Find the distance between the point (2,1) and the line 3x- 4y+15=0​

Keep in mind that without the population standard deviation, it is impossible to provide an exact sample size. However, this formula will give you a good starting point.

To find the sample size needed for a 99.5% confidence interval with a margin of error of 1.5, we can use the formula:

n = (Z * σ / E)^2

where n is the sample size, Z is the Z-score corresponding to the desired confidence level, σ is the population standard deviation, and E is the margin of error.

For a 99.5% confidence interval, the Z-score is approximately 2.807 (from a standard normal distribution table). Since we do not have the population standard deviation (σ), we will need to estimate it using a sample standard deviation or use a conservative approach by assuming the maximum possible value. For now, let's assume we have an estimated standard deviation.

n = (2.807 * σ / 1.5)^2

Solve for n by plugging in the estimated standard deviation (σ) and then round up to the nearest whole number, as you cannot have a fraction of a sample.
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Answer:

1400 - 2.5t =  1200 + 1.5t

t = 50

Step-by-step explanation:

A hand of 10 cards is dealt from a well-shuffled standard 52-card deck of cards. The probability that the hand contains 3 Jacks is 0.018617. So correct option is b.

In mathematics, combinations refer to the ways of selecting a group of items from a larger set without considering the order of the items. Combinations are used to count the number of possible outcomes in situations where order does not matter, such as selecting a group of people to form a committee, or selecting a subset of items from a larger collection.

The number of possible combinations of r items selected from a set of n items is given by the formula:

C(n, r) = n! / (r! * (n - r)!)

where n! represents the factorial of n, which is the product of all positive integers up to n, and r! represents the factorial of r.

To solve this problem, we need to find the probability of selecting exactly 3 jacks out of 10 cards from the 52-card deck.

The probability of selecting a jack from the deck is 4/52, since there are four jacks in the deck. The probability of not selecting a jack is 48/52, since there are 48 non-jack cards in the deck.

Using the formula for the probability of a specific combination of events occurring (nCr), where n is the total number of cards in the deck, and r is the number of jacks we want to select:

P(3 jacks) = (4/52)³(48/52)⁷ × 10C3

10C3 is the combination of 10 cards taken 3 at a time, which is equal to 10!/(3!7!) = 120.

Therefore, P(3 jacks) = (4/52)³(48/52)⁷ × 120 ≈ 0.018617

So, the answer is b) 0.018617.

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Answer:

(G) -1

Step-by-step explanation:

Let the integer be [tex]x[/tex].

Then, it folloes that [tex]-x=x^2[/tex].

Because [tex]x \neq 0[/tex], dividing both sides by [tex]x>/tex] yields [tex]x=-1[/tex].

Answer:

Step-by-step explanation:

A contrapositive statement changes "if not p then not q" to "if not q to then, not p." The converse of the conditional statement is “If Q then P.” The contrapositive of the conditional statement is “If not Q then not P.” The inverse of the conditional statement is “If not P then not Q.” if p → q, p → q, then, ∼ q →∼ p ∼ q →∼ p

A Note about Notation: Be careful with the notation  a|b

. This does not represent the rational number  ab

. The notation  a|b

 represents a relationship between the integers  a

 and  b

 and is simply a shorthand for “ a

 divides  b

.”   "Divides" as in  a|b

 is a relation (true or false), while "divided by" as in  ab

 or   a/b

 is an operation (results in a number).

The definition for “divides” can be written in symbolic form using appropriate quantifiers as follows: A nonzero integer  m

 divides an integer  n

 provided that  (∃q∈Z)(n=m⋅q).

Answer

15.71 cm

Explanation

The equivalent function is [tex]z^{1/4}[/tex].

What is a function?

Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and codomain, respectively. Initially, functions represented the idealized relationship between two changing quantities.

Here, we have

Given: Z ≠ 0

We have to find the equivalent function to [tex]\sqrt[4]{z}[/tex].

We concluded that

[tex]\sqrt[4]{z}[/tex] = [tex]z^{1/4}[/tex]

Hence, the equivalent function is [tex]z^{1/4}[/tex].

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Answer:

60

Step-by-step explanation:

An easy way to find the answer is when you see of that basically means to times(X) so that means 2/3 X 90 = 60

After diving dοwn 215.5 feet, rising 125.5 feet, and diving dοwn anοther 122.4 feet, the submarine is at a depth οf 1,063.1 feet belοw sea level.

The fοur fundamental οperatiοns οf arithmetic are additiοn, subtractiοn, multiplicatiοn, and divisiοn οf twο οr mοre quantities. Included in them is the study οf numbers, especially the οrder οf οperatiοns, which is impοrtant fοr all οther areas οf mathematics, including algebra, data management, and geοmetry. The rules οf arithmetic οperatiοns are required in οrder tο answer the prοblem.

Starting at a depth οf 1,275.5 feet belοw sea level, the submarine dives dοwn an additiοnal 215.5 feet:

1,275.5 - 215.5 = 1,060 feet belοw sea level

Then the submarine rises 125.5 feet:

1,060 + 125.5 = 1,185.5 feet belοw sea level

Finally, the submarine dives dοwn anοther 122.4 feet:

1,185.5 - 122.4 = 1,063.1 feet belοw sea level

Therefοre, after diving dοwn 215.5 feet, rising 125.5 feet, and diving dοwn anοther 122.4 feet, the submarine is at a depth οf 1,063.1 feet belοw sea level.

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Answer:

[tex]v≈41033.52 \: {ft}^{3} [/tex]

Step-by-step explanation:

Given:

A sphere

r (radius) = 99 ft

π ≈ 3,14

Find: V (volume) - ?

[tex]v = \frac{4}{3} \pi {r}^{2} [/tex]

[tex]v = \frac{4}{3} \times 3.14 \times {99}^{2} ≈41033.52 \: {ft}^{3} [/tex]

There are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to Balance out those who have only one.

To solve this problem, we need to use some basic principles of statistics and probability. Let's start by identifying the key information provided in the problem. We know that there are 20 children in the class, and that some of them have sisters. Specifically, 8 children have one sister and 6 children have two sisters. We also know that the mean (average) number of children is 1, which means that on average, each child has one sibling.

To find out how many children had no sisters, we can use the following formula:

Total number of children - (number of children with one sister x 1) - (number of children with two sisters x 2) = number of children with no sisters

Using the values from the problem, we get:

20 - (8 x 1) - (6 x 2) = 0

This means that there are no children in the class who have no sisters. While this may seem counterintuitive, it's important to remember that the mean number of children is 1, which means that some children must have more than one sibling in order to balance out the others who have only one.

In summary, the answer to the question is that there are no children in the class who have no sisters. This is because the mean number of children is 1, and some children have more than one sibling to balance out those who have only one.

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Hamilton had a 21-man company in its first (currently only ongoing) production. There are 720 ways that can play as cast.

Hamilton had a 21-man company in its first (currently only ongoing) production, so we really know a little about our army of volunteers (all of which I think are good enough to hold the show to a high standard), but that's not necessarily the case. The problem - Thomas Kail and Andy Blanken buehler use their team of 11 in their Broadway productions to great effect, but a team of the same size. It's an art choice.

When it comes to the main body, there are actually 14 named locations, with a lot of work through singing and/or dialogue, in addition to the many things the members use from Kail products. This prevents all volunteers from being an essential part because that leaves us only 3 people in total which seems a bit lackluster in some big productions.

One solution is to have some minor roles played by the band members - for example James Madison, King George III, Peggy Schuyler and Maria Reynolds - so now we have 9 key characters and 8 groups that we need to succeed. compact performance.

My preference is to follow a Broadway production, so we have 10 main actors, so the ensemble is 7 people. If necessary, with the help of a small part of the main cast, we can expand the group in many performances.

Therefore, there are 10!/7! = 720 ways .

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The  five different math vocabulary that can be used to describe each given expression 6(t+2)-8

Expression: A combination of numbers, variables, and operators that can be evaluated or simplified.

Coefficient: A number that is multiplied by a variable.

Distributive Property: The property that allows you to multiply a factor by each term inside a set of parentheses.

Simplify: To reduce an expression to its simplest form.

Linear: An expression that has no exponents or other operations besides addition, subtraction, and multiplication by a constant.

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The mean of the given data set is 2.11.

What is mean?

Mean is a statistical term which is in general meaning is average. Sum of the given data and then dividing it by the number of terms is the mean of the given data set.

In the given problem ,

x              p(x)

0              .05

1                .34

2               .26

3                 .20

4                .10

5                .05

So the mean is ∑x (p(x))

                      = (0× .05)+ (1× .34)+(2× .26)+(3× .20)+(4× .10)+(5× .05)

                    = .34 +0.52+0.6+0.4+0.25

                   = 2.11

Hence, the mean is 2.11.

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Answer:

[tex]x = 1 \frac{49}{57} [/tex]

Step-by-step explanation:

[tex]6.75x + \frac{3}{8} x = 13 \frac{1}{4} [/tex]

Multiply the whole equation by 8, to eliminate the fractions:

[tex]54x + 3x = 106[/tex]

[tex]57x = 106[/tex]

Divide both parts of the equation by 57:

[tex]x = \frac{106}{57} = 1 \frac{49}{57} [/tex]

The height of the trapezoid is 7 mm.

A quadrilateral with one set of parallel opposite sides is referred to as a trapezium.

To find the height of a trapezoid when the area and the lengths of the parallel bases are given, we can use the formula:

h = 2A / ([tex]b_1 + b_2[/tex])

where

h is the height,

A is the area,

[tex]b_1[/tex] and [tex]b_2[/tex] are the lengths of the parallel bases.

As per given information in the question.

Using the given area of 35 mm² and the lengths of the parallel bases,

For [tex]b_1[/tex] = 8 mm and [tex]b_2[/tex] = 6 mm

we get:

h = 2 x 35 / (8 + 6) = 7 mm

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Answer:

H

Step-by-step explanation:

% of 11 year olds is 24

% of 12 year olds is 16

then ratio of

11 year olds : 12 year olds

= 24 : 16 ( divide both parts by 8 )

= 3 : 2

Answer:

Calculation:

Total Amount: $227

Down Payment: $47

Interest Rate: 9.6% (0.096)

Number of Payments: 12

Remaining Balance: $227 - $47 = $180

Remaining Balance with Interest: $180 + (9.6/100 * $180) = $197.68

Amount of Payment: $197.68 / 12 = $16.47

Answer: The amount of each payment is $16.47.

Answer:

A monthly budget worksheet cause it shows your income and expenditure, so you are able to spend within your budget and it helps you know your disposable income

Option A "Reject the hypothesis" is the appropriate conclusion in this case.

As per the question,

Based on the results from the simulation trials, Peter should conclude that his hypothesis should be rejected.

The simulation showed that finches are a guaranteed bird type for only 80% of the birds, which is lower than the observed percentage of 75% finches at Peter's bird feeder.

This indicates that the predicted percentage of finches continuing at the same rate is not supported by the simulation results.

Therefore, option A "Reject the hypothesis" is the appropriate conclusion in this case.

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Answer:

This problem can be solved using the method of Lagrange multipliers. Let's define the Lagrangian function as: L(K, L, λ) = Q - λ(K + 4L - 16) Taking partial derivatives with respect to K, L, and λ, we get: dL/dK = 0 => 1 - λ = 0 => λ = 1 dL/dL = 0 => 1 - 4λ = 0 => λ = 1/4 dL/dλ = K + 4L - 16 = 0 Solving the last equation for K, we get: K = 16 - 4L Substituting this into the Lagrangian function, we get: L = Q - λ(16 - 4L + 4

Answer:

  $1.53

Step-by-step explanation:

You want to know the total tax on purchases of $4.56, 12.45, and 2.13 if the tax rate is the sum of 6.5% and 1.5%.

The tax is the product of the tax rate and the total of purchases. The tax rate will be the sum of the state and county tax rates:

  6.5% +1.5% = 8% = 8/100

The attached calculation shows the tax is $1.53 after rounding to cents.

The tax rate on Mary Lou Mason's purchases is $1.53.

What is meant by rate?

In mathematics, rate usually refers to the ratio of two quantities that have different units of measurement.

To calculate the total tax on Mary Lou Mason's purchases, we need to first calculate the total cost of her purchases, including both the prices of the items and the sales tax.

The total cost of Mary Lou Mason's purchases before taxes is:

$4.56 + $12.45 + $2.13 = $19.14

To calculate the sales tax, we need to multiply the total cost of the purchases by the sum of the state and county tax rates:

6.5% + 1.5% = 8%

So the sales tax rate is 8%.

To calculate the total tax on Mary Lou Mason's purchases, we multiply the total cost of the purchases by the sales tax rate:

$19.14 x 8% = $1.53

Therefore, the tax on Mary Lou Mason's purchases is $1.53.

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Thus, the one notebook' price n = $6 and the price of one pencil is p = $2.4.

Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. Once an equation is given in this format, finding both intercepts is rather simple (x and y). When attempting to solve systems involving two linear equations, this form is also quite helpful.

Let cost of a notebook to be 'n' dollars

Let the cost of a pencil to be 'p' dollars,

Then, the system of equations are-

3n + 5p = 30   ..eq 1

n + 10p = 30  ....eq2

multiply eq 2 with 3

3n + 30p = 90 ...eq 3

Subtract eq 3 from eq 1

3n + 5p - 3n - 30p = 30 - 90

25p = 60

p = 2.4

n + 10(2.4) = 30

n = 30 - 24

n = 6

Thus, the price of one notebook n = $6 and the price of one pencil is p = $2.4.

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if Grandson Sinko puts the forks in groups of 12, there will be no forks left over

The least common multiple (LCM) of two or more integers is the smallest positive integer that is a multiple of each of the given integers. In other words, the LCM is the smallest number that is divisible by all the numbers in a given set.

the least common multiple of 4 and 6, is 12. So if Grandson Sinko puts the forks in groups of 12, there will be no forks left over.

To find the number of forks, we can use the fact that the number of forks is three more than a multiple of both 4 and 6. Let's call the number of forks x. Then we have:

x ≡ 3 (mod 4)

x ≡ 3 (mod 6)

Using the Chinese remainder theorem, we can combine these congruences to get:

x ≡ 3 (mod 12)

This means that the number of forks is three more than a multiple of 12. So we can write:

x = 12n + 3

where n is an integer. To find the value of n, we can plug in the values of x from the first two congruences:

x ≡ 3 (mod 4) => x = 4m + 3

x ≡ 3 (mod 6) => x = 6k + 3

Setting these two expressions for x equal to each other, we get:

4m + 3 = 6k + 3

Simplifying, we get:

2m = 3k

Since 2 and 3 are relatively prime, this means that m must be a multiple of 3 and k must be a multiple of 2. So we can write:

m = 3p

k = 2q

where p and q are integers. Plugging these into the expressions for x, we get:

x = 4m + 3 = 4(3p) + 3 = 12p + 3

x = 6k + 3 = 6(2q) + 3 = 12q + 3

Since x is the same in both expressions, we can set them equal to each other:

12p + 3 = 12q + 3

Simplifying, we get:

p = q

So we can write:

x = 12p + 3

where p is an integer. Therefore, if Grandson Sinko puts the forks in groups of 12, there will be no forks left over.

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8 possible sequences in total. Thus, A tree with 8 outcomes, option 1 is correct.

A diagram with a structure of branching connecting lines, representing different processes and relationships.

Here is a tree diagram showing all the possible outcomes of Sandra tossing a coin three times:

In the diagram, each branch represents the outcome of one toss of the coin. The letters "H" and "T" represent "heads" and "tails," respectively. Each path from the top of the tree to a bottom node represents a possible sequence of coin tosses, and there are 2³ = 8 possible sequences in total.

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Complete question:

Sandra tossed a coin 3 times. Which tree diagram shows al the possible outcomes of the coin landing heads up or tails up.

A tree with 8 outcomes

A tree with 12 outcomes

A tree with 9 outcomes

A tree with 6 outcomes

The correct answer is (B) Function A is decreasing, while function B is also decreasing AND Function A is steeper.

the expression would be used as follows:

Number of boxes of donuts (N) = 6 x Number of donuts (D)

Ling bought 108 boxes of donuts.

This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought.

Equations are used to solve problems involving unknowns, such as how much a person owes for groceries or how many people are required to complete a certain task.

The expression that would show how many boxes of donuts Ling bought is:

Number of boxes of donuts (N) = 6 x Number of donuts (D)

In this expression, N represents the number of boxes of donuts Ling bought and D represents the number of donuts. This expression can be used to calculate the number of boxes of donuts Ling bought when the number of donuts is known.

For example, if Ling bought 18 donuts, the expression would be used as follows:

Number of boxes of donuts (N) = 6 x Number of donuts (D)

N = 6 x 18

N = 108

Therefore, Ling bought 108 boxes of donuts.

This expression is a mathematical equation that uses multiplication to calculate the number of boxes of donuts Ling bought. The expression can be used whenever the number of donuts is known and can be used to calculate the number of boxes of donuts Ling bought.

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The complete expression of given question is :

3 5/6 feet = 23/6 feet = 46 inches.

A mixed fraction is a type of fraction that consists of a whole number and a proper fraction. For example, 3 1/2, 2 2/3, and 5 3/8 are all mixed fractions. The whole number part represents a number of whole units, while the fraction part represents a part of a unit.

To write 3 5/6 feet as a single fraction greater than one, we can convert the mixed number to an improper fraction. To do this, we multiply the whole number (3) by the denominator of the fraction (6), and add the numerator (5), then put the result over the denominator. Like this:

3 5/6 = (3 x 6 + 5)/6 = 23/6

Therefore, 3 5/6 feet can be written as the improper fraction 23/6 feet.

To complete the expression, we can use the fact that 1 foot is equal to 12 inches. Therefore, we can convert 23/6 feet to inches by multiplying it by 12:

23/6 feet × 12 inches/1 foot = 23/6 × 12 inches

Simplifying the fraction, we get:

23/6 × 12 inches = 276/6 inches = 46 inches

Therefore, the expression is:

3 5/6 feet = 23/6 feet = 46 inches.

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To find (f-g)(1), we first need to find f(1) and g(1): f(1) = -(1)^2 - 1 - 3 = -5 g(1) = -1 Now we can substitute these values into (f-g)(x) = f(x) - g(x) and simplify: (f-g)(1) = f(1) - g(1) = (-5) - (-1) = -4 Therefore, (f-g)(1) = -4.