Using the z-distribution, it is found that since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.
At the null hypothesis, it is tested if the mean length of jail time is still of 2.5 years, that is:
[tex]H_0: \mu = 2.5[/tex]
At the alternative hypothesis, it is tested if it has increased, that is:
[tex]H_1: \mu > 2.5[/tex]
We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. [tex]\sigma[/tex] is the standard deviation of the sample. n is the sample size.For this problem, the values of the parameters are: [tex]\overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26[/tex]
Hence, the value of the test statistic is:
[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}[/tex]
[tex]z = 1.7[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, is of [tex]z^{\ast} = 1.645[/tex]
Since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.
A similar problem is given at https://brainly.com/question/24166849
Solving Equations Using Distributive Property 6(x - 3) = 36
Answer:
x=9
Step-by-step explanation:
Expand bracket
6x-18=36
Bring -18 to other side
6x=36+18
Add them
6x=54
Bring 6 to other side
x=54/6
Divide them
x=9
The fuel capacity of a popular hybrid car is 11.9 gallons. The function for this situation is f(x) = -0.02x + 11.9, where x represents miles and f(x) represents the amount of fuel remaining. What is the rate of change for this scenario?
Answer:
-0.02 gallons per mile
Step-by-step explanation:
You're in luck. The fuel consumption of the car is linear, and the slope - ie, the coefficent of the x term gives you the rate of change. In this case, it's -0.02 gallons per mile.
Calculate the slope of the line for Graph C.
Answer:
[tex]- \frac{5}{4}[/tex]
Step-by-step explanation:
Use the slope form:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
m = slope
Let:
[tex](x_1 , y_1) = (-2 , -8)\\(x_2 , y_2) = (-6 , -3)[/tex]
Plug in the corresponding numbers to the corresponding variables, and solve:
[tex]m = \frac{-3 - (-8)}{-6 - (-2)} = \frac{-3 + 8}{-6 + 2} = \frac{5}{-4} = -\frac{5}{4}[/tex]
[tex]- \frac{5}{4}[/tex] is your answer.
Help,
Is the following triangle acute, obtuse, or a right triangle
Answer:
Right-as long as it has one right angle it is a right triangle. It actually can't have more than one right angle.
Step-by-step explanation:
Find the exact length of EC.
Answer:
[tex]\sqrt{246}[/tex]
Step-by-step explanation:
The scale factor is [tex]\frac{4\sqrt{138} }{\sqrt{138}}[/tex] = 4
If AB = 6[tex]\sqrt{3}[/tex] then AC = 24[tex]\sqrt{3}[/tex] 4 times longer.
Using a² + b² = c² substitute a = 4[tex]\sqrt{138}[/tex], b = 24[tex]\sqrt{3}[/tex], and c = DC = x
[tex](4\sqrt{138})^2 + (24\sqrt{3} )^2= x^2[/tex]
2208 + 1728 = x²
3936 = x²
[tex]\sqrt{3936} = x[/tex]
4[tex]\sqrt{246[/tex] this is the length of DC
Now the length of EC is 4 times shorter, so EC = [tex]\sqrt{246}[/tex]
For reviewing purposes
Answer:
(25-16)/9=
=9/9=1 because 5^2 is 25 and 3^2 is 9 (5x5)/(3x3)
How does this image help you understand why the French surrendered to the Prussians?
Answer:
It's hard.
Step-by-step explanation:
Answer:
Step-by-step explanation:
If you look carefully at the diagram, it looks like the French have no way out. The Prussians are on the outside perimeter and can always get supplies into their position. Since they are completely surrounded, the French do not enjoy that luxury.
Furthermore (and I'm guessing here) the Prussians probably outnumbered the French. Now it is possible to get around that problem, but not terribly likely if the numbers are really lopsided.
Large boxes weigh 75 pounds, and small boxes weigh 40 pounds. a. Write an inequality that represents the numbers of large, x , and small, y, boxes a 200-pound delivery person can take on the elevator.
The inequality that represents the numbers of large, x and small, y boxes of a 200 pound delivery person is; 75x + 40y ≤ 200
Weight of large boxes = 75 pounds
Weight of small boxes = 40 pounds
Number of large boxes = x
Number of small boxes = y
Thus;
Total weight of large boxes = 75x
Total weight of small boxes = 40y
If the delivery man has 200 pound weight to deliver, then inequality is;
75x + 40y ≤ 200
Read more about Inequalities at; https://brainly.com/question/24966055
grace was born in 1995. how old will she be in 2027
Answer:
12
Step-by-step explanation:
2007 - 1995
Naomi’s recipe for baked beans calls for 715 cup of kidney beans. Each can of kidney beans holds 145 cups. How many cans of kidney beans will Naomi use to make the recipe?
Answer:
5 Cans
Step-by-step explanation:
Hoped this helped.
Use the following function rule to find f(1).
f(x) = 8^x+7
f(1) =
Given the function [tex]f(x)=8^x+7[/tex], the value of f(1) is f(1) = 15
The given function is:
[tex]f(x)=8^x+7[/tex]
To find f(1), substitute x = 1 into f(x) and evaluate for the result
[tex]f(1)=8^1+7[/tex]
Simplify the resulting equation to get the final result
f(1) = 8 + 7
f(1) = 15
Therefore, given [tex]f(x)=8^x+7[/tex], the value of f(1) is f(1) = 15
Learn more here: https://brainly.com/question/25747693
James threw a flying disk from a height of 4 feet above the ground. The disk travels a horizontal distance of 30 feet before falling to the ground. the height of the disk, in feet, at a distance of x feet from james, is modeled on the graph.
the domain represents the _____ the flying disk. The range of this function is [___, ___]. for this function, the range represents the flying disk’s _________
Answer:
the domain represents the horizontal flying of the disk. The range of this function is [0, 7]. For this function, the range represents the flying disk's possible heights
I just need answers ;-;
Answer:
1. 5⁴
2. d¹⁰
3. w⁶
Round 2,861 to the nearest hundred
Hey there!
2,891
= 200,000 + 800 + 90 + 01
= two-hundred thousand, eight hundred ninety one
Thousand:
2,000
Hundred:
900
Tens:
90
Ones:
1
Based on that information we can answer your question
SIMPLIFY IT
ANSWER: 2,900
[2,000 + 900 + 0 + 0]
[two thousand + nine hundred]
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
Karen saw a laptop for sale in 2004.
In March 2005, the price of this laptop was reduced 20%.
In June 2005, the price of this laptop was reduced by one sixth of the March 2005 price.
Compared with the 2004 price, what percentage discount would Karen obtain by buying this laptop in June 2005?
Answer:
Step-by-step explanation:
Let X be the initial price in March 2004.
Let X' be the price for March 2005.
Let X" be the price for June 2005.
March 2005: The price was reduced by 20%. Thus, X' = 0.8X
June 2005: The price was reduced by 1/6 of the March 2005 price: Thus,
X" = X' - (1/6)X'
Substituting, we have X" = (0.8X) - (1/6)(0.8X)
X" = (0.8X) - (1/6)(0.8X)
X" = (0.8X) - (0.1333X)
X" = 0.6667X
The June 2005 price is 0.6667 of the 2004 price. That's a (1-0.6667) or 33.33% reduction.
Nathan earned $105.70 at his job when he worked for 7 hours. What was his hourly wage, in dollars per hour?
100 IF U GET THIS RIGHT!
Answer:
y-intercept: 3/7
Step-by-step explanation:
Our equation: y = mx + b
Given equation: y = 6x + 3/7
Now, let's compare:
y = mx + b = y = 6x + 3/7
We can tell that the y intercept is b, which is 3/7
Hoped this helped.
Answer:
y-intercept: 3/7
Step-by-step explanation:
plss answer it correctly...I need asap
Answer:
sorry I cannot understand that
Your family went out to dinner. They spent $60.45 on dinner, 7% tax, and on top of both costs they left an 18% tip. How much total did her family pay for dinner?
Answer:
The answer is $75.56 total for the family payings.
Step-by-step explanation:
First I added the percentages up together which is now 25% you might ask me why I did that well it's because it's asking us the total of the payings in percentages so that's why I did that, next I used percentage calculations which is 25% of 60.45 and got the answer $15.11 which is the tax+ the tip now we just add 60.45 and 15.11 and that's how I got $75.56! Hope I helped if I did please mark brainliest it means a lot to my progression! Thanks <3
Jack estimates that a piece of wood measures 4.5 cm. If it actually measures 4.72 cm, what is the percent error of Jack’s estimate? (Show all of your work)
Answer:
ion
Step-by-step explanation:srry
Plant A Plant B WeeksHeight (inches) WeeksHeight (inches) 06 04 28 27 Part A To graph the two linear relationships, you need to know which variable is the independent variable, x, and which is the dependent variable, y. Of the two variables, weeks and height, which is the independent variable and which is the dependent? Explain your answer.
Answer:
Weeks is the independent variable and height is the dependent variable.
Step-by-step explanation:
The height of the plant depends on the weeks the plant has been growing. So the height is the dependent variable. Because the number of weeks doesn't depend on anything, the number of weeks is an independent variable.
you have 20 quaters you find 40% more in your room then you go shopping and spend 50% of the total number of quarters
Answer:
you would have 14 quarters left.
What does a residual value of â€""0. 8 mean in reference to the line of best fit?.
Residuals are used to determine how the line of best fit relates to the data points
A residual value of -0.8 means, the point is 0.8 units above the line of best fit
The residual value is given as:
[tex]\mathbf{Residual = -0.8}[/tex]
When the residual value is less than 0 (i.e. negative), then the point is above the line of best fit.
So, the interpretation of a residual value of -0.8 is that, the point is 0.8 units above the line of best fit
Read more about residuals at:
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what is 24x + 4 = 52
Answer:
x=2
Step-by-step explanation:
24x=48, x=2 (subtract 4 from both sides)
Answer:
[tex]\bf 24x+4=52[/tex]
[tex]\bf 24x+4-4=52-4[/tex]
[tex]\bf 24x=48[/tex]
[tex]\bf \cfrac{24x}{24}=\cfrac{48}{24}[/tex]
[tex]\boxed{\bf x=2}[/tex]
⊱ ────── {.⋅ ✯ ⋅.} ────── ⊰
Yasmine is making party favors for her birthday party. She has 2/5 meter of yarn to make
bracelets for 5 people. How much of a meter can Yasmine use for each bracelet?
Write out the problem. Then create a model to represent the quotient.
Answer: 0.5 hope this helps if not i'm sorry
The graph below represents the path of a squirrel traveling up and down a tree over time.
The position of the squirrel can be calculated using the function p (t) = at? + b + c.
What is the value of a?
What is the value of b?
What is the value of c?
Answer:
a= -1
b= 7
c= 0
Step-by-step explanation:
equation is
y=h(x)(x-7)
let x be 5 and y be 10 to solve for a
10=h(5)(5-7)
10=h(-10)
h=-1
now equation is
y= -x²+7x
so a=-1
b=7
c=0
The value of a is -1, the value of b is 7 and the value of c will be equal to zero.
What is an expression?Mathematical actions are called expressions if they have at least two terms that are related by an operator and include either numbers, variables, or both.
Adding, subtraction, multiplying, and division are all reflection coefficient operations. A mathematical operation such as reduction, addition, multiplication, or division is used to integrate terms into an expression.
As per the data provided in the question,
y = h(x) × (x-7)
let x be 5 and y be 10 to solve for a
10=h(5) × (5-7)
10 = h(-10)
h = -1
now equation is
y = -x²+7x
So,
a = -1
b = 7
c = 0
To know more about expression:
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1. Susan completed her journey of running in 10 minutes. If she ran 85 miles, how many
minutes did she run in one minute?
Answer:
850 this what I think it is
Step-by-step explanation:
that's what I think I don't know if that's the right answer
Answer:
8.5
Step-by-step explanation:
divide 10 by 10 to get to 1
divide 85 by 10 and u get 8.5
1=8.5
Find the unit rate to 30 1/2 and 1 1/4
Answer:
24.4
Step-by-step explanation:
yw
How can coordinate proof be used to show segments are congruent?
Answer:
The coordinate proof is a proof of a geometric theorem which uses ... and/or y -axis until it does.) To Prove: ¯XY is parallel to ¯PR and. XY=12PR. Proof:.
Help would be much appreciated! :)
Answer:
[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4} = x^2 + 5x - 4 + \frac{3x - 8}{x^2 + 5x - 4}[/tex]
General Formulas and Concepts:
Algebra I
Terms/Coefficients
ExpandingAlgebra II
Polynomial Division
Long DivisionSynthetic DivisionStep-by-step explanation:
Step 1: Define
Identify.
[tex]\displaystyle \frac{x^4 + 10x^3 + 25x^2 + 3x - 24}{x^2 + 5x - 4}[/tex]
Step 2: Long Division
See attachment.
Multiply quotient a and divisor, then subtract from dividend: [tex]\displaystyle x^2(x^2 + 5x - 4) = x^4 + 5x^3 - 4x^2 \leftarrow \text{red 1}[/tex]Multiply quotient b and divisor, then subtract from new dividend: [tex]\displaystyle 5x(x^2 + 5x - 4) = 5x^3 + 25x^2 - 20x \leftarrow \text{red 2}[/tex]Multiply quotient c and divisor, then subtract from new dividend: [tex]\displaystyle 4(x^2 + 5x - 4) = 4x^2 + 20x - 16 \leftarrow \text{red 3}[/tex]Write remainder: [tex]\displaystyle \frac{r(x)}{b(x)} = \frac{3x - 8}{x^2 + 5x - 4}[/tex]Please excuse the bad handwriting.