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Using proportions, it is found that:

a) The graph for the distance-time journey is given at the end of the answer.

b) The average speed for the whole journey was of 25 miles per hour.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using basic arithmetic operations such as multiplication or division from the rates of the variables.

Proportions are applied to find the relation between velocity, distance and time, as velocity is distance divided by time, that is:

v = d/t.

Then, applying cross multiplication, the distance is given by:

d = vt.

On the first interval of his trip, for the first 15 minutes = 1/4 of an hour, he traveled at a velocity of 40 mph, hence the distance is:

d = 40 x 1/4 = 10 miles.

During the second interval, of 25 minutes, from 15 minutes to 40 minutes, he stopped, hence his distance remained constant at 10 miles.

During the third interval, of 20 minutes = 1/3 of an hour, Tim completed the journey at a velocity of 45 mph, hence the complete distance is given by:

d = 10 + 45 x 1/3 = 10 + 15 = 25 miles.

The graph with these three intervals is given at the end of the answer.

He drove a distance of 25 miles in one hour, hence his average speed is given as follows:

v = d/t = 25/1 = 25 miles per hour.

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Answer:

x=8

Step-by-step explanation:

83+(12x+1)=180

It equal to 180 because the line measures to 180.

Then write out the equation and solve.

Answer: Hi this would be the arrow that goes to the left and the dot on the right, so something like ← and dot. Hope this helps, I know this is confusing but try your best.

Step-by-step explanation:

Answer:

After solving the inequality, we get:

[tex]x\leq -10[/tex]

With the plotted inequality given.

Step-by-step explanation:

Step 1: Manipulate and solve the inequality

The inequality is given as:

[tex]\frac{1}{2}x+8\leq 3[/tex]

Make [tex]x[/tex] the subject of the inequality to solve it:

[tex]\frac{1}{2}x+8\leq 3\\\\\text{Subtract 8 from both sides of the equation:}\\\frac{1}{2}x+8-8\leq 3-8\\\\\text{Simplify:}\\\frac{1}{2}x\leq -5\\\\\text{Multiply by 2 on both sides of the inequality:}\\2\times \frac{1}{2}x\leq -5\times 2\\\\\text{Simplify:}\\x\leq-10[/tex]

Step 2: Plot the inequality

After solving the inequality, we get:

[tex]x\leq -10[/tex]

Which means that [tex]x[/tex] consists of all values that are equal to and less than [tex]-10[/tex].

On a number line, when the inequality includes the value, it is denoted by a closed circle.

With all this information, let's plot the number line:

The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.

Denoting the distance in feet between the wall and the base of the ladder by x and the angle in radians between the ladder and the ground by y, it is noted;

cos(y) = x/10

which implies;

y = arccos(x/10)

Denoting time in seconds by t, it is further noted that;

[tex]\frac{dx}{dy} = \frac{dy}{dx} \frac{dx}{dt}[/tex]  (chain rule)

Noting (using a standard table of derivatives for convenience)

[tex]\frac{dy}{dx}= -\frac{1}{\sqrt{1-(0.1x)^2} }(0.1)[/tex] (also by chain rule)

The above equation changes as;

[tex]\frac{dy}{dx}= -\frac{0.1}{\sqrt{1-0.1x^2} }[/tex]

It is noted from the question that in this particular system;

[tex]\frac{dx}{dt} = 0.5[/tex]  feet per second

So (denoting the derivative as a function of x)

[tex]\frac{dy}{dt}(x)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01x^2} }[/tex]

At last;

[tex]\frac{dy}{dt}(8)=\frac{dy}{dx} \frac{dx}{dt} = - \frac{0.05}{\sqrt{1-0.01(64)} }[/tex]

         = [tex]\frac{0.05}{\sqrt{1-0.64} }[/tex]

         = [tex]\frac{-0.05}{\sqrt{0.36} }[/tex]

         = -5/60

         = -1/12 radians per second

The angle between the ladder and the ground changes when the bottom of the ladder is 8 ft from the wall is -1/12 radians per second.

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⇒The line passes through the points (3,0) and (1,-3) I will use them to find the gradient of the line. Note this information is from the graph.

⇒[tex]m=\frac{y_{2}-y_{1} }{x_{2} -x_{1} } \\m=\frac{-3-0}{1-3} \\m=\frac{3}{-2} \\m=-\frac{3}{2}[/tex]

In the year 1998, movie tickets will be greater than $5.50 as determined by solving the equation y=4.25[(1.035)^x].

What is an equation?

A movie ticket cost $4.25 in 1990.

The inflation rate is about 3.5%

Rate increased ,r=100%+3.5%=103.5%=1.035

equation generated is,

y=4.25[(1.035)^x]

Solving the equation for each year, we get the following data:

Tabulating the data

Year         cost

1990         4.25

1991          ....

....              ....

1998          5.5964~ 5.6

In the year 1998, the will be greater than $5.50.

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The value of m = -10, which we get by solving the given equation

The given equation is

0.61m - 1.51m = 9

⇒-0.9m = 9                  (we get the minus sign because 0.61  is smaller than 1.51)

⇒-0.9m/(-0.9) = 9/(-0.9)       (dividing both sides of the equation by -0.9)

⇒m = -90/9

⇒m = -10

Thus on solving the given equation we get the value of m as -10

That is m=-10

Solve another equation for x

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a. The line equation is given by:

Where m is the slope of the line and b is the y intercep.

In this case y is the number of active pilots and x is the year.

In order to obtain the line equation of the function, you use the information about a pair of years in the given table, in order to calculate the slope of the line. You can select whichever two years with its number of active pilots.

For example, for years 1980 and 1990, you have that the pilots were 182,097 and 149,666 respectively.

To calculate the slope of the line, you use the following formula:

Then, the slope of the line is negative.

If you consider the zero point of the year axis, as the year 1980, the y intercept of the function will the value of the active pilots in that years, which is 182,097.

Finally, the line equation is:

b. For the year 2003, you have that x is:

x = 2003 - 1980 =23

You replace this value of x into the linear equation:

The number of active pilots for 2003 is 107,506

Answer:

y = 3x - 1

Step-by-step explanation:

In order for lines to be parallel, they must have the same slope.

The slope of y = 3x - 8 is 3.

Now, we can solve it using point-slope form. Remember that m = 3, x₁ = -2 and y₁ = -7:

y − y₁ = m(x − x₁)

y - (-7) = 3(x - (-2))

y + 7 = 3(x + 2)

Distribute 3 and isolate y:

y + 7 = 3x + 6

y = 3x - 1

Answer:

x = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

using the rule of exponents

[tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex] , then

[tex]8^{x}[/tex] = 2

[tex]2^3)^{x}[/tex] = 2 , that is

[tex]2^{3x}[/tex] = [tex]2^{1}[/tex]

since the bases on both sides are equal, both 2, then equate the exponents

3x = 1 ( divide both sides by 3 )

x = [tex]\frac{1}{3}[/tex]

Accurate Whole numbers .

What is accurate whole number?

Accuracy is defined by the number of significant digits while precision is identified by the location of the last significant digit. For instance the number 1234 is more accurate than 0.123 because 1234 had more significant digits.

What does function mean?

Each element of x is given exactly one element of y via a function from a set x to a set y. The sets x and y are collectively referred to as the function's domain and codomain, respectively.

The following details must to be taken into account:

The term "whole number" refers to a number that is free of fractions and decimals.

It calculated the number of household online devices in relation to the number of occupants.

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The value of the function f(0) = 1, obtained from the graph.

For the given question;

The graph for the function is given.

For finding the value of function f(0), simply see the value of y with respect to x = 0.

f(0) = 1, taken from graph.

Thus, the value of function f(0) is found as 1.

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The density of the material of mass 200 g and volume 10.4 ml is 19.2 g/ml.

According to the question,

We have the following information:

Density is defined as the mass per unit volume.

So, we have the formula of density:

Density = Mass/volume

Mass of the metal object = 200 g

Volume of the metal object = 10.4 ml

Density = 200/10.4 g/ml

Density = 19.231 g/ml

Now, we will round it off to nearest 1 decimal point.

We know that when the digit is greater than 5 then the number is increased by 1 and when the digit is less than 5 then the number remains same.

So, we have:

Density = 19.2 g/ml

Hence, the density of the metal object is 19.2 g/ml.

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A unit rate means a rate for one of something.

The number of boxes packed in 18 hours is 216 boxes.

A unit rate means a rate for one of something.

We write this as a ratio with a denominator of one. 

We have,

From the graph, we see that,

In 5 hours, there are 60 boxes packed.

This can be written as:

5 hours = 60 boxes

Similarly,

1 hour = 12 boxes

3 hours = 36 boxes

The number of boxes packed in 18 hours:

1 hour = 12 boxes

Multiply both sides by 18.

18 hours = 18 x 12 boxes

18 hours = 216 boxes

Thus,

The number of boxes packed in 18 hours is 216 boxes.

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Answer:

A = 135 cm²

Step-by-step explanation:

the area (A) of a trapezium is calculated as

A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )

where h is the perpendicular height between the bases b₁ and b₂

here h = 9 , b₁ = 19 , b₂ = 11 , then

A = [tex]\frac{1}{2}[/tex] × 9 × (19 + 11) = 4.5 × 30 = 135 cm²

Answer:

a) ∠13

b) ∠13

c) ∠2

Step-by-step explanation:

a) ∠ 8  + ∠13 = 180°  

Co - interior angles are supplementary, when m // l

b) ∠5 ≅ ∠13

If m // l, the corresponding angles are congruent.

c) ∠5 + ∠2 = 180°

∠5 and ∠2 are co interior angles and they are supplementary if a // b.

Answer:

20002

Step-by-step explanation:

100*20=2000

2000*10=20000

20000+2=20002

Answer:

Solve for x by simplifying both sides of the equation, then isolating the variable.

x=17

Step-by-step explanation:

The amount that Georgina has invested in savings account and CD are $ 2500 each.

Given that:-

Total amount invested in savings account and CD = $ 5000.

APY in savings account = 0.6 %

APY in CD = 0.9 %

Total interest earned = $ 37.5

Let the amount invested in savings account be x.

Hence, according to the data given in the question, we can write,

Amount invested in CD = 5000 - x

Interest in savings account in a year = x*(0.6)*1/100 = 0.006x

Interest in CD in a year = (5000-x)*(0.9)*1/100 = (0.009)(5000-x) = 45 - 0.009x

Hence,

0.006x + 45 - 0.009x = 37.5

45 - 37.5 = 0.009x-0.006x

7.5 = 0.003x

x = 7.5/(0.003)

x = 7500/3 = 2500

Hence, Georgina has invested $2500 in each savings account and CD.

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a) 10 percent people arrive before 7 am.

b) 64 percent of the people arrive after 7:59 am.

Here, we are given the following data-

Time                                No. of people

before 7 am                           15

7am to 7:59 am                     39

8am to 8:59 am                    75

9am to 9:59 am                    21

a) the number of people who arrive at the office before 7am = 15

The total number of people in the office = 150

Thus, the percentage of people surveyed who arrived before 7 am = (15/150)*100

= (1/10)*100

= 10

Thus, 10% people arrive before 7 am.

b) The number of people who arrive after 7:59 am = 75 + 21

= 96

Thus, the percentage of people surveyed who arrived after 7:59 am =

(96/150)*100

= (0.64)*100

= 64

Thus, 64 percent of the people arrive after 7:59 am.

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You can use the Alternate Exterior Angle Theorem to prove that the 2 angles shown on the drawing are congruent to each other.

MK = 50

to get from 13 to 53

times 1 plus 40

10 times 1 plus 40 =50

The equation of the linear function is: 3x + y = 1.

How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y - y₁ = m(x - x₁), where m is the slope and c is the y-intercept.

Given, the line passes through the points (-2, 7) and (2, -5).
Now, using the formula established in the literature, we get:
Slope = m = (y₂ - y₁)/(x₂ - x₁) = (-5 - 7)/(2 - (-2)) = -12/4 = -3
Equation of the linear function: y - 7 = (-3)(x - (-2)) ⇒ y - 7 = (-3)(x + 2)
⇒ y - 7 = -3x - 6 ⇒ 3x + y = 1
Thus, the equation of the linear function is: 3x + y = 1.

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Answer:

Step-by-step explanation:

2x+3

x=3divides2

On a hot summer day, 606 people used the public swimming pool; daily admission prices are $1.75 for children and $2.50 for adults; admission receipts totaled $1357.50; 396 adults and 210 children swam at the public pool that day.

Therefore,

1.75C + 2.50A = 1357.50

C + A = 606

C = 606-A

1.75(606 - A) + 2.50A = 1357.5

1060.5 - 1.75A + 2.50A = 1357.5

1060.5 + 0.75 A = 1357.5

0.75 A = 297

A = 297/0.75

A = 396

No of adults = 396

Therefore children = 606-396

No of children = 210

396 adults and 210 children swam at the public pool that day

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Answer:

1.265 x 10-10

Step-by-step explanation:

ANSWER

y - 3 = -8/5 (x + 5)

EXPLANATION

The point-slope form of the equation of a line, that has a slope m and passes through point (x1, y1) is:

In this problem m = -8/5 and the given point is (-5, 3). The equation is:

Answer:

6cm by 1.5cm

18cm by 4.5cm

80cm by 20cm

Step-by-step explanation:

The error interval for the area will be expressed as 64.2< a < 63.93

Error intervals may be defined as the limits of accuracy when a number has been rounded or truncated. They are the range of possible values that a number could have been before it was rounded or truncated. According to the question, Area of circle = 78.1 cm² and Area of square = 21.4 cm². If we round the area to one decimal point, we get the Area of circle = 78.1 + 0.05   and = 78.1 - 0.05 that is 78.15 and 78.05. Also, the Area of square = 21.4 - 0.05 and = 21.4 + 0.05 we get 21.35 and 21.45. Now, Area of shaded region in the form m < a < n. So, n = 78.15 - 21.35

=> n= 56.8 and

m = 78.05 - 21.45

=> m = 56.6

Area of shaded region is 56.6< a < 56.8.

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