Two cars raced at a race track. the faster car traveled 20 mph faster than the slower car. in the time that the slower car traveled 165 miles, the faster car traveled 225 miles. if the speeds of the cars remained constant, how fast did the slower car travel during the race? distance (mi) rate (mph) time (h) slower car 165 r startfraction 165 over r endfraction faster car 225 r 20 startfraction 225 over r 20 endfraction 55 mph 60 mph 75 mph 130 mph

Answer:

153 in²

Step-by-step explanation:

[tex]\sf \boxed{\text{\bf Area of rectangle = length * width}}[/tex]

[tex]\sf \boxed{\text{\bf Area of square = side *side}}[/tex]

Figure I:

   length = 12 in

   width = 6 in

Area of figure I = 12 * 6

                         = 72 in²

Figure II:

      length = 13 in

      width = 5 in

Area of figure II = 13 * 5

                          = 65 in²

Figure III:

       side = 4 in

Area of figure III = 4 * 4

                           = 16 in²

Area of irregular shape = 72 + 65 + 16

                                      = 153 in²

The answer is 114.5%.

Let the original population be denoted by x.

Now, let's go through the percentage increase per year.

Year 1

Year 2

Year 3

Year 4

Overall increase : 214.5% - 100% = 114.5%

Hence, the overall percentage increase in these 4 years is 114.5%.

The total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

Any data that may be shown as dots or tiny circles is called a dot plot. Given that the height of the bar created by the dots indicates the numerical value of each variable, it is comparable to a bar graph or a simple histogram. Small amounts of data are shown using dot plots.

In the question, we are informed that Mrs. Kelley asked her students to plot the number of books they read over the summer. a dot plot titled books read over the summer goes from 0 to 7. 0 has 1 dot, 1 has 3 dots, 2 has 6 dots, 3 has 2 dots, 4 has 3 dots, 5 has 1 dot, 6 has 2 dots, and 7 has 0 dots.

We are asked to find the total number of students that plotted the number of books they read using the dot plot.

The dot plot is attached to the solution.

The total number of students = The total number of dots = 1 + 3 + 6 + 2 + 3 + 1 + 2 + 0 = 18.

Thus, the total number of students that plotted the number of books they read was 18, making the 4th option, a correct choice, using the dot plot.

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The numbers are arrange in order of consecutive numbering, terminal-digit numbering, and middle-digit numbering to give a value.

Methods of arranging numbers:

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Answer:

a) 175 m

b) 20 cm

Explanation:

scaled size → actual size

1 cm represents 25 m

a)

In the scaled size on the map, the distance from church to village is 7 cm.

Then actual size,

1 cm → 25 m

7 cm → (25 × 7) m

7 cm → 175 m

b)

half a kilometer = 0.5 km = 500 m

Then scaled size,

25 meter → 1 cm

500 meter → 500/25 cm = 20 cm

Answer:

Graph X

Step-by-step explanation:

First, convert the equation into slope-intercept form. The first step is the bring the x to the right side by subtracting 8x from both sides: -y=-8x-4. Now multiply both sides by -1: y=8x+4. Now, if you know about the slope-intercept form, you'll know that 4 is the y-intercept and that [tex]\frac{8}{1}[/tex] is the slope. 8 is the rise and 1 is the run, so the answer is graph X.

The value of the given expression is 9/10. The properties of real numbers, such as commutative and distributive are used for solving this expression.

The properties are:

The given expression is

(-3/7) × 6/5 + (3/2) - (6/5) × 1/14

applying commutative law (a + b = b + c)

⇒ (-3/7) × 6/5 - (6/5) × 1/14 + (3/2)

again applying commutative law (a × b = b × a)

⇒ (-3/7) × 6/5 - 1/14 × (6/5)+ (3/2)

applying distributive law (a × (b + c) = a × b + b × c) in reverse order

⇒ (-3/7 - 1/14) × (6/5)+ (3/2)

⇒ (-7/14) × (6/5)+ (3/2)

⇒ (-1/2) × (6/5)+ (3/2)

⇒ (-6/10) + (3/2)

⇒ (-6 + 15)/10

⇒ 9/10

Thus, the required value is 9/10 and the suitable properties are commutative and distributive.

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Answer:

12.5%

Step-by-step explanation:

27-24=3

3/24=1/8

1/8=0.125

0.125 in percent is 12.5%

Step-by-step explanation:

Plug in known values

[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]

Divide both sides by 5.825

[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]
Cube both sides

[tex]12.1738 = \frac{3590}{P}[/tex]

Multiply both sides by P

[tex]12.1738P = 3590[/tex]

Divide both sides by 12.1738

[tex]P = 294.895[/tex]

Round to nearest hp

[tex]P = 295[/tex]

So if you look at the radical, it's possible for it to be mistake for a square root, and not a cube root. This was Daniels mistake, so his steps were

[tex]13.4 = 5.825\sqrt[3]{\frac{3590}{p}}\\[/tex]

Divide both sides by 5.825

[tex]2.3004 = \sqrt[3]{\frac{3590}{P}}\\[/tex]

Square both sides

[tex]5.29197 = \frac{3590}{P}[/tex]

Multiply both sides by P

[tex]5.29197P = 3590[/tex]

Divide both sides by 5.29197

[tex]p\approx 678.385[/tex]

He also probably rounded during his steps, which would explain how he got 679 instead of 678 when rounding in the final, but either way his answer is completely off, and this is due to him mistakenly thinking the cube root was a square root.

Answer:

length = 235 yd

width = 58 yd

Step-by-step explanation:

Let the width be W.

L = 4W + 3

perimeter = 2(L + W)

perimeter = 2(4W + 3 + W)

perimeter = 2(5W + 3) = 10W + 6

We are told the perimeter = 586 yd

10W + 6 = 586

10W = 580

W = 58

L = 4W + 3 = 4(58) + 3 = 232 + 3 = 235

length = 235 yd

width = 58 yd

Answer:

y=[4]x + [12]

Step-by-step explanation:

Remember that parallel lines have identical slopes; and to make a line which passes through a point we will use point-slope form.

Familiarize yourself with point-slope form:

[tex]y-y1=m(x-x1)[/tex]

If the line is parallel to [tex]y=4x+11[/tex] the slope must be 4.

[tex]y-y1=4(x-x1)[/tex]

And we know the point it must pass through is (-2,4), so we can fill those values in too.

[tex]y-4=4(x+2)[/tex]

Now all we have to do is solve for y:
[tex]y-4=4(x+2)\\y-4=4x+8\\y=4x+12[/tex]

Answer:

[tex]y = 4x + 12[/tex]

Step-by-step explanation:

The solution is in the attached image

The solution of the given equation is :

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

Since cos2θ + sin2θ = 1, sin2θ = 1 - cos2θ

So, the given equation is equivalent to 2(1 - cos2θ) - cosθ = 1

-2cos2θ - cosθ + 1 = 0

2cos2θ + cosθ - 1 = 0 (multiplying the entire equation by -1)

(2cosθ - 1)(cosθ + 1) = 0 (taking common)

cosθ = 1/2 or cosθ = -1 (on equating it to zero)

cosθ = 1/2 when θ = π/3 + 2kπ or 5π/3 + 2kπ

cosθ = -1 when θ = π + 2kπ

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Answer: 147.2 miles

Step-by-step explanation:

We can answer this by knowing the formula [tex]speed=\frac{distance}{time}[/tex]. Here, the speed is 46 miles/hour and the time is 3.2 hours. Let's put these values into the formula and solve for distance.

[tex]46=\frac{distance}{3.2}\\46*3.2=\frac{distance}{3.2}*3.2\\d=147.2[/tex]

Alex traveled 147.2 miles.

By the integral test, the series is convergent.

The sequence [tex]k^3/e^{k^4}[/tex] is clearly positive and decreasing for [tex]k\in\Bbb N[/tex]; then by the integral test,

[tex]\displaystyle \int_1^\infty \frac{x^3}{e^{x^4}} \, dx \le \sum_{k=1}^\infty \frac{k^3}{e^{k^4}}[/tex]

and

[tex]\displaystyle \int_1^\infty \frac{x^3}{e^{x^4}} \, dx = \frac14 \int_1^\infty e^{-u}\, du = \frac1{4e} < \infty[/tex]

By using the integral test, series converges

What is an integral test for convergence and divergence?

⇒ It is used to prove the divergence or convergence of series. This test is called the integral test, which compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

How to know if a series is converging or diverging?

If the limit exists and is a finite number (a number less than infinity), we say the integral converges. If the limit is ±∞ or does not exist, we say the integral diverges.

let aₓ= f (x) is any function

⇒ In order for the integral test to work The function must be positive it has to be continuous and it has to be decreasing when x≥1

If the integral converges it means the series is also converging

If the integral diverges it means the series is also diverging

The sequence [tex]k^{3} /{e^{k^{4} }[/tex] is clearly positive and decreases for k∈N then by the integral test,

[tex]\int\limits^\infty_1 {x^{3} /e^{x^4} dx[/tex] [tex]\leq\displaystyle \sum^{\infty}_{k = 1} {x^{3} /e^{x^{4}[/tex]

and

[tex]\int\limits^\infty_1 {x^{3} /e^{x^4} dx[/tex][tex]=1/4\int\limits^\infty_1 {x^{3} /e^{-u} du[/tex]

⇒ [tex]1/4 < \infty[/tex]

So it comes with a finite value hence the series converges

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The solution to the equation is x = 1.62

The equation is given as:

[tex]x =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we split the equations as follows:

y = x

[tex]y =\sqrt{x\ -\ \frac{1}{x}}+\sqrt{1-\ \frac{1}{x}}[/tex]

Next, we graph the equations (see attachment)

From the attached graph, the equations intersect at

(x, y)= (1.62, 1.62)

Remove the y value

x = 1.62

Hence, the solution to the equation is x = 1.62

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Rationalize the right side first. Expand and simplify.

[tex]x = \sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x} + \sqrt{1 - \dfrac1x}\right) \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(\sqrt{x - \dfrac1x}\right)^2 - \left(\sqrt{1 - \dfrac1x}\right)^2[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = \left(x - \dfrac1x\right) - \left(1 - \dfrac1x\right)[/tex]

[tex]x \left(\sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}\right) = x - 1[/tex]

Rearrange terms as

[tex]\dfrac{x - 1}x = \sqrt{x - \dfrac1x} - \sqrt{1 - \dfrac1x}[/tex]

[tex]\dfrac{x - 1}x + \sqrt{\dfrac{x - 1}x} = \sqrt{x - \dfrac1x}[/tex]

Substitute

[tex]y = \sqrt{\dfrac{x-1}x} = \sqrt{1 - \dfrac1x} \\\\ \implies y^2 = 1 - \dfrac1x \implies x = \dfrac1{1-y^2}[/tex]

(noting that [tex]y>0[/tex]) so that

[tex]x - \dfrac1x = \dfrac1{1-y^2} - (1-y^2) = \dfrac{2y^2 - y^4}{1-y^2}[/tex]

and the equation transforms to

[tex]y^2 + y = \sqrt{\dfrac{2y^2 - y^4}{1-y^2}}[/tex]

[tex]y + 1 = \sqrt{\dfrac{2 - y^2}{1-y^2}}[/tex]

Solve for [tex]y[/tex].

[tex](y+1)^2 = \left(\sqrt{\dfrac{2-y^2}{1-y^2}}\right)^2[/tex]

[tex]y^2 + 2y + 1 = \dfrac{2 - y^2}{1 - y^2}[/tex]

[tex]-y^4 - 2y^3 + 2y + 1 = 2 - y^2[/tex]

[tex]y^4 + 2y^3 - y^2 - 2y + 1 = 0[/tex]

[tex]\left(y^4 + 2y^3 + y^2\right) - 2y^2 - 2y + 1 = 0[/tex]

[tex](y^2 + y)^2 - 2(y^2 + y) + 1 = 0[/tex]

[tex]\left(y^2 + y - 1\right)^2 = 0[/tex]

[tex]y^2 + y - 1 = 0[/tex]

[tex]y = \dfrac{-1 \pm \sqrt5}2[/tex]

Since [tex]y>0[/tex], we take the positive root. Then

[tex]y = \sqrt{\dfrac{x-1}x} = \dfrac{-1 + \sqrt5}2[/tex]

Solve for [tex]x[/tex].

[tex]\left(\sqrt{\dfrac{x-1}x}\right)^2 = \left(\dfrac{-1 + \sqrt5}2\right)^2[/tex]

[tex]\dfrac{x-1}x = \dfrac{6 - 2\sqrt5}4 = \dfrac{3 - \sqrt5}2[/tex]

[tex]x - 1 = \dfrac{3-\sqrt5}2x[/tex]

[tex]\dfrac{-1+\sqrt5}2 x = 1[/tex]

[tex]x = \dfrac2{-1+\sqrt5}[/tex]

Rationalize to clean up the answer.

[tex]x = \dfrac2{-1+\sqrt5}\cdot\dfrac{-1-\sqrt5}{-1-\sqrt5} = \boxed{\dfrac{1+\sqrt5}2} \approx 1.6108[/tex]

i.e. the golden ratio constant.

the graphed equation is:

y = -|x| + 1

On the graph, we can see an absolute value equation, which opens downwards, and passes through the points (1, 0) and (0,1).

The general absolute value equation is:

y = a*|x - b| + c

Because the vertex is at the point (0, 1), we know that:

b = 0, c = 1

Replacing that we get:

y = a*|x| + 1

Now, this must be zero when we evaluate in x = 1, then:

0 = a*|1| + 1

a = -1

Then the graphed equation is:

y = -|x| + 1

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Answer:

C

Step-by-step explanation:

the sum of the exterior angles of a polygon = 360°

sum the 4 exterior angles and equate to 360

8x + 9x + 5 + 5x + 4 + 9x + 3 = 360 , that is

31x + 12 = 360 ( subtract 12 from both sides )

31x = 148 ( divide both sides by 31 )

x ≈ 11.23 ( to 2 dec. places )

then exterior angle at B is

9x + 3 = 9(11.23) + 3 ≈ 104° → C

The approximate measure of exterior angle B in the polygon is 104° option (C) is correct.

A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.

[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]

It is given that:

A polygon is given in the picture with angle measures.

As we know,

The sum of the exterior angles of a polygon = 360°

8x + 9x + 5 + 5x + 4 + 9x + 3 = 360

31x + 12 = 360

31x = 148

x ≈ 11.23

= 9x + 3 = 9(11.23) + 3

≈ 104°

Thus, the approximate measure of exterior angle B in the polygon is 104° option (C) is correct.

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Answer: Answer is B, Mark me brainliest please

Step-by-step explanation:

1. The value of the linear correlation coefficient r is given as 0.8159. The correct option is a. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables

2. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

This is the data that we get when we try to get the existing relationship that is in existence between the variables that are used in a regression equation.

The value of r was calculated using a statistical tool online. The graph showed us it was not a straight line. The value of the r = 0.8159

The results of the test is in the attachment

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Answer:Answer:

12 (D)

Step-by-step explanation:

The first one is 2:1.2 so i did x10 on it to get 20:12.

Step-by-step explanation:Oh and hey if it's right u have to make me brainliest i need award

Using the volume for rectangular prisms, the volume of the chimney is: 216 in.³.

The volume of a rectangular prism = (length)(width)(height).

The Chimney in Emily's house is a composite solid consisting of two rectangular prism. To find the volume, we have to decompose the figure into two rectangular prisms. Then solve for the volume of each before finding the total volume.

Volume of the bigger rectangular prism = (length)(width)(height) = (4)(4)(12)

Volume of the bigger rectangular prism = 192 in.³

Volume of the smaller rectangular prism = (length)(width)(height) = (4)(2)(3)

Volume of the smaller rectangular prism = 24 in.³

The volume of the chimney = volume of the two rectangular prism

The volume of the chimney = 192 + 24

The volume of the chimney = 216 in.³

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Sophie will pay money equivalent to $ 100 for 15 m at the same store.

The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service.

A country's monetary system is referred to as its currency.

In the case of Gareth,

Money paid for 9 m of climbing = $ 60

Money paid per m of climbing = $ 60/9

Thus, money paid by Sophie for 15 m of climbing = 15 * 60/9

                                                                                    = $ 100

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The number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

The equation is given as:

a+b+c+d+e+f = 2006

In the above equation, we have:

Result = 2006

Variables = 6

This means that

n = 2006

r = 6

The number of solutions is then calculated as:

(n + r - 1)Cr

This gives

(2006 + 6 - 1)C6

Evaluate the sum and difference

2011C6

Apply the combination formula:

2011C6 = 2011!/((2011-6)! * 6!)

Evaluate the difference

2011C6 = 2011!/(2005! * 6!)

Expand the expression

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006 * 2005!/(2005! * 6!)

Cancel out the common factors

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/6!

Expand the denominator

2011C6 = 2011 * 2010 * 2009 * 2008 * 2007 * 2006/720

Evaluate the quotient

2011C6 = 9.12 * 10^16

Hence, the number of solutions of a+b+c+d+e+f = 2006 is 9.12 * 10^16

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Answer:

210 = 6!/1!•1!•1!•1!•1!•1!

Step-by-step explanation:

We can use the stars and bars method to solve this problem. Imagine we have 2006 stars and we want to distribute them among 6 bins (a, b, c, d, e, and f). We can represent the stars as follows:

... * (a stars)

| * * * ... * (b stars)

| | * * * ... * (c stars)

| | | * * * ... * (d stars)

| | | | * * * ... * (e stars)

| | | | | * * * ... * (f stars)

The bars divide the stars into 6 bins, and the number of stars in each bin represents the value of the corresponding variable (a, b, c, d, e, or f).

To ensure that each variable is a positive integer, we can add 1 to each variable and distribute the remaining stars. For example, if we add 1 to a, b, c, d, e, and f, the equation becomes:

(a+1) + (b+1) + (c+1) + (d+1) + (e+1) + (f+1) = 2012

Now we have 6 stars and 5 bars, and we can use the stars and bars formula to find the number of solutions:

Number of solutions = (6+5-1) choose (5-1) = 10 choose 4 = 210

Therefore, the equation a+b+c+d+e+f=2006 has 210 positive integer solutions.

Expressing the answer in the form x!/x!•x!, we have:

210 = 6!/1!•1!•1!•1!•1!•1!

The stars and bars formula is a combinatorial formula that allows us to count the number of ways to distribute identical objects into distinct groups.

Suppose we have n identical objects and k distinct groups. We can represent the objects as stars and the groups as bars. For example, if we have 7 objects and 3 groups, we can represent them as:

| | |

The bars divide the 7 stars into 3 groups, and the number of stars in each group represents the number of objects in that group.

The stars and bars formula tells us that the number of ways to distribute n identical objects into k distinct groups is:

(n+k-1) choose (k-1)

where "choose" is the binomial coefficient. This formula can be derived using a technique called "balls in urns" or by using generating functions.

In the example above, we have n = 7 objects and k = 3 groups, so the number of ways to distribute the objects is:

(7+3-1) choose (3-1) = 9 choose 2 = 36/2 = 18

Therefore, there are 18 ways to distribute 7 identical objects into 3 distinct groups.

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Answer:  1.51

Step-by-step explanation:

        [tex]\frac{w + 7.1}{3} =2.87[/tex]

   [tex]3(\frac{w+7.1}{3})=3(2.87)[/tex]

      w + 7.1 = 8.61

w + 7.1 - 7.1 = 8.61 - 7.1

               w = 1.51

The key features of the above given functions are correctly matched to their corresponding definition.

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More than 50% of Americans rely upon television broadcasts for their news.

News, current occasions and ancient programming can help make younger humans extra aware of other cultures and those. Documentaries can help increase vital thinking about society and the arena. television can help introduce teens to classic Hollywood movies and overseas movies that they might not otherwise see.

It broadens the know-how of various cultures, and promotes tolerance and international information of worldwide issues. Through contemporary affairs, discovery, lifestyle, cooking indicates and children's programs, television encourages medical and cultural interest.

Agree with and effect: television is the most relied on a form of marketing and stays maximumly probable to make consumers chortle, circulate them to tears or cause feelings. For example, television is with the aid of a long way the maximum relied on shape of video advertising in Canada. 70% of 18-34-year-olds named tv the most truthful compared to 12% for online video.

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[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]

So, the correct answer is Option 1.

Answer:12

Step-by-step explanation:

Answer:

8.  -3, 16

9.  -3, 4.5

Step-by-step explanation:

See attached worksheet.