Question 3
Suppose you take a trip that covers 147.4 km and takes 8.6 hours.
What is your average speed (km/h)?
Question 4
1 pts
1 pts

Answer:

  7.7 km

Step-by-step explanation:

This question is asking you to find the third side of a triangle in which two sides and an angle not between them are given. The law of sines provides the necessary relationships.

The Law of Sines tells you that triangle side lengths are proportional to the sine of the opposite angle. For this triangle TPJ, the relation is ...

  t/sin(T) = p/sin(P) = j/sin(J)

We are given T=68°, p=5.2 km, t=7.5 km, and we are asked to find the length of j, the TP distance.

We know the sum of angles in a triangle is 180°, and the sine of an angle is equal to the sine of its supplement. This lets us fill in the Law of Sines equation like this:

  7.5/sin(68°) = 5.2/sin(P) = j/sin(68°+P) . . . . . solve for j

This can be solved in two steps. First, we find angle P, then we use that to find length j.

  sin(P) = 5.2/7.5 × sin(68°) ≈ 0.642847

  P = arcsin(0.642847) ≈ 40.0045°

Now, we can find j:

  j = 7.5 × sin(68° +40.0045°)/sin(68°) ≈ 7.693 . . . km

The distance from the tower to the plane is about 7.7 km.

__

Additional comment

We have used T, P, and J to refer to the vertices at the tower, plane, and jet.

The triangle can also be solved using the Law of Cosines. In that case, the missing side will be the solution to a quadratic equation with irrational coefficients.

The probability of correctly rejecting the null hypothesis when the null hypothesis is false is the power

From the question, we have the following highlights

The statement that represents the probability of the above highlights is power

Hence, the statement that completes the blank is power

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Answer:

C

Step-by-step explanation:

Sin represents opposite/hypotenuse. Thus, when A is the reference angle, 21 is the measure of the opposite side (CB) and 29 is the measure of the hypotenuse (AB).

Cos represents adjacent/hypotenuse. Therefore, when A is the reference angle, 20 is the measure of the adjacent side (AC) and 29 is the measure of the hypotenuse (AB).

Answer:

51

Step-by-step explanation:

Translate the problem into an equation and solve the equation.

(x - 9)/6 = 7

x - 9 = 42

x = 51

Answer: 51

Answer:

51

Step-by-step explanation:

Create an equation.

[tex]\frac{(x-9)}{6} = 7[/tex]

Multiply 6 to both sides.

x-9 = 42

Add 9 to both sides.

x=51

To check if this is correct follow the steps given in the question.

51-9=42

42÷6=7

It is correct.

Hope this helps!

There are 12 motorcycles in a company.

According to the statement

The ratio of cars, trucks, and motorcycles is 4:3:2.

The total number of cars and trucks is 42.

then

4x + 3x =42

7x = 42

x = 6.

now put these values in the ratio of vehicles.

Number of cars = 4*6 = 24

Number of truck = 3*6 = 18

Number of motorcycle  = 2*6 = 12

So, There are 12 motorcycles in a company.

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Answer: 5

Step-by-step explanation:

We have the equation of the line is of the form [tex]y=-\frac{1}{6}x+b[/tex].

Substituting in the coordinates (12,3), we get that:

[tex]3=-\frac{1}{6}(12)+b\\\\3=-2+b\\\\b=5[/tex]

Answer:

Option A

Step-by-step explanation:

  In a arithmetic sequence, difference between any two consecutive term is constant.

  a₁ = 9  & d = 7

         t₁ = 9

         t₂ = a₁ + d

             = 9 + 7

             = 16

         t₃ = t₂ + d = 16+ 7

            = 23

        t₄ = t₃ + d

            = 23 + 7

            = 30

        t₅ = t₄ + d

           = 30 + 7

           = 37

9,16,23,30,37,.......

The polynomial which can be used to support the idea that the set of polynomials is closed under multiplication is: A. (5x - 1)(3x² + 4x).

A polynomial can be defined as a mathematical expression which comprises intermediates (variables), constants, and whole number exponents with different numerical value, that are typically combined by using mathematical operations such as:

In Mathematics, a set is considered as closed under a multiplication operation, if the multiplication performed on two (2) elements of the set produces an element of the same set.

Note: The exponents of the variables are added when multiplying polynomials in accordance to the rules of exponents.

For option A, we have:

P = (5x - 1)(3x² + 4x)

P = 15x³ - 3x² + 20x² - 4x

P = 15x³ - 23x² - 4x.

For option B, we have:

P = (9x⁻³ - 5)(3x - 17)

P = 27x⁻² - 15x - 153x⁻³ + 85.

In conclusion, we can infer and logically deduce that the polynomial (5x - 1)(3x² + 4x) can be used to support the idea that the set of polynomials is closed under multiplication.

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The equation of parabola from graph is y = a(x + 1)² - 4.

According to the statement

we have to determine the parabola equation from the graphical representation.

So,

For this purpose we know that

Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

The general equation of parabola is y = a(x-h)2 + k

And The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

So, The equation of parabola from graph is y = a(x + 1)² - 4.

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Disclaimer: This question was incomplete. Please find the full content below.

Question:

Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.

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In Mathematics, two geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.

Since we know that rigid motions preserve both the side length and angle measure, this ultimately implies that congruent segments have the same (equal) length.

Thus, line segment UV ≅ line segment XY i.e UV = XY and as such the side lengths are as follows:

SU = VX = 43 feet.

For the congruent angles, we have:

<J ≅ <K i.e m<J = m<K

m<S = m<V = 38°.

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The cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is d(t) = 6cos([tex]\pi[/tex]t).

As long as its length is constant, a pendulum completes each swing (or oscillation) in precisely the same amount of time. Any particular pendulum oscillates for a fixed amount of time.

Calculation for the cosine function-

The given function is: cosine function, d = acos(bt).

As, the pendulum takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right.

The total time 't' by the pendulum is 2 sec.

Calculate the angular speed of the pendulum by-

ω = 2[tex]\pi[/tex]f

   = 2[tex]\pi[/tex]×(1/2)

ω = [tex]\pi[/tex] which is 'b' value of the given function.

As given, the distance of the pendulum from the centre is half of the total distance.

a = 12/2

a = 6

Substitute the obtained values in the cosine function, d = acos(bt),

d(t) = 6cos([tex]\pi[/tex]t)

Therefore, the cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds) is  d(t) = 6cos([tex]\pi[/tex]t).

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The complete question is -

Starting at its rightmost position, it takes 1 second for the pendulum of a grandfather clock to swing a horizontal distance of 12 inches from right to left, and 1 second for the pendulum to swing back from left to right. Write a cosine function, d = acos(bt), to model the distance, d, of the pendulum from the center (in inches) as a function of time t (in seconds).

Answer:

a=6

The period is 2 seconds.

b=pi

t=0.5

d=4.243

Step-by-step explanation:

He travels 620miles at the same speed.

Given that joe travels 434 miles in 7 hours.

An object's speed is determined by how quickly it moves. It is the distance a body travels in one unit of time.

Firstly, we will find the speed when the distance is 434 miles and the time is 7 hours by using the formula

Speed=Distance/Time

Substitute the values in the formula, we get

Speed=434miles/7 hours

Speed=62 miles/hour

Now, we will find the distance when time is 10 hours, we get

62=distance/10

Multiply both sides by 10, and we get

62×10=(distance/10)×10

620miles=distance.

Hence, in 10 hours at the same speed, he travels when joe travels 434 miles in 7 hours is 620miles.

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The best explanation for the formula is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

The area of a sector of a circle equals measure of the central angle subtended by the sector over the angle measure of a full circle multiplied by the area of the circle.

A full circle has an angle measure of 360 degrees.

The area of a circle = pi(r²).

Therefore, the formula for the shaded sector of a circle would be represented by the formula: ∅/360 × πr².

Here, we have:

Central angle (∅) = measure of angle ZYX

Measure of full circle = 360 degrees

Area of a circle = πr². (area formula for the circle that contains the sector)

Therefore, the statement that best explains the formula, (m∠ZYX)/360 × πr², used for finding the shaded sector in the circle is: A. The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector.

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Answer:

its the first answer "The central angle measure of the sector divided by the total angle measure of a circle multiplied by the area of the circle will yield the area of the sector."

Step-by-step explanation: i got it right because im smort

Answer:

No solution

Step-by-step explanation:

The equations:

2x – 3y = 10 → equ(1)

–4x + 6y = 20 → equ(2)

Using elimination method, and solving with y, we have:

3( –4x + 6y = 20) → equ(3)

6( 2x – 3y = 10) → equ(4)

Opening the bracket, we have:

–12x + 18y = 60

+12x – 18y = 60

From the above, we can see that both x and y are now eliminated, thereby giving us: 0 = 120 which makes no sense to me as it looks incorrect.

Therefore, there is no solution to the given equation.

I hope this helps

Answer:

One

Step-by-step explanation:

The best that describes the type of association shown in the scatter plot is positive linear association.

Given the scatter plot below represents the amount of dog food a brand recommends based on the weight of the dog.

Amount of Food per day cups:

20

40

60

No

We are required to find the type of association shown in the given scatter plot.

It is a positive linear association. The slope is positive so the linear association is also positive and linear mean generally in a line not on a curve like a nonlinear association.

Hence the given graph is of positive linear association.

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Answer:

480

Step-by-step explanation:

First, lets solve for the area of the 3 rectangles in the prism

One can be found by doing 17*9. The other, 8*9, the last 15*9

Next, lets solve for the 2 triangles. This is found with...

1/2(8)(15). This turns out to be 60, and we multiply that by 2 since there are 2 of those triangles.

Add everything up:

72+153+135+120 = 480

Answer:

100

Step-by-step explanation:

Lets first find the area of the greater square:

[tex]8*14=112[/tex]

And now the area of the cut inside of the square:

[tex]3*4=12[/tex]

Now subtract the area cut from the area of the greater square:

[tex]112-12=100[/tex]

Answer: (0, 3)

Step-by-step explanation:

     The y-intercept of the line is where the line intercepts the y-axis. In other words, the coordinate value of the line when x is 0.

Answer: (3, 0)

Step-by-step explanation:

y-intercept = y=a number and x=0

So, y=3, x=0.

(3, 0)

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

This question is incomplete, the complete question is:

Which of the following is equivalent to 5 sqrt 13³ ?.

A) 13^2.

B)13^15.

C)13^(5/3).

D)13^(3/5)

Given the expression; 5 sqrt 13³

This can be represented as; ⁵√13³

To convert from radical form to exponential form, we use apply the radical rule;

[tex]\sqrt[n]{a^m} = a^{m/n}[/tex]

Hence,

[tex]\sqrt[5]{13^3} = 13^{3/5}[/tex]

The exponential form of ⁵√13³ is [tex]13^{3/5}[/tex].

Hence, option D) is the correct answer.

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Answer:

197.82 m^2

Step-by-step explanation:

The area of a circle is

a = πr^2  The radius is half of the diameter.  They give us the diameter so we need to talk half of that number to use for the diameter.  The diameter is the length from the center of the circle to the edge of the circle.

We will find the area of the big circle and  subtract out the area of the little circle to bind the blue area.

Outer circle

a = πr^2

a = 3.14(12)^2

a = 3.14(144)

a = 452.16

Inner Circle:

a = πr^2

a = 3.14(9)^2

a = 3.14(81)

a =254.34

Lastly, subtract 254.34 from 452.16 to get  197.82

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

We are told that Jeri finds a pile of money with at least $200.

Now, let x be  the additional amount over the  original amount of $200.

The greater side of the  inequality will be expressed as;

Original  pile  =  (200 + x)

After  she gives away $80 and as such she has;  (120 + x)

And  she gives (1/3)  of  this away  which means she will have;

=  (1/3) (120 + x)

Thus, she  must  have  (2/3)  of this left

=  (2/3)(120 + x) = amount in her right pocket

The lesser  side of the inequality is expressed as;

(x + 200)  -  200   =   x

Thus, we now have  that;

2[120 + x ]/3  >  x

240 + 2x  >  3x

240 > 3x - 2x

240 > x

x < 240

Thus, we can conclude that the original  amount could be on the interval   (200, 440)

The possible values of the number of dollars in the original pile of money is on the interval (200, 440)

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Answer:

Step-by-step explanation:

The time it will take before your investment is worth $6000 = 7 years

The amount of money invested per month = $150

Therefore the amount principally invested yearly;

= 12 × 150 = $1,800

Simple interest = $6000

Rate = 4%

Time = ?

Using the formula for Simple interest (SI)= P×T×R/100

Make T the subject of formula,

T = SI × 100/P×R

T = $6000×100/1800×4

T = 600000/7200

T= 83 months/ 12 = 7 years

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The height of the center of the frame has to be 15ft.

Slope of the tarp is given as 2/5

The height is said to be 10 feet

The width is given as 25

25/2 = 12.5

AB/BC = 2/5

AB/12.5 = 2/5

cross multiply to find AB

5AB = 25

AB = 5

The height = 10 feet + 5 feet

= 15 feet

Hence the center of the frame has to be 15 feet.

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The amount of material needed for the entire kite is 48 square inches

The given parameters:

KI =6 inches

ET = 8 inches

KT=10 inches

Area of ΔKIT = 17 square inches

Start by calculating the area of the bottom triangle using:

A = 0.5 * Base * Height

This gives

A = 0.5 * 10 * 6

Evaluate

A = 30

The amount of material is

A = 30 + 17

A = 47

Hence, 48 square inches of material is used for the entire kite,  quadrilateral KITE

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The value of the car in 2014 is 154709

The given parameters are:

Initial, a = 599,99

Rate, r = 7%

The value of the car in t years is

Value = a * (1 + r)^t

This gives

Value = 59999 * (1 + 7%)^t

2014 is 17 years from 1997.

So, we have:

Value = 59999 * (1 + 7%)^14

Evaluate

Value = 154709

Hence, the value of the car in 2014 is 154709

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Answer:

$8 each scarf

Explanation:

Let the selling price for each scarf be x,

Formula:

unit amount(selling price - cost price) = total profit

Stepwise:

100(x - 3) = 500

100(x) - 100(3) = 500

100x - 300 = 500

100x = 500 + 300

100x = 800

x = 8

The correct option is B. Reread the directions for each section.

If you have time left after completing the test don't reread the directions for each section.

In order to find the various problem kinds and their point values during the test preview, you must read the complete test. Mark the questions that you can answer quickly and easily.

The benefits of previewing the test are-

Therefore, resolve each issue by re-entering the solution into the equation or performing the opposing operation needed to provide the appropriate response. Do not leave the testing room until the bell has rung or after you have gone over each problem twice.

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The complete question is-

All of the following are suggestions of things to do if you have time left after completing the test except

A. Look at your answer sheet to make sure its filled properly

B. Reread the directions for each section

C. Return to the questioms you were unsure of

D. Make sure your answers correspond to the correct questions

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

Transformation is the movement of a point from its initial location to a new location. Types of transformation are translation, reflection, rotation and dilation.

Figure ABCD was translated 2 units to the right so as to obtain figure A'B'C'D'

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