angles a and b are vertical angles. If mA = (5x – 24)° and m B = (3x + 24),
then find the value of x.

(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:

Hope this helps!

Step-by-step explanation:

1.  9.38

2. 9.80

3. 11

4. 9.85

5.  15.23

6.  15

7. 9.95

8. 27

9. 26.96

10. 14.14

Step-by-step explanation:

on the picture

if it's helpful ❤❤❤❤❤

THANK YOU.

Answer: 156.38 m

Step-by-step explanation:

Using the arc length formula, the answer is \(2\pi(8^2) \cdot \frac{140}{360} \approx 156.38\)

The GCD of 5! and 7! is 2^3 * 3^1 * 5^1 = 120.

the greatest common divisor of 5! and 7! is 120.

To find the greatest common divisor (GCD) of 5! and 7!, we need to factorize both numbers and identify the common factors.

First, let's calculate the values of 5! and 7!:

5! = 5 * 4 * 3 * 2 * 1 = 120

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1 = 5,040

Now, let's factorize both numbers:

Factorizing 120:

120 = 2^3 * 3 * 5

Factorizing 5,040:

5,040 = 2^4 * 3^2 * 5 * 7

To find the GCD, we need to consider the common factors raised to the lowest power. In this case, the common factors are 2, 3, and 5. The lowest power for 2 is 3 (from 120), the lowest power for 3 is 1 (from 120), and the lowest power for 5 is 1 (from both numbers).

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Answer:

Simultaneous question

Step-by-step explanation:

let first nomber be x and the second be y

make an equation

x+y=-17

x-y=41

x+x= -17+41

2x=23

x-y=41

11.5-y=41

-y=41-11.5

-y = 29.5

Therefore the numbers are 11.5 and -29.5

Answer:

(h+k)(2) = 5

(h-k)(3) = 9

3h(2) + 2k(3) = 17

Step-by-step explanation:

The given expression in simplified radical form is  2x⁴ y³  \(\sqrt[4]{2y^3}\)

Define Radicals.

The term "radical" is used to represent the square root or nth roots.

Expression with a square root is referred to as a radical expression.

Radicand: The value or phrase contained within the radical symbol.

Given expression is,

\(\sqrt[4]{32x^1^6 y^1^5}\)

Rewrite this expression,

we know, 2⁵ = 32

\(\sqrt[4]{(2x^4.y^3)^4 .y^3 .2}\)

You see this expression is equal to given expression i.e, \(\sqrt[4]{32x^1^6 y^1^5}\)

Take out the term from under the radical,

2x⁴ y³  \(\sqrt[4]{2y^3}\)

Hence, the given expression in simplified radical form is  2x⁴ y³  \(\sqrt[4]{2y^3}\)

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The equation of the parabola as described in the task content is; f (x) = -3 (x - 5)² + 9.

It follows from the task content that the equation of the parabola which has the same shape as f(x)=-3 x² but with vertex (5,9) in the form f (x) = a (x-h)² + k be determined.

Recall that the vertex of a quadratic equations of the given form is defined by the coordinates (h, k).

On this note, the required equation of the parabola by substitution of h and k is;

f (x) = -3 (x - 5)² + 9.

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The range of the data is the difference between the highest and lowest values, which is 8 inches. Adding another plant with a height of 14 inches would not change the range, so the range would remain 8 inches.

Data is a collection of facts, figures, or information that can be processed and used to draw conclusions or make decisions. It can be stored in a variety of formats, including numerical, text, images, audio, and video. Data can be collected from a variety of sources, such as surveys, observations, experiments, or transactions. It can be used to inform decisions in areas such as business, health care, education, and research. Data can be analyzed to gain insight, develop strategies, identify trends, and make predictions. Data is a valuable resource and is increasingly important in today's digital age.

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Answer:

4) choice 1) 14.7 cm

5) choice 2) 14.8 cm

Step-by-step explanation:

4) 10^2 + 10^2 + 4^2 = 216

sq rt 216 = 14.7

5) 14^2 + 3^2 + 4^2 = 221

sq rt 221 = 14.86

Answer:

A-

First we do 72/88 to get the percentage. When the math is done you get 81.81% so that means that Will got an 81.81% on the test.

B-

Now we will do 81/88 to get the percentage because Cheng got 81 points. When that math is done we see that Cheng got a 92.04% on the test.

C-

To get Rob's percentage we need to do 75/88 because Rob got 75 points. When we calculate that we recieve 85.23% meaning he got that on the test.

D-

Now to figure out who got the highest percentage and who got the lowest is simple. The max points doesn't change so it varies on who got the highest and lowest points. We can see that Cheng received the highest with 81/88 (92.04%) and Penny received the lowest with 68/88 (77.27%).

(a) Will's per cent correct on the test is 81.8%.

(b) Cheng's per cent correct on the test is 92.0%.

(c) Rob's per cent correct on the test is 85.2%.

(d) The highest percentage is 98.9% for Minowa and the lowest percentage is 77.3% for Penny.

Given a table which shows the test scores of 5 students.

Total score possible = 88

(a) The percentage score of Will is:

\(\text{W}=\frac{72}{88} \times100\)

    \(%\)\(=81.8%\)

(b) The percentage score of Cheng is:

\(\text{C}=\frac{81}{88} \times100\)

   \(=92.0%\)

(c) The percentage score of Rob is:

\(\text{W}=\frac{75}{88} \times100\)

    \(=85.2%\)

(d) Now, find the percentage score for Penny and Minowa.

For Penny,

\(\text{P}=\frac{68}{88} \times100\)

   \(=77.3%\)

For Minowa,

\(\text{M}=\frac{87}{88} \times100\)

   \(=98.9%\)

So, the highest percentage is 98.9% for Minowa.

The lowest percentage is 77.3% for Penny.

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Answer:

x = 16

m<Y = 34°

Step-by-step explanation:

∆XYZ is an isosceles ∆. An isosceles ∆ has two equal sides, as well as the bases of the isosceles triangle are congruent. In this case, therefore:

<X = <Z

(6x - 23)° = (4x + 9)

Solve for x

6x - 23 = 4x + 9

Collect like terms

6x - 4x = 23 + 9

2x = 32

Divide both sides by 2

x = 16

m<Y = 180° - (m<X + m<Z) (sum of ∆)

m<Y = 180 - ((6x - 23) + (4x + 9))

Plug in the value of x

m<Y = 180 - ((6(16) - 23) + (4(16) + 9))

m<Y = 180 - (73 + 73)

m<Y = 34°

Answer:

8:26 AM

Step-by-step explanation:

9:00 a.m. to 10:00 a.m constitute one hour

1 hour = 60 minutes

as we have to distribute time within 1 hour only, it is better to take it in minutes as we have to divide it into three parts.

Given break duration = 8 minutes

let time before break and after break be x minutes.

Thus,

Time before break + interval duration+Time after break = 60 minutes

x + 8 + x = 60

=> 2x = 60-8 = 52

=> x = 52/2 = 26

Thus, first lesson should end at 26 minutes

so time will be 8 Am + 26 minutes = 8:26 AM

Thus, break will start at 8:26 AM.

Answer:

Step-by-step explanation:

plug g(x) into fx (x+5)(x+5)-1

Answer:

There is no table, but here's a formula;

48 miles multiplied by x amount of gallons

Step-by-step explanation:

Answer:

if sam paid 500$ that would mean he would be a gym member for 20 months.

Answer: 11x-75y

Step-by-step explanation: Hope this is what you're looking for.

Answer:

11x -75y

Step-by-step explanation:

To solve this problem you first have to distribute and simpify.

In this problem you have a -(61x+27y), the parentnesses and the - sign in front tells us you need to distribute the parentnessess. Doing this gives us an answer of -61x -27y.

The next step is to combine like terms and simiplfy.

\((72x-61x)+(-48y-27y)\\\\11x -75y\)

So know we have our answer.

Answer:

2/9

Step-by-step explanation:

Answer:

2/9

Step-by-step explanation:

A rectangular tank measuring 40 cm long, 30 cm wide and 35 cm high was filled with water to a hight of 15 cm. 4800 cm3 of water were poured into water ,The new height of the water in the tank is approximately 19.83 cm.

To find the new height of water in the tank after pouring in 4800 cm³ of water, we can use the concept of ratios.

First, let's calculate the initial volume of water in the tank before pouring in the additional water. The initial volume can be calculated as the product of the length, width, and initial height:

Initial volume = 40 cm * 30 cm * 15 cm = 18,000 cm³

Next, we add the volume of the water poured in:

Total volume = Initial volume + Volume poured in = 18,000 cm³ + 4800 cm³ = 23,800 cm³

To find the new height, we divide the total volume by the base area of the tank (length * width):

New height = Total volume / (Length * Width) = 23,800 cm³ / (40 cm * 30 cm) = 19.83 cm (rounded to two decimal places)

As a result, the tank's new water level is roughly 19.83 centimetres high.

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9514 1404 393

Answer:

Step-by-step explanation:

1. The negative leading coefficient (-2) tells you the parabola opens downward.

__

2. The fact that the parabola opens downward tells you the vertex is a maximum.

__

3. For quadratic ax^2 +bx +c, the axis of symmetry is x = -b/(2a). For this parabola, that is x = -4/(2(-1)) = 2. The y-value of the vertex is f(2) = -2^2+4(2)-3 = -4+8-3 = 1. The y-intercept is the constant, c = -3.

Answer:

gay

Step-by-step explanation:

i mean it starts with a g doesnt it?

Answer:

google?

Step-by-step explanation:

There are can be can be many things found on the pages starting with the letter g.

Answer:

The measure of angle ADE is equal to 62 degrees.

Step-by-step explanation:

Firstly, I want to remind you that the sum of the interior angles in a quadrilateral are 360 degrees. Now, we are given that CD || BA and CB || DA, which means that this quadrilateral is a parallelogram. This is important because we know that the opposite angles in a parallelogram are congruent, which means that angle C is congruent to angle A and angle B is congruent to angle D. Therefore, the measure of angle A is also 73 degrees. Next, we can represent angle D as x, which means that angle B is equal to x, so the sum of angle D and B is 2x. Finally, we can set up an equation where we solve for the value of x, and then subtract it with 45 degrees:

2x + 2(73) = 360

2x + 146 = 360

2x = 214

x = 107 = B = D

Now, we can subtract the measure of angle D with 45 degrees to get the measure of angle ADE:

ADE = 107 - 45

ADE = 62

Answer:

Step-by-step explanation:

Let T represent table and B represent bench. The garden table costs $62 less than the bench. T = B - 62. plug T = B - 62 into T + B = 788. B - 61 + B = 788. This gives us 425. B = 425.

Answer:

The probability of not picking a pink jelly bean: 11/15    

Step-by-step explanation:

As we know that the maximum value of the probability of an event would always be 1.

Given that the probability of picking a pink jelly bean out of a bag is 4/15.

Thus, the probability of not picking a pink jelly bean can be calculated by subtracting 4/15 from the maximum probability '1'.

i.e.

Probability of not picking a pink jelly bean = max probability - 4/15

                                                                       = 1 - 4/15

                                                                      = 11/15

Therefore, the probability of not picking a pink jelly bean: 11/15                                                                    

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

24 games.

Step-by-step explanation:

To do this, half of 6 is 3.

So, we would simply just split 48 in half by dividing it by 2.

48 / 2 = 24.

The hockey game will play 24 games in 3 weeks.

Answer: B. 4

Step-by-step explanation: The interquartile range is just the distance in between the upper and lower quartiles. Therefore, to find the interquartile range, the equation in this case is 7 - 3, which equals 4.