For every 1 girl in Mr Hegarty's class there are 4 boys. What is the ratio of boys to girls in the class? Give your answer in its simplest form.

Answer:

x = 26, y = 9

Step-by-step explanation:

Let one number be x, and the other be y. Set the equations:

x + y = 35

x - y = 17

First, isolate the x in the first equation. Subtract y from both sides

x + y (-y) = 35 (-y)

x = 35 - y

Plug in 35 - y for x in the second equation

(35 - y) - y = 17

35 - 2y = 17

Isolate the variable. Note the equal sign, what you do to one side you do to the other side. Do the opposite of PEMDAS. First, subtract 35 from both sides

35 (-35) - 2y = 17 (-35)

-2y = -18

Isolate the variable (y). Divide -2 from both sides

(-2y)/-2 = (-18)/-2

y = -18/-2

y = 9

Plug in 9 for y in one of the equations.

x + y = 35

x + 9 = 35

Isolate the variable (x). Subtract 9 from both sides

x + 9 (-9) = 35 (-9)

x = 35 - 9

x = 26

~

Answer:

Alright well Convert fraction to an decimal, then multiply by 100

0.02714285% Hope this helps have a nice day :)

Step-by-step explanation:

Answer:

-21

Step-by-step explanation:

3(-7)

3*7 =21

A positive times a negative is a negative

-21

Answer:

3x-7=21 ( i think )

Step-by-step explanation:

when you have a parenthesis beside a number you always multiply. A negative times a positive is a negative,

Answer:

The probability that both spinners will land on 2 is A) 1/12.

Step-by-step explanation:

To get this answer you must:

-First, take the total number of outcomes and set that as you denominator, which would be 3.

-Since, your looking for the probability of two, and there is only one two you would put one as your numerator. By now you should have a fraction of: 1/3.

-Next, do the same exact thing for the next graph. Take the total number of outcomes for the graph which is 4, and set that as your denominator.

-Then, set one as your numerator since there is only one two in the other graph. You should now have a second fraction of: 1/4.

-Lastly, multiply both of the fractions. Multiply both of the numerator together and you should get one. Then, multiply both of the numbers which would result in you getting a  number of 12.

1/3(1/4) = 1/12.

Answer:

16,383 or C

Step-by-step explanation:

Answer:

Option 3rd is correct.

Step-by-step explanation:

Given: 3 + 12 + 48 + 192 + .......

We have to find : Sum of first seven term of the given Geometric series.

First term , a = 3

Common ratio , r = [tex]\frac{12}{3}=4[/tex]

Sum of the n term of series,  [tex]S_n=\frac{a(1-r^n)}{1-r}[/tex]

So,

[tex]S_7=\frac{3(1-4^7)}{1-4}[/tex]

[tex]S_7=\frac{3(1-4^7)}{-3}[/tex]

[tex]S_7=-(1-16384)[/tex]

[tex]S_7=-(-16383)[/tex]

[tex]S_7=16383[/tex]

Therefore, Option 3rd is correct.

Answer:

x= 6.6

LM= 33

MN= 17.2

LN=50

Step-by-step explanation:

10x-16= 5x+2x+4 (LN=LM+MN)

10x-16=7x+4

3x-16=4

3x=20

x=6.6

then plug 6.6 back into equation and round to the nearest whole number.

Answer:

b) 6(x + 4)

Step-by-step explanation:

The given word phrase "The product of 4 more than x and 6"

4 more than x = 4 + x

The product "4 + x" and 6

6(x + 4)

Answer: b) 6(x + 4)

The ratio of the triangle is 55/1.1, which is 50/1.

This means that the building is 50/1 = x/5

x = 250

The office building is 250 m tall.

The height of the office building is calculated using similar triangle ratios, by setting up a proportion between the tree's dimensions and the building's shadow, and solving for the building's height to get 250 meters.

To calculate the height of the office building using similar triangle ratios, compare the tree's height and shadow length to those of the building. Since the tree is 5 m tall and casts a 1.1 m long shadow, we can set up a proportion with the building's shadow, which is 55 m long.

Step-by-step calculation:

Write the proportion using the tree's height and shadow: 5 m (tree height) / 1.1 m (tree shadow) = building height / 55 m (building shadow).

Cross multiply to find the building's height: 5 m × 55 m = 1.1 m × building height.

Perform the calculations: 275 m² = 1.1 m × building height.

Divide both sides by 1.1 m to solve for building height: building height = 275 m² / 1.1 m.

Complete the division: building height = 250 m.

Answer: no correlation is suggested bc it's al over the graph or the scatter plot or whatever u wanna call it. but there is no correlation.

Step-by-step explanation: hope this helps ;D

Answer:

560 miles per hour

Step-by-step explanation:

First, what you do is divide 224 by 4.

224 ÷ 4 = 56

You do this because you need to find the rate it goes in one hour.

Next, you do 56 times 10.

56 × 10 = 560

Hope that helps!

560miles per hour is the jets speed .

Speed is the time rate at which an object is moving along a path,

Given,

A train went 224 miles in 4 hours

A jet is ten times as fast as the train.

We need to find the jets speed.

Speed = Distance / time

Train speed=224/4

=56miles/hour

So train travels 56 miles in one hour.

As given, A jet is ten times as fast as the train

So we have to multiply 10 with the 56

10×56

560miles per hour

Hence, 560miles per hour is the jets speed .

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Answer:

So, the company profit if   75 pairs of jeans are sold is $1450

Step-by-step explanation:

The number of pairs of jeans that have been sold is represented by x

We are given

The profit is the difference between the revenue and the cost , 20x-50

Let's assume profit function as P(x)

[tex]P(x)=20x-50[/tex]

There are 75 pairs of jeans

so, x=75

we can plug x=75 and find profit

[tex]P(75)=20\times 75-50[/tex]

[tex]P(75)=1500-50[/tex]

[tex]P(75)=1450[/tex]

So, the company profit if   75 pairs of jeans are sold is $1450

Answer:

8 teams

5 girls and 4 boys

Step-by-step explanation:

To determine how many teams we can have , we need to determine the greatest common factor.

 girls:40 = 5*8

boys:32 = 4*8

The greatest common factor is 8

So we will have 8 teams

There will be 5 girls and 4 boys on each team

Answer:

1. y = 2/3 x +2

2.  y = -x -8

Step-by-step explanation:

The slope intercept form of a line is y = mx+b where m is the slope and b is the y intercept

1. y = 2/3 x +2

2.  y = -x -8

ANSWER:

1. y = 2/3x + 2

2. y = -1x + -8

ABOUT SLOPE INTERCEPT FORM:

Hope this helps you!!! :)

Answer:

Step-by-step explanation:

no because x can equal anything. It should at least write down a second number for it to be solved correctly.

Answer:

2 minutes 40 sec

Step-by-step explanation:

Recall that distance = rate times time.

Thus, time = distance / rate.

Here,

time = 280 ft / (1.75 ft/sec) = 160 sec, or 2 minutes 40 sec

To calculate the time it takes to travel 280 feet on a moving walkway at an airport moving at a pace of 1.75 feet per second, we use the formula time = distance/pace. This equates to approximately 160 seconds.

The question is asking about the time it takes to transport someone along a distance of 280 feet by a moving walkway in an airport, given that the pace of the walkway is 1.75 feet per second. To answer this, you use the formula of time = distance/pace. So we have time = 280 feet / 1.75 feet per second. This calculation will give you the answer in seconds. When you do this calculation, you will find that it takes approximately 160 seconds to cover that distance on the moving walkway.

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[tex]200,000+20,000+3,000+200+20+8=223,228\\\\200,000\\.\ 20,000\\.\ \ 3,000\\.\ \ \ \ \ 200\\.\ \ \ \ \ \ \ 20\\\underline{+\qquad\ 8}\\223,228[/tex]

Answer:

The slope is 3

Step-by-step explanation:

To find the slope we can use the formula

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

Using the points (5,14) and (-5,-16)

m= (-16-14)/ (-5-5)

  = -30/-10

 = 3

Answer:

C) ∠6 and ∠7

Step-by-step explanation:

We have been given that lines a and b are parallel. We are asked to find the angle on line b that will be congruent to angle 3.

We can see that angle 3 is under the line a and on the left side of transversal.

We know that the corresponding angles and alternate interior angles formed by two parallel lines are equal.

We can see that angle 7 corresponds to angle 3 and angle 6 is alternate interior angle of angle 3.

Therefore, angle 7 and angle 6 will be congruent with angle 3 and option C is the correct choice.

Answer:

3. The number of months Megan will wait to sell the gadget.

Step-by-step explanation:

We have been given that Megan purchased a new gadget for her technology hobby. She plans to sell it sometime in the future, however, its value depreciates monthly.

The expression below shows the depreciated sales value of the gadget: [tex]2020-22m[/tex]

From above expression we can see that gadget's original value is $2020 and its value falls by $22 every month and m represents the number of months after which Megan will sell her gadget.

Therefore, the variable m represents the number of months Megan will wait to sell the gadget and 3rd option is the correct choice.  

The variable m represents the number of months Megan will wait to sell the gadget and 3rd option is the correct choice. The variable m in the expression 2020 – 22m represents the number of months Megan will wait to sell the gadget.

The original value of the gadget is 2020, and the monthly depreciation value is 22.

So, the expression 2020 – 22m represents the amount of money Megan will get when she sells the gadget after m months.

If Megan waits for 0 months to sell the gadget, then m = 0 and she will get

2020 – 22 * 0 = $2020.

If Megan waits for 1 month to sell the gadget, then m = 1 and she will get

2020 – 22 * 1 = $1998.

Therefore, the variable m in the expression 2020 – 22m represents the number of months Megan will wait to sell the gadget.

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Answer in #1 it ads up by 8

Number 1 is Add by 8

& I'm not sure about number 2

The longest side of a triangle is opposite the largest interior angle, same goes to the opposite. The shortest side of a triangle is opposite the smallest interior angle.

Hope this helps! <3

Answer:

Largest angle

Step-by-step explanation:

In any triangle, the longest side is opposite the largest angle.  The smallest side is opposite the smallest angle.

Answer:

They are equivalent

Step-by-step explanation:

2x+14 = 8

Lets solve for x

Subtract 14 from each side

2x+14-14 = 8-14

2x = -6

Divide by 2

2x/2 = -6/2

x = -3

They are the same

Answer:

Yes

Step-by-step explanation:

Solving for 2x+14=8

Subtract 14 on both sides: 2x= 8-14

2x = -6

Divide by 2: x = -3

-3 = -3

Hope this helps!!

Answer:

Option B is correct.

Value of cos(a+B) is,  [tex]\frac{16}{65}[/tex]

Step-by-step explanation:

Using the formula:

[tex]\cos(a+B) = \cos a \cos B -\sin a \sin B[/tex]

Given the values:

[tex]\cos a = \frac{3}{5}[/tex] and [tex]\sin B = \frac{5}{13}[/tex]

Using trigonometric identity:

[tex]\sin^2 \theta + \cos^2 \theta =1[/tex]

or

[tex]\sin \theta = \sqrt{1-\cos^2 \theta}[/tex]

or

[tex]\cos \theta = \sqrt{1-\sin^2 \theta}[/tex]

Find the value of sin a and cos B;

Using trigonometric identity:

[tex]\sin a = \sqrt{1-\cos^2 a}[/tex]

[tex]\sin a = \sqrt{1-(\frac{3}{5})^2}[/tex] = [tex]\sqrt{1-\frac{9}{25}} = \sqrt{\frac{25-9}{25}}=\sqrt{\frac{16}{25} } =\frac{4}{5}[/tex]

Similarly;

[tex]\cos B = \sqrt{1-\sin^2 B}[/tex]

[tex]\cos B = \sqrt{1-(\frac{5}{13})^2}[/tex] = [tex]\sqrt{1-\frac{25}{169}} = \sqrt{\frac{169-25}{169}}=\sqrt{\frac{144}{169} } =\frac{12}{13}[/tex]

Substitute these given values equation [1] we have;

[tex]\cos(a+B) =\frac{3}{5} \cdot \frac{12}{13}-\frac{4}{5} \cdot \frac{5}{13}[/tex]

[tex]\cos(a+B) =\frac{36}{65}-\frac{20}{65}[/tex]

then;

[tex]\cos(a+B) =\frac{36-20}{65}=\frac{16}{65}[/tex]

Since, the angles a and B are in first quadrant angles therefore the value of cos(a+B) is, [tex]\frac{16}{65}[/tex]

To find cos(a + B), use the formula cos(a + B) = cos(a)cos(B) - sin(a)sin(B). Substitute the given values of cos(a) = 3/5 and sin(B) = 5/13, and solve for cos(B) using the Pythagorean identity. Then substitute all the values into the formula and simplify to find cos(a + B) = 16/65.

To find cos(a + B), we can use the formula:

cos(a + B) = cos(a)cos(B) - sin(a)sin(B)

Given that cos(a) = 3/5 and sin(B) = 5/13, we can substitute these values into the formula:

cos(a + B) = (3/5)(cos(B)) - (sin(a))(5/13)

To find cos(B), we can use the Pythagorean identity:

cos²(B) + sin²(B) = 1

Substituting the given value of sin(B), we can solve for cos(B):

cos(B) = √(1 - (5/13)²)

Now we can substitute the values of cos(a), sin(B), and cos(B) into the formula for cos(a + B):

cos(a + B) = (3/5)(√(1 - (5/13)²))) - (5/13)(5/13)

Simplifying this expression gives us the final answer: cos(a + B) = 16/65.

Answer:

Brandon pays $49.74 in total

Step-by-step explanation:

$46.49 x 1.07 = $49.74

Answer:

121 is a rational number because it can be expressed as the quotient of two integers: 121/ 1

Step-by-step explanation:

The number 121 is not a irrational number

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

The number 121

When evaluated, we have

The number 121 = 121

The above number is represented by the quotient of 2 integers

using the above as a guide, we have the following:

We can conclude that the number is a rational number

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Answer:

The sale price is $13.43

Step-by-step explanation:

In order to find the sale price of an item, we multiply it by the remaining percentage of cast left. Since we are subtracting 44% of the cost, that means that we are paying 56% of it. Therefore, we can multiply the cost by 56%

23.99 * .56 = $13.43

Answer: $13.43

Step-by-step explanation:

make your 22% a decimal by dividing it by 100 equaling 0.22 then since its markDOWN you subtract 1.00 - 0.22 equaling 0.88 then multiply 0.88 by $23.99 which is supposed to equal $13.43

Answer: Inconsistent

Step-by-step explanation:

y = 3x + 4   → m = 3, b = 4

y = 3x + 3   → m = 3, b = 3

These equations have the same slope but different y-intercepts so they are parallel lines which means they will never intersect.

NOTES

Answer:

Inconsistent

Step-by-step explanation:

Answer:

Distribute so it would be 18+27f-39

Step-by-step explanation:

Step 1: Distrbute 3 into (9f - 13)

3 • 9f = 27f

3 • 13 = 39

18 + 27f - 39

Step 2: Solve like-terms

(18 and 39 are the only like terms. 27f and 39 aren't like terms since 39 doesn't have a variable therefore, you can't solve 27f - 39)

39 - 18 = 21

ANSWER:

27f - 21

Hope this is correct!

The inequality y ≥ x^2-4 satisfies (0,0) but the inequality y < 2x-1

does not satisfy (0,0).  

          Substitute (x,y)=  (0,0) in the above inequality

                                   0 ≥ (0^2)-4

                                         0 ≥ -4

              The above inequality is true.

             Hence, (0,0) is the solution of inequality (i)

          Substitute (x,y)=  (0,0) in the above inequality

                                0 < 2(0) - 1

                                0 <  -1

                The above inequality is not true.

          Hence (0,0) does not satisfy the above inequality (ii).

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