are 4:1 and 8:3 eqivalent ratios?

The train will take 10 seconds to cross 1 electric pole at the speed of 54 kilometres per hour.

The time taken will be calculated by the formula- time = distance/speed.

Now firstly converting the speed to meter per second.

As we know, 1 km is 1000 meters and 1 hour has 3600 seconds. Thus, speed = (54 × 1000)/3600

Cancelling zero and performing multiplication and division

Speed = 15 m/s.

Keep the values in formula -

Time = 150/15

Performing division

Time = 10 seconds

Hence, it takes 10 seconds by the train.

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By using percentage, it can be calculated that-

Sticker price of the car =  $14291.75

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage

For example 11% means [tex]\frac{11}{100}[/tex] . Here 11 is expressed as a fraction of 100

This is a word problem on percentage

Base price of the car = $15455.40

Cost of option = $585

Destination charge = $675

The dealer's cost is 85% of the base and 82% of the options

Sticker price of the car = [tex]\frac{85}{100}\times 15455 + \frac{82}{100} \times 585 + 675[/tex]

                                      = 13137.09 + 479.7 + 675

                                      = $14291.75

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Using the provided equation and derivative for the rate, The initial value is 100 and the rate is 40.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

in mathematics, the rate of change of a function with respect to a variable. Derivatives are fundamental to the solution of problems in calculus and differential equations.

y= 40x + 100

x=0 for initial value, We get y=100.

apply derivative on y with respect to x , We get

[tex]\frac {dy}{dx} =40[/tex]

rate =40

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Answer:

Fossil

are impressions of plants or animals embedded in rock and preserved. They may be in the form of a body or trace.

The age of the fossils is determined by the Radioactive carbon dating technique in which the half-life of carbon and found radioactive elements is determined to calculate the age of a fossil

The results obtained by using proportions to calculate are:

A) Valerie takes (4.995 ≅) 5 hours to drive to work on average after 10 days.

B) Valerie takes (9.4911 ≅) 9.5 hours to drive a total of 224.2 miles to work.

C) Valerie takes (20.98 ≅) 21 days to drive a total of 247.8 miles to work.

Proportions are the two ratios that are related by equality between them. I.e., w : x = y : z

We can rewrite them as

w/x = y/z or wz = xy

By using this relation, we can solve any of the variables.

It is given that,

Valerie takes, on average, 30 mins, to drive the 11.8 miles to her job every day.

So, from this, we can find the time taken by her for driving 1-mile using proportions.

I.e.,

for 11.8 miles → 30 min

then 1 mile → X min

⇒ 11.8 : 1 = 30 : X

⇒ 11.8X = 30

∴ X = 30/11.8 = 2.54 mins

A) The time it takes for her to drive to work on average after 10 days:

for 10 days, she drives 11.8 × 10 = 118 miles

So, the time taken for 118 miles × 2.54 min = 299.72 min

We know that for 60 min it is 1 hour, then for 299.72 min, it is 4.995 hours that is on average Valerie takes 5 hours to drive for 10 days.

B) The time it takes for her to drive a total of 224.2 miles to work:

We know that for 1 mile she takes 2.54 min, then for 224.2 miles, she takes 224.2 × 2.54 = 569.468 min

That means 569.468 min/60 = 9.49 hours ≅ 9.5 hours

Thus, she takes 9.5 hours to drive 224.2 miles.

C) The number of days she takes to drive a total of 247.8 miles to work:

We know that for 1 mile she takes 2.54 min, then for 247.8 miles, she takes 247.8 × 2.54 = 629.412 min

If she takes 30 min to drive per day, then the number of days for 629.412 min is

= 629.412 min/30 = 20.98 days ≅ 21 days.

Thus, she takes 21 days for driving 247.8 miles.

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Answer:

Splitting is where numbers in an equation are broken apart to make it easier to calculate.

Step-by-step explanation:

Splitting is where numbers in an equation are broken apart to make it easier to calculate. Ex:

21 * 7

20 * 7 + 1 * 7 =

140 + 7

147

The option that describes the viable solution for the system is D.

all real number values, with x >=0 and y>=0​

Here we have the following system of inequalities:

-y ≤ 3x + 4

-3x - 3y ≤ 9

We can rewrite the second inequality to get:

-3y ≤ 9 + 3x

-y ≤ 9/3 + 3x/3

-y ≤  3 + x

Then our system of inequalities becomes:

-y ≤  3 + x

-y ≤ 3x + 4

So, as long as x and y are both positive or 0, the system is true (this is a rough estimation), but that is enough to conclude that the correct option is D.

all real number values, with x >=0 and y>=0​

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Answer:

420

Step-by-step explanation:

60 x 7 = 420

Answer: 420

Step-by-step explanation:

If you have 7 songs on each CD then you have 60 CD'S just take 7 and times it by 60.

The required mean of the distribution of x + y for the given data is 2.07.

A statistical distribution, or probability distribution, portrays how values are dispersed for a field. As such, the measurable dissemination shows which values are normal and exceptional. There are numerous sorts of measurable appropriations, including the chime formed typical conveyance.

We have,

mean = 1 and Standard deviation = 0.94

In distribution of Y

mean = 1.07 and standard deviation = 1.04

mean of distribution X + Y = ?

Then,

the mean of the distribution of X+Y

= mean of x + mean of y

=  1 + 1.07

= 2.07

Thus, the required mean is 2.07.

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Answer: -4

Step-by-step explanation:

Answer: 13.1

Step-by-step explanation:

(2.5)+(7*9)/(5) = 2.5+63/5 = 65.5/5 = 13.1

Answer:

13.1

Step-by-step explanation:

Given rational expression:

[tex]\dfrac{m+(7 \cdot 9)}{n}[/tex]

To determine the value of the given expression when m = 2.5 and n = 5, substitute the given values into the expression and solve.

[tex]\begin{aligned}m=2.5, n=5 &\implies \dfrac{2.5+(7 \cdot 9)}{5}\\\\&\implies \dfrac{2.5+63}{5}\\\\&\implies \dfrac{65.5}{5}\\\\&\implies \dfrac{65.5 \cdot 2}{5 \cdot 2}\\\\&\implies \dfrac{131}{10}\\\\&\implies 13.1\end{aligned}[/tex]

Answer: The speed was 4.1 MB/sec.

We first find the amount that was transferred within the first 125 seconds:

549-36.5=512.5

Now we divide this by 125, the number of seconds:

512.5/125 = 4.1

The speed of the transfer is 4.1 megabytes per second.

It took 235 seconds for the drive to be completely filled.

Step-by-step explanation:

Answer: It's either 60 or 232

Note: I'm not that good, in problem solving but i thought i can try.

Message: If this helps, let me know by giving me a thanks! :)

According to the given statement the probability that the hand contain exactly 2 face card is [tex]\frac{1}{221}[/tex].

Calculating a result or perhaps the probability that an event would ever occur is known as simple probability. Probability statistics are used by insurance firms to calculate the probability that they'll have to give out a claimed. By dividing one possible outcome by all other possible possibilities, one may determine a basic probability.

A regular 52-card deck is used to deal a poker hand, which consists of 4 cards.

The total number of cards in a deck 52

Number of faces cards in a deck = 2

Number of cards not face cards = 50

The total number of combinations of drawing 4 cards out of 52 cards = [tex]={ }^{52} C_4[/tex]

Now , the combination of 4 cards such that exactly 2 of them are face cards =  [tex]{ }^{2} C_2 \times{ }^{50} C_2[/tex]

That probability that perhaps the collection will comprise exactly six face cards is as follows:

= [tex]\frac{{ }^{2} C_2 \times{ }^{50} C_2}{{ }^{52} C_4}[/tex]

[tex]=\frac{\frac{2 !}{2 ! 0 !} \times \frac{50 !}{2 ! 48 !}}{\frac{52 !}{4 ! \times 48 !}}[/tex]

=[tex]\frac{1}{221}[/tex]

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The three formulas for slope are: Slope formula, slope-intercept formula, and at the point-slope formula

 1. Slope formula  : (y2-y1) / (x2-x1)

 2. Slope intercept formula:  y = mx + b

 3. Point slope formula: y - y1 = m(x - x1)

The slope is defined as the steepness of a line, which is described by the ratio of the vertical change between two points (rise) over the horizontal change between the same two points (run). The first formula is the most commonly used and is used when we know two points in a line. The second formula is a for the  slope and y-intercept and  the third one is the slope of a line and  a point on the line.

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To find the maximum number in a list of numbers, we go through the whole list of numbers and compare each values.

We know that the maximum number is nothing but a number having the largest value in the data set.

To find the maximum number in a list of numbers, we go through the whole list of numbers and compare each values.

The maximum number in the list is the largest value found when all values have been compared.

For example, in the list of numbers 23, 98, 76, 90, 17, 71

the maximum number is 98

Therefore, the maximum number in the list is the largest value found when all values have been compared.

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The 0.75 represents the cost of the custom of each t-shirt and 9.99 represents the cost of custom shipment. And the total cost of 12 t-shirts is $18.99.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The cost (in dollars) of a uniquely crafted shirt is addressed as 0.75n + 9.99, where n is the number of words in the plan.

The cost of 12 t-shirts will be given as,

⇒ 0.75n + 9.99

⇒ 0.75 x 12 + 9.99

⇒ 9 + 9.99

⇒ 18.99

The 0.75 represents the cost of the custom of each t-shirt and 9.99 represents the cost of custom shipment. And the total cost of 12 t-shirts is $18.99.

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The residual, if the cupric chloride had an etching rate of 5 [tex]\frac{\mu m}{min}[/tex], is given as follows:

-2 [tex]\frac{\mu m}{min}[/tex]

For a data-set, the definition of a residual is that it represents the difference of the actual output value by the predicted output value, that is:

Residual = Observed - Predicted.

The predicted etching rate for a temperature of x in this problem is given by the line of best fit, defined as follows:

y = 2 + 1/5x.

Hence, for a temperature of 25ºC, the estimated etching rate is given as follows:

y = 2 + 1/5(25) = 2 + 5 = 7.

The observed etching rate is of 5 units, hence the residual is calculated as follows:

Residual = Observed - Predicted.

Residual = 5 - 7

Residual = -2.

The problem is given by the image shown at the end of the answer.

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The formula of time is time: distance/speed

Time is an important concept in physics, and it can be expressed in a variety of ways. The most common way to describe time is with the equation t = d/s, where t is time, d is the change in position of an object, and s is the speed of the object. This equation is known as the time-distance formula.  The time-distance formula can be used to calculate the time it takes for an object to travel a certain distance., also the time-distance formula can also be used to calculate the distance an object travels in a certain amount of time.

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The regression model is assumption of ols assumes that there is no correlation between the error and the independent variables

What is the Assumption of Linearity?

Linearity Assumption (OLS Assumption 1) - The model will be inaccurate and therefore unreliable if it is fitted to data that is not linearly connected. Extrapolating from the model is likely to produce inaccurate results. As a result, you must always draw a graph of the observed and anticipated values. The linearity assumption is confirmed if the graph is symmetrically distributed over the 45-degree line. By applying non-linear transformations to the independent variables, you can change the functional form of the regression if the linearity requirements are violated.

The OLS assumption of no multi-collinearity says that there should be no linear relationship between the independent variables.

Hence, The regression model is the assumption of ols assumes that there is no correlation between the error and the independent variables.

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There are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

What is permutation?

A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

In order to fix 7 − letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contains exactly one a and exactly two b, we know that For a sequence having n letters, it is called n letter sequence. Such sequences exist with 26^n cases with repetition of letters are allowed.

So, the number of desired cases are,

= [tex]\frac{7_P_3(24)^4}{2} = 34836480[/tex]

Hence, there are 34836480 number of 7-letter sequences (formed from the 26 letters in the alphabet, with repetition allowed) contain exactly one a and exactly two bs.

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Answer:

No, A and B do not have the same solution.

To find the solution to A, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting x from both sides of the equation and then adding 2 to both sides. This gives us:

4x + 2 - x = 6 - x + 2

3x = 8

x = 8/3

To find the solution to B, we need to isolate the variable x on one side of the equation and solve for its value. We can do this by subtracting 2 from both sides of the equation. This gives us:

5x + 2 - 2 = 6 - 2

5x = 4

x = 4/5

As we can see, the solutions to A and B are different, so A and B do not have the same solution. The solution to A is x = 8/3, and the solution to B is x = 4/5.

Step-by-step explanation:

The slope (m) of the line that passes through the points (-8, 2) and (-11, 3) is -1/3.  

What is the slop of the line?

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).

We have,

The line that passes through the points (-8, 2) and (-11, 3),

Slop (m) = ?

The slope formula is:

m =  (y₂-y₁) ÷ (x₂-x₁)

so here,

m = (3 - 2) ÷ (-11 - (-8))

m = 1 ÷ (-3)

m = -1/3

Hence, the slope (m) of the line that passes through the points (-8, 2) and (-11, 3) is -1/3.  

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In the inverse variation function, when x and y are given, the value of k will be K = x * y.

Inverse variation states that when the value of one quantity increases, then the value of another quantity decreases in the same proportion. It includes a relationship between variables that are mentioned as y=k/x where x and y are variables and k is constant.

Distance and speed can be taken as a great example of inverse variation. When speed increases distance decreases.

When 'K' is constant, we can find it by multiplying the x-coordinate by the y-coordinate. So,  we can say that in an inverse variation function, when x and y are given, the value of 'k' will be K =x*y.

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The completed statement that described the situation indicated by the graph of the linear system of equations representing Carson and Romeo distance from the shore is presented as follows;

The graph of the system of equations show that Romeo was floating close to Carson and then swam alongside Carson

The system of equations represented on the graph has an infinite number of solutions because the two lines in the system of equations are the same line

A system of linear equations are a set of linear equations that are formed by the same variables, and which work together.

The points on the graph of the equation, obtained from a diagram of a similar question online are; (0, 5), (1, 6), (2, 7), (3, 8), (4, 9) (5, 10)

Therefore, the slope of the equation representing the distance from the shore is, m = (6 - 5)/(1 - 0) = 1

The y-intercept, the point where x = 0, is (0, 5), which indicates that the y-intercept is c = 5

The equation of the line in slope-intercept form, y = m·x + c, therefore is; y = x + 5

Please find attached the graph in the question of the equation created with MS Excel

The details of the question obtained from a similar question on the internet indicate that the graph of the equation of Carson's distances and the graph of the equation of Romeo's distances are the same straight lines.

The y-intercept of the graph represent the location where the Carson and Romeo where initially floating, therefore;

Romeo was floating close to Carson

The coinciding graphs indicates that Carson and Romeo swam side by side

The equations of the distances which are equivalent, indicates that the system of equations has an infinite number of solutions

The reason the system of equations have an infinite number of solutions is because the two lined overlap

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Answer:

[tex]\frac{5}{3}[/tex]

Step-by-step explanation:

Because the problem is written as:

[tex]x^{3}[/tex] =

You look for the option that would equal      [tex]\frac{125}{27}[/tex] when multiplied by itself 3 times,

[tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] =  [tex]\frac{125}{27}[/tex]

C.  [tex]\frac{5}{3}[/tex]  is your answer ( because  [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] =  [tex]\frac{125}{27}[/tex]   )

[tex]x^{3}[/tex] = [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] x [tex]\frac{5}{3}[/tex] =  [tex]\frac{125}{27}[/tex]  

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Answer:

The initial value in the given table is 41. This is the total cost to rent a costume for 1 day, which is the smallest number of days listed in the table. The initial value represents the fixed refundable security deposit that the costume rental store charges, which is a constant amount that does not depend on the number of days the costume is rented for.

Step-by-step explanation:

Triangle ABC to triangle A'B'C' is enlarged by the dilation.

Dilation is the process of enlarging a shape, figure, or line. In mathematics, dilation means Reducing the object's size by dilation is a change. The items are enlarged or shrunk through dilation. An image that retains the original shape is created by this alteration. A dilation in mathematics is a function f from a metric space M into itself that fulfills the formula d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number. A resemblance of the space exists in Euclidean space when a dilation like this occurs.

The query leads us to believe that:

Triangle A'B'C' is created by enlarging triangle ABC.

The diagram also demonstrates that triangle A'B'C"s side lengths are longer than ABC's.

The dilation is hence an augmentation

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Answer:

The dilation is an enlargement because the image, triangle A'B'C', is larger than the pre-image, triangle ABC.

Step-by-step explanation:

edge 2023

y= 3x + 4

Slope: 3

y-intercept: (0,4)

y= -2x - 3

Slope: -2

y-intercept: (0,-3)