How much of the circle is shaded? Write your answer with as a simplified fraction, with an explanation. Thank you.

At the end of 5 years, with the 3.1% interest rate, your savings account will grow to $349.47.

Use the concept of percentage defined as:

A figure or ratio that may be stated as a fraction of 100 is a percentage. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion, therefore, refers to a component per hundred. Per 100 is what the word percent means.

Given that,

A new savings account is opened with $300.

The account earns a 3.1% interest rate per year.

The interest is calculated yearly.

The duration of the investment is 5 years.

After the first year,

Savings will increase by 3.1% of $300, which is $9.30.

So, your balance at the end of the first year will be $309.30.

For the following years,

you will continue to earn 3.1% interest on the new balance each year. Here's a breakdown of your balance at the end of each year:

Year 1: $309.30

Year 2: $309.30 + 3.1% of 309.30 = $318.88

Similarly

Year 3: $328.77

Year 4: $338.96

Year 5: $349.47

Hence,

At the end of 5 years, with the 3.1% interest rate, your savings account will grow to $349.47.

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Hello!

If you do not know 1 question;

100-20=80

If you do not know 2 question;

20+20=40 100-40=60

If you do not know 3 question;

20+20+20=60 100-60=40

If you do not know 4 question;

20+20+20+20=80 100-80=20

If you do not know 5 question;

20+20+20+20+20=100 100-100=0

The vertex of the function f(x) = 5x²+ 10x + 8 and indicate Minimum at (-1, 3)

To find the vertex of the function f(x) = 5x² + 10x + 8 using the completing-the-square method, follow these steps:

Step 1: Write the function in the form (ax² + bx + c).

f(x) = 5x² + 10x + 8

Step 2: Identify the coefficient of x² and divide it by 2. This gives us (b/2a).

In this case, a = 5, b = 10, so (b/2a) = 10 / (2 * 5) = 1.

Step 3: Square the result from Step 2 [(b/2a)²].

(1)² = 1.

Step 4: Add and subtract the result from Step 3 to the function inside the parentheses.

f(x) = 5x² + 10x + 1 - 1 + 8

Step 5: Group the terms.

f(x) = (5x² + 10x + 1 - 1) + 8

Step 6: Factor the quadratic expression inside the parentheses and simplify.

f(x) = 5(x² + 2x + 1) + -5 + 8

f(x) = 5(x + 1)² + 3

Now the function is in the form f(x) = a(x - h)² + k, where (h, k) represents the vertex of the parabola.

Comparing the function with this standard form, we can see that the vertex is at (-1, 3). The value of 'h' represents the x-coordinate of the vertex, and 'k' represents the y-coordinate of the vertex.

Therefore, the correct answer is:

Minimum at (−1, 3)

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am going to assume you know how to calculate standard deviation, as it is long and tedious to type up. If you really don't understand how to calculate them, I will explain it. The standard deviation is larger in data set 1 than 2, because the spread is larger. The larger the spread, the larger the deviation of the numbers in the set are from the mean (average) number. The standard deviation in 1 is greatest. 2 is in the middle, and 3 is the lowest standard deviation. Hope this helps, good luck.

Answer:

Larger the standard deviation larger the spread present in data.

Step-by-step explanation:

Standard Deviation is the square root of sum of square of the distance of observation from the mean.

[tex]Standard deviation(\sigma) = \sqrt{\frac{1}{n}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}}}[/tex]

where, [tex]\bar{x}[/tex] is mean of the distribution.

It  is used to measure dispersion (spread) of the data. Larger the standard deviation larger the dispersion (spread) present in data.

The Standard deviation of 1st data set is 39.53

The Standard deviation of 2nd data set is 15.81

The Standard deviation of 3rd data set is 7.91

Hence,

(Spread of 1st data set) > (Spread of 2nd data set) > (Spread of 3rd data set)

Answer:

b

Step-by-step explanation:

Answer:

MH is not the correct name for the line segment.

Step-by-step explanation:

Consider the provided information.

A line segment is a line having a starting and end point or we can say portion of a line between two points.

We can represents a line segment by single over bar over the letters.

For example: Consider the figure 1.

The line segment shown in figure 1 is represented by either:

[tex]\overline {GH}\ or\ \overline {HG}[/tex]

The above notation can be read as line segment GH or line segment HG.

Now consider the provided statement. We need to identify the correct name for the line segment.

Option A) MH is wrong notation for the line segment.

Option B) [tex]\overline {MH}[/tex] is the correct notation for the line segment.

Option C) Line segment MH is correct name for the line segment.

Option D) [tex]\overline {HM}[/tex] is the correct notation for the line segment.

Hence, MH is not the correct name for the line segment.

To find the volume of the box, convert all units to inches, then apply the formula for the volume of a rectangular prism, resulting in 2,121.6 cubic inches.

To calculate the volume of the box with dimensions given in inches and feet, we first need to convert all units to the same system. Since the width is given in feet (1.3 feet), we convert it to inches knowing that 1 foot equals 12 inches. Thus, 1.3 feet is equal to 1.3 × 12 = 15.6 inches.

To find the volume of the box, you need to multiply the length, width, and height together:

Convert the dimensions to a consistent unit, such as inches.

Calculate: 17 inches x 1.3 feet x 8 inches = 176.8 cubic inches.

Therefore, the volume of the box is 176.8 cubic inches (in3).

Now, with all dimensions in inches: the length is 17 inches, the width is 15.6 inches, and the height is 8 inches. Applying the formula for the volume of a rectangular prism, V = l × w × h, we get:

V = 17 inches × 15.6 inches × 8 inches = 2,121.6 cubic inches.

Therefore, the correct option is 2121.6 cubic inches (in3).

Answer:

125

Step-by-step explanation:

Answer:

The best prediction for the number of times a 4 will be drawn from the pile is:

                        125

Step-by-step explanation:

It is given that:

A set of cards contains cards numbered 1 – 8.

So, the theoretical probability that 4 comes up is:

Ratio of Number of favorable outcome( outcome of 4) to the total umber outcome(i.e. 8 )

Hence, Theoretical Probability that 4 is drawn=1/8

Now, out of 1000 trials the best prediction of number of times 4 is drawn is:

(The probability of drawing 4)×(Number of experiments or trials)  

=(1/8)×1000

=125

20% of 235 is the number 47.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

Percentage is usually denoted by the symbol '%'.

Let x be the unknown number.

Given that 20% of the number x is 47.

Mathematically, this can be written as,

20% × x = 47

(20/100) x = 47

0.2x = 47

x = 47 / 0.2

x = 235

Hence the unknown number is 235.

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The answer is B. He could increase the sample size.

The Cold War was a prolonged period of geopolitical tension between the United States and the Soviet Union, involving an arms race, proxy wars, and a race for technological superiority, but avoiding direct military conflict due to the threat of nuclear annihilation.

The two superpowers that engaged in the Cold War were the United States and the Soviet Union. The Cold War was a period of geopolitical tension between these two countries that began shortly after the end of World War II and lasted until the collapse of the USSR in 1991. This era was characterized by political and ideological conflicts that were expressed through proxy wars, the arms race, propaganda, and competition in technological advancements such as the space race.

While it was called a 'war', the Cold War did not result in direct military conflict between the two nations. Instead, the struggle for global supremacy was played out through indirect means, including support for opposing sides in regional conflicts such as the Korean War, the Vietnam War, and the Soviet-Afghan War. The fear of Mutually Assured Destruction (M.A.D.) due to both nations possessing extensive nuclear arsenals was a deterrent against a 'hot' war.

The Cold War impacted almost every aspect of international relations and domestic policies within the superpower nations and their allies, with each side attempting to limit the influence and spread of the other's ideology. The United States followed a policy of containment to prevent the spread of communism, and the Soviet Union tried to expand its socialist model and create a buffer zone against the West.

The set 8, 15, 17 is a Pythagorean triple because 8^2 + 15^2 = 17^2. A triangle with sides of 6, 7, and 10 is an obtuse triangle, because 10^2 > 6^2 + 7^2.

The set of numbers, 8, 15, 17, represents a Pythagorean triple. A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2. In this case, 8^2 + 15^2 = 64 + 225 = 289, and 17^2 = 289, so the equation is satisfied.

Furthermore, a triangle with sides 6, 7, and 10 would be described as obtuse. In any triangle, if the square of the length of the longest side is greater than the sum of the squares of the other two sides, then the triangle is obtuse. Thus, if 10^2 > 6^2 + 7^2, or 100 > 36 + 49, then the triangle is obtuse. Since this statement holds true, the triangle is indeed obtuse.

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The correct options are: B. 8, 15, 17 and A. obtuse

We can use the Pythagorean theorem to determine which set of numbers is a Pythagorean triple. The theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a2 + b2 = c2.

The correct Pythagorean triple is 8, 15, 17.

To determine the type of triangle with side lengths 6, 7, and 10, we use the idea that for a triangle with sides a, b, and c (where c is the longest side):

For the triangle with sides 6, 7, and 10:

[tex]6^2+7^2=36+49=85[/tex] and [tex]10^2=100[/tex].

Since 100 > 85, the triangle is obtuse.

To make x the subject of the equation, you can rearrange the equation x = 5t - a.

To make x the subject of the equation, we need to isolate the variable on one side of the equation. Here's how:

Therefore, to make x the subject, the equation is x = 5t - a.

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