Scallops eject water from their shells to provide a thrust force. A 29 g scallop accelerates from rest straight up to escape a predator, reaching a
speed of 4.10 m/s in 0.15 s. What is the ratio of the net force to the weight of the scallop (Fnet/Weight) for this motion? (Hint: Remember that
grams are a measurement of mass, not force). Round to three decimal places and express in terms of SI units.

We have the relation:

y = 4x + 3

Since the slope (4) and the y-intercept (3) were already found, we need now to graph this line.

In order to do so, we can find two points belonging to this line and then draw a line that passes through those points.

The first point can be (0, 3), since we know that the y-intercept is 3, i.e., y = 3 for x = 0.

Now, to find a second point we can choose a value for x, let's say x = 1, and use it in the equation of the line to find the corresponding value of y:

y = 4x + 3 , x = 1

y = 4 * 1 + 3

y = 4 + 3

y = 7

So, (1, 7) is another point we can use.

Now, we can select the second button on the toolbox to draw a line through the points (0, 3) and (1, 7):

The mean of the number of shoes according to the obtained results is; 8.49.

The median of the number of pairs of shoes obtained is; 9.

It follows from the complete task content that the mean and median of the data set are to be evaluated;

Since the mean is the average of all obtained data values, it follows from the mean formula;

Mean = Sum Total/Total Frequency

Mean = { ( 8 × 4 ) + ( 4 × 5 ) + .......+ (13 × 4) } / 65

Mean = 552/65

Mean = 8.49.

Also, the median of the set of 65 data values can be guessed to be the 33rd term.

On this note, the data value which corresponds to a cumulative frequency of 33 upon orderly arrangement is the median term.

Hence, since; 8 + 5 + 4 + 4 + 7 = 28; Hence, upon addition of 14, we have; 42.

Therefore, the median of the number of pairs of shoes is; 9 pairs of shoes.

Remark; The complete task requires that the mean and median be determined.

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Answer:

The solution to the question will be explained better using the image below

Concept:

The formula to calculate momentum is given below as

The first momentum will be

The second momentum will be

Since they are moving in different directions,

We will substract both momentums

Hence,

The momentum of a system that consists of two objects should be 20 kg m/s in the direction of the negative x-axis

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

function G(x)

Step 02:

discrete finite function:

range:

we must analyze the function to find the solution.

range:

{ 3 , 5 , 8 }

The answer is:

range:

{ 3 , 5 , 8 }

Answer:

First you will put the numbers in order least to greatest. So, it would be -4.5, -4, -3.5, -2, -1, 0, 1.5, 2, 2.5, 4, 6. 0 is the median because it in in the middle here’s how. You cross out -4.5 and 6 then 4 and -4 then -3.5 and 2.5 then 2 and -2 then -1 and 1.5 and you’re left with just the 0

Step-by-step explanation:

Step 1:

Draw the rectangle with the given dimensions

Step 2:

Next, apply the Pythagoras theorem

Opposite = 12

Adjacent = 18

Hypotenuse = L the side facing right angle

Step 3:

Final answer

The length of the diagonal is 21.6

Answer:

8 ( x + 3y + 2z) we can take 8 common in the whole expression

The slope of the line through (-10, 1) and (0, -4) is  [tex]\frac{-1}{2}[/tex].

The slope of the line is m=   [tex]\frac{y_{2}-y_{1} }{x_{2-x_{1} } }[/tex]

                                          =  [tex]\frac{ (-4)- (1)}{0- (-10)}[/tex]

                                          = [tex]\frac{-5}{10}[/tex]

                                          = [tex]\frac{-1}{2}[/tex]

Slope is a measure of the steepness of a line or part of it connecting two points.

The slope of a line is the ratio of the amount by which y increases when x increases by some amount. The slope shows how steep the line is, or how much y increases as x increases.

Types of slopes

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Notice that s stands for the slant height of the pyramid, and this height is the height of each one of the lateral triangular faces.

We will need to use the next formulas

Therefore, the surface area is

Lateral Area=116.1 m^2

As for the volume, the volume of a regular pyramid is

In our case,

Therefore,

Volume= 77.9 m^3

The algebraic expression for the statement the product 7 and the square of a number is 7x²

Algebraic expressions are described as mathematical expressions that consist of arithmetic terms, factors, constants, variables and coefficients.

These expressions are also composed of arithmetic operations which may include;

From the information given, we have that;

The product 7 and the square of a number

Now, let the number be x

The square of x is x²

This statement is expressed as;

7x²

Thus, the expression is 7x²

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The complete question:

The product 7 and the square of a number. Write the algebraic expression

The value of n is 0.06.

Given:

The mass of Earth is 5.97 × 10²⁴ kg.

The mass of Mercury is 3.29 × 10²³ kg.

The ratio of the mass of Earth to the mass of Mercury is represented as 1: n.

The ratio of the mass of Earth to the mass of Mercury can be calculated as,

= mass of Earth/mass of Mercury

⇒  [tex]\frac{5,97*10^{24} }{3.29*10^{23} } = \frac{1}{n}[/tex]

⇒ n = 0.0551

⇒ n ≅ 0.06 ( 2 significant figures)

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Answer:14 becuase

Step-by-step explanation:so your dad left you because he $H!T hates you and he want to divorces your mom and he told me to say $H!T you to you

The missing value for which there is one solution of the equation are 13, -11 and 11.

For the given question,

The expression is given as;

(4/3)(-9x + 12) - x = _x - 9

Putting, 13, -11 and 11 will given the one solution of the equation.

Except -13 as expression is not defined for it.

Put -13 at the blank space and solve it,

-12x + 48 - x = - 13 x - 9

- 13x + 48 = -13x - 9

-13x will get cancelled.

Thus,

48 = -9

But,

48 ≠ -9

Thus, -13 is not a solution of the expression.

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For the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to  y = x² - 14x + 48 .

As given in the question,

From the table of ordered pairs, it is observed that the zeros of the quadratic function are at x = 6 and x = 8. The zeros are the points where the y value of the function becomes zero.

An equation of the function in the standard form is given by :

y = (x - 6)(x - 8)

⇒y = x (x - 8) - 6 (x - 8)

⇒ y = x² -8x -6x +48

⇒ y = x² -14x + 48

The quadratic function is represented as the product of the zeros of the graph when plotted on a Cartesian plane.

Therefore, for the given table of ordered pairs, the quadratic function is represented in equation in standard form is equal to  y = x² - 14x + 48 .

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Using the subtraction between integers, it is found that the distance between -17 and 9 is given by:

B. -26.

When we subtract a positive by a negative, the result is always positive.

This is because the result will take the negative makes the signal of the negative number being inverted, then the negative becomes a positive and is added to the first amount.

For this problem, the numbers are given by:

-17 and 9.

The distance between two points on a number line is given by the subtraction between them, hence:

9 - (-17) = 9 + 17 = 26.

The negative meant that the signal of the -17 was inverted and the number became 17, then it was added with 9 resulting in 26.

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The sum of the weight of the empty box and the 940 feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kg.

A number is expressed using scientific notation when it contains a number larger than 1 but less than 10, that multiplies a power of 10

The empty weight of the box = 56.7 grams

The number of feathers added = 940 feathers

Mass of one feather (unit weight) = 0.000567 kilogram

The total weight of the box with the 940 feathers is found as follows;

56.7 grams = 0.0567 kilograms

Mass of the empty box in kilograms = 0.0567 kilograms

Total mass of the 940 feathers 0.000567 × 940 = 0.53298 kilograms

The total weight of the box with the 940 feathers inside is; 0.0567 kilograms + 0.53298 kilograms = 0.58968 kilograms

The total weight of the box and the feathers = 0.58968 kilograms =

[tex]5.8968 \times {10}^{ - 1} [/tex]

kilograms

Rounding the coefficient to the nearest tenth gives;

The total weight of the box and the feathers is approximately [tex]5.90 \times {10}^{ - 1} [/tex] kilograms

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The final answer to the function given as here can be answered as 15 when formulated properly with the formulas substituted to it.

Any kind of mathematical phrase, rule, or law that can be used to establish the link between an independent variable and a dependent variable.

This function can be solved as

Given f(x) = 4x – 1,

as in here f (4) = 4 x 4 – 1

f (4) = 15

A function is a kind of rule that has the ability to produce one output for a single input. This is illustrated by the equation y=x2. Any kind of input present for x results in an absolute single output for y. Considering that x is the input value, we would state that y is a function of x.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to the output.

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( 1 ) If p varies directly as q, for p = 4.5 when q = 12, then the relationship between p and q is p = kq represented as 4.5 = (8/3)12

( 2 ) If p and q is 16 then the direct variation is 1

Any time one quantity directly affects the other, such as when one quantity rises relative to the other and vice versa, there is a direct variation between the two variables. It is the relationship between two variables where one of the variables is a fixed multiple of the other. Since the two variables are directly correlated, they are also known as directly proportional.

There are two kinds of proportionalities: direct variation and inverse variation. When two quantities are multiplicatively connected by a constant, the relationship is said to be proportional. In a direct variation, the ratio of the two quantities stays the same, whereas in an inverse variation, the product of the two quantities stays the same.

If p varies directly as q

for p = 4.5

when q = 12

Then p = kq

4.5 = 12k

k = 12/4.5

k = 8/3

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The cost of 11 inches of wire will be 44 cents

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

The 15 inches of wire costs 60 cents, so the cost of 1 inch of wire is;

Rate = 60/15 =4 cents

So the cost of 1 inch of wire which is the rate of 4 cents.

Now we have to find the cost (in cents) of 11 inches wire.

We know the cost of 1 inch of wire cost 4 cents so the cost of 11 inches of wire is;

= Total inches of wire x Price of 1 inch of wire

= 4 x 11

= 44

Tehrefore, The cost of 11 inches of wire is 44 cents

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Distance using absolute value for each example are given below:

As given in the question,

Distance Using Absolute Value

Difference between each set of points on the number line and also confirming it by writing an absolute value statement for each.

1) –15 and 35

Distance Using Number Line     –15 – (–35) = –15 + 35 = 20

Absolute Value Statement    |–15 – (–35)| = 20

2) 47 and –12

Distance Using Number Line    47 – (–12) = 47 + 12 = 59

Absolute Value Statement     |47 – (–12)| = 59

3) –43 and 27

Distance Using Number Line     –43 – (–27) = –43+27 = – 16

Absolute Value Statement      |–43 – (–27)| = 16

4) –10 and 4

Distance Using Number Line     –10 – 4 = –14

Absolute Value Statement     |–10 – 4| = 14

5) 50 and –25

Distance Using Number Line     50 – (–25) = 50 + 25 = 75

Absolute Value Statement     |50 – (–25)| = 75

6) 36 and –19

Distance Using Number Line     36 – (–19) = 36+19 = 55

Absolute Value Statement    |36 – (–19)| = 55

7) –30 and –40

Distance Using Number Line    –30 – (–40) = –30 + 40 = 10

Absolute Value Statement    |–30 – (–40)| = 10

8) –2 and –45

Distance Using Number Line     –2 – (–45) = –2 + 45 = 43

Absolute Value Statement    |–2 – (–45)| = 43

9) 18 and 46

Distance Using Number Line     18 – 46 = –28

Absolute Value Statement    |18 – 46| = 28

10) –10 and –44

Distance Using Number Line      –10 – (–44) = –10 + 44 = 34

Absolute Value Statement    |–10 – (–44)| = 34

11) –28 and 41

Distance Using Number Line       –28 – 41 = –69

Absolute Value Statement     |–28 – 41| = 69

12) 7 and –9

Distance Using Number Line       7 – (–9) = 7+9 = 16

Absolute Value Statement      |7 – (–9)| = 16

13) –52 and 28

Distance Using Number Line       –52 – 28 = –80

Absolute Value Statement      |–52 – 28| = 80

14) 22 and –50

Distance Using Number Line       22 – (–50) = 22 + 50 = 72

Absolute Value Statement       |22 – (–50)| = 72

15) –4 and –31

Distance Using Number Line       –4 – (–31) = –4 + 31 = 27

Absolute Value Statement       |–4 – (–31)| = 27

16) 19 and 51

Distance Using Number Line       19 – 51 = –32

Absolute Value Statement     |19 – 51| = 32

17) 0 and –38

Distance Using Number Line       0 – (–38) = 0+ 38 = 38

Absolute Value Statement      |0 – (–38)| = 38

18) 2 and –14

Distance Using Number Line       2 – (–14) = 2+14 = 16

Absolute Value Statement       |2 – (–14)| = 16

Therefore, distance using absolute value for each example are given below:

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Answer:

c is the answer

Step-by-step explanation:

1.5 x 3 =4.5

4.5 - 0.25

= 4.25

The test score ratio for studying 2 : 2 : 1 hours is represented as

44 : 44 : 22

The comparison of two similar quantities or the relationship between them is known as a ratio. Using ratio symbols or words, ratios can be expressed in three different ways while maintaining their meaning.

To put it another way, ratios can be expressed by putting a fraction bar, the word "to," or the ratio symbol ":" between the two values being compared.

If 2 hours of studying = 44 marks

If 3 hours of studying = 66 marks

If 4 hours of studying = 88 marks

Then total sum of hours of studying = 9 hours

9 hours of studying = Sum of all marks

                                 = 44 + 66 + 88

                                 = 198

1 hour of studying = 198/9

                              = 22 marks

So, the test score ratio for studying 2 : 2 : 1 hours is represented as

44 : 44 : 22

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a. The elements are in this sample space = 8.

b.  "there are more heads than tails" = 1.

c. Probability that there are more heads than tails = 1/8.

d. Probability for equal number of heads and tails = 0.

The formula for calculation the probability is;

P(E) = number of times E occurs/ number of times experiment is performed

The sample space of flipping three coins.

S = HHH, HHT, HTH, HTT, THH, THT, TTH, TTT

a. The elements are in this sample space.

The total element present on the sample space is 8.

b.  "there are more heads than tails"

Sample space for more heads than tails is only HHH.

S = 1

c. The probability that there are more heads than tails.

Probability = number of heads than tails/total outcome

Probability = 1/8

d. The probability that there are an equal number of heads and tails

S = 0; Non outcome has equal number of head ans tail.

Probability = 0.

Thus, the probabilities of different situations are obtained.

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Value of b is  2Ah - B.

The area that an object's shape designates as being within it. The amount of space occupied by a figure or any other two-dimensional geometric shape in a plane is known as its area. Area is the entire amount of space occupied by the shape of an object or a flat (2-D) surface.

On a piece of paper, draw a square with a pencil. Two dimensions make it up. A shape's area on paper is the space it takes up.

Numerous 2-D shapes, such as circles, triangles, squares, rectangles, parallelograms, and trapezoids, may be found all around us. On paper, you can trace each of these shapes. Since every shape is distinct and varied, its area is also determined in a different way.

Given Data

A= [tex]\frac{1}{2}[/tex]h ( B + b)

For the value of b

b + B = 2Ah

b = 2Ah - B

Value of b is  2Ah - B.

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Based on the given ratio, the total number of chocolate chip and oatmeal raisin cookies in the cookie box is 10.

The ratio refers to the numerical relationship that one value or number bears to another.

Ratios are fractional values, showing how much a value is contained in another, or in relation to another.

Ratios are depicted using the ratio sign (:), fractions, decimals, or percentages, like proportions.

The ratio of chocolate chip cookies to oatmeal raisin cookies = 1:4

The sum of ratios = 5 (1 + 4)

The number of chocolate chip cookies in the cookie box = 2

Using the above ratio, there will be 8 oatmeal raisin cookies, that is 2/1 x 4

The total number of cookies (both types) in the cookie box = 10 (2/1 x 5).

Thus, we can conclude that based on the relative sizes of both cookies, the total number in the box is 10.

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The product (a - b)(a + b) is called the special binomial product, when simplified it is called algebraic identity of two squares and, when simplified it is equivalent to a² - b²

An equivalent, simpler (typically shorter) mathematical expression is substituted for the original one through the process of simplification.

In propositional logic, simplification is a valid immediate inference, argument form, and inference rule that draws the conclusion that if the conjunction A + B is true, then A + B is true as well. By deriving one of the conjuncts of a conjunction on a line by itself, the rule enables the brevity of longer proofs.

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The angle 4 is an alternate angle to 80° and this tells us that; ∠4 = 80°

Alternate angles are defined as the angles that occur on opposite sides of the transversal line and have the same size. Thus, Alternate angles are always equal.

These interior alternate angles can be gotten by drawing a Z shape which produces two different types of alternate angles namely alternate interior angles and alternate exterior angles.

Now, we are given that only one known angle in the image which is 80°. However, we see that the angle we want to find which is angle 4 is an alternate angle to the known angle.

Thus, by definition of alternate angles, we can say that ∠4 = 80°

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[tex] {x}^{2} - x - 1 = x + 2 \\ {x }^{2} - x - 1 - x - 2 = 0 \\ {x}^{2} - x - x - 1 - 2 = 0 \\ {x}^{2} - 2x - 3 = 0 \\ (x - 3)(x + 1) = 0 \\ x - 3 = 0 \\ \\ or \\ x + 1 = 0 \\ \\ x = 3 \\ \\ or \\ \\ x = - 1[/tex]

WHEN x=3

[tex]y = 3 + 2 \\ y = 5[/tex]

When x=-1

[tex]y = - 1 + 2 \\ y = 1[/tex]

NOW WE HAVE A PAIR OF SOLUTIONS AS

Answer:

0.04122137404 is the answer

Answer: 0.041221374

Step-by-step explanation: According to Bing, 0.041221374 is your answer.