(c) A total of 1800 students attend St. John's College. The ratio
of teachers to students is 1:25.
(i) How many teachers are there at the college.
Three-quarters of the students own laptop computers.
(ii) How many students DO NOT own laptop computers?

In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.

Given that,

In the picture there are 2 problems.

We have to find the difference and similarities of question in the picture.

The similarities are they 2 are word problems.

Another similarity is they two have to find 2 question.

1. How much money for 10 days and How many days to collect the money $1.05?

2.How much gallon of water need for 50 minutes and How much time take to fill the pool?

Another similarity is they two have to justified the answer in a mathematical model.

Now,

The difference is,

First question has given sisters and money problem where as the second has given pool and gallon water problem.

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The inverse of the given function, y = 16x² + 1 is: B. y = ±√(x - 1)/16

In Mathematics, an inverse function can be defined as a type of function that is obtained by reversing (undoing) the operation of a given function (f(x)).

Generally speaking, a given function (f(x)) and its inverse function has the following property f⁻¹(f(x)) = x.

In order to determine the inverse of the given function, we would interchange input value (x) and the output value (y) as follows:

y = 16x² + 1

x = 16y² + 1

Subtracting 1 from both sides, we have:

16y² + 1 - 1 = x - 1

16y² = x - 1

Dividing both sides by 16, we have:

y² = (x - 1)/16

Taking the square root of both sides, we have:

y = ±√(x - 1)/16

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Answer:

12.5

Step-by-step explanation:

-3\4÷[-0.06]

convert -0.06to fraction

-3\50

then divide

-3\4÷-3\50

sign changes

-3\4 ÷ 50\3

=50\4

=12.5

Answer: -5x >[-3x,4x,1.5x] 10>[11] 6xy>[-7.85xy, -98xy, 155xy]

Step-by-step explanation:

Answer:

Step-by-step explanation:

Expand · Evaluate Fractions · Linear Equations · Quadratic Equations ... 7 + 4 s = 10 ( 6 - 9 s ). 7+4s=10(6−9s) ... 7 + 4 s = 10 ( 6 - 9 s ).

Answer:

-10b × 90

Step-by-step explanation:

-10 * b =-10b

10 *9=90

Your welcome :)

The total number of t-shirts sold by Tom equals to 17 t-shirt.

Basically, a profit refers to the difference between the revenue that an entity has received from its outputs and the opportunity costs of its inputs.

We need to note that he made a total profit of $125. From here, we will proceed to use that data to solve other sections.

From the total profit of $125, he also made a profit of $40 from selling hats. That means that the T-shirt sales alone gives him a profit of $85 ($125 - $40).

Total quantity of t-shirt sold is computed as follows:

= Total profit from t-shirt / Profit per shirt

= $85 / $5

= 17 t-shirt

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Answer:

24%

Step-by-step explanation:

[tex]16.12 - 13 = 3.12\\3.12 * 100 = 312 \\312 / 13 = 24[/tex]

24% more chocolate

1.00 + 0.24 = 1.24

13 * 1.24 = 16.12

The simplified expression for the rate of change of f'(x) is x²(2 ln(2x) - 1)/4 + c.

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

It is given that:

f'(x) = xIn(2x)

To find the simplified expression for the rate of change of f'(x) integrate the function:

∫f'(x) dx = ∫xIn(2x) dx

Using integration by parts:

∫uv dx = uv - ∫u'v

After solving:

∫xIn(2x) dx = x²(2 ln(2x) - 1)/4 + c

Thus, the simplified expression for the rate of change of f'(x) is x²(2 ln(2x) - 1)/4 + c.

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Answer: B

Step-by-step explanation:

[tex](f+g)(x)=f(x)+g(x)\\\\=\frac{x}{2}-3+4x^2 +x-4\\\\=4x^2 +\frac{3x}{2}-7[/tex]

The total number of outcomes is 24.

In probability theory, an outcome is a possible result of an experiment or trial.

When a number cube is rolled there are 6 distinct outcomes

{1,2,3,4,5,6} = 6

Again when a spinner is spun there are 4 possible outcomes

The total number of outcomes = 6 × 4 = 24

Hence there are 24 distinct outcomes.

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Ignore the angles of triangle DEF. They complicate things when they don't need to be like that.

The distance from E to F is 3 units since there are 3 spaces between the points. Or you could subtract the x coordinates of each point, so 7-4 = 3.

So far we have one pair of congruent sides

EF = BC = 3

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

Let's use the distance formula to find the distance from D to E

[tex]D = (x_1,y_1) = (3,-1) \text{ and } E = (x_2, y_2) = (7,-4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-7)^2 + (-1-(-4))^2}\\\\d = \sqrt{(3-7)^2 + (-1+4)^2}\\\\d = \sqrt{(-4)^2 + (3)^2}\\\\d = \sqrt{16 + 9}\\\\d = \sqrt{25}\\\\d = 5\\\\[/tex]

Segment DE is exactly 5 units long.

We have another pair of congruent sides between the two triangles

AB = DE = 5

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

We'll use the distance formula one last time to find the length of side FD.

[tex]D = (x_1,y_1) = (3,-1) \text{ and } F = (x_2, y_2) = (4,-4)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(3-4)^2 + (-1-(-4))^2}\\\\d = \sqrt{(3-4)^2 + (-1+4)^2}\\\\d = \sqrt{(-1)^2 + (3)^2}\\\\d = \sqrt{1 + 9}\\\\d = \sqrt{10}\\\\\sqrt{10} \approx 3.162278 \approx 3.2\\\\[/tex]

Side FD is approximately 3.2 units long, which matches with AC = 3.2

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

Here are the three paired sides that are congruent to one another

Since we have three pairs of congruent sides, we can use the SSS (side side side) congruence theorem to prove the triangles are congruent.

Congruent triangles are identical copies or clones of one another. One triangle is just a reflected and translated version of the other.

This means they have the same corresponding angle measures, and the same corresponding side lengths.

Answer:

Ramu's sister's Age= 28

ramus age=×

28=5×+3

5×=28-3

=25

×=25/5

×=5

so the age of Ramu is 5 years old.

Answer:

25 because 5×5= 25 and 25+3=28 so ramu's age is 25

Answer:

Yes, the relation {(3,2), (4,1), (5,9), (6,12), (7,12)}is a function.

Step-by-step explanation:

Answer:

It's a triangle just like you, except you're acute one.

Step-by-step explanation:

Answer:

7, -5

Step-by-step explanation:

-5, -7   after a rotation of 270 degrees lands in quadrant 2 left y positive where x negative. while 90 degree clockwise is equal to 270 degree counterclockwise  = 7 ,-5      What are the coordinates of the image after a rotation of 90 clockwise?

When the point is rotated through 90° clockwise about the origin, the point M (h, k) takes the image M’ (k, -h). Therefore, the new position of point M (-2, 3) will become M’ (3, 2).

How do you calculate a 90 degree rotation?

The rule for a rotation by 90° about the origin is (x,y)→(−y,x) .

What is the image of point 3/5 If the rotation is?

Answer: The image point will be (-3, -5) .

How do you find the coordinates of the image of a point after a 270 degree rotation?

Answer – To find the coordinates of point (x,y) after a 270° counterclockwise rotation about the origin, multiply the x-coordinate by -1 and then interchange the x- and y-coordinates.

How do you find the rotation point?

The x coordinate of the rotated point is rcos(θ), and the y coordinate is rsin(θ). If you plug in 5 and 66.87 for r and θ, you find that the rotated point (x1,y1) = (1.964, 4.598).

What is 270 degrees rotated?

270 Degree Rotation When rotating a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means, we switch x and y and make x negative.

What is 90 degrees counterclockwise?

90 Degree Rotation When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

How do you rotate a point 90 degrees clockwise?

Answer: To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x).

What is a 90 degree rotation clockwise?

Answer: To rotate the figure 90 degrees clockwise about a point, every point(x,y) will rotate to (y, -x). Let’s understand the rotation of 90 degrees clockwise about a point visually.

How do you calculate a 90 degree rotation? The general rule for rotation of an object 90 degrees is (x, y) ——–> (-y, x). You can use this rule to rotate a pre-image by taking the points of each vertex, translating them according to the rule, and drawing the image.

When to rotate point c 180 or counterclockwise?

And this process could be repeated if you wanted to rotation Point C 180 degrees or 270 degrees counterclockwise: Point C after a 180-degree rotation. Point C after a 270-degree rotation. This example should help you to visually understand the concept of counterclockwise geometry rotations.

How to calculate the coordinate point of rotation?

The following formula can be used to calculate the coordinate point in the x-y plane that has rotated by some angle (θ) about the x-axis. Note these formulas are for clockwise rotation. X=xcos (θ)+ysin (θ) Y=−xsin (θ)+ycos (θ) Where X is the new X coordinate. Y is the new Y coordinate. and θ is the angle of rotation.

What is the definition of rotation in geometry?

Rotation Geometry Definition: A rotation is a change in orientation based on the following possible rotations: 90 degrees clockwise rotation 90 degrees

Answer:

The Answer is 1 1/8

Step-by-step explanation:

When Stanley ate 3/8 of a pizza and his brother ate 3/4 of a pizza, the amount eaten in all is 1 1/8 of the pizza.

A fraction simply means a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, Stanley ate 3/8 of a pizza and his brother ate 3/4 of a pizza.

Therefore, the amount eaten by both of them will be:

= 3/8 + 3/4

= 3/8 + 6/8

= 9/8

= 1 1/8.

The amount is 1 1/8.

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The two numbers are 10 and 6.

Now, let's take the larger number to be x and the smaller number to be y.

According to the question,

We have the following details:

The difference between two numbers = 4

So, we have the following expression:

(x-y) = 4 .... (1)

The sum of the smaller number and three times the larger number = 36

So, we have the following expression:

(3x+y) = 36 ....(2)

Now, we will use the elimination method to solve these equations. So, we will add equation 1 and 2.

(Please note that the left hand side is added to the left hand side and the right hand side numbers are added to the right hand side numbers.)

(x-y+3x+y) = (4+36)

4x = 40

x = 40/4 (4 is in multiplication on the left hand side. So, it is in the division on the right hand side.)

x = 10

Now, putting the value of x in equation 1,

(x-y) = 4 .... (1)

(10-y) = 4

-y = 4-10

-y = -6

y = 6

Hence, the larger number is 10 and the smaller number is 6.

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Answer:

807

Step-by-step explanation:

because u multipy 3x19x14+18/2 and u get 807

Answer:

807

Step-by-step explanation:

3*19*12=798

18/2 = 9

798 + 9 = 807

Answer:

15 to 20 minutes

Step-by-step explanation:

Answer:

10-15

Step-by-step explanation:

i took the test

Answer:

20%

Step-by-step explanation:

10% of 55 is 5.5 so 20% is 11 which is how much extra he paid

The equation of the line in slope intercept form with slope 1/3 and passes through ( - 6, 0) is y = 1/3x + 2.

In mathematics, the slope or gradient of a line is a number that indicates the line's steepness as well as its X and Y directions. The letter "m" stands for slope. The ratio of the "vertical change" to the "horizontal change" between any two separate points on a line is used to compute the slope.

The equation of the line in point-slope form is expressed as:

y - y₁ = m( x - x₁ )

where m is the slope.

So, m = 1/3

( x₁, y₁ ) is the point on the line = ( - 6, 0)

Substituting the values,

y - 0 = 1/3( x + 6 )

y = 1/3( x + 6 )

y = 1/3x + 6/3

y = 1/3x + 2

Hence, the equation in slope-intercept form of the line is y = 1/3x  + 2.

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Combine X. which is 2x, -5x, x.

we combine -2x and -5x and gives me -3x.

2x -10 -5x -1 +x

now i combine the last x, which is -3x and x and gives us -2x.

-3x -10 -1 +x

now we just combine the rest of the numbers. -10 and -1 and gives me -11.

-2x -10 -1

we have now combine all the numbers and there's nothing else to combine. we're done combining.  :))

ANSWER:

-2x-11

Answer:

Step-by-step explanation:

Problem 12:

r(x) = 2

Since x will always be 2, it will always be a straight line.

Problem 14:

(I'm assuming the square is on the x)

g(x) = x^2-3

First, start on the y-intercept, and go down 3 as the starting value is -3. You can then substitute a number to find the next point.

For example, if you want to find if x = 1, what y will be:

1^2-3

1-3

-2

You can then do this for the rest of the points to the point.

Answer:

Below in bold.

Step-by-step explanation:

The relation between the height of the ladder and distance from the ground is given by Pythagoras Theorem:

h^2 = 13^2 - L^2

h = (169 - L^2)^1/2

Finding the derivative:

dh/dL = 1/2(169 - L^2)^-1/2 * -2L

         = -L / (169 -L^2)^1/2

dL/dt = 6

So, dh/dt = dh/dL * dL/dt

               = -6 * L/ (169 - L^2)^1/2

               = -6 * 12 / (169 - 12^2)^1/2

                = -72/5 ft /second

                 = -14.4 ft/second.

It's negative because the distance from the ground is decreasing.

Given,

Total no. of bushels = 240

On average, no. of bushels sold by the farmer each day = [tex]15\frac{3}{5}[/tex] =[tex]\frac{78}{5}[/tex]

Therefore,

total  no. of bushels sold by the farmer at the end of 6th day

= [tex]15\frac{3}{5}[/tex] x 6 = [tex]\frac{78}{5}[/tex] x 6 = 78 x 1.2  =  93.6

So, no. of bushels left = 240 - 93.6 = 146.4

Hence, the change in bushels is of 93.6 after 6 days of sale.

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Answer: Option D

Step-by-step explanation:

Step-by-step explanation:

As we know domain of a function is represented by x values on the graph and y values represents the range of the function.

From the given table domain will be the set of all real numbers.

Range of the same function will be y > 4

Option D is the answer. there you go o(*￣︶￣*)o it was hard to but now its easy

The Compound Interest of Principle 2000 will become 2420 within 2 years when the rate of interest is 21%

Compound interest = P(1 + R ÷ 100) to the power of n,

where P = Principle

           R = Rate of Interest

           n = no. of years

According to the given question,

Principle(P) =Rs2000

Rate of interest (R) =?

no. of years(n) = 2 years

given CI (Compound Interest) = Rs2420

CI = 2000(1 + R ÷ 100)² = 2420

    = 20(100 +R) = 2420

    = 100 + R = 2420 ÷ 20

    = 100 + R = 121

    = R = 121 - 100

    = R = 21%

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The translation of y = |x| left 9 units and up 11 units is y = |x+9|+11 .

The process of translating an existing graph or equation into a new graph is known as graph translation.

We know that for translation we have to change the x-coordinate and the y-coordinate by the amount that is stated in the translation.

Therefore from the graph we can see that the graph of y =|x| is represented by the blue line and the graph of  translation y = |x+9|+11 is represented by the red line.

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Christopher would be able to purchase 3 oranges but if the grocery store only sells them in bags of 4 then he would not have enough money to purchase any.

To find our answer we do 4 divided by 1.29 and that is how many he can afford which is 3.1

pls give brainliest

Answer:

He bought 3 oranges

Step-by-step explanation

Divided $1.72 by 4 which gives $0.43

So each orange cost $0.43

0.43 times 3 equals $1.29

Answer:

1. (3 + 7) ÷ 2 = 5

2. (4 + 9) x 3 = 39

3. 10 ÷ (4 x 5) = 1/2

4.(1 + 2) ÷ 20 = 3/20