(I found x but I don’t know how to figure out y)

Using the definition of **congruent triangles**, the missing values are:

x = 35

y = 30°

What are Congruent Triangles?Given that the two **triangles** in the image above are **congruent**, it implies that all its corresponding angles and corresponding side lengths have equal measure.

Therefore, we have:

2x - 10 = x + 25

Solve for x:

2x - x = 10 + 25

x = 35

Plug in the value of x to find the missing angles:

y + 90 + (2x - 10) = 180 [**triangle sum theorem**]

y + 90 + (2(35) - 10) = 180

y + 90 + 60 = 180

y = 30°

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A leaky faucet is losing water and is filling a 5-gallon bucket every 20 hours. At that

rate, how many gallons of water will the faucet leak in

48 hours?

Show your

work.

To find the number of gallons of water leaked by the faucet in 48 hours, we need to multiply the number of gallons leaked per hour by the number of hours:

gallons leaked per hour = 5 gallons / 20 hours = 5/20 gallons/hour

gallons leaked in 48 hours = (5/20 gallons/hour) * 48 hours = (5/20) * 48 gallons

gallons leaked in 48 hours = 12 gallons

So, the faucet will leak a total of 12 gallons in 48 hours.

gallons leaked per hour = 5 gallons / 20 hours = 5/20 gallons/hour

gallons leaked in 48 hours = (5/20 gallons/hour) * 48 hours = (5/20) * 48 gallons

gallons leaked in 48 hours = 12 gallons

So, the faucet will leak a total of 12 gallons in 48 hours.

**Answer:**

**Step-by-step explanation:**

We can start by finding the amount of water the leaky faucet loses in one hour:

5 gallons / 20 hours = 0.25 gallons per hour

This means that the leaky faucet loses 0.25 gallons of water every hour.

To find how many gallons of water the faucet will leak in 48 hours, we can multiply the rate of leakage per hour by the number of hours:

0.25 gallons/hour x 48 hours = 12 gallons

Therefore, the leaky faucet will lose 12 gallons of water in 48 hours.

a manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 430 gram setting. it is believed that the machine is underfilling the bags. a 21 bag sample had a mean of 421 grams with a standard deviation of 15 . assume the population is normally distributed. a level of significance of 0.1 will be used. find the p-value of the test statistic. you may write the p-value as a range using interval notation, or as a decimal value rounded to four decimal places.

A manufacturer working at the 430 gram setting, and a 21 bag sample had a mean of 421 grams with a standard deviation of 15. The** p-value** of test statistic is 0.0074.

To test whether the bag filling machine works correctly at the 430 gram setting, we can conduct a one-sample t-test. The null **hypothesis **is that the true mean weight of the bags filled by the machine is equal to 430 grams, and the alternative hypothesis is that the true mean weight is less than 430 grams.

The **test statistic** is calculated as:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values given in the problem, we get:

t = (421 - 430) / (15 / sqrt(21)) = -2.77

The degrees of freedom for the t-**distribution **are n - 1 = 20.

Using a t-table or calculator, we can find the p-value associated with a t-score of -2.77 and 20 degrees of freedom. The **p-value** turns out to be 0.0074 (rounded to four decimal places).

Since the p-value is less than the level of significance of 0.1, we can **reject **the null hypothesis and conclude that the bag filling machine is underfilling the bags at the 430 gram setting.

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The table shows how many hours Sara spent at several activities one Saturday.

Activity Hours

Soccer practice 222

Birthday party 333

Science project 111

What is the ratio of hours spent at soccer practice to hours spent at a birthday party?

The **ratio** of hours spent at soccer practice to hours spent at a birthday party are **2 for every 3**.

**What is a ratio?**

A **ratio** is produced by **comparing** or condensing **two** related pieces of **data**. Looking at the reciprocity of the relationship allows us to calculate the number of times one quantity is equal to another. To put it simply, a **ratio** is a number that can be used to **represent** one thing as a **proportion** of another.

We are given that for soccer practice, Sara spends 2 hours and for birthday party, she spends 3 hours.

So, the **ratio** of hours spent at soccer practice to hours spent at a birthday party is **2 for every 3.**

Hence, the **ratio** is **2 for every 3.**

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Question: The table shows how many hours Sara spent at several activities one Saturday.

Activity "Hours

Soccer practice 2

Birthday party 3

Science project 1

What is the ratio of hours spent at soccer practice to hours spent at a birthday party?

Choose 1 answer:

1 for every 2

2 for every 1

2 for every 3

3 for every 2

*FIND THE SLOPE OF THE LINE THROUGH EACH PAIR OF POINTS*

d. (-4, 3) and (-6, -8)

e. (-7, -1) and (-7, 2)

f. (9, 4) and (-6, 4)

slope = y2 - y1

______

x2 - x1

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{-8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-8}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{(-4)}}} \implies \cfrac{-11}{-6 +4} \implies \cfrac{ -11 }{ -2 } \implies \cfrac{11 }{ 2 } \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{-7}~,~\stackrel{y_2}{2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{(-1)}}}{\underset{\textit{\large run}} {\underset{x_2}{-7}-\underset{x_1}{(-7)}}} \implies \cfrac{2 +1}{-7 +7} \implies \cfrac{ 3 }{ 0 } \implies \stackrel{\textit{vertical line}}{{\Large \begin{array}{llll} unde fined \end{array}}} \\\\[-0.35em] ~\dotfill[/tex]

[tex](\stackrel{x_1}{9}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{-6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{-6}-\underset{x_1}{9}}} \implies \cfrac{ 0 }{ -15 } \implies \stackrel{\textit{horizontal line}}{\text{\LARGE 0}}[/tex]

keep in mind that whenever you notice the x-coordinates are the same, it's a vertical line, and whenever the y-coordinates are the same, is a horizontal line.

express 2x^2 + 8x in the form a(x + b)^2 + c

The **vertex** form **equivalent** to the given expression; 2x² + 8x as required to be determined in the task content is; 2 (x + 2)² + 8.

The vertex form equivalent of the given expression can be determined as follows;

2x² + 8x

2 (x² + 4x)

2 ( (x + 2)² + 4)

= 2 (x + 2)² + 8.

Ultimately, the **vertex form** equivalent of the given **expression** as required is; 2 (x + 2)² + 8.

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40° rcm Find the value of z. zem This sector of a circle has radius r and perimeter 20 cm. find the value of z

The value of **length** of z is 5.06 cm.

What is the value of length z?

The value of **length** of z is calculated by determining the **radius** of the sector as shown below;

The formula for the **perimeter** of a **sector** is given as;

P = 2r + (θ/360) × 2πr

where;

r is the radius of the sector20 cm = 2r + (40/360) x 2πr

20 = 2r + 0.7r

20 = 2.7r

r = 20/2.7

r = 7.4 cm

A perpendicular bisector of 40⁰ will cut line z into two equal parts, the **length** of half of z is calculated as;

sin (20) = (z/2) / r

r x sin (20) = (z/2)

2r x sin (20) = z

2 x 7.4 cm x sin(20) = z

5.06 cm = z

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A cardboard box in the shape of a rectangular prism has the

dimensions shown.

a. Write a polynomial that represents the volume of the box.

b. The volume of the box is 60 cubic inches. What are the

length, width, and height of the box?

On solving the provided question, we can say that Volume of **cuboid **- L X B X H=> volume = (x+6)*(x-2)*(x-1) => [tex]V = x^3 + 3x^2 - 16x + 12[/tex]

A cuboid is a solid or **three-dimensional** form in geometry. A cuboid is a convex polyhedron having 8 vertices, 12 sides, and 6 rectangular faces. Another name for a cuboid is a cuboid. A cube is a cuboid with six square faces. Boxes include things like books and bricks. The following are the key variations between cubic and cubic: In contrast to a cube, which has rectangular faces, a **cube **has six equally sized square faces. Even though the cube and cuboid structures have a similar appearance, they differ in some ways in terms of side length, diagonal, and area.

The dimensions are:

Length =(x + 6), Width = (x - 2) and Height = (x -1)

Volume of cuboid - L X B X H

volume = (x+6)*(x-2)*(x-1)

[tex]V = (x+6)(x^2 - 3x +2)[/tex]

[tex]V = x^3 - 3x^2 + 2x + 6x^2 - 18x + 12[/tex]

[tex]V = x^3 + 3x^2 - 16x + 12[/tex]

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Question content area top

Part 1

A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In the results of the gender-selection technique, 887 births consisted of 451 baby girls and 436 baby boys. In analyzing these results, assume that boys and girls are equally likely.

a. Find the probability of getting exactly 451 girls in 887 births.

b. Find the probability of getting 451 or more girls in 887 births. If boys and girls are equally likely, is 451 girls in 887 births unusually high?

c. Which probability is relevant for trying to determine whether the technique is effective: the result from part (a) or the result from part (b)?

d. Based on the results, does it appear that the gender-selection technique is effective?

a. The probability of getting exactly 451 girls in 887 births is 0.0578.

b. The probability of getting 451 or more girls in 887 births is 0.0478. To determine if 451 girls in 887 births is unusually high, we compare this probability to a **significance level (alpha)** of choice and then either reject or accept the null hypothesis.

c. The **probability** from part (b) is more relevant for trying to determine whether the technique is effective because it considers a range of outcomes that are consistent with the hypothesis that boys and girls are equally likely.

d. Based on the results, we can reject the **hypothesis** that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.

**Probability** is the likelihood of an event occurring or not occurring.

Mathematically;

Probability = expected outcomes/possible outcomea. To find the probability of getting exactly 451 girls in 887 births, we can use the **binomial distribution** with n = 887 and p = 0.5 (since boys and girls are equally likely).

The probability of getting k girls is given by the formula:

P(k girls) = (n choose k) * p^k * (1-p)^(n-k)

Plugging in the values, we get:

P(451 girls) = (887 choose 451) * 0.5^451 * 0.5^436

P(451 girls) = 0.0578 (rounded to four decimal places)

b. To find the probability of getting 451 or more girls in 887 births, we can add up the probabilities of getting 451, 452, 453, ..., up to 887 girls. The cumulative binomial distribution is used to determine the probability of getting k or fewer girls:

P(k or fewer girls) = sum((n choose i) * p^i * (1-p)^(n-i), i = 0 to k)

Since we want the probability of getting 451 or more girls, we can subtract the probability of getting 450 or fewer girls from 1:

P(451 or more girls) = 1 - P(450 or fewer girls)

= 1 - sum((887 choose i) * 0.5^i * 0.5^(887-i), i = 0 to 450)

= 0.0478

d. To determine if the gender-selection technique is effective, we need to compare the probability of getting 451 or more girls (from part (b)) to a significance level (alpha) of our choice.

Using an alpha set to 0.05, the probability of getting 451 or more girls in 887 births is 0.0478, it is less than 0.05. Therefore, we reject the **hypothesis** that boys and girls are equally likely and conclude that the gender-selection technique is effective in increasing the likelihood of having a girl.

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Solve for x. P S (6x-21)° T Q R

**Answer:**

x = 11

**Step-by-step explanation:**

You want to know the **measure of x** in a **square** marked with one portion of the **bisected corner** **angle** as being **(6x -21)°**.

We presume quadrilateral PQRS is a square, so each of the corner angles is 90°, and each of the diagonals bisects the corner angles. That mean ...

(6x -21)° = 90°/2

6x = 66 . . . . . . . . . . divide by °, add 21

** x = 11** . . . . . . . . . . . divide by 6

which of the following is a difference between panel and pooled cross-sectional data? group of answer choices a panel data set consists of data on different cross-sectional units over a given period of time while a pooled data set consists of data on the same cross-sectional units over a given period of time. a panel data set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time a panel data consists of data on a single variable measured at a given point in time while a pooled data set consists of data on the same cross-sectional units over a given period of time. a panel data set consists of data on a single variable measured at a given point in time while a pooled data set consists of data on more than one variable at a given point in time.

From the following, a panel **data** set consists of data on the same cross-sectional units over a given period of time while a pooled data set consists of data on different cross-sectional units over a given period of time is the difference between panel and pooled cross-sectional data.

**Panel data **refers to samples of the same cross-sectional units observed at multiple points in time.

For example we will follow the same set of households X, Y and Z, for each time period we collect data i.e. in 1990 and we will also interview the **same households** in 1995.

**Pooled data** occur when we have a “time series of cross sections,” but the observations in each cross section do not necessarily refer to the same unit.

For example we will take household income data on households X, Y and Z, in 1990. And then we will take the same income data on households G, F and A in 1995. Although we are interested in the same data, we are taking different samples (using different households) in **different time periods**.

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The concession stand at a football game had 3,903 soft pretzels and 2,804 hard pretzels before the game began. When they count the food after the game, there is a total of 1,683 pretzels left. How many pretzels were sold?

**Answer:**

5024

**Step-by-step explanation:**

3903+2804= 6707

6707-1683=5024

The box-and-whisker plot below represents some data set. What percentage of the data values are greater than 24?

The **percentage** of the data values are greater than 24 is 75%.

A box and **whisker** plot is a special type of graph that is used to show groups of number data and how they are spread. It shows the median, which is the middle value of the numbers in your **data**, the lowest number, the highest number and the quartiles, which divides the data into four equal groups.

So as per the given question box-whisker plot represents some data set. There is a number 24 just corresponding to it there is a vertical line which shows that 24 is the first **quartile** of the data and here 24 is the 75th percentile.

It means that there is 75% values are greater than 24.

Therefore, the **percentage** of the data values are greater than 24 is 75%.

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PLEASE HELP IS DUE TOMORROW:The average American throws away 2.5 pounds of empty cans a month (mostly during the winter months). At this rate, how many years will it take the average American to throw away a ton of empty cans? (Show work please)

1 ton = 2000 pounds

2000/2.5 = 800 months

800/12 = ~66.67 years

**Answer:**

your answer would be 66.6: do the math: 2.5 a month times 12 months in a year=30. 1 ton =2000 pounds. 2000 divided by 2.5 =800. 800 divided by 12=66.6

**Step-by-step explanation:**

Give the starting value a, the growth factor b, and the growth rate r if q = abt = a(1 r)t. write r as a percent. q = 79 (1.002) superscript t a. a. a = 79 b = 1.002 r = 0.2% b. a = 79.158 b = 1.002 r = 0.002% c. a = 79 b = 0.002 r = 1.002% d. a = 79.158 b = 0.002 r = 0.2%

r as a **percent** is a) a = 79, b = 1.002, and r = 0.2%.

The **formula** given, q = abt = a(1+r)t, represents exponential growth, where a is the starting value, b is the growth factor, r is the growth rate, t is the time period, and q is the final value after t periods.

Given q = 79(1.002)^t, we can see that:

a = 79 (the starting value)

b = 1.002 (the growth **factor**)

r = 0.2% or 0.002 (the growth rate, expressed as a decimal)

So, the correct answer is a) a = 79, b = 1.002, and r = 0.2%.

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Find the radius of the circle circumscribed around an equilateral trapezoid, if the bases of the trapezoid are 9 and 15, and the height is 5.

To find the radius of the circle circumscribed around an equilateral trapezoid, we need to first find the length of the diagonal of the trapezoid. The diagonal is equal to the height of the trapezoid times the square root of 3, since the trapezoid is equilateral.

So, the length of the diagonal is 5 * √3 = 8.66 meters.

Next, we need to find the midpoint of the two diagonals of the trapezoid, which is the center of the circumscribed circle. The midpoint is found by averaging the length of the two diagonals, which are equal in length:

(9 + 15) / 2 = 12

So, the radius of the circumscribed circle is equal to half the length of the diagonal:

8.66 / 2 = 4.33 meters.

Therefore, the radius of the circle circumscribed around the equilateral trapezoid is 4.33 meters.

So, the length of the diagonal is 5 * √3 = 8.66 meters.

Next, we need to find the midpoint of the two diagonals of the trapezoid, which is the center of the circumscribed circle. The midpoint is found by averaging the length of the two diagonals, which are equal in length:

(9 + 15) / 2 = 12

So, the radius of the circumscribed circle is equal to half the length of the diagonal:

8.66 / 2 = 4.33 meters.

Therefore, the radius of the circle circumscribed around the equilateral trapezoid is 4.33 meters.

Which ordered pair is the solution to the equation 2x + 3y = x + 5y

a.) (1, 3)

b.) (4,2)

**Answer:**

B

**Step-by-step explanation:**

We start by trying out option A

2(1) + 3(3) = 9

1 + 5(3) = 15

9 and 15 are not equal to one another.

This means it has to be the other option, B.

what is the probability that the sample mean annual insurance cost is greater than $620? show your work.

The **probability **of the sample mean annual insurance cost being greater than $620 is **very low**, that is **0.00317% **which indicating that it is unlikely to happen by chance.

Probability is a branch of mathematics that deals with the likelihood of an event **happening**. It is used in various fields, such as **insurance**, finance, and science.

To calculate the **probability**, we need to use the central limit theorem, which states that the distribution of sample means of a population approaches a normal distribution as the sample size increases. We also need to know the mean and standard deviation of the population.

Assuming that the **population **is normally distributed, we can use the following formula to calculate the probability:

z = (x - μ) / (σ / √(n))

where z is the z-score, x is the sample **mean**, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, we don't know the population mean and standard deviation, but we can use the sample mean and** standard deviation** as estimates. Let's say we have a sample of 100 insurance costs with a mean of $600 and a standard deviation of $50.

Now, we can calculate the **z-score:**

z = (620 - 600) / (50 / √(100)) = 4

The z-score of 4 indicates that the sample mean of $620 is 4 standard deviations away from the mean of $600. We can use a standard normal distribution table or a calculator to find the probability of getting a z-score of 4 or higher. The probability is very small, approximately 0.0000317 or 0.00317%.

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7. A polygon has vertices at F(-5, 2), G(-3, 2), H(-3, 4), J(1, 4), K(1, 1), L(4, 1), M(4, -2), N(6, -2), P(6, -3), and Q(-5, -3). Graph the figure on the coordinate plane. Then find the area and perimeter of the figure.

The **area **of the figure is 52 square units

The **perimeter **of the figure is 36 units

The graph is attached

How to the perimeterThe **perimeter **of the **figure **is found by summing the **length **of the **sides **

F(-5, 2) - G(-3, 2) = 2 units

G(-3, 2) - H(-3, 4) = 2 units

H(-3, 4) - J(1, 4) = 4 units

J(1, 4) - K(1, 1) = 2 units

K(1, 1) - L(4, 1) = 3 units

L(4, 1) - M(4, -2) = 3 units

M(4, -2) - N(6, -2) = 2 units

N(6, -2) - P(6, -3) = 1 units

P(6, -3) - Q(-5, -3) = 11 units

Q(-5, -3) - F(-5, 2) = 5 units

The **perimeter **= 2 + 2 + 4 + 2 + 3 + 3 + 2 + 1 + 11 + 5 = 36 units

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Use proportions to determine 23% of what number is 81.3. Round to the nearest hundredth.

18.7

23% of 81.3 is 18.699 rounded to the nearest hundredth is 18.7

23% of 81.3 is 18.699 rounded to the nearest hundredth is 18.7

HELP AAHHHHHHH FFASDF

**Answer: **

**Step-by-step explanation:**

Diane obtains a loan for home renovations from a bank that charges simple interest at an annual rate of 9.65%. Her loan is for $17,100 for 76 days. Assume

1

365

De not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas.

each day is

of a year Answer each part below.

(a) And the interest that will be owed after 76 days.

$

(b) Assuming Diane doesn't make any payments, find the amount owed after 76 days.

?

I need help fast

a) The **simple interest** that will be owed the bank by Diane after 76 days is $343.59.

b) The final amount that Diane will repay the bank after 76 days is $17,443.59.

What is the simple interest?The **simple interest** is an interest system that does not **compound interest**.

**Compounding interest** means that interest is added to the principal before subsequent interests are computed.

But under the simple interest system, interest is based on the **principal** from one period to the next.

The loan amount = $17,100

**Simple interest rate** = 9.65%

Loan period = 76 days

Total interest = $17,100 x 9.65% x 76/365 = $343.59

Final amount = $17,443.59 ($17,100 + $343.59)

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A theater sells adult and children tickets. Adult tickets sell for $10 and child sells for $5. Yesterday they sold off 50 tickets and made $40. How many adult and child tickets did the theater sell?

The theater **sold **30 adult tickets and 20 children tickets.

An equation of degree one is known as a linear equation.

A linear equation of two **variables **can be represented by ax + by = c.

Let, The number of adult tickets be 'x' and the number of children tickets be 'y'.

Therefore, 10x + 5y = 400...(i) and x + y = 50...(ii)**×10** ⇒ 10x + 10y = 500...(iii)

Now, Subtracting equation (i) from equation (iii) we have,

5y = 100.

y = 20, and hence x = 30.

So, They have sold 30 **adult **tickets and 20 **children **tickets.

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The total mass of a box and some oranges was 25 kg. The total mass of

the same box and some apples was 11 kg. The mass of the oranges was

3 times the mass of the apples.

Find the mass of the oranges.

In a case whereby the total mass of a box and some oranges was 25 kg. The** total mass** of the same box and some apples was 11 kg. The mass of the oranges was 3 times the mass of the apples, the **mass** of the **oranges **is 21kg.

The **concept** that will be used here is simplificatiopn.

We can set up as:

let a represent the box

let b represent the orange

lect c represent the apple

Then a + b = 25

a+ c = 11 ....................................................(2)

b = 3c.......................................(3)

substract equation 2 from 1

b-c = 11 ....................................(4)

substitute eqn 3 into 4

b-c = 14

3c - c =14

2c= 14

c= 7

from eqn 3

b = 3c

b = 3*7 =21

Then mass of orange = 21 kg

from eqn 2

a+ c = 11

a= 11-7= 4

mass of empty box = 4kg

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This composite figure is made up of three simpler shapes. What is the area of

the figure?

5 cm

10 cm

3 cm

4 cm

6 cm

**Answer:**

The figure is made up of a rectangle and two triangles. The dimensions of the rectangle are 10 cm by 5 cm, so the area of the rectangle is 10 * 5 = 50 cm^2.

Each of the two triangles has a base of 4 cm and a height of 3 cm, so the area of each triangle is (1/2) * 4 * 3 = 6 cm^2. The total area of the two triangles is 2 * 6 = 12 cm^2.

The total area of the figure is the sum of the areas of the rectangle and the triangles: 50 + 12 = 62 cm^2.

**Step-by-step explanation:**

5 3/5 + 1/2 = ? what is the answer

**Answer:**

61/10

**Step-by-step explanation:**

Convert the mixed number to an improper fraction

28 / 5 + 1 / 2

= 61/10

**Answer: **

Simplified form: 6 1/10

Improper form: 61/10

**Step-by-step explanation:**

5 3/5 + 1/2

= 28/5 + 1/2

Then, you multiply both fractions so that the denominator is the same number. In this case, multiply the fraction (numerator and denominator) on the left by 2 and on the right by 5.

= 56/10 + 5/10

This way, you can add the numbers because they have the same denominator.

=61/10

State how the triangles are congruent using SSS, SAS, ASA, AAS, or

HL. If they are not congruent, type NOT.

**Answer:**

SAS

**Step-by-step explanation:**

There are two pairs of congruent sides, and the pair of angles between the congruent sides is also congruent.

Given f(x)=(1)/(x), explain the how the graph of the nee function g(x)=(1)/(x-3)-5 transforms from the graph of f(x).

The function f(x) is **translated **3 units **right **and 5 units **down **then the function f(x) is **coincident **with the function g(x).

A function is an **assertion**, conception, or regulation that establishes a **partnership **between two variables.

The **functions **f(x) and g(x) are given below.

f(x) = 1 / x

g(x) = 1 / (x - 3) - 5

Translate the function 3 units **right**, then replace x with (x - 3). And translate the function 5 units **down**, then replace f(x) with (g(x) + 5). Then we have

g(x) + 5 = 1 / (x - 3)

g(x) = 1 / (x - 3) - 5

The function f(x) is **translated **3 units **right **and 5 units **down **then the function f(x) is **coincident **with the function g(x).

More about the **function **link is given below.

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Use a graphing calculator to find an equation of the line of best fit for the data. Round the slope to the nearest tenth and the y

-intercept to the nearest integer.

For the given table -

The **equation **for line of best fit is Y = -1.000 · X + 11.25**.**

The **correlation coefficient **is** **-0.443533**.**

x and y have** negative **and **strong **correlation.

**What is correlation coefficient?**

A statistical concept known as the **correlation coefficient **aids in establishing a relationship between expected and actual values gained through statistical experimentation. The estimated** correlation coefficient's **value explains how well the expected and actual values match.

The table of data is given.

The formula for **equation** of the line of best fit is -

Y = b·X + a

On adding the values in a graphing calculator the **equation** is -

Y = -1.000 · X + 11.25

Here, the **slope** is -1 and **y-intercept** is 11.25.

The formula for **correlation coefficient** is -

r = [n(∑xy) - (∑x)(∑y)] / [n∑x² - (∑x²)][n∑y² - (∑y²)]

n = Number of values or elements

∑x = Sum of 1st values list

∑y = Sum of 2nd values list

∑xy = Sum of the product of 1st and 2nd values

∑x² = Sum of squares of 1st values

∑y² = Sum of squares of 2nd values

For the given table the values are -

n = 8, ∑x = 68, ∑y = 22, ∑xy = 145, ∑x² = 620, ∑y² = 274

Plug in all the values in the** equation** -

r = [8(145) - (68)(22)] / [8(620) - (620)][8(274) - (274)]

r = -0.443533

When the values of two variables grow while one variable's values fall. The **correlation coefficient **would be negative in that situation.

The weak and adverse association is indicated by the **coefficient's **negative value. And if "r" keeps moving in the direction of -1, the relationship is moving in the negative direction.

Therefore, the equation is Y = -1.000 · X + 11.25 and r value is -0.443533.

To learn more about **correlation coefficient** from the given link

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m varies directly as n, and m=14 when n=7

a) write an equation that relates m and n

b) find m when n = 16

c) find n when m = 30

**Answer:**

see explanation

**Step-by-step explanation:**

(a)

given m varies directly as n then the equation relating them is

m = kn ← k is the constant of variation

to find k use the condition m = 14 when n = 7

14 = 7k ( divide both sides by 7 )

2 = k

m = 2n ← equation of variation

(b)

when n = 16 , then

m = 2 × 16 = 32

(c)

when m = 30 , then

30 = 2n ( divide both sides by 2 )

15 = n

Stevens high school has 800 students every Wednesday 3% of the students stay after for chess club how many students attend chess club on Wednesdays

**Answer: To find out how many students attend chess club on Wednesdays, we need to calculate 3% of the 800 students at Steven's high school. To do this, we multiply the number of students by 3% (which is equivalent to 0.03):**

**800 x 0.03 = 24**

**So, 24 students attend chess club on Wednesdays.**

**Step-by-step explanation:**

Answer:

Step-by-step explanation:

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