You are selling lemonade for $1.50, a bag of kettle corn for $3, and a hot dog for $2.50 at a fair. Write and simplify an expression for the amount of money you receive when p people buy one of each item

Answer:

-2x^6 + 7x^4 + 3x³ - 3x² + 11x + 20

Step-by-step explanation:

(-2x³ + x - 5)(x³ - 3x - 4) = -2x^6 + 6x^4 + 8x³ + x^4 - 3x² - 4x - 5x³ + 15x + 20

= -2x^6 + 7x^4 + 3x³ - 3x² + 11x + 20

B is the same thing but switching which trinomial is written first.

Answer:

Arc BC = 117°

Step-by-step explanation:

Angle D is an inscribed angle that intercepts arc ABC. According to the Inscribed angle theorem of a circle, m<D = ½ of arc ABC.

Thus,

104° = ½(AB + BC)

104° = ½(91° + BC)

Multiply both sides by 2

104*2 = 91 + BC

208 = 91 + BC

Subtract both sides by 91

208 - 91 = BC

117 = BC

Arc BC = 117°

Answer:

-16

Step-by-step explanation:

This equation is showing -8 multiplied by 2, and when they are multiplied, the sum of those two numbers is -16.

Answer:

=-16

Step-by-step explanation:

(-8)2

= 2×-8

= -16

Answer:

82

Step-by-step explanation:

78 + 4 = 82

Answer:

82 students

Step-by-step explanation:

The chart has a total of 82 students in the 18 to 22 age category, as 78 + 4 = 82.

Answer:

Total probability = 0.002 or 1 / 495

Step-by-step explanation:

Given:

Number of men = 8

Number of women = 4

Total number of person = 12

Find:

All four members will be women

Computation:

1st women probability = (4/12)

2nd women probability = (3/11)

3rd women probability = (2/10)

4th women probability = (1/9)

Total probability = (4/12)×(3/11)×(2/10)×(1/9)

Total probability = 24 / 11,880

Total probability = 0.002 or 1 / 495

The probability that all four members of the search committee will be women is 1.42%.

Since a board of directors consists of eight men and four women, and a four-member search committee is randomly chosen to recommend a new company president, to determine what is the probability that all four members of the search committee will be women the following calculation should be performed:

Therefore, the probability that all four members of the search committee will be women is 1.42%.

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Answer:

Step-by-step explanation:

The general form of a quadratic equation is ax²+bx+c = 0

Given the quadratic equation x²+4x+9=0 in its standard form, on comparing with the general equation we can get the value of the constant a, b and c as shown;

ax² = x²

a = 1

bx = 4x

b = 4

c = 9

The quadratic formula is given as x = -b±√(b²-4ac)/2a

Substituting the constant;

x = -4±√(4²-4(1)(9))/2(1)

x = -4 ±√(16-36)/2

x = -4±√-20/2

x = -4±(√-1*√20)/2

Note that √-1 = i

x = -4±(i√4*5)/2

x = (-4±i2√5)/2

x = -4/2±i2√5/2

x = -2±i√5

The solution to the quadratic equation are  -2+i√5 and  -2i-√5

Answer:

Step-by-step explanation:

A matrix is a set of numbers organized in rows and columns to represent the variables in a situation, and the determinant is used to find the inverse of a matrix which helps you solve for different variable values.

Answer: A matrix or matrices is a rectangular grid of numbers or symbols that is represented in a row and column format. A determinant is a component of a square matrix and it cannot be found in any other type of matrix. ... A determinant is a number that is associated with a square matrix.

Step-by-step explanation:

Answer:

49000

Step-by-step explanation:

since it's the same worth

Answer:

49000

Step-by-step explanation:

since there was the same worth given to all

Answer:  4+2 x (14-3)

Step-by-step explanation:

Answer:

The coefficient of x²

a) 1

b) -4

the coefficient of x² is the number in front of the x²(variable).

Coefficient= Constanta

I hope this helps

if u have question let me know in comments ^_^

Answer:

a) 1.

b) -4.

Step-by-step explanation:

The coefficient is the number  multiplying x2. If it is 1 it is usually omitted.

Answer:

the answer is $27.90

Step-by-step explanation:

if you do 15 times 2.79 you will get $41.85

then do 25 times 2.79 and you will get $69.75

then subtract 69.75 from 41.85 and your answer will be $27.90

i hope this helps this is the only way i could find the answer!

$29.4864 money will you save by driving your friend's car.

Given that, your car gets 15 miles per gallon and your friend's car averages 25 mpg.

You decide to go on a road trip to St. George Island, which is 361 miles away.

A unit of volume for measuring liquids. 1 gallon = 4 quarts = 8 pints = 16 cups = 128 fluid ounces. 1 US gallon = 231 cubic inches = 3.785411784 liters exactly.

Gallons needed for your car =361/15=24.06 gallons

Cost of 24.06 gallons of gas=24.06×2.79=$69.774

Gallons needed for friends car =361/25=14.44 gallons

Cost of 4.44 gallons of gas=14.44×2.79=$40.2876

Hence, while driving a friend's car you will save 69.774-40.2876=$29.4864

Therefore, $29.4864 money will you save by driving your friend's car.

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Answer:

We need 1/8 cup

Step-by-step explanation:

We can use ratios to solve

1/2 cup         x cups

------------  = -----------------

20 cookies     5 cookies

Using cross products

5 * 1/2 = 20x

Divide each side by 20

5/2 * 1/20 = 20x/20

5/40 =x

1/8 =x

We need 1/8 cup

Answer:

Step-by-step explanation:

step 1: you know that 1/2 c of oil makes 20 cookies.

step 2: if you only have 1/4 c (half of 1/2 cup), then you can make 10 cookies.

Step 3: 1/8 c would make 5 cookies.

Answer:

2/3

Step-by-step explanation:

Less than 5 is 1,2,3,4 and 4 out of 6 is also equal to 2/3

Answer:

[tex]2\sqrt{3}+3[/tex]

Step-by-step explanation:

[tex]$\frac{3}{2 \sqrt 3 - 3}$[/tex]

Rationalize the fraction.

[tex]$\frac{3}{2 \sqrt 3 - 3}\cdot \frac{2 \sqrt 3 + 3}{2 \sqrt 3 + 3} =\frac{6\sqrt{3}+9 }{12-9} =\frac{6\sqrt{3}+9 }{3} =2\sqrt{3}+3 $[/tex]

Note that I used the positive signal because we would have a difference of squares.

Answer:

1. Tan θ = √11/5

2. Cosec θ = 6√11 /11

3. Cos θ = 5/6

Step-by-step explanation:

Let the side opposite to angle θ be y.

The value of y can be obtained by using the pythagoras theory as follow:

b² = 6² – 5²

b² = 36 – 25

b² = 11

Take the square root of both side.

b = √11

1. Determination of Tan θ

Tan θ =?

Opposite = √11

Adjacent = 5

Tan θ = Opposite /Adjacent

Tan θ = √11/5

2. Determination of Cosec θ.

We'll begin by calculating the Sine θ. This is illustrated below:

Sine θ =?

Opposite = √11

Hypothenus = 6

Sine θ = Opposite /Hypothenus

Sine θ = √11/6

Now, we shall determine Cosec θ as follow:

Cosec θ = 1/Sine θ

Sine θ = √11/6

Cosec θ = 1 ÷ √11/6

Cosec θ = 1 × 6/√11

Cosec θ = 6/√11

Rationalise the denominator

Cosec θ = 6/√11 × √11/√11

Cosec θ = 6√11 /11

3. Determination of Cos θ.

Cos θ =?

Adjacent = 5

Hypothenus = 6

Cos θ = Adjacent / Hypothenus

Cos θ = 5/6

Problem 1

a^2+b^2 = 25^2+20^2 = 225+400 = 625

c^2 = 25^2 = 625

We get the same output of 625.

This shows that a^2+b^2 = c^2 is true for (a,b,c) = (15,20,25). We have a pythagorean triple and this is a right triangle. This is also scalene as all three sides are different lengths.

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

Problem 2

a^2+b^2 = 3^2+3^2 = 18

while c^2 = 1^2 = 1

So a^2+b^2 = c^2 is not a true equation for this a,b,c set of values. We do not have a right triangle. Instead we have an acute triangle based on these rules below

We see that we have the form a^2+b^2 > c^2 since 18 > 1.

This acute triangle is also isosceles because a = b.

Answer:

Triangle A is a scalene triangle.

Triangle B is an isosceles triangle

Exaplanation for the 1st Answer:

A scalene triangle is a triangle whose all side lengths are different.

Triangle A has the side lengths are 15, 20, 25. All these lengths are different, so this is a scalene triangle.

Explanation for the 2nd Answer:

An isosceles triangle has 2 sides lengths the same and the other side length different. Triangle B has side lengths of 3, 3, 1. Two side lengths are same, but 1 side length is different. So, this is an isosceles triangle.

Answer:

-6

Step-by-step explanation:

To solve this problem, you should move all of the variables onto one side, and all of the constants onto the other side as such:

3x-4=2x-10

   +10    +10

3x+6=2x

-3x     -3x

6=-x

/-1   /-1

x=-6

Hope this helps!

P.S. Please give me brainliest. Thanks :)

Answer:

[tex]x = -6[/tex]

Step-by-step explanation:

Looking at the expression [tex]3x - 4 = 2x - 10[/tex], our goal is to get rid of the x term on one side.

To do this, we can subtract 2x from both sides which gets us

[tex]x - 4 = -10[/tex]

Add 4 to both sides:

[tex]x = -6[/tex]

Hope this helped!

[tex]\left(\dfrac{1}{1+2i}+\dfrac{3}{1-i}\right)\left(\dfrac{3-2i}{1+3i}\right)=\\\\\left(\dfrac{1-2i}{(1+2i)(1-2i)}+\dfrac{3(1+i)}{(1-i)(1+i)}\right)\left(\dfrac{(3-2i)(1-3i)}{(1+3i)(1-3i)}\right)=\\\\\left(\dfrac{1-2i}{1+4}+\dfrac{3+3i}{1+1}\right)\left(\dfrac{3-9i-2i-6}{1+9}\right)=\\\\\left(\dfrac{1-2i}{5}+\dfrac{3+3i}{2}\right)\left(\dfrac{-3-11i}{10}\right)=\\\\\left(\dfrac{2(1-2i)}{10}+\dfrac{5(3+3i)}{10}\right)\left(\dfrac{-3-11i}{10}\right)=[/tex]

[tex]\dfrac{2-4i+15+15i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{17+11i}{10}\cdot\dfrac{-3-11i}{10}=\\\\\dfrac{-51-187i-33i+121}{100}=\\\\\dfrac{70-220i}{100}=\\\\\dfrac{70}{100}-\dfrac{220i}{100}=\\\\\boxed{\dfrac{7}{10}-\dfrac{11}{5}i}[/tex]

Answer:

A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.

Step-by-step explanation:

Answer:

C.) A car slows to stop at a stop sign. Once traffic is clear, the car speeds up.

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

Plug in t = 12 in the expression

[tex]5-\frac{t}{3}=5-\frac{12}{3}[/tex]    

         = 5 - 4/1

          = 5 - 4

           = 1

Answer:

[tex]\Huge \boxed{1}[/tex]

Step-by-step explanation:

[tex]\displaystyle 5-\frac{t}{3}[/tex]

The value of [tex]t[/tex] in the expression is 12.

Replace the [tex]t[/tex] variable with 12.

[tex]\displaystyle 5-\frac{12}{3}[/tex]

Evaluate the expression.

[tex]5-4[/tex]

[tex]1[/tex]

Answer:

Técnicas orales y de cálculo mental de multiplicación y división entera . ... conjunto de múltiplos de 10 es un subconjunto de los números pares. Si ... La clase vacía ∅ se representa por la notación 0, la clase unitaria por 1, la clase binaria por 2, etc. En ... 5 x (5 x (5 x (5 + 4) + 3 ) + 2) + 1 ; x significa el signo de multiplicar. 8.

Step-by-step explanation:

Técnicas orales y de cálculo mental de multiplicación y división entera . ... conjunto de múltiplos de 10 es un subconjunto de los números pares. Si ... La clase vacía ∅ se representa por la notación 0, la clase unitaria por 1, la clase binaria por 2, etc. En ... 5 x (5 x (5 x (5 + 4) + 3 ) + 2) + 1 ; x significa el signo de multiplicar. 8.

Answer:c

Step-by-step explanation:

Answer:

Rational, integer, natural, whole, rational numbers

Step-by-step explanation:

17 is a rational, integer, natural, whole, and is a rational number. I'm not totally sure why rational is on there, since rational and rational number should be the same thing. Basically it's everything but "only". If rational is supposed to mean irrational, then it's not irrational.

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

Explanation:

The rule f(x,y) = (x+1,y-1) says to add 1 to the x coordinate and subtract 1 from the y coordinate. So let's say the input point is (7,2). This would move it to (8,1).

Now let's say that you accidentally erased the "(7,2)", but you still have the "(8,1)". You'd have to work through the steps backwards to get back to (7,2)

So you'll effectively use this rule g(x,y) = (x-1, y+1) which is the inverse transformation. Whatever f(x,y) does, the g(x,y) function will undo it and go opposite. We'll subtract 1 from the x coordinate and add 1 to the y coordinate.

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

So that's what we'll do with the set of points { (1,1), (4,2), (2,-1) }

We have (1,1) become (0,2) after applying the g(x,y) rule

(4,2) becomes (3,3) after using g(x,y)

(2,-1) becomes (1,0) after using g(x,y)

Therefore, the domain is { (0,2), (3,3), (1,0) }

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

The mapping diagram is shown below.

Answer:

6 = n

Step-by-step explanation:

-3=n/2-6

Add 6 to each side

-3+6 = n/2 -6+6

3 = n/2

Multiply each side by 2

3*2 = n/2 *2

6 = n

━━━━━━━☆☆━━━━━━━

▹ Answer

n = 6

▹ Step-by-Step Explanation

-3 = n/2 - 6

Multiply both sides by 2:

-6 = n - 12

Rearrange the terms:

-n -6 = -12

Calculate:

-n = -6

Change the signs:

n = 6

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

316

Step-by-step explanation:

Answer:

$26 for each child

Step-by-step explanation:

35 * 3 = 105 / 4 = 26.25

Answer:

0

Step-by-step explanation:

Chalice with purified water = 4

With spoiled milk = 5

With flat soda = 6

Probability of Jones drinking from a chalice with purified water after Donovan had drank from 3 = 1/3

Probability = required outcome / Total possible outcomes

Total possible outcomes = (4 + 5 + 6) = 15

After Donovan drinks 3 :

Total possible outcomes = (15 - 3) = 12

If the probability of Jones choosing a chalice with purified water is 1/3 then :

(Required outcome / Total possible outcomes) =1 /3

(Required outcome / 12) = 1 / 3

Required outcome * 3 = 12

Required outcome = 12 / 3

Required outcome = 4

Therefore, since initial number of chalice with purified water is 4,

4 - 4 = 0

Then Donovan did not drink from a chalice containing purified water.

Answer:

the floor area of the production line =20000 m^2

Step-by-step explanation:

From the question we were told two thirds of the floor of the factory is taken up by the production line.

If we denote the total area of the factory as "y" then

the Area of the production line can be express algebraically as

2/3 × y = 2y/3

The rest of floor area of warehouse space will be

y- 2y/3 = y/3

From the rest of floor area, we were told three fifths is taken up by the office space, then this office space's area can be expressed in m^3 as

3/5 × y/3 = y/5

The remaining space left will now be for

warehouse, by we were given warehouse space omas 2000m^2.

Then from here we can get value of y

2y/15 = 2000

2y = (2000×15)

2y= 30000

y= 15000m^2

Therefore, the floor area of the production line can be expressed as

(2 ×30000)/3

= 20000 m^2

Quit easily done!