On a scale drawing of a fence, 3.75 inches represents 24 feet. What os the actual length of a fence that is 2.8 inches long in the drawing?

Option C: We can say with 95% confidence that the true mean number of books people read in the past year is between 9.41 and 11.39 books.

A confidence interval is a set of values created from a sample of data that, at a given level of confidence, are likely to include the true population parameter. It is employed to estimate a population parameter that is unknown, like the mean or proportion.

On the other hand, a prediction interval is a set of values that, given a certain level of confidence, are likely to include the value of an upcoming observation from the same population. Based on the sample data, it is used to forecast how a future observation will turn out.

The confidence interval is given by the formula:

CI = x ± t*(s/√n)

Now, for 95% confidence interval, the level of significance is α = 0.05.

Also, α/2 = 0.025 and t = 1.962 we have:

CI = 10.4 ± 1.962*(16.6/√1012)

CI = 10.4 ± 0.99

CI = (9.41, 11.39)

Hence, we can say with 95% confidence that the true mean number of books people read in the past year is between 9.41 and 11.39 books.

Learn more about confidence interval here:

https://brainly.com/question/24131141

#SPJ1

P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is used in many areas of science, such as statistics, physics, and engineering, as well as in everyday life to make informed decisions based on the likelihood of various outcomes.

The probability of drawing a green block on the first draw is 4/20 (since there are 4 green blocks out of a total of 20 blocks in the bag).

Since the block is being replaced back into the bag after each draw, the probability of drawing a yellow block on the second draw is still 3/20.

Therefore, the probability of drawing a green block followed by a yellow block is:

P (green, then yellow) = P(green) * P(yellow) = (4/20) * (3/20) = 0.03 or 3%

To know more about probability visit:

https://brainly.com/question/11234923

#SPJ1

Answer: 8,336

Step-by-step explanation:

So 1 meter is equal to 100 centimeters. All you have to do is multiply 83.36 by 100.

83.36 * 100 = 8,336

Hope this helps!!! :)

Answer:

We have supplementary angles.

123 + 3x = 180

3x = 57

x = 19

Answer:

x = 19

Step-by-step explanation:

Angle on a straight line add up to 180

123 + 3x = 180

3x = 180 - 123

3x = 57

3x/3 = 57/3

x = 19

According to the information, f(x) = 5(x-3)(x+5) and g(x) = (x-3)(x+5).

To have vertical asymptotes at x = 3 and x = -5, the denominator of the function must have factors of (x-3) and (x+5), respectively. We can write the denominator as g(x) = (x-3)(x+5).

To have a horizontal asymptote of y = 5, the degree of the numerator must be the same as the degree of the denominator. Also, the leading coefficients of the numerator and denominator must be equal. Therefore, we can write the numerator as f(x) = 5(x-3)(x+5).

The function can be written as:

f(x) 5(x-3)(x+5)

y(x) = -------------- = -----------------

g(x) (x-3)(x+5)

This function satisfies all the given conditions: it has vertical asymptotes at x = 3 and x = -5, a horizontal asymptote of y = 5, and is continuous for all x ≠ 3, -5. Therefore, f(x) = 5(x-3)(x+5) and g(x) = (x-3)(x+5).

Learn more about function in: https://brainly.com/question/21145944

#SPJ1

Answer:

To solve for the value of z in the equation 6 = 1/2 × z, we can use algebraic manipulation. First, we can multiply both sides of the equation by 2 to eliminate the fraction:

2 × 6 = 2 × (1/2 × z)

Simplifying the right side:

12 = z

Therefore, the value of z is 12.

Step-by-step explanation:

The airplane traveled a total of 5530 miles in all three trips.

What is addition?

Addition is one of the basic arithmetic operations in mathematics, which combines two or more quantities to produce a single quantity called the sum. The quantities being added are called addends, and the symbol used to represent the addition operation is the plus sign (+).

To find the total number of miles that the airplane traveled in all three trips, we need to add up the number of miles it traveled on each trip:

Total miles traveled = 2372 + 1283 + 1875

Total miles traveled = 5530

Therefore, the airplane traveled a total of 5530 miles in all three trips.

To learn more about addition visit the link:

https://brainly.com/question/25421984

#SPJ1

well, let's say the regular price is "x", which oddly enough is the 100%, and we know the store is doing a 25% sale, that means the new prices are 100% - 25% = 75%, 75% of the regular price, so when buying item for "$x", the sale price will just be

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{75\% of x}}{\left( \cfrac{75}{100} \right)x}\implies \text{\LARGE 0.75}\cdot x[/tex]

Make use of Excel, MATLAB, or Python to perform the curve fitting and find the cubic model for the given data.

To find a cubic model for the given data, we can use the method of least squares to fit the data points into a cubic polynomial of the form:

y = ax^3 + bx^2 + cx + d

where y represents the percentage of alternative and nuclear energy use, x represents the year, and a, b, c, and d are the coefficients to be determined.

Given the data points:

(2000, 10.7696)

(2003, 10.6167)

(2005, 10.6213)

(2008, 11.1977)

(2010, 11.7184)

(2011, 11.9921)

(2012, 12.0645)

Make use of Excel, MATLAB, or Python to perform the curve fitting and find the cubic model for the given data.

Once you have the cubic model, you can plug in x = 2016 to predict the alternative energy use for 2016.

Read more about cubic models here:

https://brainly.com/question/28990074

#SPJ1

we can rewrite cos³(x) in terms of first powers of cosine as:

cos³(x) = (1/4)(3cos(x) + cos(3x))

What is power-reducing identity?

trigonometric identities that enable us to translate higher-order trigonometric expressions into lower-order trigonometric expressions.

We can use the power-reducing identity:

[tex]cos^3(x) = (1/4)(3cos(x) + cos(3x))[/tex]

To see how this identity is derived, we start with the double-angle identity:

[tex]cos(2x) = 2cos^2(x) - 1[/tex]

Rearranging this equation, we get:

[tex]cos^2(x) = (1/2)(1 + cos(2x))\\\\cos^3(x) = (1/2)cos(x)(1 + cos(2x))\\\\cos^3(x) = (1/2)cos(x) + (1/2)cos(x)cos(2x)\\\\cos^3(x) = (1/2)cos(x) + (1/2)cos(x)[2cos^2(x) - 1]\\\\cos^3(x) = (1/2)cos(x) + (1/2)(2cos^3(x) - cos(x))\\\\cos^3(x) = (1/4)(3cos(x) + cos(3x))[/tex]

Therefore, we can rewrite cos³(x) in terms of first powers of cosine as:

cos³(x) = (1/4)(3cos(x) + cos(3x))

To know more about power-reducing identity visit,

https://brainly.com/question/30944807

#SPJ1

Step-by-step explanation:

y = x and y = 4

(x + y)²

(4 + 4)² = (8)² = 64

Answer:

The answer is ⁵√a²

Step-by-step explanation:

a⅖=⁵√a²

The scale factor used to dilate triangle ABC with vertices at A(−1, −1), B(1, 1), C(0, 1) into triangle A'B'C' with vertices at A′(−3, −3), B′(3, 3), C′(0, 3) is 3.

In mathematics, a scale factor is a number that scales, or multiplies, some quantity. In the context of geometry, the scale factor is the ratio of lengths in a pair of similar geometric figures or the ratio of the areas of two similar geometric figures. When one figure is transformed into another by dilation, the scale factor is the ratio of the lengths of corresponding sides. The scale factor can be greater than 1, less than 1, or equal to 1 (meaning no change in size).

We can determine the scale factor by comparing the lengths of sides of the two triangles.

The length of side AB is,

AB = [tex]\sqrt{[(1 - (-1))^2 + (1 - (-1))^2]}[/tex] = [tex]\sqrt{8}[/tex]

Similarly the length of side A'B' is,

A'B' = [tex]\sqrt{[(3 - (-3))^2 + (3 - (-3))^2]}[/tex] = [tex]\sqrt{72}[/tex]

So the scale factor will be,

A'B' / AB = [tex]\frac{\sqrt{72} }{\sqrt{8} }[/tex] = [tex]\sqrt{9}[/tex] = 3

Therefore, the scale factor used to dilate triangle ABC into triangle A'B'C' is 3.

To know more about scale factor visit:

brainly.com/question/30215119

#SPJ1

Answer:

The correct answer is B: Saturday.

The relationship between Monday and Thursday is that they are two days apart in a typical Monday-to-Sunday week. Similarly, Friday is also two days apart from Tuesday in a typical week, so the relationship between Friday and Tuesday would be the same as the relationship between Monday and Thursday. Therefore, the correct answer is B: Saturday.

Answer:

The surface area is 720 in^2

Answer:

The dimensions that maximize the area of the garden are 200 feet by 100 feet.

The largest area for the garden would be 20,000 square feet

Step-by-step explanation:

Let the length of the garden be x feet and the width be y feet. One side of the garden is adjacent to the barn, which is 50 feet long. Since only three sides need to be fenced, we can set up the following equation for the perimeter:

x + 2y = 400

We need to find the dimensions that will maximize the area of the garden, which is given by A = xy. First, we will express y in terms of x using the perimeter equation:

y = (400 - x) / 2

Now, substitute y in the area equation:

A(x) = x(400 - x) / 2

A(x) = (400x - x^2) / 2

To maximize the area, we need to find the critical points of the function A(x). We do this by taking the first derivative and setting it to 0:

A'(x) = (400 - 2x) / 2

A'(x) = 200 - x

Now, set A'(x) to 0 and solve for x:

200 - x = 0

x = 200

Now, substitute x = 200 back into the equation for y:

y = (400 - 200) / 2

y = 200 / 2

y = 100

So, the dimensions that maximize the area of the garden are x = 200 feet (length) and y = 100 feet (width). Now we can find the largest possible area:

A = xy

A = (200)(100)

A = 20,000 square feet

The largest possible area for the garden is 20,000 square feet.

The ordered pairs for the equation y = -7x + 8 are (0, 8), (1, 1), and (-1, 15).

To find ordered pairs for the equation y = -7x + 8, we can substitute different values of x and solve for y.

Let's choose three values of x:

When x = 0, y = -7(0) + 8 = 8. So one ordered pair is (0, 8).

When x = 1, y = -7(1) + 8 = 1. So another ordered pair is (1, 1).

When x = -1, y = -7(-1) + 8 = 15. So another ordered pair is (-1, 15).

Therefore, the ordered pairs  are (0, 8), (1, 1), and (-1, 15).

Learn more about  ordered pairs for the equation here:https://brainly.com/question/2055583

#SPJ1

Answer:

x > 3

Step-by-step explanation:

−8 + x/3 > -7

x/3 > 1

x > 3

We can't simplify anymore, so the answer is x > 3

Answer:

5146

Explanation:

There are 5 nickels in a quarter,

5 - 1 = 4,

There are 4 sides in a quadrilateral,

and 6 would make the digital root 7.

5146 -> 5 + 1 + 4 + 6 = 16

16 -> 1 + 6 = 7

Answer:

On the first draw, there are 10 numerals out of 36 cards.

P(first card is a number) = 10/36 = 5/18

On the second draw, there are 9 numerals out of 35 cards.

P(second card is a number) = 9/35

The probability of both events is the product:

P(both cards are numbers) = P(first card is a number) x P(second card is a number)

= 5/18 x 9/35

= 1/2 x 1/7 (cancel a 5 and a 9).

= 1/14

There are 13 $20 bills and 16 $5 bills 6 in the collection.

A system of linear equations is a set of two or more linear equations involving the same variables. The solution to a system of linear equations is the values of the variables that satisfy all the equations in the system.

To solve the following problem use variables and form linear equations according to the given conditions in the problem. Solve the equation for the values of variables.

Here we have

Part of the proceeds from a garage sale was ​$340 worth of ​$5 and ​$20 bills. There were 3 more ​$5 bills than ​$20 ​bills

Let's use variables to represent the number of $5 and $20 bills.

Let x be the number of $20 bills, then the number of $5 bills is x + 3.

The total value of the $20 bills is 20x,

The total value of the $5 bills is 5(x + 3) = 5x + 15.

According to the problem,

The total value of the bills is $340, so we can set up the equation:

20x + 5x + 15 = 340

Simplifying and solving for x, we get:

25x = 325

x = 13

Therefore,

There are 13 $20 bills and 16 $5 bills 6 in the collection.

Learn more about Linear equations at

https://brainly.com/question/27981843

#SPJ1

Thus, the solution of the given expression is found as  [tex]2xy^{2} \sqrt{13xy }[/tex] using the prime factorization.

A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the initial set of prime numbers are 2, 3, 5, 7, 11, and so forth.

Nevertheless, we may also apply the so-called prime factorization, which actually involves using factor trees, for numbers. The technique of expressing all numbers as the product of primes is known as prime factorization.

Given that:

= [tex]\sqrt{52x^{3 }y^{5} }[/tex]

Find the prime factors of 52:

52 = 2 x 2 x 13

x³ = x².x

y⁵ = y².y².y

Put obtained values in expression:

= [tex]\sqrt{(2)(2)(13).x^{2 }.x.y^{2} .y^{2}. y }[/tex]

Now, for the value to take out of the square root, make a pair with the power two and bring it as 1.

= [tex]2xy^{2} \sqrt{13xy }[/tex]

Thus, the solution of the given expression is found as  [tex]2xy^{2} \sqrt{13xy }[/tex] using the prime factorization.

Know more about the prime factors:

https://brainly.com/question/24612438

#SPJ1

Answer: Michelle's income during 2014 was her base salary plus her commission.

Her commission was 3% of $500,000, which is 0.03 x $500,000 = $15,000.

So her total income for 2014 was $87,000 + $15,000 = $102,000.

Step-by-step explanation:

Answer:

height = 4 in

base = 5 in

Step-by-step explanation:

The area of a triangle can be found using the equation:

[tex]A = \frac{1}{2} bh[/tex]

where [tex]b[/tex] is the base of the triangle and [tex]h[/tex] is the base.

In order to plug into this equation, we need to use the relationship between the base and height. It is given that the base is 3 inches shorter than twice the height. Converting this to a mathematical equation:

[tex]b = 2h-3[/tex]

Since we are given that the area is 10 inches squared, we can now plug into the area equation to solve for the height (using the quadratic formula):

[tex]10 = \frac{1}{2} (2h-3)(h)\\2h^2 - 3h -20 = 0\\h = 4[/tex]

** We reject the negative solution of -5/2, since the triangle's height cannot be negative.

Now, we can simply plug in this height to solve for the base:

[tex]b = 2(4) - 3\\b = 5[/tex]

Answer:

a. The circumference of the base is 2πr, where r is the radius of the cylinder. Therefore, the circumference of the base is:

2π(10) = 20π

So the circumference of the base is 20π.

b. The area of the base is πr^2, where r is the radius of the cylinder. Therefore, the area of the base is:

π(10)^2 = 100π

So the area of the base is 100π.

c. The lateral area of the cylinder is given by the formula 2πrh, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the lateral area of the cylinder is:

2π(10)(2) = 40π

So the lateral area of the cylinder is 40π.

d. The total surface area of the cylinder is the sum of the lateral area and the areas of the two bases. The area of each base is πr^2, which we already calculated to be 100π. Therefore, the total surface area of the cylinder is:

2(100π) + 40π = 240π

So the total surface area of the cylinder is 240π.

e. The volume of the cylinder is given by the formula πr^2h, where r is the radius of the cylinder and h is the height (or length) of the cylinder. Therefore, the volume of the cylinder is:

π(10)^2(2) = 200π

So the volume of the cylinder is 200π.

The value of tan(R) is 2/3

What is the trigonometric ratio?

The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

using tan (θ) = opposite/Adjacent

Here, tan (R) = opposite/Adjacent

Where: opposite side = 14

Adjacent Side = 21

tan (R) = 14/21  = 2/3

tan (R) = 2/3

Hence, the value of tan(R) is 2/3

To learn more about the trigonometric ratio visit:

https://brainly.com/question/13729598

#SPJ1

The complete question is in the attached figure:

What is tan(R) =?

The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data,

Let the equation be represented as A

Now, the value of A is

Substituting the values in the equation, we get

Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A

Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil

And , number of cups of vegetable oil used by Colin to make 8 cakes A =

A = 8 x number of cups of vegetable oil used by Colin to make 1 cake

On simplifying the equation, we get

[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]

[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]

Therefore, the value of A is 5 1/3 cups

Hence, the number of cups of vegetable oil required is 5 1/3 cups

To learn more about equations click:

brainly.com/question/19297665

Complete question is-

Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.

If Colin made 8 cakes, how much oil did Colin use in all?

A. 5 1/3 cups

B. 7 1/3 cups

C. 8 2/3 cups

D. 16 1/3 cups​

In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.

The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.

Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.

To know more about French writer here:

https://brainly.com/question/17460800

#SPJ1

The area of the parallelogram is 28 square centimeters and the perimeter of the parallelogram is 30 centimeters.

Given that

Length = 7 cm

Width = 8 cm

Height = 4 cm

The area of a parallelogram can be found by multiplying the base by the height. In this case, the base is the length of the parallelogram, which is 7 cm, and the height is the height of the parallelogram, which is 4 cm.

Therefore, the area of the parallelogram is:

Area = base x height = 7 cm x 4 cm = 28 cm^2

The perimeter of a parallelogram is the sum of the lengths of all four sides.

So, we have

Perimeter = 2 x (length + width) = 2 x (7 cm + 8 cm) = 2 x 15 cm = 30 cm

Therefore, the area of the parallelogram is 28 square centimeters and the perimeter of the parallelogram is 30 centimeters.

Read more about areas at

https://brainly.com/question/24487155

#SPJ1