A yoga instructor collected student data. He found that students who had less sleep did not tend to burn more or fewer calories during class. What can he conclude?

1)There is no correlation between amount of sleep and number of calories burned.


2)There may or may not be causation. Further studies would have to be done to determine this.


3)There is a correlation between amount of sleep and number of calories burned. There is probably also causation. This is because there is likely an increase in the number of calories burned with an increase in the amount of sleep

4 + 7×6 = 4 + 42 = 46

12 + 9×3 - 1 = 12 + 27 - 1 =39 - 1 = 38

The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.

We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,

The logistic growth model is given by the equation

dN/dt=rN[(K-N)/K]

where, dN/dt = rate of change of population with respect to time,

N = population size at time t,

r = intrinsic rate of natural increase (growth constant),

K = carrying capacity.

The population size, "N" after 1 year = 7050

The initial population, "N₀" = 2500

The carrying capacity, K = 25000

We can use the following formula to find the value of the growth constant,

r = 2.303/t{ln(N_t/N₀) }........... (1)

Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)

Substituting the given values in equation (1), we get

r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69

The value of the growth constant is 0.69.

Now, we can use the logistic growth equation to find the time required for the population to reach 12900.

dN/dt=rN[(K-N)/K]

Given, N₀ = 2500 and K = 25000

Differentiating both sides with respect to t,

dN/dt = rN[(K-N)/K] + Ndr/dt

Substituting the values of N, r, and K in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}

Let the population N become 12900 at time t = t₁

Therefore, at time t = 0, the population N₀ = 2500

Also, at time t = 1, the population N₁ = 7050

Substituting these values in the above equation, we get,

dN/dt= 0.69N[(25000-N)/25000] + N₁

dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁

Solving for N₁, we get, N₁ = 7825

Substituting N₁ = 7825 in the above equation,

dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁

dN/dt= 3263.25/1.69 ⇒ 1930.4

Now, to find t1, we can use the following formula;

ln[(K-N₁)/(K-N₀)] = rt₁

Substituting the given values, we get,

ln[(25000-12900)/(25000-2500)] = 0.69t₁

On solving for t₁, we get;

t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years

Hence, the population will increase to 12900 after approximately 3.7 years.

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Answer:

Step-by-step explanation:

[tex]-13-23=-13+(-23)[/tex]    (add -23 instead of subtracting +23)

          [tex]=-36[/tex]

[tex]-13-(-23)=-13+(23)[/tex]   (add +23 instead of subtracting -23)

          [tex]=10[/tex]          

The complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

To describe the complement of the given event, we need to first understand what complement means in probability theory. The complement of an event is the set of outcomes that are not included in the event.

So, the given event is that 71% of a person's credit card purchases are seventy dollars or more. This means that 100% - 71% = 29% of the person's credit card purchases are less than seventy dollars. This is the complement of the given event.

Hence, the complement of the given event is that 29% of the person's credit card purchases are less than seventy dollars.

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It would cost approximately $45.14 to drive 225 miles in a rental car that gets 29 miles per gallon.

What is Rate?

A rate in arithmetic is a ratio that contrasts two separate values with various unit systems. For instance, if John types 50 words per minute, that means he types 50 words per minute. We are dealing with a rate because the word "per" is there. The symbol "/" can be used in place of the word "per" in issues.

When two or more similar amounts or numbers are being compared using the same units, a ratio is utilized. When referring to the ratio of one quantity "to" the second quantity in spoken language, it is frequently written with a colon.

First, we convert the gas price from liters to gallons. One liter is equal to 0.264172 gallons, so:

$1.54 per liter = $1.54 / 0.264172 gallons = $5.82 per gallon

Next, we need to calculate how many gallons of gas are needed to drive 225 miles. If the car gets 29 miles per gallon, we can calculate the gallons of gas needed as:

225 miles / 29 miles per gallon = 7.7586 gallons

Finally, we can calculate the total cost of gas as:

Total cost = gallons of gas needed x gas price per gallon

Total cost = 7.7586 gallons x $5.82 per gallon

Total cost = $45.14

Therefore, it would cost approximately $45.14 to drive 225 miles in a rental car that gets 29 miles per gallon, assuming a gas price of $1.54 per liter in France.

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The expressiοn 2(x-1)(x+1)/(-x-20) can be written as 2(x+1)/(x-5).

Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.

Tο simplify the expressiοn 2(x-1)(x+1)/(-x-20), yοu can fοllοw these steps,

Factοr the denοminatοr, (-x-20), tο get (x-5)(x+4).

Rewrite the numeratοr as 2(-1).

Substitute the factοred denοminatοr frοm step 1 intο the expressiοn, giving 2(-1)/[(x-5)(x+4)].

Factοr the numeratοr, 2(x-1)(x+1), and cancel οut the cοmmοn factοr οf (x-1) frοm the numeratοr and denοminatοr.

sο we get as, The final simplified expressiοn is 2(x+1)/(x-5).

Therefοre, The final simplified expressiοn is 2(x+1)/(x-5).

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42080.9 cubic yd

Step-by-step explanation:

           r = 17.2 yd

          h = 45.3 yd

[tex]\boxed{\bf Volume=\pi r^2h}[/tex]

               = 3.14 * 17.2 *17.2 * 45.3

               =42080.9 cubic yd

Question :-

Answer :-

[tex] \rule{180pt}{4pt}[/tex]

Diagram :-

[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{17.2 \: yd}}\put(9,17.5){\sf{45.3 \: yd}}\end{picture}[/tex]

Solution :-

As per provided information in the given question, we have been given that the Radius of a cylinder is 17.2 yd. The height of a cylinder is 45.3 yd. We have been asked to find the volume of a right circular cylinder.

To calculate the volume of a right circular cylinder, we will apply the formula below :-

[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: Volume_{(Cylinder)} = \pi r^2 h \: \: }}[/tex]

Substitute the given values into the above formula and solve for Volume :-

[tex]\sf:\implies Volume_{(Cylinder)} = \pi r^2 h[/tex]

[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(17.2 \: yd)^2(45.3 \: yd)[/tex]

[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(295.84 \:yd^2)(45.3 \: yd)[/tex]

[tex]\sf:\implies Volume_{(Cylinder)} = (928.9376 \:yd^2)(45.3 \:yd)[/tex]

[tex]\sf:\implies\bold{Volume_{(Cylinder)} = 42080.873 \: yd^3}[/tex]

Therefore :-

[tex]\\[/tex]

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Have a great day! <33

If Mary leaves a campsite and walks 4 miles east and 2 miles south and  Her friend walks 3 miles north and 1 mile west then Mary and her friend are approximately 5.83 miles apart.

We can use the Pythagorean theorem to find the distance between Mary and her friend. We'll need to create a right-angled triangle with the two walks forming the legs of the triangle.

Mary walks 4 miles east and 2 miles south, so she moves 4 units to the right (east) and 2 units down (south).

Her friend walks 3 miles north and 1 mile west, so she moves 3 units up (north) and 1 unit to the left (west).

We can see that the two walks form a right-angled triangle. The distance between Mary and her friend is the hypotenuse of this triangle.

Let's calculate the length of each leg of the triangle:

The length of the horizontal leg is 4 - 1 = 3 miles (Mary moves 4 miles to the right and her friend moves 1 mile to the left).

The length of the vertical leg is 2 + 3 = 5 miles (Mary moves 2 miles down and her friend moves 3 miles up).

Now, we can use the Pythagorean theorem:

distance² = 3² + 5²

distance² = 9 + 25

distance² = 34

distance = √(34)

≈ 5.83 miles

Therefore, Mary and her friend are approximately 5.83 miles apart.

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1. A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. 2. The point where a graph contacts the y-axis is known as the y intercept.

The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.

1. A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

2. The point where a graph contacts the y-axis is known as the y intercept. Each point on the y-axis has an x-coordinate of 0, as is known. Hence, a y-x-coordinate intercept's is 0.

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Step-by-step explanation:

To find the minimum height of the satellite during the given time period, we need to find the vertex of the parabolic function f(x) = 2x^2 - 16x + 800.

The vertex of a parabola with equation f(x) = ax^2 + bx + c is given by the formula:

x = -b / 2a and f(x) = -b^2 / 4a + c

In this case, a = 2, b = -16, and c = 800. Substituting these values into the formula, we get:

x = -(-16) / 2(2) = 4

f(x) = -(-16)^2 / 4(2) + 800 = 848

Therefore, the minimum height of the satellite during the given time period is 848 kilometers, and it occurs after 4 hours of flight time.

Given the logistic model f(x)=800/1+19e^−0.402x, he initial value is 40

You should recall that Logistic regression is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables

The given question states thus: f(x)=800/1+19e^−0.402x, what is the initial value?

The initial value is the value when the value of x = 0

This implies that f(x) = (800)/ [1 + 19e⁻⁰°⁴⁰²ˣ

Simplifying this we have

f(x) = (800) / (1 + 19e⁰)

⇒ (800)  1 + 19

Simplifying to have

f(x) = 800/20

Dividing 800/20 to get 40

f(x) = 40

In conclusion, the initial value of f(x)=800/1+19e^−0.402x is 40

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The approximate area of the park is given as follows:

450 blocks squared.

To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.

Hence the formula for the area of the rectangle is given as follows:

Area = Length x Width.

According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide, hence the length and the width are given as follows:

Hence the area of Central Park is calculated as follows:

Area = 50 x 9

Area = 450 blocks squared.

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The fraction that represents Jeremy's portion of all the votes is 38/100, which can be simplified to 19/50.

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

If Tony and Donna won 0.62 of all the votes, this means that they won 62% of the votes.

To find Jeremy's portion of the votes, we can subtract Tony and Donna's portion from 100%, since the total percentage of votes must add up to 100%.

So, Jeremy's portion of the votes would be:

100% - 62% = 38%

Therefore, the fraction that represents Jeremy's portion of all the votes is 38/100, which can be simplified to 19/50.

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Answer:

7

Step-by-step explanation:

The numbers are increasing by 4 so with that, we can skip to the last number which is 3 and add 4 giving us 7 and if we go on, we would get 11, 15, 19, 23.

Answer:

You need to first identify the dum it's always multiplication

hope this helps good luck

The number of guests at a theme park can be modeled by the function p(t), where t is measured in hours and p is the number of guests. The function p(t) is a solution to the logistic differential equation.

The formula for logistic differential equation is dp/dt = p/3 - p^2/60000. This equation models the rate of change of the number of guests at the theme park over time.

To find the solution to this equation, we can use separation of variables. First, we can rearrange the equation to get:

dp/(p/3 - p^2/60000) = dt

Next, we can integrate both sides of the equation to get:

∫dp/(p/3 - p^2/60000) = ∫dt

Using partial fraction decomposition, we can rewrite the integral on the left-hand side of the equation as:

∫(3/60000)/(1 - 3p/60000)dp = ∫dt

Integrating both sides of the equation gives us:

-20000ln|1 - 3p/60000| = t + C

Solving for p gives us:

1 - 3p/60000 = Ce^(-t/20000)

3p/60000 = 1 - Ce^(-t/20000)

p(t) = 20000 - (20000C)e^(-t/20000)

To find the value of C, we can use the initial condition p(0) = p0:

p0 = 20000 - 20000C

C = (20000 - p0)/20000

Substituting this value of C back into the equation for p(t) gives us the solution:

p(t) = 20000 - (20000 - p0)e^(-t/20000)

This is the solution to the logistic differential equation that models the number of guests at a theme park over time.

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From the given data of Nicole's wedding organization, 18 tables at the venue is sufficient for the total 145 arriving guest.

To determine whether there are enough tables for the guests, we need to calculate the total circumference required for all the guests and compare it to the total circumference of the available tables. The circumference of a circle is given by the formula C = πd, where C is the circumference, d is the diameter, and π is the constant pi, approximately equal to 3.14.

For the circular table with a diameter of 180cm, the circumference is:

C = πd

= π x 180cm                              

= 565.2cm

Each guest needs 7cm around the circumference of the table, so the total circumference required for one guest is 7cm.

For 145 guests, the total circumference required is:

Total circumference required

= 145 guests x 7cm per guest

= 1015cm

Now, we can calculate the total circumference of all the tables available:

Total circumference of all tables

= 18 tables x 565.2cm per table

= 10,174.4cm

Since the total circumference required for the guests (1015cm) is less than the total circumference of all the available tables (10,174.4cm), we can conclude that there are enough tables for the guests. Therefore, there are enough tables at the venue for the 145 guests.

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Answer:

The given expression is:

-(1)/(9)(13x)

We can use the commutative property of multiplication to rearrange the order of the factors:

-(1)/(13x)(9)

Now, we can use the associative property of multiplication to group the factors in any way we want:

-(1/13)(1/x)(1/9)

This is the simplified expression using the commutative and associative properties of multiplication.

The correct statement regarding the number of solutions of the equation is given as follows:

The function has one solution.

The function for this problem is defined as follows:

[tex]x - 8 = -\sqrt{x^2 - 8}[tex]

We can remove the term with x from the square root squaring both sides of the equality, hence:

[tex](x - 8)^2 = (-\sqrt{x^2 - 8})^2[/tex]

x² - 8 = x² - 16x + 64

16x = 72

x = 72/16

x = 4.5.

Hence the equation presented in this problem has a root, which is a solution, and the number of solutions is of one.

The function is given as follows:

[tex]x - 8 = -\sqrt{x^2 - 8}[tex]

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The statements that are true are:

(A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

(D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

(E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

Using the function A(t) = -1.4t + 96, we can determine the amount of oil, A, used in gallons for a given average temperature, t, in degrees Fahrenheit.

A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

Substituting t = 10 into the function A(t), we get:

A(10) = -1.4(10) + 96 = 80

Therefore, the statement is true.

B) The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.

Substituting t = 15 into the function A(t), we get:

A(15) = -1.4(15) + 96 = 76.5

Therefore, the statement is false.

C) The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.

Substituting t = 68.5 into the function A(t), we get:

A(68.5) = -1.4(68.5) + 96 = -2.9

Therefore, the statement is false.

D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

Substituting t = 55 into the function A(t), we get:

A(55) = -1.4(55) + 96 = 18

Therefore, the statement is true.

E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

Substituting t = 0 into the function A(t), we get:

A(0) = -1.4(0) + 96 = 96

Therefore, the statement is true.

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The given question is incomplete, the complete question is:

A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees

Fahrenheit, for those months. The scatter plot shows the data. The function A(t) = -1.4t + 96,  best fits these data.

Graph- (25,60), (40,40),(45,40),(55,20),(60,10)

Use the function  to determine which of the following statements are true. Select all that apply.

A- The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.

B- The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.

C- The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.

D- The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.

E- The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.

Answer:

8 months

Step-by-step explanation:

I got it right

The value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).

A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is sometimes referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.

Let us suppose the measure of angle = x.

For rhombus all the four angles are congruent, thus,

∠MLN = (9a + 11)°

∠KLM = (-4a + 66)°

∠JLN = x

∠KLJ = x

The sum of the angles of a quadrilateral is 360 degrees, so:

∠JKL + ∠KLM + ∠MLN + ∠NJL = 360

Since JKL and NJL are vertical angles, they are congruent:

∠JKL = ∠NJL = x

Substituting in the given angles, we get:

x + (-4a + 66) + (9a + 11) + x = 360

2x + 5a + 77 = 360

2x = 360 - 5a - 77

2x = 283 - 5a

x = (283 - 5a)/2

Now, ∠JKM = 180 - ∠JKL

∠JKM = 180 - x

∠JKM = 180 - (283 - 5a)/2

Simplifying, we get:

∠JKM = 23 + (5a/2)

Hence, the value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).

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1 hot dog costs amount $8.00 and 1 hamburger costs $10.80.

Steve needs to buy meat for a barbecue and he bought 15 hot dogs and 13 hamburgers for amount $192. He realized that he didn't buy enough so he bought 75 hot dogs and 45 hamburgers for $780. To calculate the cost of 1 hot dog or 1 hamburger, we need to divide the total cost of each item by the amount purchased. For the hot dogs, we divide $780 by 75, which gives us $8.00. For the hamburgers, we divide $780 by 45, which gives us $10.80. Therefore, the cost of 1 hot dog or 1 hamburger is $8.00 and $10.80 respectively.

Hot Dogs :  ($192 + $780) / (15 + 75) = $8.00

Hamburgers : ($192 + $780) / (13 + 45) = $10.80

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The slope of the line is

3

This means that

6mm

of rain falls every

1hr

Answer:

to find x u will do : 61+132+x=1290

x=1290-193

x=1097

Answer:

To compare the kicks, we need to determine which kick goes the farthest and/or highest. Let's analyze each kick one by one.

Stewart's kick:

Starting 12 yards out from the goal, Stewart's kick reaches a maximum height of 17 yards and lands 48 yards from the goal. We can assume that the ball lands at the same height as it was kicked. Therefore, the horizontal distance traveled by the ball is:

d = 48 - 12 = 36 yards

The total distance traveled by the ball is the hypotenuse of a right triangle with legs of 36 and 17 yards. Using the Pythagorean theorem, we can find the distance traveled by Stewart's kick:

distance = sqrt(36^2 + 17^2) ≈ 40.48 yards

Oswaldo's kick:

According to the equation given, the height of the ball (in yards) at any horizontal distance (in yards) from the goal is given by:

y = -x^2 + 14x - 24

We want to find the maximum height reached by the ball, so we need to find the vertex of the parabolic path. The x-coordinate of the vertex is given by:

x = -b / 2a = -14 / (-2) = 7

The maximum height is the y-coordinate of the vertex:

y = -(7)^2 + 14(7) - 24 = 25

Therefore, Oswaldo's kick reaches a maximum height of 25 yards.

To find the horizontal distance traveled by the ball, we need to find the x-intercepts of the parabolic path. Setting y = 0, we get:

0 = -x^2 + 14x - 24

Solving for x using the quadratic formula, we get:

x = (14 ± sqrt(14^2 - 4(-1)(-24))) / (2(-1)) ≈ 2.63, 11.37

Therefore, the ball lands at a horizontal distance of approximately 2.63 or 11.37 yards from the goal. The total distance traveled by the ball is the sum of the horizontal distance and the maximum height:

distance = 11.37 + 25 ≈ 36.37 yards

Kevin's kick:

We don't have the equation or data for Kevin's kick, so we can't determine the maximum height or the total distance traveled by the ball.

Flynn's kick:

We have a partial table of data points for Flynn's kick. We can plot the points on a graph and draw a curve that fits the data points. Here is the graph:

Flynn's Kick

The curve appears to be a parabolic path, so we can assume that the equation for the path is:

y = ax^2 + bx + c

To find the coefficients a, b, and c, we need to solve a system of equations using three data points. Let's use the data points (12, 8.75), (15, 17.2), and (18, 19.7).

Using the first data point, we get:

8.75 = a(12)^2 + b(12) + c

Using the second data point, we get:

17.2 = a(15)^2 + b(15) + c

Using the third data point, we get:

19.7 = a(18)^2 + b(18) + c

Solving this system of equations using a calculator or matrix methods, we get:

a ≈ 0.0571

b ≈ -1.

Hope this helped, I'm sorry if it didn't. If you need more help, ask me! :]

Hence, in respοnse tο the prοvided questiοn, we can say that  12x - 8 can  functiοn be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

Mathematicians research numbers and their variants, equatiοn and related structures, οbjects and their lοcatiοns, and prοspective lοcatiοns fοr these things. The term "mοdule" is used tο describe the cοnnectiοn that exists in between set οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is an input-οutput cοnnectiοn in which each inputs results in sοmething like a single, distinct return. A dοmain, cοdοmain, οr scοpe is assigned tο each functiοn. Functiοns are usually denοted by the letter f. (x). An x is used fοr entry. On capabilities, οne-tο-οne capabilities, multiple prοwess, in capabilities, and οn capabilities are the fοur majοr types οf accessible functiοns.

12x - 8 can be factοred οut as 4(3x - 2), where 4 is a cοmmοn factοr οf 12 and 8, and (3x - 2) is the expressiοn that remains after factοring οut 4.

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Complete question:

We can describe 12x-8 as an expression.

It can also be written as 4(3x-2)

4(3x-2) is a ___ of 12x-8.

What is the blank?

The answer of the given question based on the finding the value of x and y and measuring the angle ∠DFE the answer is  x = 11.8 and y = -8 and angle ∠DFE is 88° degrees.

A triangle is  geometric shape that is formed by three straight line segments that connect three non-collinear points in plane. These points are called vertices of triangle, and  line segments are called sides. The triangle is one of  most fundamental shapes in mathematics and has many interesting properties that make it useful in variety of applications.

Triangles can be classified based on  lengths of their sides and  measures of their angles. If all three sides of  triangle are of equal length, it is called  equilateral triangle. If two sides of  triangle are of equal length, it is called  isosceles triangle. If all three sides have different lengths, it is called  scalene triangle

In triangle DEF, we know that the sum of the angles is 180° degrees, so:

∠DEF + ∠DFE + ∠EFD = 180°

Substituting the given values, we have:

92° + (5x - 7) + 36° = 180°

Simplifying the equation, we get:

5x + 121 = 180

5x = 59

x = 11.8

Now we know x, then we can find y:

y = 180 - 92 - 36 - (5x - 7) = 45 - 5x

y = 45 - 5(11.8) = -8

Therefore, x = 11.8 and y = -8.

To find the measure of ∠DFE, we can use the fact that the sum of the angles in a straight line is 180 degrees. ∠DFE is opposite to angle D, which is 92°, so:

∠DFE = 180° - 92° = 88°

Thus, the measure of ∠DFE is 88° degrees.

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The total amount of water Carlos drank throughout the day is 2.65 liters.

In order to calculate the total amount of water Carlos drank throughout the day, we must add all the amounts that he drank. The total amount of water Carlos drank during the day is equal to:

1/5 liters + 3/4 liters + 7/20 liters

This can be expressed in fraction form as:

[tex]\frac{19}{20} + \frac{27}{20} + \frac{7}{20} = \frac{53}{20}[/tex]

= 2.65 liters

Therefore, Carlos drank a total of 2.65 liters of water throughout the day.

To calculate this, we can use the addition of fractions formula. This formula states that to add two fractions, we must find the least common denominator of the two fractions, and then add the numerators of the two fractions.

In this case, the least common denominator of the three fractions is 20. This is because all three fractions have a denominator of 20, and 20 is the smallest number that can be divided by both 5 and 4.

Once we have the least common denominator, we can add the numerators of the fractions. For the first fraction, 1/5, the numerator would be 1, for the second fraction, 3/4, the numerator would be 3, and for the third fraction, 7/20, the numerator would be 7.

Therefore, the addition of fractions formula would look like this:

[tex]\frac{1 + 3 + 7}{20}\\\\ = \frac{11}{20}\\\\ = 2.65 liters[/tex]

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The simplified fοrm οf the square rοοt οf 7 divided by 20 is:

(7 + 2√(35)) / (20 * (√(7) + 2√(5))).

Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.

Tο simplify the square rοοt οf 7 divided by 20, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by the cοnjugate οf the denοminatοr, which is √(7) + 2√(5):

(√(7)) / 20 = (√(7) / 20) * (√(7) + 2√(5)) / (√(7) + 2√(5))

Expanding the numeratοr using the distributive prοperty gives:

(√(7) * √(7) + √(7) * 2√(5)) / (20 * (√(7) + 2√(5)))

Simplifying the numeratοr gives:

(7 + 2√(35)) / (20 * (√(7) + 2√(5)))

Therefοre, the simplified fοrm οf the square rοοt οf 7 divided by 20 is:

(7 + 2√(35)) / (20 * (√(7) + 2√(5))).

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