Natasha and Richard are making exam papers.Each set takes Natasha 45 minutes and Richard 1 hour.Express the times Natasha and Richard take as a ratio. Give your answer in its simplest form.

Answer:

the probability that both dessert and drink are sugar free = ¼

Step-by-step explanation:

We are told that there are 5 different sandwiches, 4 different desserts and 6 different drinks.

Now, since Two of the four desserts are sugar free, then the probability that the dessert chosen is sugar free is;

P(desert sugar free) = ½

Now, three of the the 6 drinks are sugar free, then the probability that the drink chosen is sugar free is;

P(drink sugar free) = 3/6 = ½

Thus, the probability that both dessert and drink are sugar free is;

P(both sugar free) = ½ × ½ = ¼

Answer:

Step-by-step explanation:

Given the expression  sin(11pi/2 +x) =-1/2

Take the arcsin of both sides

sin⁻¹[sin(11pi/2 +x)] =sin⁻¹(-1/2)

11pi/2 + x = -30

x = -pi/6 - 11pi/2

Find the LCM

x = (-pi-33pi)/6

x = -34pi/6

x = -17pi/3

Since x is negative and sin is negative in the fourth quadrant

x =  - 17pi/2

x = -1530⁰+1440⁰ (scaling down the angle)

x = -90

x = 360 - 90 (fourth quadrant)

x = 270⁰

x = 270pi/180

x = 27pi/18

x = 3pi/2

Hence x the solution of x is 3pi/2

Answer:

B, 5pi/3

Step-by-step explanation:

edge 2020

Answer: 10 degrees

Step-by-step explanation:

-5+15=10

Answer:

c. 3/2=10/x

Step-by-step explanation:

in a proportion, you want the same category of values in the same position. For example, the number of apples goes on top in each of the fractions, and the cost goes on the bottom. then solve for x.

Answer:

362

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:1 is 60 and 2 is a k=2

Step-by-step explanation: correct me if I’m wrong

Answer:

yes

Step-by-step explanation:

also its a 45 degree angle

cuz 135-90+45

XD brainliest pls

Answer:

It's just 2

Step-by-step explanation:

When you divide a negative by a negative, it becomes positive

Answer:

41 degrees

Step-by-step explanation:

Complementary angles add to 90 degrees

<3 + <4 = 90

<3 + 49 = 90

Subtract 49 from each side

<3 = 90-49

<3 =41

The percent of the bin would be filled for 30 gallons of amounts of waste is 60 percent.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, a garbage bin can hold 50 gallons of waste.

Waste (gal) = 5

Percentage = 5/50 ×100

= 10%

Waste (gal) = 30

Percentage = 30/50 ×100

= 60%

Waste (gal) = 45

Percentage = 45/50 ×100

= 90%

Therefore, the percent of the bin would be filled for 30 gallons of amounts of waste is 60 percent.

To learn more about the percentage visit:

brainly.com/question/24159063.

#SPJ2

Answer:

(1 - 2sinα)(1 + 2sinα)

Step-by-step explanation:

1 - 4sin²α ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b)

1 - 4sin²α

= 1² - (2sinα )²

= (1 - 2sinα)(1 + 2sinα)

Answer:

The answer is 24.78 m^2

Step-by-step explanation:

I did the test

The outside circumference of the walking path is 50.24 meters and the inside circumference of the walking path is 25.12 meters then the area of the walking path is 150.72 m²

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The formula for circumference of circle is 2πr

The area of circle is πr²

Area of large circle

Given:

circumference = 50.24 m

50.24 = 2 × 3.14 × r

r = 8 m

Therefore Area = 3.14 × 8²

= 200.96 m²

Area of small circle

Given circumference = 25.12 m

⇒ 25.12 = 2 × 3.14 × r

⇒ r = 4 m

Therefore Area = 3.14 × 4²

= 50.24 m²

Area of shaded path area = area of large circle - area of small circle

= 200.96 - 50.24

= 150.72 m²

Hence,  the area of the walking path is 150.72 m²

To learn more on Circles click:

https://brainly.com/question/11833983

#SPJ3

Answer:

a=3

Step-by-step explanation:

The formula for direct proportion is

f = ka

Let f= 42 and a = 7

42 = k*7

Divide each side by 7

42/7 = k7/7

6 =k

f = 6a

Let f = 18

18 = 6a

Divide each side by 6

18/6 = 6a/6

3 =a

Answer:

a = 3

Step-by-step explanation:

Given that F is directly proportional to a, then the equation relating them is

F = ka ← k is the constant of proportion

To find k use the condition F = 42 when a = 7, thus

42 = 7k ( divide both sides by 7 )

6 = k

F = 6a ← equation of proportion

When F = 18, then

18 = 6a ( divide both sides by 6 )

3 = a

ANSWER:

2 ounces.

EXPLANATION:

it uses 1 once of gasoline every time it is on not driving and it is at a traffic light for 2 minutes then 1 + 1 = 2.

 1 ounce + 1 ounce = 2 ounces of gasoline it uses.

Answer:

B

Step-by-step explanation:

it's just option B because it is only root

Answer:

the answer would be B. (2.5, -0.5)

plug the possibilities in and solve. just because it works for one, it doesn't mean that it will work for both.

3 (2.5) - (-0.5) = 7.5 + 0.5 = 8

(2.5) + (-0.5) = 2.5 - 0.5 = 2

i hope i helped. :)

Step-by-step explanation:

Read more about system of equations at:

brainly.com/question/12895249    if im wrong

Answer:

32 is the values 21 is the integers

Step-by-step explanation:

that's may answer ty hope it's help

Answer:

No it does not  matter in which order the store applies the discount.

Step-by-step explanation:

Suppose we have the cost price = $ 100

Then 70 %  off means 70% of 100= 70 $ discount

And the remaining $ 30  is again given a discount of 20 % . That would be 20 % of $ 30=  $ 6 discount giving the discounted price of $ 24.

Now if we apply the discount of 20 % first that would give $ 80 discounted price and again applying 70 % to $ 80 would give $ 56 discount and a discounted price of $ 80 - $ 56= $ 24

Hence the order in which the discount is applied does not matter.

A. The range of the ages of the members of the Debate Team is greater than the range of the ages of the

members of the Chess Club.

Answer:

Now suppose that x1,y1 , x2,y2 , , xn,yn are the vertices of a polygon (with positive orientation). The area of the polygon is A 1 2 C xdy ydx 1 2 x1y2 x2y1 x2y3 x3y2 xny1 x1yn . The problem asks us to find the area of the pentagon with vertices 0,0 , 2,1 , 1,3 , 0,2 , and 1,1 .

Step-by-step explanation:

The area of the given triangle JKL is 16 units square.

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The sum of all three angles inside a triangle will be 180° and the area of a triangle is given as (1/2) × base × height.

Given vertices form a triangle in the coordinate plane ;

Base = 3 + 5 = 8 units

Height = 9 - 5 = 4 units.

Since the area of a triangle is given as (1/2) × base × height.

So,

Area = (1/2) × 8 × 4 = 16 unit square.

Hence "The area of the given triangle JKL is 16 units square".

For more about triangles,

https://brainly.com/question/2773823

#SPJ2

Answer:

N + B + D = 90     sum of ages is 90        (I)

B = 2 D     B is twice as old as D

N + 3 D = 90      using above equations

(N + 10) + 3 D = 100        add 10 to both sides

B + 3 D = 100             Brian is 10 yrs older than Nigel

2 D + 3 D = 100       Brian is twice the age of Dean

5 D = 100      

D = 20      Dean's age

Brian = 2 D = 40 Brian's age

90 - 60 = 30 = Nigel's age

Check:

N + 10 = B = 30 + 10 = 40 = Brian's age

Answer:

because 4 is being multiplied by 500 which has two zeros because it is a multiple of 100

Step-by-step explanation:

Answer:

Because when you multiply 500 by 4 you start with the first 0. 4x0 is 0, now you move on to the second 0. 4x0 is 0, so that one is 0 too. Now you multiply the 5. 5x4 is 20. You put the 20 first, followed by the two 0s, And you get 2,000.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

to change a mixed number into an improper fraction

a [tex]\frac{b}{c}[/tex] = [tex]\frac{ac+b}{c}[/tex] , then

9 [tex]\frac{1}{3}[/tex]

= [tex]\frac{9(3)+1}{3}[/tex]

= [tex]\frac{27+1}{3}[/tex]

= [tex]\frac{28}{3}[/tex]

Answer:

we use the same program

Step-by-step explanation:

28/3 Is the answer!

(by the way you can use a simplify calculator

for most of the problems it gives you.)

Hopefully this helps you!

-Keira

AnTo divide mixed numbers Change each mixed number to an improper fraction.

Multiply by the reciprocal of the divisor, simplifying if possible.

Put answer in lowest terms.

Check to be sure the answer makes sense.

Step-by-step explanation:

Answer:

If u have mixed fractions, like [tex]3\frac{1}{2}[/tex], you will have to change it to improper fraction([tex]\frac{7}{2}[/tex]) to divide with ease.

let's give an example of how to divide fractions.

1. [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{1}{3}[/tex]

Now, you will invert the numbers on the right side, and that will cause the division sign to change into multiplication sign.

[tex]\frac{2}{3} / \frac{1}{3} \\\\\frac{2}{3} X \frac{3}{1}\\\\2[/tex]

2. let's have another example:

[tex]2\frac{1}{3} / 3\frac{1}{2}\\\\\frac{7}{3} / \frac{7}{2} \\\\\frac{7}{3} X \frac{2}{7} \\\\\frac{2}{3}[/tex]

as a simplified fraction, the answer is 4/77

as a decimal it is about 0.0519480519480519

Answer:

x = 76

Step-by-step explanation:

-4(x-26) = -4x + 104

-4x + 104 = -200

-4x = -304

x = 76

The solution of the equation is x= 76.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given, equation –4(x – 26) = –200

–4(x – 26) = –200

-4x + 104 = -200

-4x = -200-104

-4x = -304

x = 304/4

x= 76

Therefore, the solution of the equation is x= 76.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ2

Answer:

A. Total area of Alaska is considerable larger than total area of Connecticut.

B. Population of California is considerably larger that population of Alaska.

Step-by-step explanation:

A. What is the difference in total area of Alaska and Connecticut?

According to the US government, total areas of Alaska and Connecticut are 663,268 square miles ([tex]6.633\times 10^{5}[/tex] square miles) and 5,567 square miles ([tex]5.567\times 10^{3}[/tex] square miles), respectively.

The difference between both quantities is:

[tex]x = 6.633\times 10^{5}\,mi^{2}-5.567\times 10^{3}\,mi^{2}[/tex]

[tex]x = 6.577\times 10^{5}\,mi^{2}[/tex]

Which means that total area of Alaska is considerable larger than total area of Connecticut.

B. What is the difference in total population of California and Alaska?

According to the US government, total populations of California and Alaska are 39,512,223 people ([tex]3.951\times 10^{7}[/tex] people) and 710,249 people ([tex]7.103\times 10^{5}[/tex] people), respectively.

The difference between both quantities is:

[tex]x = 3.951\times 10^{7}\,people - 7.103\times 10^{5}\,people[/tex]

[tex]x = 3.880\times 10^{7}\,people[/tex]

Which means that population of California is considerably larger that population of Alaska.

Answer:

25

Step-by-step explanation:

The sum of all of the angles inside of a triangle is 180 degrees. That means we know that:

[tex](x+26)+(x+14)+(4x-10)=180[/tex]

We can then combine like terms:

[tex]6x+30=180[/tex]

We want to get 6x alone, so we can subtract 30 from both sides:

[tex]6x=150[/tex]

Then we want to get x alone, so we can divide both sides by 6:

[tex]x=25[/tex]

Now we know that x is 25.

Answer:

113

Step-by-step explanation:

c/b(cheeseburger)-2x

h/b(hamburgers)-x

2x+x=339

3x=339(divide both sides by 3)

x=113