Answer:
[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]
[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]
Step-by-step explanation:
For this case we have the following info given:
[tex]n_1 = 41 , \bar X_1 =42700 , s_1 = 2030[/tex]
[tex]n_2 = 41 , \bar X_2 =36375 , s_2 = 1360[/tex]
And for this case we want a 98% confidence interval. The significance would be:
[tex] \alpha= 1-0.98=0.02[/tex]
The degrees of freedom are:
[tex] df = n_1 +n_2 -2= 41+41 -2= 80[/tex]
And the critical value for this case is:
[tex] t_{\alpha/2}= 2.374[/tex]
And the confidence interval would be given by:
[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]
And replacing we got:
[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]
[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]
1/4 ÷ 3/8 simplest form
Answer:
2/3
Step-by-step explanation:
divide by a fraction = multiply by reciprocal
1/4 * 8/3
2/3
Answer:
⅔
Step-by-step explanation:
= ¼ ÷ ⅜
= ¼ × ⁸/3
= ⅔
Have a great day !
Pls cam someone help me
Extremely confused with both if poss xxxx
Answer:
1. Red red blue blue
2. Red blue red blue
Step-by-step explanation:
A 50 percent chance
Which of the following is parallel to
2Y = 6X + 4?
A. Y = -3X + 3
B. Y = 3X + 4
C. Y = x + 3
D. Y = -2X - 3
E. Y= 1/2 X + 3
Answer:
B. y = 3x + 4
Step-by-step explanation:
Step 1: Find slope-intercept form of 1st equation
2y = 6x + 4
2y/2 = 6x/2 + 4/2
y = 3x + 2
A parallel line has the same slope but different y-intercept:
y = -3x + 3 (No, different slope)
y = 3x + 4 (Yes, same slope, different y-int)
y = x + 3 (No, different slope)
y = -2x - 3 (No, different slope)
y = 1/2x + 3 (No, different slope)
A director of the library calculates that 10% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 899 books would be less than 11%? Round your answer to four decimal places.
Answer:
0.8413
Step-by-step explanation:
p = 0.10
σ = √(pq/n) = 0.01
z = (x − μ) / σ
z = (0.11 − 0.10) / 0.01
z = 1
P(Z < 1) = 0.8413
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
We have,
We can use the normal approximation to the binomial distribution to find the probability that the proportion of books checked out in a sample of 899 books would be less than 11%.
First, we need to calculate the mean and standard deviation of the binomial distribution:
Mean:
np = 899 × 0.1 = 89.9
Standard deviation:
√(np(1-p)) = √(899 × 0.1 × 0.9) = 9.427
Next, we need to standardize the sample proportion of 11% using the formula:
z = (x - μ) / σ
where x is the sample proportion, μ is the mean of the distribution, and σ is the standard deviation of the distribution.
Substituting the values we have, we get:
z = (0.11 - 0.1) / 0.9427 = 0.1059
Using a standard normal distribution table or calculator, we can find that the probability of getting a z-score less than 0.1059 is 0.5425.
Therefore,
The probability that the proportion of books checked out in a sample of 899 books would be less than 11% is approximately 0.5425.
Rounded to four decimal places, the answer is 0.5425.
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Consider the following. x = 6 sin y , 0 ≤ y ≤ π, x = 0; about y = 4
(a) Set up an integral for the volume V of the solid obtained by rotating the region bounded by the given curve about the specified axis.
(b) Use your calculator to evaluate the integral correct to four decimal places.
Answer:
12pi(8-pi), or
183.158 to third decimal place
Step-by-step explanation:
The geometry is indicated in the attached figure.
A. by integration
We will find the volume of the solid by the method of shells, i.e. we will integrate strips parallel to the axis of rotation to form many thin shells, then integrate to get the sum of all these shells.
For each shell, of thickness dy, we integrate strips of length located at y
L(x) = y(x)
and area
L(x)dy
Each strip is at a distance of (4-y) from
for which the volume of each shell equals
dV = 2*pi*(4-y)*L(x)dy = 2*pi*(4-y)*y(x) dy
The total volume of the solid can be obtained by integrating y from 0 to pi
integral( dV ) from 0 to pi
= integral (2*pi*(4-y)*y(x) dy) for y from 0 to pi
= 12*pi(-sin(y)+y*cos(y)-4*cos(y)) for y from 0 to pi
=12(8-pi)*pi
= 183.158
B. Using Pappus theorem
Pappus theorem simplifies the calculation of volume of revolution by multiplying the area of the rotating region by 2pi times the distance between the centroid and the rotation axis.
Here the area of the figure is A=2*6=12, (2 is the area under the sine curve from 0 to pi), or
A = integral (6sin(x))dx, x from 0 to pi
= 6 cos(x), x from 0 to pi
= 6(1- (-1))
= 12
Distance from centroid to axis of rotation = (4-pi/2)
Volume = 2*pi*A*(4-pi/2) = 2*pi*12*(4-pi/2)
= 12pi(8-pi)
=183.158 as before
The distance d of a particle moving in a straight line is given by d(t) = 2t3 + 5t – 2, where t is given in seconds and d is measured in meters. Find an expression for the instantaneous velocity v(t) of the particle at any given point in time. Question 1 options: 6t3 – 5 5t3 + 6 6t2 + 5 5t2 – 6
Answer:
(C)[tex]6t^2+5[/tex]
Step-by-step explanation:
Given the distance, d(t) of a particle moving in a straight line at any time t is:
[tex]d(t) = 2t^3 + 5t - 2, $ where t is given in seconds and d is measured in meters.[/tex]
To find an expression for the instantaneous velocity v(t) of the particle at any given point in time, we take the derivative of d(t).
[tex]v(t)=\dfrac{d}{dt}\\\\v(t) =\dfrac{d}{dt}(2t^3 + 5t - 2) =3(2)t^{3-1}+5t^{1-1}\\\\v(t)=6t^2+5[/tex]
The correct option is C.
Answer:
6t2+5
Step-by-step explanation:
What is the area of the triangle?
9 4 12
Answer:
13.636
Step-by-step explanation:
The area can be found using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2.
For the given triangle, ...
a=9, b=4, c=12, s=(9+4+12)/2 = 12.5
A = √(12.5(3.5)(8.5)(0.5)) = √185.9375 ≈ 13.636
The area of the triangle is about 13.636 square units.
Answer:
24 units\
Step-by-step explanation:
choose the function that has domain x ≠ -3 range y ≠ 2.
The function is f(x)= 2x+1/x+3.
How to find the domain of a function?A work domain is a set of all possible inputs for a job. For example, the domain f (x) = x² is all real numbers, and the domain g (x) = 1 / x is all real numbers except x = 0. And we can define the special functions of its most limited domains.
Which function has the domain and range?The function domain f (x) is a set of all values defined by the function, and the scope of the function is a set of all values taken by f. (In grammar school, you probably call the domain a set of substitutes and a set of solutions.
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Answer:
B
Step-by-step explanation:
i got it right! :)
A human resources specialist is investigating a government claim that the unemployment rate is less than 5%. To test this claim, a random sample of 1500 people is taken and its determined that 61 people are unemployed. The following is the setup for this hypothesis test:
H0:p=0.05
Ha:p<0.05
Find the p-value for this hypothesis test for a proportion and round your answer to 3 decimal places.
The following table can be utilized which provides areas under the Standard Normal Curve:
z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
-1.8 0.036 0.035 0.034 0.034 0.033 0.032 0.031 0.031 0.030 0.029
-1.7 0.045 0.044 0.043 0.042 0.041 0.040 0.039 0.038 0.038 0.037
-1.6 0.055 0.054 0.053 0.052 0.051 0.049 0.048 0.047 0.046 0.046
-1.5 0.067 0.066 0.064 0.063 0.062 0.061 0.059 0.058 0.057 0.056
-1.4 0.081 0.079 0.078 0.076 0.075 0.074 0.072 0.071 0.069 0.068
Answer:
P-value =0.062
At a signficance level of 0.05, there is not enough evidence to support the claim that the unemployment rate is less than 5%.
Step-by-step explanation:
This is a hypothesis test for a proportion.
The claim is that the unemployment rate is less than 5%.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi=0.05\\\\H_a:\pi<0.05[/tex]
The significance level is 0.05.
The sample has a size n=1500.
The sample proportion is p=0.041.
[tex]p=X/n=61/1500=0.041[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.05*0.95}{1500}}\\\\\\ \sigma_p=\sqrt{0.000032}=0.0056[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi+0.5/n}{\sigma_p}=\dfrac{0.041-0.05+0.5/1500}{0.0056}=\dfrac{-0.0087}{0.0056}=-1.5401[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z<-1.5401)=0.062[/tex]
As the P-value (0.062) is greater than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the unemployment rate is less than 5%.
The four-member math team at Pecanridge Middle School is chosen from the math club, which has three girls and five boys. How many different teams made up of two girls and two boys could be chosen?
Answer:
30 ways
Step-by-step explanation:
Given the following :
Number of boys in school (n1) = 5
Number of girls in school (n2) = 3
Total number of team members to be selected = 4
Number of boys required in team(r1) = 2
Number of girls required in team(r2) = 2
How many different teams made up of two girls and two boys could be chosen?
= (2 boys from 5) * (2 girls from 3)
Using combination :
5C2 * 3C2
Recall :
nCr = n! ÷ (n-r)! r!
5C2 = 5! ÷ (5-2)! 2!
5C2 = 5! ÷ 3!2!
5C2 = (5*4) / 2 * 1 = 10ways
3C2 = 3! ÷ (3-2)! 2!
3C2 = 3! ÷ 1!2!
3C2 = (3) / 1 = 3ways
3C2 = 3/1 = 3ways
10 * 3 = 30 ways
Write the equation of each line in slope intercept form (If possible please show work)
Hope it make sense now :)
PLEASE HELP ME OUT
Move point b to different locations in the coordinate plane. What do you notice about the relationship between BG and GF? Explain in terms of <BGF
Answer:
BG is always perpendicular to GF. The measure of angle BGF is always 90 degree
Step-by-step explanation:
Answer:
is always perpendicular to . The measure of is always 90°.
Step-by-step explanation:
Plato Awnser
Solve by completing the square: 5x2 + 20x + 32 = 0
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The non-even numbers are 1, 3, and 5 on the dice.
3 numbers out of 6.
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
Total sides of 6-sided die = 6
Numbers not even = 3
Probability of not getting an even = 3/6
=> 1/2
7. Factor by grouping.
6p2 - 17p - 45
A (2p - 9)(3p + 5)
B (2p + 9)(3p + 5)
7096
Oc
C (2p - 9)(3p - 5)
90%
D (2p + 9)(3p - 5)
ping
Answer:
Step-by-step explanation: 4
Please answer this correctly
Answer:
60%
Step-by-step explanation:
Total Cards = 5
Even Numbers = 3
P(even) = 3/5
In %age:
=> 60%
Answer:
60%
Step-by-step explanation:
The numbers that are even from the list are 2, 4, and 6.
3 numbers are even out of 5 total numbers.
3/5 = 0.6
P(even) = 60%
PLEASE HELP!! 2. Helen and Stephen both simplify the exponential expression .
Helen:
Stephen:
Unfortunately, they both made an error. Identify where each person made his or her error and explain in words what he or she did wrong. Then, correctly simplify the expression.
Answer:
We start with the expression:
exp( (4/3)*ln(2) - 1)
Here we can use that:
exp(ln(x)) = x.
and e^(a + b) = e^a*e^b.
the first step here is:
e^((4/3)*ln(2) - 1) = e^((4/3)*ln(2)*e^(-1)
So the first step of Stephen is correct, but the first step of helen is not, you can not simplify the expression in that way.
now, we have that:
a*ln(x) = ln(x^a)
then we can write:
(4/3)*ln(2) = ln(2^(4/3))
and e^(ln(2^(4/3)) = 2^(4/3)
then we have:
e^((4/3)*ln(2)*e^(-1) = 2^(4/3)/e
now we can write this as:
∛(2^4)/e
here is where stephen makes the mistake, he uses the 4 in the rooth and the 3 in the power.
so the expression actually is:
∛(16)/e
Write the function whose graph is the graph of y= Vx, but is translated 5 units downward.
Answer:
y = Vx - 5
Step-by-step explanation:
shift down is -5
y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
The function y = Vx represents the square root function, which is a graph of a half of a parabola opening upwards and passing through the point (0, 0).
To translate this function 5 units downward, we need to subtract 5 from the function. Therefore, the function we need is:
y = Vx - 5
This is the square root function shifted downward by 5 units.
The graph of this function will be the same as the graph of y = Vx, but shifted 5 units downward.
Hence, y = Vx - 5 is the function whose graph is the graph of y= Vx, but is translated 5 units downward.
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PLEASE HELP!!! How many 2-digit numbers are among the terms of the arithmetic sequence 2, 7, 12, 17, ...?
Step-by-step explanation:
The difference between. Each numbers is 5 so, it's answer is 22 and 27
Brainliest to whoever gets this correct! Does this graph show a function? Explain how you know.A.No; there are y-values that have more than one x-value.B.No; the graph fails the vertical line test.C.Yes; the graph passes the vertical line test.D.Yes; there are no y-values that have more than one x-value.
Answer:
B. No; the graph fails the vertical line test.
Step-by-step explanation:
If you hold a pencil up to the graph, the parabola would technically touch the pencil at more than one point. That means it failed the test, and therefore it is not a function.
hope this helped :)
Find the missing side and round the answer to the nearest tenth. Thanks.
Answer:
22.2
Step-by-step explanation:
The missing side is x
cos19° = 21/x switch x and cos19° x = 21/cos 19°x = 22.21≈ 22.2
please simplfy this equation
Answer:
0
Step-by-step explanation:
√12 can be rewritten as √2²·3 = 2√3
√75 can be rewritten as √5²·3 = 5√3
2/5 * 5 = 2
so
2√3 - 2/5 * 5√3 = 2√3 - 2√3 = 0
Answer:
0
Step-by-step explanation:
Which expression correctly represents “six more than the product of five and a number, decreased by one”?
Answer:
Step-by-step explanation:
Product of 5 and a number: 5n
Six more than that would be 5n + 6
Finally, "six more than the product of 5 and a number, decreased by one" would be
5n + 6 - 1, or 5n + 5
Answer: A) 6 + 5n - 1
Step-by-step explanation: edge. 2022
PLEASE HELP I’LL MARK BRAINLIEST If 1 equals 1 2/3 how much does 1 1/2 equal?
Answer:
0.9 (9/10)
Step-by-step explanation:
(see picture)
Help me find volume for this given radius please
Answer:
see below
Step-by-step explanation:
The volume of a sphere is given by
V = 4/3 pi r^3
= 4/3 pi ( 7)^3
= 1372/3 pi in^3
Using 3.14 for pi
V =1436.0266666 in^3
Using the pi button
1436.75504 in^3
Try it
Evaluate the function g(x) = -2x² + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2) - 5
g(-2) = -2(4) - 6-5
g(-2) = ?
g(0) =?
g(3) =?
Answer:
g(-2) = -19g(0) = -5g(3) = -14Step-by-step explanation:
When you have several evaluations to do, it is often convenient to put the formula into a graphing calculator or spreadsheet.
__
If you must evaluate a polynomial by hand, it is often easier if the expression is written in "Horner form":
g(x) = (-2x +3)x -5
Then we have ...
g(-2) = (-2(-2) +3)(-2) -5 = 7(-2) -5 = -19
g(0) = (-2(0) +3)(0) -5 = -5
g(3) = (-2(3) +3)(3) -5 = (-3)(3) -5 = -14
What is the answer? ACB ~ EFD
Answer:
y=4solution,
[tex] \frac{ac}{ef} = \frac{cb}{fd} \\ or \: \: \frac{12}{y} = \frac{15}{5} \\ or \: 15 \times y = 12 \times 5( \: cross \: multiplication) \\ or \: 15y = 60 \\ or \: y = \frac{60}{15} \\ y = 4[/tex]
Hope this helps...
Good luck on your assignment..
Answer:
The value of y is 4
Step-by-step explanation:
What is similarity ?
In Euclidean geometry, two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.
Given,
ΔACB~ΔEFD
The proportional sides are equal.
[tex]\frac{AC}{EF}=\frac{CB}{FD}=\frac{AB}{DE} \\\frac{12}{y}=\frac{15}{5} \\y=12*\frac{5}{15}\\\\ y=4[/tex]
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Do 2b+ b and 3b have the same value for all values of b? explain your reason
Answer:
Yes
Step-by-step explanation:
b is as in 1b so. . .
2 + 1 = 3
We can plug in b or as "b"
2b + b = 3b
So yes in whatever case 2b + b's value will always equal 3b's value
Answer:
yes
Step-by-step explanation:
because you can use any number to put for B and they will have the same value as an example we will use 3 for b so 2b = 6 + b = 9 and 3b = 9
PLEASE ANSWER FAST!! THANK YOU :)
Answer:
option 1 both statements are true
Step-by-step explanation:
Prove by PMI -- Principle of Mathematical Induction
1) n³ + 2n
n= 1 , 1³ +2*1 = 1+2 = 3 = 3*1 ---->divisible by 3
n = 2 ; 2³ + 2*2 = 8+4 = 12 = 3*4 ----> is divisible by 3
Assume that It is valid for n = k ;
[tex]k^{3}+2k[/tex] = 3*m -----(I) , for all m ∈ N
We have to prove for n =k +1 , the statement is true.
n = k+1, [tex](k+1)^{3}+2(k +1) =k^{3}+3k^{2}+3k +1 +2k +2[/tex]
= k³ + 3k² + 3k + 3 + 2k
= k³ + 2k + 3k² + 3k + 3
= 3m + 3 (k² + k + 1)
= 3(3 + [k² + k + 1] ) is divisible by 3
Therefore, this statement is true
2) [tex]5^{2n}-1\\[/tex]
[tex]n=1 ; 5^{2}-1 = 25 -1 = 24 divisible by 24\\\\n = 2 ; 5^{2*2}-1 = 5^{4}-1 = 625 - 1 = 624 divisible by 24[/tex]
This statement is also true
1. The graph of yf(x) is translated 3 units right and 4 units down. What is the equation of the translation
image in terms of the function ?
A. Y-3 = f(x+4)
B. y + 4 = f(x-3)
C. y + 3 = f(x-4)
D. y - 4 = f(x + 3)
Answer:
D.y-4=f(x+3)
Step-by-step explanation:
The correct translation would be y-4 because the y-coordinate moves down 4 units and f(x+3) because the x-coordinate would move 3 spaces to the right.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
The equation of the translation image of the function is y - 4 = f(x + 3).
which is the correct answer would be an option (D).
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Vertical shifting of a graph is done by adding any arbitrary constant to the function in shifting.
For example, If shift up by 1 unit, add 1 to the function
If shift down by 4 units, subtract 4 from the function
To determine the graph of y (x) is translated as 3 units right and 4 units down.
The x-coordinate will increase by 3 if we move it to the right.
If we shift it downward, it will become negative and read as y - 4.
So y - 4 = f(x + 3)
Therefore, the equation of the translation image of the function is y - 4 = f(x + 3).
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