a rectangular corn hole area at the recreation center has a width of 5 feet and a length of 10 feet. if a uniform amount is added to each side, the area is increased to 84 square feet. what is the amount added to each side

Final answer:

Glenn crashed in 30% of the races.

Explanation:

To find the percentage of races Glenn crashed, you can set up a proportion. A proportion is an equation that states that two ratios are equivalent. Since Glenn raced 30 times and crashed 9 times, the ratio of crashes to total races is 9 crashes out of 30 races.

You can set up the proportion as follows:
Crashes / Total Races = Percentage of Crashes / 100

Plugging in the known values gives us this:
9 / 30 = Percentage of Crashes / 100

To solve for the percentage of crashes, you multiply both sides of the equation by 100:
(9 / 30)
100 = Percentage of Crashes

Simplifying gives us:
(9/3) 10 = Percentage of Crashes

Hence, the percentage of races that Glenn crashed is 30%.

Answer:

The total number of possible outcomes are:

64

Step-by-step explanation:

It is given that:

Louisa spins the spinner below twice.

The spinner is numbered from 1-8.

Now, on spinning the spinner twice we obtain the sample space as:

(1,1)   (1,2)....................(1,8)

(2,1)  (2,2)...................(2,8)

(3,1)   (3,2)..................(3,8)

(4,1)   (4,2)..................(4,8)

(5,1)   (5,2)..................(5,8)

(6,1)   (6,2)..................(6,8)

(7,1)   (7,2)..................(7,8)

(8,1)   (8,2)..................(8,8)

Hence, the total number of outcomes is equal to the number of elements in sample space.

Hence, the total number of possible outcomes are:

64

Answer:

[tex]x=44-y[/tex]

Step-by-step explanation:

Let x represents the number of glasses of iced tea .

Let y represents the number of glasses of lemonade.

Now we are given that She has only 44 cups in which to serve the drinks

Since y is the number of glasses of  lemonade out of 44 glasses

So, remaining glasses = [tex]44-y[/tex]

So, remaining glasses is for iced tea .

So, No. of iced tea glasses =  [tex]x=44-y[/tex]

Hence She can serve [tex]x=44-y[/tex] number of glasses of iced tea serve.

152.04 is right i just took the test

your welcome ;)

Answer:

The mean of something is the "average"

For example, if the mean of people in the households of 7th-grade students is 4.3, this means that if you go to a random house of a 7th-grade student, you can expect around 4 people in there.

Now, for the  7th-grade students, the mean is 4.5, just a 0.2 bigger. (This means that, on average, there is more people in the 8th-grade student's households)

So Principal Coleman can infer that the amount of people in the households of  7th-grade students and 8th-grade students is almost the same, wherein the 8th-grade students there is a small chance of finding more people, but this difference is almost depreciable.

The difference in the number of cars manufactured in August and September is 15 cars.

The difference in the number of cars manufactured in August and September can be calculated as follows:

By the fundamental theorem of calculus,

[tex]\displaystyle\frac{\mathrm d}{\mathrm dx}\int_0^x\cos^{-1}t\,\mathrm dt=\cos^{-1}x[/tex]

so that

[tex]f'(0.3)=\cos^{-1}0.3\approx1.266[/tex]

A 'while loop' can be programmed with conditions to adjust a 'user value'. If 'user value' is greater than 80, 5 would be subtracted from it. If it is less than 0, 10 would be added to it. This loop continues until 'user value' does not meet either condition.

The question asks for a while loop in programming that modifies a value (user value) based on these conditions: if the user value is less than 0, it should be increased by 10 and if it's greater than 80, it should be decreased by 5. Here's a representative code for that:

while(user value < 0 || user value > 80) {

if(user value > 80) {user value -= 5; } else if(user value < 0) {user valuable += 10;}

This loop will continue to execute until the user value is not less than 0 or greater than 80.

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what polynomial models the total number of common and Endler's guppies

your answer will be:

7.3x^2+0.8+1.3

Step-by-step explanation:

this answer correct for 2022

The area of Ava's rectangular rug is 5382 square yards, calculated by multiplying the width (23 yards) and the length (234 yards).

To find the area of Ava's rectangular rug, we need to multiply its length and width:

Area = length × width

Using the given dimensions: 23 yards wide and 234 yards long:

Area = 23 × 234

First, let's perform the multiplication:

23 × 234 = 5382 square yards

Thus, the area of the rug is 5382 square yards as an improper fraction, which cannot be simplified further as a mixed number. Since the measurements are whole numbers, converting to a mixed number doesn't apply in this case.

Solution: We are given that:

5 people can paint 7 walls in 21 minutes

Therefore, 1 person can paint 7 walls in [tex] 21 \times 5=105 [/tex] minutes

Which means 1 person can paint 1 wall in [tex] \frac{105}{7} =15 [/tex] minutes

Now, 3 people can paint 1 wall in [tex] \frac{15}{3} =5 [/tex] minutes

Therefore, 3 people can paint 5 walls in [tex] 5 \times 5=25 [/tex] minutes

Answer:

25 :)

Step-by-step explanation:

Final answer:

To determine the length of the apothem of a regular octagonal stop sign given its side length and area, use the formula for the area of a regular polygon, solve for the apothem, and then calculate it to be approximately 15 inches when rounded to the nearest whole number.

Explanation:

The student is asking how to find the length of the apothem of a regular octagonal stop sign with side lengths of 12.6 inches and a total area of 770 square inches. The apothem of a regular polygon is a line from the center to the midpoint of one of its sides and is also the radius of the inscribed circle within the polygon.

To find the apothem's length, we can use the formula for the area of a regular polygon: Area = (1/2) × Perimeter × Apothem. The perimeter (P) of the octagon is the length of one side multiplied by 8 (since an octagon has eight sides). Therefore, the perimeter is 12.6 in × 8 = 100.8 in.

We can rearrange the area formula to solve for the apothem (a): Area = (1/2) × P × a becomes a = Area × 2 / P. Substituting the known values, we get: a = 770 in² × 2 / 100.8 in, which calculates to an apothem length of approximately 15.24 inches. Round this to the nearest whole number to get an apothem length of 15 inches.

The joint probability of x1 and y2 is  P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.

In the joint probability of x1 and y2 is  P (Y₂/X₁ )= P(Y₂ ∩ X₁ )/ P (X₁).

Therefore:

P(Y₂ ∩ X₁ )

=0.40 x 0.75

= 0.3

Therefore by following the law of conditional probability, the outcome of the The joint probability of x1 and y2 is  P (Y₂/X₁ ) = P(Y₂ ∩ X₁ )/ P (X₁) will be 0.3.

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A capitalist economic system is built on the respect of private property and competition. Hard work and free enterprise benefit citizens more than the government can. For the most part, government intervention is reduced. However, the government does provide security and some basic services, like infrastructure, to its citizens.

Socialist and communist systems endure more government control. Citizens of these economies have a limited amount of freedom by law. The government controls the market place and the production of most goods and services.

^ My answer from Edge

The solution to the equation (4j - 2) / 2 = 4j + 5 is j = -3. The equation was simplified by eliminating fractions and isolating the variable j through algebraic steps.

To solve the equation (4j - 2) / 2 = 4j + 5 for the variable j, you can follow these steps:

1. First, simplify both sides of the equation:  

  (4j - 2) / 2 = 4j + 5

2. Multiply both sides of the equation by 2 to eliminate the fraction:

  4j - 2 = 2 * (4j + 5)

3. Distribute the 2 on the right side:

  4j - 2 = 8j + 10

4. Move the variable terms to one side of the equation and the constants to the other side. You can do this by subtracting 8j from both sides:

  4j - 8j - 2 = 10

5. Combine like terms:

  -4j - 2 = 10

6. Add 2 to both sides to isolate the variable term:

  -4j = 10 + 2

  -4j = 12

7. Finally, divide both sides by -4 to solve for j:

  j = 12 / -4

  j = -3

So, the solution to the equation is j = -3.

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Final answer:

This answer explains how to prove that angle KAL is 90 degrees in a parallelogram using angle bisectors.

Explanation:

To prove: m∠KAL = 90°

Given: KLMN is a parallelogram, KA - angle bisector of ∠K, LA - angle bisector of ∠L.

Proof:

Proved that the measure of angle KAL is 90 degrees, which means that angle KAL is a right angle.

To prove that [tex]\( m\angle KAL = 90^\circ \)[/tex], we need to use the properties of angle bisectors and parallelograms.

Step 1: Identify the properties of a parallelogram.

In a parallelogram, opposite sides are equal in length, and opposite angles are equal. Also, adjacent angles are supplementary, meaning they add up to 180 degrees.

Step 2: Apply the properties to parallelogram KLMN.

Since KLMN is a parallelogram, we have:

[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]

[tex]\[ m\angle K = m\angle M \][/tex]

[tex]\[ m\angle L = m\angle N \][/tex]

Step 3: Use the properties of angle bisectors.

An angle bisector divides an angle into two equal parts. Therefore, we have:

[tex]\[ m\angle KAK = m\angle KAA \][/tex]

[tex]\[ m\angle LAL = m\angle LAA \][/tex]

Step 4: Express the angles in terms of the bisected angles.

Since KA is the angle bisector of [tex]\( \angle K \)[/tex], we can express [tex]\( m\angle KAK \)[/tex]and [tex]\( m\angle KAA \)[/tex] as half of [tex]\( m\angle K \)[/tex]:

[tex]\[ m\angle KAK = m\angle KAA = \frac{1}{2}m\angle K \][/tex]

Similarly, since LA is the angle bisector of [tex]\( \angle L \)[/tex], we can express [tex]\( m\angle LAL \)[/tex] and [tex]\( m\angle LAA \)[/tex] as half of [tex]\( m\angle L \)[/tex]:

[tex]\[ m\angle LAL = m\angle LAA = \frac{1}{2}m\angle L \][/tex]

Step 5: Use the supplementary angle relationship.

Since [tex]\( \angle K \)[/tex] and [tex]\( \angle L \)[/tex] are supplementary, we have:

[tex]\[ m\angle K + m\angle L = 180^\circ \][/tex]

Dividing both sides by 2, we get:

[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]

Step 6: Substitute the expressions for the bisected angles.

[tex]\[ m\angle KAK + m\angle LAL = 90^\circ \][/tex]

[tex]\[ \frac{1}{2}m\angle K + \frac{1}{2}m\angle L = 90^\circ \][/tex]

Step 7: Recognize that [tex]\( m\angle KAL \)[/tex] is the sum of [tex]\( m\angle KAK \)[/tex]and[tex]\( m\angle LAL \)[/tex].

[tex]\[ m\angle KAL = m\angle KAK + m\angle LAL \][/tex]

Step 8: Substitute the values from Step 6 into the equation from Step 7.

[tex]\[ m\angle KAL = \frac{1}{2}m\angle K + \frac{1}{2}m\angle L \][/tex]

[tex]\[ m\angle KAL = 90^\circ \][/tex]