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Let [tex]x,y,z[/tex] denote the amounts (in liters) of the 20%, 30%, and 60% solutions used in the mixture, respectively.

The chemist wants to end up with 72 L of solution, so

[tex]x+y+z=72[/tex]

while using twice as much of the 60% solution as the 30% solution, so

[tex]z = 2y[/tex]

The mixture needs to have a concentration of 35%, so that it contains 0.35•75 = 26.25 L of pure acid. For each liter of acid solution with concentration [tex]c\%[/tex], there is a contribution of [tex]\frac c{100}[/tex] liters of pure acid. This means

[tex]0.20x + 0.30y + 0.60z = 26.25[/tex]

Substitute [tex]z=2y[/tex] into the total volume and acid volume equations.

[tex]\begin{cases}x+3y = 72 \\ 0.20x + 1.50y = 26.25\end{cases}[/tex]

Solve for [tex]x[/tex] and [tex]y[/tex]. Multiply both sides of the second equation by 5 to get

[tex]\begin{cases}x+3y = 72 \\ x + 7.50y = 131.25\end{cases}[/tex]

By elimination,

[tex](x+3y) - (x+7.50y) = 72 - 131.25 \implies -4.50y = -59.25 \implies \boxed{y=\dfrac{79}6} \approx 13.17[/tex]

so that

[tex]x+3\cdot\dfrac{79}6 = 72 \implies x = \boxed{\dfrac{65}2} = 32.5[/tex]

and

[tex]z=2\cdot\dfrac{79}6 = \boxed{\dfrac{79}3} \approx 26.33[/tex]

Answer:

x² + y² + 8x - 8y + 7 = 0

Step-by-step explanation:

Formula: (x - a)² + (y - b)²= r²

where,

a = -4

b = 4

Substitute a and b

( x - (-4))² + (y - 4)² = 5²

(x + 4)² + (y - 4)² = 25

Open Bracket( )

(x + 4) (x + 4) = x² + 4x + 4x + 16

(y - 4) (y - 4) = y² - 4y - 4y + 16

x² + 4x + 4x + 16 + y² - 4y - 4y + 16= 25

Collect Like Terms

x² + y² + 8x - 8y + 16 + 16 - 25 = 0

x² + y² + 8x - 8y + 7 = 0

Therefore,

x² + y² + 8x - 8y + 7 = 0

Is The Equation Of The Given Circle.

0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out. This can be obtained by using the formula for probability.

Probability is the chance of occurrence of an event.

⇒ The formula for finding probability,

Probability = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Here it is given in the question that,

Therefore by using the formula of probability we get,

⇒ Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ outcomes}[/tex]

Probability (Junior Athletics being sold out) = [tex]\frac{Number\ of\ events\ sold\ out}{Total\ number\ of\ events}[/tex]

Probability (Junior Athletics being sold out) = 5/7

⇒ Probability (Junior Athletics being sold out) = 0.7

Hence 0.7 is the new probability of the event being sold out given that total number of events is 7 and 5 events are sold out.

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Answer:

5

Step-by-step explanation:

3 x |12 - x| - 4

3 x |12 - 15| - 4

3 x 3 - 4

9 - 4

5

We can write the integration domain as

[tex]D = \left\{(x,y) \mid -1 \le y \le 1 \text{ and } 2y-2 \le x \le -y+1\right\}[/tex]

so that the integral is

[tex]\displaystyle \iint_D -\sin(y+x) \, dA = \int_{-1}^1 \int_{2y-2}^{-y+1} -\sin(y+x) \, dx \, dy[/tex]

Compute the integral with respect to [tex]x[/tex].

[tex]\displaystyle \int_{2y-2}^{-y+1} -\sin(y+x) \, dx = \cos(y+x)\bigg|_{x=2y-2}^{x=-y+1} \\\\ ~~~~~~~~ = \cos(y+(2y-2)) - \cos(y+(-y+1)) \\\\ ~~~~~~~~ = \cos(3y-2) - \cos(1)[/tex]

Compute the remaining integral.

[tex]\displaystyle \int_{-1}^1 (\cos(3y-2) - \cos(1)) \, dy = \left(\frac13 \sin(3y-2) - \cos(1) y\right) \bigg|_{y=-1}^{y=1} \\\\ ~~~~~~~~ = \left(\frac13 \sin(3-2) - \cos(1)\right) - \left(\frac13 \sin(-3-2) + \cos(1)\right) \\\\ ~~~~~~~~ = \boxed{\frac13 \sin(1) - 2 \cos(1) + \frac13 \sin(5)}[/tex]

Answer:

(3+3) x (3+1)

Step-by-step explanation:

nice

We have give 4 numbers that are 1,3,3,3. we have to apply operations on it to make it 24.

» (1 + 3) × (3 + 3)

» (4) × (6)

» 24

Here's our answer..!!

hope this helps

by

aman10we

The value of x after solving this equation is 2

Polynomial is made up of two terms, namely Poly (meaning “many”) and Nominal (meaning “terms.”). A polynomial is an expression composed of variables, constants, and exponents, combined using mathematical operations such as addition, subtraction, multiplication, and division (No division operation by a variable). Based on the number of terms present in the expression, it is classified as monomial, binomial, and trinomial. For example P(x) = x2-5x+11

Given here, the equation as : (4x - 5)^4 = 81.​

(4x - 5)^4 = 3⁴.​

4x - 5    = 3

      x     = 2

Hence, the value of x is equal to 2

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So, making x subject of the formula, x = [m - 2pt³ ±√(m²  - 4pt²m)]/{2t⁵}

Since p = √(mx/t) - t²x

So, p + t²x = √(mx/t)

Squaring both sides, we have

(p + t²x)² = [√(mx/t)]²

p² + 2pt²x + t⁴x² = mx/t

Multiplying through by t,we have

(p² + 2pt²x + t⁴x²)t = mx/t × t

p²t + 2pt³x + t⁵x² = mx

p²t + 2pt³x + t⁵x² - mx = 0

t⁵x² + 2pt³x - mx + p²t = 0

t⁵x² + (2pt³ - m)x + p²t = 0

Using the quadratic formula, we find x.

[tex]x = \frac{-b +/-\sqrt{b^{2} - 4ac} }{2a}[/tex]

where

Substituting the values of the variables into the equation, we have

[tex]x = \frac{-(2pt^{3} - m) +/-\sqrt{(2pt^{3} - m)^{2} - 4(t^{5})(p^{2}t) } }{2t^{5} }\\= \frac{-(2pt^{3} - m) +/-\sqrt{4p^{2} t^{6} - 4pt^{2}m + m^{2} - 4p^{2}t^{6} } }{2t^{5}}\\= \frac{-(2pt^{3} - m) +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}\\= \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

So, making x subject of the formula,  [tex]x = \frac{m - 2pt^{3} +/-\sqrt{m^{2} - 4pt^{2}m } }{2t^{5}}[/tex]

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Answer: [tex]\frac{10\pi}{3}[/tex] m

Step-by-step explanation:

[tex](2)(\pi)(4) \left(\frac{150}{360} \right)=\frac{10\pi}{3}[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

The side opposite to the largest angle is the longest side of a triangle.

[tex] \qquad \large \sf {Conclusion} : [/tex]

hence, we can conclude that longest side is e

( since it's opposite angle is the largest, i.e 86° )

Answer: -3/7

Step-by-step explanation:

The first step is to find the slope of the line

y = mx + c where m is the slope of the line
Rearrange the equation and we get

3y = 7x + 7
y = 7x/3 + 7/3

So the slope of the line 7x - 3y = -7 is 7/3

There is another rule that states: The product of the slopes of two lines perpendicular to each other is -1

So, the slope of the line perpendicular to 7x - 3y = -7 is -1/(7/3) = -3/7

Answer: 5 times

Step-by-step explanation: The distance from his house to school and back is 0.4 km. Since he traveled 2km in a week, we have to divide 2 by0.4. 0.4x5 = 2 so he went to school 5 times a week.

Answer:

no solution

Step-by-step explanation:

16x - 32y = 27 → (1)

8x - 16 = 16y ( subtract 16y from both sides )

8x - 16 - 16y = 0 ( add 16 to both sides )

8x - 16y = 16 → (2)

multiply (2) by - 2 and add to (1)

- 16x + 32y = - 32 → (3)

add (1) and (3) term by term

0 + 0 = - 5

0 = - 5 ← not possible

this indicates the system has no solution

(b)

the solution to a system is the point of intersection of the 2 lines

since there is no solution, no point of intersection, then

this indicates the lines are parallel and never intersect

Answer:

a) no solution

b) the two lines never intersect

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases} 16x-32y=27\\8x-16=16y \end{cases}[/tex]

To solve by linear combination (elimination):

Step 1

Write both equations in standard form: Ax + By = C

[tex]\implies 16x-32y=27[/tex]

[tex]\implies 8x-16y=16[/tex]

Step 2

Multiply one (or both) of the equations by a suitable number so that both equations have the same coefficient for one of the variables:

[tex]\implies 16x-32y=27[/tex]

[tex]\implies 2(8x-16y=16) \implies 16x-32y=32[/tex]

Step 3

Subtract one of the equations from the other to eliminate one of the variables:

[tex]\begin{array}{l r l}& 16x-32y & = 32\\- & 16x-32y & = 27\\\cline{1-3}& 0 & =\:\: 5\end{array}[/tex]

Therefore, as 0 ≠ 5, there is no solution to this system of equations.

Part (b)

The solution to a system of equations is the point(s) of intersection.

As there is no solution to the given system of equations, this tells us that the two lines never intersect.

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The expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.

The expression is:

6²- (3² + 2²)

The shaded area:

Shaded area=6²- (3² + 2²)

Shaded area=36-(9+4)

Shaded area=36-13

Shaded area=23 square inches

Therefore the expression involving exponents to represent the shaded area in square inches of the diagram is: 6²- (3² + 2²). The shaded area in squares inches of the diagram is: 23 square inches.

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The values of h and r to maximize the volume are r = 4 and h = 2

From the question, we have the following equation

2r + 2h = 12

Divide through by 2

r + h = 6

Subtract r from both sides of the equation

h = 6 - r

Hence, the formula for h in terms of r is h = 6 - r

The volume of a cylinder is

V = πr²h

Substitute h = 6 - r in the above equation

V = πr²(6 - r)

Hence, the function V(r) is V = πr²(6 - r)

V = πr²(6 - r)

Expand

V = 6πr² - πr³

Integrate

V' = 12πr - 3πr²

Set to 0

12πr - 3πr² = 0

Divide through by 3π

4r - r² = 0

Factor out r

r(4 - r) = 0

Divide through by 4

4 - r = 0

Solve for r

r = 4

Hence, the single critical point on the interval [0. 6] is r = 4

We have:

V = πr²(6 - r)

and

V' = 12πr - 3πr²

Determine the second derivative

V'' = 12π - 6πr

Set r = 4

V'' = 12π - 6π* 4

Evaluate the product

V'' = 12π - 24π

Evaluate the difference

V'' = -12π

Because V'' is negative, then the single critical point is a global maximum

We have

r = 4  and h = 6 - r

Substitute r = 4  in h = 6 - r

h = 6 - 4

Evaluate

h = 2

Hence, the values of h and r to maximize the volume are r = 4 and h = 2

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a. Line AB and line BC are not congruent because their distance of separation are not equal

b. Line AC and line BD are not congruent because their distance of separation are not equal

From the number line drawn, we have the following deductions;

Line AB = -5 to -2 = 3

Line BC = -2 to 0 = 2

Line AC = -5 to 0 = 5

Line AD = -5 to 5 = 10

Line BD = -2 to 5 = 7

We can see that;

a. Line AB and line BC are not congruent because their distance of separation are not equal

b. Line AC and line BD are not congruent because their distance of separation are not equal

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Answer: Rational, Irrational, Rational, Natural, Natural, Integer

Step-by-step explanation:

-4.2 is a rational number as it can be converted into a fraction

3√5 is an irrational number as it can't be converted into a fraction

5/3 is a rational number as it is a fraction

9 is a natural number as it is a positive whole number

√16 is a natural number as despite the square root, √16 is 4 which is a natural number

-8/2 is an integer as -8/2 is -4 which is a negative whole number

Answer:

Area under the graph = 6 sq.units

I've shown the complete calculation over the attached page

Angle HEJ measures 15 degrees.

Answer:

7x + 2.25y = 440

Step-by-step explanation:

Ashlee sells lunches for $7.00 and drinks for $2.25.

One busy Saturday, Ashlee sold $440.00 worth of lunches and drinks.

The number of lunches sold is x.

The number of drinks sold is y.

The appropriate equation will be:

= (7 × x) + (2.25 × y)

7x + 2.25y = 440

Using it's concept, the percentage of employees with 8 or more years at the company reported that email is their preferred method of communication is:

D. 44.79%.

The percentage of an amount a over a total amount b is given by a multiplied by 100% and divided by b, that is:

P = a/b x 100%

In this problem, there are 96 employees with 8 or more years of experience, of which 43 prefer email, hence the percentage is:

P = 43/96 x 100% = 44.79%.

Hence option D is correct.

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Check the picture below.

[tex]sin(EDG )=\cfrac{\stackrel{opposite}{10}}{\underset{hypotenuse}{10\sqrt{3}}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\implies sin(EDG )=\cfrac{1}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{sin(EDG )=\cfrac{\sqrt{3}}{\sqrt{3^2}}\implies sin(EDG )=\cfrac{\sqrt{3}}{3}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos(EDG )=\cfrac{\stackrel{adjacent}{10\sqrt{2}}}{\underset{hypotenuse}{10\sqrt{3}}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\implies cos(EDG )=\cfrac{\sqrt{2}}{\sqrt{3}}\cdot \cfrac{\sqrt{3}}{\sqrt{3}} \\\\\\ \stackrel{\textit{rationalizing the denominator}}{cos(EDG )=\cfrac{\sqrt{6}}{\sqrt{3^2}}\implies cos(EDG )=\cfrac{\sqrt{6}}{3}}[/tex]

Answer:

i think 10 because in triangle there is 180 and 180-170 = 10

Answer:

Step-by-step explanation:

hjhj

In the given figure, the measure of the central angle CAD is 80°, the major arc is arc CBD, and minor arc is arc CD. The measure of arc BEC is 2.27r and that of arc BC is 0.87r.

About the Central Angle:

An angle formed by two radii of a circle is known as a central angle. Thus, arc BC and arc CD both subtends central angles at the center.

Since BD is the diameter of the circle,

∠BAC + CAD = 180°

It is given that ∠BAC = 100°

⇒ ∠CAD = 180° - 100°

⇒ ∠CAD = 80°

About Major Arc:

The arc which subtends an angle greater than 180° at the center, is called a major arc.

Angle subtended by arc BEC = 360° - m(arc CD)

= 360° - 80°

= 280° > 180°

∴ Arc BEC is the major arc

About Minor Arc:

The arc which subtends an angle less than 180° at the center, is called a minor arc.

⇒ Arc CD is the minor arc.

Calculating arc BEC and arc BC:

Let us assume the radius of the circle is r.

Then, the formula of the measure of an arc is given by,

θ × (π/180) × r

Here, θ is the angle ( in degrees) subtended by the arc at the center.

Arc BEC = 260 × (π/180)r  ......... [Put π = 3.14]

= 2.27r

Similarly, arc BC = 100 ×(π/180) × r .......... [Put π = 3.14]

= 0.87r

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Answer:

b = 133, a = 47

Step-by-step explanation:

If the two lines are parallel, then angle b is equal to 180-47 = 133 (same side interior angles), and angle is equal to angle 0 (alternate interior angles)

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:a = \theta[/tex]

( by Alternate interior angle pair )

[tex]\qquad \therefore\: \sf \:a = 47 \degree[/tex]

Next,

[tex]\qquad❖ \: \sf \:b = 180 - \theta[/tex]

( by co - interior angle pair )

[tex]\qquad❖ \: \sf \:b = 180 - 47[/tex]

[tex]\qquad \therefore \: \sf \:b = 133 \degree[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \: \:a = 47 \degree[/tex]

and

[tex]\qquad❖ \: \sf \:b = 133 \degree[/tex]

(i) The equation of the axis of symmetry is x = - 5.

(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.  

In this question we must find and infer characteristics from three cases of quadratic equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.

(ii) We need to transform the quadratic equation into its vertex form to determine the coordinates of the vertex by algebraic handling:

y = x² - 8 · x - 2

y + 18 = x² - 8 · x + 16

y + 18 = (x - 4)²

In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.

(iii) Now here we must apply a procedure similar to what was in used in part (ii):

y = - 2 · (x² - 4 · x + 2)

y - 4 = - 2 · (x² - 4 · x + 2) - 4

y - 4 = - 2 · (x² - 4 · x + 4)

y - 4 = - 2 · (x - 2)²

According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.  

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Answer:

5% of 15 is 0.75 i think

Step-by-step explanation:

15/5% is 0.75

The answer is 492 feet.

If we picture the scenario as a right triangle, using trigonometric ratios, this problem can be solved.

cos 60° = x / 984

1/2 = x/984

x = 984/2

x = 492 feet

Answer: 5 is the smaller number and 21 is the larger number

Step-by-step explanation: let’s have the smaller of the numbers equal x and the larger one equal y. Y = 3x + 6 their sum is 3x + 6 + x or 4x + 6. This sum minus 4 is 22 so the sum is 26. 26-6 = 4x so 4x = 20 and x = 5 so r = 15+ 6 which is 21.