Answer:
The 90% confidence level is [tex]19.15< L < 20.85[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 64[/tex]
The mean age is [tex]\= x = 20 \ years[/tex]
The standard deviation is [tex]\sigma = 4 \ years[/tex]
Generally the degree of freedom for this data set is mathematically represented as
[tex]df = n - 1[/tex]
substituting values
[tex]df = 64 - 1[/tex]
[tex]df = 63[/tex]
Given that the level of confidence is 90% the significance level is mathematically evaluated as
[tex]\alpha = 100 - 90[/tex]
[tex]\alpha =[/tex]10 %
[tex]\alpha = 0.10[/tex]
Now [tex]\frac{\alpha }{2} = \frac{0.10}{2} = 0.05[/tex]
Since we are considering a on tail experiment
The critical value for half of this significance level at the calculated degree of freedom is obtained from the critical value table as
[tex]t_{df, \frac{ \alpha}{2} } = t_{63, 0.05 } = 1.669[/tex]
The margin for error is mathematically represented as
[tex]MOE = t_{df , \frac{\alpha }{2} } * \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]MOE = 1.699 * \frac{4 }{\sqrt{64} }[/tex]
[tex]MOE = 0.85[/tex]
he 90% confidence interval for the true average age of all students in the university is evaluated as follows
[tex]\= x - MOE < L < \= x + E[/tex]
substituting values
[tex]20 - 0. 85 < L < 20 + 0.85[/tex]
[tex]19.15< L < 20.85[/tex]
If jimmy has 15 apples and give 7 to gohn how many does jimmy have?
Answer:
Hey there!
Jimmy has 15-7, or 8 apples left.
Hope this helps :)
At the bookstore near Martha's home, hardcover books cost 21 dollars. The cost of a paperback book is only 4/7 of the cost of a hardcover book. How many dollars will Martha have to pay for one paperback book?
Answer:
The cost of the paper book= $12
Step-by-step explanation:
Hardcover books costs $21
But paper book cost only a fraction of the hardcover book.
The paper book cost 4/7 of the hardcover book.
The cost of paper book= 4/7* paper book
The cost of paper book = 4/7*$21
The cost of the paper book= 4*3
The cost of the paper book= $12
Determine the t critical value for a lower or an upper confidence bound in each of the following situations. (Round your answers to three decimal places.)
a. Confidence level = 95%, df = 10
b. Confidence level = 95%, df = 15
c. Confidence level = 99%, df = 15
d. Confidence level = 99%, n = 5
e. Confidence level = 98%, df = 23
f. Confidence level = 99%, n = 32
Answer:
A. 1.812
B. 1.753
C. 2.602
D. 3.747
E. 2.069
F. 2.453
Step-by-step explanation:
A. 95% confidence level, the level of significance = 5% or 0.05
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 10 degrees of freedom = 1.182
B. 95% confidence interval = 0.05 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.05 significance level with 15 degrees of freedom = 1.753
C. 99% confidence interval = 0.01 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 15 degrees of freedom = 2.602
D. 99% confidence interval = 0.01 level of significance; DF (n - 1) = 5- 1 = 4
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 4 degrees of freedom = 3.747
E. 98% confidence interval = 0.02 level of significance
Using t-table, the critical value for a lower or an upper confidence bound at 0.02 significance level with 23 degrees of freedom = 2.069
F. 99% confidence interval = 0.01 level of significance; df (n - 1) = 32 - 1 = 31
Using t-table, the critical value for a lower or an upper confidence bound at 0.01 significance level with 31 degrees of freedom = 2.453
Solve the equation below for x. -1 2(3x - 4) = 11
Answer:
x= 37/36
Step-by-step explanation:
−12(3x−4)=11
Step 1: Simplify both sides of the equation.
−12(3x−4)=11
(−12)(3x)+(−12)(−4)=11(Distribute)
−36x+48=11
Step 2: Subtract 48 from both sides.
−36x+48−48=11−48
−36x=−37
Step 3: Divide both sides by -36.
−36x
−36
=
−37
−36
x=
37
36
Answer:
x=
37
36
-1/2(3x-4) = 11
Multiply both sides by -2:
3x-4 = -22
Add 4 to both sides:
3x = -18
Divide both sides by 3:
X = -6
The number that, when increased by 30% equals 78
Answer:
60
Step-by-step explanation:
x + 0.30x = 78
1.30x = 78
x = 60
Answer:
The answer is 60.
Step-by-step explanation:
here, let another number be x.
according to the question the number when increased by 30% will be 78. so,
x+ 30% of x =78
now, x+ 30/100×x =78
or, x+0.3x=78
or, 1.3x=78
Therefore the another number is 60.
Hope it helps...
Maddy and her cousin work during the summer for a landscaping company. Maddy’s cousin has been working for the company longer, so her pay is 30% more than Maddy’s. Last week, Maddy’s cousin worked 27 hours, and Maddy worked 23 hours. Together, they earned $493.85. What is Maddy’s hourly pay?
Answer:
Maddy's hourly pay is $8.50
Step-by-step explanation:
First, we need to use the information given to us to form a system of equations to determine either Maddy's pay, or her cousin's pay. In this case, we are interested in Maddy's pay.
We know her cousin makes 30% more than Maddy, which means she makes 100% of what Maddy makes, and an additional 30%. So we have our first equation:
C = M + .3M = 1.3M, where C is the amount the cousin makes and M is Maddy's pay.
The second piece of information is that in one week, Maddy worked 23 hours, and her cousin worked 27, and together they made $493.85. So now we have our second equation:
27C + 23M = 493.85, where C is the amount the cousin makes and M is the amount Maddy makes.
Now we simply substitute are value of C from the first equation into the second equation like such:
27(1.3M) + 23M = 493.85
And now we solve for M to find Maddy's pay.
27(1.3M) + 23M = 493.85
35.1M + 23M = 493.85
58.1M = 493.85
M = 8.5
To verify our answer is correct, let's find the value of money earned per hour by the cousin using the first equation:
C = 1.3(8.5) = 11.05
Now let's see if the number of hours worked by each and their pay adds up to the 493.85 from the previous week:
27(11.05) + 23(8.5) =? 493.85
298.35 + 195.5 =? 493.85
493.85 == 493.85
So, now we have confirmed that Maddy makes $8.50 per hour, and her cousin makes $11.05 per hour.
Cheers.
Based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25. A random sample of 52 claims showed that 43 were made by single people under the age of 25. Does this indicate that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company? State the null and alternate hypothesis then give the test statistic and your conclusion.
Answer:
We conclude that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.
Step-by-step explanation:
We are given that based on information from a large insurance company, 67% of all damage liability claims are made by single people under the age of 25.
A random sample of 52 claims showed that 43 were made by single people under the age of 25.
Let p = population proportion of claims made by single people
So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 67% {means that the insurance claims of single people under the age of 25 is smaller than or equal to the national percent reported by the large insurance company}
Alternate Hypothesis, [tex]H_A[/tex] : p > 67% {means that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of claims made by single people under the age of 25 = [tex]\frac{43}{52}[/tex] = 0.83
n = sample of claims = 52
So, the test statistics = [tex]\frac{0.83-0.67}{\sqrt{\frac{0.67(1-0.67)}{52} } }[/tex]
= 2.454
The value of z-test statistics is 2.454.
Since in the question, we are not given the level of significance so we assume it to be 5%. Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 2.454 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the insurance claims of single people under the age of 25 is higher than the national percent reported by the large insurance company.
Calculate the side lengths a and b to two decimal places
A. a= 10.92 b=14.52 <--- My answer
B. a= 11 b= 15
C. a=4.18 b=3.15
D. a= 11.40 b=13.38
Answer:
Option (D)
Step-by-step explanation:
In the picture attached,
An obtuse angle triangle ABC has been given.
By applying Sine rule in the triangle,
[tex]\frac{\text{SinB}}{b}=\frac{\text{SinA}}{a}=\frac{\text{SinC}}{c}[/tex]
Since, m∠A + m∠B + m∠C = 180°
45° + 110° + m∠C = 180°
m∠C = 180°- 155° = 25°
[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=\frac{\text{Sin25}}{7}[/tex]
[tex]\frac{\text{Sin110}}{b}=\frac{\text{Sin45}}{a}=0.060374[/tex]
[tex]\frac{\text{Sin110}}{b}=0.060374[/tex]
b = [tex]\frac{\text{Sin110}}{0.060374}[/tex]
b = 15.56
b ≈ 15.56
[tex]\frac{\text{Sin45}}{a}=0.060374[/tex]
a = [tex]\frac{\text{Sin45}}{0.060374}[/tex]
a = 11.712
a = 11.71
Therefore, Option (D) will be the answer.
The image of a parabolic lens is traced onto a graph. The function f(x) = (x + 8)(x – 4) represents the image. At which points does the image cross the x-axis?
Answer:
[tex]\large \boxed{\sf \ \ \ (-8,0) \ \text{ and } \ (4,0) \ \ \ }[/tex]
Step-by-step explanation:
Hello,
from the expression of f(x) we can say that there are two zeroes, -8 with a multiplicity of 1 and 4 with a multiplicity of 1.
So the image of the parabolic lens crosses the x-axis at two points:
(-8,0)
and
(4,0)
For information, I attached the graph of the function.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A man bought certain number of litches
at 20 per Rs 100 and an equal no. of 30 per
Rs 100. He mixed them and sold them at
25
per Rs 100. Find his
gain or loss
percent?
Answer: The loss is 4%
Step-by-step explanation:
Lets call litches that are 20 pcs per Rs 100 - litches A
that are 30 pcs per Rs 100- litches B
So a man can buy 2 pcs A per Rs 10
and 3 pcs B per Rs 10
OR
6x pcs A per Rs 30x
and 6x pcs B per Rs 20x
Now he gonna sell the 12x litches for y Rs
Lets find y from the proportion
12x cost y
25 cost 100
y/12=100/25
y=48 Rs
So the man bought 6x A + 6x B for 20x+30x=50 Rs
And then he sold them for 48 Rs
Obviously the man gonna loose the money.
Lets find the losses in %
(50-48)/50*100=200/50=4%
The loss is 4%
One number is 6 more than another. Their product is -9. Need help fast
Answer: the numbers are 3 and -3
Step-by-step explanation:
let the unknown number be x
The first UNKNOWN NUMBER = X
The second unknown number is = 6 + x
Their product = -9
(X)(6 + X) = -9
6x +[tex]x^{2}[/tex]=-9
[tex]x^{2}[/tex] +6x +9=0
we multiply the coefficient of x which is 1 with 9
now, we look for two numbers that when multiplied will give us 9 and when added will give 6 and that is 3 and 3
[tex]x^{2}[/tex] +3x+3x +9 = 0
x(x+3) +3(x+3) = 0
(x +3 ) = 0
or (x +3)=0
x +3 =0
x=0 -3
x =-3
x +3=0
x =0-3
x =-3
since the numbers are the same ,we pick one
therefore,the first number =x =-3
the second number is 6 + x=6 + (-3)
6-3=3
The length of needles produced by a machine has standard deviation of 0.04 inches. Assuming that the distribution is normal, how large a sample is needed to determine with a precision of ±0.005 inches the mean length of the produced needles to 98% confidence?
Answer:
The sample size is [tex]n = 87[/tex]
Step-by-step explanation:
From the question we are told that
The standard deviation is [tex]\sigma = 0.04 \ inches[/tex]
The precision is [tex]d = \pm 0.005 \ inches[/tex]
The confidence level is [tex]C =[/tex]98%
Generally the sample size is mathematically represented as
[tex]n = \frac{ Z_{\frac{\alpha }{2} } ^2* \alpha^2 }{d^2}[/tex]
Where [tex]\alpha[/tex] is the level of significance which is mathematically evaluated as
[tex]\alpha = 100 - 98[/tex]
[tex]\alpha = 2[/tex]%
[tex]\alpha = 0.02[/tex]
and [tex]Z_{\frac{\alpha }{2} }[/tex] is the critical value of [tex]\alpha[/tex] which is obtained from the normal distribution table as 2.326
substituting values
[tex]n = \frac{2.326 ^2* 0.02^2 }{0.005^2}[/tex]
[tex]n = 87[/tex]
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (
This question is incomplete
Complete Question
A normal population has a mean of 61 and a standard deviation of 13. You select a random sample of 16. Compute the probability that the sample mean is: (Round z values to 2 decimal places and final answers to 4 decimal places.)
(a) Greater than 64
(b) Less than 57
Answer:
(a) Greater than 64 = 0.1788
(b) Less than 57 = 0.1094
Step-by-step explanation:
To solve the above questions we would be using the z score formula
The formula for calculating a z-score :
z = (x - μ)/σ,
where x is the raw score
μ is the population mean = 61
σ is the population standard deviation = 13
(a) Greater than 64
z = (x - μ)/σ,
where x is 64
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 64 - 61 ÷ 13/√16
z = 3/3.25
z = 0.92308
Approximately, z values to 2 decimal places ≈ 0.92
Using the z score table of normal distribution to find the Probability (P) value of z score of 0.92
P(z = 0.92) = 0.82121
P(x>64) = 1 - P(z = 0.92)
= 1 - 0.82121
= 0.17879
Approximately , Probability value to 4 decimal places = 0.1788
(b) Less than 57
z = (x - μ)/σ,
where x is 57
μ is the 61
σ is the 13
In the above question, we are given the number of samples = 16
Sample standard deviation = popular standard deviation/ √16
= 13/√16
z = 57 - 61 ÷ 13/√16
z = -4/3.25
z = -1.23077
Approximately, z values to 2 decimal places ≈ -1.23
Using the z score table of normal distribution to find the Probability (P) value of z score of -1.23
P(z = -1.23) = P(x<Z) = 0.10935
Approximately , Probability value to 4 decimal places = 0.1094
What does 1/6 of 1272 equal?
Answer:
212
Step-by-step explanation:
Answer:
212
Step-by-step explanation:
you have to first divide 1272 by 6 or you can find a number that you can multiply it by so what times 6 equals 1272 so it is guess and check meathodso 200x6 = 1200, and 12x6= 721200+72=1272 and 200+12=212A customer has $10 to spend at the concession stand. Hotdogs cost $2 each and drinks cost $2.50 each. Graph the inequality that illustrates this situation. Use the space below to explain what the answer means.
Answer:
Please refer to the graph in the attached area.
Step-by-step explanation:
Given:
Total money available with the customer is $10.
Cost of each hotdog is $2.
Cost of each drink is is $2.50.
To find:
The graph of inequality.
Solution:
Let number of hotdogs bought = [tex]x[/tex]
Total cost of hotdogs = [tex]2x[/tex]
Let number of drinks bought = [tex]y[/tex]
Total cost of drinks = [tex]2.5y[/tex]
Total cost = [tex]2x+2.5y[/tex]
And total money available is $10.
So, the total cost calculated above must be lesser than or equal to $10.
Hence, the inequality is:
[tex]2x+2.5y<10[/tex]
Also there will be two conditions on variables [tex]x[/tex] and [tex]y[/tex]:
[tex]x\ge0\\y\ge0[/tex]
To graph this, let us find the points on the equivalent equation:
[tex]2x+2.5y = 10[/tex]
Finding two points on the equation.
First put x = 0 [tex]\Rightarrow[/tex] y = 4
Then put y = 0, [tex]\Rightarrow[/tex] x = 5
So, two points are (0, 4) and (5, 0).
Now, plotting the line.
Having point (1,2) in the inequality:
2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)
Please refer to the graph of inequality in the attached graph.
Find the perimeter and area of the figure. Round to the nearest tenth if necessary. 33.7 mm; 108 mm2 33.7 mm; 54 mm2 30.7 mm; 50.2 mm2 33.7 mm; 53.2 mm2
Answer:
Perimeter: 33.7 mm
Area: 54 mm
Step-by-step explanation:
If you do 12 + 9.7 + 12 you will get the perimeter, and to get the area you would use the formula A = [tex]\frac{1}{2}[/tex] x base x height. Since the base is 12 and the height is 9, you would do 12 x 9 x 0.5 to get 54 mm for the area of the triangle.
Resultado de x²-3x=0
Answer:
0, 3
Step-by-step explanation:
Hola,
[tex]x^2-3x=0\\\\x*x-3*x=0\\\\x(x-3)=0\\\\x= 0 \ or \ x=3\\[/tex]
Espero que esto ayudes
Answer:
x = 0 O x = 3
Step-by-step explanation:
[tex]x^2-3x = 0[/tex]
tomando x común
x(x-3) = 0
Ya sea,
x = 0 O x-3 = 0
x = 0 O x = 3
G(x) = 5x + 3
Find g(b2)
Answer:
g(2) =10x+6
Step-by-step explanation:
g(x) =5x+3
g(2)=5x+3
g(2)=10x+6
have a great day
Pretty much Self explanatory :) I don't understand this...
Answer:
Step-by-step explanation:
you have to keep going cause if you count the fives there's a 25 but right next to the 25 there's 24 all you have to do is watch what your doing just watch your steps
Use Euler's Formula to find the missing number. Vertices: 11 Edges: 34 Faces: _______
Answer:
I think the correct answer is 45.
Step-by-step explanation:
a circle has a radius of 6/7 units and is centered at (-2.3,0) What is the equation of the circle
Answer:
(x+2.3)^2 + (y) ^2 = (6/7)^2
Step-by-step explanation:
The equation of a circle can be written as
(x-h)^2 + (y-k) ^2 = r^2 where ( h,k) is the center and r is the radius
(x- -2.3)^2 + (y-0) ^2 = (6/7)^2
(x+2.3)^2 + (y) ^2 = (6/7)^2
Write the equation of the graph shown below in the factored form f(x) = (x + 2) (x - 1) (x - 3) f(x) = (x - 2) (x + 1) (x + 3) f(x) = (x + 2) (x + 1) (x + 3) f(x) = (x - 2) (x - 1) (x - 3)
Answer:
[tex]f(x)=(x-1)\,(x-3)\.(x+2)[/tex]
which agrees with the first answer shown in the list of possible options.
Step-by-step explanation:
Notice that there are three roots for this polynomial clearly shown on the graph's crossings of the x axis: x = 1, x = 3, and x = -2.
Therefore, based on such, we can write three binomial factors of the form [tex](x-root)[/tex] for the polynomial:
[tex]f(x)=(x-1)\,(x-3)\.(x-(-2))=(x-1)\,(x-3)\.(x+2)[/tex]
5 1/2 to improper fraction
Answer:
[tex]5 \frac{1}{2} = \frac{(5 \times 2) + 1}{2} = \frac{11}{2} [/tex]
So the answer is 11/2 .
Answer:
The answer is 11/2
Step-by-step explanation:
Simply multiply 2 and 5 to get 10 and then add 1 to get 11 so 11/2
When the input is 4, the output of f(x) = x + 21 is
Answer:
25Step-by-step explanation:
When the input is 4, the output of f(x) = x + 21 is f(4).
Substitute x = 4 to f(x):
f(4) = 4 + 21 = 25
Answer:
25
Step-by-step explanation:
We can find the output by plugging in 4 as x into the function:
f(x) = x + 21
f(4) = 4 + 21
f(4) = 25
In how many ways can you put seven marbles in different colors into four jars? Note that the jars may be empty.
Answer:
128
Step-by-step explanation:
You have two jars and seven marbles.
You do 2^{7}.
That is 128
Answer:
16384
Step-by-step explanation:
Its correct :)
How do I find the 5th term of a sequence defined by the given rule? f(n)= 6.5n + 4.5 Can someone also explain the rule(s)? I'm having trouble understanding all of this
Answer:
30.5
Step-by-step explanation:
This sequence is defined by f(n)=6.5 + 4.5
The term inside the parentheses (n) is the value you should input to get an output.
n varies from 0 to infinity
Now to find the fifth term put in mind that 0 is the first term.
This means that f(5) isn't the fifth term. In fact, it's the sixth term. So f(4) is the fifth term.
To find f(4) replace n by 4.
f(4) = 6.5 *4 +4.5 = 26+4.5=30.5
-6+4q+(-6q)−6+4q+(−6q)minus, 6, plus, 4, q, plus, left parenthesis, minus, 6, q, right parenthesis ?
Answer:
-16-5q
Step-by-step explanation:
-6+4q-6q-6+4q-6q-6+4q-6q= -18-6q
Answer:C
Step-by-step explanation: 100% correct I did it on Khan Academy
w=pv for p, how do you get the answer?
Answer:
you need to have values for w and v
but u basically have to do
MOVE V TO THE OTHER SIDE
SO
W/V=P
Step-by-step explanation:
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
Another math problem. Can you solve it? I can't... For a good answer I'll make it 'The Best' I hope you can help me... Thanks
Answer:
[tex]\boxed{\sf \ \ \ 10^2+11^2+12^2=13^2+14^2 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
let's note a a positive integer
5 consecutive integers are
a
a+1
a+2
a+3
a+4
so we need to find a so that
[tex]a^2+(a+1)^2+(a+2)^2=(a+3)^2+(a+4)^2\\<=>\\a^2+a^2+2a+1+a^2+4a+4=a^2+6a+9+a^2+8a+16\\<=>\\3a^2+6a+5=2a^2+14a+25\\<=>\\a^2-8a-20=0\\<=>\\(a+2)(a-10)=0\\<=>\\a = -2 \ or \ a = 10\\[/tex]
as we are looking for positive integer the solution is a = 10
do not hesitate if you have any question
In triangle ABC a=34 b=18 and c=17 Find m?A
Answer:
152.53°
Step-by-step explanation:
The Law of Cosines is useful for finding an angle when sides are given.
a^2 = b^2 +c^2 -2bc·cos(A)
A = arccos((b^2 +c^2 -a^2)/(2bc))
A = arccos((18^2 +17^2 -34^2)/(2(18)(17))) = arccos(-543/612)
A ≈ 152.53°