if PQ+PR=72 cm, then what is the value of sinR? (look at the file)

For the given time taken to cover 20 miles from upstream and downstream the rate of Rick paddles in still water is 6.5mph and rate of current is 1.5mph.

Let us consider 'x' be the rate at which Rick paddles in still water

'y' be the rate of the current

Distance covered while going in upstream = 20 miles

Time taken while going 20 miles upstream = 4 hours

Rate of upstream = 20 / 4

⇒ x - y = 5 miles /hours    ___(1)

Distance covered while going in downstream = 20 miles

Time taken while going 20 miles downstream = 2.5hours

Rate of downstream = 20 / 2.5

⇒ x + y = 8 miles /hours    ___(2)

Solve (1) and (2) we get,

x - y = 5

x + y = 8

2x = 13

⇒ x = 6.5miles per hour

y = x - 5

⇒ y = 1.5 miles per hour

Therefore, the rate of the Rick paddles in the still water is 6.5mph and the rate of the current is 1.5mph.

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The square root of 224 in long division is 14.96

The term square root in math is defined as  a factor of a number that, when multiplied by itself, gives the original number

Here we know that we need to find the square root of √224.

In order to solve this one we have to do the following steps,

Here we have to start dividing the digits from the right side into pairs of two by drawing a line on top of them. In the case of 224, then we have two pairs 24 and 2.

And then we have to find a number(z) whose square is ≤ 2.

Then the value of z will be 1 as 1 × 1 = 1 ≤ 2.

Here we get the value of quotient and the remainder as 1 and now we have to add the divisor z with itself and get the new divisor 2z (2).

And then we have to drag down the next pair and find a number (n) such that 2n × n ≤ 124 here we have the value of n comes out to be 4.

Finally we have to add a decimal in the dividend (224) and quotient (14) simultaneously.

Here we have to add 2 pairs of zero in the dividend after the decimal  and repeat the above step for the remaining three pairs of zero.

Complete Question:

Finale the square root of √224 and go step by step to reduce the radical.

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The expression 4× 4 × 5 × 10 = 800 in the field of math.

Algebra is a branch of mathematics that is used to manipulate symbols and equations in order to solve problems. Algebra helps to solve problems involving unknown quantities and to develop relationships between different variables. It is a powerful tool that can be used to solve and analyze a variety of mathematical problems and equations.

Algebra can be used to solve equations, simplify expressions, and find solutions to linear and quadratic equations. Through algebra, we can also find the slope of a line, the area of a triangle, and the volume of a cube. Algebra is an invaluable tool that is useful in many areas of mathematics and science.

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The expression of the statement is 3x² - 8

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

A mathematical statement

The mathematical statement is given as

Three times the square of a number minus eight

Represent the number with x

So, we have

Three times the square of x minus eight

Express as squares and numbers

This gives

3 * x² minus 8

So, we have

3x² - 8

hence. the expression is 3x² - 8

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The length of the diagonal support lumber is given as follows:

161.5 inches.

The figure is a rectangle, hence the diagonals have equal measure, and thus the value of x can be obtained as follows:

15x + 13.25 = 17x + 4.5.

2x = 9

x = 4.5.

Hence the length of the  diagonal support lumber is obtained as follows:

2 x (15 x 4.5 + 13.25) = 161.5 inches.

We multiply by 2 as we are given half the length of the diagonal.

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The distance of Naudia from starting point based on distance travelled is 13 miles.

The distance travelled by Naudia and distance from starting point will form right triangle. Distance between Naudia and her final destination is the straight line or hypotenuse.

So, the expression will be -

Distance of South² + distance of East² = Distance from starting point

Distance form starting point = 2² + 3²

Distance form starting point = 4 + 9

Distance form starting point = 13 miles

Thus, the required distance is 13 miles.

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Answer:

Equation is   x-5 = 37

Reason:

x = starting temperature

We start with x degrees, and decrease by 5 degrees.

We go from x to x-5

The x-5 is now 37 degrees

Therefore, we arrive at the equation x-5 = 37

To solve this equation, add 5 to both sides and you'll get x = 42

Nice work on getting the correct value of 42.

The table that represents the proportional relationship would be table A. Option A

In this table we can see that in option A, there is a constant for which the values of the y are gotten. This is common on all of the values in A

For instance 2² = 4

3² = 9

4² = 16

0² = 0

The power of 2 is the constant that when applied on the values it gives the corresponding solution.

This shows the constant proportional relationship that is in existence between the values in x and the y solution

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Throughout the solar system, solar energy is continuously emitted by the sun. The Earth is warmed by solar energy, which also affects the weather, the wind, and the survival of plant and animal life. Electromagnetic radiation, which is a kind of energy, heat, and light, is released from the sun (EMR).

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The results of the multiplications are: 1) x²+6x-16 (2) x²+8x+15 (3) x²-2x-63 (4) 6x+x-15 (5) 4x²-17x-15 (5) x²+13x+42

The given equations are

1) (x+8)(x-2)

Opening the brackets to have and collecting like terms  to have

x²-2x+8x-16

x²+6x-16

2) (x+5)(x+3)

Opening the brackets to have and collecting like terms  to have

= x²+3x+5x+15

x²+8x+15

3) (x+7)(x-9)

Opening the brackets to have and collecting like terms  to have

x²9x+7x-63

x²-2x-63

4) (2x-3)(3x+5)

Opening the brackets to have and collecting like terms  to have

6x²+10x-9x-15

6x²+x-15

5) (4x+3)(x-5)

Opening the brackets to have and collecting like terms  to have

4x²-20x+3x-15

4x²-17x-15

6)  (x+7)(x+6)

Opening the brackets to have and collecting like terms  to have

x²+6x+7x+42

x²+13x+42

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We should administer 2.05 ml/hr.

A sort of neurotransmitter and hormone is dopamine. It affects a variety of vital bodily processes, such as mobility, memory, rewarding pleasure, and motivation. Dopamine levels are linked to a number of neurological and mental health conditions.

To determine the ml/hr to administer, we first need to calculate the dose of dopamine in mg/kg/min. We can use the following formula:

dose (mg/kg/min) = 4 mcg/kg/min x 10^-3 (to convert from mcg to mg)

dose (mg/kg/min) = 0.004 mg/kg/min

Next, we need to calculate the total dose in mg/min. We can use the following formula:

dose (mg/min) = dose (mg/kg/min) x weight (kg)

dose (mg/min) = 0.004 mg/kg/min x 64 kg = 0.256 mg/min

Now we need to convert the dose from mg/min to ml/hr, using the following formula:

ml/hr = dose (mg/min) x weight (kg) / concentration (mg/ml) x 60 min/hr

ml/hr = 0.256 mg/min x 64 kg / 400 mg/250 ml x 60 min/hr

ml/hr = 2.048 ml/hr

To round to the nearest tenth, we will round 2.048 to 2.05 ml/hr. Therefore, we should administer 2.05 ml/hr.

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The graph of a line passing through the points (2, -4) and (0, 0). The correct answer would be an option (A).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The table represents a linear relationship.

x: −1   0    1    2

y:  2   0  −2  −4

As per the points, the graph has been attached below

Here we can see that the shown graph of a line passing through the points (2, -4) and (0, 0)

So the attached graph shows this relationship.

Hence, the correct answer would be option (A).

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Answer:

there is 30 ways

Step-by-step explanation:

There are 6 people who can be president x 5 other people who can be vice president. so there is 30 ways

The probability that the first bar Iesha selects will be lemon and the second will be raisin= 2/45.

What is probability ?

Probability can be defined as the ratio number of favourable outcomes and total number of outcomes.

Note this selection is done without replacement hence after each selection sample size will reduce

Given data,

Samples 3 chocolate chip bars,

2 peanut butter bars,

1 lemon bar, and

4 raisin bars

Sample size S= [3+2+1+4]= 10

Probability that first selection is lemon = 1/10

Probability that second selection is raisin = 4/9

Hence the probability that the first bar Iesha selects will be lemon and the second will be raisin= 1/10*4/9 = 4/90= 2/45

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The weight of the hedgehog in grams is 281 grams

The first step is to determine the unit of conversion of pounds to grams.

1 pound = 453.592 grams

In order to convert the weight of the hedgehog to grams, multiply the unit of conversion by the weight of the hedgehog in pounds. Multiplication is the product of two or more numbers,

Weight of the hedgehog in grams = 0.62 x 453.592 grams = 281 grams

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Ratio of apple juice to water will make the same recipe is  42.60

Ratios are used to compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula would be A/B. This signifies that you are dividing data A by data B. If A is five and B is ten, your ratio will be 5/10.

Add the elements of the ratio together to get the total number of shares.

Subtract the total value from the total number of shares.

Multiply by the number of necessary shares.

A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to one.

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The values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given expression is:

-15< 3n < 6

Divide all the sides of the equation with 3 to isolate the value of n.

-15 / 3 < 3n/3 < 6/3

-5 < n < 2

Hence, the values of n for the given expression such that -15< 3n < 6 is -5 < n < 2.

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The mean height of the members of the football club is 163.4 to rounded to 1 decimal place.

The mean height It is calculated by summing up all the data values and dividing by the total number of data points. The mean can also be represented by the point at which the frequency polygon would balance if it were a physical object.

The values with their corresponding frequencies are:

height: 120 × frequency: 8 = 960

height: 140 frequency: 11 = 1549

height: 160 frequency: 17 = 2720

height: 180 frequency: 18 = 3240

height: 200 frequency: 10 = 2000

sum frequency = 64

sum of all data values = 10460

mean height = 10460/64

mean height = 163.4375

Therefore, the mean height of the members of the football club is 163.4 to rounded to 1 decimal place.

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We assume that we have a plot given like the graph attached.

We have n points and we need to find How many of the 9 people listed in the scatterplot have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

So for this case we need to have the predicted value  y^  and the real value y. We are going to put these two values and the difference

    yi                          yi^                       |yi - yi^|

    157                      161.5                        4.5

    163                      163.1                        0.1

    175                      167                           8.0

    171                       170.5                        0.5

    173                      172.5                        0.5

    173                      174.3                        1.3

    172                      176                           4.0

    183                      178                           5.0

    178                      180                           2.0

So as we can see we have 4 points out of the 9 who satisfy the condition

|yi - yi^| >= 3.

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Answer:

400 pounds equal to 0.2 tons

As per the asked equation the value of P(x<6) will be c=1

The probability of an event is always between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

Given the information provided, P(x-1)=0.178, P(x>1)=0.822, it's not possible to calculate P(x<6) because the information provided doesn't give us the complete picture of the probability distribution function, also we don't know the type of distribution used to calculate the probabilities. So we can't infer anything about P(x<6) from the information given.

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Answer:

1.  5 inches in 2 days

2.  y = (5/2)x. where y is rainfall and x is days.

3.  Yes

4.  (5/2)

5.  2.5"/day

6.  37.5 Inches

Step-by-step explanation:

See attached worksheet

.

The light travels 3.784 x 10 ^13 kilometers in 4 years .As Given that, light travels 1 meter in 1/299,772,458 of a second.

In 4 years how many kilometers it will travel?

covert 4 years into seconds.

since it is given that 1 year = 365.25 days.

           4 years in seconds = 4 x 365.25 x 24 x 60 x 60

                                            = 126230400 sec

          1 m in 1/299,772,458 sec

          x km in 126230400 sec

(let x be the distance travelled)

          x = 126230400 x 299,772,458

             = 3.784 x [tex]10^13\\[/tex] km.

Therefore , The light travels 3.784 x 10 ^13 kilometers in 4 years .

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The complete question :

if light travels exactly 1 meter in 1/299,772,458 of a second, how many kilometers does it travel in 4.00 years? for this question,

1 year = 365.25 days.

4/5 + 5/6

24+25/30

49/30

hope it will help you

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(x,y) = (1, -1). Option (c) is the correct answer.

Given equations:

5x + 2y = 3   ..(1)

4x - 8y = 12   ..(2)

Solving using the elimination method:

so, 4x = 8y + 12 or x = 2y + 3   ..(3)

Now, substituting the x in equation(1) from equation(3)

so we get,

5(2y+3) + 2y = 3

10y + 15 + 2y = 3

12y = -12

y = -1

Putting the value of y in equation(3)

x = 2(-1) + 3 = 1

x = 1

Therefore, (x,y) = (1, -1)

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Answer: Option C, (-1,1)

Step-by-step explanation:

The solutions of the system of inequalities are the points on the purple region, one example of a solution is (-2, -2)

When we have a system of inequalties (so we have 2 or more inequalities) the solutions are the points (x, y) that are solutions of both inequalities at the same time.

Here we can see the graph of a system, such that the solution set of one of the inequalities is represented by the red shaded area, and the solution set of the other inequality is represented by the blue shaded area.

The solution set of the system is represented by the intersection between the areas, which is the purple area.

So any point on that region is a solution to the system, for example, the point (-2, -2) is a solution.

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The value of {z} is equivalent to 13.

Given is that SX = z, TW = 6z - 76 and UV = 3z - 24.

We can write -

{z} + {6z - 76} = {3z - 24}

7z - 76 = 3z - 24

7z - 3z = - 24 + 76

4z = 52

z = 13

Therefore, the value of {z} is equivalent to 13.

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The volume is increasing at a rate of 784 * pi cubic inches per second.

The volume of a sphere is given by the formula V = (4/3) * pi * r^3, where r is the radius of the sphere.

We can find the rate of change of the volume with respect to time by taking the derivative of V with respect to time.

dV/dt = (4/3) * pi * 3r^2 * dr/dt

Given that the radius is increasing at a rate of 2 in/sec, we can substitute this value into the equation and find the rate at which the volume is increasing:

dV/dt = (4/3) * pi * 3 * 9^2 * 2 in^3/sec = 784 * pi in^3/sec

So, when the radius of the snowball is 9 inches, the volume is increasing at a rate of 784 * pi cubic inches per second.

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Answer: Volume of a right prism = BH where B is the area of the base and H is its height.

So Volume = 16 × 12 = 192 cm^3

Step-by-step explanation:

The ordered pair could represent the image of point C(5, 2) after the dilation is (2.5, 1)

If we have a general point (x, y) and we apply a dilation with the origin as the center of a scale factor k, then the coordinates of the image after the dilation is (k*x, k*y)

Here we want to see which point can be the image of (5, 2) after the dilation, it will must have the form (k*5, k*2)

The only point that has this form is the one on the third option, where we can write:

(2.5, 1) = (k*5, k*2)

Then we have two equations:

2.5 = k*5

1 = k*2

Solving these we should get the same value of k.

2.5/5 = k = 0.5

1/2 = k = 0.5

so that is the correct option.

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