Answer:
11/16, 3/5, 7/10
Step-by-step explanation:
Please help
A town has a population of 14000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 41500?
Answer:
65.9
Step-by-step explanation:
Max bought a new pair of basketball shoes that were on sale for 25% off. If the regular price of the shoes was $75.95, what is the amount of discount?
On a map, the scale is ½ inch to 300 miles. If the trip from Corpus Christi to El Paso is 600 miles, how far apart will those cities appear on the map (in inches)?
Answer:
Step-by-step explanation:
How many miles from El Paso to Corpus Christi?
The total driving distance from El Paso, TX to Corpus Christi, TX is 699 miles or 1 125 kilometers.
Answer:
1 inch
Step-by-step explanation:
1/2 inch = 0.5 inch
0.5/300 = n/600
0.5 * 600 = n * 300
300 = 300n
1 = n or n = 1
The portion of the parabola y²=4ax above the x-axis, where is form 0 to h is revolved about the x-axis. Show that the surface area generated is
A=8/3π√a[(h+a)³/²-a³/2]
Use the result to find the value of h if the parabola y²=36x when revolved about the x-axis is to have surface area 1000.
Answer:
See below for Part A.
Part B)
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
Step-by-step explanation:
Part A)
The parabola given by the equation:
[tex]y^2=4ax[/tex]
From 0 to h is revolved about the x-axis.
We can take the principal square root of both sides to acquire our function:
[tex]y=f(x)=\sqrt{4ax}[/tex]
Please refer to the attachment below for the sketch.
The area of a surface of revolution is given by:
[tex]\displaystyle S=2\pi\int_{a}^{b}r(x)\sqrt{1+\big[f^\prime(x)]^2} \,dx[/tex]
Where r(x) is the distance between f and the axis of revolution.
From the sketch, we can see that the distance between f and the AoR is simply our equation y. Hence:
[tex]r(x)=y(x)=\sqrt{4ax}[/tex]
Now, we will need to find f’(x). We know that:
[tex]f(x)=\sqrt{4ax}[/tex]
Then by the chain rule, f’(x) is:
[tex]\displaystyle f^\prime(x)=\frac{1}{2\sqrt{4ax}}\cdot4a=\frac{2a}{\sqrt{4ax}}[/tex]
For our limits of integration, we are going from 0 to h.
Hence, our integral becomes:
[tex]\displaystyle S=2\pi\int_{0}^{h}(\sqrt{4ax})\sqrt{1+\Big(\frac{2a}{\sqrt{4ax}}\Big)^2}\, dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax}\Big(\sqrt{1+\frac{4a^2}{4ax}}\Big)\,dx[/tex]
Combine roots;
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax\Big(1+\frac{4a^2}{4ax}\Big)}\,dx[/tex]
Simplify:
[tex]\displaystyle S=2\pi\int_{0}^{h}\sqrt{4ax+4a^2}\, dx[/tex]
Integrate. We can consider using u-substitution. We will let:
[tex]u=4ax+4a^2\text{ then } du=4a\, dx[/tex]
We also need to change our limits of integration. So:
[tex]u=4a(0)+4a^2=4a^2\text{ and } \\ u=4a(h)+4a^2=4ah+4a^2[/tex]
Hence, our new integral is:
[tex]\displaystyle S=2\pi\int_{4a^2}^{4ah+4a^2}\sqrt{u}\, \Big(\frac{1}{4a}\Big)du[/tex]
Simplify and integrate:
[tex]\displaystyle S=\frac{\pi}{2a}\Big[\,\frac{2}{3}u^{\frac{3}{2}}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[\, u^\frac{3}{2}\Big|^{4ah+4a^2}_{4a^2}\Big][/tex]
FTC:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[(4ah+4a^2)^\frac{3}{2}-(4a^2)^\frac{3}{2}\Big][/tex]
Simplify each term. For the first term, we have:
[tex]\displaystyle (4ah+4a^2)^\frac{3}{2}[/tex]
We can factor out the 4a:
[tex]\displaystyle =(4a)^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =8a^\frac{3}{2}(h+a)^\frac{3}{2}[/tex]
For the second term, we have:
[tex]\displaystyle (4a^2)^\frac{3}{2}[/tex]
Simplify:
[tex]\displaystyle =(2a)^3[/tex]
Hence:
[tex]\displaystyle =8a^3[/tex]
Thus, our equation becomes:
[tex]\displaystyle S=\frac{\pi}{3a}\Big[8a^\frac{3}{2}(h+a)^\frac{3}{2}-8a^3\Big][/tex]
We can factor out an 8a^(3/2). Hence:
[tex]\displaystyle S=\frac{\pi}{3a}(8a^\frac{3}{2})\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Simplify:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
Hence, we have verified the surface area generated by the function.
Part B)
We have:
[tex]y^2=36x[/tex]
We can rewrite this as:
[tex]y^2=4(9)x[/tex]
Hence, a=9.
The surface area is 1000. So, S=1000.
Therefore, with our equation:
[tex]\displaystyle S=\frac{8\pi}{3}\sqrt{a}\Big[(h+a)^\frac{3}{2}-a^\frac{3}{2}\Big][/tex]
We can write:
[tex]\displaystyle 1000=\frac{8\pi}{3}\sqrt{9}\Big[(h+9)^\frac{3}{2}-9^\frac{3}{2}\Big][/tex]
Solve for h. Simplify:
[tex]\displaystyle 1000=8\pi\Big[(h+9)^\frac{3}{2}-27\Big][/tex]
Divide both sides by 8π:
[tex]\displaystyle \frac{125}{\pi}=(h+9)^\frac{3}{2}-27[/tex]
Isolate term:
[tex]\displaystyle \frac{125}{\pi}+27=(h+9)^\frac{3}{2}[/tex]
Raise both sides to 2/3:
[tex]\displaystyle \Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}=h+9[/tex]
Hence, the value of h is:
[tex]\displaystyle h=\Big(\frac{125}{\pi}+27\Big)^\frac{2}{3}-9\approx7.4614[/tex]
You seem to have left out that 0 ≤ x ≤ h.
From y² = 4ax, we get that the top half of the parabola (the part that lies in the first quadrant above the x-axis) is given by y = √(4ax) = 2√(ax). Then the area of the surface obtained by revolving this curve between x = 0 and x = h about the x-axis is
[tex]2\pi\displaystyle\int_0^h y(x) \sqrt{1+\left(\frac{\mathrm dy(x)}{\mathrm dx}\right)^2}\,\mathrm dx[/tex]
We have
y(x) = 2√(ax) → y'(x) = 2 • a/(2√(ax)) = √(a/x)
so the integral is
[tex]4\sqrt a\pi\displaystyle\int_0^h \sqrt x \sqrt{1+\frac ax}\,\mathrm dx[/tex]
[tex]=\displaystyle4\sqrt a\pi\int_0^h (x+a)^{\frac12}\,\mathrm dx[/tex]
[tex]=4\sqrt a\pi\left[\dfrac23(x+a)^{\frac32}\right]_0^h[/tex]
[tex]=\dfrac{8\pi\sqrt a}3\left((h+a)^{\frac32}-a^{\frac32}\right)[/tex]
Now, if y² = 36x, then a = 9. So if the area is 1000, solve for h :
[tex]1000=8\pi\left((h+9)^{\frac32}-27\right)[/tex]
[tex]\dfrac{125}\pi=(h+9)^{\frac32}-27[/tex]
[tex]\dfrac{125+27\pi}\pi=(h+9)^{\frac32}[/tex]
[tex]\left(\dfrac{125+27\pi}\pi\right)^{\frac23}=h+9[/tex]
[tex]\boxed{h=\left(\dfrac{125+27\pi}\pi\right)^{\frac23}-9}[/tex]
Simplify each expression. (Will Give Brainlest)
Answer:
0.88
Step-by-step explanation:
-5.37 + 8.14 - 1.89
-5.37 + 6.25
= 0.88
Step-by-step explanation:
please i worked on paper worksheet
please see it
1. Assume that men’s weights are normally distributed with a mean given by = 172lb and a standard deviation given by =29lb. Using the Central Limit Theorem to solve the following exercises(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.
Answer:
1) 0.99348
2) 0.55668
Step-by-step explanation:
Assume that men’s weights are normally distributed with a mean given by = 172lb and a standard deviation given by =29lb. Using the Central Limit Theorem to solve the following exercises
When given a random number of samples, we use the z score formula:
z-score is z = (x-μ)/σ/√n where
x is the raw score
μ is the population mean
σ is the population standard deviation.
(1) If 36 men are randomly selected, find the probability that they have a mean weight greater than 160lb.
For x > 160 lb
z = 160 - 172/29/√36
z = 160 - 172/29/6
z = -2.48276
Probability value from Z-Table:
P(x<160) = 0.0065185
P(x>160) = 1 - P(x<160) = 0.99348
(2) If 81 men randomly selected, find the probability that they have a mean weight between 170lb and 175lb.
For x = 170 lb
z = 170 - 172/29/√81
z = 170 - 172/29/9
z = -0.62069
Probability value from Z-Table:
P(x = 170) = 0.2674
For x = 175 lb
z = 175 - 172/29/√36
z = 175- 172/29/6
z = 0.93103
Probability value from Z-Table:
P(x = 175) = 0.82408
The probability that they have a mean weight between 170lb and 175lb is calculated as:
P(x = 175) - P(x = 170)
0.82408 - 0.2674
= 0.55668
Kevin and his children went into a restaurant and he bought 31.50
um kevin bought 31.50 of what? food?
multiply 4-6i and -4+2i
Answer:
-4 + 32i
Step-by-step explanation:
use the distributive property to multiply
remember: i^2 = 1
(4 - 6i)(-4 + 2i)
-16 + 8i + 24i - 12i^2
-16 + 32i - 12(- 1)
-16 + 32i +12
-4 + 32i
Answer:
4 - (6 * i)) * ((-4) + (2 * i)) =
-4 + 32 i
Step-by-step explanation:
PlEASE HELP ILL GIVE OUT BRAINLEIST
If you have five red balls and five blue balls in a jar what’s the probability of the first ball being red?
Answer:
red balls = 5
blue balls = 5
total balls = 5 blue+5 red
= 10
[tex]p(first \: ball \: being \: red) = \frac{red \: balls}{total \: balls} [/tex]
[tex]p(first \: ball \: being \: red) = \frac{5}{10} = \frac{1}{2} [/tex]
Answer:
Step-by-step explanation:
Total number of red balls = 5
Total number of blue balls = 5
Total number of balls in jar = 5 + 5
= 10
Probability of the first ball being red = total number of the red ball/total number of balls in the jar
= [tex]\frac{5}{10}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, the probability of the first ball being red = [tex]\frac{1}{2}[/tex], 50% or 0.5 (in any way you are instructed to write it in)
MY NOTES ASK YOUR TEACHER Jack has decided to advertise the sale of his car by placing flyers in the student union and the dining hall of the college. He estimates that there is a probability of 0.4 that a potential buyer will read the advertisement and that, if it is read, the probability that the reader will buy his car will be 0.1. Using these estimates, find the probability that a potential buyer will read the ad and will buy Jack's car.
Answer:
The probability that a potential buyer will read the advert and will buy Jack's car is 0.04
Step-by-step explanation:
Estimate 1: There's a 0.4 probability that a potential buyer will read the advert.
Estimate 2: There's a 0.1 probability that whoever reads the advert will buy his car.
- As you can see, the probability of success of this event decreases; from the point of Jack placing an advert, to the point of someone purchasing his car.
- That someone reads the advert does not mean that he or she would be interested in or capable of purchasing the car.
- That someone has the capacity to buy the car (potential buyer) does not mean they'll eventually buy it.
- So altogether, there is a low probability of each reader purchasing the car, and that's 0.1
In the calculation of probability, "and" represents multiplication. Hence,
0.4 × 0.1 = 0.04
Prove that for any natural value of n the value of the expression (n+2)^2-(n-2)^2 is a multiple of 8.
Answer:
We have the expression:
(n + 2)^2 - (n - 2)^2
Let´s break the parentheses:
(n + 2)^2 = n^2 + 4*n + 4
(n - 2)^2 = n^2 - 4n + 4
Then:
(n + 2)^2 - (n - 2)^2 = (n^2 + 4*n + 4) - (n^2 - 4n + 4) =
= (n^2 - n^2) + (4 - 4) + (4n - (-4n)) = 4n - (-4n) = 8*n
Then for any natural value of n, 8*n will be a multiple of 8.
How do you work this problem? 10x2 +25x
Answer:
x=-5/2,0
Step-by-step explanation:
It is solved by first factorizing it
10x²+25x=5x(2x+5)=0
Finding the zeros
5x=0x=0/5=0
2x+5=0
x=-5/2
Therefore x is -5/2 or 0
Lydia receives a $2,000 gift and wants to open a savings account. Which bank interest would be the best for her if the current inflation rate is 3.5%?
Answer:
the best interest rate would be a minimum of 3.5% annual interest
Step-by-step explanation:
An inflation rate of 3.5% would mean that the buying power of Lydia's money would decrease by 3.5% every single year. Therefore, the best interest rate would be a minimum of 3.5% annual interest. That way she would at least maintain the same buying power with her money as the day that she first placed it in the account. Any interest rate higher than 3.5% would be even better as Lydia will begin to make a profit from her savings.
rewrite using a single positive exponent 5^6/5^4
Answer:
5²Step-by-step explanation:
We can divide exponents by subtract 4 from 6. So, now we have 5^2 or 25.
The other way to solve to check our answer is to do the math.
5^6 = 15625
5^4 = 625
15625/625 = 25
So, we know we have the correct answer.
The population of Garden City in 1995 was 2,400. In 200, the population was 4,000. Write a linear equation in slope-intercept form that represents this data.
Answer:
[tex]y = 320x +2080[/tex]
Step-by-step explanation:
Given
Population in 1995 = 2400
Population in 2000 = 4000
Required
Determine the linear equation
Let the years be represented with x.
In 1995, x = 1 i.e. the first year
In 2000, x = 6
Let y represents the population
When x = 1; y = 2400
When x = 6; y = 4000
First, we calculate the slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{4000 - 2400}{6 - 1}[/tex]
[tex]m = \frac{1600}{5}[/tex]
[tex]m = 320[/tex]
Next, we calculate the line equation as follows:
[tex]y - y_1 = m(x - x_1)[/tex]
[tex]y - 2400 = 320(x - 1)[/tex]
[tex]y - 2400 = 320x - 320[/tex]
[tex]y = 320x - 320 + 2400[/tex]
[tex]y = 320x +2080[/tex]
are any of these equations linear or nonlinear if yes what is the standard form
a. y=-7+6x
b. y=2x+5
Answer:
both are linear
a) 6x - y = 7
b) 2x - y = -5
Step-by-step explanation:
Helppp pleaseee, abc= dce. If ac=5 and bc=7 cd=?
Answer:
CD = 5
Step-by-step explanation:
Given that ∆ACB is congruent to ∆DCE, it follows that their corresponding angles and corresponding side lengths are congruent to each other. Thus:
AC is congruent to CD,
BC is congruent to EC, and
AB is congruent to DE.
Since AC = 5, therefore CD = 5.
If each of two complementary angles has the same measure, then each angle will equal _____.
22.5°
90°
180°
45°
Answer:
45
Step-by-step explanation:
what is this answer!!!!!!!!
Step-by-step explanation:
what is this answer
(3x + 40) + (5x - 52) = 180°
8x - 12 = 180°
8x = 180 + 12
8x = 192
8x = 24
x = 3
What is the solution for this inequality?
need help fast please!
Answer:
[tex]x\geq -4[/tex]
Step-by-step explanation:
[tex]-10x\leq 40[/tex]
divide by -10, which means you need to flip the inequality sign since youre dividing by a negative number
[tex]x\geq -4[/tex]
Answer:
The anwer is D
Step-by-step explanation:
up up up......
Perform the following operation
and express the answer in
scientific notation.
6.300x10^-5 – 7.200x10^-3
[?]*10
Answer:
Step-by-step explanation:
6.3 x10^-5 -7.200 x10^-3= - 0.007137=7.137x10-3
Answer:-7.137 x 10^-3
Step-by-step explanation:
what type of transformation maps abc onto def
Answer:
The answer is translation :)
Select the expressions that are equivalent to 34
Answer:
81 9^2
Step-by-step explanation:
3•3= 9
3•3=9
9•9=81
and 9•9=81
When a gas is kept at a constant temperature and pressure on it changes, its volume changes according to the following formula, known as Boyle’s law
where P1 and V1 are the pressure (in atm) and the volume (in litres) at the beginning, and P2 and V2 are the pressure and the volume at the end. Find the final pressure P2 if V1 = 1.5 litres, P1 = 4.5 atm and V2 = 3.5 litres. Round to the nearest tenth of a atm.
Answer: Approximately 1.9 atm
============================================
Work Shown:
[tex]P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = \frac{6.75}{3.5}\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\[/tex]
If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.
Note the increase in volume leads to the reduction of pressure, and vice versa. The two variables have an inverse relationship.
-----------
As a check,
[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\[/tex]
We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.
A more accurate check could be
[tex]P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\[/tex]
which has the two sides much closer to one another. This helps us verify the answer.
Aden started with 6 cups of water. Throughout the day he drank the following amounts: 1 1/3 cups, 1 1/2 cups, 1 2/3 cups, and 3/4 cup. How many cups of water are left?
A. 2/3
B. 3/4
C. 1 1/3
D. 1/4
Answer:
B. 3/4 cup of water
Step-by-step explanation:
1 1/3 + 1 1/2 + 1 2/3 + 3/4 = 5 1/4
6 - 5 1/4 = 3/4
Answer: B or 3/4
Step-by-step explanation:
ok first add all the amounts he drank together
1 1/3 + 1 1/2 + 1 2/3 + 3/4
because the denominators are all different, you have to change them to a common denominator, which is 12. i've also changed them to improper fractions.
1 1/3 = 4/3 = 16/12 1 1/2 = 3/2= 18/12 1 2/3 = 5/3= 20/12 3/4 = 9/12
now add them all together
16/12 + 18/12 + 20/12 + 9/12 = 63/12
now convert the original 6 cups to an improper fraction with the denominator of 12
6 = 72/12
now subtract 63/12 (the amount he drank) from 72/12 (the amount he started with)
72/12 - 63/12 = 9/12
9/12 is able to be simplified to 3/4
so the correct answer is B, or 3/4
which of the following represents the equation with a slope of 3 and a y-intercept of 2?
Answer:
c is the correct answer
Step-by-step explanation:
which statement is true regarding the functions on the graph?
Answer:
f(3)=g(3)
Step-by-step explanation:
the only one i see is that
f(3)=g(3)
because the two functions intersect there
that means the two values are the same
Is this a function???
Answer:
pfft no lol
Step-by-step explanation:
yeah no
have a good day! :)
plz give me brainliest
Answer:
yes
Step-by-step explanation:
i think,because it goes past the center it all
After the movie premiere 99 out of 130 people surveyed said they liked the movie.
What is the experimental probability that the next person surveyed will say he or she liked the movie?
What is the experimental probability that the next person surveyed will say he or she did not like the movie?
Answer:
99 over 130 multiplied by 100 over 1