Answers
Answer:
Step-by-step explanation:
hello,
so we know y in terms of t and x in terms of t and we need to find y in terms of x
[tex]x=21t^2<=>\sqrt{x}=\sqrt{21}*t \ \ as \ \ t>=0 \ \ So\\t=\sqrt{\dfrac{x}{21}}[/tex]
and then
[tex]y=f(x)=3\sqrt{\dfrac{x}{21}}+5=\sqrt{\dfrac{9x}{21}}+5=\sqrt{\dfrac{3x}{7}}+5[/tex]
hope this helps
Related Questions
=IF(5 > = 2 * 4,11,IF(25/2 > 5 * 3,15, a friend tells you that they always call people they would like to date. identify the converse error 74))
Answers
Answer:
4+10-284-4819+2948929
Which best describes the structure outlined in the bridge.
Answers
Answer:D
Step-by-step explanation:
The red line in the figure is an altitude of triangle HJL. Using right angle trigonometry, write an equation involving sinL
Answers
Answer:
B.
Step-by-step explanation:
According to SohCahToa, when using Sin to find a side value, you must use opposite over hypotenuse.
So in this case to find x, you would do the Sin(L)=x/y
Answer:
B. Sin(L)=x/y indeed!
Step-by-step explanation:
Two fair dies are rolled. What is the conditional probability thatat least one lands on 6 given that the dies land on different numbers?
Answers
Answer:
33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
All outcoms of the dices:
Format(Dice A, Dice B)
(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)
(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)
(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)
(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)
(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)
(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)
36 in all
Total outcomes:
In this question, we want all with no repetition.
There are 6 repetitions, they are (1,1), (2,2), ..., (6,6). So 36 = 6 = 30 outcomes.
Desired outcomes:
One landing on six:
(6,1), (6,2), (6,3), (6,4), (6,5), (1,6), (2,6), (3,6), (4,6), (5,6).
10 desired outcomes.
Probability:
10/30 = 0.3333
33.33% conditional probability thatat least one lands on 6 given that the dies land on different numbers
A model for consumers' response to advertising is given by the equation N(a)=2600 + 470ln (a) Where N(a) is the number of units sold, a is the amount spent on advertising, in thousands of dollars, & a≥1.
Required:
a. How many units were sold after spending $1,000 on advertising?
b. Find N′(a).
c. Find the maximum value, if it exists.
d. Find lim a→[infinity] N′(a).
Answers
Answer:
a. [tex]N(1)=2600[/tex]
b. [tex]N'(a) = 470/a[/tex]
c. N(a) has no maximum value, max N'(a) = 470 (when a = 1)
d. lim a→[infinity] N′(a) = 0
Step-by-step explanation:
a.
the variable 'a' is the amount spent in thousands of dollars, so $1,000 is equivalent to a = 1. Then, we have that:
[tex]N(1)=2600 + 470ln(1)[/tex]
[tex]N(1)=2600 + 470*0[/tex]
[tex]N(1)=2600[/tex]
b.
To find the derivative of N(a), we need to know that the derivative of ln(x) is equal (1/x), and the derivative of a constant is zero. Then, we have:
[tex]N'(a) = 2600' + (470ln(a))'[/tex]
[tex]N'(a) = 0 + 470*(1/a)[/tex]
[tex]N'(a) = 470/a[/tex]
c.
The value of 'ln(a)' increases as the value of 'a' increases from 1 to infinity, so there isn't a maximum value for N(a).
The maximum value of N'(a) is when the value of a is the lower possible, because 'a' is in the denominator, so the maximum value of N'(a) is 470, when a = 1.
d.
When the value of 'a' increases, the fraction '470/a' decreases towards zero, so the limit of N'(a) when 'a' tends to infinity is zero.
In 4 days, the price of a share of stock rose 3/4 of a point. On a average, what was the change in stock each day?
Answers
Answer:
0.15 or 15%
Step-by-step explanation:
If the price of a stock rose 3/4 on a point, it means that 1x became 1,75x (x + 3/4x). X is the price of the stock here.
To calculate how much the price went up each day on average, we will create exponential equation.
x = price of the stock
y = average daily change
[tex]x*y^{4} =1.75x[/tex] divide by x
[tex]y^{4} = 1.75[/tex]
We will calculate it using logarithms.
y = 1.15016, rounded to 1.15
We see that the stock goes up 0.15 points every day.If we multiply it by 100%, we get 15%
A store buys sneakers for $20.00 and marks them up 250%. What is the selling price?
Answers
Answer:
[tex]\$45[/tex]
Step-by-step explanation:
[tex]20+(2.5*20)=45[/tex]
Marking up means that the new value is added onto the original value.
As we are increasing the original price by 250% of the price, we need to multiply it by 2.5, as that is equal to 250%
Answer:
20*2.5 = $50 Gross margin $70 Selling price
Step-by-step explanation:
Name the major arc and find its measure.
Answers
Answer:
ADB = Major Arc
arc measure = 310
Step-by-step explanation:
major arc measure = 360 - 50 = 310
how are the values of the eights related in 880
Answers
Answer:
8 is in the hundreds place as well as in the tens place.
Step-by-step explanation:
We use the base 10 system. 880 would represent eight hundred and eighty. So our 0 would be the ones place, 8 in the tens place, and 8 also in the hundreds place.
A kite 100 ft above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle (in radians) between the string and the horizontal decreasing when 200 ft of string have been let out? rad/s g
Answers
Answer:
0.015 radians per second.
Step-by-step explanation:
They tell us that at the moment the speed would be 6 ft / s, that is, dx / dt = 6 and those who ask us is dθ / dt.
Which we can calculate in the following way:
θ = arc sin 100/200 = pi / 6
Then we have the following equation of the attached image:
x / 100 = cot θ
we derive and we are left:
(1/100) * dx / dt = - (csc ^ 2) * θ * dθ / dt
dθ / dt = 0.01 * dx / dt / (- csc ^ 2 θ)
dθ / dt = 0.01 * 6 / (- csc ^ 2 pi / 6)
dθ / dt = 0.06 / (-2) ^ 2
dθ / dt = -0.015
So there is a decreasing at 0.015 radians per second.
The horizontal distance and the height of the kite are illustration of rates.
The angle is decreasing at a rate of 0.24 radian per second
The given parameters are:
[tex]\mathbf{Height =y= 100ft}[/tex]
[tex]\mathbf{Speed =\frac{dx}{dt}= 6fts^{-1}}[/tex]
[tex]\mathbf{Length = 200}[/tex]
See attachment for illustration
Calculate the angle using the following sine ratio
[tex]\mathbf{sin(\theta) = \frac{100}{200}}[/tex]
[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]
The horizontal displacement (x) is calculated using the following tangent ratio:
[tex]\mathbf{tan(\theta) = \frac{100}{x}}[/tex]
Take inverse of both sides
[tex]\mathbf{cot(\theta) = \frac{x}{100}}[/tex]
[tex]\mathbf{cot(\theta) = \frac{1}{100}x}[/tex]
Differentiate both sides with respect to time (t)
[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot \frac{dx}{dt}}[/tex]
Substitute known values
[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{1}{100} \cdot 6}[/tex]
[tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]
Recall that:
[tex]\mathbf{sin(\theta) = \frac{1}{2}}[/tex]
Take inverse of both sides
[tex]\mathbf{csc(\theta) = 2}[/tex]
Square both sides
[tex]\mathbf{csc^2(\theta) = 4}[/tex]
Substitute [tex]\mathbf{csc^2(\theta) = 4}[/tex] in [tex]\mathbf{-csc^2(\theta) \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]
[tex]\mathbf{-4 \cdot \frac{d\theta}{dt} = \frac{6}{100}}[/tex]
Divide both sides by -4
[tex]\mathbf{\frac{d\theta}{dt} = -\frac{24}{100}}[/tex]
[tex]\mathbf{\frac{d\theta}{dt} = -0.24}[/tex]
Hence, the angle is decreasing at a rate of 0.24 radian per second
Read more about rates at:
https://brainly.com/question/6672465
co
Which graph represents the inequality?
-2
1-1
-12
1
1 2
NE
1
Y>-
2
2
А
++
1 -1
-12
ou
-2
od
1
NIE
1
B
1 2
2
2
---
Oto
-2
-1
1 2
-12
-
NIE
NI
12
D
-2
1 - 1
1
0
1
1 2
NIS
2
NI
Answers
Answer:
A
Step-by-step explanation:
Given the equality y > -½, it means the values of y is greater than -½.
The values of y would range from 0 upwards. I.e. 0, ½, 1, 1½, 2. . .
Thus, when graphed on a number line, the circle that appears like "o" would start from -½, and the "o" would not be full or shaded to indicate that -½ is not included in the values of y, which are greater than -½. Since the values of y are greater than -½ the direction of the arrow that indicates values of y would point towards our far right, to indicate the values included as y.
Therefore, the graph that indicates the inequality y > ½ is A
Answer:
A
Step-by-step explanation:
all my points!!!!!!!!!!!!!! Brainleist will be given
Answers
Answer:
18-22 = 1
23-27 = 3
28-32 = 3
33-37 = 3
Answer:
18-22 = 1
23-27 = 3
28-32 = 3
33-37 = 3
Write one to two paragraphs about what you have learned from this process. When you read, see, or hear a statistic in the future, what skills will you apply to know whether you can trust the result?
Answers
Answer:
The answer is below
Step-by-step explanation:
What must be applied to know if the result is true or reliable is a test statistic, since due to it we can calculate how true or rather what is the probability that this data will occur. There are many types of test statistic, use the one that best fits the data.
The veracity of the medium where the information comes from is also important, whether they took a representative sample or not, among other parameters.
Write 17857000012 in words
Answers
Answer:
Seventeen billion, eight hundred fifty-seven million and twelve.
Step-by-step explanation:
Answer:
17,857,000,012 = 17 billion 857 million 12
Step-by-step explanation:
Bye lad!
If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Answers
Answer:
The range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).
Step-by-step explanation:
The complete question is:
The lengths of pregnancies in a small rural village are normally distributed with a mean of 267 days and a standard deviation of 17 days. If you were to draw samples of size 47 from this population, in what range would you expect to find the middle 98% of most averages for the lengths of pregnancies in the sample?
Solution:
As the sample size is large, i.e. n = 47 > 30, the central limit theorem can be used to approximate the sampling distribution of sample mean by the normal distribution.
So,[tex]\bar X\sim N(\mu,\ \frac{\sigma^{2}}{{n}})[/tex]
The range of the middle 98% of most averages for the lengths of pregnancies in the sample is the 98% confidence interval.
The critical value of z for 98% confidence level is,
z = 2.33
Compute the 98% confidence interval as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}[/tex]
[tex]=267\pm 2.33\cdot\frac{17}{\sqrt{47}}\\\\=267\pm5.78\\\\=(261.22, 272.78)\\\\\approx (261, 273)[/tex]
Thus, the range of middle 98% of most averages for the lengths of pregnancies in the sample is, (261, 273).
which one doesn't belong ? please help thx :)
Answers
Answer:
THE CURVED ONE
Step-by-step explanation:
THE OTHER ONES R STRAIGHT LINES
THE ONE ON THE TOP RIGHT CORNER IS A PARABOLA
HOPE I HELPED
PLS MARK BRAINLIEST
DESPERATELY TRYING TO LEVEL UP
✌ -ZYLYNN JADE ARDENNE
Matt wants to plot a garden. He was 48 meters to work with. He wants the length of the garden to be 3 times the width of the garden because he has many types of vegetables to grow. What is the width of the garden.
Answers
Answer: The width of the garden is 6 Meters
Step-by-step explanation:
3x + x = 24
The length is 3x and the width is x
24 / 4 = 6
x= 6
The width of the garden is 6 Meters
Answer:
x = 6
Step-by-step explanation:
3x + x = 24
24 / 4 = 6
x = 6
Determine the point estimate of the population proportion, the margin of error for the following confidence interval, and the number of individuals in the sample with the specified characteristic, x, for the sample size provided. Lower bound equals 0.345, upper boundequals0.895, nequals1000
Answers
Answer:
For this case we have the following confidence interval given:
[tex] 0.345 \leq p \leq 0.895 [/tex]
And for this case we want to find the estimated proportion like this:
[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]
And the margin of error for this case would be given by:
[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]
Step-by-step explanation:
For this case we have the following confidence interval given:
[tex] 0.345 \leq p \leq 0.895 [/tex]
And for this case we want to find the estimated proportion like this:
[tex]\hat p= \frac{0.345 +0.895}{2}= 0.62[/tex]
And the margin of error for this case would be given by:
[tex] ME= \frac{0.895-0.345}{2}= 0.275[/tex]
Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r=0.767, n=25 A. Critical values: r= +0.396, no significant linear correlation B. Critical values: r= +0.487, no significant linear correlation C. Critical values: r = +0.396, significant linear correlation D. Critical values: r = + 0.487, significant linear correlation
Answers
Answer:
C. Critical values: r = +0.396
Step-by-step explanation:
Hello!
A linear correlation for two variables X₁ and X₂ was calculated.
For a sample n= 25 the sample correlation coefficient is r= 0.767.
Be the hypotheses:
H₀: ρ = 0
H₁: ρ ≠ 0
α: 0.05
For this hypothesis test, the rejection region is two-tailed, and the degrees of freedom are Df= n-2= 25-2= 23
So using the Pearson product-moment correlation coefficient table of critical values, under the entry for "two tailed tests" you have to cross the level of significance and the degrees of freedom to find the corresponding critical value:
[tex]r_{n-2;\alpha }= r_{23;0.05}= 0.396[/tex]
Since the calculated correlation coefficient is greater than the critical value, you can reject the null hypothesis, this means that the correlation is significant at level 5%
I hope this helps!
Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the answer is an interval, enter your answer using interval notation. If the answer is a finite set of values, enter your answers as a comma separated list of values.)
Answers
Answer:
(0, 16]
Step-by-step explanation:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)
According to the ratio test, if we define L such that:
L = lim(n→∞) |aₙ₊₁ / aₙ|
then the series will converge if L < 1.
aₙ = (-1)ⁿ⁺¹ (x−8)ⁿ / (n 8ⁿ)
aₙ₊₁ = (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹)
Plugging into the ratio test:
L = lim(n→∞) | (-1)ⁿ⁺² (x−8)ⁿ⁺¹ / ((n+1) 8ⁿ⁺¹) × n 8ⁿ / ((-1)ⁿ⁺¹ (x−8)ⁿ) |
L = lim(n→∞) | -n (x−8) / (8 (n+1)) |
L = (|x−8| / 8) lim(n→∞) | n / (n+1) |
L = |x−8| / 8
For the series to converge:
L < 1
|x−8| / 8 < 1
|x−8| < 8
-8 < x−8 < 8
0 < x < 16
Now we check the endpoints. If x = 0:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (0−8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -(-1)ⁿ (-8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -(8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° -1 / n
This is a harmonic series, and diverges.
If x = 16:
∑ₙ₌₁°° (-1)ⁿ⁺¹ (16−8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° (-1)ⁿ⁺¹ (8)ⁿ / (n 8ⁿ)
∑ₙ₌₁°° (-1)ⁿ⁺¹ / n
This is an alternating series, and converges.
Therefore, the interval of convergence is:
0 < x ≤ 16
Or, in interval notation, (0, 16].
Determine whether the sequence converges or diverges. If it converges, find the limit. an = 9 + 14n2 n + 15n2 Step 1 To find lim n → [infinity] 9 + 14n2 n + 15n2 , divide the numerator and denominator by the highest power of n that occurs in the fraction. This is n .
Answers
Answer:
The sequence ConvergesStep-by-step explanation:
Given the sequence [tex]a_n = \frac{9+14n^{2} }{n+15n^{2} }[/tex]
To find the limit of the sequence, we will first divide the numerator and the denominator through by the highest power of n which is n² as shown;
[tex]\lim_{n \to \infty} \frac{9/n^{2} +14n^{2}/n^{2} }{n/n^{2} +15n^{2}/n^{2} }\\ \lim_{n \to \infty} \frac{9/n^{2} +14 }{1/n +15n^{2}/n^{2 }}\\[/tex]
As [tex]n[/tex] tends to [tex]\infty[/tex], [tex]\frac{a}{n}[/tex] tends to zero where n is any constant, The limit of tyhe sequence as n tends to infinity becomes;
[tex]= \frac{9/\infty+14 }{1/\infty+15 }\\= \frac{0+14}{0+15} \\= 14/15\\[/tex]
Therefore [tex]\lim_{n \to \infty} \frac{9+14n^{2} }{n+15n^{2} } = 14/15[/tex]
Since the limit of the sequence gave a finite number , the sequence converges.
Note that the only case when the sequence diverges id when the limit of the sequence is infinite
A baby’s t-shirt requires 2/9 yards of fabric. How many t-shirts can be made from 38 yards?
Answers
Answer:
8 and 4/9 i think... i am sorry if i am wrong
Step-by-step explanation:
Consider a data set containing the following values:
70 65 71 78 89 68 50 75
The mean of the preceding values is:
70.75.
The deviations for the mean have been calculated as follows:
-0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25
a. If this is the sample data, the sample variance is _____ and the sample standard deviation is ___
b. If this is a population data, the population variance is_____ and the population standard deviation is_____
Answers
Answer:
a. 125.0714; 11.1835.
b. 109.4375; 10.4612.
Step-by-step explanation:
Given the following data;
70, 65, 71, 78, 89, 68, 50, 75.
Mean = 70.75
The deviation for the mean of the data is -0.75, -5.75, 0.25,7.25,18.25,-2.75,-20.75, and 4.25.
We would then find the square of this deviation;
[tex]=(-0.75)^2+(-5.75)^2+( 0.25)^2+(7.25)^2 +(18.25)^2+(-2.75)^2+(-20.75)^2 +(4.25)^2[/tex]
[tex]=0.5625+33.0625+0.0625+52.5625+333.0625+7.5625+430.5625+18.0625[/tex]
= 875.5
Next is to find the population variance;
[tex]V = \frac{875.5}{8}[/tex]
Variance, V = 109.4375
The population standard deviation is the square root of the population variance;
[tex]Sd = \sqrt{109.4375}[/tex]
Standard deviation, Sd = 10.4612
To find the sample variance;
[tex]V = \frac{875.5}{8-1}[/tex]
[tex]V = \frac{875.5}{7}[/tex]
Variance, V = 125.0714
The sample variance is;
[tex]Sd = \sqrt{125.0714}[/tex]
Standard deviation, Sd = 11.1835
Therefore,
a. The sample variance is 125.0714 and the sample standard deviation is 11.1835.
b. If this is a population data, the population variance is 109.4375 and the population standard deviation is 10.4612.
Answer:
C. 20.67
Step-by-step explanation:
I got it right on edge :)
please help fast ! Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match the fractions with equivalent percentages.
Answers
Answer:
13/20<--->65%
21/25<--->84%
3/4<--->75%
2/5<--->40%
3/5<--->60%
To find the matching pairs, divide the fraction and move the decimal point to your answer 2 places to the right to then get a percentage.
Ex: 1/2= .50->5.0->50.->50%
The image did not show the rest of the answers, but I worked with what information I received from the current image, producing 5 sets of answers. If there are more than 5 sets, please send a second image with your question so we can help you with the rest.
Hence the correct match of fractions to their equivalent percentages are;
13/20 = 65%
21/25 = 84%
3/4 = 75%
2/5 = 40%
3/5 = 60%
Percentages and fractionsFractions are written as a ratio of two integers. In order to convert fractions to percentage, we will simply multiply the fraction given by 100.
For the fraction 13/20
13/20 * 100 = 13 * 5
13/20 = 65%
For the fraction 21/25
21/25 * 100 = 21 * 4
21/25 = 84%
For the fraction 3/4
3/4 * 100 = 3 * 25
3/4 = 75%
For the fraction 2/5
2/5 * 100 = 2 * 20
2/5 = 40%
For the fraction 3/5
3/5 * 100 = 3* 20
3/5 = 60%
Hence the correct match of fractions to their equivalent percentages are;
13/20 = 65%
21/25 = 84%
3/4 = 75%
2/5 = 40%
3/5 = 60%
Learn more on percentages here: https://brainly.com/question/24304697
#SPJ9
Which of the following shows the union of the sets? {3, 6, 9, 12, 15} {1, 6, 12, 18, 24}
Answers
Answer:
A ∪ B = {1,3,6,9,12,15,18,24}
Step-by-step explanation:
Let A = {3,6,9,12,15}
B = {1,6,12,18,24}
So,
A ∪ B = {3,6,9,12,15} ∪ {1,6,12,18,24}
A ∪ B = {1,3,6,9,12,15,18,24}
Answer:
{1,3,6,9,12,15,18,24}
Step-by-step explanation:
The union is joining of the elements of the sets
{3, 6, 9, 12, 15}U {1, 6, 12, 18, 24}
= {1,3,6,9,12,15,18,24}
2jenxnwioznxjwhjjjjjhdhwbxnoaowbfnxiw
Answers
What is your question?
Answer:
yeah what's your question?
The slope of a line is 1, and the y-intercept is -1. What is the equation of the line written in slope-intercept form? y = 1 - x y = -x - 1 y = x - 1
Answers
y=x-1
Step by step explanation:
Y intercept is the value of y when x=0 thus y=-1 if x is 0
Slope in equation y=mx+c is the value before x,which is 1
y=1x+c
Thus y=x+c
Please mark as brainliest
What is the value of this expression when n approaches infinity?
Answers
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
The claim that the mean amount of sleep for adults is less than 7 hours. Choose the correct statement about null and alternative hypothesis.
a) H0: µ > 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
b) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
H2: µ > 7 hours (second alternative hypothesis and original claim)
c) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
d) H0: µ < 7 hours (null hypothesis)
H1: µ ≥≥ 7 hours (alternative hypothesis and original claim)
Answers
Answer:
c) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
Step-by-step explanation:
The hypothesis test is performed in order to see if a sample outcome gives evidence to reject a null hypothesis and support the researchers claim.
In this case, the claim is that the mean amount of sleep for adults is less than 7 hours.
For this claim, the alternative hypothesis will state the researcher's claim: the mean amount of sleep for adults is significantly less than 7 hours.
The null hypothesis will state the opposite: the mean amount of sleep for adults is not significantly less than 7 hours. In this case, it is the same to claim that the mean amount is 7 hours.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=7\\\\H_a:\mu< 7[/tex]
In a family, the probability that a child is female is 0.6. if there are thee children in the family, what is the probability that 1. Exactly 2 are girls 2. At least 1 is a boy
Answers
Answer:1.P(exactly 2 kids are girls)=3/8
2. P(at least 1 is boy)=7/8
Step-by-step explanation:
1.P(exactly 2 kids are girls)=N(outcomes with 2 girls) /Total number of outcomes.
All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8
Outcomes where are exactly 2 girls are:
ggb,gbg, bgg - total 3 outcomes
So P(exactly 2 are girls)=3/8
2. P(at least 1 is boy)=Number of outcomes , where are at least 1 boy (1,2 or all 3 kids are boys)/ Total number of outcomes
All possible outcomes are ggb,gbg, bgg, gbb, bgb, bbg, ggg, bbb - total 8
Outcomes, where at least 1 kid is boy: ggb,gbg, bgg, gbb, bgb, bbg, bbb - total 7
P(at least 1 is boy)=7/8