Mike is training for a race. He wants his pace to be proportional throughout the race. The table relates the number of hours he ran and the distance that he traveled. Hours 0.5 1.0 1.5 2.0 Miles 3 6 8 12 Mile then graph these points (hours, miles) to determine whether or not his pace was proportional. Mike determined his pace was proportional because the graph passes through the origin. Which statement best describes his error? Multiple choice question. cross out A) The graph passes through the point (1, 1). cross out B) The graph does not pass through the origin. cross out C) The graph both passes through the origin and is a straight line. cross out D) While the graph does pass through the origin, it is not a straight line.

Answer:

The total number of employees the company have is;

Explanation:

Given that an international company has 29,200 employees in one country.

If this represents 31.7% of the company's employees.

let n represent the total number of employees the company have;

Solving for n;

Therefore, the total number of employees the company have is;

The formula to calculate the time taken is given to be:

The total time taken is going to be the sum of the time taken to cross the river and the time taken to go from the point on the opposite bank to the toll gate.

The

Given:

Let's graph the equation.

Apply the formula:

Where:

a = 6

b = 3

Thus, we have the following:

Subsitute -θ for θ to know thw axis of symmetry:

Now, solve for θ = 1 and -1:

Since sinθ is not equal to sin(-θ), the pole will be the point of symmetry.

To find the x-intercept, substitute 0 for θ:

Hence, the limacon will cross the x-axis on both sides at x = 6 and -6.

Since the addition is with the sine function, the limacon will face down.

Now, input different values for θ and solve for r.

We have:

When θ = pi/2:

When θ = pi:

When θ = 9pi/6:

Thus, we have the points:

Using the coordinates we have the graph:

- Tan²θ is the left side expression as the difference of two squares in trigonometric ratios.

What do trigonometric ratios represent?

(sec θ+1)(sec θ-1)= tan² θ

use ( a+ b ) ( a - b) = a² - b²

= 1² - sec²θ                                   { we know that 1 + tan²θ = sec²θ}

= 1 - sec²θ

= - tan²θ

     LHS = RHS

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Answer:

Explanation:

Here, we want to get the mean utilit bill over the period

Mathematically, that means we have to find the average of his utility bills in that period

To get this,we have to divide the sum of all these values by the count of these values (5)

Mathematically, we have this as:

The inequality is x > -3

The second choice is the correct answer.

The finished graph of g(x) = 2f(x - 1) would be as seen in red.

We were provided a graph of the function f(x).

g(x) = 2f is another function definition (x -1).

Now we must use the drawing tool(s) to create the proper graph of a function g(x) = 2f (x -1).

which can be discovered through transformation.

f(x) becomes f (x-1)

Then, f(x-1) becomes 2f (x-1)

f(x-1) shifts this same graph of f(x) by one unit to the right.

Whereas 2f(x-1) extends the graph of f(x-1) by a factor of 2. So we just need to double the y-coordinates of the points on the graph.

As a result, the finished graph of g(x) would be as seen in red.

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Answer:here x=-4

Step-by-step explanation:

3(-4)-3=-15

The x intercept is the value of x when y = 0

Looking at the equation,

2x + 3y = 12

If we substitute y = 0 into the equation, it becomes

2x + 3*0 = 12

2x + 0 = 12

2x = 12

x = 12/2

x = 6

Therefore, the statement is false

Given that Line a is parallel to Line b (Line a ║ Line b), the triangle that is similar to ΔJKH is 1. ΔMKN

Similar triangles are triangles that have congruent corresponding angles, and in which all three corresponding sides are proportional.

The given parameter is Line a is parallel to Line b, which gives: a║b

Two triangles are similar if they satisfy the following conditions:

According to alternate angles theorem, the angles ∠JHK in ΔJKH is congruent to the ∠KNM in triangle ΔMKN

Similarly, the angle ∠HJK in ΔJKH is congruent to the ∠KMN in ΔMKN

Therefore, ΔJKH is similar to ΔMKN by Angle-Angle, AA similarity postulate.

The correct option for the triangle similar to ΔJKH is option 1. ΔMKN

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The socially ideal dose of 40 flu vaccines may be determined by the external beneficial effect. While a $10 subsidy for each flu shot would bring the market equilibrium's result into line with the ideal situation for society.

In order to determine customer interest in and market demands for products that are currently in development, hypothetical scenario marketing uses product surveys and made-up scenarios. Utilizing hypothetical marketing can assist small business owners in allocating resources to product categories where customers have shown a need and desire.

The presented example is a positive externality situation since there is an external social benefit and the market equilibrium quantity is lower than the level of output that would be considered optimal for society because it ignores the external benefit. The subsidy is applied to either produce internalities or address externalities per unit.

At each level, there will be a $20 rightward shift in the marginal social benefit curve. With this external benefit effect in mind, 40 shots of the flu vaccine would be the most beneficial for society. The market equilibrium result would be identical to the socially ideal equilibrium with a $10 subsidy for each flu vaccine.

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Answer: Out of the given options, we need to pick a relationship that is proportional:

In general, an equation that represents a proportional relationship has the following form:

Therefore, the following is a proportional equation:

Option-(A)

Explanation:

Because there is a constant multiple or a coefficient, and it indeed matches the form of equations that are proportional.

Answer:

  (b)  {2, 4, 6}

Step-by-step explanation:

You want the range of the relation {(1, 2), (2, 4), (3, 2), (4, 6)}.

The range of a relation is the set of possible output values. When values are listed as ordered pairs, it is the set of second numbers of those pairs.

The list of second numbers is ...

  2, 4, 2, 6

When these are expressed as a set, duplicates are removed, and they are listed in order:

  {2, 4, 6} . . . . the range of the relation

Determine the unit price of 32 oz for $3.29.

Determine the unit price for 24 oz for $2.59.

The unit price of 32 oz for $3.29 is less. So the better buy round is 32 oz for $3.29.

We will solve as follows:

*We have the equations:

&

We solve then for the second equation [Either for A or B], that is:

Now, we replace in the first equation and solve for B:

Now, we replace the value of B in the second equation:

So, the investor has 80 shares on stock A and 120 shares on stock B.

Answer: It is 10000 times larger

The measure of the given polygon's angle is 2340°

Polygons are two-dimensional closed objects in geometrical mathematics where n number of line segments cross each other to generate n number of vertices. A triangle is a polygon with three sides, for instance.

In an n-sided polygon, there are n inner angles.

The total of all interior angle measurements in a polygon is always constant and is denoted by the notation "n" for the number of sides in the polygon.

the formula is ;

Sₙ = ( n - 2 ) 180°

Here in question n is given as 15

Thus Sₙ = ( n - 2 ) 180° becomes

Sₙ = ( 15 - 2) 180

13 × 180

= 2340 °

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Answer:

y = 1/3x + 7

Step-by-step explanation:

A line includes the points (9,10) and (6,9). What is its equation in point-slope form?

slope = change in rise/change in run

so:

slope = change in y/change in x

you are given two points in (x , y) format, points are: (9,10) and (6,9) [second in each pair are the y values]. Figure change in y and x:

y: 10 - 9 = 1

x: 9 - 6 = 3

so slope =y/x = 1/3

slope intercept form is: y = mx + b where m = slope. Substitute in value previously found for slope:

y = 1/3x + b

Now, you need to find y intercept, or b. Using one of the points given, we will use the first one (9,10), calculate for b:

y = 1/3x + b

10 = 1/3(9) + b

10 = 3 + b

subtract 3 from both sides:

10 - 3 = 3 + b - 3

b = 7

Put this into your equation: y = mx + b

y = 1/3x + 7

The graph that represents the proportional relationship between x and y with a unit rate of 4/5 is shown in the image below.

If the relationship between x and y is a proportional relationship, the equation that models the relationship between x and y can be expressed as y = mx. Here, the unit rate is represented by the value of  in the equation.

This means that, the graph that represents the proportional relationship between x and y would have a slope of the value of m. m, which is the slope of the line, is the ratio of the rose of the line to the run of the line.

Thus, where m = 4/5, the equation that represents the proportional relationship would be:

y = 4/5x.

Therefore, the graph below shows the proportional relationship between x and y which is represented by the equation, y = 4/5x.

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Answer:

I'm pretty sure it's 1800!!

In the equation y = 3x + 2, the expression f(x) would replace which part of the equation.

Answer: y will be replaced by the expression f(x).

Answer:

The scale factor is 5 / 2

Explanation:

The scale factor is the ratio of the side lengths of the bigger triangle to the smaller triangle.

The scale factor is also the ratio of the corresponding sides of the two traingles.

The ratio of MP to XZ is

Simplification gives

Hence, the scale factor is 5 /2 or 2.5.

Using the Pythagorean Theorem and implicit differentiation, it is found that the tip of the person's shadow is moving toward the post at a rate of 0.393 m/sec when the person is 4 m from the post.

The Pythagorean Theorem is a geometry axiom that relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, stating that the hypotenuse squared is the sum of the legs squared, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

In the context of this problem, we have that:

Hence the following relation between these variables is established:

d² = x² + y².

Applying implicit differentiation, the rate of change of the distance is given as follows:

[tex]d\frac{dd}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]

The height remains constant, hence:

[tex]\frac{dy}{dt} = 0[/tex]

The other parameters are given as follows:

Hence the distance at the desired instant is:

d² = 4² + 3.15²

d = sqrt(4² + 3.15²)

d = 5.091 m

The rate of change of the distance is found as follows:

5.091dd/dt = 4 x 0.5

dd/dt = 2/5.091

dd/dt = 0.393 m/sec.

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The equivalent expression to 8(t+8) is 8t+64 and the equivalent expression to 8t+8 is 4(2t+2) and 4t+8+4t.

The given expressions are 8(t+8) and 8t+8.

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Now, 8(t+8)

Using distributive property a(b+c)=ab+ac, simplify 8(t+8)

That is, 8t+64

Take common factor in 8t+8 is 4(2t+2) and 8t+8=4t+8+4t

Therefore, the equivalent expression to 8(t+8) is 8t+64 and the equivalent expression to 8t+8 is 4(2t+2) and 4t+8+4t.

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Answer: $19

Step-by-step explanation:

Since we want 30 copies, let x=30.

[tex]C(30)=0.15(30)+14.50=19[/tex]

She spends the cost of $0.46 if she purchases the items in the city where she lives.

The percentage is defined as a ratio expressed as a fraction of 100.

The given data  below as:

Cost of the shirt = $11.99

Cost of the shoes = $35.50

Cost of the belt = $6.75

Cost of the socks = $3.00

Total cost of the items = 11.99 + 35.50 + 6.75 + 3.00

Total cost of the items = $57.24

In the city she lives in, the sales tax rate is 7.15%.

Total cost of the items with tax of 7.15%

= 57.24 × 7.15/100 + 57.24 = 4.092 + 57.24 = $61.33

In another city, the sales tax rate is 6.35%

Total cost of the items with tax of 6.35%

= 57.24 × 6.35/100 + 57.24 = 3.633+ 57.24 = $60.87

Hence, she spends the cost of $0.46 if she purchases the items in the city where she lives.

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Answer:

1)D and 2)A

Step-by-step explanation:

1) D

When you dived B by 4 on both sides , you get A

2) A

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For the given probability distribution, the missing value is 5/17.

A probability distribution is a mathematical function used in probability theory and statistics that estimates the likelihood that various possible outcomes of an experiment will occur. In terms of its sample space and event probability, it is a mathematical description of a random phenomena.

For the given distribution,

Let the missing value be x

we know that sum of probabilities = 1

⇒ 0 + 0 + 7/17 + x + 5/17 = 1

⇒ 12 / 17 + x = 1

⇒ x = 1 - 12/17

⇒ x = 5 / 17

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