Answer:
0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes
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 establishes 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.
Mean of 50 minutes and a standard deviation of 10 minutes.
This means that [tex]\mu = 50, \sigma = 10[/tex]
Class size of 30 students
This means that [tex]n = 30, s = \frac{10}{\sqrt{30}}[/tex]
What is the probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes.
This is the p-value of Z when X = 48.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{48.5 - 50}{\frac{10}{\sqrt{30}}}[/tex]
[tex]Z = -0.82[/tex]
[tex]Z = -0.82[/tex] has a p-value of 0.2061
0.2061 = 20.61% probability, given a class size of 30 students, the average time to complete the test is less than 48.5 minutes
• A certain test consists of multiple-choice questions
and essay questions in the ratio of 5:2. If the test
contains 6 essay questions, what is the total number
of questions on the test?
Answer: 21
Step-by-step explanation:
My teacher just did it
Roger has found a home to be purchase for $120,372 and has agreed to pay 28% down. Find the amount of Roger's down payment. Find the amount of money that Roger would need to borrow through a mortgage in order to purchase the home.
If Roger found a 30 year mortgage with a 5.9% APR. Find Roger's monthly payment. Using the monthly payment how much did Roger pay over the life of the mortgage?
Round your answer to the nearest cent.
Answer:
He needs to borrow: 86667.84
His monthly payment would be: 514.06
He would pay a total of: 185061.6 over the life of the loan
Step-by-step explanation:
roger would need to borrow .72*120372= 86667.84
2.)
calculate the effective rate .059/12= .004916667
[tex]86667.84=x\frac{1-(1+.004916667)^{-30*12}}{.004916667}\\x=514.0585984[/tex]
which we round to 514.06
3.) he is going to pay a total of 514.06*30*12= 185061.6 over the life of the loan
PLEASE HELP ASAP!!! I don’t know how to do this problem or where to start! How do I solve this?
Answer:
W = 4.95
Step-by-step explanation:
You want to start by writing down what you know, and forming a system of equations.
L= length W= width
2L+2W=14.7
L= 2.4
On the left side of the equation, you're adding all your side lengths, and on the right, is the total perimeter. (Also could be written L+L+W+W = 14.7)
You would then substitute L from the bottom equation into the top equation to get:
2(2.4) +2W=14.7
Solving:
4.8+2w=14.7
W= 4.95
To check your answer simply add all the sides together and make sure it equals your perimeter. You can also plug W and L back into the original equation.
if the smaller side of a rectangle was increased by 7 cm, it would be exactly 55% of the 110 cm longer side. Find the area of the rectangle
Answer:
5886 cm
Step-by-step explanation:
start by finding 55% of 110 which is 60.5. then subtract by 7 and then you get 53.5
then multiply 53.5 by 110 = 5885 cm
write the volume formula beside the solid figure
Answer:
cube(v=l×l×l)
cylinder (v= πr^2h)
cone(v=1/3πr^2h)
rectangular prism (v= area of base×lenght)
pyramid (v=1/3×area of base×h)
Step-by-step explanation:
Cube:-a^3
Cuboid:-lbh
Cylinder :-pi r^2h
Cone:-1/3pi r^2h
In the word PARADISE,how many pairs are there which have as many letters between them in the word as in the alphabet?
Answer:
three
P A R
A R A D
A D I S E
P Q R
A B C D
A B C D E
There are three such pairs of letters.
For the inequality 4x2>y−3, where is the graph shaded and is the curve solid or dotted?
Answer:
Dotted Curve
Shaded Area includes the Origin.
Step-by-step explanation:
I am assuming that you mean 4x² > y-3.
Since the inequality sign is greater than, the line would be dotted. The curve would be solid if the inequality was an 'X or equal to' sign.
----------------------------------
4(0)² > 0 - 3
0 > -3
Since the given statement is true, the origin is a solution and we would shade below the curve.
----------------------------------
See the graph attached.
Hope this helps.
(2x+3)(5x-8)
10x7€ 16x+158–24
10x2-x-24
Answer:
16X+134
Step-by-step explanation:
Describe the motion of a particle with position (x, y) as t varies in the given interval. (For each answer, enter an ordered pair of the form x, y.) x = 1 + sin(t), y = 3 + 2 cos(t), π/2 ≤ t ≤ 2π
Answer:
The motion of the particle describes an ellipse.
Step-by-step explanation:
The characteristics of the motion of the particle is derived by eliminating [tex]t[/tex] in the parametric expressions. Since both expressions are based on trigonometric functions, we proceed to use the following trigonometric identity:
[tex]\cos^{2} t + \sin^{2} t = 1[/tex] (1)
Where:
[tex]\cos t = \frac{y-3}{2}[/tex] (2)
[tex]\sin t = x - 1[/tex] (3)
By (2) and (3) in (1):
[tex]\left(\frac{y-3}{2} \right)^{2} + (x-1)^{2} = 1[/tex]
[tex]\frac{(x-1)^{2}}{1}+\frac{(y-3)^{2}}{4} = 1[/tex] (4)
The motion of the particle describes an ellipse.
round 3,236 to the nearest hundred
Answer:
3,200
Step-by-step explanation:
3 is less than 5 so you round down to 3,200
If X is a normal random variable with mean 6 and standard deviation 2.0, then find the value x such that P(X > x) is equal to .7054. Group of answer choices5.28
5.46
4.92
7.28
Answer:
Step-by-step explanation:
If X is a normal random variable with a mean of 6 and a standard deviation of 3.0, then find the value x such that P(Z>x)is equal to .7054.
-----
Find the z-value with a right tail of 0.7054
z = invNorm(1-0.7054) = -0.5400
x = zs+u
x = -5400*3+6 = 4.38
We have just performed a one-way ANOVA on a given set of data and rejected the null hypothesis for the ANOVA F test. Assume that we are able to perform a randomized block design ANOVA on the same data. For the randomized block design ANOVA, the null hypothesis for equal treatments will ________ be rejected.
Answer:
The answer is "sometimes".
Step-by-step explanation:
A one-way ANOVA was merely performed on one collected data and the null hypothesis was rejected after an ANOVA F test. Assume we could randomize ANOVA block design with the same information. This null hypothesis for full equality is sometimes rejected for the randomized complete block design ANOVA. Therefore we understand the use of randomized ANOVA block if the null hypothesis is denied of a one-way ANOVA but the rejection of a null RBD ANOVA hypothesis isn't conditional mostly on denial of the yet another ANOVA null.
one number is seven less than the second number. five times the first is 9 more than 6 times the second. find the numbers
Step-by-step explanation:
2nd number = x
1st number = x - 7
5 (x - 7) = 6x + 9
5x - 35 = 6x + 9
- x = 44
x = - 44
1st number = -51
2nd number = -44
Proof: 5 (-51) = 6(-44) + 9
-255 = -264 + 9
-255 = -255
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
જ્યારે જહાંગીરની ઉંમર 18 વર્ષ થશે ત્યારે અકબરની ઉંમર 50 વર્ષ થર્શ.
જ્યારે અકબરની ઉંમર જહાંગીરની ઉંમર કરતા 5 ઘણી હશે ત્યારે
અકબરની ઉમર કેટલી હશે?
A) 36
B) 40
C) 44
D) 48
Answer:
C: 44
Step-by-step explanation:
The area of a circle is 3.142cm square.find the radius and diameter of the circle
Answer:
50.24 or 50.272
Step-by-step explanation:
Square radius and then times by 3.14 or 3.142
4^2*3.14 = 50.24
4^2*3.142 = 50.272
) A patient drank 12 ounces of orange juice. How many milliliters did the patient drink?
Answer:
[tex]Drink = 354.882\ mL[/tex]
Step-by-step explanation:
Given
[tex]Drink = 12oz[/tex]
Required
Equivalent in mL
We have:
[tex]1\ oz = 29.5735\ mL[/tex]
So:
[tex]Drink = 12 * 29.5735mL[/tex]
[tex]Drink = 354.882\ mL[/tex]
Circle O has radius 5 m with an arc AB intercepted by a central angle of π5π5 radians. What is the length of arc AB expressed in terms of ππ?
Answer:
I am assuming that you meant to write π/5.
Step-by-step explanation:
Radius r = 5 meters
Circumference = 2πr = 10π
Central angle θ = π/5 radian
Arc length = 10π × θ/(2π radians)
= 5θ
= π meters
Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n
inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer,
while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches
greater than the box he originally planned to build?
O 3n2 + 2n
312 + 3n+3
O 6n2 + 3n
O 6n2 + 3n+3
Given:
Edge of a cubic box = n inches.
He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.
To find:
How many cubic inches greater than the box he originally planned to build?
Solution:
Edge of a cubic box is n inches, so the volume of the original cube is:
[tex]V_1=(edge)^3[/tex]
[tex]V_1=n^3[/tex]
According to the given information,
New width of the box = n+1
New length of the box = n+2
New height of the box = n
So, the volume of the new box is:
[tex]V_2=Length\times width\times h[/tex]
[tex]V_2=(n+2)(n+1)n[/tex]
[tex]V_2=(n^2+2n+n+2)n[/tex]
[tex]V_2=(n^2+3n+2)n[/tex]
[tex]V_2=n^3+3n^2+2n[/tex]
Now, the difference between new volume and original volume is:
[tex]V_2-V_1=n^3+3n^2+2n-n^3[/tex]
[tex]V_2-V_1=3n^2+2n[/tex]
So, the volume of new box is 3n^2+2n cubic inches more than the original box.
Therefore, the correct option is A.
I NEED HELP ILL MARK!!!
Answer:
c) tan
Step-by-step explanation:
For the 63-deg angle, YZ is the opposite leg. The unknown side, AY, is the adjacent leg. The trigonometric ratio that relates the opposite and adjacent legs is the tangent.
Answer: c) tan
Find the value of z, the measure of the subtended arc.
86°
47°
188°
94°
Answer:
188 degrees
Step-by-step explanation:
The measure of the arc is the center angle, that is double of the circumference one
94 * 2 = 188 degrees
kxndjdkdkdkkdkskskdkdjdjdjskskskdjdjddjd
Answer:
Not a functionFunctionFunctionNot a functionNot a functionHope this helps!
When the suns rays are at an angle of 39° the distance from the top of Dakotas head to the tip of the shadow is 77 inches, about how tall is Dakota?
Answer:
48.45in
Step-by-step explanation:
To get the height of Dakota, we will use the SOH CAH TOA
Given the following
angle of elevation = 39degrees
distance from the top of Dakotas head to the tip of the shadow = 77in (Hyp)
Required
Height of Dakota (Opp)
Sin 39 = opposite/hyp
Sin39 = H/77
H = 77sin39
H = 77(0.6293)
H = 48.45in
Hence the Dakota is 48.45in
For what values of the variable, do the following fractions exist: y^2-1/y+y/y-3
For what values of the variable, do the following fractions exist: b+4/b^2+7
For what values of the variable, do the following fractions exist: a/a(a-1)-1
PLEASE HELP NEED ANSWER ASAPPPP!!!! WILL GIVE BRAINLIEST TO FIRST CORRECT ANSWERRRR!!!
Answer:
Remember that the division by zero is not defined, this is the criteria that we will use in this case.
1) [tex]\frac{y^2 - 1}{y} + \frac{y}{y - 3}[/tex]
So the fractions are defined such that the denominator is never zero.
For the first fraction, the denominator is zero when y = 0
and for the second fraction, the denominator is zero when y = 3
Then the fractions exist for all real values except for y = 0 or y = 3
we can write this as:
R / {0} U { 3}
(the set of all real numbers except the elements 0 and 3)
2) [tex]\frac{b + 4}{b^2 + 7}[/tex]
Let's see the values of b such that the denominator is zero:
b^2 + 7 = 0
b^2 = -7
b = √-7
This is a complex value, assuming that b can only be a real number, there is no value of b such that the denominator is zero, then the fraction is defined for every real number.
The allowed values are R, the set of all real numbers.
3) [tex]\frac{a}{a*(a - 1) - 1}[/tex]
Again, we need to find the value of a such that the denominator is zero.
a*(a - 1) - 1 = a^2 - a - 1
So we need to solve:
a^2 - a - 1 = 0
We can use the Bhaskara's formula, the two values of a are given by:
[tex]a = \frac{-(-1) \pm \sqrt{(-1)^2 + 4*1*(-1)} }{2*1} = \frac{1 \pm \sqrt{5} }{2}[/tex]
Then the two values of a that are not allowed are:
a = (1 + √5)/2
a = (1 - √5)/2
Then the allowed values of a are:
R / {(1 + √5)/2} U {(1 - √5)/2}
Please help me on this
Answer:
58.8 in²
Step-by-step explanation:
you have no calculator ?
since you clearly have a computer or smart phone - there are calculator apps on all of them.
you really just need to use the given numbers and multiply and add them following the formula. so, what is your problem ?
anyway,
2pi×r×h + 2pi×r²
h = 5.9
r = 1.3
2pi × 1.3 × 5.9 + 2pi × 1.3² = 2pi × 7.67 + 2pi × 1.69 =
= 58.8 in²
In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 21% of your total grade, each major test is worth 25%, and the final exam is worth 29%. Compute the weighted average for the following scores: 60 on the lab, 81 on the first major test, 69 on the second major test, and 79 on the final exam. Enter your answer as a whole number.
Answer:
[tex]Weighted\ Average = 73[/tex]
Step-by-step explanation:
Given
[tex]Lab = 21\%[/tex]
[tex]Tests = 25\%[/tex]
[tex]Exam = 29\%[/tex]
[tex]Lab\ Score = 60[/tex]
[tex]First\ Test = 81[/tex]
[tex]Second\ Test = 69[/tex]
[tex]Exam = 79[/tex]
Required
The weighted average
To do this, we simply multiply each score by the corresponding worth.
i.e.
[tex]Weighted\ Average = Lab\ worth * Lab\ score + Tests\ worth * Tests\ score.....[/tex]
So, we have:
[tex]Weighted\ Average = 21\% * 60 + 25\% * 81 + 25\% * 69 + 29\% * 79[/tex]
Using a calculator, we have:
[tex]Weighted\ Average = 73.01[/tex]
[tex]Weighted\ Average = 73[/tex] --- approximated
If angles A and B are consecutive interior angles, what is the measure of
angle B if angle A measures 75°?
A. 105
B. 75
C. 180°
O
D. 90°
SUBMIT
Answer:
A
Step-by-step explanation:
180 - 75 = 105
(ar^b) ^4 = 16r^20 where a and b are positive integers work our a and b
Answer:
a = 2
b = 5
Step-by-step explanation:
Given :
(ar^b)^4 = 16r^20 ; a and b are positive integers :
Opening the bracket :
a^4r^4b = 16r^20
a^4 = 16 - - - - - (1)
r^4b = r^20 - - - (2)
a^4 = 16
Take the 4th root of both sides :
(a^4)^(1/4) = 16^1/4
a = 2
From (2)
r^4b = r^20
4b = 20
Divide both sides by 4
4b/4 = 20/4
b = 5
Hence ;
a = 2
b = 5
Andrew worked over 40 hours this week. He earns $12 an hour and gets paid time and a half for overtime. If x represents total hours worked, which equation will result in the
amount of money earned for the week?
Answer:
y = 480 + 1.5 (x-40)
Step-by-step explanation:
sometimes its better to answer the question and make the formula from that
40 x 12 = 480
1.5 for overtime
x
y = 480 + 1.5 (x-40)
Okay, let's calculate the year end adjustment for overhead. Based on the data below, determine the amount of the year end adjustment to cost of goods sold due to over or under allocated manufacturing overhead during the year
Answer:
the adjustment made to the cost of goods sold is -$2,014
Step-by-step explanation:
The computation of the adjustment made to the cost of goods sold is given below:
Total actual overhead expenses $110,822
Less: Total overheads allocated -$112,836
Adjustment made to the cost of goods sold -$2,014
Hence, the adjustment made to the cost of goods sold is -$2,014
The same should be considered
A researcher designs an experiment by manipulating the following variables: temperature (low or high), illumination level (low or high), and time of testing (day or night). For a repeated measures design, how many participants would the researcher require in order to have 10 participants per condition?
Answer:
10
Step-by-step explanation:
As it could be inferred from the name, repeated measure design may be explained as experimental measures involving multiple (more than one) measures of a variable on the same observation, subject or participants which are taken at either various times or periodic intervals, different levels, different conditions. Hence, a repeated measurement taken with the same sample but under different treatment conditions. Therefore, since the measurement will be performed on a the same subjects(paired) , then the number of subjects needed will be 10. As it is this same samples that will be used for the other levels or conditions.
