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
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.
What are the like terms in the expression below? Select two options. 3.6 p minus q minus 4 + StartFraction r over 3 EndFraction + StartFraction 3 over 7 EndFraction q
Answer:
the like terms are - q and (3/7)q
Step-by-step explanation:
3.6 p minus q minus 4 + StartFraction r over 3 EndFraction + StartFraction 3 over 7 EndFraction q = 3.6p - q- 4 + r/3 + (3/7)q
The like terms are the terms with same letters, alphabet .
For the above expression, the like terms are -q and (3/7)q
All others do not have a like term.
Answer:
-q and 3/7q btw sorry im late
Step-by-step explanation:
write -4i+(1/4-5i)-(-3/4+8i)+17i as a complex number in the standard form
Answer:
1
Step-by-step explanation:
Eliminate parentheses using the distributive property.
= -4i +1/4 -5i +3/4 -8i +17i
= (1/4 +3/4) +i(-4 -5 -8 +17)
= 1 + 0i
= 1
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
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.
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
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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which graph represents the compound inequality
Answer: C
Step-by-step explanation:
When looking at compound inequalities, the inequalities are very important. You can see that on the graphs, there are some points that have a white open circle and others have blue, closed circle. The 2 different circles tells you the inequality itself. If you see ≤ or ≥, it is a closed circle. This is a closed circle because it is less than/greater than or equal to. That means it is also equal to the point, therefore it is a closed circle. If you see < or >, it is an open circle. That means it is not closed because it is greater than. It is not equal to on that specific point.
Now that we have covered the basics, we can start to eliminate. our first condition is n<-2. Above, we have established that < is an open circle. We can eliminate A and B because the points on -2 are both closed circles.
That leaves us with C and D. Since C and D both follow the points, let's look carefully at what the inequality tells us. n<-2 means n is less than -2. This means the arros should be pointing in the left side. As you go more towards the negative, the smaller the number becomes.
We can eliminate D because at -2, the numbers are going towards the right, not the left.
Therefore, our answer is C.
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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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:
my family left at 4am this morning on a trip to the mountains if the car average for 60 miles per hour for 600 miles what time would they arrive at their destination
Answer:
They would arrive at their destination at 2pm.
Step-by-step explanation:
We have that:
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance and t is the time.
We first have to find how long the trip takes.
60 miles per hour, so [tex]v = 60[/tex]
600 miles, so [tex]d = 600[/tex]
Then
[tex]v = \frac{d}{t}[/tex]
[tex]60 = \frac{600}{t}[/tex]
[tex]60t = 600[/tex]
[tex]t = \frac{600}{60}[/tex]
[tex]t = 10[/tex]
The trip lasts 10 hours. Your family left at 4am. When they arrive.
10 hours after 4 am is 10 + 4 = 14 hours, which in the am/pm scale is 2 pm.
So they would arrive at their destination at 2pm.
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
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
In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 54 inches, and standard deviation of 8 inches. What is the probability that the height of a randomly chosen child is between 38.9 and 61 inches
Answer:
77.98% probability that the height of a randomly chosen child is between 38.9 and 61 inches
Step-by-step explanation:
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.
In this question:
[tex]\mu = 54, \sigma = 8[/tex]
What is the probability that the height of a randomly chosen child is between 38.9 and 61 inches
This is the pvalue of Z when X = 61 subtracted by the pvalue of Z when X = 38.9. So
X = 61
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{61 - 54}{8}[/tex]
[tex]Z = 0.875[/tex]
[tex]Z = 0.875[/tex] has a pvalue of 0.8092
X = 38.9
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{38.9 - 54}{8}[/tex]
[tex]Z = -1.89[/tex]
[tex]Z = -1.89[/tex] has a pvalue of 0.0294
0.8092 - 0.0294 = 0.7798
77.98% probability that the height of a randomly chosen child is between 38.9 and 61 inches
(-16) - (+12) + (-୨)
Answer:
-37
Step-by-step explanation:
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 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
Bella is making button barrettes. She allows each of her friends to reach into er bag of buttons and randomly pick a color.
Answer:
Total no. of buttons = 300 + 700 + 1000
+ 500 = 2500
Possibility for a person to pick a pink button = 300/2500 = (3/25)%
Amount of pink buttons she can expect her friends to pick = 50(3/25) = 6
She can expect to make 6 pink barrettes
Step-by-step explanation:
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:
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
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
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
pls help me this my my second assignment help me!!!
Answer:
Step-by-step explanation:
F/4 = 18
Multiply both sides by 4
F = 72 N
answer is A
Answer:
72N
Step-by-step explanation:
pressure=force/Area
MAKE FORCE SUBJECT OF THE FORMULA
:. FORCE=PRESSURE ×AREA
Force=18Nm² × 4m²
Force= 18N ×4
:. Force=72N
PLEASE MARK AS BRILLIANT ANSWER
how do I make more than 1 question (30 points)
CLICK ON THE POIN AND SCHROOL DOWN
Answer:
By asking the question.
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).
A homeowner finds that there is a 0.15 probability that a flashlight does not work when turned on. If she has three flashlights, find the probability that at least one of them works when there is a power failure. Find the probability that the second flashlight works given that the first flashlight works.
Answer:0.9966
Step-by-step explanation:
Given
Probability that flash light does not work is [tex]P_o=0.15[/tex]
If owner has 3 three flashlights then
Probability that atleast one of them works [tex]=1-P(\text{none of them works})[/tex]
Probability that flashlight will work [tex]=1-P_o=1-0.15[/tex]
[tex]=0.85[/tex]
Required Probability[tex]=1-0.15\times 0.15\times 0.15[/tex]
[tex]=1-0.003375[/tex]
[tex]=0.9966[/tex]
Now, Probability that second works given that first works is given by
[tex]P=P(\text{First works})\times P(\text{Second works})[/tex]
[tex]P=0.85\times 0.85[/tex]
[tex]P=0.7225[/tex]
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
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!
For f(x) = x3 – 7x2 + 8x + 16, a. Find f(10) using synthetic division.
Answer:
Dear user,
Answer to your query is provided below
The value of f(10) using synthetic division is 396.
Explanation:
Cubic polynomials cannot be factorized by splitting the middle term. Quadratic polynomials can be factorized by splitting the middle term.
A cubic polynomial can have a maximum of three linear factors. To factorize a cubic polynomial, we first find a factor by hit and trial method or using factor theorem and reduce it into the product of a quadratic polynomial and a linear polynomial. The quadratic polynomial can then be factorized in linear factors.
The value of f(10) using synthetic division method is 396.
What is synthetic division?"The synthetic division is a method for manually performing Euclidean division of polynomials, with less writing and fewer calculations than long division."
The given function is:
f(x) = x³ – 7x² + 8x + 16
Therefore using synthetic division, we get:
(10) | (1) (- 7) (8) (16)
| (10) (30) (380)
|............................................
(396)
Therefore, f(10) = 396.
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