Given Information:
Sample size = n = 25
Mean age of client = 46 years
Standard deviation of age of client = 5 years
Confidence level = 95%
Required Information:
Width of the confidence interval = ?
Answer:
[tex]$ \text {width of CI } = \pm 2.064 $\\\\[/tex]
Step-by-step explanation:
The width for the true mean client age is given by
[tex]$ \text {width of CI } =\pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]
Where n is the sample size, s is the standard deviation of age of client, and [tex]t_{\alpha/2}[/tex] is the t-score corresponding to 95% confidence level.
The t-score corresponding to 95% confidence level is
Significance level = 1 - 0.95 = 0.05/2 = 0.025
Degree of freedom = n - 1 = 25 - 1 = 24
From the t-table at α = 0.025 and DF = 24
t-score = 2.064
[tex]$ \text {width of CI } = \pm (2.064)(\frac{5}{\sqrt{25} } ) $\\\\[/tex]
[tex]$ \text {width of CI } =\pm (2.064)(\frac{5}{5 } ) $\\\\[/tex]
[tex]$ \text {width of CI } = \pm (2.064)(1) $\\\\[/tex]
[tex]$ \text {width of CI } = \pm 2.064 $\\\\[/tex]
Therefore, width of the 95% confidence Interval for the true mean client age is approximately ±2.064.
Bonus:
The corresponding 95% confidence interval is given by
[tex]$ \text {Confidence Interval } = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $[/tex]
Where x_bar is the mean client age
[tex]$ \text {Confidence Interval } = 46 \pm 2.064 $[/tex]
[tex]$ \text {Confidence Interval } = (43.936, 48.064) $[/tex]
[tex]$ \text {Confidence Interval } = (44, 48) $[/tex]
Which means that we are 95% sure that the true mean client age is within the range of (44, 48) years.
what is equal to 12/10
Answer:
6/5, or 1.2
Step-by-step explanation:
The right answer is 6/5
Look at the attached picture
Hope it will help you
Good luck on your assignment
Which is the completely factored form of 4X cubed +10 X squared minus 6X
Answer:
2x(2x - 1)(x + 3)
Step-by-step explanation:
4x^3 + 10x^2 - 6x =
Factor out the common factor 2x.
= 2x(2x^2 + 5x - 3)
Factor the trinominal.
= 2x(2x - 1)(x + 3)
Answer:
[tex]=2x\left(2x-1\right)\left(x+3\right)[/tex]
Step-by-step explanation:
[tex]4x^3+10x^2-6x\\\mathrm{Factor\:out\:common\:term\:}2x:\quad 2x\left(2x^2+5x-3\right)\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\x^3=x^2x\\=4x^2x+10xx-6x\\\mathrm{Rewrite\:}6\mathrm{\:as\:}2\cdot \:3\\\mathrm{Rewrite\:}10\mathrm{\:as\:}2\cdot \:5\\\mathrm{Rewrite\:}4\mathrm{\:as\:}2\cdot \:2\\=2\cdot \:2x^2x+2\cdot \:5xx-2\cdot \:3x\\\mathrm{Factor\:out\:common\:term\:}2x\\=2x\left(2x^2+5x-3\right)\\\mathrm{Factor}\:2x^2+5x-3:\quad \left(2x-1\right)\left(x+3\right)[/tex]
[tex]2x^2+5x-3\\\mathrm{Break\:the\:expression\:into\:groups}\\=\left(2x^2-x\right)+\left(6x-3\right)\\\mathrm{Factor\:out\:}x\mathrm{\:from\:}2x^2-x\mathrm{:\quad }x\left(2x-1\right)\\2x^2-x\\\mathrm{Apply\:exponent\:rule}:\quad \:a^{b+c}=a^ba^c\\x^2=xx\\=2xx-x\\\mathrm{Factor\:out\:common\:term\:}x\\=x\left(2x-1\right)\\\mathrm{Factor\:out\:}3\mathrm{\:from\:}6x-3\mathrm{:\quad }3\left(2x-1\right)\\6x-3\\\mathrm{Rewrite\:}6\mathrm{\:as\:}3\cdot \:2\\=3\cdot \:2x-3[/tex]
[tex]\mathrm{Factor\:out\:common\:term\:}3\\=3\left(2x-1\right)\\=x\left(2x-1\right)+3\left(2x-1\right)\\\mathrm{Factor\:out\:common\:term\:}2x-1\\=\left(2x-1\right)\left(x+3\right)\\=2x\left(2x-1\right)\left(x+3\right)[/tex]
What is x to the nearest tenth?
Answer:
x= 13.7 (nearest tenth)
Step-by-step explanation:
Please see attached picture for full solution.
Daniel is packing his bags for his vacation. He has
5
55 unique socks, but only
4
44 fit in his bag
Answer:
yes
Step-by-step explanation:
Find the GCF.
6m3n and 8mn2
Answer:
[tex]2mn[/tex]
Step-by-step explanation:
[tex]6m^3n,\:8mn^2[/tex]
Find the GCD of [tex]6,\:8[/tex]:
[tex]6[/tex]
[tex]=2\cdot \:3[/tex]
[tex]8[/tex]
[tex]=2\cdot \:4[/tex]
[tex]=2\cdot \:2\cdot \:2[/tex]
So the prime factor common to 6, 8 is:
[tex]2[/tex]
So the factor common to [tex]6m^3n,\:8mn^2[/tex]:
[tex]=2mn[/tex]
PLEASE HELP ME PLEASE LOOK AT THE PICTURE I NEED AN ANSWER ASAP
Answer:
1st one is 2. 2nd one is 5. 3rd one is less than. 4th one is, is smaller
Step-by-step explanation:
Please help me understand this!!
Step-by-step explanation:
3 + 15 + 75 + 375 + 1,875
This is a geometric series. The first term is 3, the common ratio is 5, and the number of terms is 5.
∑₁⁵ 3 (5)ⁿ⁻¹
∑₀⁴ 3 (5)ⁿ
3 + 12 + 48 + 192 + 768
This is a geometric series. The first term is 3, the common ratio is 4, and the number of terms is 5.
∑₁⁵ 3 (4)ⁿ⁻¹
∑₀⁴ 3 (4)ⁿ
4 + 32 + 256 + 2048 + 16,384
This is a geometric series. The first term is 4, the common ratio is 8, and the number of terms is 5.
∑₁⁵ 4 (8)ⁿ⁻¹
∑₀⁴ 4 (8)ⁿ
2 + 6 + 18 + 54 + 162
This is a geometric series. The first term is 2, the common ratio is 3, and the number of terms is 5.
∑₁⁵ 2 (3)ⁿ⁻¹
∑₀⁴ 2 (3)ⁿ
How would you simplify a negative square root?
Provide a detailed explanation, with an example, to receive full credit.
Answer:
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
Given a negative square root √(-x);
From our knowledge of complex numbers, we know that
i^2 = -1 and vise versa
To simplify
√(-x) = √((x)(-1)) = √((x)(i^2))
√(-x) = √(i^2) × √x = i√x
For example;
Simplify √-9
√-9 = √(-1×9) = √-1 × √9
√-9 = √(i^2) × √9 = i × 3
√-9 = 3i
Step-by-step explanation:
The square root of a number A, is a number B such that, when it is multiplied by itself, the result is A.
If A × A = B
Then √B = A.
Now the multiplication of two numbers gives a positive number if both numbers are positive, or both numbers are negative.
2 × 2 = -2 × -2 = 4
3 × 3 = -3 × - 3 = 9
And so on.
So, the square root of 4 = 2 or -2
The square root of 9 = 3 or -3
But if one of the numbers is positive while the other is negative, then the result is negative.
2 × -2 = -4
3 × -3 = -9
Clearly, √(-4) ≠ 2 ≠ -2
√(-9) ≠ 3 ≠ -3
It is impossible to find the square root of negative numbers on the real line. This gives rise to the introduction of Complex Number.
Let i² = -1, then we have that
√(-1) = i.
This is the idea of Complex number, and it helps solve the problem of the negative square roots, and every negative number can be written as the multiplication of -1 and the inverse of the number.
-A = -1 × A
So, √(-A) = √(-1 × A)
= √(-1) × √A
= i × √A
= i√A
Example, to simplify √(-16)
√(-16) = √(-1 × 16)
= √(-1) × √16
= i × ±4
= ±4i
Marc drives his car 500 miles using 20 gallons of gas. How many miles per gallon does his car get
Answer:
25 miles per gallon
Step-by-step explanation:
We want to find miles per gallon so take the miles and divide by the gallons
500 miles / 20 gallons
25 miles per gallon
Answer:
[tex]= 25 \: \: \: miles \: \: \: per \: \: \: gallon \\ [/tex]
Step-by-step explanation:
You have to find miles per gallon.
So to solve that you have to divide miles by gallon.
[tex] \frac{500}{20} \\ = 25 \: \: \: miles \: \: \: per \: \: \: gallon[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
A carpenter bought some tools to build chairs. The cost of the materials for each chair was the same. The total cost y (tools and materials) to make x chairs is shown in the graph below. The cost of the tools was $_____ and the cost of materials for one chair was $________
Answer:
Cost of tools: $100
Cost for each chair: $25
Step-by-step explanation:
You can see that before 1 chair, the cost is at 100. This means that the cost of the tools is $100. Another way to determine this is to see that at 1 chair, the cost is $125. At 2, it's $150, and at 3 it's $175, etc. This tells you that the cost to produce each chair is $25, but it also tells you that the tools cost 100 dollars, since the total cost at 1 chair is $125, and each chair only costs $25.
Hope this helps!
Answer:
100,25
Step-by-step explanation:
Which of these generalizations is true?
A. All rectangles are squares.
В. All parallelogram s are rectangles.
C. All squares are parallelograms.
D. All trapezoids are parallelograms.
PLEASE HELP QUICKLY !THANK YOU :)
Find the mass of lamina bounded by circles x2 + y2 = 1 and x2 + y2 = 4in the first quadrant if the density is (x2 + y2). Could please anyone solve this...
Since density is equal to mass per unit volume, mass is equal to density times volume. So we split up the lamina into tiny regions with "volume" (area) equal to dA, multiplied by the density, and integrated over the entirety of the lamina.
This is best done in polar coordinates:
[tex]\begin{cases}x=u\cos v\\y=u\sin v\end{cases}\implies\mathrm dA=\mathrm dx\,\mathrm dy=u\,\mathrm du\,\mathrm dv[/tex]
so that [tex]x^2+y^2=u^2\cos^2v+u^2\sin^2v=u^2[/tex].
The lamina is then the set of points
[tex]L=\left\{(u,v)\mid1\le u\le2\land0\le v\le\dfrac\pi2\right\}[/tex]
Now compute the integral: the mass of the lamina is
[tex]\displaystyle\iint_L(x^2+y^2)\,\mathrm dA=\int_0^{\pi/2}\int_1^2u^3\,\mathrm du\,\mathrm dv=\frac\pi2\int_1^2u^3\,\mathrm du=\frac{15\pi}8[/tex]
If Triangle M N O is congruent to triangle N M O, what statement best describes triangle MON?
The triangle is scalene.
The triangle is equilateral.
The triangle is isosceles and possibly equilateral.
The triangle is isosceles but definitely not equilateral.
Answer:
The answer is c
Step-by-step explanation:
The statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.
The congruent triangles are:
Triangle MNO and Triangle NMO
The above means that:
Sides MN and NO or MN and MO are equal
So, the triangles are isosceles triangles
However, it is possible that sides NO and MO are congruent
Hence, the statement that best describes triangle MON is (c) The triangle is isosceles and possibly equilateral.
Read more about congruent triangles at:
https://brainly.com/question/1675117
The ACT is an achievement test given nationally with normally distributed scores. Tim
scored a 24 on the mathematics portion of his ACT. The mean for the mathematics portion of
the ACT was 22.0 and the standard deviation was 5.1. What percent of the population scored
higher than Tim on the mathematics portion of the ACT?
Answer:
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 22, \sigma = 5.1[/tex]
Tim scored 24. What percent of the population scored higher than Tim on the mathematics portion of the ACT?
The proportion is 1 subtracted by the pvalue of Z when X = 24. The percentage is the proportion multiplied by 100.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 22}{5.1}[/tex]
[tex]Z = 0.39[/tex]
[tex]Z = 0.39[/tex] has a pvalue of 0.6517
1 - 0.6517 = 0.3483
34.83% of the population scored higher than Tim on the mathematics portion of the ACT
The students in Mr. Sanchez's class are converting distances measured in miles to kilometers. To estimate the number of kilometers, Abby takes the number of miles, doubles it, then subtracts 20% of the result. Renato first divides the number of miles by 5, then multiplies the result by 8. Write an algebraic expression that shows the process that both students used. Abby's expression: Renato's expression:
Step-by-step explanation:
Abby’s Expression:
Double m, giving 2m. She then takes 20% of the result, which we can write 0.2(2m). Finally she subtracts this from 2m, giving 2m−(0.2)2m
2m − (0.2)2m
Renato’s Expression:
Divide m by 5, giving m ÷ 5 = m/5, and then multiplies the result by 8, giving:
8(m/5)
What is the product? [-3 4 2 +5] * [3 -2 1 0]
Answer:
So the answer is the first one
[tex]\left[\begin{array}{ccc}1&0&-2\\&&\\&&\end{array}\right] +\left[\begin{array}{ccc}1&2&3\\&&\\&&\end{array}\right][/tex]
The answer is [ 2 2 1]
look at the attached picture
Hope it helps
Good luck on your assignment
3. Candace drew quadrilateral ABCD with vertices A(3, 3), B(5, 3), C(7, 1), and D(1, 1). Miguel wants to dilate Candace's quadrilateral by a scale factor of 5/5. Which statement is true? *
A-Quadrilateral ABCD is smaller than quadrilateral A'B'C'D'.
B-The algebraic expression of the dilation is (x, y) -> (5x, 5y).
C-The coordinates of quadrilateral A'B'C'D' will be A'(15, 15), B'(9, 15), C'(5, 35), D'(5, 5).
D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Answer:
D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Step-by-step explanation:
The scale factor is equal to 1. Hence, the quadrilateral A'B'C'D' will be identical to quadrilateral ABCD, whose vertices are the same.
The algebraic expression of the dilation is:
[tex](x',y') = (x,y)[/tex]
Besides, the coordinates of the new quadrilateral are A'(3, 3), B'(5, 3), C'(7, 1), and D'(1, 1)
And quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Therefore, the right answer is D.
Answer: D-Quadrilateral A'B'C'D' will be congruent to quadrilateral ABCD.
Step-by-step explanation: just did a test with this question and got it right. Hope this helped! thx for the points :D
Find the product. (3x 2 - 5x + 3)(3x - 2)
Answer:
9x^3-21x^2+19x-6
Step-by-step explanation:
First you have to distribute the first equation into the second since the two are being multiplied:
(3x^2-5x+3)(3x-2)
9x^3-6x^2-15^2+10x+9x-6
(simplify)
9x^3-21x^2+19x-6
9x^3-21x^2+19x-6
First you have to distribute the first equation into the second since the two are being multiplied:
(3x^2-5x+3)(3x-2)
9x^3-6x^2-15^2+10x+9x-6
(simplify)
9x^3-21x^2+19x-6 is the answer to the question
1. Michel buys a leash for his dog. The leash is 6 ft 3 inches. How long, in inches, is the leash?(1 ft = 12 inches)
A) 48 inches
B) 51 inches
C) 72 inches
D) 75 inches
2. What is the area of a triangular garden with base of 6 ft and a height of 9 ft? (A = 1/2BH)
A) 27 square feet
B) 48 square feet
C) 54 square feet
D) 24 square feet
Answer:
1 = D 75 inches
2 = A 27
Step-by-step explanation:
1 - 6.3 times 12 = 75.6
2 - 6 times 9 = 54
54/2 = 27
:)
what is the solution to 2.8(2+0.5n)=2.4(n+1.2)
Answer:
Step-by-step explanation:
The ratio of Adriana's age to her aunt's age is 7:10. In 2 years the sum of their ages will be 123. How old is Adriana's aunt now?
Answer:
70.35Step-by-step explanation:
The sum of 7 and 10 is 17. So 123 / 17 = 7.235 (roughly)
7.235 x 10 (for Adriana's aunt's age) equals 72.35
And to double check: We can find adriana's age by doing. 7.235 x 7 = 50.645. If we add 50.645 and 72.35 we get 122.995 which is roughly 123 and the reason why it is not 123 on the dot is because 123 / 17 is roughly 7.235 the full expanded one is: 7.23529411765
You may try checking with the full number without estimating but i am sure of my answer
Parker invested $7,800 in an account
paying an interest rate of 1.7%
compounded continuously. Assuming no
deposits or withdrawals are made, how
much money, to the nearest dollar, would
be in the account after 11 years?
Answer:
A=9404
Step-by-step explanation:
Answer:
9404
Step-by-step explanation:
Find the point based on the parametric
equations. t = 3
X = 1 - 2t
y = 4t + 1
Answer:
(-5,13)
Step-by-step explanation:
because t=3
[tex]x = 1 - 2 \times 3 = - 5 \\ y = 4 \times 3 + 1 = 13[/tex]
Given: 1; -5; -13 ; -23 ; ...
Derive a formula for the nth term in the pattern.
Answer:
f(n) = -n^2 -3n +5
Step-by-step explanation:
Suppose the formula is ...
f(n) = an^2 +bn +c
Then we have ...
f(1) = 1 = a(1^2) +b(1) +c
f(2) = -5 = a(2^2) +b(2) +c
f(3) = -13 = a(3^2) +b(3) +c
__
Here's a way to solve these equations.
Subtract the first equation from the second:
-6 = 3a +b . . . . . 4th equation
Subtract the second equation from the third:
-8 = 5a +b . . . . . 5th equation
Subtract the fourth equation from the fifth:
-2 = 2a
a = -1
Then substituting into the 4th equation to find b, we have ...
-6 = 3(-1) +b
-3 = b
and ...
1 = -1 +(-3) +c . . . . . substituting "a" and "b" into the first equation
5 = c
The formula is ...
f(n) = -n^2 -3n +5
triangle ABC a = 4 and m angle C=30 If the area of the triangle is 6 what is the length of side b
Answer:
6m = b
Step-by-step explanation:
The area of triangle when angle and sides are given = 1/2* sin angle*ab
Area = 1/2 * sin 30 * 4*b
Area = 6m²
6 = 1/2 * sin 30 * 4*b
(6*2)/(sin 30 * 4)= b
12/(0.5*4) = b
12/2 = b
6m = b
I need to know if the graph makes sense based on how Naoya shoots, everything is in the photo.
Answer:
Not correct
Step-by-step explanation:
Sample 8 has one free throw, sample 9 has 3 free throw success,
sample 10 has 3 free throw success
sample 11 has 5 free throw success
sample 12 has 5 free throw success
sample 13 has 2 free throw success
sample 14 has 1 free throw success;
See one sample should contain 15 free throw and the probability of success should be 0.7
Let's look at sample 8
Total no of success is 1
Total no of free throws 15
Probability is 1/15 = 1/15 * 100 =6.67%
Similarly you can do so for the others.
Meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories. Use the 68-95-99.7 rule to answer the following questions. NOTE. This web site 68-95-99.7 rule graphically depicts the 68-95-99.7 rule and may help with the following questions. a. What is the approximate percentage of the Chipotle meals that have more than 471 calories
Answer:
The approximate percentage of the Chipotle meals that have more than 471 calories is 95%.
Step-by-step explanation:
We are given that meal can be considered symmetric and mound-shaped with mean 1075 calories and standard deviation 302 calories.
Let X = Chipotle meals having calories
So, X ~ Normal([tex]\mu=1075, \sigma^{2} =302^{2}[/tex])
Now, the 68-95-99.7 rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.So, the approximate percentage of the Chipotle meals that have more than 471 calories is given by;
[tex]\frac{X-\mu}{\sigma} = \frac{471-1075}{302}[/tex]
= -2
Since, it is stated above that 95% of the data values lies within two standard deviation points which means 95% values lies between -2 and 2 z score values.
SO, the approximate percentage of the Chipotle meals that have more than 471 calories is 95%.
Use the fundamental theorem of calculus to find the area of the region between the graph of the function x^5 + 8x^4 + 2x^2 + 5x + 15 and the x-axis on the interval [-6,6]. Round off your answer to the nearest integer.
A) 25,351 units^2
B) 149,473 units^2
C) 3,758 units^2
D) 2,362 units^2
Answer:
The area of the region is 25,351 [tex]units^2[/tex].
Step-by-step explanation:
The Fundamental Theorem of Calculus: if [tex]f[/tex] is a continuous function on [tex][a,b][/tex], then
[tex]\int_{a}^{b} f(x)dx = F(b) - F(a) = F(x) | {_a^b}[/tex]
where [tex]F[/tex] is an antiderivative of [tex]f[/tex].
A function [tex]F[/tex] is an antiderivative of the function [tex]f[/tex] if
[tex]F^{'}(x)=f(x)[/tex]
The theorem relates differential and integral calculus, and tells us how we can find the area under a curve using antidifferentiation.
To find the area of the region between the graph of the function [tex]x^5 + 8x^4 + 2x^2 + 5x + 15[/tex] and the x-axis on the interval [-6, 6] you must:
Apply the Fundamental Theorem of Calculus
[tex]\int _{-6}^6(x^5+8x^4+2x^2+5x+15)dx[/tex]
[tex]\mathrm{Apply\:the\:Sum\:Rule}:\quad \int f\left(x\right)\pm g\left(x\right)dx=\int f\left(x\right)dx\pm \int g\left(x\right)dx\\\\\int _{-6}^6x^5dx+\int _{-6}^68x^4dx+\int _{-6}^62x^2dx+\int _{-6}^65xdx+\int _{-6}^615dx[/tex]
[tex]\int _{-6}^6x^5dx=0\\\\\int _{-6}^68x^4dx=\frac{124416}{5}\\\\\int _{-6}^62x^2dx=288\\\\\int _{-6}^65xdx=0\\\\\int _{-6}^615dx=180\\\\0+\frac{124416}{5}+288+0+18\\\\\frac{126756}{5}\approx 25351.2[/tex]
Carole ordered 4 dresses for $80 each, a $25 sweater, and a coat. The cost of the items without sales tax was $430. What was the cost of the coat?
Explanation:
The equation for the total cost of the clothes is 4×80+25+c=430, where c is the cost of the coat.
320 + 25 + c = 430
345 + c = 430
345 - 345 + c = 430 - 345
c = 85
The cost of the coat was $85.
Answer:
$85 for the coat
Step-by-step explanation:
1 dress = $80
4 dress =$80×4
=$320
sweater=$25
coat=?
4 dresses plus the sweater cost :
$320+$25=$345
The cost of all the item $430
cost of the coat :
$430-$345=$85
