Answer:
f = 4 pi
Step-by-step explanation:
f + 3 pi = 7 pi
f = 7 pi - 3 pi
f = 4 pi
Answer:
f = 4 pi
Step-by-step explanation:
f + 3 pi = 7 pi
Subtract 3 pi from each side
f + 3 pi -3pi = 7 pi -3 pi
f = 4 pi
Below are two different functions, f(x) and g(x). What can be determined about their y-intercepts?
X: 1,3,5
——————
G(X): 0,4,8
A)The function f(x) has a higher y-intercept
B)The function gx has a higher y intercept
C) They both have the same y intercept
D) The relationship between y intercepts cannot be determined
Answer: D) relationship between y intercepts cannot be determined
The graph of f(x) is a vertical line. It is completely parallel to the y axis, so it never crosses the y axis. We need the graph to cross the y axis somewhere in order to form a y intercept. Therefore f(x) does not have a y intercept. So we cannot compare y intercepts if f(x) doesn't have one at all.
15. Jim had 103 red and blue marbles. After giving of his blue marbles and 15 of his red marbles
to Samantha, Jim had as many red marbles as blue marbles. How many blue marbles did he
originally have?

This question above is incomplete
Complete Question
Jim had 103 red and blue marbles. After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles. How many blue marbles did he have originally?
Answer:
70 Blue marbles
Step-by-step explanation:
Let red marbles = R
Blue marbles = B
Step 1
Jim had 103 red and blue marbles.
R + B = 103.......Equation 1
R = 103 - B
Step 2
After giving 2/5 of his blue marbles and 15 of his red marbles to Samantha, Jim had 3/7 as many red marbles as blue marbles
2/5 of B to Samantha
Jim has = B - 2/5B = 3/5B left
He also gave 15 red marbles to Samantha
= R - 15
The ratio of what Jim has left
= Red: Blue
= 3:7
= 3/7
Hence,
R - 15/(3/5)B = 3/7
Cross Multiply
7(R - 15) = 3(3/5B)
7R - 105 = 3(3B/5)
7R - 105 = 9B/5
Cross Multiply
5(7R - 105) = 9B
35R - 525 = 9B............ Equation 2
From Equation 1, we substitute 103 - B for R in Equation 2
35(103 - B) - 525 = 9B
3605 - 35B - 525 = 9B
Collect like terms
3605 - 525 = 9B + 35B
3080 = 44B
B = 3080/44
B = 70
Therefore, Jim originally had 70 Blue marbles.
The price of a used textbook after a 35% markdown is $28.60. What was the original price?
Answer:
28.60×.35=10.01
10.01+28.60=$38.61
Below are two different functions, f(x) and g(x). What can be determined about their slopes?
f(x)= 4x + 2
A) function f(x) has a larger slope
B) the function g(x) has a larger slope
C) they both have the same slope
D) the relationship between slopes cannot be determined
===================================================
Explanation:
The slope of f(x) is 4, since the equation y = 4x+2 has slope m = 4. Compare this to y = mx+b.
The slope of g(x) is 5. Note how if we started at (0,-2) on the red line and moved up 5 and to the right 1, we arrive at (1,3) which is another point on the red line. You could use the slope formula
m = (y2-y1)/(x2-x1)
to get the same result.
Since the slope of f(x) is 4 and the slope of g(x) is 5, we see that g(x) has a larger slope. The g(x) line is steeper compared to f(x).
The given graph shows the cigarette consumption (in billions) in the United States for the years 1900 to
2007
Choose the best estimate for the number of cigarettes smoked in 2000.
420 billion
Qi 400 billion
380 billion
450 billion
Answer:
The answer is below
Step-by-step explanation:
The graph used to estimate the consumption (in billions) in the United States for the years 1900 to 2007 is attached.
The year is plotted on the x axis and the number of cigarettes is on the y axis. To estimate the number of cigarattes smoked in year 2000, we have to find the y coordinate that corresponds to an x coordinate of 2000. This is done by drawing a line vertically to touch the graph from the point 2000 on the x axis. The point it touches the graph is then traced to the y axis to get the consumption as shown in the graph attached.
From the graph the number of cigarettes smoked in 2000 is about 420 billion cigarettes
Suppose that it snows in Greenland an average of once every 27 days, and when it does, glaciers have a 26% chance of growing. When it does not snow in Greenland, glaciers have only a 4% chance of growing. What is the probability that it is snowing in Greenland when glaciers are growing? (Round your answer to four decimal places.)
Answer:
0.1998
Step-by-step explanation:
This is a conditional probability question.
We solve this question using Bayes's Theorem of conditional probability.
P(A|B) = [P(B|A) × P(A)] ÷ [(P(B|A) × P(A))+ (P(B|A') × P(A'))]
Based on the information in the question, we have the following values.
Suppose it snows in Greenland once every 27 days.
Probability (it snows) = P(A) = 1/27
= 0.037037037
Approximately = 0.0370
Probability ( it doesn't snow) = P(A') = 1 - 0.0370 = 0.963
Probability ( that when it snow, glaciers grow) = P(B|A) = 26% = 0.26
Probability( that is doesn't snow , glaciers grow) = P(B|A)' = 4% = 0.04
Using the Bayes's Theorem of conditional probability
Probability that it is snowing in Greenland when glaciers are growing is =
P(A|B) = [P(B|A) × P(A)] ÷ [(P(B|A) × P(A))+ (P(B|A') × P(A'))]
= [0.26 × 0.0370] ÷ [(0.26 × 0.0370) + (0.04 × 0.963)]
= 0.00962 ÷( 0.00962 + 0.03852)
=0.00962 ÷ 0.04814
= 0.199833818
Approximately to 4 decimal places ≈ 0.1998
Therefore, probability that it is snowing in Greenland when glaciers are growing is 0.1998
15 POINTS!!!!!!!!!!!!!!
If an object is dropped from a height of h meters and it’s the ground in t seconds, then t = *square root* h/4.9. Suppose that an object is dropped from the top of a building that is 290.57 meters tall. How long does it take to hit the ground?
Round your answer to the nearest tenth....
?????? Seconds
Please state how many seconds first...
Answer:
7.7 seconds
Step-by-step explanation:
t = √(h / 4.9)
t = √(290.57 / 4.9)
t = √59.3
t ≈ 7.7
A project has an initial cost of $60,000, expected net cash inflows of $14,000 per year for 9 years, and a cost of capital of 14%. What is the project's IRR? Round your answer to two decimal places.
Answer:
74
Step-by-step explanation:
60,000 + 14,000
ANS 14%
ANSWER: 74
The project's IRR is approximately 13.45%.
We have,
To calculate the project's internal rate of return (IRR), we need to find the discount rate at which the net present value (NPV) of the project's cash flows is equal to zero.
Given:
Initial cost (C0) = $60,000
Net cash inflow per year (CF) = $14,000
Number of years (n) = 9
Cost of capital (r) = 14% = 0.14
To calculate the IRR, set up the equation:
[tex]0 = C0 + (CF / (1 + r)^1) + (CF / (1 + r)^2) + ... + (CF / (1 + r)^n)[/tex]
[tex]0 = 60,000 + (14,000 / (1 + r)^1) + (14,000 / (1 + r)^2) + ... + (14,000 / (1 + r)^9)[/tex]
By using a financial calculator or software, the IRR for this project is found to be approximately 13.45% when rounded to two decimal places.
Therefore,
The project's IRR is approximately 13.45%.
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Find the average value of the function y = 6 - x2 over the interval [-1, 4]
Answer:
The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].
Step-by-step explanation:
The average value of a function over an interval is represented by this integral:
[tex]\bar y = \frac{1}{b-a}\cdot \int\limits^{b}_{a} {f(x)} \, dx[/tex]
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds of the interval, dimensionless.
[tex]f(x)[/tex] - Function, dimensionless.
If [tex]a = -1[/tex], [tex]b = 4[/tex] and [tex]f(x) = 6 - x^{2}[/tex], the average value of the function is:
[tex]\bar y = \frac{1}{4-(-1)}\int\limits^{4}_{-1} {6-x^{2}} \, dx[/tex]
[tex]\bar y = \frac{6}{5}\int\limits^{4}_{-1} \, dx - \frac{1}{5}\int\limits^{4}_{-1} {x^{2}} \, dx[/tex]
[tex]\bar y = \frac{6}{5}\cdot x |_{-1}^{4} - \frac{1}{15}\cdot x^{3}|_{-1}^{4}[/tex]
[tex]\bar y = \frac{6}{5}\cdot [4-(-1)]- \frac{1}{15}\cdot [4^{3}-(-1)^{3}][/tex]
[tex]\bar y = \frac{5}{3}[/tex]
The average value of the function [tex]f(x) = 6 - x^{2}[/tex] over the interval [tex][-1,4][/tex] is [tex]\frac{5}{3}[/tex].
find the values of x and y please and thank you
Answer:
x=26
y=9
Step-by-step explanation:
5x-17+3x-11=180
8x=180+17+11
8x=208
x=26
3(26)-11=78-11=67
2y+5=90-67
2y=90-67-5
2y=18
y=9
Addy’s monthly water bills for last year are $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26. Express the formula for the mean using sigma notation and calculate the mean water bill for the year. Extend Your Understanding
Answer:
Σ( xi ) / n ; $29
Step-by-step explanation:
Given the following data:
X= $27, $31, $30, $26, $25, $27, $37, $33, $32, $28, $26, $26
Number of observations (n) = 12
Mean formula (m) = ( Σ xi ) / n
Where i = each individual value in X
Mean water bill for the years is thus :
m = Σ [(27 + 31 + 30 + 26 + 25 + 27 + 37 + 33 + 32 + 28 + 26 + 26)] / 12
m = 348 / 12
m = 29
Hence, the mean water bill for the year is $29
is ray AB same as ray BA?
Answer:
Yes
Step-by-step explanation:
Because a - - - - - - - - - - b
Same as b-----------------a
There are three different colored balls: orange, green and purple. The probability of randomly choosing orange ball from a bag is 45%. The probability of randomly choosing a green ball from bag is 0.10. Explain how likely it is, in relation to 0, for Jared to randomly choose a purple ball from the bag. * l
Answer:
Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probabiity = expected outcome/total outcome
Let the total outcome be 100% = 1.0
Given three different colored balls: orange, green and purple. If the probability of randomly choosing orange ball from a bag is 45%. The probability of randomly choosing a green ball from bag is 0.10
The probability of choosing both orange ball and green ball is 0.45+0.10 = 0.55.
Since the total outcome of probability is 1, then the probability for Jared to randomly choose a purple ball from the bag will be expressed as;
Pr(purple) = 1 - [Pr(green)+Pr(orange)]
Pr(purple) = 1 - [0.45+0.10]
Pr(purple) = 1 - 0.55
Pr(purple) = 0.45
Hence it is 45% likely for Jared to randomly choose a purple ball from the bag.
what is the square root 3175 by division method
56.347..........
just simply put the value 3175 under division root and make pairs of 31 and 75.Now think of a number whose square will be nearest to 31 and that ll be 5.Now write 5 in the quotient and 5 also 5 under the divider.Now by multiplying 5 with the 5 in the quotient you ll get 25 write this under 31.And by adding 5 in the divider 5 youll get 10.write this under the divider.no by subtracting 25 from 31 you ll get 6 and by bringing 75 down it ll be 675.Now think of a number again and write it with 10.Like 6 into 6 is 36 and when you multiply 6 with 106 you ll get nearest number to 675 that ll be 636.Now because its giving a remainder just add a .0 in the question and continue to solve it the same way.And as it ll be a continuous answer so just add continuty dots........ or just round it off to nearest whole number
Answer:
56.347138347923
Step-by-step explanation:
Suppose the following are the city driving gas mileages of a selection of sport utility vehicles (SUVs). 19, 20, 19, 20, 18, 21, 17, 19, 24, 23, 21, 21, 17, 20, 20, 18 (a) Find the sample standard deviation (rounded to two decimal places). (b) In what gas mileage range does Chebyshev's inequality predict that at least 75% of the selection will fall
Answer:
answer below
Step-by-step explanation:
from the question the
mean = ∑x/n
∑x = 317
n = 16
mean = 19.8125
x x-Ц x-Ц²
19 -0.8125 0.66015625
20 0.1875 0.03515625
19 -0.8125 0.66015625
20 0.1875 0.03515625
18 -1.8125 3.28515625
21 1.1875 1.41015625
17 -2.8125 7.91015625
19 -0.8125 0.66015625
24 4.1875 17.53515625
23 3.1875 10.16015625
21 1.1875 1.41015625
21 1.1875 1.41015625
17 -2.8125 7.91015625
20 -0.8125 0.66015625
20 -0.8125 0.66015625
18 -1.8125 3.28515625
∑(x-Ц)² = 56.44
s.d = 1.9
b.
19.81 + 2*1.9= 23.61
19.81-2*1.9 = 16.01
=
HELP PLS! Kaitlyn is about to retire from gymnastics. Over her career she was lucky to stay healthy enough to compete in many meets. Create a Frequency Table and Histogram of the medals she won each season. 30, 42, 56, 63, 18, 44, 53, 70, 72 ,78, 59, 66 Create a frequency table with five intervals. Then use that information to create a histogram.
Answer:
272 thats the umm..never mind heheh
please help square root math
Answer:
2<∛13<3 1<∛6<2
Step-by-step explanation:
Lets find the integers a and b ∛13 lies between.
a<∛13<b
a³<13<b³
=> a=2 so 2³=8 and b=3 so 3³=27 8<13<27
Similarly a<∛6<b
a³<6<b³
a=1 and b=2
Mr. Beeson has $220 in the bank and $12 in his billfold. He has bills of $76 and $188 to pay. Use a
integer to express his total balance.
Answer:
Your answer is -32
Step-by-step explanation:
First you add $220 and $12 together giving you $232
Then you subtract $76 from the $232 giving you $156
Then subtract $188 from $156 giving you a total of -$-32
If (a^2 + b^2) (x^2 +y^2) = (ax + by )^2 then which relation is true?
Answer:
Step-by-step explanation:
Hello,
Let's develop both expressions and try to re factorise.
[tex]\forall (a,b,x,y) \in \mathbb{R}^4 \\ \\ (a^2+b^2)(x^2+y^2)=(ax+by)^2\\ \\<=>(ax)^2+(ay)^2+(bx)^2+(by)^2=(ax)^2+(by)^2+2(ax)(by)\\ \\<=> (ay)^2+(bx)^2-2(ay)(bx)=0\\ \\<=> (ay-bx)^2=0\\ \\<=> ay-bx=0\\ \\<=> \boxed{\sf \bf ay=bx}[/tex]
Thanks
What is -3 1/4 +1 1/2 on a number line
Which is a reasonable first step that can be used to solve the equation 2 (x + 6) = 3 (x minus 4) + 5?
Answer:
x=19
Step-by-step explanation:
2(x+6)=3(x-4)+5
2x+2*6=3x-3*4+5
2x+12=3x-12+5
12+12-5=3x-2x
19=x
Answer:
distribute 2 to (x+6) and 3 to (x-4)
Step-by-step explanation:
B is the midpoint of AC. Find the coordinates of C. B(-3,-3) and A(-1,-1)
Step-by-step explanation:
Let coordinates of B be ( x , y )
X coordinate of B = (-1 + x) / 2 = - 3
Y coordinate of B = (-1 + y) / 2 = -3
Therefore, coordinates of B are ( - 5, - 5 ).
Hitomi, Ben, and Gayle bought 3 pumpkins that weighed 15 pounds altogether. Ben and
Gayle's pumpkins each weighed the same amount.
Hitomis pumpkin weighed pounds. How much did Gayle's pumpkin weigh?
Answer:
5
Step-by-step explanation:
15/3=5 when the y are 3 it division
Answer:
What the other guy said
Step-by-step explanation:
Solve for x.
x + 3x + 5 =21
Answer:
x=4
Step-by-step explanation:
In order to solve for x, we must isolate x on one side of the equation.
x+3x+5=21
First, combine like terms. x and 3x are both terms with variables, and can be combined.
(x+3x) + 5=21
4x + 5=21
5 is being added to 4x. The inverse of addition is subtraction. Subtract 5 from both sides of the equation.
4x+5-5= 21-5
4x= 16
x is being multiplied by 4. The inverse of multiplication is division. Divide both sides by 4.
4x/4=16/4
x= 16/4
x=4
Let's check our solution. Plug 4 in for x and solve.
x+3x+5=21
4+3(4)+5=21
4+12+5=21
16+5=21
21=21
This solution checks out, so we know our answer is correct.
x is equal to 4, x=4.
Answer:
x = 4
Step-by-step explanation:
x + 3x + 5 = 21
4x + 5 = 21
4x = 21 - 5
4x = 16
x = 16/4
x = 4
verify:
4 + 3*4 + 5 = 21
4 + 12 + 5 = 21
What is 12+24=2(6+ )
Answer:
[tex]\huge \boxed{x=12}[/tex]
Step-by-step explanation:
Let the unknown number be x.
12+24=2(6+x)
Switch sides.
2(6+x)=12+24
Expand brackets.
12+2x=12+24
Subtract 12 from both sides of the equation.
12+2x-12=12+24-12
2x=24
Divide both sides of the equation by 2.
(2x)/2=24/2
x=12
12+24=2(6+x )
36=2(6+ )
36\2=(6+x)
18=(6+x)
18-6=x
12=x
the answer is 12
A company producing tennis racquets found that 3% of the racquets they produce are defective. The racquets are sent to shops in boxes of 6 and the shops send back boxes with more than one defective racquet. If a box is chosen at random and opened, what is the probability that it is sent back
Answer:
0.82
Step-by-step explanation:
The question says that three percent (3 out of 100) of the rackets (racquets) produced by the company are found to be defective.
First thing to calculate is the probability that 1 in a box of 6 rackets are defective.
That probability is gotten by cross multiplying, as illustrated below;
3 - 100
x - 6
x = (6×3)/100 = 18/100 = 0.18
Since the probability of having/finding 1 defective racket in a box of 6 is 0.18, the probability of finding more than 1 (minimum of 2 and maximum of all six) defective rackets in same box would be (1 - 0.18) = 0.82
What is the probability of drawing a spade or a jack from a standard deck of 52 cards?
Answer:
4/13
Step-by-step explanation:
There are 4 jacks in the deck and 13 spades. However 1 jack is a spade so we have a total of 16 cards which are either a jack or a spade. Therefore there are (13 + 4 - 1)/52 cards which are not a jack or a spade. Divided 16/52, thus the probability is 4/13.
The probability of drawing a spade or a jack from a standard deck of 52 cards is;
P(drawing either a spade or jack) = 4/13
We are told that the standard deck of cards has 52 cards.
Thus;
N = 52
Now,in a pack of cards there are usually 4 Jacks and 13 spades.
However, among the 4 Jacks, 1 of them is a spade. This means that 1 card will be both a spade and a jack. Thus,
Possible number of Jack's and spades = 13 + 4 - 1 = 16
Thus;
P(drawing either a spade or jack) = 16/52 = 4/13
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Identify the y-intercept of the function, f(x) = 2x2 + x - 4.
HELP ME WITH THIS ONE PLEASE ✊
(The problem is in the picture)
Answer/Step-by-step explanation:
Length of rectangle = [tex] l [/tex]
Width of rectangle = [tex] \frac{1}{3} of l - 1 = \frac{1}{3}l - 1 = \frac{l}{3} - 1 [/tex]
A. Expression for finding area of the rectangle:
Area of rectangle is given as [tex] length*width [/tex]
[tex] Area = l(\frac{l}{3} - 1) [/tex]
Or
[tex] Area = l*\frac{l}{3} - l*1 [/tex]
[tex] Area = \frac{l^2}{3} - l [/tex]
b. Expression for finding perimeter:
Perimeter of rectangle is given as [tex] 2(Length + Width) [/tex]
[tex] Perimeter = 2(l + (\frac{l}{3} - 1)) [/tex]
Or
[tex] Perimeter = 2(l) + 2(\frac{l}{3} - 1) [/tex]
[tex] Perimeter = 2l + \frac{2l}{3} - 2) [/tex]
c. Quotient of Perimeter divided by area:
[tex] 2(l + (\frac{l}{3} - 1)) [/tex] ÷ [tex] l(\frac{l}{3} - 1) [/tex]
[tex]2(l + (\frac{l}{3} - 1))[/tex] ÷ [tex]\frac{l^2 - 3l}{3}[/tex]
Change the ÷ to × and flip the fraction on your right upside down.
[tex]2(l + (\frac{l}{3} - 1)) * \frac{3}{l^2 - 3l}[/tex]
[tex]2l + 2(\frac{l}{3} - 1) * \frac{3}{l^2 - 3l}[/tex]
What is the pattern sequence for 1,2,5,6,9
Answer:
maybe : 1,2,5,6,9,10,13,14,17,
Step-by-step explanation:
I think it's in odd/even number pattern but it'll always skip a number???
or it's just in +1 then +3 pattern
The next terms of the pattern 1,2,5,6,9 are 10, 13,14,17,18,21.
What is sequence?Sequence is a collection of terms which are related in some way which is common to all the terms or some of the terms.
How to find terms of sequence?The pattern is given as 1,2,5,6,9 and we have to find the next terms of the pattern.
The First term is 1, the second term is 2. The difference between them is 1.
Second term is 2 and the third term is 5. The difference between them is 3.
Third term is 5 and the fourth term is 6. The difference between them is 1.
Fourth term is 6 and fifth term is 9. The difference between them is 3.
If we observe pattern in them them we can find that in first term they have added 1 , in second term 3 , in third term 1, in fourth term 3. It means first add 1 and then 3.
The next terms will be :
9+1=10
10+3=13
13+1=14
14+3=17
17+1=18
18+3=21.
Hence the next terms of the pattern 1,2,5,6,9 are 10,13,14,17,18,21.
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