Answer:
The 90% confidence interval is [tex] 87.95 < \mu < 92.05 [/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 28[/tex]
The sample mean is [tex]\= x = 90[/tex]
The standard deviation is [tex]s= 60[/tex]
Generally given that the sample size is not large enough i.e n < 28 then we will make use of the t distribution table
Generally the degree of freedom is mathematically represented as
[tex]df = n- 1[/tex]
=> [tex]df = 28 - 1[/tex]
=> [tex]df = 2 7[/tex]
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.10[/tex]
Generally from the student t distribution table the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of [tex]df = 2 7[/tex] is
[tex]t_{\frac{\alpha }{2} , 27 } = 2.052[/tex]
Generally 95% confidence interval is mathematically represented as
[tex]\= x -E < \mu < \=x +E[/tex]
=> [tex]90 - 2.052 < \mu < 90 + 2.052 [/tex]
=> [tex] 87.95 < \mu < 92.05 [/tex]
Wilma is tiling her bathroom with tiles that measure 1 foot along each side. The bathroom is 15 feet long and 10 feet wide. She can lay 30 tiles per hour. Which of the following can be used to find the total number of hours it will take Wilma to cover the floor with tiles?
Answer:
(15 * 10) / 30 = x
Step-by-step explanation:
Since each tile is 1 foot on each side this means that each tile will cover 1 square foot (1ft * 1ft = 1sq. ft.). We would now need to find the square footage of the bathroom by multiplying the bathroom length by its width. Then we can divide that square footage by 30 tiles per hour to find out how long it will take to cover the floor with tiles.
(15 * 10) / 30 = x
150 / 30 = x
5 hours = x
Finally, we can see that at a pace of 30 tiles per hour, Wilma will be able to finish tiling her bathroom in 5 hours.
Mrs. Browning bought ice cream treats for 6 children. Each child picked either a sundae or a milkshake. The sundaes cost $2 each and the milkshakes cost $5 each. If Mrs. Browning spent a total of $21, how many of each type of treat did she buy?
Answer:
3 milkshakes 3 sundaes
Step-by-step explanation:
First write the equation.
y = total cost
x = cost of sundae
z = cost of milkshake
21=2x+5z
x+z=6 or x = 6-z
substitute in x = 6-z into the first equation
21 = 2(6-z) + 5z
21 = 12 - 2z + 5z
21 = 12 + 3z
subtract 12 from both sides
21 - 12 = 12 - 12 + 3z
9 = 3z
divide both sides by 3
3 = z
so she bought 3 milkshakes.
That means x+z = 6 and z=3 so
x+ 3 = 6, then x=3 as well, so she bought 3 sundaes.
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Answer:
she bought 3 sundaes and 3 milkshakes
Step-by-step explanation:
let's call the amount of milkshakes M.
let's call the amount of sundaes S.
you know that in total, there are 6 children.
so, you can make the following equation:
M + S = 6
if the milkshakes cost 5$ each, then the cost of the milkshakes can be expressed as 5m
if the sundaes cost 2$ each, then the cost of the sundaes can be expressed as 2S
you also know that Mrs. Browning spent 21$ in total.
so, you can make the following equation:
5m + 2S = 21
this is a system of equations.
using the first equation, you know that M = 6 - S
you can substitute M for 6 - S in the second equation
5m + 2s = 21
5(6 - s) + 2s = 21
30 - 5s + 2s = 21
30 - 3s = 21
30 = 21 + 3s
30 - 21 = 3s
9 = 3s
3 = snow that you know how many sundaes there are, you can substitute that into the first equation:
m + s = 6
m + 3 = 6
m = 6 - 3
m = 3The value of a car depreciates every year ata constant rate, Gary bought a car for $25,000 in the year 2013. If the value of the car is expected to depreciate 15% annually, what can Gary expect for the value of his car in the year 2017?
Answer:
Step-by-step explanation:
15×4(which is the difference in the year)=60%(this is the depreciation percent)
The value of the car in 2017=40/100×25000=$10000
In triangle $XYZ,$ $\angle Y = 45^\circ$ and $\angle Z = 60^\circ.$ If $XZ = 4,$ then what is $XY$?
[asy]
unitsize(3 cm);
pair X, Y, Z;
X = (0,1);
Y = (-1,0);
Z = (1/sqrt(3),0);
draw(X--Y--Z--cycle);
label("$45^\circ$", Y + (0.3,0.1), fontsize(10));
label("$60^\circ$", Z + (-0.2,0.1), fontsize(10));
label("$X$", X, N);
label("$Y$", Y, SW);
label("$Z$", Z, SE);
label("$4$", (X + Z)/2, NE);
[/asy]
Answer:
[tex]XY = 4.9[/tex]
Step-by-step explanation:
[tex]\angle Y = 45^\circ[/tex]
[tex]\angle Z = 60^\circ[/tex]
[tex]XZ = 4[/tex]
Required
Determine the length of XY?
This question is supported with the attachment.
To solve for the length of XY, we make use of the sine law which states:
[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} = \frac{sin\ C}{c}[/tex]
In this case:
[tex]\frac{sin\ \angle Y}{XZ} = \frac{sin\ \angle Z}{XY} = \frac{sin\ X}{YZ}[/tex]
Substitute in, the following values:
[tex]\angle Y = 45^\circ[/tex]
[tex]\angle Z = 60^\circ[/tex]
[tex]XZ = 4[/tex]
The expression becomes:
[tex]\frac{sin\ 45}{4} = \frac{sin\ 60}{XY}[/tex]
Cross multiply
[tex]XY * \sin\ 45 = 4 * \sin\ 60[/tex]
Make XY the subject
[tex]\frac{XY * \sin\ 45}{\sin\ 45} = \frac{4 * \sin\ 60}{\sin\ 45}[/tex]
[tex]XY = \frac{4 * \sin\ 60}{\sin\ 45}[/tex]
[tex]XY = \frac{4 * 0.8660}{0.7071}[/tex]
[tex]XY = \frac{3.4640}{0.7071}[/tex]
[tex]XY = 4.89888276057[/tex]
[tex]XY = 4.9[/tex] --- approximated
Answer:
XY = 4.9
Step-by-step explanation:
Que es un Monomi i un Polinomi?
Answer: Traducción Española
Polynomi es un término matemático que muestra la suma de monomios. Monomi es un problema matemático donde las variables y constantes pueden estar solas o multiplicarse.
Step-by-step explanation:
English translation:
Polynomi is a mathematical term that shows the sum of monomials. Monomi is a mathematical problem where variables and constants can stand alone or multiply.
Question
You flip a coin 10 times and get heads 6 times. Based on this experiment, what is the probability of flipping a coin and
getting heads?
Select the correct answer below:
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A biology student wants to determine if using a fertilizer would help promote the growth of new babies in spider plants. The student has access to 90 baby spider plants of three varieties: green, variegated, and curly. There are 30 plants of each variety. They all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. The numbers 1–30 are written on slips of paper, placed in a hat, and mixed thoroughly. A plant is selected and a slip of paper is drawn. If the slip has the numbers 1–15, then the plant will receive fertilizer. If the slip has the numbers 16–30, the plant will not receive fertilizer. A green spider plant is selected and a slip of paper is drawn. This plant is placed in the treatment group indicated by the number, and the slip is not put back in the bag. The slips are mixed again, the next green spider plant is selected, and a slip is drawn. The plant is placed in the treatment group indicated by the number. This procedure is repeated until all 30 green spider plants are assigned to treatments. The numbered slips are placed back in the bag and this procedure is repeated for the remaining types of spider plants. After one year, the shoots will be counted for each plant.
Which of the following best describes the design for this experiment?
observational study
matched pairs design
randomized block design
completely randomized design
Answer:
Randomized block design
Step-by-step explanation:
From the question, we can see the following:
- There are 30 plants of each variety. This means that they are divided into variety subgroups which we will call blocks.
- Now, we are told each plant in each block all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light. This means that each plant in each block is assigned a treatment condition.
- The procedure is repeated by subjecting each plant one after the other in teach Block to different treatments and this will reduce variability.
Looking at all the statements above, it is clear that this is a randomized block design because a randomized block design is when the experimenter/researcher divides members/participants into subgroups called blocks in a manner that the variability within the blocks is less than the variability between the blocks. Thereafter, the participants within each block will now be randomly assigned to treatment conditions.
The best describe about the design for this experiment is random block design.
A randomized block design is an experimental design where the experimental units are in groups called blocks. The treatments are randomly allocated to the experimental units inside each block.
When all treatments appear at least once in each block, we have a completely randomized block design.
There are 30 plants of each variety. This means that they are divided into variety subgroups which we will call blocks.
Each plant in each block all are potted in the same amount and type of soil, given the same amount of water, and exposed to the same amount of light.
This means that each plant in each block is assigned a treatment condition.
The procedure is repeated by subjecting each plant one after the other in teach Block to different treatments and this will reduce variability.
The statements above, it is clear that this is a randomized block design because a randomized block design is when the experimenter/researcher divides members/participants into subgroups called blocks.
In a manner that the variability within the blocks is less than the variability between the blocks. Thereafter, the participants within each block will now be randomly assigned to treatment conditions.
Hence, The best describe about the design for this experiment is random block design.
To know more about Random block design click the link given below.
https://brainly.com/question/20165310
The elves are loading all of the toys from Santa's workshop to the sleighs. They filled 2 small sleighs and 9 big sleighs with 241 toys. Later, they filled 14 small sleighs and 13 big sleighs with 437 toys. How many toys can fit on each type of sleigh?
Answer:
2*9=18 14*13=182 18+182=200
Step-by-step explanation:
well you multiply 2 times 9 and you get 18 and then you multiply 14 times 13 and you get 182 and then you 18+182 and that will give you 382.
A store bought a pair of shoes for $50 and sold it for $80. What percentage was the markup?
Must show work.
(Percent change = amount of change x 100 )
original amount
Correct answer get's brainliest) Just something to post
Answer: 60%
Step-by-step explanation: theres a $30 increase between the two prices. To find the percent change just take the difference of money over the original price. In this case it would be 30/50 or 60%
A system of equations is graft on the grid
Which system of equations does the graph represent?
A. y = x - 4
y = 0.5x – 2
B. y=-x+4
y= 0.52x + 2
C. y= -2 - 4
y=0.5x – 2
D. y= x +4
y = -0.5x + 2
Need help on number 2 plz I appreciate it thank you so much
Answer:
[tex] \angle PQR [/tex], [tex] \angle SQR [/tex], and [tex] \angle PQS [/tex]
Or
angle PQR, angle SQR and angle PQS
Step-by-step explanation:
The three different angles in the diagram are angle PQR, angle SQR and angle PQS.
Another way of writing this is using an angle sign before the alphabets follows. Thus:
[tex] \angle PQR [/tex], [tex] \angle SQR [/tex], and [tex] \angle PQS [/tex]
What is the equation of the following line? Be sure to scroll down first to see all the options
Answer:
A. y=5x
Step-by-step explanation:
A consultant for an association of personnel directors wants to find the proportion of clerical personnel that change jobs because they are bored with their work. The consultant queries a random sample of 400 clerical workers who recently changed jobs, 200 of which state that they changed jobs because they were bored. The consultant wishes to prepare a 95% confidence interval for the true proportion changing jobs because of boredom. What is the margin of error for this interval
Answer:
the margin of error for this interval is 0.049
Step-by-step explanation:
The computation of the margin of error for this interval is shown below;
Given that
n = 400
x = 200
Now
p = x ÷ n = 200 ÷ 400 = 0.5
Now the margin of error is
= [tex]z \times \sqrt{\frac{p(1-p)}{n}} \\\\1.96 \times \sqrt{\frac{0.5 \times 0.5}{400} }[/tex]
= 0.049
Hence the margin of error for this interval is 0.049
Can some one help me plz
Answer:
4h
2d
Step-by-step explanation:
How do I know if the function is a linear function?
Answer:
This is not a linear function.
Step-by-step explanation:
It is a quadratic function. If you were to make a table of the x and y values of the function it would look like this:
x y
0 -4
1 -1
2 8
Just by looking at these three values, we can see that they do not increase at a consistent rate. It increases by 3 from 0 to 1, but increase by 9 from 1 to 2. You can tell if a function is linear by seeing if it increases at a constant rate. (In this case it does not)
According to the scores on the last math test, 80%, or 20. of the students in the class received an A Find the number of students in the entire class.
Answer:
25 students
Step-by-step explanation:
.8x = 20
x = 25 students
A jar contains 24 blue marbles 16 red marbles and 14 white marbles find the simplified ratio of total marbles to red marbles
Answer:
27:2
Step-by-step explanation:
plz help mezzzzzaZzZzZzZzZzZ
Answer:
1/33Step-by-step explanation:
Typically you would want to solve this equation by dividing both sides by 3 but we need to find an equivalent equation that gives the same answer. 3 divided by 3 is the same as 3 times 1/3. Thus;
3x * 1/3 = 9 * 1/3
x = 3
Best of Luck!
Answer:
3
Step-by-step explanation:
3x = 9
= 3x/3 = 9/3
= 3
Distribute 2(-3x + 5)
Answer:
= −6x+10
Step-by-step explanation:
Answer:
-6x+10
Step-by-step explanation:
Multiply the 2 by each figure in the parenthesis. So, it becomes the sum of (2)-3x and 2(5), which is -6x+10.
Find the HCF and LCM of 28 and 40
Step-by-step explanation:
The HCF of 28 and 40 is 4, and the LCM is 280.
Step-by-step explanation:
this is the answer..........
Write the equation 8x - 5y = 20 in
slope intercept form.
Answer:
The equation in slope-intercept form is y = 8/5x-4.
I hope this helps! Have a nice day!!
Kendal bought x boxes of cookies to bring to a party. Each box contains 12 2 points
cookies. Someone else brought 24 cookies. Let 'y' represent the total
number of cookies at the party. Show an equation in SLOPE-INTERCEPT
FORM that models this situation. Kendal brings 60 boxes to the party. How
many cookies in total were at the party?
Answer:
744 cookies
Step-by-step explanation:
PLZ MARK BRAINLIEST ON THE TOP RIGHT CLICK THE CROWN.
Free fall reaches 216km per hour. What is rate in meters per second.? How many meters fall during 20 seconds free fall?
Given,
Rate of free fall = 216 km/h
Solution,
km/h to m/s is converted as follows :
[tex]216\ \dfrac{km}{h}=216\times \dfrac{1000\ m}{3600\ s}\\\\=60\ m/s[/tex]
So, the rate of fall is 60 m/s.
If t = 20 s
Assume, initial velocity = 0
It will move under the action of gravity.
Using equation of motion,
[tex]h=ut+\dfrac{1}{2}gt^2\\\\h=0+\dfrac{1}{2}\times 10\times 20^2\\\\h=2000\ m[/tex]
Hence, this is all for the solution.
express 25 as a power with base 5
Answer: 5
Step-by-step explanation:
Answer:
5^2 or 5 to the power of 2
Step-by-step explanation:
5x5=25
If 20 assemblers can complete a certain job in 6 hours, how long will the same job take if the number of assemblers is cut back to 12?
Given,
Total number of assemblers = 20
They work a job in 6 hours.
To find,
Time to complete the work if the number of assemblers is cut back to 12.
Solution,
Initially,
20 assemblers = 6 hours
1 hour = [tex]\dfrac{20}{6}[/tex] assemblers
If assemblers are 12 then,
[tex]t=\dfrac{20}{6}\times 12\\\\=40[/tex]
Hence, 40 hours will be required if the number of assemblers is cut back to 12.
Ali took five Math tests during the semester and the mean of his test score was 85. If his mean after the first three was 83, What was the mean of his 4th and 5th tests
Answer:
88
Step-by-step explanation:
Mean of five test = 85
Sum of five tests = 85*5 = 425
Mean of first three test =83
Sum of first three test = 83 * 3 = 249
Sum of 4th and 5th test scores = 425 - 249
= 176
Mean of his 4th and 5th test = 176/2 = 88
PLEASE HELP ME WITH THIS!! WRITE DOWN BELOW WHAT I CAN PUT INTO THIS QUESTION PLEASE! I WILL BE COPYING AND PASTING YOUR RESPONSE ONTO THE ANSWER BOX
nonpurchasers to total customer 37 and 13
CAN SOMEBODY PLEASE HELP ME!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
x-intercept=-2
y-intercept=3
It is known that the mean cholesterol level for all Americans is 190. Construct the relevant hypothesis test to show that only children have an average higher cholesterol level than the national average. We tested 100 children and find out the mean is 198. You can use your own confidence level. (All Americans Standard Deviation is 15)
Answer:
95% of confidence intervals are
(197.706 , 198.294)
Step-by-step explanation:
Explanation:-
Given sample size 'n'=100
Mean of the sample x⁻ = 198
The standard deviation of the Americans =15
95% of confidence intervals are determined by
[tex](x^{-} - Z_{\alpha } \frac{S.D}{\sqrt{n} } , x^{-} +Z_{\alpha } \frac{S.D}{\sqrt{n} })[/tex]
Level of significance = 0.05
Z₀.₀₅ = 1.96
= [tex](198 - 1.96 \frac{15}{\sqrt{100} } , 198 +1.96\frac{15}{\sqrt{100} })[/tex]
= ( 198 -0.294 ,198 +0.294)
= (197.706 , 198.294)
95% of confidence intervals are
(197.706 , 198.294)
