A pool takes 3,185 gallons to fill. After 2.5 hours the pool is filled with 1,625 gallons how long will it take to fill the whole thing

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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sin^-1(-1/2) enter directly into a calculator and you'll find your answer

Answer:

(C.) 5/13

Step-by-step explanation:

The sine proportion is opposite / hypotenuse

Given the reference angle, the side measuring 5 units is the opposite side and the side measuring 13 units (and opposite of the right angle) is the hypotenuse

Thus, sine is 5/13

A- the area of the plot as a function of x. is 6 x^2 +10x-5

B- the perimeter of the plot as a function of x is 10x+8

A rectangle plot of land has a width of 3x+5 feet,

and a length of 2x-1 feet.

A) the area of the plot as a function of x is given by

A= length * width

  = ( 2x-1) * ( 3x+5)

  =6 x^2 +10x-5

B) the perimeter of the plot as a function of x

P = 2( l+ W)

  = 2 (( 2x-1) +( 3x+5))

  = 2( 5x +4)

  = 10x +8

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Answer:

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

or log4(16x^6)

Step-by-step explanation:

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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Answer:

(9,1), Z(5,1)

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer 10.5

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 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 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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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 probability that the proportion of the sample who are iphone users is between 45% and 50% be 22.87%.

The probability that more than 50% of americans are iphone users be 11.12%.

(a)We know, p = 0.47 and n = 100. First, we should check our conditions for the sampling distribution of the sample proportion.

np = (100)(0.47) = 47 and n(1 - p) = (100)(1 - 0.47) = 53

Since, X will have a sampling distribution that is approximately normal with mean = 0.47

and

standard deviation =  √(0.47)(0.53)/100 ≈ 0.05

P(0.45<X<0.50) = P((0.45 - 0.47)/0.05 < Z < (0.50-0.47)/0.05)

P(0.45<X<0.50)  ≈ 0.2287

Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 22.87% chance that we would see a sample proportion between 45% and 50% when the sample size is 100.

(b) Now, p = 0.47 and n = 50.

np = (50)(0.47) = 23.5 and n(1 - p) = (50)(1 - 0.47) = 26.5

Since, X will have a sampling distribution that is approximately normal with mean = 0.47

and

standard deviation =  √(0.47)(26.5)/50 ≈ 0.25

P(X>0.50) = P(Z > (0.50-0.47)/0.25)

P(X>0.50)  ≈ 0.1112

Therefore, if the true proportion of Americans who own an iPhone is 47%, then there would be a 11.12% chance that we would see a sample proportion more than 50% when the sample size is 50.

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Answer:

pick any two points

im going to chose (1,3) and (3,7)

so the equation y2-y1/x2-x1

1 = x1

3=y1

3=x2

7=y2

so 7-3/3-1 is 4/2

which is 2

Answer:

(-11/24)

Step-by-step explanation:

  3         5

------- - -------

  8         6

 3(3)    5(4)

------- - -------

 8(3)     6(4)

  9        20       - 11

------- - ------- = -------

  24      24        24

I hope this helps!

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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The vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.

From the graph:

vertex:

The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry.

here vertex = (-2,2)

Axis of symmetry:

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric.

x = -2.

Parabola:

It is clearly visible that the parabola is facing downward so it is a downward parabola.

Therefore the vertex is (-2,2), axis of symmetry is x = -2 and the parabola is downward.

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The probability that the second ball drawn is a purple ball  is (e) 0.5833

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

Green balls = 10

Purple balls = 14

This means that the total number of balls is

Total = 10 + 14

Evaluate the equation

So, we have

Total = 24

From the question, we understand that the ball is replaced

So, the probability that the second ball is purple ie

P(second purple) = purple/total

This gives

P(second purple) = 14/24

Evaluate

P(second purple) = 0.5833

Hence, the probability is (e) 0.5833

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The empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.

For the given question.

Therefore, it follows that we are doing an experimental calculation based on the observation whether George will indeed be able to stand again the following time.

empirical probability = 3/146

Thus, the empirical likelihood that George can stand up on his own the very next time Angie knocks him over would be 3/146.

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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 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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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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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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y≤-3x+4 has lesser than or equal to symbol so we shade the below line.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Relationship between two expressions or values that are not equal to each other is called 'inequality.

y≤-3x+4 is the given inequality.

The sign of the inequality will let you know which half-plane to shade. If the symbol ≥ or > is used, shade above the line. If the symbol ≤ or < is used shade below the line.

In the inequality we have lesser than or equal to symbol so we shade the below line.

Hence, y≤-3x+4 has lesser than or equal to symbol so we shade the below line.

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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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Answer:

140

Step-by-step explanation:

2x+5x+40=180

7x+40=180

7x=140

x=20

5x+40=BCD

5(20)+40

100+40

140

Answer:  

150 marks

Step-by-step explanation:

Every meter has 5 marks.

30 meters × 5 marks = 150 marks

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:

D

Step-by-step explanation: