The median age of the sales representatives is 37.5 years.
Explanation:To find the median ages of the sales representatives, we first need to order the ages in ascending order:
Since there are 25 data values, the middle value will be the median age. To find the middle value, we divide the number of data values by 2, which gives us 12.5. Since the median is the average of the two middle values, we can take the average of the 12th and 13th values in our ordered list:
Median age = (37 + 38) / 2 = 37.5 years
Law of cosines: a2 = b2 + c2 – 2bccos(A). What is the measure of S to the nearest whole degree?
Answer:
I think the answer is 77.
Step-by-step explanation:
hello can you please help me posted picture of question
Solve the lp problem. if no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. hint [see example 1.] (enter empty if the region is empty. enter unbounded if the function is unbounded.) maximize p = x − 2y subject to x + 4y ≤ 9 x − 5y ≤ 0 6x − 3y ≥ 0 x ≥ 0, y ≥ 0.
This linear programming problem can be solved by graphing the given inequalities to determine the feasible region. If this region is empty, there are no solutions. If the function is unbounded in this region, the maximal value can be infinitely large.
Explanation:To solve this linear programming problem, we first need to identify its feasible region which is defined by its constraints. The constraints of this problem are as follows:
x + 4y ≤ 9 x - 5y ≤ 0 6x - 3y ≥ 0 x ≥ 0, y ≥ 0By graphing these inequalities we can identify the feasible region as the intersection of these inequalities. If the feasible region is empty, it means that there is no solution that satisfies all the constraints. If the objective function p = x - 2y is unbounded, it means that the maximum value of p can be infinitely large within this feasible region. By investigating both these situations, we should be able to determine whether an optimal solution exists or not.
Learn more about Linear Programming here:https://brainly.com/question/34674455
#SPJ2
What is the surface area of the cylinder in terms of Pi? radius is 14in and height is 18 in A. 896 pi in^2 B. 504 pi in^2 C. 392 pi in^2 D. 350 pi in^2
Answer:
The answer is 896pi in.^2
Step-by-step explanation:
It may seem confusing as you get an answer in the thousands by plugging in the formula, but remember they are asking you to find the answer in "terms of pi". This means you have to divide the answer by 3.14.
2814/3.14 = 896pi in^2
Hope this helped!
a triangle has an area of 12 centimeters to the second power and a base of 8 centimeters what is the height of the triangle show you work will mark brainiest
QM Q4.) Find the solution set
The square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.
The equation using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Where:
a is the coefficient of the x² term
b is the coefficient of the x term
c is the constant term
In the equation x² - x = 2, we have:
a = 1
b = -1
c = 2
Plugging these values into the quadratic formula, we get:
x = (1 ± √((-1)² - 4(1)(2))) / 2(1)
Simplifying the expression, we get:
x = (1 ± √(1 - 8)) / 2
Evaluating the square root, we get:
x = (1 ± √(-7)) / 2
Since the square root of a negative number is imaginary, there are no real solutions to the equation x² - x = 2.
For similar question on quadratic formula.
https://brainly.com/question/29159682
#SPJ12
In a large population, very close to 25% of the observations will fall below the 25th percentile (Q1), and close to 75% fall below the 75th percentile (Q3). The Web site of the Educational Testing Service reports that on the SAT Verbal test, with a possible perfect score of 800, the 89th percentile of 1,475,623 scores nationwide is a score of 670. What is the best estimate of exactly how many scores were below 670?
Answer:
1,313,000
Step-by-step explanation:
Hi please help :)
What is the value of b in the given quadratic regression equation?
Y= -0.139x^2 + 1.667x
A. 1
B. 1.667
C. 0
D. -0.139
Answer:
The answer on edge 2021 is 1.667
Step-by-step explanation:
I got a 50% and it showed the answer
The value of b in the quadratic regression equation is 1.667.
The value of b in the given quadratic regression equation is 1.667.
To find the value of b, you can look at the coefficient of the linear term in the quadratic equation ,, In this case, the linear term is 1.667x, so the value of b is 1.667.
hello can you please help me posted picture of question
What is the measure of < L ? Need help
Length contraction is the shortening of an object's measured length when it is moving relative to the observer's frame. The formula for length contraction is L = L0√(1 - (v^2/c^2)).
Explanation:Length contraction (L) is the shortening of the measured length of an object moving relative to the observer's frame. It occurs when an object is moving at a significant fraction of the speed of light. The formula for length contraction is L = L0√(1 - (v2/c2)), where L0 is the rest length of the object, v is its velocity, and c is the speed of light.
Learn more about Length contraction here:https://brainly.com/question/10272679
#SPJ3
A leak in a water tank causes the water level to decrease by 3.6×10−2 millimeters each second.
About how many millimeters does the water level in the tank decrease in 5 hours, or 1.8×104 seconds?
Drag and drop the values to the boxes to express the answer in scientific notation.
Answer:
just to sum up the answer it is 6.5*10^2
Is 0.6 and 0.60 equal to each other
hey can you please help me posted picture of question
System.out.print((k%3) + " "); if ((k % 3) == 0) k = k + 2; else k++; } what is printed as a result of executing the code segment? question 21 options:
a. 0 2 1 0 2
b. 0 2 0 2 0 2
c. 0 1 2 1 2 1 2
d. 0 2 0 2 0 2 0
e. 0 2 1 0 2 1 0
A cartoon in the shape of a cube measuring 8 inches tall is filled with colored plastic cubes measuring 1 inch across each face. The cubes sell for 25cent each. How much would it cost to buy all of the cubes in the carton? Enter your answer in the box?
jenny is diving into a swimming pool from a diving board. The expression below represents Jenny's vertical height, in feet, above the surface of the water after x seconds. -16x^2 +12x+10. Which statement best describes the term 10?
A. Jenny's initial height above the surface of the water
B. The time it takes Jenny to reach the surface of the water
C. The horizontal distance from the diving board Jenny travels
D. the maximum height Jenny reaches.
Answer:
A. Jenny's initial height above the surface of the water
Step-by-step explanation:
Given : The expression below represents Jenny's vertical height, in feet, above the surface of the water after x seconds. [tex]-16x^2 +12x+10.[/tex]
To Find: Which statement best describes the term 10?
Solution:
[tex]h(x)=-16x^2 +12x+10.[/tex]
Substitute x = 0 i.e.time = 0 seconds
[tex]h(x)=-16x^2 +12x+10.[/tex]
[tex]h(0)=-16(0)^2 +12(0)+10.[/tex]
[tex]h(0)=10[/tex]
so, at time 0 the height was 10
So, 10 is the initial height.
Thus Option A is correct.
A. 10 is Jenny's initial height above the surface of the water.
A tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. compute the amount of salt (in pounds) in the tank at the first moment when the tank is filled.
Final answer:
The amount of salt in the tank, described by the differential equation, reaches 5 pounds after 50 minutes with an initial amount of 10 pounds and a rate of change defined by the given equation.
Explanation:
Let's start with the given differential equation: A'(t) = (2 gal/1 min) * (0 lb/1 gal) - (1 gal/1 min) * A(t) / (50 + (2 - 1)t gal).
By simplifying the equation, we get A'(t) + A(t) / (50 + t) = 0. Multiplying through by (50 + t) gives (50 + t)A'(t) + A(t) = 0. Recognizing that ((50 + t)A(t))' equals zero, we integrate to find (50 + t)A(t) = C, where C is a constant.
With the initial condition A(0) = 10, we find 10 = C / (50 + 0), which simplifies to C = 500. So, the equation describing the amount of salt in the tank is A(t) = 500 / (50 + t).
To determine when the tank will be filled, we solve 50 + t = 100, which gives t = 50 minutes. Plugging this into A(t) yields A(50) = 500 / (50 + 50) = 5 lb.
21$is 75% of what amount?
In quadrilateral $ABCD$, we have $AB=3,$ $BC=6,$ $CD=4,$ and $DA=4$.
If the length of diagonal $AC$ is an integer, what are all the possible values for $AC$?
To find the possible integer lengths for diagonal AC in quadrilateral ABCD, the Triangle Inequality Theorem is used. Possible integer values for AC are constrained between the sum and the difference of the lengths of the sides forming triangles ABC and CDA, resulting in potential lengths of 4, 5, 6, and 7.
Explanation:The question pertains to finding all possible integer values for the diagonal AC of a quadrilateral ABCD given the lengths of the sides. To determine the possible lengths of AC, we need to inspect the properties of triangles that could form within the quadrilateral upon drawing this diagonal. The quadrilateral could possibly be a rectangle, a square, or a parallelogram, but without further information, we assume it is an irregular quadrilateral.
By using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, we can determine possible values for AC. Since ABCD is a quadrilateral with sides AB = 3, BC = 6, CD = 4, and DA = 4, diagonal AC can create two triangles, ABC and CDA. For triangle ABC, the sum of sides AB and BC is 9, so AC must be less than 9. Similarly, for triangle CDA, the sum of sides CD and DA is 8, so AC must be less than 8. Therefore, the maximum value for AC is 7. However, AC must also be greater than the difference of the sides, 3 for triangle ABC and 0 for triangle CDA. This leaves us with possible integer values of 4, 5, 6, and 7 for AC.
Let f = ay i + bz j + cx k where a, b, and c are positive constants. let c be the triangle obtained by tracing out the path from (7, 0, 0) to (7, 0, 2) to (7, 6, 2) to (7, 0, 0). find f · dr
c.
The task involves evaluating the line integral of a vector field along a path to determine the work done by the field. Since the path does not traverse in the x-direction, only the y and z components of the vector field contribute to the integral. The calculation involves parameterizing each segment and summing up the individual integrals.
Explanation:The student's question involves finding f · dr along a path c in a vector field. The vector field is given as f = ay i + bz j + cx k, and the path c is a triangle with vertices at (7, 0, 0), (7, 0, 2), and (7, 6, 2). The dot product of a vector field with a differential displacement vector (dr) represents the work done by the field along that path.
To find the integral of f · dr along the path c, we would parameterize each segment of the path and evaluate the line integral. However, since the vector field has constants multiplied by either i, j, or k, and the path only moves parallel to the y and z axes, the components involving x do not contribute to the integral. Therefore, for each segment of the path, we will only consider the y and z components of the vector field. The line integral along the path is then the sum of the integrals over each segment of the triangle.
In this example, since the x-component of the field does not change and the path does not move in the x direction, the integral over the x components will be zero.
Calculation Steps:
Parameterize each segment of the path.Evaluate the integral of f · dr over each segment.Add the integrals from each segment to get the total work done by the field along path c.
Suzy randomly picks marbles form a bag containing 13 identical marbles. how many possible outcomes are there of she selects 10 marbles?
Answer:
286 possible outcomes.
Step-by-step explanation:
We have been given total 13 identical marbles
We need to select 10 out of 13
We will use combination:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
here,n=13 and r=10 on substituting the values in the formula we get:
[tex]^13C_{10}=\frac{13!}{10!(13-10)!}[/tex]
[tex]^13C_{10}=\frac{13\cdot 12\cdot 11\cdot10!}{10!\cdot 3!}[/tex]
[tex]\Rightarrow ^13C_{10}=\frac{13\cdot12\cdot11}{3\cdot2\cdot1}[/tex]
[tex]\Rightarrow 286[/tex]
So, there are 286 possible outcomes.
Possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].
Further explanation:
The formula of combination can be expressed as,
[tex]\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex]
Given:
A bag contains [tex]13[/tex] identical marbles.
Calculation:
Suzy randomly picks [tex]10[/tex] marbles from a bag of [tex]13[/tex] identical marble.
The number of possible outcomes that she can select [tex]10[/tex] marbles can be obtained as,
[tex]{\text{Possible}}\,{\text{outcomes}} = {\,^{13}}{C_{10}}[/tex]
Substitute [tex]13[/tex] for [tex]n[/tex] and [tex]10[/tex] for [tex]r[/tex] in equation [tex]{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex] to obtain the possible outcomes that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles.
[tex]\begin{aligned}{\text{Possible}}\,{\text{outcomes}}&= {\,^{13}}{C_{10}} \\ &= \frac{{13!}}{{10!\left( {13 - 10} \right)!}} \\ &= \frac{{13!}}{{10!\left( {3!} \right)}} \\ &= \frac{{13 \times 12 \times 11 \times 10!}}{{10!\, \times 3 \times 2 \times 1}} \\ &= 286\\\end{aligned}[/tex]
Hence, possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].
Learn more:
1. Learn more about inverse of the function https://brainly.com/question/1632445
2. Learn more about range and domain of the function https://brainly.com/question/3412497
3. Learn more about profit and loss https://brainly.com/question/2479097
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Combination
Keywords: Suzy, picks, marbles, 13 identical marbles, 10 marbles, possible, outcomes, select, combination, randomly picks, a bag contains 13 marbles.
rewrite 5/6 with the denomintaior of 12
How many points should be plotted when creating a scatterplot from the table of values below? Pages in Book vs. Time Needed to Read Number of pages in book Time needed to read book (hours) 200 18 175 15 275 21 225 18 400 30 350 26
Answer: 6
Step-by-step explanation:
Given table: Number of pages in book Time needed to read book (hours)
200 18
175 15
275 21
225 18
400 30
350 26
The number of observations in the above table = 6
When we create a scatter-plot from the table of values the number of points should be plotted =6.
Hence, the number of points should be plotted when creating a scatter-plot from the given table of values =6
Q # 7 please solve. the math
A 9 cm tall cone shaped paper cup can hold up to 58.9 cm3 of water. What is the minimum amount of paper needed to make the paper cup, assuming no overlap in the paper? Use 3.14 for π.
Answer:
A minimum of 93 cm squared
Step-by-step explanation:
4/5 decomposed in 2 different ways
Lot 21 is a trapezoid with the two bases
perpendicular to the road. The scale drawing
below uses the scale 1/2 inch = 40 feet.
Base 1=3.5 inches
Base 2=5 inches
height=4 inches
What is the approximate area of Lot 21?
(1 acre = 43,560 square feet)
A 1/2 acre
B 2 acres
C 2 1/2 acre
D 3 acres
Kim's family spends $62.50 on a dinner they leave an 18% tip how much is their total bill after
Find the area of the figure show steps
The actual income for this month has been reduced 200