You are a furniture restorer who is mixing a solution of olive oil and lemon juice. The solution is for polishing wooden furniture to give it a shine and a fresh scent. You fill 50% of a cup with lemon juice and 25% of a quart with olive oil. Afterwards, you mix the olive oil and the lemon juice in another container. How many cups of the solution do you have for polishing wooden furniture? 1.5 2.0 2.5 4.5 5.0

Answer:

[tex]2x^3+9x^2+16x+21[/tex]

Step-by-step explanation:

So we have the expression:

[tex](x+3)(2x^2+3x+7)[/tex]

Use the distribute property. Multiply each term on the right by (x+3):

[tex](2x^2)(x+3)+(3x)(x+3)+(7)(x+3)[/tex]

Distribute further:

[tex]=(2x^3+6x^2)+(3x^2+9x)+(7x+21)[/tex]

Combine like terms:

[tex]=(2x^3)+(6x^2+3x^2)+(9x+7x)+21\\=2x^3+9x^2+16x+21[/tex]

A polynomial in standard form has terms in descending order based on degree.

And we have that. Thus, we are done :)

Answer:

y= 2/3x +5

Step-by-step explanation:

(0,5) is the y intercept and the slope is 2/3 so we can use the y intercept form

y = mx+b where m is the slope and b is the y intercept

y= 2/3x +5

Answer:

y= 2/3x+5

Step-by-step explanation:

Okay, to write the equation of a line you need two values. The y intercept and the slope. The y intercept has an x coordinate of zero, and lucky us, the point you were given has an x coordinate of zero so that's done. You were also given the slope, so you don't have to calculate it. Anyways, the formula of a line is written in slope intercept form usually, so y=mx+b. Just fill in the gaps, m= the slope and b=the y intercept. The slope is 2/3, and the y intercept is 5. So, inserting in the variables you get y=2/3x+5.

Hope that helps!

Answer:

picked

Step-by-step explanation:

It is the only one that sounds correct.

Answer:

hi,

i think the answer can be picked

Step-by-step explanation:

picked is the answer

Answer:

(-3,-2) is the midpoint

Step-by-step explanation:

To find the midpoint

Add the x coordinates and divide by 2 to find the x coordinate of the midpoint

(-1+-5) /2 = -6/2 = -3

Add the y coordinates and divide by 2 to find the y coordinate of the midpoint

(-5+-9) /2 = -4/2 = -2

(-3,-2) is the midpoint

Step-by-step explanation:

To solve, we have to use the midpoint formula:

[tex]M=(\frac{x_{1}+x_{2} }{2} ,\frac{y_{1}+y_{2} }{2})[/tex]

Our points:

(-1, -5) (-5, 9)

Our x1 is -1, and our x2 is -5. Our y1 is -5, and our y2 is 9.

[tex]M=(\frac{-1+(-5) }{2} ,\frac{-5+9 }{2})[/tex]

[tex]M=(\frac{-6 }{2} ,\frac{4}{2})[/tex]

[tex]M=(-3 ,2)[/tex]

Answer: our midpoint: (-3, 2)

Answer:

AC = 10 units

Step-by-step explanation:

From the picture attached,

Triangle ABC is a right triangle.

Opposite side of the right angle B = Hypotenuse (AC)

and the other two legs are AB and BC

Pythagoras Theorem states

(hypotenuse)² = (leg 1)² + (leg 2)²

AC² = AB² + BC²

AC² = (6)² + (8)²

AC² = 36 + 64

AC² = 100

AC = √100

AC = 10

Therefore, length of the hypotenuse (AC) = 10 units will be the answer.

Answer:

l=w=h=15

Step-by-step explanation:

Volume of a cube= l*w*h

where l=w=h

[tex]l = {}^{3} \sqrt{ v} \: \: \: l = {}^{3} \sqrt{3375} = 15 [/tex]

15*15*15=3375

Hope this helps ;) ❤❤❤

The measure of each side of the cube will be 15 inches.

The Volume of the cone is the amount of quantity, which is obtained in the 3-dimensional space. Volume is defined as the space occupied by an object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of the cube or Cuboid

The cube has all the sides equal means that the length, width, and height of the cube will be the same. Let's suppose the length, width, and height of the cube is a.

The volume of a cube will be given by the formula:-

Volume = side³ = a³

a³ = 3375

a = ∛3375

a = ∛( 15 x 15 x 15 )

a = 15 cubic inches.

Therefore, the measure of each side of the cube will be 15 inches.

To know more about volume follow

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Answer:

(b

Step-by-step explanation:

the line graph is showing this: x<10

Answer:

Option H (the third option)

Step-by-step explanation:

A person must be at least 10 years old.

Let the person's age be x years

therefore, he has to be x≥ 10 (the person's age has to be equal or more than 10 )

Answer:

b/2-1 has a verbal phrase can be one minus the quotient of b and 2.

Answer:

14.6 feet

Step-by-step explanation:

Let A be the area of a square and S be the length of one of its sides.

The area of a square is A = S². We know A = 214 in this problem, so:

214 = S²

√214 = S

S ≈ 14.629 ≈ 14.6 feet (to the nearest tenth of a foot)

Answer:

w=6

Step-by-step explanation:

Since the triangles are similar, we can use ratios to solve

4          3

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

8           w

4w = 3*8

4w = 24

Divide by 4

4w/4 = 24/4

w = 6

Answer:

As hard as this may seem, it's actually quite simple. Because these two figures are similar, their sides can be compared.

See how on the left side of both of the triangles the numbers are 4 and 8? This shows that the left triangle is twice as small as the right one, which means that if you multiply any of the sides of the triangle on the left by 2, you'll get the triangle on the right.

We can apply this to w. Look at the left triangle on the bottom and see how there is a 3. Well, we've already noticed how the triangle on the left just needs to be multiplied by 2 in order to get to the one on the right, so that's what we should do! When you multiply 3 by 2, you get 6 which is w.

So, long answer short, w is 6.

Answer:

[tex]321_{10} = 101000001_{2}[/tex]

[tex]1023_{10} = 1111111111_2[/tex]

[tex]100632_{10} = 11000100100011000_{2}[/tex]

Step-by-step explanation:

Given

a) 321

b) 1023

c) 100632

Required

Convert to decimal

To convert each of these to binary, we have to divide the quotient by 2 and we take note of the remainder;

Solving (a)

321 / 2 = 160 R 1

160 / 2 = 80 R 0

80 / 2 = 40 R 0

40 / 2 = 20 R 0

20 / 2 = 10 R 0

10 / 2 = 5 R 0

5 / 2 = 2 R 1

2 / 2 = 1 R 0

1 / 2 = 0 R 1

Hence;

[tex]321_{10} = 101000001_{2}[/tex]

Solving (b)

1023 / 2 = 511 R 1

511 / 2 = 255 R 1

255 / 2 = 127 R 1

127 / 2 = 63 R 1

63 / 2 = 31 R 1

31 / 2 = 15 R 1

15 / 2 = 7 R 1

7 / 2 = 3 R 1

3 / 2 = 1 R 1

1 / 2 = 0 R 1

Hence;

[tex]1023_{10} = 1111111111_2[/tex]

Solving (c)

100632 / 2 = 50316 R 0

50316 / 2 = 25158 R 0

25158 / 2 = 12579 R 0

12579 / 2 = 6289 R 1

6289 / 2 = 3144 R 1

3144 / 2 = 1572 R 0

1572 / 2 = 786 R 0

786 / 2 = 393 R 0

393 / 2 = 196 R 1

196 / 2 = 98 R 0

98 / 2 = 49 R 0

49 / 2 = 24 R 1

24 / 2 = 12 R 0

12 / 2 = 6 R 0

6 / 2 = 3 R 0

3 / 2 = 1 R 1

1 / 2 = 0 R 1

Hence;

[tex]100632_{10} = 11000100100011000_{2}[/tex]

Answer:

The  95% confidence interval is [tex]0.1193 < p <0.4407[/tex]

Step-by-step explanation:

From the question we are told that

   The sample size is  [tex]m = 30[/tex]

   The sample proportion is  [tex]\r p = 0.28[/tex]

Given that the confidence interval is  95% then the level of significance is mathematically represented as

           [tex]\alpha = 100 - 95[/tex]

           [tex]\alpha = 5\%[/tex]

          [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of the [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is

        [tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{ \alpha }{2} } * \sqrt{\frac{ ( \r p (1 - \r p ))}{n} }[/tex]

=>    [tex]E = 1.96 * \sqrt{\frac{ (0.28 (1 - 0.28 ))}{ 30} }[/tex]

=>   [tex]E = 0.1607[/tex]

The  95% confidence interval is  

     [tex]\r p - E < p < \r p + E[/tex]

=> [tex]0.28 - 0.1607 < p < 0.28 + 0.1607[/tex]

=> [tex]0.1193 < p <0.4407[/tex]

Answer:

301.189

Step-by-step explanation:

Given the table :

Source of Variation - - SS - - - df - - - MS - - - - F

Regression - - - - - -3177.17 - - -2 - - 1588.6

Residual - - - - - - - - ______ --17 - - -17.717

Total - - - - - - - - - - 3478.36 - - 19

Calculate the SSR, Sum of Square residual

The Sum of Square RESIDUAL (SSR), Mean Square Residual (MSR) and Degree of Freedom RESIDUAL (DFR) are related by the formular :

MSR = SSR / DFR

Hence,

SSR = MSR × DFR

Fr the table ;

MSR = 17.717 ; DFR = 17

SSR = (17.717 × 17)

SSR = 301.189

=====================================

Work Shown:

Multiply the first coefficient (6) and the last term (-7) to get -42. We need to find factors of -42 that add to -19

Turns out that those two numbers are -21 and 2, which you find by trial and error.

-21 * 2 = -42

-21 + 2 = -19

Break up -19x as -21x+2x and use the factor by grouping method

6x^2 - 19x - 7

6x^2 - 21x + 2x - 7

(6x^2 - 21x) + (2x - 7)

3x(2x - 7) + 1(2x - 7)

(3x+1)(2x-7)

The factorization represents the length*width, since this product is equal to the rectangle's area.

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

Plug x = 15 into each factor

3x+1 = 3*15+1 = 46

2x-7 = 2*15-7 = 23

The length and width are 46 and 23

Answer:

Step-by-step explanation:

Hello, please consider the following.

We will multiply the numerator and denominator by

[tex]3-\sqrt{3}[/tex] to get rid of the root in the denominator.

Let's do it!

[tex]\begin{aligned}\dfrac{\sqrt{12}}{\sqrt{3}+3}&=\dfrac{\sqrt{2^2*3}*(3-\sqrt{3})}{(3+\sqrt{3})*(3-\sqrt{3})}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{3^2-\sqrt{3}^2}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{9-3}\\\\&=\dfrac{2\sqrt{3}*(3-\sqrt{3})}{6}\\\\&=\dfrac{6\sqrt{3}}{6}-\dfrac{2*3}{6}\\\\&=\sqrt{3}-1\\\\\large &\boxed{=-1+\sqrt{3}}\\\end{aligned}[/tex]

Thank you

Step-by-step explanation:

Here,

[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} [/tex]

is given.

Now, rationalizing it,

[tex] = \frac{ \sqrt{12} }{ \sqrt{3} + 3} \times \frac{ \sqrt{3} - 3 }{ \sqrt{3} - 3} [/tex]

now, simplifying it,

[tex] = \frac{ \sqrt{12 } \times \sqrt{3 } - 3 }{( { \sqrt{3} )}^{2} - 9} [/tex]

or, simplifying it we get,

[tex] = \frac{3}{ - 6} [/tex]

= 1/ -2

Hope it helps...

Answer:

1) -2x

2) 6x - 17

3) -16x

4) 3m - 5

5) 2m

6) 2x - 9

7) 9x

8) 6x + 8

Step-by-step explanation:

1) = x(7-9) = x(2) = 2x

2) x(-2+8) - 7 - 10 = x(6) - 17 = 6x - 17

3) x(-10-6) + 3 - 3 = x(-16) + 0 = 16x

4) m(2+1) - 6 + 1 = 3m - 5

5) m(10-8) = m(2) = 2m

6) x(1+1) - 5 - 4 = 2x - 9

7) x(4+5) = x(9) = 9x

8) x(7-1) + 3 + 5 = 6x + 8

Answer:

5.09 units

Step-by-step explanation:

Given equation

[tex]y=2\ln x=f(x)[/tex] in the interval [tex]1\le x\le 4[/tex]

So we integrate [tex]y[/tex] in the given interaval

[tex]\int f(x)=2\int\limits^4_1 {\ln x}dx[/tex]

Let us integrate [tex]\ln x[/tex] first.

let

[tex]u=\ln x, dv=dx[/tex]

[tex]du=\dfrac{1}{x}, v=x[/tex]

[tex]\int\ln x dx=udv[/tex]

Using integration by parts we get

[tex]uv-\int vdu[/tex]

[tex]=x\ln x-\int x\dfrac{1}{x}dx[/tex]

[tex]=x\ln x-dx[/tex]

[tex]=x\ln x-x+C[/tex]

So here

[tex]\int f(x)=2\int\limits^4_1 {\ln x}dx\\ =2(x\ln x-x)_1^4\\ =2[(4\ln 4-4)-(1\ln 1-1)]\\ =2[4\ln 4-4+1]\\ =5.09\ units[/tex]

The area of the the region between the curve and horizontal axis is 5.09 units.

Answer:

Step-by-step explanation:

From the question

P=2L+2W

where

L is the length

W is the width

To make W the subject move 2L to the left side of the equation

That's

2W = P - 2L

Divide both sides of 2 to make W stand alone

We have

[tex]W = \frac{P - 2L}{2} [/tex]

when

P = 70

L = 22

W is

[tex]W = \frac{70 - 2(22)}{2} \\ W = \frac{70 - 44}{2} \\ W = \frac{26}{2} [/tex]

We have the final answer as

Hope this helps you

Answer:

Width W = 13

Step-by-step explanation:

P = 2L + 2W

if the perimeter P = 70

and Length L = 22

find the Width W

P = 2L + 2W

70 = 2(22) + 2W

70 - 44 = 2W

26 = 2W

W = 26 / 2

W = 13

therefore,

the Width W = 13

check:

P = 2L + 2W

70 = 2(22) + 2(13)

70 = 44 + 26

70 = 70   --- OK

Answer: $139.23

Step-by-step explanation: Take 50% of original dress price and add price of shoes. Subtract 10% of that.

The correct answer is A. Mean

Explanation:

In the analysis of numerical data, means refers to the average value. This is found by adding all the values, in this case, all the salaries and then dividing the total by the total of values, in this case, 235. This sample statistic is affected by each of the values that are added, due to this, if a value changes or was corrected, the mean needs to be revised. Also, this does not occur in the case of the minimum (lowest value), the median (value in the middle), or in the mode (most frequent value.)

Answer:

5 miles.

Step-by-step explanation:

We would be using the Pythagoras Theorem to solve for this.

I have attached a diagram to better help you to better understand my explanation this.

The shortest distance from her playground to her house = Hypotenuse

Pythagoras Theorem for a triangle =

c² = a² + b²

Where c = Hypotenuse

a = 3 miles due west

b = 4 miles north

c² = 3² + 4²

c² = 9 + 16

c² = 25

c = √25

c = 5 miles

Therefore, the shortest distance to Alicia's home from the playground is 5 miles.

Answer: 20, 40, 60, 80, 100,....

Step-by-step explanation:

Given that :

It is possible to create teams of 4 for a relay race with no student leftover

Also,

It is possible to create teams of 5 for dodgeball with no student left over from the same class

To deduce the possible number of students in the class, then the number of students should be a multiple of both 4 and 5

Multiples of 4 include = 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100,....

Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,....

Multiples common to both 4 and 5 : 20, 40, 60, 80, 100,....

Answer:

A. 32 units

Step-by-step explanation:

First, we need to find all of the side lengths of triangle using distance formula:

Now, we can calculate length of PQ, QR and PR sides by using their vertices and above formula:

For perimeter we add up the length of all of its sides:

Answer:

Step-by-step explanation:

Given the equation of a plane in rectangular coordinates to be y = 4x.

The cylindrical coordinates of the axis is as given below;

x = rcosθ

y = rsinθ

z = z

Since there is no z coordinate in the equation of the plane given, we will only substitute x = rcosθ and y = rsinθ into the equation y = 4x and simply the result as shown;

y = 4x

rsinθ = 4( rcosθ)

rsinθ = 4rcosθ

sinθ = 4cosθ

sinθ - 4cosθ = 0

Hence the equation for the plane in cylindrical coordinate is expressed as sinθ - 4cosθ = 0

The equation of the plane y=4x in cylindrical coordinates is,  [tex]sin\theta-4cos\theta=0[/tex]

To find the equation of plane in cylindrical coordinates,

We have to substitute ,

                      [tex]x=rcos\theta\\\\y=rsin\theta\\\\z=z[/tex]

Given equation of plane is, [tex]y=4x[/tex]

Substitute values in equation of plane.

                   [tex]rsin\theta=4(rcos\theta)\\\\sin\theta=4cos\theta\\\\sin\theta-4cos\theta=0[/tex]

Learn more about the equation of plane here:

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Answer:

utv = 24° wtx=113°

Step-by-step explanation:

I solved in the picture

hope this helps ^-^

Answer:

Step-by-step explanation:

[tex] \sf{x + 3x - 36}[/tex]

Here, we have to collect like terms.

_________________________________

▪️What do you mean by like terms ?

⇒Like terms are those which have the same base. While adding or subtracting like terms, we should add or subtract the coefficients of like terms.

_________________________________

Let's add the like terms :

Answer : 4x - 36

Hope I helped!

Best regards!

I assumed you are referring to the Net (take away by the seller after removing their commissions).

Answer:

Selling price

Step-by-step explanation:

To determine what amount goes to the seller, we multiply the selling price of a commodity in question by the percentage (commissions) to the seller.

Note that the resulting amount is the value of the commission paid to the seller, the actual net is gotten by substracting the selling price from the commission paid.

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Hi my lil bunny!

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[tex]\boxed{ a^2 b^2 + -a^2 + -b^2 + 1 + 4ab}[/tex]

Let's simplify step-by-step.

[tex]( a^2 - 1 ) ( b^2 -1) + 4ab[/tex]

Distribute:

[tex]=( a^2) (b^2) + (a^2) (-1) + ( -1) (b^2) + (-1) (-1) + 4ab[/tex]

[tex]= a^2 b^2 + -a^2 + -b^2 + 1 + 4ab[/tex]

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Have a great day/night!

❀*May*❀

Answer:

a²b² - a² - b² + 4ab + 1

Step-by-step explanation:

( a²- 1) ( b²- 1) + 4ab

(a²b² - a² - b² + 1) + 4ab

a²b² - a² - b² + 4ab + 1

Answer:

Step-by-step explanation:

1. If x represents a number, then x^2 represents its square. If y represents a second number, then the sum of that square and the second number is ...

  x^2 + y

__

2. The difference of a number (n) and 7 is (n-7). Three times that difference is ...

  3(n - 7)

__

3. If x represents a number, then the product of 37 and a number is 37x. 9.85 less than that is ...

  37x - 9.85