Answer:
a. 0.94 = 94% probability that the firm will make at least one hire.
b. The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.
Step-by-step explanation:
There is only a 6% chance that it will not make any hires
This means that P(X = 0) = 0.06.
16% chance that it will make all three hires.
This means that [tex]P(X = 3) = 0.16[/tex]
60% chance of hiring at least two candidates.
This means that:
[tex]P(X = 2) + P(X = 3) = 0.6[/tex]
[tex]P(X = 2) + 0.16 = 0.6[/tex]
[tex]P(X = 2) = 0.44[/tex]
Probability of one hire:
The sum of all probabilities, from no hires to three hires, is 1. So
[tex]P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1[/tex]
[tex]0.06 + P(X = 1) + 0.16 + 0.44 = 1[/tex]
[tex]P(X = 1) = 0.66 = 1[/tex]
[tex]P(X = 1) = 0.34[/tex]
a. What is the probability that the firm will make at least one hire?
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.06 = 0.94[/tex]
0.94 = 94% probability that the firm will make at least one hire.
b. Find the expected value and the standard deviation of the number of hires.
Expected value:
[tex]E(X) = 0.06*0 + 0.34*1 + 0.44*2 + 0.16*3 = 1.7[/tex]
Standard deviation:
[tex]S(X) = \sqrt{0.06*(0-1.7)^2 + 0.34*(1-1.7)^2 + 0.44*(2-1.7)^2 + 0.16*(3-1.7)^2} = 0.8062[/tex]
The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.
A plumber and his assistant work together to replace the pipes in an old house. The plumber charges $30 an hour for his own labor and $20 an hour for his assistant's labor. The plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $2000. How long did the plumber and his assistant work on this job
Answer:
The plumber worked 50 hours, and his assistant worked 25 hours.
Step-by-step explanation:
Since a plumber and his assistant work together to replace the pipes in an old house, and the plumber charges $ 30 an hour for his own labor and $ 20 an hour for his assistant's labor, and the plumber works twice as long as his assistant on this job, and the labor charge on the final bill is $ 2000, to determine how long did the plumber and his assistant work on this job the following calculation must be performed:
40 x 30 + 20 x 20 = 1200 + 400 = 1600
50 x 30 + 25 x 20 = 1500 + 500 = 2000
Therefore, the plumber worked 50 hours, and his assistant worked 25 hours.
Question 2 (Essay Worth 10 points)
(02.03, 02.05 MC)
The linear function f(x) = 0.5x + 80 represents the average test score in your math class, where x is the number of the test taken. The linear function g(x) represents the average
test score in your science class, where x is the number of the test taken.
x g(x)
1 81
2 83
3 85
Part A: Determine the test average for your math class after completing test 2. (2 points)
Part B: Determine the test average for your science class after the completing test 2. (2 points)
Part C: Which class had a higher average after completing test 4? Show work to support your answer. (6 points)
Answer:
(a) [tex]f(2) = 81[/tex]
(b) [tex]g(2) = 83[/tex]
(c) Test average for maths class after test 2 is greater
Step-by-step explanation:
Given
[tex]f(x) = 0.5x + 80[/tex]
[tex]x \to g(x)[/tex]
[tex]1 \to 81[/tex]
[tex]2 \to 83[/tex]
[tex]3 \to 85[/tex]
Solving (a): f(2)
We have:
[tex]f(x) = 0.5x + 80[/tex]
[tex]f(2) = 0.5*2+80[/tex]
[tex]f(2) = 1 + 80[/tex]
[tex]f(2) = 81[/tex]
Solving (b): g(2)
From the table:
[tex]g(x) = 83[/tex] when [tex]x = 2[/tex]
So:
[tex]g(2) = 83[/tex]
Solving (c): Which is greater f(2) or g(2)
In (a) and (b),
[tex]f(2) = 81[/tex]
[tex]g(2) = 83[/tex]
Hence, test average for maths class is greater
A 16 ft ladder leans against the side of a house. The bottom of the ladder is 9 ft away from the side of the house. Find x, the angle of elevation of the ladder. Round your answer to the nearest tenth of a degree. (plz help listing BRAINLIST)
Answer:
55.8
Step-by-step explanation:
cos(x)=9/16
x=55.8
The angle of elevation of the ladder is approximately 60.5 degrees.
To find the angle of elevation (x) of the ladder, we can use trigonometry. The ladder, the side of the house, and the ground form a right triangle. The length of the ladder is the hypotenuse of the right triangle, and the distance from the bottom of the ladder to the house is one of the legs.
Using the tangent function:
tan(x) = opposite/adjacent
tan(x) = 16 ft / 9 ft
Now, solve for x:
x = arctan(16/9)
Using a calculator, we find
x ≈ 60.5 degrees
So, the angle of elevation of the ladder is approximately 60.5 degrees.
To know more about probabilities here
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please answer !!! quickly thank you!
Answer:
B) this line has zero slope.
Step-by-step explanation:
it doesn't increase or decrease. it is a constant; zero
Answer:
This line has zero slope.
Step-by-step explanation:
The slope of the line doesn't change it just stays straight.
Are (2, 5) and (5, 2) the same location? Why or why not?
Answer:
They are not in the same location
Step-by-step explanation:
Well because we have x axis and y axis, x always has to go first. In (2, 5) 2 is first and has to start from the x axis and 5 is the y axis. And the (5,2) is the opposite and the places would be in totally different places on the coordinate plane.
Answer: No
Step-by-step explanation: The order of coordinates for a given point is very important. For example, (2, 5) and (5, 2) represent two very different points on a coordinate system, as shown in the picture below.
A given point, such as (2, 5), is often reffered to as
an ordered pair because the order of coordinates is very important.
PLEASE HELP!!!!!!!!!!!!!!!!!!
which undefined term can contain parallel lines?
A spinner is divided into 4 equal sections numbered 1 through 4. It is spun twice, and the numbers from each spin are added.
What is the probability that the sum is less than 6?
Answer:
4equal to plus 5 eul is to be 9
Write the solution of one-half of two-thirds of three out of four-fifths of 200
Answer:
53 1/3
Step-by-step explanation:
200×4/5=160
160×2/3=106 2/3
106 2/3×1/2=53 1/3
Step-by-step explanation:
200×1/2=100
100×2/3=66.6666666667
so, the question is wrong
Choose the best selection for the
quadrilateral with vertices at the
following points:
(-5,0), (0,4), (5,0), (0,-4)
Hint: Start by graphing the points.
Distance Formula: d= (x2 – x1)2 + (72 - yı)2
A. Rectangle
B. Square
C. Rhombus
D. Trapezoid
9514 1404 393
Answer:
C. Rhombus
Step-by-step explanation:
The symmetry of the coordinates tells you the figure has equal-length sides, but the angles are not right angles. Such a figure is a rhombus.
The time it takes to build a house (T), varies directly with the floor area (A), and inversely with the number of workers (W). What is the equation that models this situation?
Answer:
T = k * (A/W)
Step-by-step explanation:
Evaluate the expression.
4!
Answer:
4! = 24
Step-by-step explanation:
4! = 4 * 3 * 2 * 1
4! = 24
will mark brainliest
Answer:
equation 1or 2 divide
3x+y=7
2x+5y=22
or, equation 1 multiple 5
15x+5y=35
2x+5y=22
or,13x=13
therefore x=1 again
value of x put the y in equation 2
2.1 + 5y=22
5y=11
therefore y=11/5
I’m not sure what it’s asking?
b and c will be reduced
Step-by-step explanation:
exterior angle= sum of other two angles
in the pic the sum is 152 so the exterior angle should've been 152 but it has been decreased so b and c will also decrease........
A worker is exposed to 98 dB for five hours and 82 dB for three hours, giving an eight-hour working day. On average, what noise level is this worker exposed to?
Answer:
92 dB
Step-by-step explanation:
Use the mean formula, mean = sum of elements / number of elements.
Since it is a 8 hour work day, there are 8 elements.
mean = sum of elements / number of elements
mean = (98 + 98 + 98 + 98 + 98 + 82 + 82 + 82) / 8
mean = 736 / 8
mean = 92
So, the average noise level is 92 dB
The Camden street Debate team is planning a trip to Florida. The trip cost $17,250
for 15 students to attend. How much is the cost per student? Write a equation to
help you solve the model.
Answer:
Step-by-step explanation:
divide the cost to the students.
use x
x+15= 17250
move 15 other side. which becomes negative
Answer: it is 1,150 per student
Step-by-step explanation: simple 17,250 divided by 15 = 1,150 now double check by 1,150 times 15 =17,250 so I am correct it is 1,150 per student
Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 16 feet and a height of 19 feet. Container B has a diameter of 20 feet and a height of 15 feet. Container A is full of water and the water is pumped into Container B until Container A is empty.
To the nearest tenth, what is the percent of Container B that is empty after the pumping is complete?
18.9% is the answer
Step-by-step explanation:
volume of a cylinder = πd²/4 x h
where d is diameter and h is height of cylinder.
thus
vol of A is
[tex]vol \: of \: a \: = \pi \times \frac{ {d}^{2} }{4} \times h \\ = \pi \times \frac{ {16}^{2} }{4} \times 19 \\ = \pi \times 4 \times 16 \times 19 \\ = 3818.24[/tex]
and
[tex]vol \: of \: b = \pi \times \frac{ {20}^{2} }{4} \times 15 \\ = \pi \times 5 \times 20 \times 15 \\ = 4710[/tex]
difference in vol of a and b is
[tex]diff \: = vol \: of \: b \: - vol \: of \: a \\ = 4710 - 3818.24 \\ = 891.76[/tex]
this volume will remain empty after container A is pumped into container B.
this volume as a percentage of total volume of B is
[tex]\% = \frac{diff \: vol}{total \: vol} \times 100 \\ = \frac{891.76}{4710} \times 100 \\ = 18.9\%[/tex]
Suppose that the distance of fly balls hit to the outfield (in baseball) is normally distributed with a mean of 247 feet and a standard deviation of 41 feet. Use your graphing calculator to answer the following questions. Write your answers in percent form. Round your answers to the nearest tenth of a percent. a) If one fly ball is randomly chosen from this distribution, what is the probability that this ball traveled fewer than 216 feet
Answer:
77.5% probability that this ball traveled fewer than 216 feet.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean of 247 feet and a standard deviation of 41 feet.
This means that [tex]\mu = 247, \sigma = 41[/tex]
What is the probability that this ball traveled fewer than 216 feet?
The probability as a decimal is the p-value of Z when X = 216. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{216 - 247}{41}[/tex]
[tex]Z = 0.756[/tex]
[tex]Z = 0.756[/tex] has a p-value of 0.775
0.775*100% = 77.5%
77.5% probability that this ball traveled fewer than 216 feet.
Each side of a square is (7 + 3x) units. Which is the perimeter of the square?
In circle R, What is the name of line segment BE and AD?
a diameter is a line that starts from the circumference to the other part of the circumference
Help with both please
Answer:
Step-by-step explanation:
12. To find the carpet needed. Find the area :
The figure is combination of semi circle and a rectangle.
So Area = Area of semi circle + Area of rectangle
[tex]Area \ of \ semi \ circle = \frac{1}{2} \pi r^2 = \frac{1}{2} \pi \times 25 = 39.25 \ ft^2 \\\\Area \ of \ rectangle = Length \times Breadth = 15 \times 10 =150 \ ft^2[/tex]
Area = 150 + 39.25 = 189.25 sq ft
13. Cost per square feet = $$9.95
Therefore cost for 189.25 square feet = 9.95 x 189.25 = $1883.04
Zara and John are hiking on a trail that 2 miles long .there are signs to mark each eighth of a mile along the trail
The weights (in ounces) of 28 tomatoes are listed below. 1.1 1.6 1.8 1.9 2.0 2.3 2.3 2.5 2.5 2.5 2.5 2.6 2.6 2.6 2.8 2.9 2.9 3.0 3.1 3.1 3.1 3.3 3.4 3.5 3.5 3.6 3.9 4.9 What is the five number summary?
Answer:
2.6 2.6 2.8 2.9 2.9
Step-by-step explanation:
used median for the five numbers.
Help troll or report Help plsssss
Answer:
11. (a) 3/4+1/2=5/4
(b) 4/5= 8/10 , 16/20
12. 8 children don't like choc ice cream
Step-by-step explanation:
11. 3/4 +2/4=5/4(change 1/2 by making it the same as the one next to it)
12. 3/5 of 20 = 12
20-12=8
Type the correct answer in each box. Use numerals instead of words. if necessary, use / for the fraction bar(s).
Find the sum. Write your answer in simplest form.
Answer:
[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]
Step-by-step explanation:
Given
See attachment for question
Required
Solve
We have:
[tex]\frac{11}{12} - \frac{1}{3}[/tex]
Take LCM and solve
[tex]\frac{11}{12} - \frac{1}{3} = \frac{11 - 4}{12}[/tex]
[tex]\frac{11}{12} - \frac{1}{3} = \frac{7}{12}[/tex]
Answer:
1
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Find the sum. Write your answer in simplest form.
Step-by-step explanation:
2x + y = 3
x - 2y = -1
If equation two is multiplied by -2 and then the equations are added, the result is
3y = 5
5y = 5
-3y = 3
9514 1404 393
Answer:
5y = 5
Step-by-step explanation:
-2(x -2y) +(2x +y) = -2(-1) +(3) . . . . -2 times [eq2] + [eq1]
-2x +4y +2x +y = 2 +3 . . . . eliminate parentheses
5y = 5 . . . . . . . . collect terms
What is the vertex and equation of the axis of symmetry of the graph of y=x^2-6x-7
Answer:
Vertex: (3,16)
Axis of symmetry: x = 3
Step-by-step explanation:
The vertex is the minimum or maximum of the graph.
The x -coordinate of the vertex is the equation of the axis of symmetry of the parabola.
In the figure below, which term best describes point A?
S
A
R
A. Incenter
B. Orthocenter
C. Centroid
D. Circumcenter
And then next time we will come back and
find the area for brainlest
Answer:
A = 30 units²
Step-by-step explanation:
The area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the perpendicular height )
Here b = 12 and h = 5 , then
A = [tex]\frac{1}{2}[/tex] × 12 × 5 = 6 × 5 = 30 units²