(2 Fruit juice A is composed of 2 parts apple juice and 1 part grape juice.
Fruit juice B is composed of 1 part apple juice and 2 parts grape juice.
When A and B are mixed, the new mixture has 10 kg of apple juice and
8 kg of grape juice. How many kilograms does each type of original
fruit juice weigh

Answer

{-10, 9}

Step-by-step explanation:

The above are Simultaneous equations

These are two or more equations that share same variables.

8X + 10Y = 10--------(1)

5X + 4Y = -14-------(2)

40X + 50Y = 50 ---------(3)

40X + 32Y = - 112--------(4)

18Y = 162

[tex] \frac{18y}{18} = \frac{162}{18} \\ y = 9[/tex]

40X + 50Y = 50

40X + 50(9) = 50

40X + 450 = 50

40X = 50 - 450

40X = - 400

{-10, 9}

(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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The lowest common multiple of the expressions 3xyz^2 and 9x^2y + 9x^2 is 9x^2z^2(y + 1)

The expressions are given as:

3xyz^2 and 9x^2y + 9x^2

Factorize the expressions

3xyz^2 = 3 * x * y * z * z

9x^2y + 9x^2 = 3 * 3 * x * x * (y + 1)

Multiply the common factors, without repetition

LCM = 3 * 3 * x * x * (y + 1) * z* z

Evaluate the product

LCM = 9x^2z^2(y + 1)

Hence, the lowest common multiple of the expressions 3xyz^2 and 9x^2y + 9x^2 is 9x^2z^2(y + 1)

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Step-by-step explanation:

21) f(x)=1/x-6. g(x)=7/x+6

f(g(x))=f(7/x+6)=1÷7/x+6 - 6=x+6/7 - 6

g(f(x))=g(1/x-6)=7÷1/x-6 - 6 =7(x-6) - 6

simplify forward

25)f(x)=|x| g(x)=5x+1

f(g(x))=f(5x+1)=|5x+1|=5x+1=g(x)

g(f(x))=g(|x|)=5|x|+1=5x+1=g(x)

The psi that the TPMS would trigger a warning for this car is = 23.36 psi

The target tire pressure of the car is = 32 psi (pounds per square inch.)

The Tire pressure monitoring systems (TPMS) warns the car below 27% of 32psi

That is , 27/100 × 32

= 864/100

= 8.64psi

Therefore, 32 - 8.64 = 23.36. When the car is below 23.36psi, TPMS would trigger a warning for this car.

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Complete question:

Tire pressure monitoring systems (TPMS) warn the driver when the tire pressure of the vehicle is 27% below the target pressure. Suppose the target tire pressure of a certain car is 32 psi (pounds per square inch.)

At what psi will the TPMS trigger a warning for this car? (Round your answer to 2 decimal place.) When the tire pressure is above or below?

The vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

The optimization equation is given as

z=−3x+5y

The constraints are given as:

x+y≥−2

3x−y≤2

x−y≥−4

Next, we plot the constraints on a graph and determine the points of intersections

See attachment for the graph

From the attached graph, the points of intersections are

(-3, 1), (3, 7) and (0, -2)

So, we have:

(0, -2)

(-3, 1)

(3, 7)

Hence, the vertices of the feasible region are (0, -2), (-3, 1) and (3, 7)

So, the complete parameters are:

Optimization Equation:

z=−3x+5y

Constraints:

x+y≥−2

3x−y≤2

x−y≥−4

Vertices of the feasible region

(0, -2)

(-3, 1)

(3, 7)

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Answer:

ratio = 4

Step-by-step explanation:

According to the given table:

• the number of days with no fire incidents

  = 16

• the number of days with more than 5 fire incidents

  = 2 + 2

  = 4

Conclusion :

the ratio of the number of days with no fire incidents

to the number of days with more than 5 fire incidents is :

16 to 4 (16 : 4)

Then

The ratio = 4

If the formula, =MID("ABCDEFGHI",3,4) is used, the result yielded would be CDEF.

When using the =MID function on a spreadsheet, the number after the text in the formula would show the position of the text from the left that the function would begin to count from.

The text in the third position from the left as shown in ABCDEFGHI is C so we need to start counting from letter C.

The second number in the function would then show the number of texts that needs to be counted and selected from the row of letters. That number is 4.

So from the letter C, you'll count 4 letters including the letter C itself.

The result you get would therefore be C, D, E, F which are the four letters from C.

In conclusion, the formula =MID("ABCDEFGHI",3,4) would yield the result, "C, D, E, F,."

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Answer:

Step-by-step explanation:

The correct value of w is 20 as the width of a rectangle must be positive. A quadratic function always has 2 zeroes and in a case like this the negative one is ignored.

If we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.

Given two equations x-2y=5 and 4x+12y=-20.

We are required to find the value of x and y through substitution method.

Equation is like a relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Equation can be a linear equation,quadratic equation, cubic equation or many more depending on the power of variable.

They can be solved as under:

x-2y=5---------------1

4x+12y=-20--------2

Finding value of variable x from equation 1.

x=5+2y--------------3

Use the value of variable  x in equation 2.

4x+12y=-20

4(5+2y)+12y=-20

20+8y+12y=-20

20y=-20-20

20y=-40

y=-40/20

y=-2

Use the value of variable y in equation 3.

x=5+2y

x=5+2*(-2)

x=5-4

x=1

Hence if we solve the equations x-2y=5 and 4x+12y=-20 then we will get x=1 and y=-2.

Question is incomplete as it should include one more equation x-2y=5.

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Rewriting the left-hand side as follows,

[tex](2\cos\theta-6\sin \theta)^2 +(6\cos \theta+2\sin \theta)^2\\\\=4\cos^2 \theta-24\cos \theta \sin \theta+36 \sin^2 \theta+36 \cos^2 \theta+24 \cos \theta \sin \theta+4 \sin^2 \theta\\\\=40\cos^2 \theta+40 \sin^2 \theta\\\\=40(\cos^2 \theta+\sin^2 \theta)\\\\=40[/tex]

The option B is correct, The second expression gives the correct value -24.

According to the statement

we have given that the some expression and a = -2 and b = 3 and we have to which expression gives a output of answer -24 after put the values in the expressions.

So, For this purpose

First expression:

[tex]a\sqrt{16} + b - 10[/tex]

Put a = -2 and b = 3

then

[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]

Second expression:

[tex]a(\sqrt{16} + b) -10[/tex]

Put a = -2 and b = 3

then

[tex]a(\sqrt{16} + b) -10\\-2(4 +3) -10\\-14-10\\-24[/tex]

Now,

Third expression:

[tex]a\sqrt{16} + (b - 10)[/tex]

Put a = -2 and b = 3

then

[tex]a\sqrt{16} + (b - 10)-2*4 + (-7)\\-8-7\\-15[/tex]

Now,

Fourth expression and first expression are same,

So,

Fourth expression:

[tex]a\sqrt{16} + b - 10[/tex]

Put a = -2 and b = 3

then

[tex]= -2\sqrt{16} + 3 - 10\\= -8 -7\\= 15[/tex]

The second expression gives the correct value -24.

So, The option B is correct, The second expression gives the correct value -24.

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If the cost of goods manufactured of $918,700 and cost of goods sold is $955,448. The average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.

Using this formula to determine the average manufacturing cost per unit

Average manufacturing cost per unit= Total cost/Number of units produced

Where:

Total cost=$918,700+$955,448=$1,874,148

Number of units produced=18,374 units

Let plug in the formula

Average manufacturing cost per unit=$918,700+$955,448/18,374

Average manufacturing cost per unit=$1,874,148/18,374

Average manufacturing cost per unit=$102 per unit

Therefore the average manufacturing cost per unit assuming 18,374 units were produced is $102 per unit.

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Using the Empirical Rule, it is found that the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

It states that, for a normally distributed random variable:

Considering the mean of 110 and the standard deviation of 15, we have that:

These values are both the most extreme within 2 standard deviations of the mean, hence the proportion of people in a population with IQ scores between 80 and 140 is of 0.95 = 95%.

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Answer: $2250

Step-by-step explanation:

Given information

Dimension of the room = 20 feet × 15 feet

Cost of tiles = $7.50 / ft²

Derived formula from the given information

Total cost = Floor area × Cost of tiles

Substitute values into the formula

Total cost = Floor area × Cost of tiles

Total cost = (20 × 15) × (7.5)

Simplify by multiplication

Total cost = 300 × (7.5)

[tex]\Large\boxed{Total~cost~=~2250~Dollars}[/tex]

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Answer:

in case you don't understand feel free to ask bye.

An angle is produced at the point where two or more lines meet. Thus the value of LP required in the question is approximately 14.

Two lines are said to be perpendicular when a measure of the angle between them is a right angle. While parallel lines are lines that do not meet even when extended to infinity.

From the question, let the length of LP be represented by x.

Thus, from the given question, it can be deduced that;

LM ≅ PN = 20

KP = KN - PN

    = 30 - 20

KP = 10

LP = x

Also,

<MLP is a right angle, so that;

< KLP = < KLM - <PLM

         = 126 - 90

<KLP = [tex]36^{o}[/tex]

So that applying the Pythagoras theorem to triangle KLP, we have;

Tan θ = [tex]\frac{opposite}{adjacent}[/tex]

Tan 36 = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{Tan 36}[/tex]

  = [tex]\frac{10}{0.7265}[/tex]

x = 13.765

Therefore the side LP ≅ 14.

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Step-by-step explanation:

f(x)=-3x+4

f(a)= -3a +4

So,

2f(a)= f(a) + f(a)

=(-3a +4) +(-3a + 4)

=-3a + 4 -3a - 4

=-6a

f(2a)=2(-3a + 4)

=-6a +8

f(a+2)=(-3a + 4) + 2

= -3a +4 +2

= -3a + 6

f(a) + f(2)= -3a +1+5

because, f(2)= -3(2)+1

=-6+1

=5

and f(a)= -3a+1

Answer:

[tex]\sf 28 \frac{1}{3} \:ft=28.3\:ft\:(nearest\:tenth)[/tex]

Step-by-step explanation:

Given information:

Let x be the unknown length of the other side of Mr Kelly's house.

To solve, set up a ratio with the given information and the defined unknown, then solve for x:

[tex]\textsf{20 ft : 6 strides = x ft : 8.5 strides}[/tex]

[tex]\implies \sf 20:6 = x:8.5[/tex]

[tex]\implies \sf \dfrac{20}{6}=\dfrac{x}{8.5}[/tex]

[tex]\implies \sf x=\dfrac{20 \cdot 8.5}{6}[/tex]

[tex]\implies \sf x=\dfrac{170}{6}[/tex]

[tex]\implies \sf x=28 \frac{1}{3} \:ft[/tex]

[tex]\implies \sf x=28.3\:ft\:(nearest\:tenth)[/tex]

Therefore, the length of the other side of Mr Kelly's house that takes him 8.5 strides to walk is 28.3 ft (nearest tenth).

Let that be x

Answer:

  x = 23; not extraneous

Step-by-step explanation:

A solution is extraneous if it does not satisfy the original equation. Extraneous solutions can sometimes be introduced in the process of solving radical and rational function equations.

Squaring both sides of the given equation, we get ...

  √(3x +12) = 9

  3x +12 = 81 . . . . . . square both sides

  x +4 = 27 . . . . . . . divide by 3

  x = 23 . . . . . . . . . . subtract 4

There is only one solution, and it satisfies the equation:

  √(3×23 +12) = √81 = 9

The solution x = 23 is not extraneous.

Answer: x = 23; not extraneous

Step-by-step explanation:

Usando la distribución hipergeométrica,  la probabilidad de que ambas estén numeradas con el valor 1, es: 0.0222 = 2.22%.

La fórmula es:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Los parámetros son:

Los valores de los parámetros son:

N = 10, k = 2, n = 2.

La probabilidad de que ambas estén numeradas con el valor 1, es P(X = 2), entonces:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,10,2,2) = \frac{C_{2,2}C_{8,0}}{C_{10,2}} = 0.0222[/tex]

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The Pythagorean theorem states that:

[tex]a^2+b^2=c^2[/tex]

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

Let a represent the length of one leg.

Because the hypotenuse is 14 cm longer than a leg, we can say that the hypotenuse's length is 14 + a.

Plug these into the Pythagorean theorem:

[tex]a^2+b^2=c^2\\a^2+a^2=(14+a)^2\\2a^2=14^2+2(14)a+a^2\\2a^2=196+28a+a^2\\a^2=196+28a\\a^2-196-28a=0\\a^2-28a-196=0[/tex]

Factor using the quadratic formula:

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

[tex]a=\dfrac{-(-28)\pm \sqrt{(-28)^2-4(1)(-196)}}{2(1)}\\\\a=14\pm14\sqrt{2}\\\\a=14+14\sqrt{2}[/tex]

We know that it's plus because subtracting results in a negative value, and length cannot be negative.

This is the length of each side.

Because the hypotenuse is 14 cm longer, we can say that the hypotenuse is [tex]28+14\sqrt{2}[/tex].

Leg length = [tex]14+14\sqrt{2}[/tex]

Hypotenuse length = [tex]28+14\sqrt{2}[/tex]

1) Based on the information, the following taxation calculations can be made:

a) Gross Pay per pay period: $500

b) Taxable Income per pay period: $425

c) Since you pay 11% in federal taxes, the Federal tax withholding per pay period is $46.75.

2) The State tax withholding per pay period is $20.

3) The calculation of FICA, Medicare, and the Net Pay per pay period is as follows:

FICA withholding per pay period: $25.50

Medicare withholding per pay period: $6.16

Net Pay per pay period = $326.59

Total hours worked per pay period = 40 hours

Rate per hour = $12.50

Pay periods per month = 2

Gross pay per pay period = $500 (40 x $12.50)

Health care = $25

401K deduction = $50

Total deductions per pay period = $75

Taxable income per pay period = $425 ($500 - $75)

Federal taxes = 11%

Federal tax withholding per pay period: $46.75 ($425 x 11%)

Annual taxable income = $10,200 ($425 x 24)

State withholding tax (annual) = $480 {$120 + ($10,200 - $5,000) x 5%}

State withholding tax per pay period = $20 ($480/24)

FICA withholding per pay period: $25.50 ($425 x 6.2%)

Medicare withholding per pay period: $6.16 ($425 x 1.45%)

Gross Pay $500

Total deductions $75

Taxable income = $425

Federal Withholding = $46.75

State Withholding = $20

]FICA Withholding = $25.50

Medicare Withholding = $6.16

Net Pay per pay period = $326.59

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Angles is known to be opposite each other when two lines cross called vertical angles  due to the fact that they are opposite each other at a vertex.

Vertical Angles are known to be often called Vertically Opposite Angles and this is described as the scenario when two lines intersect one another, then the opposite angles, is made as a result of the intersection which is known to be called vertical angles or what we say as vertically opposite angles.

Note that A pair of vertically opposite angles are said to be often always equal to one another.

Hence, based on the scenario above, Angles is known to be opposite each other when two lines cross called vertical angles  due to the fact that they are opposite each other at a vertex.

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Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

An equation is an expression that shows the relationship between two or more numbers and variables.

In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.

Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)

Hence:

0.1x + 0.05y + 0.25z = 4.6   (1)

Also:

x = 3y   (2)

And:

z = y + 4  (3)

From the equations:

x = 18, y = 6, z = 10

Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

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Answer:

See below

Step-by-step explanation:

Here is HOW to solve this problem:

b = pounds of blue candy      then   r =  11-b = pounds of red candy

.79b = cost of blue candy             1.29 (11-b) = cost of red candy

   these two costs sum to   11.19  

.79b    + 1.29 ( 11-b)  = 11.19        Now you can solve for 'b'  the 'r' = 11-b

Answer:

Red candy =5

Blue candy = 6

Step-by-step explanation:

Let the pounds of red candy be x and blue candy y. Then y=11-x

Also 1.29x + 0.79y=11.19

1.29x+0.79(11-x)=11.19

0.5x=11.19–8.69

0.5x=2.5

X=5

Red candy =5

Blue candy = 6

Answer: c) {1,245; 1,224; 1,203; 1,182; …}

Step-by-step explanation:

Concept:

For this question, we just go by eliminating each answer until we get the correct one

Given information

Common difference = -21 (decreasing sequence)

Answer Choice: a) {873, 894, 915, 936, …}

894 - 873 = 21

915 - 895 = 21

936 - 915 = 21

Since the common difference is 21, not -21

[tex]\large\boxed{FALSE}[/tex]

Answer Choice: b) {32, 20, 8, -4, …}

20 - 32 = -12

8 - 20 = -12

-4 - 8 = -12

Since the common difference is -8, not -21

[tex]\large\boxed{FALSE}[/tex]

Answer Choice: c) {1,245; 1,224; 1,203; 1,182; …}

1224 - 1245 = -21

1203 - 1224 = -21

1182 - 1203 = -21

Since the common difference is -21

[tex]\Huge\boxed{TRUE}[/tex]

Answer Choice: d) {1,563; 1,587; 1,611; 1,635; …}

1587 - 1563 = 24

1611 - 1587 = 24

1635 - 1611 = 24

Since the common difference is 24, not -21

[tex]\large\boxed{FALSE}[/tex]

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Based on the task content given; the initial fee and the fee per stop is $2 and $1.5 respectively.

let

x + 3y = 6.50

x + 7y = 12.50

7y - 3y = 12.50 - 6.50

4y = 6

y = 6/4

y = 1.5

x + 3y = 6.50

x + 3(1.5) = 6.50

x + 4.5 = 6.50

x = 6.50 - 4.5

x = 2

Therefore, the initial fee and the fee per stop is $2 and $1.5 respectively.

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Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.

Given the data in the question;

Since the scenario form a right angle triangle, we use trig ratio.

tanθ = Opposite / Adjacent

tan( 26° ) = 34ft / x

We solve for x
x = 34ft / tan( 26° )

x = 34ft / 0.4877

x = 70ft

Given the height of the tree and the angle of elevation from point B, the distance between the tree is from point B is approximately 70ft.

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