Answer:
50
Step-by-step explanation:
The amount of 4% butterfat milk is equal to x quarts , When 1% butterfat milk is equal to 75-x. The amount of butterfat in 4% butterfat milk is x/100*4=0.04x
The amount of butterflat in 1% butterfat milk is (75-x)/100= 0,75-0.01x
1The amount of butterflat in 75 quarts of 3% butterfat milk (our desired mixture) is 75/100*3= 2.25
This quantity (2.25) is the sum of butterfat from 4% butterfat milk and 1% butterfat milk(the sum of 0.04x and 0.75-0.01x)
the equation is
0.04x+0.75-0.01x=2.25
0.03x=1.5
x=50
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)
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.
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.
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.
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
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.
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.
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.
Pls solve x it’s urgent
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
Kyla can cut and split a cord of wood in 5.5 hr. Ronson can cut and split a cord of wood in 6.5 hr. How long will it take them, working together, to cut and split a cord of wood?Give your answer as a fraction or a mixed number.
Answer:
[tex]178.75\text{ minutes or }\frac{35.75}{12}\text{ hours}[/tex]
Step-by-step explanation:
Let's find each person's hourly rate. If Kyla can cut and split a cord of wood in 5.5 hours, Kyla can cut and split [tex]\frac{1}{5.5}[/tex] of a cord of wood in one hour. Similarly, Ronson can cut and spit [tex]\frac{1}{6.5}[/tex] of a cord of wood in one hour.
Therefore, working together, they can split [tex]\frac{1}{5.5}+\frac{1}{6.5}=\frac{12}{35.75}[/tex] of a cord of wood.
Thus, it will take them [tex]\frac{35.75}{12}=178.75\text{ minutes or }\frac{35.75}{12}\text{ hours}[/tex] to cut and split a cord of wood.
Area: Change in Dimensions
A rectangle FGHJ has a width of 3 inches and a length of 7 inches
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.
A certain cosine function has an amplitude of 7. Which function rule could model this situation?
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
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.)
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
What is 33000000000000+4555556656666
Answer:
785556656666-Answer s
In the case of normally distributed classes, discriminant functions are linear (straight lines, planes, and hyperplanes for two-, three-, and n-dimensional feature vectors, respectively) when the covariances matrices of corresponding classes are equal.
a. True
b. False
Answer:
True
Step-by-step explanation:
When covariance matrices of corresponding class are identical and diagonal matrix and their class probability is same then the class is normally distributed and its discriminant functions are linear.
combine like terms
-7+5x-2=15
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]
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.
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
What is the simplified expression for the
expression below? 4(x+8)+5(x-3)
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.
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
Suppose that Aces can be either high or low; that is, that {A, 2, 3, 4, 5} is a straight, and so is {10, Jack, Queen, King, Ace}. Moreover, a hand that is an Ace-high beats a King-high, etc. The number of ways of getting a five card hand that is a straight flush from a standard deck of cards is (Q) ________?? The probability of being dealt a five card hand that is a straight flush from a well shuffled standard deck of cards is (Q) _______??
Answer:
If OR is exclusive in the question, meaning that Ace can either be high or low but not both would give you 36 possible combinations. However the question isn't exactly stated in a way that makes it easy to interpret this. Your logic is right though, and it could be an error on your sources part. The possible combos are
A 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
5 6 7 8 9
6 7 8 9 10
7 8 9 10 J
8 9 10 J Q
9 10 J Q K
10 J Q K A
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
Answer:
X^2 + 3x - 10=0
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?
Find the solution to the system of equations.
x + y + z = 11
y + z = 12
Z= 8
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.
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.
Eric wrote the number 57,378 how many times greater is the value of the 7 in the thousands place than in the tens place
Answer:
100 times greater.
Step-by-step explanation:
57,378
The units digit is 8, and it's weight is: [tex]8 \times 10^0[/tex]
The tenths digit is 7, and it's weight is: [tex]7 \times 10^1[/tex]
The hundredths digit is 3, and it's weight is: [tex]3 \times 10^2[/tex]
The thousands digit is 7, and it's weight is: [tex]7 \times 10^3[/tex]
How many times greater?
We have to divide them, so:
[tex]\frac{7 \times 10^3}{7 \times 10^1} = \frac{10^3}{10^1} = 10^2 = 100[/tex]
So 100 times greater.
Find the measure of the missing angles.
83°C
b
Answer:
[tex]m\angle b=97^{\circ},\\m\angle c= 97^{\circ}[/tex]
Step-by-step explanation:
Vertical angles are angles on opposites sides of an intersection of two lines. Therefore, [tex]\angle c[/tex] and [tex]\angle b[/tex] are vertical angles. Similarly, the angle opposite to the angle marked 83 degrees is also equal to 83 degrees. Vertical angles are always equal.
Since there are 360 degrees in a circle, we have the following equation:
[tex]\angle c+\angle b+83+83=360,\\2\angle c+166=360,\\2\angle c=194,\\\angle c=\frac{194}{2}=\boxed{97^{\circ}}[/tex]
Since [tex]\angle c[/tex] and [tex]\angle b[/tex] are vertical angles and vertical angles are also equal, the measure of angle [tex]b[/tex] is also [tex]\boxed{97^{\circ}}[/tex]
You collect test scores on four members of a population which you can safely assume is approximately Normally distributed and test the hypotheses 0 : 100 : 100 H versus H µ µ = > a . You obtain a P-value of 0.052. Which of the following statements is true?
Answer:
0.052 > 0.05, which means that there is not significant evidence that the population mean is less than a.
Step-by-step explanation:
At the null hypothesis, we test if:
[tex]H_0: \mu \geq a[/tex]
At the alternative hypothesis, we test if:
[tex]H_1: \mu < a[/tex]
Standard significance level of 0.05:
If the p-value > 0.05: no significant evidence that the population mean is less than a.
p-value < 0.05: significant evidence that the population mean is less than a.
You obtain a P-value of 0.052. Which of the following statements is true?
0.052 > 0.05, which means that there is not significant evidence that the population mean is less than a.
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 ____.
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]
If three times a number added to 8 is divided by the number plus 7, the result is four thirds. Find the number.
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.
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
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.
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
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.
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.
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]
A calculator was used to perform a linear regression on the values in the table. The results are shown to the right of the table. What is the line of best fit?
Answer:
the answer is c y=-3.6x+12.8
write your answer as an integer or as a decimal rounded to the nearest tenth
9514 1404 393
Answer:
8.7
Step-by-step explanation:
We have the side adjacent to the angle and we want the hypotenuse. The relevant trig relation is ...
Cos = Adjacent/Hypotenuse
Solving for the hypotenuse, we find ...
VW = XW/cos(36°) = 7/0.80901
VW ≈ 8.7
