Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:
[tex]6\sigma = 800 - 200[/tex]
[tex]\sigma = 100[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
To ensure a margin of error of 20, we solve for n when M = 20, hence:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]
[tex]20\sqrt{n} = 1.96 \times 100[/tex]
[tex]\sqrt{n} = 1.96 \times 5[/tex]
[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]
n = 96.04.
Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.
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x2 +kx+12
What are two numbers that k could be so that each expression could be factored??
Answer:
K could be 7 or 8
Step-by-step explanation:
If K was to be 7, the equation would be x^2 + 7x + 12 = (x+3)(x+4)
If K was to be 8, the equation would be x^2 + 8x + 12 = (x + 2)(x + 6)
The table has data reflecting the measured population of Complete the descriptors of the regression equation for
North Carolina in terms of years since 1920
this data
The data is best modeled by
function
The value of a is
and the value of c is
the value of b is
The function can be best modeled by a linear regression and the values of a, b and c are -6, 100 and 240, respectively
The function typeFrom the table, we can see that as the number of years increases, the population increases.
This implies that the function can be best modeled by a linear regression.
The values of a, b and cA linear regression equation is represented by
ax + by = c
Next, we enter the data in a statistical calculator.
From the statistical calculator, we have the following summary:
Sum of X = 225Sum of Y = 27.505Mean X = 37.5Mean Y = 4.5842Sum of squares (SSX) = 3937.5Sum of products (SP) = 231.4875The regression equation is then represented as:
y = bx + a
Where:
b = SP/SSX = 231.49/3937.5 = 0.05879
a = MY - bMX = 4.58 - (0.06*37.5) = 2.37952
So, we have:
y = 0.05879x + 2.37952
Approximate
y = 0.06x + 2.4
Multiply through by 100
100y = 6x + 240
Rewrite as:
-6x + 100y = 240
Hence, the values of a, b and c are -6, 100 and 240, respectively
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Answer:
The data is best modeled by an exponential function.
The value of a is 2.653, the value of b is 1.01, and the value of c is not used
Step-by-step explanation:
EDGE answers
3.8% of a population are infected with a certain disease. There is a test for the disease, however the test is not completely accurate. 93.9% of those who have the disease test positive. However 4.1% of those who do not have the disease also test positive (false positives). A person is randomly selected and tested for the disease. What is the probability that the person has the disease given that the test result is positive?
The conditional probability that the person has the disease given that the test result is positive is of 0.4750 = 47.50%.
What is Conditional Probability?
Conditional probability is the probability of one event happening, considering a previous event. The formula is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which:
P(B|A) is the probability of event B happening, given that A happened.[tex]P(A \cap B)[/tex] is the probability of both A and B happening.P(A) is the probability of A happening.In this problem, the events are:
Event A: Positive test.Event B: Has the disease.The percentages associated with a positive test is:
93.9% of 3.8%(has the disease).4.1% of 100 - 3.8 = 96.2%(does not have the disease).Hence:
[tex]P(A) = 0.939(0.038) + 0.041(0.962) = 0.075124[/tex]
The probability of both a positive test and having the disease is given by:
[tex]P(A \cap B) = 0.939(0.038) = 0.035682[/tex]
Hence the conditional probability is given by:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.035682}{0.075124} = 0.4750[/tex]
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Trevor uses 2 ounces of almonds in each bag of trail mix he makes
The line on the graph which represents the same relationship between quantities. is line B; y = 2x
Line graphNumber of almonds = 2 ounces
Bags of trail mix = x
Total mix = y
The equation:
y = 2 × x
y = 2x
Complete question:
Trevor uses 2 ounces of almonds in each bag of trail mix he makes.
Bags of Trail Mix Almonds (oz.)
6 Line on the graph represents the same relationship between quantities.
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Solve for the values of x and y.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: x = 6 \:\: units[/tex]
[tex]{\qquad \tt \rightarrow \: y = 20° } [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
Two sides and their opposite angles of a Triangle are given equal.
[tex]\large \textsf{ For x :} [/tex]
[tex]\qquad \tt \rightarrow \: 2x - 1 = x + 5[/tex]
[tex]\qquad \tt \rightarrow \: 2x - x = 5 + 1[/tex]
[tex]\qquad \tt \rightarrow \: x = 6 \: \: units[/tex]
[tex] \large\textsf{For y :} [/tex]
[tex]\qquad \tt \rightarrow \: 3y - 10 = y + 30 [/tex]
[tex]\qquad \tt \rightarrow \: 3y - y = 30 + 10[/tex]
[tex]\qquad \tt \rightarrow \: 2y = 40[/tex]
[tex]\qquad \tt \rightarrow \: y = 20 \degree[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Which of the following points would fall on the line produced by the point-slope form equation y - 2 = 3(x - 5) when graphed?
(4, 5)
(6, 5)
(5, 5)
(1, 4)
The point is (6, 5).
What is graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
Given :
y - 2 = 3(x - 5)
Those point will satisfy after putting the value of x and y we get LHS= RHS.
take (4, 5)
5-2 = 3(4-5)
3= -3
Hence, not satisfied.
take, (6, 5)
5-2 = 3(6-5)
3= 3
Hence, satisfied.
take, (5, 5)
5-2 = 3(5-5)
3= 0
Hence, not satisfied.
take, (1, 4)
4-2 = 3(1-5)
2= -12
Hence, not satisfied.
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need answers right now
Which of the following is a solution to this inequality?
y<2/3x+2
O (0, 3)
O (-3, 1)
O (3,5)
O (1, 2)
Answer: D
Step-by-step explanation:
We can substitute in each of the coordinate pairs.
A) We get 3 < (2/3)(0)+2, which is false.
B) We get 1 < (2/3)(-3)+2, which is false.
C) We get 5 < (2/3)(3)+2, which is false.
D) We get 2 < (2/3)(1)+2, which is true.
hey
can someone solve this 4 me
Answer:
∠a = 50°
∠b = 130°
∠c = 130°
Explanation:
Following Vertical Angles Theorem:
∠(2a - 50) = ∠a2a - 50 = a2a - a = 50a = 50A straight line has 180° angle measure, ∠c and ∠a lies on a straight line
∠c + ∠a = 180°∠c + 50° = 180°∠c = 180° - 50°∠c = 130°Also, following vertical angle theorem:
∠b = ∠c∠b = 130°Which rational number is equivalent to 5.5?
Answer:
11/2
Step-by-step explanation:
Multiply by 2/2 to remove the decimal.
Part A
Which shapes can you use to model the log and the board?
Answer:
A cylinder
Step-by-step explanation:
Hope this helps :)
PLEASE HELP IF YOU DO YOU BELIEVE IN JESUS THANK YOU SO MUCH
These steps outlined were used to construct the perpendicular bisector of
Answer: ZT = ZS
Step-by-step explanation: ZT = ZS must be true under all circumstances. This is because a perpendicular bisector of a line cuts the line into two equal pieces. It is the midpoint of the entire line. Thus, ZT is the same as ZS since the line is equally cut in half and thus are the same.
Mary Lou received $5,000 from her grandparents for her college education 8 years prior to her enrolling in college. Mary Lou invested the money at 5.5% compounded semiannually. How much money would she have in her savings account when she is ready to enroll in college? A: The balance in her account would be $__________ when she is ready to enroll in college. (Round your answer to the nearest cent.)
Answer:
The total amount , principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
Step-by-step explanation:
Compound interest is based on the principal amount and the interest that accumulates on it in every period.
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
First, convert R as a percent to r as a decimal
r = R/100
r = 5.5/100
r = 0.055 rate per year,
Then solve the equation for A
A = P(1 + r/n)^nt
A = 5,000.00(1 + 0.055/2)^(2)(8)
A = 5,000.00(1 + 0.0275)^(16)
A = $7,717.55
The total amount accrued, principal plus interest, with compound interest on a principal of $5,000.00 at a rate of 5.5% per year compounded 2 times per year over 8 years is $7,717.55.
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Find how many quarts of 6% butterfat milk and 3% butterfat milk should be mixed to yield 45 quarts of 4% butterfat milk. Find how many quarts of 6 % butterfat milk and 3 % butterfat milk should be mixed to yield 45 quarts of 4 % butterfat milk .
Answer:
See below
Step-by-step explanation:
x = amount of 6% milk.... amount of fat = .06x
45-x = amount of 3% milk ...amount of fat = .03 (45-x)
Amount of fat in final mix of 45 quarts = .04 (45)
Inputs = output
.06x + .03(45-x) = .04(45)
.06x + 1.35 - .03x = 1.8
.03x = .45
x = 15 quarts of 6% then 30 quarts of 3%
Help me please I beg you
Given market demand Qd=50-p, and market supply p=Qs+5.what would be the state of the market if market price was fixed at Birr 25 per unit?
The state of the market if market price was fixed at Birr 25 per unit is excess demand
Quantity demandedQd = 50 - p
p = Qs + 5
p - 5 = Qs
if market price was fixed at Birr 25 per unit?
Qd = 50 - p
= 50 - 25
Qd = 25
Qs = p - 5
= 25 - 5
Qs = 20
The state of the market if market price was fixed at Birr 25 per unit is excess demand (demand greater than supply) leading to an increase in price.
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Im stuck on this to could you guys explain how you do this
The required equation of a line is y = -3x- 1
Equation of a lineThe equation of a line in slope-intercept form is expressed as:
y = mx + b
where
m is the slope
b is the y-intercept
Using the coordinate point (0, -1) and (-1, 2)
Slope = 2-(-1)/-1-0
Slope = 3/-1
Slope =-3
Since the line crosses the y-axis at (0, -1), hence the value of b is -1
Determine the equation
y = mx + b
y = -3x + (-1)
y = -3x- 1
Hence the required equation of a line is y = -3x- 1
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Need help with this please!! :)
From this diagram, select the
pair of lines that must be
parallel if angle 1 is congruent to angle 8. If there is no pair of lines, select "none".
Answer:
Line L is parallel to Nangle 1 is equal to angle 4 ( vertically opposite angles)
if angle 1 is congruent to angle 8
then angle 4 is also congruent to angle 8
then slope of line L and n is equal
that is L is parallel to n
If a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2018? Be careful to treat the year 2000 as the beginning; let x be the number of years since the year 2000.
The answer is not 2,100
The population at the end of the year 2018 will be 2150.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that:-
If a population of a town is recorded at 1,200 in the year 2000 and the population increases by exactly 50 people each year, what will be the population of the town in 2018.
The population will be calculated as the year 2000 is also considered:-
P = Total years x Increase per year
P = 19 x 50
P = 2150
Therefore the population at the end of the year 2018 will be 2150.
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Make sure you click the image for full picture
Answer:
See below.
Step-by-step explanation:
19.
The spinner has 12 equal-sized sections.
1/3 of 12 = 4
A number that appears in exactly 4 sections has a probability of 1/3. The number 3 appears exactly 3 times.
A number that appears more than 4 times has a probability greater than 1/3. The number 0 appears exactly 5 times.
A number that appears fewer that 4 times has a probability of less than 1/3.
Both 1 and 2 appear fewer than 4 times.
Answer:
Probability greater than 1/3: 0
Probability equal to 1/3: 3
Probability less that 1/3: 1, 2
20.
The amount of concentrate is 12 gallons.
The total amount of drink is 40 gallons.
The fraction of the concentrate out of the total is 12/40.
12/40 = 0.3
0.3 of each gallon is concentrate.
Color the bottom up to 0.30
Giving 20 points for the answer.
Answer:
B, A, C
Step-by-step explanation:
add the like terms together (ending in x2 with x2, ending in x with x etc )
Answer:
B A C
Step-by-step explanation:
combining like terms
Algebra 2 point slope form help
The slope of the line is
[tex]\frac{-1-4}{-1-0}=5[/tex]
So, the equation of the line in point-slope form is [tex]\boxed{y+1=5(x+1)}[/tex]
2x+3y=7
2x - 3y = 4
Its asking me to find x
Need number 2 please!!
Answer:
A
Step-by-step explanation:
note that i = [tex]\sqrt{-1}[/tex]
given
- 1 + 2i[tex]\sqrt{3}[/tex]
= - 1 + [tex]\sqrt{2^2(-1)3}[/tex]
= - 1 + [tex]\sqrt{-12}[/tex]
A rectangular aquarium is 1m 20cm long, 90cm wide and 50cm deep. How many cubic centimeters of water can it hold
Answer:
540,000 cubic centimeters
Step-by-step explanation:
1 meter and 20 centimeters is equal to 120 centimeters.
[tex]120 \times 90 \times 50 = 540000[/tex]
Mark divided a basket of apples evenly into small bags. The number of bags was equal to the number of apples in each bag. Which could be the total number of apples?
A. 25 B. 27 C. 20 D. 18
There are 5 bags and each bag has 5 apples and total there are 25 apples , Option A is the correct answer.
What is a Perfect Square ?A perfect square is a number which can be written as the product of an integer with itself.
It is given that Mark divided a basket of apples evenly into small bags.
Let there be n no. of bags and therefore n number of apples in each bag
Then the total number of apples will be
n * n
n²
The value of total number of apples should be a perfect square,
In the option given only 25 is the perfect square
Therefore the equation can be made as
n² = 25
n = 5
There are 5 bags and each bag has 5 apples and total there are 25 apples.
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pls help with thisc...................................
Answer:
D
598*47+38=
28106+38=
28134
Assume that the function f is a one-to-one function.
a. if f(3)=9, find ^-1 (9)
b. if f^-1(-8)=-9 , find f(-9)
Answer:
a. 3
b. -8
Step-by-step explanation:
let me know if you want an explanation
Gavin likes biking. He never misses a chance to go for a ride when the weather is nice. This week his goal is to bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before. What does the result in part d mean?
Answer:
Total Miles he drives first day = 8 miles
Total Miles he drive second day = 12miles
Total Miles he drives third day = 18miles
Total Miles he drives fourth day = 27 miles
Step-by-step explanation:
This is a problem of linear equations in 1 variable:
The linear equations in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.
It is given in the question that ,
This week his goal is to drive bike about 65 total miles over four days. Each day, he wants to ride 1.5 times as far as he rode the day before.
Let, on the first day, he drives x miles. On second day, he drives 1.5x. On the third day, he drives 1.5(1.5x) and on the fourth day, he drives 1.5(1.5(1.5x)).
So the equation is :
x +1.5x + 1.5(1.5x) + 1.5(1.5(1.5x)) = 65miles
x + 1.5x + 2.25x + 3.375x = 65miles
8.125x = 65 miles
x = 65/8.125 miles
x = 8 miles
so after solving the equation we get, on the first day Gavin drives 8 miles
similarly, on the second day he drives 12miles
on third day 18 miles
and on the fourth day 27miles
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