Three interior angles of a quadrilateral measure 55, 117 and 120 degrees. What is the measure of the fourth interior angle?

Mark should pay $0.1692 for one draw.

To calculate how much Mark should pay for one draw, we need to find the expected value, which is the sum of the products of each outcome's probability and its associated value.

Calculate the probabilities:

Probability of drawing a club: [tex]\( \frac{13}{52} = \frac{1}{4} \)[/tex]

Probability of drawing an ace: [tex]\( \frac{4}{52} = \frac{1}{13} \)[/tex]

Probability of drawing the ace of clubs: [tex]\( \frac{1}{52} \)[/tex]

Calculate the expected values:

Club: [tex]\( 0.45 \times \frac{1}{4} = 0.1125 \)[/tex]

Ace: [tex]\( 0.55 \times \frac{1}{13} = 0.0423 \)[/tex]

Ace of clubs: [tex]\( 0.75 \times \frac{1}{52} = 0.0144 \)[/tex]

Sum the expected values:

[tex]\( 0.1125 + 0.0423 + 0.0144 = 0.1692 \)[/tex]

Thus, Mark should pay $0.1692 for one draw.

Answer:

The answer appears to be A

Step-by-step explanation:If you redrew the answer backwards, the reflection would match the first one

Answer:

Step-by-step explanation:

The 90% confidence interval for the population mean is (140.4, 147.6), derived from a sample with a mean of 144 and a standard deviation of 12.

Let's break down the steps used to calculate the 90% confidence interval for the population mean:

- Sample mean ([tex]\bar{x}[/tex]): 144

- Sample standard deviation (s): 12

- Sample size (n): 30

- Critical value at 90% confidence (z): 1.645

The formula for the confidence interval is:

[tex]\[ (\bar{x} - z \cdot \frac{s}{\sqrt{n}}, \ \bar{x} + z \cdot \frac{s}{\sqrt{n}}) \][/tex]

Calculate the standard error (SE):

SE = s / sqrt(n)

SE = 12 / sqrt(30)

SE ≈ 2.188

Calculate the margin of error (ME):

ME = z * SE

ME = 1.645 * 2.188

ME ≈ 3.594

Calculate the lower limit (L):

L = [tex]\bar{x}[/tex] - ME

L = 144 - 3.594

L ≈ 140.406

Calculate the upper limit (U):

U = [tex]\bar{x}[/tex] + ME

U = 144 + 3.594

U ≈ 147.594

So, the 90% confidence interval for the population mean is approximately (140.406, 147.594), which rounds to (140.4, 147.6) when considering the appropriate level of precision. Therefore, the correct answer is (D) (140.4, 147.6).

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A polynomial function is an algebraic expression with one or more terms. The real zeros can be found by setting the function equal to zero and solving for x. The imaginary zeros can be found using the complex conjugate theorem.

A polynomial function is an algebraic expression that consists of one or more terms. The real zeros of a polynomial function are the values of x that make the function equal to zero. To find the real zeros, set the polynomial function equal to zero and solve for x using methods such as factoring, synthetic division, or the quadratic formula.

The imaginary zeros of a polynomial function are the values of x that make the function equal to a complex number. These can be found by using the complex conjugate theorem. If a + bi is a zero, then a - bi is also a zero, where a and b are real numbers and i is the imaginary unit, sqrt(-1).

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⇒A theorem is a statement that can be easily prove using a corollary

False Statement

Corollary Means , a Theorem written in another way , when it has been proved.

For Example:The Sum of Angles of Triangle is 180°.-----Theorem

Corollary→If  three distinct rays intersect at three points , and sum of interior Angles formed at their point of Intersection is 180°, then it is a Triangle.

Correct Statement will be:

     A theorem is a statement that can be easily proved using an Axiom or Postulate.

A function is a relationship that maps elements from one set (the inputs) into elements of another set (the outputs). Such that each input can be mapped into only one output.

The correct option is B: {(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}

Using the general definition, to find which set of ordered pairs does not represent a function, we need to see in which set we have the same input (the first element of the ordered pair) assigned to two different outputs (the second element of the ordered pair).

Here the one that does not represent a function is option B:

{(0, 1.5), (3, 2.5), (1, 3.3), (1, 4.5)}

Because we have the input x = 1 assigned to two different outputs, y = 3.3 and y = 4.5

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In 24 hours, you will have 48 cells if you start with cell A and keep making cells at the same rate.

If it takes three hours to produce two cells, we can calculate the production rate as follows:

Production rate of A = 2 cells / 3 hours

Now, we want to find out how many cells will be produced in 24 hours:

Number of cells produced in 24 hours = Production rate of A × Number of hours

Number of cells produced in 24 hours = (2 cells / 3 hours) × 24 hours

Number of cells produced in 24 hours = 2 cells/hour × 24 hours

Number of cells produced in 24 hours = 48 cells

Therefore, if you start with cell A and continue producing at the same rate, you will have 48 cells in 24 hours.

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The next step that Kate should take in construction of an equilateral triangle after using a straight edge to construct the given line segment is;

Option B; Place the point of the compass on point A and draw an arc, using AB as the width for the opening of the compass.

This is about steps involved in constructing an equilateral triangle which means 3 equal sides.

Thus, option B is the correct next step.

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The correct answer is a.(4, 4) because when you substitute x = 4 and y = 4 into the inequality y > -2x + 6, the inequality holds true, indicating that (4, 4) is a solution.

To determine which of the given points is a solution to the inequality y >
-2x + 6, we substitute the x and y values of each point into the inequality and check if the inequality holds true.

Therefore, the correct answer is a.(4, 4), since it is the only point that satisfies the inequality y > -2x + 6.

Answer:

all work is shown and pictured

Answer:

y= -1/3x+5

Step-by-step explanation:

The equation of the line passing through the points (- 1, -6) and (7, 2)  will be → y = x - 5. The slope will be [m] = 1 and the y - intercept will be -5.

The slope intercept of a straight line is -

y = mx + c

Where -

[m] is the slope of the line.

[c] is the y - intercept.

Given is a straight line passing through the points (- 1, -6) and (7, 2)

We have a straight line that passes through the coordinates as follows -

(- 1, -6)

(7, 2)    

The slope of the line can be calculated using the formula -

m = (y₂ - y₁)/(x₂ - x₁)

m = (2 + 6)/(8)

m = 8/8

m = 1

The line is passing through the point (7, 2). We can write -

y = mx + c

y = x + c       [m = 1]

2 = 7 + c

c = 2 - 7

c = -5

The equation of the straight line will be -

y = x - 5

Now, the slope of the line will be [m] = 1 and the y - intercept will be -5.

Therefore, the equation of the line passing through the points (- 1, -6) and (7, 2)  will be → y = x - 5. The slope will be [m] = 1 and the y - intercept will be -5.

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Answer:

all numbers are real

Step-by-step explanation:

1 pound = 0.453592 kg

5 x 0.453592 = 2.26796 kg

 round to 2.27 kg