Answer:
$20 of credit left on the card
Step-by-step explanation:
If we say that the prepaid phone card has 25 minutes on it since Maya paid 25 dollars for it. We can multiply 25 times 4 which equals 1 dollar per 4 minutes. Then, we can divide 20 by 4 to get 5 which means that she used 5 dollars of call time. We can now subtract 25-5 and we get 20. This tells us that there is 20 dollars left on the card.
Hope this helps!!! PLZ MARK BRAINLIEST!!!
Answer:
b
Step-by-step explanation:
Keisha, a scheduler at Mangel-Wurzel Transport, gets a call from a regular customer needing to move 70.3 m^3 of rock and soil, which Keisha knows from previous experience has an average density of 880 kg/m^3. Keisha has available a dump truck with a capacity of 9 m^3 and a maximum safe load of 5300. kg. Calculate the number of trips the dump truck will have to make to haul the customer's load away.
Answer:
Step-by-step explanation:
You take 70.3m^3 multiple with 880kg /m^3 divide with 5300.kg will give you the answer cause I tried it and it worked 100% true.
I hope tis helps .
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,100 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,100 and $14,700. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)
Answer:
[tex] P(X<12000)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]
Then we can conclude that the probability that your bid will be accepted would be 0.41
Step-by-step explanation:
Let X the random variable of interest "the bid offered" and we know that the distribution for this random variable is given by:
[tex] X \sim Unif( a= 10100, b =14700)[/tex]
If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:
[tex] P(X<12000)[/tex]
And for this case we can use the cumulative distribution function given by:
[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]
And using this formula we have this:
[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]
Then we can conclude that the probability that your bid will be accepted would be 0.41
A study conducted by Harvard Business School recorded the amount of time CEOs devoted to various activities during the workweek. Meetings were the single largest activity averaging 18 hours per week. Assume that the standard deviation for the time spent in meetings is 5.2 hours. To confirm these results, a random sample of 35 CEOs was selected. This sample averaged 16.8 hours per week in meetings. Which of the following statements is correct?
a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
b. The interval that contains 95% of the sample means is 17.1 and 18.9 hours. Because the sample mean is not between these two values, we do not have support for the results of the CEO study by the Harvard Business School.
c. The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
d. The interval that contains 95% of the sample means is 15.7 and 20.3 hours. Because the sample mean is between these two values, we do not have support for the results of the CEO study by the Harvard Business School
Answer:
a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
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, we have that:
[tex]\mu = 18, \sigma = 5.2, n = 35, s = \frac{5.2}{\sqrt{35}} = 0.879[/tex]
95% of the sample means:
From the: 50 - (95/2) = 2.5th percentile.
To the: 50 + (95/2) = 97.5th percentile.
2.5th percentile:
X when Z has a pvalue of 0.025. So X when Z = -1.96.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]-1.96 = \frac{X - 18}{0.879}[/tex]
[tex]X - 18 = -1.96*0.879[/tex]
[tex]X = 16.3[/tex]
97.5th percentile:
X when Z has a pvalue of 0.975. So X when Z = 1.96.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]1.96 = \frac{X - 18}{0.879}[/tex]
[tex]X - 18 = 1.96*0.879[/tex]
[tex]X = 19.7[/tex]
95% of the sample means are between 16.3 and 19.7 hours. This interval contains the sample mean of 16.8 hours, which supports the study.
So the correct answer is:
a. The interval that contains 95% of the sample means is 16.3 and 19.7 hours. Because the sample mean is between these two values, we have support for the results of the CEO study by the Harvard Business School.
In similar polygons, corresponding angles should not have equal measures.
True or false
Answer:
The answer is false
Step-by-step explanation:
For two polygons to be similar, both of the following must be true: Corresponding angles are congruent. Corresponding sides are proportional.
Find the vertex of the graphed function.
f(x) = |x-4| +3
AY
00
6
4
2
Y
4
The vertex is at
Answer:
The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).
5.27 + 3.5
Find the value of
7.9 - 4.36
Give your answer as a decimal.
Write down all the figures on your
calculator display.
Answer:
The value of 7.9-4.36 is 3.54
The value of 5.27 + 3.5 is 8.77
Step-by-step explanation:
On August 1, 2021, a company accepts an $8,000, 9-month note receivable. For 2021, the company reports interest revenue of $200. What is the interest rate on the note?
Answer:
6%
Step-by-step explanation:
We have to calculate the interest rate in the note, we must follow the following steps, calculate the amount of time remaining from the year 2021, as follows:
interest is for 5 months i.e. from Aug 01 to Dec 31 for year 2021 , so it means it would be 5/12 months.
We have to calculate the interest as follows:
I = P * R * T
We replace:
200 = 8000 * R * 5/12
we solve for R
200 * 12/5 = 8000 * R
R * 8000 = 480
R = 480/8000
R = 0.06
Which means that the interest rate on the note is 6%
I NEED HELP ASAP PLEASE!!! I REALLY NEED HELP!
Answer:
D.
Step-by-step explanation:
One slope is positive and one negative, so one line should go up and one down. B or D.
y = 1/2 x - 1 line goes up and y-int. = - 1. Answer D.
y = - 1/2 x + 3 line goes up and y-int. = 3. Answer D.
What is the value of (4-2): – 3 x 4?
-20
-4
4
20
Answer:
4
Step-by-step explanation:
In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample was $108.50 with a standard deviation of $16.
a) Formulate the null and alternative hypotheses to determine whether or not the average room price is significantly different from $112.
b) Compute the test statistic.
c) Using the p-value approach, what is your conclusion? Let alpha = .05.
d) Using the critival value approach, what is your conclusion? Let alpha = .05.
e) Write a concluding statement based on your answers above.
Answer:
C
Step-by-step explanation:
The standard form of an absolute value function is f(x) = a|x- h| + k. Which of the following represents the vertex?
(-k,h)
(-h,k)
(k,h)
(h,k)
Answer:
(h, k) is the point that represents the vertex of this absolute value function
Step-by-step explanation:
Recall that the vertex of an absolute value function occurs when the expression within the absolute value symbol becomes "zero", because it is at this point that the results in sign differ for x-values to the left and x-values to the right of this boundary point.
Therefore, in your case, the vertex occurs at x = h, and when x = h, then you can find the y-value of the vertex by looking at what f(h) renders:
f(h) = a | h - h | + k = 0 + k = k
Then the point of the vertex is: (h, k)
Answer:
D on edg2020
Step-by-step explanation:
Took the test
Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) 1 2 , 1 3 , 1 3 , 1 4 , 1 4 , 1 5 , 1 5 , 1 6 , ...
Answer:
if the sequence is:
12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.
Now, if the sequence is
1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5
so the terms after the first one repeat, we could group the terms with the same denominator and get:
1/2, 2/3, 2/4, 2/5..... etc.
So the terms after the first one are aₙ = 2/n.
Now, a criteria to see if a sequence converges if seing if:
[tex]\lim_{n \to \infty} a_n = 0[/tex]
and here we have;
[tex]\lim_{n \to \infty} 2/n[/tex]
that obviusly tends to zero, so we can conclude that this sequence converges.
then the limit is:
There exist a n' such that for any n > n' then IL -aₙI < ε
where L is the limit
I2/n - 0I = I2/nI < ε
then this is true if n > 2/ε = n'
6 identical toys weigh 1.8kg how much would 4 weigh
Answer:
1.2kg
Step-by-step explanation:
6 identical toys weigh 1.8kg.
1 toy would weigh:
1.8/6 = 0.3
0.3 kg.
Multiply 0.3 with 4 to find how much 4 identical toys would weigh.
0.3 × 4 = 1.2
4 identical toys would weigh 1.2kg
Answer:
[tex]1.2kg[/tex]
Step-by-step explanation:
6 identical toys weigh = 1.8kg
Let's find the weight of 1 toy ,
[tex]1.8 \div 6 = 0.3[/tex]
Now, lets find the weigh of 6 toys,
[tex]0.3 \times 4 = 1.2kg[/tex]
The number of bacteria in a refrigerated food product is given by N ( T ) = 22 T 2 − 123 T + 40 , 6 < T < 36 , where T is the temperature of the food. When the food is removed from the refrigerator, the temperature is given by T ( t ) = 8 t + 1.7 , where t is the time in hours. Find the composite function N ( T ( t ) ) : N ( T ( t ) ) = Find the time when the bacteria count reaches 8019. Time Needed = hours
Answer:
[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]
Time for bacteria count reaching 8019: t = 2.543 hours
Step-by-step explanation:
To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:
[tex]N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40[/tex]
[tex]N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40[/tex]
[tex]N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1[/tex]
[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]
Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:
[tex]8019 = 1408t^2 - 385.6t - 105.52[/tex]
[tex]1408t^2 - 385.6t - 8124.52 = 0[/tex]
Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.
Please help me with this math problem, I am lost
Answer:
y= 2x +7
Step-by-step explanation:
Slope-intercept form:
y= mx +c, where m is the slope and c is the y-intercept.
Given that the slope is 2, m=2.
y= 2x +c
Given that the y-intercept is -7, c = -7.
y= 2x +7
The FDA regulates that fresh Albacore tuna fish that is consumed is allowed to contain 0.82 ppm of mercury or less. A laboratory is estimating the amount of mercury in tuna fish for a new company and needs to have a margin of error within 0.023 ppm of mercury with 97% confidence. Assume the population standard deviation is 0.143 ppm of mercury. What sample size is needed? Round up to the nearest integer, do not include any decimals. Answer:
Answer:
[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]
So the answer for this case would be n=183 rounded up to the nearest integer
Step-by-step explanation:
Information provided
[tex]\bar X[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
[tex]\sigma = 0.143[/tex] represent the population standard deviation
n represent the sample size
[tex] ME = 0.023[/tex] the margin of error desired
Solution to the problem
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.023 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The confidence level is 97% or 0.97 and the significance would be [tex]\alpha=1-0.97=0.03[/tex] and [tex]\alpha/2 = 0.015[/tex] then the critical value would be: [tex]z_{\alpha/2}=2.17[/tex], replacing into formula (5) we got:
[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]
So the answer for this case would be n=183 rounded up to the nearest integer
The weights of steers in a herd are distributed normally. The variance is 10,000 and the mean steer weight is 1400lbs. Find the probability that the weight of a randomly selected steer is between 1539 and 1580lbs. Round your answer to four decimal places.
Answer:
[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]
And we can find this probability using the normal standard table with this difference:
[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]
Step-by-step explanation:
Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(1539,1580)[/tex]
Where [tex]\mu=1400[/tex] and [tex]\sigma=\sqrt{10000}= 100[/tex]
We are interested on this probability
[tex]P(1539<X<1580)[/tex]
And we can solve the problem using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]
And we can find this probability using the normal standard table with this difference:
[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]
If AYWZ - AYXW, what is true about ZXWZ?
O ZXWZ is an obtuse angle.
ZXWZ is a right angle,
ZXWZ is congruent to ZWXY.
ZXWZ is congruent to ZXZW.
Answer:
<XWZ is a right angle
Step-by-step explanation:
Since <YWZ and <XWY both equal 45 degrees, So, <XWZ is a right angle.
Given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,
Similar TrianglesTriangles that are similar possess equal corresponding angles.
We are given that:
ΔYWZ ~ ΔYXW
Therefore:∠YWZ = ∠XWY = 45 degrees
Thus:∠YWZ + ∠XWY = ∠XWZ
45 + 45 = ∠XWZ
∠XWZ = 90 degrees (right angle).
Therefore, given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,
Learn more about similar triangles on:
https://brainly.com/question/2644832
5+10/x=x+8 Solve the equation with steps
Answer:
2 and -5
Step-by-step explanation:
[tex]5+\dfrac{10}{x}=x+8 \\\\\\-3+\dfrac{10}{x}=x \\\\\\-3x+10=x^2 \\\\\\x^2+3x-10=0 \\\\\\(x+5)(x-2)=0 \\\\\\x=2,-5[/tex]
Hope this helps!
Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site stays on the site for 10 minutes. Company B is concerned that the mean time is significantly less than 10 minutes. Company B collects the times (in minutes) below for a sample of 19 users. Assume normality.
Time: 1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2
Conduct the appropriate hypothesis test for Company B using a 0.08 level of significance.
a) What is the critical value for the test? Give your answer to four decimals.
b) What is the appropriate conclusion?
A. Reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.
B. Fail to reject the claim that the mean time is 10 minutes because the test statistic is larger than the critical point.
C. Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
D. Fail to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
Answer:
a) Critical value = -1.4052
Since we are checking if the mean time is less than 10 minutes, the rejection area would be
z < -1.4052
b) Option C is correct.
Reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
That is, the mean time is significantly less than 10 minutes.
Step-by-Step Explanation:
a) Using z-distribution, the critical value is obtained from the confidence level at which the test is going to be performed. Since the hypothesis test tests only in one direction (checking if the claim is less than 10 minutes significantly)
P(z < Critical value) = 0.08
From the z-tables, critical value = -1.4052
Since we are checking if the mean time is less than 10 minutes, the rejection area would be
z < -1.4052
b) We first give the null and alternative hypothesis
The null hypothesis is that there isn't significant evidence to suggest that the mean time is less than 10 minutes.
And the alternative hypothesis is is that there is significant evidence to suggest that the mean time is less than 10 minutes.
To now perform this hypothesis test, we need to obtain the test statistic
Test statistic = (x - μ)/σₓ
x = sample mean = (Σx/N)
The data is
1.2, 2.8, 1.5, 19.3, 2.4, 0.7, 2.2, 0.7, 18.8, 6.1, 6, 1.7, 29.1, 2.6, 0.2, 10.2, 5.1, 0.9, 8.2
Σx = 119.7
N = Sample size = 19
x = sample mean = (119.7/19) = 6.3
μ = standard to be compared against = 10 minutes
σₓ = standard error = (σ/√N)
where N = Sample size = 19
σ = √[Σ(x - xbar)²/N]
x = each variable
xbar = mean = 6.3
N = Sample size = 19
Σ(x - xbar)² = 1122.74
σ = (√1122.74/19) = 7.687
σₓ = (7.687/√19) = 1.7635
Test statistic = (x - μ)/σₓ
Test statistic = (6.3 - 10)/1.7635
= -2.098 = -2.10
z = -2.10 and is in the rejection region, (z < -1.4052), hence, we reject the null hypothesis and the claim and say that the mean time is significantly less than 10 minutes.
The test statistic is less than the critical point, hence, we reject the null hypothesis and the claim and conclude that the mean time is less than 10 minutes.
Hope this Helps!!!
The critical value for the test based on the sampling distribution is -1.4052 and one needs to reject the claim.
How to explain the sampling distribution?From the complete information given, the descriptive statistics from the sample information has been given. The sample mean and variance are given. Therefore, the value of the test statistics from the information is -1.4052.
Also, the conclusion is to reject the claim since the test statistic is smaller than the critical point.
Therefore, the correct option is to reject the claim that the mean time is 10 minutes because the test statistic is smaller than the critical point.
Learn more about sampling on:
https://brainly.com/question/17831271
if segment ac and segment bc are tangent to circle o find the value of x
Answer:
x = 150°
Step-by-step explanation:
Start by cutting the shape into two triangles by bisecting the 30°
Now we have two triangles that have two angles 90° and 15°
Subtract 15° from 90°, you'll get 75°
Double 75° because x is split into 2
150° = x
Also, were given 3 angles, this is a quadrilateral.
90° + 90° + 30° = 210°
360° - 210° = 150°
Answer:
150°
Step-by-step explanation:
OA⊥AC and OB⊥BC
∠A+∠B+∠C+∠O=360°
90°×2+30°+x=360°
x=360°-210°=150°
Please show work for number 3 and 4!
Answer:
Three: x = 400
Four : 9
Step-by-step explanation:
Three
a = 10*√2
2a = √(2x) Square both sides.
4a^2 = 2x Divide both sides by 2
2a^2 = x Put a = 10√2 into a^2
2(10√2)^2 = x Square a
2(100*2) = x Multiply the result by 2.
2(200) = x
x = 400
Four
x^(a^2) / x ^(b^2) = x^36
Substitute a + b = 4 in for b.
x^(a^2) / x^(4 - a)^2 = x^36
Subtract powers
x^(a^2 - (4 - a)^2 = x^36
x^(a^2 - (16 - 8a + a^2) = x^36
Gather like terms
x^(8a - 16) = x^36
The powers are now equal
8a - 16 = 36
Add 16 to both sides
8a = 36 + 16
8a = 52
Divide by 8
a = 6.5
Solve for b
a + b = 4
6.5 + b = 4
b = 4 - 6.5
b = - 2.5
a - b = 6.5 - (- 2.5) = 9
PQR is an isosceles triangle in which PQ = PR
Mand N are points on PQ and PR such that angle MRQ = angle NQR.
Prove that triangles QNR and RMQ are congruent.
Answer and Step-by-step explanation: Congruent triangles are triangles with the same three sides and same three angles.
There many ways to determine if 2 triangles are congruent.
One of them is ASA or Angle, Side, Angle and it means that if two angles and the included side of one triangle are equal to the corresponding angles and side on the other triangle, they are congruent.
In this case, angle MRQ and angle NQR are equal. The included side of both triangles are the same QR, so it can be concluded that triangle QNR is congruent to triangle RMQ.
The image in the attachment shows the angles and their included side, which are colored.
You're pretty sure that your candidate for class president has about 6565% of the votes in the entire school. But you're worried that only 100100 students will show up to vote. How often will the underdog (the one with 3535% support) win? To find out, you
Answer:
You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.
a. describe-how-you-will-simulate a component.
b. describe-how-you-will-simulate a trial.
c. describe-the-response-variable
Step-by-step explanation:
Part A:
A component is one voter's voting. An outcome is a vote in favor of our candidate.
Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.
Part B:
A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.
And counted how many people voted for each candidate. Whoever gets the majority of the votes wins the trial.
Part C:
The response variable is whether the underdog wins or not.
To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.
please help, me find the area of Letter E.
Answer:
7.005 m^2.
Step-by-step explanation:
We can split this into one vertical rectangle 3.45 * 0.9 m^2
2 rectangles 2 * 0.75 = 1.5 m^2
1 rectangle 1.2 * 0.75 m^2
= 3.105 + 2 * 1.5 + 0.9
= 7.005 m^2.
The number of songs enjoyed by the band Metallica by a sample of six teachers is also below. 2,13,5,11,3,14. What is the mean of this sample? (line over the x) X=? What is the standard deviation of this sample? S=?
Answer:
8
Step-by-step explanation:
2,3,5,11,13,14
Mean= 8
Standard deviation= 4.830
The demand for the video games provided by Mid-Tech Video Games Inc. has exploded in the last several years. Hence, the owner needs to hire several new technical people to keep up with the demand. Mid-Tech gives each applicant a special test that Dr. McGraw, the designer of the test, believes is closely related to the ability to create video games. For the general population, the mean on this test is 100. Below are the scores on this first test for the applicants. 95 105 120 81 90 115 99 100 130 10 The owner is interested in the overall quality of the job applicants based on this test. Compute the mean and the median scores for the 10 applicants. What would you report to the owner
Answer:
Mean: 94.5.
Median: 99.5
Standard deviation: 33.1
We can tell the owner that the applicants don't have a score significantly below from 100.
Step-by-step explanation:
First, we analize the sample and calculate the statistics (mean, median and standard deviation).
Mean of the sample:
[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(95+105+120+81+90+115+99+100+130+10)\\\\\\M=\dfrac{945}{10}\\\\\\M=94.5\\\\\\[/tex]
The median, as the sample size is an even number, can be calculated as the average between the fifth and sixth value, sort by value:
[tex]\text{Median}=\dfrac{99+100}{2}=99.5[/tex]
The standard deviation is:
[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((95-94.5)^2+(105-94.5)^2+(120-94.5)^2+. . . +(10-94.5)^2)}\\\\\\s=\sqrt{\dfrac{9834.5}{9}}\\\\\\s=\sqrt{1092.7}=33.1\\\\\\[/tex]
To tell if this sample has a value significantly lower than the expected score of 100, we should make a hypothesis test.
The claim is that the mean score is significantly lower than 100.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]
The significance level is 0.05.
The sample has a size n=10.
The sample mean is M=94.5.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.1.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{33.1}{\sqrt{10}}=10.467[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{94.5-100}{10.467}=\dfrac{-5.5}{10.467}=-0.53[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=10-1=9[/tex]
This test is a left-tailed test, with 9 degrees of freedom and t=-0.53, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=P(t<-0.53)=0.306[/tex]
As the P-value (0.306) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the mean score is significantly lower than 100.
A student said that the y-intercept of the function y = 3 · 4x is 4. What is their mistake? What is the actual y-intercept?
Answer:
The y intercept is 0Step-by-step explanation:
the equation of a line is given as
[tex]y= mx+c[/tex]
where
m= is the slope
c= is the y intercept
their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)
Please answer this correctly
Answer:
No
Step-by-step explanation:
There is the same amount of teachers in each department of the school.
He asks 7 different departments of the school and collects the data he wants to.
I think it is not bias
Answer:
no
Step-by-step explanation:
This sample of teachers in the school is not likely to be biased.
The following questions pertain to the properties of the STANDARD NORMAL distribution. (a) True or False: The distribution is bell-shaped and symmetric. True False (b) True or False: The mean of the distribution is 0. True False (c) True or False The probability to the left of the mean is 0. True False (d) True or False The standard deviation of the distribution is 1. True False
Answer:
a. The distribution is bell-shaped and symmetric: True.
b. The distribution is bell-shaped and symmetric: True.
c. The probability to the left of the mean is 0: False.
d. The standard deviation of the distribution is 1: True.
Step-by-step explanation:
The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].
It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.
We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where [tex] \\ x[/tex] is the raw score that we want to standardize.
Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:
(a) True or False: The distribution is bell-shaped and symmetric
Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.
(b) True or False: The mean of the distribution is 0.
Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]
If [tex] \\ x = \mu[/tex]
[tex] \\ z = \frac{\mu - \mu}{\sigma}[/tex]
[tex] \\ z = \frac{0}{\sigma}[/tex]
[tex] \\ z = 0[/tex]
Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.
(c) True or False: The probability to the left of the mean is 0.
Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].
(d) True or False: The standard deviation of the distribution is 1.
Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.
In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].
In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.
Answer:
A: true
B: true
C: false
D: true