A flower vase has 5 white lilies, 4 pink roses, and 6 yellow carnations. one flower is chosen at random and given to a woman. another flower is then chosen at random and given to a different woman. what is the probability that both flowers are pink roses?

a)

The robot made the turn at the point (-20, 15).

b)

The equation of the second line on which the robot traveled is:

y = (4/3)x + 35.

c)

The distance between the starting position and the final position is 20.51 feet.

d)

The equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

Example:

The slope of the line y = 2x + 3 is 2.

The slope of a line that passes through (1, 2) and (2, 3) is 1.

We have,

a.

To find the coordinates of the point at which the robot made the turn, we need to determine its position after traveling for 60 seconds along the initial northeast path.

The distance the robot covers in 60 seconds is:

distance

= speed x time

= (1/2) x 60 = 30 feet

The initial path has a slope of -3/4 (since it passes through (4, -3) and

(0, 5)), so the robot's new path after turning right will have a slope of the negative reciprocal of -3/4, which is 4/3.

We know that the robot traveled 30 feet along the initial path, so we can use the slope and distance traveled to find the endpoint of the initial path:

y = mx + b, where m is the slope and b is the y-intercept

-3 = (-3/4)(4) + b

b = 0

So the equation of the initial path is y = (-3/4)x.

The endpoint of the initial path is (-20, 15) (since the initial path passes through (0, 5) and (-20, 15)).

The robot made the turn at the point (-20, 15).

b.

Since the robot turned right, its new path will be perpendicular to the initial path.

We know the robot's position after turning (i.e., the endpoint of the initial path), so we can use this point and the slope of the new path to find the equation of the new path.

The slope of the new path is 4/3, so the equation of the new path is:

y - 15 = (4/3)(x + 20)

Simplifying this equation, we get:

y = (4/3)x + 35

The equation of the second line on which the robot traveled is:

y = (4/3)x + 35.

c.

From the last equation in part (b), we have:

9(y - 5)² = 29 - 16x² - 12x

Taking the square root of both sides and solving for y, we get:

y = 5 ± √((29 - 16x^2 - 12x)/9)

Since the robot is traveling along the new path for 80 seconds, we want to find y when t = 80.

Substituting t = 80 into the equation for y and simplifying, we get:

y = 5 + √(17/9)

So the robot's final position is approximately (20.50, 6.63).

The distance between the starting position and the final position is:

distance

= √((20.50 - 0)² + (6.63 - 5)²)

= √(421.17)

= 20.51 feet.

d.

The robot needs to travel along a path that is perpendicular to the second line on which it traveled in order to return to its starting position.

The slope of the second line is 4/3, so the slope of the path back to the starting position is -3/4 (the negative reciprocal of 4/3).

We know the robot's final position and the slope of the desired path, so we can use the point-slope form to find the equation of the path:

y - 5 = (-3/4)(x - 0)

Simplifying this equation, we get:

y = (-3/4)x + 5

So the equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.

Setting the two equations equal to each other and solving for x, we get:

(4/3)x + 35 = (-3/4)x + 5

Multiplying both sides by 12 to eliminate fractions, we get:

16x + 420 = -9x + 60

Solving for x, we get:

x = -16.8

Substituting this value of x into either equation, we get:

y = (4/3)(-16.8) + 35

y = 13.60

So the intersection point is approximately (-16.8, 13.60).

To find how long it will take the robot to get there, we can use the distance formula between the robot's final position and the intersection point:

distance = √((-16.8 - 20.50)² + (13.60 - 6.63)²) ≈ 40.49 feet.

Since the robot travels at a constant speed of 1/2 foot per second, it will take approximately 80.98 seconds (rounded to two decimal places) for the robot to return and recharge.

Thus,

The robot made the turn at the point (-20, 15).

The equation of the second line on which the robot traveled is:

y = (4/3)x + 35.

The distance between the starting position and the final position is 20.51 feet.

The equation of the line the robot needs to travel along in order to return and recharge is y = (-3/4)x + 5.

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Let us suppose the distance between the sandbox and garden is x feet.

Apply the sine law in the given triangle, we have

[tex]\frac{x}{\sin 65^{\circ}}=\frac{36}{\sin 104^{\circ}}\\ \\ \text{On coss multiplying, we get}\\ x\sin 104^{\circ}=36\sin 65^{\circ}\\ \\ x=\frac{36\sin 65^{\circ}}{\sin 104^{\circ}}\\ \\ x\approx 33.6[/tex]

Therefore, in the nearest foot,  the distance between the sandbox and garden is 34 foot.

Answer:

Hello! The correct answer is 34 ft.

Step-by-step explanation:

I am just confirming!

The inequality the graph represent is y > x - 2.

Inequality is defined as the relation which makes a non-equal comparison between two given functions. An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.

We are given that;

The number line

Now,

The slope of the line is 1 and the y-intercept is -2,

so we can write y = x - 2 for the equation of the line.

The line is dashed, so we know that y is not equal to x - 2.

The region above the line is shaded, so we know that y is greater than x - 2.

Therefore, by the inequality the answer will be y > x - 2.

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Answer:

[tex]x=\frac{5}{(10-a-b)}[/tex]

Step-by-step explanation:

4+3x-ax=9-7x+bx

take all variable terms at one side and all constant terms at one side,

3x+7x-bx-ax=9-4

10x-ax-bx=5

x(10-a-b)=5

[tex]x=\frac{5}{(10-a-b)}[/tex]

Answer: The correct options are (b) and (d).

Explanation:

It the polar form [tex]r^2=x^2+y^2[/tex], where

[tex]x=r\cos \theta,y=r\sin \theta[/tex]

The polar coordinate are in the form of [tex](r,\theta)[/tex].

From the given figure it is noticed that the value of r is 4 and [tex]\theta=\frac{\pi}{2}[/tex] or [tex]90^{\circ}[/tex] .

So the point is defined as [tex](4,90^{\circ})[/tex] and option b is correct.

The value,

[tex](r\cos \theta, r\sin \theta)=(0,4)[/tex]

Check the each option if we get the same value then that option is correct.

For option a.

[tex](r\cos \theta, r\sin \theta)=(-4\cos 90^{\circ} , -4\sin 90^{\circ})=(0,-4)[/tex]

Therefore option (a) is incorrect.

For option c.

[tex](r\cos \theta, r\sin \theta)=(4\cos (-90)^{\circ} , 4\sin (-90)^{\circ})=(0,-4)[/tex]

Therefore option (c) is incorrect.

For option d.

[tex](r\cos \theta, r\sin \theta)=(-4\cos (270)^{\circ} , -4\sin (270)^{\circ})\\(-4\cos (360-90)^{\circ} , -4\sin (360-90)^{\circ})=(0,4)[/tex]

Therefore option (d) is correct.

For option (e).

[tex](r\cos \theta, r\sin \theta)=(-4\cos (-270)^{\circ} , -4\sin (-270)^{\circ})\\(-4\cos (270)^{\circ} , 4\sin (270)^{\circ})=(0,-4)[/tex]

Therefore option (e) is incorrect.

Answer:

1. A

2. B, D

3. A, D, E

4. C

5. A

Step-by-step explanation:

The ship's speed in deep water is 0.045 nautical miles per minute. In shallow water, the ship's maximum speed typically decreases due to increased drag and turbulence.

To find the speed of the ship in very deep water:

Answer: f(x) > g(x).

If f(x) = 1000(3)x and g(x)=8x

fx=3000x

f=3000x/x

f=3000

g(x)=8x

g=8x/x

g=8

For whatever amount of X (positive), the statement f(x) > g(x) is true.

The measure of a complementary angle to a 27 degree angle is 63 degrees because two angles are complementary if their measures add up to 90 degrees. This is calculated by subtracting the given angle from 90.

The measure of an angle is given as 27°, and you are asked to find the measure of a complementary angle. In mathematics, two angles are considered complementary if their measures add up to 90 degrees. Therefore, to find the measure of a complementary angle, you subtract the given angle from 90 degrees.

So, to solve this problem, you would simply subtract 27 from 90.
The calculation would look like this:
90-27 = 63. Therefore, the measure of the complementary angle is 63°.

Answer:

b

Step-by-step explanation:

The standard deviation for the given test scores can be calculated by finding the mean, computing the squared differences from the mean, averaging those squared differences to get the variance, and then taking the square root of that variance. The standard deviation for the scores is approximately 2.449.

The student is likely seeking assistance with the concept of standard deviation, which is a measure of dispersion or distribution around the mean in a set of data. The question at hand requires calculating the standard deviation for a small dataset consisting of three scores from a chemistry seminar. To find the standard deviation, one would first need to calculate the mean of the test scores, then find the variance by averaging the squared differences between each score and the mean, and finally, take the square root of the variance.

Step-by-step Calculation:

The standard deviation of the test scores in Prof. Miller's advanced chemistry seminar is approximately 2.449.

To find the interval of 68% of the data, use the empirical rule. The probability a man weighs more than 170 lbs or less than 128 lbs can be found using the normal distribution curve.

To find the interval in which 68% of the data lies, we can use the concept of the empirical rule. According to the empirical rule, approximately 68% of the data falls within one standard deviation of the mean.

Since the standard deviation is 14 pounds and the mean is 142 pounds, one standard deviation above the mean is 142 + 14 = 156 pounds, and one standard deviation below the mean is 142 - 14 = 128 pounds.

Therefore, the interval in which 68% of the data lies is from 128 pounds to 156 pounds.

The probability that a man picked at random from the unit will weigh more than 170 pounds can be found by calculating the area under the normal distribution curve to the right of 170 pounds.

The probability that a man picked at random from the unit will weigh less than 128 pounds can be found by calculating the area under the normal distribution curve to the left of 128 pounds.

The radius of the circle that includes the footbridge, given the bridge's arc length and height, is 14.1 ft.

The problem relates to the geometry of a circle, specifically the concept of the arc length and radius. Given the arc length (L) and the height of the arc (h), we can use these to find the radius (r) of the circle using the formula r = L²/(8h) + h/2.

Here, the arc length is the horizontal length of the footbridge, which is 27 ft and the height h is the height of the bridge, 10 ft.

Substituting these values into the formula we get:

r = (27² ft)/(8*10 ft) + 10 ft/2 = 729/80 + 5  = 14.1 ft

So, to the nearest tenth of a foot, the radius of the circle that includes the footbridge is 14.1 ft.

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The rates charged per hour by the first and second mechanics will be  $105 and $50.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that two mechanics worked on a car, the first mechanic worked for 10 hours, and the second worked for 15 hours. together they charged a total of 1800.

Suppose x is the hourly rate for the first mechanic and y is the hourly rate of the second.

If the total money earned is 1800.

10x + 15 y = 1800  ---- (1)

If both have their individual rates the sum of the hourly rate is,

x+ y = 15            -------- (2)

Rearrange the equation,

x = 155- y

Substitute the value of x in equation 1 we get,

10x + 15 y = 1800

10(155-y) + 15y = 1800

1150 - 10y + 15y = 1800

5y = 250

y = 50

Substitute the value of y in equation 2 we get,

x = 155- y

x= 155 - 50

x = 105

Thus, the rates charged per hour by the first and second mechanics will be  $105 and $50.

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Answer:

his answer is right.

The measure of the angle m∠FLD is 45 degrees.

A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides. The given figure shows a parallelogram ABCD which as AB parallel to CD and AD parallel to BC.

In a parallelogram, opposite angles are equal and since it is a quadrilateral, the angles add up to 360°.

[tex]\rm \angle NKL = \angle LMN = X\\\\\angle KLM = \angle KNM = 3X\\\\ 2(x+3x) = 360\\\\ 80x = 360\\\\ x=\dfrac{360}{80}\\\\ x = 45[/tex]

The figure LFND is another quadrilateral where:

[tex]\rm \angle LFN = \angle NDL =90\\\\ \angle FND = 3x[/tex]

The measure of the, m∠FLD is;

[tex]\rm (90\times 2)+3x+ (angle\ FLD) = 360\\\\m \angle\ FLD = 360- 180- (3\times 45)\\\\ m \angle\ FLD = 360 - 315\\\\ m \angle\ FLD = 45[/tex]

Hence, the measure of the angle m∠FLD is 45 degrees.

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Answer:

B.) 2 lb 2 oz

Step-by-step explanation:

$1.79 for 20 ounces gives us

1.79/20 = $0.0895 ≈ $0.09 per ounce.

1 lb = 16 oz.; this means that 2 lb = 2(16) = 32 oz.

$2.59 for 2 lb 2 oz then gives us

2.59/34 = $0.07617647059 ≈ $0.08 per ounce.

The second choice is cheaper by 1 cent.