Answer:
This question is incomplete, i will answer it as:
"The initial population of a town is A, and it grows with a doubling time of 10 years. What will the population be in X years?"
Ok, the growth of a population usually is an exponential growth, so we can write this as:
P(t) = A*exp(r*t)
Where A is the initial population.
r is the rate of growth, and t is our variable, in this case, number of years.
Now we know that when t = 10y, the population doubles, so we should have:
P(10y) = 2*A = A*exp(r*10y)
2 = exp(r*10)
ln(2) = r*10
ln(2)/10 = r = 0.069.
Then our equation is:
P(t) = A*exp(0.069*t)
Now, if we want to know the population in X years, we need to replace the variable t by X
P(t = X) = A*exp(0.069*X)
as a sales person at Trending Card Unlimited, Justin receives a monthly base pay plus commission on all that he sells. If he sells $400 worth of merchandise in one month, he is paid $500. If he sells $700 worth of merchandise in one month, he is paid $575. Find justin's salary if he sells $2500 worth of merchandise
Answer:
$1025
Step-by-step explanation:
We can use the 2-point form of the equation of a line to write a function that gives Justin's salary as a function of his sales.
We start with (sales, salary) = (400, 500) and (700, 575)
__
The 2-point form of the equation of a line is ...
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
salary = (575 -500)/(700 -400)(sales -400) +500
salary = 75/300(sales -400) +500
For sales of 2500, this will be ...
salary = (1/4)(2500 -400) +500 = (2100/4) +500 = 1025
Justin's salary after selling $2500 in merchandise is $1025.
A ball is thrown from a height of 20 meters with an initial downward velocity of 5 m/s. The ball's height h (in meters) after t seconds is given
by the following.
h=20-5t-5t²
How long after the ball is thrown does it hit the ground?
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)
Answer:
1.56 seconds
Step-by-step explanation:
When the ball hits the ground, h = 0.
0 = 20 − 5t − 5t²
Divide both sides by -5.
0 = t² + t − 4
Solve with quadratic formula.
t = [ -1 ± √(1² − 4(1)(-4)) ] / 2(1)
t = (-1 ± √17) / 2
The time must be positive, so:
t = (-1 + √17) / 2
t ≈ 1.56
in science class savannah measures the temperature of a liquid to be 34 celsius. her teacher wants her to convert the temperature to degrees fahrenheit. what is the temperature of savannah's liquid to the nearest degress fahrenheit
What will happen to the median height of the outlier is removed?
{75, 63, 58, 59, 63, 62, 56, 59)
Answer:
The meadian decreases by 1.5 when the outlier is removed.
Step-by-step explanation:
Well first we need to find the median of the following data set,
(75, 63, 58, 59, 63, 62, 56, 59)
So we order the set from least to greatest,
56, 58, 59, 59, 62, 63, 63, 75
Then we cross all the side numbers,
Which gets us 59 and 62.
59 + 62 = 121.
121 / 2 = 60.5
So 65 is the median before the outlier is removed.
Now when we remove the outlier which is 75.
Then we order it again,
56, 58, 59, 59, 62, 63, 63
Which gets us 59 as the median.
Thus,
the median height decreases by 1.5 units when the outlier is removed.
Hope this helps :)
Simplify.
Remove all perfect squares from inside the square roots.
Assume a and b are positive.
Answer:
9a^2sqrt(ab)
Step-by-step explanation:
The first noticable thing is that 81 has a perfect square of 9.
So it is now 9sqrt(a^5b)
you can split the a^5, to a^4 × a.
you can now take the sqrt of a^4, which is a^2, and pull it out from the sqrt
You are now left with 9a^2sqrt(ab)
Answer:
9a^2sqrt(ab)
Step-by-step explanation:
may someone assist me?
Answer:
28
Step-by-step explanation:
Let x be the missing segment
We will use the proportionality property to find x
24/16 = 42/x
Simplify 24/16
24/16= (4×6)/(4×4)= 4/6 = 3/2
So 3/2 = 42/x
3x = 42×2
3x = 84
x = 84/3
x= 28
Solve for qqq. 3\left(q+\dfrac43\right) = 23(q+ 3 4 )=2
pls answer this
Answer:
19/3Step-by-step explanation:
Given the expression [tex]3\left(q+\dfrac43\right) = 23[/tex], we are to find the value of q;
[tex]3\left(q+\dfrac43\right) = 23\\on\ expansion\\\\3q + 4/3(3) = 23\\\\3q+4 = 23\\\\subtract \ 4\ from \ both\ sides \ of \ the \ equation\\\\3q+4-4 = 23-4\\\\3q = 19\\\\Diviide \both\ sides \ by \ 3\\\\3q/3 = 19/3\\\\q = 19/3[/tex]
Hence the value of q is 19/3
Answer:
-2/3
Step-by-step explanation:
Don't worry about it, i got connections.
Jessie is adept at Imagining abstract concepts and applying advanced mathematical formulas while creating flowcharts for her programs. Jessle has strength in which
skill?
communication
Answer:
Design thinking skills
Step-by-step explanation:
The design thinking skills is observable in individuals who can effectively use Intuition to create prototypes of abstract objects.
Jessie thus shows that she possess design thinking skills by been able to imagine abstract concepts at the same and she applies advanced mathematical formulas which in turn provides solutions to problems.
On August 21, 2009, the World Health Organization announced its prediction that the number of new cases of H1N1 (swine flu) virus would double every 4 days for several months. As of July 27, 2009, the number of new cases was 15,784. Determine the instantaneous growth rate for the virus (rounded to the nearest ten-thousandths).
Answer:
growth rate = 0.1733 per day, or 17.33% per day
Step-by-step explanation:
Since the doubling time is 4 days, the growth factor over a period of t days is ...
2^(t/4)
Then the growth factor for 1 day is
2^(1/4) ≈ 1.189207
The instantaneous growth rate is the natural log of this:
ln(1.189207) ≈ 0.1733 . . . per day
In a small private school, 55 students are randomly selected from 1313 available students. What is the probability that they are the fivefive youngest students?
Complete Question
In a small private school, 5 students are randomly selected from 13 available students. What is the probability that they are the five youngest students?
Answer:
The probability is [tex]P(x) = 0.00078[/tex]
Step-by-step explanation:
From the question we are told that
The number of student randomly selected is r = 5
The number of available students is n = 13
Generally the number of ways that 5 students can be selected from 13 available students is mathematically represented as
[tex]n(k)=\left n} \atop {}} \right.C_r = \frac{n ! }{(n-r ) ! r!}[/tex]
substituting values
[tex]\left n} \atop {}} \right.C_r = \frac{13 ! }{(13-5 ) ! 5!}[/tex]
[tex]\left n} \atop {}} \right.C_r = \frac{13 * 12 * 11 * 10 * 9 *8! }{8 ! * 5 * 4 * 3 * 2 *1}[/tex]
[tex]\left n} \atop {}} \right.C_r = 1287[/tex]
The number of method by which 5 youngest students are selected is n(x) = 1
So
Then the probability of selecting the five youngest students is mathematically represented as
[tex]P(x) = \frac{n(x)}{n(k)}[/tex]
substituting values
[tex]P(x) = \frac{1}{1287}[/tex]
[tex]P(x) = 0.00078[/tex]
The amount of carbon-14 present in a paint after t years is given by y equals y Subscript o Baseline e Superscript negative 0.00012 t Baseline . The paint contains 27% of its carbon-14. How old are the paintings?
Answer:
The painting is [tex]t = 10911.1 \ years \ old[/tex]
Step-by-step explanation:
From the question we are told that
The amount of carbon present after t year is
[tex]y(t) = y_o * e ^{-0.00012t}[/tex] {Note ; This is the function }
Here [tex]y(t)[/tex] is the amount of carbon-14 after time t
[tex]y_o[/tex] the original amount of carbon-14
Now given that the paint as at now contain 27% of the original carbon-14
Then it mean that
[tex]y(t) = 0.27 y_o[/tex]
So the equation is represented as
[tex]0.27 y_o = y_o * e ^{-0.00012t}[/tex]
=> [tex]0.27 = * e ^{-0.00012t}[/tex]
=> [tex]ln(0.27) = -0.00012t[/tex]
=> [tex]- 1.30933 = -0.00012t[/tex]
=> [tex]t = \frac{-1.30933}{-0.00012}[/tex]
=> [tex]t = 10911.1 \ years[/tex]
Please HELP best answer will receive a BRAINLIEST. Given the probability density function f ( x ) = 1/3 over the interval [ 4 , 7 ] , find the expected value, the mean, the variance and the standard deviation.
Answer:
Step-by-step explanation:
Assume that f(x) = 0 for x outside the interval [4,7]. We will use the following
[tex]E[X^k] = \int_{4}^{7}x^k f(x) dx[/tex]
[tex]Var(X) = E[X^2]- (E[X])^2[/tex]
Standard deviation = [tex] \sqrt[]{Var(X)}[/tex]
Mean = [tex]E[X][/tex]
Then,
[tex]E[X] = \int_{4}^{7}\frac{1}{3}dx = \frac{7^2-4^2}{2\cdot 3} = \frac{11}{2}[/tex]
[tex]E[X^2] = \int_{4}^{7}\frac{x^2}{3}dx = \frac{7^3-4^3}{3\cdot 3} = 31[/tex]
Then, [tex]Var(x) = 31-(\frac{11}{2})^2 = \frac{3}{4}[/tex]
Then the standard deviation is [tex]\frac{\sqrt[]{3}}{2}[/tex]
Am I right or wrong?
You are absolutely right.
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
x+y>0
x + y +5<0
Answer:
Step-by-step explanation:
x+y>0, x>0, when y=0
x+y<-5 x<-5 when y=0
since the sign is only< then it is dotted line, and since one is greater and is less than they actually do not intersect
Answer:
No solution with slanted lines
Step-by-step explanation:
Question 3
34° Celsius is equal to
o
Fahrenheit
Hi
Below the formulas to convert Celsius into Fahrenheit.
9/5 C +32 = degree in fahrenheit.
Where C is the degree in celsius. So have a try and find the answer.
The top and bottom margins of a poster are each 9 cm and the side margins are each 6 cm. If the area of the printed material on the poster is fixed at 864 cm2, find the dimensions of the poster with the smallest area.
Answer:
the dimensions of the poster with the smallest area is 36cm by 54cm
Step-by-step explanation:
✓Let us represent the WIDTH of the printed material on the poster as "x"
✓Let us represent the HEIGHT of the printed material on the poster as "y"
✓ The given AREA is given as 864 cm2
Then we have
864 cm2= xy ...................eqn(1)
We can make "y" subject of the formula.
y= 864/x .......................eqn(2)
✓The total height the big poster which includes the 9cm margin that is at the bottom as well as the top is
(y+18)
✓The total width of the poster which includes the 6cm margin that is at the bottom as well as the top is
(x+12)
✓Then AREA OF THE TOTAL poster
A= (y+18)(x+12) ...................eqn(3)
Substitute eqn (2) into eqn(3)
A= ( 18+ 864/x)(x+12)
We can now simplify by opening the bracket, as
A=18x +1080 +10368/x
A= 18x +10368/x +1080
Let us find the first derivative of A which is A'
A'= 18-(10368/x²)
If we set A' =0
Then
0= 18- (10368/x²)
18= (10368/x²)
x²= 10368/18
x²= 576
x=√576
x=24
The second derivatives will be A"= 2(10368)/x³ and this will be positive for x> 0, and here A is concave up and x=24 is can be regarded as a minimum
The value of "y" when x=24 can now be be calculated using eqn(2)
y= 864/x
y= 864/24
y=36cm
✓The total width of the poster= (x+12)
= 24+12=36cm
✓The total height big the poster= (y+18)=36+18=54cm
the dimensions of the poster with the smallest area is 36cm by 54cm
Answer:
The total width of the paper [tex]=36 cm.[/tex]
The total height of the paper [tex]=54cm[/tex]
Step-by-step explanation:
Given information:
Top margin of the paper = 9 [tex]cm\\[/tex]
Bottom margin of the paper = 6 [tex]cm\\[/tex]
Area of the printed material = [tex]864[/tex] [tex]cm^2[/tex]
Let, the width of the printed material = [tex]x[/tex]
And the height of the printed material = [tex]y[/tex]
So, Area [tex]x \times y=864[/tex] [tex]cm^2[/tex]
After including margins;
Width of the paper [tex]= (x+12)[/tex]
Height of the paper [tex]= (y+18)[/tex]
Area [tex](A) = (y+18) (x+12)[/tex]
[tex]A=18x+(10368/x)+1080\\[/tex]
Take first derivative:
[tex]A'= 18- (10368/x^2)[/tex]
When [tex]A'=0[/tex]
Then,
[tex]18-(10368/x^2)=0\\x^2=576\\x=24[/tex]
Now ,when we take second derivative and check if it is positive or not ,
We find that it is grater than zero so the obtained value can be consider as minimum and can be proceed for further solution.
Hence ,
[tex]x \times y=864\\y=864/24\\y=36\\[/tex]
Now ,
The total width of the paper
[tex]= 24+12\\=36 cm.[/tex]
And , total height of the paper
[tex]=36+18\\=54 cm.[/tex]
For more information visit:
https://brainly.com/question/14261130
Solve for x −ax + 2b > 8
Answer:
x < -( 8-2b) /a a > 0
Step-by-step explanation:
−ax + 2b > 8
Subtract 2b from each side
−ax + 2b-2b > 8-2b
-ax > 8 -2b
Divide each side by -a, remembering to flip the inequality ( assuming a>0)
-ax/-a < ( 8-2b) /-a
x < -( 8-2b) /a a > 0
Answer: [tex]x<\frac{-8+2b}{a}[/tex]
[tex]a>0[/tex]
Step-by-step explanation:
[tex]-ax+2b>8[/tex]
[tex]\mathrm{Subtract\:}2b\mathrm{\:from\:both\:sides}[/tex]
[tex]-ax>8-2b[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}[/tex]
[tex]\left(-ax\right)\left(-1\right)<8\left(-1\right)-2b\left(-1\right)[/tex]
[tex]ax<-8+2b[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}a[/tex]
[tex]\frac{ax}{a}<-\frac{8}{a}+\frac{2b}{a};\quad \:a>0[/tex]
[tex]x<\frac{-8+2b}{a};\quad \:a>0[/tex]
The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard. Discuss the practical consequences of making a Type I and a Type II error. (continue #5) A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4. Find the p-value of the test. Do you think that H0 should be rejected? Explain. To what type of error are you now subject?
Answer:
Step-by-step explanation:
From the summary of the given statistics;
The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:
Null hypothesis:
[tex]H_0: \mu = 0.60[/tex]
Alternative hypothesis:
[tex]H_a: \mu < 0.60[/tex]
Type I error: Here, the null hypothesis which is the new engine has a mean level equal to .6g/ml is rejected when it is true.
Type II error: Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.
Similarly;
From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.
Sample size n = 64
sample mean [tex]\overline x[/tex] = .5 g/ml
standard deviation σ = .4
From above, the normal standard test statistics can be determined by using the formula:
[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]
[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]
z = -2.00
The p-value = P(Z ≤ -2.00)
From the normal z distribution table
P -value = 0.0228
Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.
Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.
need help with these 3 questions (giving brainiest if you can answer with equations)
Problem 10
Answer: approximately 57.39159 kmExplanation: You'll use the equation cos(28) = d/65 to solve for d to get d = 65*cos(28) = 57.39159 approximately. We use the cosine ratio because it ties together the adjacent and hypotenuse.
=====================================
Problem 11
Answer: approximately 10.46162 metersExplanation: This time we use the sine rule. We have the height as the opposite side (which is unknown, call it x) and the hypotenuse is the ladders length (11). So we have sin(72) = x/11 which solves to x = 11*sin(72) = 10.46162
=====================================
Problem 12
Answer: approximately 16.05724 cmExplanation: Now we use the tangent rule to connect the opposite and adjacent sides.
tan(37) = 12.1/x
x*tan(37) = 12.1
x = 12.1/tan(37)
x = 16.05724 approximately
There are three points on a line, A, B, and C, so that AB = 12 cm, BC = 13.5 cm. Find the length of the segment AC . Give all possible answers.
Answer:
AC = 25.5 or 1.5
Step-by-step explanation:
If they are on a line and they are in the order ABC
AB + BC = AC
12+13.5 = AC
25.5 = AC
If they are on a line and they are in the order CAB
CA + AB = BC
AC + 12 =13.5
AC = 13.5 -12
AC = 1.5
If they are on a line and they are in the order ACB
That would mean that AB is greater than BC and that is not the case
1. An architect is designing a house for the Mullet family. In the design he
must consider the desires of the family and the local building codes. The
rectangular lot on which the house will be built has 91 feet of frontage
on a lake and is 158 feet deep.
Answer:
An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
-------------------------------
The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
hope it helpsss
Step-by-step explanation:
Answer: An architect is designing a house for the Frazier family. In the design he must consider the desires of the family and the local building codes. The rectangular lot on which the house will be built has 91 feet of frontage on a lake and is 158 feet deep.
The building codes states that one can build no closer than 10 ft. to the lot line. Write an inequality and solve to see how long the front of the house facing the lake may be.
------
length = 91 - 2*10 = 71 ft.
-------------------------------
The Fraziers requested that the house contain no less 2800 ft square and no more than 3200 ft square of floor sample. Write an inequality to represent the range of permissible widths for the house.
---------
2800 <= area <= 3200
2800 <= (length)(width) <= 3200
2800 <= 71w <= 3200
39.44 <= width <= 45.07
Find the slope of the line passing through the points (3, 4) and (8, -3).
Answer:
-7/5
Step-by-step explanation:
We can find the slope using the slope formula
m = ( y2-y1)/(x2-x1)
= ( -3 -4)/(8-3)
= -7/5
Answer:
-7/5
Step-by-step explanation:
Hey there!
To find the slope of a line with 2 given points we'll use the following formula,
[tex]\frac{y^2-y^1}{x^2-x^2}[/tex]
-3 - 4 = -7
8 - 3 = 5
-7/5
Hope this helps :)
When do you reject the null hypothesis?
You reject the Null Hypothesis when you have a small P-Value. Here is an example! Also we never accept the null hypothesis, think of it like this if we bring someone to court you wouldn't say their innocent of a crime, you only know that if they do not get convicted of the crime they are not guilty in the eyes of the law. Same thing applies here, since there could be several answers that satisfy our assumptions made, we can not be certain that 1 of those assumptions is the REAL answer it's just AN answer.
Does anyone know the answers to these?
Step-by-step explanation:
a. The point estimate is the mean, 47 days.
b. The margin of error is the critical value times the standard error.
At 31 degrees of freedom and 98% confidence, t = 2.453.
The margin of error is therefore:
MoE = 2.453 × 10.2 / √32
MoE = 4.42
c. The confidence interval is:
CI = 47 ± 4.42
CI = (42.58, 51.42)
d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.
e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.
If mZNOM = 30°, then what is the length of the minor arc
NM?
Answer:
Option (B)
Step-by-step explanation:
To determine the length of arc of a circle we use the formula,
Length of arc = [tex]\frac{\theta}{360}(2\pi r)[/tex]
Where θ = measure of the central angle subtended by the arc
r = radius of the circle
For the circle given in the picture attached,
Length of arc NM = [tex]\frac{30}{360}(2\pi)(2)[/tex]
= [tex]\frac{4\pi }{12}[/tex]
= [tex]\frac{\pi }{3}[/tex]
Therefore, length of [tex]\widehat{NM}=\frac{\pi }{3}[/tex]
Option (B) will be the answer.
Answer: C
Step-by-step explanation:
4#/12 = #
What is the output of the function f(x) = x + 21 if the input is 4?
When the input is 4, the output of f(x) = x + 21.
Work Shown:
Replace every x with 4. Use the order of operations PEMDAS to simplify
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
The input 4 leads to the output 25.
Edgar accumulated $5,000 in credit card debt. If the interest rate is 20% per year and he does not make any payments for 2 years, how much will he owe on this debt in 2 years by compounding continuously? Round to the nearest cent.
Answer:
$7200
Step-by-step explanation:
The interest rate on $5,000 accumulated by Edgar is 20%.
He does not make any payment for 2 years and the interests are compounded continuously.
The amount of money he owes after 2 years is the original $5000 and the interest that would have accumulated after 2 years.
The formula for compound amount is:
[tex]A = P(1 + R)^T[/tex]
where P = amount borrowed = $5000
R = interest rate = 20%
T = amount of time = 2 years
Therefore, the amount he will owe on his debt is:
[tex]A = 5000 (1 + 20/100)^2\\\\A = 5000(1 + 0.2)^2\\\\A = 5000(1.2)^2\\[/tex]
A = $7200
After 2 years, he will owe $7200
Answer:7,434.57
Explanation: A= 5000(1+0.2/12)^12•2
Write the following exponential expression in expanded form 28 to the 6th power. Enter your answer in the following format a • a• a
Answer:
28 • 28 • 28 • 28 • 28 • 28
Step-by-step explanation:
The exponent signifies the number of times the base appears as a factor in the product. Here, the base 28 is a factor 6 times:
28×28×28×28×28×28
In figure, MN : NP = 9:1. If MP = 2. Find the distance from M to point K (not shown) that is a midpoint of PN.
Answer:
1.9 units
Step-by-step explanation:
Since we have ...
MN : NP = 9 : 1
then ...
NP : MN+NP = 1 : (9+1) = 1 : 10
If MP is 2 units, then NP is 1/10 × 2 units = 0.2 units. Point K will be half that distance from N or P, so will be 0.1 unit from P.
So, the distance from M to K, the midpoint of NP is ...
2 units - 0.1 units = 1.9 units
Answer:
1.9
Step-by-step explanation:
helpppp with this will give bralienst but need hurry
Answer:
20.25is how much each friend gets.Step-by-step explanation:
40.50/2 = 20.25
You have to divide by 2. This way both of the people will get the same amount of money.
Answer:
each friend will get
Step-by-step explanation:
20 .25
as 40 .50 ÷ 2 = 20 .25
hope this helps
pls can u heart and like and give my answer brainliest pls i beg u thx !!! : )