Find the circumference and area of the circle.

Using an exponential function and integration, it is found that over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.

Exponential function:

A decaying exponential function is modeled by:

⇒ A (t) = A (0) (1 - r)ⁿ

In which:

A(0) is the initial value.

r is the decay rate, as a decimal.

In this problem:

In the first year, the country emits 80,000 kilotons, hence . A (0) = 8000

Emissions will decrease 2.5% in each successive year, hence r = 0.026

Then, the equation for the amount emitted each year is:

⇒ A (t) = A (0) (1 - r)ⁿ

⇒ A (t) = 80000 (1 - 0.025)ⁿ

⇒ A (t) = 80,000 (0.975)ⁿ

The total amount emitted over the course of the 11 year period is:

T = ∫ 0 to 11 ( A (t) ) dt

Hence:

T = ∫ 0 to 11 ( 80000 (0.974)ⁿ ) dt

Applying the Fundamental Theorem of Calculus:

T = 763,968 kilotons

Hence, Over the entire 11 year period, the country will emit 763,968 kilotons of carbon dioxide.

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Hi Annie. I was interested in engaging you about your post because of my differing view. However, I think I am open to changing my views because I am not dogmatic. Do you think I am too pliable?

Throughout the Civil War, African Americans assumed crucial roles in the Union war effort. From enlisting as soldiers to acting as laborers and even spies, their contributions left an indelible impact on history.

Despite being subjected to rampant discrimination and racism from both Confederacy and Union forces, these individuals exhibited incredible heroism and bravery.

Excelling in dangerous missions that often led them to become prisoners of war, they persevered as they fought for the freedoms of themselves and others.

Hari Jones' TED talk shines a much-needed light on this overlooked aspect of history, revealing not only the extensive involvement of African American soldiers but also the pivotal role played by women in areas such as nursing, cooking, and espionage.

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The length of the other legs of the isosceles right triangle is 13 + 13√2 centimetres.

The hypotenuse of an isosceles right triangle is 13 centimetres longer than either of its legs.

An isosceles right triangle is a right triangle whose legs are the same length. The sides of a right triangle can be found using Pythagoras's theorem.

Therefore,

let

y = other legs

Therefore,

(x + 13)² = x² + x²

(x + 13)(x + 13) = 2x²

x² + 13x + 13x + 169 = 2x²

x² - 26x - 169 = 0

Therefore, using the quadratic formula,

[tex]\frac{-b+\sqrt{b^{2} - 4ac } }{2a}[/tex]

where

x = 13 ± 13√2

Therefore, we can only use positive values

x = 13 + 13√2

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Answer:

x = 72 cm

Step-by-step explanation:

Because the two figures are similar, we can create a proportion between one set of similar sides (i.e., the side measuring 48 cm and the side measuring 6 cm) and another set (the side measuring x cm and the side measuring 9 cm.  This, will allow us to solve for x:

[tex]\frac{6}{48}=\frac{9}{x}\\ 432=6x\\ 72=x[/tex]

Another way to solve would have been to notice that the scale factor used to create the bigger puzzle piece is 8 since 6 * 48.  In order for the smaller figure to be considered similar to the larger, every side had to be multiplied by the same scale factor.  Since the scale factor is 6, x must be 72 cm as 9 * 8 = 72  

The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].

In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:

Complex number (rectangular form)

z = r · (cos θ + i sin θ)

Complex number (polar form)

[tex]z = r\cdot e^{i\cdot \theta}[/tex]

Where:

Division between two complex numbers in polar form:

[tex]\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}[/tex]

This number is equivalent to the following expression in rectangular form:

z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]

If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:

z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]

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The expression that represents the total amount that Ignatio and his friends spent is 15t

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

After spending on t games, we have

f(t) = Rate * t

Substitute the known values in the above equation, so, we have the following representation

f(t) = 15 * t

Evaluate

f(t) = 15t

Hence, the expression that represents the total amount that Ignatio and his friends spent is 15t

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a) The average slope or rate of change between (0, 1) and (2, 4) is 3/2.

b) The average slope or rate of change between (-2, 1/4) and (-1, 1/2) is 1/4.

c) The slope or rate of change is not constant between these two pairs of points, since the average slopes are different.

d) The function connecting these pairs of points is not a linear function.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The average slope or rate of change between two points (x1, y1) and (x2, y2) on a line is given by:

average slope = (y2 - y1) / (x2 - x1)

For the points (0, 1) and (2, 4), the average slope is:

average slope = (4 - 1) / (2 - 0) = 3/2

For the points (-2, 1/4) and (-1, 1/2), the average slope is:

average slope = (1/2 - 1/4) / (-1 - (-2)) = 1/4

When the average slopes of these two pairs of points differ, the slope or rate of change is not constant. As a result, the function connecting these point pairs is not linear.

Because a linear function has a constant slope, a function with a variable slope cannot be linear.

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The percentage of females that do not satisfy the requirement is given as follows:

55.17%.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is obtained by the equation presented as follows:

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

The mean and the standard deviation are given as follows:

[tex]\mu = 998, \sigma = 202[/tex]

The proportion that does not satisfy the requirement is the p-value of Z when X = 1025, hence:

Z = (1025 - 998)/202

Z = 0.13

Z = 0.13 has a p-value of 0.5517.

Hence the percentage is given as follows:

0.5517 x 100% = 55.17%.

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Answer:

A multi-step-word problem is like a puzzle with lots of pieces. Multi-step word problems are math problems that have more than one operation. An operation is addition, subtraction, multiplication, or division. Multi-step word problems can have any combination of these operations

The value of A, B, C,D are 33, 36,25 and 16 respectively

A word problem is a math problem written out as a short story or scenario. We use this word problem to solve the unknowns.

The total number of students is 60 and 24 students prefer volley ball. therefore the number of students that prefer basketball = 60-24 = 36 students

Since 11 student are girls that prefer basketball, therefore the number of boys that prefers basketball = 36-11 = 25

C = 25

and B = 36

55% of the students are boys, therefore the number of boys = 55/100 × 60 = 33

A = 33

therefore the number of boys that prefer volley ball= 33-25 = 8

Number of girls = 60-33 = 27

therefore number of girls that prefer volley ball = 27-11 = 16

D= 16

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The calculated value of the area of the real room is 10.67 cm²

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

In the drawing, 3cm represents 4cm

This means that

Scale factor = 4/3

Also, we have the dimension of the scale drawing to be

Dimension = 3cm by 2 cm

So, the area of the bedroom in the scale is

Area = 3cm * 2cm

For the actual room, we have

Area = 3cm * 2cm * (4/3)²

Evaluate the exponent

Area = 3cm * 2cm * (16/9)

Evaluate the products

Area = 10.67 cm²

This means that the real area is 10.67 cm²

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Answer:

18+5f

Step-by-step explanation:

6+9f+5+4+3-4f

=11+5f+7

=18+5f

Answer:

18 + 5f

Step-by-step explanation:

To simplify the expression 6 + 9f + 5 + 4 + 3 - 4f, we must combine like-terms.

6 + 5 + 4 + 3 = 18 (6,5,4, and 3 are like-terms because they are all normal integers)

18 + 9f - 4f (9f and 4f are like-terms because they have the same variable f)

18 + 5f

Answer:

245 inches

Step-by-step explanation:

Yards->Inches

1 yard = 36 inches

Therefore, 6 yards = 36 x 6 = 216 inches

Feet->Inches

1 feet = 12 inches

Therefore, 2 feet = 2 x 12 = 24 inches

Adding all inches,

=> 216 + 24 + 5

=> 245 inches

An inequality to show the number of people  is  p ≥ 12

Let p be the number of people on the bus. We know that there are at least 12 people on the bus, so we can write:

p ≥ 12

This inequality means that the number of people on the bus, p, must be greater than or equal to 12.

To graph this inequality, we can draw a horizontal line at y = 12 on the y-axis, and shade the area above the line, since any value of p that is greater than or equal to 12 satisfies the inequality.

Here's a graph of the inequality attached

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Answer:

angle 5 is 120 since there is Z shape with angle 3

Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

The triangle has one solution. The remaining side c ≈ 4 and remaining angles B = 30°; C = 31°.

Option D is correct.

if angle A is obtuse and if a > b then the triangle has one solution

We are given ∠ = 119° which is obtuse and side a= 7 and side b - 4 i.e 7>4 so, the triangle has one solution.

Finding remaining sides c and ∠B and ∠C

Using the Law of sines to find ∠B

a/sin A = b/sin B

7/sin 119° = 4/sin B

7 * sin B = 4 * sin 119

7*sin B = 4(0.874)

sin B = 3.496/7

B = sin^-1(0.4994)

B = 29.96 = 30°

We know that sum of angles of triangle = 180°

So, 180° = 119° + 30° +∠C

180° = 149° + ∠C

=> ∠C = 180° - 149°

∠C = 31°

Now finding c

b/sin B = c /sin C

4/Sin 30 = c/sin 31

4* sin 31 = c*sin 30

4*0.515 = c* 0.5

=> c =  4*0.515/0.5

c = 4.12 ≈ 4

So, Option D one solution; c ≈ 4; B = 30°; C = 31° is correct.

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Determine whether the given triangle has no solution, one solution or two solutions. Then solve the triangle. Round measures of sides to the nearest tenth and measures of angles to the nearest degree

A = 119°, a=7, b=4

Question 7 options:

one solution; c ≈ 7; B = 30°; C = 119°

no solution

one solution; c ≈ 4; B = 31°; C = 30°

one solution; c ≈ 4; B = 30°; C = 31°

The fraction expression 2 1/2 - 4 1/4 when evaluated is -1 3/4

To solve 2 1/2 - 4 1/4, we need to convert the mixed numbers into improper fractions, then find a common denominator and subtract the two fractions.

First, we convert 2 1/2 and 4 1/4 into improper fractions:

2 1/2 = 5/2

4 1/4 = 17/4

Next, we find a common denominator. In this case, the smallest common denominator is 4:

5/2 = 10/4

17/4 = 17/4

Now we can subtract the fractions:

10/4 - 17/4 = -7/4

Finally, we can convert the resulting improper fraction back into a mixed number:

-7/4 = -1 3/4

Therefore, 2 1/2 - 4 1/4 = -1 3/4.

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Answer:

( -6, 6)

Step-by-step explanation:

The equation 5ʷ ⁺ ³ = 17 when solved for w is approximately w = 0.41

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

5ʷ ⁺ ³ = 17

Take the logarithm of both sides of the equation

So, we have

w + 3 = ln(17)/ln(3)

Evaluate the quotient on the left side of the equation

This gives

w + 3 = 2.59

So, we have

-3 + w + 3 = 2.59 - 3

Evaluate

w = 0.41

Hence, the equation when solved for w is approximately w = 0.41

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The finance charge for Sandra Lazzaro, using the average daily balance method, is $13.63.

The average daily balance is one of the methods for computing the finance charges (interest and other fees).

The average daily balance method uses the balance owed at the end of each day of the billing period, and not the balance owed at the end of the week, month, or year.

Billing period for the credit card = 31 days

Unpaid credit card balance = $750

Payment made three days before month-end = $600

Finance charge rate per month = 2.2%

Method = Average daily balance

Day        Description    Amount    Average Balance

1 - 28     Balance           $750       $21,000 ($750 x 28 days)

29 - 31   Payment        -$600       $-1,800 ($600 x 3 days)

31           Total                              $19,200

Average daily balance = $619.35 ($19,200 ÷ 31)

Finance charge = $13.63 ($619.35 x 2.2%)

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The value of the stock at the end of the two weeks would be 70, which is 30% lower than the starting value of 100.

What is Algebraic expression ?

An algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, exponents, and roots. It typically represents a mathematical relationship or formula and can be used to solve problems and make predictions.

Assuming you started with a value of 100, the value of the stock would be lower after these two weeks.

In the first week, the stock dropped by 60%, which means its value decreased to 40% of its original value. Therefore, the value of the stock at the end of the first week would be:

100 * 0.4 = 40

In the second week, the stock increased in value by 75%. Therefore, the value of the stock at the end of the second week would be:

40 * 1.75 = 70

Therefore, the value of the stock at the end of the two weeks would be 70, which is 30% lower than the starting value of 100.

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a) When Nevaeh makes $1,975 in sales for the week, her total earnings, based on her base salary and sales commission rate, are $695.

b) When she makes x in sales for the week, her total earnings are represented by the equation, y = 300 + 0.2x.

The total earnings for the week can be determined using the equation y = 300 + 0.2x, where x represents her total sales for the week while 0.2 represents a 20% sales commission.

The base salary, in this situation, is $300.

Guaranteed (base) salary per week = $300

Sales commission = 20% of sales

Sales for the week = $1,975

a) Total earnings = $695 ($300 + $1,975 x 20%)

Sales for the week = x

b) Total earnings, y = $300 + 0.2x ($300 + 0.2x)

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The thickness of the said metal piece is 560 micrometers

Solving this question would require us to switch the thickness of the metal from meters to micrometers.

So, 1 meter is equivalent to 1,000,000 micrometers; and when 0.00053 meters is multiplied by 1,000,000, we get:

0.00053 m * 1,000,000 = 560 µm

Consequently, the thickness of the said metal piece is 560 micrometers.

A metal piece's thickness is defined as the distance, measured perpendicular to its opposing surfaces, between those surfaces. It is a crucial aspect in determining the strength and longevity of the metal object and is often stated in length measures like millimeters, inches, or micrometers.

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What is the thickness of the metal piece in micrometers, given that it is 0.00053 meters thick?

Answer:

  (x -6)² +(y +2)² = 128

Step-by-step explanation:

You want the equation of the circle centered at (6, -2) through point (14, 6).

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

For center (h, k) = (6, -2), we can find the value of r² knowing that it will be the value that lets the point (14, 6) satisfy the equation.

  (14 -6)² +(6 -(-2))² = r² = 8² +8² = 128

The circle equation is ...

  (x -6)² +(y +2)² = 128

If the Amethyst Woodstar species of hummingbird beats its wings about 80 times per second and there are 60 seconds in a minute, it beats its wings D. 43,200 times in 9 minutes.

The number of times that the Amethyst Woodstar species of hummingbird beats its wings in 9 minutes can be determined using the mathematical operation of multiplication.

The number of times it beats its wings = 80 seconds per second

The total number of minutes involved = 9 minutes

1 minute = 60 seconds

The total number of times it beats in 9 minutes = 43,200 (80 x 60 x 9)

Thus, using multiplication operation, the number of times the bird beats its wings is Option D.

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Answer:

X       H(x)=2x+3

-4       -5

0        3

1         5

2        7

3        9

When a student is chosen at random, the student is more likely to be from Mrs Johnson's class.

The probability that the student got A in the first semester will be 0.15.

When a student is chosen at random, the student is more likely to be from Mrs Johnson's class. It should be noted that this is because 152 students out of 300 are from her class compared to Dixon who has 148 students.

The probability that the student got A in the first semester will be:

= 46 / 300

= 0.15

The probability for the last question will be:

= 14 / 148

= 0.095.

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