The population of a certain species of fish has a relative growth rate of 1.1% per year. It is estimated that the population in 2010 was 12 million. a. Find an exponential model n(t)= no e^rt for the population t years after 2010. b. Estimate the fish population in the year 2015. c. After how many years will the fish population reach 14 million? d. Sketch a graph of the fish population.
Answers
Answer:
(a) n(t) = P(0)*e^(0.010939940t)
(b) 12,674,681 (nearest unit)
(c) 14 years (nearest year)
Step-by-step explanation:
rate = 1.1% / year = 1.011
(a)
P(0) = 12,000,000 = population in 2010
In compound interest format, after t years
P(t) = P(0)* (1.011)^t
Given format = P(0)* e^(rt)
therefore
e^(rt) = 1.011^t use law of exponents
(e^r)^t = 1.011^t
e^r = 1.011
r = log_e(1.011) = 0.010939940 (to 9 decimal places)
required formula is
n(t) = P(0)*e^(0.010939940t)
(b)
in 2015,
P(0)=12000000, n = 5 (years after 2010)
n(5) = 12000000*e^( 0.010939940 * 5 ) = 12,674,680.6 = 12,674,681 (nearest unit)
(c)
to reach 14 million, we equate
n(t) = 14,000,000
12,000,000 *e^(0.010939940*t) = 14,000,000
e^(0.010939940*t) = 14000000/12000000 = 7/6
take log on both sides
0.010939940*t = log(7/6)
t = log(7/6) / 0.010939940 = 14.091 years = 14 years to the nearest year.
See graph attached. Y-axis is in millions, x-axis is in years.
a) [tex]n(t) = 12e^{0.011t}[/tex]
b) The estimate for the population in 2015 is of 12.7 million.
c) The fish population will reach 14 million after 14 years.
d) The sketch is given at the end of this answer.
------------------------------------
Item a:
The exponential model is:
[tex]n(t) = n(0)e^{rt}[/tex]
In which:
n(0) is the population is 2010.r is the growth rate, as a decimal.Population of 12 million, thus [tex]n(0) = 12[/tex]Growth rate of 1.1%, thus [tex]r = 0.011[/tex].
Thus, the model is:
[tex]n(t) = 12e^{0.011t}[/tex]
Item b:
2015 is 2015 - 2010 = 5 years after 2010, thus this is n(5).
[tex]n(5) = 12e^{0.011(5)} = 12.7[/tex]
The estimate for the population in 2015 is of 12.7 million.
Item c:
This is t for which n(t) = 14, thus:
[tex]n(t) = 12e^{0.011t}[/tex]
[tex]14 = 12e^{0.011t}[/tex]
[tex]e^{0.011t} = \frac{14}{12}[/tex]
[tex]\ln{e^{0.011t}} = \ln{\frac{14}{12}}[/tex]
[tex]0.011t = \ln{\frac{14}{12}}[/tex]
[tex]t = \frac{\ln{\frac{14}{12}}}{0.011}[/tex]
[tex]t = 14[/tex]
The fish population will reach 14 million after 14 years.
Item d:
At the end of this answer, the sketch is given.
A similar problem is given at https://brainly.com/question/23416643
Related Questions
Use Lagrange multipliers to solve the given optimization problem.
Find the maximum value of f(x, y)-xy subject to x + 2y 52.
fmax=______
Also find the corresponding point
(x, y)=__________.
Answers
Answer:
fmax = xy = 26 × 13 = 338
(x,y) = (26,13)
Step-by-step explanation:
Given that:
f(x, y) = xy
subject to x + 2y = 52
So;
x = 52 - 2y
and;
f(x, y) = xy
f(x, y) = (52- 2y) y
f(x, y) = 52y - 2y²
In order to maximize this function;
52y - 2y² = 0
26 y - y² = 0
26 - 2y = 0
-2y = -26
y = -26/-2
y = 13
Again:
x = 52 - 2y
x = 52 - 2(13)
x = 52 - 26
x = 26
fmax = xy = 26 × 13 = 338
(x,y) = (26,13)
Mai invests $20,000 at age 20. She hopes the investment will be worth $500,000 when she turns 40. If the interest compounds continuously, approximately what rate of growth will she need to achieve her goal? Round to the nearest tenth of a percent.
Answers
Answer:
[tex]\approx[/tex] 17.5% per annum
Step-by-step explanation:
Given:
Money invested = $20,000 at the age of 20 years.
Money expected to be $500,000 at the age of 40.
Time = 40 - 20 = 20 years
Interest is compounded annually.
To find:
Rate of growth = ?
Solution:
First of all, let us have a look at the formula for compound interest.
[tex]A = P \times (1+\frac{R}{100})^T[/tex]
Where A is the amount after T years compounding at a rate of R% per annum. P is the principal amount.
Here, We are given:
P = $20,000
A = $500,000
T = 20 years
R = ?
Putting all the values in the formula:
[tex]500000 = 20000 \times (1+\frac{R}{100})^{20}\\\Rightarrow \dfrac{500000}{20000} =(1+\frac{R}{100})^{20}\\\Rightarrow 25 =(1+\frac{R}{100})^{20}\\\Rightarrow \sqrt[20]{25} =1+\frac{R}{100}\\\Rightarrow 1.175 = 1+0.01R\\\Rightarrow R \approx17.5\%[/tex]
So, the correct answer is [tex]\approx[/tex] 17.5% per annum and compounding annually.
Answer:
16.1%
Step-by-step explanation:
(the other person is wrong, trust me)
27) Jake tells a joke to 3 people and each of those people tells the joke to 3 more people,
and so on. How many people will hear the joke in the 4th round of jokes told? How
many people will hear the joke in total after the fourth round?
Answers
Answer:
15
Step-by-step explanation:
Answer:
12 people heard the joke?
Step-by-step explanation:
Which statement describes the order of rotational symmetry for an isosceles triangle?
Answers
Answer: it should be b, 1. :)
Step-by-step explanation:
Which of the following is a rational function?
F(x)=8x^2-21x+45
F(x)= 3 root of X +17
F(x)= 16x
F(x)= 5x/x^2-25
Answers
What is the area of the shaded region? 21 mm2 24 mm2 42 mm2 48 mm2
Answers
Answer:
B or 24 mm2
Step-by-step explanation:
Just did the test :)
The area of the shaded region is 24mm^2
What is the area of triangle?Let b be the base and h be the height of the triangle. The area of the triangle is given by bh/2 square units.Step 1: Find area of the larger triangle
Here base b = 5 mm
Height h = 12 mm
Area of the larger triangle = (5*12)/2 = 60/2 = 30mm^2
Step 2: Find area of the smaller triangle
Here base b = 3 mm
Height h = 4 mm
Area of the smaller triangle = (3*4)/2 = 12/2 = 6 mm^2
Step 3: Find area of the required shaded region
Area of the required shaded region = Area of larger triangle - Area of smaller triangle
= 30 mm^2 - 6 mm^2
=24 mm^2
Hence, the area of the shaded region is 24mm^2
Learn more about area of triangle here:
https://brainly.com/question/17335144
#SPJ2
6.52
65.2
0.652
order it least to greatest which comes first?
Answers
Answer:
Hey! The answer will be below!! :)
Step-by-step explanation:
In least to greatest the answer will be....
0.652, 6.52, 65.2
0.652 comes first because since the decimal point is between the 0 and 6
It’s also because 0 is less than 6 and 65.
Here is a easy way to do this, when you have this kind of question.
First look where the decimal is.
Pretend it’s a whole number like, 0.652 becomes 0
And 6.52 becomes 6, also 65.2 becomes 65
You have to use the decimal to find out least to greatest, also you will have to round the number.
So remember, when ever you have this kind of question...after the decimal point like 65.2 you take away the .2 and just have 65....this will help you do least to greatest faster! :)
Hope this helps!
Answer:
0.652, 6.52, 65.2
Step-by-step explanation:
You have to round to find the answer in a easy way.
Least to greatest would be 0.652, 6.52, 65.2
Hop it will help u
Identify the P-VALUE used in a hypothesis test of the following claim and sample data:
Claim: "The proportion of defective tablets manufactured in this factory is less than 6%."
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective. Test the claim at the 0.05 significance level.
Answers
Answer:
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
Step-by-step explanation:
Step(i):-
Given Population proportion P = 0.06
Sample size 'n' = 500
A random sample of 500 tablets from this factory is selected, and it is found that 20 of them were defective.
Sample proportion
[tex]p^{-} = \frac{x}{n} = \frac{20}{500} =0.04[/tex]
Null hypothesis :H₀: P = 0.06
Alternative Hypothesis :H₁:P<0.06
Level of significance = 0.05
Z₀.₀₅ = 1.96
Step(ii):-
Test statistic
[tex]Z = \frac{p^{-} -P}{\sqrt{\frac{P Q}{n} } }[/tex]
[tex]Z = \frac{0.04 -0.06}{\sqrt{\frac{0.06 X 0.94}{500} } }[/tex]
Z = - 2
|Z|= |-2| = 2
Step(iii):-
The calculated value Z = 2 > 1.96 at 0.05 level of significance
Null hypothesis is rejected
Alternative Hypothesis is accepted
The proportion of defective tablets manufactured in this factory is less than 6%."
A researcher wants to study the relationship between salary and gender. She randomly selects 297 individuals and determines their salary and gender. Can the researcher conclude that salary and gender are dependent?
Answers
Answer:
The researcher cannot conclude that salary and gender are dependent.
Step-by-step explanation:
A dependent variable is a variable, for example "Salary" that depends on an independent variable, e.g. "Gender." Salary is the dependent variable while gender is the independent variable. This means that the value of salary changes in relation to the gender and not vice versa. Two variables become dependent if they change based on another independent variable that is operating on them. In this research, the researcher is not trying to measure gender but the relationship between salary and gender. To achieve her purpose, she shows that salary depends on gender and not that gender depends on salary.
on a map 1 inch represents 4 miles how many miles are represented by 3-1/2 ?
Answers
Answer:
10 miles
Step-by-step explanation:
1 inch = 4 miles
3 - 0.5 = 2.5
2.5 * 4 = 10 miles
Which of the following is the standard deviation of the random variable x
Answers
Answer: B. 1.414
Step-by-step explanation:
let x be the random variable denotes the number of die.
Numbers on 5-faced die = 1,2,3,4,5
Probability of getting any number = [tex]\dfrac{1}{5}[/tex]
Mean = [tex]\bar {x}=\sum p_ix_i[/tex]
[tex]\\\\\Rightarrow\bar{x}=\dfrac{1}{5}(1)+\dfrac{1}{5}(2)+\dfrac{1}{5}(3)+\dfrac{1}{5}(4)+\dfrac{1}{5}(5)\\\\=\dfrac{1}{5}(1+2+3+4+5)\\\\=\dfrac{1}{5}(15)=3[/tex]
Standard deviation: [tex]\sigma=\sum \sqrt{\dfrac{(x_i-\bar{x})^2}{N}}[/tex]
[tex]=\sqrt{\dfrac{(1-3)^2+(2-3)^2+(3-3)^2+(4-3)^2+(5-3)^2}{5}}\\\\=\sqrt{\dfrac{4+1+0+1+4}{5}}\\\\=\sqrt{\dfrac{10}{5}}\\\\=\sqrt{2}\approx1.414[/tex]
Hence, the standard deviation of the random variable x is 1.414.
Thus, the correct option is B.
Match the information on the left with the appropriate equation on the right.
Answers
Answer:
Step-by-step explanation:
1). Equation of a line which has slope 'm' and y-intercept as 'b' is,
y = mx + b
If slope 'm' = 1 and y-intercept 'b' = -3
Equation of the line will be,
y = x - 3
x - y = 3
2). Equation of a line having slope 'm' and passing through a point (x', y') is,
y - y' = m(x - x')
If the slope 'm' = 1 and point is (-1, 2),
The the equation of the line will be,
y - 2 = 1(x + 1)
y = x + 1 + 2
y = x + 3
x - y = -3
3). Equation of a line passing through two points [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] will be,
[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]
If this line passes through (-2, 3) and (-3, 4),
[tex]y-3=\frac{(4-3)}{(-3+2)}(x+2)[/tex]
y - 3 = -1(x + 2)
y = -x - 2 + 3
y = -x + 1
x + y = 1
hi if anyone is good with extraneous solutions pleaseeeeeee help meeee tessa solves the equation below by first squaring both sides of the equation√x^2-3x-6=x-1 what extraneous solution does tessa obtain x=
Answers
Answer:
x = -7/5
Step-by-step explanation:
If we square both sides of the equation, we get:
[tex]\sqrt{x^2-3x-6}=x-1\\ (\sqrt{x^2-3x-6})^2=(x-1)^2\\x^2-3x-6=x^2-2x+1\\[/tex]
Then, solving for x, we get:
[tex]x^2-3x-6=x^2-2x+1\\-3x-6=2x+1\\-6-1=2x+3x\\-7=5x\\\frac{-7}{5}=x[/tex]
So, x is equal to -7/5
Answer:
its -7
Step-by-step explanation:
gots it right!
Which of the following points is collinear with (2, 1) and (3, 3)?
O (0,0)
O (1,-1)
O (4,4)
O(-1,-2)
HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!??????????!!!!!!!!!
Answers
Answer:
O (1,-1) is collinear with (2, 1) and (3, 3).
Step-by-step explanation:
equation of line in point slope form is
y-y1/x-x1 = m
where m is the slope of line
slope of line is given by
m = (y2-y1)/(x2-x1)
where(x1,x2) and (y1,y2) are points on the given line
_______________________________________
Given point
(2, 1) and (3, 3)?
m = 3-1/3-2 = 2
Equation of line
y-1/x-2 = 2
=> y-1 = 2(x-2)
=> y-1 = 2x-4
=> y= 2x-4+1
=> y = 2x-3
col-linear points are one which lie on the same line
To solve the problem we will check which of the given points satisfy the equation of line derived above.
y = 2x-3
(0,0)
if we put value of x = 0 the above equation we should get y =0
y = 2*0 -3 = -3
since -3 is not equal to 0, hence (0,0) is not collinear with (2, 1) and (3, 3).
1,-1
y = 2*1 -3 = -1
since -1 is equal to -1, hence (1,-1) is collinear with (2, 1) and (3, 3).
(4,4)
y = 2*4-3 = 5
since 5 is not equal to 4 , hence (4,4) is not collinear with (2, 1) and (3, 3).
(-1,2)
y = 2*-1 -3 = -5
since -5 is not equal to 2, hence (-1,2) is not collinear with (2, 1) and (3, 3).
Hence answer is O (1,-1) s collinear with (2, 1) and (3, 3).
6 ≤ x+ 15 plzzzzz helpppp
Answers
Answer:
[tex]\large \boxed{\sf \ \ x \geq -9 \ \ }[/tex]
Step-by-step explanation:
Hello, please find below.
[tex]6\leq x+15\\\\\text{*** subtract 15 from both sides ***}\\\\6-15=-9\leq x \\\\x \geq -9[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Farmer Hanson is putting together fruit baskets. He has 240 apples and 150 pears. What is the largest number of baskets he can put together so that he can have the same number of apples and same number of pears in each basket considering no fruit is left out?HELP NOWWWWW
Answers
Answer: The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
Step-by-step explanation:
Given, Farmer has 240 apples and 150 pears.
The largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out = GCF(240,150)
Prime factorization of 240 and 150 :
[tex]240=2\times2\times2\times2\times3\times5\\150=2\times3\times5\times5[/tex]
Greatest common factor of 240 and 150 = [tex]2\times3\times5=30[/tex]
Hence, the largest number of baskets he can put together so that he can have the same number of apples and the same number of pears in each basket considering no fruit is left out is 30.
An accountant receives a salary of $262,000 per year. During the year, he plans to spend $99,000 on his mortgage, $54,000 on food, $32,000 on clothing, $41,000 on household expenses, and $28,000 on other expenses. With the money that is left, he expects to buy as many shares of stock at $250 per share as possible. Using the equation below, determine how many shares will he be able to buy? What was the sum of the accountant's expenses?
Answers
Answer:
Number of shares = 32 shares
Accountant total expenses= $254000
Step by step explanation:
The accountant salary is $262000
He spends $99000 on mortage
Spends $54000 on foods
Spends $32000 on clothing
Spends $41000 on household
Spends $28000 on others
Total expenses= 99000+54000+32000+41000+28000
Total expenses =$254000
Remaining money = 262000-254000
Remaining money= $8000
If shares = $250 for one
To know the amount he buys with the remaining money
We divide remaining money by shares cost
= $8000/$250
= 32 shares
What is the vertex of this parabola y=-5x^2-10x-13
Answers
Step-by-step explanation:
Vertex for your equation is (-1, -8)
An article reports that when each football helmet in a random sample of 34 suspension-type helmets was subjected to a certain impact test, 24 showed damage. Let p denote the proportion of all helmets of this type that would show damage tested in the prescribed manner.
Required:
a. Calculate a 99% Cl for p.
b. What sample size would be required for the width of a 99% Cl to beat most .10, irrespective of p ?
Answers
Answer:
a
[tex]0.5043 < p <0.9075[/tex]
b
[tex]n = 24[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 34
The number of damaged helmets is x = 24
Now the proportion of damaged helmets is mathematically represented as
[tex]\r p = \frac{k}{n }[/tex]
substituting values
[tex]\r p = \frac{24}{34 }[/tex]
[tex]\r p = 0.7059[/tex]
Given that the confidence level is 99% the level of significance can be evaluated as
[tex]\alpha = 100 - 99[/tex]
[tex]\alpha = 1[/tex]%
[tex]\alpha = 0.01[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]
The reason we are obtaining critical values of [tex]\frac{\alpha }{2}[/tex] instead of [tex]\alpha[/tex] is because
[tex]\alpha[/tex] represents the area under the normal curve where the confidence level interval ( [tex]1-\alpha[/tex]) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]is just the area of one tail which what we required to calculate the margin of error
The margin of error is mathematically represented as
[tex]MOE = Z_{\frac{\alpha }{2} } * \sqrt{\frac{\r p ( 1 - \r p)}{n} }[/tex]
substituting values
[tex]MOE = 2.58 * \sqrt{\frac{ 0.7059 ( 1 - 0.7059)}{34} }[/tex]
[tex]MOE =0.2016[/tex]
The 99% confidence interval for p is mathematically represented as
[tex]p-MOE < p < p + MOE[/tex]
substituting values
[tex]0.7059 - 0.2016 < p <0.7059 + 0.2016[/tex]
[tex]0.5043 < p <0.9075[/tex]
The sample size required for the width of a 99% Cl to beat most 0.10, irrespective of p ? is mathematically represented as
[tex]n \ge \frac{ Z_{\frac{\alpha }{2} } * \sqrt{\r p (1- \r p )} }{\frac{\sigma }{2} }[/tex]
Here [tex]\sigma = 0.10[/tex] telling us that the deviation from the sample proportion is set to 0.10 irrespective of the value of [tex]\r p[/tex]
so the sample size for this condition is
[tex]n \ge \frac{ 2.58 * \sqrt{ 0.7059 (1- 0.7059)} }{\frac{0.10 }{2} }[/tex]
[tex]n \ge 23.51[/tex]
=> [tex]n = 24[/tex]
Tunde and Martha are married and share their income. Tunde earns $1,500 per year less than Martha. If their annual income is $47,500, how much does each earn?
Answers
Answer:
p=2m
p+m=51
take the 2m and plug that in for p -> 2m+m=51
3m=51
m=51/3
m=17 then plu the value of m into Paula's points
p=2(17)
p=34
Please answer this correctly without making mistakes Please simplify the correct answer
Answers
Answer:
1/5 are towboats
Step-by-step explanation:
In order to find the answer, we need to find the total number of flag vessels. We can find this by adding all the categories together
30k + 10k + 10k= 50k
In total there are 50,000 flag vessels
Of those 50,000, 10,000 of them are tow boats
10,000/50,000 can be simplified to 1/5
1/5 are towboats
Answer:
1/5
Step-by-step explanation:
Well to find the fraction we first need to know the total amount of Flag Vessels.
30,000 + 10,000 + 10,000 = 50,000
If there are 10,000 towboats we can make the following fraction.
10,000/50,000
Simplified
1/5
Thus,
the answer is 1/5.
Hope this helps :)
Five less than the product of 14 and Vanessa's height Use the variable v to represent Vanessa's height.
Answers
Answer:
14v - 5
Step-by-step explanation:
The product of 14 and v is 14v. 5 less than that is 14v - 5.
Answer:
7v = 119
Step-by-step explanation:
what is the area of the shaded region between the two z-scores indicated in the diagram? z=-1.24 and z= 0.84
Answers
Answer:
0.6921 (69.21%)
Step-by-step explanation:
The area of the shaded region between the two z-scores refer to the probability between the two z-scores value( The total area under a standard normal distribution curve is 1)
So the area we want to determine in this case is as follows;
P(-1.24<z<0.84) = P(z<0.84) - P(z<-1.24)
What we use to calculate this finally is the standard normal distribution table
We use this to get these values so we can calculate the probability.
Using the standard normal distribution table;
P(-1.24<z<0.84) = 0.69206 which is approximately 0.6921
Find the length L of the curve
[tex]y = \sqrt{x} [/tex]
from the point P(0,0) to the point Q(4,2)
Answers
Answer:
4.647 to the nearest thousandth.
Step-by-step explanation:
The formula for the length of an arc between x = a and x = b is
a
∫ √( 1 + (f'(x))^2) dx
b
Here f(x) = √x so
we have ∫ (√( 1 + (1/2 x^-1/2))^2 ) between x = 0 and x = 4.
= ∫ ( √( 1 + 1/(4x)) dx between x = 0 and x = 4.
This is not easy to integrate but some software I have gives me the following
length = √17 + 1/8 log(33 + 1/8 √17)
= 4.647.
Brenda is going from $(-4,5)$ to $(5,-4)$, but she needs to stop by the origin on the way. How far does she have to travel?
Answers
Answer:
[tex]\boxed{D = 6.4 units}[/tex]
Step-by-step explanation:
She stops by (0,0)
She further needs to travel to (5,-4)
Let's calculate the distance using the Distance Formula:
Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
D = [tex]\sqrt{(5-0)^2+(-4-0)^2}[/tex]
D = [tex]\sqrt{(5)^2+(-4)^2}[/tex]
D = [tex]\sqrt{25+16}[/tex]
D = [tex]\sqrt{41}[/tex]
D = 6.4 units
She needs to travel 6.4 units more.
Answer:
2sqrt41
Step-by-step explanation:
Origin=(0,0)
Brenda wants to go from (-4,5) to (0,0) and then to (5,-4). So we need to calculate the distance from (-4,5) to (0,0), and the distance of (0,0) to (5,-4).
The distance formula is sqrt (x2-xs1)^2+(y2-y1`)^2.
So: sqrt (5-0)^2+(-4-0)^2
sqrt (5^2+-4^2)
sqrt 25+16
sqrt 41
Now we need to figure out the distance from (0,0) to (5,-4)
sqrt(0-5)^2+(0-(-4))^2
sqrt(-5^2+4^2)
sqrt 25+16
sqrt 41
sqrt 41+sqrt 41
2sqrt41
a man is 3 times as old as his son . the sum of their ages is 48 years .how old is the son ? how old is the dad?
Answers
Answer:
son is 12
dad is 36
Step-by-step explanation:
Say the son is x years old.
Then the father is 3x. Also 3x+x must be 48.
So 4x = 48 => x= 48/4 = 12
Let x be how old the son is. We know that the dad is 3 times older and their sum is 48. Creating an equation to represent this situation gives us:
[tex]x+3x=48[/tex]
[tex]4x=48[/tex]
Divide both sides by 4
[tex]x=12[/tex]
The son is 12 years old, but we want to find the age of the dad. Since we know the dad is 3 times older, multiply 12 with 3
[tex]12 \times 3 = 36[/tex]
The dad is 36 years old. Let me know if you need any clarifications, thanks!
Sum of two consecutive integers is -221
Answers
Answer:
-111 and -110
Step-by-step explanation:
If x is the lesser integer, and x+1 is the next integer, then:
x + x+1 = -221
2x = -222
x = -111
x+1 = -110
The two integers are -111 and -110.
Answer:
-111,-110
Step-by-step explanation:
Let n represent the first integer. Then n+1 will represent the next consecutive integer.
Translate into an equation.
We can restate the given information in one sentence as "The sum of the integers is −221."
As an equation this sentence is represented as:
n+n+1=−221
Solve the equation.
n+n+1=-221
2n+1=−221
2n=−222
n=−111
So, n=−111 is the first integer and n+1=−110 is the second integer.
100 POINTS!!!! Answer to the picture below.
Answers
Answer:
A 23 of people who prefer plan 1 are from the 35-45 age group and 42% of people from the 46-55 age group prefer plan 2.
Step-by-step explanation:
add everyone who prefers plan 1 = 60
age 36-45 / total of plan 1 = 14/60 = .23 or 23%
add everyone in age group 46-55 = 50
in age group 46-55 and prefers plan 2 = 21 / 50 = 0.42 or 42%
Answer:
[tex]\boxed{\mathrm{Option \ B}}[/tex]
Step-by-step explanation:
Total people in 36 - 45 age group = 50
Who prefer plan I = 14
%age of people preferring plan 1 among 36-45 age group:
=> [tex]\frac{14}{50} * 100[/tex]
=> 0.28 * 100%
=> 28%
Now,
Total People in 46-55 age group = 50
Those who prefer plan II = 21
%age of people preferring plan II among 46-55 age group:
=> [tex]\frac{21}{50} * 100[/tex]
=> 0.42 * 100%
=> 42%
A population consists of 8 items. The number of different simple random samples of size 3 that can be selected from this population is
Answers
Answer:
The correct answer will be "56".
Step-by-step explanation:
Use a combination of 8 things taken 3 at a time :
⇒ [tex]8_{C_{3}}[/tex]
⇒ [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]
⇒ [tex]\frac{8!}{(3!5!)}[/tex]
⇒ [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]
⇒ [tex]8\times 7[/tex]
⇒ [tex]56[/tex]
Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.
Using the principle of combination :
nCr = [n! ÷ (n-r)! r!]Hence, we have ;
8C3 = [8! ÷ (8 - 3)! 3!]
8C3 = [8! ÷ 5!3!]
8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)
8C3 = 8 × 7
8C3 = 56
Hence, there are 56 different possible samples.
Learn more : https://brainly.com/question/25581049
What are the vertical asymptote(s) of y= (x-6)/(x+8) (x-7)
Answers
Answer:
x = -8 and x= 7
Step-by-step explanation:
recall that for a rational expression, the vertical asymptotes occur at x-values that causes the expression to become undefined. These occur when the denominator becomes zero.
Hence the asymptototes will occur in x-locations where the denominator , i.e
(x+8)(x-7) = 0
solving this, we get
(x+8) = 0 ----> x = -8
or
(x-7) = 0 ------> x = 7
hence the asymptotes occur x = -8 and x= 7
Answer:
x = -8 and x = 7.
Step-by-step explanation:
The vertical asymptotes are lines that the function will never touch.
Since no number can be divided by 0, the function will not touch points where the denominator of the function is equal to 0.
[tex]\frac{x - 6}{(x + 8)(x - 7)}[/tex], so the vertical asymptotes will be where (x + 8) = 0 and (x - 7) = 0.
x + 8 = 0
x = -8
x - 7 = 0
x = 7
The vertical asymptotes are at x = -8 and x = 7.
Hope this helps!