Last year a business earned 4.1*10^6 dollars in income.This year the business earned 2.05*10^8 dollars in income.Which best describes how this year’s earnings compare to last year’s earnings

the best approximation of the area of the circle with a diameter of 17 meters is approximately 226.99m².

Why it is and what is diameter?

The diameter of the circle is 17 meters, which means the radius is half of the diameter, or 8.5 meters.

The formula for the area of a circle is:

A = πr²2

where A is the area and r is the radius.

Substituting the value of the radius into the formula, we get:

A = 3.14 x 8.5²2

A = 3.14 x 72.25

A ≈ 226.99

Therefore, the best approximation of the area of the circle with a diameter of 17 meters is approximately 226.99 m².

In geometry, the diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest chord (a line segment connecting any two points on a circle) of the circle, and it divides the circle into two equal halves, also known as hemispheres.

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Answer:

the answers are 6.773 and 2.448

Answer:

its D

Step-by-step explanation:

calculator

Answer:

1/360

Step-by-step explanation:

A full circle corresponds to a central angle of 360°.

A 1° angle corresponds to 1/360 of a full circle.

Answer:

1/360

Step-by-step explanation:

1° angle corresponds to 1/360 of a whole circle

The number of malaria cases in 2017 is 2700.

Let the dependent variable, y is malaria cases in thousands and the independent variable, x is the year.

Here, x is the number of years starting in the year 2000.

The required model is obtained as \(y = 299e^{0.1295x}\)

Now, the predicted number of malaria cases in the year 2017, that is, x = 17 years can be computed as,

\(y = 299e^{0.1295(17)}\\\\= 299(9.020\\\\= 2700\)

Hence, the number of malaria cases in 2017 is 2700.

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Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

The length of the air strip is 451feet

Perimeter is the sum of length of the sides used to made the given figure. A regular figure with n-sides has n equal sides in it, and they are the only parts of it(that means, nothing more than those equal lengthed n sides).

Given;

Perimeter= 8876feet

Let the length be x

and the width be y

Then, length will be x= 10+35y

Perimeter of rectangle= 2l+2b

8876=2(10+35y)+y

8876=20+700y+y

y=12.6

x=10+35y

x=451

Therefore, the length by the given perimeter will be 451feet

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Answer:

\(\Huge \boxed{a=5}\)

\(\rule[225]{225}{2}\)

Step-by-step explanation:

\(8+a=13\)

Subtracting 8 from both sides:

\(8+a-8=13-8\)

\(a=5\)

\(\rule[225]{225}{2}\)

We can see here that matching the steps for constructing a congruent line segment to their pictures, we have:

Step 1 - Picture a

Step 2 - Picture b

Step 3 - Picture c

Step 4 - Picture c.

Any portion of a line with two ends and a set length is referred to as a line segment. It differs from a line that has neither a beginning nor an end and can be stretched in both directions.

The endpoints of a line segment can be used to define it. The portion of the line that begins at point A and finishes at point B, for instance, is known as the line segment AB.

A ruler or measuring tape can be used to determine the length of a line segment. The distance between two line segments' endpoints is the segment's length.

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Answer:

Step-by-step explanation:

The sum of the length of the sides is the perimeter of the triangle.

The perimeter of the triangle is 5\(\sqrt{10}\) + \(\sqrt{13}\).

The sum of the length of the sides is the perimeter of the triangle.

d = \(\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}\)

Lets take (-2, 4) and (-2, 1).

\(d = \sqrt{(-2+2)^2 + (1 - 4)^2}\\\\d = \sqrt{0 + -3^2} \\\\d = \sqrt{9} \\\)

d = 3

Now, let's take the points (-2, 1) and (-4,-2).

d = \(\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}\)

\(d = \sqrt{(-4+2)^2 + (-2-1)^2}\\\\d = \sqrt{-2^2 + -3^2} \\\\d = \sqrt{4 + 9} \\\)

d = \(\sqrt{13}\)

Now, let's take the points (-2, 4) and (-4,-2).

d = \(\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}\)

\(d = \sqrt{(-4+2)^2 + (-2-4)^2}\\\\d = \sqrt{-2^2 + -6^2} \\\\d = \sqrt{4 + 36} \\\)

d = 40 = 2\(\sqrt{10}\)

The sum of the length of the sides is the perimeter of the triangle d= 3 + \(\sqrt{13}\) + 2\(\sqrt{10}\)

The perimeter of the triangle is 5\(\sqrt{10}\) + \(\sqrt{13}\).

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Answer:

Keith spent 37 and a half minutes dusting.

Step-by-step explanation:

Given that Keith spent 2 1/2 of hours doing chores, and I have spent 1/4 of that time dusting, to determine how much time did Keith spend dusting, the following calculation must be performed:

1/2 = 0.5

1/4 = 0.25

2.5 x 0.25 = X

0.625 = X

1 = 60

0.625 = X

0.625 x 60 = X

37.5 = X

Therefore, Keith spent 37 and a half minutes dusting.

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

area = length × width = 12 1/3 × 1 1/3

the easiest way to do this multiplication is to simply bring all to full fractions :

12 1/3 = (3×12 + 1)/3 = 37/3

1 1/3 = (3×1 + 1)/3 = 4/3

so our multiplication is

37/3 × 4/3 = 37×4/(3×3) = 148/9 = 16 4/9 m²

Answer:

\((a)\ m+ 2.1 > n + 2.1\)

\((b).\ m - (-4) > n - (-4)\)

\((c)\ 9 +m> 6 + n\)

Step-by-step explanation:

Given

\(m > n\)

Required

Select true inequalities

\((a)\ m+ 2.1 > n + 2.1\)

Subtract 2.1 from both sides

\(m > n\)

This is true

\((b).\ m - (-4) > n - (-4)\)

Open brackets

\(m + 4 > n + 4\)

Subtract 4 from both sides

\(m > n\)

\((c)\ 9 +m> 6 + n\)

\(m> -9+6 + n\)

\(m> n-3\)

This is also true

Answer:

A,B,D

Step-by-step explanation:

Answer:

Step-by-step explanation:

6x + 9 = -3x - 21 -6 solve for x​

combine similar terms: 6x + 3x = -21 - 6 - 9

simplify: 9x = -36

divide 9 each side x = -4

Step-by-step explanation:

6x+9=-3x-21-6

6x+3x=-21-6-9

9x=-36

X=-36/9

X=-12

The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.

Given are two numbers which are showed in the prime factorized form.

A = 3² × 5⁴ × 7

B = 3⁴ × 5³ × 7 × 11

Prime factorization is the factorization of a number in terms of prime numbers.

In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.

A = 3² ×         5³ × 5 × 7

B = 3² × 3² × 5³ ×       7 × 11

Bring down the primes in each column.

LCM = 3² × 3² × 5³ × 5 × 7 × 11

        = 3898125

Hence the LCM is 3898125.

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Answer:

x = 30

Step-by-step explanation:

1/2(x+6) = 18

Expand brackets or use distributive law.

1/2(x) + 1/2(6) = 18

1/2x + 6/2 = 18

1/2x + 3 = 18

Subtract 3 on both sides.

1/2x + 3 - 3 = 18 - 3

1/2x = 15

Multiply both sides by 2.

(2)1/2x = (2)15

x = 30

Answer:

30

Step-by-step explanation:

If a sample consists of 600 test scores, 516 of them would be at or below the 86th percentile. If a sample consists of 600 test scores, 228 of them would be at or above the 62th percentile.

A percentile is a score that compares a specific score to the scores of the other members of a group. It displays the proportion of other scores that a given score outperformed. For instance, if you have a test score of 75 and are placed in the 85th percentile, it signifies that your score is greater than those of 85% of other test takers.

Given that,

In general, 70 % of the values in a data set lie at or below the 70th percentile.

20 % of the values in a data set lie at or above the 20th percentile.

Generally percentile defines the percentage of a data set that is below or at a value that is being considered.

Hence the percentage of the values of a data set that lies below or at the 16th percentile is  16%

Also  the values of a data set that lies below or at the 24th percentile is  24%

Given a sample of 600 test scores , the number of test scores that will be at or below the 86th percentile is 86% of  600 which is mathematically represented as:

K = \(\frac{86}{100}\) × 600

K = 516 test scores

Given a sample of 600 test scores , the number number of test scores that will be above  the 62 th percentile is (100 - 62 = 38 )% of  600 which is mathematically represented as:

a = \(\frac{38}{100}\) × 600

a = 228 test scores.

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Answer:

ANSWER 5.3 miles

See IMAGE FOR SOLUTION

The area of the region bounded by the graphs y = x² and y = x + 6 over the domain of [-3, 4] is 41.33 square units.

To plot the graphs of f(x) = x² and g(x) = x + 6 on the same axis, we can create a coordinate system with x-values ranging from -3 to 4.

We can start by evaluating the y-values for each function within this domain.

For f(x) = x²:

When x = -3, y = (-3)² = 9

When x = -2, y = (-2)² = 4

When x = -1, y = (-1)² = 1

When x = 0, y = (0)² = 0

When x = 1, y = (1)² = 1

When x = 2, y = (2)² = 4

When x = 3, y = (3)² = 9

When x = 4, y = (4)² = 16

For g(x) = x + 6:

When x = -3, y = -3 + 6 = 3

When x = -2, y = -2 + 6 = 4

When x = -1, y = -1 + 6 = 5

When x = 0, y = 0 + 6 = 6

When x = 1, y = 1 + 6 = 7

When x = 2, y = 2 + 6 = 8

When x = 3, y = 3 + 6 = 9

When x = 4, y = 4 + 6 = 10

Plotting these points on a graph, Graph is given at the bottom.

b) Shaded and display the region bounded by the graphs f(x) and domain of [-3, 4]:

To shade and display the region bounded by the graphs f(x) = x² and the domain of [-3, 4], we need to shade the area between the two curves over this domain.

The shaded region represents the area enclosed by the two curves.

c) Evaluate the area from x = -2 to x = 3:

To find the area of the region bounded by the graphs, we need to determine the points of intersection between the two curves. By setting the two equations equal to each other, we can solve for x:

x² = x + 6

Rearranging the equation, we get:

x² - x - 6 = 0

Factoring the quadratic equation, we have:

(x - 3)(x + 2) = 0

This gives us two solutions: x = 3 and x = -2. These are the x-coordinates of the points of intersection.

By evaluating the definite integral of the difference between the two curves over the interval [-2, 3], we can find the area of the region bounded by the graphs.
Using the integral notation, we have: ∫[from -2 to 3] (x + 6 - x²) dx

Integrating each term separately, we have:

∫(x dx) = (1/2)x² + C1

∫(6 dx) = 6x + C2

∫(x² dx) = (1/3)x³ + C3

To find the definite integral over the interval [-2, 3], we evaluate each integral at the upper and lower limits and subtract:

∫[from -2 to 3] (x + 6 - x²) dx = [(1/2)(3)² + C1 + 6(3) + C2 + (1/3)(3)² + C3] - [(1/2)(-2)² + C1 + 6(-2) + C2 + (1/3)(-2)² + C3]

Simplifying, we have:

= [(1/2)(9) + C1 + 18 + C2 + (1/3)(27) + C3] - [(1/2)(4) + C1 - 12 + C2 + (1/3)(-8) + C3]

= [4.5 + C1 + 18 + C2 + 9 + C3] - [2 + C1 - 12 + C2 - 8/3 + C3]

= (4.5 + 18 + 9) - (2 - 12 - 8/3)

= 31.5 + 2/3

≈ 41.33 square units

Therefore, the area of the region bounded by the graphs y = x² and y = x + 6 over the interval [-2, 3] is approximately 41.33 square units.

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Answer:

O a=0

Step-by-step explanation:

Answer:

121 unit^2.

Step-by-step explanation:

The area = height/2 * ( sum of the opposite parallel  lines)

= h/2(BC + AD

h = BF = 14 - 3 = 11 units.

BC   = 13 - 5 = 8 units.

AD = 16 - 2 = 14 units.

Area = (11/2)(8 + 14)

= 5.5 * 22

= 121 unit^2.

Answer:

121

Step-by-step explanation:

To find the total distance of Alanah's trip to the arena, we need to add up the distances of each segment of her trip. We can use the distance formula to calculate the distances between the different points.

First, let's calculate the distance between Alanah's house (A) and Mia's house (M). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((4 - 2)^2 + (14 - 10)^2)

distance = sqrt(4 + 16)

distance = sqrt(20)

distance ≈ 4.5

So the distance between A and M is approximately 4.5 miles.

Next, let's calculate the distance between Mia's house (M) and Teresa's house (N). Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((14 - 6)^2 + (16 - 12)^2)

distance = sqrt(64 + 16)

distance = sqrt(80)

distance ≈ 8.9

So the distance between M and N is approximately 8.9 miles.

Finally, let's calculate the distance between Teresa's house (N) and the arena. Using the distance formula, we get:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

distance = sqrt((16 - 10)^2 + (8 - 16)^2)

distance = sqrt(36 + 64)

distance = sqrt(100)

distance = 10

So the distance between N and the arena is exactly 10 miles.

Now we can add up the distances of the three segments to get the total distance of Alanah's trip to the arena:

total distance = 4.5 + 8.9 + 10

total distance ≈ 23.4

Therefore, the total distance of Alanah's trip to the arena is approximately 23.4 miles

First find the area of the square, then the triangle.

15 times 17 = 255 sq. yd

Triangle:

(5 times 5)/2 = 12.5 sq. yd

Your answer is 267.5 sq. yd

Hope this helps.

Answer:

Step-by-step explanation:

5s + 6c = 23.91

2s + 7c = 17.89

10s + 12c = 47.82

-10s - 35c = -89.45

-23c = -41.63

c =  $1.81 for a large coffee

2s + 7(1.81) = 17.89

2s = 5.22

s = $2.61 for a scone

The value of the ratio of tan(90°-R) using the sketch is PR/PQ

From the question, we have the following parameters that can be used in our computation:

The right triangles (see attachment)

From the right triangle, we have the following readings

Opposite of 90 - R = PR

Adjacent of 90 - R = PQ

The ratio of tan(90°-R) is then calculated as

tan(90°-R) = Opposite/Adjacent

So, we have

tan(90°-R) = PR/PQ

Hence, the ratio of tan(90°-R) using the sketch is PR/PQ

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Answer:

b because -4°F plus 4°F would be 0°F

Given the equation

First, open the bracket on the left-hand side.

Next, add 35 to both sides of the equation.

To solve for x, divide both sides by 5.

The value of x is 12.

Answer:

Step-by-step explanation:

Initial volume of mixture is 100 ml with oil to water ratio of 1 : 4.

First, let's find the volume of each component.

If the oil is x then water is 4x according to ratio and their sum is 100 ml:

So, we have 20 ml of oil and 80 ml of water.

Now, let's added volume of oil be y. Then we have the ratio:

So, we have 40 ml of oil and 80 ml of water.

Lastly, let's added water be z. Then we have the ratio:

We must add 40 ml of water.