Answer:
48$
Step-by-step explanation:
80% of 80 is 64 which means she spent 16$ and saved 64$
so 64-16=48$
answer = 48$
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.
Use special right triangle ratios to find the length of the hypotenuse. Right Triangle Trig.
Answer:
11 sqrt(2)
Step-by-step explanation:
We know that in a 45 45 90 triangle, the lengths of the sides are x, x ,x sqrt(2)
the length of x is 11
so the lengths of the sides are 11, 11, 11 sqrt(2)
The hypotenuse is 11 sqrt(2)
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]
Identify the errors made in finding the inverse of
y = x2 + 12x.
x= y2 + 12x
y2 = x - 12x
y2=-11x
y=-11x, for x > 0
Describe the three errors?
Step-by-step explanation:
y = x2 + 12x.
x= y2 + 12x would also be 12 y
y2 = x - 12x would be -x
y2=-11x
y=[tex]\sqrt{-11x}[/tex], for x > 0 negative square root not possible
Describe the three errors?
The three errors made in finding the inverse of y = x² + 12x are,
⇒ First mistake to write 12y in place of 12x.
⇒ Second mistake to write the expression y² = x - 12x.
⇒ Third mistake because it never possible negative square root for x > 0.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ y = x² + 12x
Here, The process are,
⇒ y = x² + 12x.
⇒ x = y² + 12x
There is first mistake to write 12y in place of 12x.
⇒ y² = x - 12x
There is second mistake.
⇒ y² = -11x
⇒ y = √-11x, for x > 0
There is third mistake because it never possible negative square root for x > 0.
Learn more about the mathematical expression visit:
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PlEASE HELP ILL GIVE OUT BRAINLEIST
What’s the answer to this radical function
Step-by-step explanation:
We have,
[tex]f(x) = - 2 \sqrt[3]{x + 7} [/tex]
Taking limit,
[tex] \lim _{x \rarr \infty } f(x) \\ = \lim _{x \rarr \infty } - 2 \sqrt[3]{x + 7} [/tex]
If x approaches to positive infinity,
this implies f(x) approaches to negative infinity
Can someone help me find the value of X please?
Answer:
x = -4
Step-by-step explanation:
A circle is 360 degrees.
Anyway, first add 85 + 35 + 115 and you will get 235.
Now subtract 235 from 360.
360 - 235 = 125 degrees
Now to find x, do
-32x - 3 = 125
-32x = 128
-32x/-32 = 128/-32
x = -4
Hope it helped! My answer is expert verified.
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
A local grocery store decides to offer a free piece of fresh fruit (banana or apple) to all shoppers in the produce department. The store is conducting an observational study to determine which type of fruit is selected more often. At the end of the first day, the store found that twice as many shoppers select an apple.
The grocery store then repeats the observational study for 14 days. All studies yield similar results. What generalization can be made from the results of this study?
A.
Given the choice of a banana or an apple, twice as many shoppers will select an apple.
B.
The results are inconclusive; therefore, a generalization cannot be made regarding which type of fruit is preferred by most shoppers.
C.
There is not enough information to generalize the study’s results.
D.
Given the choice of any type of fruit, twice as many shoppers will select an apple.
Answer:
A.
Step-by-step explanation:
If the results are similar (A) should be your answer!
Option A is correct.
What is generalization?Generalization is a process which leads to something more general and whose product consequently refers refers to an actual or potential manifold in a certain way.
According to the given question
"At the end of the first day, the store found that twice as many shoppers select an apple"
So, the generalization can be made from the above result is " from the given choice of a banana or an apple, twice as many shoppers will select an apple".
Hence, option A is correct.
Learn more about generalization here:
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Consider two bases B = {b1, b2, b3} and C = {c1, c2, c3} for a vector space V such that
b1 = c1 + 3c3, b2 = c1 + 4c2 - c3, and b3 = 5c1 - c2. Suppose vector x = b1 + 6b2 + b3. That is,
suppose space left square bracket bold italic x right square bracket subscript B space equals open square brackets table row 1 row 6 row 1 end table close square brackets . Find space left square bracket bold italic x right square bracket subscript B space, the coordinates of the vector x in basis C.
y = 230x + 100
Is this proportional or non proportional?
Proportional equations are of the form y = kx, for some fixed constant k. The k value is the constant of proportionality.
The +100 at the end is why we don't have a proportional equation.
Visually all proportional equations go through the origin, meaning the lines have y intercept of 0. For y = 230x+100, the y intercept is 100.
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.
GIVING BRAINLIEST AND STARS
13)
Using a map scale of 1/2 inch = 10 miles, what would be the distance on the map between two cities that are actually 120 miles
apart?
A)
6 inches
B)
8 inches
C)
10 inches
D)
12 inches
Answer:
A) 6 Inches
Step-by-step explanation:
1/2=10 to find how many inches we need to get 120 miles, you have to find the conversion rate.
Conversion rate is 120 ÷ 10 which equals 12.
Now we multiply the conversion rate (12) times 1/2 to get an answer of 6 inches.
i'd appreciate a brainliest :)
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)
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
A scooter travels 30 feet in 2 seconds at a constant speed.
Answer:
The scooter is going faster.
Step-by-step explanation:
30/2 = 15ft/s
55/4 = 13.75ft/s
(the question was cut off so I used the information I had) Hope this helped!
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
please answer these questions
Step-by-step explanation:
you need to multiple first by second
Marlye asked students in her school whether they prefer scary movies or comedies. She found that 35 students prefer scary movies while 65 students prefer comedies. What percent of the students questioned prefer scary movies? 30% 35% 50% 65%
2
SEE ANSWERS
Answer:
The answer is 35%
Step-by-step explanation:
If we add together 35 and 65 we get 100. This means altogether there are 100 kids in her school. Out of those 100 kids, 35 like scary movies. We can write this as the fraction 35/100. This is equivalent to 0.35 or 35%.
Answer:
35%
Step-by-step explanation:
35+65
= 100
[tex]\frac{35}{100} * 100[/tex]
= 35%
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]
HELP PLS!!
Provide the length of x
Answer:
10
Step-by-step explanation:
the mid-segment, 5, is parallel to the base of the triangle and the side that the mid-segment is parallel to is always double the length of the mid-segment, so the base of the base is 10. this triangle is an equilateral triangle so the side, x, is also 10.
Which describes the missing number plotted on the number line?
A. the opposite of -4
B. the opposite of 4
C. the absolute value of -4
D. the absolute value of 4
5,10,20,40,80 determine if the pattern illustrates geometric sequence or not..
Answer:
This is a geometric sequence since there is a common ratio between each term. In this case, multiplying the previous term in the sequence by 2 gives the next term.
.
10 more than a number w is -2.6
Answer:
10 + w = -2.6
Step-by-step explanation:
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.
Find the quotient for 3/2 divided by 3/5
Answer:
2.5
Step-by-step explanation:
Answer:
5/2
Step-by-step explanation:
To divide fractions, you flip the second fractions and change it to multiplication.
(3/2) / (3/5) =
(3/2) x (5/3)
To multiply them, you just multiply their numerators together to get the new numerator and multiply the denominators together to get the new denominator.
(3/2) x (5/3) =
(3 x 5) / (2 x 3) =
15/6
This can be reduced to:
5/2
Please give me the correct answer
Because here there are 5 zeroes so 0.00003 can be written as 3/100000 , here 100000 = 10⁵ . Now , 3/10⁵ → 3 × 1/10⁵ → 3 × 10-⁵
Hence , 0.00003 = 3 × 10-⁵ . So it is -5
Bryson can travel 28 1/4 miles in 1/2 hour. What is his average speed in miles per hour?
Answer:
56 if rounding but 56.50 if not
Step-by-step explanation:
rate
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
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