. Verify the concepts you havelearned about the Law of Acceleration in doing some problem – solving exercises.1.The rising concern among athletic trainers regarding concussions among football playershas prompted numerous studies of the effectiveness of protective head gears.

1.One study suggests that concussions may result from impacts rated at 740 m/s2. If a player’s head mass (with helmet) is 6 kg and considered to be a free body, then what net force would be required to produce an acceleration of 740 m/s2?2.Captain John Stapp of the U.S. Air Force tested the human limits of acceleration by riding on a rocket sled of his own design.


2.His rocket sled, known as the Gee Whiz, had a mass of about 82 kg. What net force would be required to accelerate Gee Whiz and 82 kg Stapp at 450 m/s2 (the highest acceleration tested by Stapp)?3.Space Shuttle Max is one of the extreme rides in Enchanted Kingdom.

3.The first of its kindin the country, the roller coaster ride inverts its riders six times. If during one of its operations, a 53 kg boy experiences a net force of 1800 N at the bottom of its roller coaster loop, how fast would he be accelerating at this location ​

Answer: Most employers expect their exempt employees to work the number of hours necessary to get their jobs done. It doesn't matter if that takes more or fewer than 40 hours per week. Even if your exempt employee works 70 hours in a week, you are still only required to pay them their standard base salary If you use a payroll processing service, there is a cost for each check processed. But either way, processing paychecks more frequently will cost more, such as if you process paychecks every other week (26 times a year) rather than bi-monthly (24 times a year).

Step-by-step explanation:

The temperature at a depth of 4000 m will be 1.1 degrees Celsius.

The equation is defined as a mathematical statement that has a minimum of two terms containing variables or numbers that are equal.

Given that the temperature varies inversely with the depth

Let T be the temperature and D be the depth, then the inverse variation equation is:

T = k/D  

Where variation constant = k

If the temperature at 2000 m is 2.2 degrees Celsius, then the equation is:

2.2 = k/2000

k = 4.400

So T = 4400/D

when D = 4000 m

T = 4400/4000

T = 44/40

T = 1.1  

Thus, the temperature at a depth of 4000 m will be 1.1 degrees Celsius.

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An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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the total posible is

Julia points

Julia had less than 80 points

The missing dimensions from the given expression should be completed with the following:

(81.) A) 2

(82.) AD) x

(83.) E) 12

The expression as a product should be written as: DE) 2(x + 12).

In Mathematics and Geometry, a factored form can be defined as a type of quadratic expression that is typically written as the product of two (2) linear factors and a constant.

In this scenario and exercise, we would complete the table above by showing the factored form and expanded form of each of the given expressions as follows;

        x           12

2      2x         24

Note: 2x/2 = x.

         24/2 = 12.

(2x + 24) = 2(x + 12).

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Answer:

A

Step-by-step explanation:

You know that you can simplify 6/9 because both the numerator (top number) and denominator (bottom number) can be divided by 3. Therefore, you divide them by 3 to get 2/3. 2/3 cannot be simplified anymore. 2/3 is equal to 2/3. Therefore, the answer is A.

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Answer:

  15 mph

Step-by-step explanation:

The cyclists will cover distance at a rate proportional to their speed. So, the distance ratio is ...

  faster cyclist distance : slower cyclist distance = 3 : 1

Then the faster cyclist covers 3 : (3+1) = 3/4 of the total distance, or (3/4)(40 mi) = 30 mi.

That distance took 2 hours for the faster cyclist, so the speed was ...

  speed = distance/time = 30 mi/(2 h) = 15 mi/h

Therefore, the longest length of pencil that John can hide in the pencil holder is approximately 127.32 cm (rounded to two decimal places).

Given that John has a 100 cm³ pencil holder, the longest length of pencil he can hide in the pencil holder can be found by using the formula for the volume of a cylinder which is given by: V = πr²h where r is the radius of the cylinder and h is the height of the cylinder.The volume of a cylinder can also be expressed as V = lwh where l is the length of the cylinder, w is the width of the cylinder and h is the height of the cylinder.

If we assume that the pencil is cylindrical in shape, then its volume can be given by V = πr²l where r is the radius of the pencil and l is the length of the pencil.Since the volume of the pencil holder is given to be 100 cm³, then we have:100 = πr²h (Equation 1)

Now, we need to find the value of l that can fit inside the pencil holder. We can use the formula for the volume of the pencil to do this as follows:

V = πr²lLet V = 100 cm³ and

r = 0.5 cm

(since the pencil holder is cylindrical in shape, we can assume that it has a radius of 0.5 cm)Then, we have:100 = π(0.5)²lSolving for l, we get:

l = 100 / (π(0.5)²)

l = 100 / (0.7854)l ≈ 127.32 cm

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\( \sqrt[3]{b {}^{2} } = b {}^{ \frac{2}{3} } \)

\(f(4) = 2(3) {}^{4} = 2 \times 81 = 162\)

\(f( \frac{1}{2} ) = \frac{1}{3} (9) {}^{ \frac{1}{2} } + 5 = \frac{ \sqrt{9} }{ 3} + 5 = 6\)

\(f(5) = - 4(2) {}^{ - 5 + 1} = - 4(2) {}^{ -4} = \frac{2 {}^{2} }{2 {}^{4} } = \frac{1}{2 {}^{2} } = \frac{1}{4} \)

\(f(10) = 2e {}^{0.15 \times 10} = 2e {}^{1.5} = 8.96\)

\(y = 10(b) {}^{x} \: \: \\ 10 = 10(b) {}^{0} \: duh \\ 2 = 10b {}^{1} \\ b = \frac{2}{10} = \frac{1}{5} \)

\(y = a(b) {}^{x} \\ 3 = a(b) {}^{0} \\ a = 3 \\ \\75 = 3(b) {}^{2} \\ b {}^{2} = 25 \\ b = + 5 \: \: \: or \: \: \: \: b = - 5\)

\(s = 1000(1 + \frac{0.045}{4} ) {}^{4 \times 10} = 1564.38\)

\(s = 2500.e {}^{0.07 \times 20} = 10138\)

Answer:

Step-by-step explanation:

5-3=2x2=4

ANSWER IS:4

It is true, Mai can conclude that the diagonal WY bisects the angles ZWX and ZYX

Since Mai has proven triangles WYZ and WYX to be congruent by the SSS triangle Congruence Theorem, she can conclude that:

Diagonal WY bisects angles ZWX and ZYX because:

all corresponding parts of both triangles are congruent. (Option A).

If two triangles are proven to be congruent to each other, it means that all three pairs of corresponding sides and angles of both triangles are congruent and equal to each other.

Thus, since Mai has proven triangles WYZ and WYX to be congruent by the SSS Triangle Congruence Theorem, therefore, all corresponding parts of both triangles are congruent.

If this is so, then Mai can conclude that angles ZWX and ZYX are bisected by diagonal WY. (Option A is correct).

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Answer:

60km is 37 Miles

it is a decimal- 37.2 Miles

Step-by-step explanation:

divide 60 by 1.609

Answer: using this we can say that 60km is 37.5 miles

Step-by-step explanation:

first you divide 60 and 8 which gives us 7.5

using this we multiply 7.5*5=37.5

No, the inference is not valid because it excluded those who were not online and so did not see the poll.

To improve the poll, the news show could have conducted it in a more representative manner by surveying a larger sample of people from a variety of backgrounds

The poll's results may have been influenced by various factors, including but not limited to the order in which the comedians were presented, the demographics of the respondents, and the fact that it was conducted online, possibly excluding those without internet access. Overall, the poll's representative accuracy is questionable.

To enhance the accuracy of the survey, the broadcast could have implemented a more inclusive method by polling a wider range of individuals from diverse backgrounds. An alternate method for conducting the poll would have been by personal or telephonic means, enabling individuals without internet connectivity to participate.

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We can see that g(x) is a translation of 4 units to the left of f(x), then:

g(x) = log₃(x + 4).

Here we can see that g(x) is a shift of f(x). Is clear that the asymptote of g(x) is 4 units to the left of the asymptote of f(x), so we can say that g(x) is a shift of 4 units to the left of f(x).

Remember that for a given function f(x), an horizontal shift of N units is given by:

g(x) = f(x + N).

Then a shift of 4 units to the left is written as:

g(x) = log₃(x + 4).

Then the correct option is the last one.

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Answer: 9/30

Step-by-step explanation:

a) A table and a graph for this situation is shown in the image below.

b) You can use the table or graph to predict how many weeks it will take Martha to earn enough money to pay for the new computer by comparing the week when her savings are both equal.

c) Since the x-value and y-value in both the table and the graph increase simultaneously, it is an example of linear growth.

In this scenario, the variable x would represent the number of weeks while the variable y would represent the total amount of savings. Since Martha received $200 for her birthday and makes $150 each week, a linear equation in slope-intercept form that models the situation is given by;

y = mx + c

y = 150x + 200

Next, we would use an online graphing calculator to make a table and a graph for this situation as shown in the image attached below.

Part b.

The table and the graph both have the total amount of savings (y) equal to $1,850 when x is equal to 11 weeks. This ultimately implies that, it would take Martha between 11 weeks to save enough money to buy this new computer.

Part c.

By critically observing the table and the graph, we can logically deduce that there is a linear relationship between the variables because both the x-value and y-value increase simultaneously.

Therefore, this is an example of a linear growth.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

4 and ∠6 are vertical angles, so ∠4 is congruent to ∠6.

∠4 and ∠6 are alternate interior angles, so ∠4 is congruent to ∠6.

Step-by-step explanation:

Answer:

2.72/3=0.907 (correct to three decimal places)

Step-by-step explanation:

Answer:

8-2^x7

Step-by-step explanation:

Answer:

x = -1,375

y = -5

Step-by-step explanation:

{-8x + y = 6, / : (-1)

{-8x + 3y = -14;

Multiply the first equation by -1, so that we could eliminate 8x:

+ {8x - y = -6,

{-8x + 3y = -14;

----------------------

4y = - 20 / : 4

y = -5

Now, make x the subject from the first equation (you can do it from the 2nd one instead):

8x = -6 + y / : 8

x = -0,75 + 0,125y

x = -0,75 + 0,125 × (-5) = -0,75 - 0,625 = -1,375

The only place that the function is increasing is [-3, -1].

(learn your interval notation).

At x = -3, y = -11

In the increasing intervals of a given function, one must determine the intervals where the function has a positive first derivative. To find these intervals, first, find the critical values or the points at which the first derivative of the function is equal to zero.

at x = -2, y = -6 (-6 is greater than -11);

and at x = -1, y = -1 (-1 is greater than -6).

The next x value, 0, returns a y value of -2.

But -2 is less than -1, the value before it, So it begins decreasing again at x = 0.

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The width of the rectangular base of the pyramid is approximately 3.74 cm, and the length is approximately 11.22 cm (since it is given as 3x+1).

The base of a pyramid can be any polygon, such as a square or a triangle, but the height must always be measured perpendicular to the base.

Dimensions refer to the number of coordinates needed to specify the location of an object in space.

Based on the given information, we can set up an equation to solve for x, which is the width of the rectangular base of the pyramid:

Volume of pyramid = 1/3 × base area ×height

96 = 1/3 ×(3x+1) × x ×12

Simplifying the equation:

96 = 4x² + (4/3)x

Multiplying both sides by 3 to eliminate the fraction:

288 = 12x² + 4x

Rearranging the equation into a quadratic form:

12x² + 4x - 288 = 0

Dividing both sides by 4 to simplify the equation:

3x² + x - 72 = 0

We can then use the quadratic formula to solve for x:

x = (-b ± \(\sqrt{(b^2-4ac)}/2a\)

where a = 3, b = 1, and c = -72.

Plugging in the values:

x=(-1±\(\sqrt{1^2-4(3)(-72)} /2(3)\))

x=(-1±\(\sqrt{1+864} /6\))

x = (-1 ±\(\sqrt{865} /6\) )

Since the width of the base cannot be negative, we take the positive solution:

x = (-1 + √(865) / 6

Therefore, the width of the rectangular base of the pyramid is approximately 3.74 cm, and the length is approximately 11.22 cm (since it is given as 3x+1).

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Answer:

Step-by-step explanation:

To simplify the fraction, write the multiples of the numerator and denominator.

Hence, the simplified fraction is 3/20.

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Answer:

good day of school and➕➕ I have a great day of school and I have a great day☀☀☀ of school and➕➕ I

The solution is ± √5

The value of the equation is given by x = ± √5

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is given by

x² = 5   be equation (1)

On simplifying the equation , we get

x² = 5

Taking the radical form , radical notation is the usage of a root in an expression, such as the square or cube root

So , taking square roots on both sides of the equation , we get

The value of x = ±√5

Therefore , the value of A is ±√5

Hence , The value of the equation is given by x = ± √5

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Step-by-step explanation:

from which text book please

The half life of the radioactive Rutherford-265 is;

13.1 hours.

It follows from the task content that the given function represents the decay function of the radioactive material. Since half-life corresponds to the point at which only half of the starting material remains, hence we have;

(1/2) = e ^(-0.053t)

By taking the natural log of both sides, we have;

-0.6931 = -0.053t

Hence, t = -0.6931/ -0.053 = 13.1 hours.

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