Answer:
A 99.9% confidence interval for the population mean is [22.31, 59.91] .
Step-by-step explanation:
We are given the following sample values;
X = 45.3, 42.3, 53, 49, 15.2, 52.3, 45.6, 39.6, 39.4, 16.1, 54.4.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean = [tex]\frac{\sum X}{n}[/tex] = 41.11
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex] = 13.59
n = sample size = 11
Here for constructing a 99.9% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 99.9% confidence interval for the population mean, [tex]\mu[/tex] is;
P(-4.587 < [tex]t_1_0[/tex] < 4.587) = 0.999 {As the critical value of t at 10 degrees of
freedom are -4.587 & 4.587 with P = 0.05%}
P(-4.587 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 4.587) = 0.999
P( [tex]-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.999
P( [tex]\bar X-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.999
99.9% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-4.587 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+4.587 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]41.11-4.587 \times {\frac{13.59}{\sqrt{11} } }[/tex] , [tex]41.11+4.587 \times {\frac{13.59}{\sqrt{11} } }[/tex] ]
= [22.31, 59.91]
Therefore, a 99.9% confidence interval for the population mean is [22.31, 59.91] .
Eli has 7 games on his phone. His sister has 6 more than him. Which ratio compares the number of games on Eli’s phone to the number of games on his sister’s phone?
a. 6:13
b. 7:13
c. 6:7
d. 7:6
Answer:
B: 7:13
Step-by-step explanation:
Answer:
7:13
i get it correct on the work sheet
An equilateral triangle measures 3 1/2 inches on one side.what is the perimeter of the triangle
Answer:
10.5 inches
Step-by-step explanation:
Equalilateral triangle means all the 3 sides are equal
So perimeter of equilateral triangle=3(side)
=>3(3.5)
=>10.5
Customers at a certain pharmacy spend an average of $54.40, with a standard deviation of $13.50.What are the largest and smallest amounts spent by the middle 50% of these customers?
Answer:
Largest is [tex]x_2 = \$ 63.506[/tex]
Smallest is [tex]x_1 = \$ 45.29[/tex]
Step-by-step explanation:
From the question we are told that
The mean is [tex]\mu = \$ 54.40[/tex]
The standard deviation is [tex]\sigma = \$ 13.50[/tex]
The largest and the smallest amount spent by 50% of the costumer is mathematically represented as
[tex]P(x_1 < X < x_2) = P(\frac{ x_1 -\mu}{\sigma } < \frac{X - \mu }{ \sigma } < \frac{ x_2 -\mu}{\sigma } ) = 0.50[/tex]
=> [tex]P(x_1 < X < x_2 ) = P(\frac{x_1 - 54.40}{ 13.50} < X < \frac{x_2 - 54.40}{ 13.50} ) = 0.50[/tex]
Given that this is normally distributed we have that
[tex]P(X <- \frac{x_1 - 54.40}{ 13.50} ) = 0.25[/tex]
and
[tex]P(X < \frac{x_2 - 54.40}{ 13.50} ) = 0.25[/tex]
From the normal distribution curve that z-score having a probability of 0.25 is
0.6745
So
[tex]\frac{x_1 - 54.40}{ 13.50} = -0.6745[/tex]
=> [tex]x_1 = \$ 45.29[/tex]
and
[tex]\frac{x_2 - 54.40}{ 13.50} = 0.6745[/tex]
=> [tex]x_2 = \$ 63.506[/tex]
If 50 percent of the families in a certain city subscribe to the morning newspaper, 65 percent of the families subscribe to the afternoon newspaper, and 85 percent of the families subscribe to at least one of the two newspapers. What percentage of the families subscribe to both newspapers?
Answer: 30%
Step-by-step explanation:
Given, Percent of families subscribe to the morning newspaper = 50%
Percent of families subscribe to the afternoon newspaper = 65%
Percent of families subscribe to at least one of the two newspapers. = 85%
Now, percentage of the families subscribe to both newspapers = % for morning newspaper + % for afternoon newspaper - % for at least one of the two newspapers
= (50+65 - 85) %
= 30 %
Hence, the percentage of the families subscribe to both newspapers = 30%
please helppppppppp meeeeee
Answer:
2 1/4
Before Simplifying:
9/4
After Simplifying:
2 1/4
Answer: the exact form is 9/4 decimal form is 2.25 and the mixed number form is 2 and 1/4.
Step-by-step explanation:
so take 9/10 and turn 4/10 into 10/10 and the when you divied use KFC and you turn your division sign into a multiplication sign then you just multiply 9/10 and 10/10 and you get 90/40
Then you just take the zero's off and you have 9/4 which equals 2 and 1/4
2 and 1/4 is your answer.
please answer thank you!!
Answer:
C
Step-by-step explanation:
Distribute
-6x + 20 = 15
C
just distribute
hope it helps
At the store, Jason find the volume of a soda pack is 423.9 in.³. If each cylinder shaped can has a height of 6 inches and a diameter of 3 inches, how many soda cans are in a pack? (Use 3.14 for pi)
Answer : The correct option is, (A) 10
Step-by-step explanation :
First we have to calculate the volume of cylinder shaped can.
Formula used:
Volume of cylinder = π r² h
where,
r = radius of cylinder
h = height of cylinder
Given:
Diameter of cylinder = 3 in
Height of cylinder = 6 in
Radius of cylinder = [tex]\frac{Diameter}{2}=\frac{3in}{2}=1.5in[/tex]
Now putting all the given values in the above formula.
Volume of cylinder = π r² h
Volume of cylinder = 3.14 × (1.5 in)² × 6 in
Volume of cylinder = 42.39 in³
Now we have to determine the number of soda cans are in a pack.
Number of soda cans are in a pack = [tex]\frac{\text{Volume of soda pack}}{\text{Volume of cylinder shaped can}}[/tex]
Number of soda cans are in a pack = [tex]\frac{423.9in^3}{42.39in^3}[/tex]
Number of soda cans are in a pack = 10
Therefore, the number of soda cans in a pack are 10.
Jade receives total employment benefits that are 17.5% of her gross annual pay. If Mary has a gross annual pay of $60,500, how much in total job benefits does she receive?
A. $71,087
B. $81,087
C. $61,087
D. $51,087
Answer:
A. $71,087
Step-by-step explanation:
The name jade and Mary contradict each other, let's assume both jade and Mary refers to the same person
Jade receives job benefits of 17.5% of her annual gross pay
Jade has an annual gross pay of $60,500
how much in total job benefits does she receive?
Total job benefits received = 17.5% of $60,500 + $60,500
= (17.5 / 100 * 60,500) + 60,500
= (0.175 * 60,500) + 60,500
= 10,587.5 + 60,500
= $71,087.5
The rounded value closest to the answer in the option is $71,087
Officer Brimberry wrote 24 tickets for traffic violations last week, but only 9 tickets this week. What is the percent decrease? Give your answer to the nearest tenth of a percent Help me please
Amount of decrease: 24 - 9 = 15
Percent of decrease = (15 / 24) x 100
Percent = 62.5%
21+6x; x= -2 evaluate
Steps to solve
21 + 6x when x = -2
~Substitute
21 + 6(-2)
~Simplify
21 - 12
~Subtract
9
Best of Luck!
What number should be placed in the box to help complete the division calculation of 2635 divided by 17
Answer:
divided
Step-by-step explanation:
divided 26 goes into 17. than right your numder up tope. that is hoow you divited it is easy just try.
-5x² – 2x+10 - x² + 7x +5
Answer:
-6x² + 5x + 15
Step-by-step explanation:
Combine like terms. Like terms are terms with the same amount of variables.
Reorder based on descending powers:
-5x² - x² + 7x - 2x + 10 + 5
(-5x² - x²) + (7x - 2x) + (10 + 5)
(-6x²) + (5x) + (15)
-6x² + 5x + 15 is your answer.
~
f(x) = (2x + 1)(x - 2)(x + 3)
Answer:
f(3) = 42.
Y-intercept is (0, -6).
X-intercepts are (-0.5, 0), ( 2, 0) and (-3, 0).
Step-by-step explanation:
f(3) = (2(3) + 1)(3 - 2)(3 + 3)
= 7 * 1 * 6
= 42.
The y intercept occurs when x = 0:
y-intercept = (2(0) + 1)(0 - 2)(0 + 3)
= 1 *-2*3
= -6.
Calculate the x-intercepts:
(2x + 1)(x - 2)(x + 3) = 0 so
(2x + 1) = 0 or (x - 2) = 0 or (x + 3) = 0
So x = -0.5, 2 or -3.
If someone rode for 2 hours at 3 miles per hour, how far would they go?
Answer:
Six miles
Step-by-step explanation:
You multiply the two by the three (2x3) and get six (6)
I need help to find the slope of the line
what is 0.26 rounded to the nearest tenth.
Answer:.3
Step-by-step explanation: if it is 5 or above it rounds up
Please help!! Thanksss
Answer:
b
Step-by-step explanation:
complimentary which means both angles are the same and on the opposite sides of each other
im not sure if the explanation is correct but im pretty sure the answer is
WILL GIVE BRAINLIEST! Prove that a quadrilateral ABCD with vertices A(–1, –2), B( 2, –5), C(1, –2), and D( –2, 1) is a parallelogram. Find the point of intersection of the diagonals of parallelogram ABCD. Provide your complete solutions and proofs in your paper homework and enter the numeric answers online.
Answer:
(0,-2)
Step-by-step explanation:lol rsm hw
ok so just take average of two points (-1, -2) (1, -2)
-1+1=0/2=0
-2+(-2)=-4/2=-2
You can do this with B and D too
Have fun in rsm
10 − 2(22 + 1) ÷ 23
help me pls thanks
Answer:
8
Step-by-step explanation:
Help i dont understand pls help :(
Answer:
B. -2
Step-by-step explanation:
All you have to do is look at 2 on the x axis and see where it lines up on the graph with the y axis. In this case, when you trace the line of 2 it matches up with -2 on the graph.
what is the average rate of change
Answer:
The average rate of change between two input values is the total change of the function values (output values) divided by the change in the input values.
It is a measure of how much the function changed per unit, on average, over that interval.
evaluate 3 + 6 x 4 - 16/2
Answer:
19
Step-by-step explanation:
Find the volume of the solid shown or described. If necessary round to the nearest tenth. What is the volume of the shed?
Answer:
Volume of shed = 38 m³
Step-by-step explanation:
Given:
Length = 5 m
Width = 2 m
Height of wall = 3 m
Height of triangular shed = 1.6 m
Find:
Volume of shed
Computation:
Volume of shed = Volume of walls + Volume of triangular shed
Volume of shed = [lbh] + [1/2][Base area]h
Volume of shed = [(5)(2)(3)] + [1/2][(5)(2)]1.6
Volume of shed = [30] + [8]
Volume of shed = 38 m³
A nurse is preparing to administer dopamine 2 mcg/kg/min by continuous IV infusion for a client who weighs 110 lb. Available is dopamine
400 mg in 250 mL of D5W. The nurse should set the IV pump to deliver how many ml/hr administer? (Round the answer to the nearest
tenth.)
Answer:
3.7ml/hr
Step-by-step explanation:
From the question
A nurse is preparing to administer dopamine 2 mcg/kg/min by continuous IV infusion
Step 1
The patient weighs 110lb(pounds
Convert the patients weight to kilogram
1 lb = 0.454kg
110lb =
Cross Multiply
110lb × 0.454kg
= 49.94kg
The patient weight = 49.94kg
Step 2
The dosage to to be administered by the nurse = 2 mcg/kg/min
If 1 kg = to be administered 2mcg/min
49.94 kg =
(49.94kg × 2mcg/min)/1
= 99.88mcg/min
Therefore, for the patient's body weight, the patient's dosage = 99.88mcg/min
Step 3
Available dopamine is 400mg in 250ml
We have to convert this to mcg
Hence,
1 mg = 1000mcg
400mg =
Cross Multiply
= 400mg × 1000mcg
= 400000mcg
Hence, the available dopamine is administer in 250ml/400000mcg
Part 3
Since 60 minutes is 1 hour
The nurse should set the IV pump to deliver how many ml/hr
(99.88mcg/min × 250ml × 60mins)/ 400000mcg
= 3.7455ml/hr
Approximately to the nearest tenth = 3.7ml/hr
A Ferris wheel at a carnival has a radius of 38 feet. Suppose a passenger is traveling at 5 miles per hour. (A usual fact: 1 mi = 5280 ft).A) Find the angular speed of the wheel in radians per minute.B) Find the number of revolutions the wheel makes per hour.
Answer:
a
[tex]w = 11.58 \ rad/minutes[/tex]
b
[tex]R_h = 111 \ revolution\ per \ hour[/tex]
Step-by-step explanation:
From the question we told that
The radius of the wheel is [tex]r = 38 \ ft[/tex]
The speed of the passenger is [tex]v = 5 \ miles /hr = \frac{26400}{3600} = 7.33 \ ft / s[/tex]
Generally the angular speed is mathematically represented as
[tex]w = \frac{v}{r}[/tex]
=> [tex]w = \frac{7.3}{ 38}[/tex]
=> [tex]w = 0.193 \ rad/s[/tex]
now converting the seconds to minutes
[tex]w = 0.193 *60[/tex]
[tex]w = 11.58 \ rad/minutes[/tex]
Generally number of revolutions the wheel makes per minutes is mathematically represented as
[tex]R = \frac{11.58 }{2 \pi}[/tex]
[tex]R = 1.84 \ rpm[/tex]
Generally number of revolutions the wheel makes per hour is mathematically represented as
[tex]R_h = R * 60[/tex]
=> [tex]R_h = 1.84 * 60[/tex]
=> [tex]R_h = 111 \ revolution\ per \ hour[/tex]
At a convention there are 7 math instructors, 5 computer science instructors, 3 statistics instructors and 4 science instructors. If an instructor is selected at random, find the probability of selecting a math or science instructor. (Write your answer as a decimal, rounded to the nearest hundredth.)
Answer:
11/19
Step-by-step explanation:
By substituting in the values of the variables, complete the addition number sentence that corresponds to the diagram below,
Answer:
[tex] a + b + c = 5 + 6 + 11 = 22 [/tex]
Step-by-step explanation:
Variable "a" and "b" represents distances on the numberline.
Variable "c" is the combined distance of the values of variable "a" and variable "b" on the numberline.
a = length of red line = |5 - 0| = |5| = 5
b = length of blue line = |11 - 5| = |6| = 6
c = length of black line (red+blue) = |11 - 0| = |11| = 11
Therefore:
[tex] a + b + c = 5 + 6 + 11 = 22 [/tex]
One cup of yogurt contains 13 g of protein. Convert this to milligrams
Answer: 13000.00mg :) hope this helps
1/2 - 1/5
I don’t know how to do these problems
Answer: 3/10
Step-by-step explanation: Since our denominators of 2 and 5have no
factors in common, our least common denominator is 2 · 5 or 10.
In order to get a denominator of 10 in each fraction,
we multiply top and bottom of the first fraction by 5
and top and bottom of the second fraction by 2.
That gives us 5/10 - 2/10 which is 3/10.
A recipe for 24 cookies calls for 6 tablespoons of sugar. Which of the amounts below would be a correct ratio of cookies to sugar if you were to use the recipe?
Answer:
1:4
Step-by-step explanation:
0.25 tablespoons of sugar will be used per cookie
Answer:
4 cookies per tablespoon of sugar
Step-by-step explanation:
24 cookies divided by 6 tablespoons of sugar equal 4 cookies per tablespoon of sugar