In June 2020, Parks Canada closed the Bow Valley Parkway (Highway 1A) to vehicle traffic
between Banff and Castle Junction near Johnston Canyon. This made for a bike ride that cut
through a small piece of Canada’s beautiful Rocky Mountains. A group of friends decide to cycle
the trip, 25 km each way, from Banff to Johnston Canyon and back. They ride towards Johnston
Canyon straight into the wind, and then have the wind at their backs on the return trip. The wind
adds or subtracts 5 km/h from their speed. If the group of friends wants to complete the round trip
in 3 hours, algebraically find the average speed with no wind the group needs to cycle. Complete
the distance speed time chart to help solve the question. Round your answer to the nearest
hundredth of a km/h.

Answer: 37km

Step-by-step explanation:

Answer:

ellipses

a pair of parallel straight

Step-by-step explanation:

Answer: 10xy³ - x²y + 3xy

Step-by-step explanation:

To simplify the expression (3xy³ + 8x²y - 3xy) + (7xy³ - 9x²y + 6xy), we can combine like terms.

Adding the corresponding terms together, we have:

3xy³ + 7xy³ = 10xy³

8x²y - 9x²y = -x²y

-3xy + 6xy = 3xy

Combining these terms, the simplified expression becomes:

10xy³ - x²y + 3xy

Therefore, the correct option is:

O 10xy³ - x²y + 3xy

a) The data in the above table about the statistics class asked the city where they live are b) Quantitative and Discrete.

b) The completion of the frequency distribution for the data is as follows:

Class            Frequency

Fort Pierce          7

Port St. Lucie      6

Vero Beach        7

Sebastian           4

Okeechobee     6

Total                 30

c) The completion of relative frequency and percentage distribution for the data is as follows:

Class            Frequency    Relative Frequency    Percentage

Fort Pierce          7                       0.233                     23.3%

Port St. Lucie      6                      0.200                     20.0%

Vero Beach        7                       0.233                     23.3%

Sebastian           4                        0.133                      13.3%

Okeechobee     6                       0.200                    20.0%

Total                 30

Class            Frequency    Relative Frequency        Percentage

Fort Pierce          7                 0.233 (7/30)           23.33% (7/30 x100)  

Port St. Lucie      6                0.200 (6/30)           20.00% (6/30 x100)  

Vero Beach        7                 0.233 (7/30)           23.33% (7/30 x100)  

Sebastian           4                  0.133 (4/30)            13.33% (4/30 x100)  

Okeechobee     6                 0.200 (6/30)           20.00% (6/30 x100)  

Total                 30

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a) Time-Series

b) Quantitative and Discrete

c) Cross-Sectional Qualitative

d) Quantitative and Continuous

If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.

In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:

a² + b² = c²

where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.

We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:

a + b + c = 4x + 3

Substituting the given side lengths, we get:

(x + 7) + (x - 7) + c = 4x + 3

Simplifying, we get:

2x + c = 4x + 3 - 7 + 7

2x + c = 4x + 3

Solving for c, we get:

c = 2x + 3

We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.

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Answer:

23.35 minutes

Step-by-step explanation:

Brendan finished in 22.5 minutes. Tobias finished 85 seconds after. Just add 85 seconds to 22.5 minutes. There are 100 second in 1 minute. Since Brendan is already at 22.5, there is only 0.5 left to get to 23. 0.5 in this case means 50 seconds. You do 85 - 50 = 35. Now, you are at 23 minutes. Add 35 seconds to that to get to 23.25 minutes.

Based on the given data, we can estimate that approximately 36 out of the next 100 books that come down the chute will be nonfiction.

To estimate the number of nonfiction books out of the next 100, we can use the ratio of nonfiction to the total number of books that came down the chute so far today.

The total number of books that came down the chute so far is:

41 (fiction) + 23 (nonfiction) = 64

The ratio of nonfiction books to the total number of books in library is:

[tex]23/64[/tex]

To estimate the number of nonfiction books out of the next 100, we can multiply the ratio by 100:

[tex](23/64)*100=35.9375[/tex]

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The answers to all parts are shown below.

The law of uninhibited decay is a first-order chemical reaction, which means that the rate of the reaction is proportional to the concentration of compound A.

The rate law can be written as:

rate = k[A]

where k is the rate constant and [A] is the concentration of compound A.

From the given data, we can use the following equation to determine the rate constant:

ln([A]t/[A]0) = -kt

where [A]t is the concentration of compound A at time t, [A]0 is the initial concentration of compound A, k is the rate constant, and t is the time.

Using the given data:

[A]t = 0.37 M

[A]0 = 0.40 M

t = 30 minutes = 0.5 hours

ln(0.37/0.40) = -k(0.5)

k = 0.0486 h⁻¹

(a) How much of compound A will remain after 2 hours?

Using the same equation and substituting the known values:

ln([A]t/[A]0) = -kt

ln([A]t/0.40) = -0.0486 x 2

[A]t/0.40 = e⁻(⁹⁷² /¹⁰⁰⁰⁰)

[A]t = 0.25 M

Therefore, after 2 hours, 0.25 M of compound A will remain.

(b) How long will it take until 0.10 M of compound A remains?

Substituting the known values into the equation again:

ln([A]t/[A]0) = -kt

ln(0.10/0.40) = -0.0486t

t = 4.26 hours

Therefore, it will take approximately 4.26 hours until 0.10 M of compound A remains.

(c) After 2 hours, the amount of compound A remaining will be 0.25 M.

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Step-by-step explanation:

(35-24.8) / 6.2  = z-score of  + 1.645  corresponding to   .9495  =

           ~ 95th percentile

In triangle ABC, side BC (a) is 15 cm, side AC (b) is 13.30 cm, and side AB (c) is 12.23 cm. Also angle A is 70°, B is 50°, and C is 60°

Using the Law of Sines and the fact that the sum of the angles in a triangle is 180 degrees.

The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. Using this, we can find the lengths of the other sides of triangle ABC.

Let's denote side AB as c, BC as a, side AC as b, and angle C as ∠C.

Using the Law of Sines, we have:

sin(∠A) / a = sin(∠B) / b

Substitute in the known values, we get:

sin(70°) / 15 = sin(50°) / b

Make b the subject of the formula:

b = (15 * sin(50°)) / sin(70°)

Using a calculator, we can find the value of b:

b = (15 * 0.766) / 0.9397

  = 12.23 cm

Therefore side AC = b = 12.23 cm

Now, to find side AB (c), we can use the Law of Sines again:

sin(∠B) / b = sin(∠C) / c

But ∠C is unknown. To find ∠C, we apply the sum of angle in a triangle rule

∠A + ∠B + ∠C = 180

70 + 50 + ∠C = 180

∠C = 180 - 70 - 50

∠C = 60°

Substitute the values in the Sine rule equation

sin(50°) / 12.233 = sin(60) / c

Make c the subject of the formula

c = (12.233 * sin(60)) / sin(50°)

c = (12.233 * sin(60°)) / sin(50°)

  = 13.30 cm

Therefore, the lengths of the sides of triangle ABC are:

Side AB = c = 12.23 cm

Side BC = a = 15 cm

Side AC = b = 13.30 cm

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The simplified expression of (3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) is (b) -a³b - 8ab²

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

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab)

Open the bracket

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = 3a³b - 4ab² + 5ab -4a³b - 4ab² - 5ab

Evaluate the like terms

So, we have

(3a³b-4ab² + 5ab) - (4a³b + 4ab² + 5ab) = -a³b - 8ab²

Hence, the simplified expression is (b) -a³b - 8ab²

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The animal that swims at a top speed of 0. 33 miles per minute would be the Dolphin .

To find the animal that swims at a top speed of 0. 33 miles per minute, you need to convert their top speeds in miles per hour to miles per minute.

For every 1 mile per hour, the equivalent in minutes is 0.0166667 miles per minute.

Speed of Swordfish is:

= 60 mph x 0.0166667

= 1 mile per minute

Speed of Tuna :

= 45 mph x 0.0166667

= 0. 75 miles per minute

Dolphin :

= 20 mph x 0.0166667

= 0. 33 miles a minute

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The median total of amount Franky earned is A = $81.67 per day.

Given data ,

For the first five days: $(100 + x) per day

For the next two days: $(175 + 2x) per day

For the final three days: $(75 + 2x) per day

Now , the average amount she earns is $80 per day

So , Average earnings = Total earnings / Total number of days

Average earnings = [(100 + x) * 5 + (175 + 2x) * 2 + (75 + 2x) * 3] / 10

Simplifying the equation:

80 = [500 + 5x + 350 + 4x + 225 + 6x] / 10

Multiplying both sides by 10:

800 = 1075 + 15x

Subtracting 1075 from both sides:

15x = -275

Dividing both sides by 15:

x = -18.33

For the first five days: $(100 - 18.33) = $81.67 per day

For the next two days: $(175 + 2*(-18.33)) = $138.34 per day

For the final three days: $(75 + 2*(-18.33)) = $38.34 per day

Arranging the earnings in ascending order: $38.34, $38.34, $38.34, $81.67, $81.67, $81.67, $81.67, $138.34, $138.34

The median is the middle value when the earnings are arranged in ascending order. In this case, the middle value is $81.67

Hence , the median is $81.67

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Answer: 19

Step-by-step explanation: The best way is to set this up with synthetic division (as the attached image).

Hope this helps!

Answer:

The answer is B:14

Step-by-step explanation:

When you simply multiply 5% by 14, you get 0.7. So you know that 5% of 14 is 7.

Answer:

4x = 100, so x = 25

The correct answer is C.

The number of weeks that the puppies weigh the same amount will be A. 6 weeks.

The equation that has no solution is A. 13 - 7x = -7x + 13.

The option determined from the graph is B. The ordered pair (25, 6) is a solution to y = x + 40 and y = 3x + 15.

Puppy A weighs 4 1/5 pounds at birth and gains 3/4 pound each week. Puppy B weighs 5 2/3pounds at birth and gains 1/2 pound each week.

After how many weeks will the puppies weigh the same amount will be calculated thus:

4 1/5 + 3/4x = 5 2/3 + 1/2x

4.2 + 0 75x = 5.67 + 0.5x

Collect the like terms

5.67 - 4.2 = 0.25x

Divide

x = 1.47 / 0.25

x = 6

Hence ,the number of weeks that the puppies weigh the same amount will be A. 6 weeks.

It should be noted that the equation that has no solution is A. 13 - 7x = -7x + 13. This is because the values gives 0 all through.

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The options 2nd and 3rd are the monomials with degree 2.

Given are the expressions we need to find the monomials with degree 2.

So,

The general form of a monomial with degree 2 is:

ax²

The highest exponent of a polynomial's variable(s) in any of its terms is referred to as the polynomial's degree in mathematics.

It controls the polynomial's behavior and complexity.

A non-negative integer is used to represent the degree.

And,

A monomial is a mathematical expression consisting of a single term. It is composed of a coefficient multiplied by one or more variables raised to non-negative integer exponents.

Here, the monomials can be 2x² and x²

Hence the options 2nd and 3rd are the monomials with degree 2.

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The probability is very high and the event is very likely to occur.

option B.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

If the probability of a rolling a number greater than 1 on a six sided cube die  is 5/6, it implies that the chances of obtaining a number greater than 1 is very high.

We will convert 5/6 to percentage to see the actual value of 5/6.

5/6 x 100%

= 83.33 %

So the value of this probability is very high and the event is very likely to occur.

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Diego is correct as the number of groups result to 6/5 or 1 1/5.

We have to find the number of groups of 5/6 in 1.

So, we need to perform the division as

= 1/ (5/6)

= 1 x 6/5

= 6/5

= 1 1/5

Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.

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The closest length to the arc from point C to point D is 16.34 ft (option c).

To find the length of the arc from point C to point D, we need to calculate the circumference of the circle and then find the fraction of the circumference represented by the central angle.

The circumference of a circle can be calculated using the formula:

Circumference = 2 × π × radius

Given the radius of 18 feet, the circumference is:

Circumference = 2 × π × 18 = 36π feet

To find the length of the arc, we need to find the fraction of the circumference represented by the central angle of 52°. The fraction is calculated by dividing the central angle by 360° and then multiplying it by the circumference.

Length of the arc = (Central angle / 360°) * Circumference

Length of the arc = (52° / 360°) × 36π

Length of the arc = (13/90) × 36π

Length of the arc = 468π / 90

Length of the arc ≈ 16.41 ft

Among the given options, the closest length to the arc from point C to point D is 16.34 ft (option c).

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Out of the following 30 samples, you may expect that about 12 will be portions of vanilla cake.

To solve this problem, use the concept of probability and make a prediction based on the past data.

In this case, out of the 10 pieces of cake that have been taken, 4 are vanilla and 6 are coconut.

Therefore, the probability of selecting a piece of vanilla cake from the tray is 4/10, or 2/5.

To predict how many of the next 30 samples will be pieces of vanilla cake, multiply the probability of selecting a vanilla cake by the total number of samples:

(2/5) x 30 = 12

So expect that out of the next 30 samples taken, approximately 12 of them will be pieces of vanilla cake.

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It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.

To solve this problem, we can use the formula:

time = amount of work / rate

In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:

time = 750 / 15 = 50 minutes

This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.

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We can use the formula for the volume of a pentagonal pyramid to solve this problem:

Volume = (1/3) × Base Area × Height

We know that the base area is 12 cm² and the volume is 48 cubic centimeters. We can substitute these values into the formula and solve for the height:

48 = (1/3) × 12 × Height

Multiplying both sides by 3 gives:

144 = 12 × Height

Dividing both sides by 12 gives:

Height = 12

Therefore, the height of the pentagonal pyramid is 12 centimeters.

The measure of angle BGF from the given parallel lines is 108°.

Given that, measure of angle BGF=4x+28 and the measure of angle EHD = 2x+32.

1) From the given figure, angle BGF and angle EHC are interior alternate angles.

Angle FHC and angle EGA are corresponding angles.

Angle FHC and angle EGA are exterior alternate angles.

2) angle BGF+angle EHD=180°

3) 4x+28+2x+32=180°

6x+60=180

6x=120

x=20

Angle BGF=4x+28=108 °

Angle EHD = 2x+32

= 112°

Angle FHD=180-112=68°

Angle EGB=180-108=72°

Therefore, the measure of angle BGF from the given parallel lines is 108°.

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The surface area of the prism is 248.88 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.

Base area = 61.94 cm²

height = 5cm

perimeter = 5 × 5 = 25cm

SA = 2 × 61.94 + 25 × 5

SA = 123.88+ 125

SA = 248.88 cm²

Therefore the surface area of the prism is 258.88 cm²

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Answer:

194.4

Step-by-step explanation:

V=l*w*h

V=12*4.5*3.6

V=194.4