Answer:
The maximum life expectancy for humans is approximately 87 years.
Step-by-step explanation:
We have to calculate the point in which both linear functions (Life expectancy from birth and Life expectancy from age 65) intersect, as this is the point in which is estimated to be the maximum life expectancy for humans.
NOTE: to simplify we will consider t=0 to the year 1900, so year 2010 becames t=(2010-1900)=110.
The linear function for Life expectancy from birth can be calculated as:
[tex]t=0\rightarrow y=45\\\\t=110\rightarrow y=78.7\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{78.7-45}{110-0}=\dfrac{33.7}{110}=0.3064\\\\\\y=0.3064t+45[/tex]
The linear function for Life expectancy from age 65 can be calculated as:
[tex]t=0\rightarrow y=75\\\\t=110\rightarrow y=84.5\\\\\\m=\dfrac{\Delta y}{\Delta t}=\dfrac{84.5-75}{110-0}=\dfrac{9.5}{110}=0.0864\\\\\\y=0.0864t+75[/tex]
Then, the time t where both functions intersect is:
[tex]0.3064t+45=0.0864t+75\\\\(0.3064-0.0864)t=75-45\\\\0.22t=30\\\\t=30/0.22\\\\t=136.36[/tex]
The time t=136.36 corresponds to the year 1900+136.36=2036.36.
Now, we can calculate with any of both functions the maximum life expectancy:
[tex]y=0.0864(136.36)+75\\\\y=11.78+75\\\\y=86.78\approx87[/tex]
The maximum life expectancy for humans is approximately 87 years.
What is the mixed number3 3/8 as a fraction
Answer: Mixed Number to Fraction
Mixed Numbers to Improper Fraction
Mixed Numbers Improper Fraction
3 3/4 15/4
3 3/8 27/8
3 8/9 35/9
Hope this helps!!
How do I find the value of x for which line a is parallel to line b?
Answer:
x = 20
Step-by-step explanation:
3x + 6x = 180, if you make them supplementary then they will be parallel
9x = 180
x = 20
Want to donate to a better cause? Consider micro-lending. Micro-lending is a process where you lend directly to entrepreneurs in developing countries. You can start lending at $25. Kiva.org boasts a 99% repayment rate. The average loan to an entrepreneurs is $388.44 and the average loan amount is $261.14. With a total amount loaned of $283,697,150, how many people are lending money if the average number of loans per lender is 8?
Answer:
135,797
Step-by-step explanation:
If the total loan amount is $283,697,150 and the average loan amount is $261.14, then the number of loans is ...
$283,697,150/$261.14 = 1,086,379.5
If the average number of loans per lender is 8, then the number of lenders is ...
1086379.5/8 = 135,797 . . . . people lending money
An amount was invested at % r per quarter. What value of rwill ensure that accumulated amount at the end of one year is 1.5 times more than amount invested? Correct to 2 decimal places
Answer:
42.67%
Step-by-step explanation:
The annual growth factor for interest at annual rate r compounded quarterly is ...
(1 +r/4)^4
You want that value to be 1.5:
1.5 = (1 +r/4)^4
1.5^(1/4) = 1 +r/4
(1.5^(1/4) -1) = r/4
4(1.5^(1/4) -1) = r ≈ 0.426728
The rate r must be about 42.67%.
_____
Comment on the wording
We interpreted the problem to mean the end-of-year amount is 1.5 times the beginning-of-year amount. That is, it is "1.5 times the amount invested."
The word "more" is typically used when addition is involved. For example, "25% more" means 25% of the original is added to the original. We occasionally see "more" where "x times more" is intended to mean "x times", rather than "x times the amount, added to the original amount."
13. Carla drew two acute non-overlapping
angles that share a ray and labeled them
ZJLK and Z KLM. The two angles have
different measures. Carla says
ZILM is
greater than a right angle.
An acute angle is open
less than a right angle.
Answer:
An acute angle is open
Step-by-step explanation:
An acute angle is an angle that is less than [tex]90^{0}[/tex]. Two or more acute angles are set to be complementary if their sum equals a right angle.
Clara's diagram involves two acute angles JLK and KLM with both sharing the side LK.
If the acute angles are complementary angles, then JLM would be a right angle.
If the acute angles are not complementary angles, then JLM would be less than a right angle.
So the appropriate choice to select is an acute angle is open. Which implies that JLM may be a right angle or not depending on the degrees of the acute angles involved.
If log10y=2, what does y equal?
Answer:
[tex]y=100[/tex]
Step-by-step explanation:
I don't know if by the 10 you mean the base is 10 or it's being logged with the y, but I'm assuming the base is 10. If that's not right, message me and I'll fix my answer. If,
[tex]log_an=x\\a^x=n[/tex]
Then,
[tex]log_1_0y=2\\10^2=y\\100=y[/tex]
Seventy-six percent of sunflower seeds will germinate into a flower, and a sample of 800 such sunflower seeds is randomly selected. The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
Answer:
12.08
Step-by-step explanation:
For each sunflower, there are only two possible outcomes. Either it germinates, or it does not. The probability of a sunflower germinating is independent of other sunflowers. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Seventy-six percent of sunflower seeds will germinate into a flower
This means that [tex]p = 0.76[/tex]
Samples of 800:
This means that [tex]n = 800[/tex]
The standard deviation for the number of sunflower seeds that will germinate in such samples of size 800 is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.76*0.24} = 12.08[/tex]
Find the VOLUME of this composite solid.
Answer:
(294π +448) cm³ ≈ 1371.6 cm³
Step-by-step explanation:
The half-cylinder at the right end has a radius of 7 cm, as does the one on top. Together, the total length of these half-cylinders is 8 cm + 4cm = 12 cm. That is equivalent in volume to a whole cylinder of radius 7 cm that is 6 cm long.
The cylinder volume is ...
V = πr²h = π(7 cm)²(6 cm) = 294π cm³
__
The cuboid underlying the top half-cylinder has dimensions 4 cm by 8 cm by 14 cm (twice the radius). So, its volume is ...
V = LWH = (4 cm)(8 cm)(14 cm) = 448 cm³
Then the total volume of the composite figure is ...
(294π +448) cm³ ≈ 1371.6 cm³
What is another way to write 2×5 without using the multiplication sign?
Answer:
see below
Step-by-step explanation:
You could write it as 2+2+2+2+2 or 5+5 bc multiplication is like repeated addition.
Answer:
You can use the repeated additional as given below.
Step-by-step explanation:
2+2+2+2+2 or 5+5
Factorizar e indicar cuántos factores primos tiene -3+3x^2+y-x^2*y-y^2+x^2*y
Example and answer,will give brain
Answer:
b) -2/5
Step-by-step explanation:
b is -2/5 because its negative and goes down at a rate of 0.4 or 2/5
a , ummmm IDK that, sorry
Brainliest, crown to me
-5,-20,-80 find the common ratio
Answer:
The common ratio is 4
Step-by-step explanation:
To find the common ratio take the second term and divide by the first term
-20/-5 = 4
To verify take the third term and divide by the second
-80/-20 = 4
The common ratio is 4
Answer:
4
Step-by-step explanation:
To find the common ratio, divide one term by the term before it.
-20 ÷ -5 = 4
-80 ÷ -20 = 4
Each number is multiplied by 4 to get to the next number.
I hope this helps :))
Write the equation of the line shown in the graph above in slope-intercept form. Question 3 options: A) y = –2∕3x + 1 B) y = –x + 2∕3 C) 2x + 3y = 3 D) y = 2∕3x + 1
Answer:
A) y = -2/3x + 1
Step-by-step explanation:
Slope - intercept form is y = mx + b, where m is the slope and b is the y - intercept.
The line is falling from left to right, so it has a negative slope.
y = -mx + b
The line has a slope of -2/3.
y = -2/3x + b
The line has a y - intercept of 1.
y = -2/3x + 1
I hope this helps :)
A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
Slope - intercept form is y = mx + b,
where m is the slope and b is the y - intercept.
The line is falling from left to right, so it has a negative slope.
y = -mx + b
As, the line passes through (0,1) and (1.5,0)
The line has a slope of -2/3.
y = -2/3x + b
The line has a y - intercept of 1.
y = -2/3x + 1
hence, A) y = -2/3x + 1, the equation of the line shown in the graph above in slope-intercept form.
To learn more on Equation 0f Straight-Line click:
brainly.com/question/11116168
#SPJ2
Select the correct answer
Why are online payment services necessary?
OA
Individuals who sell items online cannot afford to deal with credit card companies.
B.
It is too risky to use credit cards online, and online payment services have better security
C. Government regulations require all online transactions be made using online payment services.
D.
Online payment services are the only payment method that individuals who sell items online trust.
Reset
Nalut
Answer:
B
Step-by-step explanation:it is really too risky to use credit card online because for someone who doesnt now if the busines is really considered as a trustful source or just a scam.
Answer:
Its A.) Individuals who sell items online cannot afford to deal with credit card companies.
Step-by-step explanation:
On plato
I will mark brainly-ist to who ever helps me
Find the value of the logarithm.
log 110
Round your answer to the nearest thousandth.
Answer:
4.700
Step-by-step explanation:
Find the number in the thousandth place 0 and look one place to the right for the rounding digit 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5.
brainliesssss plssssssssssssss
Write an expression without exponent that is equivalent to 2 to 3rd power nd 4 to the 3rd power
Answer:
8 and 64
Step-by-step explanation:
[tex]2^3[/tex] and [tex]4^3[/tex]
[tex]2^3=8[/tex]
[tex]4^3=64[/tex]
Mary is three quarters of Cameron's age. Mary is 24 years old. How old is Cameron?
Answer:
32 years oldStep-by-step explanation:
3/4=24 so 1/4= 24÷3= 8
1/4=8
So to get 4/4 or Cameron's age it is 8×4=32yrs
[tex]answer \\ 32 \: years \: old \\ solution \\ mary's \: age = 24 \\ let \: cameron's \: age \: be \: x \\ given \\ \frac{3}{4} x = 24 \\ or \: x = 24 \times \frac{4}{3} \\ x = 32 \\ hope \: it \: helps[/tex]
Find x
PLEASE HELP ME !! 11 POINTS !
Answer:
5
Step-by-step explanation:
Since this is a right triangle we can use trig functions
sin theta = opp /hyp
sin 30 = x / 10
10 sin 30 = x
10 * 1/2 = x
5 =x
what function is increasing? will give brainlist !
Answer:
Option B.
Step-by-step explanation:
Option A.
f(x) = [tex](0.5)^{x}[/tex]
Derivative of the given function,
f'(x) = [tex]\frac{d}{dx}(0.5)^x[/tex]
= [tex](0.5)^x[\text{ln}(0.5)][/tex]
= [tex]-(0.693)(0.5)^{x}[/tex]
Since derivative of the function is negative, the given function is decreasing.
Option B. f(x) = [tex]5^x[/tex]
f'(x) = [tex]\frac{d}{dx}(5)^x[/tex]
= [tex](5)^x[\text{ln}(5)][/tex]
= [tex]1.609(5)^x[/tex]
Since derivative is positive, given function is increasing.
Option C. f(x) = [tex](\frac{1}{5})^x[/tex]
f'(x) = [tex]\frac{d}{dx}(\frac{1}{5})^x[/tex]
= [tex]\frac{d}{dx}(5)^{(-x)}[/tex]
= [tex]-5^{-x}.\text{ln}(5)[/tex]
Since derivative is negative, given function is decreasing.
Option D. f(x) = [tex](\frac{1}{15})^x[/tex]
f'(x) = [tex]-15^{-x}[\text{ln}(15)][/tex]
= [tex]-2.708(15)^{-x}[/tex]
Since derivative is negative, given function is decreasing.
Option (B) is the answer.
Which number best represents the location of the point on the line?
X
-4.44
-T
11
3
_V17
RETRY
Answer:
- 11 over 3 Just did it on edg 2021
Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is very favorable, so a potential customer has decided to move forward with a purchase agreement unless it can be demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 lightbulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using computer software, which gave the following results.
Variable N Mean St Dev SEMean Z P-Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
1. What conclusion would be appropriate for a significance level of.05?
2. What significance level would you recommend?
Answer:
a) For this case since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 750 hours
b) We can use a significance level minimum of 2% in order to ensure the conditions in favor to the alternative hypothesis and then the potential customer will decide to move forward with a purchase witht his condition.
Step-by-step explanation:
For this case we have the following info given after conduct the following system of hypothesis:
Null hypothesis: [tex]\mu \geq 750[/tex]
Alternative hypothesis: [tex]\mu< 750[/tex]
The output is:
Variable N Mean St Dev SEMean Z P-Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
For this case the statistic calculated was:
[tex] z = -2.14[/tex]
And the p value calculated is:
[tex] p_v =p(z<-2.14) = 0.016[/tex]
Part a
For this case since the p value is lower than the significance level of 0.05 we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly lower than 750 hours
Part b
We can use a significance level minimum of 2% in order to ensure the conditions in favor to the alternative hypothesis and then the potential customer will decide to move forward with a purchase witht his condition.
It took jack 4 and half minutes to do 100 multiplication facts how long it takes him to do 150
Answer:
6.75 min
Step-by-step explanation:
100 facts/4.5 min = 150 facts/x min
x=(150*4.5)/100=6.75
Two competing gyms each offer childcare while parents work out Gym A charges $9.00 per hour of childcare. Gym B
charges $0.75 per 5 minutes of childcare. Which comparison of the childcare costs is accurate?
Answer:
They charge an equal amount of money each hour.
Answer:
Gym B and Gym A charge the same hourly rate for childcare.
Step-by-step explanation:
answer on edge
Brian invests £6300 into his bank account.
He receives 4.9% per year compound interest.
How much will Brian have after 2 years?
Give your answer to the nearest penny where appropriate.
Answer:
Amount that Brian has after 2 years = £6932.53
Step-by-step explanation:
To find, the amount that Brian will have after 2 years:
Formula for amount where compound interest is applicable:
[tex]A = P \times (1+\dfrac{R}{100})^t[/tex]
Where A is the amount after t years time
P is the principal.
R is the rate of interest.
In the question, we are given the following details:
Principal amount,P = £6300
Rate of interest,R = 4.9%
Time,t = 2 years
Putting the values in formula:
[tex]A = 6300 \times (1+\dfrac{4.9}{100})^2\\\Rightarrow 6300 \times (\dfrac{104.9}{100})^2\\\Rightarrow 6932.53[/tex]
Hence, Amount that Brian has after 2 years = £6932.53
Answer:
THE ANSWER IS ABOVE
Step-by-step explanation:
hahahaha
The average number of children a Japanese woman has in her lifetime is 1.37. Suppose that one Japanese woman is randomly chosen. a. In words, define the random variable X. b. List the values that X may take on. c. Give the distribution of X.X~ _____(_____,_____) d. Find the probability that she has no children. e. Find the probability that she has fewer children than the Japanese average.
Answer:
a. X: amount of children that a Japanese woman has in her lifetime.
b. X can take natural numbers (all positive integers) as values.
c. X~Poi(1.37).
d. P(X=0)=0.2541
e. P(X<1.37)=0.6022
Step-by-step explanation:
a) This can be modeled with a Poisson distribution.
We let the variable X be the amount of children that a Japanese woman has in her lifetime.
The parameter of the Poisson distribution is λ=1.37.
This is also the value of the mean and the standard deviation.
b) X can take all positive integer values.
c) X is modeled as a Poisson variable with λ=1.37.
d) This can be calculated as:
[tex]P(0)=\lambda^ke^{-\lambda}/k!=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\[/tex]
e) Having fewer children than the average means that she has one or none children.
This can be calculated as:
[tex]P(X<1.37)=P(0)+P(1)\\\\\\P(0)=1.37^{0} \cdot e^{-1.37}/0!=1*0.2541/1=0.2541\\\\P(1)=1.37^{1} \cdot e^{-1.37}/1!=1.37*0.2541/1=0.3481\\\\\\P(X<1.37)=0.2541+0.3481=0.6022[/tex]
The ability of ecologists to identify regions of greatest species richness could have an impact on the preservation of genetic diversity, a major objective of the World Conservation Strategy. A study used a sample of n = 33 lakes to obtain the estimated regression equation
y = 3.89 + 0.033x1 + 0.024x2 + 0.023x3 − 0.0080x4 − 0.13x5 − 0.72x6
where y = species richness, x1 = watershed area, x2 = shore width, x3 = poor drainage (%), x4 = water color (total color units), x5 = sand (%), and x6 = alkalinity.
The SSR and SSE have been calculated to be:_________.
SSR = 752.25 and SSE = 300.9.
ANSWER:
I believe you wish to calculate the sum of squares total (SST) for this regression analysis. The sum of squares total is 1053.15
Step-by-step explanation:
The sum of squares total is numerically derived by adding the sum of squares regression (regression sum of squares) to the sum of squares error (error sum of squares). The regression sum of squares here is 752.25 and the error sum of squares is 300.9
This gives us a total sum of squares of 1053.15
Sums of squares tell if a linear regression of one variable (or variables) on another is good or not.
The squared differences between the observed dependent variable and its mean is a measure of the total variability of the data set.
So the SST is equal to 752.25 + 300.9 = 1053.15
Calculating the standard deviation (σ) for a list of n data values: 1. Calculate the average value. 2. Subtract the average value from each individual data value and enter the results in a column to the right of the data values. 3. Square each of the results obtained in step 2, and enter these in a new column to the right. 4. Sum the squares obtained in step 3. 5. Divide the result from step 4 by (n - 1) (the total number of measurements minus 1). 6. Take the square root of the result from step 5. This is the standard deviation. Expressed as an equation, the standard deviation of n measurements of data value x is: σ = ( Σ (x - xavg)2 / (n - 1) )1/2 Using the 6 steps above (or the spreadsheet function), calculate the standard deviation for the six values on page 16 and enter your answer below. Enter your result with only one sig fig, and remember to use a zero before the decimal point for values less than 1, for example 0.05 or 0.01.
Answer:
Step-by-step explanation:
The missing list of the data values for the question are as follows:
1 1.03
2 1.01
3 0.96
4 0.96
5 0.99
6 1
7 1.01
8 0.98
9 1.02
10 1.03
11 1
12 0.99
13 1
14 0.97
15 1.01
[tex]x_i[/tex] [tex](x_i - \bar x)[/tex] [tex](x_i - \bar x)^2[/tex]
1 1.03 0.03 0.0009
2 1.01 0.01 0.0001
3 0.96 -0.4 0.0016
4 0.96 -0.4 0.0016
5 0.99 -0.1 0.0001
6 1 0.0 0.0
7 1.01 0.1 0.0001
8 0.98 -0.2 0.0004
9 1.02 0.2 0.0004
10 1.03 0.3 0.0009
11 1 0.0 0.0
12 0.99 -0.1 0.0001
13 1 0.0 0.0
14 0.97 -0.03 0.0009
15 1.01 0.1 0.0001
The average value for x is calculated as:
[tex]\bar x = \dfrac{14.96}{15}[/tex]
[tex]\bar x = 0.997 \\ \\ \bar x \approx 1.00[/tex]
[tex]\sum (x-x_i)^2 = 0.0072[/tex]
[tex]\dfrac{\sum (x-x_i)^2 }{n-1}= \dfrac{0.0072}{15-1} \\ \\ = \dfrac{0.0072}{14} \\ \\ = 0.00051[/tex]
[tex]\sigma = \sqrt{\dfrac{\sum (x-x_i)^2 }{n-1}} = \sqrt{0.00051} \\ \\ \sigma =0.0226 \\ \mathbf { \\ \sigma =0.02 \ to \ one \ significant \ figure}[/tex]
The sum of a number and twenty-one is sixty-four.
Answer:
43
Step-by-step explanation:
If X + 21 = 64
then subtract 64 by 21 and you get 43
Using the data in the table, use the exponential smoothing method with alpha=0.5 and a February forecast of 500 to forecast
sales for May
Month Demand
January 480
February 520
March 535
April 550
May 590
June 630
Answer:
Step-by-step explanation:
The formula to calculate the forecast could be determine by using the exponential smoothing method :
[tex]Ft = F(t-1) + \alpha [A(t-1) - F(t-1)][/tex]
Where ,Ft is the Forecast for period t
F(t-1) is the Forecast for the period previous to t
A(t-1) is the Actual demand for the period previous to t
[tex]\alpha[/tex] = Smoothing constant
To get the forecast for may and june the above formula with [tex]\alpha =0.5[/tex] and april forecast of 500 will be used
For march
[tex]=500+0.5(520-500)\\\\=500+0.5\times20\\\\=500+10\\\\=510[/tex]
For April
[tex]=510+0.5(535-510)\\\\=510+0.5\times25\\\\=510+12.5\\\\=522.5[/tex]
For May
[tex]=522.5+0.5(550-5225)\\\\=522.5+0.5\times27.5\\\\=522.5+13.75\\\\=536.25[/tex]
So forecast for May = 536.25
Quick Start Company makes a 12-volt car batteries. After many years of product testing, the company knows the average life of a Quick Start battery is normally distributed, with mean=45 months and a std. deviation = 8 months.
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries (to the nearest month)
Answer:
The company will expect to replace 13.03% of batteries.
The company should guarantee the batteries for 35 months.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 45, \sigma = 8[/tex]
If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?
This is the pvalue of Z when X = 36. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{36 - 45}{8}[/tex]
[tex]Z = -1.125[/tex]
[tex]Z = -1.125[/tex] has a pvalue of 0.1303.
The company will expect to replace 13.03% of batteries.
If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries
They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.28 = \frac{X - 45}{8}[/tex]
[tex]X - 45 = -1.28*8[/tex]
[tex]X = 34.76[/tex]
Rounding to the nearest month
The company should guarantee the batteries for 35 months.