The height of a triangle is twice the length of its base. The area of the triangle is 50m^2. Find the height and base to the nearest tenth of a meter

The value of y is 50

Using the expression given:

substitute the value of q into the expression

Now we have :

y = 10 × 5

y = 50

Hence, the value of y is 50

Answer:

The answer is $704.73

Step-by-step explanation:

Answer:

The answer is A. $704.73

Step-by-step explanation:

Final answer:

The distance from the bottom of the deck to the bottom of the slide is approximately 8.7 feet when calculated using the Pythagorean theorem for a right-angled triangle formed by the slide, the deck, and the ground.

Explanation:

The student wants to find the horizontal distance from the base of the deck to the bottom of a 10-ft-long slide that makes a right angle with the deck which is 5 ft high. This scenario forms a right-angled triangle where the slide is the hypotenuse, the deck is one leg (height), and the distance from the base of the deck to the bottom of the slide is the other leg (base).

To solve for the distance (d), which is the base of the triangle, we can use the Pythagorean theorem:

a² + b² = c²

where

Plugging the known values into the equation, we get:

5² + d² = 10²

25 + d² = 100

d² = 100 - 25

d² = 75

d = √75

d ≈ 8.7 ft (to the nearest tenth)

Jessica added exactly ¼ cup of vanilla powder, weighing 32 grams, to her recipe. This is the perfect amount as stated by the cake recipe.

Jessica is tasked with following a cake recipe that requires 32 grams of vanilla powder. She knows that 1 cup of vanilla powder weighs 128 grams. Since she added only ¼ cup of vanilla powder, we need to calculate if this amount is equivalent to the required 32 grams.

First, let's determine how many grams are in ¼ cup of vanilla powder:

Therefore, Jessica has added the perfect amount of vanilla powder to her recipe.

The simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year is $56.

The subject of your question is simple interest calculation. The formula for calculating simple interest is: principal amount x interest rate x time. You are asked to calculate the simple interest paid on a $1,400 loan with an annual interest rate of 4% for 1 year. Let's proceed step-by-step:

So, the simple interest paid on the loan for 1 year is $56.

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The median size of the four water parks, given as 66, 70, 60, 60 acres, is 63 acres.

To find the median of the sizes of the four water parks, we first need to list the sizes in ascending order. Given the sizes are 66, 70, 60, 60, the arranged list becomes 60, 60, 66, 70.

As there are four numbers, the median is the average of the middle two numbers. So by adding 60 and 66 and then dividing by 2, we find that the median size of the water parks is 63 acres.

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Answer:

Based on calculations the correct answer is A

Step-by-step explanation:

The coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).

To find the coordinates of the point that divides the line segment AB in the ratio of 1:4, we can use the formula:

x = (x1 + 1/n * (4 * x2)) / (1 + 1/n)

y = (y1 + 1/n * (4 * y2)) / (1 + 1/n)

Substituting the given coordinates into the formula, we have:

x = (10 + 1/4 * (4 * 2)) / (1 + 1/4) = 8

y = (4 + 1/4 * (4 * 8)) / (1 + 1/4) = 6

Therefore, the coordinates of the point that divides the line segment AB in the ratio of 1:4 are (8, 6).

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Answer:

Option: B is the correct answer.

Enjoying movies and concerts are not independent since,

[tex]P(movies|concerts)\neq P(movies)[/tex]

and  [tex]P(concerts|movies)\neq P(concerts)[/tex]

Step-by-step explanation:

We know that if two events A and B are independent then:

[tex]P(A\bigcap B)=P(A)\times P(B)[/tex]

where P denote the probability of an event.

Now, we know that:

[tex]P(movies|concerts)=\dfrac{P(movies\bigcap Concerts)}{P(concerts)}[/tex]

Similarly:

[tex]P(concerts|movies)=\dfrac{P(movies\bigcap Concerts)}{P(movies)}[/tex]

If movies and concerts are independent then:

[tex]P(movies|concerts)=P(movies)[/tex]

Similarly:

[tex]P(concerts|movies)=P(concerts)[/tex]

We have:

[tex]P(movies)=0.6[/tex]

[tex]P(concerts)=0.55[/tex]

[tex]P(concerts|movies)=\dfrac{0.25}{0.6}[/tex]

[tex]P(movies|concerts)=\dfrac{0.25}{0.55}[/tex]

Hence,

Enjoying movies and concerts are not independent

Since,

[tex]P(movies|concerts)\neq P(movies)[/tex]

and  [tex]P(concerts|movies)\neq P(concerts)[/tex]

#1) 163.81 m

#2) About 9.8 laps.

#3) 1314 square meters

Explanation

#1) We first add all of the horizontal and vertical sections:

30+8+6+6+12+30+20 = 112 m

Now we find the distance around each curve.  The distance around a circle is the circumference; the formula for circumference is 

C=πd. 

We will use 3.14 for π for each curve:

Curve 5:  The radius is 3, so the diameter is 2*3 = 6.  This is 1/4 of a curve, so we multiply the circumference by 1/4:

1/4(3.14)(6) = 4.71

Curve 4:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 3:  This is 1/2 of a curve, so we will multiply the circumference by 1/2.  The radius is 2.25, so the diameter is 2*2.25 = 4.5:

1/2(3.14)(4.5) = 7.065

Curve 2:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 1:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 9:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 8:  This is another 1/4 curve with a radius of 3, so the distance around is 4.71.

Curve 7:  This is another 1/2 curve with a radius of 2.25, so the distance around is 7.065, just as curve 3.

Curve 6:  This is 1/2 of a curve with a radius of 3, so the distance around is 1/2(3.14)(2*3) = 9.42

The total distance around the curved parts is:

4.71+4.71+7.065+4.71+4.71+4.71+4.71+7.065+9.42 = 51.81

Together this gives us 112+51.81 = 163.81.

#2) To find the number of laps it takes to go 1609 meters, divide:

1609/163.81 = 9.8

#3) To find the rectangular area, we first need the total distance across and the total distance vertically.

Horizontally, we have a radius of 3, a horizontal distance of 30, and another radius of 3:

3+30+3 = 36

(looking at the right hand side)

Vertically, we have a radius of 3, vertical distance of 8, radius of 3, radius of 2.25, radius of 2.25, radius of 3, vertical distance of 12, and radius of 3:

3+8+3+2.25+2.25+3+12+3 = 36.5

The area is then 36(36.5) = 1314 m²

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The number is given by the equation n = 8

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the number be represented as n

And , a number is the same as the square root of the product of 8 and the number

Substituting the values in the equation , we get

n = √ ( 8 x n )   be equation (1)

On simplifying the equation , we get

n = √8n

Taking squares on both sides of the equation , we get

n² = 8n

Divide by n on both sides of the equation , we get

n = 8

Therefore , the number is 8

Hence , the equation is n = 8

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1,000,000,000 social Security numbers can be formed using the numerals 0-9.

A combination is grouping or sub-setting of items from a set where the order in which the selection is being made does not matter.

[tex]^{n}C_r = \frac{n!}{(n-r)!r!}[/tex]

where, n = Total number of items to be selected from.

r = Number of items to be selected.

According to the given problem,

Social security number contains nine digits.

A digit can be any number between 0-9.

For the first digit there are 10 choices which is 0-9 and the amount of numbers to be chosen is 1.

Thus there are [tex]^{10}C_{1}[/tex] ways for filling up first spot.

Similarly for the second digit , numbers available are 10 and numbers to be chosen is 9.

Thus there are [tex]^{10}C_{1}[/tex] ways for achieving this.

Same for third, fourth .. . . ninth digit.

Using the formula of combination, total number of ways would be,

= [tex]9 ~times~~ ^{10}C_{1}[/tex]

= [tex](\frac{10!}{1!\times (10-1)!})^9[/tex]

= 1000,000,000 ways

Hence we can conclude that there are 1000,000,000 ways of choosing 10 numbers from 0 to 9 for nine spots.

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One degree is equal 0.01745329252 radians:

1° = π/180° = 0.005555556π = 0.01745329252 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = α(degrees) × π / 180°

or

radians = degrees × π / 180°

Convert 30 degrees angle to radians:

α(radians) = α(degrees) × π / 180° = 30° × 3.1459 / 180° = 0.5236 rad

The angle α in radians is equal to the angle α in degrees times pi constant divided by 180 degrees:

α(radians) = (α(degrees) / 180°) × π

Convert 30 degrees angle to radians in terms of pi:

α(radians) = (α(degrees) / 180°) × π = (30° / 180°) × π

 = (1/6) × π = π/6 rad = 0.166667π rad

Final answer:

To convert degrees to radians, multiply the number of degrees by π and then divide by 180, or simply multiply by π/180. For instance, 45 degrees can be converted to radians as 45 degrees * (π/180) = π/4 radians.

Explanation:

To convert degrees to radians, you can use the basic formula that π radians equal 180 degrees. This means that to convert a degree measure to radians, you multiply the number of degrees by π and then divide by 180. This can be simplified to multiplying the number of degrees by π/180.

For example, if you wanted to convert 45 degrees to radians, you would perform the following calculation:

That means 45 degrees is equivalent to π/4 radians. Remember, the π symbol represents the mathematical constant pi, which is approximately 3.14159.

Answer:

7.

Step-by-step explanation: