Lorenzo uses 2 1/2 cups of vinegar in his salad dressing recipe. How much vinegar would Lorenzo use to make 4 2/5 recipes?

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{4})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{3}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{3}{5}}(x-\stackrel{x_1}{10}) \\\\\\ y-4=- \cfrac{3}{5}x+6\implies {\Large \begin{array}{llll} y=- \cfrac{3}{5}x+10 \end{array}}[/tex]

The values of the variables "a", "b", and "c" are 3.06, 169.74, and 0, respectively. The total amount Gary will pay is $769.74.

Gary purchased a S750 TV on a credit card with a 22% annual percentage rate, and he wants to pay it off in payments of $200 per month. The table shows the information for the first four months after Gary used his credit card. We need to calculate the values of the missing variables and the total amount he will pay.

The variable "a" is the interest charged on the left amount in the third month.

a = (366.68 - 200)*0.018333 = 3.06

The variable "b" is the monthly amount paid by Gary. It is less than or equal to $200, depending on the payment amount. Since the amount to be paid is $169.74, which is less than $200, he will pay the whole amount in one go.

b = 169.74

The variable "c" is the interest charged on the left amount in the fourth month. Since then, the entire amount has been paid.

c = 0

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The volumes of the 20% solution, 35% solution, and 80% solution used by the chemist are 18 liters, 12 liters, and 24 liters, respectively.

The chemist has three different acidic solutions. The first solution contains 20% acid, the second contains 35% acid, and the third contains 80% acid. She created 54 liters of a 50% acid mixture, using all 3 solutions. The number of liters of 80% solution used is 2 times the number of liters of 35% solution used.

Let the amounts of 20% solution, 35% solution, and 80% solution used be x, y, and z. We already know that z = 2y. We can write equations as given below.

The sum of the volumes must be equal to the final volume.

x + y + z = 54

x + y + 2y = 54

x = 54 - 3y

Now we will write the equation using the concentrations of the acid.

50%*54 = 20%*x + 35%*y + 80%*z

27 = 0.2(54 - 3y) + 0.35y + 0.8(2y)

2700 = 20(54 - 3y) + 35y + 80(2y)

2700 = 1080 - 60y + 35y + 160y

1620 = 135y

y = 1620/135 = 12

z = 2y = 2*12 = 24

x = 54 - 3y = 54 - 36 = 18

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Answer:

[tex]a_1=3[/tex]

[tex]a_n=a_n_-_1+2[/tex]

Step-by-step explanation:

Recursive formula : an = a(n-1) + d

where d = common difference , an = nth term, and n = number of terms

Because we are just writing the recursive formula rather than the explicit formula, the only defined term will be "d" or the common difference.

Here, the common difference is +2. This is evident as you must add 2 to get to 5 and then add 2 to get to 7 etc.

So d = 2

Plugging this into the recursive formula we get an = a(n-1) + 2

Also it's very important to state the first term which is 3 so a1 = 3

The value of the expression, 2w+4x, is 28 when w = 4 and x = 5.

According to the question,

We have the following expression:

2w+4x

We have the following values of w and x:

w = 4 and x = 5

Now, in order to find the value of the given expression, we will put these values in the expression.

So, we have this:

2*4+4*5

Now, we will first multiply the integers and then we will add the obtained results together:

8+20

28

Hence, the value of the expression, 2w+4x, is 28 when w = 4 and x = 5.

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The dividend growth rate of Kiefer service company is 0.16% . Dividend growth rate can be determined by using the return rate formula.

Dividend growth rate is the annual rate of growth that a particular stock's dividends experience over a specified period of time.

We have given that ,

Common stocks sells or current price = $36.84

Market rate of return (R) = 25.8 %

Annual dividend (D) = $1.61

Rate of return is defined as net gain or loss of। an investments over a specified time period . It is expressed as a percentage of investment initial cost .

Using the formula,

Rate of return = (D1/ current price )+growth rate where,

D1 --> divided of previous year

putting all the values in above formula we get,

15.8 = ( 1.61/36.84) + growth rate

=> growth rate= 15.8 - (1.61/36.84) = 15.756

Hense, the dividend growth rate for Kiefer service company is 0.16%.

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Answer:

x=9

Step-by-step explanation:

I assume you want me to solve for x.

6x+22=13x-41

Subtract 6x from both sides.

22=7x-41

Add 41 to both sides.

63=7x

Divide both sides by 7.

x=9.

CHECK:

6x+22=54+22=76

13x-41=117-41=76

76=76

So, x=9

Approximately Carlo takes 2 minutes time to sing the song.

Given that, Ariel sings a song in 5.92 minutes. Carlos sings the same song in 7.73 minutes.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

Now,

Difference of singing time = 7.73-5.92

= 1.81 minutes

≈ 2 minutes

Hence, approximately Carlo takes 2 minutes time to sing the song.

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Answer:6400 multiplied  by 13% (0.13)  then multiply that answer by 52 , for weeks in the year.  

Step-by-step explanation:

6400*.013= $832.00

832*52= $43264.00

The range of the given function is represented as {y | -5 ≤ y ≤ 5 , y ∈ R} .

Range of a function is defined as the possible values of y or the dependent variable in relation to the values of x.

Here from the graph we can see that the greatest value y achieves is 5.

The lowest value of y from the graph is -5 for all the values of x.

Hence the range will be {-5 ≤ y ≤ 5}

Now the graph is continuous, so we accept all values of y, hence y ∈ R .

Therefore the range will be: {y | -5 ≤ y ≤ 5 , y ∈ R} .

The set of all possible values for the results of the dependent variable, or the entire set of all possible values when the domain is substituted, is the range of a function.

The steps to find the range is:

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Answer:

Step-by-step explanation:

You want the equation of the line with slope 3/5 that passes through point (5, 3).

The point-slope form of the equation of a line with slope m through point (h, k) is ...

  y -k = m(x -h)

You have m=3/5, (h, k) = (5, 3), so your equation is ...

  y -3 = 3/5(x -5) . . . . point-slope form of desired equation

This can be simplified to ...

  y -3 = 3/5x -3

  y = 3/5x . . . . . . . add 3

Answer:

4

Step-by-step explanation:

you can use the formula y=mx+b where b is 4

the dimensions of the dumpster that will minimize its surface area

length l = 6.32

width w =  1.58

height h = 0.39

Length = l

width = w

height = h

given that length is four times its width

l = 4w

Now, the formula for the surface area of a cube is;

S = 2lh + 2lw + 2wh

substitute l = 4w in the above equation

S = 2(4w)h+2(4w)w+2wh

S = 8wh+8[tex]w^{2}[/tex]+2wh

S = 10wh + 8[tex]w^{2}[/tex]

formula for the volume of a cube is;

V = lwh

now substitute l=4w in the above equation

V = (4w)wh

V = 4[tex]w^{2}[/tex]h

h = 4[tex]w^{2}[/tex]/V

Put V/2w² for h in the surface area equation to get;

S= 8w² + 10w(V/4w²)

 = 8w² + 5V/2w

given that volume V = 25.6 substitute that in the above equation

S = 8w² + 5(25.6)/2w

  = 8w² + 128/2w

Since we want to minimize the surface area, let us find the first derivative of S to get;

S' = 16w - 128/2w²

At S' = 0

0 = 16w-  128/2w²

16w =  128/2w²

32w³ = 128

w³ = 128/32

w³ = 4

w = [tex]\sqrt[3]{4}[/tex]

w = 1.58 yds

since l = 4w substitute the value of w in that

l = 4(1.58) = 6.32

h = 4[tex]w^{2}[/tex]/V = 4([tex]1.58^{2}[/tex])/25.6

h = 0.39

the dimensions are

length l = 6.32

width w =  1.58

height h = 0.39

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The Natural Unemployment Rate based on the information is 5%.

The natural rate of unemployment is the lowest unemployment rate when inflation is stable, or the unemployment rate when inflation is not accelerating. The natural rate of unemployment (NAIRU) is the rate of unemployment caused by all factors other than changes in aggregate demand. Potential GDP estimates are based on the long-term natural rate.

The unemployment rate is the proportion of the total labor force that is unemployed but actively looking for work and willing to work. Cyclical unemployment is associated with an industry's business cycle. It is a direct result of a drop in consumer demand, which has resulted in a drop in labor demand. If cyclical unemployment rises, it indicates that the economy is slowing, which is not good.

Cyclical unemployment occurs when labor forces are reduced as a result of business cycles or economic fluctuations. If you are cyclically unemployed, it means that your employer has laid you off to save money during a period of slow business.

In this case, the unemployment will be:

= Actual unemployment rate - Cyclical unemployment rate

= 12% - 7%

= 5%

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Answer:

1

3

6

are all the correct answers because they made the most sense and looked the most proportional

Answer:

ones: 0

tenths: 9

thousandths: 3

Step-by-step explanation:

Because 0 is at the beginning of the whole "part" of the number, it is a "one" in place value (confusing right??) for example, in the number 54,743, 3 would be the digit in the ones place.

Because 9 is one decimal place across the example number, it is a tenth - because you would need 10 lots of 0.1 in order to make a whole number.

Because 3 is three decimal places across the example number, it is a thousandth - because you would need 1000 lots of 0.001 to make a whole number.

A good way of remembering these decimal place values is by using the number of zeros after 10, 100, 1,000, 10,000, and so on (one zero is a ten-th, two zeros is a hundred-th, etc, etc.)

Step-by-step explanation:

The drawing has the side dimension of 7.6 cm

  since each cm represents 90 m   the ACTUAL park is

        7.6 x 90 = 684 meters

  similarly, the bottom of the drawing has the dimension 9.1 cm which represents    9.1 x 90 = 819 m

the area of the park is then

Area =  height x width =     684 m x 819 m = 560 196 m^2

OR  in one step:

Area of the actual park is then

(7.6 cm * 90 m / cm )   X  ( 9.1 cm * 90 m/cm ) = 560 196 m^2

The greatest stress is experienced by object 2.

Stress is defined as force divided by area

Given: the table containing values of force and area for objects

Object 1

Stress = 72/6.46×10⁻⁵ =  1114551.084 N/m²

Object 2

Stress = 185/4.56×10⁻⁵ =  4057017.544 N/m²

Object 3

Stress = 406/5.07×10⁻⁴ =  792899.4083 N/m²

Object 4

Stress = 512/1.14×10⁻³ =  449122.807 N/m²

Therefore, object 2 is experiencing the greatest stress

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The only common factor (different than 1) between x and y is 29, so the greatest common divisor is 29.

Here we have two real numbers that are written as a product between their corresponding prime factors.

These numbers are:

x = 2*3*5*7*11*13*17*19*23*29

y = 29*31*37*41*43*47*53*59*61*67

Again, all of these are prime numbers, so the only common divisors between the two numbers are the factors that appear in both numbers.

And we can see that the only common factor between x and y is 29, then the greatest common divisor between x and y is 29.

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Mia's error in her thinking was that she interchanged the coordinate of both the x- and y-axis. Also, the point would actually be located at (5, 8).

In Mathematics, a reflection across the x-axis would maintain the same x-coordinate while the sign of the y-coordinate would change from positive to negative. Therefore, a reflection across the x-axis is given by this transformation rule:

(x, y)                   →               (x, -y)

In Geometry, a reflection across the y-axis of a graph is given by this transformation rule (x, y) → (-x, y).

(x, y)                   →               (-x, y)

(-5, -8)                   →            (5, -8)

Next, we would apply another reflection across the x-axis of a graph as follows:

(x, y)                   →               (x, -y)

(5, -8)                   →            (5, 8)

In conclusion, we can logically deduce that Mia was wrong in her calculations.

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Answer:

the value of x is 135 i believe

Step-by-step explanation:

sorry if im wrong

Answer:

Angle BAC =50

Step-by-step explanation:

Since O is the circumcenter and angle BOC is the angle subtended by the arc BC at the center and angle BAC is the angle subtended by arc BC

The length of the swimming pool is 30 feet

The width of the swimming pool is 15 feet

The volume of the swimming pool is 16875 gallons

Given,

Length of the rectangular swimming pool = 2x

Width of the rectangular swimming pool = x

A small concrete walkway surrounds the pool.

The width of the walkway = 2 feet

The area of the walkway = 196 square feet

We have to find the dimensions of the pool;

Here,

Area of rectangle = length x width

Area of walkways = (4x + 8x) + 4 x 4 = 196

12x + 16 = 196

12x = 196 - 16

12x = 180

x = 180/12

x = 15

That is,

Width of the pool is 15 feet

Length of the pool = 2 × x = 15 x 2 = 30 feet

Now,

If the depth of the pool is 6 feet, we have to find the amount of water that the pool can hold if the height of water is 1 foot below the top of the pool.

That is,

Volume of pool = length x width x depth

Here, depth = 6 - 1 = 5 feet

So,

Volume = 15 x 30 x 5 = 2250 cubic feet

Convert cubic feet to gallons

2250 x 7.5 = 16875 gallons of holding capacity

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Answer: y=-2x

Step-by-step explanation: Use the slope formula

-8-2/4-(-1)

-10/5=-2

y=-2

Answer:

y = - 2x

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

with (x₁, y₁ ) = (- 1, 2 ) and (x₂, y₂ ) = (4, - 8 )

m = [tex]\frac{-8-2}{4-(-1)}[/tex] = [tex]\frac{-10}{4+1}[/tex] = [tex]\frac{-10}{5}[/tex] = - 2 , then

y = - 2x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (- 1, 2 )

2 = 2 + c ⇒ c = 2 - 2 = 0

y = - 2x + 0 , that is

y = - 2x ← equation of line

Answer:

I think that the correct answers are C and D. I have questions. how many answers can I choose? what is the original photograph size? don't choose an answer until I get the information that I need

Answer: 5/6 windows in an hour, 6/5 hours, 72 minutes

Step-by-step explanation: the general formula used is 1/Oliver+1/sister=1/together and you plus in to find the amount of windows in an hour. Once solved, you take the reciprocal of that and that is the hours. Then you solve for the amount of minutes.

Answer:

[tex]f(x) = (x+1)(x-2)(x+4)[/tex]

        [tex]= (x^{2} +x-2x-2)(x+4)\\\\= (x^{2} -x-2)(x+4)\\\\= x^{3}-x^{2}-2x+4x^{2} -4x-8\\\\= x^{3} +3x^{2} -6x-8[/tex]

Solving an equation we will see that x = 13, then the measure of interior angle G is 63°.

Here we have the 3 interior angles of a triangle defined with a variable x.

m∠E = (5x + 6)°

m∠F = (4x - 6)°

m∠G = (5x - 2)°

Now, remember that the sum of the interior angles of a triangle is always equal to 180°.

Then we can write:

(5x + 6)° + (4x - 6)° +  (5x - 2)° = 180°

We can solve this for x.

14x - 2 = 180

14x = 180 + 2

x = 182/14 = 13

Now that we know the value of x, we can find the value of angle G.

m∠G = (5x - 2)° = (5*13 - 2)° = (15 - 2)° = 63°

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The volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.

According to the question,

We have the following information:

The side of the base is 18cm, the length of the upper side is 7.5cm and the height of the trunk is 20.4cm.

Now, we know that the trunk of a regular quadrangular pyramid is in the shape of a cuboid.

And the following formula is used to find the volume of cuboid:

Length*breadth*height

​ Volume of a trunk of a regular quadrangular pyramid = 7.5*18*20.4

Volume of a trunk of a regular quadrangular pyramid = 2754 cubic centimeters

Hence, the volume of a trunk of a regular quadrangular pyramid is 2754 cubic centimeters.

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