Hey circle has a diameter of 30 cm what is the circumference?


Use 3.14 for pie and do not round your answer be sure to include the correct unit in your answer 

Answer: Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

Step-by-step explanation:

To find all values of x for which f(x) = g(x), we can set the two functions equal to each other and solve for x:

-x² + 5 = -2x + 2

Expanding the right-hand side:

-x² + 5 = -2x + 2

-x² + 2x + 3 = 0

Solving for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1, b = 2, and c = 3

x = (-2 ± √(2² - 4(1)(3))) / 2(1)

x = (-2 ± √(4 - 12)) / 2

x = (-2 ± √(-8)) / 2

Since the square root of a negative number is not a real number, there are no real solutions to this equation, and therefore no values of x for which f(x) = g(x).

Answer:

199 cm²

Step-by-step explanation:

in the picture

Answer: x =1, y = -1

Step-by-step explanation:

-10x+4y=-14

7x+5y=2

Let's eliminate y.

5(-10x+4y= -14)

4(7x + 5y=2)

[ I multiplied the first equation by the coefficient of y in the second equation and did the same in the second equation].

=> -50x+20y =-70

     28x+20y = 8

Notice how the coefficients of y are the same. We can subtract the 2 equations to eliminate y.

Thus,

-78x = -78 ( y has been eliminated)

∴ x=-78/-78 =1.

Put the value of x in any equation to find y.

7x + 5y =2

=> 7(1) + 5y =2

7+5y=2

5y = 2-7

5y = -5

y = -1.

Hope this helps :)

Step-by-step explanation:

the equation we use here is [items to choose from] to the power of [required items]; in this case, we get [tex]10^{3}[/tex].

The length of the two sides of the given right triangle is 5√2

A triangle with an angle right angle is called a right triangle.

Given that, a right triangle, with an acute angle of 45° and the length of hypotenuse is 10 units,

We need to find the length of two sides u and v,

The sum of a triangle is 180°, and if one angle is 90° and the other is 45° therefore, the third is also 45°

Now, we know that, sides opposite to equal angles are equal,

Therefore, v = u,

Now, using the Pythagoras theorem,

10² = v²+u²

v² + v² = 100

2v² = 100

v² = 50

v = 5√2

u = 5√2

Hence, the length of the two sides of the given right triangle is 5√2

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The statement "If f(n) = O(g(n)) and g(n) = Ω(h(n)), then f(n) = Θ(h(n))" is actually true.

This can be proven using the formal definitions of the O-notation, Ω-notation, and Θ-notation:

f(n) = O(g(n)) means that there exist positive constants c and n0 such that |f(n)| ≤ c|g(n)| for all n ≥ n0.

g(n) = Ω(h(n)) means that there exist positive constants c' and n0' such that |g(n)| ≥ c'|h(n)| for all n ≥ n0'.

f(n) = Θ(h(n)) means that there exist positive constants c1, c2, and n1 such that c1|h(n)| ≤ |f(n)| ≤ c2|h(n)| for all n ≥ n1.

If we assume that f(n) = O(g(n)) and g(n) = Ω(h(n)), we can use the definitions above to show that f(n) = Θ(h(n)).

Since g(n) = Ω(h(n)), we have |g(n)| ≥ c'|h(n)| for some positive constants c' and n0', and since f(n) = O(g(n)), we have |f(n)| ≤ c|g(n)| for some positive constants c and n0.

Combining these two inequalities, we get:

|f(n)| ≤ c|g(n)| ≤ c(c'/c)|h(n)|

Therefore, f(n) = Θ(h(n)) with constants c1 = 1 and c2 = c(c'/c), and n1 = max(n0, n0').

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Answer:

Part A: If (26)x = 1, the value of x is approximately 0.03846.

Part B: If (50)x = 1, the possible value of x is approximately 0.02.

Step-by-step explanation:

Part A: To find the value of x in the equation (26)x = 1, we need to find the value that, when raised to the power of 26, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 26 and taking the natural logarithm of both sides.

Using the formula x = 1/26, we get:

x = 1/26 = 0.03846

So, the value of x in the equation (26)x = 1 is approximately 0.03846.

Part B: To find the possible values of x in the equation (50)x = 1, we need to find the values that, when raised to the power of 50, will equal 1. This value can be found by taking the reciprocal (or multiplicative inverse) of 50 and taking the natural logarithm of both sides.

Using the formula x = 1/50, we get:

x = 1/50 = 0.02

So, the possible value of x in the equation (50)x = 1 is approximately 0.02.

So the simplified expression of the expression given in the question is: 1.17 - 3.99a

To simplify the expression, we can combine the like terms, which are terms with the same variable and exponent. Starting with the first two terms: 1.17 - 0.07a. The next two terms are the opposite of each other, so we can add them: 1.17 - 0.07a + (-3.92a) = 1.17 - 0.07a - 3.92a. Finally, we can simplify the expression by combining the like terms, which are terms with the same variable: 1.17 - 0.07a - 3.92a = 1.17 - (0.07 + 3.92)a = 1.17 - 3.99a. So the simplified expression is: 1.17 - 3.99a

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Complete Question

Combine like terms to simplify the expression:

1. 17 − 0. 07 + ( − 3. 92 )  1. 17−0. 07a+(−3. 92a)

Option d) [tex]y= 30.5(0.7)^x[/tex] is the function that best models the number of game systems sold in millions x years since 2015.

In mathematics, a function is a rule that associates each element in one set (called the domain) with a unique element in another set (called the range). The rule specifies how the input values (the elements of the domain) are transformed into output values (the elements of the range).

A function can be represented using various notations, such as f(x), where f is the name of the function and x is the input value, or y = f(x), where y is the output value and x is the input value. The function can be defined explicitly, as in[tex]f(x) = x^2,[/tex] or implicitly, as in the equation of a circle, [tex]x^2 + y^2 = r^2[/tex], where y is a function of x.

To determine which function best models the number of game systems sold, we need to observe the trend in the data.

We can see that the number of game systems sold is decreasing as time goes on, which means the function should be decreasing as well.

Option a) [tex]y=21.35(0.7)^x[/tex] is an exponential function with a base less than 1, which means it would also be decreasing. However, it starts with a higher initial value than the data suggests.

Option b) [tex]y= 30.5(21.35)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function does not match the trend in the data.

Option c) [tex]y= 30.5(1.3)^x[/tex] is an exponential function with a base greater than 1, which means it would be increasing. This function also does not match the trend in the data.

Option d) [tex]y= 30.5(0.7)^x[/tex]is an exponential function with a base less than 1, which means it would be decreasing. Additionally, this function passes through all three data points, and it has a starting value that matches the first data point. Therefore, option d) is the function that best models the number of game systems sold in millions x years since 2015.

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The mean for the number of students who work full-time in

samples of size 16 are 3.5.

We understand The expected value, also known as the expected average in the field of probability theory, is a generalization of the weighted average.

Given, 22% of all students work full-time, per a college poll.

Now, If we choose a sample of 16 students the mean number of students working full-time is,

= 16(22/100)

= 16×0.22

= 3.5.

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The probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

Simply put, probability is the liability that commodity will do. When we do not know how an event will turn out, we can bandy the liability or liability of several issues. Statistics is the study of events that follow a probability distribution.

a) We need to find p(x<68.15)

Standardize x to z, we have, z = (68.15-μ)/σ

=(68.15-57)/8.1

=1.38

Reading from standard normal tables,

p(z<1.38) =0.9162.

Therefore, the probability that a randomly chosen child has a height of less than 68.15 inches is 0.9162.

b) We need to find p(x>54.4)

Standardize x to z, we have, z = (54.4-μ)/σ

=(54.4-57)/8.1

=-0.32

Reading from standard normal tables,

p(z>-0.32) = 0.6255

Therefore, the probability that a randomly chosen child has a height of more than 54.4 inches is 0.6255.

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The right triangle ABC with right angle at vertex B has the length of the segment is; 4√2 unit.

The Pythagorean theorem state that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.

We can find the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can find that side BC is equal to the length of side AB.

The side lengths are 8/2 = 4

Now, Another side length that is x

So , the equation formed is;

xcos45 = 4

x/√2 = 4

x = 4√2

Hence the length of the segment is; 4√2 unit.

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There are 35 ways to choose two toppings for a pizza, one topping from a group of 5 kinds of meats and the other topping from a group of 7 kinds of vegetables.

The multiplication rule of counting in Permutation and Combinations states that if there are n ways to perform one task and m ways to perform a second task, then there are n x m ways to perform both tasks in sequence.

The number of ways to choose a meat topping from 5 kinds of meats = 5.

The number of ways to choose a vegetable topping from 7 kinds of vegetables = 7.

Using the multiplication rule, the number of ways to choose one meat topping and one vegetable topping is = 5 x 7 = 35 ways.

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The volume of the silo of cylinder shape containing grain is 8625.24 cubic units.

The volume of the cylindrical shaped grain silo will be calculated by the formula -

Volume = πr²h, where r represents radius and h represents height of the cylinder.

Now, as we know radius is half of the diameter. So, radius = 17/2

Performing division on Right Hand Side of the equation

Radius of the cylinder = 8.5

Keep the values in formula to find the value of volume of silo

Volume = π × 8.5² × 38

Taking square and performing multiplication on Right Hand Side of the equation

Volume = 8625.24 cubic units

Hence, the volume is 8625.24 cubic units.

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Answer:

X = 48

Step-by-step explanation:

x/4 - 6 = x/12 + 2​

= 3x-72=x+24

= 3x=x+96

= 2x=96

= x=48

Answer:

x=48

Step-by-step explanation:

You can solve by x by simplifying both sides of the equation, then isolating the variable

The given statement is transitive property.

Transitive property is also called transitive property of equality when we have two equal values and either of this value is equal to third value.

DE≅XY AND [tex]\hat{DE}$$\approx\hat{XY} and \hat{XY}$$\approx$$\YZ, then\hat{DE}$$\approx$$\hat{YZ}[/tex]

This is a transitive property.

Here we have three values, initially first two values are equal and second & third values are equal.

Which gives any one of the value of first and second equals third value.

This is the transitive property.

Hence, the given statement is transitive property.

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The variability of the data is very small (close to 0) because all the scores are approximately the same.

The variability of these data can be calculated using the variance formula, which is the average squared difference from the mean. In this case, the mean is 3.8 (the sum of 4, 4, 4, 4, and 3 divided by 5). Therefore, the variance is 0.08 (the sum of the squared differences [4-3.8, 4-3.8, 4-3.8, 4-3.8, 3-3.8] divided by 5). This indicates that the variability of the data is very small (close to 0) because all the scores are approximately the same.

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Answer:

AAS

Step-by-step explanation:

There are two pairs of congruent angles, and the pair of congruent sides is not included in between the angles.

The solution of x in the rhombus is 3

From the question, we have the following parameters that can be used in our computation:

The rhombus

Also, we have

LN = 14

AN = x + 4

Using the above as a guide, we have the following equation:

LN = 2 * AN

Substitute the known values in the above equation, so, we have the following representation

2 * (x + 4) = 14

Evaluate the expression

x + 4 = 7

Subtract 4 from both sides

so, we have the following representation

x = 3

Hence, the solution is 3

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Answer:

Solution to system of inequalities is y≥ 3x-2

Graph attached

Step-by-step explanation:

We have the following two inequalities:
y>-3x-5

y≥ 3x-2

To get the solution and graph

1. Graph each inequality separately

2. Choose a test point to determine which side of the line needs to be shaded

3. The solution will be the area where the shadings from each inequality overlap one another

The graph is attached. The heavily shaded region is the set of all points which satisfy all inequalities

We see that any point that satisfies y≥ 3x-2  also satisfies y>-3x-5

In other words, the solution set for y≥ 3x-2 is a subset of the solution set for   y>-3x-5

The solution of the equation are as follows:

y = 15

v = 28

r = 95.5

m = 30

d = 54

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.  The equation can be solved by finding the value of the variables.

A variable is a number represented with letter in an equation.

Therefore, let's solve the equation.

y + 4 - 1 = 18

y = 18  - 4 + 1

y = 15

v - 7 = 9 + 12

v = 12 + 9 + 7

v = 28

53.5 + 44 = 2 + r

r = 53.5 + 44 - 2

r = 95.5

m + 18 + 23 = 71

m = 71 - 18 - 23

m = 30

22 + 15 = d - 17

d = 22 + 15 + 17

d = 54

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The size of width of each lumber piece will be 3.875 inches.

Logic is the arrangement of all those concepts, whereas algebra is the study of abstract concepts.

Making something a little less complicated while both making it easier to attain or understand is the concept of clarity.

Mrs. Harris intends to divide the breadth of a piece of timber that is 11 ⁵/₈ inches broad into three equal pieces.

Convert the mixed fraction number to a decimal number. Then we have

11 ⁵/₈ = 11 + ⁵/₈

11 ⁵/₈ = 11.625 inches

The width of each lumber piece is given as,

⇒ 11.625 / 3

⇒ 3.875 inches

The size of width of each lumber piece will be 3.875 inches.

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Answer:

None. [tex]24+25+26[/tex] is the only valid answer

Step-by-step explanation:

We can create an expression for the sum of 3 consecutive numbers.

[tex]S=x+(x+1)+(x+2)[/tex]

Which we can simplify to

[tex]S=x+x+1+x+2[/tex]

[tex]S=3x+3[/tex]

In this example we are given a sum of 75.

[tex]75=3x+3[/tex]

Lets solve for [tex]x[/tex].

Subtract 3 from both sides.

[tex]72=3x[/tex]

Divide both sides by 3.

[tex]24=x[/tex]

To find out what the 3 numbers are we can plug in 24 for x

[tex]x+(x+1)+(x+2)[/tex]

[tex]24+(24+1)+(24+2)[/tex]

[tex]24+25+26[/tex]

Answer:

  4 other ways (5 ways, total).

Step-by-step explanation:

You want to know how many other ways 75 can be written as the sum of consecutive whole numbers other than 24+25+26.

If 75 is written as the sum of an odd number of integers, the middle integer of the set will be 75 divided by the number of integers. The divisors of 75 are {1, 3, 5, 15, 25, 75}. If the numbers in the sum are non-negative, the number of integers involved cannot be more than √(2·75) ≈ 12. Then allowed odd numbers of integers in the sum are 3 and 5.

If 75 is written as the sum of an even number of integers, the quotient when 75 is divided by the number of integers must be 1/2 more than a whole number. Such integer divisors are 2, 6, and 10.

  37 + 38 = 75 . . . . 2 integers

  24 + 25 + 26 = 75 . . . . 3 integers (the given sum)

  13 + 14 + 15 + 16 + 17 = 75 . . . . 5 integers

  10 + 11 + 12 + 13 + 14 + 15 = 75 . . . . 6 integers

  3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 = 75 . . . . 10 integers

There are 4 other ways to use consecutive non-negative integers to make a sum of 75.

Answer:

22

Step-by-step explanation:

x+35=56

56-35=22

x=22

Answer:

maximum value = 135

Step-by-step explanation:

the maximum value is situated at the right end of the whisker.

each division on the number line is 5 units

so maximum value = 125 + 2 units = 125 + 10 = 135

Based on the Venn diagram, the number of people in each set are follows:

The number of people in each set in the Venn diagram is calculated as follows:

The universal set has a total of 50 people

Let the intersection of A and B be x

A∩B = x

The number of people in A alone = 24 - x

The number of people in B alone = 30 - x

x + (24 - x) + (30 - x) + 7 = 50

61 - x = 50

x = 61 - 50

x = 11

A∩B = 11

Hence;

The number of people in A alone = 24 - 11

The number of people in A alone = 13

The number of people in B alone = 30 - 11

The number of people in B alone = 19

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A bag of 15 scrabble tiles contains three each of the letters a, c, e, h, and n. The chance of spelling "chance" is approximately 0.0108 or about 1.08%.

First, we need to count the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n" from the 15 tiles in the bag. To do this, we use the combination formula:

C(n, r) = n! / (r! * (n - r)!)

where n is the total number of items and r is the number of items we want to choose. For example, to choose two "c"s from three, we can calculate:

C(3, 2) = 3! / (2! * (3 - 2)!) = 3

We can use this formula to calculate the number of ways to choose two "c"s, two "e"s, and one each of "h" and "n":

C(3, 2) * C(3, 2) * C(3, 1) * C(3, 1) = 54

Therefore, there are 54 ways to choose the required letters out of the 15 tiles in the bag.

Next, we need to count the total number of ways to choose 6 tiles from the 15 in the bag. We can again use the combination formula:

C(15, 6) = 15! / (6! * (15 - 6)!) = 5005

Therefore, there are 5005 ways to choose any 6 tiles from the bag.

Finally, we can calculate the probability of spelling "chance" by dividing the number of ways to choose the required letters by the total number of ways to choose 6 tiles:

54 / 5005 ≈ 0.0108 or about 1.08%

So the probability of spelling "chance" when picking six tiles one at a time from the bag is approximately 0.0108 or about 1.08%.

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The length of the candle that has been burning for the total of 240 minutes would be = 9 inches.

The rate at which a candle burns = 2 in/ 2 hours

That is,

2 in = 2 hour; 2 inches = 120 minutes

X in = 240 minutes

Make X the subject of formula;

X = 2×240/120

X= 480/120

X = 4+5

X = 9 inches

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Answer:

30.

Step-by-step explanation:

We can write an equation for the number of gallons of water in the bathtub using the rate of change (drainage) and the elapsed time. Let y be the number of gallons of water in the tub after t minutes. Then, the equation can be written as:

y = 42 - (drainage rate) * t

Since we know that after 2 minutes, the tub holds 30 gallons of water, we can use this information to solve for the drainage rate:

30 = 42 - (drainage rate) * 2

12 = (drainage rate) * 2

drainage rate = 6 gallons per minute

Substituting this value into the original equation, we get:

y = 42 - 6t

So, the equation that represents the number of gallons of water in the tub after 2 minutes is:

y = 42 - 6 * 2 = 42 - 12 = 30.

Answer:

The equation representing the number of gallons of water in the tub after t minutes can be represented by a linear function y = mx + b, where y is the number of gallons of water, x is the number of minutes, m is the rate of change (or the slope) and b is the y-intercept.

Since the bathtub is draining at a constant rate, the slope (m) can be found by finding the difference between the initial number of gallons of water (42) and the number of gallons after 2 minutes (30), and dividing by the difference in time (2 minutes):

m = (42 - 30) / 2 = 6 gallons per minute

The y-intercept (b) can be found using the initial conditions of the problem, when t = 0:

b = 42 - (6 * 0) = 42

Therefore, the equation representing the number of gallons of water in the tub after t minutes can be written as:

y = 6t + 42

So, after 2 minutes, y = 6 * 2 + 42 = 54 gallons of water.