Answer:
Answer is in bold form
Step-by-step explanation:
Given
radius = 3feet
Height = 6feet
Volume of the cylinder = πr²h
Volume of the cylinder = 3.14 * 3² * 6
Volume of the cylinder = 169.56ft³
volume of the cone = Volume of cylinder/3
volume of the cone = 169.56/3
volume of the cone = 56.52ft³
Volume of the sphere = 4/3πr³
Volume of the sphere = 4/3*3.14*(3)³
Volume of the sphere = 4 * 3.14* 9
Volume of the sphere = 113.04ft³
76 is what percent of 79
Answer:
79
100
0.79%
76
100
0.76%
What is this function’s input if its output is 11?
f(x) = 2x + 5
Answer:
the input x is 3
Step-by-step explanation:
2x+5=11
2x=6
x=3
Eric wants to buy a new hat
which costs $17. He made
$5 by raking leaves and
$8 by washing cars.
How much more money does he need?
Answer:
the answer is 4
Step-by-step explanation:
you subtract 13 from 17 =4
Look at the illustration.
What is WX?
Answer:
O 0.5 units
Step-by-step explanation:
so the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W'X'Y'Z is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5) = 1.5 / 9 = 1/6
Since WX has an initial measure of 3 units, therefore the measure of W'X' is:
W'X' = 3 units *(1/6) = 0.5 units
If a normal distribution has a mean of 154 and a standard deviation of 15,
what is the value that has a z-score of 1.6?
Answer:
The correct answer is - 178.
Step-by-step explanation:
The standard deviation is a measure of the amount of dispersion in a set of values.
Given:
Mean of a normal distribution (m) = 154
Standard deviation (s) = 15
z-score = 1.6
Solution:
To find: value (x) that has a z-score of 1.6
z-score is given by = x-u/15
1.6*15 = x-154
=> 154+24 = x
x = 178
Which expression is equivalent to the given expression?
6ab/(a^0b^2)^4
Answer:
,here is the answer
Step-by-step explanation:
here is your answer
solve for x 6(x-3)=8(x-4)
Answer:
7=x
Step-by-step explanation:
6(x-3)=8(x-4)
Distribute
6x -18 = 8x-32
Subtract 6x from each side
6x-18 -6x = 8x-32-8x
-18 = 2x-32
Add 32 to each side
-18+32 = 2x-32+32
14 = 2x
Divide by 2
14/2 =2x/2
7=x
[tex]\sf\purple{x= 7}[/tex]
[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]
[tex]➺\:6(x - 3) = 8(x - 4)[/tex]
[tex]➺ \: 6x - 18 = 8x - 32[/tex]
[tex]➺ \: 6x - 8x = - 32 + 18[/tex]
[tex]➺ \: - 2x = - 14[/tex]
[tex]➺ \: x = \frac{ - 14}{ - 2} [/tex]
[tex]➺ \: x = 7[/tex]
Therefore, the value of [tex]x[/tex] is 7.
[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY :}}}[/tex]
[tex]➺ \: 6(x - 3) = 8(x - 4)[/tex]
[tex]➺ \: 6(7 - 3) = 8(7 - 4)[/tex]
[tex]➺ \: 6 \times 4 = 8 \times 3[/tex]
[tex]➺ \: 24 = 24[/tex]
➺ L. H. S. = R. H. S.
Hence verified.
[tex]\red{\large\qquad \qquad \underline{ \pmb{{ \mathbb{ \maltese \: \: Mystique35ヅ}}}}}[/tex]
Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 67.5 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quadruple (4x) the sample size. What is the standard error for the new sample size
Answer:
The standard error for the new sample size will be of 33.75.
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Standard error as 67.5 for samples of a particular size.
We have that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], that is, the standard error is inversely proportional to the square root of the sample size, so if you quadruple (4x) the sample size, the standard error will be divided by half. So
67.5/2 = 33.75
The standard error for the new sample size will be of 33.75.
This is for my brother’s test
What are the measures of L1 and L2? Show your work or explain your answers.
Answer:
angle 2 is 75°osjdiajsjoasnndosnsnd
Find the interest earned on $1,000 for 1 year at a 6% rate of interest when the interest is compounded quarterly.
Answer:
1060
Step-by-step explanation:
Joseph borrows $10000 from his sister Katie at an annual interest rate of 10%. If the
interest is compounded twice a year, how much does he owe after 12 months? Give your answer in dollars.
Answer:
A = P ( 1 + r / n) ^( t * n)
where
A = the amt owed
P = amt borrowed
r = the interest rate as a decimal
n = the number of compoundings per year
t = the number of years
A = 10000 ( 1 + .10 / 2)^(2 *1) = 10000 ( 1.05)^2 = $11025
Step-by-step explanation:
Last month Rudy’s Tacos sold 22 dinner specials. The next month they released a new commercial and sold 250% of last month’s dinners. How many dinner specials did they sell this month?
Answer:
the answer is 2
Step-by-step explanation: because 250 -22 is i dont even know
Answer:
55
Step-by-step explanation:
The volume of a cone with a diameter of 9 and a height of 120
Answer: 15268.1403 unit^3 (unit: cm,m,mm)
Step-by-step explanation:
volume of a cone= 1/2*pi*r^2*h
r= radius (unit: cm,m,mm)
h= perpendicular height (unit: cm,m,mm)
volume= 1/2*pi* (9)^2* 120 = 15268.1403 unit^3
what number must you add to complete the square? x^2+24x=50
Answer:
144
Step-by-step explanation:
Divide the b term which is 24 by 2
Gives you 12, then square it.
that's 144
formula for completing squares is [tex](b/2)^{2}[/tex]
Solve for T: 10t-4x=3S Explanation plz
WILL MARK YOU IF YOU ANSWER SO PLEASE HELP
Answer:
x= 83
first take vertical opposite angle then take corresponding angles then you're done
Answer:
x value is 83 degree
because they both are alternate exterior angle
Factor completely, then place the factors in the proper location on the grid. a8 - 12a4 + 36
Answer:
[tex]{ \tt{ {a}^{8} - {12a}^{4} + 36}} \\ = { \tt{ {a}^{4} ( {a}^{2} - 12) + 36 }} \\ = ( {a}^{2} - 12)( {a}^{4} + 36) \\ [/tex]
What are the coordinates of the vertices of the triangle under the translation (x, y) -> (x + 2, y + 3)?
(−4, 5), (3, 4), (0, 0)
(6, −5), (5, 2), (1, −1)
(5, −4). (4, 3), (−1, 2)
(−5, 6), (2, 5), (−1, 1)
9514 1404 393
Answer:
(d) (−5, 6), (2, 5), (−1, 1)
Step-by-step explanation:
No answer choices have any points in common, so we only need to find one translated point to determine the correct answer choice.
For the point on the y-axis, (0, 2), the translation is ...
(x, y) ⇒ (x +2, y+3)
(0, 2) ⇒ (0 +2, 2 +3) = (2, 5) . . . . matches choice D
Find the 23rd term of the arithmetic sequence with the terms a1 27 and d = 16.
Answer:
379
Step-by-step explanation:
a23 = 27 + (23-1)(16)
= 27 + (22)(16)
= 27 + 352
= 379
If a product normal retails for $40, and a customer has a coupon for 15% off, what will the discounted price of the product be?
Answer:
$34
Step-by-step explanation:
price of the product = $40
coupon = 15% off
discount price = 15% of price of a product
=15/100 * $40
=$600/100
=$6
New price of the product = original price - discount
=$40 - $6
=$34
Suppose X has an exponential distribution with mean equal to 23. Determine the following:
(a) P(X >10)
(b) P(X >20)
(c) P(X <30)
(d) Find the value of x such that P(X
Answer:
a) P(X > 10) = 0.6473
b) P(X > 20) = 0.4190
c) P(X < 30) = 0.7288
d) x = 68.87
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Mean equal to 23.
This means that [tex]m = 23, \mu = \frac{1}{23} = 0.0435[/tex]
(a) P(X >10)
[tex]P(X > 10) = e^{-0.0435*10} = 0.6473[/tex]
So
P(X > 10) = 0.6473
(b) P(X >20)
[tex]P(X > 20) = e^{-0.0435*20} = 0.4190[/tex]
So
P(X > 20) = 0.4190
(c) P(X <30)
[tex]P(X \leq 30) = 1 - e^{-0.0435*30} = 0.7288[/tex]
So
P(X < 30) = 0.7288
(d) Find the value of x such that P(X > x) = 0.05
So
[tex]P(X > x) = e^{-\mu x}[/tex]
[tex]0.05 = e^{-0.0435x}[/tex]
[tex]\ln{e^{-0.0435x}} = \ln{0.05}[/tex]
[tex]-0.0435x = \ln{0.05}[/tex]
[tex]x = -\frac{\ln{0.05}}{0.0435}[/tex]
[tex]x = 68.87[/tex]
the points -6/5 and -5/6 will line in which quadrant
A negative x is to the left of the y axis and a negative y value is below the x axis. Any value to the left and below the axis’ will be in the 3rd quadrant.
Answer: 3rd quadrant
Help me pls I don’t know how to do this
Answer:
[tex]radius=6.68cm[/tex]
Step-by-step explanation:
Formula to find radius:
[tex]r=\frac{C}{2\pi }[/tex]
[tex]r=42/2\pi[/tex]
[tex]r=42/2(3.14)[/tex]
[tex]r=6.68cm[/tex]
hope this helps......
pleaseeeee helpppppppppppp
9514 1404 393
Answer:
maximum height: 26.5 ftair time: 2.5 secondsStep-by-step explanation:
I find the easiest way to answer these questions is to use a graphing calculator. It can show you the extreme values and the intercepts. The graph below shows the maximum height is 26.5 ft. The time in air is about 2.5 seconds.
__
If you prefer to solve this algebraically, you can use the equation of the axis of symmetry to find the time of the maximum height:
t = -b/(2a) = -(40)/(2×-16) = 5/4
Then the maximum height is ...
h(5/4) = -16(5/4)² +40(5/4) +1.5 = -25 +50 +1.5 = 26.5 . . . feet
__
Now that we know the vertex of the function, we can write it in vertex form:
h(t) = -16(t -5/4)² +26.5
Solving for the value of t that makes this zero, we get ...
0 = -16(t -5/4)² +26.5
16(t -5/4)² = 26.5
(t -5/4)² = 26.5/16 = 1.65625
Then ...
t = 1.25 +√1.65625 ≈ 2.536954
The cannon ball is in the air about 2.5 seconds.
25. Approximate the sample variance and standard deviation given the following frequency distribution: Class Frequency 0–9 13 10–19 7 20–29 10 30–39 9 40–49 11
Sample variance = 228.408
Standard deviation = 15.113
Step-by-step explanation:The well formatted frequency table has been attached to this response.
To calculate the sample variance and standard deviation of the given grouped data, follow these steps:
i. Find the midpoint (m) of the class interval.
This is done by adding the lower bounds and upper bounds of the class intervals and dividing the result by 2. i.e
For class 0 - 9, we have
m = (0 + 9) / 2 = 4.5
For class 10 - 19, we have
m = (10 + 19) / 2 = 14.5
For class 20 - 29, we have
m = (20 + 29) / 2 = 24.5
For class 30 - 39, we have
m = (30 + 39) / 2 = 34.5
For class 40 - 49, we have
m = (40 + 49) / 2 = 44.5
This is shown in the third column of the attached table.
ii. Find the product of each of the frequencies of the class intervals and their corresponding midpoints. i.e
For class 0 - 9, we have
frequency (f) = 13
midpoint (m) = 4.5
=> f x m = 13 x 4.5 = 58.5
For class 10 - 19, we have
frequency (f) = 7
midpoint (m) = 14.5
=> f x m = 7 x 14.5 = 101.5
For class 20 - 29, we have
frequency (f) = 10
midpoint (m) = 24.5
=> f x m = 10 x 24.5 = 245
For class 30 - 39, we have
frequency (f) = 9
midpoint (m) = 34.5
=> f x m = 9 x 34.5 = 310.5
For class 40 - 49, we have
frequency (f) = 11
midpoint (m) = 44.5
=> f x m = 11 x 44.5 = 489.5
This is shown in the fourth column of the attached table.
iii. Calculate the mean (x) of the distribution i.e
This is done by finding the sum of all the results in (ii) above and dividing the outcome by the sum of the frequencies. i.e
x = ∑(f x m) ÷ ∑f
Where;
∑(f x m) = 58.5 + 101.5 + 245 + 310.5 + 489.5 = 1205
∑f = 13 + 7 + 10 + 9 + 11 = 50
=> x = 1205 ÷ 50
=> x = 24.1
Therefore, the mean is 24.1
This is shown on the fifth column of the attached table.
iv. Calculate the deviation of the midpoints from the mean.
This is done by finding the difference between the midpoints and the mean. i.e m - x where x = mean = 24.1 and m = midpoint
For class 0 - 9, we have
midpoint (m) = 4.5
=> m - x = 4.5 - 24.1 = -19.6
For class 10 - 19, we have
midpoint (m) = 14.5
=> m - x = 14.5 - 24.1 = -9.6
For class 20 - 29, we have
midpoint (m) = 24.5
=> m - x = 24.5 - 24.1 = 0.4
For class 30 - 39, we have
midpoint (m) = 34.5
=> m - x = 34.5 - 24.1 = 10.4
For class 40 - 49, we have
midpoint (m) = 44.5
=> m - x = 44.5 - 24.1 = 20.4
This is shown on the sixth column of the attached table.
v. Find the square of each of the results in (iv) above.
This is done by finding (m-x)²
For class 0 - 9, we have
=> (m - x)² = (-19.6)² = 384.16
For class 10 - 19, we have
=> (m - x)² = (-9.6)² = 92.16
For class 20 - 29, we have
=> (m - x)² = (0.4)² = 0.16
For class 30 - 39, we have
=> (m - x)² = (10.4)² = 108.16
For class 40 - 49, we have
=> (m - x)² = (20.4)² = 416.16
This is shown on the seventh column of the attached table.
vi. Multiply each of the results in (v) above by their corresponding frequencies.
This is done by finding f(m-x)²
For class 0 - 9, we have
=> f(m - x)² = 13 x 384.16 = 4994.08
For class 10 - 19, we have
=> f(m - x)² = 7 x 92.16 = 645.12
For class 20 - 29, we have
=> f(m - x)² = 10 x 0.16 = 1.6
For class 30 - 39, we have
=> f(m - x)² = 9 x 108.16 = 973.44
For class 40 - 49, we have
=> f(m - x)² = 11 x 416.16 = 4577.76
This is shown on the eighth column of the attached table.
vi. Calculate the sample variance.
Variance σ², is calculated by using the following relation;
σ² = ∑f(m-x)² ÷ (∑f - 1)
This means the variance is found by finding the sum of the results in (vi) above and then dividing the result by one less than the sum of all the frequencies.
∑f(m-x)² = sum of the results in (vi)
∑f(m-x)² = 4994.08 + 645.12 + 1.6 + 973.44 + 4577.76 = 11192
∑f - 1 = 50 - 1 = 49 {Remember that ∑f was calculated in (iii) above}
∴ σ² = 11192 ÷ 49 = 228.408
Therefore, the variance is 228.408
vii. Calculate the standard deviation
Standard deviation σ, is calculated by using the following relation;
σ =√ [ ∑f(m-x)² ÷ (∑f - 1) ]
This is done by taking the square root of the variance calculated above.
σ = [tex]\sqrt{228.408}[/tex]
σ = 15.113
Therefore, the standard deviation is 15.113
A professor has been teaching introductory statistics for many years and the final exam performance has been very consistent from class to class and the scores have been normally distributed. Overall, the whole data base (i.e. population) of final scores has a mean (μ) of 24 points (out of a maximum of 30 points) and a standard deviation (Ï) of 5 points. The professor would like to revise the course design to see if student performance on the final could be improved.
The new course design was implemented in the most recent academic year. There were 100 students and the average final exam score was 24.7. The professor would like to run a hypothesis test to see if this sample of students in the recent academic year performed significantly better than the past population. In other words, the hypothesis was a comparison between the population taking the course with the new design (represented by the sample of 100 students) with the population taking the course with the old design. The professor is predicting an increase of final score with the new design, so the hypotheses should be directional, and the test should be one-tailed. The significance level is set at α = .1.
Required:
a. Identify the dependent variable for this study.
b. State the null hypothesis and alternative hypothesis using both words and symbol notation
Answer:
a) Independent variable - Design of the course
Dependent variable - Final score of the students
b) H0 - Final score >24.7
Alternate hypothesis - Final score is less than or equal to 24.7
Step-by-step explanation:
a) Independent variable - Design of the course
Dependent variable - Final score of the students
b) Null Hypothesis : Performance of student taking course with the new design is better as compared to the population of student taking the course with the old design.
H0 - Final score >24.7
Alternate hypothesis - Final score is less than or equal to 24.7
Jill calls a plumber to her house to fix the leaking faucets . The plumber charges a one-time fee of $50 plus an additional $35 per hour of labor. What are the independent and dependent variables
Answer:
independent=$50
dependent=$35X
Step-by-step explanation:
50 is the independent variable because it doesn't change.
35X is the dependent variable because it does change.
In this scenario, the independent variable is the number of hours of labor and dependent variable is the total cost.
The independent variable is the number of hours. It is the variable that we can control or change.
The dependent variable is the total cost charged by the plumber.
It depends on the number of hours of labor and is determined by the plumber's fee structure, which includes a one-time fee of $50 plus $35 per hour of labor.
The total cost is calculated based on the number of hours of labor, making it the dependent variable in this situation.
Learn more about Independent variable here:
https://brainly.com/question/32711473
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100° - y А (x+2) units Match the values based on parallelogram ABCD, shown in the figure. length of BC value of y mZDAB value of I 56 4 44 2
Answer:
BC = 4 units
Value fo y = 44
∠DAB = 56°
Value of x = 2
Step-by-step explanation:
100 - y = 12 + y (opposite angles of parallelogram are equal)
2y = 88
y = 44
Similarly,
6-x = x+2 (opposite sides of parallelogram are equal)
2x = 4
x = 2
How to solve and answer
Answer:
option A
Step-by-step explanation:
2x*(x + 3) = 6x + 4
2x *x + 2x*3 = 6x + 4 {Distributive property}
2x² + 6x = 6x + 4
Subtract 6x from both sides {Subtraction property of equality}
2x² = 4
Divide both sides by 2 {Division property of equality}
x² = 4/2
x² = 2
x = √4 {Square root property}
x = ± 2
What is the smallest number you should subtract from 456 to make it divisible by 9?