The probabilities for various binomial distribution have been determined.
The complete question is
About 5% of hourly paid workers in a region earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Complete parts (a) through (c) below.
(a) Company A has 285 employees. What is the probability that Company A will get the discount? (Round to four decimal places as needed.)
(b) Company B has 502 employees. What is the probability that Company B will get the discount? (Round to four decimal places as needed.)
(c) Company C has 1033 employees. What is the probability that Company C will get the discount? (Round to four decimal places as needed.)
What is Probability ?Probability is a stream in mathematics that study the likeliness of an event to happen .
On the basis of the given data
(a) Let X is a random variable that denotes the number of employees that earn less than prevailing average.
Here X has binomial distribution with
n=285 and p=0.05.
As np and n(1-p) are greater than 5 so using normal approximation X has normal distribution with parameters
μ= np-285 * 0.05
= 14.25
standard deviation is given by
[tex]\sigma=\sqrt{np(1-p)}=\sqrt{285* 0.05* 0.95}\\\\=3.6793[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]z=\dfrac{29.5-14.25}{3.6793}\\\\=4.14[/tex]
The probability that Company A will get the discount is given by
[tex]P(X\geq 30)=P(z > 4.14)=0.0000[/tex]
(b) Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=502 and p=0.05.
[tex]\rm \mu=np=502* 0.05=25.1[/tex]
standard deviation
[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{502\cdot 0.05\cdot 0.95}=4.8831[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]\rm z=\dfrac{29.5-25.1}{4.8831}=0.90[/tex]
The probability that Company B will get the discount is
[tex]P(X\geq 30)=P(z > 0.90)=0.1841[/tex]
(c)Let X is a random variable that denotes the number of employees that earn less than prevailing average.Here X has binomial distribution with
n=1033 and p=0.05.
[tex]\mu=np=1033\cdot 0.05=51.65[/tex]
standard deviation
[tex]\rm \sigma=\sqrt{np(1-p)}=\sqrt{1033*0.05* 0.95}=7.0048[/tex]
Applying continuity correction.
The z-score for X = 30-0.5 = 29.5 is
[tex]\rm z=\dfrac{29.5-51.65}{7.0048}=-3.16[/tex]
The probability that Company C will get the discount is
[tex]\rm P(X\geq 30)=P(z > -3.16)=0.9992[/tex]
Therefore the probabilities for various binomial distribution have been determined.
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An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with μ = 15.5 and σ = 3.6. What is the probability that during a given week the airline will lose less than 20 suitcases?
Answer:
[tex] \frac{?}{?} [/tex]
Find the area.
8 in
19 in
13 in
1976 in²
205 in²
128 in²
104 in²
Total area = 104+24 = 128 sq.in , Option C is the right answer.
The missing figure is attached with the answer.
What is Area ?The space occupied by a two dimensional figure is called Area.
The figure given in the question can be divided into two figure
A rectangle of 8 * 13 inch
and a triangle of 8 * 6 inch
The area of a rectangle is given by
Length * Breadth
8 * 13
= 104 sq.inch
The area of the triangle is given by
(1/2) * base * height
= (1/2) * 8 * 6
= 24 sq.inch
Total area = 104+24 = 128 sq.in
Therefore Option C is the right answer.
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Trigonometry is crazy
Answer:
see the attachment photo!
i hope this can help you! :)
if the degree mesures of the angles in a triangle are in the ratio 2:3:4, what is the degree measure of the largest angle
The largest angle of the triangle is equal to 80 degrees.
Concept: Angle sum property of a triangle i.e., the sum of all angles of a triangle is equal to 180 degree
Given : Degree measures of the angles in a triangle are in the ratio 2:3:4
Let one part of each angle of the triangle be x, so the different angles of triangle are 2x,3x,4x (taking the ratios given in the question and multiplying by each of them by x)
2x +3x +4x = 180x
180x = 20
The angles of a triangle are 40,60,80
The largest angle of the triangle is equal to 80 degrees.
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A linear function contains the following points.
What are the slope and y-intercepts of this function?
The slope is -1, and the value of the y-intercept is 6 if the linear function contains the points provided.
What is the slope?The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
The slope is:
[tex]\rm m =\dfrac{6-8}{0-(-2)}[/tex]
m = -1
The equation of a line:
y = mx + c
y = -x + c
Plug x = 0 and y = 6
y = 6
y-intercept is (0, 6)
Thus, the slope is -1, and the value of the y-intercept is 6 if the linear function contains the points provided.
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i need help can someone give me answers
Answer:
Step-by-step explanation:6 type
5/25=1/5=20%
1-1/5=4/5=80%
The types of candles are 6. And the probability of a small pink candle and NOT a small pink candle will be 0.20 and 0.80, respectively
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
The table is given below.
Small Medium Large Total
White 9 3 5 17
Pink 5 2 1 8
Total 14 5 6 25
The types of candles are given as,
⇒ 2 x 3
⇒ 6
The probability of a small pink candle is as,
P = 5/25
P = 0.20
The probability of NOT a small pink candle is as,
Q = 1 - P
Q = 1 - 0.20
Q = 0.80
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You are betting on a game with an expected value of -$0.33. What does this mean?
The first term of a sequence is 5.
The term-to-term rule is 'add 8'. What is the 10th term of the sequence?
Answer:
[tex]\fbox {77}[/tex]
Step-by-step explanation:
Given
⇒ a = 5
⇒ d = + 8
Solving :
⇒ a₁₀ = a + 9d
⇒ a₁₀ = 5 + 9(8)
⇒ a₁₀ = 5 + 72
⇒ a₁₀ = 77
Find the sine and the cosine of 30°.
A. sin 30° =1/2, cos 30°= √3
B. sin 30°=1/2, cos 30° = √3/2
C. sin 30° = √3/3, cos 30°= √3/4
D. sin 30° = √3/3, cos 30° = √3/2
Answer:
Option B is correct.
Step-by-step explanation:
Trigonometry is defined as the branch of mathematics dealing with the relations of the sides and angles of triangles and with the relevant functions of any angles. There are three basic trigonometric ratios: sine, cosine, and tangent. Trigonometry and its functions have an enormous number of uses in our daily life. For instance, it is used in geography to measure the distance between landmarks, in astronomy to measure the distance of nearby stars and also in the satellite navigation system.
The trigonometric function of sine for an acute angle is the ratio between the leg opposite the angle when it is considered part of a right triangle and the hypotenuse while the cosine is the ratio of the base and the hypotenuse.
Here, [tex]sin 30[/tex]° [tex]=\frac{4}{8}[/tex]
[tex]sin 30[/tex]° [tex]=\frac{1}{2}[/tex]
[tex]cos 30[/tex]° [tex]=\frac{4\sqrt{3}}{8}[/tex]
[tex]cos30[/tex]°[tex]=\frac{\sqrt{3} }{2}[/tex]
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A family originally bought a home for $654,030. Now, a few years later, the home is worth
$457,821. What was the percent of decrease in its value?
Answer:
30%
Step-by-step explanation:
First we find out the difference between them:
$654,030 - $457,821 = $196,209
Then we compare it with the original price:
196,209/654,030 = 0.3
Since 0.3 is 30%, that is 30% decrease in value.
The blue dot is what value on the number line -6 -10
Answer:
I have no clue what I could answer that question with other than (-6,-10)
A woman bought some large frames for $10 each and some small frames for $4 each at a closeout sale. If she bought 22 frames for $106, find how many of each type she bought.
Answer:
19 small frames and 3 large frames
Step-by-step explanation:
follows the steps in the attached
find the y-component of this vector
leave an explanation for brainlest
The y- component of the vector is 18.31728 m
What is Vector?A quantity that has both magnitude and direction but not position.
The y- component is
Dy = 18.6* sin80
Dy = 18.6* 0.9848
Dy= 18.31728 m
Hence, the y- component of the vector is 18.31728 m.
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What is the measure of complemnt angle
a)42° b) 35°
Answer:
90°
Step-by-step explanation:
A complement angle is the same as a right angle
Hii!
___________________________________________________________
Answer:
[tex]\sf 48\textdegree[/tex][tex]\sf 55\textdegree[/tex]Step-by-step explanation:
The sum of complementary angles is always 90 degrees.
We can find the complements of these two angles by setting up an equation.
x+42=90
Subtract 42 from both sides
x=48
This problem can be solved the same way!
x+35=90
Subtract 35 from both sides
x=55
--
Hope that this helped! Best wishes.
--
The SAT is the most widely used test in the undergraduaté admissions process, Scores on the math portion of the SAT are believed to
be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire
is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take
to ensure that the margin of error is below 20?
(You may find it useful to reference the z table. Round intermediate calculations to at
least 4 decimal places and "2" value to 3 decimal places. Round up your final answer to the nearest whole number.)
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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Solve for x: |x − 2| + 10 = 12 (1 point)
Answer:
I think that would be 1
Step-by-step explanation:
Do everything in the lines before anything else. -2 becomes a 2 and then you add that with the 12 and divide 12 on both sides to get one.
Answer:
x = 0 or 4
Step-by-step explanation:
The absolute value function can be resolved into two equations. These one- or two-step equations can be solved in the usual way.
__
negative argument-(x -2) +10 = 12
-x = 0 . . . . . . . . . simplify, subtract 12
x = 0 . . . . . . . . . multiply by -1. Check: 0 -2 is negative.
positive argumentx -2 +10 = 12
x = 4 . . . . . . . . . simplify, subtract 8. Check: 4 -2 is positive.
The two solutions are x=0 and x=4.
What is the scale factor of this dilation? Triangle A B C. Side A C is 8, C B is 10, A B is 6. Triangle A prime B prime C prime. Side A prime C prime is 4, C prime B prime is 5, B prime A prime is 3. One-fifth One-half 1 2
Answer:
0.5
Step-by-step explanation:
well you can just take one of the sides and in this case I'll use AC which originally is 8 and then in AC prime it's 4. You can simply divide the new length by the original length which is 4/8 or 0.5. So if you multiply any of the original side lengths by 0.5 you'll get the new side length.
Answer:
1/2
Step-by-step explanation:
edge 23
What is the slope of the following graph? (write your answer as a fraction unless divided by 1. Do not use spaces in your answer)
The slope of the graph is 4/5
How to determine the slopeUsing the formula
Slope = Δ y-axis / Δ x- axis
y2 = -4
y1 = 0
x2 = -5
x1 = 0
Slope = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
Substitute the values into the formula
Slope = [tex]\frac{-4 - 0}{- 5 - 0}[/tex]
Slope = [tex]\frac{-4}{-5}[/tex]
Slope = [tex]\frac{4}{5}[/tex]
Therefore, the slope of the graph is 4/5
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Find f ° g and g ° f, if they exist. f={(-4,-5),(0,3),(1,6)} and g={(-5,0),(3,-4),(6,1)}.
The composite function of f o g are (-4,-5),(0,3),(1,6). The composite function of g o f are (-5,0),(3,-4),(6,1).
What is a function?A function is defined as a relation between the set of inputs having exactly one output each.
Given;
f = {(-4,-5),(0,3),(1,6)}
g = {(-5,0),(3,-4),(6,1)}.
In order to find f o g and g o f,
f o g = f(g)
The composite function of f o g
f(-5,0) = (-4,-5)
f(3,-4) = (0,3)
f(6,1) = (1,6)
The composite function of g o f
g(-4,-5) = (-5,0)
g(0,3) = (3,-4)
g (1,6) = (6,1)
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The Function h is defined by the following rule.
h(x) = 2x-2
Complete the function table.
Answer:
[tex]\fbox {See below} \downarrow[/tex]
Step-by-step explanation:
[tex]\textsf {The function is :}[/tex]
[tex]\boxed {h(x) = 2x - 2}[/tex]
[tex]\textsf {Finding the missing values :}[/tex]
[tex]\mathsf {h(-4) = 2(-4) - 2 = -10}[/tex][tex]\mathsf {h(-2) = 2(-2) - 2 = -6}[/tex][tex]\mathsf {h(1) = 2(1) - 2 = 0}[/tex][tex]\mathsf {h(4) = 2(4) - 2 = 6}[/tex][tex]\mathsf {h(5) = 2(5) - 2 = 8}[/tex][tex]\textsf {The table :}[/tex]
[tex]\left[\begin{array}{ccc}x&f(x)\\-4&-10\\-2&-6\\1&0\\4&6\\5&8\end{array}\right][/tex]
Please answer! Will give the brainliest!
Answer: K. 3
Step-by-step explanation:
There are 30 students in total. What I did is I added everything that was in the Venn diagram and subtracted that from 30.
[tex]12+5+10=27[/tex]
[tex]30-27=3[/tex]
Therefore, there are 3 students who didn't like either English or math.
I hope this helps! Pls give brainliest!! :)
how to make 27 using 1,2,3,4 only once
Answer:
1) (4 - 2 + 1)^3
2) 3^2(4 - 1)
3) 3^4/2 + 1
It can be either one of those
Answer:
(2 * 4 + 1) * 3 =Step-by-step explanation:
how to make 27 using 1,2,3,4 only once
Remember Pemdas
(2 * 4 + 1) * 3 =
(8 + 1) * 3 =
9 * 3 =
27
In the diagram, point D divides line segment AB in the ratio of 5:3. If line segment AC is vertical and line segment CD is horizontal, what are the coordinates of point C? Diagram shows a line segment with endpoints A(2, minus 6) and B(10, 2). Point D lies on this line segment. A dashed segment extends up from point A until point C and then extends horizontally to right until point D, forming a right triangle. A. (2, -1) B. (2, -3) C. (5, -3) D. (7, -1) Reset Next
The coordinates of point C that forms the triangle is; (2, -1)
How to partition a line segment?We are told that point D divides line segment AB in the ratio of 5:3.
The line segment division formula is;
(x, y) = (m₁x₂ + m₂x₁)/(m₁ + m₂), (m₁y₂ + m₂y₁)/(m₁ + m₂)
For this question;
x₁ = 2; y₁ = -6; x₂ = 10; y₂ = 2; m₁ = 5; m₂ = 3
Thus, (x, y) gives us;
(5*10 + 3*2)/(5 + 3), (5*2 + 3*-6)/(5 + 3)
D(x, y) = (7, -1)
Now, we need to find the coordinates of C
We will use coordinate system which means the coordinate of x will be the as x coordinate of A since, AC is vertical line
And coordinate of y will be same as y in D since CD is horizontal line. Thus, coordinate of C is; C(2,-1).
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22x31
a537
b682
c492
Step-by-step explanation:
copy from there that right answer if need more then follow me Bhai or send me money
Could use some help! Brainliest to who answers :)
Answer:
N. The number of people purchasing coffee each day in a coffee shop
Step-by-step explanation:
A fraction of a person could not buy coffee because every person is a whole person. If something is not a person, it's not a person. Therefore, the only numbers you could add to this value are 0 and 1.
Which second degree polynomial function has a leading coefficient of -1 and root 4 with multiplicity 2?
f(x) = -x²-8x-16
f(x) = -x² +8x-16
f(x)=x²-8x + 16
f(x) = -x² + 8x + 16
Mark this and return
Save and Exit
Next
Subm
Answer:abc and d
Step-by-step explanation:
trust me I took the dum test
Big Oil, Inc. has a preferred stock outstanding that pays an $7 annual dividend. If
investors' required rate of return is 10 percent, what is the market value of the shares?
If the required return declines to 6 percent, what is the change in the price of the stock?
The change in the price of the stock is $46.67.
How to calculate the change in price?From the information given, the current price will be:
= Annual dividend / Required rate
= 7/0.1
= $70
The market value of the shares will be:
= 7/6%
= 7/0.06
= $116.67
Therefore, the change in the price of the stock will be:
= $116.67 - $70
= $46.67
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A country's population in 1991 was 103 million, in 1999 it was 108 million. estimate the total population in 2013
Answer:
117
Step-by-step explanation:
The total population is 117 million
28.6% of city employees ride the bus to work.Last year,29.7% of city employees rode the bus to work.What is the relative change from last year to this year
The number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.
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:-
28.6% of city employees ride the bus to work. Last year,29.7% of city employees rode the bus to work.
The relative change will be calculated as follows:-
Relative change = Present year data - Last year's data
Relative change = 28.6 - 29.7
Relative change = -1.1%
Therefore the number of employees taking the bus to an office is reduced by 1.1% from the last year. The relative change will be 1.1%.
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Josh made $35,000 in taxable income last year.
Suppose the income tax rate is 15% for the first $8500 plus 17% for the amount over $8500.
How much must Josh pay in income tax for last year?