In a certain college, 4 instructors are single out of 24 instructors employed. What is the ratio of single to married instructors?
A. 1 to 6
B. 1 to 5
C. 24 to 4
D. 20 to 24

Answer:

Let's call the number of 7,000 gallon tank cars "x1", the number of 14,000 gallon tank cars "x2", and the number of 28,000 gallon tank cars "x3".

We can write the following constraints based on the total carrying capacity of the fleet:

7,000x1 + 14,000x2 + 28,000x3 = 532,000

x1 + x2 + x3 = 25

x1, x2, x3 >= 0 (since we can't have a negative number of tank cars)

This is a linear programming problem, which can be solved using simplex method or the graphical method.

By using the graphical method, we find that there are multiple optimal solutions. For example, one solution is x1 = 11, x2 = 7, and x3 = 7. This means that the manufacturer should lease 11 7,000 gallon tank cars, 7 14,000 gallon tank cars, and 7 28,000 gallon tank cars to meet the total carrying capacity requirement of 532,000 gallons.

So, the answer to the question is: There are multiple possible combinations of how the tank cars should be leased. The combinations are obtained from the equations x1 = 11 + 7t, x2 = 7 + 7t, and x3 = 7 + 7t.

Answer:

Step-by-step explanation: Yes, that is correct. The solution to the system of equations is (x, y) = (-7, 0) which is not in the given options, so none of them are the correct answer.

Following is the frequency distribution table:

0.720- 0.730

0.730- 0.740

0.740- 0.750

Any table that shows the frequency of values for one or more variables within a set of data. a table displaying each value of the variable and its accompanying frequency for a whole-number variable in a data set.

Given:

The lower limit is given as 0.720 inches.

and, The upper limit is 0.750 inches.

Also, the width of each class is 0.010 inches.

Thus, the intervals will be:

0.720- 0.730

0.730- 0.740

0.740- 0.750

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The second telephone pole is 72 feet tall. Since the ratio of the height of the first telephone pole to the length of its shadow is 24/6 = 4.

We can use this ratio to find the height of the second telephone pole.

If the second telephone pole casts a shadow of 18 feet at the same time of day, we can set up the following proportion:

height of second pole / length of shadow of second pole = height of first pole / length of shadow of first pole

Letting x be the height of the second pole, we can plug in the values we know and solve for x:

x / 18 = 24 / 6

Multiplying both sides by 18, we get:

x = 72

Therefore, the second telephone pole is 72 feet tall.

The answer is (e) 72.

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Complete question:

On a level field a telephone pole 24 feet tall casts a shadow 6 feet long. At the same time of day, another nearby telephone pole casts a shadow 18 feel long. How many feet tall is the second telephone pole?.

a. 6

b. 12

c. 24

d. 36

e. 72

The speed of Petra will be 0.55 mile/minute.

What exactly is speed?

The definition of speed is:

The pace at which an object's location changes in any direction.

Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.

Formula for Speed

The speed formula is shown below:

s=d/t

Where,

s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.

Now,

As given petra jogs 60 miles in 110 minutes

then in one minute she will jog =60/110 mile

=0.5454 mile/min

Hence,

           The speed of Petra will be 0.55 mile/minute.

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To find the mass of her parcel, you must solve the equation for the input when the output is of 19.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

For this problem, we have that the numeric value is of $19, hence the equation must be solved for the input variable to find the mass of the parcel.

The problem is incomplete, hence the general procedure to solve it was presented.

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The equation that represents the graph of a line passing through the points (0, -1) and (1, -4) is y = -3x - 1.

What is graph?

A graph is a visual representation of data or information that shows the relationship between different variables or quantities. Graphs can take many forms, including bar graphs, line graphs, scatterplots, and pie charts, among others. They are widely used in many fields, including mathematics, science, economics, and social sciences, to help visualize and analyze data, identify patterns, and communicate findings to others in a clear and concise manner. By representing complex information in a simple, easy-to-understand format, graphs can provide valuable insights and help us make informed decisions.

The equation that represents the graph of a line passing through the points (0,-1) and (1,-4) is:

y = -3x - 1

To find the equation of a line given two points, you can use the slope-intercept form:

y - y1 = m(x - x1)

where m is the slope of the line and (x1, y1) is one of the given points.

First, we can find the slope of the line:

m = (y2 - y1) / (x2 - x1)

= (-4 - (-1)) / (1 - 0)

= -3

Next, we can choose one of the given points and substitute its coordinates and the slope into the slope-intercept form:

y - (-1) = -3(x - 0)

y + 1 = -3x

y = -3x - 1

Therefore, the equation that represents the graph is y = -3x - 1.

Option A, y = -1/3x - 1, has a slope of -1/3, which is not the slope of the line passing through the given points.

Option C, y = -1/3x + 1/3, also has an incorrect slope of -1/3, and it also does not pass through the point (0,-1).

Option D, y = -3x + 1/3, has the correct slope of -3, but it does not pass through the point (0,-1).

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The graph of the points can be seen at the end, and the relation is not a function.

The coordinate axis has two axis with numbers labeled. For any point (x, y), you need to find the value x on the horizontal axis and the value y on the vertical axis.

Then the graph of the points  ​(-7,5), (-4,-6), (-1,4), (-7,3) will be like the one at the end of the answer.

Now, is this a function?

Not, it is not, because we can see that the input -7 is being mapped into two different outputs, and a relation is a function only if each input is mapped into a single output.

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The inverse of the given function is f(x) = 2x/(1 - x)

What is a function?

A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two varying quantities.

Given function is

f(x) = x/(2+x)

Assume that y = f(x) = x/(2+x)

Solve y = x/(2+x) for x:

y = x/(2+x)

Multiply (2+x) on both sides:

y(2+x) = x

2y + xy = x

Subtract xy from both sides:

2y = x - xy

2y = x(1 - y)

x = 2y/ (1 - y)

Now replace x with y and y with x:

y = 2x/(1 - x)

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domain = all real numbers

range = y > -2

y=x²-2

range is y is -2

domain is x is

The proof of the parallelogram has been given below

We have WXYZ as a parallelogram.

XW = ZY

XW // ZY

such that

M ∠VXW = M VZY (This is alternate interior angles,)

M∠VWX = M ∠VYZ

therefore ΔVXW ≅ Δvzy

wv = yv

Then XZ bisects WY

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The following form has two parallel sides, and, in accordance with the provided assertion, its area is 21 cm².

Area is the entire amount of space occupied by a flattened (2-D) surface or form of an item. The area of a planar figure is the space that its perimeter encloses. The quantity of unit rectangles that completely encircle a closed figure's surface is its area. Square units such as cm² and m² are used to measure area.

The ratio will also be 1/2 * (bases 1 + base 2) * length since it is a trapezium.

So, 1/2 * ( 9+5) * 3

   = 1/2 * 14 * 3

   =  1/2 * 42

   =  21 cm²

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The area of the polygon is 6x√3 / 3 units².

The polygon above is a triangle. The polygon has three sides. Therefore, the area of the polygon can be calculated as follows:

area of the polygon = 1 / 2 pa

where

Therefore, the perimeter of the polygon is the sum of the whole sides. The sides of the polygon is the same. Hence, the perimeter is 3x.

where

area of the polygon = 1 / 2 × 3x × 4√3 / 3

Hence,

area of the polygon =  3 / 2 x × 4√3 / 3

area of the polygon = 6x√3 / 3 units²

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Answer:

  EF = 7

Step-by-step explanation:

You want to know the length of midsegment EF in the triangle with it labeled 43-4x and the parallel base segment labeled 32-2x.

The midsegment is half the length of the base segment, so we have ...

  (43 -4x) = 1/2(32 -2x)

  43 -4x = 16 -x . . . . . simplify

  27 = 3x . . . . . . . . add 4x-16

  9 = x . . . . . . . . divide by 3

  EF = 43 -4x = 43 -4(9) = 43 -36

  EF = 7

Answer:

Step-by-step explanation:

x - 5 = 8 - 4x

rearrange

x - 5 = -4x + 8

x + 4x - 5 = -4x + 4x + 8

5x - 5 = 8

5x - 5 + 5 = 8 + 5

5x = 13

Divide by 5

5x/5 = 13/5

x = 13/5 or 2 [tex]\frac{3}{5}[/tex]

or 2.6 as a decimal

The location of the points for quadrilateral KLMN have been plotted in the graph shown in the image attached below.

In Geometry, there are different types of quadrilateral and these include the following:

Next, we would use an online graphing calculator to construct (plot) quadrilateral KLMN on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of quadrilateral KLMN on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of quadrilateral QRST, we can reasonably infer and logically deduce that it represents a parallelogram.

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Answer:

yes

Step-by-step explanation:

Answer: To find the distance between the tops of two buildings, we first need to find the horizontal distance between the two buildings. This distance can be found using the Pythagorean theorem.

Let's call the horizontal distance between the two buildings "d".

d^2 = 12^2 + (34 - 29)^2

d^2 = 144 + 25

d^2 = 169

d = 13

So, the horizontal distance between the two buildings is 13 meters.

To find the distance between their tops, we simply add the height of each building:

distance = 34 + 29 = 63 meters

So, the distance between the tops of the two buildings is 63 meters.

Step-by-step explanation:

Answer: Given the ratio of boys to girls at the park is 4 to 5, then there are 4 boys for every 5 girls. If there are 45 girls at the park, then there are 4 * 45 / 5 = 36 boys at the park.

So, the answer is B) 36.

Step-by-step explanation:

The probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is given by the equation P = 9/17

The set formula is given in general as n(A∪B) = n(A) + n(B) - n(A⋂B), where A and B are two sets and n(A∪B) shows the number of elements present in either A or B and n(A⋂B) shows the number of elements present in both A and B.

Given data ,

Let the probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 be P

Now , the equation will be

The fraction of doctors who are general practitioners be n ( A ) = 7/17

The fraction of doctors who are under the age of 45 n ( B ) = 4/17

And ,

The fraction of doctors who are both n ( A ∩ B ) = 2/17

Now , from the set theory formula ,

n(A∪B) = n(A) + n(B) - n(A⋂B)

And , probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B )

Substituting the values in the equation , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = ( 7 / 17 ) + ( 4/17 ) - ( 2/17 )

On simplifying the equations , we get

Probability that you are randomly assigned a General Practitioner or a doctor under the age of 45 is n ( A ∪ B ) = 9/17

Hence , the probability is 9/17

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f(x) = a(b)*.

Question 1 Part C

During their team meeting both managers shared their findings. Complete the statement describing their combined results.

Double click and highlight the correct answers

• the initial number of video views was - fewer than, the same as, more than- the initial number of site visits

• The number of website visits grew by a - smaller factor than, larger factor than, the same factor as- the number of video views.

• The difference between the total number of website visits and video views after 4 weeks is - 10,935, 4,690, 8,726, 15,625

Answer:

10,935, 4,690, 8,726, 15,625

Step-by-step explanation:

Each worker would take home a net pay of $586.71.

What is the net pay?

The net pay is the amount of money that an employee takes home after all deductions have been made from their gross pay. Gross pay is the total amount of money an employee earns before taxes and other deductions are taken out.

To calculate net pay, you need to subtract all the required deductions from the employee's gross pay.

To calculate the net pay for each worker, we first need to determine their gross pay. The gross pay will depend on the number of hours they worked and whether they worked any overtime.

For the first 40 hours worked, each worker earns $15.90 per hour, so their gross pay for those hours would be:

Gross Pay for 40 hours = $15.90/hour x 40 hours = $636

For any hours worked beyond 40, the worker earns time and a half wages. This means they earn 1.5 times their regular hourly wage of $15.90, or $23.85 per hour. So, if they worked, for example, 45 hours in total, the additional 5 hours would be paid at the overtime rate, resulting in an additional gross pay of:

Gross Pay for 5 overtime hours = $23.85/hour x 1.5 x 5 hours = $178.88

Therefore, their total gross pay would be:

Total Gross Pay = Gross Pay for 40 hours + Gross Pay for 5 overtime hours = $636 + $178.88 = $814.88

Now, we need to calculate the deductions, which we are told are 28% of the gross pay. So the total deductions would be:

Total Deductions = 28% x $814.88 = $228.17

Finally, to determine the net pay, we need to subtract the total deductions from the gross pay:

Net Pay = Gross Pay - Total Deductions = $814.88 - $228.17 = $586.71

Therefore, each worker would take home a net pay of $586.71.

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The expression when simplified is 2c^3d^3(4cd^2 + 1)

From the question, we have the following parameters that can be used in our computation:

8c^4d^5+2c^3d^3

Factor out 2 from the expression

So, we have the following representation

2(4c^4d^5 + c^3d^3)

Factor out c^3d^3 from the expression

So, we have the following representation

2c^3d^3(4cd^2 + 1)

Hence, the expression is 2c^3d^3(4cd^2 + 1)

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Answer:

X    Y

0    0

2   -3

Step-by-step explanation:

The slope should look like this photo.

The volume of the candle is 6740 cubic cm

From the question, we have the following parameters that can be used in our computation:

Radius, r = 9 cm

Height, h = 26.5 cm

The volume of a cylinder is calculated as

Volume = πr²h

substitute the known values in the above equation, so, we have the following representation

Volume = 3.14 * 9² *  26.5

Evaluate the products and exponents

Volume = 6740 cubic cm

HEnce, the volume is 6740 cubic cm

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Answer:

$90.12

Step-by-step explanation:

The principal amount of the loan is ...

 (sale price)(1 + sales tax rate) - (down payment)

 = $19,725×1.0475 -2175 = $18,486.94

For a secured loan, the APR charged for an average credit rating appears to be 5.85%, so the interest for the first month is

 i = Prt = ($18,486.94)(0.0585)(1/12)

 i = $90.12

Answer: C

Step-by-step explanation:

I am fairly certain this is the right answer. Good luck on your quiz!

Answer:C

Step-by-step explanation:

I remember this from class one time hope it helps:)

Since the triangles are congruent. Then The size of angle Q is 47°

Congruent Angle:

Congruent angles are often used in architecture, construction, design, and art. Isometrics have the same angular measurements. For example, a regular pentagon has 5 sides and 5 angles, each measuring 108 degrees. Regardless of the size or scale of a regular polygon, the angles are always congruent.

Here is a list of rules for the congruence of angles.

1. The only condition for two angles to be congruent is if the measurements of the angles agree.

2. The lengths and orientations of the two sides of this congruent angle are not important.

According to the Question:

It is given that :

B = 6 cm, 12 cm and 9 cm

A = 47°

R' = 29°

If the triangle is congruent, then all the three sides and angles will be same.

Therefore,

Angle Q = Angle A

Therefore, Angle Q = 47°

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The solution of the logarithm expression  logₐ 60 is 2.1. Therefore, the answer is D.

The logarithm expression can be solved as follows; Using the logarithm rule,

Law of multiplication of logarithm,

logₐ x + logₐ y = logₐ xy

Therefore,

logₐ 2 = 4

logₐ 3 = 5

logₐ 5 = 8

Hence, let's find logₐ 60.

logₐ 5 + logₐ 3 + logₐ 2 + logₐ 2 = logₐ (5 × 3 × 2 × 2) = logₐ 60

Hence,

0.8 + 0.5 + 0.4 + 0.4 = 2.1

Therefore,

logₐ 60 = 2.1

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The value of log a 60 is 21. The correct option is D.

Logarithms are another way of writing exponents.

Logarithm is nothing but another way of expressing exponents and can be used to solve problems that cannot be solved using the concept of exponents only.

log a 60 = log a (12 x 5)

log a 60 = log a 12 x log a 5

log a 60 = log a (4 x 3) x log a 5

log a 60 = log a 4 x log a 3 x log a 5

log a 60 = 2 log a 2 x log a 3 x log a 5

Substituting the values for the logs

log a 60 = 2 (4) + 5 + 8

log a 60 = 21

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