At one really small university, there are 1,200 people. Of these students, 53% are undergraduates. 37% are graduates, and the rest are going for their doctorate. How many professors are at the university?

Answer:

w<=16

Step-by-step explanation:

600-25w>=200

25w>=600-200

25w>=400

w>=400/25

w>=16

w<=16

The pair (2, -1) is the solution the system of equations.

The given system equations are 2a+b = 3 and a - 3b = 5.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Here,

2a+b = 3 --------(1) and a - 3b = 5 --------(2)

Multiply equation (1) by 3

6a+3b=9 --------(3)

Add equation (2) and (3), we get

a - 3b+6a+3b = 5+9

⇒ 7a = 14

⇒ a = 2

Put a=2 in the equation (1), that is

2(2)+b=3

⇒ b=-1

Therefore, the pair (2, -1) is the solution the system of equations.

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Final answer:

The correct pair (a,b) that solves the given system of equations 2a + b = 3 and a - 3b = 5 is (2, -1), which is option J.

Explanation:

To find which pair (a,b) is the solution to the system of equations 2a + b = 3 and a - 3b = 5, we can use substitution or elimination. Here's a step-by-step explanation using the elimination method:

Therefore, the correct solution to the system of equations is (2, -1), which corresponds to option J.

Turn percentage into a decimal.

3% = 0.03

Multiply.

40,400 * 0.03 = 1,212

Subtract.

40,400 - 1,212 = $39,188

_______

Alice earned $39,188 last year.

_______

Best Regards,

Wolfyy :)

Answer:

The correct answer is 39,188.

Step-by-step explanation:

Alice Swanson's current earnings for this year are 40,400. Her earnings were 3% less than this last year. To find her earnings for last year, we will use the "Percent • Whole = Part" formula. But first, we must put 3% into a decimal form: 3 ÷ 100 = 0.03. Now let's solve:

40,400 • 0.03 = 1,212

1,212 is 3% of 40,400. To find Alice's earnings for last year, we will subtract her raise from her current earnings:

40,400 - 1,212 = 39,188

Hope this helps,

♥A.W.E.S.W.A.N.♥

Answer:

the third side is 40 m long

Step-by-step explanation:

The perimeter of the triangle is the sum of its three sides, and they give you what that value in meters is (120 m)

Your are given the length of two of them: 30 m and 50 m, and need to find the third one (let's call it "x" for this unknown side)

Now set the following equation:

Perimeter = side 1 + side 2 + side 3   --> replace these with the info you know

120 m = 30 m + 50 m + x   --> add 30 m and 50 m obtaining 80 m

120 m = 80 m + x  --> now solve for x (isolate the x on one side) by subtracting 80 m from both sides

120 m - 80 m = x  --> perform the subtraction 120 m - 80 m = 40 m

40 m = x

Which tells us that the third unknown side has a length of 40 m

Answer:

The third side is 40 meters long

Step-by-step explanation:

From the question, we were told that a triangular courtyard has a perimeter of 120 meters, we are to find the length of the third side if the other two sides are 30 and 50 meters.

First, we need to know that perimeter is the distance around a polygon.

Let the third side = side c, let the two sides be side A and side B

Perimeter = side A + side B + side c

side A = 30 meters

side B = 50 meters

side C = ?

Perimeter = 120 meters

We can now proceed to insert the values in the equation above

Perimeter = side A + side B + side c

      120    = 30 + 50 + side c

      120 = 80 + side c

Subtract 80 from both-side of the equation

120 - 80 = 80 - 80 + side c

40 = side c

side c = 40 meters

Therefore, the third side is 40 meters long

1. 60 tablets

2. 120 tablets

Step-by-step explanation:

1. Order: Alprazolam 2 mg take 1 tab by mouth twice a day for 30days. How many total tablets will the patient take for 1 month (30days)

As the patient has to take 1 tablet twice a day, that will be 2 tablets per day so the total number of tablets will be:

[tex]30*2 = 60\ tablets[/tex]

And

60*2 = 120 mg

2. Order: Tramadol Hychloride 10mg take 1 tab by mouth 4 times a day before meal for 30days. How many total tablets will the patient take for 30days?

As the patient has to take 4 tablets each day, that means the total tablets for one month or 30 days will be:

[tex]30* 4 = 120\ tablets[/tex]

And

120*10 = 1200 mg

Hence,

1. 60 tablets

2. 120 tablets

Keywords: Multiplication,

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Answer:

Part a) [tex]y=0.05x+1.50[/tex]

Part b) [tex]y=0.50x+0.50[/tex]

Part c) The graph in the attached figure

Part d) see the explanation

Step-by-step explanation:

The complete question is

A restaurant sells tea for $1.50 plus $0.05 per refill. A gas station store sells tea for $0.50 plus $0.50 per refill.

Part a) Write a linear function for the price of tea at restaurant

Part b) Write a linear function for the price of tea at gas station store

Part c) Graph both equations

Part c) Compare the lines in terms of slope and y-intercept

Let

y -----> the price of tea in dollars

x -----> the number of refills

we know that

The linear equation in slope intercept form is equal to

[tex]y=mx+b[/tex]

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value (value of y when the value o x is equal to zero)

Part a)

At restaurant

we have that

The slope or unit rate is equal to

[tex]m=\$0.05\ per\ refill[/tex]

The initial value or y-intercept is equal to

[tex]b=\$1.50[/tex]

substitute

[tex]y=0.05x+1.50[/tex]

Part b)

At gas station store

we have that

The slope or unit rate is equal to

[tex]m=\$0.50\ per\ refill[/tex]

The initial value or y-intercept is equal to

[tex]b=\$0.50[/tex]

substitute

[tex]y=0.50x+0.50[/tex]

Part c) Graph both equations

we know that

The easiest way to graph a line is with two points

Find the intercepts of the line

At restaurant

[tex]y=0.05x+1.50[/tex]

The y-intercept is the point (0,1.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=0.05x+1.50[/tex]

[tex]x=-30[/tex]

The x-intercept is the point (-30,0)

Plot the points and join to graph the line

see the attached figure

At gas station store

[tex]y=0.50x+0.50[/tex]

The y-intercept is the point (0,0.50)

The x-intercept is the value of x when the value of y is equal to zero

For y=0

[tex]0=0.50x+0.50[/tex]

[tex]x=-1[/tex]

The x-intercept is the point (-1,0)

Plot the points and join to graph the line

see the attached figure

Part c) Compare the lines in terms of slope and y-intercept

The slope or unit rate at the restaurant is less than the slope at the gas station store

[tex]\$0.05\ per\ refill < \$0.50\ per\ refill[/tex]

The initial value or y-intercept at the restaurant is greater than the initial value at the gas station store

[tex]\$1.50 > \$0.50[/tex]

Answer:

It is.

Step-by-step explanation:

1. Multiply 2x *x and 2x* -3 ;

2. Multiply 1*x and 1*(-3) ;

You should get: 2x^2 -6x +x -3 = 2x^2 -5x -3;

3. Add -6x +x;

In the end you get : 2x^2 -5x -3=2x^2 -5x -3

Answer:

Step-by-step explanation:

Use FOIL:

(a + b)(c + d) = ac + ad+ bc+ bd

(2x + 1)(x - 3)

= (2x)(x) + (2x)(-3) + (1)(x) + (1)(-3)

= 2x² - 6x + x - 3          combine like terms

= 2x² + (-6x + x) - 3

= 2x² - 5x - 3

Answer:

21(2x+1)

Step-by-step explanation:

42x+21=21(2x+1)

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

c = 7/5

Decimal Form:

c = 1.4

Mixed Number Form:

c = 1/2/5

Edit: I answered this on Jan 7th, 2021.

Answer:

The answer is 225 cm

Step-by-step explanation:

15×15=225

Answer:

5 or 3

Step-by-step explanation:

Answer:

It would be 11.333 minutes

Step-by-step explanation:

I solved this by setting up a cross multiplication.

60%/17 so then 40/x.

Then here cross multiplying. 60x=680. divide by 60 and x would = 11.33

The given expressions are solved and matched

To match the given expressions we need to solve the expressions with the given values of g and h and find their value.

Given that g = -7 and h = 3

[tex]\begin{array}{l}{\text { 1) } g+h=-7+3=-4} \\\\ {\text { 2) } g-h=-7-3=-10} \\\\ {\text { 3) } h-g=3+7=10} \\\\ {\text { 4) } g h=-7 \times 3=-21} \\\\ {\text { 5) } g+h^{2}=-7+3^{2}=-7+9=2} \\\\ {\text { 6) } g^{2}-h=(-7)^{2}-3=49-3=46}\end{array}[/tex]

The expressions are evaluated by substituting g = -7 and h = 3 into each one. After calculation, the matching values are found for each expression.

To evaluate each expression for g = -7 and h = 3, we'll substitute these values into the equations and perform the operations step by step.

Then, you can match each expression to its corresponding value that has been calculated:

Answer:

3:10

Step-by-step explanation:

1. Find the total number of students by doing

14 + 6= 20

2. Now make your ratio

6:20

3. To make it in simplest form, divide both sides by 2

6 divided by 2 is 3

20 divided by 2 is 10

4. Your answer is

3:10

Answer:

3:10

Step-by-step explanation:the answer would be 6:20, but that can be simplified by 2. 6 divided by 2 equals 3, 20 divided by 2 equals 10. 3:10

Let's begin by understanding your initial position, which is the school, located at coordinates (2, -1). The school is 2 blocks east and 1 block south of the center of town. This means that if you were to go to the center of town, you would travel 2 blocks west and 1 block north from the school. Now, to find out where your house is in relation to the school, we can reverse the steps you take to get from your house to the school. You’ve said you walk 5 blocks west and 2 blocks north to reach the school. Since you walk west to reach school, your house must be to the east of the school. Similarly, since you walk north to reach school, your house must be to the south of the school. To get back to your house from the school, then, you'd need to reverse both of these movements. To find the house’s position, we start with the school's position at (2, -1): 1. Since you walk 5 blocks west to get to school, let's go 5 blocks east from the school to get back to your house. Moving east means increasing the x-coordinate. So, starting from the x-coordinate of the school, which is 2, we add 5 to find the x-coordinate of your house. This gives us 2 + (-5) = -3. 2. Next, since you walk 2 blocks north to get to school, let's go 2 blocks south from the school to reach your house. Moving south means decreasing the y-coordinate. So, starting from the y-coordinate of the school, which is -1, we subtract 2 to find the y-coordinate of your house. This gives us -1 + 2 = 1. Therefore, the coordinates of your house are (-3, 1), which means your house is 3 blocks west and 1 block north of the center of town.

Final answer:

To locate the student's house on a grid, you need to reverse the movements made from the school to the house. By subtracting 5 blocks west and adding 2 blocks north from the school's coordinates (2, -1), the house's coordinates are determined to be (-3, 1).

Explanation:

The question involves a two-dimensional path on a grid, similar to the coordinates and movements given in the examples provided. To solve the problem, imagine that you start at the center of town, move 2 blocks east and 1 block south to reach the school at (2, -1), and then move from your house to the school by walking 5 blocks west and 2 blocks north.

To find your house's coordinates, you need to reverse the movements. Starting from the school's location at (2, -1), moving 5 blocks west means subtracting 5 from the x-coordinate, and moving 2 blocks north means adding 2 to the y-coordinate. Thus, the coordinates of your house would be (2 - 5, -1 + 2) which simplifies to (-3, 1).

Answer:

0.7

Step-by-step explanation:

7 millimiters equals 0.7 centimeters

Answer:

0.7 cm

Step-by-step explanation:

1 mm=0.1 cm

7 mm=0.1*7=0.7 cm

4 hours and 45 minutes

The number of miles increasing each hour is 16, 16 times 4 is 64, and to get to 76, you add an extra 3/4 of an hour, which is 45 minutes.

The distance between Antony and Lily will be 76 miles after 4.75 hours.

Speed is the unit rate in terms of distance travelled by an object and the time taken to travel the distance.

Speed is a scalar quantity as it only has magnitude and no direction.

Given that,

Antony and Lily started moving in opposite directions from the same point at the same time.

Speed of Antony = 12 mph

Speed of Lily = 4 mph

Let x be the distance traveled by Antony.

Then the distance traveled by Lily = 76 - x

Time will be the same, let it be t.

t = x /12 and t = (76 - x) / 4

x/12 = (76 - x) / 4

4x = 12 (76 - x)

4x + 12x = 912

16x = 912

x = 57

t = 57/12 = 4.75 hours

Hence the time is 4.75 hours.

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Answer:

The solution of the given system is given as  L = -12, d =16.5

Step-by-step explanation:

7 L+  5.5 d  = 6.75

L +  d  =  4.5

From (2), we get:

L +  d  =  4.5

⇒  d = 4.5 - L

Substitute the above value of d is the above first equation:

7 L+  5.5 d  = 6.75   ⇒  7 L+  5.5 (4.5 - L)  = 6.75

⇒ 7 L  +  24.75  - 5.5 L = 6.75

or, 1.5 L = 6.75 -   24.75  =  -18

or, L  = -18/1.5 =  12

or, L = -12

Now,  d = 4.5 - L  = 4.5  - (-12)  = 16.5

 or,  d = 16.5

Hence, the solution of the given system is given as  L = -12, d =16.5

Answer:

x=2

Step-by-step explanation:

2x+4=8

2x=8-4

2x=4

x=4/2

x=2

Answer:

  x = 2

Step-by-step explanation:

The equation shown is a perfectly good equation.

___

Look at what is being done to the variable. It is multiplied by 2, and 4 is added to the product.

To find the value of the variable, we reverse these operations, in reverse order. We undo the addition by adding the opposite of 4 (to both sides of the equation).

  2x +4 -4 = 8 -4

  2x = 4 . . . . . simplify

We undo the multiplication by multiplying by the inverse value, 1/2 (to both sides of the equation).

  (1/2)(2x) = (1/2)(4)

  x = 2 . . . . . simplify

_____

The rules of equations are pretty simple: whatever you do to one side, you must also do to the other side.

_____

Comment on this equation

You may notice that all of the numbers in this equation are divisible by 2. Another way to solve it is to start by dividing (both sides!) by 2:

  x + 2 = 4

Now, you have a 2nd-grade problem in addition facts: what added to 2 gives 4? Since you know your addition facts, you know the answer is 2. In algebra, we solve this by subtracting 2 (from both sides!).

  x = 2

Answer:

Part B is 271!!!

Step-by-step explanation:

a9=54

S9=9/2(6+54)=270

270+1

=271

By plugging in the ring number, 9, in the equation for the number of

cells in a ring, gives 54.

Response:

A. The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6

B. The number of cells in the ninth ring are 54 cells

Given;

The type of sequence = Arithmetic sequence

From the possible drawing of the question obtained from a similar question, we have;

Number of cells in the first ring that goes around the first cell = 6

Number of cells that go around the second ring = 12

A. The common difference of the arithmetic sequence = 12 - 6 = 6

We have that the nth term of an arithmetic sequence is; aₙ = a + (n - 1)·d

Taking the first ring as the first term, we have;

a = 6

Which gives;

The rule for the number of cells in the ring is, aₙ = 6 + (n - 1) × 6

Where;

n = The ring number

B. In the ninth ring, we have;

a₉ = 6 + (9 - 1) × 6 = 54

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The price of senior citizen ticket is $8 and that of children ticket is $14          

Let the price of ticket for senior citizen be ‘s’ and for child be ‘c’

Given that on the first day of ticket sales the school sold 3 senior citizen and 1 child ticket for a total of $38

So, an equation can formed which is as follows:

3s + c = 38  ---- eqn 1

On the Second day of ticket sales the school sold 3 senior citizen and 2 child ticket for a total of $52

3s + 2c = 52  ---- eqn 2

Multiply eqn 1 by 2

6s + 2c = 76 ---- eqn 3

Now subtract eqn 2 from eqn 2

6s + 2c = 76

(-) 3s + 2c = 52

---------------------

3s = 24

s = 8

Plug in s = 8 in eqn 2,

24 + 2c = 52

2c = 28

c = 14

Hence, the price of senior citizen ticket is $8 and that of children ticket is $14                      

To find (f o h)(4), substitute h(4) into f(x) and evaluate the expression.

To find (f o h)(4), we need to first find h(4) and then substitute that value into f(x). Let's start by finding h(4).

h(x) = - x + 3

h(4) = -4 + 3 = -1

Now, we substitute h(4) into f(x).

f(x) = -3x - 1

f(h(4)) = f(-1) = -3(-1) - 1 = 2

Therefore, (f o h)(4) = 2.

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1) There is 233.33% increase in the quantity.

2) There is 122.22% increase in the quantity.

3) There is 15% decrease in the quantity.

Step-by-step explanation:

1) Start: 3 End: 10

Change = End - Start

Change = [tex]10-3=7[/tex]

As the change is positive, therefore, it shows an increase

Percent increase = [tex]\frac{Change}{Start}*100[/tex]

Percent increase = [tex]\frac{7}{3}*100 = 233.33\%[/tex]

There is 233.33% increase in the quantity.

2) Start: 9 End: 20

Change = [tex]20-9=11[/tex]

As the change is positive, it shows an increase.

Percent increase = [tex]\frac{Change}{Start}*100[/tex]

Percent increase = [tex]\frac{11}{9}*100 = 122.22\%[/tex]

There is 122.22% increase in the quantity.

3) Start: 100 End: 85

Change = 85-100 = -15

Negative sign shows that it is a decrease in quantity.

Percent decrease = [tex]\frac{Change}{Start}*100[/tex]

Percent decrease = [tex]\frac{15}{100}*100 = 15\%[/tex]

There is 15% decrease in the quantity.

Keywords: Percentage, increase

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Answer:

1. 233.333%

2.122.2%

3.-12%

Step-by-step explanation: Hopes this helps you :)

The solution involves calculating the average speed for each driver (distance travelled divided by time). Deena's average speed was 65 mph and Kristen's was 55 mph, therefore, Deena drove at a faster rate.

To solve this question, we need to compute each driver's average speed. Average speed is calculated by dividing the total distance traveled by the total time taken to cover that distance. Mathematically, average speed = total distance/total time.

For Deena, we calculate her average speed by dividing her total distance traveled (585 miles) by the time she took to cover this distance (9 hours). Doing the division, we find Deena's average speed to be about 65 mph.

Similarly, for Kristen, we divide her total distance traveled (605 miles) by the time she took to cover this distance (11 hours). Kristen's average speed comes out to be approximately 55 mph.

By comparing the average speeds, we find Deena drove at a faster rate than Kristen.

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Answer:

378

Step-by-step explanation:

            She has 9 kinds of cards out of which she has to chose only 1.

The number of ways of doing this is 9 (she can pick any one of them).

            She has 7 kinds of cards out of which she has to chose only 1.

The number of ways of doing this is 7 (she can pick any one of them).

            She has 3 designs of first-class stamps out of which she has to chose only 1.

The number of ways of doing this is 3 (she can pick any one of them).

            She has to pick the color of pen and she has 2 to choose from.

The number of ways of doing this is 2 (she can choose any one of them).

She has to do Work 1 and Work 2 and Work 3 and Work 4.

∴By the fundamental counting principle, the total number of different ways in which the thank-you note can look is 9×7×3×2 = 378

Answer:

4$

Step-by-step explanation:

in 2000, ticket price is 75% of 8$ that is 6$. in 2005, money spent is increased by 50% of 8$ that is 12$ with same ticket price(6$). so non ticket price is increased from 2$(in 2000) to 6$(in 2005).

Answer:

4

Step-by-step explanation:

6(2005) - 2(2000) = 4

Easier to read then the one above, like its addition

Answer:

B

Step-by-step explanation:

Answer:

Option 4 - [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]

Step-by-step explanation:

To find : Which set of rational numbers is arranged from least to greatest?

Solution :

The set of rational numbers are

[tex]3,\ \frac{1}{5},\ -1.4,\ -\frac{1}{2}[/tex]

Writing all number in one form,

[tex]\frac{1}{5}=0.2[/tex]

[tex]-\frac{1}{2}=-0.5[/tex]

Now, -1.4<-0.5<0.2<3

From least to greatest the set of natural numbers are

[tex]-1.4<\ -\frac{1}{2}<\frac{1}{5}<\ 3[/tex]

So, [tex]-1.4,\ -\frac{1}{2},\ \frac{1}{5},\ 3[/tex]

Therefore, option 4 is correct.

Answer:

Option 4

Step-by-step explanation:

Answer:

$5175 per meal

Step-by-step explanation:

10% of $23.00 is $2.30, now you subtract $2.30 from $23.00 which makes $20.70. Now your getting four meals, so you split the money four ways which would be $20.70/4 which would equal $5.175 per meal

Answer:

y = x² + 2x + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here the vertex = (- 1, 4), thus

y = a(x + 1)² + 4

To find a substitute (0, 5) a point on the graph into the equation

5 = a(0 + 1)² + 4

5 = a + 4 ( subtract 4 from both sides )

a = 1, thus

y = (x + 1)² + 4 ← expand and simplify

  = x² + 2x + 1 + 4

  = x² + 2x + 5

The quadratic function to model the graph to the right is f(x) = x² + 2x + 5.

Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

[tex]\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}[/tex]

The graph of the quadratic function is given in the picture.

As we know,

(y - h)² = 4a(x - k)

(h, k) is the vertex of the parabola:

Or

y = a(x - h)² + k

From the graph:

Here the vertex = (- 1, 4)

y = a(x + 1)² + 4

Plug x = 0, and y = 5 to find the value of a

5 = a(0 + 1)² + 4

a = 1

y = (x + 1)² + 4

f(x) = x² + 2x + 5

Thus, the quadratic function to model the graph to the right is f(x) = x² + 2x + 5.

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