Pre calculus trigonometry

The amount of water in the basement is V = 22,500 gallons

Given data ,

To calculate the amount of water in the basement, we need to determine the volume of water in cubic feet and then convert it to the most appropriate units to describe the amount of water.

First, we need to convert the dimensions of the basement to feet, since the depth of the water is given in inches. 18 inches is equal to 1.5 feet, so the volume of water in cubic feet can be calculated as:

50 feet x 40 feet x 1.5 feet = 3,000 cubic feet

There are 7.5 gallons in 1 cubic foot of water, so the amount of water in the basement in gallons can be calculated as:

3,000 cubic feet x 7.5 gallons per cubic foot = 22,500 gallons

Hence , there are 22,500 gallons of water in the basement

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The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine.

Which representation is most appropriate for displaying and describing what is happening to the amount of hot chocolate over time?

The most appropriate representation for displaying and describing what is happening to the amount of hot chocolate over time is a scatter plot titled New Machine with the x-axis labeled time in seconds going from 0 to 28 and the y-axis labeled hot chocolate amount in fluid ounces going from 0 to 18, with points at 4 comma 5 and 8 comma 7 and a half and 12 comma 9 and 16 comma 11 and 20 comma 13 and 24 comma 16.

A scatter plot is a useful way to show the relationship between two variables, in this case, the amount of hot chocolate and time. Each point on the scatter plot represents a pair of values for time and hot chocolate amount. A line graph with line segments connecting each point to the next would not be appropriate because the data is not continuous, and there is no reason to assume that the relationship between time and hot chocolate amount is linear.

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Answer:

Set 1: {10, 19, 38, 50, 51}

Step-by-step explanation:

To calculate the standard deviation of a data set, we first find the mean of the data set. The mean is simply the sum of all the values in the data set divided by the number of values. For example, the mean of Set 1 is:

(10+19+38+50+51)/5=33.6

Next, we find the variance of the data set. The variance is the average of the squared differences between each value in the data set and the mean. For example, the variance of Set 1 is:

((10−33.6)^2+(19−33.6)^2+(38−33.6)^2+(50−33.6)^2+(51−33.6)^2)/5=323.84

Finally, we take the square root of the variance to get the standard deviation. For example, the standard deviation of Set 1 is:

[tex]\sqrt{323.84}[/tex]=17.99

We can repeat this process for each of the four data sets and find that Set 1 has the largest standard deviation.

There would be 35 more defective bean seeds than pumpkin seeds in the shipment.

Calculate the number of defective bean seeds:

Defective bean seeds = Total bean seeds * Defect rate for bean seeds

Defective bean seeds = 1,750 * 0.05 = 87.5

Since we can't have half a seed, we'll round it up to the nearest whole number.

Defective bean seeds = 88

Calculate the number of defective pumpkin seeds:

Defective pumpkin seeds = Total pumpkin seeds * Defect rate for pumpkin seeds

Defective pumpkin seeds = 1,750 * 0.03 = 52.5

Similarly, we'll round it up to the nearest whole number.

Defective pumpkin seeds = 53

Calculate the difference in defective seeds:

Difference in defective seeds = Defective bean seeds - Defective pumpkin seeds

Difference in defective seeds = 88 - 53 = 35

So, there would be 35 more defective bean seeds than pumpkin seeds in the shipment.

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In a shipment of 1,750 seeds of each type, with a defect rate of 5% for bean seeds and 3% for pumpkin seeds, how many more defective bean seeds would be expected than pumpkin seeds?

Answer:

Step-by-step explanation:

Answer: Cut 3 inch per person

Step-by-step explanation:

there is a 4 foot sub you take the quadrilatiral and divide it by 10 and you get 3 inches per person remember to multiply the reciprocal by 12 as there are 12 inches in a foot and you have 4 foot so the product of that reciprocal will be equal to 4 divided by your sum from adding the recriptorcal into the quadrilateral remember a quadrilateral not a duolateral or a triolatiral as there is 4 feet in the sub. >:)

Answer:

7 Cuts

Step-by-step explanation:

This is because if you do 48 inches / 6 inches = 8 sections Since each cut will create two sections, you need to make 7 cuts (one fewer than the number of sections) to get 8 equal portions.

The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

The y-intercept for each function is given as follows:

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

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Answer: D

Step-by-step explanation:

The function g(x) is defined as follows:

D. g(x) = f(x) + 4.

What is a translation?

A translation happens when either a figure or a function is moved horizontally or vertically on the coordinate plane.

The four translation rules for functions are defined as follows:

Translation left a units: f(x + a).

Translation right a units: f(x - a).

Translation up a units: f(x) + a.

Translation down a units: f(x) - a.

The y-intercept for each function is given as follows:

f(x): y = -5.

g(x): y = -1.

Meaning that g(x) is a translation up four units of function f(x), hence it is defined as follows:

g(x) = f(x) + 4.

Step-by-step explanation:

X component  = 4.5 - 2.1  =   2.4

Y component  = 7.8 - 2.1  =    5.7

Find magnitude using Pythagorean theorem

  m^2 = 2.4^2 + 5.7^2

    magnitude  = 6.18    units

Remember for a right triangle   tangent Φ = opposite leg / adjacent leg

    angle = arctan ( 5.7 / 2.4 )   = 67.2 degrees

Heracio used the computer 2 more hours to do homework than to shop online.

To solve the problem, we need to first calculate the number of hours Heracio spent on each activity:

Videos: 10% of 40 hours = 4 hours

Homework: 20% of 40 hours = 8 hours

Games: 20% of 40 hours = 8 hours

Social media: 25% of 40 hours = 10 hours

Shopping: 15% of 40 hours = 6 hours

To find out how many more hours Heracio used the computer to do homework than shop online, we need to subtract the number of hours spent shopping from the number of hours spent on homework:

8 hours (homework) - 6 hours (shopping) = 2 hours

Therefore, Heracio used the computer 2 more hours to do homework than to shop online.

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Answer:

90.95%

Step-by-step explanation:

85 * 0.07 = 5.95 5.95 + 85= 90.95

Answer:

The answer to your problem is, 90.95%

Step-by-step explanation:

Calculation:

In order to find the answer we need to

= Old score + New Score

= 85 + 7% of 85

= 85 + ( [tex]\frac{7}{100}[/tex] x 85 )

= 85 + ( 0.07 x 85 )

= 85 + 5.95

= 90.95

Which 90.95% is our answer.

Thus the answer to your problem is, 90.95%

Answer:

The linear function is y = (1/3)x - 4.

Step-by-step explanation:

The y-intercept is -4. Starting at (0, -4), go up 1 unit and then right 3 units. You will end at (3, -1). So the slope of this line is 1/3, and it follows that the function is

y = (1/3)x - 4.

The numerical expression that represents the sum of eight squared and thirty two will be 96.

A numerical expression is a mathematical expression that consists of numbers and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation.

The numerical expression that represents the sum of eight squared and thirty two is

= 8² + 32

= 64 + 32

= 96.

The question is incomplete and the complete question is '' What is the numerical expression that represents the sum of eight squared and thirty two''.

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The system of equations where the combination of the candies gives you a total of 22 points are:

x + y = 9

2x + 3y = 22

To create the equations, we shall first define the variables:

x = the number of purple candies

y = the number of yellow candies

Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.

Then, we would make sure that the total number of candies selected is 9.

The first equation represents the total number of candies selected:

x + y = 9

The second equation represents the total number of points obtained:

2x + 3y = 22

Therefore, the system of equations is:

x + y = 9

2x + 3y = 22

This is a system of linear equations.

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Step-by-step explanation:

Only ONE .....there are three sides to a triangle and you supplied 3 sides.

The rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.

2.2×10^6 feet per minute is in its scientific notation.

In scientific notation, a number is written as the product of a coefficient and a power of 10.

So, 2.2×10^6 is already in scientific notation, where the coefficient is 2.2 and the power of 10 is 6.

If you want to convert it to standard notation, you can multiply the coefficient by the power of 10:

2.2×10^6 = 2.2 x 1,000,000 = 2,200,000

Therefore, the rocket must travel at a rate of 2,200,000 feet per minute to reach escape velocity.

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The composition of functions is solved and the expressions are

a) ( g o f ) ( -1 ) = 1

b) ( g o f ) ( 0 ) = 4

c) ( f o g ) ( -1 ) = -2

d) ( f o g ) ( 4 ) = -1

Given data ,

Let the composition of function be represented as A

Now , the value of A is

a)

( g o f ) ( -1 ) = g ( f ( -1 ) )

On simplifying the function , we get

when x = -1 , f ( -1 ) = 2

g ( 2 ) = 1

So , ( g o f ) ( -1 ) = 1

b)

( g o f ) ( 0 ) = g ( f ( 0 ) )

On simplifying the function , we get

when x = 0 , f ( 0 ) = 0

g ( 0 ) = 4

So , ( g o f ) ( 0 ) = 4

c)

( f o g ) ( -1 ) = f ( g ( -1 ) )

On simplifying the function , we get

when x = -1 , g ( -1 ) = 2

f ( 2 ) = -2

So , ( f o g ) ( -1 ) = -2

d)

( f o g ) ( 4 ) = f ( g ( 4 ) )

On simplifying the function , we get

when x = 4 , g ( 4 ) = 1

f ( 1 ) = -1

So , ( f o g ) ( 4 ) = -1

Hence , the composition of function is solved

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Caroline needs to fill the 1-quart pitcher four and a half times in order to fill all 3 pint glasses.

Since Caroline has 3 pint glasses to fill, she needs to use the 1-quart pitcher multiple times. Each time she fills the pitcher, she can pour it into 2 pint glasses

From this, we can say that Caroline needs to pour a total of 3 x 1.5 = 4.5 quarts of juice.

What is a Pitcher

Pitcher is a container with a spout and handle, used for holding and pouring liquids. It is typically used for serving beverages such as water, juice, milk, or iced tea. Pitchers can be made from a variety of materials, including glass, ceramic, metal, or plastic.

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Answer:

option c) x=-6

Step-by-step explanation:

-15x = 90

= x = 90/-15

= x = (-6)

In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.

A collection of information's values' standard deviation serves as a gauge for how much variance or dispersion there is. It is a statistical word used to describe the degree to which the individual data points depart as from mean or average value that is contained in the data set. By taking taking square root of the variance—the sum of the squared deviations amongst each point in the data and the mean—we can determine the standard deviation. While a high standard deviation suggests that the data points are widely dispersed, a modest standard deviation suggests that the statistics are close to the mean.

given

(a) When the sample size, n, is 16, we can apply the following formula to create a 95% confidence interval regarding the population mean, :

x ± tα/2 * (s/√n)

where t/2 is the crucial value from the t-distribution with n-1 degrees of freedom and a confidence level of 95%, and x is the sample mean, s is the sample standard deviation, n is the sample size.

We determine that t0.025,15 = 2.131 using a t-distribution table or calculator.

When we enter the values, we obtain:

106 ± 2.131 * (10/√16)

which is equivalent to:

106 ± 5.33

In light of this, the 95% confidence interval for is (100.67, 111.33) as s is the sample standard deviation, n is the sample size.

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Answer:

B

Step-by-step explanation:

not good at explaining this concept but keep the signal its X|X and its near the square root so tadaaa

Carson can line up his textbooks on his bookshelf in 24 different ways

What is Permutation?

Permutations are a way to count the number of ways that a set of objects can be arranged in a particular order. A permutation is an ordered arrangement of objects.

What is Combination?

The combination is a way to count the number of ways that a set of objects can be selected without regard to order. A combination is an unordered selection of objects.

According to the given information:

Carson has four textbooks that he wants to line up on his bookshelf. The number of different ways that he can do this is given by the permutation formula:

n! / (n - r)!

where n is the total number of objects (in this case, 4 textbooks), and r is the number of objects that he wants to arrange in a particular order (in this case, all 4 textbooks).

On substituting the values in the formula,

4! / (4 - 4)! = 4! / 0! = 4 x 3 x 2 x 1 / 1 = 24

Therefore, Carson can line up his textbooks on his bookshelf in 24 different ways.

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Based on the data given in the table, B. Median for both coffee shops because the data distribution is not symmetric

It is better to describe the centers of distribution in terms of the median rather than the mean for both coffee shops because the data distribution is not symmetric.

The median is a better measure of central tendency in this case because it is not influenced by outliers or extreme values, which may exist in the data.

The mean, on the other hand, is sensitive to outliers and may not provide an accurate representation of the data distribution.

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The graph of the piecewise function is given by the image presented at the end of the answer.

A piece-wise function is a function that has different definitions, depending on the input of the function.

All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.

The definitions are given as follows:

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The given line AB is having endpoints A(-3,5) & B(1,-1).

To find the equation of line AB it can be written as[tex]y-y_1=(x-x_1){(y_2-y_1)/(x_2-x_1)}\\[/tex]

Substituting the given points

[tex]y-(-1)=(x-1){(5-(-1))/(-3-1)}\\[/tex]

y=-(3/2)x+1/2

For two perpendicular lines [tex]m_1*m_2=-1[/tex]

Therefore, (-3/2)*[tex]m_2[/tex]=-1

or [tex]m_2[/tex] = 2/3

Also, the midpoint of AB will be [tex]{1-(-3)}/2, {5-(-1)}/2[/tex] = (2,3).

The line passing through (2,3) & perpendicular to y=-3/2x+1/2 will be given as follows

(y-3)=(2/3)(x-2)

3y-9=2x-4

3y=2x+5 is the required equation of the line.

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The correct option regarding which bus has the least spread among the travel times is given as follows: Bus 14, with an IQR of 6.

The interquartile range is a better measure of spread compared to the range of a data-set, as it does not consider outliers.

For groups of 15 students, we have that:

The first half is composed by the first seven students, hence the first quartile is the fourth dot, which is the median of the first half.

The second half is composed by the last seven students, hence the first quartile is the eleventh dot, which is the median of the first half.

The quartiles for Bus 14 are given as follows:

Q1 = 12.

Q3 = 18.'

Hence the IQR is of:

IQR = Q3 - Q1 = 18 - 12 = 6.

The quartiles for Bus 18 are given as follows:

Q1 = 9.

Q3 = 16.

Hence the IQR is of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Hence Bus 14 is the more consistent bus, due to the lower IQR.

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Answer:

6 presents / minute

Step-by-step explanation:

We can represent the given information in a ratio:

amount of present wrapped : minutes it took to wrap

                                        2/3   :   1/9

Then, we can multiply both sides by 9 (the reciprocal of 1/9) so that the right side of the ratio is 1 minute.

presents : minutes

       2/3   :   1/9

       × 9       × 9

        6     :     1

So, Patricia can wrap 6 presents in 1 minute.

Answer:

Step-by-step explanation:

(a) The distance between two points A(x1, y1, z1) and B(x2, y2, z2) is given by the formula: AB = √((x2-x1)² + (y2-y1)² + (z2-z1)²). Substituting the coordinates of points A and B into this formula gives: AB = √((2-1)² + (-1-4)² + (3-2)²) = √(14).

(b) The direction vector of line l is given by the vector (i-j+k). The direction vector of line AB is given by the vector AB = (2-1)i + (-1-4)j + (3-2)k = i - 5j + k. The cosine of the angle between two vectors is given by the dot product of the vectors divided by the product of their magnitudes. Therefore, cos(θ) = (AB.(i-j+k)) / (|AB|.|i-j+k|) = ((i - 5j + k).(i-j+k)) / (√14.√3) = -3/√42. Hence θ = cos⁻¹(-3/√42).

©(i) Let P be the point on line l where λ = p. Then P has position vector r = (2i-j+3k)+p(i-j+k) = (2+p)i + (-1-p)j + (3+p)k. The vector AP is given by AP = r - a = ((2+p)i + (-1-p)j + (3+p)k) - (i+4j+2k) = pi - (5+p)j + pk. Taking the dot product of AP with (i-j+k), we get AP.(i-j+k)=7+3p.

©(ii) The foot of the perpendicular from point A to line l is the point on line l that is closest to point A. This point is obtained when AP is perpendicular to the direction vector of line l, which is (i-j+k). Therefore, AP.(i-j+k)=0. Substituting the expression for AP.(i-j+k), we get 7+3p=0, so p=-7/3. Substituting this value of p into the expression for r, we get r = (2-7/3)i - 8/3j + 2k. Hence, the coordinates of the foot of the perpendicular from point A to line l are (1/3,-8/3,2).

(d) The cartesian equation of a line with direction vector d and passing through a point with position vector a is given by r=a+λd. For line l, d=(i-j+k), a=(2i-j+3k), so its cartesian equation is r=(2i-j+3k)+λ(i-j+k).