Answer:
A sample size of at least 271 is required.
Step-by-step explanation:
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{1-0.9}{2} = 0.05[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.05 = 0.95[/tex], so [tex]z = 1.645[/tex]
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.
Maxium error of 0.12.
How large of a sample is required to estimate the mean usage of electricity?
We need a sample size of at least n.
n is found when [tex]M = 0.12, \sigma = 1.2[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.12 = 1.645*\frac{1.2}{\sqrt{n}}[/tex]
[tex]0.12\sqrt{n} = 1.645*1.2[/tex]
[tex]\sqrt{n} = \frac{1.645*1.2}{0.12}[/tex]
[tex](\sqrt{n})^{2} = (\frac{1.645*1.2}{0.12})^{2}[/tex]
[tex]n = 270.6[/tex]
Rounding up
A sample size of at least 271 is required.
Which is the slope of the line that passes through the points (3, 17) and
(7.25)?
Triangle ABC is rotated 180º using the origin as the center of rotation.
On a coordinate plane, triangle A B C has points (negative 4, negative 3), (negative 5, negative 2), (negative 3, negative 2). Triangle A prime B prime C prime has points (4, 3), (5, 2), (3, 2).
Which sequence of transformations will produce the same result?
a
a reflection over the x-axis and then a reflection over the y-axis
b
a translation up 4 and then a translation right 6
c
a translation up 4 and then a reflection over the y-axis
d
a translation right 6 and then a reflection over the x-axis
Answer:
a. a reflection over the x-axis and then a reflection over the y-axis
Step-by-step explanation:
If you plot it on a graph (you can use Desmos), you can see the triangles and only a. a reflection over the x-axis and then a reflection over the y-axis makes sense.
Answer:
thats c
Step-by-step explanation:
A company is producing two types of ski goggles. Thirty percent of the production is of type A, and the rest is of type B. Five percent of all type A goggles are returned within 10 days after the sale, whereas only two percent of type B are returned. If a pair of goggles is returned within the first 10 days after the sale, the probability that the goggles returned are of type B is
Answer:
[tex]\dfrac{14}{29}[/tex]
Step-by-step explanation:
Let P(A) be the probability that goggle of type A is manufactured
P(B) be the probability that goggle of type B is manufactured
P(E) be the probability that a goggle is returned within 10 days of its purchase.
According to the question,
P(A) = 30%
P(B) = 70%
P(E/A) is the probability that a goggle is returned within 10 days of its purchase given that it was of type A.
P(E/B) is the probability that a goggle is returned within 10 days of its purchase given that it was of type B.
[tex]P(A \cap E)[/tex] will be the probability that a goggle is of type A and is returned within 10 days of its purchase.
[tex]P(B \cap E)[/tex] will be the probability that a goggle is of type B and is returned within 10 days of its purchase.
[tex]P(E \cap A) = P(A) \times P(E/A)[/tex]
[tex]P(E \cap A) = \dfrac{30}{100} \times \dfrac{5}{100}\\\Rightarrow P(E \cap A) = 1.5 \%[/tex]
[tex]P(E \cap B) = P(B) \times P(E/B)[/tex]
[tex]P(E \cap B) = \dfrac{70}{100} \times \dfrac{2}{100}\\\Rightarrow P(E \cap B) = 1.4 \%[/tex]
[tex]P(E) = 1.5 \% + 1.4 \% \\P(E) = 2.9\%[/tex]
If a goggle is returned within 10 days of its purchase, probability that it was of type B:
[tex]P(B/E) = \dfrac{P(E \cap B)}{P(E)}[/tex]
[tex]\Rightarrow \dfrac{1.4 \%}{2.9\%}\\\Rightarrow \dfrac{14}{29}[/tex]
So, the required probability is [tex]\dfrac{14}{29}.[/tex]
Sara goes on a slingshot ride in an amusement park. She is strapped into a spherical ball that has a radius of centimeters. What is the volume of air in the spherical ball? Use this formula: , where r is the sphere’s radius.
A.
B.
C.
D.
Answer:
A. 4×π×3²×[tex]10^{6}[/tex]
Step-by-step explanation:
r = 3×10² = 3×100 = 300
[tex]\frac{4}{3}[/tex]×π×300³=
[tex]\frac{4}{3}[/tex]×π×27,000,000=
[tex]\frac{108,000,000}{3}[/tex]×π=
36,000,000π
Answers solved:
A. 36,000,000π
B. 108,000,000π
C. 3,600,000π
D. 32,400,000π
The solution is Option A.
The volume of the air in the spherical ball is given by the equation
V = 4π ( 3 )² ( 10 )⁶ cm³
What is a Sphere?A sphere is symmetrical, round in shape. It is a three dimensional solid, that has all its surface points at equal distances from the center. It has surface area and volume based on its radius. It does not have any faces, corners or edges.
The Surface Area of a Sphere = 4πr²
The Volume of a Sphere = ( 4/3 ) πr³
where r is the radius of the sphere
Given data ,
Let the volume of the sphere be represented as V
Now , the radius of the spherical ball be r
The value of r = 3 ( 10 )² cm
So , the volume of the spherical ball = ( 4/3 ) πr³
Substituting the values in the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x [ 3 ( 10 )² ]³
On simplifying the equation , we get
Volume of the spherical ball V = ( 4/3 ) x π x ( 3 )³ ( 10 )⁶
Volume of the spherical ball V = 4 x π x ( 3 )² ( 10 )⁶
Therefore , the value of V is 4π ( 3 )² ( 10 )⁶
Hence , the volume of the spherical ball is 4π ( 3 )² ( 10 )⁶
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A rhombus has side lengths of 25. What could be the lengths of the diagonals?
A. 22 and 40
B. 26 and 36
C. 26 and 48
D. 30 and 40
Answer:
The correct option is;
D. 30 and 40
Step-by-step explanation:
Here, we have that the rhombus is a quadrilateral with equal and parallel sides hence the length of the diagonals will be
2 × 25×sinθ and 2 × 25× cosθ
Therefore tanθ = (2 × 25×sinθ)/(2 × 25× cosθ) = (sinθ)/(cosθ)
Therefore, the root of the sum squares of both diagonals = 50
Therefore, we analyze each of the options as follows
For A. we have √(22² + 40²) = 45.65 ≠ 50 therefore these are not the length of diagonals of the rhombus in question
For B. we have √(26² + 36²) = 44.41 ≠ 50 therefore these are not the length of diagonals of the rhombus in question
For C. we have √(26² + 48²) = 55.59 ≠ 50 therefore these are not the length of diagonals of the rhombus in question
For D. we have √(30² + 40²) = 50 therefore these are possible lengths of diagonals of the rhombus in question.
PLEASE HELP- 25 points-what is the circumference of the circle. Diameter =9cm
Answer:
9π cm - exact value
28.26 cm - approximate value
Step-by-step explanation:
C = πd =9π cm - exact value
or
C=9π≈ 28.26 cm - approximate value
A certain game consists of rolling a single fair die. If a four or five comes up, you win 10 dollars; otherwise, you lose 5 dollars. Find the expected winnings for this game. Is this a fair game?
Answer:
no this game is not fair due to the fact that u have a 2/6 chance to win
Phil wishes to compare the weights of professional athletes to the weights of non-professional athletes. Phil completes a simple random sample of professional athletes and records his results in pounds: 125 147 240 186 156 205 248 152 199 207 176 Phil also completes a simple random sample of non-professional athletes and records his results in pounds: 151 161 139 128 149 160 201 173 The samples are independent and come from normally distributed populations. Use the p-value method and a 2% significance level to test the claim that the mean weights of professional and non-professional athletes are the same. What population parameter is being tested
Answer: 4
Step-by-step explanation:
A square and rectangle have the same perimeter.
The rectangle is 13 cm long and 7 cm wide What is the length of a side of the square
The length of a side of the square is 10 cm.
What is a length?Length is defined as the measurement or extent of something from end to end.
The perimeter of rectangle is obtained using the formula
perimeter = 2(length+width)
Perimeter of square is obtained using the formula
perimeter = 4(length of one side)
Length of rectangle is 13 cm.
Width of rectangle is 7 cm.
Then the perimeter of rectangle is obtained as
perimeter = 2(length+width) = 2(13+7) = 2*20=40
Perimeter of square is
perimeter = 4(length of one side) = 40
Therefore, length of one side is 10 cm.
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Which figure below has point symmetry
Answer:
Figure D
Step-by-step explanation:
Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction. Hope this helps! :)
There are five families that each have one child. Each of them hires Riley as a babysitter. Because the children she babysits are different ages, Riley charges each family a different amount. To visualize her earnings, Riley recorded and plotted her pay from each job. Using the scatterplot, calculate her average rate of pay.
Answer:
Average Rate of Pay = $ 5.23 /hr
Step-by-step explanation:
We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:
x (Hours) = 12 13 16 17 20
y ($) = 54 56 65 64 100
The statistical data calculated is:
∑x = 78, ∑x² = 1258, ∑y = 339, ∑xy = 5504, n = no. of data points = 5
Now, we use linear regression model to fit a straight line to this data.
y = a + bx --------- eqn (1)
where,
b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]
b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]
b = 5.23
and,
a = (∑xy - b∑x²)/∑x
a = [5504 - (5.23)(1258)]/78
a = -13.83
Therefore, eqn (1) becomes:
y = -13.83 + 5.23x
The graph plot of this straight line fit is provided in the attachments.
Now, we derivate the equation with respect to x, to get the average rate of pay:
Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)
Average Rate of Pay = $ 5.23 /hr
Please help which should I choose
Reasoning:
If it is at all possible to draw a single vertical line through more than one point on the curve, then the graph is not a function. With graphs (2), (3) and (4), we can draw a vertical line through more than one point on those curves, so they aren't functions. Graph (1) is the only thing left. This graph is a function because it is not possible to draw a single vertical line through more than one point. It passes the vertical line test. Any input (x) leads to exactly one and only one y output.
Nice work on getting the correct answer when you chose "graph (1)".
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
(x + 5) (x - 7)
Step-by-step explanation:
To factor this trinomial, you must split the middle term (-2x) into two terms that can be added to get -2x, and multiplied to get -35:
[tex]x^2[/tex] - 2x - 35
[tex]x^2[/tex] - 7x + 5x - 35
Group:
([tex]x^2[/tex] - 7x) (5x - 35)
Take out GCF (Greatest Common Factor):
x(x - 7) 5(x - 7)
(x + 5) (x - 7)
IF GET THESE 2 RIGHT 10 POINTS FOR BOTH BE THE GOD AND THE BRAINLYIEST!!! IF THEY ARE BOTH QUESTIONS RIGHT!!
Answer:
Step-by-step explanation:
Question 19:
Answer: C. 1.25 miles
So far, [tex]\frac{1}{10}[/tex] of the 12.5 miles is 1.25 miles. Let's see why!
Very simple all we need to is divide by 10 because our fraction is [tex]\frac{1}{10}[/tex]. So our equation is going to look something like this:
12.5 ÷ 10 = 1.25
Therefore, our answer is, C. 1.25 miles.
Phew! I don't think I would want to run 1.25 miles let alone 12.5! That's what I call dedication!
Question 20:
Answer: A. 8 bags
For this question all we need to do is divide 6.24 by 0.78 pounds of trail mix. This is to see how many bags Leon had purchased.
6.24 ÷ 0.78 = 8
Therefore our answer is 8 bags.
TIPS!!!
If you ever have questions like 19 always look for what the denominator is and divide by that.
If you ever have a question like 20 divide by the total amount of product purchased and than how much that cost was for whatever measurement it may be. (or weight)
This area model represents the product 27 and another number . What is the other number
Answer:
60
Step-by-step explanation:
Alex and Micah scored a total of 40 points in the basketball game. Micah scored four more points than twice Alex's score. How many points did Micah score?
a. 10 points
B. 28 points
C. 12 points
D. 22 points
Answer: D
Step-by-step explanation:
2x + (2x +4 ) =40
x= 9
2(9) +4 =22
What is the surface area of the triangular prism? 10mm 6mm 16mm 12mm
Answer:it would help of you included a photo because the base is measured differently from the triangles
Step-by-step explanation:
The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?
Recall the formula Cube V = 57
s=2/64
s=64+64 +64
s= √64
s=64.64.64
Answer:
The length of a side is [tex]4in^{3}[/tex]
Step-by-step explanation:
The question is not properly formatted. here is a better format .
"The volume of a cube is 64 cubic inches. Which expression represents s, the length of a side of the cube?
Recall the formula Cube [tex]v=l*l*l= l^{3}[/tex]
The problem bothers on the mensuration of solid shapes, a cube
Given data
Volume v = [tex]64in^{3}[/tex]
length l= ?
We can solve for the length by find the cube root of the volume, we have.
[tex]64= l^{3} \\l= \sqrt[3]{64} \\l= 4 in[/tex]
Answer: A or s=∛64
Step-by-step explanation: Edge2023
find the median of the list 12,18,21,25,30,43
Answer:
23
21+25=46 ÷2 =23 what you do is cancel out the numbers and find the middle
The median of the given data set 12,18,21,25,30,43 is, 23
What is median?The middle number or piece of data in a collection is known as the median. Three alternative metrics are employed in mathematics to determine the average value for a given group of integers. They are the mode, median, and mean. The measures of central tendency are this trio of measurements.
Median = {(n+1)/2}th term (for odd)
Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)
Given that,
The data set 12,18,21,25,30,43
By arranging given data set into ascending order,
12, 18, 21, 25, 30, 43
Median = [(n/2)th term + {(n/2)+1}th term]/2 (for even)
Median = (21 + 25)/2
Median = 23
Hence, the median is 23
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A pediatrician randomly selected 10 parents of his patients. Then he surveyed the parents about their opinions of different kinds of diapers. Identify the population and sample in this setting. Choose 1 answer
Answer:
c) The population is the parents of the pediatrician's patients; the sample is the
10
1010 parents of patients selected.
Step-by-step explanation:
Answer:
c) The population is the parents of the pediatrician's patients; the sample is the
10
1010 parents of patients selected.
Step-by-step explanation:
Line p passes through (8, -6) and is perpendicular to the line 2x + y = -7. The slope of line p is . The equation of line p is y = 1/2x + ?.
Answer:
y = (1/2) x -10
Step-by-step explanation:
Perpendicular lines are lines make right angles. The slopes of perpendicular lines are opposite reciprocals !
2x + y = -7 rewrite in form y=
y = -7 -2x
slope of this line is -2
perpendicular lines are opposite reciprocals so the line p has a slope = 1/2
line p passes through (8, -6) so plug in point into equation of p and get ?
y = 1/2 x +?
-6 =1/2(8) +?
-6 =4 + ? subtract 4 from both sides
-6-4 = ?
-10 = ?
y = (1/2) x -10
Karla has 3 gallons of paint. Bryant has 10 quarts of paint. How many more pints of paint does Karla have than Bryant?
Answer: 4
Step-by-step explanation:
First you need to convert to pints.
Your conversion factors are:
1 gallon = 8 pints
1 quart = 2 pints
[tex]3gallons(\frac{8pints}{1gallon}) =24pints[/tex]
[tex]10quarts(\frac{2 pints}{1quart})=20pints[/tex]
To find the difference, subtract.
24-20=4
Question 1
Write x2 + 4x – 3x3 + 6 in standard form.
a) – 3x3 + 4x + x2
b) x2 – 3x3 + 4x + 6
c) –3x3 + x2 + 4x + 6
d) 6 + 4x – 3x3 + x2
Answer:
-3x^3 + x^2 + 4x +6
Answer is C
Step-by-step explanation:
Answer: -3x^3 + x^2 + 4x +6
Answer is C
Step-by-step explanation:
How many seconds would it take to fill up one gallon
Answer:
5 seconds
Step-by-step explanation:
(60 / seconds = GPM)
60 / 5 = 12 GPM
12 GPM = 60 seconds
Simplified
1 Gallon is 5 seconds
Answer:
5
Step-by-step explanation:
Find the distance between (-10,12) and (-6,-14). Round to the nearest hundredth
Answer:
26.31 units
Step-by-step explanation:
Given: Points [tex](-10,12),(-6,-14)[/tex]
To find: Distance between the given points
Solution:
Let [tex](x_1,y_1)=(-10,12)\,,\,(x_2,y_2)=(-6,-14)[/tex]
The distance formula is used to find the distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex]
According to distance formula,
Distance = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{(-6+10)^2+(-14-12)^2}\\ =\sqrt{16+676}\\ =\sqrt{692}\\ =26.31[/tex]
So, distance between the given points is 26.31 units
What is the number of possible permutations of 5 objects taken 2 at a time? A. 10 B. 20 C. 60 D. 120
Answer:
B. 20
Step-by-step explanation:
5P2 is equal to 20 using the permutation formula.
What is the measure of angle A?
Answer:
A = 19.47
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
sin theta = opp / hypotenuse
sin A = 2/6
Take the inverse sin of each side
sin ^-1 ( sin A) = sin ^-1 (2/6)
A =19.47122063
To the nearest hundredth
A = 19.47
What’s the correct answer for this?
Answer:
B
Step-by-step explanation:
In the attached file
What is the value of x in the equation 0.7x -1.4 = -3.5?
-7
x
-3
Answer:
–3
Step-by-step explanation:
i got 90% on my quiz also may i pleas get brainliest
how many tenths are in 4600
Answer:
4600 tenths as a Fraction
Since 4600 tenths is 4600 over ten, 4600 tenths as a Fraction is 4600/10.
4600 tenths as a Decimal
If you divide 4600 by ten you get 4600 tenths as a decimal which is 460.00.
4600 tenths as a Percent
To get 4600 tenths as a Percent, you multiply the decimal with 100 to get the answer of 46000 percent.
4600 tenths of a dollar
First we divide a dollar into ten parts where each part is 10 cents. Then we multiply 10 cents with 4600 and get 46000 cents or 460 dollars and 0 cents.
Step-by-step explanation:
Hope this helped!
Stay safe!!!
Answer:
Step-by-step explanation:
To answer this, multiply 4600 by 10: 46000. There are 46000 tenths in 4600.
