Add.
-1 + 2 = 1
- 6 + (-5)

Vic and Dan are 2, 897m apart.

It is important to note that the distance between Vic and Dan is the base of CN

Let's say the distance to Dan is x

The distance to Vic is y

Using cosine ratio, we have

cos α = opposite / adjacent

α = 72°

opposite = 553. 3cm

Adjacent = x

cos  72° = [tex]\frac{553. 3}{x}[/tex]

Cross multiply

[tex]cos 72[/tex] × [tex]x[/tex] = [tex]553. 3[/tex]

[tex]0. 3090x= 553. 3[/tex]

[tex]x = \frac{553. 3}{0. 3090}[/tex]

[tex]x = 1, 790. 61[/tex] m

The distance to Vic is y

Using the cosine ratio, we have

[tex]cos 60 = \frac{553. 3}{y}[/tex]

Cross multiply

[tex]0. 5y = 553. 3[/tex]

[tex]y = \frac{553. 3}{0. 5}[/tex]

[tex]y = 1,106. 6[/tex]m

To determine how far apart Vic and Dan, we use = x + y

= 1790. 61 + 1106. 6

= 2, 897. 21m

= 2, 897m

Thus, Vic and Dan are 2, 897m apart.

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∠5 ≅ ∠8 (vertically opposite angles)

Hence, ∠1 ≅ ∠8 by the transitive property.

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line e and f are parallel lines cut by the the transversal g.

∠1 ≅ ∠4(vertically opposite angles)

Hence,

∠4 ≅ ∠8(corresponding angles)

Since, ∠1 ≅ ∠4

Then, by substitution,

∠1 ≅ ∠8 (transitive property)

∠5 ≅ ∠8 (vertically opposite angles)

Therefore, ∠1 ≅ ∠8 by the transitive property.

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See below for the solution to each question

Yes, the graph is a function.

This is because all x values have different y values

This is the set of input values of the graph.

From the graph, we have

x = 0 to x = 17

Hence, the domain is [0, 17]

This is the set of output values of the graph.

From the graph, we have

y = 0 to y = 10

Hence, the range is [0, 10]

This is the maximum point on the graph.

From the graph, we have

Maximum = (12, 10)

This is the minimum point on the graph.

From the graph, we have

Minimum = (0, 0)

These are the intervals where the y values increase as x increase.

From the graph, we have

Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)

These are the intervals where the y values decrease as x increase.

From the graph, we have

Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)

These are the intervals where the y values remain unchanged as x changes.

From the graph, we have

Constant intervals = (5, 7)

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Answer:

240π cm³ (exact)

754 cm³ (approximate)

Step-by-step explanation:

I assume the shape of the cup is a cylinder. The height of the cylinder is 15 cm.

Think of a vertical rectangle that contains the vertical axes of the cylinder.

Two sides of the rectangle are diameters of the bases of the cylinder. The other two side are heights of the cylinder. The pencil is 17 cm long and is a diagonal of this rectangle. We can find the diameter of the base of the cylinder using the Pythagorean theorem.

In a rectangle that is 15 cm long, the diagonal measures 17 cm.

a² + b² = c²

15² + b² = 17²

b = 8

The diameter of the cup is 8 cm.

radius = 8 cm/2 = 4 cm

V = πr²h

V = π(4 cm)²(15 cm) = 240π cm³ (exact)

V = 754 cm³ (approximate)

The probability that of the questions studied, all three were the test questions selected by the professor is 0.05.

We can find the probability by dividing the total number of favorable events by the total number of events.

The total number of events is given by [tex]6C_{3}[/tex].

The total number of favorable events is given by [tex]3C_{3}[/tex].

The probability is given by = Favorable events/Total number of events

= [tex]\frac{3C_{3}}{6C_{3}}[/tex]

= [tex]\frac{1}{\frac{(6)(5)(4)}{(1)(2)(3)} }[/tex]

= [tex]\frac{1}{(5)(4) }[/tex]

= 0.05

The probability that all three questions are selected by the professor for the test is found to be 0.05.

Therefore, we have found that the probability that of the questions studied, all three were the test questions selected by the professor is 0.05.

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Disclaimer: The question was incomplete, the complete question is attached below.

Question: A professor gave her students six essay questions from which she will select three for a test. A student has time to study for only three of these six questions. What is the probability that, of the questions studied, all three were the test questions selected by the professor?

A $2.00 base fare charge, and per-mile, and per-minute rates related as follows; 3•x + 7•y = 6.5 and 7•x + 14•y = 14, give the distance traveled in the third ride as 4.5 miles

The base fare = $2.00

Let x represent the per-mile rate, and let y represent the per-minute rate, we have;

The cost of Ryan's first taxi ride = $8.50

Distance traveled in the first ride = 3.0 miles

Time taken during the first ride = 7 minutes

Therefore;

2 + 3•x + 7•y = 8.5

Which gives;

3•x + 7•y = 8.5 - 2 = 6.5

Distance traveled in the second ride = 7.0 miles

Duration of the second ride = 14 minutes

The second ride cost = $16.00

Therefore;

2 + 7•x + 14•y = 16

Which gives;

7•x + 14•y = 16 - 2 = 14

Solving the above simultaneous equations by multiplying equation (1) by 2 then subtracting the result from equation (2) gives;

(7•x + 14•y) - 2 × (3•x + 7•y) = 14 - 2×6.5 = 1

x = 1

3•x + 7•y = 6.5

7•y = 6.5 - 3•x

7•y = 6.5 - 3×1 = 3.5

y = 3.5/7 = 1/2 = 0.5

Duration of the third taxi ride = 10 minutes

Cost of the third ride = $13.50

Therefore;

2 + 1×a + 10×y = $13.50

Where a is the distance traveled during the third ride, we have;

2 + 1×a + 10×0.5 = $13.50

2 + a + 5 = 13.5

a = 13.5 - 2 - 7 = 4.5

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The inverse function of g(x) is:

[tex]f(x) = -\frac{3}{x + 4}[/tex]

So the correct option is D.

Here we have the function:

[tex]g(x) = -\frac{3}{x} - 4[/tex]

Remember that two functions f(x) and g(x) are inverses if:

[tex]f(g(x)) = x\\g(f(x)) = x[/tex]

Then we must have:

[tex]g(f(x)) = -\frac{3}{f(x)} - 4 = x[/tex]

Solving for f(x), we get:

[tex]-\frac{3}{f(x)} - 4 = x\\\\ \frac{3}{f(x)} +4 = -x[/tex]

[tex]\frac{3}{f(x)} = -x - 4\\\\3 = (-x - 4)*f(x)\\\\\frac{3}{-x - 4} = f(x) = -\frac{3}{x + 4}[/tex]

Then the correct option is D.

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The reasons for the statement about the angles include:

3. Definition of linear pair.

4. Definition of supplementary angles.

5. Substitution.

6. Subtraction property of equality.

7. Definition of congruence.

The angles are supplementary because the angles 1 and 2, 2 and 3 form a linear pair and thus because of the definition of linear pair, they are supplementary angles.

The sum of angles of 1 and 2, 2 and 3 is equal to 180 because these pair of angles are supplementary angles. Supplementary angles are those angles whose sum is 180 degrees.

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The volume of cone whose area of base is 8π[tex]mm^{2}[/tex] is 32π/3 [tex]mm^{3}[/tex].

Given area of base of the cone 8π[tex]mm^{2}[/tex].

We are required to find  the volume of the cone.

We know that base of a cone used to be in circle  so the area of base of cone is equal to π[tex]r^{2}[/tex].

Area=8π   (given)

π[tex]r^{2}[/tex]=8π

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

r=[tex]\sqrt{8}[/tex]

r=2[tex]\sqrt{2}[/tex]

Volume of cone=1/3*π[tex]r^{2} h[/tex]

=1/3*π[tex](2\sqrt{2} )^{2}[/tex]*4

=1/3*8*4π

=32π/3

(We are not required to put value of π so our answer will be 32π/3.)

Hence the volume of cone whose area of base is 8π is 32π/3.

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Question is incomplete as it should also include height of cone be 4 mm.

The construction that is performed based on the information given will be D. construct a right angle.

It should be noted that construction simply means the accurate drawing of shapes, angles, and the line in geometry.

In this case, the construction that is performed based on the information given will be to construct a right angle.

It should be noted that a right angle has an angle of 90°.

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[tex] \frac{2}{y} = \frac{4}{2} [/tex]

[tex]4 = 4y[/tex]

[tex] \frac{4}{4} = y[/tex]

[tex]1 = y[/tex]

Hope it helps you any confusions you may ask!

Let's see

Verified

Step 1. You need x isolated.
[tex]x < 13+7[/tex]

When you move a number from the left to right (and its addition or subtraction, the sign stays (< ≤ > and ≥ is signs).
x<20 or in words, x is less than 20, and cannot be 20.

Answer:

x < 20

Any number less than 20 is a solution

Step-by-step explanation:

x-7 < 13

The first step to solve this inequality is to add 7 to each side

x-7+7 < 13+7

x < 20

Any number less than 20 is a solution

Answer:

The estimated result is 680, which suggests the calculator is incorrect.

answer choices would have helped, hope this helps :)

There were 74 problems in the test.

Let the student got total number of problems in the test to be X.

Percentage of correct answer = 39 %

⇒ 61% of X were incorrect

⇒61/100 x X = 45

⇒61X = 45x100

⇒X = 4500/61

⇒X=73.77

After rounding off 73.77, we get 74.

Hence, we can say that there were total of 74 problems in the test.

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When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. So that the additional information required in the question is FG ≅ IJ.

When two or more given triangles are congruent, this implies that the measures of their corresponding angles and sides are equal. Thus the congruent relations of the triangles can be with respect to their angles or/ and sides.

The two given triangles in the question would be congruent with respect to the Side-Angle-Side (SAS) postulate if the condition below is true:

i.e FG ≅ IJ

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There is a 9/25 chance that two numbers will be added together such that their total exceeds their product.

The set of positive numbers are:

{1,2,3,4,5}

We have to independently select two numbers from these sets.

We are trying to determine the likelihood that the sum is larger than the product of the integers.

When one of the chosen numbers is 1, the total will always be greater than the product because:

1*1=1 & 1+1=2

1*2=2 & 1+2=3

1*3=3 & 1+3=4

1*4=4 & 1+4=5

1*5=5 & 1+5=6

and so on.

If we select 2 as both numbers then,

2*2=4 & 2+2=4

Here sum and the product are equal.

If not, the product will be bigger than the sum.

Now, the first stage is to evaluate the total number of two combinations that are feasible:

We have 5 alternatives for the first number and 5 alternatives for the second number.

The product of the number of possibilities in each scenario yields the total number of combinations:

C= 5*5=25

The following combinations have a sum that is greater than the product :

1 and 1

1 and 2

1 and 3

1 and 4

1 and 5

2 and 1

3 and 1

4 and 1

5 and 1

So, we get 9 combinations.

So, Probability,p=9/25

Therefore it is concluded that the probability is 9/25.

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Answer:

#3

Step-by-step explanation:

To create a number line to represent x<= 0, draw a solid circle at 0 (because 0 is included), then draw an arrow extending to the left (because it's less than or equal to).

The perimeter of the quadrilateral illustrated is 30cm.

The information is incomplete. Therefore, an overview will be given. It should be noted ha perimeter simply means the addition of the sides given.

Let's assume that that we've a rectangle with length and width of 10 and 5cm.

The perimeter will be:

= 2(l + w)

= 2(10 + 5)

= 30cm

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Using proportions, it is found that their bill before adding the tip was of $27.48.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

They paid a 20.2% tip, hence 120.2% = 1.202 of the price x is equals to $33.03, hence the bill before the tip is found as follows:

1.202x = 33.03

x = 33.03/1.202

x = $27.48.

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Answer:

Step-by-step explanation:

Angle M corresponds to angle M' and

Side N'O' is the image of side NO

The vertices of each triangle must have a one-to-one correspondence. This phrase means that the measure of each side and angle of each triangle is equal to the side or angle of the other triangle.

Here it is given that Triangle MNO maps to triangle M'N'O'

We need to find that Angle M corresponds to which angle and the image of side NO

By one to one correspondence we get that

Angle M corresponds to angle M' and

Side N'O' is the image of side NO

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Answer:

555 m

Step-by-step explanation:

Because the model should have identical proportions to the real-life tower, the ratio between the height and shadow length of both diagrams should be the same.

Height (model)             Height (real)
-------------------------  =  ------------------------
Shadow (model)         Shadow (real)

Math:

 0.9 meters                   x
--------------------  =  ----------------------               <----- Ratio
 0.2 meters           123.3 meters

4.5 = x / 123.3 meters                                  <----- Divide 0.2 from 0.9

555 meters = x                                            <----- Multiply both sides by 123.3

The function g(x) is a translation of 3 units to the right and a vertical dilation by scale factor k = 2 of f(x), the graphs of both functions can be seen in the image at the end.

We know that g(x) is a transformation of the parent function f(x) = √x, such that:

g(x) = 2*f(x - 3)

g(x) = 2*√(x - 3)

Then we can see that g(x) is a translation of 3 units to the right followed by a vertical dilation of scale factor 2 of the parent function f(x).

So to graph g(x) you first need to move the whole graph of f(x) 3 units to the right, and then apply a dilation vertically.

The graph of g(x) and f(x) can be seen in the image below:

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Answer:

12/13

Step-by-step explanation:

     [tex]\sf Cos \ x = \dfrac{adjacent \ side \ to \ \angle x}{hypotenuse}\\\\[/tex]

              [tex]\sf = \dfrac{XY}{ZX}\\\\=\dfrac{36}{39}\\\\=\dfrac{36 \div3}{39 \div 3}\\\\=\dfrac{12}{13}[/tex]

your anwer would be 12/13 love

The value of positive integers in the set are 16.

According to the statement

we have given that the there is a set of numbers from 1 to n and we have to find that the how many integers in this set. and there is one condition that the numbers in the set are less than or equal to 24.

So, For this purpose,

Since [tex]$1 + 2 + \cdots + n = \frac{n(n+1)}{2}$[/tex]

the condition is equivalent to having an integer value for [tex]$\frac{n!} {\frac{n(n+1)}{2}}$.[/tex]

This reduces, when [tex]$n\ge 1$[/tex], to having an integer value for [tex]$\frac{2(n-1)!}{n+1}$[/tex]

This fraction is an integer unless n+1 is an odd prime. There are 8 odd primes less than or equal to 24,

so there are 24-8 = 16.

So, The value of positive integers in the set are 16.

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[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]=[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

[tex]\sqrt[3]{125x^{10}y^{13} } +\sqrt[3]{27x^{10}y^{13} }[/tex]

Therefore,

125 = 5³

27 = 3³

Hence,

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} }[/tex]

Hence,

Both cube root are the same now,

Therefore, we have to add them together.

[tex]5\sqrt[3]{x^{10} y^{13} } +3\sqrt[3]{x^{10}y^{13} } = 8\sqrt[3]{x^{10}y^{13} }[/tex]

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The graph depicts that at the end of the snowstorm, there was 5 inches of snow left. See the attached graph.

It is not be noted that the total amount of hours which the snow fell is:

2 + 9 = 11 hours.

Although the graph depicts a peak of 14 hours, recall that there were three hours when the snow didn't fall.

While the maximum depth of the snow was 11 inches.

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Answer:

Step-by-step explanation:

Let the fraction be x/y.

According to question we have the following equations.

The denominator of a fraction exceeds numerator by 3:

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

Change the fraction as below and solve for y:

Find the value of x using the first equation:

The fraction is:

Answer:

Original fraction = ⁴/₇

Step-by-step explanation:

Numerator:  top of the fraction

Denominator: bottom of a fraction

Let x be the original numerator.

If the denominator of a fraction exceeds the numerator by 3:

[tex]\implies \dfrac{x}{x+3}[/tex]

If the numerator is doubled and the denominator is increased by 14, then fraction becomes 2/3rd of the original fraction:

[tex]\implies \dfrac{2x}{x+3+14}=\dfrac{2}{3}\left(\dfrac{x}{x+3}\right)[/tex]

[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3(x+3)}[/tex]

[tex]\implies \dfrac{2x}{x+17}=\dfrac{2x}{3x+9}[/tex]

Cross multiply:

[tex]\implies 2x(3x+9)=2x(x+17)[/tex]

Divide both sides by 2x:

[tex]\implies 3x+9=x+17[/tex]

Subtract x from both sides:

[tex]\implies 2x+9=17[/tex]

Subtract 9 from both sides:

[tex]\implies 2x=8[/tex]

Divide both sides by 2:

[tex]\implies x=4[/tex]

Substitute the found value of x into the original fraction:

[tex]\implies \dfrac{4}{4+3}=\dfrac{4}{7}[/tex]

Therefore, the original fraction is ⁴/₇.