Answer:
The first term is 6; the common difference in 0.8.
Step-by-step explanation:
The nth term is:
[tex] a_n = a_1 + (n - 1)d [/tex]
The sum of the first n terms is:
[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]
[tex] a_{n} = a_1 + (n - 1)d [/tex]
[tex] a_{11} = a_1 + (11-1)d [/tex]
[tex] a_1 + 10d = 14 [/tex] Equation 1
[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]
[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]
[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]
[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]
[tex] 26a_1 + 325d = 416 [/tex] Equation 2
Equation 1 and Equation 2 form a system of equations in 2 unknowns.
To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.
[tex] 65d = 52 [/tex]
[tex] d = \dfrac{52}{65} [/tex]
[tex] d = \dfrac{4}{5} = 0.8 [/tex]
[tex] a_1 + 10d = 14 [/tex]
[tex] a_1 + 10 \times 0.8 = 14 [/tex]
[tex] a_1 + 8 = 14 [/tex]
[tex] a_1 = 6 [/tex]
Answer:
The first term is 6; the common difference in 0.8.
he parent function f(x) = x3 is represented by graph A. Graph A is transformed to get graph B and graph C. Write the functions represented by graph B and graph C.
Graph B represents the function g(x) =
.
Graph C represents the function h(x) =
.
The Statistical Abstract of the United States published by the U.S. Census Bureau reports that the average annual consumption of fresh fruit per person is 99.9 pounds. The standard deviation of fresh fruit consumption is about 30 pounds. Suppose a researcher took a random sample of 38 people and had them keep a record of the fresh fruit they ate for one year.
Appendix A Statistical Tables
(Round all z values to 2 decimal places. Round your answers to 4 decimal places.)
a. What is the probability that the sample average would be less than 90 pounds?
p =
b. What is the probability that the sample average would be between 98 and 105 pounds?
p =
c. What is the probability that the sample average would be less than 112 pounds?
p =
d. What is the probability that the sample average would be between 93 and 96 pounds?
p =
Answer:
Hence,
a) The probability that the sample average would be less than 90 pounds is 0.0210.
b) The probability that the sample average would be between 98 and 105 pounds is 0.5045.
c) The probability that the sample average would be less than 112 pounds is 0.9935.
d) The probability that the sample average would be between 93 and 96 pounds is 0.1341.
Step-by-step explanation:
a) [tex]P(X < 90) = P(Z < (90 - 99.9) / (30\sqrt(38)))[/tex]
= P(Z < -2.03) = 0.0210
b )[tex]P(98 < x <105) = P((98 -99.9) / (30 \sqrt(38)) < Z < (105 -99.9) / (30 \sqrt(38)))[/tex]
= P(-0.39 < Z < 1.05) = 0.5045
c ) [tex]P(X < 112) = P(Z < (112 - 99.9) / (30\sqrt(38)))[/tex]
= P(Z < 2.49) = 0.9935
d )[tex]P(93 < x < 96) = P((93 -99.9) / (30 \sqrt(38)) < Z < (96 -99.9) / (30 \sqrt(38)))[/tex]
= P( -1.42 < Z < -0.8 )
= 0.2119 - 0.0778 = 0.1341
after buying 55 books for Rs 50 each a man has rupees 3/4 of his money left how much he had at first?
Answer:
916.67 (corrected to 2 decimal places)
Hope I'm right, fingers crossed
Step-by-step explanation:
[tex]55 \times 50 = 2750 \div \frac{3}{4 } = 916.6666667[/tex]
Question 5 of 10
Select the correct answer.
The graph shows a line of best fit for data collected on the average temperature, in degrees Fahrenheit, during a month and the
number of inches of rainfall during that month.
Average Temp.
90
80
70
60
50
404
30
20
10
1 1 2 3 4 5 6
X
Inches of Rain
The equation for the line of best fit is y = -3.32x + 97.05.
Based on the line of best fit, what would be the prediction for the average temperature during a month with 13.25 inches of rainfall?
Answer:
53.06°F
Step-by-step explanation:
Given the equation of best fit :
y=-3.32x +97.05.
The average temperature for a month with 13.25 inches of Rainfall
Amount of Rainfall = x
Average temperature = y
To make our prediction ; put x = 13.25 in the equation and solve for y ;
y = -3.32x +97.05
Put x = 13.25
y = -3.32(13.25) +97.05
y = - 43.99 + 97.05
y = 53.06°F
What is the gradient of the graph shown? Give your answer in simplest form
Answer:
gradient = 2
line: y = 2x - 4
Step-by-step explanation:
Find the slope from the slope intercept formula
y = mx + b
b is the y intercept
b = -4 and the point is (0,-4)
So far the equation looks like this.
y = mx - 4
Use the other intercept (x intercept) to find m
x = 2
y = 0
0 = m*2 - 4 Add 4 to both sides
4 = 2m Divide by 2
4/2 = m
m = 2
So the gradient or slope is 2
What complex number is represented by the expression 7i^5+9i^8
Answer:
[tex]9 + 7i[/tex]
Step-by-step explanation:
[tex]7i^5+9i^8[/tex]
[tex]i^5 = i\\ i^8 = 1[/tex]
A polynomial function has a root of -6 with multiplicity 1, a root of -2 with multiplicity 3, a root of 0 with multiplicity 2, and a
root of 4 with multiplicity 3. If the function has a positive leading coefficient and is of odd degree, which statement about
the graph is true?
O The graph of the function is positive on (-6, -2).
O The graph of the function is negative on (-0, 0).
O The graph of the function is positive on (-2, 4).
O The graph of the function is negative on (4.co).
9514 1404 393
Answer:
(a) the graph is positive on (-6, -2)
Step-by-step explanation:
The roots, left to right, are ...
-6, -2, 0, 4
The odd-multiplicity roots, where the sign changes, are ...
-6, -2, 4
The function is negative to the left of -6, and positive to the right of +4. It is positive on the interval (-6, -2) and negative on the intervals (-2, 0) and (0, 4).
Answer:it’s a!!!
edge please stop deleted my answer ;)
Step-by-step explanation:
A printing machine 600 books in 3 hours. How many books will the machine print in 5
Answer:
1, 000 hrs
Step-by-step explanation:
The machine prints,
in 3 hrs = 600 books
in 1 hr = 600/ 3 hrs = 200 hrs.
in 5 hrs = 200 × 5
= 1, 000 hrs
The printing machine will print 1000 books in 5 hours.
Let's calculate how many books the printing machine will print in 5 hours based on the given information.
To do this, we'll use the concept of rates and proportions.
Given that the printing machine can print 600 books in 3 hours, we can set up a rate equation as follows:
Rate of printing = Number of books / Time taken
Let "x" be the number of books the machine will print in 5 hours. We can set up the proportion:
600 books / 3 hours = x books / 5 hours
To solve for "x," we cross-multiply:
3 * x = 600 * 5
Now, let's solve for "x":
3x = 3000
x = 3000 / 3
x = 1000
So, the printing machine will print 1000 books in 5 hours.
Given: Printing machine prints 600 books in 3 hours.
Let the number of books the machine will print in 5 hours be "x."
Using the rate formula, we can set up the proportion:
600 books / 3 hours = x books / 5 hours
Cross-multiplying:
3 * x = 600 * 5
Solving for "x":
3x = 3000
x = 3000 / 3
x = 1000
Hence, the printing machine will print 1000 books in 5 hours.
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Mackenzie earns 4% commission as a salesperson. She sold a digital camera that cost $767. How much commission did Mackenzie earn?
Answer:
like about $500 and because of the ca!erlsn
PLEASE HELP MATH⚠️⚠️⚠️⚠️⚠️
Convert this into algerbraic expression:
The difference of a number cubed and the same number
Step-by-step explanation
n^3-n.
Hope this will help you :) <3
Which value is in the domain of f(x)?
f(x) =
2x+5, |-6 < xso
- 2x + 3, 0 < x 34
N
-7
-6
5
9514 1404 393
Answer:
4
Step-by-step explanation:
The function definition tells you its domain is ...
-6 < x ≤ 4
Values -7, -6, and 5 are not in this domain.
Of the listed values, only 4 is in the domain.
Please help!!!!
I’m using Plato
1 by 4 ^ 256 is equal to 4 and 1 by 4 ^ 64 will be root 4 so here the answer will be 4 into 4 root 4
there option 4 will be correct
Please explain :)
Expand 5x(x+2)
Thanks :)
Answer:
[tex] {5 x }^{2} +10x[/tex]
Step-by-step explanation:
[tex]5x(x+2)[/tex]
[tex]5x \times x+5x \times 2[/tex]
[tex]5(x \times x)+5x \times 2[/tex]
[tex]5 {x}^{2} +5x \times 2[/tex]
[tex]5 {x}^{2} + 10x[/tex]
Hope it is helpful....Claim: Fewer than 94% of adults have a cell phone. In a reputable poll of 1004 adults, 86% said that they have a cell phone. Find the value of the test statistic.
Answer: The value of test statistic = -10.67
Step-by-step explanation:
Test statistic for proportion:
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
, where p= population proportion
n= sample size
[tex]\hat{p}[/tex] = sample proportion
AS per given,
p=0.94, n= 1004, [tex]\hat{p}=0.86[/tex]
[tex]z=\dfrac{0.86-0.94}{\sqrt{\dfrac{0.94(1-0.94)}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{\dfrac{0.0564}{1004}}}\\\\=\dfrac{-0.08}{\sqrt{0.0000561752988048}}\\\\=\dfrac{-0.08}{0.00749501826581}\\\\=-10.673756509\approx-10.67[/tex]
i.e. the value of test statistic = -10.67
Determine whether the following propositions are true or false:
(a) 5 is an odd number and 3 is a negative number.
(b) 5 is an odd number or 3 is a negative number.
(c) 8 is an odd number or 4 is not an odd number.
(d) 6 is an even number and 7 is odd or negative.
(e) It is not true that either 7 is an odd number or 8 is an even number (or both).
Answer:
a) false
b) true
c) true
d) true
e) false
Step-by-step explanation:
In a statement of the type:
p ∧ q
where ∧ means "and"
The statement is true only if both p and q are true
the statement is false if p, q, or both, are false.
and in the case of:
p ∨ q
where ∨ means "or"
The statement is true if at least one of p or q (or both) are true.
The statement is false if both are false.
Now that we know that, let's solve the problem:
a) "5 is an odd number and 3 is a negative number."
Here we have:
p = 5 is an odd number
We know that this is true
q = 3 is a negative number
This is false.
then the complete statement is false.
b) "5 is an odd number or 3 is a negative number."
here we have:
p = 5 is an odd number.
this is true
q = 3 is a negative number
because in this case we have an "or", with only p being true, the whole statement is true.
c) "8 is an odd number or 4 is not an odd number."
p = 8 is an odd number (this is false)
q = 4 is not an odd number (this is true, 4 is a even number)
Again, we have an "or", so we need only one true proposition, then the statement is true.
d) "6 is an even number and 7 is odd or negative."
p = 6 is an even number (true)
q = 7 is odd or negative (notice that we have an or, and 7 is odd is true, so this proposition is true)
Then both propositions are true, then the statement is true.
e) "It is not true that either 7 is an odd number or 8 is an even number (or both)."
This is most complex, this will be true if at least one of the propositions is false.
but:
7 is an odd number is true
8 is an even number is true.
Then both statements are true, which means that the statement is false.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck. Express the indicated degree of likelihood as a probability value between 0 and 1 inclusive.
Answer:
The probability of this event is represented by a value of 1.
Step-by-step explanation:
Probability of a certain event:
The probability of an event that is considered to be certain, that is, guaranteed to happen, is 100% = 1.
You are certain to get a heart, diamond, club, or spade when selecting cards from a shuffled deck.
This means that the probability of this event is represented by a value of 1.
Find the solution set.
The solution set for 5v2 – 125 = 0
Josephine left home traveling at 25 mph. One hour later her friend, Steve, leaves from the same place and travels the same road traveling at 50 mph. How many hours will it take Steve to catch up to Josephine?
Answer:
1 hour
Step-by-step explanation:
J = 50 mph by 2 hours
S = 50 mph by 1 hour
2-1 = 1
Identify the percent, amount, and base in this problem.
What percent of 80 is 40?
Answer:
50Step-by-step explanation:
40: 80x100 =100 =(40x100): 80 =100): 80 =4000: 80 = 50The percentage of the number 80 is 40 will be 50%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
The percentage is given as,
P = [(80 - 40) / 80] x 100
P = (40 / 80) x 100
P = 0.50 x 100
P = 50%
The percentage of the number 80 is 40 will be 50%.
More about the percentage link is given below.
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Which statement about the net is true?
The net can be folded to form a pyramid because at least one of the faces is a triangle.
The net can be folded to form a pyramid because more than one of the faces is a triangle.
The net cannot be folded to form a pyramid because one of the faces is a rectangle.
The net cannot be folded to form a pyramid because the faces that are not a base are not all triangles.
Answer:
DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD
Step-by-step explanation:
remove bracket and simplify 6x-(3x+2)
Answer: 3x - 2
Step-by-step explanation:
First to solve this, we need to know some basic information such as:
1. (-) × (-) = +
2. (+) × (-) = -
3. (+) × (+) = +
Therefore, 6x-(3x+2)
= 6x - 3x - 2
= 3x - 2
The answer to the question after removing the bracket will be 3x - 2.
$66.25 divided among 4 people
In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
Laura lives 15 miles east of Kevin’s place. Kevin lives 8 miles south of Michelle’s place. How far does Michelle live from Laura’s place?
17 miles
24 miles
32 miles
36 miles
Answer:
17 miles.
Step-by-step explanation:
Let's define:
North as the positive y-axis
East as the positive x-axis.
We know that Laura lives 15 miles east of Kevin's place.
Kevin lives 8 miles south of Michelle's place.
So, if we define the origin, (0, 0) as Laura's place.
From:
"that Laura lives 15 miles east of Kevin's place."
We have that the location of Kevin's house is 15 miles west from Laura's place, then Kevin's house is at:
(0, 0) + (-15mi, 0) = (-15mi, 0)
From Kevin lives 8 miles south of Michelle's place, we know that Michelle's live 8 miles north of Kevin's place.
Then the location of Michele's house is the location of Kevin's plus (0, 8mi).
Michelle's house is located at:
(-15mi, 0) + (0, 8mi) =(-15mi, 8mi)
Now we want to find the distance between Michelle's house and Laura's house.
Michelle's house is at (-15mi, 8mi)
Laura's house is at (0mi, 0mi)
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]D = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
Then the distance between (-15mi, 8mi) and (0mi, 0mi) is:
[tex]D = \sqrt{(-15mi - 0mi)^2 + (8mi - 0mi)^2} = 17mi[/tex]
The correct option is the first one, 17 miles.
HW HELP ASAP PLZZZZZ
Answer:
p = 15/x
x= -3
Step-by-step explanation:
For the first problem, we can expand the equation to 4px+4=64
then simplify it to:
4px=60
then divide 4x from both sides of the equation
p=60/4x
then simplify:
p=15/x
For the second problem:
plug in -5 for p so the equation would look like
4(-5x +1)=64
simplify
-20x=60
x= -3
Round 948070 to the nearest hundred? Hurry please
Answer:
9.48
Step-by-step explanation:
You return from a trip with 480 Canadian dollars. How much are your Canadian dollars worth in U.S. dollars? Use the exchange rate shown below. Currency U.S. dollars per Canadian dollar Canadian dollars per U.S. dollar Canadian dollar 0.5823 1.717 The 480 Canadian dollars are equivalent to about $ (Round to the nearest cent as needed.)
591 Dollars 42 Cents (591 Dollars when rounded)
There are 3 boxes of coins. There are 4 times as many coins in Box A as in Box B. There are 180 fewer coins in Box C than Box A. The number 2 of coins in Box B is of the total number of coins in the three boxes. 13 What is the total number of coins in the three boxes?
Answer:
Step-by-step explanation:
The answer b
A random sample of 35 employees of the local green technologies plant Greenies, who completed two years of college, were asked to take a basic mathematics test. The mean and standard deviation of their scores were 75.1 and 12.8, respectively. In a random sample of 50 employees who had only completed high school, the mean and standard deviation of the test scores were 72.1 and 14.6, respectively. Assuming equal variance between the two populations, can we infer at the .10 level of significance that students who completed two years of college had a higher average than students who had only completed high school
Answer:
There is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.
Step-by-step explanation:
The hypothesis :
H0 : μ1 = μ2
H1 : μ1 > μ2
Given :
n1 = 35 ; x1 = 75.1 ; s1 = 12.8
n2 = 50 ; x2 = 72.1 ; s2 = 14.6
Pooled variance = Sp² = (df1*s1² + df2*s2²) ÷ (n1 + n2 - 2)
df1 = n1 - 1 = 35 - 1 = 34
df2 = n2 - 1 = 50 - 1 = 49
(x1 - x2) ÷ Sp(√(1/n1 + 1/n2))
Sp² = (34*12.8^2 + 49*14.6^2) / (35+50-2)
Sp² = (5570.56 + 10444.84) / 83
Sp² = 192.95662
Sp = √192.95662
Sp = 13.89
Test statistic = (75.1 - 72.1) / 13.89 * √(1/35 + 1/50)
Test statistic = 3 / (13.89 * 0.2203892)
Test statistic = 0.980
df = n1 + n2 - 2
df = 35 + 50 - 2 = 83
Using the Pvalue calculator :
Pvalue(0.980, 83) = 0.165
α = 0.1
Pvalue > α ; We fail to reject the H0; and conclude that there is no significance evidence that students who completed two years of college had a higher average than students who had only completed high school.
Pls someone help these answers are on chegg so if u have a subscription pls answer these ill make u brainliest ! Below is a table representing data, measuring the percentage of various
groups owning a home
Percentage owning a
home
1st Generation
Hispanic Americans
N=899
43
50
2nd Generation
Hispanic Americans
N=351
1st Generation Asian
Americans N=2,684
2nd Generation Asian
Americans N=566
58
51
Test whether there is a significant difference in the proportion of
homeowners between 1st and 2nd generation Hispanic Americans. Set alpha at .05
The obtained Z test is ?
The probability of obtaining
this Z-test statistic is ?
This is _? Than our alpha level. Therefore we ___? The null hypothesis and conclude that there ____? A significant difference in the proportion of homeowners between 1 st generation and 2nd generation hispanic americans.
The table is not clear, so i have attached it.
Answer:
z statistic is -2.26
This is less than our alpha level,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans
Step-by-step explanation:
From the attached table, we can see that;
first-generation hispanic americans; (N = 899 and percentage = 43%
second-generation hispanic americans; N = 351 and percentage = 50%
first-generation asian americans; (N = 2,684 and percentage = 58%
second-generation asian americans; N = 566 and percentage = 51%
Z-score formula in this case is;
z = (p1^ - p2^)/(√(p^(1 - p^)((1/n1) + (1/n2))
Where;
p^ = (p1 + p2)/(n1 + n2)
For, hispanic americans we have;
p1^ = 0.43 × 899 = 386.57
p2^ = 0.5 × 351 = 175.5
p^ = (386.57 + 175.5)/(899 + 351)
p^ = 0.45
Thus;
z = (0.43 - 0.5)/(√(0.45(1 - 0.45)((1/899) + (1/351))
z = -2.26
From z-distribution table, we have;
P-value = 0.01191
Since we have 2 samples, then probability = 2 × 0.01191 = 0.02382
This is less than our alpha level of 0.05,therefore we reject the null hypothesis and conclude that there is a significant difference in the proportion of homeowners between first generation and second generation Hispanic Americans.
