Answer:
28/12
Step-by-step explanation:
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%
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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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]
helpppppp pleaseeee
question: Why do we need to know the mass of a robot? *
why is this in math why does my teacher does this
Answer:
To know what the answer is
Step-by-step explanation:
clearly I do not know, but I can say that we do need to know the mass bc in the future there will be more and more androids on the rising making human interaction bad.
to find out the equation take the seed and the time. (this to make it look like i answered) Taking the mass you will be able to find out how manyspeed is found by the time and masstime is found out by the mass and speedi dont know if this helpedAnswer:
Step-by-step explanation:
Identify the independent and dependent variable of the following graph. Indicate whether the graph rises, falls, or is constant.
A person's core body temperature (°F) in relation to time of day
a. Independent Variable: time of day, Dependent Variable: temperature Graph falls until morning and then steadily rises throughout the day.
b. Independent Variable: time of day, Dependent Variable: temperature Graph is constant and then rises.
c. Independent Variable: time of day, Dependent Variable: time of day Graph is constant and
then rises.
d. Independent Variable: temperature, Dependent Variable: time of day
Graph falls until morning
and then steadily rises throughout the day.
Answer:
d number is the correct answer of the question
If you rotate figure GTR 270° clockwise about the origin. What will be the coordinates of G’T’R’ (Please Help I need this done in five minutes.)
Answer:
C. G' (4,-7), R' (2,-3), T'(6,-4)
Step-by-step explanation:
Get a piece of paper and draw 2 intersecting lines, like how a graph looks like. Then get another paper that's transparent enough, and place a dot roughly where R would be. Rotate it 270* clockwise (3 times around 90 degrees), and R would be in the bottom right area. That means the figure would be around that area and you can base the coordinates from that.
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
9 lb 4 oz - 2 lb 12 oz with regrouping
Answer:
6 LB 12 OZ
Step-by-step explanation:
16 OZ in a LB
9 LB - 2 LB = 7 LB
4 OZ - 12 OZ difference of 8 OZ
4 - 4 = 0 then 16 OZ in a LB
4 remaining - 16 = 12 dropping the 7 LB to 6 LB
Answer:
6lb 8oz
Step-by-step explanation:
9lb 4oz
+16
8lb 20 oz
-2 lb 12oz =
10 more than a number w is -2.6
Answer:
10 + w = -2.6
Step-by-step explanation:
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
Based only on the information given in the diagram, it is guaranteed that
AJKL ~ AWXY.
27°
A
63"
A. True
B. False
Answer:
True
Step-by-step explanation:
Given
In JKL, we have:
[tex]\angle J = 27[/tex]
[tex]\angle K = 90[/tex]
In WXY, we have:
[tex]\angle Y = 63[/tex]
[tex]\angle X = 90[/tex]
Required
Is JKL ~ WXY?
In both triangles, we already have one similar angle (90)
Next, is to determine the third angles in both triangles.
In JKL
[tex]\angle J + \angle K + \angle L = 180[/tex]
We have that:
[tex]\angle J = 27[/tex] and [tex]\angle K = 90[/tex]
The expression becomes:
[tex]27 + 90 + \angle L = 180[/tex]
[tex]117 + \angle L = 180[/tex]
[tex]\angle L = 180-117[/tex]
[tex]\angle L = 63[/tex]
In WXY
[tex]\angle W + \angle X + \angle Y = 180[/tex]
We have that:
[tex]\angle Y = 63[/tex] and [tex]\angle X = 90[/tex]
The expression becomes:
[tex]\angle W + 63 + 90 = 180[/tex]
[tex]\angle W + 153 = 180[/tex]
[tex]\angle W = 180-153[/tex]
[tex]\angle W = 27[/tex]
The three angles in JKL are:
[tex]\angle J = 27[/tex] [tex]\angle K = 90[/tex] [tex]\angle L = 63[/tex]
The three angles in WXY are:
[tex]\angle W = 27[/tex] [tex]\angle X = 90[/tex] [tex]\angle Y = 63[/tex]
By comparing the angles, we can conclude that both triangles are similar because of AAA postulate (Angle-Angle-Angle)
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.
What is the difference between twice twenty-five and twice five and twenty?
What is the slope of
y = -5x + 14
Answer:
0
Step-by-step explanation:
Answer:
-5
Step-by-step explanation:
y=-5x+14 is in the form of y=mx+b.
m is the slope and b is the y-intercept.
So m = -5 and -5 is the slope
k/2 + 9 = 37
too lazy to do this work. lol
Answer:
K = 56
Step-by-step explanation:
Subtract 9
k/2 = 28
multiply by 2
k = 56
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
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.
What equation is parallel to
y= - 1\4x + 5 and passes through (2,-3)
QUICK
Given:
The equation of parallel line is [tex]y=-\dfrac{1}{4}x+5[/tex].
Required line passes through (2,-3).
To find:
The equation of line.
Solution:
We have,
[tex]y=-\dfrac{1}{4}x+5[/tex]
On comparing this equation with [tex]y=mx+b[/tex], where m is slope, we get
[tex]m=-\dfrac{1}{4}[/tex]
Slope of two parallel lines are always same. So, slope of required line is [tex]m=-\dfrac{1}{4}[/tex].
The required line passes through the point (2,-3) having slope [tex]m=-\dfrac{1}{4}[/tex], so the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-(-3)=-\dfrac{1}{4}(x-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)-\dfrac{1}{4}(-2)[/tex]
[tex]y+3=-\dfrac{1}{4}(x)+\dfrac{1}{2}[/tex]
Subtracting 3 from both sides, we get
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1}{2}-3[/tex]
[tex]y=-\dfrac{1}{4}(x)+\dfrac{1-6}{2}[/tex]
[tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex]
Therefore, the equation of required line is [tex]y=-\dfrac{1}{4}(x)-\dfrac{5}{2}[/tex].
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 :)
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
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)
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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What is the GCF of 88 and 66?
Answer:
the GCF would be 22 this is because that is 88 and 66 greatest common factor (gcf)
Step-by-step explanation:
have a good day!!
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]
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
dy÷dx=(x-1)(x+3) at x=2 first principal
Answer:
δy
δx = 2x − 4 + δx;
and the limit as δx → 0 is
dy
dx = lim
δx→0
µδy
δx¶
= 2x − 4.
Step-by-step explanation:
dy/2d=(2-1)(2+3)
dy/2d=4+6-2-3
dy/2d=5
dy=5(2d)=10d
2d=5/dy
dy=5×(5/dy)= 25/dy
2d=5/dy
dy^2=25
dy=√25=5
2d=5/dy=5/5=1
d=1/2
dy=1/2×10=5 y=10
plug all of the values
5/(1/2×2)=5
=
4+6-2-3=5
so finally: 5=5
any questions?
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)
4,0000000000×10,00000000
Answer:
yes 40
Step-by-step explanation:
she got it correct
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.
.
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