The radius of the hemisphere is 45 cm
Explanation:
Given:
Volume of the hemisphere, V = 60750π cm³
Radius of the hemisphere, r = ?
We know:
Volume of hemisphere = [tex]\frac{2\pi r^3 }{3}[/tex]
[tex]60750\pi = \frac{2\pi r^3 }{3} \\\\r^3 = 91125\\\\r = 45[/tex]
Therefore, the radius of the hemisphere is 45 cm
The radius of the hemisphere is 45 cm
The volume of a hemisphere is given by the formula
[tex]V = \frac{2}{3} \pi r^{3}[/tex]
Where V is the volume
and r is the radius
From the question,
V = 60750π cm³
Putting this into the formula,
We get
[tex]60750\pi = \frac{2}{3}\pi r^{3}[/tex]
∴ [tex]r^{3}= \frac{60750\pi \times 3}{2\pi}[/tex]
[tex]r^{3}= 91125[/tex]
∴ [tex]r =\sqrt[3]{91125}[/tex]
r = 45 cm
Hence, the radius of the hemisphere is 45 cm
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If you horizontally stretch the quadratic parent function, f(x) = x², by a factor
of 3, what is the equation of the new function?
O A. g(x) = x2
O B. g(x) = (3852
O C. g(x) = (3x)2
o D. g(x) = 3x²
Answer:
d
Explanation:
You multiply the X by 3
Simplify.
-6+[4-(x-2)]
Answer:
-x
Step-by-step explanation:
-6+[4-(x-2)]
Distribute the minus sign
-6+[4-x+2]
Combine like terms
-6+4 +2 -x
-x +0
-x
What is the mean absolute deviation of the data: 10, 20, 15, 17, and 13?
Answer:
2.8
Step-by-step explanation:
1) find the mean of the data set. = 15
2) find the abs value of the diff between each data value and the mean: |data value – mean|.
|10-15|=5, |20-15|=5, |15-15|=0, |17-15|=2, |13-15|=2
3) find the sum of the abs values of the diff = 14
4) divide the sum of the abs value by the number of data values = 14/5 = 2.8
what is the perimeter of this tile 10 in 8 in 6 in
Answer:
24 inches
Step-by-step explanation:
To find perimeter, simply add all the side lengths
10 + 8 + 6 = 24in
Thank me later :)
Solve for h
35=1/2h (5+2)
Answer:
10
Step-by-step explanation:
35= 1/2h(7)
1/2 of 7 is 3.5
3.5(10)=35
h=10
Answer:
Solve for h
35=1/2h (5+2)
Multiply (5+2) by 1 divided by 2, then we have
7/2h= 35
cross multiply
35 x 2h= 7
70h= 7
divide both sides by 70
h= 7/70
h= 1/10
Step-by-step explanation:
A relative frequency table is made from data in a frequency table.
Relative Frequency Table: A 4-column table with 3 rows. The first column has no label with entries likes S, T, total. The second column is labeled U with entries 26%, 21%, 47%. The third column is labeled V with entries 42%, k, 53%. The fourth column is labeled total with entries 68%, 32%, 100%.
What is the value of k in the relative frequency table? Round the answer to the nearest percent.
2%
11%
20%
33%
Answer:
k = 11 let me know if you don't understand how I got this.
Step-by-step explanation:
I'm gonna write it out
U V total
S 26 42 68
T 21 k 32
Total 47 53 100
So, you want to look at the column and row labeled total, this is the key. for the row total, it sums up everything in the column above it. so for the u column, the total value is 47 while the two values above it are 26 and 21. These two values sum to 47. This is the same for all other columns, and you can use the same reasoning with the total column as well summing rows.
This gives you two ways to solve for k. either 21 + k = 32 or 42 + k = 53. Either way gets you the answer k = 11
The value of k in the relative frequency table is 11%.
What is relative frequency?The ratio of the frequency of a particular event in a statistical experiment to the total frequency.
U V total
S 26 42 68
T 21 k 32
Total 47 53 100
As, when we add the column data 26+ 21 = 47 which shows that the total consist of sum of column data.
So,
21 + k = 32
k = 11
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Solve the four problems below. Which of the following problems can be solved by finding ? 3 divided by 1/2
a. Shauna buys a three-foot-long sandwich for a party. She then cuts the sandwich into pieces, with each piece being 1/2 -foot long. How many pieces does she get?
b. Phil makes 3 quarts of soup for dinner. His family eats half of the soup for dinner. How many quarts of soup does Phil's family eat for dinner?
c. A pirate finds three pounds of gold. In order to protect his riches, he hides the gold in two treasure chests, with an equal amount of gold in each chest. How many pounds of gold are in each chest?
d. Leo used half of a bag of flour to make bread. If he used 3 cups of flour, how many cups were in the bag to start?
Answer:
[tex](a)=6\\(b)=1\ \frac {1}{2}\\(c)=1\ \frac {1}{2}\\d=6[/tex]
Step-by-step explanation:
(a)
3 ft long when divided into half ft each will be
3ft ÷1/2 ft
We change the ÷ to × then the second part is reciprocated hence
3ft÷1/2= 3ft×2/1=6 pieces
(b)
The question requires us to get the differences. Initially, Phil makes 3 quarts of soup but the family takes only half of the original quantity to mean Phil remains with the other half.
Therefore, half of 3 is 3×1/2=3/2= 1.5 or 1 1/2
(c)
Hiding 3 pounds of gold into two equal sections means 3 is divided by 2
3÷2=1.5 or 1 1/2
(d)
If half, 0.5 represent 3 cups then full quantity represent x
0.5=3 cups
1=x
By cross multiplication
1*3/0.5=6
Put these in order from least to greatest 1/2, 1/3, 2/5, 0.6 , o.3
Answer:
0.3, 1/3, 2/5, 1/2, 0.6
Step-by-step explanation:
Answer:
ok first lets make them all decimals
1/2=0.5
1/3= 0.3333333
2/5= 0.4
ok now we got 0.5, 0.33333, 0.4, 0.6, 0.3,
now lets also add zeros to the back to make it a more clear picture
0.50, 0.33, 0.40, 0.60, 0.30 ok now put the in order
0.30 , 0.33, 0.40, 0.50, 0.60
Step-by-step explanation:
2.75 cups of water mixed with 3.5 cups of pancake mix will make 19 pancakes. How much water is needed if there is only 1.5 cups of pancake mix left?
Answer:
You would need .75 cups of water (or 3/4 cups) if there is only 1.5 cups of pancake mix left
Step-by-step explanation:
So the ratio of water to pancake mix is 2.75 : 3.5 (which makes 19 pancakes)
To get from 3.5 cups of pancake mix to 1.5 cups of pancake mix you would subtract 2 cups. Since this is a ratio, you would not only subtract 2 cups from the pancake mix, but also from the water. 2.75 - 2 = .75 Therefore, you would need .75 cups of water (or 3/4 cups) if there is only 1.5 cups of pancake mix left. Hope this helps!
Answer:
1 5/28 cups of water
Step-by-step explanation:
Water : pancake mix
2.75 : 3.5
X : 1.5
2.75/X = 3.5/1.5
X = 2.75 × 1.5/3.5
X = 33/28 or 1 5/28 cups
please help with this question its in the picture :)
Please help it’s for my brother!!
Answer:
the answers B
Step-by-step explanation:
i got B
Exterior angles of a triangle...help?
Answer:
Angle 4 is the exterior angle
Step-by-step explanation:
Exterior mean "outside"
Angle 4 is the only angle outside of the triangle
Let f(x) = 8x + 5 and g(x) = -2x - 4 Find the value of f(2) + g(5) *
Answer: lock down
Step-by-step explanation: f(x)= 8x2 + 5=21--> f(x)=21
g(x)= -2x5 - 4=-14--> g(x)=-14
f(2)+g(5) = 7
Step-by-step explanation:
Given,
f(x) = 8x+5
g(x) = -2x-4
To find f(2)+g(5)
Now,
f(2) means putting the value of x = 2 in f(x)
g(5) means putting the value of x = 5 in g(x)
f(2) = 8(2)+5 = 21
g(5) = -2(5)-4 = -14
Hence,
f(2)+g(5) = 21-14 = 7
Which is a Linear Equation?
A. Y=3-2x
B. Y= -7x^2
C. Y=2-3x^2
D. Y=-7×^3
Answer:
(A)
Step-by-step explanation:
A linear equation can be written in slope intercept form, [tex]y=mx+b[/tex].
X must be in it's first power in a linear equation. X being in any other power will result in a curved line.
This eliminates B, C and D already. X is not in it's first power in the given three options.
The best option is A.
4x + 3y = 6
-4x + 2y = 14
Answer:
x= −3/2 y=4
Step-by-step explanation:
Y= -x + 5; (2,),(5,),(0,)
Answer:
(2,3) (5,0) (0,5)
Step-by-step explanation:
Plug the x values into the equation to find your y value.
PLEASE HELP NEED ASAP
Answer:
Side WZ=9
Step-by-step explanation:
Since he two are similar you need to make a ratio of the two parallelograms
The first tells you side FE is 2 and side EH is 3 so write it like this 2/3.
Next you need to do the same thing with the second parallelogram, so you know side XW is 6 but you don't know side WZ so you'd write this one 6/x.
You can do this since FE is similar to XW, because it is the same shape just bigger.
Next you take the two fractions adn set them equal to each other.
2 6
_ = _
3 x
Now cross multiply (2 timesx and 6 times 3)
It should look like this now
2x=18
Now all you have to do is divide by 2.
The sum of the present ages of a father and his son is 80 years. When the
father's age was equal to the present age of the son, the sum of their ages
would be 40 years. Find their present ages.
Answer:
Father=60
Son=20
Step-by-step explanation:
Let the father's age be x
Let the son age be y
Present age of them
X+y=80...(1)
Since the father's age equals to the present age of the son
Y+y=40
2y=40....(2)
Make y the subject of formula by dividing both sides by 2
Y=20
Substitute the value for x into (1)
20+x=80
Substrate 20 from both sides
X=60
Therefore the father's age is 60 and the son's age is 20
A math teacher who likes baseball conducts a survey of 100 students. He asked the students about their favorite sport and about their favorite subjects in order to determine the number of students who like math or baseball. The two way table below shows part of the results of the survey. Enter the percentage of students in the survey who’s favorite subject is math or who’s favorite sport is baseball.
[this is written response, so there are no answer choices]
Answer:
46%
Step-by-step explanation:
see image attached!
HELP! WILL MARK BRAINLIEST!!!!! QUESTION IN THE PHOTO
Answer:
Step-by-step explanatio
What is the length of the third side of the window frame below
15
27
25
32
Answer:
25
Step-by-step explanation:
6. In the year of 2017, the highest number of ambulance calls in a month was 8,312. The
lowest number of ambulance calls in a month was 791 times. The difference between the
highest and lowest use in a month is about ______ calls.
a. 7,300 b. 7,500 c. 7,800
Answer: The answer would be (b), or 7,500
Step-by-step explanation:
Stack the numbers and have 8,312 on top of 791Subtract You get the answer 7,521Round to the nearest hundred by looking at the tens place, anything below 5 will round it down to 500 and anything 5 or more will round it up to 600You end up with 7,500 as your rounded answer (about is a clue word to let you know you need to round)I have a few questions!
a) x−1.27=4.09
b) 2.3−y=2.301
c) t+3.04=14.3
d) 1.1+k=5.67
Answer:
a.) x = 5.36
b.) y = - 0.001
c.) t = 11.26
d.) k = 4.57
Step-by-step explanation:
a) x−1.27=4.09
b) 2.3−y=2.301
c) t+3.04=14.3
d) 1.1+k=5.67
Solving. right?
a.) x = 4.09 + 1.27 = 5.36
b.) y = 2.3 - 2.301 = - 0.001
c.) t = 14.3 - 3.04 = 11.26
d.) k = 5.67 - 1.1 = 4.57
Liz flips a coin 50 times. The coin lands heads up 20 times and tails up 30 times. Complete each statement. The theoretical probability of the coin landing heads up is ______. Based on Liz’s results, the experimental probability of the coin landing heads up is_____. The theoretical probability is than the experimental probability in this experiment________.
Answer:
50% or 50/100 or 25/50 40% or 40/100 or 20/40MoreStep-by-step explanation:
The theoretical probability is more than the experimental probability in this experiment
What is Probability?The probability that an event will occur is measured by the ratio of favorable examples to the total number of situations possible
Probability = number of desirable outcomes / total number of possible outcomes
The value of probability lies between 0 and 1
Given data ,
Let the number of times the coin is flipped be n = 50
And , the number of times the heads is shown = 20 times
The number of times the tails is shown = 30 times
The theoretical probability of a coin being head or tail P ( A ) = 50 %
So , the experimental probability of being a head is P ( B ) = 20/50
P ( B ) = 40/100 = 40 %
Therefore , P ( A ) > P ( B )
Hence , theoretical probability is more
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Which set of ordered pairs does NOT represent y as a function of x?
Question 5 options:
{(1, 1), (2, 1), (3, 1)}
{(1, 1), (2, 2), (2, 3)}
{(1, 2), (2, 3), (3, 3)}
{(1, 2), (1, 3), (1, 1)}
Answer:
the 3rd choice
Step-by-step explanation:
Answer:
The last one {(1, 2), (1, 3), (1, 1)}
Step-by-step explanation:
This is because the domain x is repeated. For a set of ordered pairs to be a function the domain can not repeat.
What, approximately, is the mean weight for babies born
during this two-month period?
As a nurse in a maternity ward, you are tracking the
weights of newborn babies. In the month of August, 360
babies are born, with a mean weight of 8.1 pounds. In the
month of September, 291 babies are born, with a mean
weight of 7.8 pounds.
7.83 pounds
7.93 pounds
7.95 pounds
7.97 pounds
7.99 pounds
Final answer:
The approximate mean weight for babies born during the two months of August and September is calculated using a weighted average, and it is approximately 7.97 pounds.
Explanation:
To find the mean weight of the babies born during the two months, we can use the weighted average formula which takes into account the different numbers of babies born in each month and their respective mean weights.
The formula for the weighted mean is as follows:
Weighted mean = (Sum of weights × their respective frequencies) / (Total sum of frequencies)
Calculate the total weight for August: 360 babies × 8.1 pounds = 2916 pounds.Calculate the total weight for September: 291 babies × 7.8 pounds = 2269.8 pounds.Add the weights from both months: 2916 pounds + 2269.8 pounds = 5185.8 pounds.Add the number of babies from both months: 360 babies + 291 babies = 651 babies.Divide the total weight by the total number of babies: 5185.8 pounds ÷ 651 babies = approximately 7.97 pounds.Therefore, the approximate mean weight for the babies born during August and September is 7.97 pounds.
If $500 yields $51.76 in simple interest over 7yrs, what is the annual rate? Answer need to be rounded to the nearest thousandth
The annual rate of interest is 1.479%.
Step-by-step explanation:
Given,
Principle (P) = $500
Interest (I) = $51.76
Time (T) = 7 years
To find out the rate of interest (R).
Formula
Simple interest (I) = [tex]\frac{PTR}{100}[/tex]
According to the problem,
[tex]\frac{PTR}{100}[/tex] = 51.76
or, R = [tex]\frac{51.76X100}{PT}[/tex]
or, R = [tex]\frac{51.76X100}{500X7}[/tex]
= 1.4788 = 1.479% (approx)
Answer:
1.5%
Step-by-step explanation:
Principal, P = $500
Simple interest S.I. = $51.76
Period, T = 7 years
Simple interest = P*R*T / 100
Let's make rate, R the subject of formula
R = 100 * S.I. / P * T
Slot in the respective values
R = 100 * 51.76 / 500 * 7
R = 1.5%
Just Checking
2. A consumer watchdog organization received customer complaints about
the performance of one brand of batteries. To investigate, the researchers
purchased 24 of these batteries and ran them until they died. This sample
lasted a mean of 47 hours with a standard deviation of 3 hours.
a) What assumption must we make about battery life in order to use a t
model?
b) Find a 95% confidence interval for the mean lifespan of this brand of
batteries.
c) Write a conclusion based on your confidence interval.
Which of the given points would be in a table generated by the equation below?
pm + gy = 5
А. (0, 9)
B. (0, й)
C. , о)
D. (2 , 0)
26 Points!!! Select True or False for each equation.
Answer:
The first one is true, meanwhile the second is false!
Step-by-step explanation:
The first one both simplify to -3.
The second one, -6/-2 ( fraction ) simplifies to positive 3 because dividing or multiplying by 2 negative numbers cancels out the negative sign.
Hope it helps!
Answer:
1) True
2) False
Step-by-step explanation:
- 6/2 = -3