The sum of the speed of the two trains is 723.5 miles per hour. if the speed of the first train is 4.5 mph faster than that of the second train, find the speeds of each

Step-by-step explanation:

Slope = (y2 - y1) / (x2 - x1)

Slope = 5/2

x1 = -6

y1 = y

x2 = 4

y2 = 8

5/2 = (8-y) / (4 - (-6))

5/2 = (8-y) / (4+6)

5/2 = (8-y) / 10

5 x 10 = 2 x (8-y)

50 = 16 - 2y

2y = 16 - 50

2y = -34

y = -17

The speed of the humming bird when converted to miles per minute is; 0.67 miles per minute

In scientific problems, sometimes, it is necessary to change units from one to another as specifically needed.

The procedure for unit conversion is;

1. Identify the unit you have.

2. Identify the unit you desire or require.

3. Identify appropriate unit conversion factor(s).

4. Cancel units and carry out the math calculations.

5. Evaluate the result.

We are given the speed as 40 miles per hour. Now, the unit of conversion factor from mph to miles per minute is;

1 mile per hour = 1/60 miles per minute

Thus;

40 miles per hour = 40 * 1/60 = 0.67 miles per minute

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Altogether, Abby and Annie have 2,400 coins, using the Lowest Common Multiple of 75 and 80.

The lowest common multiple (LCM) of two or more numbers is the common multiple shared by the numbers.

LCM of 75 and 80 can be obtained by multiplying common prime factors of 75 and 80, and then raising them to their respective highest power, i.e. 2^4 × 3^1 × 5^2, which gives 1200.

For instance, 1,200 can be divided by both 75 and 80 evenly without a remainder.  And there is no other number less than 2,000 that 75 and 80 can divide evenly without a remainder.

Abby's coins = 1,200

Annie's coins = 1,200

Total coins = 2,400

Abby's 80 coins will have 15 groups (1,200/80)

Annie's 75 coins will have 16 groups (1,200/75)

Thus, using the LCM of 80 and 75, the total number of coins held by Abby and Annie is 2,400.

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Answer:

Step-by-step explanation:

1. Convert words to math

3/4/1/8=

3/4*8/1=

24/4=

6

3. Answer: 6

The inequality has a solution set of  {-∞, 13} in order to make it equal

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions. An inequality shows the relationship between two values in an algebraic expression that are not equal.

In the given question

8(n - 3) < 4(n + 7)

Expand the bracket

8n - 24 < 4n + 28

8n - 4n < 28 + 24

n < 13

The solution set to make the inequality equal is {-∞, 13}

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The time taken for the 5 feet of snow to accumulate is 20 hours.

In this case, Smsnow was falling at the rate of 3 inches per hour and if the snow keeps acclimating, we want to know how long will 5 feet of snow to accumulate.

Since 1 foot = 12 inches

5 feet = 5 × 12

= 60 inches

Therefore the time taken will be the division and this will be:

= 60 / 3

= 20

It'll take 20 hours.

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Answer:

2.8 x 10º

Step-by-step explanation:

Because if you travel 10 spaces in the number 280,000,00.

The bottle of grapefruit juice at store A is $6.63 less than the store B.

According to the question,

We have the following information:

The equation y = 1.75x represents what Lamonte would pay in dollars and cents, y, for a bottles of grapefruit juice at store A.

Cost of 17 bottles of grapefruit juice at store B = $36.38

Now, we will find the cost of 17 bottles at store A.

y = 1.75*17

y = $29.75

Now, the difference in their price = 36.38-29.75

Difference = $6.63

Hence, the bottle of grapefruit juice at store A is $6.63 less than the store B.

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Answer: 0.39

Step-by-step explanation:

Store A

y= 1.75x

A bottle of grapefruit juice costs 1.75 at store A

Store B

36.38$/17 bottles = 2.14$ per bottle

A bottle of grapefruit juice costs 2.14$ at store B

Store B - Store A= 2.14$ - 1.75$

=0.39

The value of the car depreciates according to the scatter plot model that is attached , from the model we can infer that the model is exponential in nature.

So from the data that is plotted in the scatter plot we can see that

The graph is exponential.

We know that the depreciation is calculated by the formula as

A = A₀(1-r)ⁿ

So it is an exponential form of equation. therefore the scatter plot model will also predict an exponential equation.

A scatter plot is a type of plot or mathematical diagram that displays values for a group of data using two or more variables and Cartesian coordinates. A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.

If the points are somehow coded according to colour, shape, or size, another variable can be seen. A series of points is used to represent the data, with each point's position on the y line determined by the value of one variable and its position on the vertical axis by the value of the other.

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a perfect square trinomial, namely   [tex]\qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2[/tex]

where the middle-term is just a product of "2 times the square root of the terms on both sides".

so let's start by grouping the terms with a variable, and then adding the last term for the trinomial, keeping in mind the middle-term is just that product.

[tex]x^2+6x+5\implies (x^2+6x) ~~ +5\implies (x^2+6x+\square^2) ~~ +5 \\\\\\ \stackrel{middle-term}{6x}=2(\sqrt{x^2})(\sqrt{\square^2})\implies 6x=2x\square\implies \cfrac{6x}{2x}=\square\implies 3=\square[/tex]

ahhhaaa!!! so our missing term from our group is 3, meaning we need to use 3², however, let's remember, all we're doing is borrowing from our very  good friend Mr Zero, 0, so if we add 3², we also have to also subtract 3²

[tex](x^2+6x+3^2-3^2) ~~ +5\implies (x^2+6x+3^2)-3^2 +5\implies {\Large \begin{array}{llll} (x+3)^2-4 \end{array}}[/tex]

The type of variable that C is can be said to be the binomial variable.

A binomial random variable counts the number of times a specific event occurs in a given number of tries or trials. To be a binomial random variable, a variable must be There is a set number of trials.

It should be noted that the features of the binomial variable include:

1: The number of observations, n, is constant.

2: Each observation is distinct.

3: Each observation denotes one of two possible outcomes ("success" or "failure").

4: The "success" probability p is the same for each outcome.

In this case, the number of coupons the family wins illustrate a binomial.

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Answer:

Page 1 of 3

1. twenty  

2. 16,49  

3. option3  

4.32  

5. 40 tickets     show your work--10= 1.00 40=4.00

Page 2 of 3

7, 14, 21, 28, 35, 42, 49, 56, 63

Page 3 of 3 (left to right)

56, 0, 21, 63, 42, 35, 14, 28, 7, 77, 84, 56, 14, 49, 63, 28, 70, 42, 21, 35, 84, 7, 77, 0, 70

Step-by-step explanation:

learn your times tables

it will help you in high school and college

The thing that can be conluded about the diagram is that the ponds are the same length. This is according to the SAS theorem.

According to the SAS theorem, if two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent.

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. If two triangles meet one of the following criteria, they are congruent. All three corresponding side pairs are equal. Two corresponding side pairs and their corresponding angles are equal.

In this case, the triangle for the frog pond and duck pond are the same.

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The balance on the Bad Debt Expense account for the year, based on the accounts receivable balance and the rates of uncollectibility is $6, 800.

First, find the uncollected receivables estimate for the year using the rates of uncollectibility.

= ∑ (Age of receivable x Rate of uncollectibility)

= (50, 000 x 1%) + ( 20,000 x 3%) + (11, 000 x 5%) + (19, 000 x 25%)

= 500 + 600 + 550 + 4, 750

= $6, 400

The Bad Debts Expense for the year would then be:

= Uncollected receivables estimate + Debit balance on Allowance for doubtful accounts

= 6, 400 + 400

= $6, 800

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Answer: (3x^2)(y^3√y)

Step-by-step explanation:

1. To simplify the radical

> break the radicand (the number under the radical sign) into a product (the result of two numbers being multiplied together) of known factors.

2. Assume all numbers are real.

Check step-by-step explanation.

In order to form the table, we must take several values of x (any values you want to evaluate) and find it's correspondent y value. This is how you  do it:

[tex]y=3x+12[/tex]

[tex]x=0, \\y=3(0)+12\\y=12[/tex]

As you may notice, we are just substituting the x value for the x variable into the equation and calculating y. Do this with several values and form a table (check attached image 1).

[tex]x=1, \\y=3(1)+12\\y=15[/tex]

[tex]x=2, \\y=3(2)+12\\y=18[/tex]

Using the calculated points, draw them in the cartesian plane. Remember that "x" means how many spaces you move horizontally, and "y" means vertical spaces.

Check attached image 2.

Let's take point (2, 18) as an example. This point is generated when you substitute the x value of 2, meaning 2 hotdogs and the souvenir hat. Then, the functions gives a result of 18, which would be the cost of those 2 hotdogs in addition to the souvenir hat. Point (0, 12), on the other hand, means that you didn't buy any hotdogs but you still have to pay $12 for the souvenir hat.

The 68.26% confidence interval for the mean of the population, using the z-distribution, is given as follows:

(15.88 ounces, 16.12 ounces).

The bounds of a z-distribution confidence interval are presented as follows:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which the parameters are given by:

The confidence level is of 68.26%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.6826}{2} = 0.8413[/tex], so the critical value is z = 1.

The values of the remaining parameters are given as follows:

[tex]\overline{x} = 16, \sigma = 1.4, n = 144[/tex]

Hence the lower bound of the interval is obtained as follows:

[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 16 - \frac{1.4}{\sqrt{144}} = 15.88[/tex]

The upper bound of the interval is obtained as follows:

[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 16 + \frac{1.4}{\sqrt{144}} = 16.12[/tex]

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Step-by-step explanation:

domain: x is any value, ⇒ x∈(-∝;+∝);

range: y is not greater, than 4, ⇒ y∈(-∝;4].

Answer:

a = 70 degrees

b = 20 degrees

c = 20 degrees

Step-by-step explanation:

First, we can find "c":

angleBCA = 90

angleBCA = angleBCD + c

90 = 70 + c

90 - 70 = c

20 = c

Knowing "c", we can find "a".

angleADC = 90

triangleADC = 180

triangleADC = angleADC + c + a

180 = 90 + 20 + a

180 = 110 + a

180 - 110 = a

70 = a

Knowing "a", we can find "b".

angle BCA = 90

triangleACB = 180

triangleACB = angleBCA + a + b

180 = 90 + 70 + b

180 = 160 + b

180 - 60 = b

20 = b

A direct variation with nonzero numbers is if y varies directly as x, and y = 6 when x = 2,

The relationship between two variables in which the variables have a constant ratio, k, where k is not equal to 0.

K is known as the constant. Assume the variables are x and y, and that y varies directly with x. We can say that the y/x ratio is equal to k, where k is not equal to zero.

This formula can also be written as y = kx where k is not equal to 0.

It's critical to understand that we can use these two ratios interchangeably depending on the problem at hand.

In the example given, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.

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The value of q after solving the inequality, 3q-9 ≤ 8q+10, is q ≤ -19/5.

According to the question,

We have the following information:

3q-9 ≤ 8q+10

Adding 9 to both sides of the inequality:

3q ≤8q+10+9

3q ≤ 8q+19

Subtracting 8q from both sides of the expression:

3q-8q ≤ 19

-5q ≤ 19

Dividing both sides by -5:

q ≤ -19/5

(More to know: inequalities can solved like an equation but the only difference is that the sign of equal has to be replaced by the signs of inequality.)

Hence, the value of q after solving the inequality, 3q-9 ≤ 8q+10, is q ≤ -19/5.

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The estimates for the number of transistors per IC, using Moore's Law, are given as follows:

Moore's Law states that the number of transistors per IC is expected to double every two years.

From the chart shown by the image at the end of the answer, the reference number is given as follows:

4000 transistors per IC in 1972.

The number of years between 1972 and 2012 is of:

2012 - 1972 = 40.

Hence the number of doubling periods is of:

40/2 = 20 doubling periods.

Thus the estimate for the number of transistors per IC in 2012 = 20 doubling periods is of:

4000 x 2^20 = 4,194,304,000 transistors per IC.

The number of years between 1972 and 2040 is of:

2040 - 1972 = 68.

Hence the number of doubling periods is of:

68/2 = 34 doubling periods.

Thus the estimate for the number of transistors per IC in 2012 = 20 doubling periods is of:

4000 x 2^34 = 6.87 x 10¹³ transistors per IC.

The chart is given by the image at the end of the answer.

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The purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.

Let us understand the post hoc tests:

Post hoc tests are an essential component of ANOVA. When at least three group means are tested for equality using ANOVA, statistically significant findings suggest that not all of the group means are equal. ANOVA results, on the other hand, do not specify which differences between pairs of means are significant. Use post hoc tests to investigate variations between various group averages while keeping the experiment-wise error rate under control.

There are a lot of post hoc tests that you can be used but the main purpose of the post hoc tests is always the same.

Thus, the purpose of post hoc tests following an Analysis of Variance is to address the question of which groups differ from one another. Option A is correct.

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Step-by-step explanation:

Its is 8 inches as 72÷9 is 8

10 kilograms of the 50% fat-content chocolate and 20 kilograms of the 20%, fat-content chocolate are used to make the required 30 kilograms.

Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.

The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.

Suppose the amount of 50% fat content chocolate is x and the amount of 20% fat content chocolate is y,

Since the candy company wants to produce 30 kilograms,

x+y=30 -----(1)

If a candy manufacturer wishes to meet the dietary requirements of its customers, it may make 30 kg of special chocolate with a 30% fat content. A specific melting procedure is used to blend local chocolate with 20% fat content with foreign chocolate with 50% fat content to create this. The resultant equation reads,

50x + 20y = 30(30)

5x+2y=90 -------(2)

After solving the equation 1 and 2 we get,

x=10

y=20

Thus, 10 kilograms of the 50% fat-content chocolate and 20 kilograms of the 20%, fat-content chocolate are used to make the required 30 kilograms.

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Answer:

36mins

Step-by-step explanation:

So, the time of travel to cover 5 1/5 miles at a speed of 8 2/3 mph is 36 minutes.

Answer:you have 2 lines that cross.

the left angle formed is equal to 3x + 8

the right angle formed is equal to 5x - 20.

the bottom angle formed is equal to 5x + 4y

since the lines are crossed, the opposite angles to each other are equal.

this means that:

3x + 8 = 5x - 20

solve for x to get x = 14 degrees.

the angle on the left side will be equal to 3(14) + 8 = 50 degrees.

the angle on the right side will be equal to 5(14) - 20 = 50 degrees.

this is at it should be since the angles are equal to each other.

since the sum of the 4 angles formed is equal to 360 degrees, the sum of the remaining 2 angles is equal to 260 degrees.

since those 2 angles are equal, then each one must be equal to 130 degrees.

one of those angles is equal to 5x + 4y.

you get 5x + 4y = 130

since x was already found to be 14, replace x with 14 to get:

5(14) + 4y = 130

solve for y to get y = (130 - 5(14)) / 4 which is equal to 15 degrees.

when x = 14 and y = 15, 5x + 4y = 5(14) + 4(15) = 70 + 60 = 130 which confirms the value of 15 for y is good.

your answers are:

x = 14 degrees

y = 15 degrees

2 of the angles measure 50 degrees each.

2 of the angles measure 130 degrees each.

Answer:

El otro extremo dista :

12.5 decímetros

Step-by-step explanation:

1 dm = 1 decímetro = 10 cm

1 m = 1 metros = 10 decímetros = 10 dm

3.5 metros = 3.5 * 10 = 35 decímetros

125 cm = 125/10 = 12.5 decímetros

Entonces:

35 dm - 12.5 dm = 22.5 dm

Answer:

Step-by-step explanation:

percentage increase = (final - initial)/initial

increase = (672 - 480)/480

               = 192/480

               = 0.4 * 100 = 40% increase