which is bigger 67/72 or 11/12

The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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It will take 28.5 seconds to Makayla to be twice as deep as Jonah.

What is an equation?

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values. For example, 3x + 5 = 15.

Given,

Jonah is at a depth of -20ft.

Makayla is at a depth of -12.5ft.

at the rate of descending is 0.5.

Given equation is

2(-20+0.25s) = -12.5-0.5s

-40 + 0.5 s = -12.5 -0.5s

0.5s + 0.5s = -12.5+40

1s = 28.5

Hence, the solution of the equation is 1s = 28.5.

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Answer:

its 63

Step-by-step explanation:

Answer:

\( \frac{15.75}{0.25} = \frac{1575}{25} \\ = 63\)

...............................

Answer:

1.25 without the sales tax and tip

Step-by-step explanation:

Answer:

A. 18x - 3y = 6

Step-by-step explanation:

By taking 3 common from the terms 18x and 3y we get,

3 (6x-3y) = 6

or, 6x - y = 6/3

or, 6x - y = 2

And,

The equation becomes,

y = 6x - 2

The equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

By taking 3 commons from the terms 18x and 3y we get,

3 (6x-3y) = 6

6x - y = 6/3

6x - y = 2

The equation becomes,

y = 6x - 2

Therefore, the equation has exactly one solution in common with the equation y=6x-2 will be 18x - 3y = 6. The correct option is A.

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Answer:

B) 9 square units

Step-by-step explanation:

Split the shape into a right triangle and a rectangle.

The rectangle is 2 by 3, so multiply 2 x 3 for the area: 6.

The triangle has a height of 3 and a base of 2. Multiply to get 6. Then divide by 2 to get: 3.

Add 6 + 3 to get 9 square units.

Hope it helps!

Answer:

calculate by yourself

Step-by-step explanation:

use sin theorem

1.

\( \frac{s}{ \sin(60) } = \frac{12}{ \sin(30) } \)

2.

\( \frac{s}{ \sin(90) } = \frac{4}{ \sin(30) } \)

3.

\( \frac{s}{ \sin(60) } = \frac{10}{ \sin(90) } \)

Given:

Where the Mean (μ ) and Standard Deviation (σ) for a Normal Distribution, you need to find:

Where "X" is the number of hours worked per worker.

In order to calculate that probability, you should approximate to a Standard Normal Distribution. Therefore, you need to find z-statistic:

The value of "X" you must use is:

Then, substituting values and evaluating, you get:

Therefore, now you need to find:

Now you need to use the Standard Normal Distribution Table in order to find the value of the probability. Then, you get:

Hence, the answer is:

Answer:

25%

Step-by-step explanation:

We are given that

Initial height of sunflower=160 cm

After increasing

Final height of sunflower=2m

We have to find the percentage increase in height.

1 m=100 cm

\(2m=2\times 100=200cm\)

Increase in height of sunflower=Final height of sunflower-initial height of sunflower

Increase in height of sunflower=200-160=40cm

Percentage increase=\(\frac{Increase\;value}{Initial\;value}\times 100\)

Using the formula

Percentage increase in height=\(\frac{40}{160}\times 100\)

Percentage increase in height=25%

Therefore, Chase ran 49/8 miles each day.

To find out how many miles Chase ran each day, we need to divide the total distance he ran (36 3/4 miles) by the number of days (6 days).

First, let's convert the mixed number into an improper fraction. 36 3/4 is equal to (4 * 36 + 3)/4 = 147/4.

Now, we can divide 147/4 by 6 to find the distance he ran each day:

(147/4) / 6 = 147/4 * 1/6 = (147 * 1) / (4 * 6) = 147/24.

Therefore, Chase ran 147/24 miles each day.

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 147 and 24 is 3.

So, dividing 147 and 24 by 3, we get:

147/3 / 24/3 = 49/8.

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Chase ran a total of 36 3/4 miles over six days. To find out how many miles he ran each day, simply divide the total distance (36.75 miles) by the number of days (6). The result is approximately 6.125 miles per day.

To solve this problem, you simply need to divide the total number of miles Chase ran by the total number of days. In this case, Chase ran 36 3/4 miles over six days. To express 36 3/4 as a decimal, convert 3/4 to .75. So, 36 3/4 becomes 36.75 miles.

Now, we can divide the total distance by the total number of days:

36.75 miles ÷ 6 days = 6.125 miles per day. So, Chase ran about 6.125 miles each day.

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Answer:

12

Step-by-step explanation:

squares have equal sides

The truck is 32.22m away from the base of the building

As a 1.5m long  man is standing on the 42m long building,

=>the height of man's site= 42+ 1.5= 43.5m

If the line of sight is directed downward from the horizontal line, then an angle is created with the horizontal line. The angle produced between the horizontal line and the observer's line of sight is known as the angle of depression if the object being observed is below the observer's level.

As given, the angle of depression = 53.5°

We know that,

tan ∝= perpendicular* base

so, ∝=53.5:

tan(53.5 )= 43.5/y

[where y= distance of the truck from the base of the building]

1.35= 43.5/y

y=43.5/1.35= 32.22m

Hence, the truck is 32.22m away from the base of the building.​

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Expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16

What do you mean by One-to-One Correspondence?

the capability of relating one object to another. For each number spoken aloud, the learner should be able to count or move one object while saying "1,2,3,4". She has not learned one-to-one correspondence if she accidentally counts an object twice or skips one of the things while counting. Before starting Giggle Facts, students must be able to match one object to each number counted.

Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practise combining groups of the same number using manipulatives or other classroom supplies.

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Answer:

A double expression

Step-by-step explanation:

Using Theorem 9.11, we can determine the convergence or divergence of the p-series given by:

1 + 1/(8√2) + 1/(8√3) + 1/(8√4) + ...

The general form of this series is:

Σ (1/(8√n))

Comparing this to a p-series, we can see that the exponent p in the denominator is 1/2, as it involves a square root:

Σ (1/n^p) with p = 1/2

According to Theorem 9.11, a p-series converges if p > 1 and diverges if p ≤ 1. In this case, p = 1/2, which is less than or equal to 1. Therefore, this p-series diverges.

Theorem 9.11 states that the p-series 1/n^p converges if p > 1 and diverges if p ≤ 1.

In this case, we have a series of the form 1/√n^p, where n = 1, 2, 3, ... Since the denominator is growing exponentially with n, the terms are decreasing to zero.

To apply the theorem, we need to compare p to 1. Since the series has a square root in the denominator, we can rewrite it as 1/(n^(p/2)√n). Thus, p/2 is the exponent of the series without the square root.

If p/2 > 1, then p > 2, and the series converges by Theorem 9.11. If p/2 ≤ 1, then p ≤ 2, and the series diverges by Theorem 9.11.

So, in this case, p/2 = 1/8, which is less than 1. Thus, p ≤ 2 and the series diverges by Theorem 9.11. Therefore, the answer is "diverges".

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Answer:

( x - 2 ) ( x + 2 ) ( x² + 4 ) - ( x² - 2 ) ( x² + 3 )

(x²– 4) (x²+4) – (x⁴ + x² – 6)

( x⁴ – 16 ) – ( x⁴ + x² – 6 )

( x⁴ – 16 ) + ( – x⁴ – x² + 6 )

– x² – 10

I hope I helped you^_^

Answer:  15 is 75% of 20.

To solve the percent problem, we can use the equation:

part = percent * whole

In this case, the "Part" is 15, and the "Percent" is 75%. We need to find the "Whole".

So we can rewrite the equation as:

15 = 75% * Whole

To solve for the Whole, we need to divide both sides of the equation by 75% or 0.75 (which is the decimal equivalent of 75%).

15 / 0.75 = Whole

Now, let's calculate the value of Whole:

Whole = 20

Therefore, 15 is 75% of 20.

In this problem, we can also solve it by setting up a proportion:

15 is to 75% as Whole is to 100%.

This can be written as:

15/75% = Whole/100%

To simplify the proportion, we can convert 75% to its decimal form, which is 0.75, and 100% to its decimal form, which is 1.

15/0.75 = Whole/1

Simplifying further, we can multiply both sides of the equation by 0.75:

(15/0.75) * 0.75 = Whole

20 = Whole

So, the Whole value is also 20.

Therefore, 15 is 75% of 20.

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The solutions for the equation are b = 0, 3.

What is the cubic equation?

A three-degree equation is referred to as a cubic equation. All cubic equations have roots that are either three real roots or one real root and two imaginary roots. Polynomials are referred to as cubic polynomials if they have a degree of three. The opposite of cubing an integer is finding the cube root of that number. It can be determined by first determining how the given integer can be divided into prime factors, and then by using the cube root formula.

To find the solution for the equation 5/3b³ - 2b² - 5, we can factor it or use the quadratic formula.

One way to factor it is to note that it is a cubic equation in terms of b, and can be written as:

5/3b³ - 2b² - 5 = (5/3b³ - 2b²) - 5 = (5/3b³ - 2b²- 5b) + (5b)

= (5/3b)(b² - 3b) + 5

So, b=0 is one solution, but we can also factor the remaining quadratic equation (b² - 3b) = 0,

b=0 and b=3 are the solutions for the equation.

Hence, the solutions for the equation are b = 0, 3.

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_________the answer is -4+5_________

Answer: 29

Step-by-step explanation:

I will explain how I got my answer and how it is correct. It is asking for the perimiter, so this is how you find it.

1. Add the lengths of all sides. (19 + 19 + 11 + 9 = 58)

2. (ONLY FOR TRIANGLES) Since this is a triangle, half that number because it is not a full square. (58 divided by 2 = 29)

Hope this helps! :)

The dimensions of the rectangle will be 4 and 6.

From the information given, we are told that the area is given by x² + 2x - 24. We will expand this as follows:

x² + 2x - 24

x² + 6x - 4x - 24

x(x + 6) + 6(x - 4)

x - 4 = 0

x = 0 + 4

Therefore, the other dimension will be:

= 24/4

= 6

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Answer:

$124.86

Step-by-step explanation:

We can find the sale price by multiplying $129.99 by (1.00 - 0.15), or 0.85, which results in $110.49.

Similarly, the final new price is (1 + 0.13)($110.49) = $124.86.

This breaks down to 1.00($110.49) = $110.49 (the sale price before tax) plus 0.13($110.49) = $14.36 (the tax on $110.49).  Adding $110.49 and $14.36 together results in $124.86.

Answer:

(-3, -3)

Step-by-step explanation:

1.) Rewrite the second equation so 3y is on one side of the equation:

3y=6+5x

2.) Substitute the given value of 3y (replacing 3y with 6+5x, since we know they equal each other) into the equation 17x=-60-3y

Should end up with this:

17x=-60-(6+5x)

3.) Solve 17x=-60-(6+5x)

Calculate Difference: 17x=-66-5x

Combine Like Terms: 22x = -66

Divided both sides by 22 to isolate and solve for x: -3

So We know x=-3, now we got to find the y value. We can use either the first or second equation to find y value, so lets use the second.

3y=6+5x

1.) We know that x=-3, so we can simply substitute x in the equation

3y=6+5x with -3

3y=6+5(-3)

2.) Solve 3y=6+5(-3)

Combine Like Term: 3y=6+-15

Combine Like Term Even More: 3y= -9

Divide by 3 on both sides to isolate and solve for y: y=-3

So now we know y=-3 and once again we know x=-3, so if we format that

(-3,-3)

^  ^

x  y

Original Width: 10.5

Original Length: 12

Scaled Width: 3.5

Scaled Length: ?

We will be using x to find the unknown scale multiplier

3.5=10.5/x

Multiply both sides by x:

3.5•x=10.5/x•x

3.5x=10.5

Divide both sides by 3.5:

3.5x/3.5=10.5/3.5

x=3

12/3=4

Scaled Width: 3.5

Scaled Length: 4

3.5•4=14

Hope this helped!

The area of the scale model would be equal to 14.

The scale factor states the scale or measurement by which a figure is bigger or smaller than the other figure. The size by which the figure would be reduced or enlarged is called its scale factor.

Given that room is 12 feet long and 10.5 feet wide. A scale model of the room is 3.5 feet wide.

Using x to find the unknown scale multiplier

Solving for x:

3.5=10.5/x

Multiply both sides by x:

3.5•x=10.5/x•x

3.5x=10.5

x = 3

To determine the length, we need to divide the original length by 3:

12/3=4

The area of the scaled model is;

(Scaled Length x Scaled Width)

Scaled Width: 3.5

Scaled Length: 4

3.5(4)=14

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A) Average number of children per household= Sum of all the number of children/number of households=> 2.35 children per household.B) The central measure calculated in the task is mean or the average number of children per household. C) the median of the data set is  3. The mode is 2.

a) Average number of children per household is calculated by summing up all the number of children per household and dividing it by the number of households.

Here,Sum of all the number of children = 1+2+4+1+1+3+2+3+6+2+5+3+2+1+3+1+4+2+5+2=47

Average number of children per household= Sum of all the number of children/number of households=> 47/20= 2.35 children per household.

b) The central measure calculated in the task is mean or the average number of children per household.

c) There are two other central measurements called the median and mode that exist.Median:

To calculate the median, we need to arrange the given data in the order of increasing magnitude. 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 5, 5, 6.

The median is the middle value in the data set. Since we have an even number of data points, the median is the average of the two middle values.

Therefore, the median of the data set is (3+3)/2= 3.

Mode: The mode is the value that appears most frequently in a data set. Here, the mode is 2 because it appears the most number of times.

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The inverse of the matrix A is:

A^(-1) = [ 0 2/15 0 ]

[ 2/15 -2/15 -2/15 ]

[ -4/15 2/15 1/15 ]

To find the inverse of the matrix A:

A = [ 1 -1 -2 ]

[ 3 -2 -8 ]

[ -2 0 15 ]

We can use the method of row operations to transform the matrix into reduced row-echelon form. We augment the matrix with the identity matrix of the same size and perform row operations until the left side of the augmented matrix becomes the identity matrix. The right side will then be the inverse of the original matrix.

[ 1 -1 -2 | 1 0 0 ]

[ 3 -2 -8 | 0 1 0 ]

[ -2 0 15 | 0 0 1 ]

Performing row operations:

R2 = R2 - 3R1

R3 = R3 + 2R1

[ 1 -1 -2 | 1 0 0 ]

[ 0 1 2 | -3 1 0 ]

[ 0 -2 11 | 2 0 1 ]

R3 = R3 + 2R2

[ 1 -1 -2 | 1 0 0 ]

[ 0 1 2 | -3 1 0 ]

[ 0 0 15 | -4 2 1 ]

R3 = (1/15)R3

[ 1 -1 -2 | 1 0 0 ]

[ 0 1 2 | -3 1 0 ]

[ 0 0 1 | -4/15 2/15 1/15 ]

R2 = R2 - 2R3

R1 = R1 + 2R3

[ 1 -1 0 | -2/15 4/15 2/15 ]

[ 0 1 0 | 2/15 -2/15 -2/15 ]

[ 0 0 1 | -4/15 2/15 1/15 ]

R1 = R1 + R2

[ 1 0 0 | 0 2/15 0 ]

[ 0 1 0 | 2/15 -2/15 -2/15 ]

[ 0 0 1 | -4/15 2/15 1/15 ]

Therefore, the inverse of the matrix A is:

A^(-1) = [ 0 2/15 0 ]

[ 2/15 -2/15 -2/15 ]

[ -4/15 2/15 1/15 ]

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Answer: 90 U.S. dollars

If 60 U.S. dollars represwnt 50 euros, we will add.

80 euros represent 90 dollars because: there are 10 more euros than dollars.

Hope this helps!

Answer: 90

50:60 = 5:6

80:90 = +10

If there is a decrease in interest rates in an economy, the impact on the consumption of households that are net savers can be analyzed in terms of the income and substitution effects.

The income effect refers to the change in consumption resulting from a change in income. When interest rates decrease, the income effect for net savers is likely to be negative. This is because the return on their savings will be lower, resulting in a decrease in the income generated from interest earnings. As a result, their overall income available for consumption may decrease, leading to a decrease in current consumption.

The substitution effect refers to the change in consumption resulting from a change in the relative prices of goods and services. In this case, a decrease in interest rates would reduce the return on savings compared to the return on other assets or investments. This can incentivize net savers to shift their savings away from low-yielding savings accounts or bonds towards alternative investments that may offer higher returns. This reallocation of savings can lead to a decrease in current consumption, as funds are redirected towards investments rather than immediate consumption.

Considering both effects, the correct answer is (c) The income effect will drive their current consumption up, but the substitution effect will drive it down. The income effect suggests a decrease in current consumption due to the lower income from reduced interest earnings, while the substitution effect indicates a decrease in current consumption due to the reallocation of savings towards other investments.

It's important to note that the actual response of net savers' consumption to a decrease in interest rates can vary depending on individual preferences, economic conditions, and other factors. The magnitude and direction of the effects may differ among households based on their specific financial situations and attitudes towards saving and spending.

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Answer:

I'd say multiply the numerators then the denominators and at the end simplify at least thats how I multiply fractions :)

Answer:

5'506 the answer is 5'506 I because I add 2'500 with 6 and I got that answer

The total amount owed when $2500 is borrowed for one year at 6% simple interest is $2650.

Simple interest is the process of finding the amount of interest if we have some principal value of money. Here a specific interest is charged only for the principal amount.

Formula for calculating the total amount in case of Simple Interest is,

A = p (1 + r t)

where, A is the total amount, p is the principal amount, r is the rate of interest and t is the time period.

Here, p = $2500

r = 6% = 6/100 = 0.06

t = 1 year

So the total amount = 2500 [1 + (0.06 × 1)]

                                 = 2500 [1 + 0.06]

                                 = 2500 × 1.06

                                 = 2650

Hence the total money owed is $2650 when $2500 is borrowed for one year at 6% simple interest.

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The mass of silver that can be plated onto an object is 0.319 g.

The amount of silver plated onto the object can be calculated using Faraday's law of electrolysis, which states that the mass of a substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the cell.

The formula for calculating the mass of silver plated is:

mass of silver plated = (current x time x atomic mass of silver) / (Faraday's constant x 1000)

current = 8.70 A, time = 33.5 minutes = 2010 seconds

Atomic mass of silver (Ag) = 107.87 g/mol

Faraday's constant = 96,485 C/mol

Substituting the values in the above formula, we get:

mass of silver plated = (8.70 A x 2010 s x 107.87 g/mol) / (96,485 C/mol x 1000)

= 0.319 g

Therefore, the mass of silver plated onto the object in 33.5 minutes at 8.70 A of current is 0.319 g.

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