Answer:
V₂ = V₁ / 8
Step-by-step explanation:
Volume of sphere with radius of 6 = 288π
Volume of sphere with radius of 3 = 36π
the difference in volume after radius is halved is reduced 8 times so formula could be:
V (when radius is halved) = prior volume ÷ 8
V₂ = V₁ / 8
Forty-two cities provided information on vacancy rates (in percent) for local apartments in the following frequency distribution.
Vacancy Rate (in percent) Frequency
0 up to 3 10
3 up to 6 9
6 up to 9 8
9 up to 12 7
12 up to 15 8
a. What is the average vacancy rate?
b. What is the variance?
c. What is the Standard Deviation?
Answer:
[tex](a)\ \bar x = 7.07[/tex]
[tex](b)\ \sigma^2 = 18.67[/tex]
[tex](c)\ \sigma = 4.32[/tex]
Step-by-step explanation:
Given
[tex]\begin{array}{cc}{Rate (\%)} & {f} & {0-3} & {10} & {3-6} & {9} & {6-9} & {8} & {9-12} & {7} & {12-15} & {8} \ \end{array}[/tex]
Solving (a): The average vacancy rate
First, we calculate the class midpoint (x). This is the mean of the class boundaries.
[tex]x = \frac{0+3}{2} = 1.5[/tex] [tex]x = \frac{3+6}{2} = 4.5[/tex] [tex]x = \frac{6+9}{2} = 7.5[/tex]
When done for the whole class, the frequency table becomes:
[tex]\begin{array}{ccc}{Rate (\%)} & {f} & {x} & {0-3} & {10} &{1.5}& {3-6} & {9} &{4.5}& {6-9} & {8} & {7.5}&{9-12} & {7} &{10.5}& {12-15} & {8} &{13.5}\ \end{array}[/tex]
The average rate is:
[tex]\bar x = \frac{\sum fx}{\sum f}[/tex]
[tex]\bar x = \frac{10*1.5 + 9*4.5+8*7.5+7*10.5+8*13.5}{10+9+8+7+8}[/tex]
[tex]\bar x = \frac{297}{42}[/tex]
[tex]\bar x = 7.07[/tex]
Solving (b): The variance
This is calculated as:
[tex]\sigma^2 = \frac{\sum f(x -\bar x)^2}{\sum f}[/tex]
[tex]\sigma^2 = \frac{10(1.5-7.07)^2 + 9(4.5-7.07)^2+8(7.5-7.07)^2+7(10.5-7.07)^2+8(13.5-7.07)^2}{10+9+8+7+8}[/tex]
[tex]\sigma^2 = \frac{784.2858}{42}[/tex]
[tex]\sigma^2 = 18.67[/tex]
Solving (c): The standard deviation.
This is calculated as:
[tex]\sigma = \sqrt{\sigma^2[/tex]
[tex]\sigma = \sqrt{18.67[/tex]
[tex]\sigma = 4.32[/tex]
What is the distance between T(9, −5) and the center of the circle with equation (x – 6)2 + (y + 1)2 =10?
Step-by-step explanation:
first, determine the coordinates values like x =9 and y=-5
so x-6 =3
Khusbu needs 650 gm flour and 30 gm sugar to bake a cake. How much
flour and sugar does he need to bake same size of 6 cakes?
Answer:
4080 gm
Step-by-step explanation:
To bake one cake, it will take us 650 gm flour and 30 gm sugar. When we add both of them together, it gives 680 gm (650+30). But this is only for one cake. To find the total amount of flour and sugar needed to bake 6 cakes, we will have to multiply 680 by 6. That will give you 4080 gm which is your final answer.
7
10
6
What is the area of the triangle shown above?
Answer:
Area of triangle = 0.5* base * height
A = 0.5*6*10
A = 30
If l=10, b=5, h=2, find the values of 2h(l+b)
Answer:
60
Step-by-step explanation:
given:
l = 10
b = 5
h = 2
to find:
2h(l + b)
substitute the given values of l , b and h
=2*2(10 + 5)
=4*15
=60
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{2h(l + b)}[/tex]
[tex]\large\text{If l = 10, b = 5, and h = 2, then substitute it into the equation!}[/tex]
[tex]\large\textsf{= 2(2)((10)+ 5)}[/tex]
[tex]\large\textsf{2(2) = \boxed{\bf 4}}[/tex]
[tex]\large\textsf{= 4(10 + 5)}[/tex]
[tex]\large\textsf{10 + 5 = \boxed{\bf 15}}[/tex]
[tex]\large\textsf{4(15)}[/tex]
[tex]\large\textsf{= \boxed{\bf 60}}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: \textst \bf 60}}}\huge\checkmark[/tex]
[tex]\large\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
find an area of a circle
The area of a circle is pi times the radius squared (A = π r²).
Find the volume of a sphere with a radius of 9 inches. Use 3.14 for π
.
Round your answer to the nearest hundredth.
Answer:
Answer = 3053.63
Step-by-step explanation:
The formula for finding the volume of a sphere is : V = 4/3 πr³
V = 4/3· π · [tex]9^{3}[/tex]
≈ 3053. 62806
Rounded to the hundreths place is 3053.63.
odd number less than 5
Answer:
1 and 3 are the odd numbers that are less than 5. 0, 2 and 4 are the even numbers that are less than 5
Step-by-step explanation:
plaz..mmnj k,mnmnm 1
Answer:
Option 1
Step-by-step explanation:
3x - 7y = -7y + 3x
They have simply been moved to opposite ends of the equation.
HELP WITH MY MATH PLEASEEE
Answer:
x = 18
Step-by-step explanation:
JM = LM
8x - 3 = 141
8x = 141 + 3
8x = 144
x = 144/8
x = 18
Answer:
since its a square each side is equal so
8x-3=141
8x=144
x=18
so
A: x=18
Hope This Helps!!!
3 points If you have the following experimental running times in seconds for some program, mark the one word hypothesis on the order of growth of the running time that best explains the given experimental evidence
Answer:
LogarithmiclinearithmiclinearAnswer:
express the following equation as two statement each using the word varies and proportional i) v(rl=4/3
Records show that 12% of all college students are foreign students who also smoke. It is also known that 40% of all foreign college students smoke. What percent of the students at this university are foreign
Answer: the percent of the students at this university are foreign = 30%
Step-by-step explanation:
Given: Probability that college students are foreign students who also smoke: P(S|F)=0.12
Probability that foreign college students smoke P(S∩F)=0.4
The probability that the students at this university are foreign :
[tex]P(F)=\dfrac{P(S\cap F)}{P(S|F)}[/tex] [By conditional probability formula]
[tex]=\dfrac{0.12}{0.4}\\\\=0.3[/tex]
Hence, the percent of the students at this university are foreign = 30%
Katy spent $2834 on a washing machine and a dryer. The dryer cost $875 less than the washing machine. How much did the dryer cost ?
Answer:
the answer is 1959
Step-by-step explanation:
2834-875=1959
PLEASE HURRY!! I WILL MARK BRAINIEST!
The pentagons JKLMN and PQRST are similar.
Find the length x of QR.
Answer:
x=2.8
Step-by-step explanation:
If JKLMN and PQRST are similar then you can look the to other sides to find the ratio that relates the two. For this specific one you are able to fin 0.4 is the relationship.
NJ is related to TP by a factor of 1.4. -> NJ*1.4=TP -> 4*1.4=5.6
The rest can be said to relate all the other sides together.
A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the wind) takes 90 minutes. Which system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? Recall the formula d = rt.
Answer:
x=12 mile/hour(the speed of the boat)
y=6 mile/hour(the speed of the current)
Step-by-step explanation:
According to the Question,
let, x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour.
Given That, A motorboat travels 9 miles downstream (with the current) in 30 minutes. Thus, x+y = 0.3 mile/minute ⇒ 0.3×60 ⇒ 18mile/hourx+y=18 ---- Equation 1
& The return trip upstream (against the wind) takes 90 minutes. Thus, x-y = 0.1 mile/minute ⇒ 0.1×60 ⇒ 6mile/hourx-y=6 ---- Equation 2
On Adding both above Equations We get,
2x=24 ⇔ x=12 mile/hour(the speed of the boat)
& x+y=18 put Value of x=12 we get ⇔ y=6 mile/hour(the speed of the current)
Is 256.78 power by 10 100 or 1000
Answer:
I would say 100 since 256.78 is closer to 100 then 1000 or 10
Step-by-step explanation:
Leila is arranging 11 cans of food in a row on a shelf. She has 4 cans of corn, 1 can of peas, and 6 cans of beets. In how many distinct orders can the cans be arranged if two cans of the same food are considered identical.
Answer:
2310 ways
Step-by-step explanation:
We are given;
Number of cans = 11
Number of cans of corn = 4
Number of cans of peas = 1
Number of cans of beets = 6
Following the rule of combination and permutations and applying it to this question, we have;
Number of ways = 11!/(6! × 1! × 4!)
Number of ways = 2310 ways
A 7-foot ladder is leaned against a building in such a way that the bottom of the ladder is 4 feet from the base of the wall. Find the angle formed between the ladder and the ground
express the standard form53630000
Answer:
5.363×10^8pls mark me as brainliestAnswer:
5.363×10^8
Step-by-step explanation:
A factory produces 2985 bulbs in a day. how many bulbs did it produce in that year.
Answer:
1089525
Step-by-step explanation:
2985 is per day of bulbs and a year has 365 days
so we multiply bulbs by day and days in a year
which will give us 1089525
Sara drives 72 miles on 3.2 gallons of gas. She uses this information to calculate how many miles per gallon she can drive. Using this result, how many miles can Sara drive on 12.3 gallons of gas?
Answer:
276.75 miles
Step-by-step explanation:
12.3/3.2 × 72 = 276.75 miles
Find the greatest common factor of the
following monomials:
22x5
34x6
Answer:
22x5 = 1
34x6 = 2
Step-by-step explanation:
This might be the answer
Answer:
2x^5
Step-by-step explanation:what equals 22 is 2,11
what equals 34 equals 2,17 and 1,34 are the factors of 34x^6
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Khan Academy
Dependent probability
In a class of 7, there are 4 students who play soccer.
If the teacher chooses 3 students, what is the probability that none of the three of them play soccer?
Answer:
[tex]\frac{12}{49}[/tex]
Step-by-step explanation:
[tex]\frac{4}{7} *\frac{3}{7} = \frac{12}{49}[/tex]
Hope this helps.
NO LINKS OR ELSE YOU'LL BE REPORTED! Only answer if you're very good at Math.No guessing please.
A private university is accepting applications for enrollment.Out of 2,000 applicants,950 meet the GPA requirements,600 volunteer for community service,and 250 both meet the GPA requirements and volunteer.Which statement correctly describes the probability that an applicant meets the GPA requirements or volunteers?
A: Because some applicants volunteer and meet the GPA requirements, the events are mutually exclusive.Thus, the probability is 65%.
B: Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 65%.
C: Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 77.5%.
D: Because no applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 77.5%.
Answer:
It is B - Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.Thus, the probability is 65%.
>3
Answer: Choice B
Because some applicants volunteer and meet the GPA requirements, the events are not mutually exclusive.
Thus, the probability is 65%.
====================================================
Explanation:
950 people meet the GPA requirements. Also, 250 both meet the GPA requirements and volunteer. This must mean 950-250 = 700 people only meet the GPA requirements, but don't volunteer. Let A = 700.
600 people volunteer. 250 both meet the GPA requirements and volunteer. This must mean 600-250 = 350 people volunteer only (ie they don't meet the GPA requirements). Let B = 350
Let C = 250 to represent the number who meet the GPA requirements and volunteer.
-----------------
In summary we found that,
A = 700 people meet the GPA requirements only (they don't volunteer)B = 350 people volunteer only (they don't meet the GPA requirements)C = 250 people both meet the GPA requirements and volunteerThat means A+B+C = 700+350+250 = 1300 people either meet the GPA requirements, volunteer, or both. This is out of 2000 people
1300/2000 = 13/20 = 0.65 = 65%
That calculation tells us that 65% of the 2000 applicants fit the conditions we're after. So that's the probability of randomly selecting someone to fit those conditions.
Because the value of C is not zero, this means we don't have mutually exclusive events. It's possible that someone fits both criteria. Mutually exclusive events cannot happen at the same time.
In other words, if we did have mutually exclusive events, then someone couldn't both meet the GPA requirements and volunteer at the same time (they would have to pick one or the other but not both).
Answer this question to receive 10 points
Answer:
153.86.
Step-by-step explanation:
Use the formula pi times radius squared.
The Table below shows the number of hours ten students spent studying for a test and their svores
Answer:
Step-by-step explanation:
By using linear regression calculator,
Linear regression equation representing the data set will be,
y = 7.79x + 34.27
Correlation coefficient of the line will be,
R = 0.98
Since, correlation coefficient of the line is (+0.98), relation between the two variables is a strong linear relationship.
That means hours spent studying has the strong relation with test scores obtained.
Erin has 5 cans of juice and drinks 1/3 of a can daily. in how many days will she empty all the cans she has? I think it's 1/15 I'm not sure though.
During the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month. State whether this increase was linear or exponential. If your food bill was $130 in one month during this period, what was it three months later?
Answer:
After three months the value of the food bill will be $ 224.64.
Step-by-step explanation:
Given that during the worst periods of hyperinflation in a certain country, the price of the food increased at a rate of 20% per month, for state whether this increase was linear or exponential, and determine, if your food bill was $ 130 in one month during this period, what was it three months later, the following calculations must be performed:
A hyperinflation raises prices exponentially (the percentage is calculated based on the increase of the previous month). Thus, to calculate the price of the food bill, the following calculation must be performed:
130 x 1.20 ^ 3 = X
130 x 1.728 = X
224.64 = X
Therefore, after three months the value of the food bill will be $ 224.64.
Common ration of 54 and 72
Answer:
answer is 18 54 an 72 is 18
College credits. A college counselor is interested in estimating how many credits a student typically enrolls in each semester. The counselor decides to randomly sample 100 students by using the registrar's database of students. The histogram below shows the distribution of the number of credits taken by these students. Sample statistics for this distribution are also provided. 25 20 8 15 10- Min Q1 Median Mean SD Q3 Max 13 14 13.65 1.91 15 18 5 5 0 00 10 12 14 16 18 Number of credits (a) What is the point estimate for the average number of credits taken per semester by students at this college
Answer:
[tex]\bar x = 13.65[/tex]
Step-by-step explanation:
Given
See attachment for graph and table
Required
Point estimate of the mean
From the attachment, we have:
[tex]\mu = 13.65[/tex]
So, the point estimate of the mean (i.e. the sample mean) is:
[tex]\bar x =\mu[/tex]
[tex]\bar x = 13.65[/tex]