The ratio of fish to snails is 3 to 2. There are 18 fish in the aquarium. How many snails are in the aquarium ?

The required solution to the given equation is x = 106.04, which is the correct answer that would be option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

The equation is given in the question following:

x - 69.80 = 36.24

We have to determine the solution to the given equation

As per the question, we have

x - 69.80 = 36.24

Add 69.80 on both sides of the equation, and we get

x - 69.80 + 69.80 = 36.24 + 69.80

x = 106.04

Hence, the correct answer would be an option (A).

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Answer:

m=5/2

Step-by-step explanation:

Answer:

n = 5/6

Step-by-step explanation:

4n - 8 = 3n - (n + 3)

4n - 8 = 3n - n - 3

4n + 3n + n = - 3 + 8

6n = 5

n = 5/6

Answer:

Substitute x = 5 into the function machine 4x = y:

4(5) = y

y = 20

Therefore, if 5 is inputted into the function machine, the output will be 20.

The probability that Betty is first in line or Mary is last in line is (n^2 - n - 1)/n(n-1), as a function of n.

We can approach this problem by considering the probability of the complementary event, i.e., the probability that neither Betty is first in line nor Mary is last in line, and then subtracting this probability from 1 to get the probability we want.

The total number of ways the n kids can line up is n!, since there are n choices for the first person in line, n-1 choices for the second person, and so on down to 1 choice for the last person.

The number of ways in which neither Betty is first in line nor Mary is last in line is (n-2)!, since there are (n-2) choices for the first person in line (excluding Betty and Mary), (n-3) choices for the second person, and so on down to 1 choice for the second-to-last person.

Therefore, the probability that neither Betty is first in line nor Mary is last in line is

[(n-2)! / n!] = 1/n(n-1)

The probability we want is

1 - 1/n(n-1) = (n^2 - n - 1)/n(n-1)

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The given question is incomplete, the complete question is:

A class with n kids lines up for recess. The order in which the kids line up is random with each ordering being equally likely. There are two kids in the class named Betty and Mary. The use of the word “or” in the description of the events, should be interpreted as the inclusive or. That is “A or B” means that A is true, B is true, or both A and B are true.

What is the probability that Betty is first in line or Mary is last in line as a function of n? Simplify your final expression as much as possible and include an explanation of how you calculated this probability.

Answer:

-3.4

Step-by-step explanation:

"| |" are absolute value which means |-4| is actually 4. However, if there is a  negative outside of the lines, than the answer is negative.

The grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

To determine the number of trees the plum grower should plant per acre to maximize her harvest, we can set up an equation and use calculus to find the optimal solution. Let's denote the number of additional trees planted as x.

The yield of each tree can be represented by the equation:

Yield = 126 - 2x

The total yield per acre is then given by:

Total Yield = (26 + x) * (126 - 2x)

To maximize the harvest, we need to find the value of x that maximizes the total yield. We can achieve this by finding the maximum point of the quadratic equation representing the total yield.

Differentiating the equation with respect to x and setting it equal to zero, we can find the critical point:

d(Total Yield)/dx = -4x + 252 - 2(26 + x) = 0

Simplifying the equation, we get:

-4x + 252 - 52 - 2x = 0

-6x + 200 = 0

x = 200/6

x ≈ 33.33

Since we cannot have a fraction of a tree, the grower should plant 33 additional trees per acre to maximize her harvest. This gives a total of 26 + 33 = 59 trees per acre.

To find the maximum harvest, we substitute the value of x into the equation for the total yield:

Total Yield = (26 + 33) * (126 - 2 * 33)

Total Yield ≈ 59 * 60

Total Yield ≈ 3540 bushels

Therefore, the grower should plant 59 trees per acre to maximize her harvest, and the maximum harvest she can achieve is approximately 3540 bushels.

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The standard form of a polynomial is: ax^n+ bx^n-1 + cx^n-2  + ......... + d

The standard form of the polynomial is 4x^3 + 2x^2  + 3x - 6

The polynomial is given as:

(4x^3 - 2x - 9) + (2x^2 + 5x + 3)

Remove the bracket

4x^3 - 2x - 9 + 2x^2 + 5x + 3

Collect like terms

4x^3 + 2x^2 - 2x + 5x - 9 + 3

Evaluate the like terms

4x^3 + 2x^2  + 3x - 6

Hence, the standard form of the polynomial is 4x^3 + 2x^2  + 3x - 6

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Answer:

Attached is the solution. Hope it helps!

Answer:

x = 44/7

Step-by-step explanation:

7x+3 = 47

Subtract 3 from each side

7x+3-3 = 47-3

7x = 44

Divide by 7

7x/7 = 44/7

x = 44/7

To determine the probability that an ADA will earn between $50 and $60 per hour, we can use the standard normal distribution and the z-score.

Given:

Mean (μ) = $52

Standard deviation (σ) = $5.50

To find the probability, we need to calculate the z-scores for the lower and upper limits, and then use the z-table or a calculator to find the corresponding probabilities.

Step 1: Calculate the z-scores

For the lower limit of $50:

z_lower = (X_lower - μ) / σ = (50 - 52) / 5.50

For the upper limit of $60:

z_upper = (X_upper - μ) / σ = (60 - 52) / 5.50

Step 2: Look up the probabilities from the z-table or use a calculator

Using the z-table or a calculator, we can find the probabilities corresponding to the z-scores.

Let's denote the probability for the lower limit as P1 and the probability for the upper limit as P2.

Step 3: Calculate the final probability

The probability that an ADA will earn between $50 and $60 per hour is the difference between P2 and P1.

P(X_lower < X < X_upper) = P2 - P1

Note: Make sure to use the cumulative probabilities (area under the curve) from the z-table or calculator.

I will perform the calculations using the given mean and standard deviation to find the probabilities. Please hold on.

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Answer:

10

Step-by-step explanation:

divide 1800 by 20 and 1800 by 18 and find the difference

The expression that can be used to find the pool's diameter in feet is 100/π

The circumference of a circle can be calculated using the formula C = 2πr, where C is the circumference, r is the radius, and π is pi. We are given that the circumference of the pool is 50 feet, so we can write:

50 = 2πr

To find the diameter, we know that the diameter is twice the radius, so:

d = 2r

Substituting 2r for d in the equation above, we get:

d = 2r = 2(50/2π) = 100/π

Therefore, the expression that can be used to find the pool's diameter in feet is 100/π, where π is pi.

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answer is

because are complementary angles A and B

answer: 4.

Step-by-step explanation:

sum of two interior angles is equal to one exterior angle....this implies that,

(6x+4) +(5x+2)= 12x-4

11x+6=12x-4.......make X the subject

11x-12x=-4-6

-x= -10......divide both sides by -1

x=10

The Justification for the 5th statement is option B Distance formula.

The distance formula is one that is seen as a mathematical formula used to calculate the distance that exist between two points in a coordinate plane.  it is seen as:

The distance between two points (x₁, y₁) and (x₂, y₂) is given by:

d = \(\sqrt{(x_{2} - x_{1} )^2 + (y_{2} -y_{1} )^2}\)

In this formula,  (0,0) to  (0, 2) will be inputted as:

d = \(\sqrt{(0 - 0 )^2 + (2 -0 )^2} = \sqrt{2^2} = 2\)

Therefore  this statement of the justification is also the distance Formula,  so we assume the distance from (0,0) to  (1, √2) that brings about 2 and is also seen as the radius of the circle.

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Answer:

Madhu played better.

Step-by-step explanation:

Change both fractions to where they have the same denominator to see which one is bigger. The smallest possible denominator between the two fractions is 117.  

To get the 13 in 6/13 to become 117, you had to multiply it by 9. Whatever you do to the denominator, you must do to the numerator.

6 x 9 = 54.

Allison's fraction is now 54/117.

To get the 9 in 5/9 to become 117, you had to multiply the 9 by 13. Whatever you do to the denominator, you must do to the numerator.

5 x 13 = 65

Madhu's fraction is now 65/117

By looking, 65 is larger than 54, so Madhu had a larger number of shots compared to shots not made than Allison.

The cost of the pyramid shape sign is $240.

A pyramid is a 3D figure that has a base made of a polygon and faces that are all triangular and connected. The conventional shape of a pyramid is created by joining each vertex of the base to a single common tip or apex. In this section, let's study more about pyramids.

We know the volume of a pyramid is (1/3)×length of the bese×width of the base×height.

∴ The volume of the pyramid with base length of 6feet, base width of 3feet and height 5 feet is,

= (1/3)×6×3×5 cubic feet.

= 30 cubic feet.

Given, The aluminum costs $8 per cubic foot.

∴ The total cost of the pyramid is = (30×8) = $240.

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Probability = (3.4 - 1.6) / (5.2 - 1.6)= 0.556Thus, P(X < 3.4) = 0.556.

Given that X has a continuous uniform distribution over the interval (1.6, 5.2] we need to find the following:(a) Determine the mean of X.

(b) Determine the variance of X.

(c) What is P(X< 3.4)?

(a) Determine the mean of X.

The mean of X can be calculated as follows:

Mean of X = (a+b) / 2Here, a = 1.6, b = 5.2

Therefore, Mean of X = (1.6 + 5.2) / 2 = 3.4

Thus, the mean of X is 3.4.(b) Determine the variance of X.

The variance of X can be calculated as follows:

Variance of X = (b - a)² / 12

Here, a = 1.6, b = 5.2

Therefore, Variance of X = (5.2 - 1.6)² / 12= 0.64

Thus, the variance of X is 0.64.

(c) What is P(X < 3.4)?

Since X has a continuous uniform distribution, the probability can be calculated as follows:

Probability = (X - a) / (b - a)Here, a = 1.6, b = 5.2, X = 3.4

Therefore, Probability = (3.4 - 1.6) / (5.2 - 1.6)= 0.556Thus, P(X < 3.4) = 0.556.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

The experimental probability of not selecting a heart is (D)P(not heart) = 77.5%

The experimental probability that a heart is selected is:

= Number of times hearts was selected / Number of times Lisa drew a card

= 9 / 40

This then means that the experimental probability of not selecting a heart is:

= 1 -  experimental probability of selecting a heart

= 1 - 9 / 40

= 31 / 40

= 0. 775

= 77. 5 %

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The question is:

Determine the experimental probability of not selecting a heart.

(A) P(not heart) = 9%

(B) P(not heart) = 10%

(C) P(not heart) = 67.5%

(D)P(not heart) = 77.5%

Answer:

144.

Step-by-step explanation:

40% shorter means she played  100 - 40 = 60% of the previous tall.

60% of 240

= 240 * 0.6

=  144 games.

Based on the information provided, the archaeological sample's estimated age is = 0.214136  years

Half life given is 5730

t₆.₅ = Ln2/k

k= ln 2/ 5730

The rate constant ,

k = 0.00012 year⁻¹

Given that 23 % of the 14C remains

then |A1|/|A2|  = 0.23

As we know ,

|A1|/|A2| = e ⁻₍kt₎

Hence, on solving the equation we get ,

ln(0.23)= -1.46967

t = -0.31471/ --1.46967

= 0.214136 years

The amount of time needed for a quantity (of substance) to decrease to half of its initial value is known as the half-life (symbol t12). In nuclear physics, the phrase is frequently used to indicate how rapidly unstable atoms decay radioactively or how long stable atoms last. The phrase is also used more broadly to describe any kind of exponential decay (or, very infrequently, nonexponential decay).

The biological half-life of medications and other compounds in the human body, for instance, is a term used in the medical sciences. Half-opposite life's in exponential growth is time's doubling.

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Therefore , the solution of the given problem of unitary method comes out to be for 10 weeks because $150 is larger than or equal to $153.

To finish a job using a unitary method, take the measurements of this minuscule subsection and divide the result by two. Simply put, the unit method removes a desired item from both specific sets and pixel subsets. 40 pens, for variable instance, will indeed cost Rs/kg ($1.01). It's conceivable that one nation will have complete control over the strategy used to achieve this. Almost all living things have a unique trait. There are open comments and additions (mathematics, algebra).

Here,

Certainly, considering that he has already saved $212 and will save an additional $150.

We need to figure out if Ben's overall savings will be greater than or equal to the stereo's price in order to see if he can purchase it after saving for 10 weeks.

Ben needs to set aside money that is at least as much as $365 - $212, or $153.

Ben will put aside $15 each week for the next ten weeks, totaling $150.

Ben will be able to purchase the stereo after putting money aside for 10 weeks because $150 is larger than or equal to $153.

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Answer: Let the side length of the square rug be x, and the dimensions of the rectangular rug be l and w.

In the first arrangement, the three rugs are arranged side by side, with the rectangular rugs aligned vertically and the square rug aligned horizontally. The length of this arrangement is l + 2x, and the width is w. We know that the length is 3 times the width, so we can write:

l + 2x = 3w

In the second arrangement, the two rectangular rugs are arranged side by side, with the square rug placed on top. The length of this arrangement is l, and the width is w + x. We know that the length is twice the width, so we can write:

l = 2(w + x)

We now have two equations with two unknowns, l and w:

l + 2x = 3w

l = 2(w + x)

Substituting the second equation into the first, we get:

2(w + x) + 2x = 3w

4x = w

Substituting this value of w into the second equation, we get:

l = 2(4x) = 8x

So the dimensions of the rectangular rug are 4x by x, and the dimensions of the square rug are x by x.

To find the value of x, we use the measurements given in the diagram:

l + 2x = 60

l = 36

Substituting into the equation l = 2(w + x), we get:

36 = 2(4x + x)

36 = 10x

x = 3.6

So the side length of the square rug is 3.6 feet.

Step-by-step explanation:

50,400 different anagrams can be made from the letters in the word statistics.

Given word : STATISTICS

Anagrams are words formed by jumbling the positions of the letters given in the word.

For such problems we do factorial of number of words and divide by the repeated letters factorials.

Total number of letters = 10

They can be permutated among themselves in 10! ways.

Some letters are repeated in word STATISTICS

Since, there are 3 S's and 3 T's and 2 I's

So, Number of anagrams = \(\frac{10!}{3!.3!.2!}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3!}{3! \times 3 \times 2 \times 1 \times 2 \times 1}\)

= \(\frac{10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4}{3 \times 2 \times 2}\)

= 10 × 9 × 8 × 7 × 2 × 5

= 50,400

50,400 different anagrams can be made from the letters in the word statistics.

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Answer:

Step-by-step explanation:

To determine the areas under the standard normal curve in the given scenarios, we need to calculate the cumulative probability using z-scores. The cumulative probability represents the area under the curve up to a specific z-score.

We can use a standard normal distribution table or a statistical software to find the cumulative probabilities. However, I can provide you with the steps to calculate these areas.

(a) Find the area under the normal curve to the left of z = -1 plus the area under the normal curve to the right of z = 1:

The area to the left of z = -1 is the cumulative probability from negative infinity up to z = -1. Let's denote this as P(Z < -1).

The area to the right of z = 1 is the cumulative probability from z = 1 up to positive infinity. Let's denote this as P(Z > 1).

To calculate these probabilities, we subtract the cumulative probability from 1 for the area to the left and right of the z-scores.

P(Z < -1) = 1 - P(Z > -1)

P(Z > 1) = 1 - P(Z < 1)

Using a standard normal distribution table or a statistical software, find the values of P(Z > -1) and P(Z < 1), and then subtract these probabilities from 1.

(b) Find the area under the normal curve to the left of z = -1.52 plus the area under the normal curve to the right of z = 2.52:

Similar to part (a), we calculate the cumulative probabilities:

P(Z < -1.52) and P(Z > 2.52)

Again, use a standard normal distribution table or a statistical software to find the values of P(Z < -1.52) and P(Z > 2.52), and then calculate the combined area.

(c) Find the area under the normal curve to the left of z = -0.26 plus the area under the normal curve to the right of z = 1.10:

Calculate the cumulative probabilities:

P(Z < -0.26) and P(Z > 1.10)

Using a standard normal distribution table or a statistical software, find the values of P(Z < -0.26) and P(Z > 1.10), and then calculate the combined area.

Once you obtain the cumulative probabilities, add them together to find the combined area under the standard normal curve in each scenario. Round the results to four decimal places as needed.

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