Work out the value of (2^3)^2 ?

Answer:

497.6 cm to 1 decimal place.

Step-by-step explanation:

→ Square root the area to find the length

√15476 = 124.4025723

→ Multiply the answer by 4 to get the perimeter

124.4025723 × 4 = 497.6102893

Answer:

497.6 cm

Step-by-step explanation:

Perimeter = 4 x a

Since area is given we must square root a

P = 4 x square root (\(\sqrt{15476}\))

P = 4 x (124.40)

P = 497.6 cm

Answer:

Step-by-step explanation:

n + 1 = 4(n - 8)

n + 1 = 4n - 32      [Multiply 4 times (n-8)]

1 = 3n - 32           [Subtract 1n from both sides]

33 = 3n               [Add 32 to both sides]

3n = 33

CHECK:

Does n + 1 = 4(n - 8) when n = 11?

n + 1 = 4(n - 8)

11 + 1 = 4(11 - 8)

11 + 1 = 4(3)

12 = 12   YES

Step-by-step explanation:

Use the Factor Theorem,

" if x-a is a factor of f(x), then f(a) =0,

So here, since x-3 is a factor then f(3)=0,

So first step, plug in 3 for x for the serperate equations.

\( {3}^{2} + ( p + q)3 - q = 0\)

\(2(3) {}^{2} + (p - 1)3 + (p + 2q) = 0\)

Simplify both equations,

\(9 + 3p + 2q = 0\)

\(15 + 4 p + 2q = 0\)

Isolate the constants,

\(3p + 2q = - 9\)

\(4p + 2q = - 15\)

We have a system of equations so let eliminate a variable, by subtracting the two equations.

\( - p = 6\)

\(p = - 6\)

Plug p back in for any one of the equations to find q.

\(3( - 6) + 2q = - 9\)

\( - 18 + 2q = - 9\)

\(2q = 4.5\)

So p is -6

q is 4.5

Annika will spend for the interest is $72.

Answer:

$72.

Step-by-step explanation:

The number of people died from aids in U.S. in 2005 are 2,30,68,96,671

Given, diseases tend to spread according to the exponential growth model.

In the early days of aids, the growth factor (i.e. common ratio; growth multiplier) was around 1.9.

In 1983, about 1700 people in the U.S. died of aids.

we have to find the number of people died from aids in 2005.

Let the exponential function, be

P(x) = AB^x

where, A is the initial population of people died of aids in U.S.

B is the growth factor of aids in U.S.

as, B = 1.9

In 1983, x = 0

P(0) = AB^0

1700 = A

Now, P(x) = 1700(1.9)^x

and the number of years from 1983 to 2005 are, 22 years

The number of people died from aids in 2005 be,

P(22) = 1700(1.9)^22

P(22) = 2,30,68,96,671

So, 2,30,68,96,671 people died from aids in 2005.

Hence, 2,30,68,96,671 people died from aids in 2005.

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Ordered pair (0, 6) and  (2, 7)  satisfy both inequalities in the system and are solutions to the system.

To identify the graph that represents the given system of inequalities y > x + 5 and y ≥ 2x + 3, we need to graph the individual inequalities and find the region where they overlap.

When we plot the graph of inequality separately:

    2. y ≥ 2x + 3:

The overlapping shaded region represents the solution to the system of inequalities.

To find two ordered pairs that are solutions to the system, we can choose any points within the overlapping region. Let's select two points:

Ordered pair 1: (0, 6)

Ordered pair 2: (2, 7)

These two points satisfy both inequalities in the system and are solutions to the system.

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The correct question is given below -

Identify the graph that represents the given system of inequalities. Also identify two ordered pairs that are solutions to the system.

y > x + 5

y ≥ 2x + 3

Answer:

Yes

Step-by-step explanation:

-3x+7=-17

      -7    -7

     -3x=-24

     _______

       x=8

The personnel director in this scenario is performing a convenience sampling.

Convenience sampling is a type of non-probability sampling method where the researcher selects participants based on their accessibility and proximity to the researcher. In this case, the personnel director chose employees from the department nearest her office for the study.

This approach may not provide a fully representative sample of the entire company's employee population, as it doesn't account for possible differences in eating habits across various departments. Therefore, the findings from this study might not accurately represent the proportion of employees who buy lunch in the cafeteria, bring their own lunches, or go out to lunch for the entire company.

To obtain more accurate results, the director might consider employing a probability sampling method, such as simple random sampling or stratified sampling, to ensure a more representative sample of the company's employees.

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Answer:

4294967293 dots

Step-by-step explanation:

Figure 1 has 5 dots.

Figure 2 has 13 dots.

Figure 3 has 29 dots.

Subtract and find different of each term:

Let \(\displaystyle \large{b_n}\) be sequence of difference (and the sequence appears to be geometric.)

So for \(\displaystyle \large{b_n}\), find the common ratio which is 2.

Hence, \(\displaystyle \large{b_n = 8(2)^{n-1}}\) - recall geometric sequence formula below:

\(\displaystyle \large{a_n = a_1r^{n-1}}\)

The sequence of difference \(\displaystyle \large{b_n=8(2)^{n-1}}\) can be simplified to:

\(\displaystyle \large{b_n=2^3(2)^{n-1}}\\\displaystyle \large{b_n=2^{n+2}}\)

Now to find the original sequence:

\(\displaystyle \large{a_n = a_1 + \sum_{k=1}^{n-1}b_k}\)

Hence:

\(\displaystyle \large{T_n=5+\sum_{k=1}^{n-1}8(2)^{k-1}}\)

Recall:

\(\displaystyle \large{\sum_{k=1}^{n-1} a_1r^{n-1} =a_1\left( \dfrac{1-r^{n-1}}{1-r}\right)}\)

Therefore:

\(\displaystyle \large{T_n=5+\sum_{k=1}^{n-1}8(2)^{k-1}}\\\displaystyle \large{T_n=5+8\left(\dfrac{1-2^{n-1}}{1-2}\right)}\\\displaystyle \large{T_n=5+8\left(\dfrac{1-2^{n-1}}{-1}\right)}\\\\\displaystyle \large{T_n=5+8(-1+2^{n-1})}\\\displaystyle \large{T_n=5-8+8(2)^{n-1}}\\\displaystyle \large{T_n=2^{n+2}-3}\)

Therefore, the sequence for 5,13,29 is \(\displaystyle \large{2^{n+2}-3}\).

Therefore, in figure 30:

\(\displaystyle \large{T_{30}=2^{30+2}-3}\\\displaystyle \large{T_{30}=2^{32}-3}\\\displaystyle \large{T_{30}=4294967293}\)

Therefore, there are 4294967293 dots in figure 30

We reflect the point (-5, -3) over the x-axis to get (-5, 3), and then translate this point down by 2 units to get the final coordinates of (-5, 1).

To reflect a point over the x-axis, we keep the x-coordinate the same, but negate the y-coordinate. Thus, reflecting the point (-5, -3) over the x-axis gives us the point (-5, 3).

Next, we need to translate the result 2 units down. To do this, we subtract 2 from the y-coordinate of the reflected point. So, subtracting 2 from the y-coordinate of (-5, 3) gives us the final coordinates:

(-5, 3) translated 2 units down is (-5, 1).

In summary, we can reflect a point over the x-axis by negating the y-coordinate, and translate a point down by subtracting a value from its y-coordinate. So, we reflect the point (-5, -3) over the x-axis to get (-5, 3), and then translate this point down by 2 units to get the final coordinates of (-5, 1).

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Answer:

3/2 is the answer

Step-by-step explanation:

Answer:

x=1 1/2

Step-by-step explanation:

9-4x=2x

4x+2x=9

6x=9

x=9/6

x=3/2

x=1 1/2

Theres the answer hope this helps! :)

Answer:

y = 2.3x

Step-by-step explanation:

y = kx  

52.9 = 23x

52.9 ÷ 23 = x

x = 2.3

By looking at the endpoints, we conclude that the correct graph is the one in the second option.

Notice that the original line ends at B = (7, 5)

And now we apply a translation of -5 on the x-axis and 3 on the y-axis, then the new coordinate of point B will be B' = (7 - 5, 5 + 3) = (2, 8)

Now let's look at the graphs, the only one with that coordinate of B'  is the second option (counting from the top).

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Here, we are given two functions and we want to find the difference between the two functions;

Looking at what we have;

(f-g)x

What this mean is that we are to subtract g(x) from f(x);

Mathematically;

Answer: 4ab2 - 3a + 13b

Step-by-step explanation:  (a•(b2))+13b)-4a)+(3ab2+a)

Factoring    4ab2 - 3a + 13b

Answer:

C

Step-by-step explanation:

Find the difference between $94.79 and $89.00 then do (5.79/89)*100 which is 6.50561797753, then round the initial answer so you get 6.50

Have a great day <3

a) X is an unbiased estimator of p. b) The Var(X) is p(1-p)/n. c) The E[X(1-X)] is (n-1)[p(1-p)/n]. d) The value of c is c = 1/(n-1).

(a) To show that X = Y/n is an unbiased estimator of p, we need to show that E[X] = p.

Since Y is a sum of n iid Bern(p) random variables, we have E[Y] = np.

Now, let's find the expected value of X:

E[X] = E[Y/n] = E[Y]/n = np/n = p.

Therefore, X is an unbiased estimator of p.

(b) To find the variance of X, we'll use the fact that Var(aX) = a^2 * Var(X) for any constant a.

Var(X) = Var(Y/n) = Var(Y)/n² = np(1-p)/n² = p(1-p)/n.

(c) To show that E[X(1-X)] = (n-1)[p(1-p)/n], we expand the expression:

E[X(1-X)] = E[X - X²] = E[X] - E[X²].

We already know that E[X] = p from part (a).

Now, let's find E[X²]:

E[X²] = E[(Y/n)²] = E[(Y²)/n²] = Var(Y)/n² + (E[Y]/n)².

Using the formula for the variance of a binomial distribution, Var(Y) = np(1-p), we have:

E[X²] = np(1-p)/n² + (np/n)² = p(1-p)/n + p² = p(1-p)/n + p(1-p) = (1-p)(p + p(1-p))/n = (1-p)(p + p - p²)/n = (1-p)(2p - p²)/n = 2p(1-p)/n - p²(1-p)/n = 2p(1-p)/n - p(1-p)²/n = [2p(1-p) - p(1-p)²]/n = [p(1-p)(2 - (1-p))]/n = [p(1-p)(1+p)]/n = p(1-p)(1+p)/n = p(1-p)/n.

Therefore, E[X(1-X)] = E[X] - E[X²] = p - p(1-p)/n = (n-1)p(1-p)/n = (n-1)[p(1-p)/n].

(d) To find the value of c such that cX(1-X) is an unbiased estimator of p(1-p)/n, we need to have E[cX(1-X)] = p(1-p)/n.

E[cX(1-X)] = cE[X(1-X)] = c[(n-1)[p(1-p)/n]].

For unbiasedness, we want this to be equal to p(1-p)/n:

c[(n-1)[p(1-p)/n]] = p(1-p)/n.

Simplifying, we have:

c(n-1)p(1-p) = p(1-p).

Since this should hold for all values of p, (n-1)c = 1.

Therefore, the value of c is c = 1/(n-1).

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The type of function that fits the given description is D. Exponential decay.

In an arithmetic sequence, the difference between consecutive terms remains constant. If the y-values of a function form an arithmetic sequence that decreases in value, it means that the difference between consecutive terms is negative.
Exponential decay functions exhibit a constant ratio between consecutive terms, resulting in a decreasing sequence. As the x-values increase, the y-values decrease at a consistent rate. This is represented by the formula y = ab^x, where b is a constant between 0 and 1.
In contrast, linear functions have a constant difference between consecutive terms, resulting in an arithmetic sequence. However, since the y-values are decreasing, the function cannot be linear.
Exponential growth functions, on the other hand, have a constant ratio between consecutive terms, but they result in an increasing sequence. The y-values of an exponential growth function increase as the x-values increase.

Therefore, based on the given information, the most appropriate type of function is D. Exponential decay.

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Answer:

Step-by-step explanation:

Q1

Q2

Q3

Q4

Answer:

Here we do not have the options, so I will answer in a general way.

We have two statements:

p = A number is greater than 25

q = A number is less than 35

We want to have:

p ^ q is true

This means:

p and q are true.

So, we need to find a number such that both conditions are meet, so we need to find a number N such that

The number N is greater than 25  (from p)

The number N is less than 35 (from q)

So N can be any number between 25 and 35

So, some of the possible values of N are:

N = 26

N = 27

N = 28.6

N = 33

N = 34

Concluding, any number N ∈ (25, 35) can be a solution.

(Note that N = 25 and N = 35 are not solutions)

Answer:

Bank A charges 10.4 a month. Bank B charges 27.00 a month

Step-by-step explanation:

Bank A step by step-

0.20 x 52 = 10.4

Bank B step by step=

52-25 = 27

27 x 1.00 = 27.00

Answer: they are parallel so there is no solution.

Step-by-step explanation:

Brayden- y=5x-1 or y-5x= -1

Howard- y=5x+1 or y-5x= 1

Vincent- y=4x+5 or y-4x= 5

In summary, they are all parallel so there is no solution. or

5y - 1 = 5y + 1

(Braydon = Howard)

Hope this helps you :) pls BRAINLEST

Answer:

The expressions for the yards gained by Brayden and Howard are 5y − 1 and 5y + 1, respectively.

If Brayden and Howard gained the same number of yards, then the equation representing this situation would be

5y – 1 = 5y + 1.

Brainliest?

Answer:

x=3

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

The length of the hypotenuse of this triangle is 30cm.

Let us assume that the length of base =  a cm

the length of perpendicular =  b cm

the length of hypotenuse =  c cm

according to Pythagoras theorem we have

\(hypotenuse^{2} = base^{2} + perpendicular^{2}\)

\(c^{2} = a^{2}+ b^{2}\)  equation 1

also given that

\(a^{2}+ b^{2} +c^{2} =1800\)  equation 2

now putting the value from equation 1 in equation 2 we get

\(c ^{2} +c^{2} =1800\\2c^{2} = 1800\\c^{2} = 900\\c = 30\)

hence, the length of the hypotenuse of this triangle is 30cm

The longest side of a right-angled triangle, or the side opposite the right angle, is known as the hypotenuse in geometry.

The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

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