At the same time a 6 foot person casts a 2 foot shadow, a nearby flagpole casts a ten foot
shadow. How tall is the flagpole?

Answer:

first we know the speed from home to school is 8mph and from school to home is half that speed so 4 miles per hour

now,

from home to school it takes: m/8 hours

and from school to home m/4 hours

we can pass it to minutes multiplying by 60

so:

from home to school it takes: m*7.5 minutes

and from school to home m*15 minutes

and now the relations between these two amount of minutes is that takes 15 more from school to home so:

7.5m+17

Step-by-step explanation:

Answer:

100 miles from shore

Step-by-step explanation:

locate 10 hours on the x- axis, go vertically up to meet the line at (10, 100 )

so after 10 hours they are 100 miles from shore

Answer:

100

Step-by-step explanation:

x-axis shows time - find where this is 10 hours

y-axis shows distance from shore.  Find where this corresponds to 10.  That is at 100 miles.

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

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

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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Answer:

none of these

Step-by-step explanation:

Answer:

43 hundreds

Step-by-step explanation:

There are 40 hundreds in 4000.  

4000/100=40.

Afterwards, you would add the other 3 hundred to the answer which would make the answer 43 since 300/100 is equal to 3, and 40 + 3 = 43

The remainder of the 76 left would be 7 tens and 6 ones also if you wanted to know.

10 one hundreds = 1000

3 one hundreds = 300

Answer:

the answer is given below with steps.

Step-by-step explanation:

tan(45) = x/24

x = tan(45) × 24

x = 24

sin(30) = 24/y

y = 24/sin(30)

y = 48

Answer:

Angles that are vertical or across from each other are congruent or equal.

Answer:

hold on..

Step-by-step explanation:

Answer:

x =  − 4

Step-by-step explanation:

I put your question in a math calculator and this is what I got. Good Luck

The features related to vectors are listed below:

Case A: u' = (- 4√41 / 41, - 5√41/ 41)

Case B: Tip coordinantes of vector v: (x, y) = (10, 10)

Case C: r = 11.402

In this question we must determine three features related to vectors: (a) unit vector, (b) the definition of a vector based on the coordinates of its base and its tip, (c) The magnitude of a resulting vector.

Case A - Unit vector

Unit vectors are vectors with magnitude 1, for the case of vector u we have the following definition:

u' = u / ||u||

Where:

Please notice that the magnitude of the vector is determined by Pythagorean theorem:

r = √[(Δx)² + (Δy)²]

Where:

Thus, the unit vector of u is:

u' = (- 4, - 5) / √[(- 4)² + (- 5)²]

u' = (- 4, - 5) / √41

u' = (- 4 / √41, - 5 / √41)

u' = (- 4√41 / 41, - 5√41/ 41)

Case B - Definition of a vector

This can be found easily by vector subtraction:

v = Tip coordinates - Base coordinates

(3, 4) = (x, y) - (7, 6)

(x, y) = (3, 4) + (7, 6)

(x, y) = (10, 10)

Case C - Magnitude of a vector

The magnitude is found by means of Pyhtagorean theorem:

r = √[(- 4 - 3)² + (- 5 - 4)²]

r = √[(- 7)² + (- 9)²]

r = 11.402

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Answer:

x=4

Step-by-step explanation:

By SAS we know that

\(\triangle ABE \sim \triangle ADC\)

by a ratio of

\(1:2\)

so we have

\(\frac{BE}{DC}=\frac{1}{2}\\\\2BE=DC\\\\2(x+2)=12\\\\2x+4=12\\\\2x=12-4\\\\2x=8\\\\x=4\)

Answer:

0650 + 500 = 1150

Step-by-step explanation:

You will need to represent the question on a triangle.

You will actually need a ruler and pencil for drawing along with a good eraser in case you make mistake.

Take your pencil and draw a point X, take ruler and rule a straight line to another point Y and rule another straight line to point Z and finally close it up at point X again.

Answer:

Step-by-step explanation:

You want points A(-4, 0), B(0, -1) and C(-3, -3) reflected across the y-axis and translated left 5 and up 2.

The reflection across the y-axis changes the sign of the x-coordinate:

  (x, y) ⇒ (-x, y)

The translation adds the translation vector to the reflected coordinates.

  (x, y) ⇒ (x -5, y +2) . . . . . . translation (by itself)

Then the result of both transformations is ...

  (x, y) ⇒ (-x -5, y +2)

For a number of points, this arithmetic is conveniently accomplished by a calculator. The result is ...

Answer:

\(\frac{30meters}{second}\)

600meters

Step-by-step explanation:

Use conversion factors that represent 1.  You can cross cancel wods just like numbers.

\(\frac{108km}{1hour}\) · \(\frac{1hour}{60 minutes}\) · \(\frac{1minute}{60seconds}\) ·\(\frac{1000meters}{1 km}\)

\(\frac{108000meters}{3600seconds}\)

\(\frac{30meters}{second}\)

\(\frac{30meters}{second}\) ·\(\frac{20seconds}{1}\)

600 meters

Helping in the name of Jesus.

Answer:

As = 256\(\pi\) or 804.25cm

Step-by-step explanation:

By formula As = \(4\pi r^{2}\)

As = 256\(\pi\) or 804.25cm

The equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

To find an equation in slope-intercept form that passes through the point (1, -2) and is perpendicular to the given equation y = 5x + 4, we need to determine the slope of the perpendicular line.

The given equation y = 5x + 4 is already in slope-intercept form (y = mx + b), where m represents the slope. In this case, the slope of the given line is 5.

To find the slope of a line perpendicular to this, we use the fact that the product of the slopes of two perpendicular lines is -1. So, the slope of the perpendicular line can be found by taking the negative reciprocal of the slope of the given line.

The negative reciprocal of 5 is -1/5.

Now that we have the slope (-1/5) and a point (1, -2), we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = (-1/5)(x - 1)

Simplifying:

y + 2 = (-1/5)(x - 1)

To convert the equation into slope-intercept form (y = mx + b), we need to simplify it further:

y + 2 = (-1/5)x + 1/5

Subtracting 2 from both sides:

y = (-1/5)x + 1/5 - 2

Combining the constants:

y = (-1/5)x - 9/5

Therefore, the equation of the line perpendicular to y = 5x + 4, passing through the point (1, -2), is y = (-1/5)x - 9/5.

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Answer:b=5

Step-by-step explanation:

The value of B for the given expression is B = (2 - 3C) / 5.

An expression in mathematics is a grouping of one or more numbers, variables, and arithmetic operations (such as addition, subtraction, multiplication, division, and exponentiation) that illustrates a relationship or calculation.

Parentheses, braces, and other grouping symbols that specify the sequence in which operations should be carried out are also permitted in expressions.

To solve for B, we need to isolate B on one side of the equation.

15B + 9C = 6

Subtract 9C from both sides:

15B = 6 - 9C

Divide both sides by 15:

B = (6 - 9C) / 15

Simplifying the right side gives:

B = (2 - 3C) / 5

Therefore, B = (2 - 3C) / 5.

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we know that

The vertical line test is a method that is used to determine whether a given relation is a function or not

A function can only have one output, y, for each unique input, x

If a vertical line intersects a curve more than once then for one value of x the curve has more than one value of y, and so, the curve does not represent a function

see the figure below to better understand

In the figure above f(x) represents a function, because the vertical line intersects the graph

Answer:

(a) \(\hat y=69.04-0.083\cdot x\)

(b) D. For every unit increase in commute​ time, the index score falls by 0.083​, on average.

Step-by-step explanation:

(a)

Form the least-squares regression line using Excel as follows:

Go to Data → Data Analysis → Regression

A dialog box will open.

Select the X and Y variable.

Press Ok.

The regression output is attached below.

The least-squares regression line is:

\(\hat y=69.04-0.083\cdot x\)

(b)

The slope of a regression line is the average rate of change in the dependent variable (y) with 1 unit change in the independent variable (x).

Here the slope value is -0.083. This value implies that with 1 minute change in the commute times the Well-Being Index​ Score falls by 0.083 units.

The intercept of a regression line is the average value of the dependent variable (y) when the independent variable (x) value is 0.

Here, the intercept value is 69.04. This value implies that for a person with commute time 0, their Well-Being Index​ Score is 69.04.

The correct option is:

D. For every unit increase in commute​ time, the index score falls by 0.083​, on average.

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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Answer:  The second description is correct for the absolute value of x

Main details: Horizontal line from 0 to the dot 6 ticks to the left, and 6 written above the line

Step-by-step explanation: breaking it down:

A number line is shown from negative 6 to positive 6 with increments of 1. All the numbers are labeled on the number line. The first part is the same in all of the descriptions

A dot is shown on a point at 6 tick marks to the left of 0. This represents -6 on the number line.

Above the number line, a bracket is shown extending from a point at 6 tick marks to the left of zero to 0. This shows the distance between 0 and -6. Important. Absolute value is the distance between two numbers

A horizontal line is shown between the brackets, This is the measuring line 6 units long.

and 6 is written on the line. Important. It is a plain number, no negative or positive! Absolute value is just that.

Answer:

The probability of winning the second prize after the first prize has been awarded is 398/399, or approximately 0.9975.

Step-by-step explanation:

After the first person is drawn, there are 399 people left in the raffle, including the person who won the first prize. So the probability of any one person winning the second prize is 1 out of 399.

However, the question is asking for the probability of the second prize being won by the person who did not win the first prize. Since there are two possible people who could win the first prize, we need to calculate the probability of the second prize being won by the person who did not win the first prize for each of these two cases and then add them together.

Case 1: The first prize is won by person A. Then there are 399 people left, including person A, and 398 of them did not win the first prize. So the probability of person B (who did not win the first prize) winning the second prize in this case is 398/399.

Case 2: The first prize is won by person B. Then there are 399 people left, including person B, and 398 of them did not win the first prize. So the probability of person A (who did not win the first prize) winning the second prize in this case is also 398/399.

Therefore, the total probability of the second prize being won by the person who did not win the first prize is:

(1/2) x (398/399) + (1/2) x (398/399) = 398/399

So the probability of winning the second prize after the first prize has been awarded is 398/399, or approximately 0.9975.

The probability of winning the second prize after the first prize winner is chosen is 0.00250627, or 0.25%.

We have,

After the winner of the first prize is chosen, there are 399 remaining contestants eligible for the second prize.

The probability of winning the second prize depends on the specific individual selected.

Probability of winning the second prize

= 1/399

= 0.00250627

Therefore,

The probability of winning the second prize after the first prize winner is chosen is 0.00250627, or 0.25%.

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Answer:

36 cm squared is the anwer

Answer:

96cm²

Step-by-step explanation:

you must find the surface area of each side then add it all up

                                                   uh i could never, sorry

Answer:

3.142

Step-by-step explanation:

Succinctly, pi which is written as the Greek letter for p, or π is the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.142.