Answer:
The area of the shaded region is [tex](77-4\pi)\ cm^{2}[/tex]
Step-by-step explanation:
we know that
The area of the shaded region is equal to the area of the rectangle minus the area of the circle
step 1
Find the area of the rectangle
[tex]A=(7)(11)=77\ cm^{2}[/tex]
step 2
Fin the area of the circle
[tex]A=\pi (2)^{2}=4\pi \ cm^{2}[/tex]
step 3
Find the area of the shaded region
[tex]77\ cm^{2}-4\pi \ cm^{2}=(77-4\pi)\ cm^{2}[/tex] -----> exact value
To find the approximate value use [tex]\pi=3.14[/tex]
[tex](77-4(3.14))=64.44\ cm^{2}[/tex] -----> approximate value
What is the equation of the line, in point-slope form, that passes through the points (-3, -1) and (-6, 8)?
A. y + 8 = -3(x - 6)
B. y - 8 = -3(x + 6)
C. y + 8 = 3(x - 6)
D. y - 8 = 3(x + 6)
Answer:
B. y - 8 = -3(x + 6)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have the points (-3, -1) and (-6, 8). Substitute:
[tex]m=\dfrac{8-(-1)}{-6-(-3)}=\dfrac{9}{-3}=-3\\\\y-8=-3(x-(-6))\\\\y-8=-3(x+6)[/tex]
The total, t, divided into 5 groups is 45
Harry made fruit punch using 2 parts orange juice to 2 parts soda water. The amount of soda water that Harry used is directly proportional to the amount of orange juice he used. How many cups of orange juice should Harry use with 18 cups of soda water?
Final answer:
To find out how many cups of orange juice Harry should use with 18 cups of soda water, set up a proportion and solve for x.
Explanation:
In this problem, we know that Harry uses 2 parts orange juice to 2 parts soda water for his fruit punch. This means that for every 2 cups of orange juice, he uses 2 cups of soda water. Since the amount of soda water is directly proportional to the amount of orange juice, we can set up a proportion to find out how many cups of orange juice Harry should use with 18 cups of soda water.
2 cups orange juice / 2 cups soda water = x cups orange juice / 18 cups soda water
To solve the proportion, we can cross multiply:
2 cups orange juice * 18 cups soda water = x cups orange juice * 2 cups soda water
36 cups orange juice = 2x cups soda water
By dividing both sides of the equation by 2, we find that Harry should use 18 cups of orange juice with 18 cups of soda water.
How do I find and what is the x?
Answer:
STEP ONE: 2x
STEP TWO: 5=X (should be the final answer)
Step-by-step explanation:
Hi Lasagna!
So basically, this is extremely simple. In order to "solve" that equation, the x has to be on one side. The easiest way to do this would be to take the 2x to the other side. If you want the 2x to go to the other side, you need to subtract it (since it is already positive, therefore it needs to cancel out). Once you do that, you must always do the same thing to the other side: subtract 2x from 3x. That should get you one x there, which you can just write as x if it's just one. Then you're all set! :D
Answer: step 1. 2 from both sides
Step-by-step explanation:
just take away the = number by doing the opposite action for ex. if it it 2x then divide both sides by 2.
Based on the records for the past several seasons a sports fan believes the probability the red team wins is 0.55. The fan also believes the probability the blue team will wins is 0.60. In a season with 180 games, how many fewer games should the fan expect the red team to win?
Answer:
The fan should expect the red team to win 9 more games than the blue team.
Step-by-step explanation:
Using proportions, it is found that over the entire season, the fan should expect the red team to win 9 less games.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, considering the proportions of the red and of the blue teams, the number of games they are expected to win is given by:
R = 0.55 x 180 = 99.B = 0.6 x 180 = 108.108 - 99 = 9, hence the fan should expect the red team to win 9 less games.
More can be learned about proportions at https://brainly.com/question/24372153
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As you leave Clark, the sign says Lutherville 75 miles, Otisburg 155 miles. If the Planet Diner is halfway between Lutherville and Otisburg, how far is it from Clark?
77.5 answer
Step-by-step explanation:
The Planet Diner, being halfway between Lutherville and Otisburg, is 115 miles away from Clark.
Explanation:To answer this question, we need to find out how far the Planet Diner is from Clark. Given that the Planet Diner is halfway between Lutherville and Otis burg, it is about half of the distance from Otis burg to Lutherville, which is 155 miles - 75 miles = 80 miles.
So, the distance from Lutherville to the Planet Diner is 80 miles / 2 = 40 miles. Since Lutherville is 75 miles away from Clark, the distance from Clark to the Planet Diner would be 75 miles + 40 miles = 115 miles.
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Please help
No idea how to do
Answer:
see explanation
Step-by-step explanation:
He cycles [tex]\frac{3}{4}[/tex] Km and jogs [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{6}[/tex]
Adding the 2 together gives the total he cycled/ jogged
[tex]\frac{3}{4}[/tex] + [tex]\frac{3}{4}[/tex] - [tex]\frac{1}{6}[/tex]
We require the denominators to be common before adding/ subtracting
The lowest common denominator of 4 and 6 is 12, hence
= [tex]\frac{9}{12}[/tex] + [tex]\frac{9}{12}[/tex] - [tex]\frac{2}{12}[/tex]
= [tex]\frac{9+9-2}{12}[/tex]
= [tex]\frac{16}{12}[/tex] = [tex]\frac{4}{3}[/tex] = 1 [tex]\frac{1}{3}[/tex] Km
Do 3/4 x 3 = 9/12
Do 1/6 x 2 = 2/12
Then do 9/12 - 2/12 = 7/12
Next you do 7/12 + 9/12 = 16/12
Then simplify. 1 4/12
Simplify again. 1 1/3
how to solve polynomial by factoring and using the zero product principle for x^3+3x^2=4x+12
Answer:
The solutions to the equation are -3,-2,2
Step-by-step explanation:
x^3+3x^2=4x+12
Subtract 4x +12 from each side
x^3+3x^2-4x-12=4x+12-4x-12
x^3+3x^2-4x-12=0
I will use factoring by grouping
x^3+3x^2 -4x-12=0
I will factor out x^2 from the first group and -4 from the second group
x^2 (x+3) -4(x+3) =0
Now we can factor out (x+3)
(x+3) (x^2-4) =0
We can use the zero product principle since the right hand side is equal to 0
x+3 =0 x^2-4 =0
x+3-3=0-3 x^2 -4+4=0+4
x=-3 x^2=4
Take the square root of each side
sqrt(x^2) = sqrt(4)
x=±2
The solutions to the equation are -3,-2,2
Bonita said that the product of 5/6 × 1 2/3 is 7/ 3. How can you tell that her answer is wrong?
Answer:
See below
Step-by-step explanation:
Because her answer is greater than 2 (7/3 = 2 1/3)
We are multiplying a number less than 2 (1 2/3) by a number less than 1 (5/6), so we have less than one of the number 1 2/3, which has to be less than 1 2/3.
let's firstly convert the mixed fraction to improper fraction.
[tex]\bf \stackrel{mixed}{1\frac{2}{3}}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{5}{6}\times \cfrac{5}{3}\implies \cfrac{25}{18}\implies 1\frac{7}{18}[/tex]
what if the measure of the smaller angle formed by the minute hand and the hour hand at 2:30
120°
hope you are having a good day :)
what is 15456415 times 45415
Answer: 701953087225 is the answer
Write the equation is logicrithmic form 3^3=27
Answer:
[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]
Step-by-step explanation:
[tex] b^y = x \Longleftrightarrow \log_b x = y [/tex]
A logarithm is an exponent. The base of the logarithm is the base of the power.
[tex] 3^3 = 27 \Longleftrightarrow \log_3 27 = 3 [/tex]
Answer:
[tex] log_3 2 7 = 3 [/tex]
Step-by-step explanation:
We are given the following equation and we are to write it in logarithmic form:
[tex] 3 ^ 3 = 27 [/tex]
We know that [tex] a ^ n = b [/tex] is written as [tex] log _ a b [/tex] when expressed in logarithmic form.
So here we have [tex] 3 ^ 3 = 27 [/tex], converting it logarithmic form we get:
[tex] log_3 2 7 = 3 [/tex]
I need help finding the value of x
Answer:
60 i think
Step-by-step explanation:
Hope this helped :)
According to the tree diagram below, what is the probability that someone buys a book that is hardcover and nonfiction
Whenever you have a decision tree like this, the probability of reaching a specific leaf is the multiplication of the probabilities of each step you have to reach the leaf.
So, in order to reach the "hardcover and nonfiction" leaf, we have to take the "buys hardcover" branch (probability 0.35), and then the "buys nonfiction" branch (probability 0.55).
Given what we said above, the probability for "hardcover and nonfiction" is
[tex]0.35\cdot 0.55=0.1925[/tex]
The probability of buying a hardcover and non-fiction book is 0.1925
How to determine the stated probabilityWe have the below parameters for our Calculation;
P(hard cover) = 0.35 P(non - fiction) = 0.55The probability that someone buys a hardcover and non- fiction book ;
P(hard cover n Non-fiction) = P(hard cover) × P(non-fiction)Now we have;
P(hard cover n Non-fiction) = 0.35 × 0.55 = 0.1925
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I need the answer plz show me the step
Answer:
f(x)/g(x) = x+6
Step-by-step explanation:
f(x) = 3x^2 +16x -12
g(x) = 3x-2
f(x) 3x^2 +16x -12
---- = -------------------
g(x) 3x-2
Factor
f(x) (3 x - 2) (x + 6)
---- = -------------------
g(x) 3x-2
Cancel the common terms
f(x) (x + 6)
---- = -------------------
g(x) 1
535 invenstment compounded continuosly for 10 years at 6 percent
Answer:
[tex]\$974.83[/tex]
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=10\ years\\ P=\$535\\ r=0.06[/tex]
substitute in the formula above
[tex]A=\$535(e)^{0.06*10}=\$974.83[/tex]
Two seniors, one from each government class are randomly selected to travel to Washington, D.C. Wes is in a class of 18 students and Maureen is in a class of 20 students. Find the probability that both Wes and Maureen will be selected.
Answer: 1 out of 19
Step-by-step explanation:
add up all of the students, wes and maureen are two people, so it's two out of thrity eight, then just simplify it and you're done <3
The probability that both Wes and Maureen will be selected is 1/360.
What is probability?Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.
Given, Wes is in a class of 18 students and Maureen is in a class of 20 students.
Now, this is an independent event, therefore, the probability that both Wes and Maureen will be selected will be,
= (1/18)×(1/20).
= 1/360.
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Which of the following is a polynomial with rootsnegative square root of 5, square root of 5, and 3
Answer:
P(x) = x³ - 3x² - 5x + 15
Step-by-step explanation:
∵ The roots of the polynomial are -√5 , √5 , 3
∴ The polynomial has 3 factors:
(x - √5) , (x + √5) , (x - 3)
∴ P(x) = (x - √5)(x + √5)(x - 3)
= (x² + √5x - √5x - 5)(x - 3)
= (x² - 5)(x - 3) = x³ - 3x² - 5x + 15
∴ P(x) = x³ - 3x² - 5x + 15
URGENTTTTTTTTTTTTT!!!!!!!!!!!
3^3 + 2^7
Step-by-step explanation:
There really is no other way that I can think of other than guessing and checking. 3^3 is 27, when subtracted from 155 gives you 128. 128 can be rewritten as 2^7, leaving your final answer as 3^3 +2^7.
"taken from MrScienceguy"
Answer:
3^3 + 2^7
Step-by-step explanation:
There really is no other way that I can think of other than guessing and checking. 3^3 is 27, when subtracted from 155 gives you 128. 128 can be rewritten as 2^7, leaving your final answer as 3^3 +2^7.
subtract (5x^2+3)-(2x^2+4x-12)
Answer:
Final answer is [tex]3x^2-4x+15[/tex]
Step-by-step explanation:
Given expression is [tex](5x^2+3)-(2x^2+4x-12)[/tex].
Now we need to subtract them.
We are allowed to subtract like terms only that has same variable with same exponent.
[tex](5x^2+3)-(2x^2+4x-12)[/tex]
[tex]=5x^2+3-2x^2-4x+12[/tex]
[tex]=5x^2-2x^2-4x+3+12[/tex]
[tex]=(5-2)x^2-4x+(3+12)[/tex]
[tex]=(3)x^2-4x+(15)[/tex]
[tex]=3x^2-4x+15[/tex]
Hence final answer is [tex]3x^2-4x+15[/tex]
Answer:
(5x² + 3) - ( 2x² + 4x - 12) = 3x² - 4x + 15
Step-by-step explanation:
The given expression is
(5x² + 3) - ( 2x² + 4x - 12)
To find the subtraction result
(5x² + 3) - ( 2x² + 4x - 12) = 5x² + 3 - 2x² - 4x + 12
= 5x² - 2x² - 4x + 3 + 12
= 3x² - 4x + 15
Therefore the correct answer is
(5x² + 3) - ( 2x² + 4x - 12) = 3x² - 4x + 15
Estimate the surface area of a cube with side length 9.9 in.
A) 100 in2
B) 400 in2
C) 600 in2
D) 1000 in2
Answer:
Estimate the surface area of a cube with side length 9.9 in.
A) 100 in²
B) 400 in²
C) 600 in²
D) 1000 in²
Step-by-step explanation:
9.9 to the nearest whole number is 10
We know the side length of the cube is 10
We work out the area of face and multiply by 6.
10 x 10 = 100
100 x 6 = 600 in²
Answer:
600 is the answer
Step-by-step explanation:
We can round each side length to 10 in. Therefore, the area of one face is 100 in2. Since there are 6 congruent faces in a cube, the total estimated surface area of 600 in2.
Will mark BRAINLIEST!!!
Answer:
C
Step-by-step explanation:
sqrt(200)
Find the highest square multiple.
200 = 100 * 2
sqrt(100) = 10
10 goes on the outside, and the one that is left, 2, goes on the inside.
Answer:
Your answer is C) [tex]10\sqrt{2}[/tex]
Step-by-step explanation:
This is because [tex]10\sqrt{2}[/tex] is [tex]\sqrt[4]{200}[/tex] simplified.
Confirming the answer above!
I hope this helps!~
In a bag of candy there are 12 blue candies, six red candies, four yellow candies, and two purple candies. What is the ratio of red to all candies? Simplify if possible
?? hold on I'ma work the problem out
Answer:
6/22
Step-by-step explanation:
Just add wanted outcomes over all outcomes
in the figure PQ is parallel to RS. the length of RP is 6 cm; the length of PT is 18 cm; the length of QT is 21 cm; what is the length of SQ?
Answer:
Option A. [tex]SQ=7\ cm[/tex]
Step-by-step explanation:
we know that
In the figure
The triangles PTQ and RTS are similar by AA Similarity Theorem
so
Remember that
If two figure are similar, then the ratio of its corresponding sides is equal
so
[tex]\frac{PT}{RT}=\frac{QT}{ST}[/tex]
we have
[tex]PT=18\ cm[/tex]
[tex]RT=RP+PT=6+18=24\ cm[/tex]
[tex]QT=21\ cm[/tex]
[tex]SQ=ST-21\ cm[/tex] ------> equation A
substitute the values and solve for ST
[tex]\frac{18}{24}=\frac{21}{ST}[/tex]
[tex]ST=21*24/18[/tex]
[tex]ST=28\ cm[/tex]
substitute the value of ST in the equation A to find the value of SQ
[tex]SQ=28-21=7\ cm[/tex]
Answer: 77cm
Step-by-step explanation:
What is the volume of a rectangular prism with the dimensions: base 3 1 2 cm, height 1 1 2 cm, and length 5 1 2 cm?
Answer:
The volume of a rectangular prism is [tex]28\frac{7}{8}\ cm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the rectangular prism is equal to
[tex]V=BHL[/tex]
Convert the given dimensions to an improper fractions
[tex]B=3\frac{1}{2}\ cm=\frac{3*2+1}{2}=\frac{7}{2}\ cm[/tex]
[tex]H=1\frac{1}{2}\ cm=\frac{1*2+1}{2}=\frac{3}{2}\ cm[/tex]
[tex]L=5\frac{1}{2}\ cm=\frac{5*2+1}{2}=\frac{11}{2}\ cm[/tex]
substitute in the formula
[tex]V=(\frac{7}{2})(\frac{3}{2})(\frac{11}{2})=\frac{231}{8}\ cm^{3}[/tex]
Convert to mixed number
[tex]\frac{231}{8}=\frac{224}{8}+\frac{7}{8}=28\frac{7}{8}\ cm^{3}[/tex]
What is 15,245 divided by 9
Answer:
1693.88888889
Step-by-step explanation:
15,245 divided by 9 or 15,245/9
The correct answer is 1,693.88889
If you round this, the answer is 1,694
Hope this helps!
Consider the table of values.
x y
-2 0
-1 2
0 6
1 12
2 20
3 30
4 42
Select the statement that is true about the table.
A.
The relationship between the variables in the table is linear because the first differences are constant.
B.
The relationship between the variables in the table is quadratic because the second differences are constant.
C.
The relationship between the variables in the table is linear because the second differences are constant.
D.
The relationship between the variables in the table is quadratic because the first differences are constant.
Answer:
B. The relationship between the variables in the table is quadratic because the second differences are constant.
Step-by-step explanation:
We have to look for the differences in the y values of the given table.
The y values are:
0, 2, 6, 12, 20, 30, 42
The differences between the consecutive values are:
2, 4, 6, 8, 10, 12
These are the first differences and are not constant. This means the relationship is not linear. Now we again find the differences between the consecutive values:
2, 2, 2, 2, 2
These are the second differences. The second differences are constant. So this means the given relationship is quadratic.
Therefore, option B gives the correct answer. The relationship between the variables in the table is quadratic because the second differences are constant.
Figure ABCD is a parallelogram what are the measures of angles B and D?
Answer:
B=65 degrees, c=65 degrees
Step-by-step explanation:
Opposite angle in a parallelogram are equal. 3n+20 = 6n-25. n=15. You then plug n in into the equations. B=65 and D=65
Answer:
the answer to this question is B. Trust me I'm not wrong.
-0.14x0.12 what is the product
Answer:
-0.14 * 0.12 = -0.0168
Step-by-step explanation:
You could multiply both numbers by 100 to make them whole integers.
-0.14 * 100 = -14
0.12 * 100 = 12
-14 * 12 = -168
Now divide by 100 twice.
-168 / 100 = -1.68 / 100 = -0.0168
Disuss the difference between fixed expenses and variable expenses as they relate to a budget?
The difference between fixed expenses and variable expenses is that fixed expenses do not change, regardless of how many items are produced. Variable expenses change based on the number of items produced.
An example of a fixed expense is the rent. The rent is always the same amount, regardless of production.
Materials would be a variable expense. You need enough material to make each item, so the more items you produce, the more material you need.