One herd consisted of eight white cows and six brown. In ten days they produced the same amount of milk as did the other herd - six white cows and ten brown - in eight days. Did the brown cows produce more milk or did the white cows?

Answers

Answer 1

The brown cows produced more milk than the white cows in the given situation.

What is same amount?

"Same amount" means that two or more quantities are equal to each other in terms of their numerical value or quantity.

According to question:

To find out whether the brown cows produce more milk or the white cows, we can make a ratio of milk produced by both the herds in one day.

For this, let’s assume the amount of milk produced by a white cow in one day is “w” and the amount of milk produced by a brown cow in one day is “b”.

Then, The amount of milk produced by eight white cows in 1 day = 8w.

The amount of milk produced by six brown cows in 1 day = 6b.

The amount of milk produced by six white cows in 1 day = 6w.

The amount of milk produced by ten brown cows in 1 day = 10b.

According to the given condition, both herds produce the same amount of milk in one day.

Therefore, 8w × 10 = 6w × 86w × 5/3

                               = 10b5w/4 = 5b/2b

                               = (5w/4) × (2/5)

                               = w/2

We can say that a brown cow produces double the milk produced by a white cow. Hence, brown cows produced more milk than the white cows in the given situation.

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Related Questions

240

Use the ratio 1. What operation can you do on both terms to find

an equivalent ratio that has 1 as the second term?

Answers

Answer:

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

hope this helps good luck

Given the logistic model f(x)=800/1+19e^−0.402x, what is the initial value? Round your answer to the nearest whole number.

Answers

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

What is  logistic model?

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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Nicole is a wedding organiser. The guests sit at a circular table with a diameter of 180cm each guest needs 7cm around the cicumference of the table. Their are 18 tables at the venu. There is a toptal of 145 guests. Are their enoughb tables

Answers

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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Jason read a total of 8 books over 4 months. If Jason has read 16 books so far, how many months has he been with his book club? Solve using unit rates. its worth 100 points

Answers

Answer:

8 months

Step-by-step explanation:

I got it right

solve the following system of equation y=x^2-32 y=x+10

Answers

x=(17,4)^2+(−340,−80)+58y= y^2−20y+68

y=y^2−20y+68

i need the answers for this? 8th grade math

Answers

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.

What is y-intercept of the graph?

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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the number of guests at a theme park can be modeled by function p(t) where t is measured in hours. p is a solution to the logistic differential equation dp over dt equals p over 3 minus p squared over 60000 comma where p(0)

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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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Stewart, Oswaldo, Kevin, and Flynn go to a soccer day at the FC Dallas’ arena, Toyota Stadium, in
Frisco, Texas. The coach has a computer and video system that can track the height and distance of
their kicks. All four soccer players are practicing up-field kicks, away from the goal.
Stewart goes first and takes a kick starting 12 yards out from the goal. His kick reaches a maximum
height of 17 yards and lands 48 yards from the goal.
Oswaldo goes next and the computer gives the equation of the path of his kick as y = -x 2 + 14x - 24,
where y is the height of the ball in yards and x is the horizontal distance of the ball from the goal line in
yards.
After Kevin takes his kick, the coach gives him a printout of the path of the ball.

Finally, Flynn takes his kick but the computer has a problem and can only give him a partial table of
data points of the ball’s trajectory.
Flynn’s Table:
Distance from the
goal line in yards

10 11 12 13 14 15 16 17 18 19 20

Height in yards 0 4.7 8.75 12.2 15 17.2 18.75 19.7 20 19.7 18.75
The computer is still not working but Stewart, Oswaldo, Kevin, and Flynn want to know who made the
best kick.

Answers

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! :]

Subtracting a number is the same as adding its opposite.

Use this understanding to complete each of the equations below.

Answers

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]          

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

Answers

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.


You fill up your gas tank in France where the gas price is $1.54 per liter. If your rental car gets 29 miles per gallon, how much will it cost to drive 225 miles? (to the nearest cent)

this is conversion math​

Answers

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 figure shown is composed of two parallelograms. find x. justify your answer

Answers

Answer:

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

x=1290-193

x=1097

Use the commutative or associative property to simplify the expression. -(1)/(9)(13x)

Answers

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.

A right circular cylinder has the dimensions shown below.
r = 17.2 yd h = 45.3 yd

What is the volume of the cylinder? Use 3.14 for tr. Round to the nearest tenth and include correct units.

Show all your work.

Answers

Answer:

42080.9 cubic yd

Step-by-step explanation:

Volume of right circular cylinder:

           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 :-

What is the volume of a right circular cylinder with a radius of 17.2 yd and a height of 45.3 yd?

Answer :-

The volume of a right circular cylinder is 42080.873 yd³.

[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 :-

The volume of a right circular cylinder is 42080.873 yd³.

[tex]\\[/tex]

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Type your answers into the boxes. Complete the following questions. 4+7 x6= 12 + 9 x3 -1 =

Answers

4 + 7×6 = 4 + 42 = 46

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

Simplify the square root of 7 divided by 20

Answers

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

(7 + 2√(35)) / (20 * (√(7) + 2√(5))).

What is the equivalent expressiοn?

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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This is the same information as you’ll use in the next question.

The equation for the period of a pendulum is given by T space equals space 2 straight pi square root of straight L over 32 end root where T is the time (in seconds) and L is the length of the pendulum (in feet).

Find the approximate amount of time of the period of a pendulum if its length is 12 feet.

Answers

The approximate amount of time period of a pendulum with a length of 12 feet is 1.85 seconds.

What is calculus?

Calculus is a branch οf mathematics that deals with the study οf change and hοw things change οver time.

We can use the given equatiοn fοr the periοd οf a pendulum:

T = 2π√(L/32)

Substituting L = 12, we get:

T = 2π√(12/32)

Simplifying:

T ≈ 1.85 seconds

Hence, the approximate amount of time of the period of a pendulum with a length of 12 feet is 1.85 seconds.

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How do I solve this, steps please!
2(x-1)(x+1) / x^2 -x-20

Answers

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

What is Algebraic expressiοn ?

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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Select whether the equation has a solution or not. x-8+-/x2-8 roots no roots

Answers

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

The function has one solution.

How to obtain the number of solutions?

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.

Missing Information

The function is given as follows:

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

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According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide. What is the approximate area of the park? Show your work.

Answers

The approximate area of the park is given as follows:

450 blocks squared.

How to obtain the area of a rectangle?

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:

Length of 50 blocks.Width of 9 blocks.

Hence the area of Central Park is calculated as follows:

Area = 50 x 9

Area = 450 blocks squared.

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JKLM is a rhombus. m/MLN = (9a + 11)° m /KLM = (-4a + 66)°
Find the m2KJM.

Answers

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

What is rhombus?

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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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, find the growth constant , and determine when the population will increase to 12900.

Answers

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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Mary leaves a campsite and walks 4 miles east and 2 miles south. Her friend walks 3 miles north and 1 mile west. How far apart is Mary from her friend?​

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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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Carlos tomo 1/5 litros de agua a las 8. 00 am; 3/4 litros de agua a las 12. 12:00 AM. Y7/20 litros de agua a las 5:00 pm. Cuantos litros de agua tomo en total durante el dia

Answers

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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This graph shows the amount of rain that falls in a given amount of time.

What is the slope of the line and what does it mean in this situation?

Select from the drop-down menus to correctly complete each statement.

The slope of the line is
Choose...
.

This means that
Choose...
mm of rain falls every
Choose...
.

Answers

The slope of the line is

3

This means that

6mm

of rain falls every

1hr

Sorry if I said it again but I need help on this question

Answers

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.

What is Triangle?

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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Use the clues to crack the code the number is greater than ten the value of the ones digit is ten times the value of the tenths digit Code number (5, 5, 7,

Answers

Given that there is only one digit left and the sum is more than 10, the third digit must be 7, which it is. and the pass code to open anything it is guarding is 5 5 7, which may be inputted.

To decode the code, we know that the number is more than 10 and has three digits: . Moreover, we are aware that the value of the ones digit is 10 times that of the tenths digit. The code is 5 5 7, as may be inferred from the provided hints.

Given that the code contains two 5s, the first digit must be 5. As the value of the ones digit is 10 times that of the tenths number, the second digit must likewise be 5, which is 5. The number is bigger than 10, hence the third digit must be 7, as it is the only one still present.

In order to open whatever it is guarding, the code, which is 5 5 7, may be input.

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find the missing number in the sequence

- 5, -1, 3​

Answers

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.

describe the complement of the given event. 71% of a person's credit card purchases are seventy dollars or more.

Answers

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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Tony, Donna, and Jeremy ran for class president. Tony and Donna together won 0. 62 of all the votes. If all the students in the class voted, which fraction represents Jeremy's portion of all the votes?

Answers

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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