A regular polygon has 12 sides find the size of each of its interior angles​

Answer:

-22+27i

Step-by-step explanation:

\(i = \sqrt{ - 1} \\ (3 - 4i)( - 6 + i) \\ = (3 - 4 \sqrt{ - 1} )( - 6 + \sqrt{ - 1} ) \\ = 3( - 6 + \sqrt{ - 1)} - 4 \sqrt{ - 1} ( - 6 + \sqrt{ - 1} ) \\ = - 18 + 3 \sqrt{ - 1} + 24 \sqrt{ - 1} - 4 \\ = - 22 + 27 \sqrt{ - 1} \\ putting \: \: \: \sqrt{ - 1 } = i \\ = - 22 + 27i\)

Hope it helps.

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To solve problems, construct one-variable equations and inequalities.

As opposed to an inequality, which links two different values, an equation declares that two expressions are equal.

Create one-variable equations and inequalities, then utilize them to solve issues.

Include simple rational and exponential equations as well as those resulting from linear and quadratic functions.

In order to answer word problems, students should be able to decipher them and create equations and inequalities.

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Answer:

20

Step-by-step explanation:

f(x) = 30

30 = 1.8x -5.4

35.4 = 1.8x

x = 35.4/1.8

x = 19.666

What will be the size of his payments at the start of each month from the ordinary simple annuity for 20 years following his retirement is  $939.85

To determine the amount, we have to use the formula;

\(A = P(1 + r/n)^(^n^t^)\)

Substitute the values, we have;

Jamal's accumulated value would be A = \(2000 * (1 + 0.09/12)^(1^2^*^1^7^)\)

= $104,137.46.

We also have that the formula for simple annuity formula is expressed as;

P = A / ((1 + r)ˣ - 1)

Such that;

Substitute the values, we get;

P = 104137.46 / ((1 + 0.09)²⁰ - 1)

P = $939.85

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What will be the size of his payments at the start of each month from the ordinary simple annuity for 20 years following his retirement is  $939.85

To determine the amount, we have to use the formula;

Substitute the values, we have;

Jamal's Saving account accumulated value would be A =

= $104,137.46.

We also have that the formula for simple annuity formula is expressed as;

P = A / ((1 + r)ˣ - 1)

Such that;

P is the payment size

A is the accumulated value

Substitute the values, we get;

P = 104137.46 / ((1 + 0.09)²⁰ - 1)

P = $939.85

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Answer:

Step-by-step explanation:

A bitmap is a digital image format that is made up of a grid of square colored dots called pixels.

Each pixel in the bitmap contains information about its color and position, which allows the computer to display the image on a screen or print it on paper. Bitmaps are commonly used for photographs, illustrations, and other complex images that require a high degree of detail and color accuracy.

However, because bitmaps store information for each individual pixel, they can be memory-intensive and may result in large file sizes. Additionally, resizing a bitmap can lead to a loss of quality, as the computer must either interpolate or discard pixels to adjust the image size.

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Check the picture below.

so the parabola looks more or less like so, with a vertex at (-3 , 10) and the directrix above it at -79/8 or namely -9⅞, now, the directrix is just 1/8 of a unit above the vertex, that's our "p" distance, and since the directrix is above the vertex, the parabola is opening downwards and "p" is negative.

\(\textit{vertical parabola vertex form with focus point distance} \\\\ 4p(y- k)=(x- h)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h,k+p)}\qquad \stackrel{directrix}{y=k-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\cap}\qquad \stackrel{p~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\)

\(\begin{cases} h=-3\\ k=-10\\ p=-\frac{1}{8} \end{cases}\implies 4(-\frac{1}{8})(~~y-(-10)~~) = (~~x-(-3)~~)^2 \\\\\\ -\cfrac{1}{2}(y+10)=(x+3)^2\implies y+10=-2(x+3)^2\implies \boxed{y=-2(x+3)^2-10}\)

Answer: Reflection over the x-axis

At a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.

What is the null hypothesis in statistics?

The null hypothesis in inferential statistics states that two possibilities are the same. The null hypothesis states that the observed difference is solely due to chance. The likelihood that the null hypothesis is true can be calculated using statistical tests.

Sample size, n =1500

The sample proportion of the chips that do not fail in the first 1000 hrs of their use, \(\hat{p} = 0.69\)

Null Hypothesis, H0: p=0.72

Alternate Hypothesis, \(Ha: p \neq 0.72\)

Test statistic,

\(z= \frac{\hat{p}-p}{\sqrt{\frac{p(1-p)}{n}}} - \frac{0.69-0.72}{\sqrt{\frac{0.72(1-0.72)}{1500}}} = -2.5877\)

Critical Value,

\(Z_{0.05/2} =\)±1.96

Now, since the absolute value of the test statistic i.e, 2.5877 is greater than the absolute value of the critical value i.e, .1.96, thus we will reject the null hypothesis.

Thus at a 0.01 significance level, we do not have enough evidence to support the claim that 72% do not fail in the first 1000 hrs of their use.

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a) There is only one triangle.

b) Please see the image attached below to see the sketch of the triangle.

c) By trigonometry, the measure of the angles are R = 55°, Q = 77.524° and P = 47.476°.

In this question we need to determine all possible triangles with the following information: PQ = 5 cm, R = 55°, QR = 4.5 cm. All missing information can be found by trigonometry. First, find the missing angle P by sine law:

PQ / sin R = QR / sin P

sin P = (QR / PQ) · sin R

sin P = (4.5 / 5) · sin 55°

sin P = 0.737

Therefore, we find the following two choices:

P₁ = 47.476° or P₂ = 132.524°

Second, compute the possible values of angle Q:

Q₁ = 180° - 55° - 47.476°

Q₁ = 77.524°

Q₂ = 180° - 55° - 132.524°

Q₂ = - 7.524° (IMPOSSIBLE)

Then, Q = 77.524°

Third, determine the value of side PR by cosine law:

PR = √(PQ² + QR² - 2 · PQ · QR · cos Q)

PR = √(5² + 4.5² - 2 · 5 · 4.5 · cos 77.524°)

PR = 5.960 cm

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Answer:

A. 5/13

General Formulas and Concepts:

Pre-Algebra

Geometry

Step-by-step explanation:

Step 1: Identify

Angle θ = C

Adjacent Leg = 10

Hypotenuse = 26

Step 2: Find ratio

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of option (C) the variability around the regression line

The standard error of the estimate in a regression-based forecast is a measure of the variability of the actual data points around the predicted values of the regression line.

It tells us how much the actual data points are likely to deviate from the predicted values, and provides a measure of the accuracy of the forecast. It is not related to the time required to derive the forecast equation, the maximum error of the forecast, or the time period for which the forecast is valid.

Therefore, the correct option is (C) The variability around the regression line.

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The give question is incomplete, the complete question is:

With regard to a​ regression-based forecast, the standard error of the estimate gives a measure of:

A. the time required to derive the forecast equation.

B. the maximum error of the forecast.

C. the variability around the regression line.

D. the time period for which the forecast is valid.

Answer: A

Step-by-step explanation: A function means that your x can only have one y but your y can have multiple x's.

Answer:

Step-by-step explanation:

To convert 20 cm to meters, we divide by 100, because 1 meter = 100 centimeters.

So, 20 cm = 20/100 m = 0.2 m

To convert 0.2 m to meters in the lowest form, we divide by 15, because 1 meter = 15 units.

So, 0.2 m = 0.2/15 m = 0.013 m

So the final answer is 0.013 m.

A) The equilibrium solutions are (0,0) and (4000, 10000), and B) The expression for dL/dA = (-20 + 0.001L) / \((L-0.0001L)^{2}\)

(a) To find the equilibrium solutions, we need to set both equations equal to 0 and solve for A and L.

From the first equation:

dA/dt = 2A - 0.02AL = 0

2A = 0.02AL

A = 0.01L

Substituting this into the second equation:

dL/dt = -0.4L + 0.001A(L) = 0

-0.4L + 0.001(0.01L)(L) = 0

-0.4L + \(0.0001L^{2}\) = 0

L(0.0001L - 0.4) = 0

Therefore, the equilibrium solutions are (0,0) and (4000, 10000).

(b) To find dL/dA, we can use the chain rule:

dL/dA = (dL/dt) / (dA/dt)

From the given equations,

dL/dt = -0.4L + 0.001AL

dA/dt = 2A - 0.02AL

Substituting A = 0.01L,

dA/dt = 2(0.01L) - \(0.02L^{2}\) = 0.02L(1 - 0.01L)

Therefore,

dL/dA = (-0.4L + 0.001AL) / (0.02L(1 - 0.01L))

Simplifying,

dL/dA = (-20 + 0.1A) / (L - 0.01AL)

Substituting A = 0.01L,

dL/dA = (-20 + 0.1(0.01L)) / (L - 0.01(0.01L)L)

dL/dA = (-20 + 0.001L) / \((L-0.0001L)^{2}\)

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If the likelihood that the Islanders will beat the Rangers in a game is 0.33, the probability that the Islanders will win at most two out of five games in a series against the Rangers is 0.132.

Probability is the chance that an expected event occurs when there are many possible outcomes.

Probability is the ratio of success over the total number of occurrences.

The probability of the Islanders beating the Rangers = 0.33

Out of five games, the probability of winning at most two = 0.132 (2/5 x 0.33)

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The descending order of the length of the four insects is as follows: 2/3 cm, 0.1 cm, 0.02 cm, 1/8 cm.

The length of four insects are 0.02 cm, 1/8 cm, 0.1 cm, and 2/3 cm.

Arrange the length in descending orderIn order to arrange the lengths of the four insects in descending order, we need to convert the fractions to decimals so that we can compare all the values.

1/8 cm = 0.125 cm

2/3 cm = 0.6667 cm

Now we have the values in decimal form, we can proceed to arrange them in descending order from the highest to the lowest value:

2/3 cm = 0.6667 cm

0.1 cm

0.02 cm

1/8 cm = 0.125 cm.

In conclusion, the lengths of four insects were arranged in descending order by first converting the fractions to decimals before comparing them.

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Let:

From that equation:

If two lines are perpendicular, then:

Given an arbitraty point:

Using the point slope equation:

Answer:

1. Quadratic function

2. y-intercept = 0

3. x-intercepts = 0, 6

4. greatest value of y = 9 when x = 3

5. y > 0

Step-by-step explanation:

2. The line crosses the y-axis at (0,0)

3. The line crosses the x-axis at (0,0) & (6,0)

4. The highest point is at 9 which is above 3; (3, 9)

5. The y value is greater than 0

I hope this helps!

Answer:

B, D, E

Step-by-step explanation:

If a line is parallel to another line, then the slope has to be the same. Thus we first want to find the slope of the line given, by using the slope formula: m = (y_1 - y_0)/(x_1 - x_0): (2 - 4)/(-2-3) = 2/5

We proceed to find the slope of the following answer choices:

A. (-3-(-5))/(-7-(-2)) = -2/5

B. (-1-1)/(-6-(-1)) = 2/5

C. (5 - 0)/(2-0) = 5/2

D. (2-0)/(6-1) = 2/5

E. (2-0)/(8-3) = 2/5

Thus, we have B, D, E

Answer:

B, D, E On Edge

Step-by-step explanation:

edge22

Answer:

Step-by-step explanation:

=> 8.2x + 9y + 2(2.5x) + 10xy

=> 8.2x + 9y + 5x+ 10xy

=> 13.2x + 9y + 10xy

Since we can't simplify it from here, 13.2x + 9y + 10xy is our answer.

1. The balloon's initial temperature was ____ °C.

2. The temperature of the oil is ____ °C.

1. To find the balloon's initial temperature, we can use the combined gas law, which states that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature. Given that the volume changes to 76.4% of its initial volume and the final temperature is -80.0 °C, we can solve for the initial temperature. First, we convert the volume change to a decimal by dividing 76.4% by 100, giving us 0.764. Plugging in the values into the combined gas law equation, we can rearrange it to solve for the initial temperature.

2. To determine the temperature of the oil, we can use the ideal gas law, which states that the pressure times the volume divided by the temperature is equal to the gas constant times the number of moles. Since the volume remains constant and we are given the initial and final pressures, we can solve for the temperature. By plugging in the values into the ideal gas law equation and solving for the temperature, we can find the temperature of the oil in °C.

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To achieve a corner frequency of 12 kHz with a capacitance (C) of 0.5 μF, the value of the resistance (R) in the simple RC lowpass filter should be approximately 13.27 kΩ.

In a simple RC lowpass filter, the corner frequency (f_c) is determined by the relationship f_c = 1 / (2πRC), where R is the resistance and C is the capacitance.

Given that the desired corner frequency (f_c) is 12 kHz and the capacitance (C) is 0.5 μF, we can rearrange the formula to solve for R:

R = 1 / (2πf_cC)

Substituting the given values, we have:

R = 1 / (2π * 12 kHz * 0.5 μF)

Converting kHz to Hz and μF to F:

R = 1 / (2π * 12,000 Hz * 0.5 * 10^(-6) F)

Simplifying the expression:

R ≈ 13,271 Ω

Therefore, to achieve the desired corner frequency of 12 kHz with a capacitance of 0.5 μF, the value of the resistance (R) in the simple RC lowpass filter should be approximately 13.27 kΩ.

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Answer:

556

Step-by-step explanation:

So, 378/189=2. So it will double two times. x2x2=x4. 139x4=556.

Answer:

556

Step-by-step explanation:

There's an initial population of 139 bacteria in a colony. If it doubles every 189 minutes, then the population would be 556 in 378 minutes from now.

189th minute= 139+139=278

Since 189+189= 378, Just double 278 again, which gives you 556.

Answer:

42

Step-by-step explanation:

Answer:

I'm not 100% sure about this but i think its 42

Step-by-step explanation:

this is what i did

32/16=2

2*21=42