The line 2x+3y=-22 is tangent to a circle centered at (-1,2) What is the tangent point?

Therefore , the solution of the given problem of unitary method comes out to be there were approximately 557 principals present.

To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.

Here,

Let's determine the principals' proportion to everyone else in the display room:

=> Number of principals divided by the total number of visitors to the display room =

=> 52/70 (number of principals / total number of visitors).

to determine the approximate number of principals present at the conference:

Estimated number of principals attending the conference = Principals as a percentage of all attendees in the exhibit hall * Total attendees =

=>  (52 / 70) * 750

=> 557 principals are expected to have attended the meeting.

As a result, it is possible to forecast that there were approximately 557 principals present at the meeting,

which corresponds to the response option "There were approximately 557 principals present."

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The probability that Julian will roll a 3 on the next roll is approximately 16.67%. The probability of rolling a 3 on a normal 6-sided die is independent of the previous rolls. This means that regardless of the outcomes of Julian's previous rolls, the probability remains the same.

Explanation

On a 6-sided die, there is 1 favorable outcome for rolling a 3 (the number 3 itself) out of 6 possible outcomes (1, 2, 3, 4, 5, and 6).

To find the probability, you can use the formula:

Probability = (Number of favorable outcomes) / (Total number of outcomes)

In this case:

Probability of rolling a 3 = 1 (favorable outcome) / 6 (total outcomes)

Probability of rolling a 3 = 1/6 ≈ 0.1667 or 16.67%

So, the probability that Julian will roll a 3 on the next roll is approximately 16.67%.

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The distance between points A and B is 2 units.

To find the distance between two points in a coordinate plane, we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Using this formula, we can find the distance between points A (-3,1) and B(-1,1) as follows:

distance = sqrt((-1 - (-3))^2 + (1 - 1)^2)

distance = sqrt(2^2 + 0^2)

distance = sqrt(4)

distance = 2

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The function is a linear function because as x increases, the y-value changes at a constant rate . The rate of change of this equation is 2.

The difference between linear and exponential functions is that  Linear functions change at a constant rate per unit interval while an exponential function changes by a common ratio over equal intervals.

We are given the function table as:

(0, -3)

(1, -1)

(2, 1)

(3, 3)

Thus, we can see that as x increases, the y-value changes at a constant rate of  + 2.

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The minimum number of weeks Kade should wait before making his purchase is 5 weeks.

Given that, Kade has $40 as his saving, and he wants to buy a video game console that costs $250 plus 8.25% sales tax.

He saves $50 each week to buy the same, we need to find the number weeks in which he can buy the game,

Total cost of the game = 250 + 250 × 8.25%

= 250 + 250 × 0.0825

= 250 + 20.625

= 270.625

Hence, he needs to save = $270.625 - $40 = $230.625

Let the number of weeks be x,

∴ 50x = 230.625

x = 4.61 ≈ 5

Hence, the minimum number of weeks Kade should wait before making his purchase is 5 weeks.

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the sample proportion (p^) is 0.4 or 40%.

To calculate the sample proportion (p^) for the number of Mizzou students with brown eyes, use the following formula:

A set is a collection of objects or groups of objects. These objects are often called elements or members of a set. For example, a group of players in a cricket team is a set.

p = (number of students with brown eyes) / (total number of students in the sample)

In this case, there are 24 students with brown eyes out of a sample of 60 students. Therefore, the numerical value of the statistic p^ is:

[tex]p = \frac{24} { 60} = 0.4[/tex]

So, the sample proportion (p^) is 0.4 or 40%.

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The numerical value of the statistic p^ for the random sample of 60 Mizzou students is 0.4, meaning 40% of the

sampled students have brown eyes.

To find the numerical value of the statistic p^ (sample proportion) for the given problem, you should follow these steps:

Identify the total number of students (n) in the sample, which is 60.

Identify the number of students with brown eyes (x), which is 24.

Calculate the sample proportion (p^) using the formula: p^ = x/n

Applying the formula:

p^ = 24/60

p^ = 0.4

So, the numerical value of the statistic p^ for the random sample of 60 Mizzou students is 0.4, meaning 40% of the

sampled students have brown eyes.

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The equation that matches the given graph can be represented by y = x + 7 , on the basis of coordinates of five different points on cartesian-plane.

What is a cartesian-plane?

A two-dimensional coordinate plane known as the cartesian plane is created when the x- and y-axes connect. The origin is the point at where the x- and y-axes cross perpendicularly. The x-coordinate and y-coordinate are the coordinates for each point on this plane. The ordinate and abcissa are other names for the x- and y-coordinates, respectively.

The points through which the given graph passes are:

(2,9) ; (3,10) ; (4,11) ; (5,12) and (6,13)

In (2,9): x=2 and y=9

y-x=7

In (3,10): x=3 and y=10

y-x=7

In (4,11): x=4 and y=11

y-x=7

In (5,12): x=5 and y=12

y-x=7

In (6,13): x=6 and y=13

y-x=7

∴ we can say that the difference of x and y coordinates in each point is 7

y-x=7

y=7+x

The required equation of the graph: y = x + 7

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The number of balls that must be selected to ensure that 4 balls of the same color are chosen is 10 balls.

To ensure that 4 balls of the same color are chosen, we must consider the worst-case scenario where we select 3 balls of each color before selecting the fourth ball. Therefore, the minimum number of balls that must be selected is:

= 3 (red balls) + 3 (blue balls) + 3 (yellow balls) + 1 (any color)

= 10 balls.

Therefore, we must select at least 10 balls to ensure that 4 balls of the same color are chosen.

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The total surface area of each figure are:

1)  2,557.3 yd²

2) 601.02 m₂

3) 3782.5 mm²

4)750 in²

1) The total surface area of a cylinder is:

2πrh + 2πr².

where:

r is radius

h is height

Thus:

TSA = 2π(11 * 26) + 2π(11)²

TSA = 2π(286) + 2π(121)

TSA = 2π(407)

TSA = 2,557.3 yd²

2) The total surface area is:

2(¹/₂ * 9 * 11.12) + (16 * 15) + (16 * 12) + (9 * 16)

= 25.02 + 240 + 192 + 144

= 601.02 m₂

3) The total surface area of a cylinder is:

2πrh + 2πr².

where:

r is radius

h is height

Thus:

TSA = 2π(14 * 29) + 2π(14)²

TSA = 2π(406) + 2π(196)

TSA = 2π(602)

TSA = 3782.5 mm²

4) The total surface area of the pyramid is:

TSA = (15 * 8) + (21 * 17) + (21 * 15) + (8 * 21)

TSA = 120 + 147 + 315 + 168

TSA = 750 in²

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Check the picture below.

Sally would have invested $1150 initially in the savings account to satisfy the conditions in the question.

A savings account is a type of bank account that helps people save money over time. It offers a safe and secure way to store money while earning interest on the balance. Unlike checking accounts, savings accounts are intended for long-term storage of funds, with a higher interest rate and regular compounding to help the balance grow. Savings accounts offer flexibility in terms of access to funds and usually allow withdrawals at any time with limits on the number of withdrawals without incurring a fee.

To determine how much money Sally initially invested in a savings account that earns 7.2% annual simple interest, we can use the formula for simple interest: I = Prt. Here, I represents the interest earned, P is the initial principal, r is the annual interest rate as a decimal, and t is the time in years.

Given that Sally earned $745.20 in interest over a period of 9 years with an annual interest rate of 7.2%, we can substitute the values into the formula and solve for P:

I = $745.20

r = 7.2% = 0.072 (decimal)

t = 9 years

Now, P = I / (rt)

P = 745.20 / (0.072 * 9)

P = $1150

Therefore, Sally initially invested $1150 in the savings account.

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The measure of angle B in the right-angled triangle ACB is 63 degrees.

What is a triangle ?

A triangle is a polygon with three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees. Triangles can be classified based on their side lengths and angle measures.

In a right-angled triangle, the sum of the two acute angles is always equal to 90 degrees. Therefore, we can find the measure of angle B in the right-angled triangle ACB by subtracting the measure of angle A and the right angle from 90 degrees.

Given that [tex]\angle A = 27^\circ[/tex], we can find the measure of angle B as follows:

[tex]\angle B = 180^\circ - \angle A - \angle C[/tex]

Since the triangle is right-angled at C, we know that [tex]\angle C = 90^\circ[/tex]. Therefore, we can substitute the values of [tex]\angle A[/tex] and [tex]\angle C[/tex] in the equation above to get:

[tex]\angle B = 180^\circ - 27^\circ - 90^\circ[/tex]

Simplifying this expression, we get:

[tex]\angle B = 63^\circ[/tex]

Therefore, the measure of angle B in the right-angled triangle ACB is 63 degrees.

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Answer:your answer is 11

Step-by-step explanation:

The price of each book must be either $38.53 or $10.8 to generate a total sales revenue of $1,24,875.

If the prices of a book is $16 then 10000 copies will be sold.

For every dollar that increase in price, 300 books will not be sold.

So if the price of a book increases $x then the total price of sold books is given by,

y = (16 + x)*(10000-300x)

Now total sales revenue of the books is $124875, that is, y = 124875.

So, (16+x)*(10000-300x) = 124875

160000 + 10000x - 4800x - 300x² = 124875

35125 + 5200x - 300x² = 0

25 (1405 + 208x - 12x²) = 0

12x² - 208x - 1405 = 0

Solving the above quadratic equation we get,

x = 22.53 or x = -5.20 (Rounding to two decimal places)

So the amount will be either (16+22.53) = $38.53 or (16-5.20) = $ 10.8.

Hence the price must be either $38.53 or $10.8.

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The translation of the question is -

"If a publisher prices a book at $16, 10,000 copies will be sold. For every dollar that increases in price, 300 books will not be sold. What must be the price each book must sell for to generate a total sales revenue of $124,875?"

The required area of the given triangle is 63 ft² respectively.

A triangle is a 3-sided polygon that is occasionally (though not frequently) referred to as the trigon.

There are three sides and three angles in every triangle, some of which may be the same.

A unique triangle and plane (i.e., a two-dimensional Euclidean space) are determined by any three non-collinear points in Euclidean geometry.

In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.

Area of a triangle:

1/2 * b * h

Now, insert values as follows:

1/2 * b * h

1/2 * 14 * 9

7 * 9

63 ft²

Therefore, the required area of the given triangle is 63 ft² respectively.

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The answer to the given question after considering the two options is true under the condition all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.      

Probability is also known as the estimation of possible changes of a particular event taking place. Furthermore, it is  important while dealing with calculations in the branch of science and mathematics. It is useful in eliminating the total changes of systematic errors, which are hampering the research population.

Some examples of probability

The probability on the event of rolling a 4 with a die is 1/6.

The probability of getting a tails while tossing a coin is 1/2.

The probability of getting  one  joker from a deck of cards is 1/51.

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The complete question is

All probabilities can be expressed as decimal values ranging from 0.00 to 1.00. True or False

Yes, it is true that all probabilities can be expressed as decimal values ranging from 0.00 to 1.00.

This is because probabilities represent the likelihood of an event occurring, and the probability of an event can range from impossible (0.00) to certain (1.00). Therefore, probabilities are expressed as decimal values between these two extremes.
Hi! Yes, all probabilities can be expressed as decimal values ranging from 0.00 to 1.00. A probability of 0.00 represents an impossible event, while a probability of 1.00 represents a certain event. Values between these two extremes indicate varying levels of likelihood for the event to occur.

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the probability of a customer choosing a sandwich on white bread with ham and either provolone or American cheese is 6/36, which simplifies to 1/6. Thus, option A is correct.

There are 3 bread options, 4 meat options, and 3 cheese options listed on the board, which gives us a total of  [tex]3 \times 4 \times 3 = 36[/tex] possible sandwich combinations.

There are two cheese options that meet this criteria, so we can create two different sandwiches: one with provolone and one with American cheese.

Each of these sandwiches can be made in [tex]3 \times 1 \times 1 = 3[/tex] ways, as there are 3 bread options but only one option each for the ham and cheese. So, the total number of sandwich combinations that meet our criteria is [tex]2 \times 3 = 6.[/tex]

Therefore, the probability of a customer choosing a sandwich on white bread with ham and either provolone or American cheese is 6/36, which simplifies to   [tex]1/6[/tex].

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The answer to this question is  x = 6

The minimum of the given expression can be found to be 3 x ∛(√2).

Use these inequalities to find the minimum of the given expression:

(a / (b + c)) + (b / (c + a)) + √(2c / (a + b)) ≥ (a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab)))

Now, simplify the expression:

(a / (√(bc))) + (b / (√(ac))) + √(2c / (√(ab))) = (√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))

Apply AM-GM inequality to the terms (√(a²/bc)), (√(b²/ac)), and (√(2c²/ab)):

AM = [(√(a²/bc)) + (√(b²/ac)) + (√(2c²/ab))] / 3 ≥ GM = ∛[(√(a²/bc)) * (√(b²/ac)) * (√(2c²/ab))]

The geometric mean (GM) is:

GM = ∛[(√(a²/bc)) x (√(b²/ac)) x (√(2c²/ab))]

GM = ∛(√(2a²b²c² / a²b²c²))

GM = ∛(√2)

Thus, the minimum of the given expression is:

= 3 x ∛(√2)

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The distance between your location and the epicenter is just slightly larger than the maximum distance that the earthquake can be felt (76 miles), so you would be able to feel the earthquake.

A triangle is a polygon with three sides and three angles. The sum of the angles in a triangle is always 180 degrees. There are different types of triangles such as equilateral, isosceles, scalene, right-angled, obtuse-angled, and acute-angled triangles. Triangles are used in geometry and other fields of mathematics to solve problems related to areas, angles, and side lengths.

Here,

Yes, you feel the earthquake.

To see why, imagine drawing a circle around the epicenter with a radius of 76 miles. This circle represents the maximum distance that the earthquake can be felt. Then, draw a line from the epicenter to your location. This line represents the distance between you and the epicenter.

To determine whether you feel the earthquake, we need to calculate the distance between your location and the epicenter using the Pythagorean theorem:

distance = √(65² + 40²)

distance ≈ 76.06 miles

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The number of bags that have zips on them is 28.

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

First, we know that the total number of bags is 110.

Next, we know that 24 of the bags have neither zips nor buttons. Therefore, the number of bags that have either zips or buttons is 110 - 24 = 86.

We also know that 32 of the bags have buttons but no zips, and 28 of the bags have zips but no buttons.

To find the number of bags that have both zips and buttons, we can subtract the number of bags that have only buttons from the total number of bags with zips, or vice versa:

Number of bags with both zips and buttons = (Number of bags with zips) + (Number of bags with buttons) - (Number of bags with either zips or buttons)

Number of bags with both zips and buttons = 28 + 32 - 86 = -26

This result is clearly nonsensical, so we can conclude that there are no bags with both zips and buttons.

Therefore, the number of bags that have zips on them is simply the number of bags with zips but no buttons, which is 28.

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Answer:

96

Step-by-step explanation:

The missing value in the table for the exponential function is 27.

An exponential function is a mathematical function of the form f(x) = a^x, where a is a positive constant called the base, and x is the variable.

To find the missing value in the table, we need to evaluate the exponential function f(x) = (3)^x for the missing value of x.

We can see that

f(1) = 3, f(2) = 9, f(4) = 81, f(5) = 243, f(6) = 729, and f(7) = 2187.

To find f(3), we can use the formula f(x) = (3)^x

f(3) = (3)^3 = 27

Therefore, the missing value is 27

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We would predict using the random sample that 175 students at the school like math.

A confidence interval is a range of values that, with a certain degree of certainty, is likely to contain the real value of a population parameter. In most cases, the level of confidence is stated as a percentage, such as 95% or 99%, and it indicates the likelihood that the parameter's actual value falls within the range. In statistics, confidence intervals are frequently used to calculate an estimate of a population parameter's value from a sample of data. A confidence interval, which offers a range of likely values for the population parameter, is constructed using the sample statistics and the variability of the data.

Given that, 14 out of 20 students like math.

Using proportions we have:

14/20 = 0.7.

Now for 250 students we have:

0.7 * 250 = 175

Hence, we would predict that 175 students at the school like math.

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Answer:

18

Step-by-step explanation:

Since it is an equilateral triangle AB=AC=5

If I sum up all sides u will get 18. How this helps.

Answer:

No, this triangle is NOT a right angle.

Step-by-step explanation:

The known fact is that the largest number is our hypotenuse. The other two numbers can go on either side.

A square plus B square equal C square is our equation

Let's plug in the numbers: 15^2+5^2=16^2

Now we solve.

Once we solve our squares and add them together, we get 250=256. Since these two number are not equal to each other, this triangle is NOT a right angle

much love to you.

95.61 degrees is equal to 95 degrees, 36 minutes, and 36 seconds or 95° 36' 36".

To convert decimal degrees to degrees, minutes, and seconds

The whole number of the decimal degree will be the degrees

Multiply the decimal part that remains by 60. The whole number of the result will be the minutes.

Multiply the decimal part that remains by 60. The resulting number will be the seconds.

So for 95.61 degrees

The whole number of 95.61 is 95 degrees.

Multiply 0.61 by 60 to get 36.6. The whole number of 36.6 is 36 minutes.

Multiply 0.6 by 60 to get 36 seconds.

Therefore, 95.61 degrees is equal to 95 degrees, 36 minutes, and 36 seconds.

In the format of degrees, minutes, and seconds: 95° 36' 36"

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( 5 - 2t ) < - 4 is an inequalty that represents t, the number of hours past midnight, when the temperature was coler than -4 degrees celsius.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.

If t is the hours past midnight then after t hours the temperature will be ( 5 - 2t ).

Now, if this temperature is colder than - 4° C, then the inequality can be written as   ( 5 - 2t ) < - 4.

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The inequality that represents t, the number of hours past midnight, when the temperature was cooler than -4 degrees celsius( 5 - 2t ) < - 4

What is  inequality?

The term "inequality" is used in mathematics to describe a relationship between two expressions or values that is not equal to one another. Inequality results from a lack of balance. When two quantities are equal, we use the symbol '=', and when they are not equal, we use the symbol. If two values are not equal, the first value can be greater than (>) or less than (), or greater than equal to () or less than equal to ().

The midnight temperature is 5 °C and the temperature is decreasing at the rate of 2°C per hour.

If t is the hours past midnight then after t hours the temperature will be

=>  ( 5 - 2t ).

Now, if this temperature is colder than - 4° C, then the inequality can be written as   ( 5 - 2t ) < - 4.

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Given a sample of 36 male mosquitos of a species with a mean lifespan of 8.88 days and a standard deviation of 6.66 days, the probability of the sample mean lifespan exceeding 10 days is approximately 0.14. So, the correct choice is option B is P ( x ˉ > 10 ) ≈ 0. 14 P( x ˉ >10)≈0. 14P, left parenthesis, x, with, \bar, on top, is greater than, 10, right parenthesis, approximately equals, 0, point, 14.

The sampling distribution of the mean lifespan is approximately normal due to the Central Limit Theorem.

The standard error of the mean is 6.66 / sqrt(36) = 1.11. The z-score for a sample mean of 10 is (10 - 8.88) / 1.11 = 1.08. Using a standard normal distribution table or calculator, the probability of a z-score greater than 1.08 is approximately 0.14.

Therefore, the answer is Choice B is P(X > 10) ≈ 0.14.

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