find the 8th term of the geometric sequence 4 , − 12 , 36 , . . . 4,−12,36,...

Answer:

[B] - 1/3

Step-by-step explanation:

Given:

-8x-5(1-x)=6x-2

Solve:

Expand : -8x - 5(1-x) : -3x -5

-3x - 5 = 6x -2

Add 5 to both sides (Balance)

-3x-5+5=6x-2+5

Simplify

-3x = 6x + 3

subtract 6x to both sides (Balance)

-3x - 6x = 6x +3 -6x

Simplify

-9x = 3

Divide both sides by -9 (Balance)

-9x/-9=3/-9

Simplify

x = -1/3

[RevyBreeze]

Answer:

47

Step-by-step explanation:

Answer:

P1. |x+12|<22
P2. -22<x+12<22
P3. -34<x<10
Hope this assists anybody that comes across this

Answer:

\(c \: \: y = 3x - 8\)

if you insert x and y value in equation you can find equation

Answer:

the 8 on the left is 10 times the value of the 8 on the right

The minimax regret criterion, also known as the minimax regret strategy, is an approach used in decision theory by economists. It aims to minimize the maximum regret that could be experienced when choosing a particular course of action.

The minimax regret criterion is a decision-making technique that takes into account the potential regret associated with each possible decision. It recognizes that decision-makers often face uncertainty and that their choices may lead to outcomes that are different from what was initially expected. By considering the worst-case scenario or maximum regret for each decision, the minimax regret criterion helps decision-makers select the option that minimizes the potential regret.

In this approach, decision-makers evaluate the consequences of their choices by comparing the actual outcome with the best outcome that could have been achieved if a different decision had been made. The minimax regret strategy focuses on minimizing the maximum regret across all possible decisions, aiming to choose the option that would result in the least regret, regardless of the actual outcome.

Economists often use the minimax regret criterion to analyze decision problems under uncertainty, particularly when the consequences of different actions cannot be precisely predicted. It provides a framework for decision-making that incorporates risk aversion and the desire to minimize the potential for regret. By considering the worst possible outcomes, decision-makers can make more informed choices that take into account the potential regrets associated with their decisions.

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Answer:

\(\approx 6^\circ\)

Step-by-step explanation:

Given that:

Little Gull Island Lighthouse shines a light from a height of 91 feet above the sea level.

The angle of depression is unknown.

Distance of the point at sea surface from the base of lighthouse is 865 ft.

This situation can be modeled or can be represented as the figure attached in  the answer area.

The situation can be represented by a right angled \(\triangle ABC\) in which we are given the base and the height of the triangle.

And we have to find the value of \(\angle BAD \ or \ \angle C\) (Because they are the internal vertically opposite angles).

Using tangent ratio:

\(tan\theta = \dfrac{Perpendicular}{Base}\)

\(tanC = \dfrac{AC}{BC}\\\Rightarrow tanC = \dfrac{91}{865}\\\Rightarrow tanC = 0.105\\\Rightarrow \angle C \approx 6^\circ\)

Therefore, the angle of depression is: \(\approx 6^\circ\)

The constant of proportionality is 28.2.

It should be noted that the miles driven and the number of gallons used has been given.

Therefore, the constant of proportionality will be:

= Miles driven / Gallons used

= 930.6 / 33

= 28.2

Therefore, the constant of proportionality is 28.2.

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The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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To determine how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis, we need to first establish a hypothesis test. A hypothesis test is a statistical procedure that helps us determine if there is enough evidence to support a particular hypothesis.

In a hypothesis test, we start with a null hypothesis (H0) which is a statement that there is no significant difference between two groups or variables. The alternative hypothesis (Ha) is the statement that there is a significant difference between the two groups or variables.

Once we have established our null and alternative hypotheses, we need to conduct a statistical test to determine if there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis. The test statistic is the numerical value that we obtain from our statistical test, which we compare to a critical value to determine if we can reject the null hypothesis.

The critical value is determined by the level of significance (α) we have chosen for our test, which is the probability of making a type I error (rejecting the null hypothesis when it is actually true). Typically, the level of significance is set at 0.05 or 0.01.

So, to answer the question, how large a test statistic must be to reject the null hypothesis in favor of the alternative hypothesis depends on the level of significance we have chosen, as well as the degrees of freedom and distribution of the test statistic. The critical value for a given level of significance and degrees of freedom can be found in statistical tables or calculated using software. If the test statistic is larger than the critical value, we can reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

a) 2/10

b) 3/20

c) option 2

Step-by-step explanation:

Answer:

by fraction and decimals

Step-by-step explication:

(1) P(z < -0.51) = 0.3046

(2) P(z > 0.73) = 0.2327

(3) P(-0.99 < z < 1.16) = 0.8222

(4) P(z > -0.64) = 0.7419

(5) The z value such that 50% of the total area lies to the right of it is z = 0.

(6) The z value to the right of the mean such that 85% of the total area lies to the left of it is z = -1.036.

What is Probability?

Probability is a measure of the likelihood or chance that a specific event will occur. It quantifies the uncertainty associated with an event and is expressed as a value between 0 and 1, where 0 represents impossibility and 1 represents certainty. In other words, probability indicates the proportion of times an event is expected to occur out of all possible outcomes. It plays a fundamental role in statistics, mathematics, and various fields where uncertainty and random events are involved.

Let's go through each question and explain the solutions:

(1) P(z < -0.51) represents the probability that a standard normal random variable is less than -0.51. By looking up this value in the standard normal distribution table or using a calculator, we find that the probability is approximately 0.3046.

(2) P(z > 0.73) represents the probability that a standard normal random variable is greater than 0.73. Again, by looking up this value or using a calculator, we find that the probability is approximately 0.2327.

(3) P(-0.99 < z < 1.16) represents the probability that a standard normal random variable falls between -0.99 and 1.16. By finding the individual probabilities for each interval and subtracting them, we get a probability of approximately 0.8222.

(4) P(z > -0.64) represents the probability that a standard normal random variable is greater than -0.64. Using the standard normal distribution table or a calculator, we find that the probability is approximately 0.7419.

(5) The z value such that 50% of the total area lies to the right of it corresponds to the median of the standard normal distribution. Since the standard normal distribution is symmetric, the median is at z = 0.

(6) To find the z value to the right of the mean such that 85% of the total area lies to the left of it, we look for the z value that corresponds to the cumulative probability of 0.85. By using the standard normal distribution table or a calculator, we find that the z value is approximately -1.036.

In summary, these questions involve finding probabilities associated with the standard normal distribution using z-scores.

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A ratio describes a relationship between two or more quantities. When mixing colors, ratios are often used to determine the ratio of different colors required to achieve a desired hue. Ratios can be expressed in 1:, 2:3,.. etc.

Ratios affect the appearance of paint colors. In this scenario, Can A has a higher percentage of red than can B. This means that the shade of pink you get with Can A is likely to be darker and more red due to the higher concentration of red.

Can B, on the other hand, has a lower percentage of red, suggesting that the resulting pink hue is lighter and less red than can A.  

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Answer:

so the answer should be g if not im sorry

Step-by-step explanation:

Answer:

1) x < -1

2) x ≥ -1

3) x ≤ -1

4) x < -1 and x > 0

5) -1 < x < 0

Explanation:

(1) f(x) > 0

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 > \:0\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x > \:2\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x > \:2^{-1}\)

\(\sf \rightarrow x < -1\)

(2) f(x) ≤ 0

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 \leq \:0\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x \leq \:2\)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x \leq \:2^{-1}\)

\(\sf \rightarrow x\geq -1\)

(3) g(x) ≥ 0

\(\sf \rightarrow -\dfrac{2}{x}-2 \:\geq \:0\)

\(\sf \rightarrow -\dfrac{2}{x} \:\geq \:2\)

\(\sf \rightarrow \dfrac{1}{x} \:\geq \:-1\)

\(\sf \rightarrow x \: \leq \:-1\)

(4) g(x) < 0

\(\sf \rightarrow -\dfrac{2}{x}-2 \: < \: 0\)

\(\sf \rightarrow x < -1 \ or \ x > 0\)

Observe the graphs a find solution for g(x) < 0

(5) f(x) < g(x)

\(\sf \rightarrow \left(\dfrac{1}{2}\right)^x-2 < -\dfrac{2}{x}-2\)

\(\sf \rightarrow -1 < x < 0\)

Answer:

okay

Step-by-step explanation:

Answer:

\(\huge\boxed{\sf \$ \ 8.79\ per\ hour}\)

Step-by-step explanation:

Work hours = 2:00 pm - 11:00 pm

So,

9 hours = $79.11

Using unitary method

9 hours = $79.11

Divide both sides by 9

1 hour = $79.11/9

1 hour = $8.79

So, Kenya is being paid $8.79 per hour.

\(\rule[225]{225}{2}\)

The simplest expression that represents the total number of beads in her bracelet design is 2b + 7.

Expression:

An expression is the  sentence with a minimum of two numbers or variables and at least one math operation.

This math operation can be addition, subtraction, multiplication, or division.

The structure of an expression is:

Expression = (Number/variable, Math Operator, Number/variable)

Given,

Jewelry Marena is using a certain number of blue beads in a bracelet

design. she will use 7 more red beads than blue beads.

Here we need to write an expression in simplest form that represents the total number of beads in her bracelet design.

Assign a variable for the unknown value.

Let b be the number of blue beads for the bracelet.

The number of red beads will be represented as b + 7.

Determine the expression for the total number of beads.

Then we can written it as,

=> b + (b +7)

=> 2b + 7.

Therefore, the total number of beads can be written as 2b + 7.

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Answer:

There are 10 cards in the stack, and 5 of them are odd (1, 3, 5, 7, and 9). There are 3 cards (1, 2, and 3) that are less than 4. Since we are replacing the first card before selecting the second, the outcomes are independent and we can multiply the probabilities of each event.

The probability of selecting an odd card on the first draw is 5/10, or 1/2.

The probability of selecting a card less than 4 on the second draw is 3/10, since there are 3 cards that meet this condition out of a total of 10.

Therefore, the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is:

(1/2) x (3/10) = 3/20

So the probability of selecting an odd card on the first draw and a card less than 4 on the second draw is 3/20.

Step-by-step explanation:

Answer:

3/20.

Step-by-step explanation:

To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is:

5/10 x 3/10 = 15/100

We can simplify this fraction by dividing both the numerator and denominator by 5:

15/100 = 3/20

So, the final answer is 3/20.

Received message. To find the probability of two independent events happening together, we multiply their individual probabilities. The probability of the first card being an odd number is 5/10, because there are 5 odd numbers out of 10 cards. The probability of the second card being less than 4 is 3/10, because there are 3 cards (1, 2, and 3) that are less than 4 out of 10 cards. Therefore, the probability of the first card being an odd number and the second card being less than 4 is: 5/10 x 3/10 = 15/100 We can simplify this fraction by dividing both the numerator and denominator by 5: 15/100 = 3/20 So, the final answer is 3/20.

By solving the given equation f(x) = \(x^{2} +3x-40\), the zeroes are -3 and 5.

To solve the given equation we have to do the factorization.

What is factorization: Factorization is the method of writing numbers as the product of their factors or divisors.  In other words, we can say finding what to multiply together to get an expression.

To do the factorization, we have to follow the steps as shown below:

 \(x^{2} +3x-40\) \(= 0\)

\(-40 = 8 * -5\\\)                        [ multiplication of 8 and -5 is -40]

\(x^{2}+8x-5x -40\) \(= 0\)

\(x(x+8) -5(x+8)\) \(= 0\)

\((x-5)(x+8)\) \(= 0\)

\(x = 5\)   and  \(x = -8\)              [ The roots or zeroes]

From the above solution, we can conclude that the zeros of the given function \(x^{2} +3x-40\) are 5 and -8.

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Answer:

P = 74

Step-by-step explanation:

14 + 60 = 74

Answer:

\(=12\sqrt{15} -40\sqrt{5}\\\)

Step-by-step explanation:

\((2\sqrt{10} )(3\sqrt{6} -5\sqrt{8} )=(2\sqrt{10} )(3\sqrt{6} )-(2\sqrt{10} )(5\sqrt{8} )\)

\(=6\sqrt{60} -10\sqrt{80}\)

\(=6\sqrt{4(15)} -10\sqrt{16(5)}\)

\(=6(2)\sqrt{15} -10(4)\sqrt{5}\)

\(=12\sqrt{15} -40\sqrt{5}\)

Hope this helps

Answer: a. y = - 1/2x + 2

b. y = -3 + 1

Step 1: 6/5

Step 2: I Do not know

Step-by-step explanation:

a. y = mx + b

The m part is the slope and the b part is the y-intercept

b. When you replace the coordinates (x and y) in the equation, you get 4 = -3(-1) + b which equals to 1 = b

Step 1. Use the rise over run equation. So you have to subtract the y coordinates on top and the x coordinates on the bottom. In this case, it's 5 - (-1) for rise and 3 - (-2) for run. In the end, the answer should be 6/5

Step 2: Sorry I do not know this one.

Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In △RST;

The vertices are, R(4, 1), S(7, 3), and T(6, 4)

Here, Translation: (x, y) → (x, y−1)

And, Reflection in the y-axis.

Hence, New coordinate of the image of △RST are,

⇒ R' = (- 4, 1 - 1) = (- 4, 0)

⇒ S' = (- 7, 3- 1) = (- 7, 2)

⇒ T' = (- 6, 4 - 1) = (- 6, 3)

Thus, Graph △RST with vertices R(4, 1), S(7, 3), and T(6, 4) and its image after the glide reflection is shown in figure.

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(a) The expected time between two successive arrivals is 100 / (25 + y).

If X has a geometric distribution with parameter p, the expected time between two successive arrivals can be calculated as the reciprocal of the probability of success, which is 1/p.

In this case, the parameter p is given as (25 + y)/100.

Therefore, the expected time between two successive arrivals is:

Expected time = 1 / p = 1 / [(25 + y)/100] = 100 / (25 + y)

So, the expected time between two successive arrivals is 100 / (25 + y).

(b) If X has an exponential distribution with parameter λ, the probability density function (PDF) of the exponential distribution is given by:

f(x) = λ * e^(-λx)

To find P(X < t), where t is a specific time value, we need to calculate the cumulative distribution function (CDF) of the exponential distribution, which is given by:

F(x) = 1 - e^(-λx)

In this case, λ is given as 1. So, the CDF becomes:

F(x) = 1 - e^(-x)

To calculate P(X > t), we can subtract P(X < t) from 1:

P(X > t) = 1 - P(X < t) = 1 - (1 - e^(-t))

Simplifying further:

P(X > t) = e^(-t)

Therefore, P(X > t) for an exponential distribution with λ = 1 is simply e^(-t)

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The probability that 2 to 4 out of 27 rubber rafts develop cracks is 0.117. The probability that a single rubber raft develops a crack is 0.12.

We can use the binomial distribution to calculate the probability that 2 to 4 out of 27 rubber rafts develop cracks. The binomial distribution is a probability distribution that describes the number of successes in a fixed number of trials. In this case, the success is a rubber raft developing a crack and the trials are the 27 rubber rafts that are tested.

The formula for the binomial distribution is:

P(X = k) = nCk p^k (1 - p)^(n - k)

where:

In this case, we want to calculate the probability that there are 2 to 4 successes (rubber rafts that develop cracks) in 27 trials (number of rubber rafts tested).

So, we can set n = 27, k = 2, and k = 3. We can then plug these values into the formula for the binomial distribution to get the following probabilities:

P(X = 2) = 27C2 (0.12)^2 (0.88)^(25) = 0.117

P(X = 3) = 27C3 (0.12)^3 (0.88)^(24) = 0.038

The total probability that 2 to 4 out of 27 rubber rafts develop cracks is the sum of these two probabilities: 0.117 + 0.038 = 0.155. However, we need to round our answer to four decimal places, so the final answer is: 0.117.

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Answer:

3

Step-by-step explanation:

Answer:

grams because it's smaller amounts measured and kilograms are high amount of measurements.