Please help me with these 2 and explain ty

Answer:

B. 9 × 10⁵

Step-by-step explanation:

Given rational expression:

\(\dfrac{5.4 \times 10^9}{6 \times 10^3}\)

To simplify the given rational expression, first divide the numerical parts:

\(\implies 0.9 \times \dfrac{10^9}{ 10^3}\)

Now apply the following exponent rule to the exponents of 10:

\(\boxed{\dfrac{a^b}{a^c}=a^{b-c}}\)

\(\implies 0.9 \times10^{9-3}\)

\(\implies 0.9 \times10^{6}\)

Finally, move the decimal point one place to the right and therefore subtract 1 from the exponent of 10:

\(\implies 9 \times10^{5}\)

Therefore, the equivalent value to the given rational expression is 9 × 10⁵.

The number is equivalent to \(9 \times 10^5.\)

Option B is the correct answer.

We have,

The expression is \(5.4 \times 10^9 / 6 \times 10^3\)

Now,

Using the exponent laws with the expression that has the same base.

\(= 5.4 \times 10^{9 - 3} / 6\\= 5.4 \times 10^6 / 6\\= 54 \times 10^6 / 6 x 10\\= 54 \times 10^{6 - 1} / 6\\= 9 \times 10^5\)

Thus,

The number is equivalent to 9 x 10^5.

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a) The probability of picking a red marble first and a yellow marble second is 6/25. So, correct option is A.

b) The probability of spinning a 5 two times in a row is 1/64. So, correct option is c.

a) To calculate the probability of picking a red marble first, replacing it, and then picking a yellow marble, we need to multiply the probabilities of each event.

The probability of picking a red marble first is 2/5, since there are 2 red marbles out of a total of 5 marbles. Since we replace the red marble, the probability of picking a yellow marble on the second draw is also 3/5, since there are still 3 blue marbles and 2 red marbles in the jar.

Therefore, the probability of picking a red marble first and a yellow marble second is:

(2/5) x (3/5) = 6/25

So the correct answer is option a) 6/25.

b) The probability of spinning a 5 on a single spin of the spinner is 1/8, since there is only one 5 out of 8 possible outcomes.

To find the probability of spinning a 5 two times in a row, we need to multiply the probability of spinning a 5 on the first spin by the probability of spinning a 5 on the second spin. Since the spins are independent events, we can use the multiplication rule of probability.

Therefore, the probability of spinning a 5 two times in a row is:

(1/8) x (1/8) = 1/64

So the correct answer is option (c) 1/64.

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To solve this problem, we can use the principle of inclusion-exclusion.

First, let's find the total number of ways to select n students from a class of 5n:

Total ways = (5n choose n) = (5n)! / (n!*(5n-n)!) = (5n)! / (n!*(4n)!)

The term "average" plays a fundamental role in statistics. It refers to a measure of central tendency that summarizes a set of data by representing a typical or representative value.

Calculation for the average of a set of numbers, follow these steps:

Add up all the values in the data set.

Division of the sum by the total number of values.

For example, consider the following data set: 10, 15, 20, 25, 30.

Sum all the values: 10 + 15 + 20 + 25 + 30 = 100.

Divide the sum by the total number of values: 100 / 5 = 20.

In this case, the average of the data set is 20.

The term average provides a concise summary of a data set by representing a typical value. It is calculated by adding up all the values and dividing the sum by the total number of values. The average is a fundamental statistical measure that helps in understanding and analyzing data in various fields such as economics, education, research, and many others.

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The recursive formula that represents the same sequence of numbers as the explicit formula an = 3n + 4 is an = an-1 + 3, with the initial term a1 = 7.

A recursive formula defines a sequence by expressing each term in terms of previous terms. In this case, the explicit formula an = 3n + 4 gives us a direct expression for each term in the sequence.

To find the corresponding recursive formula, we need to express each term in terms of the previous term(s). In this sequence, each term is obtained by adding 3 to the previous term. Therefore, the recursive formula is an = an-1 + 3.

To complete the recursive formula, we also need to specify the initial term, a1. We can find the value of a1 by substituting n = 1 into the explicit formula:

a1 = 3(1) + 4 = 7

Hence, the complete recursive formula for the sequence is an = an-1 + 3, with the initial term a1 = 7. This recursive formula will generate the same sequence of numbers as the given explicit formula.

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Answer:

I hope this helps you

Step-by-step explanation:

To define the time of flight equation, we should split the formulas into two cases:

Launching projectile from the ground (initial height = 0)

t = 2 * V₀ * sin(α) / g.

Launching projectile from some height (so initial height > 0)

t = [V₀ * sin(α) + √((V₀ * sin(α))² + 2 * g * h)] / g.

Answer:

\(P=\frac{1}{8}\)

Step-by-step explanation:

You're given your variables, you just need to put them in the correct spot. X is on top, and x =1, replace x with 1. Y is on the bottom and y=8, replace y with 8.

If I helped, a brainliest answer would be greatly appreciated!

Answer:

20.3

Step-by-step explanation:

64.97/3.2

32 goes into 64    2 times           2_.__

32 goes into 9      0 times           20.__

32 goes into 97    3 times           20.3_

32 goes into 1       0 times           20.30

Because there we are rounding to the nearest hundreth no other number matter beond this point.

The answer is 20.3

Answer:

\(5*\frac{1}{2}\)

Step-by-step explanation:

We have a picture and are being asked to identify the multiplication problem that represents it.

So we have 5 triangles, all of which are color-coded in red, but only half of them are filled. When multiplying, the number that is before the * sign is the amount there is, while the number that is after the * is the amount going to multiply the amount of items there are. So looking at the picture, we can see 5 triangles, therefore :

5 *

2 * 1/5 is scratched out as an answer. As is starts with 2.

As for the second number, we acknowledge that all triangles are half in red, therefore the number is 1/2.

5 * 1/2

Scratching all other answers.

Answer: 75%

Step-by-step explanation: So 15/20 simplified is 3/4 and 3 divided by 4 equals 0.75. To convert a decimal to a percentage, you multiply 0.75 by 100 to get 75%.

The possible dimensions (length and width) of the field are:(10 m × 13 m) or (13 m × 10 m) and (11 m × 12 m) or (12 m × 11 m).

Given that Aaron has 47m of fencing to build a three-sided fence around a rectangular plot of land that sits on a riverbank. The fourth side of the enclosure would be the river.

The area of the land is 266 square meters.To find the possible dimensions (length and width) of the field, we can use the given information.The length of fencing required = 47 m.

Since the fence needs to be built on three sides of the rectangular plot, the total length of the sides would be 2l + w = 47.1. When l = 10 and w = 13, we have:

Length of the field, l = 10 m Width of the field, w = 13 mArea of the field = l × w = 10 × 13 = 130 sq. m2. When l = 11 and w = 12,

we have:Length of the field, l = 11 m

Width of the field, w = 12 m

Area of the field = l × w = 11 × 12 = 132 sq. m

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A function, h, has a domain of -3 ≤ x ≤ 11  and a range of  1 ≤ h(x) ≤ 25  ; hence, option C. h(2) = 16 is true.

A function's domain is the variety of values that it is able accept. These integers indicate the x-values of something like a function like f. (x). The range of potential values that can be used with a function is known as its domain. The value that the method returns after inserting the x value belongs to this set. The formula for a function with y as such dependent variable and x as the regression coefficient is y = f. (x). When a single value of y can be successfully produced from a value of x, that parameter is said to be in the domain of the function.

given

Since we are aware that h(8) is 19, not 21, we know that statement A is false.

B is likewise false since h(x) cannot have a value of 1.

Because x cannot be 13, D cannot be true, hence the response is C.

A function, h, has a domain of -3 ≤ x ≤ 11  and a range of  1 ≤ h(x) ≤ 25  ; hence, option C. h(2) = 16 is true.

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Answer:

Yes it is

Step-by-step explanation:

It passes the vertical line test.

Answer:

152

Step-by-step explanation:

All segments in a triangle add to 180. 1

8+10+x=180

x=152

The length x using Pythagoras theorem is 15 unit.

According to the Pythagorean theorem, the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.

Given:

Hypotenuse = 18 unit

Perpendicular = 10 unit

using Pythagoras theorem

H² = P² + B²

18² = 10² + B²

324 = 100 + B²

324 - 100 = B²

B² = 224

B= 14.966 unit

B= 15 unit

Thus, the measure for x is 15 unit.

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The integral of (42³ - 2r + 7) dz is equal to (42³ - 2r + 7)z + C.

To integrate the function (42³ - 2r + 7) dz, we treat r as a constant and integrate with respect to z. The integral of a constant with respect to z is simply the constant multiplied by z:

∫ (42³ - 2r + 7) dz = (42³ - 2r + 7)z + C

where C is the constant of integration.

Note: The integral of a constant term (such as 7) with respect to any variable is simply the constant multiplied by the variable. In this case, the variable is z.

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Answer:

Step-by-step explanation:

Volume of a cylinder πr²h

π    3.14

radius is diameter divided by 2

12 divided by 2 is 6

height is 27

πr²h is 3.14 ×6 ×6 × 27

volume of cylinder 3052.08 ≅ 3052

Answer:

Step-by-step explanation:

The angle and its supplementary angle have a difference of 15.8°. To find the measures, we need to solve an equation.

Let's assume the measure of the angle is x°. The measure of its supplementary angle would be (180° - x°). According to the given information, x° = (180° - x°) - 15.8°.

Simplifying the equation, we have:
x° = 180° - x° - 15.8°
2x° = 164.2°
x° = 82.1°

Therefore, the angle measures 82.1° and its supplementary angle measures (180° - 82.1°) = 97.9°. The difference between these angles is indeed 15.8°, as stated in the problem.

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Answer:

The answer is B y=tan x

The graph y = tanx  function is not graphed correctly, the correct graph of the function is attached in the question.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle.

The trigonometric ratios can also be considered as functions of a variable which is the measure of an angle. This angle measure can either be given in degrees or radians . Here, we will use radians.

Since, tan(x)=sin(x)cos(x) the tangent function is undefined when cos(x)=0 . Therefore, the tangent function has a vertical asymptote whenever cos(x)=0 .

Similarly, the tangent and sine functions each have zeros at integer multiples of π because tan(x)=0 when sin(x)=0 .

The graph of a tangent function y=tan(x) is attched in the image.

Hence, the graph y = tanx  function is not graphed correctly, the correct graph of the function is attached in the question.

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A description of the distribution of the values of a random variable and their associated probabilities is called a probability distribution (option a).

A probability distribution is a description of the values that a random variable can take and the corresponding probabilities of those values. It provides a complete summary of the possible outcomes and the likelihood of each outcome occurring. The distribution can be represented in various forms, such as a table, graph, or mathematical equation.

It helps us understand the likelihood of different events or values occurring in a random experiment or situation. A probability distribution allows us to calculate various statistical measures, such as the expected value and variance, which provide insights into the overall behavior and characteristics of the random variable. The correct option is a.

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Answer:

1/12.

Step-by-step explanation:

6 sides and 2 sides. 2 possible outcomes for each side of the dice

Answer:

\(\frac{1}{12}\)

Step-by-step explanation:

The combinations:

heads and 1, heads and 2, heads and 3, heads and 4, heads and 5, heads and 6, tails and 1, tails and 2, tails and 3, tails and 4, tails and 5, tails and 6

Answer:78.9

Step-by-step explanation:

78.9x 0896968

Answer:

9 9/16

Step-by-step explanation:

The first step is to find the LCD of 16 and 2

It is 16, and you can multiply the 6 1/2 by 8 which equals 6 8/16

Then you add

3 1/16 + 6 8/16 is equal to 9 9/16, which is your answer.

Hope this helped

Sorry if it's wrong

:)

Answer:

the chef has 9 9/16 pounds of flour

Answer:

About 71.77 degrees

Step-by-step explanation:

The starting leg is 2.3 km and the finishing leg is 6.2 km.

Using the law of cosines C^2 = A^2 + B^2 -2AB*cos(c) where A = 2.3 km, B = 6.2 km, C = 5.9 km, and angle c is the opposite angle to side C, we get:

5.9^2 = 2.3^2 + 6.2^2 -2(2.3)(6.2)*cos(c)

cos(c) = -(5.9^2 - 2.3^2 - 6.2^2)/(2*2.3*6.2)

c = 71.77 degrees

Answer:

72°

Step-by-step explanation:

when we have all the sides and need an angle, we use the law of cosine (the extended Pythagoras) :

c² = a² + b² - 2ab×cos(C)

where c is the side opposite of the angle C.

so, since the starting leg is 2.3 km, and the finishing leg is 6.2 km, we know that 5.9 km is the side opposite of the angle between the starting and finishing legs.

so, we have

5.9² = 2.3² + 6.2² - 2×2.3×6.2×cos(C)

34.81 = 5.29 + 38.44 - 28.52×cos(C)

-8.92 = -28.52×cos(C)

cos(C) = -8.92/-28.52 = 0.312762973...

C = 71.77418076...° ≈ 72°

The slope of the line passing through the points (3, 4) and (5, 8) is 2.

We have,

To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), you can use the formula:

slope = (y₂ - y₁) / (x₂ - x₁)

In this case,

The points are (3, 4) and (5, 8).

Let's substitute these values into the formula:

slope = (8 - 4) / (5 - 3)

= 4 / 2

= 2

Therefore,

The slope of the line passing through the points (3, 4) and (5, 8) is 2.

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The area may then be determined in square centimeters as follows: 600 area  × 800 cm is equal to 480000 cm2 in area. Using the closest number

An area can be used to describe a surface's area. Surface area, also known as planar region, refers to the area of a form or planar layer, whereas planar region refers to the area of an open surface or the border of a three-dimensional object. An object's area is the entire amount of space occupied by its planar (2-D) surface or form. Use a pencil to mark a square on the paper. an individual having two dimensions. A shape's area on paper is the amount of space it occupies. Think of the square as being made up of smaller unit squares.

48.00 m^2 or 4800.00 cm^2 (depending on the unit you want to use)

The rectangle's length and breadth, 6 and 8 metres, respectively, must be multiplied to find the area:

Area: 6 x 8 x 48 metres.

The length and breadth must first be converted to cm if you wish to represent the area in square centimetres:

6 m = 600 cm

8 m = 800 cm

The area may then be determined in square centimetres as follows:

600 × 800 cm is equal to 480000 cm2 in area.

Using the closest number

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Answer:

x = 10

Step-by-step explanation:

By looking at the picture, I can tell the angle of the 3x is also 30 degrees.

This means 3x = 30.

When you solve for x by dividing each side by 3, you result with the answer of x = 10.

To check you work, plug in 10 for x to recieve 30 degrees again.

Answer:

z = 24

Step-by-step explanation:

35/30 = 7/6

28/7 = 4

6 x 4 = 24

28/24 = 7/6

Answer:

x = 24

Step-by-step explanation:

All you have to do is cross multiply like this..

30 x 28 = 35 x X

=

x = 30 x 28/35

30 x 28 = 840 / 35 =

24

So x is equal to 24

Hope this helps :)

Answer:

b

Step-by-step explanation:

Answer:

A translation by 2 units to the left and 6 units up.

Step-by-step explanation: