Pearce needs to choose a variable to represent the number of wallabies in an exhibit. Which variable would be the best choice? Explain.

Answer:

"An expression that represents repeated multiplication of the same factor is called a power. The number 5 is called the base, and the number 2 is called the exponent. The exponent corresponds to the number of times the base is used as a factor." -wwwmathplanet.com

Answer:

an expression tells hiw many times is base used

Answer:

1.Suppose 3 | 2x. Then we can write 2x = 3k for some integer k. Rearranging, we have x = (3/2)k. Since k is an integer, (3/2)k is also an integer, which means that x is divisible by 3. Hence, 3 | x.

First, suppose 3 | (2n^2 + 1). Then we can write 2n^2 + 1 = 3k for some integer k. Rearranging, we have 2n^2 = 3k - 1. Since 3k - 1 is odd, we can write it as 2m + 1 for some integer m. Substituting, we have 2n^2 = 2m + 1, which implies that n^2 = m + (1/2). But since m is an integer, (1/2)m is not an integer, which means that n^2 is not an integer. This is a contradiction, so our assumption that 3 | (2n^2 + 1) must be false.

Now suppose 3 - n. Then we can write n = 3k - 1 for some integer k. Substituting, we have 2n^2 + 1 = 18k^2 - 12k + 3. Factoring out 3, we have 2n^2 + 1 = 3(6k^2 - 4k + 1). But 6k^2 - 4k + 1 is always an integer, so if 3 - n, then 3 | (2n^2 + 1).

give me thanks for more! your welcome!

Step-by-step explanation:

The crank angle value when the piston is at Top Dead Center (TDC) is 0 radians or 0 degrees. The maximum ratio of the crank radius to the connected length is 0.3.

The crank angle value refers to the angle between the crankshaft and a reference point when measuring the position of the piston. When the piston is at Top Dead Center (TDC), it is at its highest point in the cylinder. The crankshaft is positioned such that the connecting rod is aligned with the crank radius and the piston is at the topmost position. This corresponds to a crank angle value of 0 radians or 0 degrees.

Regarding the maximum ratio of the crank radius to the connected length, this value is given as 0.3. The crank radius is the distance from the center of the crankshaft to the center of the crank pin, and the connected length is the distance from the center of the crank pin to the center of the piston pin. The maximum ratio of 0.3 indicates that the crank radius is 0.3 times the connected length.

It's important to note that these values are specific to the context of the problem statement provided. Different engines or mechanisms may have different values for the crank angle at TDC and the maximum ratio of crank radius to connected length.

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The SRED Credit remainder after applying the maximum SRED Credit for this year is $0. This means that the company has fully utilized the maximum SRED credit available for the current year.

The Scientific Research and Experimental Development (SRED) program is a tax incentive program offered to companies for conducting eligible research and development activities. The SRED credit is calculated based on the qualified SRED expenses incurred during the year.

In this scenario, the company has qualified SRED expenses of $10,000 for the current year. However, the SRED credit remainder is determined after applying the maximum SRED credit for the year. The maximum SRED credit represents the maximum allowable amount that can be claimed as a credit.

Since the SRED Credit remainder is $0, it indicates that the company has already utilized the maximum SRED credit available for this year. Therefore, there is no remaining credit to be applied, and the company will not receive any additional credit for its qualified SRED expenses.

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So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

Given

r= 2cost and theta = 9t

To Find

the velocity and acceleration vector

Solution

We can start by expressing the position vector r in terms of the Cartesian coordinates x and y:

x = r cos(theta) = 2cos(t)

y = r sin(theta) = 2sin(t)

To find the velocity vector, we can take the time derivative of the position vector:

v = (dx/dt) i + (dy/dt) j

where i and j are the unit vectors in the x and y directions, respectively.

Taking the derivatives:

dx/dt = -2sin(t)

dy/dt = 2cos(t)

Substituting these back into the velocity vector equation:

v = (-2sin(t)) i + (2cos(t)) j

To find the acceleration vector, we can take the time derivative of the velocity vector:

a = (d^2x/dt^2) i + (d^2y/dt^2) j

Taking the derivatives:

d^2x/dt^2 = -2cos(t)

d^2y/dt^2 = -2sin(t)

Substituting these back into the acceleration vector equation:

a = (-2cos(t)) i + (-2sin(t)) j

So the velocity vector is v = (-2sin(t)) i + (2cos(t)) j, and the acceleration vector is a = (-2cos(t)) i + (-2sin(t)) j, both in terms of t.

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Considering the given triangle :

GIVEN :

• Opposite side to angle = 34

• Adjacent side to angle = 48

• We will use Tan = opposite /adjacent trigonometric fuction tocalculate angle

CALCULATIONS:

Step-by-step explanation:

8.

the angle at a vertex (crossing point) outside of the circle (when both lines intersect with the circle arc, which is also the case for tangents) is half of the difference of both arc angles (the outer and the inner angles).

the outer angle is 250°. since the full circle is 360°, this makes the inner arc angle 360-250 = 110°.

the difference is 250-110 = 140.

and half of that difference is

140/2 = 70°.

so, x = 70°

9.

see 8.

the angle at the vertex outside the circle is half of the difference between outer and inner arc angle.

in fact, this is again about tangents (despite the picture), because the outer angle + the inner angle is again 360° (the full circle). this can only be, if the 2 lines are tangents splitting the outer and inner arc angles into 2 parts of 360° without remainder.

320 - 40 = 280

280/2 = 140

x = 140°

10.

see 8. and 9.

it is an extreme example, where the vertex of the 2 intersecting lines is exactly on the circle arc and the tangent point of the second line.

this makes the inner arc angle = 0°.

remember, the vertex angle (55°) is half of the difference of the outer (x) and inner (0°) arc angle.

55 = (x - 0)/2

110° = x

11.

remember the table question, where we found that the circle internal angle of 2 intersecting lines is half of the sum of both intersected arc angles ?

this is exactly this case again.

(120 + 50)/2 = 170/2 = 85°

x = 85°.

12.

first, like in 8. and 9., we determine the vertex angle. x is then the supplementary angle (together they have 180°) to this vertex angle, because the sum of all angles around one point on one side of a line is always 180°.

the vertex angle is

(125 - 15)/2 = 55°

x + 55 = 180

x = 125°.

13.

see 11.

the circle internal vertex angle is half of the sum of both circle arcs.

x = (70 + 30)/2 = 100/2 = 50°.

14.

again, an extreme case, where the vertex is on the circle arc. so, the second arc angle is 0°.

see also 12.

x is the supplementary angle of the vertex angle.

the vertex angle is

(80 + 0)/2 = 80/2 = 40°.

x + 40 = 180

x = 140°.

15.

it is difficult to read. I see the outer arc circle as 140°.

see 8., 9., 10.

the vertex angle x is

x = (140 - 70)/2 = 70/2 = 35°

do I sound like a broken record ? I at least feel that way. you should be able to apply the explanations from the previous questions to solve the new ones yourself.

what is not clear yet ? where do you need further explanations ?

It took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

Let L(t) be the amount of undeveloped land in acres at time t, where t is measured in years since 2002. Then, we can write:

L(t) = 30 * (7/8)^t

We know that the amount of undeveloped land we are interested in is approximately 15.39 acres. Therefore, we can set up the following equation:

15.39 = 30 * (7/8)^t

To solve for t, we can first divide both sides by 30:

0.513 = (7/8)^t

Next, we can take the natural logarithm of both sides:

ln(0.513) = ln[(7/8)^t]

ln(0.513) = t * ln(7/8)

t = ln(0.513) / ln(7/8)

t ≈ 5.3

Therefore, it took approximately 5.3 years for the amount of undeveloped land to decrease to approximately 15.39 acres, starting from 30 acres in 2002.

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Answer:

Isolate the mDivide both sides by 8:Simplify the fraction:Find the greatest common factor of the numerator and denominator:Factor out and cancel the greatest common factor:

Then you get m=1/2

Step-by-step explanation:

The rotation used in this problem is given as follows:

90º clockwise rotation.

The five more known rotation rules are given as follows:

A vertex and it's equivalent is given as follows:

A(1,3) and A'(3, -1).

Hence the rule is:

(x,y) -> (y, -x).

Which is the rule for a 90° clockwise rotation = 270º counterclockwise rotation.

The image is presented at the end of the answer.

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Answer:

90° clockwise rotation

Step-by-step explanation:

I did the exam and got it correct

Answer: 4

Step-by-step explanation:

By finding the relative frequency, we will see that we can expect that 4 out of the next 20 sundaes will have nuts.

First, we know that 2 out of the last 10 sundaes sold had nuts. So the relative frequency of sundaes with nuts is:

R = 2/10 = 0.2

(the quotient between the number of sundaes with nuts and the total number of sundaes)

Then, out of the next 20 sundaes, we can expect that the number of sundaes with nuts will be:

N = R*20 = 0.2*20 = 4

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The coordinates of V' after reflection(Dilation) across y=-x will be (3,1).

In mathematics, what is dilation?

Dilation is the process of changing the size of an object or form by shrinking or extending its dimensions based on certain scale variables. For example, a circle with radius 10 unit is decreased to a circle with radius 5 unit and there are only four basic types of transformations. They are as follows:

Some characteristics stay constant during dilation are:

Now,

Before reflection

Coordinates of V are (−3, −1).

and reflection of V is across y=-x, which will make values for x and y opposite or change the sign of coordinates.

then coordinates of V' are (3,1)

hence,

           The coordinates of V' after reflection(Dilation) across y=-x will be (3,1).

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Answer:

4,813,431.07 ft³

\(V = \frac{1}{3} \pi r^2h\\\\V = \frac{1}{3} * 3.14 * \frac{307}{2^2} * 195\)

    \(= 4,813,431.07\)

Answer:

144 in^2

Step-by-step explanation:

Using the A = s^2 and the text says that s= 12in

 the answer is 12 in * 12 in = 144 in^2

Amy will choose the second restaurant to purchase pizza. Because the second one is cheaper.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given,

the first restaurant charges a delivery fee of $6 for the entire purchase and $13 per pizza.

The second restaurant has no delivery fee and charges $16 per pizza.

And Amy will choose between two restaurants to purchase pizzas for her party.

The cost of one pizza of the first restaurant:

Cost = delivery fee + price of one pizza

        = $6 + $13

         = $19

The cost of one pizza of the second restaurant:

Cost = delivery fee + price of one pizza

          = $0 + $16

         = $16

And 16< 19

The second restaurant is cheaper.

Therefore, Amy will choose the second restaurant to purchase pizza.

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The equivalent expression for the expression that represents the amount Carmen would earn is 5000(1.0005^12)^t.

Based on the expression given, Carmen's investment is compounded monthly.

The formula for calculating future value:

FV = P (1 + r)^nm

5000(1.0005)^12t

= 5000(1.0005^12)^t

50002.5^12t

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Answer:

\(x = \sqrt{ \frac{36}{49} } = + \frac{6}{7} \: \: or \: - \frac{6}{7} \)

The weight gained by the spot dog during his time is 57/2 ounces.

An operation is a function in mathematics that converts zero or more input values, also known as "operands" or "arguments," into a clearly defined output value. The operation's complexity is determined by its operand count.

The most frequently studied operations are unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication. The nullary operation, also known as an operation of arity zero, is a constant. A ternary operation, also known as an operation of arity 3, is an example of the mixed product.

Given that, spot the Dog gained 4 3/4 ounces each week for the first 6 weeks of his life.

Convert the mixed fraction into improper fraction:

4 3/4 = 19/4 ounces

The weight gained for 6 weeks is:

19/4 (6) = 114/4 = 57/2

Hence, the weight gained by the spot dog during his time is 57/2 ounces.

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Answer:

96,470,000

Step-by-step explanation:

10^7=10,000,000

10,000,000 * 9.647= 96,470,000

Hope this helps!

Answer:

x=6 and y=0

Step-by-step explanation:

1. 15-3=12

2. 12÷2=6 6=x

3. 6-6=0 0=y

The true proportion of the side lengths of the quadrilaterals is A'B'/AB

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

Quadrilaterals ABCD and A'B'C'D

These quadrilaterals are similar

So, it means that the corresponding side lengths are proportional

So. we have

Side length = AB

Corresponding side length = A'B'

The true proportion is then represented as

k = Corresponding side length/Side length

Substitute the known values in the above equation, so, we have the following representation

k = A'B'/AB

Hence, the proportion is A'B'/AB

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Answer:

x = 10

Step-by-step explanation:

Divide both sides by 2.

(2x) / 2 = 20 / 2

x = 10

Answer:

The answer is going to be 10.

Step-by-step explanation:

1) Diving both sides by 2.

\(x = \frac{20}{2} \)

2) Simplify 20/2 to 10 because 20 ÷ 2 is 10.

\(x = 10\)

Therefor, the answer for x is x = 10.

The missing value is 6.

As per the question, y = -4. Keeping the value of y in the equations to find the value of x.

6x + 7(-4) = 4x + 4(-4)

Performing multiplication on each side of the equation

6x - 28 = 4x - 16

Rewriting the equation with identical values on each side of the equation

6x - 4x = 28 - 16

Performing subtraction on each side of the equation to find the value of x

2x = 12

Shifting 2 to Right Hand Side of the equation

x = 12 ÷ 2

Performing division on Right Hand Side of the equation

x = 6

Hence, the value of x is 6.

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The complete question is -

6x+7y=4x+4y

Complete the missing value in the solution to the equation.

(__,-4)

Answer:

Is 57, I just did it on a paper, hope it helped

Step-by-step explanation:

Answer:

ASA

Step-by-step explanation:

Answer:

$8

Step-by-step explanation:

If it's 75% of that mean 2=25%

multiply it by 4 to get 8

The median number of newspapers sold over seven weeks is 223.

The median is the middle score for a data set arranged in order of magnitude. The median is less affected by outliers and skewed data.

The formula for the median is as follows:

Find the median number of newspapers sold. (87, 87, 215, 154, 288, 235, 231)

We'll first arrange the data in ascending order.87, 87, 154, 215, 231, 235, 288

The median is the middle term or the average of the middle two terms. The middle two terms are 215 and 231.

Median = (215 + 231)/2

= 446/2

= 223

In statistics, the median measures the central tendency of a set of data. The median of a set of data is the middle score of that set. The value separates the upper 50% from the lower 50%.

Hence, the median number of newspapers sold over seven weeks is 223.

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\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Question:-}}}}\diamond\)

         Find the slope of the line that passes through (6, 9) and (9, 5).

\(\diamond\large\blue\textsf{\textbf{\underline{\underline{Answer and how to solve:-}}}}\diamond\)

\(\boxed{\\\begin{minipage}{3cm}\xrightarrow {slope\:formula\:below} \\ $\displaystyle\frac{y_2-y_1}{x_2-x_1}$ \\ \end{minipage}}}\)

Substitute 5 for y₂, 9 for y₁, 9 for x₂ and 6 for x₁:-

\(\boxed{\frac{5-9}{9-6}}\)

On simplification,

↬ \(\boxed{\frac{-4}{3}}\)

   ►So we conclude that the slope of the line is

 ►\(\boxed{-\frac{4}{3}}\) ◀︎

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Answer:

Step-by-step explanation:

Your answer

A = 73

B= 33

C = 40

D = 40

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