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Divide and give the answer in scientific notation.
8.4 x 10^7
________ 3 x 10^3


A) 5.4 x 10-4
B) 5.4 x 1021
C) 2.8 x 10-4
D) 2.8 x 104

The correct dependent variable in this experiment is the Length of wax after 10 minutes.

In the context of an experiment, the dependent variable is the variable that is being measured or tested in the experiment. It is the outcome that the experimenters are interested in observing to determine the effect of the independent variable.

 In this case, the students are investigating the thermal conductivity of copper and steel wires by observing how much wax melts over a fixed period of time when the wires are heated. The independent variable is the type of wire used (copper or steel), as this is what the students are changing to see its effect on the dependent variable.

The dependent variable is the length of wax remaining after 10 minutes because this measurement is expected to change based on the thermal conductivity of the wire. The better the thermal conductor, the more heat will be transferred along the wire, and the more wax will melt. Since the students are measuring how much wax has melted (by subtracting the length of wax after 10 minutes from the original length), this is the dependent variable.

The original length of wire and the original length of wax are control variables; they are kept constant to ensure that any differences in the dependent variable are due to the independent variable (the type of wire) and not due to other factors. The thermal conductivity of the wire is a property being indirectly measured through the observation of the dependent variable. It is not directly measured and thus is not the dependent variable.

Answer

39.8°

Explanation

To solve this we can use the trigonometric ratio tangent.

tan x = opposite / adjacent

           = 10/12

           = 0.8333...

x = tan⁻¹(0.8333..)

  = 39.8°

The best approximation for the measure of angle XYZ in the given triangle is 39.8 degrees.

To solve this we can use the trigonometric ratio tangent.

tan x = opposite side / adjacent side

We have given the,

Opposite side=10in

Adjacent side=12in

use this value in the gven formula

Therefore we get,

                tanx    = 10/12

                tanx  = 0.8333...

x = tan⁻¹(0.8333..)

x  = 39.8°

Therefore, The best approximation for the measure of angle XYZ is 39.8 degrees.

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Let

x----------> charge per hour to rent a jet sky in dollars

y----------> the total cost to rent a jet sky in dollars

we know that

First Jet Sky Company

[tex]y=24.00+2.25x[/tex] ---------> equation [tex]1[/tex]

Second Jet Sky Company

[tex]y=23.00+2.50x[/tex] ---------> equation [tex]2[/tex]

we know that

To find the number of hours for which the costs are the same

equate equation [tex]1[/tex] and equation [tex]2[/tex]

The intersection both graphs is the solution of the problem

using a graph tool

see the attached figure  

the intersection point is [tex](4,33)[/tex]

That means

For [tex]x=4\ hours[/tex]

the cost of the rent is [tex]y=\$33[/tex] in both companies

therefore

the answer is

[tex]4\ hours[/tex]

For 4 hours of booking, the charges paid to both the companies should be same. And the charge will be $ 30.

Let x be the number of hours of booking per jet ski.

First company charges $24.00 plus $2.25 per hour to rent a jet ski.

So, the total cost paid for x hours to the first company will be,

[tex]C_1=24+2.25x[/tex]

Second company charges a fee of $23.00 plus $2.50 per hour to rent the same jet ski.

So, the total cost paid for x hours to the second company will be,

[tex]C_2=23+2.5x[/tex]

Now, the charge paid to both the companies should be same. For this condition, the number of hours of booking per jet ski should be,

[tex]C_1=C_2\\24+2.25x=23+2.5x\\1=0.25x\\x=4[/tex]

Therefore, for 4 hours of booking, the charges paid to both the companies should be same. And the charge will be,

[tex]24+2.25\times4=\$33[/tex].

For visuals, refer the attached graph.

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The equation relating the total cost with the number of hours will be c = 2.25h + 5.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have North parking garage where it costs $5 to bring your car into the garage plus $2.25 for every hour the car is parked.

Assume that [h] represents the number of hours the car was parked and [c] represents the total cost. Then, we can write the equation relating the total cost with the number of hours will be -

c = 2.25h + 5

Therefore, the equation relating the total cost with the number of hours will be c = 2.25h + 5.

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[The complete question is -

At the North parking garage it costs $5 to bring your car into the garage plus $2.25 for every hour the car is parked. If h, represents the number of hours the car was parked and c, represents the total cost, which equation would model this situation?]

Answer:

P represents the population in year 0

Step-by-step explanation:

Answer:

(C)

Step-by-step explanation:

It is given that a right triangle, ACB which is right angled at C has BC = 24 inches, and AB = 25 inches.

We know that m∠C=90°,

Using the trigonometry in ΔACB, we have

[tex]sinB=\frac{AC}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinB=\frac{24}{25}[/tex]

⇒[tex]B=sin^{-1}(0.96)[/tex]

⇒[tex]B=73.7^{\circ}[/tex]

Also, [tex]sinA=\frac{CB}{AB}[/tex]

Substituting the given values, we get

⇒[tex]sinA=\frac{7}{25}[/tex]

⇒[tex]A=sin^{-1}(0.28)[/tex]

⇒[tex]A=16.3^{\circ}[/tex]

Therefore, the measure of the angles in triangle ABC are  m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°.

Thus, option C is correct.

Answer:

Answer B is correct

Answer: positive

Step-by-step explanation:

The slope of a line is given by:-

[tex]m=\dfrac{\text{rise}}{\text{run}}[/tex]

From the given picture, it can be seen that the rise in the line l is positive since the change in the y coordinates increases as we from left to right.

Similarly we can see that  the run in the line l is positive since the change in the x coordinates increases as we from left to right.

By using above formula, the slope of line m is positive.

Answer:

A. p=6.25h

because

6.25 (2) = p 12.50

6.25 (4) = p 25.00

6.25 (6) = p 37.50

6.25 (8) = p 50.00

Final answer:

After solving the original equation 2/3(6x+12)=-24, we find x = -8. Comparing this solution with the provided equations, the ones that have the same value for x are 9x+18=-24, 18x+36/2=-24, and x=-8.

Explanation:

To find which equations have the same value for x as 2/3(6x+12)=-24, we must first solve the original equation to find the value of x it yields:

2/3(6x+12) = -24
Multiply both sides by 3/2 to eliminate the fraction:
6x + 12 = -24 * (3/2)
6x + 12 = -36
Subtract 12 from both sides:
6x = -48
Divide by 6:
x = -8

Now we will compare this solution with the other equations:

Therefore, the equations that have the same value of x as the original equation are 9x+18=-24, 18x+36/2=-24, and x=-8.

The number will be greater than 54 such that a negative one-sixth of a number is less than -9.

A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.

A mathematical phrase in which the sides are not equal is referred to as being unequal.

Inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.

Let's suppose that number is x

Then,

negative one-sixth of x

-(1/6)x is less than -9

-(1/6)x < -9

-x < -54

Multiplying by - will change the sign of inequality

So,

x > 54

Hence "The number will be greater than 54 such that a negative one-sixth of a number is less than -9".

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Assuming there are 4 walls

6/4 = 1.5 rolls per wall

Answer:

A

Step-by-step explanation:

The average rate of change of the function will be -93.75.

It is the average amount by which the function changed per unit throughout that time period. It is calculated using the slope of the line linking the interval's ends on the graph of the function.

Given that the interval from x = 0 to x = 2 and the function is [tex]f(x)=250(0.5)^x[/tex].

Calculate the value of the function at x = 0 and x = 2

[tex]f(x)=250(0.5)^x[/tex].

[tex]f(0)=250(0.5)^0=250\\f(0)=250(0.5)^2=62.5[/tex].

The average rate of change will be calculated as,

Rate of change = ( 62.5 - 250 ) ( 2 - 0)

Rate of change = -93.75

Therefore, the average rate of change of the function will be -93.75.

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Answer:

B. -6

Step-by-step explanation:

There is a mistake in the question. It would have to say:

Your football team gained four yards on first down and two yards on second down during its last possession

So, your team gained 4 + 2 = 6 yards.

Calling x, the additive inverse of 6, the following equation must be satisfied:

6 + x = 0

x = 0 - 6

x = -6

Triangle is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

The other angles in the isosceles triangle are 40°.

Option D is the correct answer

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

Isosceles triangle:

One angle = 100°

We know that,

In an isosceles triangle, there are two equal sides and two equal angles opposite to the equal sides.

The sum of the three angles in the isosceles triangle is 180.

We already have,

One angle = 100°

The other two should be equal.

The sum should give us 180°.

Now,

40 + 40 = 80

100 + 80 = 180°

Thus,

The other angles in the isosceles triangle are 40°.

Option D is the correct answer

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the answer would be b. C=(2,0), A=(0,1), T=(1,4)

all x's move 2 to the right and no change in y

Solution: If a shape is being translated neither it's shape nor size changes.When we translate a shape we just move a shape or geometrical figure by certain distance either horizontally or vertically or both horizontally and vertically.

Coordinates of Triangle CAT is →C(0,0), and A(-2,1), and T(-1,4).

In option (a) vertices C has not been translated , but A and T are translated.Which is Untrue because we have to move all the vertices by same value. But x and y can have different value.

In option (b) all the coordinates C,A,and T is being translated along→ x by 2 units , horizontally right, but not translated in vertical direction.  

C(0,0)⇒C(0+2,0+0)→C(2,0)

A(-2,1)⇒C(-2+2,1+0)→C(0,1)

T(-1,4)⇒C(-1+2,4+0)→C(1,4)

In option C, Coordinates of A and B are changed but not of C, So in this case translation can't happen.

In option D , C is being translated 2 units horizontally left ,  but amount of translation in A and T are different.

So , Option (b) is true.

The measure of an interior angle of the regular polygon is 156 degrees and the polygon has 15 sides.

In a regular polygon, the measure of an exterior angle is equal to 360 degrees divided by the number of sides of the polygon. In this case, the measure of the exterior angle is given as 24 degrees. So we can set up the equation:

24 = 360 / n

Where n is the number of sides. Cross multiplying, we get:

n = 360 / 24 = 15

So the polygon has 15 sides. To find the measure of an interior angle, we can use the formula:

Interior Angle = 180 - Exterior Angle

Interior Angle = 180 - 24 = 156 degrees