A tank contains 8000 liters of a solution that is 40% acid. How much water should be added to make a solution that is 30% acid?

Step-by-step explanation:

The pythagorian theorem:

a²+b² = c²

now let a be the side of the red triangle and b the side of the orange one

so a² is the area of the red triangle and b² is the area of the orange one

Let c be the side of the blue rectangle

so c² is the area of it

then what we concluded is right

Answer:

10

Step-by-step explanation:

f(x)=-x^2+6x+1

This is a parabola that opens downward( the - coefficient of x^2)

The maximumx is at the vertex

The x coordinate is at

-b/2a  where ax^2 + bx +c  a =-1  b=6 c=1

-6/(2*-1)

-6/-2 = 3

The x coordinate of the vertex is 3

f(3) = - (3)^2 +6(3)=1

    = -9+18+1

    = 10

The vertex is ( 3,10)

The maximum value is 10

Answer:

[tex]10[/tex]

Step-by-step explanation:

[tex]f(x)=-x^2+6x+1[/tex]

x coordinate:

[tex]\frac{-b}{2a}[/tex]

[tex]a=-1\\b=6[/tex]

[tex]\frac{-6}{2(-1)} \\\frac{-6}{-2}\\ =3[/tex]

y-coordinate:

[tex]f(3)=-(3)^2+6(3)+1\\f(3)=-9+18+1\\f(3)=10[/tex]

Answer:

x=-15/2 and x=1

x=6 and x=3/4

Step-by-step explanation:

You have the following equations:

[tex]\frac{4x-3}{x+2}=\frac{2x}{x+5}[/tex]

[tex]\frac{2}{x-2}+\frac{3}{x}-\frac{9}{x+3}[/tex]

To solve both equations you can first multiply by the m.c.m of the denominators, and then solve for x, just as follow:

first equation:

[tex][\frac{4x-3}{x+2}=\frac{2x}{x+5}](x+2)(x+5)\\\\(4x-3)(x+5)=2x(x+2)\\\\4x(x)+4x(5)-3(x)-3(5)=2x(x)+2x(2)\\\\4x^2+20x-3x-15=2x^2+4x\\\\4x^2-2x^2+20x-3x-4x-15=0\\\\2x^2+13x-15=0[/tex]

In this case you use the quadratic formula:

[tex]x_{1,2}=\frac{-13\pm \sqrt{(13)^2-4(2)(-15)}}{2(2)}\\\\x_{1,2}=\frac{-13 \pm 17}{4}\\\\x_1=-\frac{15}{2}\\\\x_2=1[/tex]

Then, for the first equation the solutions are x=-15/2 and x=1

second equation:

[tex][\frac{2}{x-2}+\frac{3}{x}=\frac{9}{x+3}]x(x-2)(x+3)\\\\2x(x+3)+3(x-2)(x+3)=9x(x-2)\\\\2x^2+6x+3(x^2+3x-2x-6)=9x^2-18x\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\2x^2+6x+3x^2+3x-18-9x^2+18x=0\\\\-4x^2+27x-18=0[/tex]

Again, you use the quadratic formula:

[tex]x_{1,2}=\frac{-27\pm \sqrt{(27)^2-4(-4)(-18)}}{2(-4)}\\\\x_{1,2}=\frac{-27\pm 21}{-8}\\\\x_1=6\\\\x_2=\frac{3}{4}[/tex]

Then, the solutions for the second equation are x=6 and x=3/4

Answer:

A,C,D

Step-by-step explanation:

When b=0, there is a proportional relationship.

The slope in y=mx+b is the value next to x.

Using RISE/RUN when there is a change of 3 units in x, there is a change of 2 units in y.

Answer:

1.33,3.667

Step-by-step explanation:

Use y=mx+b for second system

which is y=5/2x+7

Now use substitution,graph, or elimination method.

Answer:

371

Step-by-step explanation:

According to the given situation the calculation of degrees of freedom for this single-sample t test is shown below:-

Degrees of freedom is N - 1

Where N represents the number of Men

Now we will put the values into the above formula.

= 372 - 1

= 371

Therefore for calculating the degree of freedom we simply applied the above formula.

The equation of line which is perpendicular to the line FG is

y = -2x -3.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

[tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]

If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].

The slope intercept form of the line is given by  y = mx + b

Where, m is the slope of a line.

According to the given question

We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.

Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]

⇒ The slope of the line which is parallel to line FG is -2

Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .

Hence, the equation of line which is perpendicular to the line FG is

y = -2x -3.

Learn more about the equation of a perpendicular line here:

https://brainly.com/question/20712656

#SPJ2

Answer:

Step-by-step explanation:

Please write this as x^2 + 5.  

Roots are ±i√5.

The corresponding factors of x^2 + 5 are (x + i√5) and (x - i√5)

Answer:

12 weeks

Step-by-step explanation:

To solve this, all you need to do is divided 24 pieces by the two he learns per week. You'll then find it will take him 12 weeks

Answer:

39858075

Step-by-step explanation:

Hello,

One basic way to see it is to compute the values.

   75 = 25 * 3

   225 = 75 * 3

   675 = 225 * 3

   etc ...

We can notice that this is multiplied by 3 every 10 years so we can compute as below.

year         population

1970 25

1980 75

1990 225

2000 675

2010 2025

2020 6075

2030 18225

2040 54675

2050 164025

2060 492075

2070 1476225

2080 4428675

2090 13286025

2100 39858075

So the correct answer is 39858075

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

60 miles

Step-by-step explanation:

Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?

Statement 1. Brian’s walking speed is twice the difference between Ashok’s walking speed and his own

Statement 2. If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds

Solution

A. Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.

Let Brian speed=b

Ashok speed=a

Brian's walking speed=2(a-b)

b=2(a-b)

Divide both sides by 2

b/2=a-b

Ashok catches up in (time)= distance /( relative rate

=30/(a-b)

=30/(b/2)

=30÷b/2

=30*2/b

=60/b.

By that time Brian will cover a distance of

distance=rate*time

=b*60/b

=2(a-b)*60/2(a-b)

=60 miles

(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.

5a=3(a+b)

5a=3a+3b

5a-3a=3b

2a=3b

Answer:

15

Step-by-step explanation:

Answer:

21.213

Step-by-step explanation:

Answer:

2, 3 , 5, 7

Step-by-step explanation:

2(x - 2)/3 < (x + 1)/2 < 3(5x + 6)/4

Considering:

    2(x - 2)/3 < (x + 1)/2

<=>(2x - 4)/3 < (x + 1)/2

<=> (2x - 4)*2 < (x + 1)*3

<=> 4x - 8 < 3x + 3

<=> 4x - 3x < 8 + 3

<=> x < 11

Considering:

     (x + 1)/2 < 3(5x + 6)/4

<=>(x + 1)/2 < (15x + 18)/4

<=>(x + 1)*4 < (15x + 18)*2

<=> 4x + 4 < 30x + 36

<=> 4x - 30x < 36 - 4

<=> -26x < 32

<=> 26x > -32

<=> x > -32/26

=> -32/26 < x < 11

The prime numbers satisfy the above inequalities: 2, 3 , 5, 7

Answer:

E

Step-by-step explanation:

i guess the dotted lines outline a square

so get the area of the square which is 6×6=36

then don't focus on the shaded part but unshaded you'll see two right angled triangles

[tex]a = 1 \div2b \times h[/tex]

you will get a total for both as 21

then get the area of the square 36-21=15

so the area becomes 15

Answer:

Money in her purse is Rs. 500.

Step-by-step explanation:

Let the money in her purse = Rs. [tex]x\\[/tex]

Let the money in her Money box = Rs. [tex]y[/tex]

As per question statement,

[tex]2x+y=1700[/tex]  ........ (1)

[tex]3x+y=2200[/tex] ....... (2)

To find: Money in her purse = ? i.e. [tex]x=?[/tex]

Let us solve for [tex]x[/tex] using the two linear equations.

We can use substitution method here i.e. find value of one variable from one equation and then substitute that value in other equation.

Using equation (1), we get the value of [tex]y[/tex] as follows:

[tex]y=1700-2x[/tex]

Now, let us put this value of y in equation (2) to find the value of [tex]x[/tex]:

[tex]3x+1700-2x=2200\\\Rightarrow x+1700 = 2200\\\Rightarrow x=2200-1700\\\Rightarrow x = Rs.\ 500[/tex]

Money in her purse is Rs. 500.

Answer:

A = 49[tex]\pi[/tex]

Step-by-step explanation:

First, we need to find the length of the wire. We can calculate this because we are given the area of the square, so we can work backwards.

Use the area formula and plug in the numbers:

A = s²

121 = s²

11 = s

We can calculate the length of the wire by multiplying 11 by 4, which is 44.

Now, we know the circumference of the circle is 44 units because that is how long the wire is.

We can work backwards again to find the radius, using the circumference formula:

C = 2[tex]\pi[/tex]r

44 = 2[tex]\pi[/tex]r

22 = [tex]\pi[/tex]r

7 = r

Now, we can find the area of the circle:

A = [tex]\pi[/tex]r²

A = [tex]\pi[/tex](7)²

A = 49[tex]\pi[/tex]

Answer: Griffin charge $79.854 to his credit card when he bought the sneakers.

Step-by-step explanation:

Griffin ordered a pair of sneakers online.

Value of each credit point = 1 cent

Then , value of 16 credit points = 16 cents = $0.16 [1$ = 100 cents]

Cost of shoes = Rs $80

Charge to credit card = (Cost of shoes) - (Value of 16 credit points)

= $(80-0.16)

= $79.84

Hence, Griffin charge $79.854 to his credit card when he bought the sneakers.

Answer:

h = V3B

Step-by-step explanation:

V = 1/3B · h

Divide volume by 1/3 B to get h by itself

V/1/3B = V3B

Answer:

The shortest altitude = 8 cm

Step-by-step explanation:

Where we have the sides given by

15 cm, 17 cm, 8 cm

From cosine rule, we have;

a² = b² + c² - 2×b×c×cos(A)

We have

For the side 15 cm,

15² = 17² + 8² - 2×17×8 cos A

-388 = -612×cos×A

A = 61.93°

17² = 15² + 8² - 2×15×8 ×cos B

0 = -240·cos B

B = 90°

Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm

Answer:

5

Step-by-step explanation:

The initial value is when x=0

When x=0, y =5

The initial value is 5

Answer:

[tex]7 < x < 37[/tex] -- Triangle 1

[tex]6.5 < x < 19.9[/tex] -- Triangle 2

[tex]22 < x < 46[/tex] -- Triangle 3

[tex]21 < x < 67[/tex] -- Triangle 4

Step-by-Step Explanation:

Given

2 sides of a triangle

1. 22 and 15

2. 13.2 and 6.7

3. 34 and 12

4. 23 and 44

Required

Determine the range of the third side in the above triangles

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]22 + x > 15[/tex]

[tex]22 + 15 > x[/tex]

[tex]15 + x > 22[/tex]

Solving

[tex]22 + x > 15[/tex]

Make x the subject of formula

[tex]x > 15 - 22[/tex]

[tex]x > -7[/tex]

Solving

[tex]22 + 15 > x[/tex]

[tex]37 > x[/tex]

Solving

[tex]15 + x > 22[/tex]

Make x the subject of formula

[tex]x > 22 - 15[/tex]

[tex]x > 7[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]37 > x[/tex] and [tex]x > 7[/tex]

Rewrite both inequalities

[tex]x < 37[/tex] and [tex]7 < x[/tex]

Combine the two inequalities

[tex]7 < x < 37[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]13.2 + x > 6.7[/tex]

[tex]13.2 + 6.7 > x[/tex]

[tex]6.7 + x > 13.2[/tex]

Solving

[tex]13.2 + x > 6.7[/tex]

Make x the subject of formula

[tex]x > 6.7 - 13.2[/tex]

[tex]x > -6.5[/tex]

Solving

[tex]13.2 + 6.7 > x[/tex]

[tex]19.9 > x[/tex]

Solving

[tex]6.7 + x > 13.2[/tex]

Make x the subject of formula

[tex]x > 13.2 - 6.7[/tex]

[tex]x > 6.5[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]19.9 > x[/tex] and [tex]x > 6.5[/tex]

Rewrite both inequalities

[tex]x < 19.9[/tex] and [tex]6.5 < x[/tex]

Combine the two inequalities

[tex]6.5 < x < 19.9[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]34 + x > 12[/tex]

[tex]34 + 12 > x[/tex]

[tex]12 + x > 34[/tex]

Solving

[tex]34 + x > 12[/tex]

Make x the subject of formula

[tex]x > 12 - 34[/tex]

[tex]x > -22[/tex]

Solving

[tex]34 + 12 > x[/tex]

[tex]46 > x[/tex]

Solving

[tex]12 + x > 34[/tex]

Make x the subject of formula

[tex]x > 34 - 12[/tex]

[tex]x > 22[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]46 > x[/tex] and [tex]x > 22[/tex]

Rewrite both inequalities

[tex]x < 46[/tex] and [tex]22 < x[/tex]

Combine the two inequalities

[tex]22 < x < 46[/tex]

Represent the third side with x

We'll make use of the following conditions to calculate  the range of the third side;

[tex]23 + x > 44[/tex]

[tex]23 + 44 > x[/tex]

[tex]23 + x > 44[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 23 - 44[/tex]

[tex]x > -21[/tex]

Solving

[tex]23 + 44 > x[/tex]

[tex]67 > x[/tex]

Solving

[tex]23 + x > 44[/tex]

Make x the subject of formula

[tex]x > 44 - 23[/tex]

[tex]x > 21[/tex]

The next step is to dismiss the inequality with negative digit; So, we're left with

[tex]67 > x[/tex] and [tex]x > 21[/tex]

Rewrite both inequalities

[tex]x < 67[/tex] and [tex]21 < x[/tex]

Combine the two inequalities

[tex]21 < x < 67[/tex]

Answer: The number of points added for r right answers is 12r. The number of points taken away for w wrong answers is 4w, so Olga's total points will be

... 12r -4w

To win, she needs this number to be more than 400. Your inequality is ...

... 12r -4w > 400

Answer:12r -4w > 400

Step-by-step explanation:

Answer:

The correct option is;

y minus x = negative 4

(y - x = -4)

Step-by-step explanation:

Given that the line y  = x - 4 of the graph passes through the points (0, -4) and (4, 0)

Comparing with the general equation of a straight line, y = m·x + c, where m is the slope and c is the y-intercept gives;

The slope of the equation y = x - 4 = 1

The y-intercept of the equation y = x - 4 = -4

Two equations will have an infinite number of solutions when they are on the same line, that is having the same slope and intercept, we check for the slope and the intercept of the given options as follows;

For y - x = -4, we have;

y = x - 4 which is the same as the given equation and both equations will have an infinite number of solutions

For y - x = -2 we have;

y = x - 2

The slope is the same as the given equation but the intercept is different giving no solution

For y - 4 = x, we have;

y = x + 4

The slope is the same as the given equation but the intercept is different giving no solution

For y + 4x = 1, we have;

y = 1 - 4x

The slope and  intercept are different giving one solution.

Answer:

y - x = -4

Step-by-step explanation:

Answer: 380

Step-by-step explanation:

Total number of players = 20

To select a captain and a vice captain :

One captain from a total of 20 players :

20 combination 1 = 20C1 = 20 ways

Total number of players left after selecting a captain = 20 - 1 = 19

Number of players left from which to select a vice captain = 19

Therefore, one vice captain from a group of 19 players :

19 combination 1 = 19C1 = 19 ways

Therefore no of different possible ways to select a captain and a vice captain :

20C1 × 19C1 = 20 × 19 = 380 Ways

Answer:

Hey there!

Discrete Data is the number of friends you invited to your last birthday party.

Hope this helps :)

Answer:

a) The number of friends you invited to your last party.

Step-by-step explanation:

Let’s take a step back what is discrete, and what continuous?

Discrete

This is the type of data with certain whole numbers not 2.36 only 2 or 3.

Continuous

This is the data being specific like 1.373.

So a)

The is discrete because you can only have like 5 friends not 7.49 friends.

b)

This is continuous because height can be 5.26 feet.

c)

Time is continuous because there can be 4.3739 minutes.

d)

Weight is also continuous it can be 6339.373 pounds.

Answer:

19008

Step-by-step explanation:

550 is equal to 11 multiplied by 50.

1. Solve for multiples of 11 between 550 and 850

11 · 51 = 561

11 · 52 = 572

11 · 53 = 583

11 · 54 = 594

11 · 55 = 605

11 · 56 = 616

11 · 57 = 627

11 · 58 = 638

11 · 59 = 649

11 · 60 = 660

11 · 61 = 671

11 · 62 = 682

11 · 63 = 693

11 · 64 = 704

11 · 65 = 715

11 · 66 = 726

11 · 67 = 737

11 · 68 = 748

11 · 69 = 759

11 · 70 = 770

11 · 71 = 781

11 · 72 = 792

11 · 73 = 803

11 · 74 = 814

11 · 75 = 825

11 · 76 = 836

11 · 77 = 847

2. Add the products together

= 19008

Answer:

77%

Step-by-step explanation:

Given the following :

Probability of winning both games = 50%

Probability of winning just the first game = 65%

Let the probability of winning the ;

First game = p(A) = 65%

Second game = p(B)

Both games = p(A and B) = 50%

What is the probability that the team will win the 2nd game given that they have already won the first game

The above question is a conditional probability question :

Probability of winning the second Given that they've already won the first = p(B | A)

p(B | A) = (A and B) / p(A)

p(B | A) = 50% / 65%

p(B | A) = 0.5 / 0.65

p(B | A) = 0.7692307

= 76.9% = 77%

Answer:

Below

Step-by-step explanation:

● a^(-2) *b^3

●(1/a^2) *b^3

● b^3 / a^2

Answer:

-1/3

Step-by-step explanation:

The slope of the line can be found by

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

    = ( 7-8)/(5-2)

    = -1/3

Answer:

-1/3.

Step-by-step explanation:

The slope can be found by doing the rise over the run.

In this case, the rise is 8 - 7 = 1.

The run is 2 - 5 = -3.

So, the slope is 1 / -3 = -1/3.

Hope this helps!