researchers collect data about juuling by asking users to keep track of the number of times per day they turn their device on and the number of inhalations each time they turn the device on. what type of data are these? group of answer choices interval nominal ratio ordinal

Answers

Answer 1

The given data is ordinal data.

This type of data is ordinal data, as the variables are collected on an ordered scale (the number of times per day the device is turned on and the number of inhalations per activation). Although the actual numerical values may not have equal distances, they can still be ordered and compared based on the magnitude of the numbers.

Ordinal data is a categorical statistical data type when the distances between the categories are unknown and the variables have naturally occurring, ordered categories. These statistics are presented on an ordinal scale, one of the four measurement levels that S. S. Stevens described in 1946.

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Related Questions

For a set of data, r = 0.27. Which is true about the correlation of the variables?
• The variables have a strong positive correlation.
• The variables have a weak negative correlation.
The variables have no correlation.
O The variables have a weak positive correlation.

Answers

The  sign of r is positive and  there is a positive and weak correlation.

What is Statistics ?

In statistics, association is any statistical relationship, whether causal or not, between two random variables or bivariate data.  One is independent and other is dependent variable.  

In the broadest sense correlation is any statistical association, though in common usage it most often refers to how close two variables are to having a linear relationship with each other.

Examples are exercise and sickness are negatively correlated.

Study hours and marks are positively correlated

When correlation is nearer -1 or +1 there is a strong correlation.  When correlation is nearer to 0 than to 1 or -1 we say that there is a negative correlation.

Hence, The  sign of r is positive and  there is a positive and weak correlation.

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Which expressions are equivalent to -56Z +28?

Answers

An expression that is equivalent to -56Z +28 can be -23z + 10 - 33z + 18

How to calculate the expression?

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

In this case, an expression that is equivalent to -56Z +28 can be:.

-23z + 10 - 33z + 18

= -23z - 33z + 10 + 18

= -56z + 28

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tara can develop 2 rolls of film in about 18 minutes. at this rate, how long will it take her to develop 8 rolls of film?

Answers

1 hour and 12 minutes is the time that will it take her to develop 8 rolls of film.

According to the question,

Tara develops 2 rolls of film in about 18 minutes.

Tara develops 1 roll of film in about  = (18 ÷2) minutes

                                                                = 9 minutes (using division)

Tara develops 8 rolls of film in about = ( 8 × 9) minutes

                                                                   = 72 minutes

we know that, 1 hour = 60minutes

Tara can develop 8 rolls of film in about = (72 ÷ 60)

                                                                   = 1 hour 12 minutes

So, Tara can develop 8 rolls of film in about 1 hour and 12 minutes.

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What are the coordinates of the image of the point (-4,12) under a dilation with a scale factor of 4 and the center of dilation at the origin?

Answers

The coordinates after a dilation of scale factor k = 4 are (-16, 48)

What are the coordinates of the image after the dilation?

If we have a general point (x, y), and we apply a dilation of scale factor k and the center of dilation is the origin, then the coordinates of the image after the dilation are (k*x, k*y)

Here we start with the point (-4, 12), and we apply a dilation of scale factor 4 and the center is the origin, then the coordinates  of the image are::

(-4*4, 12*4) = (-16, 48)

The coordinates after the dilation are (-16, 48).

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please help thank you :)

Answers

Answer:

Without exponents: a * a * a * a * a

Fill in the blank: [tex]a^5[/tex]

Step-by-step explanation:

We have to use exponent rules:

[tex]x^y * x^y = x^{y+y} \\= x^{2y}[/tex]

So for this problem, we can apply that rule here:

[tex]a^3 * a^2 = a^{3+2}[/tex]

= [tex]a^5[/tex]

^ This will be the answer to the second question.

Now, to find the equation without exponents, we can use the information we have from above. We need to use this rule: [tex]x^2 = x * x[/tex]

Since our equation is [tex]a^5[/tex], we can rewrite it as a * a * a * a * a.

Find the two solutions to the following equation: x(x + 8) = 0​

Answers

Answer: I believe the solutions your looking for would be x = 0 or x = −8

Step-by-step explanation:

x (x + 8) = 0

Step 1: Simplify both sides of the equation.

x² + 8x = 0

Step 2: Factor left side of equation.

x (x + 8) = 0

Here are factors equal to 0:

x = 0 or x + 8 = 0

x = 0 or x = −8

I hope this helps!

Answer:

Step-by-step explanation:

x inside the () is equal to -8

then that will be ( -8 + 8=0)

the x multiply by 0 is 0

You welcome

Computers depreciate rapidly. If a new computer that costs $1200 loses 40% of its value every year, what is its worth 5 years from now?

Answers

Answer:

93.312

Step-by-step explanation:

This would be decay so we use the formula [tex]y=a(1-r)^{2}[/tex]

in this case a would equal $1200, r would equal 40% (as a decimal) or 0.4 and x would equal 5

[tex]y=1200(1-0.4)^5[/tex] plug this into your calculator and you will get 93.312

I hope this helps (Lmk if im wrong )

Fran swims at 2. 2 mph in still water. The Lazy River flows at a speed of 0. 6 so how long will it take her to go 2. 4 mi upstream and 2. 4 mi downstream?

Answers

If Fran swims at 2.2 mph in still water and  Lazy River flows at a speed of 0.6 mph , the the time required by Fran to go 2.4 mi upstream is 1.5  hours and 2.4 mi downstream is 0.857  hours .

the speed of Fran in still water (rate) = 2.2 mph ;

the sped of the river (current) is = 0.6 mph  ;

The time  taken by Fran to swim 2.4 miles upstream and 2.4 miles downstream can be calculated by formula :

⇒ time = distance/(rate + current)  ;

the distance to be covered is = 2.4 miles ;

For the time taken by Fran to swim upstream , the speed of current is subtracted from the Speed of Fran ;

So , time = 2.4/(2.2-0.6) = 2.4/1.6 = 1.5 hours

For the time taken by Fran to swim downstream, the speed of current is added to the Speed of Fran ;

So , time = 2.4/(2.2 mph + 0.6) = 2.4/2.8 = 0.857 hours

Therefore , by Fran it will take 1.5 hours to travel 2.4 miles upstream and 0.857 hours to travel downstream .

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If the average rate of inflation over the last hundred years was 3. 22%, what amount of money one hundred years ago would be equivalent to a million dollars today? Show your work.


Answers

If the average rate of inflation over the last hundred years was 3.22%, the amount of money one hundred years ago would be equivalent to a million dollars today is approximately 968,805 dollars.

If the average rate of inflation over the last hundred years was 3.22%, we have to determine the amount of money one hundred years ago would be equivalent to a million dollars today.

We know that formula of inflation is:

inflation = (FP−IP)/IP × 100

where, IP stands for the initial basket price or price index.

FP stands for the basket's final price or the price index.

From the question, inflation = 3.22%, FP = 1,000,000

Now putting the values in the formula

3.22 = (1,000,000 - IP)/IP  × 100

Divide by 100 on both side, we get

0.0322 = (1,000,000 - IP)/IP

Multiply by IP on both side, we get

0.0322IP = 1,000,000 - IP

Add IP on both side, we get

1.0322IP = 1,000,000

Divide by 1.0322 on both side, we get

IP = 968,804.5

IP = 968,805(approx)

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To predict the performance of her first period class on their next quiz, á teacher randomly selects eight students from the class and takes the mean of their scorés on the last quiz. Is this sample representative of the class's performance on the quiz? Explain your reasoning.​

Answers

It's important to note that even if the sample is random, there's still a chance that the sample may not be representative of the population, this is known as sampling error.

What does reason mean?

The fundamental act of thinking about anything logically and sensibly is best described as reasoning.

It depends on how the teacher choose the class members. Because every student had an equal chance of being chosen, the sample, if the students were chosen at random, is likely to be indicative of the class' performance on the quiz. However, the sample would not be indicative of the class's performance on the quiz if the teacher arbitrarily chose the students, for instance, by selecting only the best or the worst performers.

In general, if a sample is large enough and random, it is thought to be representative of the population. The likelihood that the sample is representative of the population rises with greater sample sizes. Since only 8 students were chosen in this instance, it's possible that the results don't accurately reflect how the entire class did on the quiz.

The term "sampling error" refers to the possibility that a sample, even one drawn at random, may not be representative of the population as a whole.

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Determine which integers in the set S:{−40, −10, 20, 40} will make the inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty false

Answers

Answer: The inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty can be rewritten as:

(1/5)(m-5) <= (1/10)(m-20)

To find the integers in the set S that will make this inequality false, we need to find the values of m that do not satisfy it. We can start by simplifying the inequality:

(1/5)(m-5) <= (1/10)(m-20)

(1/5)m - (1/5)5 <= (1/10)m - (1/10)20

(1/5)m <= (1/10)m - (1/10)20 + (1/5)5

(1/5)m <= (1/10)m - 2 + (1/5)5

(4/5)m <= (1/5)5 - 2

m <= -5

So, the integers in the set S that do not satisfy the inequality are 20 and 40. These integers will make the inequality false.

Step-by-step explanation:

Melanie is comparing the price of two party planners. Party Planner 1 and Party Planner 2. Party Planner 1 uses the equation, y = 10x + 70, where x is the number of people attending the party and y is the total cost. Prices for Party Planner 2 are shown in the table. Which statement is true?

Party Planner 2
number of people attending. cost ($)
20 490
25 590
35 790
50 1,090

A. Party planner 2 charges $15 more per person than party planner 1.
B. Party planner 1 charges $20 more per person than party planner 2.
C. Party planner 1 charges $10 more per person than party planner 2.
D. Party planner 2 charges $20 more per person than party planner 1.

Answers

Party planner 2 charges $15 more per person than party planner 1.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given ,

Melanie is comparing the price of two party planners. Party Planner 1 and Party Planner 2. Party Planner 1 uses the equation, y = 10x + 70,

where x is the number of people attending the party and y is the total cost.

y=15x+75 means that they charge $15 for every person but $75 right away. For planner 2, they charge $20 a person because comparing coordinates 1 and 2,

every 5 people charge $100. So to find the amount per person for planner 2, divide 100 by 5 and you'll get 20, and

since 20 is 5 more than 15. A is true.

Therefore, Party planner 2 charges $15 more per person than party planner 1.

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the approximate time t in seconds that it takes an object to fall a distance of d feet is given by . how far will the object fall in 6 seconds?

Answers

A parachutist falls 11 seconds before the parachute opens, so 1936 ft far the parachutist fall during this time.

We have to find how far does the parachutist fall during this time.

The formula for estimating the time in seconds it will take an object to fall d feet is given below.

t = [tex]\sqrt{\frac{d}{16}}[/tex]

We merely need to enter the specified time t into the formula to find the distance answer.

11 = [tex]\sqrt{\frac{d}{16}}[/tex]

taking square on both side, we get

121 = d/16

Multiply by 16 on both side, we get

d = 1936 ft

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The complete question is:

The approximate time t in seconds that it takes an object to fall a distance of d feet is given by

t = [tex]\sqrt{\frac{d}{16}}[/tex]

Suppose a parachutist falls 11 seconds before the parachute opens. How far does the parachutist fall during this time?

Arithmetic and Geometric Sequences Grade 11

A toy car is rolling down an inclined track and picking up speed as it goes. The car travels 4 cm in the first second, 8cm in the second second, 12cm in the next second, and so on. Determine the total distance travelled by the car in 30 seconds.

Answers

Answer:

The distance traveled by the car in each second is increasing by 4 cm each time. This is an example of an arithmetic sequence, where the common difference is 4 cm.

To find the total distance traveled by the car in 30 seconds, we can use the formula for the sum of an arithmetic series:

S_n = n/2 * (a_1 + a_n)

where S_n is the sum of the first n terms of the series, a_1 is the first term (4 cm in this case), a_n is the nth term, and n is the number of terms.

Substituting the values into the formula:

S_n = 30/2 * (4 + (4 + (30 - 1) * 4))

S_n = 30/2 * (4 + 4 + 116)

S_n = 30/2 * 124

S_n = 3720 cm

So the total distance travelled by the car in 30 seconds is 3720 cm.

Find x for the picture

Answers

Answer:

x = 20

Step-by-step explanation:

Because these are alternate interior angles, 2x+20 and 3x are equivalent to each other. Therefore, we can set up this equation:

2x+20 = 3x

Now, we can solve this equation and find x:

20 = 3x-2x

x = 20

Introduction: Are the two angles equal?

These provided angle measures (3x and 2x + 20) are a pair of alternate interior angles because they satisfy the following required conditions:

The two angles must lie on the inside of the parallel lines.The two angles must lie on the opposite sides of the transversal.

Since the two angles ARE alternate interior angles, they are EQUAL! Therefore, we can equate the two angles and solve for the variable (x).

{2x + 20 is equal to 3x} ⇒ 2x + 20 = 3x

Process in solving the linear equation:

The key step in solving the linear equation is to ISOLATE the variable completely by removing the coefficient until you have 1 as the coefficient.  

There are 4 possible ways to isolate the variable:

If you have a negative integer/variable as the coefficient, you can divide the negative integer/variable on both sides of the equation. If you have a positive integer/variable as the coefficient, you can divide the positive integer/variable on both sides of the equation. If your variable is added by a positive integer/variable, you can subtract the same integer/variable on both sides of the equation. If your variable is added by a negative integer/variable, you can add the same number/variable on both sides of the equation.

Once your variable is completely isolated, simplify (if possible) on the other side of the equation. If the opposite side of the variable is simplified, you can conclude your solution for the linear equation.

Solving the Linear equation

Now, let us solve the equation using the above step by step processes.

⇒ 2x + 20 = 3x                                         (Given equation)

Isolating the variable from the constant(s) on the R.H.S:  

⇒ 2x + 20 - 2x = 3x - 2x

Simplify both sides of the equation:

⇒ 20 = x

Therefore, the solution to the linear equation (x) is 20.

__________________________________________________________

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Find the values of x and y.

Answers

Answer:

x = 7 , y = 4

Step-by-step explanation:

the triangle on the right has 3 congruent angles and is therefore equilateral with 3 congruent sides, so

3x - 5 = 5y - 4 → (1)

the triangle on the left has 2 congruent angles and is therefore isosceles with the 2 legs being congruent, so

3x - 5 = y + 12 → (2)

we have 2 equations with 3x - 5 on the left side so equate the right sides

5y - 4 = y + 12 ( subtract y from both sides )

4y - 4 = 12 ( add 4 to both sides )

4y = 16 ( divide both sides by 4 )

y = 4

Then

5y - 4 = 5(4) - 4 = 20 - 4 = 16 , so

3x - 5 = 16 ( add 5 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

What are the domain and range of f(x) =7?

Answers

Answer:

C

Step-by-step explanation:

2. The function f is defined as f(x) = - 4x³ - 4x². What is f(-4)
A. -320
B. -192
C. 16
D. 192
E. 320

Answers

And the answer is I think 16

Help Me Please!!!!!
Homework!

Answers

A graph of the inequality w ≤ 200 is shown in the image attached below.

How to graph the inequality?

In this scenario, we would solve the given inequality by making "w" the subject of formula as follows;

w/-10 ≤ -20

By multiplying both sides of the inequality by -10, we have the following:

-10 × w/-10 ≤ -20 × -10

w ≤ 200

Next, we would use an online graphing calculator to plot the inequality as shown in the graph attached below. Additionally, the circle is closed because of the less than or equal to (≤) symbol.

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The air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃ ?

Answers

At the height of 2500 m, the temperature will be T = 16 ℃.

What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.

Given is that air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃.

2 ℃ for every 500 m of elevation.

Then, for 1 m of elevation, it will change by (2/500) or (1/250) ℃

We can write the function as -

T{x} = 26 - {x/250}

Now, for T = 16 ℃, we can write -

26 - {x/250} = 16

26 - 16 = x/250

10 = x/250

x = 2500 m

Therefore, at the height of 2500 m, the temperature will be T = 16 ℃.

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selena would like to learn a new language. to gauge how common it is for people to know more than one language, she asks 10 of her friends how many languages they speak. she compiles the responses in the table below. languages spoken 2 1 1 1 2 3 1 2 1 1 use a calculator to create a relative frequency distribution for the data. what is the relative frequency of her friends who speak more than one language?

Answers

The relative frequency of Selena's friends who speak more than one language is 3/16 or 0.1875

To create a relative frequency distribution, we first need to find the total number of responses by summing up the number of languages spoken by Selena's friends. In this case, the total number of responses is 2 + 1 + 1 + 1 + 2 + 3 + 1 + 2 + 1 + 1 = 16.

Next, we need to find the relative frequency for each category, which is the number of responses in that category divided by the total number of responses. To find the relative frequency of her friends who speak more than one language, we need to add up the number of responses in categories 2, 3, and above.

In this case, the number of responses in category 2 is 2, the number of responses in category 3 is 1, and there are no responses above 3.

So the relative frequency would be (2+1)/16 = 3/16 or 0.1875

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The ordered pair (a, b)(a,b)left parenthesis, a, comma, b, right parenthesis gives the location of point P on the coordinate plane. The values of a and b have the same sign. Neither a nor b is 0. Where could point P be located on the coordinate plane?

Answers

Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.

The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant.

If both a and b have the same sign, point P could be located in one of the four quadrants:

For First quadrant (a > 0, b > 0)

For Second quadrant (a < 0, b > 0)

For Third quadrant (a < 0, b < 0)

For Fourth quadrant (a > 0, b < 0)

Hence, Point P cannot be located on either the x-axis or y-axis, as neither a nor b is 0.

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Expand the logarithm fully using the properties of logs. Express the final answer in terms of
log

x
logx.
log

7
x
3
log7x
3

Answers

The expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

What is a logarithm?

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

So, we must keep in mind the following characteristics of the logarithms in order to solve the issue:

[tex]\begin{aligned}& \log (x . y)=\log (x)+\log (y) \\& \log \left(x^y\right)=y \cdot \log (x)\end{aligned}[/tex]

Then, the expression we have:

[tex]P=\log \left(6 x^4\right)[/tex]

The factor of 6=2*3:

[tex]P=\log \left(2 \cdot 3 x^4\right)[/tex]

Apply the product's feature:

[tex]P=\log (2)+\log (3)+\log \left(x^4\right)[/tex]

Apply the exponent's property now:

P=log(2)+log(3)+4.log(x)

Therefore, the expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

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Correct question:

Expand the logarithm fully using the properties of logs. Express the final answer in

terms of log .

log 6x^4

judes water balloon is empty but filling up at a rate of 5 ml per second. Ian's water balloon contains 45ml of water of water and is losing 10 mL of water per second.

Write an equation to represent y, the amount of water in each balloon based on x, the number of seconds.

Jude:
Ian:

Answers

Answer:

Jude: y = 5x

Ian: y = 45 - 10x

Step-by-step explanation:

Jude:

y = 5x

Ian:

y = 45 - 10x

Jaya observes a marble travel along a horizontal path at a constant rate. The marble
travels of the length of the path in 43 seconds. At that rate, how many seconds
does it take the object to travel the full length?

Answers

It take 43 seconds to the object to travel the full length.

What is the concept of constant rate?

Constant rate refers to a fixed rate of change over a specific period of time. It can be used to describe a variety of situations such as the rate of population growth, the rate of inflation, or the rate of decline in a company's profits.

Constant rate can be used to measure a variety of factors in order to track progress or gauge the success of a particular strategy.

This question uses the concept of constant rate.

Constant rate means that the marble is travelling at a constant speed over the entire length of the path.

This means that the time it takes to travel the full length is the same as the time it took to travel a certain portion of the path.

In this case, it took 43 seconds to travel a certain portion of the path, so it will take 43 seconds to travel the full length.

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I need help on part b

Answers

The number of sticks in pattern number n will be 6 + (n-1)(4).

What is a pattern?

A recurring arrangement of numbers, forms, colours, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern.

The given diagram states that -

The first figure of the triangle is made using - 6 sticks.

The second figure of the triangle is made using - 6 + 4 sticks.

The third figure of the triangle is made using - 6 + 4 + 4 sticks.

Similarly, the fourth figure of the triangle will be made using - 6 + 4 + 4 + 4 sticks.

So, the pattern followed here is -

First image = 6 + (1-1)(4)

Second image = 6 + (2-1)(4)

Third image = 6 + (3-1)(4)

Fourth image = 6 + (4-1)(4)

So, for pattern n the number of sticks will be -

nth image = 6 + (n-1)(4)

Therefore, the pattern is obtained as 6 + (n-1)(4).

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Please Help!

I don't understand how to work out this question.

Answers

∠XBC is 55 degrees because it is corresponding to ∠AXY..

The angle ∠BXC is 70 degrees

How to find angles in parallel lines?

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.

Therefore, XY and BD are parallel lines.

XB = XC

ΔXBC is an isosceles triangle.

Therefore, ∠XBC is 55 degrees because it is a corresponding angle to ∠AXY.

Let's find ∠BXC.

Therefore, the base angles of an isosceles triangle are congruent.

Hence,

∠XBC = ∠BCX = 55 degrees

Therefore,

55 + 55 + ∠BXC = 180

110 + ∠BXC = 180

∠BXC = 180 - 110

∠BXC = 70 degrees

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An iron rod of length 10.38 ft is bent to form a circle. What is the radius of the circle?

Answers

The radius of circle for the given length of rod is found as 1.65 ft

Define the term perimeter of the circle?The border or entire arc length of a circle's perimeter is known as its perimeter. A circle's circumference is the term used to describe its edge.The radius of circle serves as one of the three variables in the perimeter of such a circle formula, along with two constants. The formula for calculating a circle's circumference or perimeter is as follows:

Perimeter of circle = 2 π r

In which,

r = radius of the circleπ = 3.14

When the length of the rod is bent to form the circle.

Length of rod = Perimeter of circle

10.38 = 2 π r

r = 10.38 /  2 π

r = 1.65

Thus, the radius of the circle for the given length of rod is found as 1.65 ft.

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GIVING 40 POINTS!!
Determine whether the solids are similar. Explain your reasoning.

Answers

Answer:

yes ✔‍♀️

Step-by-step explanation:

just flip it over and dividend by 1.2

Your business is expanding. You plan to offer your famous Equation Café Coffee blend
worldwide. To do this, you'll need a shipping company. DHL charges $4 for the first pound,
and $0.22 for each additional pound. MPS charges $12 for the first pound and $0.12 for each
additional pound. How many pounds will it take for DHL and MPS to cost the same amount?

Answers

Answer:

itll take 8 pounds for both DHL and MPS to cost the same

Step-by-step explanation:

since DHL charges $4 for the first pound and $0.22 for each additional pound, and MPS charges $12 for the first pound and $0.12 for each additional pound, we can write that as 4 + 0.22x = 12 + 0.12x, with the left side representing DHL and the right representing MPS.

If this equation is solved, you will find out that x = 8, which is the number of pounds that DHL and MPS will cost the same at. Therefore, they will charge the same amount for 8 pounds.

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