Find the equation of the line:Through :(1, 4), slope=9

The equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

To calculate the equivalent ratio of 1.25 : 3.75 : 7.5, we need to find a common multiplier that can be applied to all the numbers in the ratio to make them whole numbers. In this case, the common multiplier is 4 because it can be multiplied to each number to eliminate the decimals.

By multiplying each number in the ratio by 4, we get:

1.25 * 4 = 5

3.75 * 4 = 15

7.5 * 4 = 30

So the equivalent ratio of 1.25 : 3.75 : 7.5 is 5 : 15 : 30.

This means that the relative sizes or quantities represented by the original ratio are maintained in the equivalent ratio. For example, if we had 1.25 units of something, it would be equivalent to 5 units in the new ratio, and if we had 7.5 units, it would be equivalent to 30 units in the new ratio.

To more on ratio:
https://brainly.com/question/12024093
#SPJ8

At the relative extremum

What is a relative extremum?

A relative extremum is a relative minimum or maximum of a function.

Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2). This implies that dF(x)/dx = 0 at the extremum.

So, F(x) = 2ax² + bx + 3

dF(x)/dx = d(2ax² + bx + 3)/dx

= d2ax²/dx + dbx/dx + d3/dx

= 4ax + b

dF(x)/dx = 0

⇒ 4ax + b = 0

⇒b = -4ax at x = -1

b = -4a(-1)

= 4a

Since the function F(x) = 2ax² + bx + 3 has a relative extremum at the point (-1,2), we have that

F(-1) = 2a(-1)² + b(-1) + 3

= 2a - b + 3

F(-1) = 2

⇒2a - b + 3 = 2

⇒2a - b = 2 - 3

2a - b = -1

Now, b = 4a

So,  substituting b into the equation, we have that

2a - b = -1

2a - 4a = -1

-2a = -1

a = -1/-2

a = 1/2

So, b = 4a

= 4(1/2)

= 2

So,

Learn more about relative extremum here:

https://brainly.com/question/1938915

#SPJ1

Answer:

They are equivalent by Associative Property

Step-by-step explanation:

(3•6)•9 is 18•9 which is 162

3•(6•9) is 3•54 which is also 162

So the difference between the two expressions is that they are grouped differently. In the first expression the 3•6 had to be multiplied first. In the other expression the 6•9 had to be multiplied first. But really both were 3•6•9 and it's all multiplication and can happen in any order. But the order 3, 6, 9 did not change. That is Associative property that says you can multiply by grouping factors differently and still get the same answer.

Answer:

  see attached

Step-by-step explanation:

You want the graph of the circle defined by the equation ...

  (x-2)^2 + (y-7)^2 = 4.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Comparing this to the given equation, we see ...

  h = 2, k = 7, r² = 4

Then r = √4 = 2.

The circle will have its center at (2, 7) and will have a radius of 2. It is shown in the attached graph.

<95141404393>

Answer:

\(54\)

Step-by-step explanation:

Formula for average A of two numbers m and n is:

\(A=\frac{m+n}{2}\)

Substitute the value m=36 and n=72

\(A=\frac{36+72}{2}\)

This is equivalent to:

\(A=\frac{108}{2}\)

The average is:

\(A=54\)

Using a subtraction operation, the overall temperature change over those five days that Joe tracked the temperature in his town was a decrease of 3°C.

The temperature change can be computed by determining the differences in temperature from one day to the next and summing the differences.

The temperature change can also be computed by finding the difference between the ending period's temperature and the beginning period's temperature.

Days         Temperature     Change

Monday          23°C                  0

Tuesday          14°C (23 - 9)    -9

Wednesday    21°C (14 + 7)    +7

Thursday       25°C (21 + 4)    +4

Friday            20°C (25 - 5)    -5

Overall change =                  -3°C

= 20°C - 23°C = -3°C

Learn more about subtraction operations at https://brainly.com/question/4721701

#SPJ1

The values that used to create the box and whisker plot

[using these values]

Minimum value: Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

Here, we have,

Step 1: Order the data set from smallest to largest:

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

Step 2: Calculate the lower quartile (Q1), median (Q2), and upper quartile (Q3):

Q1 (25th percentile): The value that separates the lowest 25% of the data from the rest. Since we have 10 data points, the first quartile will be the average of the 2.5th and 3.5th data points. In our case, it's the average of the 2nd and 3rd data points:

Q1 = (19 + 28) / 2 = 23.5

Q2 (50th percentile or median): The value that separates the lowest 50% of the data from the rest. Since we have an even number of data points, the median will be the average of the 5th and 6th data points:

Q2 = (34 + 38) / 2 = 36

Q3 (75th percentile): The value that separates the lowest 75% of the data from the rest. Since we have 10 data points, the third quartile will be the average of the 7.5th and 8.5th data points. In our case, it's the average of the 7th and 8th data points:

Q3 = (45 + 47) / 2 = 46

Step 3: Calculate the interquartile range (IQR):

IQR = Q3 - Q1 = 46 - 23.5 = 22.5

Step 4: Determine the whiskers:

Lower whisker: The smallest value that is not smaller than Q1 - 1.5 * IQR

Upper whisker: The largest value that is not larger than Q3 + 1.5 * IQR

Lower whisker limit: 23.5 - 1.5 * 22.5 = -10

Upper whisker limit: 46 + 1.5 * 22.5 = 79.5

Our data points are all within these limits, so the lower whisker is at the smallest value, 12, and the upper whisker is at the largest value, 56.

Now, you can plot the box and whisker plot using these values:

Minimum value : Lower whisker: 12

Q1: 23.5

Q2 (median): 36

Q3: 46

Maximum value: Upper whisker: 56

Read more about whisker plot here:

brainly.com/question/27849170

#SPJ1

create a box and whisker plot for the following set of data

12, 19, 28, 32, 34, 38, 45, 47, 50, 56

The equivalent expression of the given expression is 5n/4 -3/8

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

Here, the given expression is :

(-2 ¹/₂n + ¹/₄) + (3 ³/₄n - 5/8)

simplifying the above expression by taking like considering like terms :

= -2 ¹/₂n + 3 ³/₄n +  ¹/₄- 5/8

= (15/4)n - (5/2)n + (2-5)/8

= (15-10)n/4 -3/8

= 5n/4 -3/8

Therefore, the equivalent expression of the given expression is 5n/4 -3/8.

Read more about distributive law at:

https://brainly.com/question/5637942

#SPJ1

Answer:

1.66

Step-by-step explanation:

Using the Chi square statistic (χ²) test :

χ² = Σ(Oi - Ei)² / Ei

Expected, Ei :

Freshmen = 30% * 300 = 90

Sophomore =24% * 300 = 72

Junior = 26% * 300 = 78

Senior = 20% * 300 = 60

Observed, Oi :

Freshmen = 83

Sophomore = 68

Junior = 85

Senior = 64

χ² = ((83 - 90)²/90) + ((68 - 72)²/72) + ((85 - 78)²/78) + (64 - 60)²/60)

χ² = 49/90 + 16/72 + 49/78 + 16/60

χ² = 0.544 + 0.222 + 0.628 + 0.267

χ² = 1.661

The test statistic = 1.66

Answer:

let's use c as circumference, d for diameter

lets say c increases, d is related to c, d will also increase

if c decreases, d will too.

Let's put in this way.

Pretend you're at a store,

The more you spend, the more points you get in their loyalty program

C is going to be the amount you spend

D will be how many points you get

Spend more, more points

spend less, less points

P.S

C is the independent variable, D is the dependent variable. (I think that's the right way, if not ignore the postscript aka P.S)

================================================

Work Shown:

A = old price = 320

B = new price = 400

C = percent change

C = [ (B-A)/A ] * 100%

C = [ (400-320)/320 ] * 100%

C = (80/320)*100%

C = 0.25*100%

C = 25%

The positive C value indicates a percent increase.

--------------------------------

A slightly alternative method:

A = old price = 320

B = new price = 400

C = change in price

C = B-A

C = 400-320

C = 80 is the price increase

D = percent change

D = (C/A)*100%

D = (80/320)*100%

D = 0.25*100%

D = 25%

We get the same result as before.

The correct trigonometric substitution for evaluating integral ∫√(x² + 64) dx is option B. x = 8 tan θ.

To evaluate the integral ∫√(x² + 64) dx using trigonometric substitution, use the substitution x = 8 tan θ.

Let's go through the steps to see how this substitution leads us to the solution:

1. Substitute x = 8 tan θ.

This implies dx = 8 sec² θ dθ.

2. Substitute the expression for x and dx in the integral:

∫√(x² + 64) dx becomes ∫√((8 tan θ)² + 64) * 8 sec² θ dθ.

3. Simplify the expression:

∫√(64 tan² θ + 64) * 8 sec² θ dθ = ∫√(64(sec² θ - 1)) * 8 sec² θ dθ.

4. Further simplify:

∫√(64sec² θ - 64) * 8 sec² θ dθ = ∫√(64sec² θ) * 8 sec² θ dθ.

5. Simplify the expression inside the square root:

∫8sec θ * 8 sec² θ dθ = ∫64sec³ θ dθ.

6. Integrate with respect to θ:

∫64sec³ θ dθ = 64∫sec³ θ dθ.

Now, this integral can be evaluated using standard trigonometric integral identities or integration techniques. However, it's worth noting that the original integral did not involve the variable θ, so we would eventually need to convert the result back to x by substituting x = 8 tan θ.

The correct answer is B. x = 8 tan θ.

learn more about trigonometric substitution: https://brainly.com/question/17199316

#SPJ1

For this equation you simply have to graph it.

First, you have to remember that these equations follow a formula: y=mx+b. m is the slope of you line and b is the y-intercept.

Next, you need to graph it. First, graph your b, in this case 2. You would go up 2 on you graph (graph (0,2)). Then, you would graph your slope which is 3.

Now, remember that slope equals y/x, so think of the number 3 being like 3/1. You would start at (0,2) and go up 3 points in the graph, then over 1 point (graph where you end up). You repeat that from each new point you make until you have enough points to create a straight line.

Hope this helps a bit,

The trigonometric function that models the temperature T in the South Pole in March t hours after midnight is given as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

The lowest temperature is of -54ºC, while the highest is of -50ºC, with a difference of 4ºC, hence the amplitude is given as follows:

2a = 4

a = 2.

A function with amplitude of 2 would oscillate between -2 and 2, while this one oscillates between -54 and -50, hence the vertical shift is given as follows:

d = -50.

The period is of 24 hours, hence:

2π/B = 24

24B = 2π

B = π/12.

The highest value of the cosine function should be assumed at t = 0, but it is assumed at t = 14(2 p.m.), hence the phase shift is given as follows:

c = 14.

Thus the function is defined as follows:

T(t) = 2cos(π/12(t - 14)) - 52.

More can be learned about cosine functions at brainly.com/question/21558626

#SPJ1

The biscuits should be placed 2.54 centimeters apart on the baking tray.

The unitary method is a way for solving a problem by the first value of a single unit and than finding the value by multiplying the single unit. Unitary method is a technique by which we can find the value of a single value from the value of more than one devices and the value of more than one unit from the value of a single unit. We can this method use for most of the calculations in math.

We are given that;

Elana must roll the dough into 7 inch rounds.

a) To convert this measurement to centimeters, we can use the conversion factor 1 inch = 2.54 centimeters. Therefore, 7 inches is equal to:

7 inches x 2.54 centimeters/inch = 17.78 centimeters

So, Elana must roll the dough into 17.78 centimeter rounds.

b) To rewrite all the ingredients using grams or milliliters, we need to know the density of each ingredient. Assuming that the density of each ingredient is the same as that of all-purpose flour (which is approximately 125 grams per cup), we can convert the measurements as follows:

1 cup flour = 125 grams flour

1/2 cup sugar = 100 grams sugar

2 teaspoons baking powder = 10 grams baking powder

1 teaspoon salt = 5 grams salt

1/2 cup cream = 120 milliliters cream (assuming a density of 1 gram per milliliter)

So, the rewritten ingredients are:

125 grams flour

100 grams sugar

10 grams baking powder

5 grams salt

120 milliliters cream

c) The recipe states that the oven should be preheated to 350 °F. To convert this temperature to Celsius, we can use the formula:

Celsius = (Fahrenheit - 32) x 5/9

So, the temperature in Celsius is:

Celsius = (350 - 32) x 5/9 = 176.67 °C

Therefore, Elana should heat the oven to 176.67 °C.

d) The recipe states that the biscuits should be placed on the baking tray 1 inch apart. To convert this measurement to centimeters, we can use the conversion factor 1 inch = 2.54 centimeters. Therefore, the biscuits should be placed on the baking tray:

1 inch x 2.54 centimeters/inch = 2.54 centimeters

Therefore, by unitary method answer will be 2.54 centimeters.

To learn more about the unitary method, visit;

https://brainly.com/question/23423168

#SPJ9

Answer:

(14, -2)

I could totally be wrong though, I haven't done this type of math in years.

Answer:

Step-by-step explanation:

Let h and s represent the numbers in the House and Senate, respectively. Then we have ...

  h + s = 88

  h - s = 54

Subtracting the second equation from the first gives ...

  (h +s) -(h -s) = (88) -(54)

  2s = 34 . . . . . simplify

  s = 17 . . . . . . . divide by 2

  h = 88 -17 = 71 . . . . find the other value using the sum equation

There were 71 females in the House of Representatives, and 17 females in the Senate.

To solve the question asked, you can say:  expressions  d. (Ex)2 is read as "the square of the sum of all x values."

In mathematics, an expression is a set of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation that represent quantities or values. Expressions can be as simple as "3 + 4" or as complex as they can contain functions like "sin(x)" or "log(y)" . Expressions can be evaluated by substituting values ​​for variables and performing mathematical operations in the order specified. For example, if x = 2, the expression "3x + 5" is 3(2) + 5 = 11. In mathematics, formulas are often used to describe real-world situations, create equations, and simplify complex math problems. 

a. Ex is read as "the expected value of all x values."

b. Ex2 is read as "the sum of the squared expected values of all x values."

c. E(x — i) is read as "the sum of the deviations of x values from their mean."

d. (Ex)2 is read as "the square of the sum of all x values."

To know more about expressions visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

12,621

Step-by-step explanation:

when rounding there asking for the thousands therefore you have to look at the hundreds place and since there's a six in the hundreds place the one is going to change to a 2 the answer is 12,621

Length of gz = 12 units

Length of ot = 14.4 units

Given,

Triangle EGD with centroid at Z .

Now,

As we know that centroid divides the line segment in the ratio 2:1 .

Firstly calculate the length of gz,

gu = 18 unit

gz:zu = 2:1

gz = 2/3  * 18

gz = 12 units .

Secondly calculate the length of ot,

zt = 4.8 units

oz:zt = 2:1

oz = 4.8 * 2

oz = 9.6 units

ot = 9.6+ 4.8

ot = 14.4 units

Hence with the centroid length of ot and gz can be found out .

Know more about triangles,

https://brainly.com/question/30420011

#SPJ1

\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

\( \fbox \colorbox{black}{ \colorbox{white}{n} \:  \:  \:   \:  \:  \:  \: \: \colorbox{white}{=}  \:  \:  \:  \:  \:   + \colorbox{white}{3.6}}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's solve for n ~

I hope it helps ~

Answer:

The answer is 42/19 or 2 4/19

Step-by-step explanation:

You have to divide 7 by 19/6. I say "19/6" because that's an improper fraction. You do " 7/1 divided by 19/6". Then you do KCF (Keep Change Flip). So you do "7/1 times 6/19". So now you just multiply across. And there's your answer (42/19) If you want to do a mixed number then you get 2 4/19.

Answer

\(3 \frac{5}{6} \)

Step by step explanation

\(7 = 6 \frac{6}{6} \)

\(6 \frac{6}{6} - 3 \frac{1}{6} = 3 \frac{5}{6} \)

The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

More can be learned about union and intersection at brainly.com/question/4699996

#SPJ1

Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

The domain and the range of the piecewise function in this problem are given as follows:

The function in this problem is defined for all values of x between -6 and 2, except x = 0, and assumes all values of y between 0 and 6, except y = 1, hence the domain and range are given as follows:

Learn more about domain and range at https://brainly.com/question/26098895

#SPJ1

If K is between J and L. Then:

JK +KL = JL

Since:

JK = (2x + 42) and KL = (30 - 2x)

Replacing and adding:

(2x + 42) + (30 - 2x)

2x+42+30-2x

2x-2x+24+30

54

JL =54

Answer: B

Step-by-step explanation: Hope this helps:)

The simplified form of the expression is \(-32\).

To simplify the expression, we can perform the calculations written below step by step:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\)

We follow the order of operations (PEMDAS/BODMAS):

Step 1: Simplify within parentheses:

\(\(4+6 = 10\)\).

Step 2: Perform multiplications and divisions from left to right:

\(\(-2(10) = -20\) and \(-2(4-1) = -2(3) = -6\)\).

Step 3: Evaluate the remaining additions and subtractions:

\(\(-20 + (-2) \cdot 6 = -20 - 12 = -32\)\).

Therefore, the simplified form of the expression \(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\) is \(-32\).\)

When simplifying an expression, several factors need consideration. First, apply the order of operations correctly, respecting parentheses and exponents. Next, combine like terms by adding or subtracting them. Distribute and simplify within parentheses or brackets as needed. Pay attention to negative signs and ensure their proper placement.

Finally, review the simplified expression to ensure accuracy and validity within the given context.

Note: The complete question is:

\(\(\frac{{-2(4+6)+(-2)6}}{{-2(4-1)}}\)\), calculate the simplified form of this expression.

For more questions on simplified form of the expression:

https://brainly.com/question/28323654

#SPJ8