Answer:[tex]\$1946[/tex]
Step-by-step explanation:
Given
Eric average income for four months is [tex]S_1=\$1450.25[/tex]
average Annual income [tex]S=\$1780.75[/tex]
Average income [tex]=\dfrac{\text{Total salary}}{\text{Time }}[/tex]
Sum of 4 month salary [tex]=4\times S_1[/tex]
Sum of 4 month salary [tex]=\$5801[/tex]
Average salary of remaining 8 months[tex]=S_2[/tex]
Sum of last 8 months salary[tex]=8\times S_2[/tex]
So average Salary [tex]S=\dfrac{4\times S_1+8\times S_2}{12}[/tex]
[tex]\Rightarrow 1780.75=\dfrac{4\times 1450.25+8\times S_2}{12}[/tex]
[tex]\Rightarrow 21,369=5801+8\times S_2[/tex]
[tex]\Rightarrow 15,568=8\times S_2[/tex]
[tex]\Rightarrow S_2=\dfrac{15,568}{8}=\$1946[/tex]
So, average salary of remaining 8 months is [tex]\$1946[/tex]
The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.21 minutes and a standard deviation of 1.90. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual?
Answer:
4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.
Since Z > -2 and Z < 2, this outcome is not considered unusual.
Step-by-step explanation:
Problems of normally distributed samples are solved using 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.
If [tex]Z \leq 2[/tex] or [tex]Z \geq 2[/tex], the outcome X is considered to be unusual.
In this question:
[tex]\mu = 8.21, \sigma = 1.9[/tex]
Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.
This is the pvalue of Z when X = 5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.21}{1.9}[/tex]
[tex]Z = -1.69[/tex]
[tex]Z = -1.69[/tex] has a pvalue of 0.0455.
4.55% probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase.
Since Z > -2 and Z < 2, this outcome is not considered unusual.
A scientist studying water quality measures the lead level in parts per billion (ppb) at each of 49 randomly chosen locations along a water line. Suppose that the lead levels across all the locations on this line are strongly skewed to the right with a mean of 17 ppb and a standard deviation of 14 ppb. Assume that the measurements in the sample are independent. What is the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb? Choose 1 answer: A) Plæ <15) = 0.02 B) Plū<15) – 0.16 C) Plē <15) 0.30 D) Plö < 15) – 0.44 E) We cannot calculate this probability because the sampling distribution is not normal.
Complete Question
The complete qustion is shown on the first uploaded image
Answer:
The correct option is B
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 49[/tex]
The mean is [tex]\mu = 17ppb[/tex]
The standard deviation is [tex]\sigma = 14 ppb[/tex]
Generally the standard error of this measurement is mathematically represented as
[tex]\sigma_z = \frac{\sigma}{\sqrt{n} }[/tex]
substituting values
[tex]\sigma_{\= x} = \frac{14}{\sqrt{49} }[/tex]
[tex]\sigma_{\= x} = 2[/tex]ppb
Now the probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb represented as P(X < 15 )
Next is to find the z value
[tex]z = \frac{\mu -\sigma }{\sigma_{\= x}}[/tex]
[tex]z = \frac{15-17}{2}[/tex]
[tex]z = -1[/tex]
Now checking the z-table for the z-score of -1 we have
[tex]P(X<15) = P(Z < -1 )= 0.16[/tex]
Using the normal distribution and the central limit theorem, it is found that there is a 0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], considering a sample size of at least 30 for a skewed variable.In this problem:
Mean of 17 ppb, hence [tex]\mu = 17[/tex].Standard deviation of 14 ppb, hence [tex]\sigma = 14[/tex].Sample of 49, hence [tex]n = 49, s = \frac{14}{\sqrt{49}} = 2[/tex]The probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb is the p-value of Z when X = 15, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15 - 17}{2}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.16
0.16 = 16% probability that the mean lead level from the sample of 49 measurements T is less than 15 ppb, hence option B is correct.
For more on the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
The balance on Taylor's credit card is $2000 it has an interest rate of 12.5% she wants to compare the difference between paying $75 and $100 of the monthly balance how much does she save in interest and fees if she pays $100 instead of $75?
Answer:
so she saved 82 cents in the interest the month after
Step-by-step explanation:
case 1: payment is $75
interest on 2000 = 0.125/12×2000 = $20.83
so the actual repayment on the balance = (75-20.83) = $54.17
therefore,balance =$(2000-54.7)=$1945.83
interest in the next month = $20.27
case 2: payment is $100
interest on 2000 is still $20.83
repayment = $79.73
balance = $1920.27
interest in the next month = 20.01
so she saved 82 cents in the interest the month after
Answer:
$101
Step-by-step explanation:
Check link explanation.
A self storage center is a storage room that is 8 feet long, 6 feet wide, and 10 feet high. What is the volume of the room?
Answer:
480 cubic feet
Step-by-step explanation:
The volume of any rectangular prism can be found by multiplying together the length, width and height. In this case, 8*6*10=48*10=480 cubic feet. Hope this helps!
Answer:
[tex]480 {ft}^{3} [/tex]
Step-by-step explanation:
[tex]area \\ = l \times b \times h \\ = 8 \times 6 \times 10 \\ = 48 \times 10 \\ = 480 {ft}^{3} [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Which of the following represents the graph of f(x) = 3x − 2?
graph of exponential rising up to the right, through the point 0, 3
graph of exponential rising up to the right, through the point 0, negative 1
graph of exponential rising up to the right, through the point 0, 1
graph of exponential rising up to the right, through the point 0, negative 2
Answer:
graph of exponential rising up to the right, through the point 0, negative 2
Step-by-step explanation:
I graphed the function on the graph below so you can see that it rises to the right and goes through the point (0,-2).
Answer:
graph of exponential rising up to the right, through the point 0, negative 2
Step-by-step explanation:
f(x)=3x-2
f(0)=3*0-2= -2
(0, -2) is the last given option
A well is 7 meters deep, and a snail climbs up from the bottom of the well.It climbs 3meters during the day and falls 2 meters at night.How many days can the snail crawl out of the well?
Answer:
1
Step-by-step explanation:
How many solutions does this linear system have?
y = 2x-5
-8x - 4y = -20
one solution: (-2.5, 0)
O one solution: (2.5, 0)
O no solution
O infinite number of solutions
Answer:
B (2.5, 0)
Step-by-step explanation:
2x - y = 5 (multiply all by 4)
8x- 4y = 20
-8x - 4y = - 20
eliminate the 4y
8x- 4y = 20
-8x - 4y = - 20
-------------------- –
16x = 40
x = 40/16 = 2.5
now we substitute x with 2.5
2x - y = 5
2(2.5) - y = 5
y = 0
Answer:
its B
Step-by-step explanation:
took the test
If eggs cost $3 per dozen, how much would 8 eggs cost?
Answer:
$2
Step-by-step explanation:
Because 3/12 is 0.25 and then you multiply it by 8 to get 2.
is x^2+3x+8 a monomial, binomial, or trinomial
Answer:
A trinomial
Step-by-step explanation:
Since there are three terms, x^2, 3x, and 8, it is a trinomial
A circle has a radius of 6 cm. Which calculation would be the correct calculation to work out the circumference?
Answer: C≈ 37.7cm
Step-by-step explanation: C=2πr=2·π·6≈37.69911cm
Hope this helps.
Answer:
C = 37.7 cm
Step-by-step explanation:
Circumference = 2πr
Where r = 6 cm, π = 3.14
C = 2(3.14)(6)
C = 37.69
C ≈ 37.7 cm
A kite flying in the air has a 91-ft string attached to it, and the string is pulled taut. The angle of elevation of the kite is 57 degrees. Find the height of the kite. Round your answer to the nearest tenth.
Answer:
H = 49.56 m
Step-by-step explanation:
We have,
A kite is flying in the air has a 91 ft string attached to it.
The angle of elevation of the kite is 57 degrees.
It is required to find the height of the kite. If we consider a right angled triangle, 91 ft is the hypotenuse. Let H is the height of the kite.
[tex]\cos\theta=\dfrac{H}{91}\\\\H=91\times \cos(57)\\\\H=49.56\ m[/tex]
Hence, the height of the kite is 49.56 m.
Stanford University conducted a study of whether running is healthy for men and women over age 50. During the first eight years of the study, 1.5% of the 451 members of the 50-Plus Fitness Association died. We are interested in the proportion of people over 50 who ran and died in the same eight-year period.
Required:
a. Construct a 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period.
b. Explain in a complete sentence what the confidence interval means
Answer:
a. The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).
b. It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 451, \pi = 0.015[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.015 - 1.96\sqrt{\frac{0.015*0.985}{451}} = 0.0038[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.015 + 1.96\sqrt{\frac{0.015*0.985}{451}} = 0.0262[/tex]
The 95% confidence interval for the population proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).
b. Explain in a complete sentence what the confidence interval means
It means that we are 95% sure that the true proportion of people over 50 who ran and died in the same eight-year period is (0.0038, 0.0262).
Which parent function is f(x) = x^2
O A. The linear parent function
O B. The absolute value parent function
O C. The quadratic parent function
D. An exponential parent function
Answer:
C.
Step-by-step explanation:
the standard form of a QE is ax2+bx+c. This includes x squared, and when graphed, it forms the graph of a QE, a parabola.
Hope this helps!
The parent function of f(x) = x^2 is the quadratic parent function.
We have given that,
f(x) = x^2
We have to determine the parent function of the given function.
Here the highest power of the x is 2.
We remember that the quadratic equation has the highest power is 2.
What is the formula for the quadratic equation?The standard form of a quadratic equation is ax^2+bx+c.
This includes x squared and when graphed it forms the graph of a quadratic equation is a parabola.
We have given function is f(x) = x^2
Therefore the value of the a,b and c are,
a=1
b=0 and c=0
Therefore, option C is correct.
The parent function of f(x) = x^2 is the quadratic parent function.
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ABC represents a race path. Find the total distance of the race. Round your answer to the nearest meter.
Answer:
Race covers 1911 meters.
Step-by-step explanation:
Triangle ABC represents a race path.
Total distance covered by the race = Perimeter of the triangle ABC
We will apply Sine rule in the given triangle to find the unknown sides.
By Sine rule,
[tex]\frac{SinB}{AC}=\frac{SinA}{BC}=\frac{SinC}{AB}[/tex]
[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}=\frac{Sin60}{AB}[/tex] [Since m∠A = 180° - (85 + 60)° = 35°]
[tex]\frac{Sin35}{450}=\frac{Sin85}{AC}[/tex]
AC = [tex]\frac{450\times \text{Sin85}}{\text{Sin35}}[/tex]
= 781.57 meters
[tex]\frac{Sin35}{450}=\frac{Sin60}{AB}[/tex]
AB = [tex]\frac{450\times \text{Sin60}}{\text{Sin35}}[/tex]
= 679.44 meters
Perimeter of the triangle = AB + BC + AC
= 679.44 + 450 + 781.57
= 1911.01
≈ 1911 meters
Therefore, the race covers 1911 meters.
Answer:
1911
Step-by-step explanation:
yes
A stock's price fluctuations are approximately normally distributed with a mean of $104.50 and a standard deviation of $23.62. You decide to purchase whenever the price reaches its lowest 10% of values. What is the most you would be willing to pay for the stock?
a) $80.88
b) $74.23
c) $84.62
d) $134.77
Answer:
[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]
and we can set up the following equation
tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]
And if we solve for a we got
[tex]a=104.5 -1.282*23.62=74.22[/tex]
And the best answer for this case would be:
b) $74.23
Step-by-step explanation:
Let X the random variable that represent the stocks price of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(104.5,23.62)[/tex]
Where [tex]\mu=104.5[/tex] and [tex]\sigma=23.62[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.90[/tex] (a)
[tex]P(X<a)=0.10[/tex] (b)
As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.10[/tex]
and we can set up the following equation
tex]z=-1.282<\frac{a-104.5}{23.62}[/tex]
And if we solve for a we got
[tex]a=104.5 -1.282*23.62=74.22[/tex]
And the best answer for this case would be:
b) $74.23
Select 2 strategies that we can use to add 319 +291.
Choose 2 answers:
CORRECT (SELECTED)
Add 320 + 290.
INCORRECT (SELECTED)
Add 319 + 300 + 9.
Add 310 + 300.
Answer:
I think it is 310 plus 300 and
320 plus 390
Step-by-step explanation:
A car travels at an average speed of 48 miles per hour. How long it take to travel 156 miles
Answer:
3.25 h = 3 h 15 m
Step-by-step explanation:
156 mi * 1h/48 mi = 3.25 h = 3 h 15 m
Answer: 195 min or 3 hr and 15 min
Step-by-step explanation:
We can set up a proportion to solve this problem.
[tex]\frac{48mi}{60 min} =\frac{156 mi}{x}[/tex]
[tex]48x=156*60[/tex]
[tex]48x=9360[/tex]
[tex]x=195 min[/tex]
We can also write this in terms of hours and minutes.
[tex]\frac{60 min}{1 hr} =\frac{195 min}{x}[/tex]
[tex]60x=195[/tex]
[tex]x=3.25[/tex]
3 hr and 15 min
Eighty percent of all California drivers wear seat belts. If three drivers are pulled over,
what is the probability that all would be wearing their seat belts? Write as a percent to the nearest tenth. Thanks!
Answer:
The probability that the three drivers would wear seat belts is 0.5
Step-by-step explanation:
Given
Percentage of drivers using seat belt = 80%
Number of drivers pulled over = 3
Required
Probability that all three drivers wore seat belt
First, the probability that a driver would wear seat belt has to be calculated.
Let's represent that with P(D)
P(D) is equivalent to the percentage of drivers using seat belt
[tex]P(D) = 80%[/tex]%
[tex]P(D) = \frac{80}{100}[/tex]
[tex]P(D) = 0.8[/tex]
Let the probability that the three drivers would wear seat belts be represented as P(All).
P(All) is calculated as thus;
(Probability that the first driver would wear seat belt) and (Probability that the second driver would wear seat belt) and (Probability that the first driver would wear seat belt).
Mathematically, this means
[tex]P(All) = P(D) * P(D) * P(D)[/tex]
Substitute [tex]P(D) = 0.8[/tex]
[tex]P(All) = 0.8 * 0.8 * 0.8[/tex]
[tex]P(All) = 0.512[/tex]
[tex]P(All) = 0.5[/tex] --- Approximated
Hence, the probability that the three drivers would wear seat belts is 0.5
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A
Step-by-step explanation:
(f-g)(x) means that the 2 functions are being subtracted.
[tex]3^{x}[/tex] +10x -(5x-3) =[tex]3^{x}[/tex] +10x-5x+3
simplify!
[tex]3^{x}[/tex] +5x+3
the answer is A
My rule is: y= 1/3 x+ 11/15 Find x, if y=1.
Answer:
4/5
Step-by-step explanation:
[tex]y=\dfrac{1}{3}x+\dfrac{11}{15} \\\\1=\dfrac{1}{3}x+\dfrac{11}{15}\\\\\dfrac{4}{15}=\dfrac{1}{3}x\\\\\dfrac{4}{5}=x[/tex]
Hope this helps!
Answer:
x=4/5
Step-by-step explanation:
y=1/3x+11/15
1=1/3x+11/15
4/15=1/3x
multiply both sides by 3
4/5=x
What is the length of the hypotenuse of the triangle below?
45"
312
90°
312
O A. 6/2
O B. 3.2
O C.3
O D. 9.2
O E. 6
O F. 1
Answer:
Option (E)
Step-by-step explanation:
In the figure attached,
Given a isosceles right triangle with two equal legs measuring [tex]3\sqrt{2}[/tex] units
By Pythagoras theorem,
(Hypotenuse)² = (Leg 1)² + (Leg 2)²
Since, hypotenuse = h
Leg 1 = Leg 2 = 3√2
Now we substitute the values,
h² = (3√2)² + (3√2)²
h² = 18 + 18
h = √36
h = 6 units
Therefore, length of the hypotenuse is 6 units.
Option (E) will be the answer.
Using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.
The Pythagorean TheoremGiven that the hypotenuse length of a right triangle is c, and the other legs are a and b, the Pythagorean Theorem states that: c = √(a² + b²).
Thus:
h = √((3√2)² + (3√2)²)
h = √(18 + 18)
h = √36
h = 6
Therefore, using the Pythagorean Theorem, the length of the hypotenuse is: E. 6.
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A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundredSix hundred and sixtyand sixty feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?
Answer:
Dimensions: 165 feet by 110 feet.
Maximum Area =18,150 Square feet
Step-by-step explanation:
Let the dimension of the playground be x and y.
The rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground.
Let the side parallel to one side of the playground =x
Therefore, the total length of fencing =2x+x+2y
P=3x+2y
Six hundred and sixty feet of fencing is used.
We have: 3x+2y=660
3x=660-2y
[tex]x=\dfrac{660-2y}{3}[/tex]
Area of the Playground A=xy
We write the area in terms of y by substitution of x derived above.
[tex]A(y)=y\left(\dfrac{660-2y}{3}\right )\\A(y)=\dfrac{660y-2y^2}{3}[/tex]
We want to maximize the total enclosed area.
To do this, we first find the derivative of A(y).
[tex]A'(y)=\dfrac{660-4y}{3}[/tex]
Next, we solve A'(y) for its critical point.
[tex]A'(y)=\dfrac{660-4y}{3}=0\\660-4y=0\\660=4y\\y=660 \div 4\\y=165$ feet\\[/tex]
Recall that: [tex]x=\dfrac{660-2y}{3}[/tex]
Therefore:
[tex]x=\dfrac{660-2(165)}{3}=\dfrac{660-330}{3}=\dfrac{330}{3}\\x=110$ feet[/tex]
Therefore, the dimensions of the playground that maximize the total enclosed area is 165 feet by 110 feet.
Maximum Area =165 X 110
=18,150 Square feet
Answer:
Dimensions: 165 feet by 110 feet.
Maximum Area =18,150 Square feet
Maximum Area =165 X 110
=18,150 Square feet
Simplify.
-2(x+3)+6x
−2(x+3)+6x
Distribute:
=(−2)(x)+(−2)(3)+6x
=−2x+−6+6x
Combine Like Terms:
=−2x+−6+6x
=(−2x+6x)+(−6)
=4x+−6
(-16) - (+12) + (-୨)
Answer:
-37
Step-by-step explanation:
00:00
Muriel has been a member of the Solaris Gym for 372 days,
Ben has been a member for 1 year, 2 weeks, 3 days.
Part A
Who has been a member of the Solaris Gym longer?
Use the drop-down menus to show and explain your answer.
Choose...
has been a member longer because 1 year, 2 weeks, 3 days is
Choose...
than 372 days
00:00
Part B
How much longer? Assume that it is not a leap year. Enter your answer in the box.
days
Answer:
A: Ben has been a member longer because 1 year, 2 weeks, 3 days is longer than 372 days.
B: 10 days longer
Step-by-step explanation:
1 year, 2 weeks, 3 days is 382 days -> 365 + 14 + 3 = 382
Using either the critical value rule or the p-value rule, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ______________ be rejected at the same significance level.
Answer:
Step-by-step explanation:
Using either the critical value rule or the p-value rule, a conclusion can be drawn at a level of significance (alpha)
The null hypothesis: u = hypothesized mean
Alternative hypothesis: u > u0 or u < u0 for a one tailed test
Alternative hypothesis for a two tailed test: u =/ u0
To draw a conclusion by failing to reject the null hypothesis as stated then: using critical value
Observed z score > critical z score for both the one and two tailed test.
Or using p value:
P-value > alpha for a one tailed test
P-value > alpha/2 for a two tailed test
Thus, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis will also not be rejected at the same significance level.
A recent study focused on the number of times men and women send a Twitter message in a day. The information is summarized below.
Men Sample size-25 Sample mean-20 Population standard deviation-5
Women Sample size-30 Sample mean-30 Population standard deviation-10
At the .01 significance level, is there a difference in the mean number of times men and women send a Twitter message in a day? What is the value of the test statistic for this hypothesis test?
1. 2.668
2. 2.672
3. 2.58
4. 2.40
Answer:
The value of the test statistic = 2.58
Test statistic Z = - 4.805
|Z| = 4.805 > 2.58
Null hypothesis is rejected The value of the test statistic = 2.58
There is significant difference between in the mean number of times men and women send a Twitter message in a day
Step-by-step explanation:
Step(i):-
Sample size of men n₁ = 25
mean of the first sample x₁⁻ = 20
Standard deviation of the first sample σ₁ = 5
Sample size of women n₂ = 30
mean of the second sample x₂⁻ = 30
Standard deviation of the first sample σ₂ = 10
Level of significance ∝= 0.01
Step(ii):-
Null Hypothesis : H₀: There is no significant difference between in the mean number of times men and women send a Twitter message in a day
Alternative Hypothesis :H₁:There is significant difference between in the mean number of times men and women send a Twitter message in a day
Test statistic
[tex]Z = \frac{x^{-} _{1} - x^{-} _{2} }{\sqrt{\frac{S.D_{1} ^{2} }{n_{1} }+\frac{ S.D_{2} ^{2}}{n_{2} } } }[/tex]
[tex]Z = \frac{20 - 30 }{\sqrt{\frac{(5)^{2} }{25 }+\frac{ (10)^{2} }{ 30} } }[/tex]
Z = [tex]\frac{-10}{2.081} = - 4.805[/tex]
The value of the test statistic = 2.58 C
|Z| = 4.805 > 2.58
Null hypothesis is rejected The value of the test statistic = 2.58
Conclusion:-
There is significant difference between in the mean number of times men and women send a Twitter message in a day
Reduce the fraction to lowest terms. Do not use spaces in your answer.
Answer:
-2x/yz
Step-by-step explanation:
You can cancel out terms using division and properties of exponents. x^a/x^b = x^a-b
Use a graphing calculator to sketch the graph of the quadratic equation, and then state the domain and range y=2x^2-x+3
Answer:
For the domain since we have a quadratic function then the domain would be all the real numbers:
[tex] D =[x | x \in R][/tex]
And if we want to find the range we can find the vertex:
[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]
And now we can find th coordinate of y of the vertex like this:
[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]
And then the range would be:
[tex] R=[x \geq 2.875][/tex]
Step-by-step explanation:
We have the following function given:
[tex] y = 2x^2 -x +3[/tex]
For this case we can plot the function with a calculator and we got the plot in the figure attached.
For the domain since we have a quadratic function then the domain would be all the real numbers:
[tex] D =[x | x \in R][/tex]
And if we want to find the range we can find the vertex:
[tex] v_x = -\frac{b}{2a}= -\frac{-1}{2*2}= \frac{1}{4}[/tex]
And now we can find th coordinate of y of the vertex like this:
[tex] f(V_x) = 2(\frac{1}{4})^2 -(1/4) +3 =2.875[/tex]
And then the range would be:
[tex] R=[x \geq 2.875][/tex]
I NEED HELP ASAP! Alex wants to buy carpet to cover his whole living room, except for the tiled floor. The tiled floor is 5 3/4 FT by 3 1/2 FT. WHATS THE AREA OF THE CARPET IT NEEDS TO COVER?
Answer:
53.375 or 427/8 or 53 3/8
Step-by-step explanation:
To solve this you must find the area of both the carpet and the tiled floor. You use the equation area = length x width
Carpet: 10.5 x 7 = 73.5
Tile: 5.75 x 3.5 = 20.125
The you subtract the area of the tiled floor from the carpet
73.5 - 20.125 = 53.375
(I prefer to work in decimals but most of the time they want fraction answers so 53.375 = 427/8 = 53 3/8
