Two trains leave towns 1240 kilometers apart at the same time and travel toward each other. One train travels 18 km/h faster than the other. If they meet in 5 hours, what is the rate of each train?
rate of the faster train:
rate of the slower train:

The probability of spinning an even number, flipping tails, then spinning an odd number is:

1/9   (as fraction) or 11.11% (as percent)

To find the probability of spinning an even number, flipping tails, then spinning an odd number. We need to consider the individual probabilities. That is:

We have only one even number in the spinner, and that is 2. Thus,

P(even number) = 1/3

For a coin, the probability of head or tail is 1/2. Thus,

P(tail) = 1/2

We have two odd number in the spinner, and that is 1 and 3. Thus,

P(odd number) = 2/3

Therefore, the probability of spinning an even number, flipping tails, then spinning an odd number will be:

P(even, tail, odd) = 1/3 * 1/2 * 2/3

                            = 2/18

                            = 1/9   (as fraction)

In percent:

P(even, tail, odd) =  1/9 * 100

                            = 11.11%

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Answer:

0.362 = (0 x 1) + (3/10) + (6/100) + (2/1000)

49.564 = (4 x 10) + (9 x 1) + (5/10) + (6/100) + (4/1000)

Step-by-step explanation:

If you look at the first one 0.362 the 3 is in the tenths position + 6 in the hundredths position + 2 in the thousandths position.

You work the second number the same way:

4 is in the tens position + 9 in the ones position + 5 in the tenths position + 6 in the one hundredths positions + 4 in the thousandths position.

The area of mathematics known as algebra is used to portray situations or problems using mathematical expressions.

Graph y=4x-1

To determine the slope and y-intercept, use the slope-intercept form.

Y = m x + b, where m is the slope and b is the y-intercept, is the slope-intercept form.

Using the formula y = m x + b, determine the values of m and b. m = 4 b = -1

The value of m represents the line's slope, and the value of b represents the y-intercept.

4 slope, 0 y-intercept, and 1 negative slope

Two points can be used to graph any line. Plug two x values into the equation to determine the associated y values.

Build a table with the x and values for  y:

x    y

0     1

1      3

Use the slope and the y-intercept, or the points, to graph the line.

Slope is 4, and the y-intercept is (0, 1 )

x   y

0   -1

1    3.

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Answer:

4

Step-by-step explanation:

count up from -5 to -1

so -5,-4,-3,-2,-1 and there are four numbers excluding-5

Answer:

Step-by-step explanation:

Answer:

A^n = [4^n 4^n

0 1]

Step-by-step explanation:

To find the solution for the 2x2 matrix A:

[4 4

0 1] to the nth power = [ ]

We can use matrix multiplication to raise A to the nth power. Let's start with n = 1:

A^1 = [4 4

0 1]

Now, let's solve for A^2 by multiplying A^1 by A:

A^2 = A x A^1

= [4 4 [4 4

0 1] 0 1]

= [16 16

0 1]

Next, let's solve for A^3:

A^3 = A x A^2

= [4 4 [16 16

0 1] 0 1]

= [64 64

0 1]

We can see a pattern emerging:

   A^1 = [4 4

   0 1]

   A^2 = [16 16

   0 1]

   A^3 = [64 64

   0 1]

We can generalize this pattern as follows:

A^n = [4^n 4^n

0 1]

Therefore, the solution for the 2x2 matrix A raised to the nth power is:

A^n = [4^n 4^n

0 1]

The statement that can serve as the best option for Mike would be to use his credit card to purchase the bicycle now. That is option A.

A credit card is defined as the type of card that is processed and given to an individual by their banks which gives the individual the liberty to purchase goods on credit.

Since Mike wants to buy a bicycle but has no money in his checking account, he can make use of his credit card which gives him the free liberty to buy goods on credit.

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The best option for mike in this case of borrowing money is; A: Use his credit card to purchase the bicycle now.

A credit card is defined as a type of credit facility, that is provided by banks which permits customers to borrow funds within a pre-approved credit limit. This in turn enables customers to make purchase transactions on goods and services.

Now, we are told that Mike wants to buy a bicycle, but he does not have enough money in his checking account to pay for one.

Looking at the option of a credit card above, it will be the best option for mike since he doesn't possess the total money in his account currently.

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Answer:

121 pi

Step-by-step explanation:

;)

Answer:

121π ft²

Step-by-step explanation:

area = πr²

area = π × (11 ft)²

area = 121π ft²

The equation for the line of best fit is: C. y = 0.894x + 0.535.

In order to determine the equation for the line of best fit, we would create a table of values based on the given x-values and y-values as follows;

x          y            x²        y²          xy__

5          4          25        16       20

6          6           36       36       36

9          9           81        81        81

10         11          100       121       110

14          12        196       144      168  

Sum                  438       398     415

Next, we would calculate the mean of the x and y variables as follows;

Mean = [∑(x)]/n

Mean = 44/5

Mean, \(\bar{x}\) = 8.8

Mean = [∑(y)]/n

Mean = 42/5

Mean, \(\bar{y}\) = 8.4

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) = (5-8.8)(4-8.4) + (6-8.8)(6-8.4)+(9-8.8)(9-8.4)+(10-8.8)(11-8.4)+(14-8.8)(12-8.4)

∑(x - \(\bar{x}\))(x - \(\bar{y}\)) =45.4

∑(x - \(\bar{x}\))² = (5-8.8)²+(6-8.8)²+(9-8.8)²+(10-8.8)²+(14-8.8)²

∑(x - \(\bar{x}\))² = 50.8

Now, we can determine the slope coefficient for the line of best fit:

Slope (b) = 45.4/50.8

Slope (b) = 0.894.

Lastly, we would determine the intercept (a) as follows;

\(a = \bar{y} - b\bar{x}\)

a = 8.4 - (0.894)8.8

a = 0.535

Therefore, the required equation is y = 0.894x + 0.535.

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The coordinates of the new point  is (-6, -2)

From the question, we have the following parameters that can be used in our computation:

Point = (6, 2)

Rule: 180 degrees rotation

The rule of 180 degrees rotation is

(x, y) = (-x -y)

Substitute the known values in the above equation, so, we have the following representation

image = (-6, -2)

Hence, the image is (-6, -2)

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The linear function that describes the data in the table for this problem is given as follows:

C. P(h) = h + 11.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

From the table, we have that when h increases by 1, P(h) also increases by 1, hence the slope m is given as follows:

m = 1/1 = 1.

Hence:

P(h) = h + b.

When h = 4, P(h) = 15, hence the intercept b is given as follows:

15 = 4 + b

b = 11.

Hence the rule is:

P(h) = h + 11.

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The minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

We are given that a water pumping station is to be built on a river at point P in order to deliver water to points A and B. The design requires that LAPD = /BPC so that the total length of piping that will be needed is a minimum. We need to find this minimum length of pipe.

The given figure is shown below: \(AB = 10 \ miles\)\(BC = 6 \ miles\)\(CP = 12 \ miles\). We are given that \(LAPD = LCPB\).

Now, we need to find the minimum length of pipe required for delivering the water to points A and B.The total length of the pipe, \(L_{total} = LA + AB + BP\)Since \(LAPD = LCPB\), we can say that\(AP^2 + PD^2 = BP^2 + PC^2\).

From the triangle ACP, we can say that\(AC^2 = AP^2 + PC^2\). So, we can substitute AP^2 + PC^2 with AC^2 to get\(AP^2 + PD^2 = BP^2 + AC^2\)Now, we can substitute AP = AC - PC and BP = BC + PC in the above equation to get\((AC - PC)^2 + PD^2 = (BC + PC)^2 + AC^2\).

After solving this equation, we get\(AC = \frac {37}{8}\) and \(PC = \frac {27}{8}\)Now, we can calculate the length of pipe required as follows: \(L_{total} = LA + AB + BP = 10 + 6 + \frac {27}{8} = \boxed{20.375 \ miles}\). Therefore, the minimum length of pipe required to deliver water to points A and B is approximately 20.375 miles.

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Answer:

Pizza eaten together: 5/6,

Pizza left over: 1/6

Step-by-step explanation:

~ If Ellen ate 2/4th of the pizza and John ate 1/3 of the pizza, provided that the pizza counts as a whole ( 1 )... ~

1. Let us simplify 2/4th to be ⇒ 1/2, through simple algebra

2. To see how much they ate together we would neglect that the pizza counts as a whole but simply add 1/2 by 1/3rd.

3. Through simple algebra: 1/2 + 1/3 = 3/6 + 2/6 = Pizza eaten together: 5/6

4. Now to find out how much pizza was left over, we would need the fact that a pizza ⇒ 1 whole. It would be that 1 - 1/2 - 1/3 ⇒ Pizza left over, through the Partition Postulate. In fact, the pizza left over would simply be 1 whole - the pizza eaten together ( 5/6 ).

5. Through algebra: 1 - 1/2 - 1/3 = 1 - 5/6 = Pizza left over: 1/6

Answer:

How much did they eat all together? 5/6

How much was left over? 1/6

\( \\ \)

Step-by-step explanation:

How much did they eat all together?

\( \frac{2}{4} + \frac{1}{3} \\ = \frac{6}{12} + \frac{4}{12} \\ = \frac{10}{12} \\ = \frac{5}{6} \)

\( \\ \)

How much was left over?

\( 1 - \frac{5}{6} \\ = \frac{6}{6} - \frac{5}{6} \\ = \frac{1}{6} \)

Answer:

It has the same domain and range as the function f(x) = StartRoot x EndRoot. It has the same range but not the same domain as the function f(x) = StartRoot x EndRoot. It has the same domain and range as the function f(x) = negative StartRoot negative x EndRoot.

Step-by-step explanation:

A, perpendicular line

Answer:

$153.24

Step-by-step explanation:

:/

Answer:

The equation would be:

58 times 65

The answer:

3,770

Step-by-step explanation:

Answer:

3 8

× 2 7

______

2 6 6

+ 7 6

_______

1 0 2 6

Answer:

     38

x    27

   266

+  76_

 1026

Answer:

10 5/12 cups of juice

Step-by-step explanation:

4 1/4 + 2 2/3 + 3 1/2

17/4 + 8/3 + 7/2

51/12 + 32/12 + 42/12

125/12

10 5/12

To determine how the surface area of a rectangular prism changes when all dimensions are quadrupled, we need to compare the original surface area to the new surface area.

The original surface area of the rectangular prism is given by:

SA_original = 2lw + 2lh + 2wh

where l, w, and h represent the length, width, and height of the prism, respectively.

In this case, the dimensions of the original box are:

Length (l) = 3 ft

Width (w) = 6 ft

Height (h) = 5 ft

Substituting these values into the formula, we have:

SA_original = 2(3)(6) + 2(3)(5) + 2(6)(5)

            = 36 + 30 + 60

            = 126 square feet

Now, if we quadruple all the dimensions of the box, the new dimensions would be:

Length (l_new) = 4(3) = 12 ft

Width (w_new) = 4(6) = 24 ft

Height (h_new) = 4(5) = 20 ft

The new surface area of the enlarged box is given by:

SA_new = 2(l_new)(w_new) + 2(l_new)(h_new) + 2(w_new)(h_new)

       = 2(12)(24) + 2(12)(20) + 2(24)(20)

       = 576 + 480 + 960

       = 2016 square feet

Comparing the original surface area (SA_original = 126 sq ft) to the new surface area (SA_new = 2016 sq ft), we can see that SA_new is 16 times greater than SA_original.

Therefore, the correct answer is:

1. The new surface area would be 16 times the original surface area.

24 i think

an LCM is the lowest number that applies to all numbers in your equation

The time period of the animals life cycles are,

⇒ Beluga whole = 35 years

⇒ Bengal tiger = 10 years

⇒ Elephant = 20 years

⇒ Giraffe = 25 years

⇒ Orangutan = 40 years

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

There are some animals and there ages.

Now,

Since, There are some animals and there ages are given.

Hence, The correct ages of the animals are,

⇒ Beluga whole = 35 years

⇒ Bengal tiger = 10 years

⇒ Elephant = 20 years

⇒ Giraffe = 25 years

⇒ Orangutan = 40 years

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Answer:

81

Step-by-step explanation:

3*3=9

9*3=27

27*3=81

Answer:  90

Step-by-step explanation:

3 to the fourth power =  81

81 + 9 = 90

Answer: The correct answers are -3.45 and 1.45

Step-by-step explanation: The only problem you had was you rounded it to the tenths place instead of the hundredths place.

Sorry for getting back to you late.

Answer:

Step-by-step explanation:

1 is 60 2 i 60 and 3 is 61 ;)

When two straight lines or rays intersect at a shared endpoint, an angle is generated. The exact value of cosine(7π/8) is 0.912939.

When two straight lines or rays intersect at a shared endpoint, an angle is generated. An angle's vertex is the common point of contact. Angle is derived from the Latin word angulus, which means "corner."

The given angle can be written in degree form as,

(7π/8) radian = (7π/8) × (180/π) = 157.5°

The exact value of cosine(7π/8) can be written as,

Cosine (7π/8) = Cosine(157.5°) = 0.912939

Hence, The exact value of cosine(7π/8) is 0.912939.

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Answer:

D. -sqrt(2+sqrt(2))/2

Step-by-step explanation:

Took the test and this was the correct answer

A paired t-test can be used to determine if there is a difference between the means of the two groups.

YES.

A paired t-test is appropriate for determining if there is a significant difference between the means of two groups when the data is paired or dependent. This test compares the means of two related samples to evaluate if the difference between them is statistically significant.

In a paired t-test, each observation in one group is paired or matched with a corresponding observation in the other group. The test examines the difference between the paired values and determines if that difference is significantly different from zero.

By calculating the t-statistic and comparing it to the critical values from the t-distribution, along with the degrees of freedom, we can assess if there is a significant difference between the means of the two groups.

Therefore, a paired t-test can be used to determine if there is a difference between the means of the two groups.

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1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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Answer:

False, False, A. 180

Step-by-step explanation:

A flat line is 180 degrees. A right isosceles triangle has one right angle. None of the sides on a scalene triangle are the same.

Answer:

675

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

(5t - 3) · (3t + 7)

t = 6

Step 2: Evaluate

Answer:

(5t -3)(3t+7) (im multiplying them together, if that's not what the questions asking lmk. but anyway, put them next to eachother and then plug in 6 for t)

(5(6) -3)(3(6)+7) (multiply where possible)

(30 -3)(18+7) (use the distributive property/foil to multiply the two)

540 +210 -54 -21 (add the positive numbers and subtract the negative )

750 - 75 (subtract)

675 (the answer)

Step-by-step explanation:

I hope this helps :)

Answer:

3.16227766017 is the answer

Answer: 3.16227766017

Step-by-step explanation:

Or you could round and get 3.2 or 3.16