Kwame's team will make two triangular pyramids to decorate the entrance to the exhibit. They will be wrapped in the same metallic foil. Each base is an equilateral triangle. If the base has an area of about 10.8 square feet, how much will the team save altogether by covering only the lateral area of the two pyramids? The foil costs $0.24 per square foot.

Answer:

Option C - determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.

Step-by-step explanation:

To find : Which statement best describes how to determine whether [tex]f(x) = 9-4x^2[/tex] is an odd function?

Solution :

We have a property for odd functions,

Let f(x) be an odd function then it must satisfy

[tex]f(-x)= -f(x)[/tex]

Now, we have been given the function [tex]f(x) = 9-4x^2[/tex]

For this function to be odd, it must satisfy the above property.

Replace x with -x,

[tex]f(-x)=9-4(-x)^2[/tex]

and

[tex]-f(x)=-(9-4x^2)[/tex]

Hence, in order to the given function to be an odd function, we must determine whether [tex]9-4(-x)^2[/tex] is equivalent to [tex]-(9-4x^2)[/tex] or not.

Therefore, C is the correct option.

Answer:

36π cm^2.

Step-by-step explanation:

This is a sphere . Surface area =  4πr^2.

This sphere has surface area = 4π3^2

= 36π.

The surface area of the sphere would be = 36πcm². That is option C.

Area is the measure of a region's size on a surface. The area of a plane region or plane area refers to the area of a shape or planar lamina, while surface area refers to the area of an open surface or the boundary of a three-dimensional object.

here, we have,

to calculate the surface area of a sphere:

The surface area of a sphere can be calculated through the use of the formula = 4πr²

Where,

radius (r) = 3 cm

surface area

=4πr²

= 4π × 3²

= 36π cm² ( in the terms of π)

Hence, The surface area of the sphere would be = 36πcm². That is option C.

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Jeff made $210 by selling 30 pumpkins.

Step-by-step explanation:

Given,

Selling price of each Pumpkin = $7

Number of pumpkins sold by Jeff = 30

We will multiply number of pumpkins sold by selling price per pumpkin.

Amount made by Jeff = Price per pumpkin * Number of pumpkins

Amount made by Jeff = 7 * 30 = $210

Therefore;

Jeff made $210 by selling 30 pumpkins.

Keywords: multiplication

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Answer:

45%

Step-by-step explanation:

For simplicity, let use assume there are 100 students in the school.

No. of students to complete college = (30/100) x 100 = 30 Students

President wants to increase by 50% = (50/100) x 30 = 15 Students

New set goal = 30 + 15 = 45 students.

Total number of students = 100 students

Therefore;

Rate goal % = (45/100) x 100% = 45%

The solution of the expression of the inequality - 6 ≥ 10 - 8x for x

would be;

⇒ x ≥ 2

What is Mathematical expression?

The combination of numbers and variables by using operations addition, subtraction, multiplication and division is called Mathematical expression.

Given that;

The expression of the inequality is;

⇒ - 6 ≥ 10 - 8x

Now,

Solve the inequality for x as;

The inequality is;

⇒ - 6 ≥ 10 - 8x

Add 8x both side, we get;

⇒ - 6 + 8x ≥ 10 - 8x + 8x

⇒ - 6 + 8x ≥ 10

Add 6 both side, we get;

⇒ - 6 + 8x + 6 ≥ 10 + 6

⇒ 8x ≥ 16

Divide by 8 both side, we get;

⇒ x ≥ 16/8

⇒ x ≥ 2

Hence, - 6 ≥ 10 - 8x ⇒  x ≥ 2

Thus, The solution of the expression of the inequality - 6 ≥ 10 - 8x, for x will be;

⇒ x ≥ 2

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Answer:

2.78hrs

Step-by-step explanation:

Volume of water in the pool =πr2h

V = 3.142 * 2.5² *1.7

V = 33.38m³

Emptying the pool out at 12m³ per hour

= 33.38/12

= 2.78hrs

Answer:

206

Step-by-step explanation:

We have been given that Biologists tagged 103 fish in a lake January 1. On February 1, they returned and collected a random sample of 24 fish, 12 of which had been previously tagged.

To find the number of fish in the lake, we will use proportions because ratio of tagged fish and collected fish on February 1 will be equal to ratio of tagged fish and total fish on January 1.

[tex]\frac{\text{Tagged fish}}{\text{Collected fish}}=\frac{12}{24}[/tex]

Upon substituting the number of tagged fish in our proportion, we will get:

[tex]\frac{103}{\text{Total fish}}=\frac{12}{24}\\\\\frac{103}{\text{Total fish}}=\frac{1}{2}[/tex]

Cross multiply:

[tex]1\cdot \text{Total fish}=103\cdot 2\\\\\text{Total fish}=206[/tex]

Therefore, there are approximately 206 fishes in the lake.

Answer:

500000 people

Step-by-step explanation:

The population grew by 600,000 which is 120% the earlier prediction by the town council.

Using direct proportion

600,000  -------- 120%

X              --------- 100%

X = (600000 × 100) ÷ 120 = 500000

Therefore the earlier prediction by the town council is 500000 people

The student's question is a mathematical problem calculating population growth predictions. The town council of Grand Island originally predicted a growth of 500,000 people, which is 20% less than the actual growth of 600,000 people.

To determine the prediction made by the town council, we can use the fact that the actual growth exceeded the prediction by one fifth (or 20%). If the actual growth was 600,000 people, the predicted growth can be calculated by dividing 600,000 by 1.2, as the actual growth represents 120% of the predicted value (100% original prediction + 20% excess).

Calculating the Predicted Population Growth

To find the town council's predicted growth, we can set up the equation:

Therefore, the town council had originally predicted that the population of Grand Island, Nebraska, would increase by 500,000 people between 1995 and 2005.

Answer:

The third option is correct i.e. 15 x + 30 y minus 220.

Step-by-step explanation:

We have to choose expression from the option that is equivalent to

[tex]30(\frac{1}{2}x - 2) + 40(\frac{3}{4}y - 4)[/tex]

Now, [tex]30(\frac{1}{2}x - 2) + 40(\frac{3}{4}y - 4)[/tex]

= 15x - 60 + 30y - 160

= 15x + 30y - 220

Therefore, the third option is correct i.e. 15 x + 30 y minus 220. (Answer)

Step-by-step explanation: C.

Answer:

Step-by-step explanation:

The fraction of tickets that are adult tickets is ...

  ((average price per ticket) - (child's ticket cost)) / (difference in ticket costs)

so the fraction of adult tickets is ...

  ((2881/548) -3.50)/(6.50 -3.50) = 321/548

Then the number of adult tickets is ...

  (321/548)·548 = 321

and the number of child tickets is ...

  548 -321 = 227

321 adult and 227 child tickets were sold that night.

_____

If you want to write an equation, you can let "a" represent the number of adult tickets sold. Total revenue is ...

  6.50a +3.50(548 -a) = 2881

  3.00a +1918 = 2881 . . . . . . eliminate parentheses

  3a = 963 . . . . . . . . . . . . . . . subtract 1918

  a = 321 . . . . . . . . . . . . . . . . . divide by 3

The number of child tickets is ...

  548 -a = 548 -321 = 227

Answer: if he drives the car each month, he would spend $150 lesser than when he drives the truck.

Step-by-step explanation:

The car goes 25 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is

1000/25 = 40 gallons of gas

If gasoline costs $2.50 per gallon and Jamaica chooses to buy a car, the cost of gas per month would be

2.5 × 40 = $100

The truck goes 10 miles on 1 gallon of gas. Jamaica drives 1000 miles per month, it means that the number of gallons of gas that he would use in a month is

1000/10 = 100 gallons of gas

If gasoline costs $2.50 per gallon and Jamaica chooses to buy a truck, the cost of gas per month would be

2.5 × 100 = $250

The difference between both costs is

250 - 100 = $150

Step-by-step explanation:

[tex]\lim_{n \to \infty} \sum\limits_{k=1}^{n}f(x_{k}) \Delta x = \int\limits^a_b {f(x)} \, dx \\where\ \Delta x = \frac{b-a}{n} \ and\ x_{k}=a+\Delta x \times k[/tex]

In this case we have:

Δx = 3/n

b − a = 3

a = 1

b = 4

So the integral is:

∫₁⁴ √x dx

To evaluate the integral, we write the radical as an exponent.

∫₁⁴ x^½ dx

= ⅔ x^³/₂ + C |₁⁴

= (⅔ 4^³/₂ + C) − (⅔ 1^³/₂ + C)

= ⅔ (8) + C − ⅔ − C

= 14/3

If ∫₁⁴ f(x) dx = e⁴ − e, then:

∫₁⁴ (2f(x) − 1) dx

= 2 ∫₁⁴ f(x) dx − ∫₁⁴ dx

= 2 (e⁴ − e) − (x + C) |₁⁴

= 2e⁴ − 2e − 3

∫ sec²(x/k) dx

k ∫ 1/k sec²(x/k) dx

k tan(x/k) + C

Evaluating between x=0 and x=π/2:

k tan(π/(2k)) + C − (k tan(0) + C)

k tan(π/(2k))

Setting this equal to k:

k tan(π/(2k)) = k

tan(π/(2k)) = 1

π/(2k) = π/4

1/(2k) = 1/4

2k = 4

k = 2

Answer:

[tex]m\angle R=69.4^o[/tex]

Step-by-step explanation:

we know that

In the right triangle PQR

[tex]tan(R)=\frac{PQ}{QR}[/tex] ----> by TOA (opposite side divided by adjacent side)

substitute the given values

[tex]tan(R)=\frac{8}{3}[/tex]

using a calculator

[tex]m\angle R=tan^{-1}(\frac{8}{3})=69.4^o[/tex]

Answer:

E) Choco Dream faces increasing marginal opportunity cost in the production of liquor chocolates.

Step-by-step explanation:

When Choco Dream increased their production of liquor chocolates by 500 units (to 4,500 bars per month), their opportunity was 800 units of dark chocolate. But when they needed to increase liquor chocolates by 500 more units (to 5,000 bars per month), then the opportunity cost increased to 1,000 units of dark chocolate.

That means that for the first 500 extra liquor bars, the opportunity cost = 800 dark chocolate bars / 500 liquor bars = 1.6 dark chocolate bars for every extra liquor bar.

The second increased required a higher opportunity cost = 1,000 dark chocolate bars / 500 liquor bars = 2 dark chocolate bars for every extra liquor bar.

Step-by-step explanation:

Hi,

Since there are multiple scenarios, lets first discuss the rules of developing expressions.

Using these rules we can develop the following expressions:

Tip:

In addition, the order of number doesn't matter however this is not the case in subtraction.

The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.

Answer:

Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex]   miles.

Step-by-step explanation:

Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 [tex]\frac{2}{3}[/tex] miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.

To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.

The fraction can now be written as [tex]\frac{11}{3}[/tex]. The distance of Brookside trail to the end and back is

[tex]\frac{11}{3}[/tex] +

Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 [tex]\frac{1}{2}[/tex] miles. We will add this distance twice as well to obtain the total distance traveled for this trail.

To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is [tex]\frac{5}{2}[/tex].

The distance of Forest Glen Trail to the end and back is:

[tex]\frac{5}{2}[/tex] +

The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.

[tex]\frac{22}{3}[/tex] + 5

This can be written as:

[tex]\frac{22}{3}[/tex] + [tex]\frac{5}{1}[/tex]

The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.

We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.

[tex]\frac{22}{3} + \frac{5 X 3}{1 X 3}[/tex]

= [tex]\frac{22}{3} + \frac{15}{3}[/tex]

= [tex]\frac{22+15}{3}[/tex]

= [tex]\frac{37}{3}[/tex]

To convert [tex]\frac{37}{3}[/tex] miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.

3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12 [tex]\frac{1}{3}[/tex]

Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex]   miles.

Answer:

Step-by-step explanation:

The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.

Answer:

Before stopping to eat, Leon and Marisol biked a total distance of 12    miles.

Step-by-step explanation:

Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3  miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.

To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.

The fraction can now be written as . The distance of Brookside trail to the end and back is

+

Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2  miles. We will add this distance twice as well to obtain the total distance traveled for this trail.

To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is .

The distance of Forest Glen Trail to the end and back is:

+

The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.

+ 5

This can be written as:

+

The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.

We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.

=

=

=

To convert  miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.

3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12

Before stopping to eat, Leon and Marisol biked a total distance of 12    miles.

Answer:

The average age was minimum at 1954 and the average age is 25.5.

Step-by-step explanation:

The given quadratic function is

[tex]f(x)=0.0039x^2-0.42x+36.79[/tex]

It models the​ median, or​ average, age,​ y, at which men were first married x years after 1900.

In the above equation leading coefficient is positive, so it is an upward parabola and vertex of an upward parabola, is point of minima.

We need to find the year in which the average age was at a minimum​.

If a quadratic polynomial is [tex]f(x)=ax^2+bx+c[/tex], then vertex is

[tex]Vertex=(-\dfrac{b}{2a},f(-\dfrac{b}{2a}))[/tex]

[tex]-\dfrac{b}{2a}=-\dfrac{(-0.42)}{2(0.0039)}=53.846153\approx 54[/tex]

54 years after 1900 is

[tex]1900+54=1954[/tex]

Substitute x=54 in the given function.

[tex]f(54)=0.0039(54)^2-0.42(54)+36.79=25.4824\approx 25.5[/tex]

Therefore, the average age was minimum at 1954 and the average age is 25.5.

The year when the average age at first marriage was at a minimum in a specific U.S. city was approximately 1954. The average age at first marriage for that year was approximately 28.4 years.

To find the year when the average age at first marriage was at a minimum, we need to determine the x-value at the vertex of the quadratic function. The x-value at the vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic function. For the given function f(x) = 0.0039x2 - 0.42x + 36.79, the x-value at the vertex is x = -(-0.42)/(2*0.0039) = 53.85. Since the x-value represents years after 1900, we add 1900 to get the year: 1900 + 53.85 ≈ 1954.

To find the average age at first marriage for that year, we substitute x = 53.85 into the quadratic function. f(53.85) = 0.0039(53.85)2 - 0.42(53.85) + 36.79 ≈ 28.4. Therefore, the average age at first marriage for the year 1954 was approximately 28.4 years.

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Answer:

Correct statement: a. x₁ + x₂ + x₃ > 2

Step-by-step explanation:

The variables x₁, x₂ and x₃ takes value 0 if the projects are not done and 1 if the projects are done.

Consider that at least two projects are done, i.e. 2 or more projects are done.

This can happen in:

x₁ = 0, x₂ = 1 and x₃ = 1

x₁ = 1, x₂ = 0 and x₃ = 1

x₁ = 1, x₂ = 1 and x₃ = 0

x₁ = 1, x₂ = 1 and x₃ = 1

The statement (x₁ + x₂ + x₃ > 2) will be true only when all the variables takes the value 1.

This statement implies that 2 projects are definitely done.

Thus, the correct statement is (a).

Answer:

d = $5.50 - p

Step-by-step explanation:

Answer: d = $5.50 - p

Step-by-step explanation:

Vote me Brainlets pls!

Answer: The maturity value is $43743

Step-by-step explanation:

The formula for determining simple interest is expressed as

I = PRT/100

Where

I represents interest paid on the loan.

P represents the principal or amount that was taken as loan.

R represents interest rate.

T represents the duration of the loan in years.

From the information given,

P = 42000

R = 8.3

T = 6 months = 6/12 = 0.5 years

I = (42000 × 8.3 × 0.5)/100 = $1743

The maturity value is the total amount paid after the duration of the loan. It becomes

42000 + 1743 = $43743

Final answer:

Isaac has 134 square feet of the wall left to paint after subtracting the area he has already painted (28 square feet) from the total area of the wall (162 square feet).

Explanation:

The student's question is regarding an area calculation problem. Isaac is painting a wall with dimensions of 9 feet by 18 feet and has painted a 4 feet by 7 feet section so far. To find the area left to paint, we need to calculate the total area of the wall and subtract the area that's already been painted.

Step 1: Calculate the total area of the wall

The total area of the wall is:

(Length of the wall) × (Width of the wall) = 9 ft × 18 ft = 162 square feet.

Step 2: Calculate the area that has been painted

The area that Isaac has painted is:

(Length of painted section) × (Width of painted section) = 4 ft × 7 ft = 28 square feet.

Step 3: Calculate the area left to paint

To find the remaining area to paint:

(Total area of the wall) - (Area painted) = 162 sq ft - 28 sq ft = 134 square feet.

So, Isaac has 134 square feet of the wall left to paint.

Answer: it will take 2 days and the customer will pay $49

Step-by-step explanation:

Let x represent the number of days for which the cost would be the same.

At Joseph rentals, customers will pay $47 to rent a midsize car for the first day plus two dollars for each additional day. This means that the total cost of using Joseph rental for x days would be

47 + 2(x - 1) = 47 + 2x - 2

= 45 + 2x

At Fox rental, the price for a midsize car is $36 for the first day and $13 for every additional day beyond that. This means that the total cost of using Fox rental for x days would be

36 + 13(x - 1) = 36 + 13x - 13

= 23 + 13x

At the point where renting at either companies will cost the customer the same amount, then

45 + 2x = 23 + 13x

13x - 2x = 45 - 23

11x = 22

x = 22/11 = 2

The amount that the customer will psy is

23 + 13 × 2 = 49

Answer:

The cost of 1 eraser is $0.07.

Step-by-step explanation:

Given:

The school store sells erasers. If Mrs. McBryde purchases 1000 erasers for $70.00,

Now, to find the cost of 1 eraser.

Let the cost of 1 eraser be [tex]x.[/tex]

The cost of 1000 erasers is $70.00.

So, 1000 is equivalent to $70.00.

Thus, 1 is equivalent to [tex]x.[/tex]

Now, to solve by using cross multiplication method:

[tex]\frac{1000}{70} =\frac{1}{x}[/tex]

By cross multiplying we get:

[tex]1000x=70[/tex]

Dividing both sides by 1000 we get:

[tex]x=\$0.07.[/tex]

Therefore, the cost of 1 eraser is $0.07.

Final answer:

The cost of one eraser is found by dividing the total cost of $70.00 by the number of erasers purchased, which is 1000, resulting in a cost of $0.07 per eraser.

Explanation:

To find the cost of one eraser, we divide the total cost by the number of erasers Mrs. McBryde purchased. She bought 1000 erasers for $70.00. So, we need to perform the division $70.00 ÷ 1000 erasers = $0.07 per eraser. This means each eraser costs 7 cents.

Answer:

The temperature would be -5 degrees Fahrenheit

Step-by-step explanation: It's represented by a negative integer because 15 - 20 = -5. This means the temperature outside would be -5 degrees Fahrenheit.

Hope this helps! (:

The temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees,

It is defined as the conversion from one quantity unit to another quantity unit followed by the process of division, multiplication by a conversion factor.

It is given that:

The temperature outside is 15 degrees Fahrenheit . If the temperature drops 20 degrees

=15 - 20

= -5.

A negative sign means the temperature outside would be -5 degrees Fahrenheit.

Thus, the temperature would be -5 degrees Fahrenheit if The temperature outside is 15 degrees Fahrenheit. If the temperature drops 20 degrees,

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Answer:

View Image

Step-by-step explanation:

View Image

The constant amount of depreciation in the value of boat per year is $ 500

Solution:

When he bought the boat in 2004 he paid $26,500

Therefore,

Initial value in 2004 = $ 26500

In the year 2011, Ryan's boat had a value of $23,000

Value in 2011 = $ 23000

The value of the boat depreciated linearly

If the boat depreciation is linear, then the amount by which the value of boat depreciates must be constant.

Let x be the constant depreciation in the value of boat per year

Then we can say,

Value in 2011 = Initial value in 2004 - nx

Here, "n" is the number of years

2011 - 2004 = 7 years

Therefore,

23000 = 26500 - 7x

7x = 26500 - 23000

7x = 3500

Divide both sides by 7

x = 500

Thus the rate of depreciation per year is $ 500

The annual rate of change of the boat's value is approximately -71.43 dollars.

The annual rate of change of the boat's value can be calculated using the formula for slope of a line. We subtract the initial value from the final value and divide it by the number of years the boat has depreciated. In this case, the initial value is $26,500 and the final value is $23,000. The number of years is 7 (2011 - 2004). So the annual rate of change is ($23,000 - $26,500)/7 = -$500/7 = -71.43. Therefore, the annual rate of change of the boat's value is approximately -71.43 dollars.

The student is asking about the annual rate of change in the value of a boat, which is a problem related to linear depreciation. To solve this, we need to calculate the total amount the boat depreciated over a certain period and then divide by the number of years to get the annual rate.

Ryan's boat was worth $23,000 in 2011 and was purchased for $26,500 in 2004. The total depreciation over these 7 years is $26,500 - $23,000 = $3,500. To find the annual depreciation rate, we divide the total depreciation by the number of years: $3,500 ÷ 7 years = $500 per year.

Therefore, the annual rate of change of the boat's value is $500 per year, which means the boat's value decreased by $500 every year on average.

Answer:

  about 29.7 minutes

Step-by-step explanation:

If it take c minutes for Charles to mow the lawn by himself, it takes c+16 minutes for Peter. The two of them working together can mow in one minute this fraction of the entire lawn:

  1/c + 1/(c+16) = 1/18

Multiplying by 18c(c+16), we get ...

  18(c +16) + 18(c) = c(c+16)/18

  36c +288 = c^2 +16c

  c^2 -20c = 288 . . . . . subtract 36c

  c^2 -20c +100 = 388 . . . . . add (20/2)^2 = 100 to complete the square

  (c -10)^2 = 388

  c = 10 +√388 ≈ 29.6977 . . . . . take the positive square root

It takes Charles about 29.7 minutes to mow the lawn by himself.

Part a

Angle ABC = angle CDA (given by the angle markers)

Angle BAC = angle DCA (alternate interior angles)

Segment AC = segment AC (reflexive property)

Through AAS (angle angle side) we can prove the two triangles are congruent. We have a pair of congruent angles, and we have a pair of congruent sides that are not between the previously mentioned angles.

If two triangles are congruent, they are always similar as well (scale factor = 1).

The same cannot be said the other way around. Not all similar triangles are congruent.

======================================================

Part b

Angle FGH = angle JIH (both shown to be 50 degrees)

Angle FHG = angle JHI (vertical angles)

We have enough information to prove the triangles to be similar triangles. This is through the AA (angle angle) similarity rule. Since FG and JI are different lengths, this means the triangles are not congruent.

======================================================

Part c

For each right triangle shown, divide the longer leg over the shorter leg

larger triangle: (long leg)/(short leg) = 6/3 = 2

smaller triangle: (long leg)/(short leg) = 3/2 = 1.5

The two results are different, so the sides are not in proportion to one another, therefore the triangles are not similar.

Any triangles that are not similar will also never be congruent.

======================================================

Part d

Use the pythagorean theorem to find that PQ = 5 and KL = 12

We have two triangles with corresponding sides that are the same length

So we use the SSS (side side side) triangle congruence theorem to prove the triangles congruent. The triangles are also similar triangles (scale factor = 1)

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In Mathematics, triangles can be congruent, similar, or neither. Congruency means the triangles have the same three sides and angles. Similarity means the triangles have the same shape but not necessarily the same size.

In Mathematics, particularly in Geometry, determining whether two triangles are congruent, similar, or neither is a pivotal concept. Triangles are congruent when they have exactly the same three sides and exactly the same three angles. On the other hand, triangles are similar when they have the same shape but not necessarily the same size.

To determine if triangles are congruent, you can use several postulates, including the Side-Side-Side (SSS), Side-Angle-Side (SAS), or Angle-Side-Angle (ASA) postulates. For triangle similarity, the Angle-Angle (AA) postulate is often used. In the absence of sufficient information, the triangles cannot be declared similar or congruent.

A flowchart to justify the congruence or similarity would begin by assessing if all corresponding angles and sides match. If so, the triangles are congruent. If only the angles match and the sides are proportional, then the triangles are similar. In the absence of either, the triangles are neither similar nor congruent.

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Answer:

B. 22

Step-by-step explanation:

124.06 = 2.35h + 72.36

124.06 - 72.36 = 2.35h

51.7 = 2.35h

51.7/2.35 = h

22 = h

Answer:

a. 2.28%

b. 30.85%

c. 628.16

d. 474.67

Step-by-step explanation:

For a given value x, the related z-score is computed as z = (x-500)/100.

a. The z-score related to 700 is (700-500)/100 = 2, and P(Z > 2) = 0.0228 (2.28%)

b. The z-score related to 550 is (550-500)/100 = 0.5, and P(Z > 0.5) = 0.3085 (30.85%)

c. We are looking for a value b such that P(Z > b) = 0.1, i.e., b is the 90th quantile of the standard normal distribution, so, b = 1.281552. Therefore, P((X-500)/100 > 1.281552) = 0.1, equivalently  P(X > 500 + 100(1.281552)) = 0.1 and the minimun SAT score needed to be in the highest 10% of the population is 628.1552

d. We are looking for a value c such that P(Z > c) = 0.6, i.e., c is the 40th quantile of the standard normal distribution, so, c = -0.2533471. Therefore, P((X-500)/100 > -0.2533471) = 0.6, equivalently P(X > 500 + 100(-0.2533471)), and the minimun SAT score needed to be accepted is 474.6653

Using the normal distribution, it is found that:

a) 0.0228 = 2.28% of students have SAT scores greater than 700.

b) 0.3085 = 30.85% of students have SAT scores greater than 550.

c) The minimum SAT score needed to be in the highest 10% of the population is 628.

d) The minimum SAT score needed to be accepted is 475.

In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

In this problem:

Item a:

This proportion is 1 subtracted by the p-value of Z when X = 700, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{700 - 500}{100}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772.

1 - 0.9772 = 0.0228.

0.0228 = 2.28% of students have SAT scores greater than 700.

Item b:

This proportion is 1 subtracted by the p-value of Z when X = 550, thus:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{550 - 500}{100}[/tex]

[tex]Z = 0.5[/tex]

[tex]Z = 0.5[/tex] has a p-value of 0.6915.

1 - 0.6915 = 0.3085.

0.3085 = 30.85% of students have SAT scores greater than 550.

Item c:

This is the 100 - 10 = 90th percentile, which is X when Z has a p-value of 0.9, so X when Z = 1.28.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]1.28 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = 1.28(100)[/tex]

[tex]X = 628[/tex]

The minimum SAT score needed to be in the highest 10% of the population is 628.

Item d:

This is the 100 - 60 = 40th percentile, which is X when Z has a p-value of 0.4, so X when Z = -0.25.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]-0.25 = \frac{X - 500}{100}[/tex]

[tex]X - 500 = -0.25(100)[/tex]

[tex]X = 475[/tex]

The minimum SAT score needed to be accepted is 475.

A similar problem is given at https://brainly.com/question/24663213