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The side lengths of the triangle are 8 cm, 12 cm, and 16 cm

To solve for the side lengths of the right triangle, we can use the Pythagorean Theorem, which states that for any right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). Mathematically, this is written as a^2 + b^2 = c^2.

Let's denote the shorter leg of the triangle as x. Then, according to the problem, the longer leg is x + 4 cm and the hypotenuse is x + 8 cm. Plugging these expressions into the Pythagorean Theorem, we have:

x^2 + (x + 4)^2 = (x + 8)^2

Expanding and simplifying the equation:

x2 + x2 + 8x + 16 = x2 + 16x + 64

2x2 + 8x + 16 = x2 + 16x + 64

x2 - 8x - 48 = 0

Solving this quadratic equation for x, we find:

x = 8 cm (shorter leg)

x + 4 = 12 cm (longer leg)

x + 8 = 16 cm (hypotenuse)

Therefore, the side lengths of the triangle are 8 cm, 12 cm, and 16 cm

Area of each square = 14 sq. cm.
length of each square = sqrt(14) = 3.7 cm

 length of one side  = 8 x 3.7 = 29.6 cm

Perimeter of the checker board = 4 x 29.6 = 118.4 cm

The perimeter of the checker board  118.4 cm

Area of each square = 14 sq. cm.

The square root of area is the length of one side

[tex]length of each square =\sqrt{14} = 3.7 cm[/tex]

[tex]length of one side = 8 * 3.7 = 29.6 cm[/tex]

Perimeter (P) =4 (length of side a)

[tex]P=4a[/tex]

[tex]Perimeter of the checker board = 4 *29.6 = 118.4 cm[/tex]

Therefor we get the perimeter of the checker board  118.4 cm

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To find the total number of people surveyed in 6 days with numbers tripling each day starting with 750, we calculate the number for each day and sum them up, giving a total of 273000 people surveyed.

To calculate the total number of people surveyed in 6 days if 750 people were covered on the first day and the number tripled every subsequent day. We will use an exponential growth formula to find the answer.

On Day 1: 750 people.

On Day 2: 750 × 3 = 2250 people.

On Day 3: 2250 × 3 = 6750 people.

On Day 4: 6750 × 3 = 20250 people.

On Day 5: 20250 × 3 = 60750 people.

On Day 6: 60750 × 3 = 182250 people.

To find the total number of people surveyed over the 6 days, we add up the total number of people surveyed each day:
750 + 2250 + 6750 + 20250 + 60750 + 182250 = 273000 people.

Therefore, the correct answer is C. 273000.

The premium of $200,00 term life insurance policy is $1,202

Annualized premium is the total amount paid in a year's time to keep the life insurance policy in force. The annualized premium amount of a life insurance policy does not include taxes and rider premiums.

Given, Jade wants to buy a $200,000 term life insurance policy. She is 34 years old.

Jade wants to buy a $200,000 term life insurance policy.  She is 34 years old.

Since, Jade is female.

Using table for 10-year policy: We will see the column of female.

Annual premium of life insurance per $1000 for 10-years policy term of 34-years old female = $6.01

  For $1000 life insurance premium = $6.01

  For     $1    life insurance premium = $0.00601

For $20000 life insurance premium = 200000 x 0.00601      

For $20000 life insurance premium =  $ 1,202

Therefore, The premium of $200,00 term life insurance policy is $1,202  

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Answer:

0.005377 people/m²

Step-by-step explanation:

5377 people/km² can written as

5377 × [tex]\frac{people}{km^2}[/tex]

Now we have to find the value in [tex]\frac{people}{meter^2}[/tex]

Since 1 km = 1000 meter.

So 5377 × [tex]\frac{people}{km^2}[/tex] = 5377 × [tex]\frac{people}{(1000)^2met^2}[/tex]

= [tex]\frac{5377}{(1000)^2}[/tex] people per met²

=  [tex]\frac{5377}{(1000000)}[/tex]

= 0.005377 people/m²

Final answer:

By using the principle of inclusion-exclusion, we calculate that all 20 girls on the basketball team are either over 16 years old or taller than 170 cm, as the sum of the individual criteria minus the intersection equals the total number of girls on the team.

Explanation:

To determine how many of the girls on the basketball team are either over 16 years old or taller than 170 cm, we can use the principle of inclusion-exclusion. According to the information provided, there are 20 girls on the team in total, of which 17 are over 16 years old, 12 are taller than 170 cm, and 9 satisfy both criteria. The principle of inclusion-exclusion states that the number of elements in the union of two sets is equal to the sum of the sizes of each set minus the size of their intersection.

Using this principle:

Number of girls over 16 years old: 17

Number of girls taller than 170 cm: 12

Number of girls who are both over 16 and taller than 170 cm: 9

The calculation would be as follows:

17 (over 16) + 12 (taller than 170 cm) - 9 (both) = 20

Therefore, there are 20 girls on the team who are either older than 16 or taller than 170 cm.

The reasoning is because you are subtracting 2. If you were to be adding 2, then it would be -6.

Since you are subtracting 2 it = 10.

Glad to help a Senior mod out.

Thanks, Plip.

The given sequence is 25, 10, 4.

Notice that this is a geometric sequence because here we have equal common ratio.

So, common ratio : r = [tex] \frac{a_{2}}{a_{1}} [/tex]

= [tex] \frac{10}{25} [/tex]

= 0.4

So, each term is 0.4 times of it's previous term.

Hence, to get the next term of this sequence, multiply 0.4 with the third term 4.

So, fourth / next term = 4* 0.4 =1.6

Hence, next term of this sequence is 1.6.

Hope this helps you!

Answer:

Step-by-step explanation:

the answer is 8/5 i just did it on my quiz and got it right.

Answer:

A(0, -3) ;  B(3, -2) and C(1, -1).

Step-by-step explanation:

Given  : ΔABC with vertices A(-3, 0), B(-2, 3), C(-1, 1) is rotated 180° clockwise about the origin.

To find : What are the coordinates of the vertices of the image.

Solution : We have given

Vertices A(-3, 0), B(-2, 3), C(-1, 1)  is rotated 180° clockwise.

By the rotation rule of 180° clockwise : (x ,y) →→ ( -x ,-y).

Then vertices would be

A(-3, 0) →→ A(3, 0)

B(-2, 3) →→ B(2, -3)

C(-1, 1) →→ C(1, -1).

Reflection y = -x then

A(0, -3) ;  B(3, -2) and C(-1, 1).

Therefore, A(0, -3) ;  B(3, -2) and C(1, -1).

The function f(x)=300-25x represents the decline of population in a fishing lake that was initially stocked with 300 bass. Each year, the population reduces by 25. For instance, after 4 years, the number of bass left in the lake would be 200.

The question is about a fishing lake that was initially stocked with 300 bass. As per the information given, the population of bass in the lake decreases by 25 each year. Therefore, if we let x represent the number of years, then every year, the number of bass decreases by 25x. This relationship is represented by the algebraic function f(x)=300-25x.

To provide a practical understanding, suppose you want to calculate the number of bass remaining after 4 years. You just substitute '4' in place of x in the equation. Hence, f(4) = 300 - 25 * 4 = 300 - 100 = 200. So, after 4 years, there would be 200 bass remaining in the lake.

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The equation representing the number of people, y, at the fair x hours after the gates open:

y = 68 * 1.5^(x-1)

Initial number of people: 68 (given)

Growth factor per hour: 1.5 (given)

Number of hours since gates opened: x

The equation uses the following logic:

Start with the initial number of people (68).

Multiply by the growth factor (1.5) to account for the increase after the first hour.

Since the growth factor applies after each hour, raise it to the power of (x-1) to account for the total number of times it's applied after x hours. This is because the first hour's growth is already accounted for in the initial number.

Therefore, the equation y = 68 * 1.5^(x-1) accurately represents the number of people at the fair x hours after opening.

Complete question:

When the county fair opened its gates, 68 people entered the fairgrounds. After one hour, there were 1.5 times as many people on the fairgrounds as when the gates opened. After two hours, there were 1.5 times as many people on the fairgrounds as the previous hour. If this pattern continues, write the equation representing the number of people, y, at the fair x hours after the gates open.

John can make a profit by selling ice cream from the cylindrical jar. After calculating the volume, he would earn approximately $15.70 in revenue, and by deducting the initial cost ($7), he makes a profit of around $8.70.

To determine if John will make a profit by selling the entire ice-cream cylindrical jar, we first need to calculate the volume of the jar to find out how many cones he can fill. The jar has a diagonal of 20 cm and a height that is three times its width. Assuming the width is 'w' and height is '3w', we can use the Pythagorean theorem with the jar's diagonal to find 'w', since the diagonal forms a right triangle with the width and height of the cylinder.

The formula for the Pythagorean theorem is diagonal^2 = width^2 + height^2, which gives us 20^2 = w^2 + (3w)^2. Solving for 'w', we get w = 4 cm and height = 12 cm. The volume 'V' of the cylinder is given by V = π * radius^2 * height, which gives us V = π * 2^2 * 12, therefore, V = 48π cm^3. Then, we divide the jar's volume by the volume of each ice cream cone to find the number of cones, 48π cm^3 / 30 cm^3/cone ≈ 5π cones.

Given that John sells each cone for $1, the total revenue from selling all the ice-cream cones would be approximately $5π. Since π is approximately 3.14, his total revenue would be about $15.70. Subtracting the initial cost of the jar ($7), we find that John would make a profit of approximately $8.70.

Therefore, John will indeed make a profit out of selling the jar of ice cream.