Need some help on this question please provide evidence on how you came up with the answer aswell.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

Let A represent the number of students reading Accountancy, S represent the number of students reading Sociology, and F represent the number of students reading French.

Let X be the number of students reading all three.

From the information given:

A ∩ S = 19

A + S - 27 = 120 - 53 + 19 = 86 (number of students reading Accountancy or Sociology but not French)

S - A - X = 27

S + F - X = 53

F - X = 19

A - X = 86 - 19 = 67

Total = A + S + F - (A ∩ S) - (A ∩ F) - (S ∩ F) + X = 120

Solving, we get X = 6, A = 73, S = 52, F = 25.

(1) 6 students read all three courses.

(II) 37 students read only one course.

(III) 77 students read exactly two courses.

(IV) 73 students read Accountancy irrespective of Sociology or French.

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Answer:

A) The amount of money deposited monthly

Step-by-step explanation:

y = 35x (slope) (amount deposited each month)+ 250 (y-intercept) (starting amount)

Answer: D

Step-by-step explanation:

Hope it helps

Daniella: Were you thinking of perpendicular lines?

Ori: It seems like you've got the basic idea, but your definition could be more precise.

Kaori: Yes! Well done. Here, have a cookie. You've earned it.

Answer:

1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Step-by-step explanation:

We need to find the factors of 18
which are; 1,18; 2,9; 3,6
So therefore we'd pick:
1 cm and 18 cm

2 cm and 9 cm

3 cm and 6 cm

Answer:

To solve this problem, we need to subtract the cost of the book and the total amount donated to charities from the total amount of cash Katye received for her birthday. Here are the steps:

Add up the value of the gifts Katye received:

Total value of gifts = (value of gift 1) + (value of gift 2) + ... + (value of gift 15)

Add up the value of the cash Katye received:

Total cash = $100

Subtract the cost of the book from the total cash:

Cash remaining after buying the book = $100 - $23

Determine the maximum number of $10 donations that Katye can make:

Maximum number of $10 donations = (cash remaining after buying the book) / $10

Multiply the maximum number of donations by $10 to get the total amount donated:

Total amount donated = (maximum number of $10 donations) x $10

Subtract the cost of the book and the total amount donated from the total cash:

Cash remaining = $100 - $23 - (total amount donated)

The final answer will be the cash remaining after these calculations

\(9 \times \frac{1}{4} = \frac{9}{4} \)✅

Option A⤵

\(5 \times \frac{1}{2} = \frac{1}{10} \\ ⇢  \frac{5}{2} ≠ \frac{1}{10} \)

Option B⤵

\(4 \times \frac{1}{3} = \frac{4}{12} \\ ⇢ \frac{4}{3} ≠ \frac{4}{12} \)

Option C⤵

\(9 \times \frac{1}{4} = \frac{9}{4} \\ ⇢ \frac{9}{4} = \frac{9}{4} \)

Option D⤵

\(8 \times \frac{1}{ 5} = \frac{9}{5} \\ ⇢ \frac{8}{5} ≠ \frac{9}{5} \)

Hence, option C is correct.

\(\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘\)

Answer:

Step-by-step explanation:

A

The correct option that indicates the quadrant that contains the translation of the shaded figure is the option B

B. III

A translation is a transformation in which the size, relative position of the points on the pre-image, are preserved but the location of the pre-image changes to obtain the image.

The shape of the shaded figure is an L-shape

The geometric figure in quadrant II and IV are a reflection of the shaded figure, across the y-axis and across the x-axis, respectively which is not a translation transformation.

The geometric figure in quadrant III can be obtained from the shaded figure by a translation 4 units to the left and 5 units downwards, which can be expressed as <-4, -5>, which is a translation transformation, therefore;

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Answer:

y= 8

Step-by-step explanation:

y= k/x

-8= k/4

k= -8×4= -32

y= k/x

y= -32/-4

y= 8

hope it helps!

Answer:

the answer is 8 if y= -8 when x is 4 amd

2(6k+2)=64

12k+4=64

12k=60

k=5

Answer:

a. $840

b. $1,260

Step-by-step explanation:

a. 2/5 x 2100 = 840

b. 2100 - 840 = 1,260

Answer:

-a+11

Step-by-step explanation:

hard to explain. but should be correct

Answer:

see below

Step-by-step explanation:

1.

a)

the relation is

\(y=5x+28\)

b)

\(f(x)=5x+28\)

we can use it because for every value of  x there is just one value, as the definition of function states

c)

\(f(22)=?\\\\f(22)=5(22)+28\\\\f(22)=110+28\\\\f(22)=138\)

and

\(f(?)=128\\\\5x+28=128\\\\5x=128-28\\\\5x=100\\\\x=20\)

2.

the points are

(-2,2) with

\(x_1=-2\\\\y_1=2\)

(1,-3) with

\(x_2=1\\\\y_2=-3\)

so the change in y is      \(y_2-y_1\)

\(-3-(2)=-5\)

and the change in x is   \(x_2-x_1\)

\(1-(-2)=3\)

so the slope is

\(\frac{\:Change\:in\:y}{Change\:in\:x} =\frac{-5}{3} =-\frac{5}{3}\)

and the general formula is

\(y=ax+b\)

so with a=-5/3

we plug in point 1

\(2=-\frac{5}{3} (-2)+b\\\\2=\frac{10}{3} +b\\\\6=10+3b\\\\6-10=3b\\\\-4=3b\\\\-\frac{4}{3}=b\)so the formula is

\(y=-\frac{5}{3}x-\frac{4}{3}\)

expressed as a function is

\(f(x)=-\frac{5}{3}x-\frac{4}{3}\)

3.

this is bassically all the work of number 2, so we have

(-2,-5)

\(x_1=-2\\\\y_1=-5\)

(4,31)

\(x_2=4\\\\y_2=31\)

so the slope will be

the change in y    \(y_2-y_1\)

\(31-(-5)=36\)

the change in x   \(x_2-x_1\)

\(4-(-2)=6\)

so the slope will be

\(\frac{\Delta\:y}{\Delta\:x}=\frac{36}{6} =6\)                                              (the triangle means change)

so the formula we have

\(y=mx+b\\\\y=6x+b\)

we plug some point, let's say 1

\(-5=6(-2)+b\\\\-5=-12+b\\\\-5+12=b\\\\7=b\)

so the formula is

\(y=6x+7\)

as a function is

\(f(x)=6x+7\)

so there you have it

Just as a note, for the next one, put more points :)

Answer:

200% of tickets handed out this year

Step-by-step explanation:

Let

Tickets handed out last year=x

Tickets handed out this year=2x

The number of tickets handed out this year was what percent of the number handed out last year

Last year was x%

Then, this year would be 200x%

200% tickets was handled out this year

Answer:

hi hello he they 1235

Step-by-step explanation:

hi hello he they 1235

Answer: 4032 cm^2.

Step-by-step explanation: The equation to find the surface area of a rectangular prism is SA=2(wl+hl+hw). Substitute the given values into the equation. SA=2(12x12+15x12+15x12). Simplify inside the parentheses. SA=2(144+180+180). SA=2(504). SA=1008 cm^2. This is the surface area for 1 box. Multiply the surface area by 4 to get the total surface area of 4 congruent boxes. 1008x4=4032 cm^2.

Sara calculated the unit rate as dollars per orange whereas Sara's friend Daniel calculated unit rate as oranges per dollar.

What is unit rate?

One of a given object constitutes a unit. The cost of only one of an item is its unit rate. With one as the denominator, this is written as a ratio. For instance, you would move 7 yards on average every second if you covered 70 yards in 10 seconds.

Sara said there was a ratio of 12 to 8, so the unit rate was $1.50 per orange, it means she is calculating the unit rate as dollar per oranges.

Whereas, his friend Daniel, he thought the ratio would be 8:12, so the unit rate would be 8/12 oranges per dollar.

In this way both the unit rates are correct.

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Ahem, here goes, my attempt at a minute-long rap in praise of the parallelogram:

Yo, listen up, the parallelogram is where it's at,

A shape so brilliant, the angles are sat.

Parallel sides that never converge,

Internal angles that never diverge.

Each side an equal length,

A geometry prodigy's dream length.

The diagonals intersect, another line through the middle they meet,

Creating symmetry so neat.

A rectangle it could be,

But it's oblong, not square, can't you see?

With depth and width in perfect balance we see,

A two-dimensional form of complexity.

While the square is simple, the parallelogram is hip,

A mathematical masterpiece, skip, skip, skip!

four right angles keep the shape so tight,

Parallel lines dominate left and right.

Rotated or reflected without a care,

Its structural integrity beyond compare.

triangles form at each corner you'll note,

Acute or obtuse, depends on the protractor's groove.

A versatile shape with reason and purpose galore,

The parallelogram, simply, carries the floor.

From geometry to art, its angles they intrigue,

As a basis for patterns, its potential we can truly plug.

A forgotten form that deserves more acclaim,

Put the parallelogram on geometry's game!

This shape so underrated, rarely appreciated it seems,

But with logic and virtue, strong foundations it gleams.

The parallelogram, the parallelogram, Hooray!

This is why the parallelogram is the best shape, I say!

Answer:

a). m∠AED = 70°

b). x = 10°

Step-by-step explanation:

a). Quadrilateral ABDE is a cyclic quadrilateral.

Therefore, by the theorem of cyclic quadrilateral,

Sum of either pair of opposite angle is 180°

m(∠AED) + m(∠ABD) = 180°

m(∠AED) = 180° - 110°

m(∠AED) = 70°

Since, ∠AED ≅ ∠EAD

Therefore, m∠AED = m∠EAD = 70°

b). By triangle sum theorem in ΔABD,

m∠ABD + m∠BDA + m∠DAB = 180°

110° + 40° + m∠DAB = 180°

m∠DAB = 180° - 150°

m∠DAB = 30°

m∠BAE = m∠EAD + m∠BAD

              = 70° + 30° = 100°

By angle sum theorem in ΔACE,

m∠EAC + m∠AEC + m∠ACE = 180°

100° + 70° + x° = 180°

x = 180° - 170°

x = 10°

The greatest common factor, GCF, of 8y, -12x, and 4xy is 4

From the question, we are to determine the greatest common factor of the given expressions.

The given expressions are 8y, -12x, and 4xy

To determine the greatest common factor, we will express each of the expressions as a product of their factors.

8y = 2 × 2 × 2 × y

-12x = 2 × 2 × 3 × -x

4xy = 2 × 2 × x × y

From above, we can observe that the greatest common factor is

2 × 2

= 4

Hence, the greatest common factor is 4

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Answer:

Yes

Step-by-step explanation:

8/6 simplified is 4/3

20/15 simplified is 4/3

Choose me as smartest

Answer:

85

Step-by-step explanation:

Average calculator

Answer:

Solving gives us the result, x = 2, y = -1

Step-by-step explanation:

The system of equations is,

y = 2x-5

y=-2x+3

equating the two equations, we get,

(since y = y)

\(2x-5 = -2x + 3\\4x -5 = 3\\4x = 3+5\\4x=8\\x=8/4\\x=2\)

and then since y = 2x-5

\(y=2(2)-5\\y=-1\)

so, x =2, y = -1

Answer:

Step-by-step explanation:

The first step is to calculate the volume of the cylinder:

Volume = π x (radius)^2 x height

Volume = π x (16.2 cm)^2 x 710 cm

Volume ≈ 1.468 x 10^6 cm^3

Next, we can calculate the mass of the metal required to make the pole:

Mass = Density x Volume

Mass = 6.6 g/cm^3 x 1.468 x 10^6 cm^3

Mass ≈ 9.6948 x 10^6 g or 9694.8 kg

Finally, we can calculate the cost of the metal required:

Cost = Price per unit mass x Mass

Cost = $0.78/kg x 9694.8 kg

Cost ≈ $7,561.17

Therefore, the cost of the utility pole would be approximately $7,561.17, rounded to the nearest cent.

Answer:

Step-by-step explanation:

Given

Solve for x

Answer:

2

Step-by-step explanation:

first answer deleted by moderator... even when it was correct... i did more explaining on that one, but they kindly deleted my answer and didn't even show my full answer after they had deleted it like some other moderators do which i always appreciate.

∠LMN is an obtuse angle.

==========================================

Explanation

Let's go through the answer choices to see which are true, and which are false.

Answer:c

Step-by-step explanation:

Just flip it backwards which one looks the same