Simplify this fraction
1^22 / 1^7

Answer:

Step-by-step explanation:

She is traveling via Bootle.

Crosby to Bootle is 4 miles.

Bootle to Speke is 12 miles.

That is 16 miles each way.

16  times 2 = 32 miles per day

5 times 32 for the work week.

5 times 32 = 160 miles per week

For the given triangle, m∠CBD = 63 degrees.

What is triangle?

A triangle is a two-dimensional geometric shape with three sides and three angles. It is one of the basic shapes in geometry and is formed by connecting three non-collinear points with line segments.

In a triangle, the sum of the angles is always 180 degrees.

So, we can write:

m∠ABD = m∠ABC + m∠CBD

Substituting the given values, we get:

96 = (7x - 9) + (6x + 27)

Simplifying the equation:

96 = 13x + 18

Subtracting 18 from both sides:

78 = 13x

Dividing by 13:

x = 6

Therefore:

m∠ABD = 96 degrees

m∠CBD = 6x + 27 = 6(6) + 27 = 63 degrees

m∠ABC = 7x - 9 = 7(6) - 9 = 33 degrees

To learn more about triangle visit:

https://brainly.com/question/1058720

#SPJ1

Answer:

12,750,000ft

Step-by-step explanation:

1,500 * 8,500 = 12,750,000

Answer:

15.71

Step-by-step explanation:

Triangle ABC and triangle ADE are similar triangles so we can find the length of DE using similarity ratio.

[tex] \frac{14}{22} = \frac{10}{de} [/tex]

14×DE = 220

DE = 15.71 approximately.

Volume of the sphere is equal to two-third of the volume of a cylinder.

Volume is a mathematical concept that refers to the amount of space occupied by a three-dimensional object. It is expressed in cubic units, such as cubic meters or cubic centimeters, and can be calculated using a specific formula for each type of geometric shape.

A sphere is a perfectly round, three-dimensional object that looks like a ball. It has no edges or vertices and is symmetric around its center point. The formula for calculating the volume of a sphere is V = 4/3 πr³, where V is the volume, π is a mathematical constant approximately equal to 3.14, and r is the radius of the sphere.

True.

Assume that both the sphere's and cylinder's radius is r.

Considering that the base's diameter equals the cylinder's height

⇒h = 2r

Sphere radius = cylinder radius = r

Assuming the conditions are met, the sphere's volume:

=  [tex]\frac{2}{3}[/tex] × Volume of cylinder

= [tex]\frac{4}{3}[/tex]πr³= [tex]\frac{2}{3}[/tex] × πr² × 2r

=[tex]\frac{4}{3}[/tex]πr³= [tex]\frac{4}{3}[/tex]πr³

Hence, volume of the sphere is equal to two-third of the volume of a cylinder.

To know more about cylinder visit:

https://brainly.com/question/30522025

#SPJ1

The complete question is:

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

Answer:

the amount at the end of the third year is A3 = $11,330.40.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

Where:

A = the final amount

P = the principal (initial amount)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

For the first year, the interest rate is 10%, so we have:

A1 = 8000(1 + 0.1/1)^(1*1)

A1 = 8800

After the first year, the principal becomes 8800. For the second year, the interest rate is 12%, so we have:

A2 = 8800(1 + 0.12/1)^(1*1)

A2 = 9856

After the second year, the principal becomes 9856. For the third year, the interest rate is 15%, so we have:

A3 = 9856(1 + 0.15/1)^(1*1)

A3 = 11330.4

Therefore, the amount at the end of the third year is A3 = $11,330.40.

In summary, the initial amount of $8,000 is compounded annually for three years at different interest rates. By using the formula for compound interest, we find that the amount at the end of the third year is $11,330.40.

Therefore, they will have paid the same amount after attending 9 games.

An equation is a mathematical statement that expresses the equality between two expressions or values. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division, as well as other mathematical functions. An equation typically includes an equal sign (=) that indicates that the two sides of the equation are equal in value.

Here,

Let's start by setting up an equation to represent the total cost for each person after attending a certain number of games:

For the season ticket holder: Total Cost = 136.98 + 2.5x, where x is the number of games attended

For the second person: Total Cost = 17.72x

To find the number of games at which they will have paid the same amount, we can set the two equations equal to each other and solve for x:

136.98 + 2.5x = 17.72x

136.98 = 15.22x

x = 9

To know more about equation,

https://brainly.com/question/28243079

#SPJ1

Step-by-step explanation:

Please find the attached pics for answers.

Answer:

To find out for what mileages Company A will charge less than Company B, we need to set up an inequality using the given prices and the number of miles driven, m.

For Company A, the cost is a flat rate of $104 regardless of the number of miles driven. Therefore, the inequality is simply:

104 < 65 + 0.60m

We can simplify this inequality by subtracting 65 from both sides:

39 < 0.60m

To isolate m, we can divide both sides by 0.60:

65 < m

So, Company A will charge less than Company B for any mileage greater than 65 miles. If Rachel plans to drive more than 65 miles, she should choose Company A to save money. However, if she plans to drive less than 65 miles, Company B may be the cheaper option.

The amount of work required to stretch the spring from 30.0 cm to 36.0 cm is 1.411 joules, which can be rounded to three decimal places.

According to Hooke's Law, the amount of work required to stretch or compress a spring by a certain amount is given by the formula:

W = (1/2) k (x2 - x1)²

where W is the work done (in joules), k is the spring constant (in newtons per meter), x1 is the initial displacement (in meters), and x2 is the final displacement (in meters).

In this case, the spring has a natural length of 30.0 cm, which is equivalent to 0.3 meters. To find the spring constant, we can use the fact that a 20.0-N force is required to keep it stretched to a length of 42.0 cm, which is equivalent to 0.42 meters.

Using Hooke's Law, we have

F = k (x2 - x1)20.0 N

= k (0.42 - 0.3) m

=> k = 80.0 N/m

Now we can use Hooke's Law again to find the amount of work required to stretch the spring from 30.0 cm to 36.0 cm, which is equivalent to 0.36 meters.

Using Hooke's Law, we have:

F = k (x2 - x1)W

= (1/2) k (x2 - x1)²W

= (1/2) (80.0 N/m) (0.36 - 0.3) m²W

= 1.411 J

You can learn more about Hooke's Law at: brainly.com/question/29126957

#SPJ11

The approximate standard error of the mean is 3.

Here is how to find the approximate standard error of the mean from a population of 600 elements, where a sample of 100 elements is selected, and it is known that the variance of the population is 900.

Determine the sample size n, which is 100

Find the population variance, which is 900.

Compute the population standard deviation, which is the square root of the variance, as follows:

σ = √900σ

= 30

Compute the standard error of the mean as follows:

SEM = σ/√nSEM

= 30/√100SEM

= 3

The standard error of the mean (SEM) can be calculated using the formula:

SEM = σ / √n
where σ represents the population standard deviation, and n represents the sample size. In this case, we know that the population variance is 900.

To find the standard deviation, take the square root of the variance:
σ = √900 = 30
Now, we can plug in the values into the formula:
SEM = 30 / √100
SEM = 30 / 10
SEM = 3
The approximate standard error of the mean for this sample is 3.

For similar question on standard error

https://brainly.com/question/14524236

#SPJ11

Answer:

h = 9km

Step-by-step explanation:

area of a trapezoid= ½ x (a+b) x h

117 = (2+2+11 +11) / 2 x h

h = 117 / 26÷2

h = 9km

Answer:

The three most common methods for solving quadratic equations are factoring, completing the square, and the quadratic formula.

Here's a quadratic equation you can solve by factoring:

x^2 - 4x + 3 = 0

(x - 1)(x - 3) =0

x = 1, 3

Answer:

we know the area of the parallelogram is given by a=b×h

The average speed of the round-trip for same path back to his house is given by 3 miles per hour.

The mean value of a body's speed over a period of time is its average speed. As a moving body's speed is not constant over time and fluctuates, the average speed formula is required. The values of total time and total distance travelled may be employed even when the speed varies, and with the aid of the average speed formula, we can identify a single number that sums up the whole motion.

So the average speed is simply: [tex]\frac{distance}{time}[/tex]

In case, the total time = 25 minutes + 55 minutes

which is a total of 80 minutes, or 1.33 hours.

The total distance traveled is two miles + two miles, since he jogged two miles to the park, and then he turns around and walks the same path.

So in total he traveled 4 miles.

Plugging this in to the formula gives you the equation:

[tex]v = \frac{d}{t} \\= \frac{4\ miles}{4/3 \ hour} \\= \frac{4 \ miles}{1} * \frac{3}{4} hours\\= 3mph[/tex]

Therefore, average speed of the round-trip is 3 mph.

Learn more about Average speed:

https://brainly.com/question/24739297

#SPJ4

The probability of exactly three successes in eight trials is approximately 26.61%

To find the probability of exactly three successes in eight trials of a binomial experiment with a success probability of 45%, use the binomial probability formula:

P(x) = C(n, x) * [tex]p^x[/tex] * [tex](1-p)^{(n-x)}[/tex]

where n is the number of trials, x is the number of successes, p is the probability of success, and C(n, x) is the combination function representing the number of ways to choose x successes from n trials.

In this case, n = 8, x = 3, and p = 0.45.

Calculate the probability:

P(3) = C(8, 3) * [tex]0.45^3[/tex] * [tex](1-0.45)^{(8-3)}[/tex]

P(3) = 56 * 0.091125 * 0.1721865

P(3) ≈ 0.2661

So, the probability of exactly three successes in eight trials is approximately 26.61%.

Know more about Probability here :

https://brainly.com/question/24756209

#SPJ11

The minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.

Let x be the number of tulip bulbs that Jay plants, and let y be the number of lily bulbs that Jay plants.

Since Jay wants to plant at least twice as many tulips as lilies, we have the constraint:

x ≥ 2y

Also, the total number of bulbs that Jay plants cannot exceed 60, so we have the constraint:

x + y ≤ 60

We want to minimize the total cost of the bulbs that Jay purchases, which is given by the object function:

C = 1.6x + 1.25y

To solve this problem, we can use linear programming. First, we graph the two constraints on a coordinate plane:

The shaded region represents the feasible region, which is the region that satisfies both constraints. The vertices of the feasible region are (0, 0), (40, 20), (60, 0), and (30, 15).

Next, we evaluate the object function at each vertex to find the minimum value. We have:

C(0, 0) = 0

C(40, 20) = 1.6(40) + 1.25(20) = 92

C(60, 0) = 1.6(60) + 1.25(0) = 96

C(30, 15) = 1.6(30) + 1.25(15) = 67.5

Therefore, the minimum cost occurs when Jay plants 30 tulip bulbs and 15 lily bulbs, and the minimum cost is $67.50.

Graphically, we can see that the optimal solution occurs at the intersection of the two constraints, which is the point (30, 15). This is where the slope of the object function is equal to the slope of the feasible region, which indicates that the object function is optimized at this point.

To know more about   object function. here

https://brainly.com/question/29611012

#SPJ9

Answer:

Yes,

Step-by-step explanation:

Because no x- Values repeat.

The solutions to the equation are x = -11/3 and x = 6.

In mathematics, an equation is a statement that two expressions are equal. It consists of two sides separated by an equal sign (=). The expression on the left side of the equal sign is usually called the left-hand side (LHS), while the expression on the right side is called the right-hand side (RHS).

Equations can take many different forms and can involve various types of functions and operators, such as addition, subtraction, multiplication, division, exponentiation, logarithms, trigonometric functions, and more. They can also involve one or more variables, which can be solved for to obtain a specific value or range of values that make the equation true. Equations are used extensively in mathematics, science, engineering, economics, and many other fields.

To solve the equation for x, we can start by simplifying both sides of the equation and bringing all the terms to one side:

(1)/(x²-6x) - (x)/(x²-36) = 2

We can simplify the left side of the equation by finding a common denominator:

[(1)(x-6) - (x)(x+6)] / [(x-6)(x+6)] = 2

Expanding the numerator and simplifying, we get:

(-x² + 7x - 6) / [(x-6)(x+6)] = 2

Multiplying both sides by the denominator, we get:

-x² + 7x - 6 = 2(x-6)(x+6)

Expanding the right side, we get:

-x² + 7x - 6 = 2(x² - 36)

Simplifying and rearranging, we get:

3x² - 7x - 66 = 0

We can solve this quadratic equation by factoring or using the quadratic formula:

3x² - 7x - 66 = (3x + 11)(x - 6) = 0

So either 3x + 11 = 0 or x - 6 = 0:

3x + 11 = 0 => x = -11/3

x - 6 = 0 => x = 6

Therefore, the solutions to the equation are x = -11/3 and x = 6.

To know more about quadratic  visit:

https://brainly.com/question/29011747

#SPJ1

The statements: the sample is random, the sample is an srs, and restrictions are placed on the sample, each plant has an equal chance of being selected are true.

Each tree has an equal chance of being selected. 

This sample is a simple random sample (SRS) because each tree has an equal chance of being selected and the selection of each tree is independent of the others.

Restrictions are imposed on the sample because the botanist selects only one plant from each row, based on a specific criterion (roll a cube).

Hence the following statements are true by probability

The sample is random.

The template is an SRS.

Restrictions are imposed on the sample.

Each tree has an equal chance of being selected. 

learn more about probability

brainly.com/question/31120123

#SPJ4

The logarithm expression is approximately 4.6.

To evaluate 9㏒₉⁵ - ㏒₃3⁵, we can use the logarithmic property that states:

㏒ₐ(b^c) = c x ㏒ₐ(b)

Using this property, we can simplify the expression as follows:

9㏒₉⁵ - ㏒₃3⁵

= ㏒₉(95^9) - ㏒₃(35)

= ㏒₉(1423892081) - ㏒₃(35)

We can evaluate these logarithmic terms using the change of base formula, which states:

㏒ₐ(b) = log(b) / log(a)

Using this formula, we get:

㏒₉(1423892081) = 8.032

㏒₃(35) = 3.432

Substituting these values back into the expression, we get:

9㏒₉⁵ - ㏒₃3⁵ = 8.032 - 3.432

= 4.6

The above answer is in response to the question below;

Evaluate

9㏒₉⁵ - ㏒₃3⁵

Find more exercise on logarithm;

https://brainly.com/question/20785664

#SPJ1

According to the given data the equity in the house is $30,000.

Equity is the difference between the current market value of the property and the outstanding mortgage balance on the property.

If you purchased the house for $250,000 and it is now valued at $280,000, your equity in the house can be calculated as follows:

Equity = Current market value - Outstanding mortgage balance

Assuming you took out a mortgage for the full purchase price of the house and haven't made any extra payments, your outstanding mortgage balance would be the same as the original mortgage amount, which is $250,000. Therefore, your equity in the house would be:

Equity = $280,000 - $250,000

Equity = $30,000

So, your equity in the house is $30,000.

To know more about equity visit:-

https://brainly.com/question/31458166

#SPJ1

Nolan has 270 different outfits to choose from.

What is permutation?

Ways" or permutation refers to the number of different possible outcomes or arrangements in a situation. For example, if you have 3 different shirts and 4 different pants, there are 12 ways (3 x 4) to choose one shirt and one pant. The concept of "ways" is often used in combinatorics, which is the branch of mathematics that deals with counting and arranging objects.

To find the total number of different outfits that Nolan can choose from, we need to multiply the number of options for each clothing item:

Total number of outfits = number of pants x number of t-shirts x number of sweaters or hoodies x number of shoes

Total number of outfits = 6 x 3 x 3 x 5 = 270

Therefore, Nolan has 270 different outfits to choose from.

To learn more about permutation, visit the link:

https://brainly.com/question/28065038

#SPJ1

Answer:

The scale factor would be 3,000

Step-by-step explanation:

3(3000) = 9000 millimeters

9000 x [tex]\frac{1}{1000}[/tex] = 9 to convert to meters

Helping in the name of Jesus.

To take a systematic sample of 100 companies from a population of 1,803 companies, determine the sampling interval (k) which is N/n, choose a random starting point between 1 and k, and select every kth company until 100 companies are sampled.

To take a systematic sample of 100 companies from the 1,803 companies that are members of an industry trade association, follow these steps

Determine the sampling interval (k), which is the number of companies in the population divided by the desired sample size. In this case, k = 1803/100 = 18.03. Round this number up or down to the nearest whole number based on your sampling preferences.

Choose a random starting point between 1 and k. For example, you could randomly select a number between 1 and 18.

From the starting point, select every kth company in the list of members until you have 100 companies. For example, if the starting point is 4, you would select companies 4, 22, 40, 58, 76, 94, 112, and so on until you reach 100 companies.

Important numerical values used in this process are:

Population size (N) = 1,803 companies

Desired sample size (n) = 100 companies

Sampling interval (k) = N/n = 1803/100 = 18.03

Random starting point (any number between 1 and k, depending on sampling preference)

Learn more about systematic sample here

brainly.com/question/28975411

#SPJ4

a) For a 90% confidence interval [22.25, 23.55].

For a 95% confidence interval [22.10, 23.70].

For a 99% confidence interval [21.97, 23.83].

b) For a 90% confidence interval [22.25, 23.55].

a) To construct a confidence interval for the population mean age, we can use the formula: CI = x* ± tα/2 * (σ / sqrt(n)), where x* is the sample mean age, σ is the population standard deviation, n is the sample size, and tα/2 is the critical value of the t-distribution with n-1 degrees of freedom and a given level of confidence α/2.

For a 90% confidence interval, α = 0.1 and tα/2 = 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].

For a 95% confidence interval, α = 0.05 and tα/2 = 2.093, so the interval is: 22.9 ± 2.093 * (1.5 / sqrt(20)) = [22.10, 23.70].

For a 99% confidence interval, α = 0.01 and tα/2 = 2.861, so the interval is: 22.9 ± 2.861 * (1.5 / sqrt(20)) = [21.97, 23.83].

b) If the given standard deviation of 1.5 years came from the sample instead of the population, we need to use a t-distribution with n-1 degrees of freedom to construct the interval. The formula is the same as before, but we replace σ with s, the sample standard deviation.

For a 90% confidence interval, the critical value is still 1.725, so the interval is: 22.9 ± 1.725 * (1.5 / sqrt(20)) = [22.25, 23.55].

c) If the distribution of the population is not specified, we can still form a confidence interval if we have a large enough sample size (typically, n >= 30) due to the central limit theorem. In this case, we have n = 20, so we may not have enough information to form a confidence interval if we cannot assume the population is normally distributed.

To know more on central limit theorem

https://brainly.com/question/18403552

#SPJ4

Answer:

[tex] {2}^{a} \times {2}^{b} = {2}^{a + b} = {2}^{0} [/tex]

From this, a + b = 0, meaning a and b are additive inverses of each other.

As an example, let a = 1, so b = -1.

The expression is undefined, so the sign cannot be determined.

How to determine sign for the given problem?

The following given expression can be more simplified as follows:

-9 * (0 - 3)    -    (9 * (-3/0))

= -9 * (-3) - 9 * undefined [Note: Division by zero is undefined]

= 27 - undefined

As anything subtracted from undefined remains undefined, the overall result is undefined.

Therefore, the sign of the expression cannot be determined.

Undefined values represent the absence of a meaningful result or outcome. In this case, the expression involves division by zero, which is undefined. As a result, any operation involving an undefined value will also be undefined, including subtraction. Thus, the overall result is undefined.

To learn more about expression, visit: https://brainly.com/question/29176690

#SPJ1

Answer:

ITS ZEROOOO

Step-by-step explanation:

i guesses and ended up getting it right.

The product of twice a number and four is 8 times the number.

The product means a number that you get by multiplying two or more other numbers together.

The product of twice a number and four can be represented algebraically as:

4(2x)

where x is the number we are referring to.

Simplifying the expression, we get:

4(2x) = 8x

Therefore, the product of twice a number and four is 8 times the number.

To know more about product, click here

https://brainly.com/question/13179238

#SPJ1

Answer:

Step-by-step explanation:

its a 12/14 probabiloty or a 92.5%

Step-by-step explanation:

I'll try:

7 boys choose 5   =   7! / (5!2!)  = 21 ways

4 girls  choose 2  = 4 ! / (2! 2!) =  6 ways

6 x 21 = 126 ways to choose   5 boys and 2 girls

11 cats total choose  7  =  11! /( 7! 4!)  = 330 ways to choose 7 cats

                   126 of these will be 5 boys and 2 girls

126 out of 330 = 126/330 = .382