ \ \end{array}[/tex]
This probability is calculated as:
[tex]P(x > 2) = P(3) + P(4) + P(5) + P(6\ or\ more)[/tex]
This gives:
[tex]P(x > 2) = 0.20+ 0.15 + 0.05 + 0.05[/tex]
[tex]P(x > 2) = 0.45[/tex]
the bases of a trapezoid are 8 and 6 inches it's height is 5 inches what is the area of the trapezoid?
Answer:
35 in^2
Step-by-step explanation:
The area of a trapezoid is the average of the bases times the height.
Base 1: 8, Base 2: 6, Height: 5
(8 + 6)/2 = 7
7 * 5 = 35 in^2
please help i tried this homework for about 30 min and still cant get it
Answer:
1)false
2)false
3)true
4) false
Given that f(x) = 2x and g(x)=2x+5 and h(x)=2x+2 how does g(x) and h(x) compare to f(x)
Answer:
vkjhfs cjjdjzjzjdjdjududinqbbsjz
You are borrowing $1,575 to purchase a washer and dryer using a 36 month installment plan. Determine the annual percentage rate (APR) and the monthly payment given that the interest charge is $99.32. Round your answer to the nearest whole percent and to the nearest cent.
A. %% 47.2
b. 5% 50.18
C. 4% 49.4
D. 4% 46.5
The price of an item yesterday was $40. Today, the price fell to $22. Find the percentage decrease.
Answer:
45%
Step-by-step explanation:
40 * .45 = 18
40-18 = 22
The percentage decrease of an item would be 45%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
We can determine the value of the percentage decrease by the following formula,
percentage decrease = (initial value - reduced value) / initial value × 100%
As per the given question, we have
initial value = $40, and reduced value = $22
Substitute the values in the above formula, and we get
percentage decrease = (40 - 22) / 40 × 100%
percentage decrease = (18) / 40 × 100%
percentage decrease = 0.45 × 100%
Apply the multiplication operation, and we get
percentage decrease = 45%
Thus, the percentage decrease of an item would be 45%.
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How long a ladder must you have to reach the top of a 15-foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? Round to the nearest tenth of a foot.
14.5 ft
15.5 ft
17.0 ft
19.0 ft
Answer:
15.5
Step-by-step explanation:
on edguenity
Answer:
15.5
Step-by-step explanation:
trust
A table contain 30 milligrams of medications. How many tablets will be needed to provide with 240 milligrams of medication
Answer:
8 tablets
Step-by-step explanation:
Answer:
8 tablets
Step-by-step explanation:
240/30
One year, the population of a city was 80,000. Several years later it was 66,400. Find
the percent decrease.
Answer:
The population decrease by 17%.
Step-by-step explanation:
This is because 66,400 is 83% of 80,000.
100%-83%= 17%
Therefore, the percentage of the population that decreased was 17%
These four numbers are plotted on a number line:
2 5 3 1
3352
Which is the correct ordering on the number line, from left to right?
Answer:
yes
Step-by-step explanation:
Evaluate the expression when x = 28 and y=5. x-3y
Answer:
13
Step-by-step explanation:
Substitute x for 28 and y for 5:
(28) - 3(5)
28 - 15
13
Look at the triangles shown below.
z
2
6
E
А
3 D
Which statement is true?
(Ity)
O SinceAAEC ~AADB according to the side-angle-side similarity postulate, then
2 6
(aty)
SinceAAEC ~AADB according to the side-angle-side similarity postulate, then
2
9 3
o SinceAAEC ~AADB according to the angle-angle similarity postulate, then
(1+y)
6 3
o Since AAEC ~AADB according to the angle-angle similarity postulate, then
(1+y)
NOH OH
T
Answer:c
Step-by-step explanation:
The statement which is true for the given expression triangle is, 9/(x + y) = 3/x. So option c is correct.
What is similarity of triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"
Given that,
One right angle triangle, ΔAEC
one segment BD which is intersecting sides AC & AE
ΔAEC has one similar triangle inside, which is ΔADB
Triangle ΔAEC and ΔADB similar,
So, we can say ΔAEC ≈ ΔADB
For the given similar triangles,
we can use angle-angle similarity property,
so, AE/AC = AD/AB
⇒ (3+6)/(x + y) = 3/x
⇒9/(x + y) = 3/x
Hence, the Statement C is correct
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Y-4=7(x-6) need help
Answer:
y = 7x - 39
Step-by-step explanation:
y-4= 7(x-6)
y = 7(x-6) + 4
= 7x - 42 + 4
= 7x - 38
y = 7x - 39
8 Saturday they make 13 plain glazed donuts for every 7 chocolate glazed donuts what is the ratio of chocolate glazed to plain glaze
This is equation
I don't know how to do
so can anyone tell me plz
with explanation it will help me alot ❤
Answer:
[tex] - \frac{10}{9} [/tex]
Al sumar 2x+5y-4z+9 y 2x-4y+6 se obtiene?
Answer: (Responder)
4x + y + 15 – 4z
Step-by-step explanation: (Explicación paso a paso)
(2x + 5y – 4z) + (9 + 2x – 4y + 6)
Group Like Terms (Agrupar términos similares)
2x + 2x + 5y – 4y – 4z + 9 + 6
Add Similar Elements (Agregar elementos similares)
4x + 5y – 4y – 4z + 9 + 6
4x + y – 4z + 9 + 6
Add The Numbers (Suma los números)
4x + y + 15 – 4z
Akili has two tests next week. The probability that he will pass the first test, science, is 3 4 . How he does on that test affects how he will do on his math test. If he passes science, then the probability that he will also pass the math test is 4 5 ; otherwise, the probability is only 1 3 that he will pass the math test. What is the probability he passes exactly one test
Answer:
0.2333 = 23.33% probability he passes exactly one test
Step-by-step explanation:
We have these following probabilities:
3/4 probability that he passes the first test.
If he passes the first test, 4/5 probability that he passes the math test.
If he does not pass the first test, 1/3 probability that he passes the math test.
What is the probability he passes exactly one test
Two scenarios:
Pass first(3/4 probability) and fails second(1/5 probability).
Fails first(1/4 probability) and passes second(1/3 probability). So
[tex]p = \frac{3}{4}*\frac{1}{5} + \frac{1}{4}*\frac{1}{3} = \frac{3}{20} + \frac{1}{12} = \frac{9 + 5}{60} = \frac{14}{60} = 0.2333[/tex]
0.2333 = 23.33% probability he passes exactly one test
this is confusing, i need help
Answer:
Step-by-step explanation:
2. SV ║TU
3. SV ≅TU
7. corresponding sides of congruent Δ are congruent
8. quadrilaterals that have one set of opposite sides ║ and ≅ are parallelograms
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
D
Step-by-step explanation:
3x+2x-13=47 solve for x
Please show the work
(-1 1/2) * 2/3 =
pls i need help!!
Answer: -1
Step-by-step explanation:
[tex]\bigg (-1\dfrac{1}{2} \bigg) \cdot \dfrac{2}{3} =-\dfrac{3}{2} \cdot \dfrac{2}{3} =-1[/tex]
15j + 15 i need this ASAP will give brainlyest
Answer:
15 ( j + 1)
Step-by-step explanation:
You need to factor it.
15 ( j +1 )
= 15j + 15 ✔
Which is equivalent to the expression below? |-3|
O
13
-1-31
O
3
Chicken costs $3.20 per pound, and beef costs $4.59 per pound. What is the exact cost of 3 pound of beef?
1) $9.60
2)$13.77
3)$4.17
Step-by-step explanation:
i need help with this
Answer:
just put any number for the answer if im reading it right they should all answer 0
Step-by-step explanation:
hope i helped ;)
Killian has $25 in his bank account. He wants to have at least $100. Working for his dad he earns $7.50 for each hour. Write an inequality that would help you find the number of hours he needs to work.
Answer:
Step-by-step explanation:
100-25<= 7.5x
x >= 10
Answer:
Responsability+nopartyscapes=200$!!!!
Step-by-step explanation:
find all the real zeros of the function f(x)=3x^4+11x^3-40x^2-132x+48
Answer:
2*square root 3, -2*square root 3, 1/3, -4
Step-by-step explanation:
I think the answer should be 1/x but I don’t understand how they want me to put it in.
(15 points)
Answer:
See explanation below (type a 1 (one) in each box)
Step-by-step explanation:
Notice that by using the exponent notation and properties, the given exponents can be re-written and simplified as shown below:
[tex]\frac{(x^{20})^\frac{1}{10} }{\sqrt{x^6} } =\frac{x^2}{x^\frac{6}{2}} =\frac{x^2}{x^3} =\frac{1}{x}[/tex]
As you seem to have found. Well done!
What you are expected to do, is to type the coefficient that goes in the numerator (in your case a "1", and in the box below, the exponent that x has in the denominator (in your case also a "1").
So please complete the question as shown below typing a "1" in each box:
[tex]\frac{1}{x^1}[/tex]
Select the correct answer.
Which of the following tables corresponds to the equation below?
y =
O
A.
I
0
1
3
4
5
y
1
4
16
64
256 1,024
B.
0
1
2
3
4
5
y
0
1
4
16
64
4
0
1
2
3
4
5
4
12 /
1
4
16
64
256
D.
0
1
3
4
y
1
4
8
12
16
+
Answer:
A.
Step-by-step explanation:
The table that corresponds to the equation y = ¹/₄(4ˣ) is; Table C
How to simplify an equation?We are given the equation; y = ¹/₄(4ˣ)
At the input value of x = 0;
x = ¹/₄(4⁰)
x = ¹/₄
At the input value of x = 1;
y = ¹/₄(4¹)
y = 1
At the input value of x = 2;
y = ¹/₄(4²)
y = 4
At the input value of x = 3;
Thus;
y = ¹/₄(4³);
y = 16
At the input value of x = 4;
y = ¹/₄(4⁴)
y = 64
At the input value of x = 5;
y = ¹/₄(4⁵)
y = 256
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Lincoln told his mother that 4 5/10
represents his height, in feet. Which decimal measurement represents Lincoln's height?
Answer:
[tex]4.5[/tex]
Step-by-step explanation:
In order to find the answer to this question you will first need to convert Lincolns height into a improper fraction and then convert the improper fraction into a decimal number.
[tex]L =4\frac{5}{10}[/tex]
Convert into improper fraction
[tex]4\frac{5}{10} =10 \times4=40+5=45=\frac{45}{10}[/tex]
Convert into decimal by dividing the numerator by the denominator:
[tex]45\div10=4.5[/tex]
[tex]L=4.5[/tex]
Hope this helps.