Determine the equation of the circle with center (0, -5) containing the point
(-√60,-6).

Using sine law, the length of t is 11.34 units

A fundamental conclusion of trigonometry that connects a triangle's sides and angles is known as the law of sines. It claims that the following relationship holds for any triangle with sides a, b, and c and opposite angles a, b, and c:

a / sin A = b / sin B = c / sin C

In other words, each of the triangle's three sides has a length that is equal to the sine of the angle opposite it. Any triangle, correct or not, can be related to another triangle in this way.

When some of the information is available, it is common to utilize the Law of Sines to find the triangle's unknown side lengths or angle measurements. In addition to the Law of Cosines, it can also be employed alone.

Using sum of angle of triangle;

V + U + T = 180

v + 100 + 36 = 180

v + 136 = 180

v = 180 - 136

v = 44°

8 / sin 44 = t / sin 100

t = 8 sin100 / sin44

t = 11.34

The value of t is 11.34 units

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

When you roll a di, there is a  [tex]\frac{1}{2}[/tex] chance you will either get an even or an odd number. Since this needs to happen twice, we will square this fraction, giving us:

[tex](\frac{1}{2}) ^{2} = \frac{1}{4}[/tex]

So, the probability to roll an even number and then roll an odd number is [tex]\frac{1}{4}[/tex].

Hope this helped!

Natural Numbers: 13, 17

Whole Numbers: 13, 17

Integers: -15, 13, 17

Rational Numbers: -17/13, 3.63

Irrational Numbers: √7, π/4

First, let us understand what each type of numbers are.

Natural Numbers: All positive numbers from 1 to infinity are considered natural numbers and are therefore a component of the number system. Because they don't contain zero or negative numbers, natural numbers are also known as counting numbers. They are a subset of real numbers, which only include positive integers and exclude negative, zero, fractional, and decimal numbers.

Whole Numbers: The term "whole numbers" refers to numbers devoid of fractions, which are made up of positive integers and zero. Its symbol is "W," and its range of numbers is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...}. The entire number zero denotes nothing or a null value.

Integers: Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.

Rational and Irrational Numbers: An irrational number cannot be stated using fractions, but a rational number may be expressed as the ratio of two integers with the denominator not equal to zero. Irrational numbers are non-terminating and non-recurring, whereas rational numbers have terminating decimals.

Now, in the set provided, we can classify them as follows.

Natural Numbers: 13, 17

Whole Numbers: 13, 17

Integers: -15, 13, 17

Rational Numbers: -17/13, 3.63

Irrational Numbers: √7, π/4

Thus, this is the final classification.

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If the right hand side of the equation is non-negative real number, the equation will have two solution that include all real numbers.

An absolute value equation of the form |x| = k (where k is a constant) will have two solutions, one positive and one negative, that are the same distance from 0 on the number line.

To determine if the solutions of the equation include all real numbers, you can examine the value of k. If k is a non-negative real number, then the two solutions of the equation will include all real numbers, because any real number is either positive or negative and the same distance from 0 as k.

For example, if the equation is |x| = 5, the two solutions of the equation are x = 5 and x = -5, which include all real numbers.

On the other hand, if k is a negative real number or a complex number, the equation is not valid and there are no solutions.

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1/2 as a decimal is 0.5. As a percent, it is 50%. 1/2 can be written as a decimal by dividing the numerator (1) by the denominator (2).

In this case, 1 divided by 2 is 0.5. To convert this decimal to a percent, simply multiply it by 100. 0.5 multiplied by 100 is 50%, so 1/2 as a percent is 50%.

1/2 is 0.5 as a decimal and 50% as a percent.

1/2 is equal to 0.5 when written as a decimal. This means that 1 is divided by 2, resulting in 0.5. To convert this decimal to a percentage, it is necessary to multiply it by 100. When 1/2 is multiplied by 100, it comes out to be 50%, meaning that 1/2 as a percent is 50%. This shows that 1/2 is equal to 0.5 as a decimal and 50% as a percent.

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There are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits.

There are 5 choices for the first digit, 4 choices for the second digit, and 3 choices for the third digit. This can be expressed using the combination formula:

nCr = n! / r!(n - r)!

So, the number of possible 3-digit numbers with no digit repeated can be calculated as 5C3 = 5!/(3!*2!) = 10.

Therefore, there are 10 possible 3-digit numbers which can be generated using numbers 1, 2, 3, 4, and 5 without repeating any digits. These numbers are 123, 124, 125, 134, 135, 145, 234, 235, 245, and 345.

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Reason:

The ratio of white to green is 2:5.

The ratio of green to blue is 1:3, which can be scaled up to 5:15 after multiplying both parts by 5.

Write out the ratios 2:5 and 5:15 to notice that we have the inner '5's match up. This gives a triple ratio of 2:5:15 which is the ratio of white to green to blue in that exact order.

Ignoring the middle value gives the ratio of white to blue being 2:15

For every 2 white beads, there are 15 blue beads.

The oldest type of currency still in use today, according to the claim, is metal.

Money is a good that is frequently used as a basis of economic exchange. It is used to communicate values and prices and is the primary determinant of value. By effortlessly traveling from one person to another and from one country to another, money fosters commerce.

Money is derived from the Latin term moneta, which means "coin," through the French term monnaie. It is thought that the Latin phrase came from a temple dedicated to Juno on Capitoline, being one Poland's seven hills. Juno was frequently linked to riches in ancient times.

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The relationship between Doubling and halving is that in halving we simply half one of the factors and in doubling we double the other.

The Doubling and Halving is a technique that is commonly used in Multiplication of two numbers .

Let us understand the Relationship between Doubling and Halving with help of an example ;

Example : To solve 25×16, it is not that simple to directly multiply these ,

By using the Doubling and Halving method ,

we could double the number 25 to make it 50 and

then half the number 16 to make it 8.

So , the equivalent expression becomes , [tex]50\times8[/tex] ,which is much easier to solve , that is 400 .

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Answer:

325 hamburgers were sold on Tuesday

Step-by-step explanation:

We can start solving the problem by using algebra. Let H be the number of hamburgers sold and C be the number of cheeseburgers sold. We know from the problem that:

H + C = 713 (total number of hamburgers and cheeseburgers sold)

C = H + 63 (there were 63 more cheeseburgers sold than hamburgers)

We can substitute the second equation into the first equation:

H + (H + 63) = 713

2H + 63 = 713

2H = 650

H = 325

The function increasing on interval  [0, 3] and decreasing on the interval  [-6, 0] ∪ [3, 5].

What is increasing and decreasing function?

For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.

F is rising on the interval if f′(x) > 0 on an open interval.

F is decreasing on the interval if f′(x) < 0 on an open interval.

We have to find the intervals of increasing and decreasing function from the given graph.

From graph we can see that graph is increasing on the interval [0, 3].

And decreasing on the interval [-6, 0] ∪ [3, 5].

Hence, the function increasing on interval  [0, 3] and decreasing on the interval  [-6, 0] ∪ [3, 5].

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Answer:

James is 18 and Patrick is 38

Step-by-step explanation:

Let p = Patrick's age

Let j= James' age

p = j + 20

p + 2 = 2(j+2)        Substitute j + 20 for p

j + 20 + 2 = 2j + 4  Combine like terms.

j + 22 = 2j + 4  Subtract j from both sides

j -j + 22 = 2j - j + 4

22 = j + 4    Subtract 4 from both sides

22 - 4 = j + 4 - 4

18 = j

James is 18 years old.

Substitute 18 for j  in p = j + 20

p =  18 + 20

p = 38

Patrick is 38

To round to the nearest tenth, we examine the digit in the hundredth's place (the second decimal place).

In this case, the number is 7. Since 7 is greater than or equal to 5, we round the digit in the tenth's place up by one.

7.1703171 rounded to the nearest tenth is 7.2.

Answer:

60mm

Step-by-step explanation:

240*1/4=60mm

Answer:

40 mm

Step-by-step explanation:

Given information:

To find the length of the children's shoes, multiply the length of the adult shoes by the scale factor:

[tex]\begin{aligned}\implies 240 \times \dfrac{1}{6}&=\dfrac{240 \times 1}{6}\\\\&=\dfrac{240}{6}\\\\&=\dfrac{40 \times 6}{6}\\\\&=40\; \sf mm\end{aligned}[/tex]

Therefore, the length of the children's shoes is 40 mm.

On solving the provided question, we can say that standard deviation and mean, The equivalent ACT score is using 1.545 as the z score [tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]

Standard deviation is a statistic that expresses the variability or variance of a group of numbers. While a high standard deviation suggests that the values are more dispersed, a low standard deviation suggests that the values tend to be closer to the established mean. A measure of how dispersed the data are from the mean is the standard deviation (or ). When the standard deviation is low, the data tend to be grouped around the mean, and when it is large, the data are more dispersed. The average variability of the data set is measured as standard deviation. It reveals the average deviation of each score from the mean.

[tex]X = 0.675 * 198 + 1101 = 1235[/tex]

standard deviation and mean

[tex]X = 0.675 * 3.9 + 19.2 = 21.8[/tex]

scores 1407  standardized score z for 1407

[tex]z = (X-μ)/σ = (1407-1101)/198 = 1.545[/tex]

The equivalent ACT score is using 1.545 as the z score

[tex]= > X = 1.545 * 3.9 + 19.2 = 25.5[/tex]

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The congruent sides of an isosceles triangle are each $5$ cm long, and the perimeter is $17$ cm.  the length of the base is 7 cm.To calculate the length of the base of an isosceles triangle, we can use the formula of the perimeter.

The perimeter is the sum of all sides of a triangle, so the formula is Perimeter = Side1 + Side2 + Base. In this case, the two congruent sides are each 5 cm long, and the perimeter is 17 cm. So, if we set up an equation, we have 17 = 5 + 5 + Base. We can then solve the equation for Base by subtracting 10 from both sides.

This gives us 17 - 10 = 5 + Base, and then subtracting 5 from both sides gives us 12 = Base. Then, we can divide both sides by 12 to get 1 = Base / 12. Lastly, we can multiply both sides by 12 to get 12 = Base. Therefore, the length of the base is 7 cm.

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Answer:

[tex]-11\sqrt{5}-11\sqrt{6}[/tex]

Step-by-step explanation:

Given expression:

[tex]\dfrac{11}{\sqrt{5}-\sqrt{6}}[/tex]

To rationalize the denominator, multiply the numerator and denominator by the conjugate of the denominator.

The conjugate of a binomial is where we change the sign between the two terms of the binomial.  So the conjugate of (√5 - √6) is  (√5 + √6).

[tex]\implies \dfrac{11}{\sqrt{5}-\sqrt{6}} \cdot \dfrac{\sqrt{5}+\sqrt{6}}{\sqrt{5}+\sqrt{6}}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{(\sqrt{5}-\sqrt{6})(\sqrt{5}+\sqrt{6})}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{\sqrt{5}\sqrt{5}+\sqrt{5}\sqrt{6}-\sqrt{6}\sqrt{5}-\sqrt{6}\sqrt{6}}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{5-6}[/tex]

[tex]\implies \dfrac{11(\sqrt{5}+\sqrt{6})}{-1}[/tex]

[tex]\implies -11(\sqrt{5}+\sqrt{6})[/tex]

[tex]\implies -11\sqrt{5}-11\sqrt{6}[/tex]

Yes , we can construct a triangle which has the side lengths as 11 cm 12 cm and 15 cm , because the given sides satisfies the criteria to form a triangle .

The Condition for the sides to form a triangle is that the Sum of the any two sides of the triangle must be greater than the third side of the triangle .

The sides of the triangle are given as ⇒ 11cm ,12cm and 15cm ;

On adding the two sides ,

we get ;

⇒ 11 + 12 = 23 > 15 ; True

⇒ 12 + 15 = 27 > 11 ; True

⇒ 11 + 15 = 26 > 12 ; True

So , we can see that all the three conditions are satisfied .

Therefore , the triangle can be constructed with the sides 11cm ,12cm and 15cm .

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Therefore , the solution of the given problem of linear equation comes out to be chris sold = g/8 -17.

A model of linear regression is one that follows the algebraic formula y=mx+b. The y-intercept is m, and the slope is B. Although both y and x are distinct parameters, the foregoing sentence is sometimes referred to as a "mathematical equation with two variables." Bivariate linear equations only have two variables. Application areas of linear equations result in zero in all cases. The equation for one linear equation is Y=mx+b where m is the slope and b is the y-intercept. Y=mx+b is the formula for an equation, where m stands for slopes and b for the y-intercept.

Here,

Given : there are 8 employees on the game .

chris sold 17 fewer games than what the team averaged per employee.

Thus,

g be the number of total employee selling games:

=> chris sold = g/8 -17

Therefore , the solution of the given problem of linear equation comes out to be chris sold = g/8 -17.

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The measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 137.5 degrees.

The hour hand of a 12-hour clock completes one full rotation in 12 hours while the minute hand completes one full rotation in 60 minutes. To find the measure of the angle between the hands of a 12-hour clock at 12:25 pm, we need to calculate the relative position of the hands with respect to the 12 o'clock position.

At 12:25 pm, the minute hand is pointing to the 12.25 mark on the clock which is 25 minutes after 12 o'clock and the hour hand is pointing to the 12 o'clock mark.

The minute hand moves 360 degrees every 60 minutes, so in 25 minutes, it would have moved (360/60)*25 = 75 degrees.

The hour hand moves 360 degrees every 12 hours, so in 25 minutes, it would have moved (360/12*60)*25 = (30)*25 = 750/60 = 12.5 degrees.

The angle between the hands is the absolute difference between their positions.

the angle between the hands = |75-12.5| = 62.5 degrees

However, the clock has two hands and thus we have two angles between the hands.

Therefore, the measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm is 180-62.5 = 137.5 degrees.

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Answer: The volume of a sphere can be calculated using the formula V = 4/3 * pi * r^3, where V is the volume and r is the radius of the sphere. In this case, we can use the Pythagorean theorem to find the radius of the sphere. The hypotenuse of the right triangle is 16 cm and is also the diameter of the sphere, therefore the radius of the sphere is half of the hypotenuse or 8 cm.

Now we can use this value of radius to calculate the volume of the sphere.

V = 4/3 * pi * 8^3

V = 4/3 * pi * 512

V = 2197.333 cm^3 (rounded to the nearest hundredth)

So, the volume of the sphere is 2197.333 cm^3

Step-by-step explanation:

The solution set for the function f(x) ≤ 0 as required to be determined in the task content in interval notation is; ( infinity, 3 ].

It follows from the task content that the values of x for which f(x) ≤ 0 be determined considering the given graph.

As evident in the given graph; the portion of the graph which is below the x-axis (i.e below the line f (x) = 0 ) lies in the interval; ( infinity, 3 ] for variable x.

On this note, it can be inferred that the required solution set for f(x) ≤ 0 is; ( infinity, 3 ].

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An expression that represents the height of a tree is 6.7 + 2.9.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Here, we have

Given

The initial height of the tree is 6.7 feet

The increase in height per year = 2.9 feet

Thus,

The expression will be = 6.7 + 2.9t,

Here t represents the number of years.

Hence, an expression that represents the height of a tree is 6.7 + 2.9.

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Answer: 2.55x

Step-by-step explanation:

The potential energy of a 50kg boulder at the ledge of a cliff 250m high is 122500 J.

Potential energy is the energy carried by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.

The PE energy of a boulder 250 m from the ground is given by the formula

PE = h x m x g    where h is the height above the ground, m is the mass, and g is the acceleration of gravity.

Putting the given values in the equation

PE = 250m x 50 kg x 9.8 m/s²  =  122500 J

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To determine the number of smartphones sold in 2012 with the exponential function.

What is exponential function ?

An exponential function is a mathematical function in which the variable, or the input, is in the exponent (power) of the function. It takes the form of f(x) = ab^x, where a and b are constants and x is the variable. The variable x is often time and the constant b is often greater than 1, which causes the function to grow at an increasing rate. It is often used to model growth and decay phenomena, such as population growth, radioactive decay, and others.

To estimate the number of smartphones sold in 2012, we would need to find the exponential function that models the worldwide sales of the smartphone brand from 2008 to 2011. Once we have this function, we can plug in the year 2012 as the input to estimate the number of smartphones sold in that year. However, without more information it is impossible to know the exact exponential function and the exact number of smartphones sold in 2012.

To determine the number of smartphones sold in 2012 with the exponential function.

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Answer:

The slope of the line is -10/11

Step-by-step explanation:

To find the slope with points you would use the formula [tex]m = \frac{y2 - y1}{x2 - x1}[/tex]

Now since the line crosses the y-axis at 17, that would be where the y-intercept is, meaning there is a point at (0, 17).

With that, we can find the slope with (11, 7) and (0, 17) in the formula above

So, [tex]m = \frac{17 - 7}{0 - 11}[/tex]

which will simplified to, [tex]m = -\frac{10}{11}[/tex]

So the slope is - 10/11

As per the given distribution the consumer group claims that the difference in proportions has a mean of 0.05.

The term mean in math is defined as the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Here we have given that the consumer group is investigating two brands of popcorn, R and S.

And the population proportion of kernels that will pop for Brand R is 0.90 where as the population proportion of kernels that will pop for Brand S is 0.85.

Then the difference of the mean is calculated as,

=> 0.90 - 0.85

=> 0.05

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Answer:

I don't know ooo y the same time that I can come get you if you want to