how many liters each of a 60% acid solution and a 80% acid solution must be used to produce 80 liters of a 75% acid solution​

Answer:

[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Step-by-step explanation:

Given:

Center of the ellipse is, [tex](h,k)=(-4,-3)[/tex]

Minor axis length is, [tex]2b=6[/tex]

A vertex of the ellipse is at (1, -3)

Now, distance between the center and the vertex is half of the length of the major axis.

Using distance formula for (-4, -3) and (1, -3), we get:

[tex]a=\sqrt{(1+4)^2+(-3+3)^2}=5[/tex]

Therefore, the value of half of major axis is, [tex]a=5[/tex]. Also,

[tex]2b=6\\b=\frac{6}{2}=3[/tex]

Now, equation of an ellipse with center [tex](h,k)[/tex] is given as:

[tex]\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1[/tex]

Plug in [tex]h=-4,k=-3,a=5,b=3[/tex] and determine the equation.

[tex]\frac{(x-(-4))^2}{5^2}+\frac{(y-(-3))^2}{3^2}=1\\\\\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Therefore, the equation of the ellipse is:

[tex]\frac{(x+4)^2}{25}+\frac{(y+3)^2}{9}=1[/tex]

Answer:

[tex]\frac{11}{20}[/tex]

Step-by-step explanation:

Total no. of possible outcome= 100  (from 1 to 100)

total no. of favorable outcome= 60 (50 even and 5 odd perfect square)

Hence PROBABILITY=[tex]\\\frac{55}{100}[/tex]

                                    =[tex]\frac{11}{20}[/tex]

d/dx cos^2(5x^3)

= d/dx [cos(5x^3)]^2

= 2[cos(5x^3)]

= - 2[cos(5x^3)] * sin(5x^3)

= - 2[cos(5x^3)] * sin(5x^3) * 15x^2

= - 30[cos(5x^3)] * sin(5x^3) * x^2

Explanation:

d/dx x^n = nx^(n - 1)

d/dx cos x = - sin x

Chain rule:

d/dx f(g(...w(x))) = f’(g(...w(x))) * g’(...w(x)) * ... * w’(x)

Step-by-step explanation:

f(x) = cos²(5x³)

f(x) = (cos(5x³))²

Use chain rule to find the derivative:

f'(x) = 2 cos(5x³) × -sin(5x³) × 15x²

f'(x) = -30x² sin(5x³) cos(5x³)

If desired, use double angle formula to simplify:

f'(x) = -15x² sin(10x³)

(a) The recursive rule for the sequence is:

     [tex]a_{1}[/tex] = 5 ;  [tex]a_{n}=a_{n-1}+15[/tex]

(b) The explicit rule for the sequence is: [tex]a_{n}=15n-10[/tex]

Step-by-step explanation:

The form of the recursive rule of an arithmetic sequence sequence is

[tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex] , where

The form of the explicit rule of nth term of an arithmetic sequence is

[tex]a_{n}=a+(n-1)d[/tex] , where

∵ The sequence is 5, 20, 35, 50, ….......

∵ 20 - 5 = 15 , 35 - 20 = 15 and 50 - 35 = 15

∴ The sequence is an arithmetic sequence with a common

   difference 15

∵ The form of the recursive rule of the arithmetic sequence is

   [tex]a_{1}[/tex] = first term ; [tex]a_{n}=a_{n-1}+d[/tex]

∵ First term = 5

∵ d = 15

∴ [tex]a_{1}[/tex] = 5 ;  [tex]a_{n}=a_{n-1}+15[/tex]

(a) The recursive rule for the sequence is:

     [tex]a_{1}[/tex] = 5 ;  [tex]a_{n}=a_{n-1}+15[/tex]

∵ The form of the explicit rule of nth term of an arithmetic

   sequence is [tex]a_{n}=a+(n-1)d[/tex]

∵ a = 5 and d = 15

- Substitute these values in the rule

∴ [tex]a_{n}=5+(n-1)15[/tex]

- Simplify the right hand side

∴ [tex]a_{n}=5+15n-15[/tex]

- Add like terms

∴ [tex]a_{n}=15n-10[/tex]

(b) The explicit rule for the sequence is [tex]a_{n}=15n-10[/tex]

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Answer:

Kelan gets 135 Euros.

Step-by-step explanation:

First of all you add up the ratio getting 10, with 10 you divide it from 450 getting 45. Then you multiply 3 (Kelan's Part) by 45 getting your answer. Tell me if this helped, i'd appreciate knowing.

This question is based on simple mathematics. Therefore, the answer is £135.

Given:

Harry, regan and kelan share £450 in the ratio 2 : 5 : 3.

We have to determined the money would kelan get.

According to questions,

First of all, adding  up the ratios.

We get,

2+5+3 = 10

Regan and kelan share £450. So divided £450  by 10, and solve it further.

We get,

[tex]\dfrac{450}{10} = 45[/tex]

Now, multiplying 45 by 3 (Kelan's part).

We get,

[tex]45\times3= 135[/tex]

Therefore, the money that kelan get is £135.

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Answer:

The student is expected to spend 15.4 hours doing homework

Step-by-step explanation:

The scattered plot shows there is a close correlation between the variables. A line of best fit will go through the 'center' of the points. Since we are not required to find an exact line, we'll draw it in red color as shown below

To know the equation of that line, we must take two clear points of it from the graph. We'll pick (28,4) and (4,25)

The equation of a line, given two points (a,b) and (c,d) is

[tex]\displaystyle y-b=\frac{d-b}{c-a}(x-a)[/tex]

Using the selected points

[tex]\displaystyle y-4=\frac{25-4}{4-28}(x-28)[/tex]

Simplifying and computing results, the equation is

[tex]\displaystyle y=-\frac{7}{8}x+\frac{57}{2}[/tex]

Using that equation, we can predict how many hours the students will spend doing homework if they spend 15 hours watching TV

[tex]\displaystyle y=-\frac{7}{8}(15)+\frac{57}{2}[/tex]=15.4 hours

So the student is expected to spend 15.4 hours doing homework

Answer:

4x-14

Step-by-step explanation:

8x-(14+4x)

8x-14-4x

8x-4x-14

4x-14

Answer:

2 transformations

Step-by-step explanation:

1)Reflection

2) Rotation 180 degrees clockwise

Answer:

The number is -84.

Step-by-step explanation:

-x/7-2=10

-x/7=10+2

-x/7=12

-x=12*7

-x=84

x=-84

The cost of slippers is $10.5 after discount.

Step-by-step explanation:

Given,

Price of slippers = $15

Sale = 30%

Amount of discount = 30% of price of slippers

[tex]Amount\ of\ discount=\frac{30}{100}*15\\Amount\ of\ discount=\frac{450}{100}\\Amount\ of\ discount=\$4.5[/tex]

Sale price = Price of slippers - amount of discount

[tex]Sale\ price=15-4.5\\Sale\ price=\$10.5[/tex]

The cost of slippers is $10.5 after discount.

Keywords: percentage, subtraction

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To find the cost of the slippers after the 30% discount, multiply the original price by 30% and subtract the discount from the original price. The cost of the slippers after the discount is $10.50.

To find the cost of the slippers after the 30% discount, first calculate the amount of the discount by multiplying the original price by 30% (or 0.30).

Discount = $15 × 0.30 = $4.50

Next, subtract the discount from the original price to find the sale price:

Sale Price = $15 - $4.50 = $10.50

Therefore, the cost of the slippers after the discount is $10.50.

Answer:

-3

Step-by-step explanation:

Given, f(x)=-4log2(x+3)-6

      So, for domain of f(x) ,we have to find the domain of log2(x+3) as all other things are just numbers which do not affect the domain.

For domain of f(x),    2(x+3) > 0

                    Thus,      x + 3 > 0

                                    x > -3.

So, all real numbers greater than -3 are in the domain of f(x).

You will pay 5% sales tax.

Step-by-step explanation:

Given,

Cost of item = $40

Sales tax = $2

Percent of sales tax = [tex]\frac{Sales\ tax}{Cost\ of\ item}*100[/tex]

[tex]Percent\ of\ sales\ tax=\frac{2}{40}*100\\Percent\ of\ sales\ tax=\frac{200}{40}\\Percent\ of\ sales\ tax=5\%[/tex]

You will pay 5% sales tax.

Keywords: sales tax, division

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The value of z is zero

Step-by-step explanation:

The slope is the steepness of the line.

The formula for slope is given by:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line[/tex]

Here

(x1,y1) = (1,z)

(x2,y2) = (2,8)

So,

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0[/tex]

The value of z is zero

Keywords: slope, Line

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Answer:

The number of textbooks of each type were sold is 134 math and 268 psychology books.

Step-by-step explanation:

Given:

Total number of math and psychology textbooks sold in a week is 402.

Now, let the number of math textbooks sold be [tex]x[/tex].

And, the number of psychology textbooks be [tex]2x[/tex].

According to question:

[tex]x+2x=402[/tex]

[tex]3x=402[/tex]

Dividing both sides by 3 we get:

[tex]x=134[/tex]

So, total number of math textbooks were 134 .

And, total number of psychology textbooks were [tex]2x=2\times 134[/tex]

                                                                                 [tex]=268[/tex].

Therefore, the number of textbooks of each type were sold is 134 math and 268 psychology books.

Answer:

what is the question

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

We have: [tex]$ \frac{18}{4} \times \frac{20}{7} $[/tex]

Simplifying we get: [tex]$ 18 \times \frac{5}{7} $[/tex]

⇒ [tex]$ \frac{90}{17} $[/tex]

This is equal to 5.2 ≅ 5.

So, Option C - 5 is the answer.

Answer:

The proof is given below.

Step-by-step explanation:

Given: ( the correct question and ans is as follow )

sin (x + y) = 3sin ( x - y)

To Prove

tan x = 2 tan y

Proof:

[tex]\sin (x+y) = 3\sin (x-y)[/tex]

Using the identities

[tex]\sin (A+B) = \sin A.\cos B + \cos A.\sin B\\and\\\sin (A-B) = \sin A.\cos B - \cos A.\sin B\\[/tex]

we get

[tex]\sin x.\cos y + \cos x.\sin y = 3(\sin x.\cos y - \cos x.\sin y)\\\sin x.\cos y + \cos x.\sin y = 3\sin x.\cos y - 3\cos x.\sin y[/tex]

Now we will take sin x . cos y to the left hand side and cos x . sin y to the right hand side,we get

[tex]3\sin x.\cos y - \sin x.\cos y = 3\cos x.\sin y +\cos x.\sin y\\2\sin x.\cos y =4\cos x.\sin y\\\sin x.\cos y =2\cos x.\sin y \ \textrm{4 divide by 2}\\ \frac{\sin x}{\cos x} =2\times \frac{\sin y}{\cos y} \\\textrm{we know identity }\\\frac{\sin x}{\cos x} = \tan x\\\frac{\sin y}{\cos y} = \tan y\\\therefore \tan x = 2\tan y\ ...............{PROVED}[/tex]

Answer:

B. 10.2

Step-by-step explanation:

Answer : The value of chord XY is, 10.2 units

Step-by-step explanation :

As we are given that, XY and YZ are congruent.

XY and YZ are congruent by SSA.

The ΔXOY and ΔZOY are congruent triangles.

Side OX = Side OZ           (side)

Side OY = Side OY     (common side)

∠XOY = ∠ZOY                   (angle)

That means, in this two sides and one angle of a triangle are equal to another triangle then the triangles are congruent.

So, Side XY = Side YZ

As we are given :

Chord YZ = 10.2

So, Chord YZ = Chord XY = 10.2

Hence, the value of chord XY is, 10.2 units

Answer:

$4,500

Step-by-step explanation:

4,200e^3(.023)

Answer:

123

Step-by-step explanation:

135 - 12 = 123

The concession stand made $123

Profit and loss are the terms used to identify whether a deal is profitable or not. We use these terms very often in our daily lives. If the selling price is greater than the cost price, then the difference between the selling price and cost price is called profit. If the selling price is less than the cost price, then the difference between the cost price and the selling price is called loss.

When, in a transaction, the selling price is greater than the cost price, it means we earn a profit.

When, in a transaction, the cost price is greater than the selling price, it means we incur a loss.

Given:

profit on saturday = $135

loss on sunday = $12

So,

the total profit concession stand made= $135 + (-$12)

                                                                = $135 - $12

                                                                = $123

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Answer:

$ 929

Step-by-step explanation:

Given: Original price of stay in hotel= $240 per night

           Discount= 25%

           Total taxes and fee = 29%

Now, finding the price of stay for four night.

Using unitary method to solve:

As we know original price of hotel stay per night is $240

∴ Price of four night stay at original price is [tex]240\times 4 = \$ 960[/tex]

Next, 25% discount given on the price of four night stay.

∴ [tex]960 - \frac{25}{100} \times 960 = 960 - 240[/tex]

= [tex]\$ 720[/tex]

∴Price of four night hotel stay after discount is [tex]\$ 720[/tex]

Now, 29% taxes and fees been added to the price.

Price of hotel stay after discount + Taxes paid.

[tex]720 + ( \frac{29}{100} \times 720) = 720 + 209[/tex]

= [tex]\$ 929[/tex]

∴ [tex]\$ 929[/tex] is the price to be paid for four night stay at hotel after discount and taxes.

Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 7) and (x₂, y₂ ) = (4, 6) ← 2 points on the line

m = [tex]\frac{6-7}{4-2}[/tex] = - [tex]\frac{1}{2}[/tex]

Note the line crosses the y- axis at (0, 8) ⇒ c = 8

y = - [tex]\frac{1}{2}[/tex] x + 8 ← equation of line

Answer : The slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex]  and [tex]y=\frac{-1}{2}x+8[/tex] respectively.

Step-by-step explanation :

The general form for the formation of a linear equation is:

[tex](y-y_1)=m\times (x-x_1)[/tex] .............(1)

where,

x and y are the coordinates of x-axis and y-axis respectively.

m is slope of line.

First we have to calculate the slope of line.

Formula used :

[tex]m=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]

Here,

[tex](x_1,y_1)=(2,7)[/tex] and [tex](x_2,y_2)=(4,6)[/tex]

[tex]m=\frac{(6-7)}{4-2)}[/tex]

[tex]m=\frac{-1}{2}[/tex]

Now put the value of slope in equation 1, we get the linear equation.

[tex](y-y_1)=m\times (x-x_1)[/tex]

[tex](y-7)=\frac{-1}{2}\times (x-2)[/tex]

[tex]y-7=\frac{-1}{2}x+1[/tex]

[tex]y=\frac{-1}{2}x+1+7[/tex]

[tex]y=\frac{-1}{2}x+8[/tex]

Thus, the slope of the line and equation of the line is, [tex]\frac{-1}{2}[/tex]  and [tex]y=\frac{-1}{2}x+8[/tex] respectively.

75100 > 34

75100 is greater than 34

Answer:

its <

Step-by-step explanation:

Answer: 12:40

Step-by-step explanation:

Answer:

12:40 PM

Step-by-step explanation:

By the time the plane arrives in Minnesota, the time is already 13:40 or 1:40 PM (eastern time). From eastern time to central time, the time decreases by 1 hour. 1:40 PM - 1 hour is 12:40 PM.

Answer:

Explanation:

The diagram provides the proportion of the heights to the shadows:

From that you are asked (i) to simplify the fraction of the right side to one with whole numbers.

You can do that in two steps by multiplying both numerator and denominator by 10:

You can simplify that fraction if you divide by the greatest common factor of 180 and 150, which is 30:

The second part (ii) asks to find the height of the tree, that is x. To solve for x you can multiply both sides by the denominator of the fraction on the left and then simplify:

[tex]\frac{x}{33}=\frac{6}{5}\\ \\ x=\frac{6\times 33}{5}\\  \\ x=\frac{198}{5}=39.6[/tex]

Thus, the height of the three is 39.6 feet.

a) 5000 represents the initial amount that Sue invested in a money market account

b) The annual percentage rate is 7%

c) Sue will have $7012.76 after 5 years

Step-by-step explanation:

The exponential growth function is [tex]f(t)=P(1+r)^{t}[/tex] , where

Sue invests in a money market account. The balance of the account in dollars after t years can be represented by the function [tex]5000(1.07)^{t}=B[/tex]

∵ The function is [tex]5000(1.07)^{t}=B[/tex]

∵ The form of the exponential growth function is tex]f(t)=P(1+r)^{t}[/tex]

- By comparing the two functions

∴ P = 5000

∵ P is the initial amount

∴ The initial amount is 5000

a) 5000 represents the initial amount that Sue invested in a money market account

∵ [tex](1+r)^{t}=(1.07)^{t}[/tex]

∴ 1 + r = 1.07

- Subtract 1 from both sides

∴ r = 0.07

∵ r is the annual rate in decimal

∵ 0.07 × 100% = 7%

∴ The annual rate is 7%

b) The annual percentage rate is 7%

∵ t = 5

- Substitute the value of t in the function

∴ [tex]5000(1.07)^{5}=B[/tex]

∴ B = 7012.76

c) Sue will have $7012.76 after 5 years

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Answer:

(1, -2).

Step-by-step explanation:

y=-4x+2

y=6x-8

Substitute y = 6x - 8 in the first equation

6x - 8 = -4x + 2

10x = 10

x = 1

So y = 6x - 8

= 6(1) - 8

= -2.

The pair should be (1, -2).

The equation is y=-4x+2 and y=6x-8

here we Substitute y = 6x - 8 in the first equation

So,

6x - 8 = -4x + 2

10x = 10

x = 1

Now

y = 6x - 8

= 6(1) - 8

= -2.

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Answer:

Look the square root up on the internet.

Step-by-step explanation: