Using the normal distribution and the central limit theorem, it is found that there is a 0.0029 = 0.29% probability that the sample average is LESS than 8.40.
Normal Probability DistributionIn a normal distribution 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]
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:
The mean is of [tex]\mu = 8.5[/tex].The standard deviation is of [tex]\sigma = 0.22[/tex].A sample of 37 is taken, hence [tex]n = 37, s = \frac{0.22}{\sqrt{37}} = 0.0362[/tex].The probability that the sample average is LESS than 8.40 is the p-value of Z when X = 8.4, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{8.4 - 8.5}{0.0362}[/tex]
[tex]Z = -2.76[/tex]
[tex]Z = -2.76[/tex] has a p-value of 0.0029.
0.0029 = 0.29% probability that the sample average is LESS than 8.40.
To learn more about the normal distribution and the central limit theorem, you can take a look at https://brainly.com/question/24663213
Ninja gym membership costs $33 per month after an initial membership fee. You paid a total of $338 after 5 months. Write an equation that gives you the total cost related to the months of your gym membership.
Find the 70th term of the following arithmetic sequence.
13, 22, 31, 40,
Answer:
634
Step-by-step explanation:
Nth term of an arithmetic progression is given by:
Tn=a+(n-1)d
Where 'Tn' is the Nth term of A.P. , 'a' is the first term of A.P. , 'n' is the no. of terms and 'd' is the common difference.
22-13=9, 31-22=9, 40-31=9.
So, d=9
a=13
n=70
Put the values in the Formula.
T70=13+(70-1)*9=13+69*9=13+621=634
are they congruent? 50 points please help
Answer:
Yes
Step-by-step explanation:
they were just dilated differently
Answer:
Yes
Step-by-step explanation:
The only difference is that they are dilated. And the dilation is the same from all sides.
Hope this helped!! :)
Stay safe and have a wonderful day/night!!!!!
Brainliest?!?!
A system of equations is shown below,
y = 5x + 2
10x - 2y = 12
what is the solution to the system of equations?
Find the value of the expression below for x = 3.
x2+ 5
A.8 B.11 C.14
Answer:
11
Step-by-step explanation:
Plz mark brainliest thanks
Find the circumference of a circle with a diameter of 6 cm. Leave your answer in terms of pi
9 pi cm
24pi cm
12pi cm
бpi cm
Step-by-step explanation:
diameter = 6cm
radius = diameter ÷ 2
= 6 ÷ 2
= 3cm
circumference = 2π × radius
= 2 π × 3cm
= 3π cm
-----------------------------FOLLOW ME24 pack of mountain dew for 9.99 or a pack if mountain dew for 5.99 find the unit number
Answer:
24 pack of mountain dew=9.99
1 pack of mountain dew=9.99/24=0.41625
Please tell me the answer and explain it too please!!!
Answer:
56-8=48cm²
Step-by-step explanation:
area 1 (triangle area)=1/2bh
=1/2×4×4=8cm²
area 2(rectangle area)=lw
=8×7=56cm²
the shaded area=area 2-area 1
=56-8=48cm²
Anna wants to celebrate her birthday by eating pizza with her friends. For $42.50 total, they can buy p boxes of pizza. Each box of pizza costs $8.50.
Answer: they can get 5 pizzas
Step-by-step explanation:
42.50 divided by 8.50 is 5
Answer:
They can buy 5 pizzas.
Step-by-step explanation:
HELP PLEASE
(Look at the picture)
Answer:
D is correct (I think).
Step-by-step explanation:
A and C are completely invalid, as A is a linear function and C does not go up in intervals of 25.
Answer C is a linear function and is represented by y=x+1, but there are potential other reasons that it could be considered a linear function.
Answer D cannot be solved by y=mx+b because it is an exponential function.
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answer: im in 100% sure but i think its yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
I used photomath
Which sentence best describes the main idea of a text?
A.) It states the author's opinion about a different topic.
B.) The important details in the text support it.
C.) It can stand by itself without any need for support.
D.) It always appears in the title of the text.
Answer: B
Step-by-step explanation:
I am not sure if this is correct but this is probably the most likely answer
If a⋅b+c⋅d=12, and a,b,c and d are all integers greater than 1, how many values are possible for a, if a, b, c, and d are not necessarily distinct?
Answer:
hajajhagshausuwuw8h1v2os q
the price of a stereo system is $627.50 the sales tax is 6% find the amount of the tax and the total cost
Which word best describes the degree of overlap between the
two data sets?
Low
high
none
moderate
Answer:
moderator since the lines are similar
hope it helps <3!
Step-by-step explanation:
100% correct
The overlap between both data sets can best be described as being moderate.
What is the degree of overlap between both sets?The degree of overlap shows the pairwise distance that can be observed between the variables in both data sets.
The degree of overlap above can be said to be moderate because the pairwise distance isn't too different.
Find out more on degree of overlap at https://brainly.com/question/1289628.
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An item is regularly priced at $51 . It is on sale for 35 %off the regular price
Answer:
17.85$
Step-by-step explanation:
if the expression (2x^4)^3 was written in ax^b form, which of the following would be the sum of a and b
Answer:20
Step-by-step explanation:
4(n+2)-2n=0
Distributive property
Answer:
n=-4
Step-by-step explanation:
Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have?
a.
$50,000
b.
$70,000
c.
$90,000
d.
$120,000
Answer:
The answer is 70,000 sales.
Bob gets paid an annual salary of $30,000, which means that monthly he gets:
$30,000 : 12 months = $2,500 per month
x - number of sales
Bob earns 5% commission on all sales he makes: x * 5% = x * 0.05 = 0.05x
The function is:
f(x) = 2,500 + 0.05x
Bob wants to make $6,000 this month: f(x) = 6,000
2500 + 0.05x = 6000
0.05x = 6000 - 2500
0.05x = 3500
x = 3500 : 0.05
x = 70000 sales
Step-by-step explanation:
Sales for the month should amount to $70,000
Annual salary = $30,000
Commission on sales = 5%
To make 6000 in a month :
Monthly salary = $30000 / 12 = $2500
Month earning = $2500 + 5% × (monthly sales)
Month earning = $6000
Let month sales = m
6000 = 2500 + 0.05m
6000 - 2500 = 0.05m
3500 = 0.05m
m = 3500 / 0.05
m = 70,000
Sales for the month should be 70,000
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I GIVE BRAINLIEST FOR EXPLANATION AND CORRECT ANSWER EXTRA POINTS 3
Answer:
[tex]x=8[/tex]
Step-by-step explanation:
The best way to go about this is to use a trig identity. You have the unknown opposite the angle and the hypotenuse, so its best to use the sine identity: [tex]sin(x)=\frac{O}{H}[/tex], where O is the opposite side, and H is the hypotenuse.
Set up the equation as:[tex]sin(27)=\frac{x}{17}[/tex], and solve for X.
I got x=7.718, rounded to x=8.
If I helped, a brainliest answer would be greatly appreciated!
Tasty Treats Baking Company asked all students in the senior class at Ridgemont High School the question, “Do you prefer chocolate or butterscotch Tasty Treats?” Everyone surveyed had to pick one of the two answers, and 42%, percent said they preferred chocolate.
Based on this data, which of the following conclusions are valid?
Answer:
42%, percent of all students in the senior class at Ridgemont High prefer chocolate.
Step-by-step explanation:
Answer:
42%, percent of all students in the senior class at Ridgemont High prefer chocolate.
Step-by-step explanation:
your answer awaits:
In ΔDEF, the measure of ∠F=90°, the measure of ∠D=67°, and FD = 7.4 feet. Find the length of EF to the nearest tenth of a foot.
Answer:
14.2 ft
Step-by-step explanation:
tan 66° = 32/ FD
FD = 32 / tan 66° = 32 / 2.246 = 14.2
hope it helped you
Answer:
17.4
Step-by-step explanation:
\tan D = \frac{\text{opposite}}{\text{adjacent}}=\frac{x}{7.4}
tanD=
adjacent
opposite
=
7.4
x
\tan 67=\frac{x}{7.4}
tan67=
7.4
x
7.4\tan 67=x
7.4tan67=x
Type into calculator and round to the nearest tenth of a foot.
Bill is 6 years older than Mary. The sum of their ages is 48. What are the equations used to find their ages?
Step-by-step explanation:
Mary's age = x
Billi's age = x+6
So, Mary age + Billi age = x + (x + 6)
Sum of their ages = 2x + 6
So, 2x + 6= 48
2x = 48 - 6
2x = 42
x = 42/2
Mary age = x = 21
And Billi age = x +6= 21 + 6 = 27
So Mary = 21
And Billi = 27
Lets check!
21 + 27 = 48
So therefore their ages add up to 48
So the answer is correct!
Solve for u. 3u=7.5 please help me
Answer:
2.5
Step-by-step explanation:
7.5 divided by 3 equals 2.5.
(Also next time you can use a calculator)
The measurements of a rectangular room, in a scale drawing, are 2 inches by 3
inches. The scale is inch = 3 feet. If carpet costs $1.75 per square foot, how much will
it cost to put carpet in this room?
Answer:
so,
the room (2×3) × (3×3) feet, or 6x9 feet.
6x9= 54square feet
54 x 1.75= $94.50
There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is 7/9.
There are 42 red marbles in the bag and each is equally likely to be chosen.
Work out how many marbles in total there must be.
Answer:
do 7/9*42. then you will get answer
Probability helps us to know the chances of an event occurring. The total number of red marbles in the bag is (7×42)/9.
What is Probability?Probability helps us to know the chances of an event occurring.
[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
Given that there are 42 red marbles in the bag and each is equally likely to be chosen. Also, The probability of randomly choosing a red marble is 7/9. Therefore, the total number of red marbles in the bag is,
Number of red marbles = 7/9 × 42
Learn more about Probability:
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Tanveer bought 0.7 pounds of sliced ham at his local deli. If the deli charged $6.79 per pound, how much did Tanveer pay?
$2.04
$4.75
$7.49
$9.70
Mark this and return
Answer:
Total amount of money paid by Tanveer at his local deli = $4.75
Step-by-step explanation:
Quantity of sliced ham bought by Tanveer at his local deli = 0.7 pounds
Amount of money charged by deli per pound of ham = $6.79
Now, we need to find the total amount of money paid by Tanveer at his local deli for buying the 0.7 pounds of sliced ham.
So, Total amount of money paid by Tanveer at his local deli = Quantity of sliced ham bought × Price of ham per pound
⇒ Total amount of money paid by Tanveer at his local deli = 6.79 × 0.7
⇒ Total amount of money paid by Tanveer at his local deli = $4.75
Answer:
Total amount of money paid by Tanveer at his local deli = $4.75
Step-by-step explanation:
How would you describe the correlation in the data? Explain your reasoning.
Answer:
Where is the options
Step-by-step explanation:
Answer: sorry where's the pic?
Step-by-step
Raul ate 7/8 of 1/2 a pizza. How much of the pizza did Raul eat?
Answer:
7
16
Step-by-step explanation:
7/8× 1/2=
7 × 1
8 × 2
=7/16
4.5% of what number is 99?
Answer:
2200
Step-by-step explanation:
4.5% × ? = 99
? =
99 ÷ 4.5% =
99 ÷ (4.5 ÷ 100) =
(100 × 99) ÷ 4.5 =
9,900 ÷ 4.5 =
2,200