Find the area of each triangle.

1. a = 6ft, b = 11ft, c = 12ft

2. a = 2in, b = 4in, C = 38°

Answer:

[tex]\dfrac{24}{31}[/tex]

Step-by-step explanation:

Given information:

Total number of girls = 14

Total number of boys = 17

Total number of peoples = 14 + 17 = 31

6 girls and 7 boys brought balloons.

Let A and B are two events, such that

A = Choosing a girl

B = Choosing someone who did not bring a balloon.

[tex]A\cup B[/tex] = Choosing girl or someone who did not bring a balloon.

[tex]n(S)=31,n(A)=14,n(B)=18,n(A\cup B)=14+10=24[/tex]

The probability of randomly choosing a girl or someone who did not bring a balloon is

[tex]P=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]P=\dfrac{24}{31}[/tex]

Therefore, the required probability is [tex]\dfrac{24}{31}[/tex].

The probability of randomly choosing a girl or someone who did not bring a balloon at a party is 24 out of 31, which simplifies to the fraction 24/31.

To solve this problem, we can use the concept of probability and the addition rule since the events are not mutually exclusive.

First, let's define the total number of people at the party: 14 girls + 17 boys = 31 people.

Next, we look at the number of girls who brought balloons, which is 6, meaning there are 14 - 6 = 8 girls who did not bring balloons.

Similarly, 17 boys - 7 boys who brought balloons = 10 boys who did not bring balloons.

Now, let's calculate the number of ways to choose a girl or someone who did not bring a balloon. For the girls, it's simply the total number of girls, 14. For those who did not bring balloons, we need to add the number of girls who did not bring balloons to the number of boys who did not bring balloons: 8 girls + 10 boys = 18 people who did not bring a balloon.

Combining these, the event of choosing a girl overlaps with the event of choosing someone who did not bring a balloon, so we have to subtract the number of girls who did not bring a balloon once to avoid double-counting: 14 + 18 - 8 = 24.

Thus, the probability is: 24 out of 31, which we can write as 24/31.

Answer:

50505 units

Step-by-step explanation:

The radius is the fixed distance from the center of a circle to any point on its circumference. The radius of a circle always equals half of its diameter, so to find the diameter, multiply the radius by two. ( 101010/ 2=50, 505 units)

Answer:

The answer is 288 pages are filled with hockey cards

Step-by-step explanation:

First, you need to figure out what percentage of the album is full which is 32% So, with that 32% you figure out how many pages that is. So you would find 32% of 900 which is 288 therefor, that would be your answer.

I hope this helped <3

Answer: c

Step-by-step explanation:

Answer:

complementary angles are angles that sum up to 90 degrees. that is all I can say because I can't see any diagram

Answer:

complementary angles are angles that sum up to 90°

i can't see any diagram

Answer:

A≈38.52 in²

Step-by-step explanation:

google

Answer:

Step-by-step explanation:

Answer:

There were 16.3 pounds in each of the bags

Step-by-step explanation:

The complete question is as follows;

The students put recycling bins for cans and bottles in the cafeteria and teachers lounge. At the end of last week, there was a total of 48.9 pounds of cans and bottles. They split them evenly into 3 bags. How many pounds were in each bag?

Solution;

This is a straightforward question that borders on one of the arithmetic operations which is division.

To properly understand this question, we can reframe it to mean if you have three bags containing cans and bottles with a total weight of 48.9 pounds, what is the weight of each bag if they have the same weight?

we can see we have succeeded in making the question look simpler while meaning the same thing.

To get the weight of each of the bags, what we simply do is to divide the total weight of the bags by 3

Mathematically that would be 48.9/3 = 16.3

This means that each of the bags weigh 16.3 lbs

The correct options are: B and D.  The true statements about stickers are: Katarina has 375 star stickers and 75% of the stickers are stars.

Let's analyze each statement given the information that 25% of the 500 stickers are hearts, and the remaining stickers are stars.

1. Total number of stickers: 500

2. Percentage of heart stickers: 25%

3. Percentage of star stickers: 100% - 25% = 75%

Now, let's calculate the actual numbers:

- Number of heart stickers:

[tex]\[ 25\% \text{ of } 500 = \frac{25}{100} \times 500 = 0.25 \times 500 = 125 \][/tex]

- Number of star stickers:

[tex]\[ 75\% \text{ of } 500 = \frac{75}{100} \times 500 = 0.75 \times 500 = 375 \][/tex]

Now, let's evaluate each statement:

A. Katarina has 100 heart stickers.

- False. Katarina has 125 heart stickers.

B. Katarina has 375 star stickers.

- True. Katarina has 375 star stickers.

C. The package contains 20 sheets of stickers.

- Not enough information is given to determine this. This statement is irrelevant without knowing how many stickers are on each sheet.

D. 75% of the stickers are stars.

- True. 75% of 500 stickers are stars.

E. The number of heart stickers is the same as the number of star stickers.

- False. The number of heart stickers (125) is not the same as the number of star stickers (375).

So, the true statements are:

B. Katarina has 375 star stickers.

D. 75% of the stickers are stars.

The complete question is:

Katarina bought a package of 500 stickers. 25% of the stickers are hearts. The remaining stickers are stars. Select all the statements that are true.

A.Katarina has 100 heart stickers.

B.Katarina has 375 star stickers.

C.The package contains 20 sheets of stickers

D.75% of the stickers are stars.

E.The number of heart stickers is the same as the number of star stickers.

Answer:

1. 17 whole cans

2. Yes, 38.65 in2 of metal

Step-by-step explanation:

First we need to find the surface area of the can.

The base and the top of the can have a area of pi*r^2.

If the radius is half the diameter, we have r = 3/2 = 1.5 inches, so:

A1 = pi * 1.5^2 = 7.069 in2

The side of the can has a area of pi*d*h. If the diameter is 3 inches and the height is 4.5 inches, we have:

A2 = pi*3*4.5 = 42.412 in2

So the total area of the can is:

2*A1 + A2 = 56.55 in2

To know how many cans we can make with 1000 in2 of metal, we just need to divide the total metal for the surface area of each can:

number of cans = 1000 / 56.55 = 17.684 cans

We can make 17 cans, and the metal left over is 1000 - 17 * 56.55 = 38.65 in2

Gummy Bear = 16

Lollipop = 16

Lime = 0

Ring pop = 4

Question mark (total) = 36

Answer: 4 hours

Step-by-step explanation: If you take 50 times 4 it will get you 200. Another way to look at it is the car is going 50 miles per hour, so in one hour the car has gone 50 miles, in two hours it’s gone 100, three hours it’s gone 150, so in four hours it’s gone 200 miles

Final answer:

To calculate how long it takes to travel 200 miles at a constant speed of 50 miles per hour, divide the distance by the speed. The car will take 4 hours to cover the distance.

Explanation:

To determine how long it takes a car moving at a constant speed to cover a certain distance, we use the formula time = distance \/ speed. In this case, the car is moving at a constant speed of 50 miles per hour and needs to cover a distance of 200 miles.

We can calculate the time it will take as follows:

Time = Distance \/ Speed
Time = 200 miles \/ 50 miles per hour
Time = 4 hours

Therefore, it will take the car 4 hours to travel 200 miles at a constant speed of 50 miles per hour.

Answer:

The length of BC is needed because it is the side opposite ∠A.

Step-by-step explanation:

Given the right angles triangle as shown in the attachment, we can get sin(A) without using Pythagoras theorem. Instead we will use SOH CAH TOA trigonometry identity.

According to SOH:

Sin(A) = Opposite/Hypotenuse

Sin(A) = |BC|/|AB|

Opposite side of the triangle is the  side facing ∠A.

Based on the formula, we will need to get the opposite side of the triangle which is length BC for us to be able to determine sinA since the hypotenuse is given.

Answer:

Bc is needed because it is opposite of A

Step-by-step explanation:

Answers: A fraction is a perfect square if it's reduced version (of an improper fraction if the number is greater than 1) has both numerator and denominator numbers that are perfect squares. IE: 25/36 is a perfect square because both 25 and 36 are perfect squares.

Step-by-step explanation:

So for example 5/25 is a perfect square but 2/5 wouldn't be a perfect square.

Tell me if this helped you

If a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

A fraction is a perfect square if both the numerator and the denominator of its reduced version, which is an improper fraction if the integer is greater than 1, are perfect squares. To put it another way, 25/36 is a perfect square as 25 and 36 are both perfect squares.

Thus, if a fraction can be expressed as the product of two equal fractions, it may also be expressed in its simplest form as a perfect square.

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Answer:

C

Step-by-step explanation:

I just guessed and got it right

Answer:

C. taking the square root of both sides of the equation

Answer: the total price of the trip is

$1087.5

Step-by-step explanation:

The trip costs $1450 and they have a special discount of 35% off. It means that the amount that would be taken off is

35/100 × 1450 = $507.5

The cost of the trip would be

1450 - 507.5 = $942.5

The tax rate for the package is 10%. It means that the amount of tax to be paid is

10/100 × 1450 = $145

Therefore, the total price of the trip would be

942.5 + 145 = $1087.5

Answer:

Arc AB = 80°

Arc AD= 100°

Step-by-step explanation:

Arc AB

Since AC is the diameter, it would be 180°, and since arc BC is given (100°), arc AB would be 80°

Arc AD

Since BD is a diameter, it would also be 180°. Arc ED is given and previously you found arc AB. So subtract 50 and 80 from 180 and you'll get 50° for arc AE. Add that with arc ED and you'll get 100°

Answer:

15 - 3(8³) = 3y³

Step-by-step explanation:

5 – 8³ = y³

3(5 - 8³) = 3(y³)

15 - 3(8³) = 3y³

Answer:

15-8=y

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

just check at least two

Answer:

1. 24      2. 12       3. it is a very easy concept

Step-by-step explanation:easy

Answer:

Let's suppose that the ideal blood pressure is 100 (the ideal values are between 90 and 110, i am taking the middle value)

If 125 is the 100%, and we want to go to 100, then we need to decrease by:

125 - 100 = 25

now, to calculate the percentage that represents the 25, we need to calculate:

(25/125)*100% = 20%

So to reduce his blood pressure to normal, he must reduce it by 20%

To find out by what percentage Cory must reduce his blood pressure to normal, subtract the normal from Cory's blood pressure, divide the result by Cory's initial blood pressure, and then multiply by 100. For instance, if normal blood pressure is 120, Cory must reduce his blood pressure by approximately 4%.

To calculate the percentage that Cory needs to reduce his blood pressure, we first need to know the normal blood pressure level. For example, if the normal blood pressure is considered to be 120, then we can proceed as follows:

So, Cory would need to reduce his blood pressure by approximately 4% to return to a normal level, assuming normal blood pressure is 120.

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Answer:

x =2 or x=7

Step-by-step explanation:

x^2-9x+14= 0

Now splitting the middle term we get,

x^2-7x -2x +14 =0

x(x-7) - 2(x-7) =0

(x-2) (x-7) =0

x-2=0 or x-7 =0

x =2 or x=7

The factors of [tex]x^2-9x+14[/tex] are (x - 7) and (x - 2)

"It is a mathematical statement which consists of variables and constants, and some algebraic operations."

For given question,

We have been given a quadratic expression [tex]x^2-9x+14[/tex]

We need to factorize given quadratic expression.

[tex]\Rightarrow x^2-9x+14\\\\= x^2-7x-2x+14~~~~~~~~...........(-9x=-2x-7x~~and~14=(-9)\times (-2))\\\\=x(x-7)-2(x-7)\\\\=(x-7)(x-2) ~~~~~~~~~~~~............(Seperate~out~common~terms)[/tex]

Therefore, the factors of [tex]x^2-9x+14[/tex] are (x - 7) and (x - 2)

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Answers:

Across->

Housing: Fixed, $950, $11,400, ?

Food: Variable, $650, $7,800,?

Clothing: Variable, $75, $900,?

Transportation: Fixed, $500, $6,000,?

Insurance&medical: Variable, $1,200, $14,400,?

Entertainment: Variable, $100, $1,200,?

Emergency fund: Fixed, $50, $600,?

Saving for C: Fixed, $50, $600,?

Saving for R: Fixed, $100, $1,200,?

Step-by-step explanation:If it is the cost monthly you are looking for, divide the yearly cost by 12. If you are looking for yearly cost, multiply the monthly cost by 12.

And if you would like to know what a variable and fixed expense is, the variable expense is the expense that can change, so say for instance, food isn’t gonna cost at two different places, so it’s variable. A fixed expense is an expense that is regularly paid and always the same cost.

Answer:

Housing: Fixed, $950, $11,400, 23.3%

Food: Variable, $650, $7,800, 16%

Clothing: Variable, $75, $900, 1.8%

Transportation: Fixed, $500, $6,000, 12.3%

Insurance&medical: Variable, $1,200, $14,400, 29.5%

Entertainment: Variable, $100, $1,200, 2.5%

Emergency fund: Fixed, $50, $600, 1.2%

Saving for C: Fixed, $50, $600, 1.2%

Saving for R: Fixed, $100, $1,200, 2.5%

Step-by-step explanation: Added correct percentages...

Answer:

$220.32

Step-by-step explanation:

108 x 2.04 = 220.32

The expression equivalent to the given expression is [tex]\left[\dfrac{1}{(36a^{4}b^{10})}\right][/tex] and this can be determined by using the arithmetic operations.

Given :

Expression  ---   [tex]\left[\dfrac{(2a^{-3}b^4)^{2}}{(3a^5b)^{-2}}\right]^{-1}[/tex]

The following steps can be used in order to evaluate the given expression:

Step 1 - The arithmetic operations can be used in order to evaluate the given expression.

Step 2 - Write the given expression.

[tex]\left[\dfrac{(2a^{-3}b^4)^{2}}{(3a^5b)^{-2}}\right]^{-1}[/tex]

Step 3 - Simplify the above expression.

[tex]\left[\dfrac{1}{(3a^5b)^{2}(2a^{-3}b^4)^{2}}\right][/tex]

Step 4 - Open the brackets and square the given terms in the denominator.

[tex]\left[\dfrac{1}{(9a^{10}b^2)\times (4a^{-6}b^8)}\right][/tex]

Step 5 - Multiply the terms present in the denominator.

[tex]\left[\dfrac{1}{(36a^{4}b^{10})}\right][/tex]

Therefore, the correct option is C).

For more information, refer to the link given below:

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Answer:

Density

Step-by-step explanation:

Density is the number of items per unit area. It is gotten by dividing the number of items by the area it occupies. It measures the compactness of an item in a given area. The higher the density, the more compact items are per unit area and the lesser the density, the less compact items are per unit area. It is measured in items/m²

Answer:

c:

Step-by-step explanation:

Answer:

1200 apples.

Step-by-step explanation:

The way I thought about this was, you need to figure out how many apples per percent. Thus, I divided 420 by 35, which gave me 12.

We have deduced that every percent = 12 apples.

Multiply 12 by 100 (apples per percent x total percentage)

12 x 100 = 1200

Answer: they will meet after 3 hours.

Step-by-step explanation:

Let t represent the number of hours it will take them to meet.

A walker and a cyclist are 45 miles apart. If they move towards each other, in t hours, they would have covered a total of 45 miles

Distance = speed × time

They move towards each other with speeds of 5 mph and 10 mph respectively. It means that the distance covered by the walker in t hours is 5 × t = 5t

Also, the distance covered by the cyclist in t hours is 10 × t = 10t

Since the total distance covered us 45 miles, then

5t + 10t = 45

15t = 45

t = 45/15

t = 3 hours

Answer:

vertex: (0,4) // domain: x is a real number // Range: 4

Step-by-step explanation:

got a 100%

Answer:

C,D,C in that order

Step-by-step explanation:

Answer:

3.2 miles

Step-by-step explanation:

Initial fee plus state tax first because they are static:

3.25 + 0.5 = 3.75

Remove the initial charge plus tip from total cost:

14.75 - 3 - 3.75 = 8

Divide by 0.5 to get how many 1/5 of a mile he went:

8 / 0.5 = 16

Divide 16 by 5 to get miles:

16 / 5 = 3.2 miles

Answer:

3.2 miles

Step-by-step explanation:

Initial fee plus state tax first because they are static:

3.25 + 0.5 = 3.75

Remove the initial charge plus tip from total cost:

14.75 - 3 - 3.75 = 8

Divide by 0.5 to get how many 1/5 of a mile he went:

8 / 0.5 = 16

Divide 16 by 5 to get miles:

16 / 5 = 3.2 miles