Answer:
15 inches
Step-by-step explanation:
As the square cake was cut in two equal pieces, we have that one side of the rectangle is the double of the other side, so we have that:
2*Length + 2*Width = 45
Length = 2*Width
So using the value of length in the first equation, we have:
4*Width + 2*Width = 45
6*Width = 45
Width = 7.5
Length = 2*Width = 15
So each side of the original cake is equal to the length of the rectangle pieces, that is, 15 inches.
What is the probability that the proportion of people who will order coffee with their meal is between 2% of the population mean? If in a restaurant, the proportion of people who order coffee with their dinner is .9. A simple random sample of 144 patrons of the restaurant is taken.
Answer:
57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.
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 normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
For a proportion p in a sample of size n, we have that [tex]\mu = p, s = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this question:
[tex]p = 0.9, n = 144[/tex]
So
[tex]\mu = 0.9, s = \sqrt{\frac{0.9*0.1}{144}} = 0.025[/tex]
What is the probability that the proportion of people who will order coffee with their meal is within 2% of the population mean?
This is the pvalue of Z when X = 0.9 + 0.02 = 0.92 subtracted by the pvalue of Z when X = 0.9 - 0.02 = 0.88. So
X = 0.92
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.92 - 0.9}{0.025}[/tex]
[tex]Z = 0.8[/tex]
[tex]Z = 0.8[/tex] has a pvalue of 0.7881
X = 0.88
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.88 - 0.9}{0.025}[/tex]
[tex]Z = -0.8[/tex]
[tex]Z = -0.8[/tex] has a pvalue of 0.2119
0.7881 - 0.2119 = 0.5762
57.62% probability that the proportion of people who will order coffee with their meal is within 2% of the population mean.
Fill in the blanks:-
The product of a number and its reciprocal is __________ .
PLEASE HELP.....I NEED TO SUBMIT IT NOW
Answer:
The product of a number and its reciprocal is 1.
For i.e : 4/3 and its reciprocal 3/4, 4/3 x 3/4 = 1
Hope this helps!
:)
What is 1/3 of 60% as a fraction
60% *0.01 = 0.6
1/3*0.6=0.2=2/10=1/5
Answer:
1/5
The fraction is 1/5.
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
We have two types of fractions.
Proper fraction and improper fraction.
A proper fraction is a fraction whose numerator is less than the denominator.
An improper fraction is a fraction where the numerator is greater than the denominator.
Example:
1/2, 1/3 is a fraction.
3/6, 99/999 is a fraction.
1/4 is a fraction.
We have,
60%
= 60/100
= 6/10
= 3/5
Now,
1/3 of 60%
= 1/3 x 3/5
= 1/5
Thus,
The fraction is 1/5.
Learn more about fractions here:
https://brainly.com/question/24370499
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Selecting 5 out of the 13 students will ride in a car instead of a van.
A) Permutation
B) Combination
C) Circular permutation
Answer:
combination
Step-by-step explanation:
permutation is when there is a specific order, whereas combination is when they are not in any specific pattern (in this case, 5/13 students, not in any particular order. just 5.
I don't want to explain circular permutation right now (it's difficult to explain), but it's not it from my knowledge
The number of ways selecting 5 out of the 13 students will ride in a car instead of a van is 1287.
The way of selecting 5 out of the 13 students will ride in a car instead of a van is evaluated by the combinations.
We consider the group of 5 students can be selected to ride in a car instead of a van.
Thus, for selecting a random group of the data from the universal data, we have to apply combinations to evaluate it.
Therefore, the ways can be formulated as:
[tex]^{13}C_5=\dfrac{13!}{5! \times 6!}\\=1287\;\rm{ways}[/tex]
Thus, the number of ways selecting 5 out of the 13 students will ride in a car instead of a van is 1287.
To know more about the combinations, please refer to the link:
https://brainly.com/question/10699405
A can of juice has a diameter of 6.6 centimeters and a height of 12.1 centimeters. What is the total volume of a 6-pack of juice cans? Tell the steps you used to calculate your response. *
Answer:
It was a cylinder shape
volume of cylinder is
= \pi {r}^{2} h
Radius of the can
=6.6÷2
=3.3
Volume of 6 can
6(3.142 \times {3.3}^{2} \times 12.1) \\ = 6(3.142 \times 10.89 \times 12.1) \\ = 6(34.21638 \times 12.1) \\ = 6(414.018198) \\ = 2484.109188 \\ = 2484.11 \: (2d.p.)
Answer
2484.11
Step-by-step explanation:
6 divided 2 (1+2) and 9 - 3 divided by 1/3 +1
Answer:
1
Step-by-step explanation:
Work between parenthesis first, so distribute the 2 into both digits within the parenthesis then add the together.
Now divide that number by the 6 at the beginning of the problem to get your first answer.
Now you work on the second part, divide 3 by 1/3 which would give you 9.
9-9=0
0+1=1
1 is your overall answer
Answer:
1 ; 18/4
Step-by-step explanation:
6/ 2(1+2) ; 9 - 3/(⅓ + 1)
6/ 2(3) ; 6/ (4/3)
6/6 ; 6 / (4/3)
1; (6×3)/4
1 ; 18/4
Four students were asked to write an expression which has terms that have a greatest common factor of 8c.
the expressions provided by the students are shown below.
Tanya
32C+16cd
Wyatt
8c-48cd
Xavier
36c-24c yang. 8c+40
Which student wrote the correct expression?
Answer:
Wyatt
Step-by-step explanation:
Tanya: 32c+16cd=16c(2+d)
The GCD of the terms is 16cWyatt : 8c-48cd=8c(1-6d)
The GCD of the terms is 8cXavier :36c-24c =12c(3-2)
The GCD of the terms is 12cYang: 8c+40=8(c+5)
The GCD of the terms is 8Since the expression is required to have a GCD of 8c, Wyatt wrote the correct expression.
Answer:
wyatt answered correctly
Step-by-step explanation:
How fast was a driver going if it left skid marks that were 63 feet long on wet concrete? (The coefficient of friction is 0.97)?
Answer:
Step-by-step explanation:
Let m be the mass of the vehicle
frictional force = μ mg
μ is coefficient of friction ,
deceleration = μ g
= .97 x 32
a = - 31.04 ft /s
v² = u² - 2 a s
0 = u² - 2 a s
u² = 2 a s
= 2 x 31.04 x 63
= 3911.04
u = 62.54 ft / s
Answer:
43mph
Step-by-step explanation:
Took the test
What is the Solution?
Answer: w=2 and 2=6
Step-by-step explanation:
If you substitute 6 and 2 in for w they both work, making c the correct answer
Answer:
w = 2 and w = 6
Step-by-step explanation:
Given
[tex]\frac{w}{2w-3}[/tex] = [tex]\frac{4}{w}[/tex] ( cross- multiply )
w² = 4(2w - 3) ← distribute
w² = 8w - 12 ( subtract 8w - 12 from both sides )
w² - 8w + 12 = 0 ← in standard form
(w - 2)(w - 6) = 0 ← in factored form
Equate each factor to zero and solve for w
w - 2 = 0 ⇒ w = 2
w - 6 = 0 ⇒ w = 6
For the parrallelogram, if measure of angle 2= 5x-28 and measure of angle 4= 3x-10, Find x.
Answer:
x = 9
Step-by-step explanation:
Unfortunately you didn’t provide the figure however we can use the picture below to work on:
from a property of the parallelogram (opposit angles) we know that angle 2 and 4 are equal in measure
then
5x - 28 = 3x - 10
then
5x - 3x = 28 - 10
then
2x = 18
then
x = 18/2
= 9
Find the surface area of the prism.
Answer:
9x4x5= 180cm
You would do length x width x hight
Answer:
A=202
Step-by-step explanation:
Length: 9
Width: 4
Height: 5
Formula: L*W*H
Hope this helps
The base of a triangle is 3cm and the height is 5cm. What mathematical operations described must be performed in order to find the area of this triangle
I NEED HELP FAST, 20POINTS
Which of the following statements is true?
| A | < | D |
A + B = D
C ≥ D
| B | > C
Answer:
| A | < | D |
Step-by-step explanation:
| A | is going to be 4 units since A = -4
| D | i sgoing to be 3 units since D = 3
Answer:
The answer is |A|< |D|
Step-by-step explanation:
Just did it and it was right
im lost!! can someone please help me. will vote brainliest
Answer:
Answer is >= 1. The reason is that you can't take the square root of a number and it be a rational number. So you have to avoid having a number that is negative under the square root symbol. In addition, you have to make sure you don't have a zero in the denominator because that would make the answer undefined.
Answer is C
Step-by-step explanation:
Answer:
I belive the answer is c
Try using desmos cauculater ;)
About 450 manta rays are seen near lady Elliot island each year if you were to spot one manta ray at random what is the probability that it would be clouseau
Answer:
Probability that if a manta ray is spotted at random, it would be clouseau = Total number of Clouseau spotted each year) ÷(Total number of manta rays seen each year)
Step-by-step explanation:
The information given is not enough to determine the probability.
We need to know, how many Clouseau are seen each year, then we can find the desired probability.
The Parameters:
Total number of manta rays seen each year = 450
Probability that if a manta ray is spotted at random, it would be clouseau,
P = Total number of Clouseau spotted each year, C) ÷(Total number of manta rays seen each year, T)
P = C/T
P = C/450
Rocky has 7 bottles of water. He will buy bottles of water from the store. The store has 8 cases in stock and each case contains 24 bottles of water. The store will not sell partial cases. The function that models the number of bottles of water Rocky will have after his purchase is F(c) = 24c +7, where c is the number of cases of water he buys.
What is the theoretical domain of the function?
A)
All Real Numbers
B)
All Real Numbers From 1 To 8, Inclusive
C)
{31, 55, 79, 103, 127, 151, 175, 199}
D)
All Integers From 1 To 8, Inclusive
Answer:
A)
All Real Numbers
Step-by-step explanation:
Every integer is a real number.
Can someone please help me? I keep losing points...
CORRECT ANSWERS ONLY PLEASE!!!!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Round your answer to the nearest cent.
Answer:
$14,000
Step-by-step explanation:
i = prt
i= ($70,000)(.04)(5)
i = $14,000
Answer:
$14000
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 70000 × 4/100 × 5
I = $14000
What is the solution to the inequality 1/4+x<5/6
Answer:
x < 7/12
Step-by-step explanation:
1/4+x<5/6
Multiply each side by 12 to get rid of the fractions
12*1/4+12x<5/6*12
3 + 12x < 10
Subtract 3 from each side
3+12x-3 < 10-3
12x < 7
Divide by 12
12x/12 < 7/12
x < 7/12
Answer:
A
Step-by-step explanation:
Find the volume of the sphere.
Either enter an exact answer in terms of π or use 3.14 for π.
The sphere's radius is 6.
Answer:
V≈904.78
Step-by-step explanation:
You have to multiply
6*3.14
Answer:
288π
Step-by-step explanation:
A company has been forced to reduce its number of employees. Today the company has 29% fewer employees than it did a year ago. If there are currently 142 employees, how many employees did the company have a year ago?
250 is not the answer
Step-by-step explanation:
Idk
4/7 of the students in a classroom are boys. If there are twelve girls in the class, how many total students are there?
Answer:
28 students total.
Step-by-step explanation:
Let's use a ratio:
boys : girls
4 : 3
16 : 12
To find the total, we need to add 16 and 12 which equals 28
Answer:
28 students
Step-by-step explanation:
If 4/7 of the students are boys,
then 1- 4/7 = girls
7/7 -4/7 = 3/7
total students *3/7 = girls
total students * 3/7 = 12
Multiply each side by 7/3
total students * 3/7 *7/3 = 12*7/3
total students = 28
When a cycle is sold allowing 10% discount on its marked
price a seller gains 5% and allowing 5% discount the profit is
Rs 351. Find the cost price of the cycle. (Ans: Rs. 3240)
The cost price of the cycle is Rs.3240
Represent the cost price of the cycle with x and the selling price with y
A gain of 5% when the marked price is at a discount of 10% implies that:
[tex]5\%=\frac{(1 - 10\%)y-x}{x}[/tex]
Express 10% as decimal
[tex]5\%=\frac{(1 - 0.10)y-x}{x}[/tex]
[tex]5\%=\frac{0.90y-x}{x}[/tex]
Express 5% as decimal
[tex]0.05=\frac{0.90y-x}{x}[/tex]
Cross multiply
[tex]0.05x=0.90y-x[/tex]
Collect like terms
[tex]x + 0.05x=0.90y\\[/tex]
This gives
[tex]1.05x=0.90y[/tex]
Make y the subject of the formula
[tex]y = \frac{1.05x}{0.90}[/tex]
Also, when the discount is 5% and the profit is 351, we have:
[tex]351=(1 - 5\%)y -x[/tex]
Express 5% as decimal
[tex]351=(1 - 0.05)y -x[/tex]
This gives
[tex]351=0.95y -x[/tex]
Make y the subject
[tex]0.95y = 351 + x[/tex]
Substitute [tex]y = \frac{1.05x}{0.90}[/tex]
[tex]0.95 \times \frac{1.05x}{0.90} = 351 + x[/tex]
[tex]\frac{0.9975x}{0.90} = 351 + x[/tex]
Subtract x from both sides
[tex]\frac{0.9975x}{0.90} -x= 351[/tex]
Take LCM
[tex]\frac{0.9975x - 0.9x}{0.90}= 351[/tex]
[tex]\frac{0.0975x}{0.90}= 351[/tex]
Multiply both sides by 0.90
[tex]0.0975x= 315.9[/tex]
Divide both sides by 0.0975
[tex]x= 3240[/tex]
Hence, the cost price of the cycle is Rs.3240
Read more about discounts and price at:
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Please help ASAP! I will mark BRAINLIEST! Please answer CORRECTLY! No guessing!
Answer:
C. [tex]b^{27}[/tex]
Step-by-step explanation:
Assume b is a number like 3
([tex]3^{9}[/tex])³=19683³=7625597484987
[tex]3^{24}[/tex]=282429536481
B is definitely wrong. Not even going to try.
[tex]3^{27}[/tex]=7625597484987
D is definitely wrong. Not even going to try.
Part A The circumference of a dinner plate is 19.5 inches. What is its radius? ( use π=3.14 ) Round your answer to the nearest hundredth. inches.
Circumference = PI x diameter
FInd the diamter:
19.5 = 3.14 x diameter
Divide both sides by 3.14:
Diameter = 19.5 / 3.14
Diameter = 6.21019108 inches.
Radius = diameter / 2
Radius = 6.21019108 / 2
Radius = 3.10509554 inches
Rounded to the nearest hundredth = 3.11 inches.
please Help it’s urgent
Answer:
Angle IAJ
Step-by-step explanation:
X idea again. They are opposite to each other in the immediate area around them.
Which sentence describes a benefit that short-term disability insurance offers a policyholder? A. It provides 30% to 40% of the policyholder's income for up to one year. B. It provides 10% to 25% of the policyholder's income for up to two years. C. It provides 50% of the policyholder's income for up to one year. D. It provides 40% to 60% of the policyholder's income for up to one year.
Answer:
D. It provides 40% to 60% of the policyholder's income for up to one year.
Step-by-step explanation:
Insurance is a risk sharing device where the risk is shared between the policyholder and the insurance company through regular periodic payment called premium. What Short term disability insurance does is to make do with the income of a person that has to leave his/her place of work as a result of sickness or injury. It provides financial assistance while the individual convalesces at home. The employee are liable to receive 40 to 60 % of their gross weekly income pending on the premium paid. This coverage period is 9 to 52 weeks, (i.e 2.25 to 12 months).
Answer:
D. It provides 40% to 60% of the policyholder's income for up to one year.
Step-by-step explanation:
What is the solution to the system of linear equations graphed below?
5
4 3
2
1
1
2 3
4
5
x
Answer: -5,-1
Step-by-step explanation:
Answer:
-5,-1
Step-by-step explanation:
Mr.Cho made a two way table to describe members of his family.which could describe the row and column headings for Mr.Chos table
Answer:c
Step-by-step explanation:
Took test
. You deposit $600 in an account that earns simple interest. The difference between the total interest earned after 5 years and the total interest earned after 3 years is $24. What is the annual interest rate?
Answer:
The answer is .007874989
Step-by-step explanation:
the number of subscriptions to an interior design magazine was 16,450 in 1996. Since then, the number of subscriptions has increased by 9.2% each year. find the approximate number of subscriptions in 2018.
Answer:
49,744.8 so round up to 49,745
Step-by-step explanation:
