Write 2x^9 as the product of two powers with the same base.

Answer:

6

Step-by-step explanation:

24/6 = 4

36/6 = 6

6 bags, 4 lollipops and 6 pieces of gum in each bag.

Answer:

12 bags

Step-by-step explanation:

You would need to find the GCF of both numbers: 12

24*12 = 2

38*12 = 4

12 bags with 2 lollipops and 4 pieces of gum in each

The airspeed of the plane is 500 mph and the speed of the wind is 100 mph, assuming both remain constant throughout the flight.

To solve this problem, let's denote the airspeed of the plane as "P" and the speed of the wind as "W."

On the outbound flight (against the wind), the effective ground speed of the plane is P - W. The distance traveled is 1800 miles and the time taken is 3 hours and 36 minutes, which is equivalent to 3.6 hours. Using the formula distance = speed * time, we have:

1800 = (P - W) * 3.6

On the return flight (with the wind), the effective ground speed of the plane is P + W. The distance traveled is still 1800 miles, but the time taken is 3 hours. Again, using the distance = speed * time formula, we get:

1800 = (P + W) * 3

We now have a system of equations:

1800 = (P - W) * 3.6
1800 = (P + W) * 3

Solving these equations simultaneously, we find that P = 500 mph and W = 100 mph.

To learn more about Airspeed, visit:

https://brainly.com/question/30529519

#SPJ11

A: ZABC is a right angle. (Given)

B: DB bisects ZABC. (Given)

C: m/ABD = m/CBD. (Definition of angle bisector)

D: m/ABD + m/CBD = 90°. (Sum of angles in a right triangle)

By substitution property, m/CBD + m/CBD = 90° should be m/ABD + m/CBD = 90°.

A: Given: ZABC is a right angle.

B: Given: DB bisects ZABC.

C: To prove: m/CBD = 45°

D: Proof:

ZABC is a right angle. (Given)

DB bisects ZABC. (Given)

m/ABD = m/CBD. (Definition of angle bisector)

m/ABD + m/CBD = 90°. (Sum of angles in a right triangle)

Substitute m/CBD with m/ABD in equation (4).

m/ABD + m/ABD = 90°.

2 \(\times\) m/ABD = 90°. (Simplify equation (5))

Divide both sides of equation (6) by 2.

m/ABD = 45°.

Therefore, m/CBD = 45°. (Substitute m/ABD with 45°)

Thus, we have proved that m/CBD is equal to 45° based on the given statements and the reasoning provided.

Please note that in step 5, the substitution of m/CBD with m/ABD is valid because DB bisects ZABC. By definition, an angle bisector divides an angle into two congruent angles.

Therefore, m/ABD and m/CBD are equal.

For similar question on substitution property.

https://brainly.com/question/29058226  

#SPJ8

In probability theory, a Venn diagram is a diagrammatic representation of sets that shows all possible logical relations between them. Venn diagrams are widely used in probability and statistics to visualize the relationship between different sets of data.

The given Venn diagram shows the relationship between three sets, A, B, and C. In order to calculate probabilities using a Venn diagram, we need to know the number of elements or members in each set, as well as any overlapping regions.

We can then use these numbers to calculate the probability of different outcomes.Let's consider two possible probabilities from the given Venn diagram:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22. The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3The first probability can be calculated by dividing the number of elements in the overlapping region of sets A and B (which is 0.1) by the total number of elements in set B (which is 0.5).

This gives us a probability of 0.22 or 22%.The second probability can be calculated by dividing the number of elements in the union of sets B and C (which is 0.2) by the total number of elements in either set B or set C (which is 0.6). This gives us a probability of 1/3 or approximately 33%.

Therefore, the correct probabilities are:1.

The probability that an element is in set A and set B but not in set C is 0.1/0.5 = 0.22.

The probability that an element is in set B or set C but not in set A is 0.2/0.6 = 1/3

For such more question on probability

https://brainly.com/question/30390037

#SPJ8

By merging information from several sources, a pooled estimate of the population is utilised to gain a better picture of the population mean as a whole.

When a person or organisation needs to combine data from several sources to better understand a population, they utilise a pooled estimate of the population. This can be accomplished in a number of ways, such as by integrating data from several surveys, data from various time periods, or data from various geographical regions .A more complete and accurate view of the population can be acquired by combining the data from several sources. Because it enables a more precise assessment of a population's needs and traits, this is particularly helpful for making judgements about policy or resource distribution. The comparison of several populations or the analysis of changes across time can both be done using pooled estimates. This is necessary to comprehend population change and determine the most effective resource allocation.

Learn more about population mean here

https://brainly.com/question/19538277

#SPJ4

The transfer function allow us to determine the appropriate value of Ki that satisfies the desired overshoot and settling time specifications ≈ 16.67.

To design a compensator that guarantees a steady-state error less than 0.01 and a settling time (Ts) of 5 seconds with 5% maximum overshoot (PO), we can use a proportional-integral (PI) controller.

The transfer function of the compensator can be represented as:

C(s) = Kp + Ki/s

where Kp is the proportional gain and Ki is the integral gain.

To achieve a steady-state error less than 0.01, we need to ensure that the open-loop transfer function with the compensator, G(s)C(s), has a DC gain of at least 100.

To calculate the values of Kp and Ki, we can follow these steps:

Determine the open-loop transfer function without the compensator, G(s):

G(s) = 2(s + 3)(s + 1)

Calculate the DC gain of G(s) by evaluating G(s) at s = 0:

DC_gain = G(0) = 2(0 + 3)(0 + 1) = 6

Determine the required DC gain with the compensator to achieve a steady-state error less than 0.01:

Required_DC_gain = 100

Calculate the proportional gain Kp to achieve the required DC gain:

Kp = Required_DC_gain / DC_gain = 100 / 6 ≈ 16.67

Determine the integral gain Ki to achieve the desired overshoot and settling time.

To achieve a settling time of 5 seconds and a 5% maximum overshoot, we can use standard control design techniques such as root locus or frequency response methods.

Using these methods, you can determine the proper Ki value to meet the required overshoot and settling time specifications.

For more questions on transfer function:

https://brainly.com/question/12950741

#SPJ8

The probability that a 25-year-old person from this group prefers biking is: 68/229.

The total number of people in the survey between the ages of 23 and 27 is 229. The number of people who prefer biking in this group is 68.

Therefore, the probability that a 25-year-old person from this group prefers biking is: 68/229

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor (GCF), which is 1:

68/229 = 68/229

So the probability that a 25-year-old person from this group prefers biking is 68/229.

Learn more about probability at https://brainly.com/question/24756209

#SPJ1

Answer:

y = -3x - 4

Step-by-step explanation:

Find the slope.

y2-y1/x2-x1

-9/3 = -3

-3 is the slope. You know the y-intercept is -4 since (0, -4) is a point. The y-intercept is the value of y where x = 0.

So if you know the slope is -3 and the y-intercept is -4, plug it into slope-intercept form.

y = mx+b

y = -3x - 4

Answer:

18 cm

Step-by-step explanation:

The ratio of Actual length (L) to scale length is 27 : 3.6

27 ÷ 3.6 = 7.5

Therefore, actual width (W) = scale width x 7.5

                                              = 2.4 x 7.5

                                              = 18 cm

Step-by-step explanation:

1》 x + 74° = 90°

x = 90° - 74°

x = 16°

2》 x + 134° = 180°

x = 180° - 134°

x = 46°

Answer:

y= 1/5x + -8

Step-by-step explanation: slope-intercept form= y=mx+b

y= the number on the y-axis or the simple y

m=slope

x= the number on the x-axis or the simple x

b= y-intercept

The required slope-intercept form of the equation is given as y = 1/5x - 8.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The slope intercept of the equation is given as,
y = mx + c,

From the given, we have a slope of line m = 1/5 and y-intercept, c = -8.
Now,
y = mx + c
y = 1/5x - 8

Thus, the required slope-intercept form of the equation is given as y = 1/5x - 8.

Learn more about slopes here:
https://brainly.com/question/3605446

#SPJ2

For a larger input size of 320,000 elements, it will take 240 ms to sort each half and 24 ms to merge the sorted halves, resulting in a total time of 264 ms.

The given information describes the time required for sorting and merging operations on two different input sizes. For 80,000 elements, it takes 18 ms to sort each half, resulting in a total of 36 ms for sorting. Merging the two sorted halves with 80,000 numbers in each takes 40 - 18 = 22 ms.

When the input size is doubled to 320,000 elements, the sorting time for each half increases to 240 ms, as it scales linearly with the input size. The merging time, however, remains constant at 4 ms since the size of the sorted halves being merged is the same.

Thus, the total time for sorting and merging 320,000 elements is the sum of the sorting time (240 ms) and the merging time (4 ms), resulting in a total of 264 ms.

Therefore, based on the given information, the total time required for sorting and merging 320,000 elements is 264 ms.

Learn more about total time here:

https://brainly.com/question/951637

#SPJ11

Perimeter is a measure of the area or distance around a two-dimensional shape. On a rectangle, for instance, the perimeter is the total length of the rectangle's outline, including the two widthwise borders and the two lengthwise borders.

To determine the perimeter of a shape, therefore, you add together all the dimensions that make up the shape's outer edge. Being able to find the perimeter of a shape has many applications in the real world. Say, for example, that you wanted to build a fence around your backyard. In order to purchase materials, you need to know how much fencing you'll need, and to determine that you have to figure out the perimeter of the area you want to fence in.

C. The Number Of Tokens is the right answer

The label on the x-axis option (C) number of tokens is the correct answer.

A graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The graph of a function f is the set of all points in the plane of the form (x, f(x)).

For the given situation,

Charge for admission to game room = $4.00

Charge per game token = $0.25

The equation representing the cost is y = 0.25x + 4.

From the data,

When he graphs this situation, the label on the x-axis is number of tokens.

Hence we can conclude that the label on the x-axis option (C) number of tokens is the correct answer.

Learn more about graph of a function here

https://brainly.com/question/2275360

#SPJ3

Answer:

Step-by-step explanation:

Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18

The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.

Answer:

"statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = \(4x\)

Let, Number of girls = \(5x\)

Total number of students = Number of boys + Number of girls = 270

\(\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}\)

Therefore, number of boys = 4 \(\times\) 30 = 120

And, number of girls = 5 \(\times\) 30 = 150

As per Statement 1:

Finding \(\frac{4}5\) of the number of girls:

\(\dfrac{4}{5}\times 150 = 4 \times 30 = 120\) = Number of boys.

Finding \(\frac{4}9\) of the total number of students:

\(\frac{4}{9}\times 270= 4 \times 30 = 120\) = Number of boys.

Number of boys is equal to \(\frac{4}9\) of total number of students.

So, "statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

In general, different refrigerants should not be mixed or recovered into the same cylinder.

Different refrigerants have unique chemical compositions and properties that make them incompatible with one another. Mixing different refrigerants can lead to unpredictable reactions, loss of refrigerant performance, and potential safety hazards. Therefore, it is generally recommended to avoid recovering different refrigerants into the same cylinder.

When recovering refrigerants, it is important to use separate recovery cylinders or tanks for each specific refrigerant type. This ensures that the refrigerants can be properly identified, stored, and recycled or disposed of in accordance with regulations and environmental guidelines.

The refrigerant recovery process involves capturing and removing refrigerant from a system, storing it temporarily in dedicated containers, and then transferring it to a proper recovery or recycling facility. Proper identification and segregation of refrigerants during the recovery process help maintain the integrity of each refrigerant type and prevent contamination or cross-contamination.

To maintain the integrity and safety of different refrigerants, it is best practice to recover each refrigerant into separate cylinders. Mixing different refrigerants in the same cylinder can lead to complications and should be avoided. Following proper refrigerant recovery procedures and guidelines helps ensure the efficient and environmentally responsible management of refrigerants.

To know more about cylinder visit:

https://brainly.com/question/30390407

#SPJ11

The number of different refrigerants that may be recovered into the same cylinder is zero.

When it comes to refrigerants, it is important to understand that different refrigerants should not be mixed together. Each refrigerant has its own unique properties and should be handled and stored separately. mixing refrigerants can lead to chemical reactions and potential safety hazards.

The recovery process involves removing refrigerants from a system and storing them in a cylinder for proper disposal or reuse. During the recovery process, it is crucial to ensure that only one type of refrigerant is being recovered into a cylinder to avoid contamination or mixing.

Therefore, the number of different refrigerants that may be recovered into the same cylinder is zero. It is essential to keep different refrigerants separate to maintain their integrity and prevent any adverse reactions.

Learn more:

About refrigerants here:

https://brainly.com/question/13002119

#SPJ11

Answer:

The answer is B

Step-by-step explanation:

Answer:

The focus is A. (0, 3/2)

Step-by-step explanation:

I searched it up

Answer:

To find the area of a triangle, multiply the base by the height, and then divide by 2. The division by 2 comes from the fact that a parallelogram can be divided into 2 triangles. For example, in the diagram to the left, the area of each triangle is equal to one-half the area of the parallelogram.

Step-by-step explanation:

there

Answer:yes

Step-by-step explanation:4x minus 3x is 1x, or x, and then it's just x+2

Answer:

Yes

Step-by-step explanation:

Both of these equations have the same X and Y intercepts. The X intercepts being -2,0 and the Y intercepts being 0,2

The height of the flagpole is 12.9 feet to the nearest tenth.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

The boy is 5' 3" tall and his shadow is 4 feet.

The shadow of the flagpole is 17 feet.

The boy is 5.25 feet tall.

Let the height of the flagpole is h feet.

So,

17/h = 5.25/4

h = 68/5.25

h = 12.95

h = 12.9 to one decimal place.

Therefore, h = 12.9 to one decimal place.

To learn more about the ratio;

https://brainly.com/question/13419413

#SPJ1

Answer: 7.312

Step-by-step explanation: Hope this helped but you have to first divide 4/2 which makes 2, then 2/2 which is 1, 6/2 which makes 3, then 14/2 which makes 7

4/2= 2

2/2=1

6/2=3

14/2=7

7.312

Answer:

B) 5

Step-by-step explanation:

$6000 × 0.03 = $180 - this means that every year, $180 is added to the invested amount.

We can now do $900 ÷ $180 to find out the number of years the money was invested for: $900 ÷ $180 = 5

The money was invested for 5 years

Hope this helps!

The surface with the given vector equation, r(s, t) = (s cos(t), s sin(t), s), is a circular cone.

The vector equation r(s, t) = (s cos(t), s sin(t), s) represents a surface in three-dimensional space. Let's analyze the equation to determine the nature of the surface.

In the equation, we have three components: s, cos(t), and sin(t). The presence of s indicates that the surface expands or contracts radially from a central point. The trigonometric functions cos(t) and sin(t) determine the angle at which the surface extends in the x and y directions.

By observing the equation closely, we can see that as s increases, the radius of the surface expands uniformly in all directions, while the height remains constant. This behavior is characteristic of a circular cone. The circular base of the cone is defined by s cos(t) and s sin(t), and the vertical component is determined by s.

Therefore, the surface described by the vector equation r(s, t) = (s cos(t), s sin(t), s) is a circular cone.

Learn more about  vector equation here :

https://brainly.com/question/32619742

#SPJ11

4 kilometers is the height of the given mountain.

In this case, we can consider the height of the mountain as the length of one side of a right triangle, the distance Ben climbed as the length of another side, and the distance from the base of the mountain to the center as the hypotenuse.

Let's denote the height of the mountain as h. According to the given information, the distance Ben climbed is 5 kilometers, and the distance from the base to the center of the mountain is 3 kilometers.

Using the Pythagorean theorem, we have the equation:

\(h^2 = 5^2 - 3^2\\\\h^2 = 25 - 9\\\\h^2 = 16\)

Taking the square root of both sides, we find:

h = √16

h = 4

Therefore, the height of the mountain is 4 kilometers.

Learn more about right-angle triangles here:

https://brainly.com/question/3770177

#SPJ1

Answer:

area of rectangle is 1144 area of circle is1534

Answer:

X=20

Step-by-step explanation:

Verticals angles have same degree.

3x=x+40

x=20

Answer:

The value of \(x\) would be 20°.

Step-by-step explanation:

Since vertical angles are equivalent, and ∠SRT and ∠VRW are vertical angles, you can create the equation \(3x = x + 40\) to solve for \(x\). \(3x = x+40\) ⇒ \(2x = 40\) ⇒ \(x=20\)°, so that would be the correct answer.

With the help of the figure we can say that triangles are congruent by SAS Rule

What is Congruence of Triangle?

Triangle congruence: Two triangles are said to be congruent if all three of their corresponding sides are equal and all three of their corresponding angles are equal in size. These triangles can be moved, rotated, flipped, and turned to look exactly the same.

Solution:

By SAS rule, two triangles are said to be congruent if any two sides and the angle included between the sides of one triangle are comparable to the corresponding two sides and the angle included between the sides of the second triangle.

In given figure, sides AB= PQ, BC=QR and angle between AB and BC equal to angle between PQ and QR i.e. ∠B = ∠Q. Hence, Δ ABC ≅ Δ PQR.

To learn more about Congruence of Triangles from the given link

https://brainly.com/question/2938476

#SPJ4