Answer:
8
Step-by-step explanation:
Hello,
[tex]x=3y^2<=>y=\sqrt{\dfrac{x}{3}} \ \ for \ x\geq 0[/tex]
And for y = 2, x = 3 * 2 * 2 = 12 so first, let's compute
[tex]\displaystyle \int\limits^{12}_0 {\sqrt{\dfrac{x}{3}}} \, dx =\dfrac{1}{\sqrt{3}} \int\limits^{12}_0 {\sqrt{x}} \, dx\\\\=\dfrac{1}{\sqrt{3}} \left[ \dfrac{2}{3}x^{3/2}\right]_0^{12}\\\\=\dfrac{1}{\sqrt{3}} *\dfrac{2}{3}*12*\sqrt{12}\\\\=\dfrac{2*12*2*\sqrt{3}}{3*\sqrt{3}}\\\\=2*4*2=16[/tex]
The area which is asked is 12*2 - 16 = 24 - 16 = 8
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Using integrals, it is found that the area of the region enclosed by the curves in the interval is of 27 units squared.
In this problem:
The curve is [tex]x = 3y^2[/tex], hence the integral is relative to y.The lower limit is when x = 0, hence [tex]0 = 3y^2 \rightarrow y = 0[/tex].The upper limit is when y = 2.Then, the integral for the area is:
[tex]A = \int_{0}^{2} 3y^2 dy[/tex]
[tex]A = y^3|_{y = 0}^{y = 3}[/tex]
[tex]A = 3^3 - 0^3[/tex]
[tex]A = 27[/tex]
The area of the region enclosed by the curves in the interval is of 27 units squared.
You can learn more about the use of integrals to calculate an area at https://brainly.com/question/15127807
A cylindrical grain silo, with a flat top, is 30 feet tall and has a radius of 12 feet. It is full to the top with shelled corn. If the density of shelled corn averages 45 pounds/cubic foot, what does the corn in the silo weigh to the nearest pound
Answer:
610805 pounds
Step-by-step explanation:
The volume of grain in the silo will be calculated as equal to the volume of the cylinder formed by the silo
Height of the silo [tex]l[/tex] = 30 ft
radius of the silo r = 12 ft
volume of a cylinder = [tex]\pi r^{2} l[/tex]
substituting, we have
V = 3.142 x [tex]12^{2}[/tex] x 30 = 13573.44 cubic feet
We know that density ρ = weight/volume
density of the grains in the silo = 45 pound/cubic feet
therefore,
weight of grains = density x volume
weight of grains = 45 x 13573.44 = 610804.8 ≅ 610805 pounds
A clock rotated from 12 to 6 this is
Answer:
one half
Step-by-step explanation:
Because the rotation from 12 to 6 is one-half of a complete rotation, it seems reasonable to assume that the hour hand is moving continuously and has therefore moved one-half of the distance between the 2 and the 3. source- ck12.org
Find the volume of the following figure round your answer to the nearest tenth if necessary and use pi
Answer:
Volume = 1152 x pi km^3
Step-by-step explanation:
Volume = 1/3 x pi x r^2 x h
Volume = 1/3 x pi x 12^2 x 24
Volume = 1152 x pi
Find the value of x.
x=2.86
Step-by-step explanation:
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
[tex] {24}^{2} + {32}^{2} = 40[/tex]
[tex]c = 40[/tex]
[tex]6x + 6 + 9x - 9 = 40[/tex]
[tex](6x + 9x) + (6 - 9) = 40[/tex]
[tex]15x - 3 = 40[/tex]
[tex]15x = 43[/tex]
[tex]x = 2.866[/tex]
[tex]23.16 + 16.74 = 39.9[/tex]
the
[tex]6(2.86) + 6 = 23.16[/tex]
[tex]9(2.86) - 9 = 16.74[/tex]
Simplify to create an equivalent expression.
-k-(-8k+7)
a=7k−7
b=-7k-7
c=7k+7
d=-7k+7
choose one
Answer:
a. 7k - 7
Step-by-step explanation:
Step 1: Write out expression
-k - (-8k + 7)
Step 2: Distribute negative
-k + 8k - 7
Step 3: Combine like terms
7k - 7
And we have our answer!
Which of the following functions best describes this graph? y=(x+2)(x+7)
Answer:
hope. It helps. What. I Understood
Suppose that the director of manufacturing at a clothing factory needs to determine whether a new machine is producing a particular type of cloth according to the manufacturer’s specifications, which indicate that the cloth should have a mean breaking strength of 70 pounds and a standard deviation of 3.5 pounds. A sample of 49 pieces reveals a sample mean of 69.1 pounds.
(a) State the null and alternative hypotheses.
(b) Is there evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength? (Use a 0.05 level of significance.)
(c) Compute the p-value and interpret its meaning.
(d) What will your answer be in (b) if the standard deviation is 1.75 pounds?
(e) What will your answer be in (b) if the sample mean is 69 pounds?
Answer:
a.H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
Step-by-step explanation:
Formulate the null and alternative hypotheses as
a) H0 : u1= u2 against Ha : u1≠ u2 This is a two sided test
Here ∝= 0.005
For alpha by 2 for a two tailed test Z∝/2 = ± 1.96
Standard deviation = s= 3.5 pounds
n= 49
The test statistic used here is
Z = x- x`/ s/√n
Z= 69.1- 70 / 3.5 / √49
Z= -1.80
Since the calculated value of Z= -1.80 falls in the critical region we reject the null hypothesis.
b) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
c) the p- value is 0.0359*2= 0.0718. It is greater than the value of ∝ so there isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
d) If standard deviation is 1.75 pounds
The test statistic used here is
Z = x- x`/ s/√n
Z= 69.1- 70 / 1.75 / √49
Z= -3.6
This value does not fall in the critical region.
d) There is enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
e) If the sample mean is 69 pounds
Z = x- x`/ s/√n
Z= 69.1- 69 / 3.5 / √49
Z= 0.2
This value falls in the critical region
e) There isn't enough evidence that the machine is not meeting the manufacturer’s specifications in terms of the average breaking strength.
I need answering ASAP please and thank you
Answer:
one
Step-by-step explanation:
The red graph intersects the blue graph at one point
That is the number of solutions to the system
Answer:
one
Step-by-step explanation:
I had to do this question once. It was hard. I remember the answer. it is one. You have to trust me.
Reaner Recycling collected 7/4 tons of aluminum last Saturday. If 7 ton of
aluminum can be shredded each day, how many days will it take to process what
was collected on Saturday?
Answer:
1/4
Step-by-step explanation:
since 7 tonnes can be shredded per day you need o divide the amount you have by 7
so 7/4 /7 = 1/4
so it will take 1/4 days
Answer:
[tex] \frac{1}{4} [/tex]
Step-by-step explanation:
Make a ratio
7 : 1
7/4:x
Cross multiple
7x = 7/4
Then make x a subject formula
x =1/4
solve the system with elimination 4x+3y=1 -3x-6y=3
Answer:
x = 1, y = -1
Step-by-step explanation:
If we have the two equations:
[tex]4x+3y=1[/tex] and [tex]-3x - 6y = 3[/tex], we can look at which variable will be easiest to eliminate.
[tex]y[/tex] looks like it might be easy to get rid of, we just have to multiply [tex]4x+3y=1[/tex] by 2 and y is gone (as -6y + 6y = 0).
So let's multiply the equation [tex]4x+3y=1[/tex] by 2.
[tex]2(4x + 3y = 1)\\8x + 6y = 2[/tex]
Now we can add these equations
[tex]8x + 6y = 2\\-3x-6y=3\\[/tex]
------------------------
[tex]5x = 5[/tex]
Dividing both sides by 5, we get [tex]x = 1[/tex].
Now we can substitute x into an equation to find y.
[tex]4(1) + 3y = 1\\4 + 3y = 1\\3y = -3\\y = -1[/tex]
Hope this helped!
The quotient of 8 and the difference of three and a number.
Answer: 8÷(3-x)
Answer:
Below
Step-by-step explanation:
● 8 ÷ (3-x)
Dividing by 3-x is like multiplying by 1/(3-x)
● 8 × (1/3-x)
● 8 /(3-x)
Find f(-2) given f(x) = –x^3 – 3x^2 +8
Answer:
Option A, 4
Step-by-step explanation:
f(-2) = -(-2)³-3×(-2)²+8
= 8-12+8
= 16-12
= 4
the mode of some data is 20 if each value is increased by 2 what will be the mode of the data
what is the answer
Answer:
40
Explanations
Have to multiple 20 by 2 then your answer would be 40
The mode of the increased data will be 22.
What is the mode?The mode is that specific value that is found several times in a certain observation of a set of values.
How to calculate the mode of increased value?Here, mode of some data is 20.
Therefore, 20 is the most repeated value of that data observation.
Now, the each of value is increased by 2.
Then, the mode will be (20+2)=22
Learn more about mode here :
https://brainly.ph/question/12346912
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NEED ASAP! Given: AB = 12 AC = 6 Prove: C is the midpoint of AB. A line has points A, C, B. Proof: We are given that AB = 12 and AC = 6. Applying the segment addition property, we get AC + CB = AB. Applying the substitution property, we get 6 + CB = 12. The subtraction property can be used to find CB = 6. The symmetric property shows that 6 = AC. Since CB = 6 and 6 = AC, AC = CB by the property. So, AC ≅ CB by the definition of congruent segments. Finally, C is the midpoint of AB because it divides AB into two congruent segments. Answer choices: Congruence Symmetric Reflexive Transitive
Answer:
It’s symmetric property
Answer:
Symmetry
Step-by-step explanation:
The guy above me
look at the image below plz helppppppppppppp
Answer:
150.
Step-by-step explanation
Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. She takes random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. What conclusion can be made based on the data
There are nickles and quarters worth $2.20 in total. If there are 28 coins, how many nickels are there?
let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship
Answer:
d = s x t
Step-by-step explanation:
The formula for distance.
If the Miller's spend $1200 on housing each month, then what is their total monthly budget?
Answer:
2400$
Step-by-step explanation:
Miller's Family spends 50% of their budget on housing and we know that they spent 1200$ this month, so 1200$*2 = 2400$.
Have a nice day! :-)
PLEASE HELP!!! TIMED QUESTION!!! FIRST CORRECT ANSWER WILL BE BRAINLIEST!!!
The bar graph shows the number or each item sold at a bake sale. Which statement about the graph is true?
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
Test at 5% significance level on the typist’s claim.
Using the hypothesis test for one sample mean, There is NO SIGNIFICANT EVIDENCE to support the typist's claim
[tex]H_{0} = 45\\H_{1} < 45\\\\[/tex]
The test statistic :
T = (x - μ) ÷ (s/√(n))
T = (43 - 45) ÷ (15/√70)
T = - 2 ÷ 1.7928429
T = -1.12
At α = 0.05
Pvalue :
Degree of freedom, df = 70 - 1 = 69
Pvalue = 0.1333
Decision region :
Reject [tex]H_{0}[/tex] if Pvalue < α
0.1333 > 0.05
Since Pvalue > α We fail to reject the Null
Learn more on hypothesis testing: https://brainly.com/question/20262540
Help me plz 20 points to who ever gets it right
Step-by-step explanation:
2., 3., 4., 5.
yes, you had the right idea to calculate the half distances between the coordinates. just create the absolute values of the full distance before cutting it in half.
you need to remember : we have to go this half distance from one point to the other (meaning adding our subtracting the half distance to/from the starting point).
2.
(-4, 6) to (10, -10)
in x the distance is 10 - -4 = 14. half is 7.
in y the distance is |-10 - 6| = |-16| = 16. half is 8.
so the midpoint is
(-4 + 7, 6 - 8) = (3, -2)
remember, to go the half distance in the direction towards the second point (so we have to choose properly, when to use "+" and "-" depending on the change of the coordinate : from -4 to 10 we have to add, from 6 to -10 we have to subtract, of course).
3.
(-3, -8) to (-6.5, -4.5)
in x distance : -3 - -6.5 = 3.5. half is 1.75
in y distance : -8 - -4.5 = |-3.5| = 3.5. half is 1.75
midpoint is
(-3 - 1.75, -8 + 1.75) = (-4.75, -6.25)
4.
(3, 7) to (-8, -10)
x : 3 - -8 = 11. half is 5.5
y : 7 - -10 = 17. half is 8.5
midpoint is
(3 - 5.5, 7 - 8.5) = (-2.5, -1.5)
5.
(-6, -13) to (-6.4, -3.8)
x : -6 - -6.4 = 0.4. half is 0.2
y : -13 - -3.8 = |-9.2| = 9.2. half is 4.6
midpoint is
(-6 - 0.2, -13 + 4.6) = (-6.2, -8.4)
6.
(-1, 7) to (5, 1)
x : -1 - 5 = |-6| = 6. 1/3 is 2.
y : 7 - 1 = 6. 1/3 is 2.
1/3 from C to D
(-1 + 2, 7 - 2) = (1, 5)
7.
2/3 of the way from D to C is the same point as in 6. (1/3 from C to D).
again
(1, 5)
8.
2/3 of the way from C to D.
so, we need to double what we added in 6.
(-1 + 4, 7 - 4) = (3, 3)
9.
1/3 of the way from D to C is the same point as in 8. (2/3 of the way from C to D).
again
(3, 3)
10.
exactly. Pythagoras.
the square root of the sum of the squares of the coordinate differences.
distance = sqrt((x1 - x2)² + (y1 - y2)²)
11.
(6, 8) to (-1, 8)
distance = sqrt((6 - -1)² + (8 - 8)²) = sqrt(49) = 7
12.
(5, -6) to (5, 6)
sqrt((5-5)² + (-6-6)²) = sqrt(144) = 12
13.
(-2, 0) to (11, 0)
sqrt((-2 - 11)² + (0-0)²) = sqrt(169) = 13
14.
(1, -5) to (9, 1)
sqrt((1-9)² + (-5 - 1)²) = sqrt(64 + 36) = sqrt(100) = 10
15.
ST and MT are basically the same equation.
MT is half of ST.
ST equation based on 2 points :
y – yS={(yT – yS)/(xT – xS)}(x – xS)
M = (xS + (xT - xS)/2, yS +(yT - yS)/2)
so, let's put that into the general equation :
y - yM={(yT - yM)/(xT - xM)}(x - xM)
y - (yS +(yT - yS)/2) = {(yT - (yS +(yT - yS)/2))/(xT - (xS + (xT - xS)/2))}(x - (xS + (xT - xS)/2))
16.
the two corners farthest away are (5, 10) and (9, 6).
what distance from (0, 0) is now bigger ?
since it is (0, 0), we can skip the 0s and just sum up the squares of the coordinates.
5² + 10² = 125
9² + 6² = 117
so, the corner (5, 10) is the farthest away.
THE PRICE OF AN ITEM FROM $10 TO $17. WHAT WAS THE PERCENT INCREASE IN THE PRICE OF THE ITEM?
Answer:
70%
Step-by-step explanation:
The method to find out percentage increase is by subtracting the original price from the increased price and making it into a fractional form with the denominator as 10 (out of 100%). So it results to this.
(original price - increased price) / 10
(17 - 10) / 10 = 7/10
7/10 can be converted from its fractional form to 70% i.e.its percentage.
Hope this helps and please mark as the brainliest.
Word phrase for algebraic expression 15-1.5/d
Answer: 1.5 less than 15 is divided by a number d.
Step-by-step explanation:
Oak street and elm street run parallel to each other. When main street intersects them, it forms exterior 8, measuring 60. What is the measure of 1?
Answer:
0 is the answer measure 1
What is the area of polygon EFGH?
Answer:
C. 42 square units
Step-by-step explanation:
This is a rectangle and to calculate the area of a rectangle we multiply length and width
The length of this rectangle is 7 units and the width is 6 units
6 × 7 = 42 square units
In the data set shown below, what is the value of the quartiles?
{4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}
A. Q1 = 4.6; Q2 = 5.5; Q3 = 5.95
B. Q1 = 4.7; Q2 = 5.5; Q3 = 6
C. Q1 = 4.7; Q2 = 5.5; Q3 = 5.9
D. Q1 = 4.6; Q2 = 5.5; Q3 = 5.92
Answer:
A. Q1 = 4.6; Q2 = 5.5; Q3 = 5.95
Step-by-step explanation:
{4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}
First find the median or the 2nd quartile
There are 9 data points so the middle is the 5th
4.3, 4.5, 4.7, 5, 5.5, 5.7, 5.9, 6, 6.1}
Q2 = 5.5
Now looking at the data on the left, we need to find the middle, which is Q1 or the first quartile
4.3, 4.5 , 4.7, 5,
It is between 4.5 and 4.7 so we average
(4.5+4.7)/2 = 9.2/2 = 4.6
Q1 is 4.6
We do the same for the data on the right, which is the third quartile or Q3
5.7, 5.9, 6, 6.1
(5.9+6)/2 = 11.9/2 = 5.95
Q3 = 5.95
Answer: IT'S A !!
Step-by-step explanation:
Sarah had a balance of $155 in her bank account at the start of the week. She withdrew $65.50 on Monday, $23.25 on Wednesday, and $26.45 on Thursday. On Friday she deposited $165.30. Write an expression that represents Sarah's spending.
Answer:
155 + 165.3 - 65.5 - 23.25 - 26.45
Step-by-step explanation:
She had $155 dollars in the starting = +155
She withdrew $65.5 = -65.5
She withdrew another $23.25 = -23.25
She withdrew another $26.45 = -26.45
The deposited $165.3 = +165.3
The expression looks like:
155 + 165.3 - 65.5 - 23.25 - 26.45
We could simplify the expression:
155 + 165.3 - 65.5 - 23.25 - 26.45
=> 320.3 - 88.75 - 26.45
=> 320.3 -115.2
=> 205.1
At the end of the week, she had a total of $205.10.
A potato chip manufacturer produces bags of potato chips that are supposed to have a net weight of 326 grams. Because the chips vary in size, it is difficult to fill the bags to the exact weight desired. However, the bags pass inspection so long as the standard deviation of their weights is no more than 3 grams. A quality control inspector wished to test the claim that one batch of bags has a standard deviation of more than 3 grams, and thus does not pass inspection. If a sample of 21 bags of potato chips is taken and the standard deviation is found to be 4.1 grams, does this evidence, at the 0.025 level of significance, support the claim that the bags should fail inspection
A health insurer has determined that the "reasonable and customary" fee for a certain medical procedure is $1200. They suspect that the average fee charged by one particular clinic for this procedure is higher than $1200.
Explain in context the conclusion of the test if H0 is rejected.
Answer:
For the null hypothesis to be rejected , then the conclusion of the test is that the absolute values of the z-statistic and/or the t-test statistic is greater than the critical value
Step-by-step explanation:
Here, we want to explain the conclusion of the test given that the null hypothesis is rejected.
Mathematically, the null hypothesis is as expressed as below;
H0: μ = 1,200
The alternative hypothesis H1 would be;
H1: μ > 1,200
Now, before we can reject or accept the null hypothesis, we will need a sample size and thus calculate the test statistics and the z statistics
For us to reject the null hypothesis, one of two things, or two things must have occurred.
The absolute value of the z statistic |z| or the test statistic |t| must be greater than the critical value.
If this happens, then we can make a rejection of the null hypothesis