Which of the following are solutions to the equation below?
Check all that apply.
4x2 - 81 = 0

Answer:

the answer is c hope is helps

Answer:

1.25

Step-by-step explanation:

so you multiply 1.75 by 5 which is 8.25. You subract 10 by 8.25

Answer:

the domain is D. (-infinity, infinity)

Answer:

2

Step-by-step explanation:

The table are shown below

From the question, we have:

f(x) = x^2 - 1  x <= 0

        2x - 2  0 < x <= 5

        3  x > 5

So, we make the table using the x values in the domain

x   f(x) = x^2 - 1

0                -1

-1               0

-2              3

-3             8

x   f(x) = 2x - 1

1                1

2               3

3               5

4               7

5              9

x   f(x) = 3

6         3

7         3

8         3

The domain are given in the question

So, we have the domains of the three functions to be

x <= 0, 0 < x <= 5 and x > 5

Using the table of values, we have the range of the three functions to be

f(x) >= -1, -1 < f(x) <= 9 and f(x) = 3

Here, we use a graphing calculator

The graph of the function is added as an attachment

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The length of the segment NO is 17.9

The given parameters are;

Length of side, QP = 9

Length of QO = 14

The length of  segment NO we have to find.

NO² = qo×(qp×qo)

Plug in the values of qo, qp

Which gives NO² =14(9×14)

=322

NO=17.9

Hence, the length of the segment NO is 17.9

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Given the circle below with tangent \overline{NO} NO and secant \overline{QPO} QPO ​ . If QP=9 and QO=14, find the length of \overline{NO} NO . Round to the nearest tenth if necessary. Q

Answer:

Step-by-step explanation:

The scale factor is the ratio between the man's actual height and the height of the drawing.

Scale = 64/4 = 16

Answer:

1/16

Step-by-step explanation:

the actual man is 16 times bigger than drawing.

Answer: as per question statement

we need to set up an equation first

p(t)=1200e(0.052*t)

they have given that it is relative to 1200 that means it starts to increase from 1200 at t=0 initially 1200 bacteria were present

we need to find population at t=6

we need to plug t=6 in p(t).

P(6)=1200e(0.052*6)=1639.38

1638.38 bacteria were present at that time t=6

Step-by-step explanation: I hope this helps.

Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

Given, Returns of the company for the last few years are 5%, 10%, -15%, 20%, -12%, 22%, 8%
Arithmetic Average return:
Arithmetic Average return = (sum of all returns) / (total number of returns)
Arithmetic Average return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Therefore, the arithmetic average return of the company is 2.57%.
Geometric average return:
Geometric average return = [(1+R1) * (1+R2) * (1+R3) * …….. * (1+Rn)]1/n - 1
Geometric average return = [(1.05) * (1.1) * (0.85) * (1.2) * (0.88) * (1.22) * (1.08)]1/7 - 1= 0.13
Therefore, the geometric average return of the company is 13%.
Variance:
Variance = (sum of (return - mean return)2) / (total number of returns)
Mean return = (5 + 10 - 15 + 20 - 12 + 22 + 8) / 7= 18 / 7= 2.57
Variance = [(5-2.57)2 + (10-2.57)2 + (-15-2.57)2 + (20-2.57)2 + (-12-2.57)2 + (22-2.57)2 + (8-2.57)2] / 7= 392.12 / 7= 56
Therefore, the variance of the company is 56.
Standard Deviation:
Standard Deviation = Square root of Variance
Standard Deviation = √56= 7.48
Therefore, the standard deviation of the company is 7.48%.

Thus, Arithmetic average return of the company is 2.57%.Geometric average return of the company is 13%.Variance of the company is 56.Standard deviation of the company is 7.48%.

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The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.

Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:

Diameter in kilometers = Diameter in miles × Conversion factor

Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile

Diameter in kilometers = 12,681.6 kilometers

Rounding this value to the nearest whole number, we get 12,682 kilometers.

Therefore, the correct answer is option D: 12,682 km.

Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.

Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.

Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.

In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

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a. d/dx(x^3) = 3x^2, which is the power rule for n = 3. b. d/dx(x^-1) = -x^-2, which is the power rule for n = -1. c. d/dx(x^21) = 21x^20, which is the power rule for n = 21.

(a) Let's use the forward difference quotient definition of a derivative to show that the power rule holds true for n = 3.

f(x) = x^3

f'(x) = lim(h→0) [f(x+h) - f(x)]/h

= lim(h→0) [(x+h)^3 - x^3]/h

= lim(h→0) [3x^2h + 3xh^2 + h^3]/h

= lim(h→0) [3x^2 + 3xh + h^2]

= 3x^2, since h approaches 0

So, d/dx(x^3) = 3x^2, which is the power rule for n = 3.

(b) Let's use the same approach for n = -1.

f(x) = x^-1

f'(x) = lim(h→0) [f(x+h) - f(x)]/h

= lim(h→0) [(x+h)^-1 - x^-1]/h

= lim(h→0) [1/(x+h) - 1/x]/h

= lim(h→0) [x - (x+h)]/[x(x+h)h]

= lim(h→0) [-h]/[x(x+h)h]

= -1/x^2, since h approaches 0

So, d/dx(x^-1) = -x^-2, which is the power rule for n = -1.

(c) Lastly, let's use the same approach for n = 21.

f(x) = x^21

f'(x) = lim(h→0) [f(x+h) - f(x)]/h

= lim(h→0) [(x+h)^21 - x^21]/h

= lim(h→0) [21x^20h + ... + h^21]/h

= lim(h→0) [21x^20 + ... + h^20]

= 21x^20, since h approaches 0

So, d/dx(x^21) = 21x^20, which is the power rule for n = 21.

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The optimal point values for x1, x2, λ, and μ (Lagrange multipliers) in the given problem are:

x1 = 1

x2 = 1

λ = -4

μ = 2

To solve the optimization problem using the Lagrange multipliers technique, we first construct the Lagrangian function L(x1, x2, λ) by incorporating the equality constraint:

L(x1, x2, λ) = f(x1, x2) - λ(g(x1, x2))

Where f(x1, x2) is the objective function, g(x1, x2) is the equality constraint, and λ is the Lagrange multiplier.

In this case, the objective function is f(x1, x2) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6, and the equality constraint is g(x1, x2) = x1 + x2 - 2.

The Lagrangian function becomes:

L(x1, x2, λ) = 2x1^2 - 2x1x2 + 2x2 - 6x1 + 6 - λ(x1 + x2 - 2)

To find the optimal values, we need to find the critical points by taking partial derivatives of L with respect to x1, x2, and λ and setting them equal to zero. Solving these equations simultaneously, we get:

∂L/∂x1 = 4x1 - 2x2 - 6 - λ = 0

∂L/∂x2 = -2x1 + 2 + λ = 0

∂L/∂λ = -(x1 + x2 - 2) = 0

Solving these equations, we find x1 = 1, x2 = 1, and λ = -4. Substituting these values into the equality constraint, we can solve for μ:

x1 + x2 - 2 = 1 + 1 - 2 = 0

Therefore, μ = 2.

The optimal point values for the variables in the optimization problem are x1 = 1, x2 = 1, λ = -4, and μ = 2. The Lagrange multipliers λ and μ represent the rates of change of the objective function and the equality constraint, respectively, with respect to the variables. They provide insights into the sensitivity of the objective function to changes in the constraints and can indicate the impact of relaxing or tightening the constraints on the optimal solution. In this case, the Lagrange multiplier λ of -4 indicates that a small increase in the equality constraint (x1 + x2 - 2) would result in a decrease in the objective function value. The Lagrange multiplier μ of 2 indicates the shadow price or the marginal cost of satisfying the equality constraint.

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K-fold cross-validation generally produces an estimate with lower bias compared to leave-one-out cross-validation.(option b).

Cross-validation is a popular technique used in machine learning to estimate the performance of a model on unseen data. There are different methods of cross-validation, including leave-one-out and K-fold. In leave-one-out, only one data point is left out for testing, while in K-fold, a Kth portion of the data is held out.

Now, to answer the question of which method generally produces an estimate with higher bias, we need to look at the formula for bias in cross-validation. The bias is given by the difference between the expected value of the cross-validation estimate and the true performance of the model.

For K-fold cross-validation, the expected value of the estimate is computed as the average of the estimates obtained in each of the K folds. This means that the bias is dependent on the number of folds used. The more folds used, the lower the bias is likely to be.

Hence the correct option is (b).

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Answer: D

Step-by-step explanation:

Answer:

Step-by-step explanation:

The difference between the assets and the liabilities cannot be compared.

The half-life of this isotope (in hours) is 13.0

Isotopes are variations of chemical elements that have a varied number of neutrons but the same number of protons and electrons. In other words, isotopes are different forms of the same element that have different amounts of nucleons (the sum of protons and neutrons) because of variations in the total number of neutrons in each of their individual nuclei.

An important application of isotopes is in the determination of the isotopic signature of element samples via isotope analysis. This is generally done via the process of isotope ratio mass spectrometry.

28% decay means, 72% remains.

Now,

\(N=N_{n} (\frac{1}{2})^{t/t_{12} } \\72=100(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\(\frac{72}{100} )=(\frac{1}{2} )^{\frac{6.16 hours}{t_{1/2} } } \\\)

Taking long as both sides & solving we get,

\(t_{\frac{1}{2} } = 13.0 hours\)

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Answer:

The answer is True. Just trust me on this one.

Using proportions, it is found that Product A sold 345600 units.

In this problem, we have that Product B sold 70% less, that is, 30% of Product C, which sold 39,000 units, hence:

B = 0.3 x 33000 = 9900.

Product A sold 3.5 times more than Product B. So, the number of units sold by Product A is given by:

A = 3.5 x 9900 = 346500.

Therefore, Product A sold 345600 units.

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Answer:

\(x=144\)

Step-by-step explanation:

\(We\ can\ observe\ that:\\The\ polygon\ is\ an\ octagon\ as\ it\ is\ bounded\ by\ 8\ linear\ sides.\\Hence,\\We\ know\ that,\\The\ Interior\ Angle\ Sum\ of\ a\ polygon\ with\ n\ is\ given\ by\ the\ formula:\\Interior\ Angle\ Sum=180(n-2)\\Hence,\\As\ we\ already\ know\ that,\\The\ number\ of\ sides\ in\ this\ polygon=n=8\\Hence,\\The\ Interior\ Angle\ Sum\ Of\ An\ Octagon=180(8-2)=180*6=1080\\\)

\(Hence,\\\angle 1+ \angle 2+\angle 3+\angle 4+\angle 5+\angle 6+\angle 7+\angle 8=1080\\Hence,\\129+132+136+124+141+158+116+x=1080\\Hence,\\936+ \angle x=1080\\\angle x=1080-936=144\)

Answer:

John has a sheet of paper that is 8 feet long. He cuts the length of paper into eighths, and then cuts the length of each of these \(\frac{1}{8}\) pieces into fourths. How many pieces does he have? How many inches long is each piece?

Step-by-step explanation:

Answer: y = 1x+ -2 or y=x-2

Step-by-step explanation:

y=mx+b

-10=1(-8)+b

-10=-8+b

b=-2

Answer:

y=x-2

Step-by-step explanation:

y-(-10)=1(x-(-8)

y+10=1(x+8)

y+10=1x+8

y=1x+8-10

y=1x-2

Answer:

3/8 as a percent equals 37.5%

Step-by-step explanation:

Answer:

.375

Step-by-step explanation:

We are given the following function

We are asked to find the output y when the input x is 10

Simply substitute x = 10 into the function and solve for y

Therefore, the output y is -29 when the input x is 10

Answer:

  0.92

Step-by-step explanation:

Each year, the value declines. This eliminates choices A and D.

The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...

  0.92 . . . . the third listed choice

Answer:

d, as long as distance is y(up) and time is x(across)

Step-by-step explanation:

a. the graph would go up and then slow down. b. the graph could be this. d. distance does not look like this.

Answer:

c

Step-by-step explanation:

The graph has a positive slope (it's increasing). SO the scenario has to be something increasing.

a matches but only for the first part where the speed s 0 at the stop sign then approaching a stoplight, it would slow down, so the graph would turn down at that point.

for b, air temperature doesn't increase over 24 hours, it goes up then goes down after the sun sets.

d, the walking home from school you would be getting closer with every step, so the graph would have a negative slope (slope down)

c. the runner is racing and adding more distance with time, except the flat part where time passed but they didn't add any more distance since they were on the ground. After they got up and continued to run, the graph still slopes up since the distance they are running is increasing.

Answer:

No Solution

Step-by-step explanation:

Rearrange terms

Add 19 to both sides of the equation

Simplify

Since each side of the pen is being increased by 4 feet, the total increase in perimeter would be 4 feet multiplied by 4 sides, which equals 16 feet.

To determine how many feet of additional fence Craig should purchase, we need to calculate the increase in the perimeter of the enlarged pen. Therefore, Craig should purchase an additional 16 feet of fence to build his enlarged fence.

The original size of the pen is an 8 by 8 feet square, which means each side measures 8 feet. The perimeter of the original pen is calculated by adding up the lengths of all four sides, so 8 + 8 + 8 + 8 = 32 feet.

To enlarge the pen, Craig decides to increase each side by 4 feet. After the enlargement, each side of the pen would measure 8 + 4 = 12 feet. The perimeter of the enlarged pen is calculated in the same way, by adding up the lengths of all four sides: 12 + 12 + 12 + 12 = 48 feet.

To find the additional fence Craig needs to purchase, we subtract the original perimeter from the enlarged perimeter: 48 feet - 32 feet = 16 feet. Therefore, Craig should purchase an additional 16 feet of fence to build his enlarged fence.

This calculation is based on the assumption that the pen remains a square shape after enlargement. If the shape of the enlarged pen differs from a square, the calculation would vary.

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