7.1 Lesson A Rational Existence Introduction to Rational Functions

Applying the inscribed angle theorem, we have:

a. x = 55° b. x = 60°  c. x = 92°    d. x = 84°

These theorem states that:

Inscribed angle measure = 1/2(central angle) or measure of intercepted arc.

Intercepted arc measure = central angle measure.

Therefore, we have:

a. x = 180 - 35 - 90 [tangent theorem]

x = 55°

b. x = 1/2(120) [inscribed angle theorem]

x = 60°

c. x = 2(46) [inscribed angle theorem]

x = 92°

d. m(FE) = 2(42) = 84°

m(EB) = 180 - FE = 180 - 84

m(EB) = 96°

m(AB) = 180 - m(EB) = 180 - 96

m(AB) = 84°

x = m(AB) = 84° [central angle theorem]

Learn more about the inscribed angle theorem on:

https://brainly.com/question/5436956

#SPJ1

Answer:

A.

Step-by-step explanation:

correct answer is A. 3x1=

Answer: A

Step-by-step explanation:

The next step you would take is take the square root of both sides to cancel out the square.

Which gets rid of the square on 1 side and you get ±5 on the other.

Answer:

Step-by-step explanation:

If moving due west is +16, then moving due east is going to cover up for -16 and an additonal -2 to the east. which sums up to -18. Therefore -18 is 2units to the east.

The probability that the Players are assigned to go in the order given can be found to be 0.833 %.

First, we need to find out the number of ways that the baseball players can be assigned to go and this is:

= 5 × 4 × 3 × 2 × 1 = 120 ways

However, there is only one way in which Player A is assigned to go 1st, Players B is assigned to go 2nd, Player C is assigned to go 3rd, Player D is assigned to go 4th, and player E is assigned to go 5th.

The probability is therefore:

= 1 / 120

= 0.833 %.

Find out more on probability at https://brainly.com/question/10305273

#SPJ1

The calculated value of the expression A + B is 60

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

A - B = 56

B = 2

Substitute the known values of B in the above first equation

So, we have the following representation

A - 2 = 56

Evaluate the sum

A = 58

Add B to both sides

A + B = 58 + B

So, we have

A + B = 58 + 2

Evaluate

A + B = 60

Hence the solution is 60

Read more about expression at

https://brainly.com/question/15775046

#SPJ1

An equation that is represented by the graph below include the following: 3) y = |x| - 3.

In Mathematics, the translation a geometric figure or graph downward simply means adding a digit to the value on the y-coordinate of the pre-image or function.

In Mathematics, a vertical translation to the positive y-direction (downward) is modeled by this mathematical expression g(x) = f(x) - N.

Where:

In conclusion, we can logically deduce that the graph of the parent function was y = |x| stretched away from the y-axis and translated by 3 units downward;

y = |x|

f(x) = |x| - 3

Read more on translation here: brainly.com/question/26869095

#SPJ1

The probability that exactly 2 out of 4 children will be colorblind and the other 2 will have normal color vision, assuming a probability of 1/16 for colorblindness, is approximately 0.0206 or 2.06%.

We have,

To calculate the probability, we can use the binomial probability formula:

P(2 colorblind and 2 normal) = (4 choose 2) * (1/16)² * (15/16)²

Using the formula, we can calculate:

P(2 colorblind and 2 normal) = (4! / (2! * (4-2)!)) * (1/16)² * (15/16)²

= (6) * (1/256) * (225/256)

= 1350/65536

≈ 0.0206

Therefore,

The probability that exactly 2 out of 4 children will be colorblind and the other 2 will have normal color vision, assuming a probability of 1/16 for colorblindness, is approximately 0.0206 or 2.06%.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ12

The complete question:

What is the probability that, if a couple with no known family history of colorblindness has 4 children, exactly 2 of them will be colorblind and the other 2 will have normal color vision, assuming that the probability of having a colorblind child is 1/16 due to a rare genetic mutation?

The 99% prediction that number of defects per countertop is (-19.68, 9.13), under the given condition that new employee have had 13 hours of training.

Let us assume a linear regression model where the number of defects per countertop is projected based on the number of hours of training an employee has received. The 99% prediction interval for the number of defects per countertop can be evaluated applying the formula
y' ± t(α/2,n-2) × s[y"]
here
y' = predicted value of y,
t(α/2,n-2) = t-critical value for a given level of confidence (in this case 99%)
(n-2) =degrees of freedom ,
s[y"] = standard error of the estimate.

Utilizing the given data, we can evaluate y'

y' = 6.717822 - 1.004950 × 13
= -5.276

Therefore, the standard error of the estimate  is given as 1.229787.
Applying a t-distribution table with n-2 degrees of freedom (n=1), we can get that t(α/2,n-2) = 12.706. Then, the  evaluated 99% prediction interval for the number of defects per countertop is
-5.276 ± 12.706 × 1.229787
= (-19.68, 9.13)

To learn more about  linear regression model,
https://brainly.com/question/30884929
#SPJ4

Starting with the given equation:

4x² - 30 = 34

Adding 30 to both sides:

4x² = 64

Dividing both sides by 4:

x² = 16

Taking the square root of both sides:

x = ±4

Therefore, the solutions to the equation are x = 4 and x = -4.

Checking each option:

A. x = -√√8 is not a solution.

B. x = 4 is a solution.

C. x = -8 is not a solution.

D. x = √√√8 is not a solution.

E. x = -4 is a solution.

F. x = 8 is not a solution.

Therefore, the solutions to the equation are x = 4 and x = -4, which are options B and E.

Answer:

24

Step-by-step explanation:

We can simplify this equality by squaring both sides.

[tex](\sqrt{x})^2 < 5^2[/tex]

[tex]x < 25[/tex]

We know that the greatest integer less than 25 is 24. Therefore, this is the greatest integer solution to the inequality.

Answer:

Step-by-step explanation:

A. Commutative Property of Multiplication

The length of the arc corresponding to the subtended central angle EFD would be = 7/3π. That is option C.

To calculate the length of an arc of a circle, the formula that should be used ;

= 2πr(∅/360)

where,

radius=r= 4 units

∅ = 180(30+45)

= 180- 75

= 105°

length of an arc= 2×π ×4(105/360).

= 7/3π

Learn more about circle here:

https://brainly.com/question/26594685

#SPJ1

The percentage of wheel production times that will take more than 28 hours is approximately 2.28%.

We can use the standard normal distribution table to find the percentage of production times that will take more than 28 hours. We will convert the given data into a standard normal distribution by using the formula:

z = (x - μ) / σ

Where:

x = the given production time (in this case, 28 hours)

μ = the mean production time (20 hours)

σ = the standard deviation (4 hours)

z = (28 - 20) / 4

z = 2

We can use the standard normal distribution table to find the percentage of values that are greater than 2. In the standard normal distribution table, we can find that the percentage of values that are greater than 2 is approximately 2.28%.

To know more about percentage here

https://brainly.com/question/13729841

#SPJ4

The calculated value of the area of the shaded region is 60.5 square meters

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

The figure

Where we have the shaded region to be the gray region

Also, we have

Shaded region = 2 triangles with base = 1/2 * 11 and height = 11

using the above as a guide, we have the following:

Area = 2 * area of 1 triangle

So, we have

Area = 2 * 1/2 * 11 * 1/2 * 11

Evaluate

Area = 60.5

Hence, the area of the shaded region is 60.5 square meters

Read more about area

https://brainly.com/question/24487155

#SPJ1

The null hypothesis would be that the mean tenure for CEO's is 8 years, while the alternative hypothesis would be that the mean tenure for CEO's is less than 8 years. This would be formulated as: Null hypothesis: μ = 8 years
Alternative hypothesis: μ < 8 years

The sample mean of 5.8 years is lower than the claimed mean of 8 years, suggesting that the shareholders' claim may not be valid. To test the validity of their claim, a hypothesis test can be conducted using the sample data and assuming a normal distribution of CEO tenure in the population.

To challenge the validity of the claim made by the shareholders, you can formulate a hypothesis test using the following steps:

Step 1: State the null hypothesis (H0) and alternative hypothesis (H1)
- Null hypothesis (H0): The population mean tenure for a CEO is at least 8 years (μ ≥ 8)
- Alternative hypothesis (H1): The population mean tenure for a CEO is less than 8 years (μ < 8)

Step 2: Collect and summarize the sample data
- Sample size (n): 52 companies
- Sample mean (x): 5.8 years
- Sample standard deviation (s): 5.4 years

Step 3: Since the population standard deviation is unknown and the sample size is large (n > 30), we can assume the sampling distribution is normally distributed and use a t-test to perform the hypothesis test.

Note that we cannot directly test the validity of the shareholders' claim based on the sample data alone. The hypothesis test will help determine whether there is enough evidence to reject the null hypothesis and support the alternative hypothesis, which would then challenge the claim made by the shareholders.

Learn more about standard deviation at: brainly.com/question/23907081

#SPJ11

The inequality that shows how many more boxes Mrs. Minor will have to sell is given as follows:

x ≥ 12.

The four inequality symbols, along with their meaning on the number line and the coordinate plane, are presented as follows:

She needs to sell at least 16 boxes, and has already sold 4, hence the amount that needs to be sold is:

16 - 4 = 12 boxes.

Then the inequality is:

x ≥ 12.

More can be learned about inequalities at brainly.com/question/25275758

#SPJ1

Answer:

Step-by-step explanation:

Find the equivalent for each

1. R

2. S

3. Q

4. QS  put a line over this

5. QR  put a line over

6. MN put a line over

7. LN put a line over

8.  RS put a line

9.  2

10.  6

11.  3y+5=14

        3y=9

          y=3

12.  2

The probability of winning first, second, third, and fourth prizes in specific order by Bo, Colleen, Jeff, and Rohini is equals to 0.00000020.

Number of people enter in contest = 49

The number of ways to choose the first prize winner is 49.

Since the first prize winner is no longer eligible.

The number of ways to choose the second prize winner is 48.

Since the first and second prize winners are no longer eligible.

The number of ways to choose the third prize winner is 47  .

Since the first, second, and third prize winners are no longer eligible.

and the number of ways to choose the fourth prize winner is 46 .

The total number of ways to choose four prize winners out of 49 entrants is,

= 49 x 48 x 47 x 46

= 5085024

However, probability of Bo, Colleen, Jeff, and Rohini winning the first, second, third, and fourth prizes in that specific order.

The probability of this happening is,

(1/49) x (1/48) x (1/47) x (1/46)

= 1/5085024

= 0.0000001967

=  0.00000020

Therefore, probability of Bo, Colleen, Jeff, and Rohini winning first, second, third, and fourth prizes in specific order is  0.00000020.

Learn more about probability here

brainly.com/question/28205657

#SPJ4

This is an exercise in solving problems involving quadratic functions, which is an important topic in mathematics and is used in many fields, including physics, engineering, and economics. In general, one seeks to find the critical points of a quadratic function, such as the vertex or the roots, to understand the behavior of the function in different situations.

To find the vertex of a quadratic function, we use the canonical form of the quadratic equation, which is f(x) = a(x - h)^2 + k, where (h, k) are the coordinates of the vertex. It is also possible to find the vertex using the formula -b/2a, which is derived from the general form of the quadratic equation.

In addition to finding the vertex, it is also common to find the roots of a quadratic function, which are the values of x where the function vanishes. This can be done using the general formula of the quadratic equation or by completing the square.

f(x) = 2(x + 8)² - 2

First we write the quadratic function in standard form.

Using (a + b)² = a² + 2ab + b², expand the expression.

   f(x) = 2(x² + 16x + 64) - 2

We distribute the 2 to the terms that are between the parentheses.

  f(x) = 2x² + 32x + 128 - 2 ⇒ subtract 2

  f(x) = 2x² + 32x + 126

Now we identify the coefficients a and b of the quadratic function.

a = 2, b = 32

We find the x-coordinate of the vertex by substituting a = 2 and b = 2 into x = - (b)/(2a).

     x = - (32)/(2 × 2) = - 32/4 = -8

     x = -8

Find the y-coordinate of the vertex by evaluating the function for x = -8.

   f(x) = 2(x + 8)² - 2, x = -8

  We substitute x = -8 in the equation.

    f(-8) = 2(-8 + 8)² - 2

The sum of two opposite numbers is equal to 0. The Inverse Property of Addition states that the sum of two opposite numbers is equal to 0.

f(-8) = 2 x 0² - 2

0 raised any positive power is equal to 0. We remember that a power represents a repeated multiplication of the base.

Therefore, the power 0² means that 0 is multiplied by itself 2 times, resulting in 0.

f(-8) = 2 × 0 - 2

Any expression multiplied by 0 equals 0.

f(-8) = 0 - 2

Removing the 0 does not change the value, so we remove it from the expression.

  f(-8) = -2

The vertex of the graph of the quadratic function is at (-8, -2).

  (-8,-2)

The vertex of the quadratic function f(x) = 28(x + 8)² - 2 is (-8,-2), the last option being correct.

ヘ( ^o^)ノ＼(^_^ )If you want to learn more about mathematics, I share this link to complement your learning:

https://brainly.com/question/11582506

Answer:

Yes, 86.76 is a rational number. A rational number is any number that can be expressed as a ratio of two integers (where the denominator is not zero).

86.76 can be expressed as the ratio of two integers: 8676/100, which can be simplified to 2169/25. Since 2169 and 25 are both integers, and the denominator is not zero, 86.76 is a rational number.

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

A rational number is any number that can be expressed as the ratio of two integers (i.e., a fraction where the numerator and denominator are both integers).

In this case, we can express 86.76 repeating as the fraction:

8676/100 = 8676 ÷ 100

Simplifying this fraction, we get:

8676/100 = 8676 ÷ 4 ÷ 25 = 2169/25

Since 2169 and 25 are both integers, we have expressed 86.76 repeating as a ratio of two integers, and therefore it is a rational number.

To find the actual height of the tower, we need to use the scale factor. The ratio of the scale is 1.5 inches to 10 feet, which can be simplified to 1 inch to 6.67 feet (by dividing both sides by 1.5).

Therefore, the actual height of the tower in feet would be:

24 inches × (1 inch ÷ 6.67 feet) = 3.6 feet

So the actual height of the tower is 3.6 feet.

The correct equation is $25 + 0.1($25) + 0.2($25)

Iris should first figure out how much tax she will be responsible for paying.

Her supper will set you back $25 before taxes and gratuity, and the tax percentage is 10%.

Thus, she will pay the following amount in taxes:

taxes = 0.1 * $25 = $2.50

Secondly, determine how much Iris will leave in tips. Since she will leave a 20% tip, tip is :

0.2 * $25 =$5.00.

Iris will pay her bill in full, which will include taxes, a gratuity, and the price of her dinner:

Dinner price plus taxes and tip equals the final bill.

The total due is $25 plus $2.50 plus $5.00.

$32.50 is the entire cost.

So, $25 + 0.1($25) + 0.2($25) is the equation that indicates the amount of money Iris will pay for her bill.

Learn more about percentages here:

https://brainly.com/question/29306119

#SPJ1

The area of the small triangle is equal to 25 ft².

In Mathematics and Geometry, a scale factor can be calculated or determined through the division of the dimension of the image (new figure) by the dimension of the original figure (pre-image).

In Mathematics and Geometry, the scale factor of the dimensions of a geometric figure can be calculated by using the following formula:

(Scale factor of dimensions)² = Scale factor of area

Therefore, the area of the small triangle can be calculated as follows;

Area of small triangle = (12/28)² × 135

Area of small triangle = 24.80 ≈ 25 ft².

Read more on scale factor here: brainly.com/question/29967135

#SPJ1

The population will exceed 7569 at moments beyond 7.4 years hence from 8 years (to the nearest years)​

Exponential function is a function of the form f(x) = a e^(kt)

Considering the given problem,

the initial value = a

the base factor = k

the exponents in time = t

Information given in the problem are

solving for the time wen the population will exceed 7569

7569 = 1600 x e(0.21 * t)

7569 / 1600 = e(0.21 * t)

take ㏑ of both sides

㏑ (7569 / 1600) = ㏑ e(0.21 * t)

㏑ (7569 / 1600) = 0.21t

t = ㏑ (7569 / 1600) / 0.21

t = 7.40

Learn more about exponential function here:

https://brainly.com/question/29716007

#SPJ1

Using probability, we can find:

Probability of getting zero heads = 0.25

Probability of getting 1 head = 0.5

Probability of getting 2 heads = 0.25

The ability of an event to occur is known as probability. The occurrence of random events is the subject of this branch of mathematics. The value is expressed as a number between 0 and 1. Probability has been introduced in mathematics to predict how likely events are to occur.

Here in the question,

2 coins are flipped at the same time.

The possible outcomes are as follows:

H H

H T

T H

T T

So, there are 4 outcomes of this event.

Now,

Probability that there are 0 heads in the event:

One event there is 0 heads = T T

Probability = 1/4

= 0.25

Now, events with one head are:

H T and T H

So,

Probability = 2/4

= 0.5

In the final event, we have 2 heads in one event = H H

So,

Probability = 1/4

= 0.25

To know more about probability, visit:

brainly.com/question/16484393

#SPJ1

Step-by-step explanation:

First, use law of SINES to find QS :

11.7 / sin 28  = QS / sin95

      shows QS = 24.83 cm

Now use law of COSINES to find QR

QR^2 = 10.2^2 + 24.83^2 - 2 ( 10.2)(24.83) cos ( 110)

   shows QR = 29.9 cm

Answer:

Step-by-step explanation: Hello! You know the area of a right triangle shown is 24 square feet. The formula for area of a triangle is A = 1/2(b)(h).

24 can be substituted for A.

24 = 1/2(b)(h).

From here, I will need to see the triangle shown. If you post an image of the triangle with this, I might be able to come back and help you.

Good luck!

Answer:

  14 inches

Step-by-step explanation:

You want the diameter of a circle that has a circumference of 43.96 inches.

The equation for the circumference of a circle is ...

  C = πd

Then the diameter is ...

  d = C/π

  d = (43.96 in)/3.14 = 14 in

The circle's diameter is 14 inches.

<95141404393>

The dilated points are:

G' = (1, 1)

H' = (1, 3)

J' = (4, 1)

Option C is the correct answer.

We have,

To dilate with a scale factor of 1/3, we need to multiply the coordinates of each point by 1/3.

The new coordinates of G will be:

x-coordinate: 3 × 1/3 = 1

y-coordinate: 3 × 1/3 = 1

So, the new coordinates of G are (1, 1).

The new coordinates of H will be:

x-coordinate: 3 × 1/3 = 1

y-coordinate: 9 × 1/3 = 3

So, the new coordinates of H are (1, 3).

The new coordinates of J will be:

x-coordinate: 12 × 1/3 = 4

y-coordinate: 3 × 1/3 = 1

So, the new coordinates of J are (4, 1).

Therefore,

The dilated points are:

G' = (1, 1)

H' = (1, 3)

J' = (4, 1)

Learn more about dilations here:

https://brainly.com/question/13176891

#SPJ1