Dustin has five hats, five shirts, five pairs of pants, and five pairs of shoes; he has one of each in blue, green, gray, silver, and gold (his five favorite colors). Dustin is picky about what he wears: he insists on his shoes being the same color as at least two other articles of clothing in the outfit. However, he refuses to wear all silver or all gold (because that's tacky). How many possible outfits can Dustin wear?

Answer:

First car: 30 gallons

Second car: 35 gallons

Step-by-step explanation:

Hi, to answer this question we have to write a system of equations:

Total gas consumption was 65:

x+y=65

Where:

x = gallons consumed by the first car

y = gallons consumed by the second car

The first car has a fuel efficiency of 20 miles per gallon of gas and the second has a fuel efficiency of 30 miles per gallon of gas, the two cars went a combined total of 1650 miles:

x 20+y 30 = 1650

The system is:

x+y=65 (1)

x 20+y 30 = 1650 (2)

Isolating y on (1)

y = 65-x

Replacing y= 65-x on (2):

x 20+(65-x)30 = 1650

20x +1,950-30x= 1650

20x-30x= 1650-1950

-10x= -300

x= -300/-10

x = 30 gallons

Back to (1)

y =65-x

y =65-30

y= 35 gallons

Feel free to ask for more if needed or if you did not understand something.  

Answer:

30x² cubic units

Step-by-step explanation:

The volume of an Oblique prism = Base Area × Height

This oblique prism has trapezoidal bases.

Area of a Trapezoid = 1/2 × h × ( b1+b2)

where h = height

b1 and b2 = bases of the Trapezoid.

From the question,

h = 20

b1 = x

b2 = 2x

Area of the Trapezoid =

1/2 × x ×( x + 2x)

1/2 × x × (3x)

3x²/2 square units.

Remember, the volume of an Oblique prism = Base Area × Height

Height of the prism = The distance between the 2 trapezoid bases = 20 units.

Base Area = 3x²/2 square units × 20 units

= 30x² cubic units

Answer:

d

Step-by-step explanation:

Answer:

b. y - 8 = -2/3(x + 3)

Step-by-step explanation:

Well point-slope form takes one point in this case (-3,8) and puts it into the equation.

So this is point slope form,

[tex]y -y_{1} = m(x - x_{1} )[/tex]

The 2 negatives in the -y and -x means you have to change the number to a negative to a positive to a negative.

We plug in (-3,8) to the equation.

y - 8 = m(x + 3)

Well we change the -3 to a 3 because of the negative.

So with the given slope -2/3 we plug that in for m.

y - 8 = -2/3(x + 3)

Thus,

answer choice b is correct.

Hope this helps :)

Answer:

15

Step-by-step explanation:

Opposite sides in a parallelogram are equal.

2x - 5 = x + 10

Subtract x and add 5 on both sides.

2x - x = 10 + 5

Combine like terms.

x = 15

Answer:

[tex]\boxed{\red {x= 15}}[/tex]

Step-by-step explanation:

We know that opposite sides in a parallelogram are equal.

So, in this sum value of the sides in a parallelogram

[tex]x + 10 \: \: \: and \: \: \: 2x - 5[/tex]

So now let's create an equation

[tex]x + 10 = 2x - 5[/tex]

Now let's solve for x

[tex]x + 10 = 2x - 5 \\ 10 + 5 = 2x - x \\ 15 = x[/tex]

Answer:

It has two solutions.

Step-by-step explanation:

Let as consider the given options are  

It has no solution.

It has one solution.

It has two solutions.

It has infinitely many solutions.

The given equation is

[tex]\dfrac{3}{4z}=\dfrac{1}{4z-3}+5[/tex]

Multiply both sides by 4z(4z-3).

[tex]3(4z-3)=4z+5(4z(4z-3))[/tex]

[tex]12x-9=4z+80z^2-60z[/tex]

[tex]0=-12x+9+80z^2-56z[/tex]

[tex]0=80z^2-68z+9[/tex]

It is a quadratic equation.

Therefore, it has two solutions.

Answer:

It has 1 solution

Step-by-step explanation:

I did the test I put the guys above me in and got it wrong

Answer:

(a) 63 cups

(b) 16 cups

Step-by-step explanation:

Given that the volume of the sink = (2000/3)×π in³

(a) For the cup that has diameter = 4 in. and height, h = 8 in.

The radius, r = Diameter/2 = 4/2 = 2 in.

The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×2²×8 = (32/3)×π in.³

The number of cups to scoop = (Volume of the sink)/(Volume of the cup)

The number of cups to scoop = ((2000/3)×π)/((32/3)×π ) = 125/2=62.5 cups

Rounding to the next whole number gives 62.5 cups ≈  63 cups

(b) For the cup that has diameter = 8 in. and height, h = 8 in.

The radius, r = Diameter/2 = 8/2 = 4 in.

The of a cone = 1/3×Base area × Height = 1/3 × π×r² ×h = 1/3×π×4²×8 = (128/3)×π in.³

The number of cups to scoop = (Volume of the sink)/(Volume of the cup)

The number of cups to scoop = ((2000/3)×π)/((128/3)×π ) = 125/8=15.625 cups

Rounding to the next whole number gives 15.625 cups ≈  16 cups.

Answer:

Step-by-step explanation:

The factorization of x² - 5x + 6 can be determined thinking critically about two numbers, that if we multiply those two numbers together it will result into a value of +6 and if we add those numbers together , we will have -5

The numbers are -3 and -2 ; if we multiply -3 and -2 , we have = 6

If we add -3 + (-2) ; we have,

-3-2 = -5

Now the factorization of

x² - 5x + 6 = 0 is as follows.

x² - 3x - 2x + 6

By factorization,

x(x - 3) - 2 (x - 3) = 0

(x - 2) or  (x-3) = 0

Now, using An algebra tile configuration. The diagrammatic expression showing how an algebraic tile configuration should looks like can be found in the attached image below.

Hint:

Let represent ,

1   =   x² tile

-5 = - x tiles

6  =  1 tiles

Answer:

The answer is the first tile choice.

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

Answer:

x= 118 y= 26 and z=36

Step-by-step explanation:

The sum of the measures of the angles of a triangle is 180

can be written as x+y+z=180

The sum of the measures of the second and third angles is four times the measure of the first angle.  

It can be written by:  x+y=4z

The third angle is 10 more than the second

It can be written as z=y+10

By solving the equations systems the above values can be determined.

x + y + z = 180

Substituting,

4z + z = 180

5z = 180

z = 180 / 5 = 36

z = y + 10

36 - 10 = y

y = 26

x + y + z = 180

x + 26 + 36 = 180

x = 180 - 62

x = 118

Answer:

its harddd

Step-by-step explanation:

rightttttttt

Answer:

the answer is A=2

Step-by-step explanation:

a real solution is a solution that uses real numbers. This equation has 2 real solutions.

Answer:

A. 2 real solutions

Step-by-step explanation:

One graph is a parabola and 1 graph is a straight line and they intersect twice.

Answer:

i will say c

Step-by-step explanation:

c

Answer:

B. Whole numbers from 0 to 10

Step-by-step explanation:

this is a dot graph, so only those dots, whole numbers of tickets, are valid input, that is, domain of the graph.

Answer:

6^5  * 9^5

Step-by-step explanation:

( 6*9) ^5

We know that ( ab) ^c = a^ c* b^c

6^5  * 9^5

Step-by-step explanation:

Given

Opp=8

Adj=6

Hyp=10

Answer

1)Sin<A=Opp/Hyp

8/10=4/5... Yes

2)Cos<A=Opp/Adj

8/6=4/3... No

Given

Opp=6

Adj= 8

Hyp= 10

Answer

1)Sin<B= Opp/Hyp

6/10=3/5... No

2)Cos<B= Opp/Adj

6/8=3/4... No

Hope this helps ❤❤❤

Answer:

-6

Step-by-step explanation:

x(-y + z)

Let x= 3 y =3 and z =1

3( -3+1)

Parentheses first

3 ( -2)

Then multiply

-6

Answer:

Hello! The answer to your question is -6

Steps will be provided below.

Step-by-step explanation:

This is how to solve your question:

Question:

Evaluate x(-y + z) for x = 3, y = 3, and z = 1.

Answer and how to solve:

The answer is -6 because....

If you do the steps correctly it will be...

Do the Parentheses first.

3x-(2)

Now you just multiply and you will get your answer.

Which will give you -6

SO THE ANSWER TO YOUR QUESTION IS -6

⭐️Hope this helps! :) ⭐️

Have a wonderful day! :D

Answer:

A. 770,000,000

Step-by-step explanation:

7.7x10^8 First step is to simplify

7.7x100,000,000 Then, multiply

770,000,000

Hope this helps, if it does, please consider giving me brainliest, it will help me a lot. If you still have any questions, feel free to ask.

Have a good day! :)

Answer:

(x + 4)² + (y + 1)² = 4

Step-by-step explanation:

From the graph attached,

Extreme ends of the diameter of the circle,

(-4, 1) and (-4, -3)

Center of the circle = Midpoint of the diameter

Center = [tex](\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]

           = [tex](\frac{-4-4}{2},\frac{1-3}{2})[/tex]

           = (-4, -1)

Radius of the circle = Distance between the center and extreme end

                                = 2 units

Since standard equation of the circle is,

(x - h)² + (y - k)² = r²

where (h, k) is the center and 'r' is the radius of the circle

By substituting the values in the standard equation,

(x + 4)² + (y + 1)² = 2²

(x + 4)² + (y + 1)² = 4

Answer:

71s

Step-by-step explanation:

The question we have at hand is 7s² + ___ + 13s + 6² = (7s + 6)². We can expand the perfect equation " (7s + 6)² " in order to find our solution. A perfect square consists of 3 terms, and hence the term in the blanks must add to 13s to form another term.

Applying the perfect square formula : ( a + b )² = a² + 2ab + b², let's expand the expression,

(7s + 6)² = ( 7s )² + 2( 7s )( 6 ) + ( 6 )² =  7s² + 84s + 6²

84s - 13s = 71s, which fills in the blank provided.

Answer:

RS and plane RSU

Step-by-step explanation:

I think not to sure

Answer:

[tex]\boxed{x=1}[/tex]

Step-by-step explanation:

[tex]mean=\frac{sum \: of \: terms}{number \: of \: terms}[/tex]

[tex]2=\frac{2+4+1+1+x+3+2}{7}[/tex]

[tex]2=\frac{13+x}{7}[/tex]

[tex]14=13+x[/tex]

[tex]x=1[/tex]

Answer:

to be honest I'm not sure how to do

Answer:

[tex]Side\ B = 6.0[/tex]

[tex]\alpha = 56.3[/tex]

[tex]\theta = 93.7[/tex]

Step-by-step explanation:

Given

Let the three sides be represented with A, B, C

Let the angles be represented with [tex]\alpha, \beta, \theta[/tex]

[See Attachment for Triangle]

[tex]A = 10cm[/tex]

[tex]C = 12cm[/tex]

[tex]\beta = 30[/tex]

What the question is to calculate the third length (Side B) and the other 2 angles ([tex]\alpha\ and\ \theta[/tex])

Solving for Side B;

When two angles of a triangle are known, the third side is calculated as thus;

[tex]B^2 = A^2 + C^2 - 2ABCos\beta[/tex]

Substitute: [tex]A = 10[/tex],  [tex]C =12[/tex]; [tex]\beta = 30[/tex]

[tex]B^2 = 10^2 + 12^2 - 2 * 10 * 12 *Cos30[/tex]

[tex]B^2 = 100 + 144 - 240*0.86602540378[/tex]

[tex]B^2 = 100 + 144 - 207.846096907[/tex]

[tex]B^2 = 36.153903093[/tex]

Take Square root of both sides

[tex]\sqrt{B^2} = \sqrt{36.153903093}[/tex]

[tex]B = \sqrt{36.153903093}[/tex]

[tex]B = 6.0128115797[/tex]

[tex]B = 6.0[/tex] (Approximated)

Calculating Angle [tex]\alpha[/tex]

[tex]A^2 = B^2 + C^2 - 2BCCos\alpha[/tex]

Substitute: [tex]A = 10[/tex],  [tex]C =12[/tex]; [tex]B = 6[/tex]

[tex]10^2 = 6^2 + 12^2 - 2 * 6 * 12 *Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]

[tex]100 = 36 + 144 - 144 *Cos\alpha[/tex]

[tex]100 = 180 - 144 *Cos\alpha[/tex]

Subtract 180 from both sides

[tex]100 - 180 = 180 - 180 - 144 *Cos\alpha[/tex]

[tex]-80 = - 144 *Cos\alpha[/tex]

Divide both sides by -144

[tex]\frac{-80}{-144} = \frac{- 144 *Cos\alpha}{-144}[/tex]

[tex]\frac{-80}{-144} = Cos\alpha[/tex]

[tex]0.5555556 = Cos\alpha[/tex]

Take arccos of both sides

[tex]Cos^{-1}(0.5555556) = Cos^{-1}(Cos\alpha)[/tex]

[tex]Cos^{-1}(0.5555556) = \alpha[/tex]

[tex]56.25098078 = \alpha[/tex]

[tex]\alpha = 56.3[/tex] (Approximated)

Calculating [tex]\theta[/tex]

Sum of angles in a triangle = 180

Hence;

[tex]\alpha + \beta + \theta = 180[/tex]

[tex]30 + 56.3 + \theta = 180[/tex]

[tex]86.3 + \theta = 180[/tex]

Make [tex]\theta[/tex] the subject of formula

[tex]\theta = 180 - 86.3[/tex]

[tex]\theta = 93.7[/tex]

Answer:

3

Step-by-step explanation:

We are adding 2 each time

-3 +2 = -1

-1 +2 = 1

To get the next term add 2

1 +2 = 3

Answer: 3

Step-by-step explanation:

Answer:

A. 4x¹¹ + x⁷ + 3x³ - 5x + 9

Step-by-step explanation:

order the exponents from largest to smallest. variables always come first; therefore, -5x before 9

volume=l1*l2*l3

=8*15*20=2400cm^3

Volume = length x breadth x height = 20 x 15 x 8 = 2400 sq cm

Answer:

[tex]=3/4[/tex]

Step-by-step explanation:

[tex]\frac{4\sqrt{18}}{16\sqrt{2}}[/tex]

First, simplify the fraction:

[tex]=\frac{\sqrt{18}}{4\sqrt2}[/tex]

Now, simplify the radical in the numerator (the radical in the denominator cannot be simplified:

[tex]\sqrt{18}=\sqrt{9\cdot2}=\sqrt{9}\cdot\sqrt{2}=3\sqrt{2}[/tex]

Substitute:

[tex]=\frac{3\sqrt{2}}{4\sqrt{2}}[/tex]

The radicals cancel:

[tex]=3/4[/tex]

Answer:

8 scoops of flour

Step-by-step explanation:

It asks for you to solve using unit rates so we need to find out the rate of how much flour you need to bake a single cookie since the question is about how many scoops of flour Shelby needs to bake 64 cookies.

So first, do 6/48, which is 1/8.

It takes 1/8 scoop of flour to bake one cookie.

Unit rate: 1/8 scoop of flour per cookies.

Now, we can multiply 1/8 by 64 since 64 is the number of cookies Shelby needs and 1/8 is the amount of flour for one single cookies. 1/8 * 64 = 8.

Shelby needs 8 scoops of flour to bake 64 cookies

Answer:

Mark as BRAINLIEST plz

|x-323|<50: answer

Step-by-step explanation :

For water to be a liquid, the temperature must be within 50 Kelvin of 323 K.

So, the range of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323.

The equation that can be used to determine the maximum temperature at which water is a liquid can be given by :  x < 323 + 50

The equation that can be used to determine the minimum temperature at which water is a liquid can be given by : x > 323 - 50

So the resultant equation can be written as :

|x-323|<50

The solution of inequality equation is  | x - 323 | < 50

What is an Inequality Equation?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the temperature of the water be = x Kelvin

Now , the equation will be

For water to be in the liquid state, the temperature must be within 50 kelvin (K) of 323 K

So , the value of the temperature of water will lie between 50 kelvin more than 323 kelvin and 50 kelvin less than 323

Substituting the values in the inequality equation , we get

For maximum temperature ,

x should be 50 more than 323 and

For minimum temperature ,

x should be 50 less than 323

So ,

The inequality relation is

x > 50 + 323   be equation (1)

x < 323 - 50   be equation (2)

So , the modulus function is expressed as

It always gives a non-negative value of any number or variable. Modulus function is denoted as y = |x| or f(x) = |x|, where f: R → (0,∞) and x ∈ R.

Therefore , the value is | x - 323 | < 50

Hence , The solution of inequality equation is  | x - 323 | < 50

To learn more about inequality equations click :

https://brainly.com/question/11897796

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Answer:

[tex]y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3[/tex]

Step-by-step explanation:

The region R is surrounded by 4 lines, the first one is y=x+1, the second one is y=0 or the axis x, and the third and fourth one need to be calcualted.

To find the equation of a line through the points (x1,y1) and (x2, y2) we can use the following equation:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

Then, our third line is going to be the line that passes through the points (2,0) and (4,3), so the equation is:

[tex]y=\frac{3-0}{4-2}(x-2)\\y=\frac{3}{2}x-3[/tex]

Our fourth line is the line that passes through the points (3,0) and (0,3), so the equation is:

[tex]y=\frac{3-0}{0-3}(x-3)\\y=-x+3[/tex]

Then we can say that the other three inequalities are:

[tex]y\geq 0\\y\geq \frac{3}{2}x-3\\ y\leq -x+3[/tex]

Answer:

The probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.

Step-by-step explanation:

Suppose the probability of an event occurring is [tex]P_{i}[/tex].

The probability of the given event not taking place is known as the complement of that event.

The probability of the complement of the given event will be,

[tex]1 - P_{i}[/tex]

In this case an events X is defined as a man, aged 55​ - 59, will die of cancer during the course of the year.

The probability of the random variable X is:

[tex]P (X) = \frac{300}{100000}=0.003[/tex]

Then the event of a man in this age category not dying of cancer during the course of the​ year will be complement of event X, denoted by X'.

The probability of the complement of event X will be:

[tex]P(X')=1-P(X)[/tex]

          [tex]=1-0.003\\=0.997[/tex]

Thus, the probability that a man in this age category does NOT die of cancer during the course of the​ year is 0.997.