(7,-20), (1,-3)
Find the slope of the line through each pair of points

Answer:

The answer is 2

Step-by-step explanation:

f(x)=√x+2 +2

when x=2

f(2)=√2+2 +2

f(2)=√4 +2

f(2)=2+2

f(2)=4

Answer:

f(x) = (x + 4)² - 4

Step-by-step explanation:

Write the equation f(x) = x² + 8x + 12 in vertex form by completing the square:

f(x) = (x² + 8x + (8/2)²) + 12 - (8/2)²

Simplify:

f(x) = (x² + 8x + 16) + 12 - 16

Subtract to find the 'k' value:

f(x) = (x + 4)² - 4. This is the equation in vertex form.

Answer:

y=8x2+8x−12

Step-by-step explanation:

Rewrite in vertex form and use this form to find the vertex (h,k).

(4,4)

Answer:

I THINK it would be 11.

The answers are:

The reason in the second column of a two column proof is

Option b. A theorem

The reason that should go in box 2 of the two column proof is

Option b. Definition of supplementary angles

A prior assertion upon which the legitimacy of the subsequent assertion is established.

As, When two angles are considered supplementary, their sum equals 180 degrees.

<1 + < 2= 180

A theorem states that two angles are supplementary if their measures add up to 180 degrees.

In a two-column proof, a theorem may be used as a justification in the second column.

According to the definition of supplementary angles, two angles are considered supplementary if their measures add up to 180 degrees.

The justification for including box 2 in the two column proof's box 2 is the definition of supplementary angles.

Learn more here about supplementary angles here:

brainly.com/question/17797703

#SPJ1

Answer:

126

Step-by-step explanation:

The simple interest for R 7,500 is R 1, 800, and she will get it at 3 years with interest of 8%.

Simple interest:

Simple interest means the method of calculating the interest amount for a particular principal amount of money at some rate of interest.

The formula used to calculate the simple interest is

SI = P × R × T

P = The principal is the amount that initially borrowed from the bank or invested.

R = Rate is the rate of interest at which the principal amount is given to someone for a certain time.

T= Time is the duration for which the principal amount is given to someone.

Given,

Cynthia receives a gift of r 7, 500 she decides to invest it for 3 years, she is offered two saving at 8% interest.

Here we need to find the simple interest.

We know that,

P = 7, 500

R = 8/100 = 0.08

T = 3

So, the simple interest is,

SI = 7,500 x 0.08 x 3

SI = 1800

To know more about Simple Interest here

https://brainly.com/question/25845758

#SPJ4

Answer:

The better bar to buy is the Nutty Crunch

Step-by-step explanation:

4.74 / 6 = 0.79 per bar

7.80 / 10 = 0.78 per bar

:)

Answer:

Nutty Crunch is better

Step-by-step explanation:

After the transformation of vertical compression , horizontal shift and reflection as mentioned the transformed equation is given by :

y = (-1/7)(x+ 8)³ .

As given in the question,

Given equation is :

y = x³

When the transformation is done as vertical compression with factor 1/7 it is equal to :

y = ( 1/7 )x³

Now Transformed by horizontal shift of 8 units to the left

y = ( 1 /7)( x + 8 )³

Reflection across the x -axis is given by :

y = - ( 1 /7)( x + 8 )³

Therefore, after the transformation of vertical compression , horizontal shift , and the reflection the required equation is :

y = ( 1 /7)( x + 8 )³.

The above question is incomplete, the complete question is :

What is the equation of y=x^3 with the given transformations?

Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis.

Learn more about transformation here

brainly.com/question/11709244

#SPJ4

Answer:

area = width * length = y* b/y = b =17

Step-by-step explanation:

Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ and solve for 'x'

Let's solve:

 \(x^2-2x+3=-2x+19\\x^2-2x+2x+3-19=0\\x^2-16=0\\(x+4)(x-4)=0\)

Let's find the x-values:

   \((x-4)=0\\x=4\\\\(x+4)=0\\x=-4\)

Let's find f(x)'s value for each 'x':

 \(x=4\\f(4)=-2(4)+19=-8+19=11\\\\x=-4\\f(-4)=-2(-4)+19=8+19=27\)

Answer: (4, 11), (-4,27)

Hope that helps!

#LearnwithBrainly

Answer:

It not a function... the two points would be (0,3) and (-3,0)

Step-by-step explanation:

The numbers in the second option is from the least to the greatest.

The numbers can be list from least to greatest as follows:

√5 , 4, 32, -2

32 is greater than -2.

Therefore, the numbers in first option is not from the least to the greatest.

-2,√5 , 4, 32

The number increases.

Therefore, the numbers in the second option is from the least to the greatest.

-2, 4, 32, √5

32 is greater than √5.

Therefore,  the numbers in third option is not from the least to the greatest.

-2, 3 / 2, 4, √5

4 is greater than √5.

Therefore,  the numbers in fourth option is not from the least to the greatest.

learn more on numbers here: https://brainly.com/question/2628441?referre

#SPJ1

The equation is:

7x = y

Hope it helps!!!

Answer:

c. 4

Step-by-step explanation:

f ( -2) means x = -2

so just replace x with -2

a)  the value of the constant c is 1/9. b) P[Y < X] is equal to 5/9. c) P[Y > X] is equal to 1/3. d) P[Y = X] is equal to 1/3. e) P[X < 1] is equal to 4/9.f)\(the marginal PMFs are: P_x(-1) = P_x(0) = P_x(1) = 1/3\\P_y(-2) = P_y(0) = P_y(2) = 1/3\) g) the expected values E[X] and E[Y] are both equal to 0. h)the standard deviation of X is √(2/3), and the standard deviation of Y is √(8/3) from given  probability mass function.

To answer the questions related to the given probability mass function (PMF) \(P_{x,y}(x,y),\) let's go through each question step by step:

a. To find the value of the constant c, we need to ensure that the sum of the probabilities for all possible values of x and y is equal to 1.

Summing the probabilities for the given values of x and y:

P(-1, -2) + P(-1, 0) + P(-1, 2) + P(0, -2) + P(0, 0) + P(0, 2) + P(1, -2) + P(1, 0) + P(1, 2) = 1

Using the given definition of \(P_{x,y}(x,y),\) we find:

c + c + c + c + c + c + c + c + c = 1

9c = 1

c = 1/9

Therefore, the value of the constant c is 1/9.

b. P[Y < X] represents the probability that the random variable Y is less than X. We need to sum the probabilities for all the cases where Y is less than X.

P[Y < X] = P(-1, -2) + P(0, -2) + P(0, -2) + P(1, -2) + P(1, 0) + P(1, 2)

Using the given definition of \(P_{x,y}(x,y),\) we find:

P[Y < X] = c + 0 + c + c + c + c = 1/9 + 0 + 1/9 + 1/9 + 1/9 + 1/9 = 5/9

Therefore, P[Y < X] is equal to 5/9.

c. P[Y > X] represents the probability that the random variable Y is greater than X. We need to sum the probabilities for all the cases where Y is greater than X.

P[Y > X] = P(0, 2) + P(-1, 0) + P(-1, 2)

Using the given definition of \(P_{x,y}(x,y),\) we find:

P[Y > X] = c + c + c = 1/9 + 1/9 + 1/9 = 3/9 = 1/3

Therefore, P[Y > X] is equal to 1/3.

d. P[Y = X] represents the probability that the random variable Y is equal to X. We need to sum the probabilities for all the cases where Y is equal to X.

P[Y = X] = P(-1, -1) + P(0, 0) + P(1, 1)

Using the given definition of \(P_{x,y}(x,y),\) we find:

P[Y = X] = c + c + c = 1/9 + 1/9 + 1/9 = 3/9 = 1/3

Therefore, P[Y = X] is equal to 1/3.

e. P[X < 1] represents the probability that the random variable X is less than 1. We need to sum the probabilities for all the cases where X is less than 1.

P[X < 1] = P(-1, -2) + P(-1, 0) + P(0, -2) + P(0, 0)

Using the given definition of \(P_{x,y}(x,y),\) we find:

P[X < 1] = c + c + c + c = 1/9 + 1/9 + 1/9 + 1/9 = 4/9

Therefore, P[X < 1] is equal to 4/9.

f. To find the marginal PMFs \(P_x(x)\) and \(P_y(y),\) we need to sum the probabilities of \(P_{x,y}(x,y),\) over the respective variable.

\(P_x(x)\) = P(x, y) for all possible values of y.

\(Py(y)\) = P(x, y) for all possible values of x.

Using the given definition of \(P_{x,y}(x,y),\) we have:

\(P_x(-1) = P(-1, -2) + P(-1, 0) + P(-1, 2)\\= c + c + c\\= 1/9 + 1/9 + 1/9\\= 3/9 = 1/3\)

\(P_x(0) = P(0, -2) + P(0, 0) + P(0, 2)\\= c + c + c\\= 1/9 + 1/9 + 1/9\\= 3/9 = 1/3\\P_x(1) = P(1, -2) + P(1, 0) + P(1, 2)\\= c + c + c\\= 1/9 + 1/9 + 1/9\\= 3/9 = 1/3\)

\(P_y(-2) = P(-1, -2) + P(0, -2) + P(1, -2)\\= c + c + c\\= 1/9 + 1/9 + 1/9\\= 3/9 = 1/3\\P_y(0) = P(-1, 0) + P(0, 0) + P(1, 0)\\= c + c + c\\= 1/9 + 1/9 + 1/9\\= 3/9 = 1/3\)

\(P_y(2) = P(-1, 2) + P(0, 2) + P(1, 2)\\= c + c + c\\= 1/9 + 1/9 + 1/9\\= 3/9 = 1/3\\Therefore, the marginal PMFs are:\\P_x(-1) = P_x(0) = P_x(1) = 1/3\\P_y(-2) = P_y(0) = P_y(2) = 1/3\)

g. To find the expected values E[X] and E[Y], we need to sum the products of each variable's value and its corresponding probability from their marginal PMFs.

E[X] = (-1)(1/3) + (0)(1/3) + (1)*(1/3) = 0

E[Y] = (-2)(1/3) + (0)(1/3) + (2)*(1/3) = 0

Therefore, the expected values E[X] and E[Y] are both equal to 0.

h. To find the standard deviations Ox and Oy, we need to calculate the variances Var(X) and Var(Y) first. The standard deviation is the square root of the variance.

\(Var(X) = E[(X - E[X])^2]\\= (-1 - 0)^2*(1/3) + (0 - 0)^2*(1/3) + (1 - 0)^2*(1/3)\\= 2/3\\Var(Y) = E[(Y - E[Y])^2]\\= (-2 - 0)^2*(1/3) + (0 - 0)^2*(1/3) + (2 - 0)^2*(1/3)\\= 8/3\\O_x = \sqrt{(Var(X))} = \sqrt{2/3} \\O_y = \sqrt{(Var(Y))} = \sqrt{8/3}\)

Therefore, the standard deviation of X is √(2/3), and the standard deviation of Y is √(8/3).

To know more about the probability mass function refer here :

brainly.com/question/30070005#

#SPJ4

Answer:

30 more

Step-by-step explanation:

hope it helps friend.

Answer: x=-3 x √2

Step-by-step explanation:

Answer:

x = 24

Step-by-step explanation:

I think the question is \( \sqrt{x+1}+4=-1 \)

\( \sqrt{x+1}=-5 \)

\( x+1=25 \)

x = 24

Rounding to three decimal places, the 95% confidence interval for the population proportion of times that the bats would follow the point is (0.565, 1.035).

To find the 95% confidence interval for the population proportion, we can use the formula for calculating confidence intervals for proportions:

Confidence Interval = Sample Proportion ± Margin of Error

The sample proportion is the number of successes (bats going to the correct feeder) divided by the sample size (total number of trials). In this case, the sample proportion is 8/10, which simplifies to 0.8.

The margin of error depends on the desired level of confidence. For a 95% confidence interval, the critical value is 1.96.

Margin of Error = Critical Value * Standard Error

The standard error is calculated as the square root of [(sample proportion * (1 - sample proportion)) / sample size]. In this case, it is sqrt[(0.8 * (1 - 0.8)) / 10], which simplifies to 0.12.

Now we can plug in the values:

Confidence Interval = 0.8 ± (1.96 * 0.12)

Calculating the confidence interval:

Confidence Interval = 0.8 ± 0.2352

Simplifying the interval:

Confidence Interval = (0.5648, 1.0352)

know more about 95% confidence interval here:

https://brainly.com/question/29680703

#SPJ11

Answer:

x = 18311.61 m

Step-by-step explanation:

It is given that, An observer (O) spots a bird flying at a 55° angle from a line drawn horizontal to its nest. The distance from the observer (O) to the bird (B) is 15,000 ft. We need to find the distance between the bird and the nest. It is based on trigonometry. So,

\(\sin (35)=\dfrac{\text{opposite}}{\text{hypotenuse}}\)

Let x is the distance between the bird and the nest

So,

\(\sin (55)=\dfrac{15000}{x}\\\\x=\dfrac{15000}{ \sin(55)} \\\\x=18311.61\ m\)

So, the distance between the bird and the nest is 18311.61 m.

Answer:

8,604

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

3x-7=2x(isosceles triangle)

x=7

AC=3(7)-7=21-7=14

The length of the side AC in the given triangle is 14 units.

A polygon with three sides, angle and vertex is called a triangle.

Given is a triangle ABC, with sides, AB = 2x, AC = 3x-7 and BC = 4x-10,

We need to find the length of AC,

According to the figure, ∠B ≅ ∠C, therefore, according to the theorem of triangles, that sides opposite to congruent angles are congruent,

Therefore, AC = AB

2x = 3x-7

x = 7

AC = 3(7)-7

AC = 14

Hence, the length of the side AC in the given triangle is 14 units.

Learn more about triangle, click;

https://brainly.com/question/2773823

#SPJ7

The length of the microorganism in millimeters is 0.005 mm.

The theory behind converting length units from one unit to another is based on the conversion factor principle. In the International System of Units (SI), the conversion factor between two units of length can be obtained by comparing the number of meters represented by each unit. For example, 1 millimeter is equal to 0.001 meters, and 1 micrometer is equal to 0.000001 meters.

To convert from one unit of length to another, we multiply the length by the appropriate conversion factor. In this case, to convert from micrometers to millimeters, we multiply the length in micrometers by 0.001 to obtain the length in millimeters.

To convert the length of the microorganism from micrometers (μm) to millimeters (mm), we divide by 1000.

5 μm / 1000 = 0.005 mm

Therefore, the length of the microorganism in millimeters is 0.005 mm.

To learn more about conversions click on,

https://brainly.com/question/30510574

#SPJ4

49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

Learn more about calories

brainly.com/question/22374134

#SPJ4

Answer:

See Below

Step-by-step explanation:

150 = p + 78    ------ you want to get the p to one side and the other number the the other side of the =

(78 - 150) = p (78 - 78)   ---- what ever you do to one side you do to the other

72 = p

s - 51 = 12 (same thing as above)

s (-51 + 51)  = 12 + 51

s = 63

65 = blank + 7 ( you can put a letter like x or y because they number is not determined yet)

65 = x + 7 (same as above)

( 7 - 65 ) = x ( 7 - 7 )

58 = x

0.449 is the probability that at least one of the three residents does not own a cell phone.

The area of mathematics known as probability is concerned with how random events turn out. The definition of probability is chance or potential for a result. It clarifies the likelihood of a specific occurrence. We frequently say things like, "It will probably rain today," "He'll probably pass the test," "There's very little chance we'll get a storm tonight," and "It'll probably get expensive again for onions." We insert the word probability in place of all the phrases chance, doubt, maybe, probable, etc. in all of these sentences. In essence, probability is the forecasting of an outcome that is either based on the analysis of past data or the variety and quantity of alternative outcomes.

P(X≥1) = 0.45 (approximately)

Let X be the random variable, then X follows a binomial distribution with probability of success, p and number trials, n.

The probability distribution is given as:

P(X) = nCx * p^x * (1 – p)^(n – x)

Where p is Probability of success, n is number of trials and x is total number of successes.

Probability of having phone is 82% = 0.82

Probability of not having phone is 100% – 82% = 0.18.

Since the trials are interested in those that are not having phone, then probability of success, p = 0.18.

Number of trials, n = 3.

P(X ≥ 1) = 1 – P(X < 1) = 1 – P(X = 0)

P(X = 0) = 3C0 * (0.18)^0 * (0.82)^(3) = 1 * 1 * 0.551368 = 0.551368

P(X ≥ 1) = 1 – 0.551368 = 0.448632 ≈ 0.449

To know more about Probability, visit:

https://brainly.com/question/11234923

#SPJ4

The right response is 21 days, minus any days that the location was unavailable or inaccessible.

This is due to the fact that taxpayers have 21 days starting from the date of the Notice of Deficiency to file a petition with the Tax Court, as per the Internal Revenue Service. However, the taxpayer can be given longer time to submit the petition if their place of residence or business was inaccessible or unavailable as a result of a natural disaster..

Upon receiving a Notice of Deficiency, the Internal Revenue Service (IRS) gives taxpayers 21 days to file a petition with the Tax Court. This petition is a formally filed motion asking the court to consider the proposed assessment of the IRS and resolve the taxpayer's disagreements with the agency.

Therefore, the right response is 21 days, minus any days that the location was unavailable or inaccessible.

To know more about tax payer, visit:

https://brainly.com/question/16781281

#SPJ4

Answer:

41/20

Step-by-step explanation:

or 2 1/20

The "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

In statistics, a confidence interval describes the likelihood that a population parameter would fall between a set of values a predetermined percentage of the time.

Thus, the "correct" statement is that the odds ratio appears statistically significant when the whole 95% confidence interval is much less than 1.

To know more about the confidence interval, here

https://brainly.com/question/14825274

#SPJ4

Karen has made 76 calls today to secure donations at the call center.

Let's assume that Karen has made x calls so far today. According to the information given, she has convinced 18% of the people she has called to donate. This means that 18% of x calls have resulted in successful donations, which can be written as 0.18x.

Karen wants to be just over the 25% mark by convincing 12 out of the next 30 people she calls to donate. This means that the total number of successful donations should be slightly more than 25% of the total number of calls made. Representing this mathematically, we have (0.18x + 12)/(x + 30) > 0.25.

Simplifying the inequality, we have 0.18x + 12 > 0.25(x + 30). Solving for x, we find that x > 76.

Therefore, Karen has made 76 calls so far today to secure donations at the call center in order to be just over the 25% mark by convincing 12 out of the next 30 people she calls to donate.

Learn more about inequality here:

https://brainly.com/question/32386266

#SPJ11