04.02 Comparing Functions
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The height of the object at the time t = 1 second is given by 1174 feet.

Given the height of tower is 1190 feet.

The height of the object at time t seconds is given by,

h(t) = [tex]-16t^2[/tex] + 1190

So the height of the object after time t = 1 second is given by,

h(1) = [tex]-16\times 1^2+1190[/tex] = -16 + 1190 = 1174 feet

Hence the height of the object at the time t = 1 second is 1174 feet.

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The value of the expression − || 6c − 16b || + 1 if a = −12, b = 34, and c = −23 is - 681.

We that the modulus always gives a positive quantity.

For example: || -5 || = 5, etc.

We are given;

a = −12, b = 34, and c = −23.

We need to find − || 6c − 16b || + 1.

The solution of an algebraic expression is obtained by substituting the given values in the expression.

Substitute the given value in the above expression, we will get;

− || 6c − 16b || + 1

= − || 6 * -23 − 16 * 34 || + 1

=  − || - 138 − 544 || + 1

= − || - 682 || + 1

= − 682 + 1

= - 681

So, the value of − || 6c − 16b || + 1 is - 681.

Thus, the value of the expression − || 6c − 16b || + 1 if a = −12, b = 34, and c = −23 is - 681.

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The equation representing the cost of the canoe rental company is given by y = 30x + 20 .

Let the total cost for renting a canoe be y.

Let the canoe is being rent for x hours.

now the cost for renting the canoe at 30 dollars per hour = 30x

Total cost of renting the canoe = 30x + 20

But the total cost is y.

Hence the equation to represent this situation is given by

y = 30x + 20 which is a straight line of the form y = mx +c, where the slope is 30 and the y-intercept is 20.

Now we will plot the graph for this equation.

At x = 0 , y = 20

At x = 1 , y = 50

At x= -3 , y = -70

Hence the graph of the line passes through these points on the cartesian plane.

The graph of the line is attached below.

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The resulting dilation of the figure with the scale factor of 3/4 is given by the graph at the end of the answer.

Dilation on a image

Dilation in a image means multiply the coordinates of each vertex of the figure by the scale factors.

Given,

Here we have the triangle in the given figure.

Now, we have to find the dilation of the figure with the scale factor of 3/4.

Here from the original figure graph, the vertices are obtained as follows:

S(-8,-4), T(4, -4) and U(4,8)

Now we have to use the dilation scale factor of 3/4,

Which means that the coordinates are multiplied by 3/4,

Then the new coordinates of the resulting image are given as follows:

S(-8, -4) => ((-8 x 3/4), (-4,3/4)) => S'(-6, -3)

T(4, -4) => ((4 x 3/4), (-4,3/4)) => T'(3, -3)

U(8, 4) => ((8 x 3/4), (4,3/4)) => U'(6, 3)

Now, we have to plot these new coordinates on the graph, then we get,

the graph like the following.

Here the dilated figure is given by the graph at the end of the answer, having the same format as the original figure, just with smaller side lengths due to the dilation with a scale factor less than 1.

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The slope of the line is 1/5 and it means the each headband uses 1/5 yards of fabrics

First choose two points

The first point = (3, 3/5)

The second point = (5, 1)

The slope of the line is the change in y coordinate with respect to the change in x coordinate of the line

The slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where [tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line = (1- 3/5) / (5 -3)

= (2/5) / 2

= 1/5 yards per headband

Hence, the slope of the line is 1/5 and it means the each headband uses 1/5 yards of fabrics

The complete question is

The table shows the amount of fabric Camille used based on the number of headbands that she made. Find the slope, and explain what it means in the context of the situation.

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Answer:

100 square meters

Step-by-step explanation:

[tex] {x}^{2} + 6x + 8x = 240[/tex]

[tex] {x}^{2} + 14x = 240[/tex]

[tex] {x}^{2} + 14x - 240 = 0[/tex]

[tex](x - 10)(x + 24) = 0[/tex]

[tex]x = 10[/tex]

x = -24 will not work (it is extraneous).

[tex] {x}^{2} = 100[/tex]

So the area of the square region is 100 square meters.

The number of elements in the list that are divisible by 10 is 10, 20, 30, 1000, 5000, 60000, etc.

Given:

the number of elements in the list that are divisible by 10. (hint: the number x is divisible by 10 if x % 10 is 0.) div ten

The number is divisible by 10 and the last digit is zero.

suppose take 10:

= 10/10 = 1

It is divisible.

= 10%10

The last digit or remainder is zero.

Therefore the number of elements in the list that are divisible by 10 is 10, 20, 30, 1000, 5000, 60000, etc.

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The intermediate form for the limit , [tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ is  ∞/∞

Given,

The limit ; [tex]\lim_{x \to \infty} \frac{e^{2x} }{x^{5} }[/tex]

L'Hospital's rule;

A general technique for assessing indeterminate forms like 0/0 or / is the L'Hospital rule. L'Hospital's rule is applied to calculate the limits of indeterminate forms for calculus derivatives. It is possible to use the L Hospital rule many times.

By using L'Hospital's rule the intermediate form is;

[tex]\lim_{x \to \infty} \frac{e^{2x} }{x^{5} }[/tex] = [tex]\lim_{x \to \infty}[/tex] e²∞/ ∞⁵

 [tex]\lim_{x \to \infty} \frac{e^{2x} }{x^{5} }[/tex] =  [tex]\lim_{x \to \infty}[/tex] e∞/∞

[tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ = [tex]\lim_{x \to \infty}[/tex] 2e²ˣ / ∞

[tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ = [tex]\lim_{x \to \infty}[/tex] 2e∞/∞ = ∞/∞

That is,

The intermediate form for the limit , [tex]\lim_{x \to \infty}[/tex] e²ˣ/x⁵ is  ∞/∞

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Answer:

G is correct.

Step-by-step explanation:

[tex] - 2 + 4(5) = - 2 + 20 = 18[/tex]

[tex] - 3( - 2) + 2(5) = 6 + 10 = 16[/tex]

So G (-2, 5) is correct.

Answer:

x=-20

y=10

z=-19

Step-by-step explanation:

It is given that the shape is a rhombus, which means all four sides are equal. This means we can set up the equations:

5y-4=46   --> 5y=50 --> y=10

-2x+6=46 --> -2x=40 --> x=-20

-2z+8=46 --> -2z=38 --> z=-19

The number of days that it take Olivia to collect at least 54 1/3 cups of sugar is 12 days.

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Olivia needs to gather at least 54 1/3 cups of sugar.

The expression will be illustrated thus:

15 2/3 + 3 1/3d ≥ 54 1/3

Collect like terms

3 1/3d ≥ 54 1/3 - 15 2/3

3 1/3d ≥ 38 2/3

Divide

d ≥ 38 2/3 ÷ 3 1/3

d ≥ (116 / 3 × 3/10)

d ≥ 11 3/5

She needs 12 days.

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Answer: SAS (Side angle side)

From the given statements it was found that statement p is false. So, -3x + 8x - 5x is equal to 0 not x.

In p statement,

-3x + 8x - 5x = x is given.

Let us check it.

-3x + 8x - 5x = 8x - 8x = 0

So, we can say statement p is false.

In q statement,

(3x)(5y) = 15xy is given.

Let us check it.

(3x)(5y) = 15xy

So, we can say statement is q is true.

Therefore, from the given statements it was found that statement p is false. So, -3x + 8x - 5x is equal to 0 not x.

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Answer:

[tex] \rm \implies \frac{1}{3} (5x - 8) + \frac{2}{3} x \\ \\ \rm \implies \frac{5}{3} x - \frac{8}{3} + \frac{2}{3} x \\ \\ \rm \implies \frac{5x + 2x}{3} - \frac{8}{3} \\ \\ \rm \implies \frac{7x}{3} - \frac{8}{3} \\ \\ \rm \implies 2 \frac{1}{3} x - 2 \frac{2}{3} [/tex]

If you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than 665 grams.

In statistics, mean is the ratio of sum of all the observations and total number of observations in a data set.

How to calculate their mean weight will be greater than how many grams?
Given that from the question

Mean = 641 grams

standard deviation 24 grams

If you pick 25 fruits at random, then 15% of the time, their mean weight will be greater than how many grams?

The formula for the calculating the x value in the normal distribution is,

x = μ + zσ

The level of significance is = 15% = 0.15

Therefore,

z = (=normsinv (1 - α))

= (=normsinv (1-0.15))

= (=normsinv(0.85))
= 1.036

The critical value of z is 1.036

z = 1.036

(x - μ) / σ = 1.036

x = μ + 1.036σ

= 641 + 1.036*23

= 641 + 23.828

= 664.828

= 665grams (rounded to the nearest gram)

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The volume of the largest right cylinder that fits in a sphere of radius 4 units is 143 m².

Let the diameter of the cylinder be “d" and the height of the cylinder be “h".

Given radius of the sphere = r = 4m

Diameter of the sphere = d = 2r = 2×4 = 08 m

As the cylinder is inscribed in the sphere

Therefore, the diameter of the cylinder be “d" is equal to the height of the cylinder be “h".

i.e, d = h

By Pythagoras Theorem, In triangle ABC

AB²+BC²=AC²

Or, d²+h² = (8)²

Or, h²+h² = 64

Or, 2h² = 64

Or, h² = 64/2

Or, h = √32

And d =√32

Or, r = d/2

       = √32/2 =16/√32

Or, r = 16/√32

Volume of the cylinder = πr²h

                                       =22/7 × (16/√32 )² × √32

                                       = 22/ 7 × 8 ×√32

                                       = 142.229

Rounding up the value 142.229 in 143 m³

Therefore, the largest volume of the cylinder = 143 m³

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Answer:

  (a)  y -5= -2(x -2)

Step-by-step explanation:

You want the equation of the line perpendicular to y = (1/2)x - 2 that contains the point (2, 5).

Perpendicular lines have slopes that are opposite reciprocals of one another. The slope of the given line is the x-coefficient: 1/2. Its opposite reciprocal is ...

  -1/(1/2) = -2

The point-slope equation of a line is ...

  y -k = m(x -h) . . . . . . . . line with slope m through point (h, k)

You want a line with slope -2 through point (2, 5), so its equation is ...

  y -5 = -2(x -2)

Answer:vvvvvvvvvvvvvvvvvv55555

Step-by-step explanation:

a) Karmila have 5 pieces of ribbon each 3/4 m long

b) the length of ribbon left over​ =   1 m

A roll of ribbon was 8m long.

Karmila cut 6 pieces of ribbon each length 2/3

Total length of 6 pieces of ribbon having length 2/3 would be,

6 * (2/3) = 4 m

This means, after cutting 6 pieces of ribbon, the length of the remaining ribbon = 4 m

Then we need to cut the remaining ribbon into some pieces each of length 3/4

Let t be the number of pieces.

So, we get an equation

(3/4) * t = 4

t = 4 * (4/3)

t = 16/3

t = 5 1/3

t ≈ 5

This means, Karmila have 5 pieces of ribbon each 3/4 m long and the length of ribbon left over​ =  1m

Therefore, a) Karmila have 5 pieces of ribbon each 3/4 m long

b) the length of ribbon left over​ =   1 m

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4.8 inches is the height of a trapezoid with an area of 24 square inches if the two bases measure 4 inches and 6 inches.

Using the formula for the area of a trapezoid, which is:

Area = (1/2)(b1 + b2)h

In this formula, b1 and b2 are the lengths of the two bases of the trapezoid, and h is the height of the trapezoid. In our problem, we know that the area is 24 square inches, and the lengths of the two bases are 4 inches and 6 inches. We want to solve for h, the height of the trapezoid.

Plugging in the known values, we get:

24 = (1/2)(4 + 6)h

24 = (1/2)(10)h

24 = 5h

4.8 = h

Therefore, the height of the trapezoid is 4.8 inches.

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The number of ways of selecting a committees of 5 members from  a group of 10 people will be 252

Combination is a method to calculate different ways to select items from a set / group regardless of the order.

ⁿCₓ = n! / (n-x)! x!

Total number of people in group is 10

Number of people require to form committee is 5

By using Combination ,

¹⁰C₅ = 10! / (10 - 5 )! 5!

= 10×9×8×7×6×5! / 5! × 5!

Cancelling 5! from numerator and denominator

= 10×9×8×7×6 / 5!

expanding the factorial

= 10×9×8×7×6 / 5×4×3×2×1

= 252

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Exponential model representing the amount of Iodine-125 remaining in the tumor after t days is f(t) = 0.5 *[tex]e^{-0.0115t}[/tex] and number grams of Iodine-125 after 60 days is 0.2507 grams

Given:

A tumor is injected with 0.5 grams of Iodine-125, which has a decay rate of 1.15% per day.

The formula for exponential decay is f(t)=a*e^kt where a is the original amount of the substance, k is the decay rate and t is the time elapsed. You are given the decay rate of 1.15% or -0.0115. For this problem t is left as is since we are creating a function of time.

f(t) = 0.5 *[tex]e^{-0.0115t}[/tex]

After 60 days

= 0.5 * [tex]e^{-0.0115*60}[/tex]

= 0.5*e^-0.69

= 0.5*0.50157

f(t) = 0.2507 grams

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Answer:

Step-by-step explanation:

The of miles the group walked in 3 weeks is 44 miles

What is proportion?

Proportion can be defined as the mathematical comparison of two elements or numbers.

From the information given, we have that;

• in 1 week people walked 62 miles

• in the second week reduced to 58 miles

• in week 3 they walked 14 fewer miles during week 2

to determine the many miles did the group walk in 3 weeks, we can reduce

58 miles - 14 miles less during week 2

=44 miles.

so, number of miles the group walked in 3 weeks is 44 miles.

Answer:5.08

Step-by-step explanation:

When You fill up your car with 15 gallons of gasoline. then it weighs 90 pounds of weight.

the weight of an object is the force acting on the object due to gravity.

Given

A car with 15 gallons of gasoline is filled.

We need to find the weight of the gasoline

We know that 1 gallons of gasoline is 6 pounds

So now for 15 gallons will be fifteen times of 6 pounds

15×6

90 pounds

90 pounds is the weight of the gasoline.

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Answer:

Step-by-step explanation:

A septagon (7 sided polygon) adds up to 900 degrees. When adding up the given interior angle measures, you get 771. Subtract 771 from 900 and you get the answer of 129.

Answer:

x= 129°

Step-by-step explanation:

Interior angles: 180(n-2) where n=sides

=180(7-2)

=180(5)

=900°

130°+118°+135°+128°+126°+134°+x=900

771+x=900

x=900-771

x= 129°

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The amount that the painter will charge is $519.75.

From the information illustrated, the painter can paint 175 square feet per hour and she charges $0.54 per square foot and then paints for 5.5 hours.

The amount that she will charge will be:

= Number of square foot × Amount charged × Number of hours

= 175 × $0.54 × 5.5

= $519.75

The amount is $519.75.

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