Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 100 miles per hour. The westbound train
travels at 90 miles per hour. How long will it take for the two trains to be 304 miles apart? ( this is timed plz someone help)

The number that does not belong with the other three is D. 10 x 9.2 ⁻¹³

With the first three numbers, the base of the exponential that is being multiplied by the first number is 10. These numbers are:

With the last number however, we see that the base of the exponential is 9. 2 and not 10 like the others. This is why 10 x 9 . 2 ⁻¹³ does not belong with the rest.

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Step-by-step explanation:

360÷100×20

=72

so 360+72

=432

pls give brainliest!!

Answer:

see the work below

Step-by-step explanation:

20.)    x = √32²+32² = √2048 = 45.25

y = 32(sin60) = 27.7

z = 32(cos60) = 16

22.)   x = 7√3 / cos60 = 24.25 = 14√3

y = 14√3 / tan30 = 42

sin30 = 14√3 / (z+7√3)

z + 7√3 = 14√3 / sin30

z = 14√3/√sin30 - 7√3 = 36.37 = 21√3

24.) z = 18(tan30) = 10.4

h = √10.4² + 18² = √432 = 20.785

x = y

2x² = 20.785²

x = √20.785²/2 = 14.7

y = 14.7

Answer:

Question 20:

Question 22:

Question 24:

Step-by-step explanation:

A 45-45-90 triangle is a special right triangle where the measures of its sides are in the ratio 1 : 1 : √2.  Therefore, the formula for the ratio of the sides is b : b : b√2 where:

A 30-60-90 triangle is a special right triangle where the measures of its sides are in the ratio  1 : √3 : 2.  Therefore, the formula for the ratio of the sides is c: c√3 : 2c where:

Side x is the hypotenuse of a 45-45-90 triangle with congruent legs measuring 32 units. Therefore b = 32.

\(\implies x=b\sqrt{2}=32\sqrt{2}\; \sf units\)

Side y is the side opposite the 60° angle in a 30-60-90 triangle with a hypotenuse of 32 units. Therefore, 2c = 32 so c = 16.

\(\implies y = c\sqrt{3}=16\sqrt{3}\; \sf units\)

Side y is the side opposite the 30° angle in the same 30-60-90 triangle.

\(\implies z=c = 16\; \sf units\)

Side x is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 7√3 units. Therefore c = 7√3.

\(\implies x=2c=2 \cdot 7 \sqrt{3}=14\sqrt{3}\; \sf units\)

Therefore, other leg of the same triangle (opposite the 60° angle) measures c√3 = 7√3 · √3 = 21 units.

Side y is the hypotenuse of a 30-60-90 triangle with the leg opposite the 30° angle measuring 21 units. Therefore c = 21.

\(\implies y=2c=2 \cdot 21 = 42\; \sf units\)

Side z is the leg of the same 30-60-90 triangle opposite the 60° angle.

\(\implies z=c\sqrt{3}=21\sqrt{3}\; \sf units\)

Side z is the side opposite the 30° angle in a 30-60-90 triangle with the other leg (opposite the 60° angle) measuring 18 units. Therefore, c√3 = 18, so c = 18/√3 = 6√3 units.

\(\implies z=c = 6\sqrt{3}\; \sf units\)

Therefore, the hypotenuse of the same triangle measures 2c = 12√3 units.

Sides x and y are the congruent legs of a 45-45-90 triangle with hypotenuse measuring 12√3 units. Therefore b√2 = 12√3, so b = 6√6.

\(\implies x=6 \sqrt{6}\; \sf units\)

\(\implies y=6 \sqrt{6}\; \sf units\)

The journal entries for the bonds transactions of Shunda Corporation are as follows:

1. Debit Cash $23,829,684

Credit Bonds Payable $22,000,000

Credit Bonds Premium $1,829,684

2. Debit Interest Expense $834,039

Debit Bonds Premium $155,961

Credit Cash $990,000

3. Debit Interest Expense $828,580

Debit Bonds Premium $161,420

Credit Cash $990,000

b. Bond Interest Expense for the first year is as follows:

Annual interest paid = $1,980,000

Premium amortized = $317,381

Interest Expense = $1,662,619

c. The bonds sell for more than their face amount because the market rate of interest is less than the contract interest rate. Investors are willing to pay more for bonds that pay a higher rate of interest (contract rate) than the rate they could earn on similar bonds (market rate).

Face value of bonds = $22,000,000

Bonds Proceeds = $23,829,684

Bonds Premium = $1,829,684 ($23,829,684 - $22,000,000)

Coupon interest rate = 9%

Semi-annual interest payment = $990,000 ($22,000,000 x 9% x 1/2)

Effective market interest rate = 7%

1. Cash $23,829,684 Bonds Payable $22,000,000 Bonds Premium $1,829,684

2. Interest Expense $834,039 Bonds Premium $155,961 Cash $990,000

3. Interest Expense $828,580 Bonds Premium $161,420 Cash $990,000

Interest Payment at 4.5% $990,000

Interest Expense            = $834,039 ($23,829,684 x 3.5%)

Amortized Premium =        $155,961

Bond's carrying value = $23,673,723 ($23,829,684 - $155,961)

Interest Payment at 4.5% $990,000

Interest Expense            = $828,580 ($23,673,723 x 3.5%)

Amortized Premium =        $161,420

Bond's carrying value = $23,512,303 ($23,673,723 - $161,420)

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Answer:

Q1: \(\frac{3}{4}\)

Q2: \(\frac{83}{100}\)

Step-by-step explanation:

Q1: 12 : 16 = 3 : 4 = \(\frac{3}{4}\)

Q2: 8.3 : 10 = \(\frac{83}{100}\)

Answer:

x = 4

Step-by-step explanation:

\( - 2x - 4 + 5x = 8\)

Step 1: Collect like terms and simplify

\( - 2x + 5x = 8 + 4 \\ 3x = 12\)

Step 2: Divide both sides of the equation by 3

\( \frac{3x}{3} = \frac{12}{3} \)

Simplify

\(x = 4\)

Answer:

x=4

Step-by-step explanation:

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Given statement solution is :- Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

To determine which company will provide the lowest total cost for 12 lunches, let's calculate the costs for both Carla's Catering and Dan's Diner.

Carla's Catering:

Using the equation provided, y = 6.75x + 25, where x represents the number of lunches:

For x = 12:

y = 6.75(12) + 25

y = 81 + 25

y = 106

The total cost for 12 lunches from Carla's Catering is $106.

Dan's Diner:

We are given the following data points for Dan's Diner:

Number of Lunches (x) Total Cost (y)

5 $57.50

10 $100.00

15 $142.50

From this data, we can calculate the rate at which the cost increases per lunch:

Rate = (Change in Total Cost) / (Change in Number of Lunches)

Rate = (100 - 57.50) / (10 - 5)

Rate = 42.50 / 5

Rate = 8.50

Now, let's calculate the cost for 12 lunches using the rate:

For x = 12:

y = 100 + (8.50 * (12 - 10))

y = 100 + (8.50 * 2)

y = 100 + 17

y = 117

The total cost for 12 lunches from Dan's Diner is $117.

Comparing the costs:

Carla's Catering: $106

Dan's Diner: $117

Carla's Catering provides the lowest total cost for 12 lunches, and the difference is $11.00.

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Answer:

the y-intercept for the first one is 4. remember y=mx+b!! b is the y-intercept. The second question the y-intercept is 4

Answer for 18 is 1. for the last question, the answer is -1/3. I attached an image to show the work for the last 3 problems but for the first one you don’t rlly need to show work.

Answer:

11331 non fiction books

Step-by-step explanation:

Given :

Total books = 67982

Childrens section = 1/3 of total

Number of children's books :

(1/3 * 67982) = 22660 books (approximately)

Books left :

67982 - 22660 = 45,322 books

Fiction books:

75% of remaining

0.75 * 45322

33991.5

= 33991 books

If the only section left is non - fiction, then

Non - fiction books = (45322 - 33991) = 11331

The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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After solving the quadratic equation, the roots are (x - 2) and (x + 7).

To determine values for various parameters, quadratic functions are employed in a variety of engineering and scientific disciplines. A parabola is used to graphically illustrate them.

The direction of the curve is determined by the highest degree coefficient. Quadratic is a derivative of the term quad, which signifies square.

As per the given equation in the question,

x² + 5x - 14 = 0

b² - 4ac

5² - 4(1)(-14)

25 + 56 = 81

Use the equation,

-b ± \(\sqrt{b^2-4ac}/2a\)

Substitute the values,

(-5 + 9)/2 = 2 and,

(-5 - 9)/2 = -7

Therefore, the root will be (x - 2) and (x + 7).

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Answer:

OB. 12

Step-by-step explanation:

Since the die is a fair six-sided die and the question uses should... we know that a roll of "4" has a 1/6 chance to land every time the die is rolled.

1. 72 rolls * 1/6 chance to roll a 4 = 12 times

Answer:

b*b^5

Step-by-step explanation:

Answer:

-48

Step-by-step explanation:

Take two points such as (3.-27) and (5.-41).

Find the slope from the points using the formula

\(\frac{y_2-y_1}{x_2-x_1}\) . The setup should look like \(\frac{-41-(-27)}{5-3}\) = -7.

Therefore, our slope is -7.

Now we can use point slope form to find an equation.

\(y-y_1=m(x-x_1)\).

Substituting the point (3,-27) in, we get \(y-(-27)=-7(x-3)\).

This equation simplifies to \(y=-7x-6\).

Now that we have an equation for our table, we can insert 6 into our equation.

\(y=-7(6)-6=-48\)

∴ When  \(x=6, y =-48\)

Answer:

9

Step-by-step explanation:

I would guess it looks like this - if not then tell me

\( \frac{18}{ \frac{2 \times 3}{5 - 2} } \)

2×3=6

5-2=3

Then there's only

\( \frac{18}{ \frac{6}{3} } \)

Which is equal to

\( \frac{18}{1} \times \frac{3}{6} = \frac{54}{6} = \frac{9}{1} = 9\)

Answer:

Step-by-step explanation:

There are two scenarios, (5 - 2) in denominator and 5 in denominator as it is not clear. Solving both:

------------------------

Answer:

h ≈ 11 ft

Step-by-step explanation:

there are 2 similar triangles created , small one on the left and the larger outside one.

corresponding sides are in proportion, that is

\(\frac{h}{4+5}\) = \(\frac{John}{5}\)

\(\frac{h}{9}\) = \(\frac{6}{5}\) ( cross- multiply )

5h = 54 ( divide both sides by 5 )

h = 10.8 ≈ 11 ft ( to the nearest foot )

Answer:

11 ft ^﹏^

Step-by-step explanation:

Answer:

4. 9.1 – 10 = 0.2x

X= -4.5

Step-by-step explanation:

Let's solve for x in the equations given below

1. 9.1 = -0.2x + 10

9.1 - 10 = -0.2x

-0.9= -0.2x

-0.9/-0.2= x

4.5 = x

2. 10 = 9.1 + 0.2x

10-9.1 = 0.2x

0.9= 0.2x

0.9/0.2 = x

4.5 = x

3. 10 – 0.2x = 9.1

10-9.1= 0.2x

0.9= 0.2x

0.9/0.2= x

4.5 = x

4. 9.1 – 10 = 0.2x

-0.9 = 0.2x

-0.9/0.2= x

-4.5 = x

The different equation is equation 4

Reason because it's answer gave a negative value of x while others gave a positive value of x.

But in magnitude they all have same value of x

Answer:Its D

Step-by-step explanation:

I just did it on ed

Result is x = - 2 and y = 1.6 so the ordered pair ( -2, 1.6) is the solution of the system equations.

It is a mathematical expression that shows the equalities between two or more terms. There are different types of equation such as linear equation, quadratic equation, exponential equation and so on.

Given, the two systems of equation.

y = - 0.5x + 0.6

and y = x + 3³₅

rewrite the second equation and get y = x +18/5

                                                       5y = 5x + 18 ....  equation 2

                   the first equation is multiplied by 5 and we get.

                                               5y = - 2.5 x + 3

                                               5y = 5x +18

                                            -          -     -

                        we will now solve the above equations by addition method.

                                       0 = - 7.5 x - 15

                                    7.5 x = - 15

                                     x = -2

        putting the value of x in any equation, we get the value of y = 1.6

    x = - 2 and y =1.6

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Answer:

Dollars per passenger would be $252.
The maximum revenue is $63,404.

Step-by-step explanation:

Let's define the number of passengers above 212 as x.

The revenue function is given by R(x) = (212 + x)(292 - x).

We can expand and simplify the revenue function:

\(R(x) = 212 * 292 + 212 * (-x) + x * 292 + x * (-x)\)

= \(61804 - 212x + 292x - x^2\)

= \(-x^2 + 80x + 61804\)

The revenue function is a quadratic function in the form\(R(x) = -x^2 + 80x + 61804\), representing a downward-opening parabola.

To find the x-coordinate of the vertex (which gives the number of passengers for maximum revenue), use the formula \(x = -b/2a\), where \(a = -1\) and \(b = 80\).

\(x=\frac{-80}{2*(-1)}\)

\(= \frac{80}{2}\)

\(= 40\)

Therefore, the number of passengers above 212 for maximum revenue is 40.

Substitute x = 40 into the revenue function to find the maximum revenue:

\(R(x) = -(40)^2 + 80(40) + 61804\)

\(= -1600 + 3200 + 61804\)

\(= 61804 + 1600\)

\(= 63404\)

Hence, the maximum revenue is $63,404.

To determine the fare per passenger, subtract x from the base fare of $292:

Fare per passenger = Base fare - x

\(= 292 - 40\)

\(= 252\) Dollars per passenger.

The expression without absolute value bars is 3.84.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

|√10 - 7 |

= | 3.16 - 7 |

= | -3.84 |

= 3.84

Thus,

The value of the expression is 3.84.

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Answer:

3,0,-6,0

Step-by-step explanation:

x1=3 because 3+0+0=3

since x2 and s2=0.

Answer:

• A change from 54 to 81 represents a positive change (increase) of 50%

Answer:

  B. The graph of K has a greater y-intercept

  D. The graph of J has a greater slope.

Step-by-step explanation:

Given a table for function J and an equation for function K, you want to know which has the greater slope, and which has the greater y-intercept.

The y-intercept is the value of the function when x=0. We see from the table that y=2 corresponds to x=0 for function J.

We see from the equation for function K that the constant is 8. This is the value of y when x=0.

Function K has the greater y-intercept (8 vs. 2).

The slope is the change in y-value when x increases by 1 unit. We see from the table that y=7 when x=1, so the change in y from x=0 to x=1 is 7-2 = 5. The slope of function J is 5.

The equation for function K has an x-coefficient of 3. This means a change in x of 1 unit will result in a change in y of 3 units. The slope of function K is 3.

Function J has the greater slope (5 vs. 3).

Additional comment

Both functions are graphed in the attachment. The y-intercepts have their points labeled. The graph with the steeper slope is the blue line, function J.

The correct statement regarding the transformation is given as follows:

Dilation bu a scale factor of 0.5 about the origin. Then reflect over the x-axis.

The true statements about the dilation are given as follows:

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

For this problem, the coordinates of the dilated line segment are half the coordinates of the original line segment, hence the scale factor is given as follows:

k = 0.5.

The y-coordinate then has the signal exchange, hence the figure is also reflected over the x-axis.

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a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Answer:

All of them except a trapezoid

Step-by-step explanation:

The playground has two pairs of sides that are congruent to each other (70 = 70, 50 = 50), but a trapezoid only has ONE pair of sides that are congruent to each other; the other two are not the same. Therefore, this playground can be any shape besides a trapezoid.

Answer:

does this have to do with graphs

Answer:

6781632 ft ^ 3

Step-by-step explanation:

The first thing is to know the formula for the volume of a pyramid:

V = 1/3 * Ab * h

That is, it is one third of the product between the area of the base and the height.

The base area would be:

Ab = l ^ 2

the side equals 156 ft, replacing:

Ab = 156 ^ 2

Ab = 24336 ft ^ 2

now, replacing in the volume formula:

V = 1/3 * 24336 * 836

V = 6781632

Which means that the volume of the pyramid is 6781632 ft ^ 3