Select all valid probabilities.
a. 110%
b. 0.25
c. 50%
d. 50/49
e. 49/50
f. 1.01
g. 1

Answer:

Third term=4

Step-by-step explanation:

Given:

C(n)=4/9(-3)^n-1

Find the third term

Let n=3

Substitute n=3 into the equation

C(n)=4/9(-3)^n-1

C(3)=4/9(-3)^3-1

Step 1: evaluate the power 3-1

C(3) = 4/9(-3)^2

Step 2: evaluate (-3)^2

C(3) = 4/9(9)

It can be rewritten as

C(3) = 4/9*9

9 numerator will strike 9 denominator out leaving 4

C(3)=4

Therefore, the third term=4

C(3)=4

ANSWER

28.285 units

EXPLANATION

We are given the square EFGH and we need to find the perimeter.

The perimeter of a square is given as:

P = 4 * L

P = 4L

where L = length of the side of the square

To find the length of the side of the square, we have to find the distance between a pair of adjacent vertices of the square.

Let us pick E(0, 5) and F(5, 0).

The distance between the two points is:

where (x1, y1) = (0, 5)

(x2, y2) = (5, 0)

Therefore, the length of the square (distance between the two points) is:

Therefore, the perimeter of the square is:

P = 4 * 7.071

P = 28.284 units

The system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

Equation modelling is the process of writing a given mathematical statement (or word problem) in the form of a mathematical equation for the correct analysis of the given problem (or situation).

Given is that Jordan's t-shirt business sells long sleeve shirts for $18 and short sleeve shirts for $13. He needs to make at least $350 to buy a new heat press machine.

Let {S} represent the short sleeves and {L} represents the long sleeves. So, we can model the equations as -

S + L < 30

13S + 18L ≥ 350

Therefore, the system of inequalities that will model the given scenerio are -

S + L < 30

13S + 18L ≥ 350

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According to a recent survey, nearly half of the respondents cited better pay as their primary reason for changing jobs.

The survey was conducted on a national level and the results indicate that a majority of people are looking to increase their earnings by switching jobs.

Other reasons are:

In conclusion, the survey clearly showed that the main reason for job changes among respondents was better pay. However, various other factors also play a role in an individual's decision to switch jobs, such as working conditions, career paths, and location.

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The polynomial function in expanded form is f(x) = x² - 3x² + 4x - 2.

A polynomial function with rational coefficients that has the given numbers as zeros, considering their conjugates . Since 1+i is a zero, its conjugate 1-i must also be a zero.

Using the zero-product property,  that if a polynomial has a zero at a given number, then the polynomial must have a factor of (x - zero). Therefore, the polynomial function with the given zeros can be written as:

f(x) = (x - (1+i))(x - (1-i))(x - 1)

Expanding this expression,

f(x) = ((x - 1) - i)((x - 1) + i)(x - 1)

= ((x - 1)² - i²)(x - 1)

= ((x - 1)² + 1)(x - 1)

= (x² - 2x + 1 + 1)(x - 1)

= (x² - 2x + 2)(x - 1)

= x² - 2x² + 2x - x² + 2x - 2

= x² - 3x²+ 4x - 2

.

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Answer:

The magnitude of the vector is 5.

Step-by-step Explanation:

The magnitude of a vector |v| can be found using the Pitagoras theorem, according to the figure below:

The magnitude can be calculated as:

In this exercise,

x = -3

y = 4

So,

The magnitude of the vector is 5.

The correct answers about school's population and year are - a. 744, b. 4 years, c. 186 and d. 1208.

The population growth between 2004 and 2008 = population in 2008 - population in 2004

Population growth = 1766 - 1022

Population growth = 744

Time taken for population to reach = final population year - initial population year

Time taken = 2008 - 2004

Time taken = 4 years

Average population growth per year = (final - initial year)/(final - initial population)

Average population growth per year = (1766 - 1022)/(2008 - 2004)

Average population growth per year = 744/4

Average population growth per year = 186

(Year 2004 - year 2001) × Average = (Population in year 2004 - population in year 2000)

3 × 186 = 1766 - Population in year 2000

558 = 1766 - Population in year 2000

Population in year 2000 = 1766 - 558

Population in year 2000 = 1208

Thus, the answers are 744, 4 years, 186 and 1208.

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Answer:

C) y = 2x - 3 and y = -2x - 1.

Hope this helps you!

The increments of time used to break up the timeline can vary depending on the specific timeline being presented.

The increments of time used to break up the timeline can vary depending on the context and purpose.

However, common time increments include years, months, weeks, or days, which are displayed on the x-axis (horizontal) to divide the timeline into easily understandable segments.

For example, in a historical timeline, the increments might be years, decades, or centuries. In a project timeline, the increments might be weeks or months.

The x-axis (horizontal) is typically where these increments are marked and can help to visualize the timeline more clearly.

Ultimately, the increments chosen should be appropriate for the task at hand and allow for effective planning and tracking of progress.

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Answer:

1152

why cant you bing it?

Answer:

15

Step-by-step explanation:

Answer: 1/16

Step-by-step explanation:

Given that there are 4 green marbles, when Dan takes a marble the first time, the probability is 1/4 as there are 4 green marbles. When he puts it back and draws another one, the probability is still 1/4 because Dan didn't take the marble out of the bag(this is known as with replacement)

∴ the total probability of drawing 2 green marbles with replacement is 1/4 × 1/4= 1/16

Hope this helps

Answer:

D) \(4*ln(2)\)

Step-by-step explanation:

Find the inverse function of f(x):

\(f(x)=log_2(2x)\)

\(y=log_2(2x)\)

\(x=log_2(2y)\)

\(2^x=2y\)

\(2^{x-1}=y\)

\(f^{-1}(x)=2^{x-1}\)

Take the derivative of the inverse function:

\(\frac{d}{dx}(f^{-1}(x))\)

\(\frac{d}{dx}(2^{x-1})\)

\(\frac{d}{dx}(e^{(x-1)(ln2)})\) <-- Logarithmic Differentiation

\(ln(2)*e^{(x-1)(ln(2))\)

\(ln(2)*2^{x-1}\)

Substitute x=3:

\(ln(2)*2^{3-1}\)

\(ln(2)*2^2\)

\(4*ln(2)\)

Answer:

Choice b. \(q\) has to be false.

Step-by-step explanation:

Consider the truth table of \(p \implies q\) (\(p\) implies \(q\)).

The only combination where \(p \implies q\) is false is when \(p\) is true and \(q\) is false. Hence, the \(q\!\) here must be false.

You have the following expression:

In order to determine if z=-5 is a solution to the previous equation, replace z=-5 and verify the equation, just as follow:

Hence, z=-5 is a solution of the given equation

Answer:  y - 6 = -3/5 ( x - 5 )

Step-by-step explanation: ask for explanation, and ill give it!

Answer:

Step-by-step explanation:

Y=3x-9

Using the test statistic, at the 0.05 level of significance, we do not find sufficient evidence to support the political scientist's claim and hence reject the null hypothesis.

To determine whether there is enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65%, we can perform a hypothesis test using the given data.

Let's set up the null and alternative hypotheses:

H₀: p ≤ 0.65 (Null hypothesis: The proportion of college students interested in election results is 65% or less)

Ha: p > 0.65 (Alternative hypothesis: The proportion of college students interested in election results is more than 65%)

We are given that the sample size is 265 college students, and out of this sample, 180 students say they're interested in their district's election results.

To perform the hypothesis test, we'll calculate the test statistic, which is the z-statistic in this case, using the formula:

z = (p - p₀) / √(p₀(1-p₀)/n)

Where p is the sample proportion, p₀ is the hypothesized proportion under the null hypothesis, and n is the sample size.

Let's calculate the sample proportion:

p = 180 / 265 ≈ 0.679

Now, we can calculate the test statistic:

z = (0.679 - 0.65) / √(0.65(1-0.65)/265) ≈ 1.295

Next, we'll compare the test statistic with the critical z-value at a 0.05 level of significance (α = 0.05) for a one-tailed test.

Using a standard normal distribution table or a statistical calculator, the critical z-value at α = 0.05 is approximately 1.645.

Since the test statistic (1.295) does not exceed the critical z-value (1.645), we fail to reject the null hypothesis. In other words, we do not have enough evidence to support the political scientist's claim that the proportion of college students interested in their district's election results is more than 65% based on this sample.

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Answer:

\(70\ \text{kilometers}\)

Step-by-step explanation:

The scale of the map is 1 centimeter distance on the map represents 20 kilometers of actual distance.

The distance between the two cities is 3.5 centimeters on the map

\(1\ \text{centimeters on the map}=20\ \text{kilometers of actual distance}\)

So,

\(3.5\times 20=70\ \text{kilometers}\)

So, the distance between the two cities is \(70\ \text{kilometers}\).

Answer:

{-2,11}

Step-by-step explanation:

write common number from three set: A,B and C

Based on the base case and the inductive step, we can conclude that every string in the set S, generated by the recursive rules, begins with the character 'a'.

To prove that every string in the set S begins with the character 'a', we can use mathematical induction to demonstrate the property for all strings generated by the recursive rules.

**Base Case:**

The base case states that the string 'a' is in the set S. This string clearly begins with the character 'a', so the property holds for the base case.

**Inductive Step:**

Now, we assume that the property holds for a string x, which means that x begins with the character 'a'. We need to show that the property also holds for the strings generated by the recursive rules using x.

**Rule 1:**

According to Rule 1, if x ∈ S, then xb ∈ S. Let's assume that x begins with 'a' since we are assuming that the property holds for x. We need to show that xb also begins with 'a'.

If x begins with 'a', then we can represent it as x = 'a' + y, where y is a string that can be empty or contain characters other than 'a'. Now, applying Rule 1, we have xb = ('a' + y) + 'b' = 'a' + (y + 'b'). Since 'a' + (y + 'b') is of the form 'a' + z, where z = y + 'b', we can conclude that xb begins with 'a'. Hence, the property holds for xb.

**Rule 2:**

According to Rule 2, if x ∈ S, then xa ∈ S. Again, assuming that x begins with 'a', we need to show that xa also begins with 'a'.

Using the same representation for x as above (x = 'a' + y), we have xa = ('a' + y) + 'a' = 'a' + (y + 'a'). Since 'a' + (y + 'a') is of the form 'a' + z, where z = y + 'a', we can conclude that xa begins with 'a'. Therefore, the property holds for xa.

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1. We should understand that question is missing, but, the amount 1 that Mia has to pay back if she takes the loan will be Loan amount plus the interest on it.

2. The banks 2 and other financial institutions did offer cash loans to people that did not apply for it because they knew that had favorable credit worthiness, that is, they repay loan as at when due.

Creditworthiness is how a lender determines whether you will default on your debt obligations or whether you are creditworthy. Creditors consider your creditworthiness before approving new credit for you.

Several factors influence it, including your repayment history and credit score. When determining the likelihood of default, some lending institutions consider available assets as well as the number of liabilities you have.

The credit report shows how much debt you have, as well as the high balances, credit limits, and the current balance of each account. It will also flag any relevant information for the potential lender, such as past due amounts, defaults, bankruptcies, and collection items.

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The transformation of System A into System B is:

Equation [A2]+ Equation [A 1] → Equation [B 1]"

The correct answer choice is option D

How can we transform System A into System B?

To transform System A into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

System A:

-3x + 4y = -23 [A1]

7x - 2y = -5 [A2]

Multiply equation [A2] by 2

14x - 4y = -10

Add the equation to equation [A1]

14x - 4y = -10

-3x + 4y = -23 [A1]

11x = -33 [B1]

Multiply equation [A2] by 1

7x - 2y = -5 ....[B2]

So therefore, it can be deduced from the step-by-step explanation above that System A is ultimately transformed into System B as 1 × Equation [A2] + Equation [A1]→ Equation [B1] and 1 × Equation [A2] → Equation [B2].

The complete image is attached.

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Answer:

The correct option is;

b. y = x², \(y = \left | x \right |\)

Step-by-step explanation:

The equations are

1) y = x

\(\lim_{x\rightarrow -\infty }f\left (x \right )=-\infty\)

2) y = x²

\(\lim_{x\rightarrow -\infty }f\left (x \right )=+\infty\)

3) y = x³

\(\lim_{x\rightarrow -\infty }f\left (x \right )=-\infty\)

4) \(y = \left | x \right |\)

\(\lim_{x\rightarrow -\infty }f\left (x \right )=+\infty\)

5) y = 1/x

\(\lim_{x\rightarrow -\infty }f\left (x \right )=0\)

6) y = eˣ

\(\lim_{x\rightarrow -\infty }f\left (x \right )\rightarrow 0\)

7) y = √x

\(\lim_{x\rightarrow -\infty }f\left (x \right )= \infty\sqrt{(-1)}\)

8) y = ㏑x

\(\lim_{x\rightarrow -\infty }f\left (x \right )= \infty\sqrt{(-1)}\)

9) y = sin x

\(\lim_{x\rightarrow -\infty }f\left (x \right )=\) undefined

10) y = cos x

\(\lim_{x\rightarrow -\infty }f\left (x \right )=\) undefined

11) y int (x)

\(\lim_{x\rightarrow -\infty }f\left (x \right )=-\infty\)

12) \(y = \dfrac{1}{1 + e^{-x}}\)

\(\lim_{x\rightarrow -\infty }f\left (x \right )=0\)

Therefore, the correct options are y = x² and \(y = \left | x \right |\)

Answer:

Step-by-step explanation:

Given the equation x + 5 = 1, to get the solution to the equation, we need to find the value of x

Step 1: Subtract 5 from both sides of the equation

x+5-5 = 1-5

x = 1-5

Step 2: Find the value of the unknown variable x

x = -4

The solution to the equation is x = -4

Answer:

100 + 6.98 = 106.98
81,636 x 106.98 / 100

= 87,334. 19

Step-by-step explanation:

Answer:Taking into account the definition of weigth, the correct answer is option A: the mass of the object is 50 kg.First, you  have to know that mass is an indicator of the amount of matter that makes up a body. Its unit in the International System is the kilogram (kg).The mass of an object will always be the same, no matter where it is located.On the other side, bodies are subjected to the action of forces, such as the force of gravity or electromagnetic forces. So, weight is the action exerted by the force of gravity on the body. That is, weight is a measure of how much force gravity exerts on the mass of an object.The weight of an object is measured in Newton (N) and will vary according to the force of gravity that acts on it.The expression for the calculation of the weight is:P= m×gwhere:P is the weight of a body.m is its mass.g is the gravity or acceleration with which bodies fall.In this case, you know that:P= 980 Nm= ?g= 19.6 Replacing in the expression for the calculation of the weight:980 N= m× 19.6 Solving:m= m=50 kgFinally, the correct answer is option A: the mass of the object is 50 kg

Step-by-step explanation:

Answer:

∠ V = 58°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , then

∠ WYX = 180° - (52 + 24)° = 180° - 76° = 104°

∠ VYU = ∠ WYX = 104° ( vertically opposite angles )

Then

∠ V = 180° - (104 + 18)° = 180° - 122° = 58°