Express the following in exponen
(-13) X ... X (-13).
35 times
Exponential notation

\(2~~,~~\stackrel{2-5}{-3}~~,~~\stackrel{-3-5}{-8}~~,~~...~\hspace{10em}\stackrel{common~difference}{d = -5} \\\\[-0.35em] ~\dotfill\\\\ n^{th}\textit{ term of an arithmetic sequence} \\\\ a_n=a_1+(n-1)d\qquad \begin{cases} a_n=n^{th}\ term\\ n=\stackrel{\textit{term position}}{64}\\ a_1=\stackrel{\textit{first term}}{2}\\ d=\stackrel{\textit{common difference}}{-5} \end{cases} \\\\\\ a_{64}=2+(64-1)(-5)\implies a_{64}=2+(-315)\implies a_{64}=-313\)

Answer:

-313 is the 64th term

Step-by-step explanation:

you take the second term an minus the first term with the second one {2-(-3)}

{=5} then you take two an minus five

it gives you -3 then you press minus five again it gives you negative eight then you press (equals to)until you reach the term you looking for

Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.

In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.

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Answer:

A. Covering the entire box is the surface area, which is 664 in.

Step-by-step explanation:

I did the test myself. Have a great day/night! Good luck with the rest of your test! <3

1. We know that it is exponential growth since it has a positive exponent.

2. The exponential growth rate is 1%.

Exponential growth is a pattern of growth in which a quantity grows over time at an ever-increasing rate. The rate of expansion in an exponential growth process is proportional to the quantity's current value.

It's vital to keep in mind that exponential growth is an idealized concept and may not always be possible in practical circumstances.

Given that;

2 = 1 + r

r = 2- 1

r = 1%

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Answer:

7s + 2t

Step-by-step explanation:

4s + 2t + s + s + s

7s + 2t

Answer:

-4(2x+5) = -8x-20

Step-by-step explanation:

Hope this helps!

Answer:

120 days

Step-by-step explanation:

There are 31 days in January, 28 in February (this was not a leap year), 31 in March and 30 in April. All you have to do now is add 31 + 28 + 31 + 30 for a final answer of 120 days!

Answer:

120

Step-by-step explanation:

January: 31

February: 28

March: 31

April: 30

31+28+31+30=120

Solution :

Given initial velocity, v= 48 ft/s

Acceleration due to gravity, g = \($12\ ft/s^2$\)

a). Therefore the maximum height he can jump on Mars is

     \($H_{max}=\frac{v^2}{2g}$\)

     \($H_{max} = \frac{(48)^2}{2 \times 12}$\)

               = 96 ft

b). Time he can stay in the air before hitting the ground is

   \($T=\frac{2v}{g}$\)

  \($T=\frac{2 \times 48}{12}$\)

     = 8 seconds

c).  Considering upward motion as positive direction.

     v = u + at

We find the time taken to reach the maximum height by taking v = 0.

     v = u + at

     0 = 16 + (12) t

     \($t=\frac{16}{12}$\)

        \($=\frac{4}{3} \ s$\)

We know that, \($S=ut + \frac{1}{2}at^2$\)

Taking t =  \($=\frac{4}{3} \ s$\)  , we get

\($S=16 \times\frac{4}{3} + \frac{1}{2}\times(-12) \times \left(\frac{4}{3}\right)^2$\)

\($S=\frac{32}{3}$\)  feet

Thus he can't reach to 100 ft as it is shown in the movie.

d). For any jump whose final landing position will be same of the take off level, the final velocity will be the initial velocity.

Therefore final velocity is = -16 ft/s

Answer:

They are both the same because the coefficient of -0.52 is negative and 0.52 is a positive which makes 0.52 a stronger coefficient.

Answer:

do it on a calculater

Step-by-step explanation:

but it equels  2 and 22║27

Solving an equation in algebra - mathematics will BOMDAS rule. Multiplication, division, addition, and subtraction are performed before.

However, in order to simplify things, if there are any exponential or logarithmic components, solve them first before applying BOMDAS to reduce them to a single solvable term. This is required by the rules.

So the list goes as

1. Exponents

2. Roots

3. Multiplication

4. Division

5. additional

6. Subtraction

However. Using a regular or scientific calculator will generate a lot of debate. A scientific calculator will adhere to the principles, while a typical calculator will evaluate from left to right or precisely the operator used first.

Using a scientific calculator, 5+2x3=11 instead of the normal one's 5+2x3=21.

Furthermore, the preferred behavior norm for division and multiplication is different.

Thus, people's difficulty with mathematics is not unjustified. The choice of how you want to approach it is ultimately up to you.

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The Intermediate Value Theorem (IVT) states that for any continuous function f(z) and any real number a, if f(a) and f(b) have opposite signs, then there exists a number c in the interval (a,b) such that f(c) = 0.

The IVT states that if a continuous function has different signs (positive or negative) at two points in its domain, then it must have a zero in between those two points. In the case of the function f(z) = 26z^53 + 3, we are asked to find an integer n such that there exists a zero of the function in the interval [n/4, (n + 1)/4].

To find the solution, we can use the IVT by considering two points in the interval with opposite signs. For example, if we take n = 1, then the interval is [1/4, 2/4]. We can evaluate the function at the two endpoints of the interval and look for opposite signs:

f(1/4) = 26 * (1/4)^53 + 3 > 0

f(2/4) = 26 * (2/4)^53 + 3 < 0

Since the function has opposite signs at the endpoints, the IVT guarantees that there exists a zero of the function in the interval [1/4, 2/4]. This means that for n = 1, the IVT is satisfied and the function has a zero in the interval [1/4, 2/4].

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Complete Question:

For which integer n, 0 < n < 3 , does the IVT say that f(z) 26 53 + 3 has & zero in the interval [n/4, (n + 1)/4]?

The measures of the angles are ∠1 = 127°, ∠2 = 53°, ∠3 = 127°, ∠4 = 37°, ∠5 = 53°, ∠6 = 90°, ∠7 = 37°, ∠8 = 143°, ∠9 = 37° and ∠10 = 143°

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

The transversal lines and the other lines

So, we have

∠1 = 180 - 53

Evaluate

∠1 = 127°

Also, we have

∠5 = 53°

By vertical angles, we have

∠2 = 53°

∠3 = 127°

Next, we have

∠4 = 127 - 90°

∠4 = 37°

Solving further, we have

∠6 = 90°

By corresponding angles, we have

∠7 = 37°

∠9 = 180 - 90 - 53°

∠9 = 37°

∠10 = 90 + 53°

∠10 = 143°

∠8 = 143°

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The given equation, 16x² - y² + 16z² = 4, represents a quadric surface known as an elliptic paraboloid.

To determine the classification, we can examine the coefficients of the squared terms. In this case, the coefficients of x², y², and z² are positive, indicating that the surface is bowl-shaped. Additionally, the signs of the coefficients are the same for x² and z², indicating that the bowl opens upward along the x and z directions.

The negative coefficient of y², on the other hand, means that the surface opens downward along the y direction. This creates a cross-section in the shape of an elliptical parabola.

Considering these characteristics, the given equation represents an elliptic paraboloid.

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The recursive geometric sequence that models this situation is:

\(f(n) = 0.9f(n-1)\)

\(f(1) = 90000\)

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

It can be represented by a recursive sequence as follows:

\(f(n) = qf(n-1)\)

With f(1) as the first term.

In this problem, the sequence is: 90.000: 81,000; 72,900; 65,610, hence:

\(q = \frac{65610}{72900} = \cdots = \frac{81000}{90000} = 0.9\)

\(f(1) = 90000\)

Hence:

\(f(n) = 0.9f(n-1)\)

\(f(1) = 90000\)

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Answer: 2 log y - log 25

Step-by-step explanation:

Notes: Division expands to subtraction.  Exponent expands to multiplication.

\(log\bigg(\dfrac{y}{5}\bigg)^2\\\\\\=log\bigg(\dfrac{y^2}{5^2}\bigg)\\\\\\=log(y^2)-log(5^2)\\\\\\=\large\boxed{2log(y)-log(25)}\)

The statement a base class cannot contain a pointer to one of its derived classes is false because a base class can indeed contain a pointer to one of its derived classes.

In object-oriented programming, a base class can have a pointer to one of its derived classes. This is known as upcasting or polymorphism. Upcasting allows for the flexibility of treating derived class objects as instances of the base class.

By using pointers, a base class can refer to derived class objects and access their member functions and variables. This enables the base class to work with different derived classes without needing to know their specific types.

Pointers to derived classes can be stored in base class member variables or passed as function parameters. This allows for dynamic binding and the ability to invoke overridden functions based on the actual derived class type at runtime.

This concept is fundamental to achieving polymorphism and code reusability in object-oriented programming languages like C++ and Java. It facilitates the implementation of inheritance hierarchies and the ability to work with objects of different derived classes through a common base class interface.

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Answer:

Open the image. (Hope you don't mind about bad writing)

Using the formal definition of the derivative we get the required proof is f '(0) + 3 f '(-1) = 0.

Let's find the derivative of the function by using the formal definition of the derivative.

Firstly, we need to find the difference quotient, f(x + h) - f(x)/h.ƒ (x) = 2x² + 3x − 5f(x + h) = 2(x + h)² + 3(x + h) − 5 = 2(x² + 2hx + h²) + 3x + 3h - 5f(x + h) - f(x) = 2(x² + 2hx + h²) + 3x + 3h - 5 - 2x² - 3x + 5f(x + h) - f(x) = 2x² + 4hx + 2h² + 3hƒ(x + h) - ƒ(x)/h = 2x + 4h + 3(because, (a + b)² = a² + 2ab + b²)

Then we find the limit as h approaches 0.f'(x) = lim (h→0) [ƒ(x + h) - ƒ(x)]/h= lim (h→0) [2x² + 4hx + 2h² + 3h - 2x² - 3x + 5]/h= lim (h→0) [4hx + 2h² + 3h + 5]/h= lim (h→0) 4x + 2h + 3= 4x + 3 (Therefore, the derivative of the function f(x) is 4x + 3)f'(-1) = 4(-1) + 3= -1f '(-1) = -1 and f '(-1) = -7

Let's substitute in the formula:f '(0) + 3 f '(-1) = 0 ƒ(x + h) - ƒ(x)/h = 2x + 3ƒ'(0) = 2(0) + 3 = 3

Now, substituting the values in the given formula:f '(0) + 3 f '(-1) = 03 + 3(-1) = 0-3 = 0

Therefore, the required proof is f '(0) + 3 f '(-1) = 0.

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The "count to infinity" problem in distance vector routing occurs when a routing loop arises due to a node receiving updates from its neighbor nodes that advertise new routes.

When the node that receives updates from its neighbors realizes that a new route is available, it adds the cost of that route to its existing distance vector table, and then broadcasts the updated table to its neighbors.

However, if a route has been lost, then the node that originally advertised that route will not be aware of this change, and will continue to advertise the lost route to its neighbors.

If the receiving node updates its distance vector table with the advertised lost route, then it will have a larger number in its distance vector table, which will lead to a longer path being chosen.

This process can continue indefinitely, resulting in a count to infinity situation where nodes advertise increasingly longer paths, and the network becomes unstable. To prevent this, several techniques have been developed, such as split horizon, poison reverse, and route holddown.

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Answer:

y = 5x + 4

Step-by-step explanation:

Hope it helps.

Answer:

option B

1/ 3x^2(a-b)

Step-by-step explanation:

The probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

To calculate the probability of rolling all six numbers at least once when rolling a six-sided die 12 times, we can use the concept of permutations.

The total number of possible outcomes when rolling a six-sided die 12 times is 6^12 since each roll has six possible outcomes. This represents the denominator of our probability calculation.

Now, let's calculate the numerator, which represents the number of favorable outcomes where we get all six numbers at least once. We can use the concept of derangements (or the principle of inclusion-exclusion) to determine this.

A derangement is a permutation in which none of the elements appear in their original position. In our case, we want to find the number of derangements for a set of six elements (the six numbers on the die).

The formula to calculate the number of derangements for a set of n elements is given by n! * (1 - 1/1! + 1/2! - 1/3! + ... + (-1)^n/n!).

Using this formula, we can calculate the number of derangements for six elements:

Number of derangements = 6! * (1 - 1/1! + 1/2! - 1/3! + 1/4! - 1/5! + 1/6!) = 265

Therefore, the numerator of our probability calculation is 265.

Finally, we can calculate the probability by dividing the numerator by the denominator:

Probability = Number of favorable outcomes / Total number of possible outcomes = 265 / 6^12

Calculating this value:

Probability ≈ 0.0263

So, the probability of rolling all six numbers at least once when rolling a six-sided die 12 times is approximately 0.0263, or about 2.63%.

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Answer: C.

Step-by-step explanation:

If ABCD gets rotated 180ᴼ, you will be able to see the reflection of ABCD to A’B’C’D’. Then just reflect across the x-axis (horizontal) to transform ABCD onto A’B’C’D’.

Answer:

Step-by-step explanation:

I have taken Biology

Congruent triangles are also frequently employed in architectural designs, carpet patterns, stepping stone patterns, and geometric art.

The following are the two most typical instances of this: Equilateral triangles are used to make truss bridges, which are built on both sides.

Congruence :

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. A term used to describe an object and its mirror counterpart is congruence. If two things or shapes superimpose on one another, they are said to be congruent. They are identical in terms of size and shape. Line segments having the same length and angles with the same measure are congruent in the context of geometric figures.

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The proportional equation for the number of oranges ( n ) and the cost of oranges ( p ) is given by p = 0.42n

The proportion formula is used to depict if two ratios or fractions are equal. The proportion formula can be given as a: b::c : d = a/b = c/d where a and d are the extreme terms and b and c are the mean terms.

The proportional equation is given as y ∝ x

And , y = kx where k is the proportionality constant

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

Given data ,

Let the proportion equation be represented as A

Now , the value of A is

Let the cost of one orange be k

Let the cost of 6 oranges be = $ 2.52

So , the cost of 1 orange k = 2.52 / 6 = 0.42

Now , let the number of oranges be n

Let the total cost of n oranges be p

On simplifying , we get

The total cost of n oranges p = cost of 1 orange k x number of oranges n

p = 0.42n   be equation (1)

Hence , the proportion equation is p = 0.42n

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The area of the triangle is 31.54 square units

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

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

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

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

a. range: 4

b. 5 students

c. mean: 8

Step-by-step explanation:

range: subtract the smallest number from the largest number in the data.

10 - 6 = 4

students amount was counted by the number of marks given.

mean: add the data together. (40) divide the sum by the number of marks provided. (5)

40 divided by 5 equals 8

Answer:

4   244   8

Step-by-step explanation:

10 - 6 = 4 is the range

6x5 = 30   7x4 = 28  8x7 = 56 9x10 = 90 10x4 = 40 244 students

mean = 6+7+8+9+10 = 40/5 = 8