Answer:
The order in which you solve the operations will provide different results and to be able to get the right answer you have to be familiar with the order of operations to know the appropiate steps to solve an operation. According to the order of operations in mathematics, exponents are given precedence over addition and multiplication. Because of that, the exponent is the first you have to solve.
3 + 2 * 3^2
3+2*9
Then, mutiplication is given precedence over addition:
3+18
Now, you can solve the addition and the result is: 21
Because of this, the answer is:
• 3 +( 2 * (3^2)) = 21
When Sam simplified the expression 3.5 - (-4.1), she got -0.6.
What mistake did Sam likely make when she simplified
the expression?
Answer:
She forgot to combine the 2 negative signs and turn it into a positive.
Step-by-step explanation:
When you subtract a negative, you are adding the number. So if we have 3.5 - (-4.1), it would equal 3.5 + 4.1, which is 7.6
Answer:
She subtracted a negative incorrectly by simply subtracting a positive when subtracting a negative means to add a positive.
Step-by-step explanation:
She subtracted 3.5 - 4.1 which is -0.6
The problem is subtracting -4.1 which means to add 4.1
3.5 - (-4.1) = 3.5 + 4.1 = 7.6
She did: 3.5 - (-4.1) = 3.5 - 4.1 = -0.6 which is incorrect.
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
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
Which of the following shows the union of the sets? {3, 6, 9, 12, 15} {1, 6, 12, 18, 24}
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}
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).
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.
According to a polling organization, 22% of adults in a large region consider themselves to be liberal. A survey asked 200 respondents to disclose their political philosophy: Conservative,Liberal, And Moderate. Treat the results of the survey as a random sample of adults in this region. Do the survey results suggest the proportion is higher than that reported by the pollingorganization? Use an alpha =0.05 level of significance.
75- Liberal
65- Moderate
61- Conservative
Answer:
Step-by-step explanation:
Using the proportion test
Null hypothesis: p <= 0.22
Alternative hypothesis: p > 0.22
Using the formula
z score = p - P /√ (P(1-P)/n)
Where p is 74/200= 0.37, P = 0.22, n = 200.
0.37-0.22 / √(0.22(1-0.22)/200)
0.15 / √(0.22(0.78)/200)
0.15 / √(0.1716/200)
0.15/ √0.000858
0.15 / 0.02929
= 5.1212
To help arrive at a conclusion, we have to find the p value, using a p value calculator at the 0.05 level of significant, the p value is less than 0.00001... Thus we would reject the null as there is sufficient statistical evidence to prove that the proportion is higher than that reported by the polling organization.
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.
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
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
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:
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 .
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
What is the value of this expression when n approaches infinity?
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
The red line in the figure is an altitude of triangle HJL. Using right angle trigonometry, write an equation involving sinL
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:
What is the value of x? The figure contains 2 lines that intersect to form what looks like an x. Two of the 4 angles in the x are labeled. The left angle is labeled open parenthesis 3 x minus 3 close parenthesis degrees. The right angle across from it is labeled open bracket 6 open parenthesis x minus 10 close parenthesis close bracket degrees. Enter your answer in the box. x =
Answer:
[tex]x=38.5^\circ[/tex]
Step-by-step explanation:
Given that the left angle = [tex](3x-3)^\circ[/tex]
The right angle across from it [tex]= 6(x-10)^\circ[/tex]
The other two angles are x and x.
We know that the sum of angles at a point equals 360 degrees.
Therefore,
[tex](3x-3)^\circ+6(x-10)^\circ+x+x=360^\circ\\3x-3+6x-60+2x=360\\11x-63=360\\11x=360+63\\11x=423\\x=38.5^\circ[/tex]
The value of x is approximately 38.5 degrees.
2jenxnwioznxjwhjjjjjhdhwbxnoaowbfnxiw
What is your question?
Answer:
yeah what's your question?
Question 1
You can ride a taxi and pay a flat rate of $25 to go anywhere in the city, or you can pay a
base rate of $15 and $1 per mile. For which trip would it make more sense to pay the base
rate and 1$ per mile?
15 mile trip
9 mile trip
25 mile trip
O 12 mile trip
Answer:
9 mile trip
Step-by-step explanation:
$15 + $15 = $30
$15 + $9 = $24
$15 + $25 = $40
$15 + $12 = $27
$30 > $25
$24 < $25
$40 > $25
$27 > $25
Write 17857000012 in words
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!
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?
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.
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
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!
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_____
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 :)
help me pls i need to graduatE
Answer:
The answer is option D.
LJ = 3.5Step-by-step explanation:
To find LJ we use the sine rule
From the picture
LK / sin J = LJ / sin K
LK = 9
J = 89°
K = 23°
So now LJ is
9 / sin 89° = LJ / sin 23°
Make LJ the subject
That's
LJ = 9 sin 23° / sin 89°
LJ = 3.51
The final answer is
LJ = 3.5Hope this helps you.
what are the multiples of 5,6,8,9?
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
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
which one doesn't belong ? please help thx :)
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
A die is rolled 8 times. Find the probability. P(getting even numbers 7 times)
Answer:
The probability of getting even 7 times out of 8 is 1/256. Hope this helps!!
Step-by-step explanation:
21/7 = 3 is the answer of your question
1. A fruitseller bought 200 apples for Rs 300.40 of them were rotten and thrown away.
She sold the rest at Rs 2.25 each. Find its gain or loss percent.
253
A Book of Mathematics-8
Answer:
ok I am tellin6 to you
Step-by-step explanation:
ok I will tell to you
Part A: The polynomial in standard form is Select a Value
Answer:
2nd Option
Step-by-step explanation:
Standard Form: ax² + bx + c
This can be modified to fit any degree polynomial, as long as the highest degree is first, and then decreasing. So our answer is B.
Is the area of this shape approximately 57 6 cm ? If not, give the correct area.
O True
O False
Answer: True
Step-by-step explanation: Taking the triangle from the left and moving it to the right creates a rectangle. From there just do 12.8×4.5.
A lumber company has just taken delivery on a shipment of 10,000 2 ✕ 4 boards. Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other. Let A = {the first board is green} and B = {the second board is green}.
(a) Compute P(A), P(B), and P(A ∩ B) (a tree diagram might help). (Round your answer for P(A ∩ B) to five decimal places.)
(b) With A and B independent and P(A) = P(B) = 0.1, what is P(A ∩ B)?
Answer:
Step-by-step explanation:
Given That:
Let A = {the first board is green} and B = {the second board is green}.
A lumber company has just taken delivery on a shipment of 10,000 2×4 boards.
Suppose that 10% of these boards (1000) are actually too green to be used in first-quality construction. Two boards are selected at random, one after the other.
We are to compute the following probabilities :
P(A)
P(B)
P(A ∩ B)
To start with the probability P(A)
[tex]P(A) = \dfrac{1000}{10000}[/tex]
P(A) = 0.1
[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]
where;
[tex]P(B|A) = \dfrac{N(B|A)}{N-1}[/tex]
[tex]P(B|A) = \dfrac{999}{9999}[/tex]
[tex]P(B|A) =0.0999[/tex]
[tex]P(B|A') = \dfrac{N(B|A')}{N-1}[/tex]
[tex]P(B|A') = \dfrac{1000}{999}[/tex]
[tex]P(B|A') = 0.10[/tex]
Recall that :
[tex]P(B) = P(B|A)*P(A)+P(B|A')*P(A')[/tex]
[tex]P(B) = 0.0999*0.1+0.10*(1-0.1)[/tex]
[tex]P(B) = 0.00999+0.10*(0.9)[/tex]
[tex]P(B) = 0.00999+0.09[/tex]
[tex]P(B) = 0.0999[/tex]
P(A ∩ B) = P(B|A)B
P(A ∩ B) = 0.0999 × 0.10
P(A ∩ B) = 0.00999
(b)
Given that A and B are independent; Then:
P(A ∩ B) = P(A) × P(B)
0.00999 = 0.1 × 0.09999
0.00999 = 0.00999
As such A and B are independent
However; when P(A ∩ B) = P(A) = P(B) = 0.1
P(A ∩ B) = P(A) × P(B)
P(A ∩ B) = 0.1 × 0.1
P(A ∩ B) = 0.01
Check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a).
9x^2 - y^2 = 1
Answer:
Step-by-step explanation:
The question is incomplete. Find the complete question in the attached file.
a) Given the expression 9x^2 - y^2 = 1
Differentiating implicitly will give;
[tex]18x-2y\frac{dy}{dx} = 0\\[/tex]
We can then make dy/dx the subject of the formula as shown;
[tex]18x = 2y\frac{dy}{dx}\\\frac{dy}{dx} = \frac{18x}{2y} \\\frac{dy}{dx} = \frac{9x}{y} \\y' = \frac{9x}{y}[/tex]
b) In order to solve the question explicitly, we will first have to make x the subject of the formula before differentiating.
[tex]9x^{2} -y^{2} = 1\\9x^{2} = 1+ y^{2}\\y^{2} =9x^{2}- 1\\y^{2} = 9x^{2} - 1\\y = \sqrt{9x^{2}- 1 } \\[/tex]
Using chain rule to solve the equation;
let;
[tex]u = 9x^{2} -1\\ y = u^{1/2}[/tex]
du/dx = 18x
dy/du = [tex]1/2u^{-1/2}[/tex]
dy/dx = dy/du * du/dx
dy/dx = [tex]1/2u^{-1/2} * 18x[/tex]
[tex]\frac{dy}{dx} = \frac{1}{2}({9x^{2}-1 } )^{-1/2} * 18x\\\frac{dy}{dx} = 9x({9x^{2} -1 } )^{-1/2} \\\frac{dy}{dx} = 9 x(\sqrt{{\frac{1}{9x^{2} -1} } }) \\\frac{dy}{dx} = \frac{9x}{\sqrt{9x^{2}-1 } }[/tex]
c) In order to confrim that solutions to part (a) and (b) are consistent, we will substitute [tex]y = \sqrt{9x^{2} - 1 } \\[/tex] into the answer in (a) as shown;
From (a) [tex]\frac{dy}{dx} = \frac{9x}{y} \\[/tex]
[tex]y' = \frac{9x}{ \sqrt{9x^{2} - 1 } \\} } \\}[/tex]
This shows that they are consistent
Please help need to do corrections and can't figure out this homework question??
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)
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]
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
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]