Answer:
3.12732 × 10⁹ beats
Step-by-step explanation:
Given that, in 1 min, the heart of an individual makes 70 beats, the number of beats the heart of the healthy individual makes in 85 years can be calculated as follows:
1 yr = 365 days, therefore,
85yrs = 85*365 = 31,025 days
1 day = 24 hours
31,025 days = 31,025*24 = 744,600 hours.
1 hr = 60 mins
744,600 hours = 744,600*60 = 44,676,000 mins
This means the individual lived for 44,676,000 mins (85yrs)
If 70 beats are made in 1 min, therefore, in 85yrs, the individual will make:
44,676,000*70 = 3,127,320,000 beats = 3.12732 × 10⁹ beats in 85yrs
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).
5 red balls, 2 white balls and 3 blue balls are arranged in a row. If the balls of the same color are not distinguished from each other. How many possible ways can they be ordered?
Answer:
27720
Step-by-step explanation:
So let's assume that in any arrangement we are not able to distinguish the balls having the same colour, so only different orders of the colours involved are counted.
If we number these balls we have 12 different numbers, 3 of which belong to the white balls, 4 belong to the blue balls and the final 5 belong to the red balls. They could be arranged in 12! different ways. Pick any of these arrangements.
The white balls in this arrangement are now ordered because I gave these balls a number. But I specifically stated in the first alinea that we were not interested in all these possible orders of the white balls within a sequence of 12 balls. So we must correct for these orders, there are 3! of these, each one leading to exactly the same visual order of white balls. The other colours lead to a correction of 4! and 5!. Moreover, these corrections are independent of each other. I can change the position of the white balls without interrupting the order of the colours of the remaining balls. So we should divide by the product of 3!,4! and 5!.
Total number of arrangement = 3,628,800
Arrangement based problem:Given that;
Number of red ball = 5
Number of white ball = 2
Number of blur ball = 3
Find:
Total number of arrangement
Computation:
Total number of balls = 5 + 2 + 3
Total number of balls = 10
Total number of arrangement = 10!
Total number of arrangement = 3,628,800
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(16x²+24xy+9y²)÷(4x+3y)
Answer:
4x + 3y
Step-by-step explanation:
Answer:
4x+3y
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
=
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:
Consider the points R and S in the figure. How many different lines pass through
both R and S? Explain.
Answer:
Here we have two points R and S.
How many lines pass through both R and S?
Well, we can have only one line that passes through both R and S.
Because we are working with lines, we can only see a plane X-Y here.
Then the points R and S can be written as:
R = (x1, y1) and S = (x2, y2)
Now, a line or a linear relationship can be written as:
y = a*x + b
where a is the slope and b is the y-axis intercept.
For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:
a = (y2 - y1)/(x2 - x1).
Now, let's suppose that we have two different lines that pass through points R and S.
From above, both lines must have the same slope, because they pass through the same points.
y1 = a*x + b
y2 = a*x + c
So the only thing that our lines can have different is the y-intercept, but the y-intercept acts as a vertical shift.
This means, if we have different values in the y-intercept, we will have two parallel lines.
And two parallel lines can never pass through the same points, which means that we can not have different values for the y-intercept.
Then the two lines must be identical.
Then there is only one line that passes through points S and R at the same time,
The new 12 mile hiking trail is 150% of the length of the original trial. How long was the original trial?
Answer:
The answer is 8 milesStep-by-step explanation:
Let the original trail be x
From the question 150% of the trail is
12 mile
That's
150% of x = 12
So we have
[tex] \frac{150}{100} x = 12 \\ \\ \frac{3}{2} x = 12[/tex]
Multiply through by 2
That's
[tex]2 \times \frac{3}{2} x = 12 \times 2[/tex]
We have
3x = 24
Divide both sides by 3
We have the final answer as
x = 8
Therefore the length of the original trail is
8 milesHope this helps you
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
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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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
Identify the y-intercept of the function, f(x) = 2x2 + x - 4.
is ray AB same as ray BA?
Answer:
Yes
Step-by-step explanation:
Because a - - - - - - - - - - b
Same as b-----------------a
a bicycle is traveling at 17 mph. How many feet will it cover in 50 seconds?
Answer:
1246 2/3 feet
Step-by-step explanation:
17 miles/hour * 5280 feet/1 mile * 1 hour/60 minutes * 1 minute/ 60 seconds =
24.93 feet/second * 50 seconds = 1246 2/3 feet
Answer: about 25 feet
Step-by-step explanation:
( the exact number for the problem would be 24.933.... so round )
convert 17 miles into a # of feet
convert 1 hr into a # of secs
# of feet=89760
# of secs=3600
divide 89760/3600
you get 24.9333..........
Round to the nearest tenth and get 25
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 ).
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:
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
for which of the following problems would the calculation of 1.5 / 0.25 be appropriate
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
Suppose Sora is arguing with her mother, Jane. Jane believes that Sora eats mostly candy and doesn't eat enough fruits and vegetables, but Sora claims that she eats candy, fruits, and vegetables equally often. To test Sora's claim, Jane carefully monitors Sora's eating habits for several weeks. She records the number of times that Sora eats fruits, vegetables, and candy.
Jane conducts a chi-square test for goodness-of-fit to test Sora's claim. Jane's results are summarized in the table
Type of food Fruits Vegetables Candy
Observed 62 54 84
Test proportion 0.333 0.333 0.333
Expected 66.667 66.667 66.667
Contribution to chi-square 0.327 2.407 4.506
Chi-square statistic: 7.2400
Degrees of freedom: 2
What is the p-value for Jane's chi-square test for goodness-of-fit? Round your answer to three decimal places.
Answer:
0.027
Step-by-step explanation:
The p-value for Jane's chi-square test for goodness of fit is computed by using value of test statistic and degree of freedom.
Using Excel function CHISQ.DIST.RT(7.24,2) for computing p-value for chi-square goodness of fit test. 7.24 is the value of test statistic and 2 is degree of freedom. The resultant value is 0.026783. By rounding off to three decimal places the required p-value is 0.027.
distinguish between everyday Mathematics and Academic Mathematics
Answer:
Everyday mathematics would include lower-level math skills and comprehension, such as adding 5 cups of flour and 2 cups of sugar to some batter. Academic mathematics would include more complex math skills and comprehension, such as quadratic equations and interval notation.
Step-by-step explanation:
Everyday mathematics would include lower-level math skills and comprehension, such as adding 5 cups of flour and 2 cups of sugar to some batter. Academic mathematics would include more complex math skills and comprehensions, such as quadratic equations and interval notation. With one, you could pick up such skills just by living life. With the other, there is a higher chance that attending an educational institute would bestow such skills and understanding.
Answer:
???
Step-by-step explanation:
???
Solve for a
y = ax2 + bx + c
Answer:
Non-answer
Step-by-step explanation: Don't like my answer? Let me know!
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "x2" was replaced by "x^2".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
y-(a*x^2+b*x+c)=0
STEP
1
:
Equation at the end of step 1
y - ax2 - xb - c = 0
STEP
2
:
Solving a Single Variable Equation
2.1 Solve y-ax2-xb-c = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
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
write an equivalent unit rate to eating chips in 1/4 mins
Answer:
Here we have the case where:
"one chip is eaten in 1/4 mins."
(that means unit rate, the amount of a given variable that we need to do a unit of another variable)
Then the unit rate would be:
4 chips per minute.
Or, in a more mathematical way to write this:
4 chips/min.
Now we could write this in other units, for example.
We know that 1 min = 60s.
Then we have that (1/4) min = 60s/4 = 15s.
Then we have the unit rate:
1 chip every 15 seconds, or:
(1/15) chips/second.
Now, the variable in this case is time, t = time, let's multiply bot our unit rates by the same amount of time, and see if we have the same outcome.
Let's use t = 2 min.
1) (4chips/min)*2min = 8 chips.
2) ((1/15) chips/second)*2min
First, 2 min = 120 seconds.
((1/15) chips/second)*2min = ((1/15) chips/second)*120seconds = 8 chips.
So both unit rates are equivalent.
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
f(x) = 3x2 + 5x – 14 Find f(-9 )
Answer:
[tex]\huge\boxed{f(-9) = 184}[/tex]
Step-by-step explanation:
[tex]f(x) = 3x^2 +5x-14[/tex]
Put x = -9
[tex]f(-9) = 3(-9)^2+5(-9)-14\\f(-9) = 3(81) -45-14\\f(-9) = 243-45-14\\f(-9) = 198-14\\f(-9) = 184[/tex]
Steps to solve:
f(-9) = 3(-9)^2 + 5(-9) - 1
~Solve using PEMDAS
f(-9) = 3(81) - 45 - 1
f(-9) = 243 - 45 - 1
f(-9) = 198 - 1
f(-9) = 197
Best of Luck!
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
What is -3 1/4 +1 1/2 on a number line
Question Details
Find the distance between X(-3, 8) and Y (6, -6).
Round answer to the nearest tenth. Pls show work
Answer:
16.64
Step-by-step explanation:
Distance between any two points (x1,y1) and (x2,y2) is given by
Distance = [tex]\sqrt{(x1-x2)^{2} + (y1-y2)^{2} }[/tex]
Given point
X(-3, 8) and Y (6, -6).
The distance XY will be
[tex]XY = \sqrt{(-3-6)^{2} + (8 - (-6)^{2} }\\XY = \sqrt{(-9)^{2} + (8 +6)^{2} }\\XY = \sqrt{81 + 196 }\\XY = \sqrt{277 }\\XY = 16.64[/tex]
Thus, distance between X(-3, 8) and Y (6, -6) is 16.64 , rounded to nearest tenth.
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 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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