How do you find the sides of a 45 45 90 triangle when given the hypotenuse?

Katie is correct. Any number with 4 as a factor will also have 8 as a factor; therefore, any number with 8 as a factor will have 4 as a factor.

Katie is correct. Any number that is a multiple of 8 will also be a multiple of 4 because 8 is divisible by 4. For example, 8 is a multiple of 4 (8 = 2 x 4) and 16 is a multiple of 8 (16 = 2 x 8) and also a multiple of 4 (16 = 4 x 4). So, any number that is a multiple of 8 will also be a multiple of 4.  So any number that is a multiple of 8 will also be a multiple of 4. Note that 80 is a multiple of 8, but not 4.

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The equation equivalent to the equation x + y = 3 is 6x + 6y = 18.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x + y = 3

Multiply 6 on both sides.

6x + 6y = 18

Thus,

The equation that is equivalent is 6x + 6y = 18.

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Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.

Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..

Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.

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The values of x are 5 or 13.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given is an equation, [tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] - x = -8

[tex]\sqrt{2x-1}[/tex] = -8+x

Squaring both sides,

2x-1 = x²+64-16x

x²-16x-2x+1+64 = 0

x²-18x+65 = 0

Factorizing the equation,

x²-18x+65 = 0

x²-13x-5x+65 = 0

x(x-13)-5(x-13) = 0

(x-5)(x-13) = 0

x = 5 or 13

Hence, the values of x are 5 or 13.

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With a mass of 50 kg, Becky used 588 watts power to sprint up a 3.0 m high set of stairs in 2. 5 seconds. She is able to run up a 4.5 m high flight of stairs in 3.75 s.

Work (in joules) equals your weight (in newtons) x the height of the stairs (in meters.) The power you now possess is equal to the sum of your labor times the duration of that labor, or: Work (measured in joules) divided by time equals power, measured in watts (in seconds.)

Given that mass of Becky is 50 Kg

gravity of earth is 9.8 m/s²

height of stairs is 3.0 m

time taken to run up in stairs is 2.5 s

Power = work done/ time taken

P = (50*9.8*3.0)/2.5

P = 1470/2.5

P = 588 watt

Becky is able to run up a 3.0 m high flight of stairs in 2.5 s

She is able to run up a 4.5 m high flight of stairs in t =  (2.5 * 4.5)/3

t = 11.25/3

t = 3.75 s

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When  C.I. is given as 80% then the margin of error will be 1.9591% as calculated from the given data.

We are given that the first margin of error (MOE) is 3%.

Also,  confidence interval

first C.I.=95%

second C.I.=80%

Therefore , MOE at 80% will be ,

The formula for proportion is given as (P),

P=x/n , here 64%.

The values are same or constant as in general, this means standard deviation is also constant

Now formula for MOE is given by

MOE = Z x ( SD ) / √n

where ,  Z is value for confidence interval

MOE ∞ Z-value

So we can say that ,

MOE = k x Z ( where k = proportionality constant).

So , for 95 % Z=1.96 and for 80% Z=1.28

MOE then calculated will be , 1.95% .

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Answer:

50x - 200y = 75

3x + y = -5

Step-by-step explanation:

Standard form of a line

Ax + By = C

0.5x +-2y -0.75  Multiply through by 100

50x - 200 - 75 = 0  Add 75 to both sides

50x - 200y = 75

y = -3x - 5  Add 3x to both sides

3x + y = -5

Answer: No

Step-by-step explanation:

Look at the 3 numbers in the sequence,

Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)

However, for the sequence listed above

Looking at 1st and 2nd term,

Ratio = 110/120 = 11/12

Looking at 2nd and 3rd term,

Ratio = 105/110 = 21/22 which is not the same as 11/12.

Hence, since the ratio is not the same, this sequence is not a geometric sequence.

In Python, __main__ is the name of the environment where top-level code is run.

We know that in Python, the main function acts as the starting point of execution for any software program.

As we know the program executes only when it runs directly, and if it is imported as a module, then it will not run, the execution of the program starts only when the main function is defined in Python.

__main__ is the name of the top-level scope in which top-level code executes.

Also, all the functions and modules will be executed in the top-level scope __main___ in the interpreter shell.

Using the top-level scope __main__ increases the reusability.

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1/7 is the probability that the product is an odd number.

What is the simple definition of probability?

A probability is a number that expresses the possibility or likelihood that a specific event will take place.

                   Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Total Cards are 7

2 cards out of 7 cards can be selected in ⁷C₂   = 21  ways

Product would be odd if both cards are odd

3 , 5 , 7  are odd cards

2 cards out of 3 Can be selected   in ³C₂  = 3  ways

( 3 , 5) , ( 3 , 7) , ( 5 , 7)

Hence probability  the product of the numbers on the 2 cards  is odd number

= 3/21

= 1/7

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y = -3x + 12   is the equation  for the line containing the side opposite the side containing the first two vertices.

Given coordinates:

(-3,4) ; (-2,1) ; and (2,6)

let us solve for the slope.

Since , parallel sides have the same slope.

m = y2-y1 / x2-x1

m = 1 - 4 / -2-(-3)

m = -3 / 1

m = -3

y = mx + b

Since , (2,6) is a point which passes through the line . Hence , it must satisfy the equation.

Therefore,

6 = -3(2) + b

6 = -6 + b

6 + 6 = b

12 = b

On Substituting , values of m and b in y = mx +b , we get y = -3x +12 which is the required equation of the line.

Hence, y = -3x + 12   is the equation  for the line containing the side opposite the side containing the first two vertices.

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Answer:

Step-by-step explanation:

Derivation of composite functions concept.

h'(x)=g'(f(x))·f'(x)=(sin(5x))'×(5x)'=cos(5x)×5=5cos(5x)

Answer : in California there are 24 volcanoes while in Alaska there are 36 volcanoes.

Step-by-step explanation:

Total number of volcanoes = 60.

40% of the volcanoes where in California.

i.e 100% - 40% = 60%.

60% of the volcanoes were in Alaska.

In California = 40/100 × 60 = 24 volcanoes.

In Alaska = 60/100 × 60 = 36 volcanoes.

Answer: The table shows the number of pictures that a printer can print at different intervals of time (measured in minutes). To find the rate in pictures per minute, we need to divide the number of pictures printed by the number of minutes it took to print them.

For example, at 2 minutes the printer printed 16 pictures. The rate of pictures printed per minute is 16 pictures / 2 minutes = 8 pictures/minute.

Similarly, at 4 minutes the printer printed 32 pictures. The rate of pictures printed per minute is 32 pictures / 4 minutes = 8 pictures/minute

And, at 6 minutes the printer printed 48 pictures. The rate of pictures printed per minute is 48 pictures / 6 minutes = 8 pictures/minute.

And, at 8 minutes the printer printed 64 pictures. The rate of pictures printed per minute is 64 pictures / 8 minutes = 8 pictures/minute.

From this it can be seen that the printer has a constant rate of 8 pictures per minute, independent of the number of minutes, it is producing 8 pictures/min.

The value 15 is not related to the table, so it's not the rate, and 16 is not the rate either, it is the number of pictures printed at 8 minutes.

Step-by-step explanation:

We convert 10 pounds to Dollars and get 12.2 United states Dollars.

Exchange rate is the rate at which one currency can be exchanged to another currency. The rate represents the relative value of one currency against the currency from another country. Currency conversion means convert one currency to another at an exchange rate.

We can convert pound to dollar by using currency exchange rate determined by the world market. The exchange rate is vary depending on the current situation of two country in which currency is converted between. The rate may be differed from one day to another.

1 pound sterling = 1.22 United States Dollar

10-pound sterling = 12.2 US Dollars

1 pound sterling = 1.76 Australian Dollar

10-pound sterling = 17.6 Australian Dollars

1 pound sterling = 1.64 Canadian Dollar

10-pound sterling = 16.4 Canadian Dollars

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Answer:

It's neither:

x =√ 9.000 = 3.00000 or :

x =√ 9.000 = -3.00000 or :

x =√ 8.000 = 2.82843 or :

x =√ 8.000 = -2.82843

Four solutions

Answer:

x^4 - 17x^2 + 72 = (x^2 - 9)(x^2 - 8)

Step-by-step explanation:

First, we need to find two numbers that multiply to give us 72 and whose sum is -17. We can see that 8 and 9 multiply to give us 72, and their sum is 8 + 9 = 17. Since we want the sum to be negative, we need to change one of the signs. So we write -(8 + 9) = -17.

Next, we write the expression as the product of two binomials. We factor out the common factor x^2 from the first two terms: x^4 - 17x^2 + 72 = x^2(x^2 - 17) + 72

Now, we complete the square in the first binomial. To do this, we need to add and subtract (17/2)^2 = (8.5)^2 = 72.25 inside the bracket:

x^2(x^2 - 17) + 72 = x^2(x^2 - 17 + 72.25 - 72.25) + 72 = x^2(x^2 - 17 + 72.25) - 72.25 + 72

Now we can rewrite the square of a binomial :

x^2(x^2 - 17 + 72.25) = x^2((x-8.5)^2)

Finally, we can combine the two binomials

x^2((x-8.5)^2) + 72 = (x^2(x-8.5)^2) + 8(9)

So the expression x^4 - 17x^2 + 72 factors completely as (x^2 - 9)(x^2 - 8)

Hope this helps!

The probabilities are given as follows:

a) No injuries: 0.4493 = 44.93%.

b) More than two injuries: 0.0474 = 4.74%.

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following equation:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

The parameters are:

The mean for this problem is of:

[tex]\mu = 0.8[/tex]

The probability of no injuries is of P(X = 0), hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

The probability of more than two injuries is of:

P(X > 2) = 1 - P(X <= 2)

In which:

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

Hence:

[tex]P(X = x) = \frac{e^{-\mu}\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-0.8}(0.8)^{0}}{(0)!} = 0.4493[/tex]

[tex]P(X = 1) = \frac{e^{-0.8}(0.8)^{1}}{(1)!} = 0.3595[/tex]

[tex]P(X = 2) = \frac{e^{-0.8}(0.8)^{2}}{(2)!} = 0.1438[/tex]

Then:

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To find the coordinates of a point in a coordinate system, do the inverse. Start at the point and trace a vertical line up or down to the x-axis. There you have your x-coordinate. Then repeat the process, but this time follow a horizontal line to determine the y-coordinate.

A point is identified by its ordered pair of (x, y). The first number represents the x-coordinate, while the second represents the y-coordinate.

To graph a point, you draw a dot at the coordinates of the ordered pair. It's usually a good idea to begin at the beginning.

An ordered pair of integers, such as an x-coordinate, which is a number on the x-axis, and a y-coordinate, which is a number on the y-axis, can be used to identify each point. Parentheses are used to indicate ordered pairings (x-coordinate, y-coordinate). The starting point is at (0,0).

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So the number of parcels that Helen delivered on Monday ​is 120 parcels.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.

An equality of two ratios is a percentage. We use proportions to construct comparable ratios and find solutions to problems involving unknown numbers.

If on Wednesday Helen delivered 50% fewer parcels than on Tuesday, then on Tuesday Helen delivered 72 / (1 - 0.5) = 72 * 2 = 144 parcels.

On Tuesday Helen delivered 20% more parcels than on Monday, so the number of parcels Helen delivered on Monday is (144 / 1.2) = 120

So Helen delivered 120 parcels on Monday.

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Answer:

  25%

Step-by-step explanation:

Of the 12 girls and 16 boys in Mr. Johnson's class, 3 girls and 4 boys wear glasses. You want to know the percentage of students in the class who wear glasses.

The percentage is the fraction multiplied by 100%. The fraction is the ratio of glasses-wearers to total students.

  percentage = (girls w/ glasses + boys w/ glasses)/(girls + boys)×100%

  percentage = (3 +4)/(12+16) × 100% = 7/28 × 100% = 25%

25% of the students in Mr. Johnson's class wear glasses.

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The members voted 2 more for mars than earth.

The Solar System has at least eight planets: the terrestrial planets Mercury, Venus, Earth and Mars, and the giant planets Jupiter, Saturn, Uranus and Neptune.

Given here, Mars has 8 votes while earth has 6 votes

Thus difference in votes is =8-6

                                              = 2

Hence, Mars got two more members than earth

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The modulus of 2 - 3i is √13. So, the correct option is d.

Modulus is a mathematical operation used to find the remainder when dividing two numbers. This is called a percent sign (%) and is represented by a single number such as 12. Used to determine if two numbers are divisible (no remainder). You can also use the modulus to compare two numbers to see which is greater or lesser. Additionally, this module can be used to calculate the distance between two points on the coordinate plane.

It is computed by taking the square root of the sum of the squares of the real and imaginary components, so √(2^2 + (-3)^2) = √13. The modulus of a complex number, also called absolute value, is a measure of distance from the origin.

Let z = -2 - 3i

z = (-2) + (-3)i

Modulus of z = √((-2)² + (-3)²)

√(4 + 9) = √13

Modulus of z = √13

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Therefore , the solution of the given problem of triangle comes out to be

OAC angle arc is = 55 degrees.

Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.

Here,

Half of the arc AB is the measure of angle OAC, hence the measure of angle OAC is:

OAC = 0.5 times 220 degrees.

110 degrees is OAC.

If the angle OAC is measured as a quarter of an arc AB, then the angle OAC is measured as follows:

OAC equals 0.25 x 220 degrees

OAC = 55 degrees

Therefore , the solution of the given problem of triangle comes out to be

OAC angle arc is = 55 degrees.

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The simplified form of the given radical expression is rational.

Exponent can be defined as the method of expressing large numbers in terms of powers. Exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6.

We are asked to determine whether the simplified form of  2√3.√12

To solve our given problem we will use exponent property for radicals

           √m.√n = a√m.n

          2√3.√12=2√3.12

            2√3.√12=2√36

             2√3.√12=2×6

              2√√3.√12=12

The simplified form of the given radical expression is rational.

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Since our given radical expression simplifies to a rational, therefore, our answer is yes

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Answer:

For the first line its distributive property
The 2nd is combining like terms

4th is simplifying it

Im not sure about the last one since its just the answer of the problem

Step-by-step explanation:

Answer:

  y = -x +3

Step-by-step explanation:

You want the equation of the line through the points (-3, 6) and (5, -2) in slope-intercept form.

The slope can be found using the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (-2 -6)/(5 -(-3)) = -8/8 = -1

The y-intercept can be be found using the formula ...

  b = y -mx

  b = 6 -(-1)(-3) = 3

The equation in slope-intercept form is ...

  y = mx +b

Using the found values, the equation is...

  y = -x +3

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Answer: Assuming that the selection of the toll booth is a random and independent event, the probability that Mr. Espinoza chooses the middle toll booth on Monday is 1/5 (or 20%), since there are five total toll booths and the middle booth is one of those options. Similarly, the probability that he chooses the middle booth on Tuesday is also 1/5 (or 20%).

To find the probability that he chooses the middle booth on Monday and Tuesday, we can multiply the probabilities of each event.

Probability of selecting middle booth on Monday AND selecting middle booth on Tuesday = (1/5) * (1/5) = 1/25 = 0.04 or 4%

So, Mr. Espinoza will select the middle toll booth on Monday and Tuesday with a probability of 4%. This means that the chance that both events will happen is low and quite rare, but not impossible.

Step-by-step explanation:

The smallest amount that Byron could have converted is £73.44.

An exchange rate is the rate at which one currency can be exchanged for another currency. It is the value of one country's currency against another country's currency. Exchange rates fluctuate based on supply and demand for a particular currency, as well as economic and political factors.

Exchange rates are typically quoted as the value of one currency in terms of another currency. For example, an exchange rate of 1.2 US dollars (USD) to 1 Euro (EUR) means that 1 EUR can be exchanged for 1.2 USD.

There are two types of exchange rates, Floating and Fixed exchange rate.

According to question :-

To determine the smallest amount that Byron could have converted, we can use the exchange rate from shop A, which is €47.20 for £40.

If we divide the amount of euros he received (€68.44) by the exchange rate (€47.20 for £40), we get:

€68.44 ÷ €47.20/£40 = £73.44

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The graph of tan(x/4) < 1/5 over the interval 0<= x<=2pi radians is attached. An approximate solution to the trigonometric inequality tan(x/4)<1/5 over the interval 0<= x<=2pi radians is 0 <= x < 0.7896.

y = 1/5 is a horizontal straight line parallel to x-axis.

Plot of tan(x/4)<1/5 over the interval 0<= x<=2pi radians is attached. The shaded region is the solution.

tan(x/4) < 1/5

Taking tan inverse on both sides

tan⁻¹(tan(x/4)) < tan⁻¹(1/5)

x/ 4 <  tan⁻¹(1/5)

Multiplying by 4 on both sides

x < 4tan⁻¹(1/5)

x < 0.7896

Applying the limits of intervals

0 <= x <= 2pi ≈ 6.28

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