Using the t-distribution, as we have the standard deviation for the sample, it is found that it can be concluded that the holes are being punched an average of 1. 84 cm.
What are the hypotheses tested?At the null hypotheses, it is tested if the mean is of 1.84 cm, that is:
[tex]H_0: \mu = 1.84[/tex]
At the alternative hypothesis, it is tested if the mean is different of 1.84 cm, that is:
[tex]H_1: \mu \neq 1.84[/tex]
What is the test statistic?The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\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.s is the standard deviation of the sample.n is the sample size.Considering the hypothesis and the given sample, it is found that the parameters are as follows:
[tex]\overline{x} = 1.85, \mu = 1.84, s = 0.0235, n = 12[/tex].
Hence, the test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{1.85 - 1.84}{\frac{0.0235}{\sqrt{12}}}[/tex]
[tex]t = 1.47[/tex]
What is the decision?Considering a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.1 and 12 - 1 = 11 df, the critical value is of [tex]|t^{\ast}| = 1.7959[/tex]
Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis and it can be concluded that the holes are being punched an average of 1. 84 cm.
More can be learned about the t-distribution at https://brainly.com/question/16313918
a binder normally costs $8.99. use this information to answer the questions below
Answer:
You are asking a question that cannot be solved by anyone outside of your school.
Step-by-step explanation:
What information is below?
3. How many 3 digit all even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
Step-by-step explanation:
Only 3 numbers are possible at units place (2, 4 & 6) as we need even number.
But at tens & hundreds place all 6 are possible
Number of 3 digit even numbers
= 3x6x6 = 108
36
Step-by-step explanation:[tex]Solution:[/tex]
[tex]6\times6=36[/tex]
[tex]such\ as:[/tex]
[tex]11\ \ \ 22\ \ \ 33\ \ \ 44\ \ \ 55\ \ \ 66\\ 12\ \ \ 21\ \ \ 31\ \ \ 41\ \ \ 51\ \ \ 61\\ 13\ \ \ 23\ \ \ 32\ \ \ 42\ \ \ 52\ \ \ 62\\ 14\ \ \ 24\ \ \ 34\ \ \ 43\ \ \ 53\ \ \ 63\\ 15\ \ \ 25\ \ \ 35\ \ \ 45\ \ \ 54\ \ \ 64\\ 16+263646+56\\ 6+6+6+6+6+6\\ =36.[/tex]
I hope this helps you
:)
In the image below, why must triangle A'B'C be similar to ABC?
(Don't mind the chosen answer)
Answer: Option (3)
Step-by-step explanation:
You can get 2 pairs of corresponding angles from the parallel segments, meaning that they are similar by angle-angle.
PLEASE HELP ME! AFCVGBHNJMK
The sum of two numbers is 27. One number is 2 times as large as the other. What are the numbers?
Answer:
9 and 18
Step-by-step explanation:
let the numbers be x and 2x
so that x+2x=27
3x=27
x=9
so the numbers are 9 and 18.
I hope this will help
Answer:
9 and 18[tex] \\ [/tex]
Step-by-step explanation:
It is given that, the sum of two numbers is 27 and one of the number is 2 times as large as the other.
[tex] \\ [/tex]
Let us assume the one number as x and as state in the question, one of the number is 2 times as large as the other (x) . So, the other number will be 2x .
[tex] \\ [/tex]
Now,
[tex] \\ {\longrightarrow \pmb{\sf {\qquad x + 2x = 27 \:}}} \\ \\[/tex]
Adding like terms we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad 3x = 27 \:}}} \\ \\[/tex]
Dividing both sides by 3 we get :
[tex]\\ {\longrightarrow \pmb{\sf {\qquad \frac{3x}{3} = \frac{27}{3} \:}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad {x} = {9} \:}}} \\ \\[/tex]
So,
One of the number is 9.[tex] \\ [/tex]
Now,
[tex] \\ {\longrightarrow \pmb{\frak {\qquad Other \: number = 2x \:}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad Other \: number = 2(9) \:}}} \\ \\[/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad Other \: number = 18 \:}}} \\ \\[/tex]
Therefore,
The two numbers are 9 and 18.Mr bean contributed 500 naira to a business, Mr. Benson contributed 300 naira, and Mr. Robinson contributed 200 naira. what is Mr bean's share if they share a profit of 2000 naira according to the amount each contributed
Answer:
Mr Bean will get 1000 naira.
Step-by-step explanation:
They invested in the ratio of 5:3:2 , meaning that Mr Bean will get half the profit. 1/2 X 2000 = 1000
A tank having length, breadth and height 10 m, 9 m and 8 m respectively. How much petrol does it hold? Ans: 720000 liter
720000 liter
Step-by-step explanation:[tex]Known:\ a=10\ m,b=9\ m,h=8\ m.[/tex]
[tex]Because:\ V=abh\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (Volume\ caculation\ formula)[/tex]
[tex]Thus:\ V=10\times9\times8=720\ m^3[/tex]
[tex]Because\ 1\ m^3=1000\ L\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (unit\ conversion)[/tex]
[tex]Thus\ 720\ m^3=720000\ L[/tex]
I hope this helps you
:)
what number is 0.1 more than 149.99
Answer:
150.09
Step-by-step explanation:
0.1 = 1/10 + 149.99= 150. the leftover of 0.09 then is finally added to 150 which then you get 150.09
Please mark brainliest!
Answer:
The answer should be 150.09
Step-by-step explanation:
Adding one tenth to 149.9 will equal 150. The remaining 0.09 will be added to 150 and the final answer is 150.09
Hope This Helps
Have A Great Day
~Zero~
Simon's dog jumped into
a stream at a 68° angle from the corner of a bridge. simon crossed the bridge and walked downstream to meet the dog
part a: how long is the bridge, in feet?
part b: how many feet did the dog swim?
The length of the bridge and the length the dog swam are 12.12 feet and 32.36 feet respectively
The problem forms a right angle triangle.
What is a right angle triangle?A right angle triangle has one of its angles as 90 degrees. The sides and angle can be found using trigonometric ratios.
Therefore, the length of the bridge and the length the dog swam can be calculated as follows:
tan 68° = opposite / adjacent
tan 68° = 30 / x
cross multiply
x = 30 / tan 68
x = 12.12 ft
length of the bridge = 12.12 ft
The length the dog swim is as follows:
sin 68°= opposite / hypotenuse
sin 68° = 30 / h
h = 30 / sin 68
h = 32.3561767942
The distance the dog swimmed = 32.36 ft
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Write an exponential function Y=ab^x for a graph that includes (-1.0,6) and (1, 15).
Answer: perimeter: 40.79
Area: 84
Step-by-step explanation:
perimeter: (√3² + 6²) + (√1² + 6²) + 7 + 6 + 6 + 9 = 40.79
area: ((9 + 6) x 6) / 2 + ((6 + 7) x 6) / 2) = 45 + 39 = 84
Help to solve the equation
Answer:
n = -1.25
Step-by-step explanation:
S(ABCD) = AB × AD
S(ABCD) = 2n × (4n + 5)
S(ABCD) = CD × AD
2n × (4n + 5) = CD × (4n + 5)
n = -1.25
PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)
Tim wants to buy soda. He can choose a 6-pack of 0.355-liter cans or a 2-liter bottle. Which statement is true?
A. The 6-pack contains 0.130 liters more soda.
B. The 2-liter bottle contains 0.130 liters more soda.
C. The 2-liter bottle contains 0.645 liters more soda.
D.The 6-pack contains 0.645 liters more soda.
The true statement is that the 6-pack contains 0.130 litres more soda.
He can choose a 6-pack of 0.355-liter cans or a 2-liter bottle.
6 pack of 0.355-liter cans. Therefore, let's establish the following proportion.
Proportional relationship1 pack = 0.355 litre can
6 pack = ?
cross multiply
volume of soda = 6 × 0.355 = 2.13 litres
The 6-pack of 0.355-liter cans contains 2.13 litres of soda.
difference = 2.13 - 2.00 = 0.13 litres
Therefore, the 6-pack contains 0.130 litres more soda
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y+2x=2 find the slope of every line perpendicular to the graph of the equation
Answer:
[tex]m_{perpendicular}[/tex] = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
y + 2x = 2 ( subtract 2x from both sides )
y = - 2x + 2 ← in slope- intercept form
with slope m = - 2
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-2}[/tex] = [tex]\frac{1}{2}[/tex]
please guys help me if u answer it correctly I will brainlist u
Answer:
1= 40, 25, 10
2= 9,375, 46,875, 234,375
3= 234, 729, 2,187
4= 192, 384, 768
The points 4,0 and 7,6 lie on a particular line, what is its equation in slope - intercept form?
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{6}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{7}-\underset{x_1}{4}}}\implies \cfrac{6}{3}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{2}(x-\stackrel{x_1}{4})\implies y = 2x-8[/tex]
the question is
on the image.
Answer:
PR = 7.99 cm (2 dp)
Step-by-step explanation:
Pythagoras' Theorem: a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
From inspection of the triangle:
a = PRb = PQ = 12.1 cmc = RQ = 14.5 cmSubstituting the given values into the formula;:
⇒ a² + b² = c²
⇒ PR² + 12.1² = 14.5²
⇒ PR² + 146.41 = 210.25
⇒ PR² = 210.25 - 146.41
⇒ PR² = 63.84
⇒ PR = ±√(63.84)
⇒ PR = ±7.99 (2 dp)
As distance is positive, PR = 7.99 cm (2 dp) only
She says that the coffee cup fountain actually holds about 400 gallons of coffee.
The newscaster claims that if the coffee fountain really broke, the 400 gallons of coffee would cover the
equivalent of half a city block.
You look up some information.
• One gallon of water covers about 13.8 square feet.
• Near the mall, an average city block is about 300 feet by 300 feet.
Assume the fountain holds 400 gallons of coffee. Using the information given, determine whether the
newscaster's claim is correct.
• Construct an argument that supports or refutes the newscaster's claim.
Include mathematics to support your argument.
https://www.perfection-events.com/content/back-basics-coffee-essentials
Since the area 400 gallons will cover, 5520 square feet is less than the area of half a city block which is 45000 square feet, the Newscasters claim is wrong.
What is the area of the city block?The area of the city block is calculated from the product of the dimensions provided:
The city block is in form of a square, hence it's area = side × side
Dimension of city block = 300 feet by 300 feet.
Area of city block = 90000 square feet
Half of area of city block = 45000 square feet
1 gallon covers 13.8 square feet
400 gallons will cover = 400 × 13.8 = 5520 square feet
The area 400 gallons of coffee will cover is less than 45000 square feet.
Therefore, the news caster's claim is wrong.
Learn more about area at: https://brainly.com/question/3948796
Elena drives for 3 hours at 44mph claire drives 144miles in 4 hours how far would elena travel if she drove for 3hours at the same speed as claire?
Answer:
108 miles
Step-by-step explanation:
144m/4h = 36m/1h or 36mph
36mph · 3 = 108m
Jim rented a truck for one day. there was a base fee for $19.95 and there was an additional charge of 91 cents for each mile driven. Jim had to pay $243.81 when he returned the truck. For how many miles did he drive the truck?
Answer:
Jim travelled 246 Miles.
Step-by-step explanation:
Pls help me!!! I need to find what b is??
Answer:
[tex]\frac{10 \sqrt{3} }{3} = b[/tex]
Step-by-step explanation:
Hi there!
We are given a right triangle (notice the right angle), one angle with a measure of 30° and another with 60°
We are also given that one of the legs (one of the sides that makes up the right angle) is 5
We want to find what b is
This triangle is a special right triangle, a 30-60-90 triangle
In a 30-60-90 triangle, if the hypotenuse (the side opposite from the right angle) is b, the leg that is opposite from the 30° angle is [tex]\frac{b}{2}[/tex], while the leg that is opposite from the angle that is 60° is [tex]\frac{b\sqrt{3} }{2}[/tex]
In this case, we're given that the side opposite from the 60 degree angle is 5, meaning that 5 is equal to [tex]\frac{b\sqrt{3} }{2}[/tex]
So we can set 5 equal to [tex]\frac{b\sqrt{3} }{2}[/tex], to solve for b:
5=[tex]\frac{a\sqrt{3} }{2}[/tex]
Multiply both sides by 2
5*2=b√3
10=b√3
Now divide both sides by √3
[tex]\frac{10}{\sqrt{3} } =b[/tex]
rationalize the denominator
[tex]\frac{10 * \sqrt{3} }{\sqrt{3} *\sqrt{3} }[/tex] = b
[tex]\frac{10 \sqrt{3} }{\sqrt{9}}[/tex]= b
[tex]\frac{10 \sqrt{3} }{3} = b[/tex]
The answer can be left as that.
Hope this helps!
Damian owns a small business selling bagels. he knows that in the last week 40 customers paid cash, 66 customers used a debit card, and 18 customers used a credit card.
if next week, he is expecting 300 customers, about how many would you expect to pay with cash? round your answer to the nearest whole number.
Sonia uses a 20% off coupon when she order from Uber eats original price of the order is $50 how much money does Sonya save
Answer:
she saves $40
Step-by-step explanation:
first of all, you find 20% of $50, that is,
(20/100) * $50
then you get: $10
next step is to subtract this answer from the $50, that is: $50 - $10 = $40
have a great day!!
We get the amount of price removed as a result of free coupon as below:
[tex] \frac{20}{100 } \times 50 = \frac{1000}{100} = 10 \\ coupon = 10dollars[/tex]
Therefore, Sonya saved $10
(b) The volume of water in a container is
directly proportional to the cube of its depth.
When the depth is 12 cm, the volume is 576 cm3.
Calculate
(i) the volume when the m is 1300 cm?. [2]
Answer:
See below.....Something is wrong with your question
Step-by-step explanation:
v = k d^3 or k = v/d^3 = 576/12^3 = 1/3
when depth (??? m??) is 1300 :
1/3 = v / (1300^3) = 732 333 333 .3 cm^3
help me with the dementions of this triangle
Answer:
20
Step-by-step explanation:
I'm not too sure why 22 is there. Triangle = (bh) / 2
90 x 2 = 180. 180 / 9 = 20, therefore, base is 20.
Answer:
First, we must know the formula for the area of a triangle.
A = BH x 1/2
Where 'b' represents the base, and 'h' represents the height.
Multiplying by 1/2 basically means dividing the result of (base x height) by 2.
Now we plug in what we know, given the dimensions shown.
We know that the area is 90 square units.
We also know that the height is 9, so;
A = BH x 1/2
90 = B(9) x 1/2
Solve for B:-
90 = 9b(we reverse b9 because they both serve as the same thing) x 1/2
90 = 9b x 1/2
Dividing by 1/2 also means multiplying by 2, so we multiply 2 to both sides to get rid of 1/2;
*2 *2
180 = 9b
To isolate b(base) we divide by 9 from both sides because the inverse operation of multiplication is division.
÷ 9 ÷ 9
20 = b, our base is 20 square units.
Please Help!!
Cherry Hill Orchards produced 500 tons of cherries during their first year of business, 2012. Since then, the cherry harvest continues to increase in production by 5. 7% over the previous year.
Write an exponential function, f(x), that models the tons of cherries produced by Cherry Hill Orchards x years after 2012.
Enter your answer by filling in the boxes.
f(x)= -------- * ( )^x
Answer:
[tex]f(x)=500*(.057)^x[/tex]
Step-by-step explanation:
Tom had 90 cookies and sold 60% of them.scott had 150 cookies and sold 2/3 of them.dawn sold 46 cookies.what percentage of the cookies sold were sold by dawn?
Answer:
Step-by-step explanation:
Tom: 90 cookies total 60% were sold
Tom: 90 * 60/100 = 54 cookies
Scott: 150 cookies and 2/3 were sold
Scott: 150 * 2/3 = 300/3 = 100
Dawn: sold 46 cookies
Total Sold = 46 + 100 + 54
Total Sold = 200
Answer
Dawn: % = (46 / 200) * 100 = 23%
Which of the following functions represents an exponential decay with a 15% rate of change where A represents the initial value and x represents time in years
The function that represent this exponential decay is given as y = A(0.85)ˣ
What is an exponential function?
An exponential function is in the form:
y = abˣ
Where a is the initial value and b is the multiplication factor.
Given that A is the initial value, there is a decay of 15%, hence:
b = 100% - 15% = 0.85
The function that represent this exponential decay is given as y = A(0.85)ˣ
Find out more on exponential function at: https://brainly.com/question/12940982
helppppppppppppppppppppppp
Answer:
0.13m
Step-by-step explanation:
1m = 100cm
0.13m = 13cm
Answer:
0.13 meters
Step-by-step explanation
In metric measures the conversion from meters to centimeters is
1 meter = 100 centimeter
because centi means one hundredth and meter means the unit meter.
Therefore, 1 cm = 0.01 meter. Now you just multiply 13 on both sides and you get 13 cm = 0.13 meters
Circle A has a radius of 9.0 cm. The shortest distance between B and C on the circle is 8.5 cm. What is the approximate area of the shaded portion of circle A?
30.0 cm²
38.25 cm²
56.5 cm²
254.5 cm²
Answer:
38.25 cm²
Step-by-step explanation:
We use the formula for the length of an arc to find the central angle of the sector of the circle.
Then we use the formula for the area of a sector of a circle to find the area.
Length of arc of circle of radius r:
[tex] s = \dfrac{n}{360^\circ}2 \pi r[/tex]
s = arc length
n = measure of the central angle of the sector
[tex] s = \dfrac{n}{360^\circ}2 \pi r[/tex]
[tex] 8.5~cm = \dfrac{n}{360^\circ}2 \pi \times 9.0~cm[/tex]
[tex] n = 54.1^\circ [/tex]
Area of sector of circle of radius r:
[tex] A = \dfrac{n}{360^\circ} \pi r^2[/tex]
A = area of sector of circle
n = measure of the central angle of the sector
[tex] A = \dfrac{54.1^\circ}{360^\circ} \pi (9.0~cm)^2[/tex]
[tex] A= 38.25~cm^2 [/tex]
The nth term of a sequence is n2 + 5 (a) (i) Find the first two terms of this sequence. (ii) Is 126 a term of this sequence? You must show how you get your answer
Answer:
126 is a term in the sequence. Please check my assumption on the correct formula.
Step-by-step explanation:
I will assume that n2 + 5 is actually n^2 + 5.
Starting with n=0, use the formula to calculate successive values of n. The attached table is the result of n from 0 to 22. At n=11, the result is 126, so 126 is a term in the sequence.
If the expression is actually n2 + 5, calculate the values for y = 2n + 5. 126 would not be a term in this sequence.
So what are the chances of getting a 100% effort out of someone who never tries than someone who does??
Answer:
someone who doesn't try would have a lower chance of 100% effort and someone who dose try would have a much higher chance of 100% effort
Step-by-step explanation:
i hope this helps!!