Suppose that 24 inches of wire costs 72 cents. At the same rate, how much (in cents) will 49 inches of wire cost?

The most appropriate choice for Probability will be given by-

Probability of rolling a sum of 10 on a standard pair of six sided dice = \(\frac{1}{12}\)

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probality of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here,

Total number of outcomes = 36

Favourable outcomes = {(4,6), (5,5), (6,4)}

Number of favourable outcomes = 3

Probability of rolling a sum of 10 on a standard pair of six sided dice = \(\frac{3}{36}\)

                                                                                                                  = \(\frac{1}{12}\)

To learn more about probability, refer to the link-

https://brainly.com/question/25839839

#SPJ4

Given the building that can be modeled as a

right rectangular prism with dimentions

8 * 2 3/4 * 2 3/4

Volume is given by

since we have 850 bricks

the volume occupied by 850 bricks is therefore

then

the cost of the 850 bricks is

cost of bricks is $3085.50

The answer is `dy/dx = 2x*(x²+1)^8√(x^4 + x²)`. Hence, the correct option is `(x²+1)^8`.

The given function is `y

= ∫₀x²√t(t² + t)⁸dt`. We need to calculate the derivative of this function.The derivative of the given function is `dy/dx`.To calculate it, we need to use the Fundamental Theorem of Calculus (Part 1). According to it, if `f(x)` is continuous on the closed interval [a, b] and `F(x)` is the antiderivative of `f(x)` on the interval `[a, b]`, then the definite integral of `f(x)` from `a` to `b` can be calculated by evaluating `F(b) - F(a)`. Therefore, we can differentiate `y` by finding its antiderivative with respect to `t` and substituting `x²` for `t`, then multiplying the result by the derivative of `x²` with respect to `x` which is `2x`. That is:`dy/dx

= 2x*√(x^4 + x²)^8`.The answer is `dy/dx

= 2x*(x²+1)^8√(x^4 + x²)`. Hence, the correct option is `(x²+1)^8`.

To know more about correct visit:

https://brainly.com/question/23939796

#SPJ11

Answer:

Your answer is 8.

Answer:

Step-by-step explanation:

-24

Answer:

9 times 5 + c

Step-by-step explanation:

well, for the piece-wise function, we know that hmmm x = -1, -1 is less 1, so the subfunction that'd apply to that will be -2x + 1, because on that section "x is less than or equals to 1".

so f(-1) => -2(-1) + 1 => 3.

Answer:3

Step-by-step explanation:

In this case x=-1 so you will use the top equation because x<1

so f(-1) = -2(-1) + 1

          = 2+1

           =3

The final cost of the item after a 35% discount and 9.8% sales tax is $53.54.

The given problem is related to percentage discounts and sales tax and can be solved using the following steps:

Step 1: Firstly, we need to determine the discount amount, which is 35% of the original price. Let's calculate it. Discount = 35% of the original price = 0.35 x $75 = $26.25

Step 2: Now, we will calculate the new price after the discount by subtracting the discount amount from the original price.New Price = Original Price - Discount AmountNew Price = $75 - $26.25 = $48.75

Step 3: Next, we need to calculate the amount of sales tax. Sales Tax = 9.8% of New Price Sales Tax = 0.098 x $48.75 = $4.79

Step 4: Finally, we will calculate the final cost of the item by adding the new price and the sales tax.

Final Cost = New Price + Sales Tax Final Cost = $48.75 + $4.79 = $53.54

Therefore, the final cost of the item after a 35% discount and 9.8% sales tax is $53.54.I hope this helps!

For more such questions on final cost

https://brainly.com/question/29509552

#SPJ8

The sample minimum isn't an unbiased estimator as D. The mean of the sampling distribution of the sample minimums is 16, which is not 15.

A sampling distribution simply means a probability distribution that is obtained from a larger number of samples drawn from a population.

From the complete question, the sample minimum isn't an unbiased estimator as the mean of the sampling distribution of the sample minimums is 16, which is not 15.

In this case, the minimum of the ages of the officer is 15.

Learn more about sampling on:

https://brainly.com/question/24466382

Step-by-step explanation:

-4x+1+6-(-9x)

-4x+7-(-9x)

5x+7

1.5 dollars per candy bar because 13.50 divided by 9 is 1.5 :)

The ideal amount of flour for 5 cakes is 40 cups of flour. The ratio of flour to cake for baking is 8 cups of flour for 2 cakes. This means for each cake, there should be 4 cups of flour. Therefore, for 5 cakes, it would be 5 multiplied by 4, which is equal to 40. This amount of flour should be enough to produce moist, light, and fluffy cakes.

If the baker uses more than 40 cups of flour, it could lead to overly dense and dry cakes, because the extra flour will absorb all the moisture and leave the cakes dry. On the other hand, using less than 40 cups of flour could lead to the cakes being too light and airy. Not having enough flour can lead to a dry and tough texture.

Therefore, the baker should use 40 cups of flour when making 5 cakes. Following the 8 cups of flour to 2 cakes ratio ensures that the cakes will have the perfect texture and consistency. This is why 40 cups of flour is the ideal amount for a baker to make 5 cakes.

To learn more about perfect ratio:

https://brainly.com/question/29758642

#SPJ4

Answer:

Step-by-step explanation:

(cos 4a*cos 2a+sin 4a*sin 2a)/sin 4a

=[cos (4a-2a)]/sin 4a

=(cos 2a)/sin 4a

=(cos 2a) /(2 sin 2a cos 2a)

=1/(2 sin 2a)

=1/2 csc 2a

Answer:

the number is 5

Step-by-step explanation:

6n + 3 = 33

6n = 30

n = 5

Answer:

1.15

Step-by-step explanation:

Answer:

The slope of the function is 3

Step-by-step explanation:

To find the slope

*This method works for any other two other points and the work is in the attachment above*

The terminal ray of α falls in the third quadrant (where cosine is negative), we can conclude that: cos(α) = -3/5.

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to calculate the lengths of sides and angles in triangles, and to solve problems involving angles, distances, and heights. The three primary trigonometric functions are sine, cosine, and tangent, which describe the ratios of the sides of a right triangle. Other trigonometric functions include cosecant, secant, and cotangent, which are the reciprocals of the primary trig functions. Trigonometry has many applications in science, engineering, and technology, including astronomy, physics, navigation, and surveying.

Here,

Since the reference angle of α has a sine value of 4/5, we can use the Pythagorean identity sin²(θ) + cos²(θ) = 1 to find the cosine of the reference angle:

cos²(θ) = 1 - sin²(θ)

= 1 - (4/5)²

= 1 - 16/25

= 9/25

Taking the square root of both sides gives us:

cos(θ) = ± √(9/25)

= ± (3/5)

To know more about trigonometry,

https://brainly.com/question/26719838

#SPJ1

1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

Learn more about Transformations here :

https://brainly.com/question/23186655

#SPJ1

Answer:

The Answer is C. 50

Step-by-step explanation:

To pack 600 granola bars, 50 boxes are needed.

The correct option is C.

To determine how many boxes are needed for 600 granola bars, we divide the total number of granola bars by the number of granola bars that can be packed in one box.

Number of boxes = Total granola bars / Granola bars per box

Number of boxes = 600 / 12

Number of boxes = 50

So, 50 boxes are needed to pack 600 granola bars.

The correct answer is option C: 50.

To confirm this, let's see the reasoning: Since each box can hold 12 granola bars, to get 600 granola bars, you need to divide 600 by 12. The result is 50, which means you need 50 boxes to pack 600 granola bars. Option C, with 50, is the correct answer. Options A, B, and D do not provide the accurate number of boxes required for 600 granola bars.

To learn more about the division;

https://brainly.com/question/13263114

#SPJ3

There are 16 possible 2-letter code words letters can be repeated. There are 12 possible 2-letter code words adjacent letters must be different.

If letters can be repeated, the number of possible 2-letter code words that can be formed from the given letters is determined by the formula:

Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter)

Since we have 4 letters available (W, C, M, J), and we can repeat letters, the number of choices for each letter is 4.

Therefore, the number of possible 2-letter code words with repeated letters is:

4 * 4 = 16

If adjacent letters must be different, the number of possible 2-letter code words is determined as follows:

Number of possibilities = (number of choices for the first letter) * (number of choices for the second letter, excluding the previously chosen letter)

For the first letter, we have 4 choices. For the second letter, we have 3 choices because we need to choose a letter different from the first letter.

Therefore, the number of possible 2-letter code words with adjacent letters different is:

4 * 3 = 12

To summarize:

The number of possible 2-letter code words with repeated letters is 16.

The number of possible 2-letter code words with adjacent letters different is 12.

To learn more about code here:

https://brainly.com/question/32676392

#SPJ4

The probability that a randomly selected woman is taller than 5 ft 10 in (70 inches) is approximately 0.0143 or 1.43%.

To find the probability that a randomly selected woman is taller than 5 ft 10 in, we need to convert the height to inches and then calculate the probability using the Normal distribution.

5 ft 10 in is equivalent to 5(12) + 10 = 70 inches.

Let's calculate the z-score corresponding to a height of 70 inches using the formula: z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation. In this case, x = 70 inches, μ = 63.8 inches, and σ = 2.8 inches.

\(z=\frac{70-63.8}{2.8} = 2.214\)

Using a standard Normal distribution table or calculator, we can find the probability associated with this z-score.The probability of a randomly selected woman being taller than 5 ft 10 in (70 inches) can be found by calculating the area under the Normal distribution curve to the right of z = 2.214.

P(Z > 2.214) = 1 - P(Z ≤ 2.214)

By looking up the corresponding probability in the standard Normal distribution table or using a calculator, we find that P(Z ≤ 2.214) ≈ 0.9857.

Therefore, P(Z > 2.214) = 1 - 0.9857 =0.0143.

Thus, the probability that a randomly selected woman is taller than 5 ft 10 in (70 inches) is approximately 0.0143 or 1.43%.

To know more about "Probability" refer here:

https://brainly.com/question/32004014#

#SPJ11

The solution are x < -1 or x ≥ 4.

A graph of the inequality is shown below.

The interval notation for the inequality is [-∞, ∞].

In Mathematics and Geometry, an inequality is a relation that compares two (2) or more numerical data, number, and variables in an algebraic equation based on any of the inequality symbols;

Next, we would solve the given inequality for x as follows;

1 - 2x > 3

-2x > 3 - 1

-2x > 2

x < -1

2x - 4 ≥ 4

2x ≥ 4 + 4

x ≥ 4

Therefore, the interval notation for this inequality 1 - 2x > 3 or 2x -4 ≥ 4 is [-∞, ∞].

Read more on inequality here: brainly.com/question/30665021

#SPJ4

Complete Question:

Solve, graph, and give interval notation for the inequality: 1 - 2x > 3 or 2x -4 ≥ 4.

Draw:

Interval notation for the above graph is:

if the statement is true for some positive integer n, it must also be true for n+1. This completes the inductive step and demonstrates that the statement P(n) holds for all positive integers n.

In the inductive step, we need to prove that the statement P(n) implies P(n+1), where P(n) is the given statement: 13 + 23 + 33 + ... + n313⁢ + 23⁢ + 33⁢ + ...⁢ + n3 = (n(n + 1)2)2(n⁢(n⁢ + 1)2)2 for the positive integer n.

To prove the inductive step, we need to show that assuming P(n) is true, P(n+1) is also true.

In other words, we assume that the formula holds for some positive integer n, and our goal is to show that it holds for n+1.

So, in the inductive step, we need to demonstrate that if 13 + 23 + 33 + ... + n313⁢ + 23⁢ + 33⁢ + ...⁢ + n3 = (n(n + 1)2)2(n⁢(n⁢ + 1)2)2, then 13 + 23 + 33 + ... + (n+1)313⁢ + 23⁢ + 33⁢ + ...⁢ + (n+1)3 = ((n+1)((n+1) + 1)2)2((n+1)(n+1 + 1)2)2.

By proving this, we establish that if the statement is true for some positive integer n, it must also be true for n+1. This completes the inductive step and demonstrates that the statement P(n) holds for all positive integers n.

Learn more about integer here

https://brainly.com/question/31048829

#SPJ11

1. In this context, f(t) = g(t) means that Fran and George will have saved the same amount of money for the summer trip at time t.

2; In this context, f(t) + g(t) represents the total combined savings of Fran and George at time t.

3. The new function rule h(t) is h(t) = 35t + 1000.

4 In this case, the y-intercept is 1000, which means they already have $1000 saved up before they began saving specifically for the summer trip.

1. It represents the point in time when their projected savings will be equal.

2. It is the sum of the amount of money Fran has saved (according to f(t)) and the amount of money George has saved (according to g(t)).

3. To find a new function rule, h(t), that represents the amount of money Fran and George raise together, we simply add their individual savings functions together:

h(t) = f(t) + g(t)

= (20t + 550) + (15t + 450)

= 35t + 1000

So the new function rule h(t) is h(t) = 35t + 1000.

4. The y-intercept of the new function, h(t), is the value of h(0), which can be calculated as:

h(0) = 35(0) + 1000

= 0 + 1000

= 1000

In terms of the context, the y-intercept of the function h(t) represents the amount of money Fran and George already have saved before they start working (at time t = 0). In this case, the y-intercept is 1000, which means they already have $1000 saved up before they began saving specifically for the summer trip.

Learn more about functions on

https://brainly.com/question/11624077

#SPJ1

The width of the box is 3 ft that can be produced using the minimum amount of material.

Consider a box with length 'l', width 'w' and height 'h',

Volume V = l × w × h

Surface area S = 2(lw + wh + hl)

It is given that,

Volume of the box V = 36 cubic feet and l = 2w

Using the formulae,

V = 2w × w × h = 2w²h ...(1)

S = (2w² + 2wh + 4wh) = 2w² + 6wh ... (2) (here only single lw is considered since it is open top)

From equation (1),

36 = 2w²h

⇒ w²h = 18

⇒ h =18/w²

equation (2) becomes

S = 2w² + 6w(18/w²) = 2w² + 108/w ...(3)

So, for a minimum amount of material, the width of the box is,

On differentiating the surface area w.r.t 'w'

S' = 4w - 108/w²

For a minimum amount, substituting S' = 0 we get,

0 = 4w - 108/w²

⇒ 4w = 108/w²

⇒ 4w³ = 108

⇒ w³ =  27

∴ w = 3 feet

Therefore, the width of the given box is 3 feet.

Learn more about volume and surface area here:

https://brainly.com/question/13522634

#SPJ4

Answer:

ljj

Step-by-step explanation:

llk

Yes , the series is an arithmetic sequence of common difference 2

What is Arithmetic Progression?

An arithmetic progression is a sequence of numbers in which each term is derived from the preceding term by adding or subtracting a fixed number called the common difference "d"

The general form of an Arithmetic Progression is a, a + d, a + 2d, a + 3d and so on. Thus nth term of an AP series is Tn = a + (n - 1) d, where Tₙ = nth term and a = first term. Here d = common difference = Tₙ - Tₙ₋₁

Sum of first n terms of an AP: Sₙ = ( n/2 ) [ 2a + ( n- 1 ) d ]

Given data ,

Let the number of terms n = 20

The number of tiles in the first row = 10 tiles

The number of tiles in the second row = 2 more than first row

The number of tiles in the second row = 12 tiles

The number of tiles in the third row = 14 tiles

So , the sequence will be , 10 , 12 , 14 , 16 ...

The number of terms n = 20

The first term a = 10

The common difference d = second term - first term

The common difference d = 12 - 10 = 2

The series is an arithmetic sequence and the 20th term of the sequence will be

a₂₀ = a + ( n - 1 )d

a₂₀ = 10 + ( 19 ) 2

a₂₀ = 10 + 38

a₂₀ = 48 tiles

Hence , the series is an arithmetic sequence

To learn more about arithmetic progression click :

https://brainly.com/question/1522572

#SPJ5

Answer:

She can bake 8 dozen cookies in 112 minutes.

Step-by-step explanation:

70/5 =14

112/14= 8