2. An Olympic sized pool holds 6.6 x 105 gallons. How many liters is that? (1 gallon = 3.79 Liters)
a. 1.7 x 105 L
b. 2.5x 106 L
c. 1.7 x 104 L
d. 2.5 x 107 L

a) The final coordinates are given as follows:

b) The rotation rule is given as follows: (x,y) -> (y,-x).

The five more known rotation rules are given as follows:

The rotation in this problem is the last rotation, 270º counterclockwise about the origin, hence the rule is given as follows:

(x,y) -> (y,-x).

The rule is applied to each of the vertices X, Y and Z to obtain the vertices of the reflected triangle X', Y' and Z'.

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Answer:

42

Step-by-step explanation:

determinant of matrix

= 5(2) - 8(-4)

= 10 - (-32)

= 10 + 32

= 42

Answer:

32

Step-by-step explanation:

the determinant of matrix

[tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex] = ad - bc

then

[tex]\left[\begin{array}{ccc}5&-4\\8&2\\\end{array}\right][/tex]

= (5 × 2) - (- 4 × 8) = 10 - (- 32) = 10 + 32 = 42

The probability for these are

Probability(a dime and then a quarter)=3/76

Probability(two pennies)=33/95

 Probability(a quarter and then a penny)=9/95

What is probability?

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.

Probability of event to happen P(E) = Number of favourable outcomes/Total Number of outcomes

Now,

Quarters=3, Dimes=5 and Pennies=12

Total=20

Probability(a dime and then a quarter)=5/20*3/19=15/380=3/76

Probability(two pennies)=12/20*11/19=132/380=33/95

 Probability(a quarter and then a penny)=3/20*12/19=36/380=9/95

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The component of u+v along the length of u and v  is (6.3, 0.66).

A vector is quantity which has both magnitude and direction. A magnitude is the length of the vector.

Here in the question u and v makes angle with the positive x axis.

||u||= 4 and θu =6  and  ||v|| = 1, θv = 4

To determine the component of u = |u||(cosu, sinu)

Component of u = 6(0.9, 0.1) = (5.4, 0.6)

Component of v = ||v||(cosv sinv)

Component of v  along the x axis = 1(0.9, 0.06 ) = (0.9, 0.06)

In the question value of u+v needs to be find.

Value of u + v = (5.4 + 0.9 , 0.6+ 0.06)

Value of the component form of u + v = (6.3, 0.66).

Hence, the component of u+v along the length of u and v is (6.3, 0.66).

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The solution to the system of equations is 6x – 2y = -14 with x = -4 and y = -5

4x – 3y = -31

To find x or method, you must first make one of the words the same so that they may cancel out.

To determine the x terms, we will make the y terms the same in this example.

To do so, multiply the first equation by three, yielding:

18x – 6y = - 42

And multiply the second equation by two to get:

8x – 6y = - 62

Now that we have the y terms, you may cancel them out.

You now have the following two equations:

18x = -42

8x = -62

The next step is to combine them, since the preceding – and – form a +.

This implies that you are left with one equation

26x = -104

Now divide by 26 on each side to get:

x = -4

As you have x, you substitute it into one of the ORIGINAL equations.

6x – 2y = -14

Substitute x in:

6(-4) – 2y = -14

-24 – 2y = -14

Add 24 on each side to get:

-2y = 10

y = -5

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Answer:

48.53 = 49 feet

Step-by-step explanation:

sin 0 = opposite/hypotenuse

sin 68 = AB/AC = 45/x

x = 45/sin 68 = 45/0.9272 = 48.53

48.53 rounded = 49 feet

Answer:

You have let out 48.5 feet of string

Step-by-step explanation:

Attached is a sketch of the problem.

We can use SOH CAH TOA to find our answer.

In this acronym, O is the opposite side, A is the adjacent side, and H is the hypotenuse. S is for the SIN function. C is for the COS function. T is for the TAN function.

We can calculate the length of the string by using the SIN function.

So we can say the sine of angle x is the opposite side divided by the hypotenuse.

[tex]sin(x)=\frac{O}{H}[/tex]

Lets solve for [tex]H[/tex].

Multiply each term by [tex]H[/tex].

[tex]H*sin(x)=\frac{O}{H} *H[/tex]

Simplify the right side by cancelling the common factor of [tex]H[/tex].

[tex]H*sin(x)=O[/tex]

Divide both sides of the equation by [tex]sin(x)[/tex].

[tex]\frac{H*sin(x)}{sin(x)} =\frac{O}{sin(x)}[/tex]

Simplify the right side by cancelling the common factor of [tex]sin(x)[/tex].

[tex]H=\frac{O}{sin(x)}[/tex]

Now lets evaluate the length of the string.

In this example we are given

[tex]x=68\\O=45[/tex]

[tex]H=\frac{45}{sin(68)}[/tex]

[tex]H=48.5341[/tex]

Answer:

Yesterday I have received amount of be with you i need to pay

The interval on which the profit function is increasing is [0, 25).

Given that:

The cost function is, C(x) = 1.2x - 0.012x²

The revenue function is, R(x) = 3.6x - 0.06x²

Here, x i is the number of units sold, and 0 ≤ x ≤ 150.

The profit function is:

P(x) = R(x) - C(x)

      = (3.6x - 0.06x²) - (1.2x - 0.012x²)

      = 2.4x - 0.048x²

Find P'(x).

P'(x) = 2.4 - 0.096x

The profit function is increasing when P'(x) > 0.

2.4 - 0.096x > 0

2.4 > 0.096x

25 > x

That is x < 25.

Hence the function is increasing in the interval [0, 25).

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The length of side b of the given right angle triangle using law of sines is; b = 12.044 m

The law of sines states that when we divide side "a" by the sine of angle A, it is equal to side "b" divided by the sine of angle B, and also equal to side "c" divided by the sine of angle C

Thus;

a/sin A = b/sin B = c/sinC

The parameters are;

B = 42°

c = 18m

Since c is the hypotenuse, it is the side that will be opposite the right angle and so;

C = 90°

Thus, using sine rule;

c/sinC = b/sin B

18/sin 90 = b/sin 42

b = (18 * sin 42)/1

b = 12.044 m

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The area expressions are (2x + 1) * (x^2 + 4x - 5) and 2x^3 + 9x^2 - 6x - 5

The missing figure is added as an attachment

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

Length = 2x + 1

Width =  x^2 + 4x - 5

The area is calculated as

Area = (2x + 1) * (x^2 + 4x - 5)

When expanded, we have

Area = 2x^3 + 8x^2  -10x + x^2 + 4x - 5

Evaluate the like terms

Area = 2x^3 + 9x^2 - 6x - 5

Hence, the area expression is 2x^3 + 9x^2 - 6x - 5

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a)The set of integers between 1 and 50, divisible by 8 are given as.

S={ 8,16,24,32,40,48}

b ) Hence, the set {-5,1}

c) The list of set of outcomes when a coin is tossed until a tail or three heads appear will be.

S={T,HT,HHT,HHH}

d) S={Europe, Asia, Australia, North America, South America, Africa, Antarctica.}

a) We have to find a list of integers between 1 and 50, divisible by 8.

Keep in mind that the S is the event that represents the sample space. The set of integers between 1 and 50, divisible by 8 are given as.

S={ 8,16,24,32,40,48}

b)  We need to list the set S= {[tex]x| x^2+4x-5=0}[/tex]}

[tex]x^2+4x-5=0\\\\x^2+5x-x-5=0\\x(x+5)-(x+5)==\\(x+5)(x-1)=0\\\\x=-5 , x=1[/tex]

Hence, the set {-5,1}

c) c) We have to find a list of the set of outcomes when a coin is tossed until a tail or three heads appear.

Let T denote the event that tail appeared.

Let H denote the event that head appeared.

The list of set of outcomes when a coin is tossed until a tail or three heads appear will be.

S={T,HT,HHT,HHH}

d) We need to list the set

S={x ∣ x is a continent}.

There are 7 continents:

S={Europe, Asia, Australia, North America, South America, Africa, Antarctica.}

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​

A truth table deconstructs a logic function by outlining all possible outcomes the function might achieve.

A truth table offers a way to map out the potential truth values in an expression and predict their results. The table has a row for each conceivable combination of truth values and a column for each variable in the expression. There is also a column that displays the results of each set of values.

For propositional logic formulations, this tool builds truth tables. There are numerous formats available for entering logical operators. As an illustration, the propositional formula p q r could be represented as p / q -> r, p and q => not r, or p && q ->!r. You can enter the connectives and as T and F.

P Q (Q ∧ P)

F F F

F T F

T F F

T T T

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The probability that it will snow on both days, given the chances of snow on Saturday and Sunday, is 24.5%.

The chance of it snowing on both days is calculated by multiplying the probability of it snowing on Saturday by the probability of it snowing on Sunday. If the probabilities are independent, we can assume that one event occurring doesn't affect the other event, therefore the probability of both events happening is just the product of the individual event probabilities.

So, the chance of it snowing on both days is:

P(Saturday and Sunday) = P(Saturday) x P(Sunday)

P(Saturday and Sunday) = 0.35 x 0.70

P(Saturday and Sunday) = 24.5 %

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Using properties of triangles, Correct options are A,B and D. AE = EB, EG || AC and AC = 2 EG.

A triangle has three sides, three angles, and three vertices, which are its characteristics.

A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

Any two triangle sides can add up to a length that is longer than the third side.

A triangle's total angles are always 180 degrees.

A triangle's outside angles are always a sum of 360 degrees.

The total of the parallel interior and exterior angles is additional.

From the given figure,

As E is the mid point of BA,

So, BE = EA

As it is clearly seen that EG is parallel to AC = EG||AC

Further,

As, EG is intersecting AB and BC at mid points,

⇒ AC = 2EG

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Answer:

20

Step-by-step explanation:

1/5 = 20/100

Answer:

Step-by-step explanation:

In a​ right-skewed distribution, which of the following is​ true? The mean tends to be greater than the median.

Based on the exponential function, the sales of MP3 players in 2008 is $1.82 billion.

An exponential function is a function that has the general form y = abˣ

where

a ≠ 0,

b is the base b is a constant (b is a positive real number and b ≠ 1)

x is the independent variable whose domain is the set of real numbers.

Using the equation for exponential growth

y = ab^x

y = 0.88

a = 0.08

0.88 = 0.08bˣ

bˣ = 0.88/0.08

bˣ = 11

x = 4

Hence;

b⁴ = 11

b = 1.82

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The amount of juice for 30% orange juice is 22 liters,

and the amount of juice for 5% orange juice is 3 liters mixed together in order to get 25 Liters.

When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."

There are both one-variable and two-variable linear equations.

Given One canned juice drink is 30% orange juice, another is 5% orange juice,

Let x and y be the amount of 30% and 5% orange juice respectively,

according to condition

0.30x + 0.05y = 0.27(25) .........(1)

x + y = 25.........(2)

Multiply the second equation by -0.05,

0.30x + 0.05y = 0.27(25)

-0.05x - 0.05y = -0.05(25)

Add equation to eliminate y,

0.30x - 0.05x + 0.05y - 0.05y = 0.27(25) - 0.05(25)

Solve for y,

0.25x = 5.5

x = 5.5/.25

x = 22

substitute value of x in equation,

x + y = 25

(22) + y = 25

y = 25 - 22

y = 3

Hence the amount of 30% orange juice is 22 liters and the amount of 5% orange juice is 3 liters.

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Answer:

206

Step-by-step explanation:

cube volume = 5*5*5 +3*3*3 = 125+81 = 206

The object that is about 15 cm is pencil.

The fundamental idea in the study of science and mathematics is measurement. The qualities of an object or event can be quantified so that we can compare them to those of other objects or occurrences. When discussing the division of a quantity, measurement is the word that is used the most frequently.

Given:

Measurement = 15 cm

As, the average length for the pencil varies from 7 cm - 17 cm.

and, average length for the desk is 120 cm.

and, the average length for the paper is 30.3 x 40.6cm.

and, the average length for the clip is 4 cm.

and, the average length for the television is 40 cm.

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Answer: X^2 - 9 can be factored into (X - 3)(X + 3) which is the difference of squares.

The difference of squares factorization of X^2 - 9 is (X - 3)(X + 3)

Step-by-step explanation:

The number of feet that canyon wall away from the person will be 3,300 feet.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

Sound travels about 750 miles per hour. If you stand in a canyon and sound a horn, you will hear an echo.

Convert the speed in feet per second. Then we have

Speed = 750 x 5280 / 3600

Speed = 1,100 feet per second

Let 'n' be the number of seconds. Then the distance is given as,

1,100 = (d / 2) / n

d = 2,200 n

If n = 1.5, then we have

d = 2,200 x 1.5

d = 3,300 feet

The number of feet that canyon wall away from the person will be 3,300 feet.

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a. To find the average rate of growth between each pair of years, we can use the formula: (end value - start value) / (end year - start year).

2004 to 2006: (12,440 - 8,574) / (2006 - 2004) = 3,866 / 2 = 1,933 locations/year

2006 to 2007: (15,006 - 12,440) / (2007 - 2006) = 2,566 / 1 = 2,566 locations/year

2005 to 2006: (12,440 - 10,238) / (2006 - 2005) = 2,202 / 1 = 2,202 locations/year

b. To estimate the instantaneous rate of growth in 2006, we can take the average of the last two rates of change from part (a).

(2,566 + 2,202) / 2 = 2,384 locations/year

c. To estimate the instantaneous rate of growth in 2006 by measuring the slope of the tangent line through (2005, 10,238) and (2007, 15,006), we can use the formula:

(15,006 - 10,238) / (2007 - 2005) = 4,768 / 2 = 2,384 locations/year

d. To estimate the instantaneous rate of growth in 2007 by measuring the slope of the tangent line through (2006, 12,440) and (2008, 16,676), we can use the formula:

(16,676 - 12,440) / (2008 - 2006) = 4,236 / 2 = 2,118 locations/year

e. Comparing the growth rates from part (c) and (d), we can see that the growth rate in 2007 is less than the growth rate in 2006. So we can conclude that 2. The rate of growth is decreasing.

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Answer:

42=3.5x+2y

Step-by-step explanation:

3.5 is the cost of the cakes and 2 is the cost of the oreos. 42 is how much Francis can spend

The average speed is 0 m/s since the object does not move.

Since the object does not change its position, it does not move. Therefore, its average speed is 0 m/s.

The object in question does not move in a closed path, meaning that its position remains the same throughout the entire path. As a result, its average speed is 0 m/s. This is because average speed is the total distance traveled divided by the total time taken, and since the object does not move its distance traveled is 0 and its time taken is also 0. Therefore, when the object goes around the closed path, its average speed is 0 m/s.

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The hypothesis of the conditional statement is;

Option A: we walk home from school

A hypothesis is defined as an educated guess while using reasonable thought patterns, about the answer to a scientific question.  Now, the hypothesis can either be supported or not supported at all, but then it depends on the data gathered.

A conditional statement is defined as a set of rules performed provided a certain condition is met. Thus, it is sometimes referred to as If-Then statement because if a condition is said to be met, then an action is said to have been performed " .

Thus, the conditional statement here is: " we walk home from school ".

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The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.

Original cylinder: The original cylinder has a radius of 2 units and a height of 13 units, and its volume is given by the formula: V = πr²h = π * 2² * 13 = 104π cubic units.

Scaled cylinder 1: The first scaled cylinder has a scale factor of 2, so its radius is 2 * 2 = 4 units and its height is 13 * 2 = 26 units. Its volume is given by: V = πr²h = π * 4² * 26 = 672π cubic units.

Scaled cylinder 2: The second scaled cylinder has a scale factor of 3, so its radius is 2 * 3 = 6 units and its height is 13 * 3 = 39 units. Its volume is given by: V = πr²h = π * 6² * 39 = 1764π cubic units.

Scaled cylinder 3: The third scaled cylinder has a scale factor of 4, so its radius is 2 * 4 = 8 units and its height is 13 * 4 = 52 units. Its volume is given by: V = πr²h = π * 8² * 52 = 3072π cubic units.

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Answer:

2/n+2

Step-by-step explanation:

On evaluating the fraction 3 3/4 the cost of 3 3/4 kg of sugar is $30.

What is fraction?

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.

The cost of 1 kg of sugar is = $ 80

The amount of sugar is given in fractional form - 3 3/4 kg

The equation for cost of 3 3/4 kg sugar is -

Cost = 3 3/4 × 8

Solve the fractional part first -

Cost = 15/4 × 8

Simplify the equation -

Cost = 15/4 × 8

Cost = 120/4

Cost = 30

Therefore, the cost value is obtained as $ 30.

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If the cost of 1 kg of sugar is $8, what is the price of 3 3/4 kg?

The lighthouse is 8.88 m tall.

What is the ratio?

A ratio is a mathematical comparison of two or more quantities. It expresses the relationship between the values of the quantities in terms of a numerical fraction.

This problem can be solved using similar triangles. Since the ratio of the heights of Pythagoras and the lighthouse is the same as the ratio of their corresponding shadow lengths, we can set up the following proportion:

(Height of lighthouse) / (Height of Pythagoras) = (Shadow length of lighthouse) / (Shadow length of Pythagoras)

Plugging in the given values:

(Height of lighthouse) / 1.78 = 26 / 3.08

To solve for the height of the lighthouse, we can cross-multiply and divide:

(Height of lighthouse) = (26 / 3.08) * 1.78

The lighthouse is approximately:

(26/3.08)*1.78 = 8.88 m

Hence, The lighthouse is 8.88 m tall.

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