HOW CAN YOU USE SUBTRACTION TO DESCRIBE DIVISION? GIMME AN EXAMPLE PLS :(

Answer:

2/7

Step-by-step explanation:

put the total number of boys over the total number of stuedents

10/35 then simplify by dividing top and bottom by 5      2/7

Answer:

2/7

Step-by-step explanation:

10/35

reduce fraction

10÷5=2

35÷5=7

There are a total of 15,504 different groups of five students that could be selected for the competition from the 20 students in the math club.

To arrive at this answer, we can use the combination formula, which is given by:

nCk = n! / (k! * (n-k)!)

where n is the total number of students in the math club (20), and k is the number of students selected for the competition (5).

Substituting these values into the formula, we get:

20C5 = 20! / (5! * (20-5)!) = 15,504

Therefore, there are 15,504 different groups of students that could be selected for the competition.

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Answer:

True

Step-by-step explanation:

Answer:

(3a + 8b) (3a - 8b)

Step-by-step explanation:

The difference in two perfect "squares" in the scenario would be the (8b) and (-8b).

The 3a would stay consistent through out the whole.

Answer:

The standard notation would be 141.7

Step-by-step explanation:

The Florist who charges less for delivering 8 standard flower arrangements is Binder's Bouquets

The amount less is $ 35. 08

The cost of eight standard flower arrangements from Green's Flowers is :

= 15 + ( 45 x 8 )

= $ 375

The cost of a single flower arrangement from Binder's Bouquets is:

= 59. 99 - 20. 00

= $ 39. 99

The cost of 8 flower arrangements is :

= 20 + ( 39. 99 x 8 )

= $ 339. 92

Binder's Bouquets is cheaper by :

= 375 - 339. 92

= $ 35. 08

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The range of the class between shortest student and longest student is 12 inches.

Range is the difference between highest and lowest possible values.

R= (higest value)-(lowest value)

Tallest student= 63 inches

Shortest student= 51 inches

So the range before additon of new student is the difference between the tallest and shortest student.

R= 63(tallest student) - 51(shortest student) = 12inches

Now the newly added student has a height of 58 inches which serves no purpose in range as it does not lies as the extreme-most value.

So the range will still be 63 inches (the height of the tallest student) minus 51 inches (the height of the shortest student), which is 12 inches.

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The minimum wage set by the government at $7.50 per hour does not result in a pay cut for unskilled workers, as it is below the equilibrium wage of $8.00 per hour.

The wage rate remains unchanged, and the labor market remains in balance.

The statement is false.

False.

The equilibrium wage in the market for unskilled labor is $8.00 per hour, which means that the market naturally sets the wage rate at this level, based on the forces of supply and demand.

The government then sets a minimum wage at $7.50 per hour.

Since the minimum wage is below the equilibrium wage, it does not directly impact the wage rate for unskilled workers.
The equilibrium wage represents the point at which the supply of labor (the number of workers willing to work at a given wage) equals the demand for labor (the number of workers that employers are willing to hire at a given wage).

In this case, both workers and employers are satisfied with the $8.00 per hour wage, and the labor market is balanced.
The government sets a minimum wage below the equilibrium wage, it essentially sets a wage floor that is not binding. Employers are still willing to pay the equilibrium wage of $8.00 per hour, and workers are still willing to accept this wage.

The wage for unskilled workers remains at $8.00 per hour, and there is no pay cut of 50 cents per hour.

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In order to calculate the z-scores for the given Confidence Interval (CI) levels, we need to use the Z-table. It is also known as the standard normal distribution table. Here are the z-scores for the given Confidence Interval levels:1. 68% CI: The confidence interval corresponds to 1 standard deviation on each side of the mean.

Thus, the z-score for the 68% \(CI is ±1.00.2. 85% CI\): The confidence interval corresponds to 1.44 standard deviations on each side of the mean.

We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.85)/2)z = invNorm(0.925)z ≈ ±1.44\)Note that invNorm is the inverse normal cumulative distribution function (CDF) which tells us the z-score given a certain area under the curve.3. 99% CI: The confidence interval corresponds to 2.58 standard deviations on each side of the mean. We can calculate the z-score using the following formula:\(z = invNorm((1 + 0.99)/2)z = invNorm(0.995)z ≈ ±2.58\)

Note that in general, to calculate the z-score for a CI level of (100 - α)% where α is the level of significance, we can use the following formula:\(z = invNorm((1 + α/100)/2)\) Hope this helps!

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The mathematical formula v = 1/3 πr²h is the formula for calculating the volume of a cone.

The volume of a cone is the amount of space or the capacity of the cone.

The formula for determining the volume of a cone is:

Volume, v = ¹/₃ πr²h

where

For example:

Calculate the volume of a cone if r= 2 cm and h= 5 cm.

V= ¹/₃ × 22/7 × 2² × 5

V = 20.95 cm³

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the third side must be greater than 8 and less than 16.

To determine the range of possible lengths for the third side of the triangle, we can use the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.

So, for a triangle with sides of 4 and 12, the third side must satisfy:

12 - 4 < third side < 12 + 4

which simplifies to:

8 < third side < 16

what is triangle?

A triangle is a geometric shape with three sides and three angles. It is formed by connecting three non-collinear points in a plane. The sum of the interior angles of a triangle is always 180 degrees, and there are various types of triangles based on their side lengths and angle measures.

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The probability that, in an hour, at least 4 cars will enter the car wash is 0.94.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

Cars enter a car wash according to a Poisson process at a mean rate of 2 cars per half an hour.

Here the value of λ is:

λ = 2 cars/half an hour

λ = 4 cars/hour

The probability that, in an hour, at least 4 cars will enter the car wash:

P(x = 4) = 4⁴e⁻⁴/5

After solving:

P(x = 5) = 0.937 ≈ 0.94

Thus, the probability that, in an hour, at least 4 cars will enter the car wash is 0.94.

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In order to calculate the time it will take for Andrew to settle the loan, we can use the formula for compound interest. So, it will take Andrew approximately 5.22 years to settle the loan.

The formula is given as A = P(1 + r/n)^(nt), Where: A = the final amount, P = the principal (initial amount borrowed), R = the annual interest rate, N = the number of times the interest is compounded in a year, T = the time in years.

We know that Andrew borrowed R200 000 from a bank at an annual interest rate of 5.25% compounded quarterly and that he will make repayments of R6 000 at the end of every 3 months.

Since the first repayment will be made 3 months from now, we can consider that the initial loan repayment is made at time t = 0. This means that we need to calculate the value of t when the total amount repaid is equal to the initial amount borrowed.

Using the formula for compound interest: A = P(1 + r/n)^(nt), We can calculate the quarterly interest rate:r = (5.25/100)/4 = 0.013125We also know that the quarterly repayment amount is R6 000, so the amount borrowed minus the first repayment is the present value of the loan: P = R200 000 - R6 000 = R194 000

We can now substitute these values into the formula and solve for t: R194 000(1 + 0.013125/4)^(4t) = R200 000(1 + 0.013125/4)^(4t-1) + R6 000(1 + 0.013125/4)^(4t-2) + R6 000(1 + 0.013125/4)^(4t-3) + R6 000(1 + 0.013125/4)^(4t)

Rearranging the terms gives us: R194 000(1 + 0.013125/4)^(4t) - R6 000(1 + 0.013125/4)^(4t-1) - R6 000(1 + 0.013125/4)^(4t-2) - R6 000(1 + 0.013125/4)^(4t-3) - R200 000(1 + 0.013125/4)^(4t) = 0

Using trial and error, we can solve this equation to find that t = 5.22 years (rounded to 2 decimal places). Therefore, it will take Andrew approximately 5.22 years to settle the loan.

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Answer:

8x²+16x+8=0

x²+2x+1=0

D=4-4=0

x0=-2/2=-1

Answer:

Step-by-step explanation:

\(8x^2+16x+8=0\)                  {divide both sides by 8}

\(x^2+2x+1=0\\\\a=1\,,\quad b=2\,,\quad c=1\\\\x=\dfrac{-2\pm\sqrt{2^2-4\cdot1\cdot1}}{2\cdot1}=\dfrac{-2\pm\sqrt{4-4}}2=\dfrac{-2\pm0}2=-1\)

the size of the union of the three sets is: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |A ∩ C| - |B ∩ C| + |A ∩ B ∩ C| = 3  × 24 million - 3 × 1.4 million + 1.2 million ≈ 69 million

A combination is a way of selecting a subset of objects from a larger set without regard to their order. The formula for the number of combinations of n objects taken r at a time is:
C(n, r) = n! / (r! ×  (n - r)!)
where n! means the factorial of n, which is the product of all positive integers up to n. For example, 5! = 5 ×  4 ×  3 ×  2 ×  1 = 120.
To apply this formula to our problem, we first need to count the total number of coins in the pile. Since there are at least 16 of each type, the minimum total is:
16 + 16 + 16 + 16 = 64
But there could be more coins of each type, so the total could be larger than 64. However, we don't need to know the exact number, only that it is large enough to allow us to choose 16 coins from it.
Using the formula for combinations, we can calculate the number of different collections of 16 coins that can be chosen from the pile:
C(64, 16) = 64! / (16! × (64 - 16)!) ≈ 1.1 billion
That's a very large number! It means there are over a billion ways to choose 16 coins from a pile that contains at least 16 of each type.
To answer the second part of the question, we need to count the number of collections that contain at least 3 coins of each type. One way to do this is to use the inclusion-exclusion principle, which says that the number of elements in the union of two or more sets is equal to the sum of their individual sizes minus the sizes of their intersections, plus the sizes of the intersections of all possible pairs, minus the size of the intersection of all three sets, and so on.
In this case, we can consider three sets:
- A: collections with at least 3 pennies
- B: collections with at least 3 nickels
- C: collections with at least 3 dimes
- D: collections with at least 3 quarters
The size of each set can be calculated using combinations:
|A| = C(48, 13) ≈ 24 million
|B| = C(48, 13) ≈ 24 million
|C| = C(48, 13) ≈ 24 million
|D| = C(48, 13) ≈ 24 million
Note that we have to choose 3 coins of each type first, leaving 4 coins to be chosen from the remaining 48 coins.
The size of the intersection of any two sets can be calculated similarly:
|A ∩ B| = C(43, 10) ≈ 1.4 million
|A ∩ C| = C(43, 10) ≈ 1.4 million
|A ∩ D| = C(43, 10) ≈ 1.4 million
|B ∩ C| = C(43, 10) ≈ 1.4 million
|B ∩ D| = C(43, 10) ≈ 1.4 million
|C ∩ D| = C(43, 10) ≈ 1.4 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 43 coins.
The size of the intersection of all three sets can also be calculated:
|A ∩ B ∩ C| = C(38, 7) ≈ 1.2 million
Note that we have to choose 3 coins of each type first, leaving 1 coin to be chosen from the remaining 38 coins.

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Answer:

  (a) negative three halves (-3/2)

Step-by-step explanation:

You want the slope of the line through points (1, 0) and (3, -3).

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-3 -0)/(3 -1) = -3/2

(a) The slope of the line is -3/2.

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(2, 2), (3, 1), (4, 2) are ordered pairs are in the solution set of the system of linear inequalities.

What are linear inequalities, exactly?

A mathematical expression that compares two expressions using the inequality symbol is known as a linear inequality. The expression may be either a numerical or an algebraic expression, or it may be both.

                               x - 5 > 3x - 10 is an illustration of a linear inequality. Since greater than is utilized in this inequality, the LHS is indubitably greater than the RHS. The inequality is represented by the formula 2x 5 x (5/2).

y >-1/3x+2

y < 2x + 3

The answer is "None" of the given choices satisfy the linear inequality. Each choice has a point (2,2) which dissatisfy the equation.

(2, 2), (3, 1), (4, 2)

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Answer:

c

Step-by-step explanation:

the -2 causes a shift 2 units right

The equation for inverse variation is m = k/h

The value of k = 2100

A relationship between two variables in which the product is a constant. When one variable increases the other decreases in proportion so that the product is unchanged. If b is inversely proportional to a, the equation is of the form b = k/a (where k is a constant). Equation: y = 60/x

Let number of machines = m

Let number of hours = h

Therefore;

m = k/h

where k = constant of proportionality

For m = 35

and h = 60

35 = k/60

k = 2100

also for m = 15

and h = 140

15 = k/140

k = 2100

therefore, the equation for inverse variation is m = k/h

while the value of k = 2100.

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Step-by-step explanation:

(x+6)(x−4)

x²- 4x+6x - 24

x² + 2x - 24

Answer:

x²+2x-24

Step-by-step explanation:

see attachment below

The partial derivatives are:

∂z/∂x = -x / (3z)

∂z/∂y = 0

To find the partial derivatives ∂z/∂x and ∂z/∂y, we differentiate the equation x^2 + 4y^2 + 3z^2 = 1 with respect to x and y, while treating y and z as constants.

Differentiating with respect to x:

2x + 0 + 3(∂z/∂x)(2z) = 0

Simplifying the equation:

2x + 6z (∂z/∂x) = 0

Rearranging the equation:

∂z/∂x = -2x / (6z) = -x / (3z)

Differentiating with respect to y:

0 + 8y + 0 = 0

Simplifying the equation:

8y = 0

This equation implies that y = 0, so there is no dependence of z on y.

Therefore, the partial derivatives are:

∂z/∂x = -x / (3z)

∂z/∂y = 0

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Answer:

V = 24pi

or 75.36 ( using 3.14 for pi)

or 75.39822369 ( using the pi button)

Step-by-step explanation:

The volume of a cylinder is given by

V = pi r^2 h

We know the radius and the height

V = pi (2)^2 * 6

V = pi 4*6

V = 24 pi

If we approximate pi by 3.14

V = 3.14 * 24 = 75.36

If we use the pi button

V =75.39822369

Answer:

Step-by-step explanation:

V=pi r^2 h

r = 2

h = 6

V = 3.14 * 2 * 2 * 6

V =75.36

The area of the flower beds can be calculated as follows:

    area of the flower beds = total area - sod area

                                     = 400 - 162

                                     = 238 square feet

    the area of each flower bed is equal to the area of the four flower beds combined, so we can write the equation as follows:    

    4 * (x * x) = 238

a. the width of each flower bed is x feet.

a. to solve the problem, let's assume the width of each flower bed is x feet. we can draw a diagram to visualize the scenario.

    -------------------------

    |         x             |

    |   ----------------   |

    |   |              |   |

    | x |   sod area   | x |

    |   |              |   |

    |   ----------------   |

    |         x             |

    -------------------------

b. we know the total area of the backyard is 16 feet by 25 feet, which is 16 * 25 = 400 square feet. we also know that the sod area is 162 square feet. solving the equation:

    4x² = 238

    x² = 238/4

    x² = 59.5

    x ≈ √59.5

    x ≈ 7.72 (rounded to two decimal places)    

    the approximate width of each flower bed is 7.72 feet    

the sod dimensions will be approximately 16 feet by 25 feet, with flower beds around the four edges that are approximately 7.72 feet wide.

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Based on the vertical angles theorem we can assume that the angles are equal to each other so:

7x-25 = 4x + 2

Now find the value of x

Subtract 4x to both sides

3x - 25 = 2

Add 25 to both sides

3x = 27

Divide by 3 to isolate x

x = 7

Answer:

D

Step-by-step explanation:

This arithmetic sequence can be represented by 9(n-1)+18

Plug in 8 for the variable

9(8-1)+18

9(7)+18

63+18

81

r = 5% = 0.05

t = 4 years

n = 4 (quarterly)

A = 1000

P = ?

1000 = P (1.2199) ==> P = 1000/1.2199 = 819.74

Answer:

$819.74

With regards to the probabilities of getting each color in the game played by Larry and Jessica, the correct answer is B. No, the probabilities are NOT equally likely.

In the game being played by Larry and Jessica, the colors that can be picked by either person include:

The probability of picking blue is:

= Number of blue sections / Total sections

= 3 / 8

The probability of picking red is :

= 3 / 8

The probability of picking green is:

= 2 / 8

= 1 / 4

The probabilities are therefore not equally likely.

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