A display of gift boxes has 1 box in the top row. 3 boxes in the next row, 5 boxes in the next row, and so on. there are 7 rows in all. how many gift boxes are in the display?

complete square = 100 square yards

 triangle = 1/2 x base x height = 1/2 x 10 x 5 = 25 square yards

100-25 = 75 square yards

shaded area = 75 square yards

Probability of an event is the measure of its chance of occurrence. The probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

Binomial distributions consists of n independent Bernoulli trials.

Bernoulli trials are those trials which end up randomly either on success (with probability p) or on failures( with probability 1- p = q (say))

Suppose we have random variable X pertaining binomial distribution with parameters n and p, then it is written as

[tex]X \sim B(n,p)[/tex]

The probability that out of n trials, there'd be x successes is given by

[tex]P(X =x) = \: ^nC_xp^x(1-p)^{n-x}[/tex]

For the given case, as failing or working of chips usually doesn't depend on other chips' working condition, so they're independent(assuming). There are two cases for each chip's working(random experiment) that it is either working or failed.

If we take Success of the considered binomial experiment(working status of chip) = Chip working fine

Then, as per given data, we have

P(chip working fine ) = 1  - P(chip not working) = 1 - 0.02 = 0.98 = Probability of success in Bernoulli experiment (chip's working status).

There are n = 5 chips, p = probability of success = 0.98, q = 1-p = 0.02

If we take X = number of chips of of 5 chips working, then:

[tex]X \sim B(n = 5, p = 0.98)[/tex]

Then, the needed probability is P(Exactly two chips fail) = P(Exactly 5-2 = 3 chips work) = P(X  = 3)

And thus,  the needed probability is calculated as:

[tex]P(X = 3) = \: ^5C_3(0.98)^3(0.02)^2 = \dfrac{5.4.3}{3.2.1} \times 0.941192 \times 0.0004 = 0.003764768[/tex]

(using the probability mass function of binomial distribution).

Thus, the probability that of 5 delivered chips, exactly 2 will fail is 0.003764768 or approx 0.0004

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place the equation for g ( x^2-5) over the equation for f(4x+1)

 so you get

x^2-5/4x+1

B is the answer

To make [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream. This calculation is done by multiplying [tex]\frac{2}{5}[/tex] cup (the amount required for a whole pie) by [tex]\frac{3}{4}[/tex].

To calculate the amount of cream needed for making [tex]\frac{3}{4}[/tex] of a nelly cream pie when the full pie requires [tex]\frac{2}{5}[/tex] cup of cream, we simply multiply these two fractions. To do this, first convert the mixed number [tex]\frac{3}{4}[/tex] to an improper fraction. We already have it in the proper format, so we can directly multiply:

([tex]\frac{2}{5}[/tex]) * ([tex]\frac{3}{4}[/tex]) = (2*3)÷(5*4)  = [tex]\frac{3}{10}[/tex]

Therefore, for [tex]\frac{3}{4}[/tex] of a nelly cream pie, you would need [tex]\frac{3}{10}[/tex] cup of cream.

I hope you got the idea

Let us say that:

x = width of walkway

So the area is:

(12 + 2x) (15 + 2x) = 238

2x because we must add x on both sides of length and width

Expanding:

180 + 24x + 30x + 4x^2 = 238

4x^2 + 54x = 58

By completing the square:

x^2 + 13.5x + 45.5625 = 60.0625

(x + 6.75)^2 = 60.0625

x + 6.75 = ±7.75

x = -14.5, 1

Since dimension cannot be negative, therefore:

width = 1 ft

Final answer:

The width of the walkway around the garden is 3.87 ft.

Explanation:

The width of the walkway around the garden can be found by subtracting the area of the garden from the total area of the garden with the walkway.

the answer is x=9

i'm not good at showing my work, but I'm positive in my answer I'm an honors student.

area of a circle = PI x r^2

r = 8.4/2 = 4.2

using 3.14 for PI

 area = 3.14 x 4.2^2 = 55.3896 square cm

 round answer as needed

When dividing 1 1/2 by 1/3, the quotient 4 1/2 indicates that each person receives half of a whole unit, which in our model is half of a pizza.

(a) To model the quotient 1 1/2 ÷ 1/3, imagine you have 1 1/2 units of something, like 1 1/2 pizzas. Now, if you divide each pizza into thirds, you'd have 3 halves of pizza. So, 1 1/2 pizzas divided by 1/3 pizza per person equals 4 people, each getting 1/2 of a pizza.

(b) The half in the quotient represents the portion of each whole unit (in this case, pizza) that each person receives. In our model, it signifies that each of the 4 people receives half of a pizza.

Answer: The answer is [tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

Step-by-step explanation:  Given that

[tex]\sin \theta=\dfrac{3}{4}[/tex] and [tex]\theta[/tex] is in Quadrant I.

We are to find the value of [tex]\cos \theta.[/tex]

We have the following trigonometric identity :

[tex]\sin^2\theta+\cos^2\theta=1\\\\\Rightarrow \cos^2\theta=1-\sin^2\theta\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\sin^2\theta}\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\left(\dfrac{3}{4}\right)^2}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{1-\dfrac{9}{16}}\\\\\\\Rightarrow \cos \theta=\pm\sqrt{\dfrac{7}{16}}\\\\\\\Rightarrow \cos \theta=\pm\dfrac{\sqrt{7}}{4}.[/tex]

Since [tex]\theta[/tex] lies in the first quadrant, so cosine of [tex]\theta[/tex] will be positive.

Thus,

[tex]\cos \theta=\dfrac{\sqrt{7}}{4}.[/tex]

The probability that the player will make next free throw is obtained as 0.795.

Probability is the branch of Mathematics that deals with the measurement of the chance of occurrence of a random event.

The probability of any event always lie in the close interval of 0 and 1 [0,1].

The total number of free throws is 220.

And, the number of throws by the player is 175.

Now, the probability can be found as below,

P(free throws) = Throws by the Player ÷ Total throws

⇒ 175 ÷ 220 = 0.795

Hence, the probability for the next free throw can be estimated as 0.795.

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The area of the enlarged figure will be 327.68 square units

The scale factor will be the ratio of the similar sides of a rectangle.

For the given triangles, the required scale factors will be expressed as:

[tex]\frac{4}{8} =\frac{a}{25.6}\\\frac{1}{2} =\frac{a}{25.6}\\2a = 25.6\\a=\frac{25.6}{2} \\a=12.8[/tex]

Next is to get the area of the bigger rectangle:

[tex]Area = Length \times Width\\Area=a\times 25.6\\Area=12.8\times 25.6\\Area=327.68 units^2[/tex]

Hence the area of the enlarged figure will be 327.68 square units

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1/5(15x-20) = 1/3(12x-9)

multiply the 15 and 20 on the left by 1/5 to get

3x-4

 now multiply 12 and 9 by 1/3 to get

4x-3

 now you have 3x-4 =4x-3

now solve for x

3x-4 =4x-3

subtract 3 x from each side:

-4 = x-3

 add 3 to each side

-1 = x

x = -1

divide 72.9 by 2.7

72.9 / 2.7 = 27 miles per gallon

Answer:

27 mi/gal

Step-by-step explanation:

The car mileage refers to the number of miles that a vehicle can run per gallon of fuel. A higher car mileage is desirable because it means that the vehicle has a better performance (travels more distance per gallon of fuel.) A driver uses 2.7 gallons of gasoline to drive her car 72.9 miles. The car mileage is:

72.9 miles / 2.7 gallon = 27 miles/gallon

The car can travel 27 miles per gallon of gasoline.

Answer:

Troy spent $9.09.

Step-by-step explanation:

Troy spent 20 Swiss Francs to stay one night in a youth hostel.

1 U.S. Dollar = 2.2 Swiss franc

We have to convert 20 Swiss franc to U.S. dollars.

So we divide 20 by 2.2 to convert Swiss franc to U.S. dollars.

= [tex]\frac{20}{2.2}[/tex] = 9.09090909 ≈ $9.09

Troy spent $9.09 to stay one night in a youth hostel.