Answer:
We accept H₀ we don´t have enough evidence to support that the mean thickness is greater than 41 mm
Step-by-step explanation:
Sample Information:
Results:
41.8
40.9
42.1
41.2
40.5
41.1
42.6
40.6
From the table we get:
sample mean : x = 41.35
sample standard deviation s = 0.698
Hypothesis Test:
Null Hypothesis H₀ x = 41
Alternative Hypothesis Hₐ x > 41
The test is a one-tail test
If significance level is 0.01 and n = 8 we need to use t-student distribution
From t-table α = 0.01 and degree of freedom df = n - 1 df = 8 - 1
df = 7 t(c) = 2.998
To calculate t(s) = ( x - 41 ) / s/√n
t(s) = ( 41.35 - 41 ) / 0.698/√8
t(s) = 0.35 * 2.83/ 0.698
t(s) = 1.419
Comparing t(s) and t(c)
t(s) < t(c)
t(s) is in the acceptance region we accept H₀
What is the equation of the line that passes through the point (1,7)and has a slope of -1
?
Answer:
y = -x + 8
Step-by-step explanation:
First, plug in the slope.
y = mx + b
y = -1x + b
y = -x + b
Then, plug in the point.
7 = -(1) + b
7 = -1 + b
8 = b
Five minivans and three trucks are traveling on a 3.0 mile circular track and complete a full lap in 98.0, 108.0, 113.0, 108.0, 102.0, 101.0, 85.0, and 95.0 seconds, respectively. Assuming all vehicles are traveling at constant speeds, what is the time-mean speed of the minivans
Answer:
The time-mean speed of the minivans is of 105.8 seconds.
Step-by-step explanation:
Mean of a data-set:
The mean of a data-set is the sum of all values in the data-set divided by the number of values.
Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.
Thus, the mean is:
[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]
The time-mean speed of the minivans is of 105.8 seconds.
prove that tan theta * sin theta = (1 - cos^2 theta)/(sqrt(1 - sin^2 theta))
Answer:
This identity holds as long as [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex].
For the proof, make use of the fact that:
[tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] (definition of tangents,) and
[tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] (Pythagorean identity,) which is equivalent to [tex]1 - \cos^{2}(\theta) = \sin^{2}(\theta)[/tex].
Step-by-step explanation:
Assume that [tex]\displaystyle \theta \ne k\, \pi + \frac{\pi}{2}[/tex] for all integer [tex]k[/tex]. This requirement ensures that the [tex]\tan(\theta)[/tex] on the left-hand side takes a finite value. Doing so also ensures that the denominator [tex]\sqrt{1 - \sin^2(\theta)}[/tex] on the right-hand side is non-zero.
Make use of the fact that [tex]\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}[/tex] to rewrite the left-hand side:
[tex]\begin{aligned} & \tan(\theta) \cdot \sin(\theta) \\ =&\; \frac{\sin({\theta})}{\cos({\theta})} \cdot \sin(\theta) \\ =&\; \frac{\sin^{2}(\theta)}{\cos(\theta)}\end{aligned}[/tex].
Apply the Pythagorean identity [tex]\sin^{2}(\theta) = 1 - \cos^{2}(\theta)[/tex] and [tex]\cos(\theta) = \sqrt{1 - \sin^{2}(\theta)}[/tex] to rewrite this fraction:
[tex]\begin{aligned} & \frac{\sin^{2}(\theta)}{\cos(\theta)}\\ =\; &\frac{1 - \cos^{2}(\theta)}{\cos(\theta)}\\ =\; & \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}\end{aligned}[/tex].
Hence, [tex]\displaystyle \tan(\theta) \cdot \sin(\theta) = \frac{1 - \cos^{2}(\theta)}{\sqrt{1 - \sin^{2}(\theta)}}[/tex].
There are 28 chocolate-covered peanuts in 1 ounce (oz). Jay bought a 62 oz. jar of chocolate-covered peanuts.
Problem:
audio
How many chocolate-covered peanuts were there in the jar that Jay bought?
Enter your answer in the box.
Answer:
1,736 chocolate cover peanuts
Step-by-step explanation:
do 28×62 hope this helps
Answer:
1736 chocolate-covered peanuts
Step-by-step explanation:
[tex]\frac{1}{62} :\frac{28}{y}[/tex]
1 · y = 62 · 28
y = 1736
Shawn thinks that helium prices next year might increase by 10%. He plans to buy 7 small balloons and x large balloons. He creates the following equation to find the total price for next year’s helium:P
Answer:
P = 7.7 C + 1.1 XC
Step-by-step explanation:
From the question, it is noted that the price of helium required to fill each of the balloons would increase by 10%. Let the current price of helium be C, so that;
10% of C = 0.1 C
The price of helium next year = C + 0.1 C
= 1.1 C
Cost of 7 small balloons = 1.1 C * 7
= 7.7 C
Cost of X large balloons = 1.1 C * X
= 1.1 XC
The total price, P for helium next year = 7.7 C + 1.1 XC
Thus, the equation to find the total price of helium that would fill the balloons next year is;
P = 7.7 C + 1.1 XC
Juan borrowed $1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%. What is the amount of interest he paid at the end of the loan
Answer:
The amount of interest he paid at the end of the loan is $ 311.85.
Step-by-step explanation:
Given that Juan borrowed $ 1500 from a credit union for 7 years and was charged simple interest at a rate of 2.97%, to determine what is the amount of interest he paid at the end of the loan, the following calculation must be performed:
(1500 x 0.0297) x 7 = X
44.55 x 7 = X
311.85 = X
Therefore, the amount of interest he paid at the end of the loan is $ 311.85.
PLS HELP ASAP !!! WILL MARK BRAINLIEST !!
Answer:
c is equal to e
Step-by-step explanation: a
one lap around a field is 4/5 of a mile .Adrian ran these laps . how far did he run?
A school class of 120 students is driven in 3 buses to a symphonic performance. There are 36 students in one of the buses, 40 in another, and 44 in the third bus. When the buses arrive, one of the 120 students is randomly chosen. Let X denote the number of students on the bus of that randomly chosen student, find E(X).
Answer:
40.2667
Step-by-step explanation:
P(X=36)= 36/120
P(X=40)= 40/120
P(X=44)=44/120
E(X) = 36(36/120)+40(40/120)+44(44/120)=1208/30=40.2667
hope this helps
If a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
It is given that:
A school class of 120 students is driven in 3 buses to a symphonic performance.
There are 36 students on one of the buses, 40 on another, and 44 on the third bus.
From the data given:
Let X be the total number of passengers on the bus carrying that randomly selected student,
Total number of students = 120
Let:
Probability:
P(X = 36) = 36/120
Probability:
P(X = 40)= 40/120
Probability:
P(X = 44)=44/120
E(X) = 36(36/120) + 40(40/120) + 44(44/120)
E(X) = 1208/30
E(X) = 40.26
Therefore, if a school class of 120 pupils is transported by three buses to a symphonic concert, the value of E(X) is 40.26.
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What is the integer x
so that x/9
lies between 71/7
and 113/11 ?
Answer:
(A) 89 (B) 91 (C) 92 (D) 95 4.If |x−2| = p, where x < 2, then x+1 equals (A) −2 (B) 3− p (C) |2p−2| (D) 2p−2 5.A
Step-by-step explanation:
Following are the calculation to the find the value of x:
Given:
Please find the question.
To find:
x=?
Solution:
[tex]\frac{71}{7} <\frac{x}{9} < \frac{113}{11}\\\\10 <\frac{71}{7} < 11 \\\\10< \frac{113}{11}<11\\\\\frac{x}{9} >10\\\\x>90\\\\\text{When}\ x=91 \\\\\frac{71}{7} > \frac{91}{9}\\\\x=92\\\\ \frac{71}{7}< \frac{92}{9} <\frac{113}{11}\\\\[/tex]
so, x= 92 \\\\
by compare score value x= 92
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NEED HELP ASAP!!
use the vertical line test to determine if the relation whose graph is provided is a function
(graph and answers pictured)
Answer:
Yes, this graph represents a function
Step-by-step explanation:
The function passes the vertical line test, which tests for if any input has more than one unique output by moving a vertical line from left to right. If the vertical line doesn't pass 2 or more points at a time, then the function is indeed a function.
Answer:
The graph does represent a function
Step-by-step explanation:
The function is at about 30y = x^3
PLEASE HELP!!!
WILL MARK BRAINLIEST!!!!
If the measure of 0 is 90, then angle B=____
Multiple choice!
Thank you!!!
Answer:
angle B is 45 degree.
Step-by-step explanation:
since both radius are equal in a circle the triangle formed is ann isosceles triangle.
base angle of an isosceles triangle are equal
angle B be x
angle A = angle B (being base angles of a triangle)
then angle A is also x
angle A + angle B + angle C =180 degree (sum of interior angles of a triangle)
x + x + 90=180
2x =180-90
x=90/2
x=45 degree
Wally bought a television for $987.00. The finance charge was $205 and she paid for it over 24 months. (Finance Ch arg e: #Months)(12) Amount Financed Use the formula Approximate APR to calculate her approximate APR. Round the answer to the nearest tenth.
Answer:
10.4%Step-by-step explanation:
Principal is $987.Finance charge is $205Time is 2 yearsAPR = ((Finance charge/Principal)/Time)*100% (simplified for this case)APR = ((205/987)/2)*100% = 10.4% Carrie works due south of her apartment. Her friend Sarah works due east of the
apartment. They leave for work at the same time. By the time Carrie is 5 miles from
their apartment the distance between them is 1 mile more than Sarah's distance
from the apartment. How far from the apartment is Sarah?
Answer:
3 miles
Step-by-step explanation:
5-1+2=3
From the calculation done using the pythagoras theorem, the distance from Sarah's apartment is 12m
What is the pythagoras theoremThis theorem states that in a right angled triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.
Using the pythagoras theorem
BC² = AB² + AC²
The sides of the triangle are x, x - 1 and 5
x² = (x-1)² + 5²
x² = (x-1)(x-1) +25
x² = x²-x-x -1 + 25
collect like terms
2x = 24
divide through the equation by 2
x = 24/2
= 12m
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Helppppppppp
What is the solution to the equation below ?
Answer: x=3
Step-by-step explanation:
First we're going to get rid of the fraction by multiplying both sides by the square root of x-2
Now square both sides
[tex](\sqrt{3x })^2=3^2(\sqrt{x-2 })^2\\3x=9(x-2)[/tex]
Next use the distributive property
[tex]3x=(9)(x)-(9)(2)\\3x=9x-18[/tex]
Now subtract 9x from both sides
[tex]3x-9x=9x-18-9x\\-6x=-18[/tex]
Finally divide -6 on both sides
[tex]\frac{-6x}{-6} =\frac{-18}{-6} \\x=3[/tex]
Find the equation of the least squares regression line. Show all calculations, and be sure to define any variables used.
a tv cost £800 plus VAT at 20% what is the total cost of the tv?
Answer:
Given:
Cost = £ 800
Tax = 20%
To find:
The total cost
Solution:
Total cost = Cost + Tax
Tax = 20 % of cost
20 / 100 * 800
Tax = £ 160
Hence,
Total cost = £ 800 + £ 160
Total cost = £ 960
HELP I WILL GIVE BRAINLYEST PLSSS HELP
Answer:
The answer is 0.5
Answer:
rhe answer is r= .50
Step-by-step explanation:
125-75=50
Evaluate f(x) =
f(x) = x for x = 4.
3
Answer:
x=3
Step-by-step explanation:
A study of college football games shows that the number of holding penalties assessed has a mean of penalties per game and a standard deviation of penalties per game. What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be penalties per game or less
Answer:
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
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
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
We have that:
The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].
Sample of n games:
This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]
What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?
The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.
All of the benches in a park are red or blue. The ratio of red benches to blue benches in the park is 3 : 4. Based on this information, which of the following statements is true?
A. For every 4 benches in the park, 3 are red.
B. For every 7 benches in the park, 4 are red.
C. For every 3 red benches in the park, there are 4 blue benches.
D. For every 3 red benches in the park, there are 7 blue benches.
(I'll give brainly, likes, follow, etc for anybody who answers this question with some explanation.)
Answer:
The answer is C
Step-by-step explanation:
3 : 4
^ ^
II II
red blue
find the value of x, do not round until the final answer.
thank you!
Answer:
[tex]x\approx 5.48[/tex]
Step-by-step explanation:
Draw a line from the center of the circle O to the end of either side of the line marked as 4. This line represents two things:
A radius of the circleThe hypotenuse of a right triangle with legs 5.1 and 2In this case, both are important. Since [tex]x[/tex] is also a radius of the circle, the line must be equal to [tex]x[/tex], since all radii of a circle are equal. To find the length of this line, use the Pythagorean Theorem:
[tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse of the triangle and [tex]a[/tex] and [tex]b[/tex] are the two legs of the triangle.
Since we're solving for the hypotenuse and the two legs are 5.1 and 2, we have:
[tex]5.1^2+2^2=c^2,\\26.01+4=c^2,\\c^2=30.01,\\c=5.47813836992\approx \boxed{5.48}[/tex] (round as necessary).
Example 3:
In how many ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf?
Solution:
Answer:
10
Step-by-step explanation:
5
C
3
5!/(3!(5-3)!)
5!/(3!x2!)
120/12
10
In 10 ways can a supermarket manager display 5 brands of cereals
in 3 spaces on a shelf.
What is Combination?Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order. Permutations and combinations can be mixed up.
Given:
Total brands of cereals= 5
Using Combination, C(n, r)
= n!/ r! (n- r)!
So, the number of ways
= C(5, 3)
= 5!/(3!(5-3)!) 5
= 5 x 4 x 3! / 3! x 2!
= 5 x 4 /2
= 10
Thus, the total number of ways is 10.
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Which expression gives the measure of XYZ?
V
110°
w
D
42
O A. 110° - 42°
O B. 2(110° + 42°)
O c. 2(110° - 42°)
OD. 110° +420
Answer:
1/2( 110+42)
Step-by-step explanation:
Angle Formed by Two Chords= 1/2(sum of Intercepted Arcs)
<<XYZ = 1/2( 42+110)
Consider the following data. 15,−4,−10,8,14,−10,−2,−11
Step 1 of 3: Determine the mean of the given data
Step 2 of 3: Determine the median of the given data.
Step 3 of 3: Determine if the data set is unimodal, bimodal, multimodal, or has no mode. Identify the mode(s), if any exist.
Answer:
(a) The mean is 0
(b) The median is -30
(c) The mode is unimodal
Step-by-step explanation:
Given
[tex]Data: 15,-4,-10,8,14,-10,-2,-11[/tex]
Solving (a): The mean.
This is calculated using:
[tex]\bar x = \frac{\sum x}{n}[/tex]
So, we have:
[tex]\bar x =\frac{15-4-10+8+14-10-2-11}{8}[/tex]
[tex]\bar x =\frac{0}{8}[/tex]
[tex]\bar x =0[/tex]
Solving (b): The median
First, arrange the data
[tex]Sorted: -11,-10, -10, -4, -2,8,14,15[/tex]
There are 4 elements in the dataset. So, the median is the mean of the 4th and 5th item.
[tex]Median = \frac{-4-2}{2}[/tex]
[tex]Median = \frac{-6}{2}[/tex]
[tex]Median = -3[/tex]
Solving (c): The mode
The item that has occurs most is -10.
Hence, the mode is -10. The dataset is unimodal because it has only 1 mode (-10).
Alex is planning to surround his pool ABCD with a single line of tiles. How many units of tile will he need to surround his pool? Round your answer to the nearest hundredth.
Answers:
8.96
10.48
13.42
20.42
Answer:19.82
Step-by-step explanation:
Got it right i did it on a test
What is the measure of each angle of a regular 24-gon? If necessary, round to the
nearest tenth.
Answer:
165°
Step-by-step explanation:
Find the interior angle measure by using the formula, ((n - 2) x 180°) / n
Plug in 24 as n:
((n - 2) x 180°) / n
((24 - 2) x 180°) / 24
(22 x 180°) / 24
3960 / 24
= 165
So, the measure of each angle is 165°
Answer:
163.6
Step-by-step explanation:
180•(22-2)=180•20 =3600
3600/22= 163.636363…
PLEASE HELP
Libby flips a quarter 2 times in a row.
What is the probability of the quarter landing on heads at least 1 time?
A. 1/4
B. 1/3
C. 3/4
D. 1/2
Standard form for -3x^+ x=13
Answer:
to put the equation into standard for we must multiply the terms on the right side of the equation. To multiply these two terms you multiply each individual term in the left parenthesis by each individual term in the right parenthesis.
Step-by-step explanation:
y
=
(
x
−
13
)
(
x
−
12
)
becomes:
y
=
(
x
×
x
)
−
(
x
×
12
)
−
(
13
×
x
)
+
(
13
×
12
)
y
=
x
2
−
12
x
−
13
x
+
156
We can now combine like terms:
y
=
x
2
+
(
−
12
−
13
)
x
+
156
y
=
x
2
+
(
−
25
)
x
+
156
y
=
x
2
−
25
x
+
156
What is 30 rounded to the nearest whole number percent?
Answer:
Thirty rounded to the nearest whole number percent is 30% (%=percent)
Step-by-step explanation:
Well, you see that if you have 30 out of one hundred then that's when all you have to do is go with the same number and just add percent or % to the end.
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Hope this Helps
This is just evidence
