Suzy is competing in a long-distance au
bicycle race. In the first 6 hours, she completed 132 miles of the race. If she
plans to ride 7 hours per day, how many
days will it take for her to complete the
616-mile race at the same rate?
A 2
B 4
C 6
D 8

The average rate of change of f(x) over the interval [-4, -1], with coordinates, (-4, -3) and (-1, 3) is 2

The average rate of change of a function over an interval is found from the change in the output values of the function over the period indicated, divided by the change in the input values of the function over the specified interval.

Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex]

The interval over which the average rate of change of the function is required = [-4, -1]

The formula for the average rate of change over the interval, [-4, -1], can be presented as follows;

Average rate of change = [tex]\dfrac{\Delta y}{\Delta x}[/tex]  =  [tex]\dfrac{f(-1) - f(-4)}{\left(-1 - (-4)\right)}[/tex]

The coordinates of the points of the graph of the function in the indicated range are; (-1, 3), and (-4, -3)

f(-1) = 3, f(-4) = -3, therefore;

Average rate of change = [tex]\dfrac{3 - (-3)}{-1 - (-4)}[/tex] = 2

The average rate of the function over the specified interval is 2

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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:

4√130 or just  √480

Step-by-step explanation:

You set up each number for pythagorean theorem as a squared plus b squared equals c squared. Then you solve for b squared and simplify into radical form, or...

your answer is 21.9

A regression model could be used to estimate the wage gender gap by comparing the earnings of men and women.

Regression is a statistical technique used in the fields of finance, investing, and other areas that aims to assess the nature and strength of the relationship between one dependent variable and another. In this case, the dependent variable would be the gender gap in wages and the independent variable would be the earnings of men and women. The regression model would be used to calculate the difference between the two variables, which would indicate the wage gender gap.

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The original price of the swimming pool is $1030.

From the information, the swimming pool is on sale for $875.50 and the sale price is discounted 15% from the original price.

Let the original price be x.

This will be illustrated as:

(x - 15% × x) = 875.50

x - 0.15x = 875.50

0.85x = 875.50

Divide

x = 875.50 / 0.85

x = 1030

The original price is $1030.

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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:

Step-by-step explanation:

4.) - 20

5.) 66 i

Feel free to double check with a calculator

(Hope that helps!)

Step-by-step explanation:

remember, an exponent n just means that the base is multiplied by itself n times.

so, e.g.

a³ = a×a×a = (a×a)×a

a⁶ = a×a×a×a×a×a = (a×a)×(a×a)×(a×a)

as you can see, any even exponent can be written as products of squares.

and any odd (uneven) exponent can be written as product of squares multiplied by one base.

a square of a real number is always positive. therefore, an even exponent of a real number is always positive.

and an odd exponent has the sign of the base (as the result of these multiplications is the product of the squares, that are always positive and one instant of the base, and +×+ = +, +×- = -).

and 1^n = 1

no matter how often I multiply 1 by 1, I get 1 as result.

also : -×- = +

1.

f(x) = x^n, n is even

f(1) = 1^n = (1×1)×(1×1)×...×(1×1) = 1×1×1×...×1 = 1

f(-1) = (-1)^n = (-1×-1)×(-1×-1)×...×(-1×-1) = 1×1×1×...×1 = 1

2.

g(x) = x^n, n is odd

g(1) = (1×1)×(1×1)×...(1×1)×1 = 1×1×1×...×1×1 = 1

g(-1) = (-1×-1)×...×(-1×-1)×-1 = 1×1×...×1×-1 = -1

The probability that Jordan misses a free throw is 0.16

From the question, we have the following parameters that can be used in our computation:

Odds in favour = 21 : 4

Represent the odds as a fraction

So, we have the following representation

Odds in favour = 21/4

To convert the odds to probability, we make use of the following equation

Probability = Numerator/(Numerator + Denominator)

Substitute the known values in the above equation, so, we have the following representation

Probability = 21/(21 +4)

Evaluate the sum

Probability = 21/25

The probability that he misses is

Misses = 1 - 21/25

Evaluate the probability

Misses = 4/25

So, we have

Misses = 0.16

Hence, the probability is 0.16

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The required solution of the given inequality is given as x > -3.

Given that,
To determine the solution of the given inequality, 2.4x−6>−13.2.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

here,
2.4x−6>−13.2.
2.4x > -7
x > -3

Thus, the required solution of the given inequality is given as x > -3.

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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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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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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

Using an exponential decay equation, the function that models the balance is y = 1800(1 + 0.081)⁻ˣ at a rate of 8.1%

Exponential function, as its name suggests, involves exponents. But note that, an exponential function has a constant as its base and a variable as its exponent but not the other way round (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). An exponential function can be in one of the following forms.

In mathematics, an exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

To solve this problem, we need to find the rate at which the payment is calculated on.

The general equation for an exponential decay is given as

A = P(1 + r)⁻ˣ

Substituting the values and solving for r

1540 = 1800(1 + r)⁻²

r = 0.081

r = 8.1%

Comparing the third month to ascertain values

1410 = 1800(1 + r)⁻³

r = 0.081

r = 8.1%

The rate which the payment is calculated is 8.1%

An exponential equation that models the balance after y months will be

y = 1800(1 + 0.081)⁻ˣ

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Answer:

A, B, D, E, F, G, H

Step-by-step explanation:

If triangle A'B'C' is a reflection of triangle ABC across line l, the following statements must be true:

A. Line l bisects segment AB.

B. Line l bisects segment CC’.

D. Line BB’ is perpendicular to line l.

E. Angle ABC is congruent to angle A’ B’ C’.

F. Triangles ABC and A’ B’ C’ are congruent.

G. Segment BC is congruent to segment B’ C’.

H. The distance from point A to line l is the same as the distance from point A’ to line l.

Statements C and H are not necessarily true. The angle ABC may not be 60 degrees, and the distance from point A to line l may not be the same as the distance from point A’ to line l.

The probability of the magazine is a sports magazine is 0.065.

What do you mean by probability?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities. A number between 0 and 1 represents the likelihood of an event, with 0 generally denoting impossibility and 1 denoting certainty.

According to data in the given question,

We have the given information:

The number of sports magazines = 25

The number of news magazines = 11

The number of travel magazines = 2

Now, we will calculate the probability of the magazine is a sports magazine,

Total number of magazine = 25+11+2 = 38

To find the probability that the random selected magazine is a sports magazine divide the amount of sports magazines by the total amount of magazines:

P( sports magazine ) = Number of sports magazine/Total number of magazine

[tex]=\frac{25}{38}\\ =0.065[/tex]

Therefore, the required probability is 0.065.

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Grandfather, two fathers and two sons purchased a total of three tickets.

What is a Mathmatical riddle?

Children must convert a few lines from a real-life incident into the appropriate set of mathematical equations in order to solve a math mystery. Mathematical riddles can be cracked by kids utilizing logic, inventive problem-solving, and common sense.

All three tickets:

Grandfather and His Son's Father

Father and his father's son.

Son.

Two fathers and two sons, then.

As a result, a total of 3 tickets were purchased by a grandfather, two fathers and two sons.

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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]

Answer:

1/ y= 1/5x

2/ y= 3/5x

3/ y= 6/5x

Step-by-step explanation: Our original equation is y=mx+b

Where m is the slope and b is the y-intercept.  Since there is no y-intercept, so we just say it is 0 and only put in the slope to the equation.

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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(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 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)

Answer:

r ≠ E – V/r

Step-by-step explanation:

E ≠ V + Ir

E – V ≠ Ir

divide both sides by I

E – V/I ≠ r

r ≠ E – V/r

i hope i helped

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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If $10,000 is invested at x percent simple annual interest for n years, the total amount of interest would be F = 10,000n(x/100)

Simple interest is calculated based on the principle of a loan or the initial deposit into a savings account. Simple interest doesn't compound, so a creditor will only charge interest on the principal sum, and a borrower will never be required to pay interest on interest that has already accrued.

F = P(1+rt), formula for simple rate of interest

Here,

=> Future value is F

=> Present value is P

=> Rate is R

=> Time is t

Substituting x for r

And, n for t

Also, 10,000 in for P

F = 10,000(1+xn)

The formula tells us principal + interest,

F = 10,000(xn)

Now, to get the x into terms of a percentage,

F = 10,000(n * x/100)

F = 10,000n(x/100)

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The preparation of the bond that should be reported on the balance sheet is presented below:

E-tech initiatives limited plans to issue $500,000, 10-year, 4 percent bonds. Interest is payable annually on december 31. All of the bonds will be issued on january 1, 2022.

We need to present it on balance sheet balance sheet if they are issued at 97.

E-Tech Initiatives Limited

Partial balance sheet

As on January 2, 2019

Liabilities

Long term Liabilities

Bond Payable $500,000

Add: Premium on Bond $10,000  ($510,000 - $500,000)

Carrying value $510,000 ($500,000 * 97%)

Therefore, The preparation of the bond that should be reported on the balance sheet is presented above.

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Option D is the correct answer.

What is distribution?

To “distribute” means to divide something or give a share or part of something.

From the given information , 83 + 68 + 85 + 64 = 300 students.

30 % = freshmen, 24% =sophomores, 26% = juniors , 20% = seniors

Class            Observed frequency      Expected proportion

Freshman            83                                   0.30

Sophomores        68                                   0.64

juniors                  85                                    0.26

seniors                  64                                   0.20

Total                     300                                     1              

The expected number of students in freshman class can be calculated as

Expected Frequency = Total number of value x Expected Proportions

                                    = 300 x 0.30

                                    = 90

Therefore, the expected number of students in freshman class = 90

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