Step-by-step explanation:
[tex]U _{ {12}^{th} } = a {r}^{(n - 1)} \\ = 5 \times {5}^{12 - 1} \\ = 244140625 \\ {12}^{th} \: term \: is \: 244140625[/tex]
Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a standard deviation of minutes. Test the hypothesis that against the alternative that if a random sample of the test times of high school seniors has a standard deviation . Use a level of significance.
Complete question :
Past experience indicates that the time required for high school seniors to complete a standardized test is a normal random variable with a mean of 35 minutes. If a random sample of 20 high school seniors took an average of 33.1 minutes to complete this test with a standard deviation of 4.3 minutes, test the hypothesis, at the 0.05 level of significance.
Answer:
We conclude they there is significant evidence to support the claim That time required for high school seniors to complete test is less than 35 minutes.
Step-by-step explanation:
H0 : μ = 35
H1 : μ < 35
Sample size, n = 20
Standard deviation, s = 4.3
xbar = 33.1
Test statistic :
T = (xbar - μ) ÷ (s /√n)
T = (33.1 - 35) ÷ (4.3 /√20)
T = - 1.9 ÷ 0.9615092
T = - 1.976
The Pvalue can be obtained from the test statistic using a Pvalue calculator :
Pvalue at 0.05 ; df = 19 is 0.0314
Since, Pvalue < α ; We reject the Null and conclude that time required for high school candidate to complete test is less than 35 minutes
The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F. What is the probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal? Do not write probability in terms of percentage. Round your answer to two decimal places.
Answer:
0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, 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.
The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F.
This means that [tex]\mu = 57, \sigma = 10[/tex]
Sample of 25:
This means that [tex]n = 25, s = \frac{10}{\sqrt{25}} = 2[/tex]
of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal?
This is 1 subtracted by the pvalue of Z when X = 59. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59 - 57}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.84
1 - 0.84 = 0.16
0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.
Please help with this question it is due today I will give 20 points. Thank you and may God bless you! :)
I would say A but please wait for someone else to answer to make sure it's not wrong I would hate for you to get this wrong
A bicycle is originally priced at $60. The online retailer gives a discount and the bicycle is now priced at $42. Enter the percentage discount for the cost of the bicycle.
Answer:
30% ywww
Step-by-step explanation:
Define the following terms using your own words. (2-3 sentences only)
1. Frequency
2 Class size
3. Ogive
4. Variance
5. Range
Answer:
Frequency: the rate at which something occurs over a particular period of time or in a given sample.Class size :Class size is the average number of students per class, calculated by dividing the number of students enrolled by the number of classes..O give :Ogive is the curve which is constructed by plotting cumulative frequency data on the graph paper, in the form of a smooth curve.Variance: The term variance refers to a statistical measurement of the spread between numbers in a data set. Range: The range, the difference between the largest value and the smallest value.A piecewise function is given.
Find f(-4)
Answer:
3
Step-by-step explanation:
For x<=0, f is constant: f(x) =3
-4<0, so f(-4)=3
What is m ZPQR?
R
(x + 3)
(3x + 5)
S.
Р
Answer:
3 x 2 − 2 x -5
Step-by-step explanation:
The base and height of a triangle are 9 yards and 10 yards respectively. Find the area of the triangle.
Answer:
45
Step-by-step explanation:
1/2×9×10
since the formula says half base times height, so therefore
Area =45
An agricultural scientist collected data to study the relationship between the amount of nitrogen added to a cornfield and the number of
bushels of corn produced. This is the regression line of the data, where y is measured in bushels of corn and x is measured in pounds of
nitrogen.
y = 0.43x + 28.5
What is the meaning of the slope of the regression line?
O A. For every 0.43 pounds of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
OB. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
-
OC. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 28.5 bushels.
OD. For every 28.5 pounds of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels.
Answer:
D.
Step-by-step explanation:
just done the assignment
Linear regression line is a algebraic model to show the relationship between the two models by putting the value of the one variable to get the value of other.. For every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels. Therefore the option B is the correct option.
Given information-The equation of the experiment to know the relationship between the amount of nitrogen added to a cornfield and the number of bushels of corn produced is,
[tex]y=0.43x+28.5[/tex]
Linear regression lineLinear regression line is a algebraic model to show the relationship between the two models by putting the value of the one variable to get the value of other.
Linear regression line can be represent as,
[tex]y=Ax+B[/tex]
Here x is the explanatory variable and y is the dependent variable. A is the slope of the line and B is the intercept.
In the given equation there are two variable given.
Variable x represent the amount of nitrogen added, and the variable y, represents the number of bushels of corn produced.
As putting the value of x the y increases with value of number 0.43. Thus as we are increasing the value of the nitrogen with unit 1 the number of bushels of corn produced is increased by unit 0.43.
Hence for every 1 pound of nitrogen added to the field, the amount of corn yielded increases by 0.43 bushels. Therefore the option B is the correct option.
Learn more about the linear regression here;
https://brainly.com/question/25311696
How many odd numbers are between 10 and 50?
Answer:
There are 20 odd numbers between 10 and 50
Step-by-step explanation:
Here are all the odd numbers! Hope this helps!
11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49
what is the smallest subset of the number -8,546,999 belong to
Answer:
its 4
Step-by-step explanation:
Verify the conclusion of Green's Theorem by evaluating both sides of the equation for the field F= -2yi+2xj. Take the domains of integration in each case to be the disk. R: x^2+y^2 < a^2 and its bounding circle C.
Answer:
hello your question is incomplete below is the complete question
verify the conclusion of Green's Theorem by evaluating both sides of the equation for the field F= -2yi+2xj. Take the domains of integration in each case to be the disk. R: x^2+y^2 < a^2 and its bounding circle C: r(acost)i+(asint)j, 0<t<2pi. the flux is ?? the circulation is ??
answer : attached below
Step-by-step explanation:
Attached below is the required verification of the conclusion of Green's Theorem
In the attached solution I have proven that Green's theorem ( ∫∫c F.Dr ) .
i.e. ∫∫ F.Dr = ∫∫r ( dq/dt - dp/dy ) dx dy = 4πa^2
The standard gasoline engine for the 2017 Toyota Corolla includes the following data: Configuration: In-line four-stroke, four-cylinder engine Bore: 3.17 in Stroke: 3.48 in Compression ratio: 10.6:1 Assuming an ideal Otto cycle to describe this engine. Consider the working fluid to be air, modeled as an ideal gas with variable specific heat. Determine: (a) The total engine volume VBDC for all cylinders (cu.in). (b) The mass of air (lbm) contained in the engine assuming ambient conditions of 540 R and 14.7 psia. (c) The efficiency of the engine (%). The maximum temperature that occurs during the cycle is 3600 R.
Answer:
a) The total engine volume is 30.3265 in³
b) the mass of air contained in the engine is 0.00129 lbm
c) The efficiency of the engine is 55.6%
Step-by-step explanation:
Given the data in the question;
The configuration is in line with four-stroke, four-cylinder engine.
Bore ( d ) = 3.17 in
Stroke ( L ) = 3.48 in
compression ratio ( r ) = 10.6 : 1
First, we calculate the swept Volume V₁ = π/4 × d²L
we substitute
V₁ = π/4 × (3.17 )² × (3.48) = 27.4655 in³
Now, Compression Ration; r = Vs + Vc / Vc
r = (V₁ + V₂) / V₂
we substitute
10.6 = (27.4655 + V₂) / V₂
10.6V₂ = 27.4655 + V₂
10.6V₂ - V₂ = 27.4655
9.6V₂ = 27.4655
V₂ = 2.861 in³
So
a) total engine volume
[tex]V_{BDC[/tex] = V₁ + V₂
we substitute
[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³
[tex]V_{BDC[/tex] = 27.4655 in³ + 2.861 in³
[tex]V_{BDC[/tex] = 30.3265 in³
Therefore, The total engine volume is 30.3265 in³
b) The mass of air
given that; T = 540°R, P = 14.7 psia
we know that; PV = mRT { R is constant }
we solve for m
m = PV / RT
we substitute
m = (14.7 × 30.3265) / ( 0.3704 × 1728 )540
m = 445.79955 / 345627.648
m = 0.00129 lbm
Therefore, the mass of air contained in the engine is 0.00129 lbm
c) The efficiency
from table { properties of air}
At 540°R; u₁ = 92.04 BTu/lbm, u[tex]_r[/tex]₁ = 144.32
Now process 1 - 2 ( Isentropic ) u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = V₁/V₁ = r
so, u[tex]_r[/tex]₁ / u[tex]_r[/tex]₂ = r
144.32 / u[tex]_r[/tex]₂ = 10.6
u[tex]_r[/tex]₂ = 144.32/10.6
u[tex]_r[/tex]₂ = 13.61
Thus, at u[tex]_r[/tex]₂ = 13.61, u₂ = 235 BTU/lbm, T₂ = 1340°R
Now, we know that;
P₁V₁/T₁ = P₂V₂/T₂ ⇒ (P₁/V₁)r = P₂/T₂
⇒ ( 14.7 / 540 )10.6 = P₂/1340
P₂ = 386.664 psia
process 2 - 3; constant volume heat addition;
Now, At T₃ = 3600°R, u₃ = 721.44 BTU/lbm, u[tex]_r[/tex]₃ = 0.6449
so, [tex]q_{in[/tex] = u₃ - u₂
we substitute
so, [tex]q_{in[/tex] = 721.44 - 235 = 486.44 BTU/lbm
Next, process 3 - 4; Isentropic
u[tex]_r[/tex]₄/u[tex]_r[/tex]₃ = V₄/V₃ = r
u[tex]_r[/tex]₄ / 0.6449 = 10.6
u[tex]_r[/tex]₄ = 6.8359
At u[tex]_r[/tex]₄ = 6.8359; u₄ = 308 BTU/lbm
∴
Heat Rejection [tex]q_{out[/tex] = u₄ - u₁ = 308 - 92.04 = 215.96 BTU/lbm
so, [tex]W_{net[/tex] = [tex]q_{in[/tex] - [tex]q_{out[/tex]
[tex]W_{net[/tex] = 486.44 - 215.96
[tex]W_{net[/tex] = 270.48 BTU/lbm
so the efficiency; η[tex]_{thermal[/tex] = ([tex]W_{net[/tex] / [tex]q_{in[/tex] ) × 100%
η[tex]_{thermal[/tex] = ( 270.48 / 486.44 ) × 100%
η[tex]_{thermal[/tex] = ( 0.55604 ) × 100%
η[tex]_{thermal[/tex] = 55.6%
Therefore, The efficiency of the engine is 55.6%
what is the midpoint of a segment with endpoints at (-4,-8) and (8,10)
Answer: Midpoint: (2, 1)
Step-by-step explanation:
Midpoint formula: ((x1 + x2)/2 , (y1 + y2)/2)
(-4 + 8)/2 = 2
(-8 + 10)/2 = 1
Answer: (2, 1)
what is the formula of finding square rood
Answer:
[tex] \huge\blue{ \mid{ \underline{ \overline{ \tt ♡ ANSWER ♡ }} \mid}}[/tex]
There's no specific formula to find the square root of a number, however we can find the square root of a number by the following methods:
i) By Prime Factorisation
ii) By Long Division
iii) By Repeated subtraction method
✏ By Prime Factorisation:Step I: Obtain the given number.
Step II: Reduce the given number into prime factors by successive division.
Step III: Now make pairs of prime factors in such a way that both the factors in each pair are equal.
Step IV: Take one factor from each pair and find the product of these factors.
Step V: The product obtained by multiplying the factors is the required square root.
✏ Long Division:Step 1: Firstly, we place a bar on every pair of digits starting from the unit digit. If the number of digits in it is odd, we put a bar on the single-digit too.
Step 2: Now we find the largest number whose square is less than or equal to the 1st number.
Step 3: Now we bring down the next bar number.
Step 4: For new divisor, we add the divisor & quotient.
Step 5: Number taken is the product of a new divisor and this digit is equal to or less than the new dividend.
✏ Repeated subtraction method:In this method, the given number is subtracted by 1, 3, 5, 7,… at every step till you get zero at the end. The number of steps in the solution is the required square root.
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
When graphed on a coordinate plane Beth’s house is located at (4, 3) and the coffee shop is located at the point (–2, –1).
What is the distance from Beth’s house to the coffee shop? Each grid line on the coordinate plane represents 1 mile.
10 miles
square root of 8
square root of 52
52 miles
Answer:
the answer is c square root 52
Step-by-step explanation:
just got a 100
The distance from Beth’s house to the coffee shop, which are graphed on a coordinate plane is √(52) units.
What is a distance formula?The distance formula is used to measure the distance between the two points on a coordinate plane.
Let the two coordinate point on a coordinate plane is ([tex]x_1,y_1[/tex]) and ([tex]x_2,y_2[/tex]). Thus, the distance between these two can be given as,
[tex]d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
When graphed on a coordinate plane Beth’s house is located at (4, 3) and the coffee shop is located at the point (–2, –1).
Here, each grid line on the coordinate plane represents 1 mile.
Using the distance formula for these point, the distance from Beth’s house to the coffee shop can be given as,
[tex]d=\sqrt{(4-(-2)^2)+(3-(-1))^2}\\d=\sqrt{6)^2+(4)^2}\\d=\sqrt{36+16}\\d=\sqrt{52}[/tex]
Hence, the distance from Beth’s house to the coffee shop, which are graphed on a coordinate plane is √(52) units.
Learn more about the distance formula here;
https://brainly.com/question/661229
what is the slope of the line.
Answer:
1 ..................or 1/1
Answer:
-1 is the slope
..................
Suppose that there is a black urn containing nine black balls and three yellow balls and there is a yellow urn containing six black balls and six yellow balls. An experiment consists of selecting at random a ball from the black urn and then (without replacing the first ball) selecting at random a ball from the urn having the color of the first ball.
1. Construct a tree diagram showing the probabilities associated with this problem. Write a probability on each branch (6 branches). Multiply the the probabilities along each path and write that number at the end of the path (4 answers).
2. Find the probability that the second ball is yellow.
Answer:
See Annex ( Tree diagram )
Step-by-step explanation:
1) Attached
2) Probability of the second ball is yellow is
P(2nd ball is yellow ) = Probability 2nd ball s yellow (if the first one was black) + Probability 2nd ball s yellow (if the first one was Yellow)
P(2nd ball is yellow ) = 0,204 + 0,045
P(2nd ball is yellow ) = 0,249
Helpppppppppppppppppppp
Answer:
95°
Step-by-step explanation:
95°
They are vertical angles.
Answer:
95 degree write it fast jakakkaoaoa
Select the correct answer.
In a sequence described by a function, what does the notation f(3) = 1 mean?
OA.
The third term in the sequence has a value of 1.
OB.
The common difference I of the sequence is 3.
O C.
The first term in the sequence has a value of 3.
OD
The common ratio of the sequence is 3.
Answer:
c is correct
Step-by-step explanation:
Answer:
c is right answer
Step-by-step explanation:
HOPE IT HELPS U
FOLLOW MY ACCOUNT PLS PLS
Challenge:
Put these in order (least to greatest)
Answer:
1 1/4, -1, -1/4, 0, 1/4, 1
Step-by-step explanation:
Answer:
-1 1/4, -1, -1/4, 0, 1/4, 1,
Step-by-step explanation:
How many faces does a triangular pyramid have?
A. 3
B. 6
C. 4
D. 5
[tex]\huge{\textbf{\textsf{{\color{navy}{An}}{\purple{sw}}{\pink{er}} {\color{pink}{:}}}}}[/tex]
C. 4.
thanks hope it helpsThe function g(x) is a transformation of the quadratic parent function, f(x)
What function is g(x)?
Answer:
Option A.
Step-by-step explanation:
The parent function is the quadratic function, that is:
[tex]f(x) = x^2[/tex]
Function g:
The function g is the function f concave down, that is, -f.
Also, for the parent function, we have that y = 1 when x = 1. On the function g, otherwise, we have that when x = 1, y = -1/3. So:
[tex]g(x) = -\frac{1}{3}f(x) = -\frac{1}{3}x^2[/tex]
The correct answer is given by option A.
-3x^2
just did it and it’s correct. Your welcome <3
A worldwide organization of academics claims that the mean IQ score of its members is 118, with a standard deviation of 17. A randomly selected group of 35 members of this organization is tested, and the results reveal that the mean IQ score in this sample is 116.8. If the organization's claim is correct, what is the probability of having a sample mean of 116.8 or less for a random sample of this size
Answer:
0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size
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 normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, 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.
The mean IQ score of its members is 118, with a standard deviation of 17.
This means that [tex]\mu = 118, \sigma = 17[/tex]
Sample of 35:
This means that [tex]n = 35, s = \frac{17}{\sqrt{35}}[/tex]
What is the probability of having a sample mean of 116.8 or less for a random sample of this size?
This is the pvalue of Z when X = 116.8. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{116.8 - 118}{\frac{17}{\sqrt{35}}}[/tex]
[tex]Z = -0.42[/tex]
[tex]Z = -0.42[/tex] has a pvalue of 0.3372
0.3372 = 33.72% probability of having a sample mean of 116.8 or less for a random sample of this size
Which fraction is the product of 5/4 x 6?
Answer:
15 x /2
Step-by-step explanation:
The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear out. The data (in kilometers) follow. Find a 99% confidence interval on the difference in the mean life.
Car Brand 1 Brand 2
1 36663 33866
2 43509 41829
3 36240 35500
4 32100 31950
5 37210 38015
6 48360 47800
7 38200 37810
8 33500 33215
a) Calculate SD =
b) Calculate a 99% two-sided confidence interval on the difference in mean life.
c) Which brand would you prefer? (brand 1/ no difference /brand 2)_____
Answer:
a) σ = 4933,64
b) CI 99% = ( - 5746 ; 7194 )
c) No difference in brands
Step-by-step explanation:
Brand 1:
n₁ = 8
x₁ = 38222
s₁ = 4974
Brand 2:
n₂ = 8
x₂ = 37498
s₂ = 4893
As n₁ = n₂ = 8 Small sample we work with t -student table
degree of freedom df = n₁ + n₂ - 2 df = 8 +8 -2 df = 14
CI = 99 % CI = 0,99
From t-student table we find t(c) = 2,624
CI = ( x₁ - x₂ ) ± t(c) * √σ²/n₁ + σ²/n₂
σ² = [( n₁ - 1 ) *s₁² + ( n₂ - 1 ) * s₂² ] / n₁ +n₂ -2
σ² = 7* (4974)² + 7*( 4893)² / 14
σ² = 24340783 σ = 4933,64
√ σ²/n₁ + σ²/n₂ = √ 24340783/8 + 24340783/8
√ σ²/n₁ + σ²/n₂ = 2466
CI 99% = ( x₁ - x₂ ) ± 2,624* 2466
CI 99% = 724 ± 6470
CI 99% = ( - 5746 ; 7194 )
As we can see CI 99% contains 0 and that means that there is not statistical difference between mean life of the two groups
(MATH) (6) ((PHOTO))
label is m
Multiply the length by the height:
6.5 x 2 = 13
The width is the volume divided by 13
Width = 52/13 = 4 m
The most expensive type of life insurance is
O limited-payment life insurance
O term insurance
O endowment life insurance
O whole-life insurance
Pls help i'll give brainlest
Answer: B. 183 cm^3
V = pi r^2 h/3
V = pi (5^2) (7/3)
V = pi (25) (2.33)
V = 183
Answer:
B.183 [tex]cm^{3}[/tex]
Step-by-step explanation:
Volume of cone is [tex]V=\pi r^{2} \frac{h}{3}[/tex]
where h=7 and r=5 (because r=d/2, where d=10)
V=[tex]5^{2}\frac{7}{3}\pi[/tex]
V=25·[tex]\frac{7}{3} \pi[/tex]
V=175/3[tex]\pi[/tex]
V=183.2595715 or 183 [tex]cm^{3}[/tex]
Ethan purchased a new cell phone for $75.00. The costs of the phone is included in his first month's bill. His cell phone plan charges $0.06 for each minute used.
if Ethan has $90.00 to spend on his first month's bill, what is the maximum number of minutes he can use?
A. 80 minutes
B. 250 minutes
C. 1,250 minutes
D. 1,500 minutes
Answer:1,250
Step-by-step explanation:
