Bob and Meena play a two-person game which is won by the first person to accumulate at least 10 points. On each turn, there is a $\frac{2}{5}$ probability that Bob will get two points and Meena will lose one point. If that doesn't happen, then Meena gets two points and Bob loses a point. Meena is now ahead 9 to 6. What is the probability that Meena will win?

Answer:

8

Step-by-step explanation:

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:)

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.

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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]

Answer:

15.6 liters

Step-by-step explanation:

Let the porridge eaten by Papa bear be 'x' liters.

Given:

Mama Bear ate 80% as much porridge as Papa Bear did.

Baby Bear ate as much as Mama Bear did.

Papa Bear ate 1.2 liters more porridge than Mama Bear did

So, porridge eaten by Mama Bear = 80% of 'x' = [tex]0.80x[/tex]

Now, Baby Bear eats same amount as Mama Bear. So,

Porridge eaten by Baby Bear = [tex]0.80x[/tex]

Papa Bear ate 1.2 liters more than Mama Bear.

Framing in equation form, we get:

[tex]x = 1.2 + 0.80x[/tex]

[tex]x-0.80x=1.2[/tex]

[tex]0.20x=1.2[/tex]

[tex]x=\frac{1.2}{0.20}=6\ liters[/tex]

So, Papa Bear ate 6 liters of porridge.

Mama Bear ate = 0.80 × 6 = 4.8 liters

Baby Bear ate = 4.8 liters.

So, total porridge = Papa Bear + Mama Bear + Baby Bear

Total porridge eaten = 6 + 4.8 + 4.8 = 15.6 liters

Answer:

Step-by-step explanation:answer is 20%

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

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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:

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].

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.

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: 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

Answer: she rented the car for 4 days.

Step-by-step explanation:

Let x represent the number of days for which Sonya rented the car.

She pays a fee of $50 for the rental plus $20 each day she had the car. This means that if she rents the car of x days, the total amount that she would pay is

20x + 50

Suppose she pays a total for $130, it means that the number of days for which she rented the car would be

20x + 50 = 130

Subtracting 50 from the left hand side and the right hand side of the equation, it becomes

20x + 50 - 50 = 130 - 50

20x = 80

x = 80/20 = 4

Answer: the small bottle holds 15 ounces while the large bottle holds 23 ounces.

Step-by-step explanation:

Let x represent the number of ounces that a small bottle holds.

Let y represent the number of ounces that a large bottle holds.

He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. It means that

2x + 2y = 76 - - - - - - - - - - - - 1

The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. This means that

4x + y = 83 - - - - - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 1, it becomes

4x + 4y = 152

4x + y = 83

Subtracting, it becomes

3y = 69

y = 69/3 = 23 ounces

Substituting y = 23 into equation 1, it becomes

2x + 2 × 23 = 76

2x + 46 = 76

2x = 76 - 46 = 30

x = 30/2 = 15 ounces

Answer:

its 15 and 19 ounces on IXL

Step-by-step explanation:

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:

= 20.83%

Step-by-step explanation:

5/24 * 100

= 20.83%

To find what percent of people did not like the movie when 5 out of every 24 people did not, we calculate 5/24 as a percentage which is approximately 20.83%, rounded to about 21% of the people.

To calculate the percentage of people who did not like the movie, we need to set up a proportion where the number of people who did not like the movie is to the total number of people. Given that 5 out of every 24 people did not like the movie, we can express this as a fraction: 5/24. To find the equivalent percentage, we set up a fraction with 100 as the denominator and cross-multiply:

5/24 = x/100

Now we cross-multiply and solve for x:

24x = 5imes 100

x = (5 imes 100) / 24

x = 500 / 24

x = 20.833...

This equates to approximately 20.83%, which can be rounded to about 21%. Therefore, about 21% of the people did not like the movie.

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.

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.

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:

B and C.

Step-by-step explanation:

A prism can be constructed from 4 sided polygons like a rectangle.

A pyramid  (not including the vertex) can be constructed from  squares of diminishing size.

The piling method allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.

The piling method, also known as the additive method or stacking method, allows for the construction of various three-dimensional shapes using polygons alone. Some of the shapes that can be constructed include prisms, pyramids, and cones.

Prisms:

A prism is a three-dimensional shape with two congruent polygonal bases and rectangular lateral faces connecting the corresponding vertices of the bases. Examples of prisms include rectangular prisms (cuboids), triangular prisms, and hexagonal prisms.

Pyramids:

A pyramid is a three-dimensional shape with a polygonal base and triangular faces connecting the vertices of the base to a single point called the apex or vertex. Examples of pyramids include square pyramids, triangular pyramids, and pentagonal pyramids.

Cones:

A cone is a three-dimensional shape with a circular base and a curved surface that connects the base to a single point called the vertex. Cones can be constructed using polygons by approximating the curved surface with a series of smaller polygons.

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Answer:

C(x) = 175√(x² + 360000) + 528000 - 100x

Step-by-step explanation:

See the attachment below (Line PR = 1mile)

C(x) = Cost of Distance across the river + Cost of Distance along the land

Calculating Distance Across the river:

In triangle OPQ,The distance across the river is represented by line y

Line y is the hypothenus of the triangle

Pythagoras theorem states that:

if one angle of a triangle is 90 degrees, then the square of the length of the hypotenuse - the side opposite the right angle - is equal to the sum of the squares of the lengths of the other two sides.

So,

y² = x² + 600²

y² = x² + 360000

y = √(x² + 360000)

If it costs $175 per foot across the river then It'll cost

175 * √(x² + 360000) to lay cables across the river.

Calculating Distance along the land

Distance along the land is represented by line QR

Line QR = Line PR - PQ.

Where PR = 1 Miles (1 mile = 5280 feet)

So, PR = 5280

Line PQ = x

So, QR = 5280 - x

If it costs $100 per foot along the land,then it'll cost

100 * (5280 - x) to lay cables along the land

= 528000 - 100x

C(x) = 175√(x² + 360000) + 528000 - 100x

Answer:

[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]

[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]

The 99% confidence interval would be given by (0.172;0.228)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

The population proportion have the following distribution

[tex]p \sim N(p,\sqrt{\frac{p(1-p)}{n}})[/tex]

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:

[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]

The confidence interval for the mean is given by the following formula:  

[tex]\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex]

If we replace the values given we got:

[tex]0.2 - 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.172[/tex]

[tex]0.2 + 2.58\sqrt{\frac{0.2(1-0.2)}{1400}}=0.228[/tex]

The 99% confidence interval would be given by (0.172;0.228)

The confidence interval for the proportion is CI = 0.20 ± 0.0275.

The formula for calculating the confidence interval for proportion is expressed as:

[tex]CI=p \pm z \cdot \sqrt{\frac{p(1-p)}{n} }[/tex]

where:

Substitute into the formula;

[tex]CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(1-0.2)}{1400} }\\CI=0.20 \pm 2.576 \cdot \sqrt{\frac{0.2(0.8)}{1400} }\\CI = 0.20 \pm 0.0275\\[/tex]

Hence the confidence interval for the proportion is CI = 0.20 ± 0.0275.

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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.

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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:

jursssursztsdigsdigssit

Step-by-step explanation:

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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:

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:

See answer below

Step-by-step explanation:

the ratio of pv against nrt is called compressibility Z and measures the deviation from an ideal gas behaviour . When Z is plotted against pressure for CH₄ for 0°C and 200°C the curves will differ because there are

- negative deviations ( Z decreases) due to intermolecular forces

- positive deviations (Z increases ) due to molecular size of gas particles

then

- at 0°C the negative deviations prevail  respect to positive deviations at lower pressures ( so Z drops below the horizontal line first ) and then Z increases when pressure increases since the effect of positive deviation is higher ( then Z increases)

- Nevertheless, at 200°C the effect of intermolecular forces is lower and thus the positive deviations always prevail ( thus you observe only Z increasing(

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:

[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.

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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.

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