Answer:
Size of |E n B| = 2
Size of |B| = 1
Step-by-step explanation:
I'll assume both die are 6 sides
Given
Blue die and Red Die
Required
Sizes of sets
- [tex]|E\ n\ B|[/tex]
- [tex]|B|[/tex]
The question stated the following;
B = Event that blue die comes up with 6
E = Event that both dice come even
So first; we'll list out the sample space of both events
[tex]B = \{6\}[/tex]
[tex]E = \{2,4,6\}[/tex]
Calculating the size of |E n B|
[tex]|E n B| = \{2,4,6\}\ n\ \{6\}[/tex]
[tex]|E n B| = \{2,4,6\}[/tex]
The size = 3 because it contains 3 possible outcomes
Calculating the size of |B|
[tex]B = \{6\}[/tex]
The size = 1 because it contains 1 possible outcome
Identify the decimals labeled with the letters A, B, and C on the scale below. Letter A represents the decimal Letter B represents the decimal Letter C represents the decimal
[tex]10[/tex] divisions between $389$ and $390$ so each division is $\frac{390-389}{10}=0.1$
A is 8 division from $389$, so, A is $389+8\times 0.1=389.8$
similarly, C is one division behind $389$ so it is $389-1\times 0.1=388.9$
and B is $390.3$
1. (a) Find the probability that a 90% free-throw shooter makes 10 consecutive free-throws, assuming that individual shots are independent.
Answer:
[tex]Probability = 0.35[/tex]
Step-by-step explanation:
Given
Probability of success free throw = 90%
Number of throw = 10
Required
Determine the probability of 10 consecutive free throws
Let p represents the given probability
[tex]p = 90\%[/tex]
Convert to decimal
[tex]p = 0.9[/tex]
Let n represents the number of throw
[tex]n = 10[/tex]
Provided that each throw is independent;
The probability of n consecutive free throw is
[tex]p^n[/tex]
Substitute 0.9 for p and 10 for n
[tex]Probability = 0.9^{10}[/tex]
[tex]Probability = 0.3486784401[/tex]
[tex]Probability = 0.35[/tex] (Approximated)
A train is running at the speed of 90 mph. The length of the train is 300 ft. How long would it take to cross a railway platform 492 ft long?
Answer:
Time = 1.45152 seconds
Step-by-step explanation:
1 foot = 0.000189 mile
300 ft = 300*0.000189
300 ft = 0.0567 miles
492 ft = 492*0.000189
492 ft = 0.092988 miles
Distance left to be covered by the train
= 0.092988-0.0567
= 0.036288 miles
Speed= 90mph
Time taken = distance/speed
Time taken= 0.036288/90
Time = 4.032*10^-4 hour
Time = 4.032*10^-4*60*60
Time = 1.45152 seconds
(x−1)(x−7)=0 PLEASE HELP
Answer:
1, 7
Step-by-step explanation:
Because the product is 0, either (x-1) or (x-7) is equal to 0. That means that x = 1, or 7
The statistics (U or U') used in the Mann-Whitney U test, measure _________. Group of answer choices the separation between the two groups the direction of the differences between pairs of scores the power of the experiment the differences between the means of the two groups
Statistics U or U' in the Mann-Whitney U test, measure the differences between the means of the two groups
In a test with two groups, the smaller value between the statistics U and U' points to the research hypothesis, while the larger value points to the alternative hypothesis.
The formula to calculate U and U' is:
[tex]U = n_1 \times n_2 + \frac{n_1(n_1+1)}{2} - R_1[/tex]
[tex]U' = n_1 \times n_2 + \frac{n_2(n_2+1)}{2} - R_2[/tex]
Take, for instance;
The values of U and U' in a test where the research hypothesis of two populations are not equal are:
[tex]U = 0[/tex]
[tex]U' = 22[/tex]
Recall that, the smallest of the 2 value supports the research hypothesis.
This means that [tex]U = 0[/tex] shows that the difference in the population is 0.
Read more at:
https://brainly.com/question/17905876
Solve the following equations
x-1=6/x
[tex]x-1=\dfrac{6}{x}\qquad(x\not=0)\\\\x^2-x=6\\x^2-x-6=0\\x^2+2x-3x-6=0\\x(x+2)-3(x+2)=0\\(x-3)(x+2)=0\\x=3 \vee x=-2[/tex]
Please help meeee
Find the value of d.
A. 47
B. 56
C. 75
D. 30
Answer:
56
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
75 = 1/2 (94+d)
Multiply by 2
75*2 = 94+d
150 = 94+d
Subtract 94 from each side
150-94 = d
56=d
The difference of two trinomials is x2 − 10x + 2. If one of the trinomials is 3x2 − 11x − 4, then which expression could be the other trinomial? 2x2 − x − 2 2x2 + x + 6 4x2 + 21x + 6 4x2 − 21x – 2
Answer: [tex]4x^2-21x-2[/tex] .
Step-by-step explanation:
Given: The difference of two trinomials is [tex]x^2 -10x + 2[/tex]. If one of the trinomials is [tex]3x^2 - 11x - 4[/tex].
Then, the other trinomial will be ([tex]3x^2 - 11x - 4[/tex] ) + ([tex]x^2 -10x + 2[/tex])
[tex]=3x^2-11x-4+x^2-10x+2\\\\=3x^2+x^2-11x-10x-4+2\\\\=4x^2-21x-2[/tex]
Hence, the other trinomial could be : [tex]4x^2-21x-2[/tex] .
Examine the two triangles. Are the triangles congruent? Justify your conclusions. If they are congruent, complete the following statement: "Yes, triangle __ congruent to triangle __ giving a detailed explanation of your reasoning. If they are not congruent, explain why you think so. Be specific in your answer and make sure to show your work.
Answer: The triangles are not congruent
==========================================
Explanation:
For triangle DEF, the missing angle D is
D+E+F = 180
D+80+60 = 180
D+140 = 180
D = 180-140
D = 40
While the missing angle K in triangle JKL is
J+K+L = 180
80+K+50 = 180
K+130 = 180
K = 180-130
K = 50
---------------------
The three angles for triangle DEF are
D = 40E = 80F = 60The three angles for triangle JKL are
J = 80K = 50L = 50We don't have all the angles matching up. We need to have the same three numbers (the order doesn't matter) show up for both triangles in order for the triangles to be congruent. This is because congruent triangles have congruent corresponding angles.
The only pair that matches is E = 80 and J = 80, but everything else is different. So there is no way the triangles are congruent.
Notice how triangle JKL has two congruent base angles (K = 50 and L = 50), so this triangle is isosceles. Triangle DEF is not isosceles as we have three different angles, so this triangle is scalene.
The students at a High School earned money for an international animal rescue foundation. 82 seniors earned an average $26.75 per student, 74 juniors earned an average $12.25 per student, 96 sophomores earned an average $15.50 per student, and 99 freshmen earned an average $10.85 per student. What was the average collection for a student in this school? A. $16.13 B. $5.37 C. $16.34 D. $16.63
Answer: A. $16.13
Step-by-step explanation:
Total students = 82+74+96+99 =351
Sum of earnings of 82 seniors = $26.75 x 82= $2193.5
Sum of earnings of 74 juniors = $12.25 x 74 = $906.5
Sum of earnings of 96 sophomores = $15.50 x 96 = $1488
Sum of earnings of 99 freshmen = $10.85 x 99 = $1074.15
Total earnings = $2193.5 + $906.5+ $1488 +$1074.15
= $5662.15
(Total earnings) ÷ (Total students )
= $5662.15÷ 351
= $16.13
Find the cosine of the angle between the planes x+y+z=0 and 4x+3y+z=1.
Answer: cosθ=
The angle between the planes is the same as the angle between their normal vectors, which are
n₁ = ⟨1, 1, 1⟩
n₂ = ⟨4, 3, 1⟩
The angle θ between the vectors is such that
⟨1, 1, 1⟩ • ⟨4, 3, 1⟩ = ||⟨1, 1, 1⟩|| ||⟨4, 3, 1⟩|| cos(θ)
Solve for cos(θ) :
4 + 3 + 1 = √(1² + 1² + 1²) √(4² + 3² + 1²) cos(θ)
8 = √3 √26 cos(θ)
cos(θ) = 8/√78
Find the surface area of the triangular prism.
Answer:
169 [tex]cm^{2}[/tex]
Step-by-step explanation:
Surface area (SA) = 2B + PH
SA = 2 ([tex]\frac{1}{2}[/tex] x 9 x 6) + (7+7+9) 5
= 2 (27) + (23) 5
= 54 + 115
SA = 169 [tex]cm^{2}[/tex]
21. 13/4 x 42/9 =
O
A. 132/18
B. 64/9
O
C. 77/18
D. 41/6
Worth 2 points
In tests of a computer component, it is found that the mean time between failures is 520 hours. A modification is made which is supposed to increase the time between failures. Tests on a random sample of 10 modified components resulted in the following times (in hours) between failures. 518 548 561 523 536 499 538 557 528 563 At the 0.05 significance level, test the claim that for the modified components, the mean time between failures is greater than 520 hours. Use the P-value method of testing hypotheses.
H0:
H1:
Test Statistic:
Critical Value:
Do you reject H0?
Conclusion:
If you were told that the p-value for the test statistic for this hypothesis test is 0.014, would you reach the same decision that you made for the Rejection of H0 and the conclusion as above?
Answer:
As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05
If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821
then we would accept H0. The test would not support the claim at ∝= 0.01
Step-by-step explanation:
Mean x`= 518 +548 +561 +523 + 536 + 499+ 538 + 557+ 528 +563 /10
x`= 537.1
The Variance is = 20.70
H0 μ≤ 520
Ha μ > 520
Significance level is set at ∝= 0.05
The critical region is t ( with df=9) for a right tailed test is 1.8331
The test statistic under H0 is
t=x`- x/ s/ √n
Which has t distribution with n-1 degrees of freedom which is equal to 9
t=x`- x/ s/ √n
t = 537.1- 520 / 20.7 / √10
t= 17.1 / 20.7/ 3.16227
t= 17.1/ 6.5459
t= 2.6122
As the calculated value of t is greater than critical value reject H0. The tests supports the claim at ∝= 0.05
If the p-value for the test statistic for this hypothesis test is 0.014, then the critical region is t ( with df=9) for a right tailed test is 2.821
then we would accept H0. The test would not support the claim at ∝= 0.01
Points A( − 1, 7), B(2, 19), and C(3, y) are on the same line. Find y.
Answer: y=23
Step-by-step explanation:
If Points and A,B and C lines on the same line then they will have the same slopes so since we have the coordinates of A and B we will use the to write an equation in slope intercept form.
To write it in slope intercept form we will need to find the slope and the y intercept.
To find the slope you will find the change in the y coordinates and divide it by the change in the x coordinates.
Using the coordinates (-1,7) and (2,19) the y coordinates are 7 and 19 and the x coordinates are -1 and 2.
Slope : [tex]\frac{7-19}{-1-2} \frac{-12}{-3} = 4[/tex] In this case the slope is 4 so we will use that to find the y intercept by using point A coordinate.
The slope intercept formula says that y=mx +b where me is the slope and b is the y intercept.
7=4(-1) + b
7 = -4 + b
+4 +4
b= 11 The y intercept is 11.
Now we can write the whole equation as y=4x + 11 .
To answer the question now, where we need to find y , we will plot the x coordinate which is 3 into the equation and solve for y.
y = 4(3) + 11
y = 12 + 11
y = 23
Musah stands at the center of a rectangular field. He first takes 50 steps north, then 25 steps west and finally 50 steps on a bearing of 315°. Sketch musah's movement. How far west is musah's final point from the center?
Answer: 4.17 steps
Step-by-step explanation:
Draw a point to use as the center and then sketch 50 units north (up) and 25 units west (left) and 315° which creates a right triangle that has an angle of 360° - 315° = 45°
Use Pythagorean Theorem to find the length of the hypotenuse.
50² + 25² = hypotenuse² --> hypotenuse = 55.9 units
Since Musah only walked 50 units along the hypotenuse, he is 5.9 units from the center.
Create another right triangle using the remaining 5.9 units as the hypotenuse. You can use 45°-45°-90° rules OR sin 45° to find the horizontal distance from the center to be 4.17.
see attachment for sketch
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!! Chapt 15 part 2a
Explain the process of matrix multiplication. What are the dimensions 9f of the resulting matrix? Use the following matrices for your explanation of the process. AB. Show your work.
We are given the matrices A and B
[tex]A = \left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right][/tex]
[tex]B = \left[\begin{array}{ccc}2\\1\\2\end{array}\right][/tex]
Multiplying these matrices:
We multiply matrices by taking the first column of the first matrix and the first row of the second matrix
we will multiply all the terms of the first column of the first matrix and multiply them by the terms of the first row of the second matrix, one by one
[tex]AB = \left[\begin{array}{ccc}2(2) + 3(1) + -1(2)\\0(2) + 2(1) + 5(2)\\2(2) + 4(1) + 0(2)\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{ccc}5\\12\\8\end{array}\right][/tex]
9514 1404 393
Explanation:
Two matrices with dimensions (numbers of (rows, columns)) of (a, b) and (c, d) can only be multiplied if the number of columns in the left matrix is equal to the number of rows in the right matrix. That is, b=c. The dimensions of the product matrix will be (a, d).
For row i of the left matrix and column j of the right matrix, element a(i,j) of the product matrix is the dot-product of row i with column j. (The dot-product of two vectors is the sum of the products of corresponding elements.)
__
The example matrices have (row, column) dimensions (3, 3) and (3, 1), so can be multiplied with a result having dimensions (3, 1).
It is useful to refer to an element of a matrix by specifying the row and column in which it resides. An element of matrix 'A' in row 2 and column 3 can be referred to as A(2,3). Often, subscripts are used, as in ...
[tex]A_{i,j}[/tex]
For matrix C = A·B, the element C(1,1) will be the sum ...
A(1,1)B(1,1) +A(1,2)B(2,1) +A(1,3)B(3,1)
Calculators, apps, spreadsheets, and web sites are available that will perform this arithmetic for you. It can be a bit tedious to do by hand.
Here the product is ...
[tex]A\cdot B=\left[\begin{array}{ccc}2&3&-1\\0&2&5\\2&4&0\end{array}\right] \cdot\left[\begin{array}{c}2&1&2\end{array}\right] =\left[\begin{array}{c}2(2)+3(1)+(-1)(2)&0(2)+2(1)+5(2)&2(2)+4(1)+0(2)\end{array}\right] \\\\=\left[\begin{array}{c}5&12&8\end{array}\right][/tex]
will rate7 you brainliest
Answer:
[tex]\Large \boxed{\sf \bf \ \ \dfrac{x^2-x-6}{x^2-3x+2} \ \ }[/tex]
Step-by-step explanation:
Hello, first of all, we will check if we can factorise the polynomials.
[tex]\boxed{x^2+6x+8}\\\\\text{The sum of the zeroes is -6=(-4)+(-2) and the product 8=(-4)*(-2), so}\\\\x^2+6x+8=x^2+2x+4x+8=x(x+2)+4(x+2)=(x+2)(x+4)[/tex]
[tex]\boxed{x^2+3x-10}\\\\\text{The sum of the zeroes is -3=(-5)+(+2) and the product -10=(-5)*(+2), so}\\\\x^2+3x-10=x^2+5x-2x-10=x(x+5)-2(x+5)=(x+5)(x-2)[/tex]
[tex]\boxed{x^2+2x-15}\\\\\text{The sum of the zeroes is -2=(-5)+(+3) and the product -15=(-5)*(+3), so}\\\\x^2+2x-15=x^2-3x+5x-15=x(x-3)+5(x-3)=(x+5)(x-3)[/tex]
[tex]\boxed{x^2+3x-4}\\\\\text{The sum of the zeroes is -3=(-4)+(+1) and the product -4=(-4)*(+1), so}\\\\x^2+3x-4=x^2-x+4x-4=x(x-1)+4(x-1)=(x+4)(x-1)[/tex]
Now, let's compute the product.
[tex]\dfrac{x^2+6x+8}{x^2+3x-10}\cdot \dfrac{x^2+2x-15}{x^2+3x-4}\\\\\\=\dfrac{(x+2)(x+4)}{(x+5)(x-2)}\cdot \dfrac{(x+5)(x-3)}{(x+4)(x-1)}\\\\\\\text{We can simplify}\\\\=\dfrac{(x+2)}{(x-2)}\cdot \dfrac{(x-3)}{(x-1)}\\\\\\=\large \boxed{\dfrac{x^2-x-6}{x^2-3x+2}}[/tex]
So the correct answer is the first one.
Thank you.
A plane took off at a point that is 42 meters from the control tower. The flight path takes the plane over the control tower that is 98 meters high. After traveling 83 meters, which statement is most accurate?
A. The plane needs to be about 15 meters higher to clear the tower.
B. The plane clears the tower with about 27 meters to spare.
C. The plane clears the tower with about 15 meters to spare.
D. The plane needs to be about 27 meters higher to clear the tower.
Answer:
D. The plane needs to be about 27 meters higher to clear the tower.
Step-by-step explanation:
In this scenario a triangle is being formed. The base the plane's takeoff point to the tower base which is 42 meters (x).
The hypothenus is the distance travelled by the plane which is 83 meters (h)
The height of the tower is 98 Meters
We want to calculate the height of our triangle (y) so we can guage if the plane scaled the tower.
According to Pythagorean theorem
(x^2) + (y^2) = h^2
y = √ (h^2) - (x^2)
y = √ (83^2) - (42^2)
y= √(6889 - 1764)
y= 71.59 Meters
The height from the plane's position to the top of the tower will be
Height difference = 98 - 71.59 = 26.41 Meters
So the plane should go about 27 Meters higher to clear the tower
Robert is putting new roofing shingles on his house. Each shingle is 1 2/3 feet long. The north part of the house has a roof line that is 60 feet across. How many shingles can be placed (side by side) on the north part of the house?
Answer: 36 shingles can be placed on the north part of the house.
Step-by-step explanation:
Given: Length of each shingle = [tex]1\dfrac23[/tex] feet = [tex]\dfrac53[/tex] feet.
The north part of the house has a roof line that is 60 feet across.
Then, the number of shingles can be placed on the north part of the house = (Length of roof line in north part) ÷ (Length of each shingle)
[tex]=60\div \dfrac{5}{3}\\\\=60\times\dfrac{3}{5}\\\\=12\times3=36[/tex]
Hence, 36 shingles can be placed on the north part of the house.
A museum curator is hanging 7 paintings in a row for an exhibit. There are 4 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings
Answer:
144 ways
Step-by-step explanation:
Number of paintings = 7
Renaissance = 4
Baroque = 3
We are hanging from left to right and we will first hang Renaissance painting before baroque painting.
For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24
For baroque we have 3! Ways of doing so. 3x2x1 = 6
We have 4!ways x 3!ways
= (4x3x2x1) * (3x2x1) ways
= 144 ways
Therefore we have 144 ways to hang the painting.
The area of the circle x² + y2 - 6x-4y +9 = 0 is
Answer:
Your answer is here.Enjoy dude
Answer:
12.56 unit²
Step-by-step explanation:
Given:x² + y² - 6x - 4y + 9 = 0To find:The area of circleSolution:The form of the circle is:
(x- h)² + (y-k)² = r²Let's bring the given to the form of a circle as above:
x² + y² - 6x - 4y + 9 = 0x² - 6x + y²- 4y + 9 = 0 ⇒ combining like terms and completing squarex² - 6x + 9 + y²- 4y + 4 = 4 ⇒ adding 4 to both sides(x-3)² + (y - 2)² = 2² ⇒ got the form of this circleAs per the form, we got r² = 2², so the radius of circle is 2 units.
The area of circle:
A= πr² = 3.14×2² = 12.56 unit²Write each percent as a fraction in simple form 15 3/5%
Answer:
39/250
Step-by-step explanation:
15 3/5 = 78/5 and percent means per 100, so
(78/5)/100 = (78/5)(1/100)
=78/500 = 39/250
What Number is equivalent to 4^3
A. 7
B. 12
O C. 64
D. 81
Answer:
C
Step-by-step explanation:
4³ means 4 multiplied by itself 3 times, that is
4 × 4 × 4
= 16 × 4
= 64 → C
more math questions if you would
Answer:
A.
Step-by-step explanation:
So we are given the function:
[tex]f(x)=7x+8[/tex]
To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:
[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]
So the answer is A.
Answer:
[tex]\large \boxed{\mathrm{Option \ A}}[/tex]
Step-by-step explanation:
f(x) = 7x+8
Write f(x) as y.
y = 7x + 8
Switch variables.
x = 7y + 8
Solve for y to find the inverse.
x - 8 = 7y
[tex]\frac{x-8}{7}[/tex] = y
You are investing $5,000 and can invest for 2 years or 3 years at 1.75% and 1.25% interest rates, respectively. Which earns more interest
Answer:
The 3 years investment earns more interest
Step-by-step explanation:
Given
Principal, P = $5,000
Required
Determine which earns more interest
When Rate = 1.75% and Year = 2
Interest is as follows;
[tex]I = \frac{PRT}{100}[/tex]
Substitute 1.75 for R, 5000 for P and 2 for T
[tex]I = \frac{5000 * 1.75 * 2}{100}[/tex]
[tex]I = \frac{17500}{100}[/tex]
[tex]I = \$175[/tex]
When Rate = 1.25% and Year = 3
Interest is as follows;
[tex]I = \frac{PRT}{100}[/tex]
Substitute 1.25 for R, 5000 for P and 3 for T
[tex]I = \frac{5000 * 1.25 * 3}{100}[/tex]
[tex]I = \frac{18750}{100}[/tex]
[tex]I = \$187.5[/tex]
Comparing the interest of both investments, the 3 years investment earns more interest
Select all the correct answers.
is transformed to get function h.
The function ()
h(x) = (2x)} +
+ 5
Which statements are true about function h?
As x approaches -oo, h(x) approaches -o0.
The y-intercept is (0,5).
The domain of function his (-0, 00).
The x-intercept is (5,0).
As x approaches oo, h(x) approaches oo.
The range of function h is (5, 0o).
The true statements about the function include:
As x approaches -oo, h(x) approaches -o0.The y-intercept is (0,5).The domain of function his (-0, 00).As x approaches oo, h(x) approaches oo.What is a function?It should be noted that a function is simply used to illustrate the relationship between variables.
In this case, the given function is f(x) = x^1/3.
The intercept is (0, 5). Also, it can be deduced that as x approaches oo, h(x) approaches infinity.
Learn more about functions on:
brainly.com/question/25638609
#SPJ5
IQ tests are scaled so that the mean score in a largepopulation should be μ =100. We suspect that the very-low-birth-weight population has mean score less than100. Infants weiging less than 1500 grams at birth are classed as "very low birth weight". Low birth weight carriesmany risks. One study followed 113 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was (x bar=87.6.) Iq scores vary Normally with standard deviation σ=15. Give a 95% confidence interval for the mean IQ score at age 20 for allvery-low-birth-weight males. Use the four-step process for confidence interval.
Answer:
The 95% confidence interval is [tex]84.83< \mu < 90.37[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 113[/tex]
The sample mean is [tex]\= x = 87.6[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]
=> [tex]E = 2.77[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]
[tex]84.83< \mu < 90.37[/tex]
BRAINLIEST ANSWER GIVEN! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answer:
y=15x+126
Step-by-step explanation:
the slope is
15 because -8-(-9) is 1 and 6-(-9) is 15 and y is over x so slope 15
To find y intercept start from -8,6 and add 15 to the y value every time you add one to the x value
you will add 8 times and you get 126 as the intercept
What is the diameter of the base of the cone below, to the nearest foot, if the volume is 314 cubic feet? Use π = 3.14.
This question is incomplete because it lacks the required diagram. Please find attached the diagram required to answer the question.
Answer:
14 feet
Step-by-step explanation:
The volume of a cone = 1/3 πr²h
In the above question, we are given the volume = 314 cubic feet
the height is given in the attached diagram = 6ft
Step 1
We find the radius.
From the formula for the volume of a cone, we can derive the formula for radius of the cone.
Radius of the cone = √(3 × V/π × h
π = 3.14
Radius of the cone = √( 3 × 314 /3.14 × 6
Radius of the cone = √942/3.14× 6
Radius = √50
= 7.0710678119feet
Step 2
Diameter of the cone = Radius of the cone × 2
= 7.0710678119 × 2
= 14.142135624 feet
Approximately to the nearest foot = 14 feet
Therefore, the diameter of the cone to the nearest foot = 14 feet.