James paid an initial fee of $6.00 for a movie rental service. Each time he rents a movie he is charged $2.00. Sarah uses a different movie
rental service that charges based on the equation y = 3x + 4, where y is the total cost and x is the number of movies rented. At what point
are the prices of the two services the same?
606

(i)  The expression for l in terms of T and g is: \(l = g(T/(2\pi ))^{2}\)

(ii) the length of the pendulum is approximately 0.362 meters

The formula for the time taken for a pendulum to complete one oscillation is given by:

\(T = 2\pi \sqrt{ (l/g)}\)

where l is the length of the pendulum and g is the acceleration due to gravity.

(i) Expressing l in terms of T and g:

We can rearrange the above formula to solve for l:

\(T = 2\pi \sqrt{(l/g)}\)

\(T/(2\pi ) = \sqrt{(l/g)}\)

\((T/(2\pi ))^{2} = l/g\)

\(l = g(T/(2\pi ))^{2}\)

So, the expression for l in terms of T and g is:

\(l = g(T/(2\pi ))^{2}\)

(ii) Finding the length of the pendulum:

We are given that T = 12 seconds for 20 oscillations. So, the time taken for one oscillation is:

T/20 = 12/20 = 0.6 seconds

Substituting this value of T into the formula for l that we obtained in part (i), we get:

\(l = g(T/(2\pi ))^{2}\)

\(l = 10(0.6/(2\pi ))^{2}\)

l = 0.362 m (rounded to 3 decimal places)

Therefore, the length of the pendulum is approximately 0.362 meters if it takes 12 seconds to complete 20 oscillations

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Answer:

Minimum Price: $230,700

Maximum Price: $261,900

Explanation:

To find the minimum and maximum prices, we need to find the z-score of the middle 70%

70% = 0.7

1 - 0.7 = 0.3

0.3/2 = 0.15

Then the inverse normal of 0.15 is -1.04

Therefore,

and

Fallis has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

To find out if Ms. Fallis has enough tiles to cover the counter, we need to calculate how many tiles are required to cover an area of 2 square meters.

Since the tiles have a side length of 3 centimeters, we need to convert the area of the counter to square centimeters.

1 square meter = 10000 square centimeters (cm²)

So, 2 square meters = 20000 square centimeters (cm²)

Now, we need to calculate the area of each tile:

Side length of each tile = 3 centimeters (cm)

Area of each tile = \((side length)^2\) = \((3 cm)^2\) = 9 square centimeters (cm²)

To cover the counter, we need to divide the total area of the counter by the area of each tile:

Number of tiles required = (Total area of counter) / (Area of each tile)

= 20000 cm² / 9 cm²

= 2222.22

Since we cannot have a fraction of a tile, we need to round up to the nearest whole number of tiles. So, Ms. Fallis needs at least 2223 tiles to cover the counter.

Since she has 2000 square centimeters (cm²) tiles, she does not have enough tiles to cover the entire counter.

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The variance of the distribution is 0.964.

What is the variance?

The squared deviation from the mean of a random variable is referred to as variance in probability theory and statistics. The square of the standard deviation is another common way to express variation. Variance is a measure of dispersion, or how far apart from the mean a group of data are from one another.

Here, we have

Given:

x    P(r)

0    0.130

1      0.346

2     0.346

3      0.154

4       0.026

We have to find the variance of the distribution.

Var(X) = E(X²) - (E(X))²...(1)

E(X²) = ∑x²Pₓ(X=x)

E(X²) = 0×0.130 + 1²×0.346 + 2²×0.346 + 3²×0.154 + 4²×0.026

E(X²) = 3.532

Now,

E(X) = ∑xPₓ(X=x)

E(X) =  0×0.130 + 1×0.346 + 2×0.346 + 3×0.154 + 4×0.026

E(X) = 1.604

Now, we put the value of E(X) and E(X²) in equation (1) and we get

Var(X)  = 3.532 - (1.604)²

Var(X)  = 0.95918

Var(X)  = 0.964

Hence, the variance of the distribution is 0.964.

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\(A = (a^2 b)(3 a^2 b) = 3(a^2 b)^2 = 3a^4 b^2 ~~ \text{units}^2,\)

Answer:

3a⁴b² units²

Step-by-step explanation:

Area of rectangle: L x B

=> Area of rectangle: LB

=> Area of rectangle = a²b x 3a²b

=> Area of rectangle = a² x b x 3 x a² x b

=> Area of rectangle = a² x b x 3 x a² x b

=> Area of rectangle = a² x a² x b x b x 3

=> Area of rectangle = a⁴ x b² x 3

Therefore, the area of the rectangle is 3a⁴b² units²

Hoped this helped.

The fraction which should go into the boxes marked A and B in their simplest form is 3/4 and 1/4 respectively.

Total number of fruits Amy has = 10

Number of Apples = 7

Number of Oranges = 3

First random pieces of fruits chosen:

Probability of choosing Apples = 6/9

Probability of choosing Oranges = 3/9

Second random pieces of fruits chosen:

Probability of choosing Apples = 6/8

= 3/4

Probability of choosing Oranges = 2/8

= 1/4

Therefore, the probability of choosing Apples or oranges as the second piece is 3/4 or 1/4 respectively.

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Answer:

linear

Step-by-step explanation:

We can write this  in the form

y = mx+b

where m is the .75 per mile and b is the 39 dollars

y = .75x + 39

If were most interested in describing the pattern of changes in the weather in a city from month to month, the type of graph that would be appropriate is the area graph.

An area graph or chart is similar to a line chart in that it has points connected by straight lines on a two-dimensional chart.

It should be noted that the area graph multiple variables are stacked on top of each other, and the area below each line is colored to represent each variable.

Therefore, the type of graph that would be appropriate is the area graph.

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By using Binomial distribution of probability, the result obtained is

Probability that it will rain on exactly zero of the five days they are there = 0.00142

What is Binomial distribution of probability?

Binomial distribution is a discrete type probability distribution, whose probability mass function is given by

P(X = x) = \({n \choose x} p^x (1-p)^{n - x}\)

Here, Binomial distribution of probability is used

Probability of rain on any given day = \(0.83\)

Probability of no rain on the given day = \(1 - 0.83 = 0.17\)

Probability that it will rain on exactly zero of the five days they are there

= \({5 \choose 0}0.83^0 0.17^{5 - 0}\\1 \times 1 \times 0.17^5\)

= \(0.17^5\)

= 0.000142

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Answer:

The answer is 4.

Step-by-step explanation:

if you havent figured that our already.

‍♀️

Answer:

x = - 4

Step-by-step explanation:

x - 5 = - 9 ( isolate x by adding 5 to both sides )

x = - 9 + 5 = - 4

Answer:

x = -4

Step-by-step explanation:

x - 5 = - 9

x - 5 + 5 = -9 + 5

x = -4

The value of f(2) as calculated by the given function is 14.

Given function:-

\(f(x)=2x^3-2\)

We have to find the value of f(2).

Putting x = 2 in the given function, we get:-

\(f(2)=2(2)^3-2\)

We know that the cube of 2 is 8. Hence, we can write,

f(2) = 2*8 -2 = 16 - 2 = 14.

Function

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range.

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Answer:

B, D, E

Step-by-step explanation:

If a line is parallel to another line, then the slope has to be the same. Thus we first want to find the slope of the line given, by using the slope formula: m = (y_1 - y_0)/(x_1 - x_0): (2 - 4)/(-2-3) = 2/5

We proceed to find the slope of the following answer choices:

A. (-3-(-5))/(-7-(-2)) = -2/5

B. (-1-1)/(-6-(-1)) = 2/5

C. (5 - 0)/(2-0) = 5/2

D. (2-0)/(6-1) = 2/5

E. (2-0)/(8-3) = 2/5

Thus, we have B, D, E

Answer:

B, D, E On Edge

Step-by-step explanation:

edge22

Answer:

52 cm

Step-by-step explanation:

Using pythagoras theorem

hypothenuos² = adjacent² + opposite²

\( {x}^{2} \: = \: {48}^{2} + {20}^{2} \\ {x}^{2} \: = \: 2304 + 400 \\ {x}^{2} \: = \: 2704 \\ x \: = \: \sqrt{2704} \\ x \: = \: 52cm\)

Answer:

The expression you provided is a binomial expression raised to the third power, where the binomial is (a^2 + 2ab + b^2). Using the binomial expansion formula for (a+b)^3, we can simplify the expression as follows:

(a^2 + 2ab + b^2)^3 = [(a+b)^2 + ab]^3 [using the identity (a^2 + 2ab + b^2) = (a+b)^2 + ab]

= [(a+b)^2 + ab][(a+b)^2 + ab][(a+b)^2 + ab]

Expanding each term, we get:

= [(a+b)^4 + 2ab(a+b)^2 + a^2b^2][(a+b)^2 + ab]

= [(a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4) + 2ab(a^2 + 2ab + b^2) + a^2b^2][(a+b)^2 + ab]

= [(a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4) + 2a^3b + 4a^2b^2 + 2ab^3 + a^2b^2][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 12a^2b^2 + 6ab^3 + b^4 + 3a^2b^2) + (2a^3b + 4a^2b^2 + 2ab^3 + a^2b^2)ab][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + (2a^4b + 6a^3b^2 + 6a^2b^3 + 2ab^4)][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a^3 + 3a^2b + 3ab^2 + b^3)][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a+b)^3][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a+b)(a+b)^2][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2ab(a+b)(a^2 + 2ab + b^2)][(a+b)^2 + ab]

= [(a^4 + 6a^3b + 13a^2b^2 + 8ab^3 + b^4) + 2a^3b + 4a^2b^2 + 2ab^3 + 2a^2b^2 + 4ab^3 + 2b^4][(a+b)^2 + ab]

Answer

9th graders in her school

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A is wrong because the teachers are not in 9th grade.

B is wrong because parents are not in 9th grade

D is wrong because the homeroom does not represent the entirety of 9th grade

Answer:

Solution,

Let the points be A and B.

A(-2,3)---->(X1,y1)

B(-5,6)---->(x2,y2)

Now,

\( \frac{y2 - y1}{x2 - x1} \\ = \frac{6 - 3}{ - 5 - ( - 2)} \\ = \frac{3}{ - 5 + 2} \\ = \frac{3}{ - 3} \\ = - 1\)

Hope this helps..

Good luck on your assignment..

The probability of getting two red counters is 27.77%, the probability of getting two blue counters is 20.38%, and the probability of getting one of each color is 51.38%.

Given that Tina has two bags of counters, Bag A and Bag B, and there are 5 red counters and 3 blue counters in bag A, while there are 4 red counters and 5 blue counters in bag B, to determine, if Tina takes at random a counter from each bag, the probability of obtaining each counter, the following calculation must be made:

Therefore, the probability of getting two red counters is 27.77%, the probability of getting two blue counters is 20.38%, and the probability of getting one of each color is 51.38%.

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Answer:

56 ounces

Step-by-step explanation:

This is what I'll do so you can see how to do it.

7 ounces --->  1/8 batch

14 ounces ----> 2/8 batch

21 ounces ---> 3/8 batch

28 ounces ----> 4/8 batch

35 ounces ---> 5/8 batch

42 ounces ---> 6/8 batch

49 ounces ----> 7/8 batch

56 ounces  ----> 8/8 batch

OR...

You could have just done 7 * 8 = 56

Hope this helps ya!!!

Answer: 12c+16d

Step-by-step explanation: 4(3c+4d)

(4)(3c+4d)

(4)(3c)+(4)(4d)

12c+16d

Answer:

Întâi faci paranteza și după de ie faci cu 4

Answer:

The dollar bills d are the independent variable while the number of quarters q are the dependent variable

Step-by-step explanation:

Here, we want to state the variable that is dependent and the one that is independent

from the question, she has to put in dollars to get the quarters

so the number of quarters she gets is dependent on the number of dollars put into the machine

Thus, we can conclude that;

The dollar bills are the independent variable while the number of quarters q are the dependent variable

Independent variables are those who are not dependent on other variables. In contrast, their exists dependent variables whose value depends on some other variable(s)' value(s).

For given case, the number of dollar bills 'd' is independent variable with respect to variable 'q'.

The number of quarters 'q' is dependent variable.

Independent variables are those who are not dependent on other variables for their evaluation.

Those variables whose value is decided by the values of other variables. This shows that the variable in consideration is dependent on other variables for its values, thus called dependent variable.

If you see it carefully, you'll see that the quarters received from the change machine is depending on how much dollar bills you're feeding to the machine.

Thus, the value of 'q' is dependent on the value of d.

But since d takes its value independent of q (it exists before q exists and doesn't need q to get its values), thus, d is not dependent on q or is independent variable with respect to q(i said "with respect to q" since d might be dependent on some other variable which we do not know right know)

Thus:

The variable 'q' is dependent variable (depends on d)

The variable 'd' is independent variable with respect to 'q.

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After dilation by a scale factor of 33, the surface area of rectangular pyramid A, the preimage is 1.12 cm²

To find the area of rectangular pyramid A given rectangular pyramid B, we need to know its scale factor.

Scale factor is the ratio of the corresponding sides of two objects.

Now, since rectangular pyramid B is the image of rectangular pyramid A, we have that (since we are dealing with areas)

(Scale factor)² = surface area of rectangular pyramid B/surface area of rectangular pyramid A

So, surface area of rectangular pyramid A = surface are of rectangular pyramid B/(scale factor)²

Since

surface area of rectangular pyramid A = surface area of rectangular pyramid B/(scale factor)²

So, substituting the values of the variables into the equation, we have

surface area of rectangular pyramid A = 1215 cm²/33²

= 1215 cm²/1089

= 1.12 cm²

So, after dilation by a scale factor of 33, the surface area of rectangular pyramid A, the preimage is 1.12 cm²

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Answer:

1742 is divided by 2.16 than answer is 418.75

You can infer causality from a correlational result, but only when the r value is greater than:

C. 1

Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.

However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.

In addition, there are other factors that need to be considered when assessing causality from a correlational result.

For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.

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Answer:

58

Step-by-step explanation:

Total area = 7 × 10 - 6 × 2 = 70 - 12 = 58 units²

The domain of a relation or function are the input values. In this image the domain is represented by the begining of the arrows (the values on the x column).

What is a one one function?

In Maths, an injective function or injection or one-one function is a function that comprises individuality that never maps discrete elements of its domain to the equivalent element of its codomain. We can say, every element of the codomain is the image of only one element of its domain.

The range are the output values. In this case they are the ends of the arrows (the values on the y column

• Domain: {5, 10, 15, 20}

• Range: {-3, -1, 1, 3}

• Description: ,this is an injective function, because it is a one to one relation

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The length of a standard basketball court is 94 feet (28.65 meters), and the width is 50 feet (15.24 meters).

A standard basketball court is rectangular in shape and follows certain dimensions specified by the International Basketball Federation (FIBA) and the National Basketball Association (NBA). The length and width of a basketball court may vary slightly depending on the governing body and the level of play, but the most commonly used dimensions are as follows:

The length of a basketball court is typically 94 feet (28.65 meters) in professional settings. This length is measured from baseline to baseline, parallel to the sidelines.

The width of a basketball court is usually 50 feet (15.24 meters). This width is measured from sideline to sideline, perpendicular to the baselines.

These dimensions provide a standardized playing area for basketball games, ensuring consistency across different courts and facilitating fair play. It's important to note that while these measurements represent the standard dimensions, there can be slight variations in court size depending on factors such as the venue, league, or specific regulations in different countries.

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