What is the length of the short side of one of the 30 60 90 triangles?

A total of 3 five ounces glass are needed so have the same alcohol as that of a 12 ounce glass.

In order to find the number of glass of capacity five ounces that will have the same capacity as that of the twelve ounce glass can be calculated as followed,

Let us say that n number of five ounces glasses are required to equate 12 ounce glass.

Now, we can write the relation,

using simple algebra,

n(Five ounces glasses) = 1 Ounce alcohol content

n = 12/5

n = 2.4

But, we have to answer an integral value, so, we will say that the required number of the glasses is 3.

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Answer:

scale factor = 3

Step-by-step explanation:

since the origin is the centre of dilatation then the scale factor is the ratio of corresponding coordinates, image to original.

given D (12, - 4 ) and D' (36, - 12 ) , then

scale factor = [tex]\frac{36}{12}[/tex] = [tex]\frac{-12}{-4}[/tex] = 3

Three cards are chosen from a pack of 52 cards. what is the probability that they are not all the same color is 0.8824 or 88.24%

The likelihood or chance that a specific event will occur is represented by a probability.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportion with a range of 0 to 1, or as percentages with a range of 0% to 100%.

Given that three cards are chosen from a pack of 52 cards.

There are 26 cards of each color (i.e. 26 cards are red color and 26 cards are of black color)

The probability of drawn first card of any one color is

P(1)= 26/52 = 1/2

The probability of drawn second card of same color is

P(2)= 25/51

The probability of drawn third card of same color is

P(3)= 24/50 = 12/25

The probability of having three cards are same color is

P = P(1)*P(2)*P(3)

P = 1/2 * 25/51 * 12/ 25

P = 6/51

So the probability that three cards are not all the same color is

P' = 1 - P

P' = 1 - 6/51

P' = (51-6)/51

P' = 45/51 = 15/17

P' = 0.8824

The likelihood that the three cards are not all red is roughly 0.8824, or 88.24%,

.

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The expression that represents the perimeter of the rhombus is 2d√17

How to determine the expression that represents the perimeter of the rhombus?

From the question, we have the following parameters that can be used in our computation:

The length of one diagonal of a rhombus is 4 times the length of the other diagonal.

This means that

Length 1 = 4 * Length 2

From the question, we have

Let d be the length of the shorter diagonal.

This means that

Length 1 = 4d

Length 2 = d

The perimeter of the rhombus from the diagonals is calculated as

P = 2√(Length 1² + Length 2²)

Substitute the known values in the above equation, so, we have the following representation

P = 2√((4d)² + d²)

Evaluate the exponents

P = 2√(16d² + d²)

So, we have

P = 2√(17d²)

Evaluate the exponents

P = 2d√17

Hence, the perimeter is 2d√17

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The required true statements for the given lines are 1 and 4.

An element or portion of a line with two endpoints is called a line segment. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters, or conventional measurements like feet or inches.

Statement A: E and C are co-linear.

It is true, E and C are lie in same line

statement 2: Lines I and m intersect at point D.

It is false, I and m intersect at point E.

statement 3: AE and DC are line segments on line I

It is false,because AE and DC are line segments placed in different line.

statement 4: EA and EC are rays on the line m.​

It is true, as EA and EC are in same line m.

Thus, required true statements are 1 and 4.

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Answer:

1 and 4

Step-by-step explanation:

Therefore , the solution of the given problem of percentage comes out to be  athletes who took move  285 to finish the race is 64%.

A percentage is what is used to describe a fraction of a whole when it is stated as a number range between 0 and 100. 100% of something, 50% of something, and 0% of something are all equal. After dividing the portion of the whole by the entire, multiply the result by 100 to arrive at a percentage.

Here,

For the table to get the total frequency is:

=> 3+6+9+7

=>9+9+7

=>25

The frequency greater than 285 is

9+7 = 16

So,

the percentage of the athletes who took move  285 to finish the race is:

=> 16/25 * 100

=> 0.64 * 100

=> 64%

Therefore , the solution of the given problem of percentage comes out to be  athletes who took move  285 to finish the race is 64%.

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Answer: The input values for this function are the number of hours traveled, represented by the variable h. Therefore, appropriate input values for this function would be any positive number representing a number of hours traveled.

For example, some appropriate input values could be:

h = 1: This represents 1 hour of travel, or a total distance of 140 miles.

h = 2: This represents 2 hours of travel, or a total distance of 280 miles.

h = 3.5: This represents 3.5 hours of travel, or a total distance of 490 miles.

Note that the input values do not have to be whole numbers, they can be any positive number representing a number of hours traveled.

Step-by-step explanation:

To fill one urn with one white ball and the second urn with the remaining nine white and ten black balls.

Probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. A coin flip is the most basic illustration. There are only two outcomes that can occur when you flip a coin: either heads or tails.

The basic probability formula is: Probability = Number of Favorable Outcomes / Total Number of Outcomes. or P(A) = f/N

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The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.

Principal, interest, taxes, and insurance make up the majority of mortgage payments. Your outstanding loan balance is reduced by the amount in the principal part. Borrowing money has a cost, which is interest. Both the interest rate and the loan balance affect how much interest you pay.

You repay your mortgage loan through monthly payments. This will often be a monthly payment that aids in your gradual mortgage repayment. There will also be taxes, insurance premiums, and loan interest due.

Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.

The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.

[tex]$& \frac{\text { Mortgage }}{\text { Acceptable Rate\% }} * 12 \\[/tex]

substitute the values in the above equation, we get

[tex]$& =\frac{954.32}{0.27} * 12[/tex]

= 42,414.22

Therefore, the annual realized income exists 42,414.22.

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The mortgage payment exists $954. 32/month then the annual realized income exists 42,414.22.

Generally speaking, mortgage payments are made up of principal, interest, taxes, and insurance. The sum in the principle component is deducted from your outstanding loan balance. Interest is a cost associated with borrowing money. The amount of interest you pay depends on both the interest rate and the loan balance.

Monthly payments are made to pay down your home loan. This will frequently be a monthly payment to help you slowly pay down your mortgage. Taxes, insurance premiums, and loan interest will all need to be paid.

Assume a mortgage repayment schedule that is reasonable, using 27% of gross monthly income.

The product of the monthly mortgage payment by 12 months, divided by the acceptable rate, yields the annual realized income.

[tex]\frac{Mortage}{Acceptable rate } *12[/tex]

substitute the values in the above equation, we get

[tex]\frac{954.32}{0.27} *12[/tex]

= 42,414.22

Therefore, the annual realized income exists 42,414.22.

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Answer: 7

Step-by-step explanation:

1. You need to know that the input value means the x-value, which means x = 3.

2. Input 3 in the function

3. Solve 3+4

4. 3+4 = 7

Answer:

put y=4 then four comes with- and 4-3=2

Logical partition - A partition within an extended partition

System partition - The partition where you place the boot loader

Primary partition - The section of the hard drive that will become the bootable drive

IBM and Microsoft initially kept internal lists of designated partition types to be used in the MBR partition table. As the market for PC operating systems and disc tools expanded and became more open, other suppliers also needed to give their products specialised partition kinds. Third parties began to merely allocate partition types on their own behalf in a largely uncoordinated trial-and-error fashion because Microsoft neither documented all of the partition types already given by them nor wished to retain foreign assignments. This resulted in several conflicting assignments, which occasionally caused serious compatibility issues between certain products. [1]

In the 1990s, a number of industry professionals including Hale Landis, Ralf D. Brown, Matthias R. Paul, and Andries E. Brouwer began investigating partition kinds.

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Geoff is therefore 15 years old.Rearranging terms in an equation to get the solution is known as "solving by rearranging.

Age of Myrka = 3x + Age of Geoff

3x + 3 = 48

3x = 48 - 3

3x = 45 x = 15

Geoff is therefore 15 years old.

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40% of Damien’s marbles are 6/5 or 1.2.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Damien has three marbles.

40% of Damien’s marbles are blue.

That means,

40% of 3 blue marbles.

So, using the percentage formula,

40% of 3,

= 40 x 3/100

= 120/100

= 12/10

= 6/5

= 1.2

Therefore, 1.2 marbles are blue.

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The equivalent expression of 5[tex]x^{3/2}[/tex] is  5√(x³). The correct option is last one.

Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).

Given:

An expression,

5[tex]x^{3/2}[/tex]

To find the equivalent expression:

We have to simplify the expression,

5[tex]x^{3.1/2}[/tex]

= 5(x³)[tex]){1/2}[/tex]

= 5√(x³)

The above expression is an equivalent expression.

Therefore, 5√(x³) is an equivalent expression.

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The equation of the line found is:

y = 3x + 1.

Since the rate of change is always the same, that is, when x changes by 1, y always changed by the same value, this is a linear equation.

Linear equation:

A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant. The standard form of linear equations in two variables is of the form Ax + By = C. where x and y are variables, A and B are coefficients, and C is a constant.

The equation of a line is given by:

y = mx + b

In which:

m is the slope, that is, by how much y changes when x changes by 1.

b is the y-intercept, which is the value of y when x = 0.

From the table, when x =0 and y =1 , thus b = 1.

When x = and y = 1 . When x =1 and y = 4 , when x = 2 and y =7  , and so on. That is, when x changes by 1, y changes by 3, and the slope is m = 3.

The equation of the line is:

    y = 3x + 1.

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The four ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula  and 4) Graphing

1. Factoring: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.

2. Completing the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.

3. Quadratic Formula: The quadratic formula is a useful tool for solving quadratic equations.

4. Graphing : is another method useful for solving quadratic equation.

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The length of the ramp is 161.62 inches when the barrel turns 47 times in being rolled up the ramp.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

The circumference of the circular base of the barrel is given by the formula C = πd, where C is the circumference and d is the diameter of the base.

In this case, d = 1.1 inches, so C = π1.1 inches = 3.46 inches.

Since the barrel turns 47 times, the distance it travels is 47 times the circumference of the base,

47 × 3.46 inches = 161.62 inches

Therefore, the length of the ramp is 161.62 inches.

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Answer:

64 sequences of 4 fish are possible.

The projected Population in 2020 is given by 4146.

Compounding is the method through which interest is added to both the principle balance already in place and the interest that has previously been paid. Thus, compounding may be thought of as interest on interest, with the result that returns on interest are magnified over time, or the so-called "magic of compounding."

Compound interest is when an amount receives interest on top of it each time interest is paid on the original amount. The main (initial) sum and the interest that has previously accrued over the course of prior periods are used to compute compound interest.

Number of years to compound is 10 years from 2010 to 2020.

The population deplition is 0.6 % = next year population is 99.4% of present.

So population after 10 years = 4403 * [tex].994\x^{10}[/tex] = 4145.84 =4146

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The exponential function that models the population of bluefin tuna after x years is given as follows:

y = 1550(0.96)^x.

The parameters of the exponential function are given as follows:

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

When he first started monitoring the population, there were about 1,550 bluefin tuna in the bay, meaning that the parameter a is given as follows:

a = 1550.

One year later, he estimated that the population of bluefin tuna had decreased to about 1,488, hence the parameter b is obtained as follows:

b = 1488/1550 = 0.96.

Hence the function is defined as follows:

y = 1550(0.96)^x.

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The probability that the sum of the 2 dice rolls will not be greater than 8 are 8 : 13.

When the probability of an event occurring is know, it is easy to calculate the probability that the event does not occur. Hence, If P(A) is the probability of event A, then 1 - P(A) is the probability that the event does not occur.

the probability that the sum of the 2 dice rolls being greater than 8 are expressed in the ratio 5:13 and expressed in fraction as 5/13

then;

probability that the sum of the 2 dice rolls will not be greater than 8 = 1 - 5/13

probability that the sum of the 2 dice rolls will not be greater than 8 = (13 - 5)/13

probability that the sum of the 2 dice rolls will not be greater than 8 = 8/13

Therefore probability that the sum of the 2 dice rolls will not be greater than 8 can be expression as the ratio 8 : 13

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Answer:

Step-by-step explanation:

122121

Answer:

36

Step-by-step explanation:

let the number be 10x+y

x - y = 3 (eq 1)

given: y = 2x (eq 2)

putting 2 in 1

x - 2x = 3

-x = 3 (we can ignore the negative sign for now because we only need to find the absolute value)

y = 6

number is 36

In an amphitheater, seat are arranged in 50 semi-circular row-facing a dome Tate. The first row contain 23 seat, and each row contain 4 more eat than the previous row. Therefore, there are 6050 seat are in the amphitheater.

Given that:

There are total 50 semi circular row.

In the first row there are 23 seats.

The given problem is AP series:

Arithmetic Series:

An arithmetic sequence is defined as an algebraic sequence in which each successive term has an equal difference. It is obtained by adding a constant to any preceding term. For the first term 'a' and the tolerance 'd' of the AP, here is a list of commonly used arithmetic progressions to solve various AP related problems:

where l is the last term in the arithmetic progression.

Now,

Sum of n terms  = n/2 [ 2a + (n-1)d]

                          = 50/2 [ 2× 23 + (50 -1)4]

                          = 25 [46 + 49×4]

                          = 25 × 242

                          = 6050

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No, I'm not agree with Noah. Because the equation 1. 20(d+5)=42 is a mathematical equation and can be false depending on the value of the variable d.

The equation 1. 20(d+5)=42 is a mathematical equation that contains a variable d. The equation states that when you multiply 20 with (d+5) the result should be 42.

The equation is true if there is a value of d that makes the equation true. For example, if d=1, then 20(1+5)=20(6)=120 which is not equal to 42, so this value of d does not make the equation true.

On the other hand, if d=-7, then 20(-7+5)=20(-2)= -40 which is equal to 42, so this value of d makes the equation true.

Therefore, the equation can be true or false depending on the value of the variable d. In general, without knowing the specific context or situation in which the equation is being used, it is impossible to determine if the equation accurately represents a situation or not.

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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 coordinates of the intersection of the diagonals of the parallelogram QRST is (0, 1/2)

The coordinates of the parallelogram QRST are:

Q = (-1, 3)

R = (5, 2)

S = (1, -2)

T = (-5, -1)

The diagonals of  parallelogram QRST are QS and RT.

Let M be the point of the intersection of the diagonals of the parallelogram QRST

The diagonals of a parallelogram bisect each other.

This means, M is midpoint of diagonals QS and RT.

Consider diagonal QS.

Let (x1, y1) = (-1, 3) and (x2, y2) = (1, -2)

Using midpoint formula the coordinates of M would be,

M =  ((x1 + x2)/2, (y1 + y2)/2)

M = ((-1 + 1)/2, (3 - 2)/2)

M = (0/2 ,  1/2)

M = (0, 1/2)

Therefore, the point of intersecton of QS and RT is (0, 1/2)

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[tex] \longmapsto \: 2(2x - 1 + x + 9) = 103 \\ \\ \longmapsto \: 2(3x + 8) = 106 \\ \\ \longmapsto \: 6x +16 = 106 \\ \\ \longmapsto \: x = \frac{90}{6} \\ \\ \longmapsto \: x = 15 [/tex]

So,

[tex]l = 2 \times 15 - 1 = 29 \\ \\ b = 2 + 15 = 17[/tex]

The perimeter of a rectangle is given by the formula P = 2(l + w), where P is the perimeter, l is the length, and w is the breadth (or width) of the rectangle.

In this case, we know that the perimeter is 106 cm, so we can set up the equation:

106 = 2(l + (X + 9))

106 = 2l + 2X + 18

We also know that the length of the rectangle is 2X - 1, so we can set this equal to l:

2X - 1 = l

Now we have a system of two equations with two unknowns (l and X). We can substitute the value of l from the second equation into the first equation and solve for X:

106 = 2(2X - 1 + (X + 9))

106 = 2(3X + 8)

106 = 6X + 16

90 = 6X

X = 15

Now that we know the value of X, we can substitute it back into the equation for the length of the rectangle to find the length:

l = 2X - 1 = 2(15) - 1 = 29 cm

And then we can use the value of X again to find the breadth:

w = X + 9 = 15 + 9 = 24 cm

So the length of the rectangle is 29 cm and the breadth is 24 cm.

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The table that is a justification for the given solution to the system of equations is table 1

The two linear equations are

y=4x-9 and

y=2x-5

We that the following points for x : -1, 0, 1, 2, 3

When we substitute the values in the two equations we will have

x           y₁              y₂

-1         -13             -9

0           -9             -5

1             -5            -3

2            -1              - 1

3            3                1

Conclusively the values of y₁, and y₂ are shown in the table above

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