Answer:
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
A reminder is that the standard deviation is the square root of the variance.
Normal probability distribution
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.
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:
[tex]\mu = 3639, \sigma = \sqrt{145161} = 381, n = 41, s = \frac{381}{\sqrt{41}} = 59.5[/tex]
Probability that the mean of the sample would differ from the population mean by less than 126 miles
This is the pvalue of Z when X = 3639 + 126 = 3765 subtracted by the pvalue of Z when X = 3639 - 126 = 3513. So
X = 3765
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3765 - 3639}{59.5}[/tex]
[tex]Z = 2.12[/tex]
[tex]Z = 2.12[/tex] has a pvalue of 0.983
X = 3513
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{3513 - 3639}{59.5}[/tex]
[tex]Z = -2.12[/tex]
[tex]Z = -2.12[/tex] has a pvalue of 0.017
0.983 - 0.017 = 0.966
96.6% probability that the mean of a sample would differ from the population mean by less than 126 miles
Before the pandemic cancelled sports, a baseball team played home games in a stadium that holds up to 50,000 spectators. When ticket prices were set at $12, the average attendance was 30,000. When the ticket prices were on sale for $10, the average attendance was 35,000.
(a) Let D(x) represent the number of people that will buy tickets when they are priced at x dollars per ticket. If D(x) is a linear function, use the information above to find a formula for D(x). Show your work!
(b) The revenue generated by selling tickets for a baseball game at x dollars per ticket is given by R(x) = x-D(x). Write down a formula for R(x).
(c) Next, locate any critical values for R(x). Show your work!
(d) If the possible range of ticket prices (in dollars) is given by the interval [1,24], use the Closed Interval Method from Section 4.1 to determine the ticket price that will maximize revenue. Show your work!
Optimal ticket price:__________ Maximum Revenue:___________
Answer:
(a)[tex]D(x)=-2,500x+60,000[/tex]
(b)[tex]R(x)=60,000x-2500x^2[/tex]
(c) x=12
(d)Optimal ticket price: $12
Maximum Revenue:$360,000
Step-by-step explanation:
The stadium holds up to 50,000 spectators.
When ticket prices were set at $12, the average attendance was 30,000.
When the ticket prices were on sale for $10, the average attendance was 35,000.
(a)The number of people that will buy tickets when they are priced at x dollars per ticket = D(x)
Since D(x) is a linear function of the form y=mx+b, we first find the slope using the points (12,30000) and (10,35000).
[tex]\text{Slope, m}=\dfrac{30000-35000}{12-10}=-2500[/tex]
Therefore, we have:
[tex]y=-2500x+b[/tex]
At point (12,30000)
[tex]30000=-2500(12)+b\\b=30000+30000\\b=60000[/tex]
Therefore:
[tex]D(x)=-2,500x+60,000[/tex]
(b)Revenue
[tex]R(x)=x \cdot D(x) \implies R(x)=x(-2,500x+60,000)\\\\R(x)=60,000x-2500x^2[/tex]
(c)To find the critical values for R(x), we take the derivative and solve by setting it equal to zero.
[tex]R(x)=60,000x-2500x^2\\R'(x)=60,000-5,000x\\60,000-5,000x=0\\60,000=5,000x\\x=12[/tex]
The critical value of R(x) is x=12.
(d)If the possible range of ticket prices (in dollars) is given by the interval [1,24]
Using the closed interval method, we evaluate R(x) at x=1, 12 and 24.
[tex]R(x)=60,000x-2500x^2\\R(1)=60,000(1)-2500(1)^2=\$57,500\\R(12)=60,000(12)-2500(12)^2=\$360,000\\R(24)=60,000(24)-2500(24)^2=\$0[/tex]
Therefore:
Optimal ticket price:$12Maximum Revenue:$360,000a geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .
Answer: [tex]\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}[/tex]
Step-by-step explanation:
a₁, 375, a₃, a₄, 81
First, let's find the ratio (r). There are three multiple from 375 to 81.
[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]
Next, let's find a₁
[tex]a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625[/tex]
Lastly, Use the Infinite Geometric Sum Formula to find the sum:
[tex]S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}[/tex]
A square has a perimeter of 12x+52 units. Which expression represents the side leagth of the square in units
Answer:
12x/2 or 52/2
Step-by-step explanation:
Ok, perimeter is length+length+width+width. 12x/2 and 52/2 could are probably the answers.
How do you write 89,700,000,000 in scientific notation? ___× 10^____
Answer:
It's written as
[tex]89.7 \times {10}^{9} [/tex]
Or
[tex]8.97 \times {10}^{10} [/tex]
Hope this helps you
Answer:
8.97 * 10 ^10
Step-by-step explanation:
We want one nonzero digit to the left of the decimal
8.97
We moved the decimal 10 places to the left
The exponent is positive 10 since we moved 10 places to the left
8.97 * 10 ^10
Researchers wanted to know whether it is better to give the diphtheria, tetanus and pertussis (DTaP) vaccine in the thigh or the arm. They collect data on severe reactions to this vaccine in children aged 3 to 6 years old. What would be the best statistical test for them to utilize?
A. One-sample chi-square
B. Linear regression
C. T-test
D. Two-sample chi-square
Answer:
D. Two-sample chi-square
Step-by-step explanation:
A chi-square test is a test used to compare the data that is observed, from the data that is expected.
In a two-sample chi-square test the observed data should be similar to the expected data if the two data samples are from the same distribution.
The hypotheses of the two-sample chi-square test is given as:
H0: The two samples come from a common distribution.
Ha: The two samples do not come from a common distribution
Therefore, in this case, the best statistical test to utilize is the two-sample chi-square test.
(0, 3) and (-2, -1)
Write an equation in slope intercept from of the line that passes through the given points.
Answer:
y = 2x + 3
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Slope-Intercept Form: y = mx + b
Step 1: Find slope m
m = (-1 - 3)/(-2 - 0)
m = -4/-2
m = 2
y = 2x + b
Step 2: Rewrite equation
y = 2x + 3
*You are given y-intercept (0, 3), so simply add it to your equation.
PLS HELP ASAP!!!!........
Answer:
aaaaha pues
Step-by-step explanation:
Answer:
what happened
Step-by-step explanation:
The graph shows a gasoline tank being filled at a rate of 2,500 gallons of gas per
hour. How will the graph change if the rate slows?
The correct answer is The line will be less steep because the rate will be slower
Explanation:
The rate of the graph is defined by the number of gallons filled vs the time; this relation is shown through the horizontal axis (time) and the vertical axis (gallons). Additionally, there is a constant rate because each hour 2,500 gallons are filled, which creates a steep constant line.
However, if the rate decreases, fewer gallons would be filled every hour, and the line will be less steep, this is because the number of gallons will not increase as fast as with the original rate. For example, if the rate is 1,250 gallons per hour (half the original rate), after 8 hours the total of gallons would be 1000 gallons (half the amount of gallons); and this would make the line to be less steep or more horizontal.
Trucks in a delivery fleet travel a mean of 100 miles per day with a standard deviation of 23 miles per day. The mileage per day is distributed normally. Find the probability that a truck drives between 86 and 125 miles in a day. Round your answer to four decimal places.
Answer:
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles
Step-by-step explanation:
Step(i):-
Given mean of the Population = 100 miles per day
Given standard deviation of the Population = 23 miles per day
Let 'X' be the normal distribution
Let x₁ = 86
[tex]Z_{1} = \frac{x_{1} -mean}{S.D} = \frac{86-100}{23} =-0.61[/tex]
Let x₂= 86
[tex]Z_{2} = \frac{x_{2} -mean}{S.D} = \frac{125-100}{23} = 1.086[/tex]
Step(ii):-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = P(-0.61 ≤ Z≤ 1.08)
= P(Z≤ 1.08) - P(Z≤ -0.61)
= 0.5 +A(1.08) - ( 0.5 - A(-0.61))
= A(1.08) + A(0.61) ( A(-Z)= A(Z)
= 0.3599 + 0.2291
= 0.5890
Conclusion:-
The probability that a truck drives between 86 and 125 miles in a day.
P(86≤ X≤125) = 0.5890 miles per day
The table shows three unique functions. (TABLE IN PIC) Which statements comparing the functions are true? Select three options. Only f(x) and h(x) have y-intercepts. Only f(x) and h(x) have x-intercepts. The minimum of h(x) is less than the other minimums. The range of h(x) has more values than the other ranges. The maximum of g(x) is greater than the other maximums.
Answer:
(A)Only f(x) and h(x) have y-intercepts.
(C)The minimum of h(x) is less than the other minimums.
(E)The maximum of g(x) is greater than the other maximums.
Step-by-step explanation:
From the table
f(0)=0 and h(0)=0, therefore, Only f(x) and h(x) have y-intercepts. (Option A)
Minimum of f(x)=-14Minimum of g(x)=1/49Minimum of h(x)=-28Therefore, the minimum of h(x) is less than the other minimums. (Option C).
Maximum of f(x)=14
Maximum of g(x)=49
Maximum of h(x)=0
Therefore, the maximum of g(x) is greater than the other maximums. (Option E)
Answer: It's B,C, and E
Step-by-step explanation:
Which steps would be used to solve the equation? Check all that apply. 2 and two-thirds + r = 8 Subtract 2 and two-thirds from both sides of the equation. Add 2 and two-thirds to both sides of the equation. 8 minus 2 and two-thirds = 5 and one-third 8 + 2 and two-thirds = 10 and two-thirds Substitute the value for r to check the solution.
Answer:
Subtract 2 and two-thirds from both sides of the equation
8 minus 2 and two-thirds = 5 and one-third
Substitute the value for r to check the solution.
Step-by-step explanation:
2 2/3 + r = 8
Subtract 2 2/3 from each side
2 2/3 + r - 2 2/3 = 8 - 2 2/3
r = 5 1/3
Check the solution
2 2/3 +5 1/3 =8
8 =8
Answer:
1, 3, 5
Step-by-step explanation:
edge
Jacqueline and Maria set up bug barns to catch lady bugs. Jacqueline caught ten more than three times the number of lady bugs that Maria caught. If c represents the number of lady bugs Maria caught, write an expression for the number of lady bugs that Jacqueline caught.
Answer:
(CX3)+10
Step-by-step explanation:
Answer:
c×3+10= j
Step-by-step explanation:
Please answer this correctly
Answer:
The second question
Step-by-step explanation:
The orca starts at -25 meters. She goes up 25 meters.
up 25 = +25
-25+25=0
Answer:
Option 2
Step-by-step explanation:
The orca swims at the elevation of -25 meters. The orca swims up 25 meters higher than before.
-25 + 25 = 0
is this right one more i think lol
Answer:
Yup P is the right one having 62.26%
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
We can set it up as
P = 33/53
Q = 20/48
R = 54/90
S = 44/83
This is because we are calculating the percent of yellow birds in the total amt. of birds in a specified park.
Now we calculate =>
P = 33/53 = around 0.62
Q = 20/48 = around 0.416
R = 54/90 = 0.6
S = 44/83 = around 0.53
We find that Park P has the greatest percentage and -->
Thus, Park P is our answer and yes, you are correct.
solve and find the value of (1.7)^2
Answer:
2.89
Step-by-step explanation:
just do 1.7×1.7=2.89
Help with one integral problem?
Answer: [tex]2\sqrt{1+tant}+C[/tex]
Step-by-step explanation:
To integrate means to find the antiderivative of the function. For this problem, we can use u-substitution.
[tex]\int\limits {\frac{dt}{cos^2t\sqrt{1+tant} } } \[/tex]
Let's first use our identities to rewrite the function. Since [tex]\frac{1}{cosx} =secx[/tex], we can use this identity.
[tex]\int\limits {\frac{sec^2t}{\sqrt{1+tant} } } \,[/tex]
[tex]u=\sqrt{1+tant}[/tex]
[tex]du=\frac{sec^2t}{2\sqrt{1+tant} } dt[/tex]
Now that we have u and du, we can plug them back in.
[tex]\int\limits {2} \, du[/tex]
[tex]\int\limits{2} \, du=2u[/tex]
Since we know u, we can plug that in.
[tex]2\sqrt{1+tant}[/tex]
This may seem like the correct answer, but we forgot to add the constant.
[tex]2\sqrt{1+tant}+C[/tex]
If the 2412 leaves are not a random sample, but the researchers treated the 2412 leaves as a random sample, this most likely made the data more:_____________.1. accurate, but not precise2. precise, but not accurate3. neither4. both accurate and precise
Answer:
2. Precise but not accurate
Step-by-step explanation:
In a high precision, low accuracy case study, the measurements are all close to each other (high agreement between the measurements) but not near/or close to the center of the distribution (how close a measurement is to the correct value for that measurement)
Lisa drew three circles to form a figure. The areas of the circles were in the
ratio 1:4:16. She then shaded some parts of the figure as shown.
What fraction of the figure was shaded?
Answer:
Fraction of the figure shaded = [tex]\frac{13}{16}[/tex]
Step-by-step explanation:
Ratio of the areas of the given circles are 1 : 4 : 16
Then the radii of the circles will be in the ratio = [tex]\sqrt{1}:\sqrt{4}:\sqrt{16}[/tex]
= 1 : 2 : 4
If the radius of the smallest circle = x units
Then the radius of the middle circle = 2x units
and the radius of the largest circle = 4x units
Area of the smallest circle = πx²
Area of the middle circle = π(2x)² = 4πx²
Area of the largest circle = π(4x)²= 16πx²
Area of the region which is not shaded in the middle circle = πx²(4 - 1)
= 3πx²
Therefore, area of the shaded region = Area of the largest circle - Area of the region which is not shaded
= 16πx² - 3πx²
= 13πx²
Fraction of the figure which is not shaded = [tex]\frac{\text{Area of the shaded region}}{\text{Area of the largest circle}}[/tex]
= [tex]\frac{13\pi x^{2} }{16\pi x^{2} }[/tex]
= [tex]\frac{13}{16}[/tex]
Una persona se dirige a un edificio y observa lo alto del mismo con un ángulo de elevación “x”, después de caminar 10m observa al mismo punto anterior con ángulo de elevación “y”, si la altura del edificio es de 30m. Calcule: "3Tgx.Ctgy + Tgx"
Answer:
3
Step-by-step explanation:
To begin with notice that
[tex]\displaymode{ \tan(x) = \frac{30}{10 + 30\cot(y)} }[/tex]
From that equation you get that
10 tan(x) + 30tan(x) cot(x) = 30
therefore
tan(x) + 3 tan(x) cot(x) = 3
please i need this answer right now !!!! Dx
Answer: the answer is d sin30degrees equal 5/x because sin is opposite over hyponuese
Find the hypotenuse of a right triangle (in cm) if one leg measures 7 cm and the other leg measures 11 cm. Round to the nearest thousandth. ____________ cm
Using the Pythagorean theorem
Hypotenuse = sqrt( 11^2 + 7^2)
= sqrt( 121 + 39)
= sqrt( 160)
= 12.694
What is the greatest common factor of the polynomial below?
20x^3 - 14x
Answer:
the correct answer is 2x
Answer:
D. 2x
Step-by-step explanation:
20x² : 1, 2, 4, 5, 10, 20, x
14x : 1, 2, 7, 14, x
The greatest common factor of the polynomial is 2x.
2x(10x² - 7)
A pet store has 10 puppies, including 2 poodles, 3 terriers, and 5 retrievers. If Rebecka and Aaron, in that order, each select one puppy at random without replacement find the probability that both select a poodle.
The probability is
Answer:
2/10 for Rebecka and either 2/9 or 1/9 for Aaron depending on if Rebecka selects a poodle or not.
Step-by-step explanation:
do some math
I don't know what to do.
Answer:
104.93 in
Step-by-step explanation:
When we draw out a picture of our triangle, we should see that we need to use sin∅ to solve:
sin23° = 41/x
xsin23° = 41
x = 41/sin23°
x = 104.931
Evaluate. Write your answer as a fraction or whole number without exponents. 1/10^-3 =
Answer:
1000
Step-by-step explanation:
=> [tex]\frac{1}{10^{-3}}[/tex]
According to the law of exponents, [tex]\frac{1}{a^{-m}} = a^{m}[/tex]
So, it becomes
=> [tex]10^{3}[/tex]
=> 1000
F (X) = x² - 2x and 6(x) = 3x+1
A) Find F(g(-4))
B) Find F(g(x)) simply
C) find g^-1 (x)
Part A
g(x) = 3x+1
g(-4) = 3(-4)+1 ... every x replaced with -4
g(-4) = -12+1
g(-4) = -11
Plug this into the f(x) function
f(x) = x^2 - 2x
f( g(-4) ) = (g(-4))^2 - 2( g(-4) )
f( g(-4) ) = (-11)^2 - 2(-11)
f( g(-4) ) = 121 + 22
f( g(-4) ) = 143 is the answer====================================================
Part B
Plug the g(x) function into the f(x) function
f(x) = x^2 - 2x
f( g(x) ) = ( g(x) )^2 - 2( g(x) ) ... replace every x with g(x)
f( g(x) ) = (3x+1)^2 - 2(3x+1)
f( g(x) ) = (9x^2+6x+1) + (-6x-2)
f( g(x) ) = 9x^2+6x+1-6x-2
f( g(x) ) = 9x^2-1 is the answerNote that we can plug x = -4 into this result and we would get
f( g(x) ) = 9x^2-1
f( g(-4) ) = 9(-4)^2-1
f( g(-4) ) = 9(16)-1
f( g(-4) ) = 144-1
f( g(-4) ) = 143 which was the result from part A
====================================================
Part C
Replace g(x) with y. Then swap x and y. Afterward, solve for y to get the inverse.
[tex]g(x) = 3x+1\\\\y = 3x+1\\\\x = 3y+1\\\\3y+1 = x\\\\3y = x-1\\\\y = \frac{1}{3}(x-1)\\\\y = \frac{1}{3}x-\frac{1}{3}\\\\g^{-1}(x) = \frac{1}{3}x-\frac{1}{3}\\\\[/tex]
The total area under the standard normal curve to the left of zequalsnegative 1 or to the right of zequals1 is
Answer:
0.3174
Step-by-step explanation:
Z-score:
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 area under the normal curve to the left of Z. Subtracting 1 by the pvalue, we find the area under the normal curve to the right of Z.
Left of z = -1
z = -1 has a pvalue of 0.1587
So the area under the standard normal curve to the left of z = -1 is 0.1587
Right of z = 1
z = 1 has a pvalue of 0.8413
1 - 0.8413 = 0.1587
So the area under the standard normal curve to the right of z = 1 is 0.1587
Left of z = -1 or right of z = 1
0.1587 + 0.1587 = 0.3174
The area is 0.3174
Write the equation of a line that goes through point (0, -8) and has a slope of 0
Answer:
Step-by-step explanation:
y + 8 = 0(x - 0)
y + 8 = 0
y = -8
what is -34/15 in decimal form
Answer:
2.26 repeating
Step-by-step explanation:
Convert the fraction to a decimal by dividing the numerator by the denominator.
hope this helpes
be sure to give brainliest
the diagram shows a circle drawn inside a square the circle touches the edges of the square
Answer:
69.5309950592 cm²
Step-by-step explanation:
Area of Square:
Area = [tex]Length * Length[/tex]
Area = 18*18
Area = 324 square cm
Area of circle:
Diameter = 18 cm
Radius = 9 cm
Area = [tex]\pi r^2[/tex]
Area = (3.14)(9)²
Area = (3.14)(81)
Area = 254.469004941 square cm
Area of Shaded area:
=> Area of square - Area of circle
=> 324 - 254.469004941
=> 69.5309950592 cm²