Answer:
Step-by-step explanation:
Given the populations P (in thousands) of a certain town in North Carolina, from 2006 through 2012 modeled by
P = 5.5e^kt,
If in 2008, the population was 7000. then;
at t = 2, P = 7000
7 = 5.5e^2k
7/5,5 = e^2k
1.2727= e^2k
Apply ln to both sides
ln 1.272 = lne^2k
ln 1.272= 2k
0.2411 = 2k
k = 0.2411/2
k = 0.1206 (to 4dp)
By 2018, the time t = 12 (2006-2018)
Substitute
P = 5.5e^(0.1206)(12)
P = 5.5e^(1.4468)
P = 5.5(4.2495)
P = 23.3722
P = 23372
Hence the population after 12 years is approx 23,372 populations
The cost of an item is $0.30 per ounce. If total cost of the item is $3.60, how many ounces are in the item?
Answer:
Example 1: - If the item's label displays the weight as 3 lb 2 oz, type the shop name and item's brand, enter 3 in the pounds field, leave the 00 (decimal) value unchanged, enter 2 in the ounces field, leave the 00 (decimal) value unchanged, fill out the Price field and Calculate to get the price per ounce
Answer:
12 ounces
Step-by-step explanation:
3.60 = .3x
divide by .3 on both sides
12 = x
Factor the difference of cubes. Select prime if the polynomial cannot be factored
Answer:
(m-(1/3))(m^2+(1/3)m+(1/9)
Step-by-step explanation:
Just use the difference of cubes
FOR 20 POINTS! GIVE REAL ANSWERS PLEASE. THANKS!
Davon's solution to the equation -2(x - 5) + 3 = -4 is shown below.
-2(x - 5) + 3 = -4
Step 1 -2x - 5 + 3= -4
Step 2 -2x - 2 = -4
Step 3 -2x = -2
Step 4 x = -1
In which step did the first mistake occur?
Step 1
Step 4
Step 2
Step 3
Answer:
8.5
Step-by-step explanation:
-2(x-5)+3=-4
Step 1 distribute
−2+10+3=−4
Step 2 add the numbers
-2x+13=-4
Step 3 subtract 13 from both sides of the equation
−2-13+13=-4-13
Step 4 get ride of the two 13
-2x=-4-13
Step 5 subtract -4 subtract 13
-2x=-17
Step 6 divide -17 by -2
-2x/-17
Step 6 answer
8.5
Identify the constant in the expression.
4w – 3r + 6
6
because it is the only number that isn't being multiplied by a letter
Peter collected 171 marbles but lost 3/4 of them on his way home through of hole in his bag when he arrived at home now many marbles did Peter have left?
The number of marbles Peter had when he arrived home was 43 marbles
What is Percentage?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %
Given data ,
The number of marbles Peter had on his way home = 171
The amount of marbles he lost on his way home = ( 3/4 ) th
Now , the amount of marbles Peter have left = 1 - amount of marbles he lost on his way home
The amount of marbles Peter have left = 1 - 3/4
= ( 1 / 4) th
So , The number of marbles Peter had left when he arrived home is =
Amount of marbles Peter have left x Number of marbles Peter had
The number of marbles Peter had left when he arrived home is = (1/4) x 171
= 171 / 4
= 42.75
≈ 43 marbles
Hence , the number of marbles Peter had left when he reached home is 43
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3/4 divided by what equals 3/16?
Give answer please
Water bottles are sold in cases of 24. Select the TWO expressions that can represent the total number of water bottles in c cases
Options:
24 X c,
24 ÷ c,
24 + c,
24 - c,
24c
Answer:
24c
Step-by-step explanation:
First off, we know what in each case there are 24 bottles. So if we have c crates and want to know the water bottles inside them, we need to multiply 24 by c resulting in 24c or 24 x c.
a shirt was originally marked as $24.95 rings up at the register as 19.96 what is the percent discount on the shirt
Answer:
The discount is 20% off
hope this helps!
2. I earned $9. I bought 4 candy bars for $0.85 each. How much money do I
have left? *
A. $5.60
B. $8.15
C. $9.85
D. $12.40
Answer:
A
Step-by-step explanation:
4 x $0.85= $3.40
$9-$3.40= $5.60
Answer:
A. $5.60
Step-by-step explanation:
4x0.85 =3.4 and 9 -3.4 = 5.6
What is the best estimate of 157 divided by 2=
What is the best estimate of 108 divided by 5=
Answer:
157 divided by 2 is 78.5 round that to get 70
108 divided by 5 is 21.6 round that to get 22
What is the value of Cosine (StartFraction x Over 2 EndFraction) if tangent x = one-half and x is in quadrant III?
[tex] - \sqrt{ \frac{5 - 2 \sqrt{5} }{10} } [/tex]
Answer:
a
Step-by-step explanation:
on edge
What is a secure line of credit?
a. A line of credit offered only to individuals with excellent credit ratings.
b. A line of credit offered to a business or corporation.
c. A line of credit backed by the government.
d. A line of credit backed by collateral.
Answer:
D. A line of credit backed by collateral.
Step-by-step explanation:
Answer:
D. A line of credit backed by collateral.
Step-by-step explanation:
did the quiz
identify a pair of factors of -35 that has a sum of -2
Answer:
5, -7
Step-by-step explanation:
Answer:
5 and -7
Step-by-step explanation:
Select all intervals in which the function P(t) is decreasing
Answer:
we conclude that the intervals in which the function P(t) is decreasing are:
x < 13 < x < 4Step-by-step explanation:
At x< 1, the function P(t) is decreasing
A function p is an increasing function on an open interval if f(y) > f(x) for any two input values x and y in the given interval where y>xA function p is a decreasing function on an open interval if f(y) > f(x) for any two input values x and y in the given interval where y>xFrom the figure, it is clear that the function seems to be increasing
from (1, 3) and then 4 to onwards.
But it is clear that the function seems to be decreasing from the x < 1 and from the interval (3, 4).
Therefore, we conclude that the intervals in which the function P(t) is decreasing are:
x < 13 < x < 4Suppose that Y has density function
f(y) = ky(1 − y) if 0 ≤ y ≤ 1 0, elsewhere
A) Find the value of k that makes f (y) a probability density function.
B) Find P(Y ≤ .4|Y ≤ .8).
C) Find the .95-quantile, i.e., find a point φ.95 such that P(Y ≤ φ.95) = .95.
I'm assuming
[tex]f(y)=\begin{cases}ky(1-y)&\text{for }0\le y\le1\\0&\text{otherwise}\end{cases}[/tex]
(a) f(x) is a valid probability density function if its integral over the support is 1:
[tex]\displaystyle\int_{-\infty}^\infty f(x)\,\mathrm dx=k\int_0^1 y(1-y)\,\mathrm dy=k\int_0^1(y-y^2)\,\mathrm dy=1[/tex]
Compute the integral:
[tex]\displaystyle\int_0^1(y-y^2)\,\mathrm dy=\left(\frac{y^2}2-\frac{y^3}3\right)\bigg|_0^1=\frac12-\frac13=\frac16[/tex]
So we have
k / 6 = 1 → k = 6
(b) By definition of conditional probability,
P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4 and Y ≤ 0.8) / P(Y ≤ 0.8)
P(Y ≤ 0.4 | Y ≤ 0.8) = P(Y ≤ 0.4) / P(Y ≤ 0.8)
It makes sense to derive the cumulative distribution function (CDF) for the rest of the problem, since F(y) = P(Y ≤ y).
We have
[tex]\displaystyle F(y)=\int_{-\infty}^y f(t)\,\mathrm dt=\int_0^y6t(1-t)\,\mathrm dt=\begin{cases}0&\text{for }y<0\\3y^2-2y^3&\text{for }0\le y<1\\1&\text{for }y\ge1\end{cases}[/tex]
Then
P(Y ≤ 0.4) = F (0.4) = 0.352
P(Y ≤ 0.8) = F (0.8) = 0.896
and so
P(Y ≤ 0.4 | Y ≤ 0.8) = 0.352 / 0.896 ≈ 0.393
(c) The 0.95 quantile is the value φ such that
P(Y ≤ φ) = 0.95
In terms of the integral definition of the CDF, we have solve for φ such that
[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=0.95[/tex]
We have
[tex]\displaystyle\int_{-\infty}^\varphi f(y)\,\mathrm dy=\int_0^\varphi 6y(1-y)\,\mathrm dy=(3y^2-2y^3)\bigg|_0^\varphi = 0.95[/tex]
which reduces to the cubic
3φ² - 2φ³ = 0.95
Use a calculator to solve this and find that φ ≈ 0.865.
Using probability concepts, it is found that
a) The value is k = 6.
b) P(Y ≤ .4|Y ≤ .8) = 0.554.
c) The 95th percentile is x = 0.86465.
The density function is:
[tex]f(y) = ky(1 - y)[/tex]
Item a:
The condition that makes it a probability density function is:
[tex]\int_0^1 f(y) dy = 1[/tex]
Thus:
[tex]\int_0^1 f(y) dy = \int_0^1 ky - ky^2 dy[/tex]
[tex]\int_0^1 f(y) dy = k(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0}^{y = 1}[/tex]
[tex]\int_0^1 f(y) dy = k(\frac{1}{2} - \frac{1}{3})[/tex]
Then
[tex]k(\frac{1}{2} - \frac{1}{3}) = 1[/tex]
[tex]k(\frac{3-2}{6}) = 1[/tex]
[tex]k = 6[/tex]
The value is k = 6.
Item b:
This probability is:
[tex]\int_0.4^0.8 f(y) dy = 6(\frac{y^2}{2} - \frac{y^3}{3})|_{y = 0.4}^{y = 0.8}[/tex]
Then
[tex]p = 6\left(\frac{0.8^2}{2} - \frac{0.8^3}{3} - \frac{0.4^2}{2} + \frac{0.4^3}{3}\right)[/tex]
[tex]p = 0.554[/tex]
Thus, P(Y ≤ .4|Y ≤ .8) = 0.554.
Item c:
This is x for which:
[tex]\int_0^x f(y) dy = 0.95[/tex]
Thus:
[tex]6(\frac{x^2}{2} - \frac{x^3}{3}) = 0.95[/tex]
[tex]-2x^3 + 3x^2 - 0.95 = 0[/tex]
Solving a cubic equation with the help of a calculator, and considering [tex]0 \leq x \leq 1[/tex], this is x = 0.86465.
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Please help, marking brainleist, show work
Answer:
Perimeter: 16x + 16
Area: 40x + 15
Step-by-step explanation:
Remember, the perimeter is the sum of all the sides of a figure, it can be found by adding up all the sides. The area is the space within the figure, in the case of a quadrilateral can be found by multiplying the length by the width. Finally, in a rectangle, the opposite sides are congruent, parallel, and intersect in 90degree (right) angles.
Using this,
1. Find the perimeter
Since opposite sides are congruent, there will be two sides with a measure of ( 8x + 3 ), and two sides with the measure of 5. Hence the sum of all the sides would be
8x + 3 + 8x + 3 + 5 + 5
Add them together,
16x + 16.
The perimeter of the figure is 16x + 16
2. Find the area,
To find the area of a rectangle, multiply the length by the width.;
( 8x + 3 ) * 5
Distribute:
40x + 15
The area of the figure is 40x + 15
9. Solve the equation.
4(6 – x) + 4 = 2 (3x + 1) – 6
Answer:
x=3.2
Step-by-step explanation:
4(6 – x) + 4 = 2 (3x + 1) – 6
24 - 4x + 4 = 6x + 2 - 6
28 - 4x = 6x -4
-4x - 6x = - 4 - 28
-10x = - 32
divide both sides
x = 16/5 or x = 3.2
hope this helps :)
How do you simplify (1/2)^2 ● 1/2 ● (1/2)^3
Answer:
1 /64
Decimal Form:
0.015625
Which expression can be used to solve the problem below? On a recent math test,
Jill scored 3 points for each of the 18 multiple choice questions she answered
correctly and 5 points for each of the 6 short response questions she answered
correctly. What was her total score on the test?
1 : 3+16 • 18+6
2 : 3+18 • 5+6
3 : 3 • 5 + 18 • 6
4 : 3 • 18 + 5 • 6
Answer:
4
Step-by-step explanation:
Because she gets 3 per multiple choice question, so 3 times 18
she gets 5 per response question, so 5 times 6
Jill total score on the test is 3 • 18 + 5 • 6. The correct option is 4.
What is multiplication?Multiplication is a mathematical arithmetic operation. It is also a process of adding the same types of expression for some number of times.
Example - 2 × 3 means 2 is added three times, or 3 is added 2 times.
Given;
Jill scored 3 points for each of the 18 multiple choice questions she answered correctly.
That means,
use the multiplication operation,
3 x 18
And 5 points for each of the 6 short response questions she answered correctly.
That means,
5 x 6
To find the total score:
Add the scores,
3 x 18 + 5 x 6
or, 3 • 18 + 5 • 6
Therefore, 3 • 18 + 5 • 6 is the required expression.
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There are 3.9 milligrams of calcium in a ½ ounce of cooked chicken. How many milligrams are in 6 ounces?
Answer:
there are 46.80 milligrams in 6 ounces.
Step-by-step explanation:
Please help me it’s very important please answer it correctly
Thank you
Answer:
a. m<CBA = m<DBA because of the definition of an angle bisector (angle bisector cuts the angle in half) We are also told that segment BD and Segment BC are congruent.
We don't know if segment AC and AD are congruent so we can't say those angles (the other two) are congruent.
b. point A and B will stay fixed because they are colinear to segment AB (on the same line)
c. Those two are needed because If those are true we can prove that they are congruent by SAS (Side Angle Side)
d. the reflection an prove that the lines and angles are congruent.
120 passengers in 4 buses = passengers per bus
Answer:
30
Step-by-step explanation:
120/4
Answer:
30
Step-by-step explanation:
Just divide 120 with 4
Hope this helps!!!!!!
To compute a student's Grade Point Average (GPA) for a term, the student's grades for cach course are weighted by the number of credits for the course. Suppose a student had these grades: 3.6 in a 5 credit Math course 2.5 in a 2 credit Music course 3.0 in a 5 credit Chemistry course 3.4 in a 5 credit Journalism course What is the student's GPA for that term? Round to two decimal places. Student's GPA=_________
Answer:
The student's GPA = 3.24
Step-by-step explanation:
To determine the student's GPA for the term,
First, we will determine the weighted grade points and then divide the result by the total credit.
The weighted grade point is the sum of the grade points in the courses.
Grade point for a course is calculated by multiplying the grade by the course credit.
For the Math course,
Grade point = 3.6 × 5 = 18.0
For the Music course,
Grade point = 2.5 × 2 = 5.0
For the Chemistry course,
Grade point = 3.0 × 5 = 15.0
For the Journalism course,
Grade point = 3.4 × 5 = 17.0
Hence,
The weighted grade point = 18.0 + 5.0 + 15.0 + 17.0
The weighted grade point = 55.0
Total credit = 5 + 2 + 5 + 5 = 17
∴ The student's GPA = 55.0 / 17 = 3.24
Hence, The student's GPA = 3.24
Helppppp meeeee 3/5 Divided by 1/9
Answer: 5.4 or 5 2/5 Hope this helps have a GREAT night
Step-by-step explanation:
Simplify the following expression (-8)-(-6)
PLEASE HELP QUICKLY!!!!! PLZZZZZZ!!!!!!!
Simplify the expression. Use positive exponents.
a14b−7c0
A. a√4b7
B. a14∙1b7
C. a14b7
D. a14b−7
Answer:
Idrk
Step-by-step explanation:
Today, 6 friends went out for lunch. Their total bill was $28.86, including tax and gratuity. They decided to split the bill equally and each paid with a $10 bill. How much money will each person get back?
Answer:
5.19
Step-by-step explanation:
first do 28.86 / 6 to find out how much each paid. then subtract that number (4.81) from 10
Answer - Every Person should get $5.19
Step-by-step explanation:
what i did is 6 x 10 = 60 then 60 - 28.86 = 31.14 / 6 = 5.19 Your welcome.
Frank ordered a set of beads. He received 70 beads in all. 21 of the beads were green. What percentage of the beads were green?
If the simple interest on $3000 for 3 years is $720 , then what is the interest rate?
Answer:
8%
Step-by-step explanation:
Starting Principal: $
3,000.00
Years:
3
Annual Interest Rate:
8
%
Results
Future Value, using...
Simple Interest: $
3,720.00
Annually Compounded Interest: $
3,779.14