At 95% confidence, the z critical value is roughly z = 1.96
You would use a reference table or calculator to determine this value. Unfortunately it's not something that can be easily/quickly found by hand.
If we're trying to estimate the population mean (mu), then we'll use this margin of error formula
E = z*sigma/sqrt(n)
Or if we want to estimate the population proportion (p), then we use this formula
E = z*sqrt(phat*(1-phat)/n)
The confidence interval then spans from (pointEstimate)-E to (pointEstimate)+E. Where "pointEstimate" represents either xbar or phat depending on the context. Other point estimates are possible. We're focusing on these two for now.
xbar estimates mu
phat estimates p
--------------------------------
An example problem:
A manager at a soda bottling plant wants to know if the contents of the cans are 20 fluid ounces (fl oz) or not. Through past observations, the manager has noted the population standard deviation (sigma) is 1.72 fl oz.
The manager gathers a random sample of 50 cans to test their contents. They find the sample mean is 18 fl oz. Conduct a hypothesis test using a confidence interval at 95% confidence to see if the cans really do have 20 fl oz of drink in them or not.
--------------------------------
Solution:
Null Hypothesis: mu = 20
Alternate Hypothesis: mu ≠ 20
This is a two-tailed test.
E = margin of error
E = z*sigma/sqrt(n)
E = 1.96*1.72/sqrt(50)
E = 0.47676
L = lower boundary of confidence interval
L = xbar - E
L = 18 - 0.47676
L = 17.52324
L = 17.52
U = upper boundary of confidence interval
U = xbar + E
U = 18 + 0.47676
U = 18.47676
U = 18.48
The 95% confidence interval is approximately (17.52, 18.48)
This is equivalent to writing 17.52 < mu < 18.48 in which we are 95% confidence in saying mu is between those endpoints.
But wait, the hypothesized mu = 20 is not in the interval 17.52 < mu < 18.48, which indicates we must reject the null hypothesis and accept the alternate hypothesis.
The soda cans do not have 20 fl oz of drink. It appears they have slightly less than 20 fl oz.
A standard toilet uses 1.6 gallons per flush. If a toilet is flushed two times per day, how much water will be used in a week (7 days)?
Total Water Used by a standard flush in a week i.e. 7 days is 22.4 gallons.
What is Multiplication?
In mathematics, multiplying implies adding equal groups. The number of items in the group grows as we multiply.
Solution:
Given that,
The standard toilet uses 1.6 gallons of water per flush
Also, it is flushed twice a day
To Find, Total water used in a week i.e. 7 days
Since, flush uses 1.6 gallons water per flush
Total water used in a day is 2*1.6 = 3.2 gallons
This implies,
Total water used in 7 days = 7 * 3.2 = 22.4 gallons
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A student earned the scores in the data set in one course.
{88, 72, 68, 78, 94}
What is the mean of the scores?
Answer:
80
Step-by-step explanation:
the mean of a data set is calculated as
mean = [tex]\frac{sum}{count}[/tex] = [tex]\frac{88+72+68+78+94}{5}[/tex] = [tex]\frac{400}{5}[/tex] = 80
Need help please is do tomorrow
Answer: 39
Step-by-step explanation:
it starts at 11 and adds 7 everytime, assuming its linear (meaning it has a constant rate of change) u would add 7 to 32 to get your 5th value
Answer: y = 39
Step-by-step explanation:
Since the line is linear, the y increases 7 every time x increases 1
Add 7 to 32 and it equals 39
Help with question pleaae
The length of triangle AB is 22.5.
Triangle A = 7.5
Triangle B = 15
Whole = 22.5
As per the given question
Figure is made of 2 triangles.
Triangle A
Triangle B
9
7
As it is 2 triangles so
So A = 7.5
B = 15
The whole is = 15 + 7.5
=22.5
Each part is 7.5 and 15 respectively and whole is 22.5 per square unit.
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What is the equation of this graphed line?
Answer:
y = 2x + 2
Step-by-step explanation:
(y-y1)/(y2-y1)=(x-x1)/(x2-x1)
(y-6)/(-6-6)= (x-2)/(-4-2)
(y-6)/-12 = (x-2)/-6
y-6 = 2x-4
y = 2x -4 + 6
y = 2x + 2
ANSWER PLEASE!
Armando lost 975 coins playing his
favorite video game. He lost the same number of coins in each of the 15 levels he played. What was the change in Armando's coins at the end of each level of the game?
Answer: 81.25
Step-by-step explanation:
Answer:
Armando lost 65 coins each level.
Step-by-step explanation:
Given information,
→ Armando lost 975 coins playing his favorite video game.
→ He lost the same number of coins in each of the 15 levels he played.
Forming the equation,
→ 15x = 975
Now required value of x will be,
→ 15x = 975
→ x = 975/15
→ [ x = 65 ]
Hence, he lost 65 coins each level.
A store owner buys sweatshirts for $16 and marks them up 20% to make a profit. The sales tax where his store is located is 7.5%. A customer considers buying one or two sweatshirts from the store. Select all the statements that apply.
One sweatshirt before tax costs $19.20.
One sweatshirt before tax costs $12.80.
The sales tax for two sweatshirts is $1.92.
The sales tax for two sweatshirts is $2.88.
Total cost for two sweatshirts is $41.28.
Total cost for two sweatshirts is $27.52.
Answer: The correct statements are:
1 SS before tax costs $19.20
Sales tax for 2 SS is $2.88
Total cost for 2 SS is $41.28
Step-by-step explanation:
$16 x 1.20 = $19.20 cost before tax
$19.20 x 0.075 = $1.44 sales tax, one shirt
Sales tax for 2 shirts = $1.44 x 2 = $2.88
Total cost of a shirt = $19.20 + $1.44 = $20.64
Total cost for 2 shirts = $20.64 x 2 = $41.28
-
Which graph represents the function f(x) = |x] – 4?
Graph for the modulus function is as follows.
What is modulus function?
A modulus function is a function that determines a number or variable's absolute value.
Main body:
Given that,
Which graph represents the function f(x) = 4⌈x⌉?
Now,
to represent the graph of Y = IxI-4 .
So,
Taking x = 0, we get
Y = IxI -4
Y = I0I -4
Y = -4
Taking x = 1, we get
Y = IxI - 4
Y = I1I -4
Y = -3
Taking x = 2, we get
Y = IxI - 4
Y = I2I - 4
Y = -2.
Taking x = -1, we get
Y = IxI - 4
Y = I-1I - 4
Y = 1 -4
Y = -3
Taking x = -2, we get
Y = IxI - 4
Y = I-2I - 4
Y = -2
Hence the graph for the function is as follows.
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How to find x here if the perimeter, diagonal, and length is given?
Answer:
see explanation
Step-by-step explanation:
(a)
perimeter (P) is calculated as
P = 2(l + b) ← l is the length and b the breadth
given l = x and P = 20 , then
2(x + b) = 20 ( divide both sides by 2 )
x + b = 10 ( subtract x from both sides )
b = 10 - x
Using Pythagoras' identity in the right triangle
x² + (10 - x)² = 8²
x² + 100 - 20x + x² = 64 ( subtract 64 from both sides )
2x² - 20x + 36 = 0 ( divide through by 2 )
x² - 10x + 18 = 0 ← as required
(b)
solve using the method of completing the square
x² - 10x + 18 = 0 ( subtract 18 from both sides )
x² - 10x = - 18
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 5)x + 25 = - 18 + 25
(x - 5)² = 7 ( take square root of both sides )
x - 5 = ± [tex]\sqrt{7}[/tex] ( add 5 to both sides )
x = 5 ± [tex]\sqrt{7}[/tex]
Then
x = 5 - [tex]\sqrt{7}[/tex] ≈ 2.35 ( to 3 significant figures )
x = 5 + [tex]\sqrt{7}[/tex] ≈ 7.65 ( to 3 significant figures )
The box plot shows the times for sprinters on a track team.
(A horizontal number line starting at 40 with tick marks every one unit up to 59. The values of 42, 44, 50, 54, and 56 are all marked by the box plot. The graph is titled Sprinters' Run Times, and the line is labeled Time in Seconds.)
Which of the following lists the range and IQR for this data?
The five number from the box plot is presented as follows:
Minimum value: 42.First quartile: 44.Median: 50.Third quartile: 54.Maximum value: 56.What does a box-and-whisker plot shows?A box and whisker plot shows five things of a distribution, listed as follows:
The data set's lowest value.The value that 75% of the measures are larger than is found in the first quartile, which is the median of the data set's lowest 50% of measurements.
50% of the data set is less than the median and 50% is more than the median, which is the midpoint value of the data set.The third quartile, which is the median of the data set's top 50% of measurements, is the value that 75% of the measures fall below.The data set's maximum value.
These numbers, which make up the five number summary, are the values highlighted on the box plot from left to right, from the minimum value to the greatest value, passing through the first quartile, the median, and the third quartile.
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(-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)
Solution to the fraction (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9) = -38
How to solve fraction?Fractions are expressed in mathematics as a number value that defines a part of a whole or group of objects
To simplify the fraction into a simple form the following steps are followed;
Evaluate (-7 + 3) x 3² + ⅖ x (-1.1 - 3.9)
(-7 + 3) x 9 + ⅖ x (-1.1 - 3.9)
Add the numbers
(-4) x 9 + ⅖ x (-1.1 - 3.9)
Evaluate the exponent
(-4) x 9 + ⅖ x (-5)
Multiply the number
-36 + ⅖ x (-5)
-36 -10/5
Subtract the number from each other
-36 -10/5
=-36-2
Answer = -38
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8x + 16x - 12 = 24x- 12
Does the equation have one,
none, or infinite solutions?
Explain why.
Answer:
Infinite solutions
Step-by-step explanation:
The equation is,
→ 8x + 16x - 12 = 24x - 12
Let's solve for the value of x,
→ 8x + 16x - 12 = 24x - 12
→ 24x - 24x = -12 + 12
→ [ 0 = 0 ]
Hence, it has infinite solution. Because, all the real numbers are suitable.
Answer:
infinite number.
Step-by-step explanation:
Comment
There is only the same letter (x) on both sides of the equation. None of the xs are raised to any power. The power is 1 for all of them. That being so, there is only ONE solution.
x^2 + 5x + 6 would give 2 solutions because the x is raised to the second power.
x^3 + x^2 + 4x + 9 would give 3 solutions.
Solution
8x + 16x - 12 = 24x - 12 This equation is a little different. Both sides are exactly the same -- 24x - 12. That means that there is an infinite number of solutions.
For example let x = 10
The right side = 240 - 12 = 228
The left side = 8*10 + 16*10 - 12 = 228
You can't come up with a number that will make the left side unequal to the right side.
Pls help me need by today
The measure of the line AC is 15√3/2
The measure of the line BC is 15/2
What is a Triangle?Triangle ABC is the display style for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces.
One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs, Right triangles follow the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs of a right triangle (a2 + b2 = c2). Special right triangles have extra characteristics that simplify computations involving them. The 3-4-5 right triangle is one of the two most well-known.
Sin 60⁰=x/15
√3/2=x/15
x=15√3/2
The measure of the line AC is 15√3/2
Cos 60⁰= y/15
1/2=y/15
y=15/2
The measure of the line BC is 15/2
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What is the last digit of the number 4^2016?
Answer:
The last number is 4
Step-by-step explanation:
Hey so basically I'm having trouble understanding this problem so if someone can help me with the answer that'd be great thx <3
Two poles of heights 9 m and 14 m stand on a plane ground. If the distance between their feet is 12 m,
then what will be the distance between their tops?
Answer:
The distance would be 13m.
Answer:
13 m
Step-by-step explanation:
this can be looked at like a triangle sorry for the bad drawing I’m in the car lol
But we know the base is 12m and the height of this triangle is 5 since the secon pole is 5m taller hence 14-9=5
So we use the Pythagorean theorem
a^2+b^2=c^2
12^2+5^2=c^2
144+25=c^2
169=c^2
Now find the square root of 169 to get the answer
13 m is the distance between the tops
Hopes this helps please mark brainliest
HELPPPPP pleaseeeeeeeeeeeeeeeeeeeee
The ratio of teachers to students is 1 to 26. Find an equivalent ratio
Answer:
2:52
Step-by-step explanation:
Multiply by 2
what is the place value of digit 4 in 405799
What is the place value of digit 4 in 405,799:
4: one hundred thousandth place
0: ten thousandth place
5: one thousandth place
7: hundredth place
9: tens place
9: ones place
Answer:
100,000 thousand
Step-by-step explanation:
The number 405799 has six digits, and each digit has a specific place value based on its position within the number. The rightmost digit, which is 9, is in the one's place. Moving to the left, the next digit is 9 again, but this time it is in the ten's place. Continuing left, the next digit is 7, which is in the hundred's place. The digit 5 is in the thousand's place, and the digit 0 is in the ten thousand's place. Finally, the digit 4 is in the hundred thousand's place, so the place value of the digit 4 in 405799 is 100,000.
what is the total cost of cake option 1
Answer:
give me the question dude......
Step-by-step explanation:
Please help me with these sorry for how many there are
Answer: 19.2, 1.7, 15.93, 0.0512
Step-by-step explanation:
We can multiply these straight across but the trick with decimals is that your answer needs to have the same decimal place distance as what you are multiplying. In the first question, we go one decimal place. In the second, we go two decimal places. In the fourth, we go four decimal places.
Mr. Carson drove 1,027 miles in April. He drove 988 miles in May. Mr. Carson used the expression below to find how many more miles he drove in April than in May -> 1,027 - 988. How many more miles did Mr. Carson drive in April than in May?
Answer:
Mr. Carson drove 39 more miles in April than in May
Step-by-step explanation:
1027-988=39
The sUm of the measures
of the interior angles of
polygon is 2,880°. How
many sides does the
polygon have?
Q1) Reggie's annual salary increased from $43,400 to
$46,300 this year and his colleague Gerald's annual
salary increased from $39,970 to $43,720. Who received
a higher rate of increase this year?
Answer:
Gerald received the higher rate of increase
Step-by-step explanation:
7 The profit function, p(x), for a company is the
cost function, c(x), subtracted from the revenue
function, (x). The profit function for the
Acme Corporation is p(x) = -0.5x² + 250x - 300
and the revenue function is r(x) = -0.3x² + 150x.
The cost function for the Acme Corporation is
1) c(x) = 0.2x² - 100x + 300
2) c(x) = 0.2x² + 100x + 300
3) c(x) = -0.2x² + 100x - 300
4) c(x) = -0.8x² + 400x - 300
The cost function for the Acme Corporation is -0.2x² + 100x - 300. a cost function, transfers an event or the values of one or more variables onto a real number that signifies the event's "cost" in real terms.
How to find cost function ?A loss function, also known as a cost function, is a function used in mathematical optimization and decision theory that transfers an event or the values of one or more variables onto a real number that intuitively represents some "cost" connected to the occurrence. A loss function is the goal of an optimization problem.
The event in question is some function of the difference between the estimated and true values for a particular instance of data, and in statistics, parameter estimation is typically done using a loss function.
Given that the profit function is
p(x) = 0.5x^2 + 250x+300
also given that the revenue is given as
r(x) = 0.3x^2 + 150x
we know that profit= revenue - cost
hence cost = revenue-profit
cost = r(x) -p(x)
cost= 0.3x^2 + 150x-(0.5x^2 + 250x+300)
cost= 0.3x^2 + 150x-0.5x^2 - 250x-300
collect like terms
cost=0.3x^2-0.5^2+150x-250x-300
The cost function for the Acme Corporation = -0.2x^2-100x-300
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I need the answer quick
6x-5=6x+5 pls help me fast
Answer:
No solution
Step-by-step explanation:
6x - 5 = 6x + 5
6x = 6x + 10
0 = 10
0 cannot be equal to 10 at anytime, so this equation has no solution
Answer: No solution.
Step-by-step explanation:
Given:
6x - 5 = 6x + 5
Add 5 to both sides of the equation:
6x = 6x + 10
Subtract 6x from both sides of the equation
0 ≠ 10
Since 0 does not equal 10, there is no solution to this equation.
Which input value produces the same output value for the two functions on the graph?
f(x) equals negative StartFraction 2 Over 3 EndFraction x plus 1. g(x) equals StartFraction 1 Over 3 EndFraction x minus 2. A coordinate grid with two lines. One line labeled f(x) passes through (negative 3, 3), (0, 1), and point (3, negative 1). The second line is labeled g(x) and passes through (negative 3, negative 3), (0, negative 2), and point (3, negative 1).
x = –3
x = –1
x = 1
x = 3
An input value that would produce the same output value for the first functions on the graph is 0. Also, an input value that would produce the same output value for the second functions on the graph is 3.
How to determine the correct input value?In this exercise, you are required to determine the input value that would produce the same output value for the two functions on the graph. This ultimately implies that, the two functions would be equated as shown below.
From the information provided above, the two functions include the following:
f(x) = -2/3(x + 1)
g(x) = 1/3(x - 2)
Equating the two equations, we have:
f(x) = g(x)
-2/3(x + 1) = 1/3(x - 2)
-2x/3 -2/3 = x/3 - 2/3
-2x/3 - x/3 = - 2/3 + 2/3
x = 0.
For the second function on the graph, the coordinates are as follows:
f(x) = (-3, 3), (0, 1), (3, -1)
g(x) = (-3, -3), (0, -2), (3, -1)
Therefore, the above function produces the same input value (x) at point 3.
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Answer:
D
Step-by-step explanation:
edge 23
Determine if the line segment YX is tangent to circle Z.
The segment XY is a tangent to circle Z.
What is tangent to a circle?
Tangent to a circle is the line that touches the circle at only one point. There can be only one tangent at a point to circle. Point of tangency is the point at which tangent meets the circle.
To check the segment YX is tangent to circle z, first we have to check that the triangle formed XYZ is right angle triangle or not.
If the triangle XYZ is a right triangle, then we have
XY² +XZ² = YZ²
3.6² +2.7² = (1.8 +2.7)²
12.96 +7.29 = 20.25 it's true.
Therefore, the segment XY is a tangent to circle Z.
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Which is the best first step when solving the following system of equations?
x+y=3
4x-y=7
O Multiply the first equation by 4.
Add the first equation to the second equation.
Multiply the second equation by -1.
Subtract the second equation from the first equation.
The best first step to solve equations, x+y = 3 and 4x-y = 7, is to add the first equation to the second equation.
According to the question,
We have the following system of equations:
x+y = 3 .....(1)
4x-y = 7 ....(2)
Now, these equations can be easily solved by adding the first equation to the second equation because we will only then have one variable which is x and y when added to -y will result in zero.
We can solve these equations by adding as follows:
x-y+4x+y = 3+7
5x = 10
x = 10/5
x = 2
Now, we can put the value of x in equation 1 to find the value of y:
2+y = 3
y = 3-2
y = 1
Hence, the correct option is B.
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Which option shows an expression meaning 4 less than 5 times
a number?
You can earn 5 coins
4n-5
5n+ 4
5n-4
4n+5
Submit
Answer: 5n - 4
Step-by-step explanation:
n is the number, 5 times the number is 5n. 4 less means subtract 4. So the correct expression is 5n - 4