Two trains start from towns 540 mi apart and travel towards each other on parallel track. They pass each other 4.5 hr later. If one train travels 20 mph faster than the other, find the rate of each train

The volume of the sand pit is V = 694.6 feet²

The volume of the rectangle is given by the product of the length of the rectangle and the width of the rectangle and the height of the rectangle

Volume of Rectangle = Length x Width x Height

Volume of Rectangle = Area of Rectangle x Height

Given data ,

Let the volume of the rectangle be represented as V

Now , the length of the sand pit = 30.2 feet

The width of the sand pit = 9.2 feet

The depth of the sand pit = 30 inches = 2.5 feet

Now , the volume of the rectangular pit = L x W x H

On simplifying the equation , we get

The volume of the rectangular pit V = 30.2 x 9.2 x 2.5

The volume of the rectangular pit V = 694.6 feet²

Hence , the volume of the rectangular sand pit is 694.6 feet²

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Answer:

y- intercept = 7

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute (4, - 1 ) into the partial equation

- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )

7 = c

that is the y- intercept = 7

volume of a cube = x³

where x the length of the side of the cube

so, the volume = (4.2)³

= 74.088 in³

The coordinates of the point R: (0, 3.4)

What is the slope?

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line

Slope PQ 5–0/ 2–6 = 5 /-4

equation of PQ y =-5/4 x +c ;

this passing through 2,5

5 =-5/4*2 +c ; C = 5 -5/2 =5/2

y =-5x/4+5/2 =-5x+10/4 ; 4y =-5x +10 ;

equation of PQ =5x +4y-10 =0 ;

slope of PR : m1 *m2 =-1 ;m2 = -1/ [-5/4 ] = 4/5

equation of PR y = mx +c this passes through [2,5]

5 = 4/5*2 +C so C = 5- 8/5 =17/5

y =4 x /5 +17/5 so coordinates of R = [0, 3.4]

Hence, the coordinates of the point R: (0, 3.4)

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Answer:

Note that the line passes through the points (1,0) and (2,6).

The measures of the angles are given as A' = 103, B' =100, c' = 80, D' = 77

∠x

125 + ∠x = 180 (angle on a straight line)

∠x = 55 degrees

∠y

∠x + ∠y + 48 = 180 angles in a triangle

55 + ∠y + 48 = 180

∠y = 77 degrees

∠D

∠d = ∠Y vertically opposite

∠a + ∠D = 180

∠A = 180 - 77

= 103 degrees

∠B  + 80 = 180

∠b = 100 degrees

∠c + ∠ b = 180

∠c = 180 - 100

= 80 degrees

hence A' = 103, B' =100, c' = 80, D' = 77

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Answer:

Step-by-step explanation:

half the base times the height

The solution to the matrix is x1 = (-555 - 356x3)/90, x2 = (138 + 89x3)/10 and x3 = free variable

To find the solution to this matrix, we need to perform row operations to put it into row echelon form or reduced row echelon form. We can do this by adding multiples of one row to another row, multiplying a row by a nonzero scalar, and swapping two rows.

Here are the row operations we can use to put this matrix into row echelon form:

1. Add 5 times the first row to the third row to eliminate the 5 in the (3,1) entry:

0 0 -9 6

0 -1 -4 4

25 35 11 38

2. Multiply the second row by -1 to make the pivot in the second row, second column equal to 1:

0 0 -9 6

0 1 4 -4

25 35 11 38

3. Add 9 times the second row to the first row to eliminate the -9 in the (1,3) entry:

0 9 0 -30

0 1 4 -4

25 35 11 38

4. Add -25 times the second row to the third row to eliminate the 25 in the (3,1) entry:

0 9 0 -30

0 1 4 -4

0 10 -89 138

5. This matrix is now in row echelon form. We can solve for the variables by back-substitution. Starting with the last row:

0 10 -89 138 | x3

We have:

10x2 - 89x3 = 138

Solving for x2, we get:

x2 = (138 + 89x3)/10

Substituting this expression for x2 in the second row, we have:

Copy code

0 1 4 -4 | (138 + 89x3)/10

Solving for x1, we get:

9x1 + 4(138 + 89x3)/10 = -30

Simplifying and solving for x1, we get:

x1 = (-555 - 356x3)/90

So the solution to the matrix is:

x1 = (-555 - 356x3)/90

x2 = (138 + 89x3)/10

x3 = free variable

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Answer: -1/2

Step-by-step explanation: The formula is y=mx+b where m is your slope and b is your y-intercept. Therefore, your b or y-intercept is -1/2

Answer:

[tex]-\frac{1}{2}[/tex]

Step-by-step explanation:

In the equation [tex]y=mx+b[/tex], m is the slope and b is the y intercept. In this equation, we are given the slope is 4 and the y intercept as [tex]-\frac{1}{2}[/tex] because the equation can be simplified to [tex]y=4x+-\frac{1}{2}[/tex]

Answer:

Step-by-step explanation:

a. The average rate of change in the cost of the hamburger during the period from 2012 to 2022 can be calculated as the difference in the cost of the hamburger divided by the number of years between the two prices.

So, the average rate of change in the cost of the hamburger is:

(6.12 - 4.32) / (2022 - 2012) = 0.18

Therefore, the average rate of change in the cost of the hamburger during this period is $0.18 per year.

b. We can use the point-slope form of a linear equation to model the cost of the hamburger as it changes over time. Let y be the cost of the hamburger in dollars, and t be the number of years since 2012. We know that the cost of the hamburger in 2012 was $4.32, so we have a starting point of (0, 4.32).

Using the average rate of change calculated in part a, we can find the slope of the line:

slope = (6.12 - 4.32) / (2022 - 2012) = 0.18

Now we can write the equation of the line as:

y - 4.32 = 0.18t

y = 0.18t + 4.32

So, the linear equation that models the cost of the hamburger in terms of years since 2012 is y = 0.18t + 4.32.

c. To find when the cost of the hamburger will reach $7.02, we can substitute y = 7.02 into the equation we found in part b and solve for t:

7.02 = 0.18t + 4.32

2.7 = 0.18t

t = 15

So, the cost of the hamburger will reach $7.02 in the year 2012 + 15 = 2027.

Answer:

Step-by-step explanation:

The digit 3 in the number 4693 has a place value of 3 tens or 30. Therefore, the value of the number 3 in the number 4693 is 30.

Answer:

First choice

Step-by-step explanation:

Answer:

Th answer is the FIRST CHOICE(A).

Have a GOOD DAY!

The dimensions of the rectangle after dilation by a sclae factor of 3 is,

Length = 15 inches

Breadth = 27 inches.

A dilation is a transformation that produces an image of a different size but with a similar overall shape to the original.

A dilation that enlarges an image is called an enlargement, and a dilation that shrinks an image is called a reduction.

The scale factor, which is employed to enlarge a mathematical entity, will determine the size of the image (compared to the original object). When the absolute value of the scaling factor is greater than 1, an expansion occurs.

The given rectangle dimension is :

width= 5 inches and

length= 9 inches.

When the sides of a rectangle are multiplied by a scale factor of 3, the rectangle is said to be dilated by that factor.

So, the width of rectangle is after dilation is 5×3 = 15  inches

So, the length of rectangle is after dilation is 9×3 = 27 inches

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Answer:

≅20.9%

Step-by-step explanation:

To find the percent decrease, we need to calculate the difference between the old value (349) and the new value (276), divide that by the old value, and then multiply by 100 to express it as a percentage.

The formula for percent decrease is:

percent decrease = ((old value - new value) / old value) x 100%

Substituting the given values, we get:

percent decrease = ((349 - 276) / 349) x 100%

percent decrease = (73 / 349) x 100%

percent decrease = 20.92%

Rounding to the nearest tenth of a percent, we get:

percent decrease ≈ 20.9%

Therefore, the percent decrease in the number of petty crimes this year is [approximately 20.9%.]

that in the second year, we use the beginning book value of $639,900

a. Sum-of-the-years’-digits method:

To compute the depreciation using the sum-of-the-years’-digits method, we first need to determine the total number of years of the asset's useful life. We do this by subtracting the salvage value from the cost and dividing by the estimated yearly depreciation.

Cost of asset = $711,000

Salvage value = $60,000

Useful life = 20 years

Yearly depreciation = (Cost - Salvage value) / Useful life

Yearly depreciation = ($711,000 - $60,000) / 20 = $32,550

To calculate the sum-of-the-years’-digits (SYD) for this asset, we add up the digits of the useful life in descending order. For a 20-year useful life, the SYD would be:

SYD = 20 + 19 + 18 + ... + 1 = 210

Using the SYD and the number of remaining years, we can calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = (20/210) x ($711,000 - $60,000) = $64,286

Year 2021:

Depreciation expense = (19/210) x ($711,000 - $60,000) = $60,952

b. Double-declining-balance method:

To compute the depreciation using the double-declining-balance (DDB) method, we first need to determine the asset's straight-line depreciation rate, which is calculated as follows:

Straight-line depreciation rate = 1 / Useful life

Straight-line depreciation rate = 1 / 20 = 0.05

The DDB depreciation rate is twice the straight-line rate, or 0.10. We can then calculate the depreciation expense for each year as follows:

Year 2020:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset

Depreciation expense = $711,000 x 0.10 = $71,100

Year 2021:

Depreciation expense = Beginning book value x DDB rate

Beginning book value = Cost of asset - Accumulated depreciation from previous years

Accumulated depreciation (2020) = $71,100

Beginning book value (2021) = $711,000 - $71,100 = $639,900

Depreciation expense = $639,900 x 0.10 = $63,990

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After Justin leaves his house he reaches a maximum distance of 20 blocks away from his house after 7 minutes of being out of his home.

To graph Justin's displacement we must use a Catersian plane. In this case we put the time on the X axis (time) and the distance on the Y axis (blocks). Once we set these parameters, we must put the information on the graph.

In the places where a time takes only the progressing of time without any displacement. Additionally, when you travel it is important to take into account the speed (blocks/minute) that Justin has to obtain a correct graph.

According to the above, after 7 minutes Justin is 20 blocks away from his house and this distance travels in 4 minutes to return home.

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The ratio of people waiting in line for the slingshot is 2:21

A ratio is a relationship between two quantities that expresses how many times one quantity is contained in the other. It can be expressed in different ways, such as with the use of a colon (:), a fraction (/), or the word "to.

From the question, the total number of people is 15 + 4 + 12 + 11 = 42

The number of people waiting for slingshot is = 4

The ratio of slingshot waiting in line = 4/42

The ratio = 2:21

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For the given percenatge of total cost, the total value of Gabe's health care coverage for the year is $9,984.

What is percentage?

Percentage is a way of expressing a fraction or a part of a whole as a portion out of 100. It is represented by the symbol "%".

We can start by using the information given to determine the total cost of the health care coverage. Let's call this cost "C". Since Gabe contributes 15% of this cost and pays $28.80 per week, we can write:

0.15C = 28.80

To solve for C, we can divide both sides by 0.15:

C = 28.80 / 0.15

= 192

So the total cost of the health care coverage is $192 per week. To find the total value of Gabe's health care coverage for the year, we need to multiply this weekly cost by the number of weeks in a year.

Assuming there are 52 weeks in a year, we have:

Total value of Gabe's health care coverage = 192 x 52

= 9984

Therefore, the total value of Gabe's health care coverage for the year is $9,984.

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Answer:

7/5, 3/2, 11/4, 15/4, 13/3.

Step-by-step explanation:

Convert all to decimal then arrange from lowest to highest

Maura will have 5, 206 points at either hotel by booking 301 nights.

To find the number of points, we shall assume that nights are denoted as n. The number of points for Hotel Elegance will be shown as :

= Signing up points + ( Number of points per night x Number of nights)

= 89 + 17 n

The number of points for Hotel Paradiso is:

= 691 + 15 n

The number of nights that Maura needs to stay for the points to be the same is :
89 + 17 n = 691 + 15 n

17 n - 15 n = 691 - 89

2 n = 602

n = 602 / 2

n = 301 nights

The number of points would be :

= 691 + 15 n

= 691 + 15 x 301

= 5, 206 points

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There are no numbers between 1.8×100 and 195%.

The representation of quantities or values using numbers is a fundamental idea in mathematics. They can be applied to measure, compare, compute, and count. Depending on the situation and the chosen notational system, numbers can be represented in a variety of ways, such as digits, words, or symbols.

Based on their attributes and traits, several sorts of numbers can be distinguished in mathematics. The following list includes some of the most typical numbers:

To identify the numbers between 1.8×100 and 195%, we need to convert both numbers to the same unit of measurement.

1.8×100 = 180

195% = 1.95 (since 195% is equal to 1.95 times the original quantity)

Now, we need to identify all numbers between 180 and 1.95. To do this, we can simply list all the numbers that are greater than 180 and less than 1.95, excluding 180 and 1.95 themselves. However, we notice that there are no such numbers, because:

Any number greater than 180 is also greater than 1.95 since 1.95 is less than 2 and 180 is greater than 2.

Any number less than 1.95 is also less than 180 since 180 is greater than 100 (which is 1% of 10,000) and 1.95 is less than 2.

Therefore, there are no numbers between 1.8×100 and 195%.

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Answer:

1 7/8

Step-by-step explanation:

i took the test

The composite function has its value to be 54168

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

f(x)=10x^2-8x

g(x)=7x-3.

Given the composite function [f o g] (11)., we have

[f o g] (11) = f(g(11))

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

g(11) =7 * 11 - 3

Evaluate

g(11) =74

So, we have

[f o g] (11) = f(74)

[f o g] (11) = 10(74)^2 - 8(74)

[f o g] (11) = 54168

Hence, the solution is 54168

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esta es la respuesta 8 B)

porque si lo restas y sumas da a 8

Answer:

Step-by-step explanation:

In a circle with a radius of 0.1, an arc length of 0.4 is intercepted by an angle. To find the angle in radians, we use the formula:

angle in radians = arc length / radius

Substituting the given values, we have:

angle in radians = 0.4 / 0.1 = 4

So the angle in radians is 4 radians, to the nearest tenth.

The equation of rational function is f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

One possible equation for a rational function with the given properties is:

f(x) = 3 + (k(x + 5)(x - 5)) / ((x + 2)(x + 6))

Here, k is a constant that determines the vertical scale of the function. We choose the factor (x + 5)(x - 5) in the numerator to make the x-intercepts at x = 5 and x = -5. We choose the factors (x + 2) and (x + 6) in the denominator to make the vertical asymptotes at x = -2 and x = -6. We choose the constant term 3 in the equation to make the horizontal asymptote at y = 3.

To determine the value of k, we can use one of the x-intercepts, say x = 5. Substituting x = 5 into the equation and setting the result to 0 (since the function has an x-intercept at x = 5) gives:

0 = 3 + (k(5 + 5)(5 - 5)) / ((5 + 2)(5 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 0 / (7 * 11)

0 = 3

This equation is not true, which means that we have made a mistake somewhere. The mistake is in assuming that the x-intercepts occur at x = 5 and x = -5. Instead, we should have x-intercepts at x = 5 and x = -1, which are the roots of the numerator (x - 5)(x + 1). So we need to adjust the numerator in the equation to (x - 5)(x + 1) in order to get the correct x-intercepts.

The correct equation for the rational function is:

f(x) = 3 + (k(x - 5)(x + 1)) / ((x + 2)(x + 6))

To determine the value of k, we can use the other x-intercept, x = -1. Substituting x = -1 into the equation and setting the result to 0 gives:

0 = 3 + (k(-1 - 5)(-1 + 1)) / ((-1 + 2)(-1 + 6))

Simplifying the right-hand side, we get:

0 = 3 + 6k / 5

Multiplying both sides by 5, we get:

0 = 15 + 6k

Solving for k, we get:

k = -15 / 6 = -5/2

So the final equation for the rational function is:

f(x) = 3 - (5/2)(x - 5)(x + 1) / ((x + 2)(x + 6))

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Answer:

Step-by-step explanation:

sh45haaa           aaaa

Answer:

A

Step-by-step explanation:

hope this helps

The probabilities are given as follows:

1) Blue eyes: 0.132.

2) Female with green eyes: 0.09.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.

The total number of people is given as follows:

20 + 25 + 30 + 15 + 10 + 12 + 15 + 20 + 10 + 10 = 167.

10 + 12 = 22 people out of 167 have blue eyes, hence the probability is given as follows:

p = 22/167 = 0.132.

15 people out of 167 are female with green eyes, hence the probability is given as follows:

p = 15/167 = 0.09.

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Equation of the line passing through (1, 5) is y = 3x + 2

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

A line with no curve is called straight line.

Given,

A line is parallel to the line y = 3x - 2

To find slope of the given line, comparing with slope-intercept equation of line

y = mx + c

Slope m = 3

Line passes through point (1 , 5)

Slope of parallel lines are equal

m' = m = 3

Equation of the line

y - y' = m'(x - x')

y - 5 = 3(x - 1)

y - 5 = 3x - 3

y = 3x + 2

Hence, y = 3x + 2 is equation of the line passing through point (1,5).

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y=3x+2 is the equation of the line which is parallel to the line y=3x-2 and passes through the point 1,5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given equation is y=3x-2

3 is the slope of given line.

The line parallel to this line will have same slope, slope is 3.

Now, the equation of line passing through 1, 5

5=3(1)+b

b=2

So slope intercept form y=3x+2

Hence,  y=3x+2 is the equation of the line which is parallel to the line y=3x-2 and passes through the point 1,5

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Answer:

- 4

Step-by-step explanation:

(f + g)(3) = f(3) + g(3)

f(3) = - 5

g(3) = 1

f(3) + g(3) = - 5 + 1 = -4

Answer:

[tex]5x^{7} -x+2[/tex]

Step-by-step explanation:

[tex]6x^{7} -x+8[/tex] minus [tex]x^{7} +2[/tex] equals to [tex]5x^{7} -x+2[/tex].

We can solve this by subtracting [tex]x^{7}[/tex] from [tex]6x^7[/tex]. This will make it [tex]5x^7[/tex].

x cannot be subtracted, so it becomes [tex]5x^7 -x[/tex].
8-6 is 2, so it becomes [tex]5x^7-x+2[/tex]