Answer:
the volume of the solid is [tex]\frac{\pi }{120}[/tex]
Step-by-step explanation:
Given the data in the question;
y = x and y = x²
so
x = x²
x - x² = 0
Radius will be; r = ( x - x² )/2
Area of the circular disk πr² = π[ ( x - x² )/2 ]²
A = [tex]\frac{\pi }{4}[/tex]( x - x² )²
So, our volume will be;
V = ₀∫¹ A(x) dx
we substitute
= ₀∫¹ [tex]\frac{\pi }{4}[/tex]( x - x² )² dx
{ lets expand; ( x - x² )² = x(x-x²) -x²(x-x²) = x² - x³ - x³ + x⁴ = x² + x⁴ - 2x³ }
so we have;
= ₀∫¹ [tex]\frac{\pi }{4}[/tex]( x² + x⁴ - 2x³ ) dx
= [tex]\frac{\pi }{4}[/tex] [tex][[/tex] [tex]\frac{x^3}{3}[/tex] + [tex]\frac{x^5}{5}[/tex] - [tex]\frac{2}{4} x^4[/tex] [tex]]^1_0[/tex]
= [tex]\frac{\pi }{4}[/tex][ [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{5}[/tex] - [tex]\frac{2}{4}[/tex] ]
= [tex]\frac{\pi }{4}[/tex][ [tex]\frac{1}{30}[/tex] ]
V = [tex]\frac{\pi }{120}[/tex]
Therefore, the volume of the solid is [tex]\frac{\pi }{120}[/tex]
Must the quadrilateral be a parallelogram?
A. Yes, both pairs of opposite sides are parallel.
B. No, both pairs of opposite sides are parallel but not congruent
C. No, both pair of opposite sides are congruent but not parallel.
D. Yes, both pairs of opposite sides are congruent.
A flower garden is the shape of a circle. The circumference of the garden is 20 meters. What is the area of the garden. Use 3.14 for pie and round your answer to the nearest whole number.
Answer:
Circumference = 2 pi r = 2*3.14 *r = 20
radius r = 20 / 2*314 = 3.185
Area = pi r^2 = 3.14 * 3.185^2 = 32 m^2 to nearest whole number
Find the other endpoint of the line segment with the given endpoint and midpoint. Endpoint 1: (−1,2) Midpoint: (9,−6) Endpoint 2=
define prism and itz color
Answer:
triangle piece of glass that different colors of light travel through
Find the area of the sector in
terms of pi.
150°
12
Area = [?]π
Enter
Aysha has 40 cubes in a bag.
18 red cubes.
13 blue cubes.
9 yellow cubes.
Aysha adds some more red cubes into the bag.
Aysha is now going to take at random a cube from the bag
The probability now that she will take a red cube is 0.5.
Work out the probability that she will take a yellow cube.
Given:
Total number of cubes = 40
Red cubes = 18
Blue cubes = 13
Yellow cubes = 9
Aysha adds some more red cubes into the bag.
The probability now that she will take a red cube is 0.5.
To find:
The probability that she will take a yellow cube.
Solution:
Let Aysha adds x red cubes into the bag. Then,
Number of total cubes = 40+x
Number of red cubes = 18+x
Probability of getting a red cube is:
[tex]P(Red)=\dfrac{18+x}{40+x}[/tex]
The probability now that she will take a red cube is 0.5. So,
[tex]\dfrac{18+x}{40+x}=0.5[/tex]
[tex]18+x=0.5(40+x)[/tex]
[tex]18+x=20+0.5x[/tex]
[tex]x-0.5x=20-18[/tex]
[tex]0.5x=2[/tex]
Divide both sides by 0.5.
[tex]x=\dfrac{2}{0.5}[/tex]
[tex]x=4[/tex]
It means Aysha adds 4 more red cubes into the bag.
Now, the total number of cubes int he bag is:
[tex]40+4=44[/tex]
Probability of getting a yellow cube is:
[tex]P(Yellow)=\dfrac{\text{Number of yellow cubes}}{\text{Total number of cubes}}[/tex]
[tex]P(Yellow)=\dfrac{9}{44}[/tex]
Therefore, the required probability is [tex]P(Yellow)=\dfrac{9}{44}[/tex].
Calculate a critical z-score for a left-tailed, right-tailed, or two-tailed test.
a. The critical z-score for a left-tailed test at a 12% significance level is -0.45.
b. The critical z-score for a right-tailed test at a 9% significance level is 1.34.
c. The critical z-score for a two-sided test at a 4% significance level is 1.75.
d. The critical z-score for a two-sided test at a 20% significance level is 0.85.
Answer:
a. Z = -1.175.
b. Z = 1.34.
c. |Z| = 2.054.
d. |Z| = 1.28.
Step-by-step explanation:
Z-score:
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
a. The critical z-score for a left-tailed test at a 12% significance level
Left-tailed test: The region of interest is the 12th percentile or below.
Thus, the critical z-score is Z with a p-value of 0.12, so Z = -1.175.
b. The critical z-score for a right-tailed test at a 9% significance level
Right-tailed test: The region of interest is the 100 - 9 = 91th percentile and above.
Thus, the critical z-score is Z with a p-value of 0.91, so Z = 1.34.
c. The critical z-score for a two-sided test at a 4% significance level is 1.75.
Two-tailed test: The region of interest is between the 4/2 = 2th percentile and the 100 - (4/2) = 98th percentile.
Thus, the critical z-score is |Z| with a p-value of 0.02 or 0.98, so |Z| = 2.054.
d. The critical z-score for a two-sided test at a 20% significance level is 0.85.
Region of interest is between the 20/2 = 10th percentile and the 100 - (20/2) = 90th percentile.
Thus, the critical z-score is |Z| with a p-value of 0.1 or 0.9, so |Z| = 1.28.
PT=3x+3 and TQ=6x-6
Use the figure to the right to find the value of PT. T is the midpoint of PQ
Answer:
PT = 12 units
Step-by-step explanation:
Given that,
PT=3x+3 and TQ=6x-6
T is the midpoint of PQ.
If T is mindpoint of PQ, it means,
PT = TQ
Substitute all the values,
3x+3 = 6x-6
Taking like terms together,
3x-6x = -6-3
-3x = -9
x = 3
So,
PT = 3x+3
= 3(3) + 3
= 9+3
= 12
So, the value of PT is equal to 12 units.
Which expression and diagram represent “three times a number”?
3 x right-arrow 3 boxes with x and 3 boxes with minus signs
3 x right-arrow 3 boxes with x
3 + x right-arrow 2 boxes with x and 3 boxes with plus signs
x + 3 right-arrow 3 boxes with plus signs
Answer:
b
Step-by-step explanation:
Answer:
took the test, it is B like the other person said!!
Use the intercepts to graph the equation x-5=y
9514 1404 393
Answer:
see beow
Step-by-step explanation:
When x=0, y=-5. The y-intercept is (0, -5).
When y=0, x-5=0, so x=5. The x-intercept is (5, 0).
Plot these two points and draw the line through them.
Question #7: Which revolution resulted from the division of society shown in this diagram?
(5 Points)
First Estate Second Estate
Third Estate
Magd
。
KUIN
பரிழப்பாகத் AARA
annu
MIA
AACAAN
Clergy
Nobles
Atées en
be eagere
1% of the people
owned 10%
of the land
2% of the people
owned 25%
of the land
Bab 2 828
Anu
AR SALE
M
Middle class, peasants, city workers
97% of the people owned 65% of the land
Source Schwartz and O'Connor Democracy and Nationalism Globe Book Company (adapted from the NYS Global History and Geography Regents
Exam August 2007
Puritan (1642)
French (1789)
Mexican (1910)
Russian (1917
Answer: French (1789)
Step-by-step explanation:
11
12
13
14
15
16
18
19
20
What is the value of x in the equation (3x + 12) = {(x + 14) – 3?
0
-24
46
0 0
Answer:
x = -24
Step-by-step explanation:
(2/3)(x/2 + 12) = (1/2)(x/3 + 14) - 3
2x/6 + 24/3 = x/6 + 14/2 - 3
2x/6 + 8 = x/6 + 7 - 3 = x/6 + 4
x/6 + 8 = 4
x/6 = -4
x = -24
-58
a
Simplify:
6
A
a4066
B
a1362
alb
D
a 40648
Answer:
wait ill work this out for you
Step-by-step explanation:
I NEED IT FASTTTTTTTTTTTTTTT
Answer:
17
Step-by-step explanation:
Max has 4/5 qt of apple juice. He drinks 1/2 qt of it. How many apple juice does he have left? (Give your answer in quarts)
Answer:
3/10 quarts.
Step-by-step explanation:
Set the denominators equal to one another.
4/5 = 8/10 (multiplied by a factor of 2)
1/2 = 5/10 (multiplied by a factor of 5)
Subtract the 5/10 from the 8/10
3/10 qt
Which equation demonstrates the additive identity property?
(7 + 4 i) + (7 minus 4 i) = 14
(7 + 4 i) + 0 = 7 + 4 i
(7 + 4 i) (1) = 7 + 4 i
(7 + 4 i) + (negative 7 minus 4 i) = 0
Answer:
b. on edge
Step-by-step explanation: just did the quiz and got it right
which linear inequality is represented by the graph
Answer:
y< -2x + 3
Step-by-step explanation:
Good luck with your questions :)
Cleo buys a new car for $18,900. The simple interest rate is 6.6% and the amount of loan (plus simple interest) is repayable in 5 years. What is the total amount that must be repaid?
Answer:
$6,237 down payment
Step-by-step explanation:
calculated [tex]18,900[/tex]×[tex]6.6%[/tex]%×[tex]5 = $6,237[/tex]
What is the value of the expression below? (27^7/3)^1/7
Answer:
3486784401/7
Step-by-step explanation:
What is the Answer
Please Help
Answer:
Step-by-step explanation:
circumference=2πr
=2*3.14*2
=12.56 km
Recounting Rectangles
How many rectangles are
there in the figure below?
Answer:
gimme a second, I'll comment
All of the following solid figures except a _____ have two bases.
Answer:
All of the following solid figures except a square pyramid have two bases.
Use the Squeeze Theorem
Answer:
See Below.
Step-by-step explanation:
We want to use the Squeeze Theorem to show that:
[tex]\displaystyle \lim_{x \to 0}\left(x^2\sin\left(\frac{2}{x}\right)\right)=0[/tex]
Recall that according to the Squeeze Theorem, if:
[tex]\displaystyle g(x)\leq f(x) \leq h(x)[/tex]
And:
[tex]\displaystyle \lim_{x\to c}g(x) =\lim_{x\to c}h(x) = L[/tex]
Then:
[tex]\displaystyle \lim_{x\to c}f(x)=L[/tex]
Recall that the value of sine is always ≥ -1 and ≤ 1. Hence:
[tex]\displaystyle -1 \leq \sin\left(\frac{2}{x}\right) \leq 1[/tex]
We can multiply both sides by x². Since this value is always positive, we do not need to change the signs. Hence:
[tex]\displaystyle -x^2\leq x^2\sin\left(\frac{2}{x}\right)\leq x^2[/tex]
Let g = -x², h = x², and f = x²sin(2 / x). We can see that:
[tex]\displaystyle \lim_{x \to 0}g(x) = \lim_{ x \to 0}h(x) = 0[/tex]
And since g(x) ≤ f(x) ≤ h(x), we can conclude using the Squeeze Theorem that:
[tex]\displaystyle \lim_{x \to 0}f(x) = \lim_{x \to 0}x^2\sin\left(\frac{2}{x}\right)=0[/tex]
100 students attended a revision lesson at the weekend.
Each student went to Maths or English or Science.
55 of these students attended on Saturday.
Over the weekend a total of 40 students went to Maths.
12 of the 27 students that went to Science went on Sunday.
10 students went to English on Saturday.
How many students went to the Maths revision lesson on Saturday?
Answer:
I am pretty sure its 30 students
Someone help me please
whats the square root of 0.0025
A 25 foot ladder is leaning against a tree. If the base of the ladder is 6 feet
away from the base of the tree, how high, to the nearest tenth, does the
ladder reach up the tree?
9514 1404 393
Answer:
24.3 ft
Step-by-step explanation:
If h is the height of the ladder up the tree, the geometry can be modeled as a right triangle with legs h and 6, and hypotenuse 25. The Pythagorean theorem gives you the relation ...
h² +6² = 25²
h² = 625 -36 = 589
h = √589 ≈ 24.3
The ladder reaches about 24.3 feet up the tree.
BRAINLIEST PLS HELP
(05.03)
Identify the initial value and rate of change for the graph shown
initial value:1,rate of change 3/5
initial value:3/5 ,rate of change 5/3
initial value :1,rate of change 5/3
initial value:5/3,rate of change:0
Answer:
the initial value is 1, rate of change 3/5
Step-by-step explanation:
rate of change is the slope, which is not zero and is def not 5/3
it started at 1, so thats the initial value
Consider the graphs shown below. Look at each trend line.
Which line does a better job capturing the trend of the data? Explain.
Answer:
GraphB
Step-by-step explanation:
To obtain the best line of fit, we need the line which minimizes the sum of the squared distances, Therefore, from visual inspection, we can conclude that the best line of fit will be one in which the distance between each individual distance and the line of best fit is minimized, for the first graph, only the upper points are close to the regression line leaving the lower values further away, however, the secubd graph gives a more uniform distance between all the data values and the regression line. Hence, it does a better job at capturing the trend in the data.
PLEASE HELP ASAP NO LINKS OR WILL BE REPORTED I NEED THIS LIKE RIGHT NOW PLEASE HURRY SHOW ALL OF YOUR WORK! (b) What is 1.363636... expressed as a fraction in simplest form? SHOW ALL OF YOUR WORK ( c) what is 5.152 expressed as a fraction in simplest form? SHOW ALL OF YOUR WORK
Answer:
1.3636363636...
can be expressed as
1 + 4/11
I tried out different fractions
1/11 is just 0.09090909...
4/11 is 4 times thar
1 = 11/11
so it's just 15/11
5.152
can be written as
[tex] \frac{5.152}{1} [/tex]
or as
[tex] \frac{5152}{1000} [/tex]
simplified with 8
[tex] \frac{644}{125} [/tex]
how to write expression for The product of ten less than a number and the number
Answer:
x-10
Step-by-step explanation:
ten is less than x
follow me for more answer