Using the normal distribution and the central limit theorem, it is found that the probability is of 0.1368 = 13.68%.
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, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem:
47% of its customers are looking to buy a sport utility vehicle (SUV), hence p = 0.47.A sample of 61 customers is taken, hence n = 61.The mean and the standard error are given by:
[tex]\mu = p = 0.47[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.47(0.53)}{61}} = 0.0639[/tex]
The probability that less than 40% of the sample are looking to buy an SUV is the p-value of Z when X = 0.4, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.4 - 0.47}{0.0639}[/tex]
Z = -1.095
Z = -1.095 has a p-value of 0.1368.
0.1368 = 13.68% probability that less than 40% of the sample are looking to buy an SUV.
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A group of friends were working on a student film that had a budget of $1400. They used $168 of their budget on costumes. What percentage of their total budget did they spend on costumes?
Answer:
12%
Step-by-step explanation:
$ spent / total budget
168 / 1400 = 0.12
0.12 = 12%
Ray YL bisects ZAY B. Find the measurement of
ZBYL.
B
(7x + 17)
(3(4x - 1))
Y
0 90
0 45
0 None of the above
0 20
Answer:
B. 45
Step-by-step explanation:
YL is the angle bisector of ∠AYB, so the two angles are congruent:
∠AYL ≅ ∠BYLSubstitute and solve for x:
7x + 17 = 3(4x - 1)7x + 17 = 12x - 312x - 7x = 17 + 35x = 20x = 4Find the value of ∠BYL:
3(4*4 - 1) = 3(16- 1) = 3(15) = 45
This is matching the answer option B.
The red angles must be equal as YL is bisector
7x+17=3(4x-1)7x+17=12x-317+3=12x-7x20=5xx=4<BYL
3(4(4)-1)3(16-1)3(15)45Option B
8.5 hours in a day what total hours they work in a week
Answer:
8.5 hrs * 5 day work week = 42.5 hrs. But usually 0.5 hr per day is considered lunch and is usually not payed so theoretically the workweek is only 40 hrs per week (full time)
Step-by-step explanation:
MAX POINTS PLEASE HELP Will make Brainliest
What is the period and frequency of the function graphed and how would the equation be written
[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]
The required equation is :
[tex]\qquad \sf \dashrightarrow \:a \cos(bx) + k[/tex]
Now, let's find the required values :
period (p) = 6
[distance between any successive Crest or trough]
a = - 4 (flipped)
b = 2π/p = 2π/6 = π/3
k = -2
Distance of starting position from origin = k
Now, plug in the values ~
[tex]\qquad \sf \dashrightarrow \: - 4 \cos( \frac{\pi}{3} x) - 2[/tex]
Not passing through origin (it's cosine)
Period:-
Difference between any two crests |-3-3||-6|6Now
Frequency:-
[tex]\\ \rm\dashrightarrow \nu=\dfrac{1}{T}[/tex]
[tex]\\ \rm\dashrightarrow \nu=\dfrac{1}{6}[/tex]
[tex]\\ \rm\dashrightarrow \nu=0.167Hz[/tex]
Pamela made a profit of $3250 after selling stocks for $10500 after 4 years. What was her average annual percentage gain?
Pamela's average annual percentage gain was = 7.7%
Calculation of annual percentage gainThe start up capital (P) = $10500
The simple interest (SI) = $3250
Time (T) = 4 years
Rate = ?
But SI = P × T × R /100
Make R the subject of formula,
R = SI × 100/P × T
R = 3250 × 100/ 10500 × 4
R = 325000/ 42000
R = 7.7%
Therefore, Pamela's average annual percentage gain was = 7.7%
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Cooper's family is going to relax at the beach all day! In preparation, Cooper made s sandwiches for them to eat when they get hungry. Cooper put 3 slices of turkey and 3 slices of ham on each sandwich.
Pick all the expressions that represent how many slices of meat Cooper used on the sandwiches.
153 = 9k HELP PLEASE THANK YOU
Answer:
17
Step-by-step explanation:
the number that has the virible with it u divide that number with the number without the varible so 153/9 = 17 and 9k/9=1 so it is 17 the answer is what you got for the number without the varible
............................................
Answer:
yoo :)
Step-by-step explanation:
Need help PLEASE lol anyway thank u
Answer:
true option is B
Step-by-step explanation:
true option is B
Find the number of faces, edges, and vertices of the solid.
The number of faces:
The number of edges:
The number of vertices:
Answer:
102
Step-by-step explanation:
first, count each rectagal,(6) then count each side of the rectangel (17). Lastly do 6x17= 102
(MAYBE WRONG)
help me guys pls pls pls
Answer:
figure area add units (?) (?)
Step-by-step explanation:
Might need a little more information
last one can be square feet square yards square inches square cm square meters etc etc It depends on the dimensions of the figure which isn't shown.
Linda counted different colored leaves on a tree. She counted 8 red leaves. She also counted 3 times as many yellow leaves as red leaves. How many yellow leaves did Linda count?
to find the number of yellow leaves you'll have to multiply number of red leaves she counted by 3.
8×3
=24
Linda counted 24 yellow leaves.
Linda counts 24 yellow leaves in total
How to determine the number of yellow leaves?The number of red leaves is given as:
Red = 8
The statement 3 times as many yellow leaves as red leaves means that:
Yellow = Red * 3
So, we have:
Yellow = 8 * 3
Evaluate the product
Yellow = 24
Hence, Linda counts 24 yellow leaves in total
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The circumference of a circle is 17π in. What is the area, in square inches? Express your answer in terms of π?
Answer:
22.97
Step-by-step explanation:
17 divided by pi is 5.41
5.41 divided by 2 is 2.075
r^2(pi)
is 2.075 x 2.075 x 3.41 is 22.97
4.
Write an equation and solve it. Anything goes as long as you address the following points:
a. The equation must start with an 'x' variable in an exponent.
b. The equation must require logarithms to solve.
c. In the solution you must use the power rule, the product rule and the quotient rule at least once each.
d. Explain each step as you solve; which rules are you using and why?
e. What challenges did you face as you were writing your problem? Did you run into any dead ends?
My problem lies in finding an exponential equation [tex]N^x=N^x[/tex] (N being any positive number) that needs all 3 rules to solve. I can come up with an equation that uses 2 of the rules but I'm stuck on adding the third. Any suggestions would be nice. Thanks
Step-by-step explanation:
hope you understand. :)
Which expression does this power represent?
10^8
10 × 8
10 × 10 × 10 × 10 × 10 × 10 × 10 × 10
10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8 × 10 × 8
8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8 × 8
Answer:
10^8 represents 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Step-by-step explanation:
Because it is to the 8th power, this means it's multiplied by itself 8 times.
Answer: It represents b 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10
Step-by-step explanation:
if a sum of money increased by 1/5 of itself every year and in 5 years amounts to Rs.8546,find the sum
Answer:
Answer :
Given : If a sum of money amounts to Rs 2200 in 5 years
Let sum of money = x
And as given : The interest is 3838 of the principal . So we get
x ( 3838 ) = 2200 - x
3x = 17600 - 8x
11x = 17600
x = 1600
So, Sum of money = Rs . 1600
Then interest = 2200 - 1600 = Rs . 600
Let Rate of interest = r %
And we know Simple interest = P × r × t100P × r × t100 , So we get
⇒1600 × r × 5100 = 600⇒16× r × 5100 = 6⇒80r = 600⇒r = 60080 = 152 = 712%⇒1600 × r × 5100 = 600⇒16× r × 5100 = 6⇒80r = 600⇒r = 60080 = 152 = 712%
So
Step-by-step explanation:
Given mn, find the value of x. + (10N+2)" ION-18)"
Answer:
16
Step-by-step explanation:
equal both using corresponding law
Making auto parts A grinding machine in an auto
parts plant prepares axles with a target diameter
p = 40.125 millimeters (mm). The machine has
some variability, so the standard cleviation of tlic
diameters is a = 0.002 mm. The machine operator
inspects a random sample of 4 uxles cach hour for
quality control purposcs and records llic sample
mcan diameter 1. Assuming that the process is work-
ing properly, what are the mean and standard devia I
fion of the sampling distribution of ? Explain.
Answer: See below
Step-by-step explanation:
Mean:
Since the sample is taken from a large population it follows the central limit theorem, which states that the sample mean is approximately equal to the population mean.
Therefore: [tex]\bold{\bar{X}=\mu=40.125}[/tex]
Standard Deviation:
Again by central limit theorem the standard deviation of the sample is calculated as:
[tex]S=\frac{\sigma}{\sqrt{n}}[/tex]
Since n=4, therefore
S = 0.001
After a successful fishing trip, Leo weighed his catch. He determined he caught a total 6.5 kilograms of fish. The recipe Leo wants to use to make fish stew lists their measurements in grams. Help Leo convert the weight of his fish from kilograms to grams.
Answer:
6 1/2 Grams
Step-by-step explanation:
Hope this helped!!
The weight of Leo's fish from kilograms to grams is 6500 grams
What is kilograms?Kilograms is the "SI unit of mass (equivalent to approximately 2.205 lb), first introduced as a unit of mass for the metric system".
According to the question,
Leo catch a total 6.5 kilograms of fish. He wants to convert kilograms into grams.
Formula to convert kilograms into grams 1 kilograms = 1000 grams
In order to find kilograms into grams only if multiply given kilogram into 1000.
6.5 × 1000 = 6500 grams
Hence, the weight of Leo's fish from kilograms into grams is 6500 grams.
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What’s the answer????
Answer:
i think its c
Step-by-step explanation:
sorry if im worng
Answer i believe its a or d
Step-by-step explanation:
im not to sure but i did try to do the math on it so.
Two angles are supplementary angles if the sum of their measures is 180 degrees. Find the measures of two supplementary angles if the measure of one angle is 3 degrees less than twice the other.
Answer:
60 degrees and 119 degrees
if the smaller angle is x, then
x + 2x - 3 = 180
3x -3 + 3 = 180 + 3
3x/3 = 183/3
x=61
2(61) - 3 = 119
A circle with radius of 1 cm sits inside a 11 cm x 12 cm rectangle.
What is the area of the shaded region?
Answer:
Hope the picture will help you.................
Use the distributive property to express 30 + 42
Answer:
it would be 6 (5 + 7) = 30 + 42 = 72
Step-by-step explanation:
hope this helps if not please let me know
Find the area of each. Round to the nearest tenth.
Answer:
346.361 Yd^2 rounded to the nearest tenth is 346.4 Yd^2
Step-by-step explanation:
The area of a disk is A=π[tex]R^2[/tex] where R=10.5 yard.
Answer:
346.2 yd^2
Step-by-step explanation:
Area of a circle: π*r^2π = 3.14radius (r) = 10.5 ydπ*r^2 <== substitute the numbers for pi(π) and radius(r)
3.14*10.5^2
3.14*110.25
346.185 <== round to the nearest tenth
346.2 yd^2
Hope this helps!
Mr. Andade had supply bag with three mechanical pencils, four blue pens, and five black pens. If he selects a writing utensil without looking, what is the probability he will select a mechanical pencil?
Answer:
1/6
Step-by-step explanation:
The sum of all writing utensils are 3+4+5 = 12,
Therefore the probability he will select a mechanical pencil is 3/12 or 1/4.
.
.
.
.
.
.
.
.
For additional info,
Probability of selecting a blue pen and black pen respectively is 4/12 or 1/3 and 5/12.
7. A hippopotamus weighs 1.5 tons. What is its weight in ounces
Please help I'll mark brainliest 2
Answer:
True
Step-by-step explanation:
To find the amount of observations all you need to do is just add up the dots. Adding the number of observations in each range should be true
nvm someone answered lol good luck!
30 divided by 14 written as a fraction
Answer:
I believe your answer is 15/7
Let's solve.
[tex]\frac{30}{14} =\frac{15 * 2}{7*2} =\frac{15}{7}[/tex]
Hope that helps!
Dante is saving money to buy a game. So far he has saved $24, which is two-thirds of the total cost of the game. How much does the game cost?
Answer:
The game costs 36$ dollars.
Step-by-step explanation:
2/3 of 36 is 24 :p
The total cost of the game Dante wants to buy is 26 dollars.
What is a fraction?A fraction describes some parts of a certain quantity. Fractions are of two types one is a proper fraction and another is an improper fraction. In a proper fraction, the numerator is smaller than the denominator and n improper fraction numerator is greater than the denominator.
Assuming The total cost of the game is x dollars.
Given that 24 dollars is (2/3)rd of the total cost of the game.
So we can write 24 is (2/3)rd of the total cost of the game.
∴ 24 = (2/3)×x.
24 = (2/3)x.
x = 24×(3/2).
x = 12×3.
x = 36 dollars.
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What is the next number in the sequence? 9….16….24….33…
Answer:
43
Step-by-step explanation:
The first increase from 9 to 16 is 7
The second increase from 16 to 24 is 8
The third from 24 to 33 is 9
Following the pattern the next increase must be by 10. 33+10=43
