Answer:
E. 0.1401
Step-by-step explanation:
The mean here has been given as 20.9
The standard deviation sd = 4.7
Random sample n = 32
Sd/√n
= 4.7/√32
= 0.8309
Probability of x less than 20
= 20-20.9/0.8309
= -0.9/0.8309
= -1.083
P(z<-1.083)
When we go to the z table
= 0.1401
Therefore the probability is 0.1401 and the answer to this question is E.
1 1/6 as an improper fraction
Answer:
The mixed number 1 1/6 converted into an improper fraction is 7/6.
Step-by-step explanation:
The improper fraction representation after converting of 1 1/6 is 7/6 where numerator is 7 and denominator is 6
To convert a mixed number to an improper fraction, we follow these steps:
Multiply the whole number by the denominator of the fraction.
In this case, multiply 1 (the whole number) by 6 (the denominator), which gives 6.
Add the numerator to the result obtained in step 1.
The numerator in this case is 1. Adding 1 to 6 gives 7.
Place the result from step 2 as the numerator of the fraction, and keep the denominator the same.
The denominator remains 6.
Therefore, the improper fraction representation of 1 1/6 is 7/6.
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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.
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.
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]
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)
Identify proportional relationships
Does the following table show a proportional relationship between the variables g and h?
g
3
6
9
9
36
81
Answer:
sure easy man the carrot is blue and green and orange there naswer soled
One year ago, Lindsey deposited $250 into a savings
account. Her balance is now $253. Two years ago, Jenn
deposited $250 into a savings account. Her balance is
now $257.50. Which account has the greater simple
interest rate? Explain.
Answer:
Jenn's account
Step-by-step explanation:
Given that:
LINDSAY'S ACCOUNT :
Principal = amount deposited = $250
Final Amount after 1 year = $253
Period (t) = 1 year
JENN'S ACCOUNT :
Principal = amount deposited = $250
Final Amount after 2 years = $257.50
Period (t) = 2 year
Using the relation :
A = P(1 + rt)
A = final amount ; r = interest rate ; t = time
Lindsay :
253 = 250(1 + r(1))
253 = 250 + 250r
253 - 250 = 250r
3 = 250r
r = 3/250
r = 0.012 ; (0.012 * 100) = 1.2%
Jenn:
257.50 = 250(1 + r(2))
257.50 = 250 + 500r
257.50 - 250 = 500r
7.50 = 500r
r = 7.50/500
r = 0.015 ; (0.015 * 100) = 1.5%
Hence, JENN'S deposit has the greater interest rate. (1.5 > 1.2)%
Answer:Sample response:Lindsay’s interest is $3 for one year. Using the formula for interest, I = prt, Lindsey’s money is earning at a rate of 1.2%. Jenn has earned $3.75 for one year. Her money is earning at a rate of 1.5%, which is a higher interest rate.
Step-by-step explanation: please make me brainliest
Find the value of the variable that results in congruent triangles
1.
Answer:
x = 26
Step-by-step explanation:
m<B = m<E = (x + 17)°
180 - (25 + 112) = (x + 17) (sum of ∆)
180 - 137 = x + 17
43 = x + 17
Subtract both sides by 17
43 - 17 = x
x = 26
What’s three more than seventeen?
Deborah spent $70 on food and clothes she spent $26 more on clothes then on food Brighton solve a system of equations to find how much Debra spent on each
Answer:
Step-by-step explanation:
You know the total will be $70.
She bought food, let's call that "F"
She spent $26 more on clothes than food. So her clothes purchase is "F+26".
So let's set-up the equation this way:
food + clothing = Total Spent
F + F + 26 = 70
2F + 26 = 70 (subtract 26 from both sides of the = sign)
2F = 44 (Divide both sides so you find out how much was spent on "F" or food.)
F = 22 (But the question doesn't stop there.)
Deborah spent $22 on food. (Remember, she spent $26 more on clothes, so we have to use our "clothes" equation? ) Deborah spent $48 on clothes. She spent a total of $70 on her purchases.
describe the relationship between the similarity ratio of two triangles and the ratio of their areas. help plz
Answer:
When two triangles are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar triangles.
Step-by-step explanation:
Theorem 60: If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.
Help me pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
A, 2 5/8 cups
Step-by-step explanation:
Since six dozen brownies is three times as much as two dozen, we can multiply 7/8 cups by 3. 3 x 7/8 = 21/8 If we simplify this fraction, it is 2 5/8. Therefore the answer is A, 2 5/8 cups.
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)
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!!
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
Please help me fast!!!. Joe and his family are touring Chicago. They want to visit the Willis Tower, hang out at Navy Pier, and shop on Michigan Avenue before their dinner reservations at 5:10 P.M. They plan to spend 1 hour and 10 minutes at the Willis Tower, 3 hours and 10 minutes at Navy Pier, and 1 hour and 15 minutes shopping. What is the latest time Joe's family can start their tour of Chicago and still make it to dinner on time?
Include A.M. or P.M. in your answer.
Answer:
11:10 am.
Step-by-step explanation:
The first thing I'm going to do is to add all the given time together
Total time = time spent at Willis tower + time spent at Navy Pier + time spent shopping
Total time = 1 HR and 10 minutes + 3 HR and 10 minutes + 1 hour and 15 minutes
Total time = (1 + 3 + 1) hr + (10 + 10 + 15) minutes
Total time = 5 hours + 35 minutes
The question doesn't make mention of how long they spent making the journey so, I'm assuming they spent 35 minutes driving around from Willis to the Pier and finally while shopping
Time = total time + time spent driving
Time = 5 hours 35 minutes + 35 minutes
Time = 6 hours and 10 minutes
Now, this time we've calculated, is what we're going to subtract from the dinner time to get our final answer
Needed time = dinner time - time
Needed time = 5:10 pm - 6:10
Needed time = 17:10 - 6:10
Needed time = 11:10
This means that they ought to start their tour by 11:10 am, so that they can meet their dinner
4,0000000000×10,00000000
Answer:
yes 40
Step-by-step explanation:
she got it correct
The cost of 3 scarves is $26.25. What is the unit price? (cost per scarf)
$8.75 because 26.25 divided by 3 equals $8.75.
hope this helps
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
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.
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It Snowed 1/2 inch on Saturday and 1 3/5 inches on Sunday. How much did it snow altogether, total?
Answer:
Fraction form: it snowed 2 1/10 inches in total, decimal form: in other words it snowed 2.1 inches.
Step-by-step explanation:
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]
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.
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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:
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
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
In the lab, Karen has two solutions that contain alcohol and is mixing them with each other. She uses 3 times as much Solution A as Solution B. Solution A is 10% alcohol and Solution B is 15% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 180 milliliters of pure alcohol?
Answer:
She uses 162 millitiers if Solution B.
Step-by-step explanation:
180 - 10% = 162
Solution A = 18 milliliters
Soultion B = 162 millitiers
"Five less than
the quotient of
a number and
3 is -7°
A. 5 - X/3-7
B. -7 +x/3
C. X3 - 5 =-7
D. 5 - 4/2 = -7
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