How many solutions are possible for the equation 5(x-3)=7x-2(x+1)

Using normal approximation: mean = 50,000, standard deviation = 500. Calculate Z-scores, find probabilities, and subtract. Result ≈ 0.3108.

To find the probability of getting between 49,800 and 50,200 heads when a fair coin is tossed 100,000 times, we can use the normal approximation to the binomial distribution since the number of trials is large.

The mean (μ) of a binomial distribution is given by n*p, where n is the number of trials and p is the probability of success (getting heads for a fair coin). In this case, n = 100,000 and p = 0.5, so μ = 100,000 * 0.5 = 50,000.

The standard deviation (σ) of a binomial distribution is given by sqrt(n*p*(1-p)). For this problem, σ = sqrt(100,000 * 0.5 * 0.5) = sqrt(25,000) = 500.

Now, we can use the normal distribution to approximate the probability of getting between 49,800 and 50,200 heads:

Z1 = (49,800 - μ) / σ = (49,800 - 50,000) / 500 = -0.4

Z2 = (50,200 - μ) / σ = (50,200 - 50,000) / 500 = 0.4

Now, we look up the corresponding probabilities for Z1 and Z2 in the standard normal distribution table (or use a calculator):

P(Z < -0.4) ≈ 0.3446

P(Z < 0.4) ≈ 0.6554

So, the probability of getting between 49,800 and 50,200 heads is approximately P(49,800 ≤ X ≤ 50,200) = P(-0.4 ≤ Z ≤ 0.4) = P(Z < 0.4) - P(Z < -0.4) ≈ 0.6554 - 0.3446 ≈ 0.3108.

Therefore, the probability is approximately 0.3108.

Two or more expressions with an Equal sign is called as Equation. The number is 16 in sentence one-half of the number is 2 less than two-thirds of the number

Two or more expressions with an Equal sign is called as Equation.

We x be the unknown number which we have to find.

Given,

one-half of the number is 2 less than two-thirds of the number

Which is one-half of the number is x/2

2 less than two-thirds of the number is 2/3 x-2

So let us form a equation

x/2 = 2x/3-2

x/2=(2x-6)/3

Apply cross multiplication

3x=2(2x-6)

Use distributive law on RHS

3x=4x-16

16=4x-3x

16=x

Hence the number is 16 in sentence one-half of the number is 2 less than two-thirds of the number

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To frame a cabin:

Lee will take 6.47 days and Ron will take 10.47 days.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

Lee can frame a cabin in 4 days less than Ron.

Ron can frame,

= 1 cabin/(x+4) days.

Lee can frame,

= 1 cabin/(x) days.

When they work together, they will do the job in 4 days.

That means,

4/x+4 + 4/(x) = 1

4(x+4+x)/x(x+4) = 1

x²-4x-16 = 0

Solving the quadratic equation,

x = 2 ± 2√5

Then,

x = -2.47 and x = 6.47.

Therefore, Lee can frame a cabin in  6.47 days and Ron will take 10.47  days.

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Answer:121

Step-by-step explanation:

Answer:16 3/10

Step-by-step explanation:

Lorraine earned $2970 in simple interest over the 9 years.

We can use the formula for simple interest, which is:

[tex]\[ I = P \times r \times t \][/tex]

where:

[tex]\( I \)[/tex] is the interest earned,

[tex]\( P \)[/tex] is the principal amount (the initial amount of money),

[tex]\( r \)[/tex] is the annual interest rate (in decimal form), and

[tex]\( t \)[/tex] is the time the money is invested for, in years.

Given:

[tex]\( P = \$5500 \)[/tex] (the principal amount),

[tex]\( r = 6\% \)[/tex] per year (which we convert to a decimal by dividing by 100.

[tex]\( r = 0.06 \)[/tex]

[tex]\( t = 9 \)[/tex] years (the time period).

Now, we can calculate the simple interest:

[tex]\[ I = \$5500 \times 0.06 \times 9 \][/tex]

[tex]\[ I = \$5500 \times 0.54 \][/tex]

[tex]\[ I = \$2970 \][/tex]

A) In standard form, the length of time the light is on is [tex]2.67 \times 10^{-2} \text{ seconds}[/tex]

B) As a decimal, the length of time the light is on is [tex]0.0267 \text{ seconds}[/tex]

Step 1: Understanding the conversion

Step 2: Converting microseconds to seconds

First, let's calculate the time in seconds as a decimal:
[tex]26700 \times 10^{-6} = 0.0267[/tex]

Step 3: Converting seconds to standard form

Standard form (also known as scientific notation) expresses numbers as a product of a number between 1 and 10 and a power of 10.

Here, [tex]0.0267[/tex] can be written as:
[tex]2.67 \times 10^{-2}[/tex]

Answer:

420

Step-by-step explanation:

400 - 20 = 380 + 40 = 420 ÷ 2 = 210 + 210 = 420.

Hey there!

400 - 20 + 40 ÷ 2 + 210

400 - 20 = 380

380 + 40 ÷ 2 + 210

40 ÷ 2 = 20

380 + 20 + 210

380 + 20 = 400

400 + 210 = 610

Answer: 610 ✅

Good luck on your assignment and enjoy your day!

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The counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

The statement is given as: "the difference of two numbers less than the greater number"

Let the numbers be x and y, where x > y.

So, the interpretation of the statement is:

x - y < x

Add x to both sides

-y < 2x

Rewrite as:

y > -2x

This means that the statement is true only when the smaller number is greater than twice the additive inverse of the greater number

Hence, the counterexample of the statement "the difference of two numbers is greater than the greater number if the smaller number is greater than twice the additive inverse of the greater number"

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The surface area to volume ratio for a cube with sides of 5 cm can be calculated using the formulas for surface area and volume of a cube. After calculating, the ratio is found to be 1.2 cm^-1.

The concept you're asking about relates to both geometry and biology, particularly cell biology. The surface area to volume ratio is important in determining how substances move in and out of cells.

To calculate the surface area and volume of a cube with sides measuring 5 cm, we use these two formulas:

Substituting 5 cm into these formulas, we get:

Finally, to get the surface area to volume ratio, divide the surface area by the volume:

So, the surface area to volume ratio for a cube with sides of 5 cm is 1.2 cm^-1.

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The y - intercept of the line is 0.

We have f(x) = 3x

We have to find the y - intercept of this function f(x).

The general equation of a straight line is as follows -

y = mx + c

where -

m - slope of line

c - intercept of line on y - axis.

According to question, we have -

f(x) = 3x

or

f(x) = 3x + 0

Comparing it with the general equation of a straight line, we get -

y = f(x)

m = 3

c = 0

Here, c is the y - intercept of the line f(x) = 3x.

Hence, the y - intercept of the line is 0.

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Area of triangle = 1/2 base x height

15.588 = 1/2 * base x 5.196

15.588 = base x 2.598

base = 15.588 / 2.598 = 6

 equi center of triangle = 1/3*5.196 = 1.732

radius of circle = Sqrt(1.732^2 + 3^2) =

 sqrt (2.999824 +9) =

sqrt(11.999824) = 3.464

rounded to nearest tenth = 3.5 inches

The radius of the circle required to inscribe an equilateral triangle with the given dimensions is; radius = 3.5 inches

Usually, when we inscribe an equilateral triangle in a circle, the distance from the centroid of that triangle to one of the vertices is;

Centroid distance to vertex = ²/₃h

Where h is the altitude of the triangle.

We are given altitude = 5.196 in

Thus;

Centroid distance to vertex = ²/₃(5.196)

⇒ 3.464 inches

Approximating to the nearest tenth gives;

Centroid distance to vertex = 3.5 inches

Now, the distance from centroid to vertex of the inscribed equilateral triangle is also the radius of the circle.

Thus; radius = 3.5 inches

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The required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.

Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.

Given:

A company added a new oil thank that holds 350 barrels of oil than its old oil tank . Together they hold 3650 barrels of oil.

According to given question we have

Let the  Capacity of old oil tank = x barrels

Let the Capacity of New oil tank = x + 350 barrels

So,

x + x + 350 = 3650

2x = 3300

x = 1650 barrels

∴Capacity of old oil tank = 1650 barrels

Capacity of New oil tank

=  x + 350

=1650 +350

=2000 barrels

Therefore, the required solution of the given question is Capacity of old oil tank and Capacity of New oil tank is 1650 and 2000 barrels respectively.

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The angle is 14 times its complement, resulting in one angle being 84 degrees and its complement being 6 degrees, following the principle that complementary angles sum up to 90 degrees.

The question mentions that the measure of an angle is 1414 times the measure of its complement. However, this seems to be a typo, and the correct interpretation might be that the angle is 14 times the measure of its complement. First, let's clarify that complementary angles sum up to 90 degrees. If we call the angle A and its complement C, then A = 14C. Knowing that A + C = 90, we can substitute the first equation into this to find C.

To find the measure of the angles, let's denote the measure of one angle as x and the measure of its complement as 90 - x (complementary angles add up to 90 degrees).

Given that x = 14 times the measure of its complement, we can set up the equation x = 14(90 - x) to solve for x. By solving this equation, we find that x = 70 degrees and 90 - x = 20 degrees. Therefore, the measure of the angle is 70 degrees and the measure of its complement is 20 degrees.

Therefore, A + C = 90 becomes 14C + C = 90, simplifying to 15C = 90. Solving for C gives C = 90 / 15, which equals 6 degrees. Subsequently, A, being 14 times C, is 14 * 6 = 84 degrees. Thus, the two angles are 84 degrees and 6 degrees.

Size is a continuous variable that can take on any value within a finite or infinite interval. Screen type is a qualitative variable that describes a characteristic of the data. Number of channels available is a discrete variable because it can only take on countable, distinct values.

In statistics, variables can be classified into different types. Size would be a continuous variable because it can take on any value within a finite or infinite interval. For example, the size of a TV screen can be 32.1 inches, 32.2 inches, 32.25 inches, and so on. On the other hand, screen type would be a qualitative variable because it describes a quality or characteristic of the data, such as LED, LCD, or Plasma. Finally, number of channels available is a discrete variable because it can only take on countable, distinct values. For instance, you could have 200, 300, or 400 channels, but not 300.5 channels.

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31 people came last year, I know this because I removed 15 from 46 which equals to 31. This can be done in many ways either by subtraction or by finding the value of x. So, we all know that 31+x = 46 to find the value of x we have to add 15. So, 31+15 = 46 therefore the answer is 31 people came last year.

Hope this helps!

An array can be utilized to represent the multiplication of two numbers in Mathematics. In this representation, the number 12 can be depicted by a 3x4 or 2x6 arrays. There can be various arrays to represent a number such as 12.

In mathematics, specifically in multiplication, arrays are often used to represent and visualize the multiplication of two numbers. The number 12 can be represented by an array in multiple ways, here we will use two ways:

Remember, for any number, there can be multiple arrays that represent it. For the number 12, for instance, other arrays such as 1 row by 12 columns (1x12) or 12 rows by 1 column (12x1) are possible as well.

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The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.

Here,

The number is 633,248.

We have to compare the values of each 3 in the number 633,248.

What is Place value?

The value represented by a digit in a number on the basis of its position in the number is called the place value.

Now,

The number is 633,248.

From right the first 3 has place in Thousand place.

So, place value of this 3 is thousands place.

And, From right the second 3 has place in Ten thousands place.

The difference of each 3 is that they have different place values.

Therefore, The second 3 is in the Ten thousand place which is 10 times larger than the first 3 which is in the Thousand place.

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