Answer:
The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].
Step-by-step explanation:
The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
z is the z-score.x is the raw score: an observation from the normally distributed data that we want standardize using [1].[tex] \\ \mu[/tex] is the population mean.[tex] \\ \sigma[/tex] is the population standard deviation.Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.
For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.
These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.
A subject earns a score of 155. How many standard deviations from the mean is the value 155?
From the question, we know that:
x = 155.[tex] \\ \mu = 155[/tex].[tex] \\ \sigma = 50[/tex].Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject earned a score that equals the population mean. Then, using [1]:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{155 - 155}{50}[/tex]
[tex] \\ z = \frac{0}{50}[/tex]
[tex] \\ z = 0[/tex]
As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:
[tex] \\ x = \mu[/tex]
Therefore
[tex] \\ z = 0[/tex]
So, the value 155 is zero standard deviations from the [population] mean.
The combined SAT scores for the students at a local high school are normally distributed with a mean of 1527 and a standard deviation of 291. The local college includes a minimum score of 1207 in its admission requirements. What percentage of students from this school earn scores that satisfy the admission requirement? P(X > 1207) =
Answer:
Step-by-step explanation:
Let x be the random variable representing the SAT scores for the students at a local high school. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 1527
σ = 291
the probability to be determined is expressed as P(x > 1207)
P(x > 1207) = 1 - P(x ≤ 1207)
For x < 1208
z = (1207 - 1527)/291 = - 1.1
Looking at the normal distribution table, the probability corresponding to the z score is 0.16
P(x > 1207) = 1 - 0.16 = 0.84
Therefore, the percentage of students from this school earn scores that satisfy the admission requirement is
0.84 × 100 = 84%
What’s the correct answer for this question?
Answer:
B
Step-by-step explanation:
The triangular prism must have a larger base than the cylinder
A company manager for a tire manufacturer is in charge of making sure there is the least amount of defective tires. If the tire manufacturing process is working properly, the average weight of a tire for a 4-door sedan is normally distributed with a mean of 22 pounds and a standard deviation of 0.76 pounds. The manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires. What proportion of tires will be rejected by this process?
Answer:
0.347% of the total tires will be rejected as underweight.
Step-by-step explanation:
For a standard normal distribution, (with mean 0 and standard deviation 1), the lower and upper quartiles are located at -0.67448 and +0.67448 respectively. Thus the interquartile range (IQR) is 1.34896.
And the manager decides to reject a tire as underweight if it falls more than 1.5 interquartile ranges below the lower quartile of the specified shipment of tires.
1.5 of the Interquartile range = 1.5 × 1.34896 = 2.02344
1.5 of the interquartile range below the lower quartile = (lower quartile) - (1.5 of Interquartile range) = -0.67448 - 2.02344 = -2.69792
The proportion of tires that will fall 1.5 of the interquartile range below the lower quartile = P(x < -2.69792) ≈ P(x < -2.70)
Using data from the normal distribution table
P(x < -2.70) = 0.00347 = 0.347% of the total tires will be rejected as underweight
Hope this Helps!!!
The proportion of the tires that would be denied for being underweight through the given process would be:
[tex]0.347[/tex]% of the total tires will be rejected as underweight.
Given that,
Interquartile Range [tex]= 1.5[/tex]
Standard Deviation [tex]= 0.76[/tex]
Considering Mean = 0
and Standard Deviation = 1
Since lower quartile = -0.67448
Upper quartile = +0.67448
IQ range = 1.34896
To find,
The proportion of tires would be rejected due to being underweight through the process would be:
1.5 of Interquartile Range = 1.5 × [tex]1.34896 = 2.02344[/tex]
Now,
1.5 of the IQ range below the lower quartile [tex]= (lower quartile) - (1.5 of Interquartile range)[/tex]
[tex]= -0.67448 - 2.02344[/tex]
[tex]= -2.69792[/tex]
The proportion of tires that would be under 1.5 of the interquartile range below the lower quartile:
[tex]= P(x < -2.69792)[/tex] ≈ [tex]P(x < -2.70)[/tex]
Using data through the Normal Distribution Table,
[tex]P(x < -2.70)[/tex] [tex]= 0.00347[/tex]
[tex]= 0.347[/tex]%
Thus, 0.347% of the total tires would be rejected as underweight.
Learn more about "Proportion" here:
brainly.com/question/2548537
You need a 55% alcohol solution. On hand, you have a 525 mL of a 45% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution? You will need _____mL of the 90% solution to obtain _____mL of the desired 55% solution.
Answer:
Let's call the amount of 90% solution x.
We can write:
45% * 525 + 90%x = 55%(x + 525)
0.45 * 525 + 0.9x = 0.55(x + 525)
Solving for x we get x = 150 so the first blank is 150 and the second blank is 525 + 150 = 675.
To test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are _____.
Answer:
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].
And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]
And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]
Step-by-step explanation:
We need to take in count that we are conducting a regression model with just one dependent variable and 3 independent variables
The degrees of freedom for the numerator on this case is given by [tex]df_{num}=df_{within}=k=3[/tex] where k =3 represent the number of independent variables.
The degrees of freedom for the denominator on this case is given by [tex]df_{den}=df_{between}=N-p-1=47-3-1 =43[/tex].
And the total degrees of freedom would be [tex]df=N-1=47 -1 =46[/tex]
And then the degrees of freedom for the numerator are 3 and for the denominator are 43 in order to find the critical value [tex]F_{3,43}[/tex]
Write a linear function f with f(−2)=6 and f(0)=−4 .
Answer:
y = -5(x) - 4
Step-by-step explanation:
Use the equation of a line and substitution.
Information given:
point 1: (-2,6)
x1 = -2 and y1 = 6
point 2: (0,4)
x2 = 0 and y2 = 4
Equation of a line: y = m(x) + b
m = slope
To find slope, you do the equation of a linear slope, which is:
m = [tex]\frac{rise}{run}[/tex] in other words m = [tex]\frac{Y2 - Y1}{X2-X1}[/tex]
plug in your values
[tex]\frac{6-(-4)}{-2-0}[/tex]
= -5
Great, we've found slope, now to find b
plug in the slope you found: y = -5(x) + b
Plug in and solve for each point given, aka (x,y) into the linear equation for both points.
FIRST POINT:
6 = -5(-2) + b
6 = 10 + b
6 - 10 = b
b = -4
SECOND POINT:
-4 = -5(0) + b
-4 = 0 + b
-4 - 0 = b
b = -4
We got -4 for both, meaning that this equation is correct, so if you add in b, your final equation will be y = -5(x) - 4.
Plug this into desmos.com/calculator, and you'll see this linear equation runs through both points given in the problem.
Answer:
f(x)=-5x-4
Step-by-step explanation:
You are given two points (-2, 6) and (0, -4)
Find the slope: m=(-4-6)/[(0-(-2)]=-5
So you have y=-5x+b
next, find the y intercept b.
the y intercept is when x=0. in this case, the y intercept is -4
so the linear function is f(x)=-5x-4
Please help. I’ll mark you as brainliest if correct!
These are 2 math problems .
Answer:
-4 503/12 ≈ 41.91667Step-by-step explanation:
To find the average rate of change, find the change in function value, and divide that by the length of the interval.
1. ((g(1) -g(-1))/(1 -(-1)) = ((-4·1³ +4) -(-4(-1)³ +4)/(2) = (-8)/2 = -4
The average rate of change of g(x) on [-1, 1] is -4.
__
2. ((g(3) -g(-2))/(3 -(-2)) = ((6·3³ +3/3²) -(6·(-2)³ +3/(-2)²))/5
= (6·27 +1/3 -6·(-8) -3/4)/5 = (2515/12)/5
= 503/12 = 41 11/12
The average rate of change of g(x) on [-2, 3] is 41 11/12.
Plz help me ASAP it’s important
Answer:
D. 6.3
Step-by-step explanation:
Well you can make a triangle with the line PQ with it's height as 2 and base as 6.
Then you can use the Pythagorean Theorem to find the length of PQ.
a²+b²=c²
2²+6²=c²
4+36=c²
40=c²
c²=40
Square root both sides
c=[tex]\sqrt{40}[/tex]
c≈6.3
Our answer is D. 6.3
8. Mr. Azu invested an amount at rate of 12% per annum and invested another amount, GH¢
580.00 more than the first at 14%. If Mr. Azu had total accumulated amount of
GH¢2,358.60, how much was his total investment?
Answer:
GH¢. 18098.46
Step-by-step explanation:
Let the first investment giving 12% interest per annum be Bank A
Let the 2nd investment giving 10% per annum be bank B
Let the first amount invested be
GH¢. X and let the second amount invested be GH¢. X + 580
Thus; In bank A;
Principal amount in first = GH¢. x
rate = 12 %
time = 1 year
Formula for simple interest = PRT/100
Where P is principal, R is rate and T is time.
So, interest in his investment = 12X/100 = 0.12X
while in bank B;
principal amount = GH¢. X + 580
rate = 14%
time = 1 yr
So, interest in his investment = [(X + 580) × 14]/100
= 0.14(X + 580)
So, total accumulated interest is;
0.12X + 0.14(X + 580) = 0.12X + 0.14X + 81.2 = 0.26X + 81.2
Now, we are given accumulated interest = GH¢. 2,358.60
Thus;
2358.60 = (0.26X + 81.2)
2358.6 - 81.2 = 0.26X
X = 2277.4/0.26
X = 8759.23
So,
first amount invested = GH¢. 8759.23
Second amount invested = GH¢. 8759.23 + GH¢. 580 = GH¢. 9339.23
Total amount invested = GH¢. 8759.23 + GH¢. 9339.23 = GH¢. 18098.46
What is the value of n in the equation: 8n+9= -n+5?
Answer:
n = -1
Step-by-step explanation:
So first subtract 9 to both sides
8n = -n - 9
Now you want the n on one side and the constant on the other
so add the single n to the n side
9n = -9
Divide 9 to both sides to solve for n
n = -1
what variable will you use to represent the number of brochures
Answer: always “X”
Step-by-step explanation:
Answer:
i would use the variable b because b = brochures.
Step-by-step explanation:
i hope this helped heh
round 3, 942,588 to the nearest thousand
Answer:
3, 943,000
Step-by-step explanation:
3, 942,588
The 2 is in the thousands place
We look at the hundreds place
There is a 5, that means we round up
2 becomes a 3
3, 943,000
Use variation of parameters to find a general solution to the differential equation given that the functions y1 and y2 are linearly independent solutions to the corresponding homogeneous equation for t > 0. ty" + (2t - 1 )y' - 2y = 6t^2 e^-2t​; y1 = 22t −​1, y2 = e^-2t
Answer:
[tex]y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]
Step-by-step explanation:
Solution:-
- Given is the 2nd order linear ODE as follows:
[tex]ty'' + ( 2t - 1 )*y' - 2y = 6t^2 . e^(^-^2^t^)[/tex]
- The complementary two independent solution to the homogeneous 2nd order linear ODE are given as follows:
[tex]y_1(t) = 2t - 1\\\\y_2 (t ) = e^-^2^t[/tex]
- The particular solution ( yp ) to the non-homogeneous 2nd order linear ODE is expressed as:
[tex]y_p(t) = u_1(t)*y_1(t) + u_2(t)*y_2(t)[/tex]
Where,
[tex]u_1(t) , u_2(t)[/tex] are linearly independent functions of parameter ( t )
- To determine [ [tex]u_1(t) , u_2(t)[/tex] ], we will employ the use of wronskian ( W ).
- The functions [[tex]u_1(t) , u_2(t)[/tex] ] are defined as:
[tex]u_1(t) = - \int {\frac{F(t). y_2(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\\\u_2(t) = \int {\frac{F(t). y_1(t)}{W [ y_1(t) , y_2(t) ]} } \, dt \\[/tex]
Where,
F(t): Non-homogeneous part of the ODE
W [ y1(t) , y2(t) ]: the wronskian of independent complementary solutions
- To compute the wronskian W [ y1(t) , y2(t) ] we will follow the procedure to find the determinant of the matrix below:
[tex]W [ y_1 ( t ) , y_2(t) ] = | \left[\begin{array}{cc}y_1(t)&y_2(t)\\y'_1(t)&y'_2(t)\end{array}\right] |[/tex]
[tex]W [ (2t-1) , (e^-^2^t) ] = | \left[\begin{array}{cc}2t - 1&e^-^2^t\\2&-2e^-^2^t\end{array}\right] |\\\\W [ (2t-1) , (e^-^2^t) ]= [ (2t - 1 ) * (-2e^-^2^t) - ( e^-^2^t ) * (2 ) ]\\\\W [ (2t-1) , (e^-^2^t) ] = [ -4t*e^-^2^t ]\\[/tex]
- Now we will evaluate function. Using the relation given for u1(t) we have:
[tex]u_1 (t ) = - \int {\frac{6t^2*e^(^-^2^t^) . ( e^-^2^t)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_1 (t ) = \frac{3}{2} \int [ t*e^(^-^2^t^) ] \, dt\\\\u_1 (t ) = \frac{3}{2}* [ ( -\frac{1}{2} t*e^(^-^2^t^) - \int {( -\frac{1}{2}*e^(^-^2^t^) )} \, dt] \\\\u_1 (t ) = -e^(^-^2^t^)* [ ( \frac{3}{4} t + \frac{3}{8} )] \\\\[/tex]
- Similarly for the function u2(t):
[tex]u_2 (t ) = \int {\frac{6t^2*e^(^-^2^t^) . ( 2t-1)}{-4t*e^(^-^2^t^)} } \, dt\\\\u_2 (t ) = -\frac{3}{2} \int [2t^2 -t ] \, dt\\\\u_2 (t ) = -\frac{3}{2}* [\frac{2}{3}t^3 - \frac{1}{2}t^2 ] \\\\u_2 (t ) = t^2 [\frac{3}{4} - t ][/tex]
- We can now express the particular solution ( yp ) in the form expressed initially:
[tex]y_p(t) = -e^(^-^2^t^)* [\frac{3}{2}t^2 + \frac{3}{4}t - \frac{3}{8} ] + e^(^-^2^t^)*[\frac{3}{4}t^2 - t^3 ]\\\\y_p(t) = -e^(^-^2^t^)* [t^3 + \frac{3}{4}t^2 + \frac{3}{4}t - \frac{3}{8} ] \\[/tex]
Where the term: 3/8 e^(-2t) is common to both complementary and particular solution; hence, dependent term is excluded from general solution.
- The general solution is the superposition of complementary and particular solution as follows:
[tex]y_g(t) = y_c(t) + y_p(t)\\\\y_g(t) = c_1*( 2t - 1 ) + c_2*e^(^-^2^t^) - e^(^-^2^t^)* [ t^3 + \frac{3}{4}t^2 + \frac{3}{4}t ][/tex]
2y + 5x – z = 4y + 6x solve for y
(show work)
Answer:
y = -z/2 - x/2
Step-by-step explanation:
2y + 5x – z = 4y + 6x
-5x. -5x
2y - z = 4y + x
+z. +z
2y = 4y + z + x
-4y -4y
-2y = z + x
÷-2. ÷-2
y = -z/2 - x/2
Mrs. Brown has 16 children in her first-grade class, and Mr. Lopez has 23 children in his second-grade class. The principal has been asked to select 1 student from one of the classes to appear at a PTA meeting. How many ways can the selection be made?
Answer: 368 ways
Step-by-step explanation: To find the total number of probabilities, you multiply all the factors together to get total outcome. 16 * 23 = 368
11+11 = 4 22+22 = 16 33+33 = ?
Answer:
36
Step-by-step explanation:
11*11=4
(1+1)*(1+1)=4
2 * 2 = 4
22*22=16
(2+2)*(2+2)=16
4 * 4 = 16
33*33=?
(3+3)*(3+3)=?
6 * 6 = 36
So the answer is 36
Series: 4, 16, 36
Answer: The answer is 36 :)
hope that helped
what is 0.035 as a simplified reduced fraction
Answer:
7/200
Step-by-step explanation:
0.035= 35/1000= 7*5/200*5=7/200
Analyze the function for domain, range, continuity, symmetry, boundedness, extrema, and asymptotes. f(x)=-2cot x
Answer:
(See explanation below for further details)
Step-by-step explanation:
The domain of the function is:
[tex]x \in \mathbb{R} - \{ \pm \pi \cdot i \}[/tex] for [tex]i \in \mathbb{N}_{O}[/tex]
The range of the function is:
[tex]f(x) \in \{-\infty, +\infty \}[/tex]
There are no absolute extrema and such function is not bounded.
Function is symmetric, whose period is π.
Lastly, the set of asymptotes is:
[tex]x = \pm \pi \cdot i[/tex], for [tex]i \in \mathbb{N}_{O}[/tex]
Answer:
Step-by-step explanation:
edge
The pressure p(in lbs/in^2) that a 160 pound persons shoe exerts on the ground when walking varies inversely with the area A(in in^2) of the sole of the shoe when the shoes have a sole area of 40 in^2 The pressure is 4 lbs/in^2 find equation that relates these variables
A=
Answer:
[tex]A = \dfrac{40}{P}[/tex]
Step-by-step explanation:
Pressure [tex]p(in lbs/in^2)[/tex] varies inversely with the area [tex]A(in$ in^2)[/tex] of the sole of the shoe.
This is written as:
[tex]P \propto \frac{1}{A}\\ $Introducing the constant of variation$\\P = \dfrac{k}{A}[/tex]
When:
[tex]When: A= 40 in^2, P =4 lbs/in^2\\$Substituting into the equation\\P = \dfrac{k}{A}\\4 = \dfrac{k}{40}\\$Cross multiply\\k=4*40\\k=160\\Therefore, the equation that connect these variables is given as:\\P = \dfrac{40}{A}\\$In terms of P\\AP=40\\\\A = \dfrac{40}{P}[/tex]
i need help asap!!!!!
Answer:
31 degrees
Step-by-step explanation:
Since RPS and QPR make up QPS, the sum of their angle measures must be 47. Therefore:
3x-38+7x-95=47
10x-133=47
10x=180
x=18
QPR=7(18)-95=126-95=31
Hope this helps!
whats the percentage of 56/100
Answer:
56%
Step-by-step explanation:
Percent means out of 100
56/100
56 out of 100
56%
Answer:
56%
Step-by-step explanation:
How much is 56 out of 100 written as a percentage? Convert fraction (ratio) 56 / 100 Answer: 56%
I will mark brainly-ist to who ever helps me
Find the value of the logarithm.
log 110
Round your answer to the nearest thousandth.
Answer:
4.700
Step-by-step explanation:
Find the number in the thousandth place 0 and look one place to the right for the rounding digit 4. Round up if this number is greater than or equal to 5 and round down if it is less than 5.
brainliesssss plssssssssssssss
(5m+100) (2m+10) what’s the value of m
Answer:
m=-30
Step-by-step explanation:
5m+100=2m+10
We want to get the variable on one side of the equation. First we subtract 100 from both sides.
5m=2m-90
Subtract 2m from both sides.
3m=-90
Divide both sides by 3.
m=-30
What’s the correct answer for this question?
Answer: Choice C
Step-by-step explanation:
Events A and B are independent if the equation P(A∩B) = P(A) · P(B) holds true.
3/10≠3/5*1/4
so event A and B are not independent.
Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.
a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.
b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.
Answer:
a) The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
We are 95% confident that the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is within 9,009 and 10,585 steps.
b) No, we can not use the confidence interval to estimate the probability of individual values. It can onlybe used to make inference about the population mean.
Step-by-step explanation:
a) We have to calculate a 99% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=9,797.
Ths sample standard deviation is s=2,313.
The sample size is N=61.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2313}{\sqrt{61}}=\dfrac{2313}{7.81}=296.15[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=61-1=60[/tex]
The t-value for a 99% confidence interval and 61 degrees of freedom is t=2.66.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.66 \cdot 296.15=787.84[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 9797-787.84=9009\\\\UL=M+t \cdot s_M = 9797+787.84=10585[/tex]
The 99% confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker is (9,009, 10,585).
b) The value of 8,500 steps is outside the confidence interval, but this means that it is an unusual value for the mean number of steps for all people in New York City who wear an activity tracker.
We can not use the confidence interval to estimate the probability of individual values.
The activity tracking devices.
The activity tracker re those devices such as watches and a bands that tells you about your physical activity such as skipping, running, and walking. They simply count the steps and tell you about the daily goals and targets. They are quite effective for monitoring blood pressure and more.
Thus answer is 9,009, 10,585 workers, 9,009, and 10,585 steps and population mean.
As per the question, the smart trackers are used by the new york people on a daily basis and they measure the footsteps of the people. A sample of random 61 people was taken and selected on the basis of the tracers. It was found that with these statistical tests a 99% confidence interval was taken for the mean on a typical workday for all people working in City that is 9,009, 10,585. The 95% confidence that the mean number of steps taken by workers of the City was within 9,009 and 10,585 steps.The confidence interval can be used to estimate the probability of the individual values. It can be used for drawing inferences for the population mean.Learn more about the trackers are electronic.
brainly.com/question/17434350.
Determine the area of the shaded region
Answer:
61.76 ft^2
Step-by-step explanation:
First find the area of the rectangle without the circle
A = l*w = 14*8 =112
Then find the area of the circle
The diameter is 8 so the radius is 8/2 =4
A = pi r^2 = 3.14 * 16 =50.24
The shaded region is the rectangle minus the circle
112-50.24 =61.76 ft^2
A laptop has a listed price of $875.98 before tax. If the sales tax rate is 6.5%, find the total cost of the laptop with sales tax included.
Round your answer to the nearest cent, as necessary.
please!
Answer:
$932.92
Step-by-step explanation:
6.5% = 0.065
(875.98) + (875.98)(0065)
(875.98) + (56.9387)
932.9187
$932.92
Answer:
$[tex]932.92[/tex]
Step-by-step explanation:
[tex]6.5/100=0.65[/tex]
Next, multiply the price by the sales tax.
[tex]875.98*0.65=56.94[/tex]
Then, add.
[tex]875.98+ 56.94=932.92[/tex]
$[tex]932.92[/tex] is the total cost of the laptop.
The lifespan (in days) of the common housefly is best modeled using a normal curve having mean 22 days and standard deviation 5. Suppose a sample of 25 common houseflies are selected at random. Would it be unusual for this sample mean to be less than 19 days?
Answer:
Yes, it would be unusual.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
Problems of normally distributed samples are solved using 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.
If [tex]Z \leq -2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered unusual.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question, we have that:
[tex]\mu = 22, \sigma = 5, n = 25, s = \frac{5}{\sqrt{25}} = 1[/tex]
Would it be unusual for this sample mean to be less than 19 days?
We have to find Z when X = 19. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{19 - 22}{1}[/tex]
[tex]Z = -3[/tex]
[tex]Z = -3 \leq -2[/tex], so yes, the sample mean being less than 19 days would be considered an unusual outcome.
What is the equation of the line perpendicular to y = 2/3 x +1 that passes through the point (12, – 6)?
Answer:
y= -3/2x+12
Step-by-step explanation:
the slope of perpendicular lines multiplied together would be -1, so the slope of the perpendicular line is -3/2. y=-3/2x+b, so -6=-18+b, so b= 12. the equation of the line is y=-3/2x+12.
Entrance to a prestigious MBA program in India is determined by a national test where only the top 10% of the examinees are admitted to the program. Suppose it is known that the scores on this test are normally distributed with a mean of 420 and a standard deviation of 80. Parul Monga is trying desperately to get into this program. What is the minimum score that she must earn to get admitted?
Answer:
The minimum score that she must earn to get admitted is 523.
Step-by-step explanation:
As the scores are normally distributed, we can calculate the probability using the z-score.
The distribution has a mean of 420 and a standard deviation of 80.
We have to calculate the z-score z* that satisfies:
[tex]P(z>z^*)=0.1[/tex]
This happens for z*=1.28155.
Then, we can calculate the score as:
[tex]X=\mu+z\cdot\sigma=420+1.28155\cdot 80=420+102.524=522.524[/tex]
