A toy company packs 20 marbles of varying sizes in containers. The function f

capacity required to hold 20 marbles with radius, 2 inches

f(x) = 40 (6+x)

If you have 5 qualified candidates to fill the positions of president and vice president, then their have 20 ways to be fill the positions.

In the given question,

If you have 5 qualified candidates to fill the positions of president and vice president, then we have to find how many ways can the positions be filled.

We have total 5 qualified question.

Their have total 2 position president and vice president.

When the one position one of president filled then their one left 4 qualified candidate for the vice president position.

So the possible ways to fill the position is find by multiplying the 5 and 4. So

Possible ways=5*4

Possible ways=20

Hence, if you have 5 qualified candidates to fill the positions of president and vice president, then their have 20 ways to be fill the positions.

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Answer:

The answer is A

Step-by-step explanation:

Count all the x's. They add up to 8.

Hope this helped.

Answer:

A. There were 8 people who rode in the bicycle race.

Step-by-step explanation:

The line plot in the picture shows the distance in miles raced by Sophie's friends.

It's required to select one of the following options:

A. There were 8 people who rode in the bicycle race.

Since each x represents one person, and there are 8 x's, this statement is true.

B. More people rode 3/4 of a mile than 1/4 of a mile. There is only one x in 3/4 and 3 x's in 1/4. This is false

C. This option is false also, there were 5 people who rode 1/4 of a mile or 2/4 of a mile.

D. There were 2 people who rode 1 mile. False

There are a total of 9 items to divide among 3 people, so the number of ways to divide the items is 84.

In mathematics, a combination is a selection of elements from a bigger group where the arrangement of the elements is irrelevant. Consider a collection of three letters, A, B, and C, for illustration. Two of these letters, AB, AC, and BC, can be chosen in one of three ways. "Combinations" of the letters A, B, and C are what these three options are referred to as.

C(n, k)=n!/(k!*(n-k))!

where the product of all positive integers from 1 to n, denoted by the symbol n!, is the factorial of n. For instance, 5! equals 1 + 2 + 3 + 4 + 5 = 120.

For example, three people divide among themselves six identical apples, one orange, one plum, and one tangerine.

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The person would need to take out a minimum of 31 socks to make sure they have at least one pair of black socks.

To make 100 percent certain he has at least one pair of black socks, the person would need to take out a minimum of 31 socks. Here's how we can determine this:

1. The person wants to have at least one pair of black socks. This means they need to select two black socks from the pile.

2. To ensure they have at least two black socks, they need to assume the worst-case scenario, where they have already selected all the blue and red socks. In this scenario, the person would have taken out 21 blue socks and 17 red socks, which totals to 38 socks.

3. Since they need to have two black socks, they subtract 2 from the total number of socks they have already taken out (38 - 2 = 36).

4. Now, the person needs to add the 15 identical black socks they haven't taken out yet.

5. Therefore, the minimum number of socks the person must take out to make 100 percent certain they have at least one pair of black socks is 36 + 15 = 51.

So, the person would need to take out a minimum of 31 socks to make sure they have at least one pair of black socks.

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Answer:

C ) 18 hope this helps !!!

Answer:

C. 18

Step-by-step explanation:

If you multiply 30%, or .3 by 60, you get 18.

Answer:

w = 1.5

Step-by-step explanation:

22(w + 2) = 77 ← distribute parenthesis on left side

22w + 44 = 77 ( subtract 44 from both sides )

22w = 33 ( divide both sides by 22 )

w = \(\frac{33}{22}\) = \(\frac{3}{2}\) = 1.5

The number Joe is thinking of is -36.

To find the number Joe is thinking of, use algebraic expression and equation.

Let x be the number Joe is thinking of

According to the problem, "Eleven more than one third of the number is -1". We can translate this into an algebraic expression such as:

x/3 + 11 = -1

To find the value of x, we'll isolate it on one side of the equation:

x/3 = -12

Next, we'll multiply both sides of the equation by 3 to cancel out the fraction:

x = -36

Therefore, the number Joe is thinking of is -36.

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The required equation for the given condition is 50x + 100y = 1000.

What is an algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

Given, the charge for every birthday party =$50

number of birthday parties = x

So, the total charge for birthday parties = 50x

the charge for every wedding  = $100

the number of weddings = y

So, the total charge for the wedding = 100y

Then,

Total amount achieve = $1000

or, 50x + 100y = 1000

Hence, the required equation is 50x + 100y = 1000.

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Answer:

60 minutes

Step-by-step explanation:

Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360°. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds.

One degree of latitude is equal to approximately 60 nautical miles or 69 statute miles. Since a minute of latitude is one-sixtieth of a degree, it follows that one degree of latitude is equal to 60 minutes.

This means that there are 60 nautical miles or 69 statute miles between two points that differ by one minute of latitude.

The minute of latitude is a widely used unit for measuring distances on Earth, particularly in navigation and aviation. It allows for precise calculations and is crucial for determining positions accurately. Understanding the relationship between degrees of latitude and minutes helps in determining distances, estimating travel times, and ensuring accurate navigation across the globe.

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If the mpc increases in value, the consumption function will become steeper.

What is MPC ?

MPC is an advanced method of process control that is used to control a process while satisfying a set of constraints. In economics, the marginal propensity to consume is a metric that quantifies induced consumption, the concept that the increase in personal consumer spending occurs with an increase in disposable income. The proportion of disposable income which individuals spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual consumes.

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The given demand and supply of the function has ,

Equilibrium price is Rs. 14 and the equilibrium quantity is equal to 40 units.

The consumer surplus for the given function is Rs. 1,080.

The producer's surplus for the given function is Rs. 40.

Demand of the function 'Qd' = -2P + 68

Supply  of the function 'Qs' = 2P + 12

The equilibrium price and quantity by setting the demand equal to the supply.

⇒ Qd =  Qs

Setting Qd equal to Qs, we get,

⇒-2P + 68 = 2P + 12

Solving for P, we get,

⇒4P = 56

⇒P = 14

Substituting P back into either the demand or supply equation, we get,

⇒Qd = -2(14) + 68

        = 40

⇒Qs = 2(14) + 12

        = 40

So the equilibrium price is Rs. 14 and the equilibrium quantity is 40 units.

The consumer's surplus,

= The area below the demand curve and above the equilibrium price.

⇒ Consumer's surplus

= (1/2) x (Equilibrium quantity) x (Difference between maximum price and equilibrium price)

⇒ Consumer's surplus = (1/2) x (40) x (68 - 14)

⇒ Consumer's surplus = Rs. 1,080

The consumer's surplus is Rs. 1,080.

The producer's surplus

= The area above the supply curve and below the equilibrium price.

⇒ Producer's surplus

= (1/2) x (Equilibrium quantity) x (Difference between equilibrium price and minimum price)

⇒ Producer's surplus = (1/2) x (40) x (14 - 12)

⇒ Producer's surplus = Rs. 40

The producer's surplus is Rs. 40.

Therefore, for the given demand and supply function we have,

Equilibrium price and the equilibrium quantity is equal to Rs. 14 and 40units.

Consumer’s Surplus  is Rs. 1,080.

Producer's surplus is Rs. 40.

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The above question is incomplete , the complete question is:

Given the demand = −2P + 68 and the supply function = 2P + 12. Calculate

The equilibrium price and the equilibrium quantity

(a) the consumer’s surplus

(b) the producer’s surplus assuming pure competition

The expression \((3xy^{-3})^{-2}\) without negative exponents is  \(\frac{y^6}{9x^2}\).

Some common rules of exponents are

xᵃ×xᵇ = xᵃ⁺ᵇ.

xᵃ/xᵇ = xᵃ⁻ᵇ.

Addition and subtraction of exponents are only possible for the same base value and when the base is different and both have the same exponent we just multiply the bases and write the exponent.

Given, An expression in exponents \((3xy^{-3})^{-2}\).

Now, Changing the place of exponents from the numerator to the denominator or vice versa changes its sign.

Therefore, \((3xy^{-3})^{-2} = 3^{-2}x^{-2}y^{6}\).

\(3^{-2}x^{-2}y^{6} = \frac{y^6}{3^2x^2}\).

\(\frac{y^6}{3^2x^2} = \frac{y^6}{9x^2}\).

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Answer:

The answer is $49.95

Step-by-step explanation:

I Took the quiz :D i hope this helps <3

Answer:

(x + 2)² = 9

x = 1 or - 5

Step-by-step explanation:

x² + 4x - 5 = 0

Solving first using completing the square method

x² + 4x = 5

x² + 4x + (4/2)² = 5 + (4/2)²

x² + 4x + 2² = 5 + 2²

x² + 4x + 4 = 5 + 4

x² + 4x + 4 = 9

Factorise

x² + 2x + 2x + 4 = 9

x(x + 2) + 2(x + 2) = 9

(x + 2)(x + 2) = 9

(x + 2)² = 9

Square root both sides

√(x + 2)² = √9

x + 2 = ± 3

x + 2 = +3

x = 3 - 2

x = 1

x + 2 = -3

x = -3 - 2

x = -5

Hence, x = 1 or - 5

1)the value of the constant c so that p(x) is \(c=\frac{1}{15}\).

2) Find the mean number of times the packet is \(\frac{2}{15}\).

a computer sends a packet of information along a channel and waits for a return signal acknowledging that the packet has been received. if no acknowledgment is received within a certain time, the packet is re-sent. let x represent the number of times the packet is sent. assume that the probability mass function of x is given,

x=0,1,2,3,4,5.

p(x)= 0,1,2,3,5=0.

{c,2c,3c,4c,5c}=1

0+c+2c+3c+4c+5c=1

15c=1

\(c=\frac{1}{15}\)

2) Find the mean number of times the packet is

p(x) for x = 0, 1, 2, 3, 4, 5 = 0, 1/15, 2/15, 3/15, 4/15, 5/15

P(X = 2) = 2/15

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The values of a, b, and c to complete the table for the inverse of the logarithmic function is 2,1 and -2 respectively.

The Inverse of the logarithmic function is an exponential function.

The given logarithmic function is,

\(f(x) = \log_{0. 5}x\)

The inverse of the given logarithmic function is,

\(f^{-1}(x) = 0.5^x.\)

Put the value of x as -1 from the table attached below, to find the value of a.

\(f^{-1}(-1) = 0.5^{(-1)}\\f^{-1}(-1) = 2\)

Similarly, put the value of x as 0 from the table attached below, to find the value of b.

\(f^{-1}(0) = 0.5^{(0)}\\f^{-1}(0) = 1\)

Now, put the value of x as 2 from the table attached below, to find the value of c.

\(f^{-1}(2) = 0.5^{(2)}\\f^{-1}(2) = -2\)

Thus, the values of a, b, and c to complete the table for the inverse of the logarithmic function is 2,1 and -2 respectively.

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Given equation of the Circle is ,

\(\sf\implies x^2 + y^2 = 25 \)

And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,

\(\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2\)

Here we can say that ,

• Radius = 5 units

• Centre = (0,0)

Finding distance between the two points :-

\(\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }\)

Here we can see that the distance of point from centre is less than the radius.

Hence the point lies within the circle .

Answer:

these points lie INSIDE THE CIRCLE

Hope it helps

have a nice day

Answer:

Option a represents a proportional relationship.

Step-by-step explanation:

A proportional relationship is a relationship where two variables are directly related to one another, meaning that their ratio is always the same. In other words, when one variable changes, the other variable also changes in the same ratio.

In the equation y = 2/3 * x, the value of y is directly proportional to the value of x, meaning that for every change in x, the corresponding change in y will always be 2/3 of that change. This is because the coefficient of x is a constant value, in this case 2/3. Therefore, as x increases or decreases, y will also increase or decrease at the same rate in proportion to x.

Option a represents a direct proportion.

Option b, c, and d are not proportional relationships because they include a constant or an operation like subtraction, addition or negative sign.

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Since i bought 1 tray of chips, and a cake, the equation is:

\($9.25 + 24 = 33.25\)

Now for the pizza, since i bought 4 pizzas for 10.50 each, with 1/3 off. The equation is:

\(10.50 * 4 = 42\)

The special is 1/3 for the pizzas:

\(1/3 * 42 = 14\)

Now adding the prices its:

\(33.25 + 14 = 47.25\)

The total: $47.25

you're welcome :D

Answer:

The pair of number that has the LCM of 60 is;

Explanation:

Given the pairs of number in the answer choices, we want to select the pair that has a LCM of 60;

Let us find the LCM of each of the pairs;

Therefore, the pair of number that has the LCM of 60 is;

Answer:

48

Step-by-step explanation:

You can use a graphing calculator like desmos or draw your own graph to figure this out. Start by graphing each of those points. Then count the width and height. Multiply them to get the area. The width and height of the rectangle were 6 and 8, so the area is 48

An approach for resolving systems of linear equations is the Gauss elimination method, commonly referred to as Gaussian elimination. It entails changing an equation system into an analogous system that is simple.

We can build the augmented matrix for the system of linear equations and apply row operations to get the reduced row-echelon form in order to locate all solutions to the system of linear equations.

[ 4  1  1  0 | 0 ]

[-1 -2  0  2 | 0 ]

[ 0  2  0  4 | 0 ]

[ 0  0  4  2 | 0 ]

We can convert this matrix to its reduced row-echelon form using row operations:

[ 1  0  0  0 | 0 ]

[ 0  1  0  2 | 0 ]

[ 0  0  1 -1 | 0 ]

[ 0  0  0  0 | 0 ]

From this reduced row-echelon form, we can see that there are infinitely many solutions to the system. We can express the solutions in parametric form

x₁ = t

x₂ = -2t

x₃ = t

x₄ = s

where t and s are arbitrary constants.

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(a) P (9,5) = 15,120

(b) P (9,9) = 362,880

(c) P (9,4) = 6,120

(d) P (9,1) = 9

(a) P (9,5) means choosing 5 objects from a total of 9 and arranging them in a specific order. Therefore, we have 9 options for the first object, 8 options for the second object, 7 options for the third object, 6 options for the fourth object, and 5 options for the fifth object. Multiplying these options together gives us P (9,5) = 9 x 8 x 7 x 6 x 5 = 15,120.

(b) P (9,9) means choosing all 9 objects from a total of 9 and arranging them in a specific order. This is simply 9! = 362,880, as there are 9 options for the first object, 8 options for the second, and so on until there is only one option for the last object.

(c) P (9,4) means choosing 4 objects from a total of 9 and arranging them in a specific order. This is calculated as 9 x 8 x 7 x 6 = 6,120.

(d) P (9,1) means choosing 1 object from a total of 9 and arranging it in a specific order. Since there is only 1 object and no other objects to arrange with it, there is only 1 way to arrange it, giving us P (9,1) = 9 x 1 = 9.

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Answer:

Second option: 32r - 8rp

Step-by-step explanation:

When you expand 8r(4-p) you get 32r - 8rp.

Answer:

= 32r - 8rp

Step-by-step explanation:

Distributive property:

8r(4 - p)

= 32r - 8rp

Steps:

8r · 4 = 32r

8r · (-p) = -8rp

= 32r - 8rp

Answer:

They are all true

Step-by-step explanation:

1. 3² +4² = 5²

3x3 + 4x4 = 5x5

  9   +  16  =  25

25 = 25

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

2. 6² + 8² = 10²

36 + 64 = 100

100 = 100

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

3. 9² + 12² = 15²

81 + 144 = 225

225 = 225

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

4. 5² +12² =13²

25 + 144 = 169

169 =169

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

Answer: w = -6

Step-by-step explanation:

-30 = 3(w + 6) + 5w

-30 = 3w + 18 + 5w

-30 = 8w + 18

-48 = 8w

w = -6

Hope this helps

Answer:

5/10

50/100

500/1000

Step-by-step explanation:

5/10 is equal to 1/2

50/100 is equal to 1/2

500/1000 is equal to 1/2

Answer:

4/3

Step-by-step explanation:

- take two easy points like ( 6, 6 ) and ( 3 , 2 ) in this case

- (y2 - y1) / (x2 - x1)

replace the values into a calculator and you'll get 4/3!

Answer:

4/3

Step-by-step explanation:

(3, 2)

(9, 10)

\(\frac{10 - 2}{9 - 3}\)

8/6 = 4/3

The glide reflection that maps ABC to A'B'C' is given as follows:

The glide reflection is a combination of a reflection with a translation.

The line of reflection passes through the midpoint of a pair of vertices, being perpendicular to the vertex.

The midpoint of segment A'B' is given as follows:

The slope of this segment is given as follows:

m = (-6 - (-2))/(6 - 4) = -1.

Then the slope of the reflection line is of:

m = 1.

(as the reflection line is perpendicular to the segment, meaning that the multiplication of their slopes is of -1).

Then:

y = x + b.

When x = 5, y = -4, then the intercept b is calculated as follows:

-4 = 5 + b

b = -9.

Thus the reflection line is of:

y = x - 9.

Then the translation is given subtracting the coordinates of one of the vertices, as follows:

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