Kyle needs 164 beads for a project. The beads are sold in packs of 2, 5, or 10. What is the least number of packs Kyle needs to buy. Explain

Translating the phrase into an algebraic expression for the difference between four times a number and 10 is 4x - 10.

An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Let the number be given as x.

Therefore, 4 times will number will be 4x.

Then, difference between four times a number and 10 will be:

= 4x - 10

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The number of handshakes that occur in Tom's workshop is 105

Given: Number of people in the workshop is 15 and Every person shakes hands once with every other person

To find: Number of handshakes

Since every person has to meet the other person only once and shake hands only once. So every handshake has only one possible combination.

Total number of combinations (handshakes) that can be possible with 15 people = [tex]15C_2[/tex]

The formula for a combination is

[tex]nC_r = \frac{n!}{r!(n-r)!}[/tex]

where n is the number of items and r is the unique arrangements.

Plugging in our numbers of n = 15 and r = 2, we get

[tex]15C_2= \frac{15!}{2!(15-2)!}\\= \frac{15!}{2! \times 13!} \\=\frac{15 \times 14 \times 13!}{2! \times 13!}\\[/tex]

On cancelling out 13! from numerator and denominator , we get

[tex]15C_2=\frac{15 \times 14}{2 \times 1}= 15 \times 7=105[/tex]

A combination is a method of picking things from a collection in which the order of selection is irrelevant. Assume we have three numbers P, Q, and R. Combination defines how many possibilities we may choose two numbers from each set.

It is feasible to count the number of combinations in smaller collections, but the possibilities of a set of combination increases with the number of groups of elements or sets. As a result, a formula has been developed to determine the number of things that can be selected.

The formula is

[tex]nC_r = \frac{n!}{r!(n-r)!} \, when \, n > r\\nC_r = 0 \, when \, n < r[/tex]

Where n = number of distinct objects to choose from

C = Combination

r = spaces to fill

The number of handshakes that occur in Tom's workshop is 105

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Step-by-step explanation:

5(2+3)-3*4²

=5*5-3*16

=25-48

=-23(A)

The values of the angles are m∠ A = 112.5°, m∠ B = 67.5°, m∠ C = 67.5°, and m ∠D = 112.5°

Considering the regular octagon, the sum of angles in an octagon is 1080°. This implies each angle in the octagon will be 1080/8 = 135°

Thus, you can label the angle as shown in the image attached

c + m<A + 135° = 360°  (the sum of angle at a point is 360°)

Since c = m<A (identical sides)

m<A + m<A + 135° = 360°

2 m<A = 360-135

m<A = 225/2 = 112.5°

m<B + m<A = 180°  (Between two parallel lines, consecutive interior angles add up to 180°)

m<B + 112.5° = 180°

m<B = 180-112.5 = 67.5°

m<C = <B    (base angles of isosceles trapezoids are equal)

m<C = 67.5°

m<D = m<A    (base angles of isosceles trapezoids are equal)

m<D = 112.5°

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Answer:

Factor for this problem is

2(2c+1)(c+2)

Answer:(c+2)(4c+2)      

Step-by-step explanation:

Factor by grouping

(c+2)(4c+2)      

Answer:

Step-by-step explanation:

Simplify parentheses : 0.5x+0.3=2.1x+9-5.5

Combine like terms : 0.5x+0.3=2.1x+3.5

Isolate the variable : -1.6x=3.2

Divide by -1.6 on both sides : x=-2

Answer:  the answer is in the picture

have a nice one

Step-by-step explanation:

The equation is [tex]36x-y=145[/tex].

The domain is (∞,-∞), {x,x∈R}.

What is the domain of a function?

The domain of a function is the set of all conceivable values that are acceptable as inputs, or alternatively, it can be interpreted as the full set of potential values for independent variables. The denominator of the fraction is not equal to zero, and the digit under the square root bracket is positive, which is an indicator of the domain.

Let us first take any 2 coordinates of the function, say (-143,-2) and (0,-71).

let us take the slope of these 2 points,

[tex]m=\frac{x_{2}-x_{1} }{y_{2}- y_{1} } \\m=\frac{-71+143}{0+2} \\m=\frac{72}{2} \\m=36[/tex]

Now, using the slope, we can find the required equation:

[tex]y-y_{1} =m (x-x_{1} )\\y+143=36(x+2)\\36x-y=145\\[/tex]

The domain for the function is (∞,-∞), {x,x∈R}.

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The two solutions of the quadratic equation are:

x  = 1.135

x= -1.468

A general quadratic equation:

a*x^2 + b*x + c = 0

Has solutions of the form:

[tex]x = \frac{-b \pm \sqrt{b^2 - 4ac} }{2a}[/tex]

Here the quadratic equation is:

3*x^2 + x - 5 = 0

So the values are:

a = 3

b = 1

c = -5

Replacing that in the quadratic formula for the solutions we will get:

[tex]x = \frac{-1 \pm \sqrt{1^2 - 4*3*(-5)} }{2*3}\\\\x = \frac{-1 \pm 7.81 }{6}[/tex]

Thus, the two solutions are:

x = (-1 + 7.81)/6  = 1.135

x = (-1 - 7.81)/6 = -1.468

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95% of the time confidence intervals like this capture the true average time between a felony.

The average of the true ranges throughout the given period is known as the average true range (ATR). ATR calculates volatility by accounting for any gaps in price movement. 14 periods, which can be intraday, daily, weekly, or monthly, are typically used in the ATR calculation. Utilize a shorter average, such as 2 to 10 periods, to gauge recent volatility. Use 20 to 50 periods for volatility over longer time spans.

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The 7th term of the sequence is 136.6875

From the question, we have the following sequence that can be used in our computation:

12, 18, 27....

In the above sequence, we can see that the previous term is multiplied by 1.5 to get the current term

Using the above as a guide,

So, we have the following representation

aₙ = 1.5aₙ₋₁

a₄ = 1.5 * 27

Evaluate the products

a₄ = 40.5

Solving further, we have

a₅ = 40.5 * 1.5

Evaluate the products

a₅ = 60.75

Solving further, we have

a₆ = 60.75 * 1.5

Evaluate the products

a₆ = 91.125

Solving further, we have

a₇ = 91.125 * 1.5

Evaluate the products

a₇ = 136.6875

Hence, the 7th term is 136.6875

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Answer:

-25

Step-by-step explanation:

10ml  of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid

percentage, a relative value indicating hundredth parts of any quantity.

We need to find how many ml of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid

Let x = number of ml of 20% acid

x mL of 20% acid plus (20 - x )mL of 100% acid  = 20 mL of 60% acid

0.20x+1.00(20-x)=0.6(20)

0.20x+20-x=12

20-0.8x=12

Subtract 20 on both sides

-0.8x=12-20

-0.8x=-8

Divide both sides by -0.8

x=10

Hence, 10ml  of 20 percent acid should be added to pure acid to make 20ml of 60 percent acid

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The standard error is decreasing on increasing number of Sample.

What is the standard error?

The population mean and sample mean are likely to deviate from one another, and the standard error of the mean, or simply standard error, shows how likely this is.

                    If a study were to be repeated using fresh samples drawn from a single population, it would be possible to calculate how much the sample mean would change.

The standard error is represented by a σ because it is a standard deviation. The subscript (M) indicates that the standard error in question is the standard error of the mean.

Now we will get the standard error for the following situations:

(a) σ_M = 12/√4 = 6

(b) σ_M = 12/√16 = 3

(c) σ_M = 12/√64 = 1.5

Hence from here, we can conclude that the standard error is decreasing on increasing number of Sample.

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The equation of the line is y=3÷5x+4.

Here, we need to figure out the slope of this curve.

if two lines are perpendicular to each other and both of their slopes exist, the product of their slopes is equal to -1.

k1 = -9-6÷1-(-4)

   = -5÷3

k2-k1  = -1

∴k2= 3÷5

y-1= 3÷5[x-(-5)]

y= 3÷5÷x+4

Hence, The equation of the line is y=3÷5x+4.

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The domain of an inverse function, f1, is the domain of a function, f(x) (x). The range of f1 is the scope of f(x) (x).

The output of a function is returned by the inverse function, which also returns the initial value. Consider the inverse relationship between the functions f and g: f(g(x)) (= g(f(x)) = x. The initial value is fetched via a function that is its inverse.

The opposite is called inverse. In mathematics, an inverse operation is one that reverses the effects of a preceding operation. Inverse operations refers to the set of two opposing operations.

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Using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.

PEMDAS stands for Parentheses, Exponents, Multiplication, Division, and Addition Subtraction (from left to right).

So, we know that:

Jenna has 50 pieces of laundry.

She removed her 10 favorite shirts.

50 - 10 = 40

She divided the rest into 8 piles.

40/8 = 5

Therefore, using simple mathematical operations, we know that Jenna has 8 piles of clothes with 5 pieces of cloth in each pile for the machine.

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The total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

It is given that, If Mars travels at 24,126 meters per second in orbit around the Sun and takes 1.88 earth years to complete its orbit,

First, we have to convert the unit from earth year to second obtained as,

1.88 earth year=  59287680 second

As we know that the distance is the multiplication of the speed and the time

Distance = speed × Time

Distance =24,126 m/sec ×  59287680 second

Distance = 1.4 × 10¹² m

If 1 meter consists of 0,000621371 miles, the obtained distance is in miles.

1 metere = 0,000621371 miles

1.4 × 10¹² m=888 × 10⁶ miles

Thus, the total distance in miles Mars travels throughout its complete orbit will be 888 × 10⁶ miles.

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Probability p(Royal flush)= 4/2598960 = 1/649740

What is Probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

A royal rush in Poker Card is five of each of the following: ace, king, queen, jack, and ten.

The ten, Jack, Queen, King, and Ace of a single suit make up a royal flush. These hands come in fours.

Total no. of ways = selecting 5 cards out of 52 cards = 52 C5 = 2598960

So, P(royal flush)= 4/2598960 = 1/649740

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Answer: D 12.54-10.67

he data in the table appears to be modeled by the function f(x) = -x^2 + 2.

To see this, let's plug in the values for x in the table and see if the resulting values for f(x) match the values in the table:

f(-2) = (-2)^2 + 2 = 4 - 2 = 2

f(-1) = (-1)^2 + 2 = 1 - 1 = 0

f(0) = 0^2 + 2 = 2

f(1) = 1^2 + 2 = 1 + 2 = 3

We can see that the resulting values for f(x) match the values in the table, so f(x) = -x^2 + 2 is a function that could represent the data.

Answer:

4

Step-by-step explanation:

Let's think of this as a cube with layers.

(Layer = height)

If the first layer has 20, and the cube has a total of 80, we can use this equation:

80 = 20 × number of layers

Let's figure out how many times we need to multiply 20 to get 80.

20 × 4 = 80

The cubes height is 4.

Answer:

Step-by-step explanation:

The volume of a room is 80 m³. The area of the floor is 20 m². The height of the room is:​

Volume = l x w x h (base area times height)

we use the inverse formula

Height = 80 : 20 =

4

Each partner needs to pay $41 to bring the balance to $0.

What is the linear equation in one variable?

The linear equation in one variable is an equation that is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

Let x be the amount each partner pays.

We can set up the equation as follows:

(-123) + 3x = 0

To solve for x, we can add 123 to both sides of the equation:

(-123) + 123 + 3x = 0 + 123

This simplifies to:

3x = 123

To solve for x, we can divide both sides of the equation by 3:

(3x)/3 = 123/3

This simplifies to:

x = 41

Therefore, each partner needs to pay $41 to bring the balance to $0.

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Answer:

61 is the mode.

Step-by-step explanation:

Remember, the mode is the most repeated number in the list. 6|1 is repeated the most times (twice).

Answer:

61 is the correct answer

Answer:

[tex]e = \frac{bd}{v - bc} [/tex]

Step-by-step explanation:

[tex] \frac{v}{b } - c = \frac{d}{e } [/tex]

[tex] = > multiply \: bothsides \: by \: e[/tex]

[tex] = > \frac{v}{b} \times e - c \times e = \frac{d}{e} \times e[/tex]

[tex] \frac{ve}{b} - ce = d[/tex]

[tex] = > multiply \: both \: sides \: by \: b[/tex]

[tex] \frac{ve}{b} \times b - ce \times b = bd[/tex]

[tex] = > ve - bce = bd[/tex]

[tex] = > e(v - bc) = bd[/tex]

[tex] = > divide \: both \: sides \: by \: (v - bc)[/tex]

[tex] = > e = \frac{bd}{v - bc } [/tex]

Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )

The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.

This statement states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

For a triangle to be Right Angled , It should obey the Pythagoras Theorem

[tex]c^{2} = a^{2}+b^{2}[/tex]

c = hypotenuse

a = perpendicular side

b = base

Hence

if c = 5 , a = 3 and b = 4

Then

[tex]c^{2} = a^{2}+b^{2}[/tex]

[tex]5^{2}= 3^{2}+4^{2}[/tex]

25 = 3 + 16

25 = 25

So

It obeys the Pythagoras Theorem

Set of Sides which will form a right angled triangle is ( 3 , 4 , 5 )

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Answer:

36

Step-by-step explanation:

[tex]\frac{1}{4}(12^2)=\frac{1}{4}(144)=36[/tex]

Answer:

-4x-12

Step-by-step explanation:

7x-8x-3x = -4x

14-26 = -12

-4x-12

The monthly payment would be an amount of $163.875.

A monthly payment is a payment made every month to pay off loans or advances. It's similar to EMI.

As per the given question, we have

Here P = $1900 , r = 3.5%, and T = 1 years

The total payback = P× r/100 × T + P

The total payback = 1900 × 3.5/100 × 1 + 1900

The total payback = 1900 × 0.04 × 4 + 1900

Apply the multiplication operation, and we get

The total payback = $1966.5

The total payback of the borrowings will be $1966.5 over a one-year period. The monthly payment for this will be,

The monthly payment = Total payback / No. of payment

The monthly payment = 1966.5/12

The monthly payment = $163.875

Therefore, the monthly payment would be an amount of $163.875.

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Answer:

12 yards

3+4+5=12

3+4=7

7+5=12

Answer:

12, needed to be multiplied ( which I don't think so) 60

Step-by-step explanation:

I really don't have a "step by step explanation" but 4+5=9+3=12

or: 4x5=20x3=60

The required probability will be 127/128 that getting at least one tail when tossing seven.

We know that the total number of sides on a coin [Tail, Heads] =2

The probability of getting a tail = 1/2

The  probability of getting no tail = 1 -1/2 = 1/2

According to the "at least once" rule, when a coin is tossed n times, the chance of obtaining at least one tail is given by:-

P(at least one tail) = 1 - [P(no tail)]ⁿ

In this case, n=7

Then, the probability of getting at least one tail is given by:-

P(at least one tail) = 1 - (1/2)⁷

P(at least one tail) = 1 - (1/128)

P(at least one tail) = 127/128

Thus, the required probability will be 127/128 that getting at least one tail when tossing seven.

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