Write the equation of the
line that is perpendicular to
y = -7/5x + 1 and goes
through (5, 3)

A) y= 7/5x-4/7

B) y= -7/5x-4/7

C) y= 5/7x-3/7

D) y= 5/7x-4/7

E) y= 1/7x+3

The completed statement with regards to Chang and Carlotta's methods used for solving the word problem is presented as follows;

A word problem in mathematics and science is the verbal presentation of the information in a scenario required to mathematically solve a problem.

The steps to solve the problem is presented as follows;

The amount in the bank account = $50

Amount made per hour by mowing lawns = $8

The number of hours put into mowing lawns in order to have a total of $130 in the account can be found by using the equation;

The amount in the account increases based on the number of hours used for mowing lawns, therefore;

130 = 50 + 8 × h

8·h = 130 - 50 = 80

h = 80/8 = 10

Ten hours of lawn mowing is required to have a total of $130 in the bank.

Chang's method involve the use of expressing the situation mathematically, by use of variables.

Carlotta's method involves the use of verbal expressions to outline the relationship between the variables, simplifying them to arrive at the determining variable that indicates the number of hours require.

Therefore;

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Using the properties of compound interest we can calculate that Jacob will have $1485 more than Brandon in his account.

Brandon invested $7,900 at the rate of 6 1/8% compounded daily.

Principal = $7900

Time = 15 years

Rate = 6 1/8% = 49/8 %

Amount earned after n years:

[tex]A=P (1+\frac{r}{n})^{nt}[/tex]  

Now we will use these values to find the amount at the end of 15 years.

P = 7900

r = 0.06625

n = 365

t = 15

[tex]A=P (1+\frac{.06125}{365})^{15\times 365}[/tex]

or, A = 19797.104...

or, A ≈ 19797.1

Again, Jacob invested the same sum at compound interest monthly at

6 5/8% .

Amount earned after 15 years:

P = 7900

r = 6.125

n = 12

t = 15

[tex]A=P (1+\frac{.06625}{12})^{15\times 12}[/tex]

or, A = 21282.383..

or, A ≈ 21282.38

Amount earned by Jacob more than Brandon

= $21282.38 - $19797.1

= $148785.283..

≈ $1485

Hence Jacob will have $1485 more than Brandon in his account.

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840 are  4-letter passwords can be formed using the letters by permutation .

What are some examples of permutation?

We are to count all possible 4-letter passwords that can be generated from the letters a, b, c, d, e, f, g .

There are 7 letters in total.

      n = 7 r = 4

 P(n , r ) = 7!/( n - r )!

  P( 7 ,4 ) = 7!/( 7 - 4)!

              = 7!/3!

             = 7 * 6 * 5 * 4 * 3 * 2 * 1/3!

              = 7 * 6 * 5 * 4

               = 840

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Answer:

f(g(x))= log4(2(8x^6))

or log4(16x^6)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Velocity = distance / time

In this problem, we need to calculate for distance, knowing time and velocity.

multiply time on both sides, on the right side the time will cancel out leaving time alone.

velocity * time = distance

40m/s * 0.46s = distance

distance = 18.4 meters

Hope it helped!

The equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

In the given question we have to find the equation of parabola in the form of f(x)=a(x-h)^2+k

The given function is f(x)=7x^2.

The given vertex = (3,5)

The equation of the parabola with the vertex of (h,k) is

y=a(x-h)^2+k

On comparing we get; a=7, h=3, k=5

Now putting the value

f(x)=7(x-3)^2+5

Hence, the equation of the parabola with the vertex (3,5) in the form of f(x)=a(x-h)^2+k is f(x)=7(x-3)^2+5.

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The rational roots of the given equation x(3x − 4) (x − 5) = 0 are x = 0, 4/3 and 5

What is Rational Number?

Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.

So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have common divisible.

x(3x − 4) (x − 5) = 0

So we can put every term equal to zero to find it's root.

1st case, x = 0

2nd, 3x-4 = 0

        3x = 4

         x= 4/3

3rd, x-5 = 0

        x = 5

Hence, the rational roots of the given equation are x = 0, 4/3 and 5

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Answer:

x = -20

Step-by-step explanation:

x/4 + 8 = 3

subtract 8 from both sides:

x/4 + 8 - 8 = 3 - 8

x/4 = -5

multiply both sides by 4:

4(x/4) = 4(-5)

x = -20

The correlation coefficient of the data (0,1132), (1,1107), (2,1000), (3,1019) is -0.89

Correlation coefficients are used to measure how strong a relationship is between two variables

Given: (0,1132), (1,1107), (2,1000), (3,1019)

x    >>>>     y     >>>>  x²  >>>>       y²  >>>>   xy

0              1132            0            1281424         0

1               1107             1            1225449       1107

2              1000           4            1000000      2000

3               1019            9            1038361       3057

................................................................................................

6               4258         14            4545234      6164

.................................................................................................

The formula for the correlation coefficient is:

r = ( n∑xy -(∑x)(∑y) ) / ( √(n∑x² - (∑x)²) .√(n∑y² - (∑y)²) )

From the table:

∑x = 6, ∑y = 4258, ∑x² = 14, ∑y² = 4545234 and ∑xy = 6164

n = 4 (number of data points)

Substituting the values into the formula will give:

r = ( 4×6164 -(6)(4258) ) / ( √(4×14 - (6)²) .√(4×4545234 - (4258²) )

r = 24656-25548 / √(20).√(50372)

r = -892/√(1007440)

r = -0.89

Therefore, the correlation coefficient is -0.89

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The probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68.

Given, that the weight of bags of all purpose flour is normally distributed with expected value 10 pounds and standard deviation 0.2 pounds.

As, we know that

P(X) = (1/s√2π)exp(-1/2((X-m)/s)^2)

where, m is the expected value

and s is the standard deviation.

Now, we have Expected value 10 pounds

and Standard Deviation 0.2 pounds

So,  the probability that of 10 randomly chosen bags of flour at least 2 are overweight be

P(X=0) + P(X=1) = (1/0.2√2π)exp(-1/2((0-10)/0.2)^2) + (1/0.2√2π)exp(-1/2((1-10)/0.2)^2)

P(X=0) + P(X=1) = 0.32

So, Required Probability be 0.68.

Now,  the probability that of 10 randomly chosen bags of flour at least 2 are overweight be 0.68

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When the patient recovery time from a specific surgical procedure is normally distributed, with a mean of 5.2 days and a standard deviation of 2.3 days, the probability of spending more than 2 days in recovery will be 0.61.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution. Information about the likelihood that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is used in epidemiology to comprehend the connection between exposures and the risk of health effects.

Here,

z=(X-μ)/σ

X=2

μ=5.2

σ=2.3

Z=(2-5.2)/2.3

Z=-1.39

-1.39+1

=0.39

1-0.39=0.61

The probability of spending more than 2 days in recovery will be 0.61 when the patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.2 days and a standard deviation of 2.3 days.

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The required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

The quadratic function is defined as a function containing the highest power of a variable is two.

The quadratic function is given in the question:

2y² + 2y - 5 = 0

Compare the given function to the standard quadratic function f(x) = ax² + b x + c.

We get a = 2, b = 2 and c = -5

Using the quadratic formula to solve the above quadratic function

[tex]y = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Substitute the values of a = 2, b = 2 and c = -5 in the above formula

[tex]y=\dfrac{-2\pm \sqrt{2^2-4\cdot \:2\left(-5\right)}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-2\pm \:2\sqrt{11}}{2\cdot \:2}[/tex]

Separate the solutions as:

[tex]y=\dfrac{-2+2\sqrt{11}}{2\cdot \:2},\:y=\dfrac{-2-2\sqrt{11}}{2\cdot \:2}[/tex]

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

Therefore, the required solutions to the given quadratic function are below as:

[tex]y=\dfrac{-1+\sqrt{11}}{2},\:y=-\dfrac{1+\sqrt{11}}{2}\quad[/tex]

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Oliver has to pay an amount of B: $90 with simple interest.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, Oliver borrowed $1,500 to purchase a riding lawn mower for his lawn care business.

The bank offered him an interest rate of 12% for 6 months.

P = $1500, r= 12% and t = 6 months or 1/2 or 0.5 years.

∴ SI = (1500×12×0.5)/100.

SI = 15×6.

SI = $90.

The amount of simple interest Oliver has to pay is $90.

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Answer:

= 7/12

Step-by-step explanation:

1 3/4 = 1 + 3/4 = 4/4 + 3/4 = (4+3)/4 = 7/4

(7/4)÷3 = 7/(4*3) = 7/12

The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.

According to the given information line using the slope and y-intercept is; y= 1/5x + 8

thus, the slope of this line is:

m = 1/5

And its y-intercept is: c= 8

The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.

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Answer:

Step-by-step explanation:

(a⁴-b⁴)/(a-b)

using..(a+b²)=(a+b)(a-b)

=(a²+b²)(a²-b²)/(a-b)

=(a²+b²)(a+b)(a-b)/(a-b)

=(a²+b²)(a+b)

⇒Note this is a fraction.

⇒For a fraction to be undefined that is of when the denominator is equal to 0

⇒Now equate what is  in the denominator with 0

⇒ [tex]k+3=0\\k=-3[/tex]

⇒So that the denominator is 0 that is of when k is equal to -3..it is then that the whole expression will be undefined.

⇒The expression is undefined when k=-3

The minimum score needed to receive a grade of A is 88.51

Let, X, be the scores of the student's

X follows Normal Distribution with mean = μ = 73 and standard deviation = σ = 11

The professor has informed us that 7.93 percent of her students received grades of A.

That is  P( X > a ) = 7.93% = 0.0793 .

We have to find a.

P( X > a ) = 7.93% = 0.0793

So, P( X <=  a ) = 1 - 0.0793 = 0.9207

Using function = NORMINV( probability , μ ,σ )

a = NORMINV( 0.9207, 73 , 11 ) = 88.51

The minimum score needed to receive a grade of A is 88.51

We have to find P( X <= 57.93 )

Using function = NORMDIST( x, μ , σ , 1 )

P( X <= 57.93 ) =NORMDIST( 57.93 , 73 , 11 , 1 ) = 0.0853 = 8.53%

8.53 percent of students failed the course

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Answer: [tex]f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

Step-by-step explanation:

Let [tex]f(y)=x[/tex].

[tex]x=(2y+1)^2\\\\\pm \sqrt{x}=2y+1\\\\-1 \pm \sqrt{x}=2y\\\\y=-\frac{1}{2} \pm \frac{\sqrt{x}}{2}[/tex]

Since the domain of the original function is the same as the range of the inverse, the rate of [tex]f^{-1}(x)[/tex] is [tex]f^{-1}(x) \geq -1/2[/tex]. This means we consider the positive case.

[tex]\therefore f^{-1}(x)=\frac{\sqrt{x}-1}{2}[/tex]

It will take 25 minutes for the two containers to have the same amount of water .

In the question ,

it is given that ,

water present in container A = 200L

water present in container B = 500L

rate at which the water is filling in container A= 6 liter/minute

rate at which the water is draining in container B = 6 liter/minute

let the time taken = m minutes ,

So , According to the question ,

the equation representing the situation is  

200 + 6m = 500 - 6m

Simplifying further , we get

6m + 6m = 500 - 200

12m = 300

m = 300/12

m = 25

Therefore , It will take 25 minutes for the two containers to have the same amount of water .

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Answer:

Step-by-step explanation:

Answer 10.5

Answer:

-3.2

Step-by-step explanation:

-5(x+1)-9=2

first simplify by distributiom

-5(x)-5(1)-9=2

simplify the multiplication

-5x-5-9=2

add the numbers

-5x-14=2

now to get x by itself on one side we undo in reverse order and move the -14 over to the other side so add 14 to both sides to cancel the -14

-5x=2+14

simplify

-5x=16

now divide both sides by -5 to get x by itself

-5x/-5=16/-5

simplify

x=-3.2 or as a fraction, [tex]-\frac{16}{5}[/tex]

The percentage decrease of the population of a city is 19%.

A percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

In this case, the population of a city was 325,000 and several years later it was 263,250.

The percentage decrease will be:

= Decrease in population / Original population × 100

= (325000 - 263250) / 325000 × 100

= 61750 / 325000 × 100

= 19%

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Work Shown:

p * q = 3p + 2q - 5

3 * 2 = 3(3) + 2(2) - 5

3 * 2 = 9 + 4 - 5

3 * 2 = 13 - 5

3 * 2 = 8

The total number of flowers is 8 flowers.

From the information given, there are 5 yellow flowers there are 3 red flowers.

It should be noted that in order to get the total value of the flowers, we have to add them. This will be:

Yellow flowers = 5

Red flowers = 3

Total flowers = Yellow + Red

= 5 + 3

= 8

The total flowers is 8.

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Complete question

There are 5 yellow flowers there are 3 red flowers.how many are in there all togerther

The point on a line that is at an equal distance from either end.

Hence, the equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].

What is midpoint ?

The point on a line that is at an equal distance from either end.

Here, the coordinates of [tex]A(1,-1),P(3,7),Q(\frac{-1}{2},\frac{7}{2})[/tex]

The general formula of the midpoint is

[tex](x_m,y_m)=(\frac{x_1+x_2}{2},\frac{y_1+t_2}{2})[/tex]

The equation of [tex]AP[/tex] is

[tex]AP=(\frac{1+3}{2},\frac{7-1}{2})\\AP=(\frac{4}{2},\frac{6}{2})\\AP=(2,3)\\[/tex]

The equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is

where [tex]AP(2,3),Q(\frac{-1}{2},\frac{7}{2})[/tex].

[tex](AP,Q)=(\frac{2+\frac{-1}{2}}{2},\frac{3+\frac{7}{2}}{2})\\(AP,Q)=(\frac{\frac{4-1}{2}}{2},\frac{\frac{6+7}{2}}{2})\\(AP,Q)=(\frac{\frac{3}{2}}{2},\frac{\frac{13}{2}}{2})\\\\(AP,Q)=(\frac{3}{4},\frac{13}{4})\\[/tex]

Hence, the equation of the line [tex]Q[/tex]  to the midpoint of [tex]AP[/tex] is [tex](AP,Q)=(\frac{3}{4},\frac{13}{4})[/tex].

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Answer:

We may use the logarithm formula,

N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.

EV is end value, SV is start value.

EV is 20000, SV is 12000, interest is 5.6% semi annual

(1+r) is obtained as,

Step-by-step explanation: