A flagpole casts a 5 foot shadow while a nearby sign cast of 1 1/4 foot shadow. Find the height of the flag pole if the sign is 4 feet high.

The slope of x - 3y = -9 is, m = 1/3, while the y-intercept (b) is 3.

The sketch of x - 3y = -9 is shown below.

To determine the slope and y-intercept of the line given by the equation x - 3y = -9, we can rewrite it in slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.

To do this, we can solve for y:

x - 3y = -9

-3y = -x - 9

y = (1/3)x + 3

Now we can see that the slope of the line is m = 1/3, and the y-intercept is b = 3.

To sketch the line, we can use the slope and y-intercept. We can start by plotting the y-intercept (0,3) on the y-axis. From there, we can use the slope of 1/3 to find additional points on the line. For example, if we move 3 units to the right along the x-axis, we can move up 1 unit (since the slope is 1/3) to get another point on the line, which is (3,4). We can repeat this process to find more points on the line and then connect them to sketch the line.

The sketch is shown below in the attachment.

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Answer:

By using trigonometric relations, we will see that:

AC = 15.6 in

AB = 8.4 in.

How to get the measures of the other two sides of the right triangle?

Here we have the right triangle where:

B = 90°

C = 40°

BC = 10 in.

Notice that is the adjacent cathetus to the angle C, then we can use the two relations:

sin(a) = (adjacent cathetus)/(hypotenuse).

tan(a) = (opposite cathetus)/(adjacent cathetus).

Where:

hypotenuse = AC

opposite cathetus = AB.

Then we will have:

sin(40°) = 10in/AC.

AC = 10in/sin(40°) = 15.6 in

tan(40°) = AB/10in

tan(40°)*10in = AB = 8.4 in.

So we can conclude that for the given right triangle we have:

AC = 15.6 in

AB = 8.4 in.

If you want to learn more about right triangles:

Step-by-step explanation:

The roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

Using the quadratic formula to solve the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex],we have

[tex]x = (-(-14) ± sqrt((-14)^2 - 4(3)(-5))) / (2(3))\\x = (14 ± sqrt(14^2 + 4(3)(5))) / (2(3))\\x = (14 ± sqrt(196 + 60)) / 6\\x = (14 ± sqrt(256)) / 6\\x = (14 ± 16) / 6\\[/tex]

Therefore, the two roots of the quadratic equation in exact square root form are:

[tex]x = (14 + 16) / 6 = 5\\x = (14 - 16) / 6 = -1/3\\[/tex]

Thus, the roots of the quadratic equation [tex]3x^2 - 14x - 5 = 0[/tex], in exact square root form, are x = 5 and x = -1/3.

A quadratic equation is a second-degree polynomial equation in one variable of the form:

[tex]ax^2 + bx + c = 0[/tex]

where x is the variable, and a, b, and c are constants. In this equation, the highest power of x is 2, and it is called the coefficient of x^2. The coefficient of x is b, and the constant term is c.

The quadratic equation is called "quadratic" because the highest power of x is a square (i.e., x^2), and the graph of the equation is a parabola.

The quadratic equation can have zero, one, or two real solutions, depending on the values of a, b, and c. The solutions can be found by using the quadratic formula:

[tex]x = (-b ± √(b^2 - 4ac)) / 2a[/tex]

where the symbol ± means "plus or minus" and the square root is of the discriminant (b^2 - 4ac).

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The least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

The space that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

To find the volume of the sidewalk in cubic feet, we first need to convert the dimensions to feet. Since 1 foot = 12 inches, we have:

Length = 24 feet + 6 inches = 24.5 feet

Width = 4 feet + 6 inches = 4.5 feet

Depth = 4 inches = 1/3 feet (since 1 foot = 12 inches, 4 inches = 4/12 feet = 1/3 feet)

The volume of the sidewalk is then:

Volume = Length x Width x Depth

= 24.5 feet x 4.5 feet x 1/3 feet

= 3.25 cubic feet

Since one bag of concrete mix makes 0.6 cubic feet of concrete, the number of bags of concrete mix that Roger needs is:

Number of bags = Volume of sidewalk / Volume per bag

= 3.25 cubic feet / 0.6 cubic feet per bag

= 5.42 bags

Since Roger cannot buy a fraction of a bag, he must buy at least 6 bags of concrete mix. Therefore, the least whole number of bags of concrete mix that Roger needs is:

Number of bags = 6

Answer: F. 16

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a) The linear function is defined as follows: y = 1 - 0.2x.

b) The slope and the intercepts are interpreted as follows:

c) The battery power is at 75% after 1.25 hours.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph touches the y-axis at y = 1, hence the intercept b is given as follows:

b = 1.

From the x-intercept, when x increases by 5, y decays by 1, hence the slope is given as follows:

m = -1/5

m = -0.2.

Hence the function is:

y = -0.2x + 1.

The battery power is of 75% = 0.75 when y = 0.75, as follows:

0.75 = -0.2x + 1

0.2x = 0.25

x = 0.25/0.2

x = 1.25 hours.

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Answer:

5pi (use the pi character button on your screen)

Step-by-step explanation:

Arc length formula is the shortest formula in all of all math!

Arc length = r•theta

r is the radius. In your question, it is 6.

"theta" is the angle in radians, which was given in your question as 5pi/6.

Fill in these given values to the formula.

Arc length

= r • theta

= 6 • 5pi/6

Simplify (the 6's cancel)

= 5pi

Answer:

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

    |          /

    |        /

    |      /

    |    /

-----|------------------

    | /         \

    |/            \

    /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

PART A:

The equations must be changed to slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, in order to be graphed in the coordinate plane.

Here is Matt's equation:

y = 40x + 50

The y-intercept of this equation is 50, while the slope is 40.

Here is Kylie's equation:

y = 50x

The slope of this equation is 50, and the y-intercept is 0. | /

   |          /

   |        /

   |      /

   |    /

-----|------------------

   | /         \

   |/            \

   /-------------\

0 1 2 3 4 5 6 x-axis

The red line shows Kylie's distance from the beginning point, while the blue line shows Matt's distance from it.

PART B:

When Matt begins driving later than Kylie, there is one circumstance in which they are never both at the same distance from the starting location at the same time. Let's imagine, for illustration, that Matt begins driving 20 minutes after Kylie. Thus, the set of equations that best describes this circumstance is:

(Matt's distance) y=40x+50

Kylie's distance is given by y = 50(x – 20).

Under this system, we deduct 20 from Kylie's x-value to reflect Matt's advantage of a 20-minute head start.

We can set the two equations equal to one another to determine how many solutions this system has:

40x + 50 = 50(x - 20) (x - 20)

40x + 50 = 50x - 1000\s100 = 10x

x = 10

This tells us that the two drivers will never be at the same distance from the starting point at the same time. There is only one solution to the system, which means the two lines will only intersect at one point, which is not on the coordinate plane we are using to graph the system.

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Answer:

10x-610x6

The equation 10x-610x6 has no real solutions because it cannot be solved for any value of x. The left side of the equation is 10x-6, and the right side is 10x+6. Since the left side is greater than the right side, no value of x can make the equation true.

Answer:

  -4

Step-by-step explanation:

You want the value of (f·g)(-1) when f(x) = x² +3x and g(x) = 2x².

The product of the functions is the product of their values for each value of x.

  (f·g)(-1) = f(-1)·g(-1) = ((-1)² +3(-1)) × (2(-1)²) = (1-3)(2·1) = (-2)(2)

  (f·g)(-1) = -4

The best option is Location 2, which you can determine by adding up the points for each site using the information below.

The complete question is:

A supply chain manager faced with choosing among four possible locations has assessed each location according to the following criteria, where the weights reflect the importance of the criteria. Use the information below to calculate total points for each location and choose the best option. Round your answers to two decimal places.

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Answer:

Step-by-step explanation:

Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.

We know that the 5th term is 729, so:

a * r^4 = 729

10th term is 3, so:

a * r^9 = 3

r^5 = 3/729

r^5 = 1/243

r = (1/243)^(1/5)

r = 1/3

a * (1/3)^4 = 729

a = 3^7

Therefore, the sequence is:

3^7, 3^6, 3^5, 3^4, 3^3, ...

The 12th term is:

3^2 = 9

The approximate percent of total students that receive no allowance and do not have a cell phone is this:

C. 47%

First, we are given some figures that stand for the number of students who receive no allowance and have no cell phones. We have to calculate the total number of students as follows:

45 + 21 + 35 + 49 = 150

The number of students who receive no allowance = 49

The number of students who have no cell phones =21

So, the percentage is = The Total number of students that receive no allowance and have no cell phones / Total number of students.

= 49 + 21 = 70

70/150 × 100

= 46.6%

Approximately this is 47%.

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From the graph of system of linear inequality there may be other possible solutions, but (20, 100) is one that satisfies all the given constraints.

Let's first define our variables and their corresponding constraints:

Let a be the number of student tickets sold.

Let y be the number of adult tickets sold.

The total number of tickets sold cannot exceed 120, so we have the constraint

a + y ≤ 120 ...eq(i)

The minimum revenue required is $670, so we have the constraint          4a + 8y ≥ 670...eq(ii)

The drama club can sell at most 30 student tickets, so we have the constraint a ≤ 30.

The drama club must sell a minimum of 80 adult tickets, so we have the constraint y ≥ 80.

The last inequality is

y ≥ 80

To solve these inequalities graphically, we will plot the lines for each constraint on a coordinate plane and shade the region that satisfies all the inequalities. The shaded region will represent all possible combinations of student and adult tickets that meet the constraints.

First, let's plot the line for the a + y ≤ 120 constraint. We can rewrite this as y ≤ -a + 120 and plot the line y = -a + 120 on the coordinate plane:

The shaded region for this constraint is below the line and includes the origin.

Next, let's plot the line for the 4a + 8y ≥ 670 constraint. We can rewrite this as y ≥ (-1/2)a + 83.75 and plot the line y = (-1/2)a + 83.75 on the same coordinate plane:

The shaded region for this constraint is above the line.

Now, let's plot the constraint a ≤ 30. We can draw a vertical line at a = 30:

The shaded region for this constraint is to the left of the line.

Finally, let's plot the constraint y ≥ 80. We can draw a horizontal line at y = 80:

The shaded region for this constraint is above the line.

To find a possible solution, we need to find the point where all four shaded regions overlap. This point represents a combination of student and adult tickets that satisfies all the constraints. One such point is (20, 100), which means the drama club can sell 20 student tickets and 100 adult tickets to meet their requirements and raise at least $670 in revenue.

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Answer:

Step-by-step explanation:

A. To plot the circles x^2+y^2=4 and x^2+y^2=1 on the same coordinate plane, we can use the standard form of the equation of a circle:

For x^2+y^2=4, the radius is 2 and the center is at the origin (0,0).

For x^2+y^2=1, the radius is 1 and the center is also at the origin (0,0)

B. To find the image of any point on x^2+y^2=4 under the transformation (x,y) to (1/2x,1/2y), we can substitute the values of x and y from the original equation into the transformation rule. Let's take the point (2,0) as an example:

(1/2x,1/2y) = (1/22, 1/20) = (1,0)

Therefore, the point (2,0) will go to the ordered pair (1,0).

C. We can notice that x^2+y^2=1 is a smaller circle that is completely contained within x^2+y^2=4, which is a larger circle. The smaller circle is a dilation of the larger one using the origin as a center and a scale factor of 1/2. This means that every point on the smaller circle is half the distance from the origin as the corresponding point on the larger circle. In other words, the smaller circle is a scaled-down version of the larger one.

The statement A and statement B are supported by the data in the table. The solution has been obtained by studying the bar graph.

What is a bar graph?

Bar graphs or bar charts are visual depictions of groups of data that are made up of vertical or horizontal rectangular bars with lengths that are equal to the data's measure.

We are given a graph showing grasshopper numbers before and after blue jays preyed on them.

From the graph, we can observe that there is no change in the number of green grasshoppers. This means that blue jays did not prey them.

Also, there is a great fall in the brown grasshoppers which means that they are most visible to the blue jays.

Hence, the statement A and statement B are supported by the data in the table.

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The complete question has been attached below

The correct sketch is B

The liquid range of water refers to the temperature range at which water exists as a liquid. At standard atmospheric pressure (1 atm), the liquid range of water is from 0 degrees Celsius to 100 degrees Celsius, or from 32 degrees Fahrenheit to 212 degrees Fahrenheit.

This means that water can exist as a liquid within this temperature range, but if the temperature falls below 0 degrees Celsius or rises above 100 degrees Celsius, it will freeze into a solid or boil into a gas, respectively.

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Answer:

6

Step-by-step explanation:

the numerator of the fraction is

6(t+h) +1 -(6t +1) = 6h

so the fraction is 6h/h =6

Answer:12

Step-by-step explanation:

Answer:

The expression "sine squared theta over the quantity 1 plus cosine theta end quantity" can be simplified to "1 - cos θ".

Answer:

1 - cos θ

Step-by-step explanation:

Robin Nest's average daily sales were $1,644 based on credit sales and net receivables.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Average daily sales are the estimated amount of sales made daily in a year.

It can be found by the formula:

= Net credit sales / Number of days in the period

Solving gives:

= 600,000 / 365 days

= $1,644

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The complete question is given below.

Robin's Nest had net credit sales for the current period of $600,000 and average net receivables were $50,000. What is Robin's Nest's average daily sales

Answer: it

Step-by-step explanation:

Answer:

To stretch the graph of f(x) horizontally by a factor of 6, we can multiply the x-values of each point on the graph by 1/6. This will make the curve wider and flatter. The equation of the transformed function will be of the form:

g(x) = cos((1/6)x)

To shift the graph of g(x) 5 units down, we can subtract 5 from the y-values of each point on the graph. The final equation of the transformed function will be:

g(x) = cos((1/6)x) - 5

So, the equation of the new function g(x) is g(x) = cos((1/6)x) - 5.

Answer: y = 2x - 7

Step-by-step explanation:

Slope-intercept form is y=mx+b

Substitute variables with their given values.

 y = 2x + b

In order to find the y-intercept, or b, we can plug the point provided, (4,1) , into y = 2x + b and solve for b.

 1 = 2(4) + b

 1 = 8 + b

-7 = b

Now we can put the y-intercept into the equation, and get y = 2x - 7 .

The solution is, the total surface area is 92 sq. inches.

Total surface area refers to the area including the base(s) and the curved part. It is the total area covered by the surface of the object. If the shape has a curved surface and base, then the total area will be the sum of the two areas.

here, we have,

Total paper required = total surface area

Surface area of a cuboid = 2[(l×b) + (l×h) + (b×h)],

Where 'l' is the length, 'b' is the breadth and 'h' is the height

For the box, total surface area = 2[(8×3) + (3×2) + (8×2)]

=2[24 + 6 + 16]

=2[46]

= 92 sq. inches

Hence, The solution is, the total surface area is 92 sq. inches.

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Therefore , the solution of the given problem of probability comes out to be  probability of  not experiencing either symptom is 0.05.

Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.

Here,

To determine if the two symptoms are independent, we need to check if the probability of one symptom changes depending on whether the other symptom is present or not.

P(pain | swelling) = 40% / 75% = 0.533

P(pain | no swelling) = 20% / 25% = 0.8

Since the conditional probabilities are not equal, the two symptoms are dependent.

(c) The probability that the victim will experience at least one of these symptoms is the probability of experiencing pain, swelling, or both. This can be calculated as:

P(pain or swelling) = P(pain) + P(swelling) - P(pain and swelling)

= 60% + 75% - 40%

= 95%

So the probability of experiencing at least one of these symptoms is 95%.

(d) The probability that a victim will have intense pain given that they have swelling is the conditional probability:

P(pain | swelling) = 40% / 75%

= 0.533

So the probability of having intense pain given that there is swelling is 0.533.

(e) The probability that a victim will experience pain but not swelling can be calculated as:

P(pain and no swelling) = P(pain) - P(pain and swelling)

= 60% - 40%

= 20%

So the probability of having intense pain without swelling is 20%.

(f) The probability that a victim will not experience either symptom is the complement of the probability of experiencing at least one symptom:

P(neither pain nor swelling) = 1 - P(pain or swelling)

= 1 - 0.95

= 0.05

So the probability of not experiencing either symptom is 0.05.

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Answer:

Step-by-step explanation:

To obtain a polynomial of lowest degree with the given zeros and leading coefficient, we can use the fact that if a polynomial has a root of multiplicity m, then the factor (x - r)^m appears in the polynomial. Therefore, we can write:

f(x) = A(x + 1/4)^2(x - 2/3)

where A is a constant that we need to determine to satisfy the condition f(0) = 2.

To find A, we substitute x = 0 into f(x) and set the result equal to 2:

f(0) = A(0 + 1/4)^2(0 - 2/3) = -A/27 = 2

Solving for A, we find that A = -54.

Therefore, the polynomial f(x) is:

f(x) = -54(x + 1/4)^2(x - 2/3)

Answer:

Customers are charged $0.003 per gallon of water used.

Step-by-step explanation:

In the given function, T = 35 + 0.003w, the coefficient of w (which is 0.003) represents the rate at which the total cost (T) increases per unit increase in the amount of water used (w). In other words, it is the cost per gallon of water used.

Therefore, the slope of the function is 0.003, and it represents the rate of change of the cost with respect to the amount of water used. Each additional gallon of water used will increase the monthly bill by $0.003.

Answer: D = √2

(please respond if im wrong)

Step-by-step explanation:

The fold is made along BE. A folds onto A′.

A′B = AB =√2 ⇒ A′C = 1

(by Pythagoras)

ΔA′BC

is therefore a right-angled isosceles triangle.

⇒∠BA′C=45∘ ⇒∠EA′D=45∘

⇒ ED = A′D = √2−1

(a) The probability that exactly 10 of the first 15 graded projects are from the second section can be calculated using the binomial probability formula:

P(X = 10) = (15 choose 10) * (35/60)^10 * (25/60)^5 = 0.0361

(b) The probability that at least 10 of the first 15 graded projects are from the second section can be calculated by summing the probabilities for 10, 11, 12, 13, 14, and 15:

P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0361 + 0.0132 + 0.0035 + 0.0007 + 0.0001 + 0.0000 = 0.0536

(c) The probability that at least 10 of the first 15 graded projects are from the same section can be calculated by summing the probabilities for 10, 11, 12, 13, 14, and 15 from both sections:

P(X >= 10) = P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13) + P(X = 14) + P(X = 15) = 0.0361 + 0.0132 + 0.0035 + 0.0007 + 0.0001 + 0.0000 + 0.0019 + 0.0003 + 0.0000 + 0.0000 + 0.0000 + 0.0000 = 0.0556

(d) The mean value and standard deviation of the number among these 15 that are from the second section can be calculated using the formulas for the mean and standard deviation of a binomial distribution:

mean = np = 15 * (35/60) = 8.75
standard deviation = sqrt(np(1-p)) = sqrt(15 * (35/60) * (25/60)) = 1.568

(e) The mean value and standard deviation of the number of projects not among these first 15 that are from the second section can be calculated using the formulas for the mean and standard deviation of a binomial distribution, with n = 45 (the remaining number of projects) and p = 35/60 (the probability of a project being from the second section):

mean = np = 45 * (35/60) = 26.25
standard deviation = sqrt(np(1-p)) = sqrt(45 * (35/60) * (25/60)) = 2.714

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Answer:

the sale price of the one-terabyte external hard drive is $274.13.

Step-by-step explanation:

To find the sale price of the one-terabyte external hard drive, we can use the following formula:

Sale price = Original price - Discount amount

where the discount amount is the amount by which the original price is reduced. The discount amount is equal to the discount rate times the original price. The discount rate is 21%, or 0.21, because the hard drive is on sale at a 21% discount.

Substituting the given values into the formula, we get:

Discount amount = 0.21 * $347 = $72.87

To find the sale price, we subtract the discount amount from the original price:

Sale price = $347 - $72.87 = $274.13

Therefore, the sale price of the one-terabyte external hard drive is $274.13.