In the figure below, if line r is parallel to line s, m

we have

1) -1/10

step 1

Between the number 0 and number 1 there are 10 spaces

so

each space is

(1-0)/10=1/10

so

-1/10 is 1 space at left of zero

answer part 1 is C

part 2) we have

1/5

Remember that

1/5 is equivalent to 2/10

so

2 spaces at right of zero

answer part 2 is D

Part 3) we have

9/10

correspond to 9 spaces at right of zero

answer part 3 is F

Part 4) we have

-0.5

-0.5=-1/2=-5/10

5 spaces at left of zero

answer part 4 is B

Part 5) we have

0.6

0.6=6/10

6 spaces at right of zero

answer part 5 is E

Part 6) we have

-4/5

-4/5=-8/10

8 spaces at left of zero

answer part 6 is A

A leaking faucet in the S&E building lab, dripping at a rate of one drop per second, will result in a water loss of approximately 4,725 liters in one year.

To calculate the amount of water lost in one year, we need to determine the number of drops per year and then convert it to liters. Since the faucet drips at a rate of one drop per second, there are 60 drops in a minute (60 seconds), which totals to 3,600 drops in an hour (60 minutes).

In a day, there would be 86,400 drops (24 hours * 3,600 drops). Considering a year of 365 days, the total number of drops would be approximately 31,536,000 drops (86,400 drops * 365 days). To convert the number of drops to liters, we need to multiply the total number of drops by the volume of each drop.

Given that each drop contains 0.150 milliliters, we convert it to liters by dividing by 1,000, resulting in 0.00015 liters per drop. Multiplying the total number of drops by the volume per drop, we find that the total water loss is approximately 4,725 liters (31,536,000 drops * 0.00015 liters/drop).

Therefore, in one year, the leaking faucet in the S&E building lab would result in a water loss of approximately 4,725 liters.

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Answer:

1.37 miles

Step-by-step explanation:

First, you have to find out how far Molly's brother and sister walked combined. 1.25+0.85=2.08. Now you subtract that from Molly's distance, 3.45. 3.45-2.08-1.37 miles.

uhm wait cz I think I had made a mistake and I need to fix it

The sentence that explains why two of the fractions shown on the number lines below are equivalent is "The fractions \(\frac{1}{2}\) , \(\frac{2}{4}\) are equivalent because both fractions have the same denominator."

The two fractions \(\frac{1}{2}\) and \(\frac{2}{4}\)  have the same denominator, which is 4. If we multiply the numerator and denominator of \(\frac{1}{2}\) by 2, we get \(\frac{2}{4}\) which means they are equivalent.

When two fractions have the same denominator, they can be easily compared and converted to their equivalent forms.

A number line is a graphical representation of numbers on a straight line, which can be used to compare numbers and determine their value and relationships. Although the number line helps in understanding the fractions, it does not have any direct relation with the equivalence of the given fractions.

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Answer:

Girls to Total:  24/32 or 3/4

Step-by-step explanation:

Girls: 24

All Students: 8+24 = 32

Girls to Total:  24/32 or 3/4

Answer:

(1) - C, \((3,\frac{\pi}{6})\)

(2) - B, \((0,-2)\)

Step-by-step explanation:

\(\text{Using the following conversions:}\\\boxed{\left\begin{array}{ccc}\text{\underline{Rect. to Polar:}}\\(x,y)\rightarrow(r, \theta)\\\\r=\sqrt{x^2+y^2}\\\\\theta=\tan^{-1}(\frac{y}{x})\end{array}\right} \ \ \boxed{\left\begin{array}{ccc}\text{\underline{Polar to Rect.:}}\\(r, \theta)\rightarrow(x,y)\\\\x=r\cos \theta\\\\y=r \sin\theta\end{array}\right}\)

Note that when doing these calculations, make sure your calculator is in radians mode.

Question #2:

Given:

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} ) \ \text{in} \ (x,y)\)

\((\frac{3\sqrt{3} }{2} ,\frac{3}{2} )\\\\\Rightarrow r=\sqrt{(\frac{2\sqrt{2} }{2})^2+(\frac{3}{2})^2} \\\\\Longrightarrow r=\sqrt{\frac{27}{4} +\frac{9}{4} } \\\\\Longrightarrow r=\sqrt{9}\\\\\therefore \boxed{ r=3}\\\\\Rightarrow \theta=\tan^{-1}(\frac{\frac{3}{2}}{\frac{3\sqrt{3} }{2}})\\\\\Longrightarrow \theta=\tan^{-1}(\frac{\sqrt{3} }{3})\\\therefore \boxed{\theta=\frac{\pi}{6} }\)

Thus, the correct option is C.

\(\boxed{\boxed{(3,\frac{\pi}{6})}}\)

Question #3:

Given:

\((2,\frac{3\pi}{2} ) \ \text{in} \ (r,\theta)\)

\((2,\frac{3\pi}{2} ) \\\\\Rightarrow x=(2)\cos(\frac{3\pi}{2})\\\\\Longrightarrow x=(2)(0)\\\\\therefore \boxed{x=0}\\\\\Rightarrow y=(2)\sin(\frac{3\pi}{2})\\\\Longrightarrow y=(2)(-1)\\\\\therefore \boxed{y=-2}\)

Thus, the correct option is B.

\(\boxed{\boxed{(0,-2)}}\)

Answer:

76.9 UNITS^2

Step-by-step explanation:

The area of the 14 by 15 rectangular shape is 210 square units, and

that of the semicircle is (1/2)(3.14)(7)^2, where 7 is half of the diameter (14).

(1/2)(3.14)(7)^2 = 76.9 UNITS^2

The expected value of the number of points Amos makes while shooting 2 free throw shots is equal to 0.812961 points.

To calculate the expected value of the number of points Amos makes when shooting two free-throw shots,

Multiply the probability of making each shot by the respective point value and sum them up.

Let us denote the probability of making a free-throw shot as p (in decimal form). I

Amos's free-throw shooting percentage is 53.1%, or 0.531.

The probability of making a free-throw shot is p = 0.531.

Now, let us calculate the expected value.

The possible outcomes when shooting two free-throw shots are,

Making both shots (probability =  p × p)

Missing the first shot and making the second one

probability = (1 - p) × p)

Missing the first shot and missing the second one

probability =  (1 - p) × (1 - p))

The point values for each outcome are,

Making both shots = 2 points

Making the second shot after missing the first one =  1 point

Missing both shots = 0 points

To calculate the expected value,

Multiply each outcome by its respective probability and sum them up,

Expected value = (2 × p × p) + (1 × (1 - p)× p) + (0 × (1 - p)× (1 - p))

Simplifying the equation,

⇒ Expected value = 2p² + (1 - p)p

⇒ Expected value = 2p² + p - p²

⇒ Expected value = p² + p

Plugging in the value of p,

⇒Expected value = (0.531)²+ 0.531

⇒Expected value = 0.281961 + 0.531

⇒Expected value ≈ 0.812961

Therefore, the expected value of the number of points Amos makes when shooting two free-throw shots is approximately 0.812961 points.

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Answer:

$33.60

Step-by-step explanation:

First we take 80% of $40.

1. $40 * 0.80 = $32

Next we take 105% of $32.

2. $32 * 1.05 = $33.60

Answer: 16,384

Step-by-step explanation:

The seven marbles have different colours, so we can differentiate them.

Now, suppose that for each marble we have a selection, where the selection is in which jar we put it.

For the first marble, we have 4 options ( we have 4 jars)

For the second marble, we have 4 options.

Same for the third, for the fourth, etc.

Now, the total number of combinations is equal to the product of the number of options for each selection.

We have 7 selections and 4 options for each selection, then the total number of combinations is:

C = 4^7 = 16,384

Answer:

the answer is 16384

Step-by-step explanation:

have a nice day.

Answer:

5.6

Step-by-step explanation:

11*7=77

11.8*7= 82.6

82.6-77=5.6

Answer:

t+3t=2-3+122

4t=121

divide both sides by four

4t/4=121/4

t=3.25

Answer:

t = 30.5

Step-by-step explanation:

t-122=\(\frac{3t}{2-3}\)

t-122=-3t           (2-3=-1, so divide by -1 to get -3t)

4t=122

t=\(\frac{122}{4}\)

t=30.5

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

The identity cos(x) tan(x) = sin(x) is verified as it simplifies to sin(x) = sin(x), which is always true.

Let's follow the steps to verify the identity cos(x) tan(x) = sin(x):

Step 1: Express the tangent function in terms of sine and cosine:

tan(x) = sin(x) / cos(x)

Step 2: Substitute the expression for tangent in the given equation:

cos(x) * (sin(x) / cos(x)) = sin(x)

Step 3: Cancel the equal numerator and denominator on the left side:

sin(x) = sin(x)

Step 4: Rewrite the simplified equation:

The equation sin(x) = sin(x) is always true for any value of x, as it represents the identity that the sine of an angle is equal to the sine of the same angle.

Therefore, the identity cos(x) tan(x) = sin(x) is verified.

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The linear equation -2(x - 2) = 4 - 2x has infinitely many solutions

A linear equation is a mathematical statement that describes a relationship between two or more variables and is written in the form of ax + by = c, where a, b and c are constants and x and y are variables. The equation is called "linear" because it is a first degree equation and it describes a straight line when graphed on a coordinate plane.

In this problem, we have to solve for the value of x

-2(x - 2) = 4 - 2x

Open the bracket

-2x + 4 = 4 - 2x

collect like terms

-2x + 2x = 4 - 4

0 = 0

This has an infinitely many solution

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Answer:

0.833333... it repeats

Step-by-step explanation:

So i say 0.83.

Answer:

0.833333...

Step-by-step explanation:

Answer:

Step-by-step explanation:

To find the least cost allocation of tasks between four people, we need to determine the assignment that results in the minimum total cost. From the given information, we can allocate tasks by assigning a number to each person for each task.

Let's denote the people as A, B, C, and D, and the tasks as 1, 2, 3, and 4. The costs for each assignment are given in the table below:

Task 1 Task 2 Task 3 Task 4

Person A 4 3 5 2

Person B 2 4 3 1

Person C 3 1 2 5

Person D 1 2 4 3

To find the least cost allocation, we need to select one task for each person such that the sum of the costs is minimized.

Based on the table, the least cost allocation would be as follows:

Person A - Task 2 (cost: 3)

Person B - Task 4 (cost: 1)

Person C - Task 3 (cost: 2)

Person D - Task 1 (cost: 1)

The total cost for this allocation is 3 + 1 + 2 + 1 = 7.

Therefore, the least cost allocation of tasks between the four people would be:

a. Person A - Task 2

b. Person B - Task 4

c. Person C - Task 3

d. Person D - Task 1

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Answer:

1.94 mm

Step-by-step explanation:

V = pi(r^2)h

V/pi(h) = r^2

r = sqrt(V/pi(h))

r = sqrt(200/pi(17))

r = 1.94 mm

The value of x is 7\(\sqrt{3}\) inches

The correct answer is an option (d)

Let us assume that in the attached diagram of right triangle the angle A measures 30 degrees.

Here, the hypotenuse measures 7 in.

We know that in right triangle, the tangent of angle θ is nothing but the ratio of opposite side of angle θ to the adjacent side of angle θ.

Consider the tan of angle A

tan(A) = opposite side of angle A / adjacent side of angle A

tan(30°) =  7 / x

We know that from the standard trigonometric table the value of tan(30°) is \(\frac{1}{\sqrt{3} }\)

Substitute this value in above equation we get,

\(\frac{1}{\sqrt{3} }\) =  7/x

We solve this equation to find the value of x.

x = 7 × \(\sqrt{3}\)

x = 7\(\sqrt{3}\) in.

Therefore, the correct answer is an option (d)

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To find the polar form of the complex numbers z1 = 2cis(θ1) and za = 6cis(θa), we need to determine their magnitudes and arguments.

For z1:

Magnitude of z1, denoted as r1, is given as 2.

Argument of z1, denoted as θ1, is the angle (in radians) between the positive real axis and the line connecting the origin to the complex number. The argument for z1 is not specified in the given information.

For za:

Magnitude of za, denoted as ra, is given as 6.

Argument of za, denoted as θa, is also not specified in the given information.

Without specific values for the arguments θ1 and θa, we cannot determine the complete polar forms of the complex numbers z1 and za. The polar form of a complex number is represented as r cis(θ), where r is the magnitude and θ is the argument.

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Answer:

4

Step-by-step explanation:

no complicated calculations are needed here

if two lines are parallel, they have the same slope

so the answer is 4

Answer:

Pontiac's Rebellion, which came closely on the heels of the French and Indian War, made the British seek more peaceful relations with Native Americans in the Ohio Valley. They issued the Proclamation of 1763, which prohibited colonists from settling in the region, as a way to avoid further conflict.

Step-by-step explanation:

The area of trapezoid $ABCD$ is $\frac{1}{2}h(a+b)$, where $h$ is the height of the trapezoid and $a$ and $b$ are the lengths of the bases $\overline{AB}$ and $\overline{CD}$, respectively.

To find the area of trapezoid $ABCD$, we need to know the lengths of the bases and the height. Let's assume that the lengths of the bases are $a$ and $b$, where $a > b$. The extensions of the legs of the trapezoid intersect at point $P$.

To calculate the area of the trapezoid, we need to find the height. Let's consider triangle $APB$ formed by the extension of the leg $\overline{AB}$, the extension of the leg $\overline{CD}$, and the line segment $\overline{AP}$. Since $\overline{AB}$ and $\overline{CD}$ are parallel, triangle $APB$ is similar to triangle $CPD$.

Using the similarity of triangles, we can set up the following proportion: $\frac{h}{a} = \frac{h+x}{b}$, where $x$ is the length of $\overline{PD}$. Cross-multiplying gives us $bh = ah + ax$. Rearranging the equation, we have $ax = (b-a)h$. Dividing both sides by $a$, we get $x = \frac{b-a}{a}h$.

Now, the height of the trapezoid, $h$, is the sum of the lengths of $\overline{AP}$ and $\overline{PD}$: $h = \overline{AP} + \overline{PD} = x + \frac{b-a}{a}h$. Simplifying the equation, we have $\frac{a}{a}h = x + \frac{b-a}{a}h$, which gives us $\frac{h}{a} = x + \frac{b-a}{a}h$.

Substituting the value of $x$, we have $\frac{h}{a} = \frac{b-a}{a}h + \frac{b-a}{a}h$. Simplifying further, we get $\frac{h}{a} = \frac{2(b-a)}{a}h$. Dividing both sides by $\frac{2(b-a)}{a}$, we find that $h = \frac{a}{2(b-a)}h$.

Finally, we can substitute the value of $h$ in the formula for the area of the trapezoid to find:

$[ABD] = \frac{1}{2}h(a+b) = \frac{1}{2}\left(\frac{a}{2(b-a)}h\right)(a+b) = \frac{a(a+b)}{4(b-a)}$.

The area of trapezoid $ABCD$ with bases $\overline{AB}$ and $\overline{CD}$ is given by $\frac{a(a+b)}{4(b-a)}$, where $a$ and $b$ are the lengths of the bases and $h$ is the height of the trapezoid.

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Answer: A googolplexian

Step-by-step explanation: A googolplexian is a number with a googol of zeros after it.

hope this helps!

please give brainliest!

Answer:

\(120^{0}\)

Step-by-step explanation:

Given: pentagon (5 sided polygon), two interior angles = \(90^{0}\) each, other three interior angles are congruent.

Sum of angles in a polygon = (n - 2) × \(180^{0}\)

where n is the number of sides of the polygon.

For a pentagon, n = 5, so that;

Sum of angles in a pentagon = (5 - 2) × \(180^{0}\)

                                                = 3  × \(180^{0}\)

                                                = \(540^{0}\)

Sum of angles in a pentagon is \(540^{0}\).

Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;

\(540^{0}\) - (2 × \(90^{0}\))  = \(540^{0}\) - \(180^{0}\)

                       = \(360^{0}\)

So that;

the measure of the interior angle = \(\frac{360^{0} }{3}\)

                                                        = \(120^{0}\)

The measure of one of its three congruent interior angles is \(120^{0}\).

If a cylinder is sliced parallel to its base. The area of the cross section is 36π inch square, then the radius of the cylinder is 6 inches

If we slice a cylinder parallel to its base, we get a circle with the same radius as the cylinder.

We are given that the area of the cross section is 36π in square units. Since the cross section is a circle, we can use the formula for the area of a circle to find the radius.

The formula for the area of a circle is:

A = πr^2

where A is the area of the circle and r is the radius of the circle.

We are given that the area of the cross section is 36π. So, we can set A = 36π and solve for r:

36π = πr^2

Dividing both sides by π:

36 = r^2

Taking the square root of both sides:

r = ±6 inches

Since radius cannot be negative, the radius of the cylinder is 6 inches

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The number of panels produced by plant B is 6000 panels.

Given that, Plant A produced 6000 panels. 2% of the panels from Plant A and 5% of the panels from Plant B were defective.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the number of panels produced by plant B be x.

Now,  2% of 6000 + 5% of x = 4% of (6000+x)

⇒ 120 + 0.05x = 0.04 (6000+x)

⇒ 120+ 0.05x = 240 + 0.04x

⇒ 0.01x=120

⇒ x=120/0.01

⇒ x=12,000 panels

Number of panels produced by plant B = 12000-6000 = 6000

Therefore, the number of panels produced by plant B is 6000 panels.

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Step-by-step explanation:

8(3x+1)

=24x+1

I'm not sure