21. Evaluate the following: 17C3. *
A. 210
B. 504
C. 35
D. 680

The equation of the parabola with focus (2,5) and directrix x=18 is (x - 18)² + (y - 5)² = (y - (5 + (18 - 2) / 2))².

A parabola is a conic section, the intersection of a right circular conical surface and a plane parallel to a generating

straight line of that surface.

The focus of a parabola is a fixed point on the interior of a parabola used in the formal definition of the curve.

The directrix is a straight line perpendicular to the axis of symmetry and placed symmetrically with respect to the focus.

The axis of symmetry is the line through the focus and perpendicular to the directrix.

The vertex of a parabola is the point where its axis of symmetry intersects the curve. It is the point where the parabola changes direction or "opens

up" or "opens down.

The directrix is a fixed straight line used in the definition of a

parabola. It is placed such that it is perpendicular to the axis of symmetry and at a distance from the vertex equal to the

distance between the vertex and focus. It is the line that is equidistant to the focus and every point on the curve.Here's

the solution to the given problem:

The distance between the directrix and the focus is equal to p = 16 (since the directrix is x = 18, the parabola opens to the left, so the distance is measured horizontally)

The vertex is (h,k) = ((18+2)/2,5) = (10,5)

Then we can use the following formula: (x - h)² = 4p(y - k)

Substitute the vertex and the value of p. (x - 10)² = 64(y - 5)

Expand and simplify. (x - 10)² + (y - 5)² = 64(y - 5)

The equation of the parabola is (x - 10)² + (y - 5)² = 64(y - 5).

for such more question on parabola

https://brainly.com/question/17987697

#SPJ11

Answer:

11

Step-by-step explanation:

Supplementary means that the sum of the two angles equal to 180, so add the two measures and make them equal to 180. Add the two x's, subtract the two constants.

Step-by-step explanation:

5n-100= profit

...............

The likelihood that the difference between two numbers rolled will be 0 is 1/6 if you roll two fair, normal six-sided dice.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

The first die can be anything.  There's a 1/6 chance that the second die will match it. Another way of saying it is that there are 36 possible combinations. Six of them are doubles.  

6/36 = 1/6

1,1    1,2    1,3    1,4   1,5     1,6  

2,1   2,2   2,3   2,4   2,5   2,6  

3,1   3,2   3,3   3,4   3,5   3,6  

4,1   4,2   4,3   4,4   4,5   4,6  

5,1   5,2   5,3   5,4   5,5   5,6  

6,1   6,2   6,3   6,4   6,5   6,6

The probability that if you roll two fair, standard six-sided dice, the difference between the two numbers rolled will be 0 is 1/6.

To know more about probability,

brainly.com/question/30034780

#SPJ4

Answer:

y=-12x-x

Step-by-step explanation:

y=mx + b

m=slope

m = -12

slope = rise / run -12/1

Answer:

Samantha makes more money with $8.40 an hour.

Explanation:

$41.50 divided by 5 is $8.30, and %50.40 divided by 6 is $8.40.

Answer:

Samantha makes more

Step-by-step explanation:

Dillon:

41.50/5 would = $8.3 an hr

Samantha:

50.40/6 would =$8.4 an hr

The expanded form of the expressions is 3y + 3x

These are mathematical expressions that are composed of terms, variables, constants and  factors with coefficients,

These expressions are also known to include mathematical or arithmetic operations, such as;

They could also be made up of fractions and decimlals

We have the expression;

3(y + x)

expand the parentheses

3y + 3x

Hence, the expression is 3y + 3x

Learn about algebraic expressions at: https://brainly.com/question/4344214

#SPJ1

Answer:

$106.64

Step-by-step explanation:

To get 14%

1. x/124 = 14/100

2. 124×14=1736

3. 1736/100= 17.36

4. 124-17.36= 106.64

Hello!

1/6 ≈ 0.167

the answer is 0.167

Answer:

p = 0.531

Step-by-step explanation:

26 + 9p = 58p

subtract 9p from both sides:

26 + 9p - 9p = 58p - 9p

26 = 49p

divide both sides by 49:

26/49 = 49p/49

0.530612 = p

rounded to the nearest hundred

p = 0.531

x= 19º, y=104º

1) For the given picture, let's find the value for x.

m∠1 = 4x, m∠2= y, m∠3=76

2) According to the Vertical Angle Theorem we can state that

∠1≅∠3 So, we write

4x = 76

x= 19º

Since∠1 and ∠2 are supplementary,∠2 and ∠2 are supplementary either we can write:

∠3+∠2=180º

76+y=180º

y=180-76

y=104

This connection makes smells particularly powerful in triggering memories and emotions.

The sense of smell is the most likely to call up mental images of specific sights, sounds, tastes, or smells. This is because the olfactory system, which is responsible for the sense of smell, is closely linked to the brain's limbic system, which is involved in emotions and memory. This connection makes smells particularly powerful in triggering memories and emotions.

The olfactory system, which is responsible for the sense of smell, is unique in its connection to the brain's limbic system, which is involved in processing emotions and memory. When we smell something, the odor molecules enter our nose and are processed by specialized sensory neurons in the olfactory epithelium. These neurons then send signals to the olfactory bulb, which is located in the brain and is the first site of olfactory processing.

From there, the olfactory information is sent to several brain regions, including the amygdala and hippocampus, which are both part of the limbic system. The amygdala is involved in processing emotions and is responsible for generating feelings of pleasure, disgust, or fear in response to smells. The hippocampus, on the other hand, is involved in forming new memories and is responsible for encoding information about the context in which a smell is experienced.

The strong connection between the olfactory system and the limbic system makes smells particularly powerful in triggering memories and emotions. For example, the scent of freshly baked bread may evoke memories of childhood mornings spent in the kitchen with a loved one, while the smell of a certain perfume may remind you of someone special. Additionally, certain smells may elicit strong emotional responses, such as the smell of smoke triggering feelings of panic and fear in someone who has experienced a fire.

Overall, the sense of smell is closely linked to our emotional and memory centers, making it a powerful tool for triggering mental images of specific sights, sounds, tastes, or smells.

To learn more about smell visit: https://brainly.com/question/31103337

#SPJ11

Answer:density = 2.9 g/cm 3

Step-by-step explanation:

Answer:

The answer is F

Step-by-step explanation:

to factor we must recognize the elements in common

the r exist on both terms, so we can divide by r on each term to factor

Answer:

7×10= 70

70-8= 62

Answer62

Answer:

5/9=1/2

12/13=1

2/13=0

Step-by-step explanation:

These are just based on what I think and also

5/9=0.55... so closer to 0.5 which =1/2

12/13 is just really close to 13/13

2/13 is really close to 0/13 rather than 6.5/13, which is 1/2

a. Paired t-test – Dependent samples. Relevant parameter: mean sales. (b) Independent samples t-test – Independent samples. Relevant parameter: rating score. (c) Chi-squared test – Independent samples. Relevant parameter:   positive/negative ratings

a. For scenario a, where Hughes records the mean sales before and after the menu change, a paired t-test would be an appropriate statistical method. The samples in this scenario are dependent because they come from the same group of customers (i.e., sales before and after the menu change). The relevant parameter in this case would be the mean sales. To determine whether the difference in mean sales before and after the change is statistically significant, a paired t-test would be used for inference.

b. In scenario b, where Hughes randomly samples 100 people and asks them to rate both menus, an independent samples t-test would be suitable for analyzing the problem. The samples in this scenario are independent because each person rates both menus separately. The relevant parameter would be the rating score. To determine if there is a significant difference in ratings between the two menus, an independent samples t-test can be used for inference.

c. In scenario c, where Hughes randomly samples 100 people and separates them into two groups, asking for positive/negative ratings for the old and new menus, a chi-squared test would be appropriate for analyzing the problem. The samples in this scenario are independent because each person belongs to either group 1 or group 2 and rates only one menu. The relevant parameter would be the proportion of positive and negative ratings for each menu. A chi-squared test can be used to assess whether there is a significant association between the menu (old or new) and the positive/negative ratings.


Learn more about Chi-squared test here: brainly.com/question/14082240
#SPJ11

Answer:

x = 7 (the number of students)

Step-by-step explanation:

let students = x , adults =y

Equation 1: the  total number of them

x+y=25  (25 because there are 5 for free)

Equation 2: the total price of them

2x+5y=104       (student cost 2$, adult cost 5$)

so we have two equations

x+y=25      (by multiply this equation by -2)

so it will be -2x-2y=-50

by adding 2 equations

-2x-2y=-50

2x+5y=104

0+3y = 54   divide both side by 3

y=18      (the number of adults)

by sub. in Equation (x+y=25)

x+18=25

x=25-18

x = 7 (the number of students)

Answer:

$12.96

Step-by-step explanation:

determine what the decimal form of 8% is

⇒ 8% = 0.08

multiply $12 by 0.08

⇒ $12 x 0.08

⇒ $0.96

add $0.96 to $12

⇒ $12 + $0.96

⇒ $12.96

new price

⇒ $12.96

Answer: The converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Step-by-step explanation:

What does it mean converse in geometry?

The converse of a statement is formed by switching the hypothesis and the conclusion. The converse of "If two lines don't intersect, then they are parallel" is "If two lines are parallel, then they don't intersect." The converse of "if p, then q" is "if q, then p."

So, in the figure below, if we can choose n║m, then ∠1≅∠2

Since  n║m , by the corresponding Angles Postulate,

∠1≅∠2.

Therefore, by the definition of congruent angles,

m∠1=m∠2

Since ∠1 and ∠2 form a linear pair, they are supplementary, so

m∠1+m∠2=180°.

Therefore, the converse of this theorem is also true; that is, if two lines n and m are cut by a transversal so that the alternate interior angles are congruent, then n║m.

Learn about more information https://brainly.in/question/14313548

#SPJ9

The probability that a customer did not order a starter is 9/10.

We have,

To find the probability that a customer did not order a starter, we can use the concept of set theory and probability.

Let's define the events:

A: Customer ordered a starter

A' (read as "A compliment"): Customer did not order a starter

Given information:

Total number of customers = 30

Customer that Ordered a starter = 3

Customer that Ordered a dessert = 5

Customer who ordered Both starter and dessert = 14

To find the probability that a customer did not order a starter (A'), we can subtract the probability of event A (customer ordered a starter) from 1.

Probability of A = Customer that Ordered a starter / Total number of customers

= 3 / 30

= 1 / 10

Probability of A' (customer did not order a starter) = 1 - Probability of A

= 1 - 1/10

= 9/10

Therefore,

The probability that a customer did not order a starter is 9/10.

Learn more about probability here:

https://brainly.com/question/14099682

#SPJ1

Answer:

Angle 5

Step-by-step explanation:

Answer:

Angle 5

Step-by-step explanation:

Angle 8 is across from angle 5 meaning they have the same degrees.

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

Sinusoids are expressions with trascendent functions, to be more specfic, trigonometric functions, whose form is described below:

T(t) = A · sin (2π · t / T + C) + B       (1)

Where:

The temperature amplitude and the middle temperature can be found by the following expressions:

A = (t' - t'') / 2      (2)

B = (t' + t'') / 2      (3)

Where t' and t'' are maximum and minimum temperatures, in degrees.

Then, we proceed to find each constant of the sinusoidal model:

A = (45 - 7) / 2

A = 38 / 2

A = 19

B = (45 + 7) / 2

B = 52 / 2

B = 26

We assume a period of 24 hours (T = 24).

If we know that t = 0, T = 24, A = 19, B = 26, T(t) = 7, then the angular phase is:

7 = 19 · sin [(π / 12) · 0 + C] + 26

- 19 = 19 · sin C

sin C = - 1

C = π

T(t) = 19 · sin (π · t / 12 + π) + 26

Then, the temperature at 9 AM is: (t = 4)

T(4) = 19 · sin (π · 4 / 12 + π) + 26

T(4) ≈ 9.545

The temperature at 9 AM is approximately 10 degrees. Neither of the answers are correct. (Correct choice: E)

To learn more on sinusoids: https://brainly.com/question/22467963

#SPJ1

The equation of the vertical asymptote of the function \(g(x)=4log_{2} (x-2)+5\) is x=2.

Vertical asymptotes are vertical lines that represent the zeros of a rational function's denominator. Asymptotes can also occur in other situations, such as logarithms. It occurs at the x-value that is outside the domain of the function, therefore the graph can never cross it.

There may be a vertical asymptote along the vertical line if a portion of the graph is about to turn vertical. At the point of x along which you discovered the vertical asymptote, the function's value changes to either ∞ or -∞. A vertical asymptote, however, must never touch the graph.

Graph the function \(g(x)=4log_{2} (x-2)+5\)

(x,y)= (3,5), (4,9), (6,13)

From graph we can see that the graph is turning to be vertical from x=2. So, the equation of vertical asymptote of the function is x=2.

To know more about vertical asymptotes, visit:

https://brainly.com/question/11743529

# SPJ4

The complete question is:

“What is the equation of the vertical asymptote of \(g(x)=4log_{2} (x-2)+5\)? enter your answer in the box.”

Answer:

0.125

Step-by-step explanation:

Becuase math

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

In hypothesis testing, if the null hypothesis is rejected, it means that there is sufficient evidence to support the alternative hypothesis. A null hypothesis is a statement that there is no significant difference or relationship between variables, while the alternative hypothesis states that there is a significant difference or relationship. To determine if the null hypothesis is true or not, we conduct a statistical test and calculate the p-value. If the p-value is less than the level of significance, usually set at 0.05, we reject the null hypothesis and accept the alternative hypothesis. Therefore, the correct answer is that the evidence supports the alternative hypothesis. This means that we have found significant results that support our research hypothesis.
Keep in mind that rejecting the null hypothesis does not prove the alternative hypothesis, but it does suggest that it's more plausible based on the data collected.

Therefore, if the null hypothesis is rejected, the evidence supports the alternative hypothesis. This means that the test results provide enough evidence to conclude that the alternative hypothesis is more likely true than the null hypothesis.

To know more about statistics visit :

https://brainly.com/question/15525560

#SPJ11