For a celebration a town is giving out miniature replicas of the towns bell.The replicas are 5 inches tall.If the scale of the replicas are 1 inch to 3 feet tall.How tall is the actual bell?

Answers

Answer 1

The actual height of the town's bell is 15 feet.

To find the actual height of the town's bell using the given scale and the height of the miniature replica, follow these steps:
1. Identify the scale:

The scale provided is 1 inch to 3 feet, which means that 1 inch on the replica represents 3 feet in reality.
2. Determine the height of the miniature replica:

The replica is 5 inches tall.
3. Apply the scale to find the actual height:

Since 1 inch represents 3 feet, we can multiply the height of the replica (5 inches) by the scale factor (3 feet) to find the actual height of the bell.

Actual height = Replica height × Scale factor.

Actual height = 5 inches × 3 feet/inch
4. Calculate the result:

Multiplying 5 inches by 3 feet/inch will give us the actual height of the bell in feet.
Actual height = 15 feet.

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Related Questions

Guys please I need help​

Answers

B

East Indians and Chinese because they are both in the continent of Asia, which is where P and Q are located.

test two different independent variables in his study. the first variable has 3 levels to it (weightlifting interventions - control, light weightlifting routine, or strenuous weightlifting routine), and the second variable is hair length and has 2 levels (short or long). this is a factorial design and will allow him to test the influence of both ivs on his dv (which is strength). using this design, if it is set up as an independent groups design, how many conditions will each participant be assigned to?

Answers

Each participant will be assigned to 6 conditions.

In a factorial design, a researcher aims to investigate the effects of multiple independent variables (IVs) on a dependent variable (DV). In this study, the researcher is examining the impact of two different independent variables: weightlifting interventions with three levels (control, light weightlifting routine, and strenuous weightlifting routine), and hair length with two levels (short or long).

To determine the number of conditions in a factorial design, you multiply the levels of each independent variable. In this case, the study has 3 levels for the first variable (weightlifting interventions) and 2 levels for the second variable (hair length). Therefore, there will be a total of 3 x 2 = 6 conditions in the study.

As the study is set up as an independent group design, each participant will only be assigned to one condition. This means that each participant will undergo a specific weightlifting intervention (control, light, or strenuous) and will have a specific hair length (short or long). The independent group design ensures that the participants' experiences in one condition do not influence their performance in another condition, thus reducing potential biases and confounds.

In summary, using a factorial design with two independent variables (weightlifting interventions with three levels and hair length with two levels), the study will have a total of 6 conditions. As it is set up as an independent groups design, each participant will be assigned to only one of these conditions.

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What scale factor is used to create a figure with an area of 16 square units from a figure with an area of 25 square units?
4/5
5/4
4
5

Answers

A a scale factor of 4/5 would be used to create a figure with an area of 16 square units from a figure with an area of 25 square units.

Calculating the scale factor

The scale factor to create a figure with an area of 16 square units from a figure with an area of 25 square units can be found using the formula:

scale factor = √(new area / original area)

Plugging in the given values, we get:

scale factor = √(16/25)

So, we have

scale factor = 4/5

Therefore, a scale factor of 4/5 would be used to create a figure with an area of 16 square units from a figure with an area of 25 square units.

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Answer: 4/5

The first person to answer was correct.

Step-by-step explanation:

I took the quiz so you don't have to! <3

Please help with three questions please this is due today

Answers

A quadratic equation is a type of polynomial equation of degree 2, which means the highest power of the variable in the equation is 2.

What is a quadratic equation?

The general form of a quadratic equation is:

ax^2 + bx + c = 0

where a, b, and c are constants and x is the variable. The coefficient a is the quadratic coefficient, b is the linear coefficient, and c is the constant coefficient.

We know that;

y = (x - 3)^2+ 36

y = x^2 -3x + 9 + 36

y = x^2 - 3x + 45

y = -3[(x + 4) (x - 5)

y = -3[x^2 - 5x + 4x - 20]

y = -3[x^2 -x - 20]

y = -3x^2 + 3x + 60

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c) How many tens are in 376

Answers

Answer:

37 tens

Step-by-step explanation:

divide the numbers

the internal auditing staff of a local manufacturing company performs a sample audit each quarter to estimate the proportion of accounts that are delinquent (more than 90 days overdue). for this quarter, the auditing staff randomly selected 400 customer accounts and found that 80 of these accounts were delinquent. what is the 95% confidence interval for the proportion of all delinquent customer accounts at this manufacturing company? (you should be using statistical software such as statcrunch.)

Answers

We will get the confidence interval for the delinquent accounts to be  0.1619, 0.2426.

Here we need to calculate the Confidence Interval for the proportion using Statcrunch.

First, we will select the option Stat. Next, we will select the option Proportion Stats. Now amongst the other available options, we will go to One Sample.

Since we have the summary available, we will select with Summary menu option.

Now the available data is clearly a binomial distribution, and hence, the confidence interval needs to be taken out with the help of normal approximation. Since this is a default in Statcrunch, we don't need to make any changes to this.

Under option # of success, we need to enter the number of delinquent accounts. This will be 80.

Now, # of observations is the sample size which is 400.

Now, we will select the confidence level for p with an interval of 0.95.

Hence we will get the interval to be 0.1619, 0.2426.

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Arianna measured a boarding school and made a scale drawing. The scale of the drawing
was 3 millimeters = 9 meters. What is the scale factor of the drawing?
() Simplify your answer and write it as a fraction.
Videa

Answers

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.

preform the indicated operation
(1)/(x^(2)-6x)=(x)/(x^(2)-36)+2
solve for x
[ sorry if im missing anything ]

Answers

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

Describe Equation?

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.

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State what each variable may be so that the equation is true. You must have at least one negative number. Explain how you chose the values for a and b. 2^a • 2^b = 2^0

Answers

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.

An oil tanker is approximately 1500 feet long. How far would 8500 oil tankers span if you placed them end to end?

Answers

Answer:

12,750,000ft

Step-by-step explanation:

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

Answer: 12,750,000ft

Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly.

Answer part a, b, and c for brainliest!!

Answers

Based on the information provided by the question, we found the following solutions:

A. Sample space of randomly selecting 2 lollipops with replacement: {GG, CC, LL, GC, GL, CL, CG, LG, LC}B. Sample space of randomly selecting 2 lollipops without replacement {GC, GL, CL, CG, LG, LC}C. The experiment of randomly selecting two lollipops without replacement shows dependent events, because the probability of the second lollipop being a certain flavor depends on what the first lollipop was.  On the other hand, the experiment of randomly selecting two lollipops with replacement shows independent events, because the first selection does not affect the probability of the second selection.What is probability theory?

An event is considered dependent if the outcome of one event affects the probability of the outcome of another event. Conversely, events are considered independent if the outcome of one event does not affect the probability of the outcome of another event.

Therefore, in the case of selecting lollipops with or without replacement, the distinction between dependent and independent events lies in whether or not the lollipop selection process affects the probability of future selections.

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Hello everyone, can you help me please?
-where n is an integer,
-Which of the following is the result of the process?​

Answers

Answer:

A) -1

Step-by-step explanation:

[tex] \dfrac{i^{2n - 3} \times i^{3n - 1}}{i^{5n - 2}} = [/tex]

[tex] = i^{2n - 3 + 3n - 1 - (5n - 2)} [/tex]

[tex] = i^{2n - 3 + 3n - 1 - 5n + 2} [/tex]

[tex] = i^{-2} [/tex]

[tex] = \dfrac{1}{i^2} [/tex]

[tex] = \dfrac{1}{-1} [/tex]

[tex] = -1 [/tex]

In this Magic Square, every row, column, and diagonal adds to 0. Copy and complete this square​

Answers

A Magic Square is a square grid of numbers in which the sum of every row, column, and diagonal is equal.

One way to approach this is to start with the center number and work outwards.

Since every row, column, and diagonal adds up to 0, the center number must be 0.

From there, we can fill in the rest of the numbers systematically.
For example, in the top row, we need to find two numbers that add up to 0.

We could choose 1 and -1, or 2 and -2, or any other pair of opposite numbers.

Let's choose 1 and -1 for the top row.

Then, we can fill in the bottom row with the same numbers in reverse order.
Next, we can fill in the left and right columns.

Since every column must add up to 0, we need to choose numbers that add up to 0 in each column.

Let's choose 3 and -3 for the left column, and 2 and -2 for the right column.

Finally, we can fill in the diagonals with the remaining numbers.

In this particular Magic Square, every row, column, and diagonal adds up to 0.

We can choose 4 and -4 for one diagonal, and 5 and -5 for the other diagonal.
By following this systematic approach, we can complete the Magic Square with the following numbers:
           3  2 -1
           0  0  0
          -3 -2  1
This Magic Square is a great example of the fascinating patterns and mathematical properties that can be found in numbers. It is also a fun puzzle to solve and can provide hours of entertainment for people of all ages.

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duck PLEASE HELP ME THIS IS URGENT I WILL GIVE BRAINLIEST ​

Answers

Answer:

The answer is B

Step-by-step explanation:

These are triangles are similar and because of that:

x/6 = (x+2.5)/(6+4)

x/6 = x/10 + 0.25

x = 6x/10 + 1.5

4x/10 = 1.5

4x = 15

x = 3.75

a sum of 8000 is compounded annually for 3 years if the rate of interest in 10% per annum for the first year 12% per annum for the second year and 15% per annum for the third year then what is the amount at the end of 3rd years?​

Answers

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.

Graph the inverse of the provided graph on the accompanying set of axes. You must
plot at least 5 points.
*Click the graph to make a point. Click it again to erase.

Answers

The inverse of the provided graph is shown in the image attached below.

What is an inverse function?

In Mathematics and Geometry, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).

In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value). By critically observing the graph, we can logically deduce the following points;

Vertex (h, k) = (-4, 6)

y-intercept (x, y) = (0, 8)

y-intercept (x, y) = (0, 4)

Point (x, y) = (5, 9)

Point (x, y) = (5, 3)

By swapping both the input value (x-value) and output value (y-value), we have:

Vertex (h, k) = (6, -4)

x-intercept (x, y) = (8, 0)

x-intercept (x, y) = (4, 0)

Point (x, y) = (9, 5)

Point (x, y) = (3, 5)

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Ja’Miles designs a sign for a store in the shape of a triangle. His design is 7.5 square feet in area, and the triangle has a height of 2.5 feet. What is the length of the base of his sign?

3 feet


0.6 feet


6 feet


10 feet

Answers

It’s the first one, 3 feet. The formula for the area of a triangle is length times height so if you use the substitution method you get the answer fast ;)

in the year 2015, the timss ranking and average scores of math achievement for fourth-graders were lowest for: korea. russia. kuwait. iran.

Answers

In the year 2015, the times ranking and average scores of math achievement for fourth-graders were option (c) Kuwait

According to the Trends in International Mathematics and Science Study (TIMSS) report for 2015, the lowest ranking and average scores of math achievement for fourth-graders were found in Kuwait. Kuwait ranked 48th out of the 49 countries that participated in the study.

It's worth noting that while Korea, Russia, and Iran also participated in the study, they did not have the lowest ranking or scores. Korea, in fact, ranked 5th overall with an average math score of 608, while Russia ranked 12th with an average math score of 544, and Iran ranked 24th with an average math score of 474.

The reasons for Kuwait's low ranking and scores in math achievement could be due to various factors, such as inadequate resources for education, lack of effective teaching methods, or low investment in STEM (science, technology, engineering, and mathematics) education.

Therefore, the correct option is (c) Kuwait

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factor the polynomial, please.
1. 2p^2+7p-6
2. -5v^2+31v-6
3. -6v^2-11v-4

Answers

To factor the polynomial 2p^2+7p-6, we need to find two numbers whose product is -12 (the product of the coefficients of the first and last terms) and whose sum is 7 (the coefficient of the middle term). The numbers are 3 and 4, so we can write:
2p^2+7p-6 = 2p^2+3p+4p-6

Now we can factor by grouping:

= (2p^2+3p) + (4p-6)
= p(2p+3) + 2(2p+3)
= (p+2)(2p+3)

Therefore, the factored form of 2p^2+7p-6 is (p+2)(2p+3).

To factor the polynomial -5v^2+31v-6, we need to find two numbers whose product is -30 (the product of the coefficients of the first and last terms) and whose sum is 31 (the coefficient of the middle term). The numbers are 30 and 1, so we can write:
-5v^2+31v-6 = -5v^2+30v+v-6

Now we can factor by grouping:

= (-5v^2+30v) + (v-6)
= -5v(v-6) + 1(v-6)
= (v-6)(-5v+1)

Therefore, the factored form of -5v^2+31v-6 is (v-6)(-5v+1).

To factor the polynomial -6v^2-11v-4, we need to find two numbers whose product is -24 (the product of the coefficients of the first and last terms) and whose sum is -11 (the coefficient of the middle term). The numbers are -8 and 3, so we can write:
-6v^2-11v-4 = -6v^2-8v+3v-4

Now we can factor by grouping:

= (-6v^2-8v) + (3v-4)
= -2v(3v+4) + 1(3v-4)
= (3v-4)(-2v+1)

Therefore, the factored form of -6v^2-11v-4 is (3v-4)(-2v+1).

with a rancher is to buy steers at each and cows at each. if the number of steers and the number of cows are both positive integers, then:

Answers

The solution is that the rancher should buy 26 steers and 13 cows

Let's start by setting up a system of equations based on the given information.

The total amount of money the rancher has is $1000, and they plan to buy steers at $25 each and cows at $26 each. Let's say they buy s steers and c cows, then we have:

$25s + $26c = $1000 (Total amount spent)

We also know that s and c are both positive integers (whole numbers greater than zero).

We can solve for s and c by using some algebraic techniques. First, let's simplify the equation by dividing both sides by $1 to get rid of the dollar sign

25s + 26c = 1000

Now we can use a technique called "integer division" to solve for s and c. We'll start by assuming that the rancher buys all steers and no cows, which gives us

25s + 26(0) = 1000

25s = 1000

s = 40

So the rancher could buy 40 steers with their $1000. However, we need to account for the fact that they can also buy cows. Let's say they buy c cows, then we can set up another equation based on the total number of animals they buy

s + c = Total number of animals

Since we don't know the total number of animals, we'll leave that as a variable for now. We can use this equation to solve for c in terms of s:

c = Total number of animals - s

Now we can substitute this expression for c into the first equation:

25s + 26c = 1000

25s + 26(Total number of animals - s) = 1000

25s + 26Total number of animals - 26s = 1000

-Taking 25s to the right side

26Total number of animals = 1000 + s

dividing both sides by 26

Total number of animals = 38 + s/26

So the total number of animals must be a whole number, which means that s/26 must be a positive integer. We can try different values of s to see which ones work

If s = 26, then s/26 = 1 and Total number of animals = 39. This gives us c = 39 - 26 = 13, so the rancher would buy 26 steers and 13 cows.

If s = 52, then s/26 = 2 and Total number of animals = 40. This gives us c = 40 - 52 = -12, which doesn't make sense since c must be a positive integer.

If s = 78, then s/26 = 3 and Total number of animals = 41. This gives us c = 41 - 78 = -37, which again doesn't make sense.

So the only solution that works is when the rancher buys 26 steers and 13 cows. This would cost

25(26) + 26(13) = $650 + $338 = $988

So the rancher would have $12 left over from their $1000 budget.

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The given question is incomplete, the complete question is:

With $1000 a rancher is to buy steers at  $25 each and cows at $26 each. If the number of steers s and the number of cows c are both positive integers, what is the solution?

There is a screenshot below showing my question. Please help asap, will name branliest plus its 10 points :)

Answers

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

At a sale, dresses were sold for $17 each. This price was 85% of a dress's original price. How much did a dress originally cost?

Answers

Answer:

To find the original price of the dress, we can use the following formula: Original price = Sale price / Discount rate In this case, we know that the sale price was $17, and the discount rate was 85%. So we can substitute these values into the formula: Original price = $17 / 0.85 Simplifying this expression, we get: Original price = $20 Therefore, a dress originally cost $20.

Is 3x-2x+ 0.5x equivalent to 0.5x

Answers

No.

You can combine like terms, so:
3x-2x+0.5x = (3-2+0.5)x = 1.5x ≠ 0.5x

no

calculating the equation, you haft to simplify it gives 1.5

it's 1.5x

2. a college admissions director wishes to estimate the mean age of all students currently enrolled. in a random sample of 20 students, the mean age is found to be 22.9 years. from past studies, the standard deviation is known to be 1.5 years and the population is normally distributed. (a) (2 points) construct a 90% confidence interval of the population mean age. then calculate a 95% confidence interval, and a 99% confidence interval. (b) (2 point) construct a 90% confidence interval for this case, assuming that the given standard deviation of 1.5 years came from the sample instead of the population. (c) (1 point) suppose that the distribution of the population is not specified. do we have enough information to form a confidence interval in that case?

Answers

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.

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Three ballet dancers are positioned on stage. Max is 2 feet straight behind Kenji and 4 feet directly left of Lindsey. When the music begins, Max twirls to Lindsey's position, then leaps to Kenji's position, and finally walks back to his original position. How far did Max travel? If necessary, round to the nearest tenth.

Answers

The total distance traveled by Max is approximately 2 + 4.5 + 4.5 = 11 feet/.

What is Cartesian plane?

The Cartesian plane, also known as the coordinate plane, is a two-dimensional plane that is used to represent and graph mathematical equations and functions. The plane is named after the French mathematician and philosopher René Descartes, who developed the concept in the 17th century.

We can use the Pythagorean theorem to find the distance between Max and Kenji, and between Max and Lindsey. Let's assume that the stage is a coordinate plane, with Max's original position at (0,0), Kenji's position at (0,2), and Lindsey's position at (-4,0).

The distance between Max and Kenji is the length of the hypotenuse of a right triangle with legs of length 2 and 4. Using the Pythagorean theorem, we have:

sqrt(2² + 4²) = sqrt(20) ≈ 4.5

So the distance between Max and Kenji is approximately 4.5 feet.

The distance between Max and Lindsey is the length of the hypotenuse of a right triangle with legs of length 4 and 2. Using the Pythagorean theorem, we have:

sqrt(4² + 2²) = sqrt(20) ≈ 4.5

So the distance between Max and Lindsey is also approximately 4.5 feet.

To find the total distance traveled by Max, we can add up the distances traveled during each part of his dance:

Twirling from Lindsey's position to Kenji's position: This distance is the same as the distance between Lindsey and Kenji, which is 2 feet.

Leaping from Kenji's position back to Max's original position: This distance is the same as the distance between Max and Kenji, which we found to be approximately 4.5 feet.

Walking from Max's final position back to his original position: This distance is the same as the distance between Max and Lindsey, which we also found to be approximately 4.5 feet.

So the total distance traveled by Max is approximately 2 + 4.5 + 4.5 = 11 feet. Rounded to the nearest tenth, this is 11.0 feet.

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Write 0.70 repeating as fraction in simplest form.

Answers

7/10 is in its simplest form

Answer:

7/10

Step-by-step explanation:

m∠CBD=6x+27 ∘ so you have to find C B D with this

Answers

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

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Rachel is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices.
Company A charges $104 and allows unlimited mileage.
Company B has an initial fee of $65 and charges an additional $0.60 for every mile driven.
For what mileages will Company A charge less than Company B?
Use m for the number of miles driven, and solve your inequality for m.

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.

Mack, Nina, Samuel, and Tara play a board game. Each of them is equally likely to go first in the game. Also, each of them is equally likely to win the game. Winning the game is independent of going first. What is the probability Samuel goes first and wins the game?
A0
B0.0625
C0.25
D0.5

Answers

The probability that Samuel goes first and wins the game is 1/16 (0.0625). The Option B is correct.

What is the probability in this case?

The probability that Samuel goes first is 1/4, since there are four players and each is equally likely to go first.

The probability that Samuel wins the game, given that he is playing, is also 1/4, since each player is equally likely to win and there are four players in total.

To find the probability that Samuel goes first and wins the game, we need to multiply these two probabilities:

P(Samuel goes first and wins) = P(Samuel goes first) x P(Samuel wins | Samuel is playing)

= (1/4) x (1/4)

= 1/16

= 0.0625

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Nolan is trying to pick out an outfit for the first day of school. He can choose from 6 pairs of pants, 3 t-shirts, 3 sweaters or hoodies, and 5 pairs of shoes. How many different outfits does Nolan have to choose from?

Answers

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.

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