Plz help ASAP and good explanation thank you

It would take 5040 cubic inches of water to completely fill the aquarium.

We know that the formula for the volume of cuboid :

V = length × width × height

Let us assume that l represents the length of the aquarium, w represent the width and h represents the height.

Here, l = 20 inches

w = 14 inches

and h = 18 inches

Using the formula for the volume of cuboid, the volume of aquarium would be,

V = l × w × h

V = 20 × 14 × 18

V = 5040 cu.in.

Therefore, it would take 5040 cu.in. of water.

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An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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The 500th term of the 7 count sequence 24,31,38,45,52 is 3517.

It should be noted that this is an arithmetic sequence. The formula is represented as:

a + (n - 1) d

where

a = first term

n = number of terms

d = common difference

Since the numbers are 24,31,38,45,52, the common difference is (3 - 25) = 7

The 500th term will be:

a + (n - 1) d

24 + (500 - 1) × 7

= 24 + (499 × 7)

= 24 + 3493

= 3517

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dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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Answer:

hello,

Step-by-step explanation:

n+2*(2n-5)=20

5n-10=20

5n=30

n=6

After considering the given data we conclude that there truth table is possible and is placed in the given figures concerning every sub question.

A truth table is a overview that projects  the truth-value of one or more compound propositions for each possible combination of truth-values of the propositions starting up the compound ones.
Every row of the table represents a possible combination of truth-values for the component propositions of the compound, and the count of rows is described by the range of possible combinations.
For instance, if the compound has just two component propositions, it comprises  four possibilities and then four rows to the table. The truth-value of the compound is projected on each row comprising the truth functional operator.
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Answer:

$112

Step-by-step explanation:

$168 per 12 hours of work

168/12 = 14

$14 per hour of work

14*8 = 112

$112 per 8 hours of work

I hope that this helped

168/12=14 . 14•8= 112

i am pretty sure this is the answer

Answer:

9/10

Step-by-step explanation:

9 is in the tenth place so the denominator is 10.

Answer:

the answer is 9/10

i) Michaelangelo's sells small, medium, large, and jumbo pizzas. - Not nominal data.

Nominal data refers to a type of categorical data where values are assigned to distinct categories or labels without any inherent order or numerical significance. In the given options, both i) and ii) involve categorical information, but only option ii) ("Michaelangelo's most-requested toppings are pepperoni, black olives, and mushrooms") describes nominal data.

In option i), the sizes of pizzas (small, medium, large, and jumbo) can be considered ordinal data as they have a specific order and imply a relative size difference. Ordinal data possesses a sequential arrangement where the categories have a meaningful relationship or hierarchy.

On the other hand, option ii) presents toppings (pepperoni, black olives, and mushrooms) as distinct categories without any inherent order or hierarchy.

Each topping represents a separate label or category, making it an example of nominal data.Therefore, option ii) ("Michaelangelo's most-requested toppings are pepperoni, black olives, and mushrooms") accurately describes nominal data.

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Answer:

2 2/5.

Step-by-step explanation:

The probability that a randomly selected passenger has a waiting time greater than 4.25 minutes is 0.5278

The uniform distributed between a and b minutes.

The probability of finding a value above x is:

P(X > x) = \(\frac{b-x}{b-a}\)

The time is evenly distributed between 0 and 9 minutes.

This implies that a=0 , b=9

Determine the likelihood that a randomly selected passenger will have to wait longer than 4.25 minutes.

p(X > 4.25) = \(\frac{9-4.25}{9-0}\)

                 = 0.5278

There is a 52.78% chance that a randomly selected passenger will have to wait longer than 4.25 minutes.

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To determine whether the series Σn=4[infinity]8/n^2 − 1 is convergent or divergent, we need to express sn as a telescoping sum.

First, we need to write out a few terms of the series to see if we can spot a pattern:

u4 = 8/4^2 - 1 = 1/3
u5 = 8/5^2 - 1/4^2 = 39/60
u6 = 8/6^2 - 1/5^2 = 77/120

Notice that each term has a denominator of the form (n+1)(n-1). We can use partial fractions to write each term as:

un = A/(n-1) - B/(n+1)

Multiplying both sides by (n-1)(n+1), we get:

un = A(n+1) - B(n-1)

Now we need to solve for A and B. Let's start with A:

u4 = A(5) - B(3) = 1/3

And now B:

u6 = A(7) - B(5) = 77/120

Solving for A and B, we get:

A = 1/2
B = 1/2

Now we can express sn as a telescoping sum:

sn = u4 + u5 + u6 + ... + un
  = (1/2)((5/3) - (3/5)) + (1/2)((6/4) - (4/6)) + ... + (1/2)((n+1)/n - (n-1)/(n+1))

Notice that most of the terms cancel out, leaving us with:

sn = (1/2)(5/3 + 6/4 + ... + (n+1)/n) - (1/2)(3/5 + 4/6 + ... + (n-1)/(n+1))

Both of the series inside the parentheses are telescoping sums, which means they converge. Therefore, sn also converges.
Hi! To determine if the given series is convergent or divergent, let's express it as a telescoping sum using partial fraction decomposition. The series is:

u_n = Σ (8 / n^2 - 1) for n = 4 to infinity.

Using partial fraction decomposition, we can rewrite 8 / (n^2 - 1) as:

8 / (n^2 - 1) = A / (n - 1) + B / (n + 1)

8 = A(n + 1) + B(n - 1)

Now, we'll find the values of A and B:

Let n = 1: 8 = 2A => A = 4
Let n = -1: 8 = -2B => B = -4

So, our decomposition becomes:

u_n = Σ [4 / (n - 1) - 4 / (n + 1)] for n = 4 to infinity.

Now, let's find the telescoping sum:

s_n = Σ (u_k) for k = 4 to n
= (4/3 - 4/5) + (4/4 - 4/6) + ... + (4/(n-1) - 4/(n+1))

When we sum the series, we observe that consecutive terms cancel out:

s_n = 4/3 - 4/(n+1)

Now, we'll check the convergence or divergence of the series as n approaches infinity:

lim (s_n) as n→∞ = lim (4/3 - 4/(n+1)) as n→∞

Since the second term 4/(n+1) approaches 0 as n approaches infinity, the limit converges to 4/3.

Therefore, the series is convergent.

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Answer:

The number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.

Step-by-step explanation:

The possible pathways are as follows:

(0, 0) → (1, 0) → (2, 0) → (3, 0) → (3, 1) → (3, 2) → (3, 3)

(0, 0) → (1, 0) → (2, 0) → (2, 1) → (2, 2) → (3, 2) → (3, 3)

(0, 0) → (1, 0) → (1, 1) → (1, 2) → (2, 2) → (3, 2) → (3, 3)

(0, 0) → (0, 1) → (0, 2) → (1, 2) → (2, 2) → (3, 2) → (3, 3)

Thus, the number of paths that are there from the ant that end at (3, 3) but never pass through (2, 3) is 4.

=======================================

Work Shown:

I'm assuming your teacher meant to say the ramp is 7 meters long and the ramp rises up 4.2 meters. It doesn't make sense the way they phrased it initially since the ramp must be the longest part (it is the hypotenuse of the right triangle).

See diagram below.

The angle of elevation is the angle made between the ramp and the ground. It's the angle amount the ramp tilts upward.

sin(angle) = opposite/hypotenuse

sin(theta) = 4.2/7

sin(theta) = 0.6

theta = arcsin(0.6)

theta = 36.869897645844

theta = 36.9

Note: inverse sine or \(\sin^{-1}\) is the same as arcsine. Make sure your calculator is in degree mode.

The probability that exactly 5 black cars and exactly 10 non-black cars drive by in a particular afternoon is approximately 0.00167.

The probability that exactly 5 black cars and exactly 10 non-black cars drive by on a particular afternoon is

, where \($X_b$\) are the number of black cars and \($X_{nb}$\) the number of non-black cars passing by the playground in the afternoon. Since the color of the cars is independent of the number of cars that drive by, we can model the number of black and non-black cars using two separate Poisson distributions with means

\($\lambda_b = \frac{1}{5}\cdot25=5$ and $\lambda_{nb}=25-5=20$\), respectively.

Plugging in the values and simplifying, we get:

\($$P(X_b=5,X_{nb}=10)=\frac{e^{-5}5^{5}}{5!}\cdot\frac{e^{-20}20^{10}}{10!}\cdot\frac{1}{5^{5}}\cdot\frac{4^{10}}{5^{10}}\approx 0.00167$$\)

Therefore, the probability that exactly 5 black cars and exactly 10 non-black cars drive by in a particular afternoon is approximately 0.00167.

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Answer:

51.1 ≈ r

Step-by-step explanation:

"A bicycle wheel travels 321 in for each revolution"- means that 321 is the circumference of the wheel that is a circle.

C = 2· π· r

What is the radius of the wheel ​?

321 = 2· π· r, divide both sides of the equation by 2 π

(321/2·π) = r , use calculator, solve and round the answer

51.1 ≈ r

Answer: To match the shapes produced by the slice through the triangular prism, we need to consider the orientation of the slice relative to the prism. Here are the matching options:

A. Perpendicular to the base: Rectangle

B. Parallel to the base: Triangle with dimensions equal to the base

C. Diagonal from vertex to vertex: Triangle with unknown dimensions

Answer:

AHHHH I LOVE YOUR PROFILE PICTURE GOKU IS THE BEST <3 :D

Answer:

The probability that the two biscuits were not the same type is 58.4%.

How much is the probability that the two biscuits were not the same type?

The probability that they are different is the opposite of the probability that they are the same.

The probability that they are the same is:

⇒ P(plain, plain) = (12/20) (11/19) = 132 / 380

⇒ P(chocolate, chocolate) = (5/20) (4/19) = 20 / 380

⇒ P(currant, currant) = (3/20) (2/19) = 6 / 380

⇒ P(same) = 132/380 + 20/380 + 6/380

⇒ P(same) = 158/380

⇒ P(same) = 79/190

Therefore, the probability that they are different is:

⇒ P(different) = 1 − 79/190

⇒ P(different) = 111/190

⇒ P(different) ≈ 58.4%

What does probability mean?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event.

Answer:

1 week

Step-by-step explanation:

Answer:

65

Step-by-step explanation:

55 + 65 + 57 = 177

there are more factors, but I found this one the quickest.

hope this helps!

The graph of the system is added as an attachment

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

f(x) = 2x + 8 for x < -1

      -2x + 7 for x > 3

The above system is a piece wise fucntion that include

Two linear equations

Next, we plot the graph

See attachment for the graph of the equation

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Using the graph method, Central Fabric should determine the most profitable numbers of bolts to purchase from mills A and B by considering profit calculations, supply and demand constraints, and plotting a profit graph.

To determine the most profitable numbers of bolts that Central Fabric should purchase from mills A and B using the graph method, we need to create a profit graph based on the given information.

Start by calculating the total available supply for each market channel:

Fabric Stores: (0.40 * Total Bolts from Mill A) + (0.20 * Total Bolts from Mill B)

Discount Stores: (0.10 * Total Bolts from Mill A) + (0.20 * Total Bolts from Mill B)

Direct Mail: (0.30 * Total Bolts from Mill A) + (0.40 * Total Bolts from Mill B)

Determine the maximum number of bolts that can be sold in each market channel:

Fabric Stores: 1,600 bolts

Discount Stores: 2,800 bolts

Direct Mail: 2,600 bolts

Calculate the profit for each combination of bolts purchased from mills A and B:

Profit from Mill A: (0.60 * Total Bolts from Mill A - 0.20 * Total Bolts from Mill A) * P8,000

Profit from Mill B: (0.80 * Total Bolts from Mill B - 0.20 * Total Bolts from Mill B) * P6,000

Plot the profit graph by considering different combinations of Total Bolts from Mill A and Total Bolts from Mill B, while taking into account the constraints of available supply and market demand.

Find the combination of Total Bolts from Mill A and Total Bolts from Mill B that maximizes the profit while satisfying the supply and demand constraints. This point on the graph represents the most profitable numbers of bolts to purchase from mills A and B.

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Answer:

11

Step-by-step explanation:

7 + z / 6 = ?

7 + 24 / 6

24 / 6 = 4

7 + 4 = 11

Answer:

11

Step-by-step explanation:

The first thing you're going to do is replace z with 24 and divide it by 6, which equals 4. Then you're going to add 7, which gets you to the answer 11.

Step-by-step explanation:

8x-2=46

collect like terms

8x=46+2

8x=48

Divide both sides by 8

8x÷8=48÷8

x=6

Thus, the probability that this song will be played on no more than two out of every four days is 35.60%.

Combination as well as permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in whatsoever order when combined. The components of the subset usually listed in a permutation in a certain order.

Since this is a combination issue, we must first determine the combination of 4 select 2, and then multiply that result by the chance of each possible outcome:

Choose 2 from a combination of 4:

C(4, 2) = 4! / (2! * 2!) = 4*3/2 = 6

This figure indicates that there are 6 alternative ways that the 2 days we want to be allocated in the 4 days could be used.

The probability of every event is now:

2 days of song playback: (0.58)²

The song wasn't played for two days: (0.42)².

Hence, the final probability is

P = C(4,2) * (0.58)² * (0.42)²

P = 6 * (0.58)² * (0.42)²

P = 0.3560

Thus, the probability that this particular song will be played on no more than two out of every four days is 35.60%.

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Answer:

15 pennies

Step-by-step explanation:

lost means subtract and gave him means add

21 -11 +5

15

Answer:

15 pennies

Step-by-step explanation:

You can start by saying that after losing 11 pennies from his original amount it is 21-11, which equals to 10.

THen the question says that his friend gives him an additional 5  pennies, which is shown by 10+5=15

THerefore, all you had to do was use the information given and add or subtract the number of pennies from the original.

Answer: 15 pennies

Hope this helped

The complete statement:

When rotated about its center, a regular hexagon has 6 rotational symmetries. In addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

Each point in a figure is transformed into a rotation by rotating it a certain amount of degrees around another point.

Given:

A regular hexagon.

There are 6 vertices in hexagons.

When rotated about its center, a regular hexagon has 6 rotational symmetries.

That means 6 lines of symmetry.

So, in addition to rotational symmetry, a regular hexagon has 6 lines of reflectional symmetry.

Therefore, a regular hexagon has 6 lines of reflectional symmetry.

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We use root mean square (RMS) speed to calculate the average speed of particles in a gas because it takes into account the speed of all particles in a distribution, regardless of direction.

It is particularly useful in studying gases because gas particles move in random directions with varying speeds. The RMS speed is the square root of the average of the squared speeds of all the particles in a gas.

The RMS speed is important because it is related to other properties of gases, such as temperature and pressure. For example, as the temperature of a gas increases, the RMS speed of its particles also increases.

This relationship is described by the Maxwell-Boltzmann distribution, which relates the speeds of gas particles to the temperature of the gas.

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