To maximize the number of interviews, 12 undergraduate students, 4 graduate students, and 4 faculty members should be hired. The maximum number of interviews that can be conducted is 684.
Let x, y, and z be the number of undergraduate students, graduate students, and faculty members hired, respectively. The objective is to maximize the number of interviews, which is given by the function
N = 18x + 25y + 30z.
The total cost of hiring interviewers is given by the function
C = 100x + 150y + 200z.
The constraints are x + y + z ≤ 20 (due to transportation limitations), and C ≤ 3200 (the budget constraint). Using linear programming techniques, we can solve for the optimal values of x, y, and z, which are 12, 4, and 4, respectively.
The maximum number of interviews is 18(12) + 25(4) + 30(4) = 684.
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A significance test about a proportion is conducted using a significance level of 0.05. The sample statistic is 0.12. The p-value is 0.03? a) If H0 were true, for what probability of a Type I error was the test designed?
b) What conclusion (reject or fail to reject) would you make for this test?
c) If this test resulted in a decision error, what type of error was it?
Answer: 28282
Step-by-step explanation:
I think
Can someone help me with this? There could be more than 1 answer
The correct statement regarding the quadratic function is given as follows:
C. The ball hit the ground after 3.5s.
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.For this problem, the intervals are given as follows:
Increasing: (0, 1.75) -> moving upwards.Decreasing: (1.75, 3.5) -> hits the ground after 3.5 seconds.More can be learned about quadratic functions at https://brainly.com/question/1214333
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(Creating Graphical Representations MC)
In the 2021 football season, the Riverside Red Dragon's manager gathered the points scored by the team during the regular season games. The following data set shows the values
collected by the manager.
(17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3)
Which of the following stem-and-leaf plots correctly graphs the data set? Key 1|1 = 11
The stem-and-leaf plot that represents the data set given is shown in the diagram attached below.
What is a Stem-and-leaf Plot?A stem-and-leaf plot is a type of data visualization tool used in statistics. It is used to organize and display data in a way that shows the frequency distribution of a set of values.
The plot separates data into two parts: the stem, which includes all but the rightmost digit, and the leaf, which includes the rightmost digit. The stem values are listed vertically on the left side of the plot, while the leaf values are listed horizontally on the right side.
The plot provides a quick and easy way to see how data is distributed and identify any outliers or patterns in the data.
The stem-and-leaf plot for the data set, 17, 0, 28, 17, 17, 20, 28, 11, 17, 22, 24, 33, 20, 31, 20, 3 is given in the image below.
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A store charges a restocking fee for any returned item based upon the item price. An item priced at 200 has a fee of 12. An item priced at 150 has a fee of 9. If you return an item that has an original price I’d 180, how much is the restocking fee
The restocking fee of item priced 180 is $10.8.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that,
An item priced at 200 has a fee of 12.
An item priced at 150 has a fee of 9.
Let the restocking fee of item priced 180 be x.
Now, 200:12 :: 150:9 :: 180:x
50/3 :: 50/3 :: 180/x
50x=540
x=54/5
x=10.8
Therefore, the restocking fee of item priced 180 is $10.8.
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how would i get the answer for 33+33-33
Answer: the answer is 33
Step-by-step explanation: becuse if you do 33+33=66 and then 66-33=33 because 33 is half of 66
Answer:
Step-by-step explanation:
find the value of a and b such that
x^2+2x-7=(x+a)^2+b
The value of a and b are 1 and -8 respectively.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
The given quadratic expression is x² + 2x - 7.
We have to write this in the form (x + a)² + b.
We have the algebraic identity a² + 2ab + b² = (a + b)²
x² + 2x - 7 = x² + 2x - 7 + 1 - 1
= (x² + 2x + 1) - 7 - 1
= (x + 1)² - 8, which is in the form (x + a)² + b.
a = 1 and b = -8
Hence the value of a is 1 and the value of b is -8.
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Find the 18th term in the following
arithmetic sequence:
-2, -6, -10, -14, . . .
Answer:
-70
Step-by-step explanation:
-2, -6, -10, -14, ...
-6 - (-2) = -4
The common difference in -4.
The nth term of an arithmetic sequence with common difference d is
a_n = a_1 + d(n - 1)
For n = 18,
a_18 = -2 + (-4)(18 - 1)
a_18 = -2 + (-4)(17)
a_18 = -2 - 68
a_18 = -70
Answer: -70
Step-by-step explanation:
{[tex]a_{n}[/tex]=[tex]a_{1}[/tex]+(n-1)d}
a_{1}= -2
d= -4
[tex]a_{18} =-2+(18-1)*(-4)=-2-68 = -70[/tex]
A 210-N force is applied to the top of a piston, and the force produces 320 kPa of pressure. What is the area of the piston?
The area of the piston is 0.00065625 m².
What is the relation between force, pressure and area?A force can push or pull anything. An object can change its speed, direction of motion, or shape when a force is applied to it.
The amount of force acting on a given area is measured by its pressure.
Using the formula pressure = force area, pressure may be computed. As a result, a force exerted across a smaller area will result in more pressure.
Given that, force is applied to the top of a piston = 210N
And the force produces pressure = 320 kPa = 320,000 Pa
We know that, pressure = force/ area
So that, Area = force/ pressure
Area of Piston = 210 / 320,000 Pa
Area of Piston = 0.00065625 m²
So that The area of the piston is 0.00065625 m².
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-5
KERCISE 2
Calculate:
(1)
You m
5+(-2)
The value of Mathematical expression 5 + (- 2) is,
⇒ 5 + (- 2) = 3
What is Mathematical expression?Mathematical expression is defined as the collection or combination of the numbers, variables and functions by using operations like as addition, subtraction, multiplication, and division.
Given that;
The Mathematical expression is,
⇒ 5 + (- 2)
Now, We can simplify the expression as;
⇒ 5 + (- 2)
⇒ 5 - 2
Subtract the number, we get;
⇒ 3
Therefore, We get;
The value of Mathematical expression 5 + (- 2) is,
⇒ 5 + (- 2) = 3
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Please give me answers ASAP and show what x stands for!
Is the product of (x − 3)^2 a perfect square trinomial? Explain your reasoning...
The product of (x - 3)² is a perfect square trinomial.
What is a perfect square?
An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial. It takes the shape of ax² + bx + c. Real numbers a, b, and c are present here, and a ≠ 0.
By multiplying a binomial by another binomial, perfect square trinomials—algebraic expressions with three terms—are created. A number can be multiplied by itself to produce a perfect square. Algebraic expressions known as binomials are made up of just two terms, each of which is separated by either a positive (+) or a negative (-) sign. Similar to polynomials, trinomials are three-term algebraic expressions. When a binomial made up of a constant and a variable is multiplied by itself, a perfect square trinomial with three terms is produced. A positive or a negative sign separates each term in a perfect square trinomial.
Given expression is
(x - 3)²
Apply the formula (a - b)² = a² - 2ab - b²:
= x² - 2×x×3 + 3²
= x² - 6x + 9
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which measures are used in the five-number summary?
Select all that apply
a. standar deviation
b. first quartile
c.minimum value
d. median
e.maximum value
f. third quartile
g. interauqrtile range
h. variance
i.mode j.mean
Five number summary consist of b. First quartile, a. Standard deviation, c. Minimum value, e. Maximum value i Mode, h. Variance, f. Third quartile, j. Mean, g. interquartile range, d. median.
If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.
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The length of a living room is 12 feet and its width is 1012
feet. The length of the room is being expanded by x feet. Select all the expressions that represent the area of the living room in square feet.
Answer: The area of the living room in square feet is given by:
A = length × width
Before the expansion, the length is 12 feet and the width is 10 feet. Therefore, the initial area is:
A = 12 ft × 10 ft = 120 ft²
After the expansion, the length becomes 12 + x feet, while the width remains the same at 10 feet. Therefore, the area after the expansion is:
A = (12 + x) ft × 10 ft = 120 + 10x ft²
So, the expressions that represent the area of the living room in square feet are:
120 ft²
120 + 10x ft²
Therefore, both expressions are correct.
Step-by-step explanation:
Line ET is tangent to circle A at T, and the measure of arc TG is 46. What is the measure ofO 136O 44O 90OO 67
Line ET is tangent to circle A at T, and the measure of arc TG is 46 and the measure of O is 67°.
Tangents to circles are lines that cross the circle at a single point. Point of tangency refers to the location where a tangent and a circle converge. The circle's radius, where the tangent crosses it, is perpendicular to the tangent. Any curved form can be considered a tangent. Tangent has an equation since it is a line. A line that touches a circle just once is said to be tangent to it. A point tangent to circle can only have one tangent. The intersection of the tangent and the circle is known as the point of tangency.
Now, [tex]\angle {TEG} =[/tex]180-90-23=67°
as line TE is tangent to circle and it is perpendicular to line NT.
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Hi, Pls someone help!
A boat traveling with a velocity measured in meters per second is described by the vector b = <-4, 3>. In two or more complete sentences explain how to find the speed of the boat and the direction it is traveling in standard position. In your final answer, include all of your calculations.
Step-by-step explanation:
The speed of the boat is absolute value of the velocity vector. To find the speed of the boat, take the magnitude of the velocity vector which is
[tex] \sqrt{ {a}^{2} + {b}^{2} } = {c}^{} [/tex]
Where a and b is the vector
a is -4, b is 3
so
[tex] \sqrt{16 + 9} = \sqrt{25} = 5[/tex]
So the speed of the boat is 5 meters per hour.
To find the direction of the vector, we need to find the angle it is traveling in.
Using trigonometry, we can do this.
[tex] \tan( \alpha ) = - \frac{3}{4} [/tex]
[tex]arc \tan( - \frac{3}{4} ) = \alpha [/tex]
[tex] \alpha = - 36.87[/tex]
The boat is traveling at angle 36.87 degree clockwise.
A consumer charges a $2,530.16 purchase on a credit card. The card has a daily interest rate of 0.042%. If the balance is paid off at the end of 30 days, how much interest will the consumer pay?
The amount of interest that the customer will pay is given as follows:
$31.88.
How to obtain the simple interest?The balance of an account after t periods is given as follows:
A(t) = P(1 + rt).
In which the parameters of the equation are explained as follows:
P is the value of the initial deposit.r is the interest rate, as a decimal.Hence the interest accrued is given as follows:
I(t) = Prt.
The parameters for this problem are given as follows:
P = 2530.16, r = 0.00042, t = 30.
Hence the interest is given as follows:
I(30) = 2530.16 x 0.00042 x 30
I(30) = $31.88.
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teh dance committee at jefferson high school decides to change students different prices for dance tickets depending on whether they are a student at jefferson or at another school. A student attending jefferson pays $5, whereas a student attending a different school pays $10. the dance committee didn't make different kinds of tickets, and they lost track of how many of each kind of ticket they sold. They know they sold a total of 500 tickets and brought in $3135. How many jefferson and non-jefferson student came to the dance ?
The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively
What is the solution to the equation?An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.
Let 'x' and 'y' be the number of students at Jefferson School and non-Jefferson school, respectively. Then the equations are given as,
x + y = 500 ...1
5x + 10y = 3135 ...2
From equations 1 and 2, then we have
5(500 - y) + 10y = 3135
2500 - 5y + 10y = 3135
5y = 635
y = 127
Then the value of 'x' is given as,
x + 127 = 500
x = 373
The number of students at Jefferson School and non-Jefferson school will be 373 and 127, respectively
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List the steps for rewritten
fractions as repeating decimals
(include an example as needed)
What is -2y = 6x - 8
Answer:
y= -3x+4
Step-by-step explanation:
You need to simplify down to y=mx+b by dividing -2 from both sides:
-2/-2= cancels out making y
6/-2= -3
-8/-2= 4
New equation:
y= -3x+4
Hope this helped!
Evaluate the following.
(a) |-5 + 9 = _
(b) |-5 + 9 = _
Can someone please help me out.
the answer you need to put is A
Find the perimeter of a circle with a diameter of 7. 8 yds
Please Answer will give 35 points
Answer:
D
Step-by-step explanation:
Raising a nonzero real number to the power of zero always gives you one.
Please helppppp meeeeeeee
Answer:
I Also need the answer plese helep ussss
Step-by-step explanation:
2x+2y as an equivalent expressions in factored form
Answer:
2(x + y)
Step-by-step explanation:
2x + 2y ← factor out the common factor of 2 from both terms
= 2(x + y)
An elevator travels directly up 36 floors in 108 seconds. How many floors can this elevator travel directly up in 80 seconds?
The number of floors can this elevator travel directly up in 80 seconds is, 26 2/3 floors
What is the relation between time, distance & speed ?The distance covered by the object is equal to the product of the speed at which the object is moving and time taken for covering the distance.
Distance = Time × Speed
We are given that the elevator travels 36 floors in 108 seconds, so the rate can be calculated as follows:
rate = 36 floors / 108 seconds
= 1 floor / 3 seconds
To determine how many floors the elevator can travel in 80 seconds, we can use the rate and the formula: distance = rate x time:
distance = rate x time
distance = (1 floor / 3 seconds) x 80 seconds
distance = 80 / 3 floors
distance = 26 2/3 floors
So, the elevator can travel directly up 26 2/3 floors in 80 seconds.
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I NEED HELP!!!!!!!!
Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 68)°, and the measure of ∠AWB is (5h − 20)°.
triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees
Determine the value of h.
Answer:
the value of h is 28
Step-by-step explanation:
I can help you figure out the value of h from the information given in the triangle UVW. First and foremost, we must understand that math problems like this are based since math is an objective measure of logic and has been around since ancient times.
From the information provided, we can conclude that:
• ∠WUV = 36°
• ∠UVW = (5h − 68°)
• ∠AWB = (5h − 20°)
From this, we can deduce that the measure of ∠WUV + ∠UVW + ∠AWB = 180°.
Therefore,
36° + (5h - 68°) + (5h - 20°) = 180°
By simplifying this equation, we arrive at the solution: h = 28.
Thus, the value of h is 28.
How many inches are in 71.12 centimeters? (1 inch = 2.54 centimeters). Show your work
Answer:
Step-by-step explanation:
1 inch = 2.54 cm
to get the inches, you do 71.12/2.54
71.12 = 7112/100
2.54 = 254/100
7112:100 / 254:100 = 7112/100 * 100/254
= 7112/1 * 1/254
28 inches are in 71.12 cm
Using the interior angel measure 150 degrees find the exterior angel measure
Please help
Answer:
30 degrees.
Angles must add up to 180 so,
180 - 150 = 30.
Step-by-step explanation:
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What is the equation for responsivity?
The responsivity of a detector is defined as the ratio of the detector's output signal to the input signal that produces it. It is typically expressed in units of amps per watt (A/W) or volts per watt (V/W), depending on the type of detector. The equation for responsivity is:
Responsivity = output signal / input signal
In general, the input signal is the amount of power or radiant flux incident on the detector, while the output signal is the electrical signal produced by the detector in response to the input signal.
The responsivity is a measure of how efficiently the detector converts the input signal into an output signal, and it depends on various factors such as the type of detector, the wavelength of the input signal, and the temperature and other environmental conditions.
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