Answer:
[tex](-2,\, 0)[/tex].
Step-by-step explanation:
Dilate a point [tex](x,\, y)[/tex] by a scale factor of [tex]r[/tex] with [tex](a,\, b)[/tex] as the center, and the resultant point would be at [tex](a + r\, (x - a),\, b + r\, (y - a))[/tex].
In this question:
Point to dilate: [tex](x,\, y) = (-8,\, 0)[/tex].
Scale factor: [tex]r = 0.25[/tex].
Center of dilation: [tex](a,\, b) = (0,\, 0)[/tex].
The resultant point would be:
[tex](0 + 0.25\, (-8 - 0),\, 0 + 0.25\, (0 - 0))[/tex], which simplifies to [tex](-2,\, 0)[/tex].
Set up an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Then use your calculator to evaluate the integral correct to five decimal places. x2 4y2
Answer:
The integral of the volume is:
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
The result is: [tex]V = 78.97731[/tex]
Step-by-step explanation:
Given
Curve: [tex]x^2 + 4y^2 = 4[/tex]
About line [tex]x = 2[/tex] --- Missing information
Required
Set up an integral for the volume
[tex]x^2 + 4y^2 = 4[/tex]
Make x^2 the subject
[tex]x^2 = 4 - 4y^2[/tex]
Square both sides
[tex]x = \sqrt{(4 - 4y^2)[/tex]
Factor out 4
[tex]x = \sqrt{4(1 - y^2)[/tex]
Split
[tex]x = \sqrt{4} * \sqrt{(1 - y^2)[/tex]
[tex]x = \±2 * \sqrt{(1 - y^2)[/tex]
[tex]x = \±2 \sqrt{(1 - y^2)[/tex]
Split
[tex]x_1 = -2 \sqrt{(1 - y^2)}\ and\ x_2 = 2 \sqrt{(1 - y^2)}[/tex]
Rotate about x = 2 implies that:
[tex]r = 2 - x[/tex]
So:
[tex]r_1 = 2 - (-2 \sqrt{(1 - y^2)})[/tex]
[tex]r_1 = 2 +2 \sqrt{(1 - y^2)}[/tex]
[tex]r_2 = 2 - 2 \sqrt{(1 - y^2)}[/tex]
Using washer method along the y-axis i.e. integral from 0 to 1.
We have:
[tex]V = 2\pi\int\limits^1_0 {(r_1^2 - r_2^2)} \, dy[/tex]
Substitute values for r1 and r2
[tex]V = 2\pi\int\limits^1_0 {(( 2 +2 \sqrt{(1 - y^2)})^2 - ( 2 -2 \sqrt{(1 - y^2)})^2)} \, dy[/tex]
Evaluate the squares
[tex]V = 2\pi\int\limits^1_0 {(4 +8 \sqrt{(1 - y^2)} + 4(1 - y^2)) - (4 -8 \sqrt{(1 - y^2)} + 4(1 - y^2))} \, dy[/tex]
Remove brackets and collect like terms
[tex]V = 2\pi\int\limits^1_0 {4 - 4 + 8\sqrt{(1 - y^2)} +8 \sqrt{(1 - y^2)}+ 4(1 - y^2) - 4(1 - y^2)} \, dy[/tex]
[tex]V = 2\pi\int\limits^1_0 { 16\sqrt{(1 - y^2)} \, dy[/tex]
Rewrite as:
[tex]V = 16* 2\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
Using the calculator:
[tex]\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy = \frac{\pi}{4}[/tex]
So:
[tex]V = 32\pi\int\limits^1_0 {\sqrt{(1 - y^2)} \, dy[/tex]
[tex]V = 32\pi * \frac{\pi}{4}[/tex]
[tex]V =\frac{32\pi^2}{4}[/tex]
[tex]V =8\pi^2[/tex]
Take:
[tex]\pi = 3.142[/tex]
[tex]V = 8* 3.142^2[/tex]
[tex]V = 78.97731[/tex] --- approximated
the measures of the angles of a triangle are shown below .solve for x
Answer:
x=17
Step-by-step explanation:
The equation is 44+60+(4×+8)=180
A χ2 goodness-of-fit test where all assumptions were met yielded the chi-square test statistic χ2=1.92 and a corresponding p-value of 0.75. The researcher interpreted the p-value as a 0.75 probability of observing a test statistic of χ2=1.92 or larger. What is wrong with the researcher’s interpretation?
Answer:
The researcher did not state that the p-value is conditional on the null hypothesis being true.
Step-by-step explanation:
The p-value or the assumed value represent the probability in which the test results that are received would be atleast extreme in that the null hypothesis would be correct
Here the wrong thing would be that researcher would not stated the p value is in conditional form based on the null hypothesis being true
Therefore the correct option is A.
PLEASE HELP DUE IN 3 minutes
Answer:D
Step-by-step explanation:
it has 2 number between 8-10 and the graph doesn't
PLZ GIVE BRAINLY
James runs 400 metres a day. He runs for five days.
What is the total distance run in kilometres
Answer:
2km
Step-by-step explanation:
400*5=2000m
2000/1000=2km
Order the steps in which to solve this expression. The value should be last.
PLEASE HELPPP.
Answer:
Exponents, Multiplication, Division (from left to right), Addition, Subtraction (from left to right), value
Step-by-step explanation:
Can someone please solve this using quadratic formula 2x^2 -7x -15=0
Solution
x=5
x= -3/2
Hopefully its good
someone help please with b (the slope is 5)
Question
Find the third degree polynomial function that has an output of 320 when x = 4, and has zeros 2 and
-8i
Answer:
[tex]f(x)=2(x-2)(x^2+64)[/tex]
Step-by-step explanation:
A standard polynomial in factored form is given by:
[tex]f(x)=a(x-p)(x-q)...[/tex]
Where p and q are the zeros.
We want to find a third-degree polynomial with zeros x = 2 and x = -8i and equals 320 when x = 4.
First, by the Complex Root Theorem, if x = -8i is a root, then x = 8i must also be a root.
Therefore, we acquire:
[tex]f(x)=a(x-(2))(x-(-8i))(x-(8i))[/tex]
Simplify:
[tex]f(x)=a(x-2)(x+8i)(x-8i)[/tex]
Expand the second and third factors:
[tex]=(x+8i)x+(x+8i)(-8i)\\\\=(x^2+8ix)+(-8ix-64i^2)\\\\=(x^2)+(8ix-8ix)+(-64i^2)\\\\=x^2-64(-1)\\\\ =x^2+64[/tex]
Hence, our function is now:
[tex]f(x)=a(x-2)(x^2+64)[/tex]
It equals 320 when x = 4. Therefore:
[tex]320=a(4-2)(4^2+64)[/tex]
Solve for a. Evaluate:
[tex]320=(2)(80)a[/tex]
So:
[tex]320=160a\Rightarrow a=2[/tex]
Our third-degree polynomial equation is:
[tex]f(x)=2(x-2)(x^2+64)[/tex]
Answer:
f(x)=2(x-2)(x^2+64)
Step-by-step explanation:
Translate the phrase into an algebraic expression.
8 less than x
Answer:
8-x is the expression for the question
Find z. Just write the number. Answer should be a whole number. PLS HELP DUE IN 10 MINS PLS
Answer:
z=13
Step-by-step explanation:
o 12h + h +17-5
Help and please
A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of a laboratory scale,that weight is weighed repeatedly. The scale readings are normally distributed with unknown mean. The population standard deviation of the scale readings is known to be 0.0003 gram.
(a) The weight is weighed FIVE times. The mean result is 10.0044 grams. Give a 98% confidence interval for the mean weight. Please keep 5 decimals in your answer.
(
,
)
(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence? Your answer must be a whole number.
Answer:
a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams
b) 49 measurements are needed.
Step-by-step explanation:
Question a:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.01 = 0.99[/tex], so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams
The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams
The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.
(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?
We have to find n for which M = 0.0001. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.0001 = 2.327\frac{0.0003}{\sqrt{n}}[/tex]
[tex]0.0001\sqrt{n} = 2.327*0.0003[/tex]
[tex]\sqrt{n} = \frac{2.327*0.0003}{0.0001}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2[/tex]
[tex]n = 48.73[/tex]
Rounding up
49 measurements are needed.
Find the rate of change in table plsss helppp!!!!
Answer:
.25 is the answer
Step-by-step explanation:
.5/2=.25
Help fast plz What is the length of the missing side? Use the Pythagorean Theorem
Answer:
10
Step-by-step explanation:
6^2+8^2=x^2
36+64=x^2
x=sqrt100
x=10
Which data set has a median of 15?
7, 16, 14, 16, 11, 7, 17
18, 9, 19, 16, 6, 20. 13
9, 17, 13, 15, 16, 8, 12
18, 15, 11, 14, 19, 15, 6
Answer: The last one is the one with the Median
Step-by-step explanation: Hope this helps ^^
Answer:
18,15,11,14,19,15,6 the last one
Find the domain and the range of the relation.
t = {(10,6), (28,- 10), (42,6), (10,10),(52,10)}
The domain of t = { ? }
Answer:
domain:{10,28,42,52}
range:{-10,6,10}
Step-by-step explanation:
Hello There!
If you didn´t know the domain is the set of x values
the x values in the given relation are
10,28,42,10 and 52
so the domain is {10,28,42,52}
The range is the set of y values
the y values in the given relations are
6,-10,6,10,10
so the range is {-10,6,10}
6A barrel holds 21 qt of oil. Trina drains the barrel at a rate of 6 c per min. How
long does it take her to empty the barrel? Show your work. (1 qt = 4 c )
Answer:
14 minutes
Step-by-step explanation:
The barrel held 21 quarts of oil, which is equal to 84 cups. Trina drains the barrel at 6 cups per minute, so to find out how much time it takes her to drain it, divide 84 by 6:
84 / 6 = 14
So, it took Trina 14 minutes to drain the whole barrel.
Figure DEFG IS A PARALLELOGRAM please help!!!!! Its timed !!!!! Ill give out most brainly and extra points !!!
Answer:
A)27 degreesStep-by-step explanation:
to understand thisyou need to know about:equationPEMDASlet's solve:according to the question
3x-20+4x+11=180
=>7x-9=180
=>7x=180+9
=>7x=189
=>7x/7=189/7
therefore
x=27Jermaine earned 175 points by finishing 5 levels of video games. At this rate, how many points will he earn if he finishes 12 levels of the video game?
Answer:
420 points
Step-by-step explanation:
5 levels of video games = 175 points
1 level = 175 ÷ 5
= 35 points
Therefore,
12 levels of video games = 35 × 12
= 420 points
Emma earned $120 babysitting. She saved 44% of his money. How much money did she save?
Answer:
$52.80
Step-by-step explanation:
First off we need to find out how much she didn't save (to make it easier)
$120 - 44% = $67.20
Well how much did she save? Lets subtract $67.20 from $120 to find our answer.
$120 - $67.20 = $52.80
Emma saved $52.80 (44%).
Hopefully this helps :3 Sorry if wrong :( plz mark brainiest if correct :D Your bootiful/handsome! Have a great day luv <3
-Bee~
In 2000 a particular school district had a total of 7982 students enrolled in school. At this time, the percent of white students who were exposed to school poverty3 was 30% whereas this was 34.5% for Black students. The number of white students in this district in 2000 was 5184 and the number of Black students was 1035. (Note these are the deomgraphics for students who identify as one of these two races alone.) In 2015, the number of students enrolled in school in this district increased to 11977. The percent of white students exposed to school poverty increased to 47.8% and the percent for Black students increased to 76.1%. The number of white students in this district in 2015 was 7306 and the number of Black students was 2037.
Suppose we want to determine if, relative to the increased size of the school district from 2000 to 2015, is the difference between the proportion of white students exposed to poverty likely due to something besides chance. Perform an appropriate statistical hypothesis test at an α = 0.05 confidence level to answer this question. Show all your work and interpret your conclusion within the context of the problem and the appropriateness of the required assumptions.
Perform the same analysis as you did but this time to determine if there is statistical evidence of an actual difference between the proportion of Black students exposed to poverty.
Answer:
Part A
There is sufficient statistical evidence to suggest that the difference between the proportion of White students exposed to poverty is likely due to something beside chance
Part B
There is sufficient statistical evidence to suggest that the difference between the proportion of Black students exposed to poverty is likely due to something beside chance
Step-by-step explanation:
Part A
The given data are;
The percent of White students exposed to school poverty in 2,000, [tex]\hat p_1[/tex] = 30%
The number of White students in the district in 2,000, n₁ = 5184
The percent of White students exposed to school poverty in 2,015, [tex]\hat p_2[/tex] = 47.8%
The number of White students in the district in 2,015, n₂ = 7,306
The significant level, α = 0.05
The confidence level = 1 - α/2 = 1 - 0.05/2 = 0.975
The critical z at 0.975 confidence level, [tex]Z_c[/tex] = 1.96
The null hypothesis, H₀; [tex]\hat p_1[/tex] = [tex]\hat p_2[/tex]
The null hypothesis, H₀; [tex]\hat p_1[/tex] ≠ [tex]\hat p_2[/tex]
The Z test is given as follows;
[tex]Z=\dfrac{\hat{p}_1-\hat{p}_2}{\sqrt{\hat{p}(1-\hat{p})\left (\dfrac{1}{n_{1}}+\dfrac{1}{n_{2}} \right )}}[/tex]
Therefore, we have;
[tex]Z=\dfrac{0.3 - 0.478}{\sqrt{0.3 \cdot (1-0.3)\left (\dfrac{1}{5184}+\dfrac{1}{7306} \right )}} = -21.3894[/tex]
Given that the actual Z is much larger than the critical Z, we reject the null hypothesis that the difference between the proportion of White students is likely due to something other than chance
Part B, we have;
The percent of black students exposed to school poverty in 2,000, [tex]\hat p_1[/tex] = 34.5%
The number of black students in the district in 2,000, n₁ = 1035
The percent of black students in the district in 2,015, [tex]\hat p_2[/tex] = 76.1%
The number of black students in the district in 2,000, n₁ = 2037
[tex]Z=\dfrac{0.345 - 0.761}{\sqrt{0.345 \cdot (1-0.35)\left (\dfrac{1}{1,035}+\dfrac{1}{2,037} \right )}} =-22,925[/tex]
Similarly, due to the large value of Z compared to [tex]Z_c[/tex], there must be other variables responsible for the difference in proportion
Select the correct answer.
Dr. Granger has two dishes of healthy cells. She exposes the cells in both dishes to different compounds that cause the number of
healthy cells to either increase or decrease exponentially.
The number of healthy cells in dish At hours after exposure is modeled by the function below.
Aft)
9,000(0.87)
The number of healthy cells in dish Bt hours after exposure to the other compound can be modeled by the table below.
t
0 1
2. 3 4
9,000 9,810 10,693 11,655 12,704
B(t)
Which of the following best describes what will happen to the number of healthy cells in each dish as t increases?
Type here to search
O
RI
11:39 PM
3/22/2021
Answer:
B. As t approaches positive infinity, A(t) approaches zero and B(t) approaches positive infinity.
Step-by-step explanation:
I got it right on my test
After a few months, Isabella's mother decides to harvest all the peas and corn and sell it at the local market. She decides on these prices: Peas are sold at $ 3 3/4 for each square foot harvested. And, corn is sold at $ 1 1/2 for each square foot harvested. Calculate how much money she made if she sold all her produce (all of her peas and corn).
D
Question 3
3 pts
Zion has 152 shares of company LMN stock. LMN issued dividend payments every
quarter that totaled $1.3 per share for the entire year. The current price for LMN
stock is $34.97 per share. What is the current dividend yield for LMN stock?
The lateral surface area is _ square inches
Answer:
180
Step-by-step explanation:
The inaugural attendance of an annual music festival is 150,00. The attendance y increase by 8% each year. (a.) Write an exponential growth function that represents the attendance after t years.
Answer:
y= 150,000(1+0.08)^t
The exponential growth equation is f ( x ) = 150,000 ( 1 + 0.08 )ˣ , where x is the number of years = t
What is exponential growth factor?The exponential growth or decay formula is given by
x ( t ) = x₀ × ( 1 + r )ⁿ
x ( t ) is the value at time t
x₀ is the initial value at time t = 0.
r is the growth rate when r>0 or decay rate when r<0, in percent
t is the time in discrete intervals and selected time units
Given data ,
Let the initial value of the function be x₀ = 150,000
Now , the initial attendance = x₀
And , the percentage of increase every year r = 8 %
So , the equation will be
f ( x ) = x₀ × ( 1 + r )ˣ , where x is the number of years = t
Substituting the values in the equation , we get
f ( x ) = 150,000 ( 1 + 0.08 )ˣ
Hence , the exponential growth equation is f ( x ) = 150,000 ( 1 + 0.08 )ˣ
To learn more about exponential growth factor click :
https://brainly.com/question/13674608
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Use square ABCD for this problem
IF AC=26,find BC.
Answer:
BC = 26Step-by-step explanation:
because in square all sides are equal
Answer:
bc=28
Step-by-step explanation:
give them brainliest
I need help it says to use 3.14 PI
Answer:
Step-by-step explanation:
[tex]\text{We have a rectangle of 100 by 50 and half a circle with a radius of 25.}\\ \\ A=100(50)+3.14(25^2)\\ \\ A\approx 6962.5\ m^2[/tex]
Plz help What is 2x+x
Answer:
The correct answer is 3x
Step-by-step explanation:
Add 2x and x
~Hoped this helped~
~Brainiliest, please?~