Answers
For this you just look at the sides.
Soh cah toa
This is good to remember.
Sin = opposite/ hypotenuse
Cos= adjacent/ hypotenuse
Tan = opposite/ adjacent
In this case you have TanZ, the side adjacent to the angle is 10 and the opposite to the angle is 24. So tanZ is 24/10 which simplifies to 12/5.
The hypotenuse is always the longest side, but the opposite and adjacent sides can change depending on the angle.
Answer:90 = ... 42 + 48) - 360
Step-by-step explanation:
Related Questions
A research team is testing a product that will minimize wrinkles among older adults. Volunteers in the age group of 40 to 45 are included in the research. The research team gives a cream to be applied on the face to one group and a placebo cream to the other group.
Answers
A punch contains cranberry juice and ginger ale in the ratio 5:3. If you require 32 L
of punch for a party, how many litres of cranberry juice and how many litres of ginger
ale are required?
Answers
6
litres of cranberry juice
Explanation:
"A fruit punch recipe calls for 3 parts of apple juice to 4 parts of cranberry juice"
Meaning: For every 3 litres of apple juice, you must add 4 litres of cranberry juice. That means if you add 6 litres of apple juice, then you must add 8 litres of cranberry juice
Now, if you add 4.5 litres of apple juice, you can think of it this way
3
apple juice
:
4
cranberry juice
4.5
apple juice
:
x
cranberry juice
x
=
4.5
×
4
3
x
=
18
3
x
=
6
Therefore, you must add
6
litres of cranberry juice
Answer link
Shwetank Mauria
Jul 25, 2018
6
liter of cranberry juice.
Explanation:
As
3
parts of apple juice are added to
4
parts of cranberry juice
and
4.5
liter of apple juice means each of three parts are
4.5
3
=
1.5
liter
and one needs
4
parts of cranberry juice i.e.
4
×
1.5
liter or
6
liter of cranberry juice.
The regression analysis can be summarized as follows: Multiple Choice No significant relationship exists between the variables. A significant negative relationship exists between the variables. For every unit increase in x, y decreases by 12.8094. A significant positive relationship exists between the variables
Answers
Answer:
A significant negative relationship exists between the variables
Step-by-step explanation:
Base on the information given in the question which goes thus : For every unit increase in x, y decreases by 12.8094. The value 12.8094 is the slope which is the rate of change in y variable per unit change in the independent variable. The sign or nature of the slope Coefficient gives an hint about the relationship between the x and y variables. The slope Coefficient in this case is negative and thus we'll have a negative relationship between the x and y variables (an increase in x leads to a corresponding decrease in y). This is a negative association.
In factons you divide the numerator and the whole number .. then denominator
Correct?
Answers
Answer:
Step-by-step explanation:
yes
A recent study of the relationship between social activity and education for a sample of corporate executives showed the following results. Social Activity Education Above Average Average Below Average College 30 20 10 High School 20 40 90 Grade School 10 50 130 The appropriate test statistic for the analysis is a(n) ______.a. F-statistic.b. t-statistic.c. Chi-square statistic.d. z-statistic.
Answers
Answer:
Chisquare statistic
Step-by-step explanation:
The most appropriate test to use here is the Chisquare test as it isemployed when testing the relationship between two variables. Both the T statistic and z statistics are the used for testing difference in means. However, in the analysis above, we are given two variables with each having its own levels. Hence, the Chisquare test is the most appropriate in this kind of situation a it measures if a difference exists between the two variables. It tests if they are related or independent of on one another
Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence. Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
Answers
Answer:
The sample size necessary is of 168.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Based on a previous study, arrival delay times have a standard deviation of 39.6 minutes.
This means that [tex]\sigma = 39.6[/tex]
Find the sample size necessary to estimate the mean arrival delay time for all American Airlines flights from Dallas to Sacramento to within 6 minutes with 95% confidence.
This is n for which M = 6. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]6 = 1.96\frac{39.6}{\sqrt{n}}[/tex]
[tex]6\sqrt{n} = 1.96*39.6[/tex]
[tex]\sqrt{n} = \frac{1.96*39.6}{6}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*39.6}{6})^2[/tex]
[tex]n = 167.34[/tex]
Rounding up:
The sample size necessary is of 168.
Area: Change in Dimensions
A rectangle FGHJ has a width of 3 inches and a length of 7 inches
Answers
Answer:
A) 21 in²
B) 42 in²
C) 84 in²
D) I) 4 in²
II) 8 in²
III) 16 in²
E) From our calculations, we can see that doubling one part of the dimensions gives an area that is twice the original one while doubling both dimensions gives an area that four times the original one.
Step-by-step explanation:
We are given dimensions of triangle as;
width; w = 3 inches
length; L = 7 inches
A) Area of triangle is;
A = Lw
A = 7 × 3
A = 21 in²
B) If we double the width, then area is;
A = 7 × (2 × 3)
A = 42 in²
Area is twice the original area
C) If we double the width and length, then we have;
Length = 7 × 2 = 14 in
Width = 3 × 2 = 6 in
Area = 14 × 6 = 84 in²
Area is four times the original one
D) Let's try a triangle with base 2 in and height 4 in.
I) formula for area of triangle is;
A = ½ × base × height
A = ½ × 2 × 4
A = 4 in²
II) If we double the width(base) , then area is;
A = ½ × 2 × 2 × 4
A = 8 in²
This is twice the original area.
III) If we double the width(base) and length(height), then we have;
A = ½ × 2 × 2 × 4 × 2
A = 16 in²
This is four times the original area
E) From our calculations, we can see that doubling one part of the dimensions gives an area that is twice the original one while doubling both dimensions gives an area that four times the original one.
You want to walk from home to a clothing store that is 1/4 miles away you stop for a rest after 1/8 miles how much farther do you have to walk
Answers
Answer:
1/8
Step-by-step explanation:
Answer: 1/8
Step-by-step explanation:
1/8 + 1/8 = 2/8 = 1/4
21-B Book Street Books sells about 700700 books each month. The pie chart displays the most popular book categories, by percentage, each month. Find the number of romance books sold each month. Round your answer to the nearest integer.
Answers
Solution :
Given data :
Total number of books sold each month= 700
The charts in the display attached below shows the most popular books category by percentages.
Percentage of romance books sold each = 8.5%
Therefore, the number of romance books sold in each month is given by :
[tex]$=8.5 \% \text{ of }\ 700$[/tex]
[tex]$=\frac{8.5}{100}\times 700$[/tex]
= 59.5
≈ 60 books (rounding off)
You can use the fact that total amount is taken as 100%.
The number of romance books in the given Streets Books is 60
How to find the percentage from the total value?Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is [tex]\dfrac{a}{100} \times b[/tex]
How to find the number of Romance books if its given that it is 8.5% of the total books present in that book collection?Since the total amount of books is 700, and its 8.5% books are romance books, thus we have:
[tex]\text{Number of Romance books} = \dfrac{700}{100} \times 8.5 = 59.5 \approx 60[/tex]
The number of romance books in the given Streets Books is 60
Learn more about percentage here:
https://brainly.com/question/11549320
4. A typical smartphone battery (yes that includes iphones) degrades at approximately 1%
battery capacity per month with typical use.
a. Construct an equation using f(t) and t that represents the relationship between
"f(t)" the battery capacity of a typical smartphone after "t" months and "L" the
number of months the smartphone has been in normal use.
b. What does the horizontal intercept represent in context? (The x-intercept)
c. What does the vertical intercept represent in context? (The y-intercept)
Answers
Answer:
a. [tex]f(t) = (0.99)^{t} 100%\\[/tex]
b. The x - intercept represents the time at which the battery life drops to 0 %.
c. The y - intercept represents the initial battery life.
Step-by-step explanation:
a. Construct an equation using f(t) and t that represents the relationship between
"f(t)" the battery capacity of a typical smartphone after "t" months and "L" the
number of months the smartphone has been in normal use.
Let the initial battery life be I.
After one month, it decreases by 1%. So, our new value, I' = initial value - decrease = I - 1%I = 99%I.
After two months, it decreases by 1% to our new value I". So, our new value, I" = initial value - decrease = I' - 1%I' = 99%I' = 99%(99%)I = (99%)²I
After three months, it decreases by 1% to our new value I'". So, our new value, I"' = initial value - decrease = I" - 1%I" = 99%I" = 99%(99%)²I = (99%)³I
We see a pattern here.
After t months, f(t)
[tex]f(t) = (0.99)^{t} 100%\\[/tex]
b. What does the horizontal intercept represent in context? (The x-intercept)
The x - intercept represents the time at which the battery life drops to 0 %.
c. What does the vertical intercept represent in context? (The y-intercept)
The y - intercept represents the initial battery life.
If three times a number added to 8 is divided by the number plus 7, the result is four thirds. Find the number.
Answers
9514 1404 393
Answer:
4/5
Step-by-step explanation:
The wording is ambiguous, as it often is when math expressions are described in English. We assume you intend ...
[tex]\dfrac{3n+8}{n+7}=\dfrac{4}{3}\\\\3(3n+8)=4(n+7)\qquad\text{multiply by $3(n+7)$}\\\\9n+24=4n+28\qquad\text{eliminate parentheses}\\\\5n=4\qquad\text{subtract $4n+24$}\\\\\boxed{n=\dfrac{4}{5}}\qquad\text{divide by 5}[/tex]
The number is 4/5.
4. Consider the function g(x) = 2x^2 - 4x+3 on the interval [-1, 2]
A.) Does Rolle's Theorem apply to g(x) on the given interval? If so, find all numbers, s,
guaranteed to exist by Rolle's Theorem. If not, explain why not. (2 pts.)
b.) Does the Mean Value Theorem apply to g(x) on the given interval? If so, find all
numbers, a guaranteed to exist by the Mean Value Theorem. If not, explain why not.
(4 pts.)
Answers
Hi there!
A.) Begin by verifying that both endpoints have the same y-value:
g(-1) = 2(-1)² - 4(-1) + 3
Simplify:
g(-1) = 2 + 4 + 3 = 9
g(2) = 2(2)² - 4(2) + 3 = 8 - 8 + 3 = 3
Since the endpoints are not the same, Rolle's theorem does NOT apply.
B.)
Begin by ensuring that the function is continuous.
The function is a polynomial, so it satisfies the conditions of the function being BOTH continuous and differentiable on the given interval (All x-values do as well in this instance). We can proceed to find the values that satisfy the MVT:
[tex]f'(c) = \frac{f(a)-f(b)}{a-b}[/tex]
Begin by finding the average rate of change over the interval:
[tex]\frac{g(2) - g(-1)}{2-(-1)} = \frac{3 - 9 }{2-(-1)} = \frac{-6}{3} = -2[/tex]
Now, Find the derivative of the function:
g(x) = 2x² - 4x + 3
Apply power rule:
g'(x) = 4x - 4
Find the x value in which the derivative equals the AROC:
4x - 4 = -2
Add 4 to both sides:
4x = 2
Divide both sides by 4:
x = 1/2
4)In order to set rates, an insurance company is trying to estimate the number of sick daysthat full time workers at an auto repair shop take per year. A previous study indicated thatthe standard deviation was2.2 days. a) How large a sample must be selected if thecompany wants to be 92% confident that the true mean differs from the sample mean by nomore than 1 day
Answers
Answer:
A sample of 18 is required.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.92}{2} = 0.04[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.04 = 0.96[/tex], so Z = 1.88.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
A previous study indicated that the standard deviation was 2.2 days.
This means that [tex]\sigma = 2.2[/tex]
How large a sample must be selected if the company wants to be 92% confident that the true mean differs from the sample mean by no more than 1 day?
This is n for which M = 1. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 1.88\frac{2.2}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 1.88*2.2[/tex]
[tex](\sqrt{n})^2 = (1.88*2.2)^2[/tex]
[tex]n = 17.1[/tex]
Rounding up:
A sample of 18 is required.
(2/3)^x-1=27/8, Find x
Answers
Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.
A business rents in-line skates and bicycles to tourists on vacation. A pair of skates rents for $5 per day. A bicycle rents for $20 per day.
On a certain day, the owner of the business has 25 rentals and takes in $425.
Write a system of equation to represent this situation, then solve to find the number of each item rented.
Show both the equations and the solution.
Answers
Answer:
5x+20y=425
Step-by-step explanation:
Its 5 bucks for x pairs of skates
Its 20 dollars for y bikes
x+y rentals have to equal 25
all of this is equal to 425. All that is left to do is test with number until the statement is true.
try :
5(5)+(20)(20)=425
x + y do equal 25, and the total is equal to 425.
Factor 12x-40 using the gcf
Answers
Answer:
4(3x-10)
Step-by-step explanation:
12x-40 = (4*3)x-(4*10) = 4(3x-10). The GCF is 4.
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $324. Find the original selling price of the ski set.
Answers
Answer:
$520.632
Step-by-step explanation:
I need some help! thank you!
Answers
Answer:
The 1st,Thrid, Fifth Option
Step-by-step explanation:
The first option is true. We can move the orginal square root function to get g(x).
The second option is false. Function g(x) which equals
[tex] \sqrt{x - 3} - 1[/tex]
Domain is all real numbers greater than or equal to 3.
The third option is true. Since minimum point we can get is 0 in a square root function. We have a vertical shift so our new minimum point is
[tex]0 - 1 = - 1[/tex]
We can take the sqr root of 0 so
So all real numbers that are greater than or equal to -1 is true.
The fourth option is false, we need to add 3 instead of subtract 3.
The fifth option is true, we can do that to get back to our original function
Which is heavier, 4- kilograms
or
4
4 kilograms?
Answers
Answer:
i think 4 4 kilograms if im wrong sorry
Step-by-step explanation:
Provided below are summary statistics for independent simple random samples from two populations. Use the pooled t-test and the pooled t-interval procedure to conduct the required hypothesis test and obtain the specified confidence interval.
x1=21, s1=4, n1=12, x2=20, s2=3, n2=15
A. What are the correct hypotheses for a right-tailed test?
b. Compute the test statistic.
c. Determine the P-value.
B. The 90% confidence interval is from ____to ____.
Answers
Answer:
(a) [tex]H_o:\mu_1 = \mu_2[/tex] [tex]H_a:\mu_1 > \mu_2[/tex]
(b) [tex]t = 0.74[/tex]
(c) [tex]p =0.2331[/tex]
(d) [tex]CI = (-2.095,4.095)[/tex]
Step-by-step explanation:
Given
[tex]\bar x_1=21,\ s_1=4,\ n_1=12,\\ \bar x_2=20,\ s_2=3,\ n_2=15[/tex]
Solving (a): The hypotheses
The test is right-tailed, means that the alternate hypothesis will contain greater than sign.
So, we have:
[tex]H_o:\mu_1 = \mu_2[/tex]
[tex]H_a:\mu_1 > \mu_2[/tex]
Solving (b); The test statistic (t)
This is calculated as:
[tex]t = \frac{\bar x_1 - \bar x_2}{\sqrt{\frac{s_1^2(n_1 - 1) + s_2^2(n_2 - 1)}{n_1 + n_2 - 2} * (\frac{1}{n_1} + \frac{1}{n_2})}}[/tex]
So, we have:
[tex]t = \frac{21 - 20}{\sqrt{\frac{4^2(12 - 1) + 3^2(15 - 1)}{12 + 15 - 2} * (\frac{1}{12} + \frac{1}{15})}}[/tex]
[tex]t = \frac{1}{\sqrt{\frac{302}{25} * (0.15)}}[/tex]
[tex]t = \frac{1}{\sqrt{12.08 * 0.15}}[/tex]
[tex]t = \frac{1}{\sqrt{1.812}}[/tex]
[tex]t = \frac{1}{1.346}[/tex]
[tex]t = 0.74[/tex]
Solving (c): The P-value
First, we calculate the degrees of freedom
[tex]df = n_1 + n_2 -2[/tex]
[tex]df = 12+15 -2[/tex]
[tex]df = 25[/tex]
Using the t distribution, the p-value is:
[tex]p =TDIST(0.74,25)[/tex]
[tex]p =0.2331[/tex]
Solving (d): The 90% confidence interval
Calculate significance level
[tex]\alpha = 1 - CI[/tex]
[tex]\alpha = 1 - 90\%[/tex]
[tex]\alpha = 0.10[/tex]
Calculate the t value (t*)
[tex]t^* = (\alpha/2,df)[/tex]
[tex]t^* = (0.10/2,25)[/tex]
[tex]t^* = (0.05,25)[/tex]
[tex]t^* = 1.708[/tex]
The confidence interval is calculated using:
[tex]CI = (\bar x - \bar x_2) \± t^* *\sqrt{\frac{s_1^2(n_1 - 1) + s_2^2(n_2 - 1)}{n_1 + n_2 - 2} * (\frac{1}{n_1} + \frac{1}{n_2})}[/tex]
[tex]CI = (21 - 20) \± 1.708 *\sqrt{\frac{4^2(12 - 1) + 3^2(15 - 1)}{12 + 15 - 2} * (\frac{1}{12} + \frac{1}{15})}[/tex]
[tex]CI = 1 \± 1.708 *1.812[/tex]
[tex]CI = 1 \± 3.095[/tex]
Split
[tex]CI = 1 - 3.095 \ or\ 1 + 3.095[/tex]
[tex]CI = -2.095 \ or\ 4.095[/tex]
[tex]CI = (-2.095,4.095)[/tex]
What is the simplified expression for the
expression below? 4(x+8)+5(x-3)
Answers
= 4x+32+5(x-3)
=4x+32+5x-15
=9x+17
Answer: 9x+17
Find the solution to the system of equations.
x + y + z = 11
y + z = 12
Z= 8
Answers
A soft drink manufacturer wishes to know how many soft drinks adults drink each week. They want to construct a 95% confidence interval with an error of no more than 0.08. A consultant has informed them that a previous study found the mean to be 3.1 soft drinks per week and found the variance to be 0.49. What is the minimum sample size required to create the specified confidence interval? Round your answer up to the next integer.
Answers
Answer:
The minimum sample size required to create the specified confidence interval is 295.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Variance of 0.49:
This means that [tex]\sigma = \sqrt{0.49} = 0.7[/tex]
They want to construct a 95% confidence interval with an error of no more than 0.08. What is the minimum sample size required to create the specified confidence interval?
The minimum sample size is n for which M = 0.08. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.08 = 1.96\frac{0.7}{\sqrt{n}}[/tex]
[tex]0.08\sqrt{n} = 1.96*0.7[/tex]
[tex]\sqrt{n} = \frac{1.96*0.7}{0.08}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.7}{0.08})^2[/tex]
[tex]n = 294.1[/tex]
Rounding up:
The minimum sample size required to create the specified confidence interval is 295.
Which of the following have both 2 and -5 as solutions?
X2+3x-10-0
X2-3x-10=0
X2+7x+10=0
X2-7x+10=0
Answers
Answer:
X^2 + 3x - 10=0
A certain cosine function has an amplitude of 7. Which function rule could model this situation?
Answers
Answer:
y = 7cos bx
Step-by-step explanation:
For a cosine function without pahse shift and vertical shift, but with amplitude given, it will also have period and thus , the formula for the cosine function is;
y = Acos bx
Where;
A is the amplitude
Period = 2π/b
Now, we are told that the amplitude is 7. Thus;
y = 7cos bx
Let f(x) = 5 + 12x − x^3. Find (a) the x- coordinate of all inflection points, (b)
the open intervals on which f is concave up, (c) the open intervals on which
f is concave down.
Answers
Answer:
A) x = 0.
B) f is concave up for (-∞, 0).
C) f is concave down for (0, ∞).
Step-by-step explanation:
We are given the function:
[tex]f(x)=5+12x-x^3[/tex]
A)
We want to find the x-coordinates of all inflection points.
Recall that inflections points (may) occur when the second derivative equals zero. Hence, find the second derivative. The first derivative is given by:
[tex]f'(x) = 12-3x^2[/tex]
And the second:
[tex]f''(x) = -6x[/tex]
Set the second derivative equal to zero:
[tex]0=-6x[/tex]
And solve for x. Hence:
[tex]x=0[/tex]
We must test the solution. In order for it to be an inflection point, the second derivative must change signs before and after. Testing x = -1:
[tex]f''(-1) = 6>0[/tex]
And testing x = 1:
[tex]f''(1) = -6<0[/tex]
Since the signs change for x = 0, x = 0 is indeed an inflection point.
B)
Recall that f is concave up when f''(x) is positive, and f is concave down when f''(x) is negative.
From the testing in Part A, we know that f''(x) is positive for all values less than zero. Hence, f is concave up for all values less than zero. Our interval is:
[tex](-\infty, 0)[/tex]
C)
From Part A, we know that f''(x) is negative for all values greater than zero. So, f is concave down for that interval:
[tex](0, \infty)[/tex]
combine like terms
-7+5x-2=15
Answers
5x = 24
Step-by-step explanation:
[tex] - 7 + 5x - 2 = 15[/tex]
Combine like terms
[tex]5x = 15 + 7 + 2[/tex]
Further Workings :
Simplify
[tex]5x = 24[/tex]
[tex] \frac{5x}{5} = \frac{24}{5} \\ \\ x = 4.8[/tex]
Pls solve x it’s urgent
Answers
Answer:
1. 55 degree
2. 50 degree
3. 88 degree
4. 50 degree
Step-by-step explanation:
1.
Angle AE interior 180-120 = 60
Angle CD interior 180-112 = 68
x = 180- (60+68) = 180-128 = 52 degree
2.
interior 180 -120= 40
interior 180- 110 = 90
x = 180 - (40+90) = 180-130 = 50 degree
3.
exterior 90-52= 38
exterior 90-40 = 50
x = 180-(52+40)= 180-92 = 88 degree
4.
interior 180- (45+50) = 180-95 = 85 degree
interior adjoining triangle 180 - 85 = 95
all angles add up to 180
interior 180- (35 + 95)= 180-130 = 50 degree
x = 50 degree
The concentration of carbon monoxide (CO) in a gas sample is measured by a spectrophotometer and found to be 85 ppm. Through long experience with this instrument, it is believed that its measurements are unbiased and normally distributed, with an uncertainty (standard deviation) of 9 ppm. Find a 95% confidence interval for the concentration of CO in this sample. Round the answers to two decimal places. The 95% confidence interval is
Answers
Answer:
The confidence interval is [tex](85 - \frac{14.81}{\sqrt{n}},85 + \frac{14.81}{\sqrt{n}})[/tex], in which n is the size of the sample.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 1.645\frac{9}{\sqrt{n}} = \frac{14.81}{\sqrt{n}}[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is [tex]85 - \frac{14.81}{\sqrt{n}}[/tex]
The upper end of the interval is the sample mean added to M. So it is [tex]85 + \frac{14.81}{\sqrt{n}}[/tex]
The confidence interval is [tex](85 - \frac{14.81}{\sqrt{n}},85 + \frac{14.81}{\sqrt{n}})[/tex], in which n is the size of the sample.
The population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year. Assuming that the world population follows an exponential growth model, find the projected world population in 2015
Answers
Answer:
The projected world population in 2015 was 8,705,121,030 people.
Step-by-step explanation:
Given that the population of the world in 1987 was 5 billion and the annual growth rate was estimated at 2 percent per year, assuming that the world population follows an exponential growth model, to find the projected world population in 2015 the following calculation must be performed :
5,000,000,000 x 1.02 ^ (2015-1987) = X
5,000,000,000 x 1.02 ^ 28 = X
5,000,000,000 x 1.741024 = X
8,705,121,030 = X
Therefore, the projected world population in 2015 was 8,705,121,030 people.
