Ms Nelson will be teaching a group math lesson with counters frist she dumps out 4 bags that have 20 counters each then she divides the counter among 6 group of students

Answer:

Option c.

Step-by-step explanation:

We have the set of real numbers greater than 8 and B the set of real numbers greater than 5 here:

A: x+2>10 ⇒ x>8

B: 2x > 10 ⇒ x>5

8∉A ; 8∈B

Note: We can see (graph) that the intervals are open, so the corresponding points do not belong to their respective sets.

Answer:

jursssursztsdigsdigssit

Step-by-step explanation:

hjnf

Answer: Lisa would need to serve 17 customers to attain the projected income.

Step-by-step explanation:

Their income on a certain day is projected to be $357.

This situation can be represented by the equation 21x + 17y = 357, where x is the number of Lisa's customers and y is the number of Daisy's customers.

On a day that Daisy is sick, the income from Daisy would be zero. For Lisa to attain the projected income of $357, the equation becomes

21x + 0 = 357

21x = 357

x = 357/21

x = 17

Answer:

Step-by-step explanation:

Given that you choose at random a real number X from the interval [2, 10].

a) Since this is a contnuous interval with all number in between equally likely

E = probability for choosing a real number is U(2,10)

pdf of E is [tex]\frac{1}{8}[/tex]

b) P(X>5) = [tex]\int\limits^10_5 {1/8} \, dx = \frac{5}{8}[/tex]

[tex]P(5<x<7) = \frac{2}{8} =\frac{1}{4}[/tex]

For

[tex]x^2-12x+35 >0\\(x-5)(x-7)>0\\x<5 or x >7[/tex]

P(X<5 or x>7) = 1-P(5<x<7)

= [tex]\frac{3}{4}[/tex]

The density function of a real number selected randomly within the range [2,10] is 1/8, with the probability of an event being the difference between the two values divided by 8. The probabilities that X is greater than 5, lies between 5 and 7 and that the inequality X^2 - 12X + 35 > 0 always holds are 5/8, 1/4 and 1 respectively.

The subject of this question is probability, particularly continuous uniform distribution. (a) A real number X selected from a certain interval [2, 10] has a continuous uniform distribution. Hence, the density function f(x) = 1/(b-a) = 1/8 for 2 ≤ x ≤ 10 and0otherwise. The probability of an event E, where E is [a,b], is the integral of f(x) from a to b, which is (b-a)/(10-2).

(b) Probability that X > 5 is the integral of f(x) from 5 to 10, which is (10-5)/8 = 5/8. Probability that 5 < X < 7 is the integral from 5 to 7, which is (7-5)/8 = 1/4. Lastly, the inequality X^2 - 12X + 35 > 0 factors out to (X-5)^2 + 10 > 0 which is always true as square number is always non-negative, thus the probability is 1.

https://brainly.com/question/22962752

#SPJ3

Answer:

[tex]R = \dfrac{16}{5}t + \dfrac{1}{5}[/tex]

where R is the R-value and t is the thickness in inches.

Step-by-step explanation:

We are given the following in the question:

The  R-value of fiberglass insulation and f its thickness have a linear relation.

Let R be the R-value and t be the thickness. Then, the equation can be written as:

[tex]R = at + b[/tex]

where a and b are constants.

When t = 3.5, R = 11

[tex]11 = 3.5a + b[/tex]

When t = 6, R = 19

[tex]19 = 6a + b[/tex]

Solving the two equation, using the elimination method, we have,

[tex]19-11 = 6a + b-(3.5a + b)\\8 = 2.5a\\\\\Rightarrow a = \dfrac{16}{5}\\\\11 = 6(\dfrac{16}{5}) + b\\\\\Rightarrow b = \dfrac{1}{5}[/tex]

Thus, the linear relationship is given by:

[tex]R = \dfrac{16}{5}t + \dfrac{1}{5}[/tex]

where R is the R-value and t is the thickness in inches.

To find a linear equation (R = mt + b) that represents the R-value of fiberglass insulation as a function of its thickness, we calculate a slope (m) of 3.2 using two known measurements. We then solve for a y-intercept (b), which is -0.5. Therefore, the equation is R = 3.2t - 0.5.

In order to derive the equation that gives the R-value as a function of the thickness, we need to use the concept of linear equations, specifically slope-intercept form (y = mx + b). First, we need to find the slope (m). Since we know two points on the line (3 ½ , 11) and (6 , 19), we calculate the slope as: m = (19-11) / (6 - 3½) = 8 / 2½ = 3.2. The y-intercept (b) is the R-value when the thickness (t) is 0. To find it, we use one of our points and the slope in the equation y = mx + b, substituting to solve for b: 11 = 3.2 * 3½ + b, hence, b = -0.5. The equation is therefore: R = 3.2t - 0.5.

https://brainly.com/question/32634451

#SPJ3

Answer:

standard deviation of the distribution = 6.325.

Step-by-step explanation:

i) standard deviation of the population σ = 20

ii) size of sample n = 10.

iii) standard deviation of the distribution = [tex]\frac{\sigma}{\sqrt{n}} = \frac{20}{\sqrt{10}} = \frac{20}{3.162} = 6.325[/tex]

Final answer:

To find the standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10, use the formula: Standard Deviation of the Distribution of Means = Population Standard Deviation / Square Root of Sample Size. By substituting the values, you get the standard deviation of 6.32.

Explanation:

The standard deviation of the distribution of means for a population with a standard deviation of 20 and sample size of 10 is calculated using the formula:

Standard Deviation of the Distribution of Means = Population Standard Deviation / Square Root of Sample Size

Substitute the values: 20 / √10 = 6.32. Therefore, the standard deviation of the distribution of means is 6.32 for this scenario.

The composite shape's area is 61.12.

Step-by-step explanation:

Step 1; To calculate the value of the composite shapes area we first divide it into shapes whose areas we know. In this case, the composite shape consists of only a circle's half and a triangle attached below it. If we can sum the individual areas of the two shapes we should be able to determine the area of the unknown shape.

Step 2; The triangle has a base length of 8 as it is from (6, 10) to (14, 10) so 14 - 6 = 8 and the height is from (10,10) and (10,1) so the height is 10 -1 = 9. So the area of any given triangle is 0.5 times the product of its base length and height. So area of this triangle = 0.5 × 8 × 9 = 36. The circle is not an entire one but only half so we calculate the entire circle's area and then half it to find its area. The diameter is 8 as the circle's ends are at (6, 10) and (14, 10) and radius = 14 - 6 / 2 = 4. The area of any circle is π times the square of its radius. So area of this circle = π × r²/2= 3.14 × 4²/ 2 = 25.12.

Step 3; Now we calculate the given composite shapes area by summing the two areas i.e areas of the half-circle and the rectangle.

Area of the composite shape = 36 + 25.12 = 61.12.

Answer: Ollie earned $9 per hour.

Step-by-step explanation:

Let x represent the amount that Ollie earned per hour.

Stan and Ollie each earned the same amount last week Stan work 20 hours and earned $13.50 per hour. This means that the total amount that Stan earned would be

20 × 13.5 = $270

Ollie worked 30 hours. This means that the total amount that Ollie earned would be

30 × x = $30x

Since they earned the same amount, then

30x = 270

x = 270/30 = $9 per hour

Answer:

$9 per hour

Step-by-step explanation:

Matt paid $70 for mp3 player.

Step-by-step explanation:

Given,

Cost of mp3 player = $149.99

Discount = 20%

Amount of discount = 20% of 149.99

Amount of discount = [tex]\frac{20}{100}*149.99[/tex]

Amount of discount = 0.2*149.99

Amount of discount = $29.99

Sale price = Cost of mp3 - Amount of discount

Sale price = [tex]149.99 - 29.99 = \$120[/tex]

Rebate = $50

Amount paid by Matt = sale price - rebate

Amount paid by Matt = 120-50 =$70

Matt paid $70 for mp3 player.

Keywords: subtraction, percentage

Learn more about subtraction at:

#LearnwithBrainly

Answer:

The answer to your question is  A = 74 ft³, B = 222 ft³, C = 222ft³

Step-by-step explanation:

Data

Total volume = 518 ft³

Prism A volume = Prism B volume / 3

Prism B volume = Prism C volume

Process

Write an equation in terms of volume of B

          Volume A + Volume B + Volume C = 518

Substitution

                B/3 + B + B = 518

                (B + 3B + 3B)/3 = 518

                               7B = 3(518)

                               7B = 1554

                                 B = 1554/7

                                 B = 222

Get the volumes

Volume A = 222/3

                 = 74

Volume B = 222

Volume C = 222

Answer: -6

Step-by-step explanation:

-4(3-1)+2

-12+4+2

-12+6

=-6

Hey there!

Just do PEMDAS

• Parentheses

• Exponents

• Multiplication

• Division

• Addition

• Subtraction

–4(3 – 1) + 2

= –4(2) + 2

= -–8 + 2

= –6

Therefore, your answer is: -6

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Number of tires that were sold is 15 and number of rims that were sold is 5. Total sales for tires is $2250 and total sales for rims is $1000

Step-by-step explanation:

Given details are selling price of tires = $150, selling price of rims = $200 and total dales = $3250

Form equation out of the given data. Let the number of rims that were sold be x. Then number of tires that were sold is 3x.

⇒ x × 200 + 3x × 150 = 3250

⇒ 200x + 450x = 3250

⇒ 650x = 3250

⇒ x = 5

Find number of tires and rims that were sold.

⇒ Number of rims that were sold = x = 5

⇒ Number of tires that were sold = 3x = 15

Find the total sales for each.

⇒ Total sales for rims = 5 × 200 = $1000

⇒ Total sales for tires = 15 × 150 = $2250

5 rims and 15 tires were sold with total sales of $1,000 for rims and $2,250 for tires.

Let x be the number of rims sold and 3x be the number of tires sold, since three times as many tires were sold as rims.

Now, we can create equations based on the given information.

The total sales for rims and tires are $3,250.

x = $3,250 / $650

3x = 3 * 5 = 15 (the number of tires sold)

Total sales for rims were $200 * 5 = $1,000, and total sales for tires were $150 * 15 = $2,250.

Answer:

Brian Peters worked for total of 45 hours.

Step-by-step explanation:

Let the total number of hours worked be 'x'.

Now Given:

Hours spent on other projects = 18 hours.

Also Given:

60% of a week's time working on drawings for a new apartment building.

Hours spent on new apartment building = [tex]60\%\times x = \frac{60}{100}x=0.6x[/tex]

We need to find the total hours worked.

Solution:

Now we can say that;

total number of hours worked is equal to sum of Hours spent on new apartment building and Hours spent on other projects.

framing in equation form we get;

[tex]x=0.6x+18[/tex]

Combining like terms we get;

[tex]x-0.6x=18\\\\x(1-0.6)=18\\\\0.4x=18[/tex]

Now Dividing both side by 0.4 we get;

[tex]\frac{0.4x}{0.4}=\frac{18}{0.4}\\\\x=45\ hrs[/tex]

Hence Brian Peters worked for total of 45 hours.

In the question, architect Brian Peters spent 60% of his total work time on a new apartment building and 40% on other projects. If those 40% equates to 18 hours, we can calculate his total work week as 45 hours by dividing 18 by 0.4.

The problem can be solved by identifying that architect Brian Peters spent 65% of his time working on other projects than the new apartment building. This implies that he spent 40% of his time on the apartment building project. Understanding that a week consists of 168 hours, we could conduct a calculation to determine his total work hours. If we take that 60% was spent on the apartment building and 40% was spent on other projects, then those 18 hours represent 40% of his total work time. Therefore, to find his total work time, we can divide 18 (hours spent on other projects) by 40%, or 0.4.

So, the calculation will be: 18/0.4 = 45 hours. This shows that Brian Peters worked a total of 45 hours within the week for all his projects. These 45 hours involve the 18 hours he spent on other projects and the remaining time he dedicated to the new apartment building drawings.

https://brainly.com/question/32197511

#SPJ3

Answer:

26.57 degrees

Step-by-step explanation:

So we need to find the angle of D in your triangle.

Since this is a right triangle we can use trigonometric functions (sin, cos, tan etc)

For this we need to use tangent since wanna do opposite over adjacent.

But since we want the angle we use tan^-1

So plug into your calculator(make sure your calculator is in degrees): tan^-1 (4/8)

We get 26.565 degrees

Answer:

Step-by-step explanation:

Triangle BCD is a right angle triangle.

From the given right angle triangle,

BD represents the hypotenuse of the right angle triangle.

With m∠D as the reference angle,

CD represents the adjacent side of the right angle triangle.

BC represents the opposite side of the right angle triangle.

To determine m∠D, we would apply

the tangent trigonometric ratio.

Tan θ = opposite side/adjacent side. Therefore,

Tan D = 4/8 = 0.5

m∠D = Tan^-1(0.5)

m∠D = 26.6° to the nearest tenth.

Answer:

The answer is 2/5

Step-by-step explanation:

I found 2 points and did y2-y1/ x2-x1 and got 2/5. And then I tested it and it worked.

Answer: the slope is 2/5

Step-by-step explanation:

The formula for determining slope is expressed as

Slope = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

y2 = final value of y

y 1 = initial value of y

x2 = final value of x

x1 = initial value of x

Looking at the graph given,

y2 = 0

y1 = - 2

x2 = 5

x1 = 0

Slope = (0 - -2)/(0 - 0) = 2/5

Answer: Coefficient of x²y² =5184

Step-by-step explanation:

18(3x + 4xy + y +3)*18(3x + 4xy + y + 3)

324( 9x² +12x²y + 3xy + 9x + 12x²y + 16x²y² + 4xy² +12xy + 3xy + 4xy² + y² + + 3y + 9x +12xy + 3y +9)

Already, x12y24x12y24 = 82944x²y²

From the expansion above, we have that: 324*16x²y²= 5184x²y²

Since, 82944x²y²/5184x²y² = 16

∴ Coefficient = 5184

The distance between the aquarium and the monkey habitat is 325 feet.

To find the distance between the aquarium and the monkey habitat, we can use the Pythagorean theorem because the aquarium and the monkey habitat form a right triangle with the gift shop.

Let's denote the distance between the aquarium and the gift shop as  a (36 feet) and the distance between the monkey habitat and the gift shop as b (323 feet). The distance between the aquarium and the monkey habitat, which we'll call c, is the hypotenuse of the right triangle.

The Pythagorean theorem states that in a 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.

[tex]\[ c^2 = a^2 + b^2 \][/tex]

Substitute the given values:

[tex]\[ c^2 = (36)^2 + (323)^2 \][/tex]

[tex]\[ c^2 = 1296 + 104329 \][/tex]

[tex]\[ c^2 = 105625 \][/tex]

Take the square root of both sides to solve for  c:

[tex]\[ c = \sqrt{105625} \][/tex]

[tex]\[ c = 325 \][/tex]

The difference between terms is the previous term divided by 4:

48/4 = 12

12/4 =3

3/4 = 0.75

Find the next two terms:

0.75/4 = 0.1875

0.1875/4 = 0.046875

Now you have 48 - 12 + 3 - 0.75 + 0.1875 - 0.046875

Answer: 38.390625

Answer:

-4

Step-by-step explanation:

The average rate of change of a function f(x) between two points x = a and x=b is given by,

[tex]f(x)=\frac{f(b)-f(a)}{b-a}[/tex]

This can be understood with a simpler example, the straight line.

In this case, the rate of change of the 'function' is given by the slope,

[tex]m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}[/tex];                

[tex](x_{1},f(x_{1})),(x_{2},f(x_{2}))[/tex] being two points on the straight line.

So, for the given problem,

a = -2

b = 2

Hence, average rate of change of [tex]f(x)=\frac{f(2)-f(-2)}{2-(-2)} =\frac{9-25}{2+2} =\frac{-16}{4} =-4[/tex]

Answer:

With side lengths 16 m, 21 m and 39 m a triangle cannot be formed.

Step-by-step explanation:

Given:

Sides of the triangle are given.

First side = 16 m

Second Side = 21 m

Third side = 39 m

We need to find whether the side length can form the triangle.

Solution:

Now we know that;

By Triangle In equality property which states that;

"The sum of length of any two side of triangle is greater than the length of the thirds side."

By applying the same in given data we get;

First Side + second side > Third side

[tex]16+21>39\\\\37>39[/tex]

which is false.

The first condition has failed itself.

So we can say that;

With side lengths 16 m, 21 m and 39 m a triangle cannot be formed.

The side lengths 16m, 21m, and 39m do not form a triangle as they do not satisfy the triangle inequality theorem, which states that for any three lengths to form a triangle, the sum of any two lengths must be greater than the third length.

In mathematics, specifically in triangle geometry, the triangle inequality theorem states that for any given three sides, the lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, if a, b, and c are the lengths of the sides:

a + b > c

a + c > b

b + c > a

Our given side lengths are 16m, 21m, and 39m. Let's check if they satisfy the triangle inequality:

16m + 21m > 39m (Is 37m > 39m? No, 37m is less than 39m, thus the inequality is not satisfied)

Therefore, the given side lengths do not form a triangle.

https://brainly.com/question/24078586

#SPJ11

Answer:

Every year they are losing 600 people a year.

Step-by-step explanation:

You take 50,000/100= 500 x 1.2=600

Answer:A)54 farms

B) 16 farms

Step-by-step explanation:

Y(1200) = (1200-1400)/100 = -200/100

Y(1200) = -2

Y(1600) = 1600-1400)/100

Y(1600) = 200/100 = 2

P(1200-1600) = (2y<-2)

2 standard deviation from the range = 68%=0.68

80 farms × 0.68 = 54 .4 approximately 54

B) 24× 0.68= 16.32 approximately 16

By using the empirical rule, it is expected that around 54 farms among the sample of 80 farms, as well as approximately 71 of 104 farms (after addition of 24 farms) will have land and building values per acre between 1300 and 1500.

The question deals with the concept of mean, standard deviation, and the empirical rule, specifically in the context of data relating to the values of land and buildings per acre on various farms.

A. Using the empirical rule, we know that approximately 68% of the population of a bell-curve distribution lies within one standard deviation from the mean. In this case, the mean is 1400 and the standard deviation is 100. So, one standard deviation above and below the mean is between 1300 and 1500. Therefore, approximately 68% of the 80 farms, or roughly 54 farms, have land and building values per acre between 1300 and 1500.

B. If we add 24 more farms to the sample, the total number of farms will be 104. Applying the same empirical rule, we'd expect approximately 68% of these, roughly 71 farms, to have land and building values per acre between 1300 and 1500.

https://brainly.com/question/35669892

#SPJ3

Answer:

Juice $0.6

Bagel $1.5

Coffee $0.3

Step-by-step explanation:

The original price is $2.40 for an orange juice (x), raisin bagel (y) and a cup of coffee(z).

The prices of the orange juice will increase by 50%:

[tex]=x+0.5x=1.5x[/tex]

The price of bagels will increase by 20%:

[tex]=y+0.2x=1.2x[/tex]

The total price of everything is $3.00.

The orange juice will cost twice as much as coffee:

[tex]x=2z[/tex]

We have the following equations:

[tex]x+y+z=2.40[/tex]

[tex]1.5x+1.2y+z=3[/tex]

[tex]x=2z[/tex]

We have 3 equations and 3 unknowns:

Solve through substitution of x=2z into both equations:

[tex]1.5x+y=2.40[/tex]

[tex]2x+1.2y=3[/tex]

Therefore before increase. Use equation before increase to solve z and not x=2z because this is after the increase.

[tex]x=0.6[/tex]

[tex]y=1.5[/tex]

[tex]z=0.3[/tex]

The original prices were $1.00 for orange juice, $0.60 for a raisin bagel, and $0.80 for coffee.

Let's denote the price of orange juice as O, the price of a raisin bagel as B, and the price of coffee as C.

Initially, we know that O + B + C = $2.40.

After the price increase, we know that (1.5O) + (1.2B) + C = $3.00 and also that 1.5O = 2C.

From the equation 1.5O = 2C, we deduce that O = 1.33C. We substitute this in the first equation to get the initial prices:

https://brainly.com/question/31571622

#SPJ3

Answer:

The violent-crime rate in a certain state of the country in that year was 1,496

Would this be an outlier?

C. Yes, because it is greater than the upper fence.

(d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?

C. The distribution of violent-crime rates is skewed right.

Step-by-step explanation:

The violent-crime rate in a certain state of the country in that year was 1,496

The lower fence is 272.8 - 1.5 x 255.5 = -110.45 crimes per​ 100,000 population.

The upper fence is 528.3 + 1.5 x 255.5 = 911.55 crimes per​ 100,000 population.

Since violent-crime rate in this certain state of the country in that year is greater than the upper fence (1496>911.55), then it is an outlier.

(d) Do you believe that the distribution of violent-crime rates is skewed or symmetric?

The distribution of violent-crime rates is not symmetric, as there are extreme values in the​ tail, which tend to pull the mean in the direction of the tail to have data are either skewed left or skewed​ right, in this case it is skewed​ right, as there are large observations in the right tail that tend to increase the value of the​ mean, while having little effect on the median.

Answer: The length is 24 inches. The width is 7 inches.

Step-by-step explanation:

Let L represent the length of the rectangle.

Let W represent the width of the rectangle.

The length of the rectangle is to be 3 inches more than triple the width. This means that

L = 3W + 3

The diagonal of the rectangle divides it into two right angle triangles and the diagonal represents the hypotenuse. The length and width represents the opposite and adjacent side. Applying Pythagoras theorem,

Hypotenuse² = opposite side² + adjacent side²

Therefore,

25² = L² + W²

625 = L² + W² - - - - - - - - - -1

Substituting L = 3W into equation 1, it becomes

625 = (3W + 3)² + W²

625 = 9W² + 9W + 9W + 9 + W²

10W² + 18W - 625 + 9 = 0

10W² + 18W - 616 = 0

Dividing through by 2, it becomes

5W² + 9W - 308= 0

5W² + 44W - 35W - 308 = 0

W(5W + 44) - 7(5W + 44) = 0

W - 7 = 0 or 5W + 44 = 0

W = 7 or W = - 44/5

Since the width cannot be negative, then W = 7

L = 3W + 3 = 7 × 3 + 3

L = 24

Answer:

8

Step-by-step explanation:

Answer:

The number of basket of apples picked by Harper and Cooper together is  [tex]5\frac{1}{4} \ \ Or \ \ 5.25[/tex].

Step-by-step explanation:

Given:

Number of basket picked by Harper = 3.5

Number of basket picked by cooper = [tex]4\frac{1}{4}[/tex]

We need to find the number of basket of apples picked by Harper and Cooper together.

Solution:

Now we can see that one number is in decimal form and other number is in mixed fraction form so we will convert both the number in simplest fraction form and then solve the same.

Number of basket picked by Harper = 3.5

Now if we divide 7 from from 2 we get the answer as 3.5 so we can say that;

3.5 can be rewritten as [tex]\frac{7}{2}[/tex]

Number of basket picked by Harper = [tex]\frac{7}{2}[/tex]

Number of basket picked by cooper = [tex]4\frac{1}{4}[/tex]

[tex]4\frac{1}{4}[/tex] can be rewritten as [tex]\frac{17}{4}[/tex]

Number of basket picked by cooper = [tex]\frac{17}{4}[/tex]

Now we can say that;

to find the number of basket of apples picked by Harper and Cooper together we will add Number of basket picked by Harper and Number of basket picked by cooper.

framing in equation form we get;

number of basket of apples picked by Harper and Cooper together = [tex]\frac{7}{2}+\frac{17}{4}[/tex]

now we will use LCM to make the denominator common we get;

number of basket of apples picked by Harper and Cooper together = [tex]\frac{7\times2}{2\times2}+\frac{17\times1}{4\times1}=\frac{14}{4}+\frac{17}{4}[/tex]

Now denominators are common so we will solve the numerators we get;

number of basket of apples picked by Harper and Cooper together = [tex]\frac{14+7}{4} = \frac{21}{4} \ \ Or\ \ 5\frac{1}{4} \ \ Or \ \ 5.25[/tex]

Hence the number of basket of apples picked by Harper and Cooper together is  [tex]5\frac{1}{4} \ \ Or \ \ 5.25[/tex].

For a semi-circle with diameter 10, the circumference is 5π, perimeter is 5π + 10, and area is 25/2π. For a circle with radius 6 and a 90-degree cut, remaining circumference is 9π, perimeter is 12π, and remaining area is 27π.

Semi-circle with Diameter 10:

a. Circumference:

The circumference of a circle is given by the formula C = π × d, where d is the diameter. For a semi-circle, it's half of the circumference of a full circle. Thus, C(semi-circle) = π × 10/2 = 5π.

b. Perimeter:

The perimeter of a shape is the sum of all its sides. For a semi-circle, it includes the curved boundary and the diameter. Therefore, P(semi-circle) = 5π + 10.

c. Area:

The area of a semi-circle is given by A(semi-circle) = 1/2 × π × r^2, where r is the radius. Substituting the given diameter, A(semi-circle) = 1/2 × π × (10/2)^2 = 25/2 × π.

Circle with Radius 6 and a 90-Degree Cut:

a. Circumference:

For the full circle, C(circle) = 2π × r = 2 × π × 6 = 12π. Since a 90-degree cut removes a quarter of the circle, the remaining circumference is C(remaining) = 3/4 × 12π = 9π.

b. Perimeter:

The perimeter includes the cut portion, so P(circle) = 12π.

c. Area:

The area of the circle is A(circle) = π × r^2 = π × 6^2 = 36π. With the cut, A(remaining) = 3/4 × 36π = 27π.

Answer:

The length of the garden is 33 feet and the width of the garden is 4 feet.                                        

Step-by-step explanation:

We are given the following in he question:

Perimeter of rectangular garden = 74 feet

Let l be the length of the garden and w be the width.

The length of the garden is 9 feet more than 6 times the width.

Thus, we can write

[tex]l = 9 + 6w\\\Rightarrow l-6w = 9[/tex]

Perimeter of rectangular garden =

[tex]2(l + w) = 74\\\Rightarrow l+w = 37[/tex]

Solving the two equation by elimination method, we get,

[tex]l-6w-(l+w) = 9 -37\\-7w = -28\\w = 4\\l = 9 + 6(4) = 33[/tex]

Thus, the length of the garden is 33 feet and the width of the garden is 4 feet.