Answer:
52
Step-by-step explanation:
24+28 = 52
52 - 24 = 28
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).
6. The number of points that Kilee scored in five basketball games was 10, 10 points
8, 9, 8, and 30. Why would it be misleading to use the mean as the center
of measure for the number of points that she scored in each game? *
Answer:
Because of the presence of an outlier (30), an extremely higher value when compared to others. Outliers affects the value of mean, thereby mean should not be used for data with outliers.
Step-by-step explanation:
For the set of data above, it would be misleading to use the mean as the center of measure for the number of points that she scored in each game because of the presence of outliers, the presence of extremely lower or extremely higher value makes the use of mean as a measure of central tendency inaccurate because the mean take into consideration all the values in a data including the outliers for its calculation, and the mean would tend to shift towards the outliers thereby misinterpreting the data. The presence of outlier which is 30 in the data given would shift the mean to the right towards 30, thereby misleading to represent the measure of central tendency. 30 is an outlier because it is extremely higher than the rest of the data (10,8,9,8,30).
In the presence of outliers it's best to use median or mode as an acceptable measure of central tendency.
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.
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
Which equation represents a line that is perpendicular to the line represented by y = 2/3x+1?
An equation that represents a line that is perpendicular to the given line is [tex]2y=3x+1[/tex].
Given the following data:
[tex]y=\frac{2}{3} x+1[/tex]
To determine an equation that represents a line that is perpendicular to the given line:
The perpendicularity of a straight line.In Mathematics, the slopes of two lines are said to be perpendicular when the product of these slopes is equal to negative one (-1).
Mathematically, this is given by the formula:
[tex]m_1 \times m_2 = -1[/tex]
Note: Slope, [tex]m_1[/tex] = [tex]\frac{2}{3}[/tex]
Substituting the given parameters into the formula, we have;
[tex]\frac{2}{3} \times m_2=-1\\\\2m_2=-3\\\\m_2=\frac{3}{2}[/tex]
For the perpendicular line:
[tex]y=mx+b\\\\y=\frac{3}{2}x +1\\\\2y=3x+1[/tex]
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sing traditional methods, it takes 11.7 hours to receive a basic driving license. A new license training method using Computer Aided Instruction (CAI) has been proposed. A researcher used the technique with 23 students and observed that they had a mean of 11.3 hours with a standard deviation of 1.4. A level of significance of 0.1 will be used to determine if the technique performs differently than the traditional method. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
Answer:
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the CAI technique performs differently than the traditional method (P-value = 0.1844).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the CAI technique performs differently than the traditional method.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=11.7\\\\H_a:\mu\neq 11.7[/tex]
The significance level is 0.1.
The sample has a size n=23.
The sample mean is M=11.3.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=1.4.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{1.4}{\sqrt{23}}=0.29[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{11.3-11.7}{0.29}=\dfrac{-0.4}{0.29}=-1.37[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=23-1=22[/tex]
This test is a two-tailed test, with 22 degrees of freedom and t=-1.37, so the P-value for this test is calculated as (using a t-table):
[tex]\text{P-value}=2\cdot P(t<-1.37)=0.1844[/tex]
As the P-value (0.1844) is bigger than the significance level (0.1), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that the CAI technique performs differently than the traditional method.
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.
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.
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
You play a game that requires rolling a six- sided dice then randomly choosing a colored card from a deck containing 3 cards, 8 blue cards, and 6 yellow cards. Find the probability that you will roll a 2 on the dice and then choose a blue card
Answer:
4/51
Step-by-step explanation:
The probability of rolling a 2 is 1/6.
There are a total of 17 cards, so the probability of a blue card is 8/17.
The probability of both events is:
(1/6) (8/17) = 4/51
We want to find the probability of rolling a 2 and then getting a blue card. We will see that this probability is equal to 0.078
First, we must find the probability of rolling a 2 with a six-sided dice.
A six-sided dice has 6 possible outcomes, only one of these is a 2, then the probability of rolling a 2 is just:
p = 1/6
Then we find the probability of drawing a blue card.
There are:
3 cards (no color)8 blue cards6 yellow cards.So there is a total of 3 + 8 + 6 = 17 cards, and 8 of these are blue, then the probability of randomly drawing a blue card is:
q = 8/17
The joint probability is given by the product of the two individual probabilities, so we get:
P = p*q = (1/6)*(8/17) = 0.078
So the probability of rolling a 2 and then getting a blue card is P = 0.078
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What is the expasion of (2x + 3)^3 ?
Answer:
(2x + 3)3
Step-by-step explanation:
Simplify: (2x+3)(3)
Answer: (2x + 3)3
Hope this helps.
(-16) - (+12) + (-୨)
Answer:
-37
Step-by-step explanation:
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:
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]
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:
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
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
What is 300+400.
I want to see how smart you are can you do this mentally????
Answer:
700
Step-by-step explanation:
Since 3 + 4 = 7, then 300 + 400 = 700
Answer: 700
Step-by-step explanation:
300+400
700
easier way to do it in your brain is
4+3 is 7 and add the 2 zeros
so the answer is 700
Hope this helps :)
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
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
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
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
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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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.
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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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
how do I make more than 1 question (30 points)
CLICK ON THE POIN AND SCHROOL DOWN
Answer:
By asking the question.
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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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