In the diagram below of triangle EFGEFG, HH is the midpoint of \overline{EG}
EG
and II is the midpoint of \overline{FG}
FG
. If m\angle GFE=87-7x∠GFE=87−7x, and m\angle GIH=51+2x∠GIH=51+2x, what is the measure of \angle GIH∠GIH?

A) The number of people who have started the rumor is N(0)=12

B) The number of students who are in the school are 1800

C) The number of days the rumor spreads to ½ the student body are 8 days.

D) The number of students who have heard the rumor when the rumor is spreading the fastest are 900.

The rate of change in students per day at this time is 281.

The rate of change is a mathematical term that describes the percentage change in value over a given time period and represents the momentum of a variable.

A) Number of people who have heard the rumor after t days is given by:

N (t) = 1800/1+149e^-0.625t

At start t=0, so from the above equation at t=0, we get

N(0)=(1800)/1+149e^0

N(0)=1800/(1+149(1))

N(0)=1800/150

N(0)=12

B) At t=∞, all of the students would have heard the rumor.  So putting t↔∞ in the above equation we get,

[tex]\lim_{t \to \infty}[/tex]N(t)=[tex]\lim_{t \to \infty}[/tex] 1800/1+149e^-0.625t

=1800/(1+0)

=1800

Therefore, the number of students in the school are 1800.

C) Putting N=1800/2 in the above equation, we get

1800/2= 1800/1+149e^-0.625t

1+149e^-0.625t=2

e^-0.625t=(2-1)/149

=1/149

Taking log on both sides, we get

ln(e^-0.625t)=ln(1/149)

-0.625t=-ln(149)

t=ln(149)/0.625

t=8.006≈8

D) N'(t)=0.625N(1-(N/1800)

=0.625(N-(N²/1800)

=(0.625/1800)(1800N-N²)

=(0.625/1800)(900²-900²+1800N-N²)

=(0.625/1800)(900²-(N²-1800N+900²)

N'(t)=(0.625/1800)(900²-(N-900)²)

For N to be maximum,

N=900

Thus, rumor is spreading fastest when 900 students have heard the rumor.

And rate of change in students per day is obtained by putting N=900 in expression of N'(t) as follows:

N'(t)=(0.625×900)(1-(900/800))

N'(t)=281.25≈281

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Answer: $1,751.4

Step-by-step explanation:

33600 = 100%

(1400*100)/33600 =

140000:33600 = 4.17

42,000 * 4.17% = 1,751.4

The number of soda bottles the machine can make in each minute is 960 bottles

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the number of soda bottles the machine can make in 1 minute be = y

Now , the equation is

Let the first point in the graph be A ( x₁ , y₁ )

The value of A ( x₁ , y₁ ) = A ( 3 , 48 )

Let the second point in the graph be B ( x₂ , y₂ )

The value of B ( x₂ , y₂ ) = A ( 7 , 112 )

Now , the slope of the line joining the points can be found out from the equation of slope

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

So , the slope of the point is m = steep of the line or inclination

Slope m = y / x

Substituting the values for x and y , we get

Slope m = 48 / 3

Slope m = 16

Therefore , the equation of line will be y = mx + c

y = 16x

Now , there are 60 seconds in a minute

So , 1 minute = 60 seconds

Substituting the value of x = 60 in the equation , we get

y = 16x

y = 16 x 60

y = 960 bottles

Therefore , the value of y = 960

Hence , The number of soda bottles the machine can make in each minute is 960 bottles

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The horse that can be fed with 44 bales of hay is 110 horses.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers. On the other hand, a fraction appears in the numerator or the denominator of a complex fraction.

Given that the average adult horse needs 2/5 bale of hay each day to meet dietary requirements and a horse farm has 44 bales of hay.

The number of horses that can be fed will be:

= Total number of hay / Fraction needed

= 44 ÷ 2/5

= 44 × 5/2

= 22 × 5

= 110

100 horses can be fed.

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Answer:

y=20x

if he charges $20 and hour multiply your hours by 20 to get the total amount of earnings

The equation 8x - 4y = -4 have y as the subject to be equal to 2x + 1 expresses in terms of x.

To solve for y in the equation 8x - 4y = -4, we must make y the subject and it should be positive as follows;

8x - 4y = -4

add 4y to both sides

8x - 4y + 4y= -4 + 4y

8x = - 4 + 4y

also to make y the subject;

- 4 + 4y = 8x

add 4 to both sides

- 4 + 4 + 4y = 8x + 4

4y = 8x + 4

factorize the right hand side

4y = 4(2x + 1)

divide through by the coefficient of y

4y/4 = [4(2x + 1)]/4

y = 2x + 1

Hence, the equation 8x - 4y = -4 has y = 2x + 1

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Answer:

90 tons

Step-by-step explanation:

given that the ration of weight from earth to mercury is 5:2, we can make an equation:

x (weight of an item on Mercury) = 0.4(weight of an item on Earth)

x=0.4(225 tons)

x=90 tons

The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.

percentage, a relative value indicating hundredth parts of any quantity.

Given,

The total number of bacteria in lab dish is 1200

The population decreases 10% per day

In first day:

10/100×1200=120

120 bacteria decreased in lab

1200-120=1080

In second day:

0.1×1080=108

1080-108=972

In third day

0.1×972=97.2

972-97.2=874.8

In fourth day

0.1×874.8=87.48

874.8-87.48=787.32

In fifth day

0.1×787.32=78.732

787.32-78.732

708.588

The population decreases more quickly from day 1 to day 3 than from day 4 to day 6.

Hence, the population decreases  more quickly from day 1 to day 3 than from day 4 to day 6.

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The equation -2g+2g has infinitely many solutions.

The method of solving equations involves determining the value of the unknown variable while maintaining the equality of the equation on both sides. When a condition on variable guarantees that two expressions in the variable have the same value, it qualifies as an equation. The equation's solution is the value of the variable for which the equation is true. An equation remains the same even when the LHS and RHS are flipped. After separating the variable whose value has to be calculated, the solution is found. We can answer it depending on the type of equation we are dealing with. Equations come in a variety of forms, including linear, quadratic, rational, and radical equations.

Consider the given equation

-2g + 2g = 0

Solve the equation,

0 = 0

This means that the equation is valid for all values of g.

Therefore, the equation can have infinitely many solutions.

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Answer:

Step-by-step explanation:

Set angle equations equal to each other(since lines are parallel)

7x-4= 5x+10

Add 4 to both sides to isolate x on left side

7x= 5x+14

Subtract 5x from both sides to get x on one side only.

2x=14

x=7

By conducting mathematical operations, we know that the group of friends will order 6 pizzas.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, a number of pizzas the friends should buy:

We know that a group is of 15 people.

They are ordering a pizza which have also 15 slices in each.

And each person wants 2 slices: That is

Then, the number of pizzas they have to order will be:

1 pizza (15 slices) * 2 = 2 pizza (30 slices)

Therefore, by conducting mathematical operations, we know that the group of friends will order 6 pizzas.

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The sum of the given two positive integers is 9.

According to the question,

We have the following information:

The product of two positive integers is 18. the positive difference of these two integers is 3.

Now, let's take the first positive integer (larger one) to be x and the second positive integer to be y.

xy = 18 ...(1)

x-y = 3

x = 3+y

Putting this value in equation 1:

(3+y)y = 18

[tex]y^{2} +3y-18 = 0[/tex]

[tex]y^{2}[/tex]+6y-3y-18 = 0

y(y+6)-3(y+6) = 0

(y+6) (y-3) = 0

y-3 = 0 and y+6 = 0

y = 3 or y = -6

Now, the number is positive so it will be 3.

Putting this value in equation 1:

xy = 18

3x = 18

Dividing by 3 on both sides of the equation:

x= 18/3

x = 6

Sum of integers = 3+6

Sum of integers = 9

Hence, the sum of the given two positive integers is 9.

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The measure of angle O in the given parallelogram is equal to 105°.

As given in the question,

Given parallelogram LMNO,

As shown in the attached diagram we have,

Measure of angle L = ( x + 40 )°

Measure of angle O = (3x)°

In the parallelogram LMNO,

LM is parallel to NO .

LO is the transversal.

∠MLO and ∠NOL are interior angles and are supplementary.

m ∠MLO + m ∠NOL = 180°

⇒ ( x  + 40 )° + ( 3x )° = 180°

⇒ 4x° = 180° - 40°

⇒x = 140° / 4

⇒ x = 35°

Measure of ∠O = 3x°

                          = 3(35°)

                          = 105°

Therefore, the measure of  ∠O  in the parallelogram LMNO with the given conditions is equal to 105°.

The complete question is :

What is the measure of angle O in parallelogram LMNO?

Diagram of parallelogram LMNO is attached.

m∠O = ?

a. 35°        b. 75°               c. 105°           d. 155°

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Answer: 105 degrees

Step-by-step explanation:

edge 2023, (Proving a Quad. is a Parallelogram)

The space between the ceiling of the one floor and the floor of the level above it will be;

⇒ 9 6/8 inches

What is mean by Subtraction?

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches.

And, The distance from the floor to the ceiling is 8 feet 2 5/8 inches.

Now,

Since, The distance from the floor of one level of a building to the floor of the level above it is 9 feet 3/8 inches.

And, The distance from the floor to the ceiling is 8 feet 2 5/8 inches.

Hence, The space between the ceiling of the one floor and the floor of the level above it will be;

⇒ 9 feet 3/8 inches - 8 feet 2 5/8 inches

⇒ (9 × 12 + 3/8) inches - ( 8 × 12 + 21/8) inches

⇒ (108 + 3/8) - (96 + 21/8) inches

⇒ 867/8 - 789/8

⇒ 78/8

⇒ 9 6/8 inches

Thus, The space between the ceiling of the one floor and the floor of the level above it will be;

⇒ 9 6/8 inches

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The simplified form of the given fraction, 3 9/10 + 4 9/10 , in its simplest form is 8 4/5

From the question, we are to write the given fraction as a mixed number in simplest form

The given fraction is

3 9/10 + 4 9/10

First, we will convert the fractions to improper fractions

39/10 + 49/10

Now, add the fractions

(39 + 49)/10

= 88/10

Write as a mixed fraction

8 8/10

Simplify the fraction

8 4/5

Hence, the fraction becomes 8 4/5

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Answer: 8.64

Step-by-step explanation:

If you add 4.44 and 4.2 you would get 8.64 pounds worth of fruits in total.

Answer:

8.64 pounds of fruit.

Step-by-step explanation:

4.2 + 4.44 = 8.64 pound of fruit

The blanks are shown below for the area of hexagon with sides equal to 12cm.

In geometry, a hexagon is defined as a six-sided polygon. The two-dimensional form contains six sides, six vertices, and six angles.

All of the fill in the blanks are answered below:

(1) The number of  equilateral triangles are 6

(2) The measure of each of the three angles in the equilateral triangle 60°

(3) If we cut an equilateral triangle down the middle the special right triangle we create is 30-60-90

(4)  The vocabulary word for the green line is perpendicular bisector.

(5) The length of the short side of one 30-60-90 triangle is 4cm

(6) What is the length of the hypotenuse of one 30-60-90 triangle is 8cm

(7) Using the properties of 30-60-90 triangles,  the length of the long leg. is 4√3cm

(8) The height of the equilateral triangle is 4√3cm

(9) The area of one equilateral triangle is ½(8)(4√3) = 16√3 cm²

(10) The area of one equilateral triangle by the number of triangles. is 8(16√3) = 128√3 cm²

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Answer:

x = -4 or 2

Step-by-step explanation:

Let the number be x.

x² + 2x = 8

Subtract 8 to both sides

x² + 2x - 8 = 0

Using mid-term break method

=> 4 × -2 = 8 (side-term), 4 - 2 = 2 (mid-term)

So, we can break the mid-term into 4 and -2.

x² + 4x - 2x - 8 = 0

Take common

x(x + 4) - 2(x + 4) = 0

Take (x+4) common

(x+4)(x-2) = 0

Either

x + 4 = 0       OR      x - 2 = 0 (Zero's method)

x = -4            OR       x = 2

[tex]\rule[225]{225}{2}[/tex]

Part a:  [In⁻]/[HIn] = 4.0 × 10⁻⁶

Part b: [In⁻]/[HIn] = 50.11, for the given phenolphthalein solution.

Using the Henderson-Hasselbalch equation to determine the indicator's pH  is as follows:

pH = pKa + log[In⁻]/[HIn]

In which,

Ka = dissociation constant of acid.

As the stated value-

Part a:

pKa = 9.7

pH = 5.3

Thus,

5.3 = 9.7 + log[In⁻]/[HIn]

log[In⁻]/[HIn]  = - 4.4

[In⁻]/[HIn] = Antilog (-4.4)

[In⁻]/[HIn] = 4.0 × 10⁻⁶

Part b:

pKa = 9.7

pH = 11.4

Thus,

11.4 = 9.7 + log[In⁻]/[HIn]

log[In⁻]/[HIn]  = 1.7

[In⁻]/[HIn] = Antilog (-4.4)

[In⁻]/[HIn] = 50.11

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Answer:4536 numbers.

Step-by-step explanation:

Since 1 st digit cannot be zero the first digit can be anything from 1–9 ( total 9)

The second digit ( any 10- 1 above)

The third digit ( any 10–2 above)

The last digit ( any 10–3 above)

Total 9x9x8x7 =

4536

:)

If water is being pumped into the trough at 2 cubic feet per minute, then the water level rising (in feet per minute) when h is 1.6 foot deep is 0.1 feet cubic per minute.

Suppose that we have a function y = f(x), and wish to find the rate of change of y with respect to a third variable t, where we do not have y expressed explicitly in terms of t. We use the chain rule in differentiation to find this rate of change in a process called implicit differentiation.

                     dy/dt = dy/dx × dx/dt

If base is equal to the height, by similar triangles:

Volume v = base x height x length/2

                = bhl/2

                = h²12/2

                = 6h².

Therefore,  

dv/dt = 12hdh/dt

         = 2 ft³/min

 Now,

dh/dt = 2/(12h)

when h = 1.6,

dh/dt = 2/(12 × 1.6) ≈ 0.1 ft³/min

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The slope of the line that contains the points (17, -12) and (7, 8), is -2.

From the question, we are to determine the slope of the line that contains the given points.

The given points are (17, -12) and (7, 8)

Using the formula for calculating slope,

m = (y₂ - y₁) / (x₂ - x₁)

Where m is the slope

Then,

The slope of the line is

m = (8 - (-12)) / (7 - 17)

m = (8 + 12) / (-10)

m = 20 / - 10

m = -2

Hence, the slope is -2

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In a simple linear regression model , if we change the input variable by 1 unit , output variable will change by its slope.

What is linear regression?

According on the value of another variable, a variable's value can be predicted using a linear regression analysis. The dependent variable is the one you're trying to forecast. The term "independent variable" refers to the variable you are using to forecast the value of the other variable.

For linear regression

Y=a + bx + error

If we neglect error

then Y=a + bx.

If x increases by 1

then Y = a +b(x+1) which implies

Y=a + bx + b.

So Y increases by its slope.

Hence their is an increase in the slope in y.

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By using the concept of percentage, it can be calculated that Karrie was late to work in 5.6 % of the days.

What is percentage?

Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.

For example 9% means [tex]\frac{9}{100}[/tex]. Here 9 is expressed as a fraction of 100

Here the concept of percentage will be used

Number of days in which Karrie was late = 14

Total number of days she worked = 250

Percentage of days Karrie was late = [tex]\frac{14}{250} \times 100[/tex] = 5.6 %

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Answer: I think it is 5

Step-by-step explanation:

Step-by-step explanation:

Also, we know that , because the unit digit is three less than tens digit, or tens digit is three more units than the unit digit. Then, the sum of the reversed number and the original number is 121, this would be expressed: Therefore, the digits are 7 and 4. The number would be 74.

Answer:

The original number is 74

Step-by-step explanation:

The answer of 74 provided by brey90 is absolutely correct. I am just providing a mathematical way of determining the number

Let the number be ab
That means [tex]b[/tex]  is in the units place and [tex]a[/tex] is in the tens place.

The actual value of this two digit number is  [tex]10a + b[/tex]  

The difference between a and b is 3:
[tex]a - b = 3[/tex]  [1]

If we reverse the number we get the number [tex]ba[/tex]

The actual value of [tex]ba[/tex] is [tex]10b + a[/tex]

The sum of [tex]ab[/tex] and [tex]ba[/tex] is 121. This means the sum of their actual values must be 121

So we get
[tex]10a + b + 10b + a = 121\\\\11a + 11b = 121\\\\[/tex]

Dividing both sides by 11 yields:
[tex]a + b = 11[/tex]  [2]

Add [1] and [2] to get:
[tex]2a = 14\\\\a = 7\\\\[/tex]

Sub for a in Equation [1] to get
[tex]7 - b = 3\\\\b = 4\\\\[/tex]

So the original number is 74

Check
Reversed is 47
74 + 47 = 121

(a) The number of ways of selecting a committee of 8 students = 45.

(b) The number of ways to select a committee with 3 seniors and 2 juniors are 105.

(c) The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the 8 must be selected as chair = 360 ways

What is combination?

A combination in mathematics is a choice made from a group of separate elements where the order of the selection is irrelevant.

Given that 10 students have volunteered for a committee. 7 of them are seniors and 3 are juniors.

a) Need to find the number of ways of selecting a committee of 8 students

The number of ways of selecting a committee of 8 students = [tex]10_C_8[/tex]

[tex]10C_8= \frac{10!}{8!(10-8)!}= \frac{10!}{8!(2!)}=45[/tex]

The number of ways of selecting a committee of 8 students = 45.

(b) Need to find the number of ways to select a committee with 3 seniors and 2 juniors

The number of ways to select a committee with 3 seniors and 2 juniors

= [tex]7_C_3(3_C_2)[/tex]

[tex]7_C_3*3_C_2 = \frac{7!}{3!*4!} *\frac{3!}{2!*1!} = 35 * 3 = 105[/tex]

The number of ways to select a committee with 3 seniors and 2 juniors are 105.

(c) Need to find the ways to make the select the committee must have 8 students (either juniors or seniors) and that one of the 8 must be selected as chair.

Number of ways = [tex]10_C_8*8_C_1[/tex]

[tex]10_C_8*8_C_1 = \frac{10!}{8!*2!} *\frac{8!}{7!*1!} = 45*8 = 360[/tex]

The number of ways to select a committee having 8 students (either juniors or seniors) and that one of the five must be selected as chair = 360 ways.

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The values of c in the given equation, 19 = | 5c - 4 |, are c = -3 and c = 4 3/5

From the question, we are to solve the given equation for all values of c

The given equation is

19 = | 5c - 4 |

From this equation, we can write that

19 = (5c - 4) and 19 = -(5c - 4)

Solving the first equation

19 = (5c - 4)

19 = 5c - 4

Add 4 to both sides of the equation

19 + 4 = 5c - 4 + 4

23 = 5c

Divide both sides by 5

23/5 = 5c/5

4 3/5 = c

Therefore,

c = 4 3/5

Solving the second equation

19 = -(5c - 4)

19 = -5c + 4

Subtract 4 from both sides of the equation

19 - 4 = -5c + 4 - 4

15 = -5c

Divide both sides by -5

15/-5 = -5c/-5

-3 = c

Therefore,

c = -3

Hence, the values of c are -3 and 4 3/5

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As per the concept of probability, there are 4,717,440 number of passwords are possible.

Probability:

In statistics, probability refers the favorable outcome of the particular event.

Given,

A password to a computer consists of 6 characters: a digit, a letter, a digit, a letter, a digit, and a letter in that order, where the numbers from 1 through 9 are allowed for digits.

Here we need to find how many different passwords are possible.

Total number of characters = 6

According to this, each password would have

5 digits of 10 digits: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9], and

one of 26 letters: [A to Z].

Here there is no repeats are allowed, and assuming only upper case letters are valid and the letter is the last character, then we can form 10*9*8*7*6 * 26 = 786,240 such passwords.

If the repetition is allowed then number of possible passwords is

786,240 * 6 = 4,717,440.

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Answer:

Step-by-step explanation:

4.) - 20

5.) 66 i

Feel free to double check with a calculator

(Hope that helps!)