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Problems 3.1–3.2
Starting at noon, the temperature changed steadily at a rate of −0.8°C every hour.

At 3 p.m., the temperature was −2.5°C.

What was the temperature at noon?

The least common denominator for each pair of fractions is as follows:

33.) = 6

33.) = 634.) = 7

33.) = 634.) = 735.) = 30

The least common denominator is defined as the lowest number that can divide a given set of numbers.

28= 2×2×7

7 = 7

The least common denominator would be 7

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Yes, this is correct. If you solve the first equation it equals the second equation.

Answer:

The exponential growth function 0f3=61025/ 04-0295254 0f=423 0fx)=(-1257 is not a valid equation.

Step-by-step explanation:

The speed of the cars are 50mph and 60mph

Let's call the speed of the slower car "x". The faster car is traveling at "x + 10 mph".

The total distance both cars travel is 660 miles, and the time it takes for them to meet is 6 hours.

Using the formula for distance = rate x time, we can set up the equation:

x * 6 + (x + 10) * 6 = 660

Expanding and simplifying, we get:

12x + 60 = 660

Subtracting 60 from both sides:

12x = 600

Dividing both sides by 12:

x = 50 mph

So the slower car is traveling at 50 mph and the faster car is traveling at 60 mph.

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We can classify them as -

There are six primary statement forms in Propositional Logic -

Given are the statements as -

We can classify them as -

Therefore, we can classify them as -

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Answer:

I don’t even know

Step-by-step explanation:

The duration of the task is 2.5 days

The task duration if Mr. Bean gets sick is 1.5 days

An equation is an expression showing two or more numbers and variables linked together by a mathematical operation. Types of equations are linear, quadratic, cubic and so on depending on the degree of the variable.

Mr. Hummer works on the task for 3 hours, Mr. Cold works on the task 9 hours, and Mr. Bean works 8 hours on the task

Total time spent on task = 3 hours + 9 hours + 8 hours = 20 hours

Working day has 8 hours, therefore:

1 working day = 8 hours

20 hours = 20 hours * 1 working day per 8 hour = 2.5 days

If Mr. Bean is sick:

Total time spent on task = 3 hours + 9 hours = 12 hours

12 hours = 12 hours * 1 working day per 8 hour = 1.5 days

The task duration if Mr. Bean gets sick is 1.5 days

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The simplified form of the exponential expression [tex]b^{n- 2}\times{b^{n-3} = b^{2n - 5}[/tex].

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An exponential expression [tex]b^{n- 2}\times{b^{n-3}[/tex].

We know, Same base multiplication is exponent addition.

Therefore,

[tex]b^{n- 2}\times{b^{n-3} = b^{n - 2 + n - 3}[/tex].

[tex]b^{n- 2}\times{b^{n-3} = b^{2n - 5}[/tex].

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The equation of the line is y = x + 6

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

The graph

On the graph, we have the following highlights

The graph intersect the y-axis at y = 6

This means that the intercept c is 6

Also, as x changes by 1, the y values changes by 1

This mean sthat the slope is 1

So, we have

y = mx + c

This gives

y = x + 6

Hence, the equation is y = x + 6

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The linear equation on the graph can be written as:

y = (3/2)*x + 6

A general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁), then the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

In this case we can see the points (0, 6)  (so the y-intercept is b = 6)  and (4, 10)

Then the slope will be:

a = (10 - 6)/(4 - 0) = 6/4 = 3/2

Then the linaer equation is:

y = (3/2)*x + 6

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A function is decreasing if as x-values increase, the y-values decrease.  Graphically this means that if you move from left-to-right, the graph goes down.

The downhill portion of this curve is on the interval [tex](1,\infty)[/tex].

Since the pavement at the new shopping mall is being laid, a transformation that is applied from brick A to brick B include the following: D. translation.

In Mathematics, a transformation can be defined as the movement of a point from its original (actual) position to a final (new) location. This ultimately implies that, when an object (pre-image) is transformed, all of its points would be transformed as well to form a new image such as the following:

In Mathematics, a translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.

In conclusion, a translation was applied to both brick A and brick B.

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Answer:

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b) $34.50

(c) 356

Step-by-step explanation:

Let x = number of minutes.

(a)

f(x) = 30, for x ≤ 200

f(x) = 0.03(x - 200) + 30, for x > 200

(b)

Here, x = 350, so x > 200.

f(x) = 0.03(x - 200) + 30

f(350) = 0.03(350 - 200) + 30

f(350) = 0.03(150) + 30

f(350) = 4.5 + 30

f(350) = 34.5

$34.50

(c)

f(x) = 0.03(x - 200) + 30

0.03(x - 200) + 30 = 34.68

0.03(x - 200) = 4.68

x - 200 = 156

x = 356

Answer:

Step-by-step explanation:

As an example, let's say I have a pond 7 feet long, 6.5 feet wide, and 3 feet deep. That gives me approximately 1,000 gallons of water. The average recommended gallons per inch of fish is 10. To calculate how many inches of fish I can fit in my pond I would divide 1,000 by 10: 1,000/10 = 100.

I know it is not the answer but I hope this helps you.

Answer: Not necessarily. Dividing the pie chart into 5 equal sections might be a way to display categorical data if the number of categories is 5. However, dividing it into 5 sections might not be the best way to display the data if the number of categories is different than 5 or if any category has a significantly higher or lower proportion than the others. In this case, it may be more appropriate to use a different scale to display the correct ratio. It is important to consider data distribution and visualization clarity before choosing how to display categorical data.

Answer:

Below

Step-by-step explanation:

sin (90 -0) = sin (90) = 1

Remember   sin^2 + cos^2 =1

  for theta       sin2 + (3/4)^2

                         sin^2 = 1 - 9/16 = 7/16

                            sin (theta) = ± sqrt(7) /4

Answer:

Below

Step-by-step explanation:

From 7 to 10 AM is THREE hours (if the times are all on the same day)

Answer:

Below

Step-by-step explanation:

The two angles at U   are equal....so the triangles have TWO equal angles: 72° and the angles at U

Answer A

Geometric mean is the square root of the two numbers after multiplying them     sqrt ( 48* 12) = sqrt( 576) = 24

Answer:

The scarf cost:

$9.91

Step-by-step explanation:

9.92 - 0.01 = 9.91

The cost of each popcorn is $0.75 while the cost of each drink is $1.25

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

Let p represent the number of popcorn and d represent the number of drinks that Liliana bought.

Liliana spends $4.00 on 2 boxes of popcorn and 2 drinks, hence:

2p + 2d = 4       (1)

Nadette spends $5.25 on 2 boxes of popcorn and 3 drinks, hence:

2p + 3d = 5.25    (2)

To solve using elimination method, subtract equation 1 from 2, hence:

d = $1.25

substitute the value of d in equation 1 to get p:

2p + 2(1.25) = 4

p = $0.75

The value of p and d are $0.75 and $1.25 respectively

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Answer:

a. Point C is at (8,8)

b. See image/expl

c. AngleABC = 140°

Step-by-step explanation:

You can just count squares to find the slope of AD. To find points along AD, go

UP1 and OVER4

UP1 and OVER4 is the slope 1/4.

Start from B and go

UP1 and OVER4.

Parallel lines have the same slope. Perpendicular lines have slopes with opposite sign and "flipped". To make CD perpendicular to AD the slope should be -4/1 or 4/-1 is the same thing. To find C go from D

UP4 and BACK1

this is the slope 4/-1

1/4 and 4/-1 are negative reciprocals (opposite sign and flipped over) so the lines will be perpendicular.

You cab use this explanation for part b. Or you the slope calculations using the coordinates. See image.

part c, see image.

The value of y when x = 28 is given as follows:

y = 0.5.

A direct proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

An inverse proportional relationship is defined as follows:

y = k/x.

When x = 7, y = 2, hence the constant k is obtained as follows:

2 = k/7

k = 14.

Hence the equation is:

y = 14/x.

When x = 28, the value of y is obtained as follows:

y = 14/28

y = 0.5.

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4(-6), 6(-4), and 12(-2). (-2). Each one adds up to -24. I am aware of this because if you multiply the two numbers and one of the numbers is negative, the result will also be negative. The item will be favorable if there are just two drawbacks.

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Answer: 3 1/2

Step-by-step explanation:

Since positive and a negative make a negative the product would be a negative. Now we multiply 2/1 (because is the same as 2) times - 7/4, which gives us - 14/4. -14/4 = 3 1/2. Have a nice day ;)

Answer:

a) Let's call the length of a call "t" (in minutes). The cost of a call can be represented as follows:

C(t) = 0.99 if t <= 20

C(t) = 0.99 + 0.07(t - 20) if t > 20

b) The domain of the function is all non-negative real numbers (t >= 0), since a call can have any non-negative length in minutes. The range of the function is all non-negative real numbers, since the cost of a call can never be negative.

c) If a call lasts 12 minutes, then the cost would be 0.99:

C(12) = 0.99

d) If a call lasts 1 hour (60 minutes), then the cost would be:

C(60) = 0.99 + 0.07(60 - 20) = 0.99 + 0.07(40) = 0.99 + 2.80 = 3.79

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

Alexia has 22$ total:
Therefore, after taking away the 10$ dollar admission fee, she has 12$ left.

12$ dolars divided by 3$ dollars per ride equal 4 rides.

The answer is 4 rides to spend exactly 22$

The area of the rectangle =  9x² +18x−16

What is the area of the rectangle?

The area of a rectangle is calculated by multiplying the height by the width. If the height of the rectangle is represented by h and the width is represented by w, then the area is given by:

A = h * w

In this case, the height of the rectangle is given as 3x - 2 yards, and the width is given as 3x + 8 yards. So, substituting these values into the formula:

A = (3x - 2) * (3x + 8)

A = (3x - 2)(3x + 8)

A = 9x² +18x−16

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The answer is:

Work/explanation:

To find the rectangle's area, we use the formula

[tex]\pmb{A=LW}[/tex]

Where A = area;

L = length;

w = width.

Plug in the data

[tex]\sf{A=(3x+8)(3x-8)}[/tex]

To multiply, use FOIL:

F = first

o = outside

i = inside

l = last

Multiply

[tex]\sf{3x\cdot3x=9x^2}[/tex]

[tex]\sf{3x\cdot(-8)=-24x}[/tex]

[tex]\sf{8\cdot3x=24x}[/tex]

[tex]\sf{8\cdot(-8)=-64}[/tex]

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

[tex]\sf{9x^2-24x+24x-64}[/tex]

[tex]\sf{9x^2-64}[/tex]

A catapult launches a pumpkin from the base of a hill. The hill follows an incline with the height in meters, y, in terms of horizontal distance in meters, x, given by the equation y=0.9x. 40m is the height, where the pumpkin lands on the hill.

The term "horizontal distance" refers to the separation between two places measured with a slope of 0%. Vertical distance is the distance following the direction of gravity, while horizontal distance is the distance along the ground surface. The distance between an observer and a building represents as that of an example of horizontal distance, and the structure's height serves as an illustration of vertical distance. A projectile's range is the horizontal distance it covers. Horizontal refers to something that is parallel to it. Anything that forms a 90-degree angle (right angle) with the horizontal or the horizon is referred to as vertical since it is the opposite of the horizontal. The line that spans from left to right is therefore considered to be horizontal.

Given that,

The hill follows an incline with the height in meters y,

in terms of horizontal distance in meters x,

The given equation becomes: y = 0.9x

The height of the pumpkin, as it is launched up hill, is given by the function:

y = -0.1x² + 4.9x

now, finding point of intersection, we get:

0.9x = -0.1x² + 4.9x    [as y = 0.9x]

or, 0.1x² - 4x = 0

or,  x (0.1x - 4) = 0

or, x = 0 (this is not possible)

and 0.1x = 4

or, x = 40

40 is the height, in meters, where the pumpkin lands on the hill.

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The amount of money that Joe needs to pay would be = $15,918.50

In the year 2018, the percentage of social security = 6.2%

Joe's taxable income= $128,400.00

The annual salary of Joe = $256,750.00

The amount of money that joe should not pay is 6.2% of $256,750.00.

That is;

= 6.2/100 × 256,750.00

= 1591850/100

= $15,918.50

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Answer: Dude this is pretty easy!

Step-by-step explanation: Use the process of elimination.

Hint: It's just subtraction or addition. Trust me it's easy.

Answer:

Step-by-step explanation:

1/4 min, 15 sec