Determine the solutions of the equation:


x = −11 and x = 5
x = −81 and x = 45
x = −99 and x = 45
x = −99 and x = 99

I dont know sorry

So sorry really wish i could help

The measurements of width w is x + 8 and height h is x - 1 when volume of a rectangular prism is given by V(x) = x³ + 3x² - 36x + 32.

Given that,

The volume of a rectangular prism is given by V(x) = x³ + 3x² - 36x + 32

We have to determine possible measures for w and h in terms of x if the

length I is x-4.

We know that,

The volume of a rectangular prism V = w×h×l

x³ + 3x² - 36x + 32 = w×h×(x-4)

w×h = \(\frac{x^3 + 3x^2 - 36x + 32}{x - 4}\)

Now, by using long division of equation

x - 4) x³ + 3x² - 36x + 32 ( x² + 7x - 8

        x³ - 4x²

----------------------------------------(subtraction)

              7x² - 36x + 32

              7x² - 28x

----------------------------------------(subtraction)

                       -8x + 32

                       -8x + 32

----------------------------------------(subtraction)

                              0

So,

w×h = x² + 7x - 8

Now, finding the root of equation

w×h = x² + 8x - x - 8

w×h = (x + 8)(x - 1)

Therefore, The measurements of width w is x + 8 and height h is x - 1.

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Answer:

y = 2x + 3  → Gradient / slope = 2 → Y - intercept = 3

y = -3x + 3 → Gradient / slope = -3 → Y - intercept = 3

Step-by-step explanation:

y = mx + c

This is the standard way an equation of a line is written. The 'm' of the line is the slope/gradient and the 'c' is the y - intercept. You can find the x-intercept by making y = 0. When the questions asks you to find the gradient you should never put 'x' after it only the number so

y = 2x + 3

Gradient / slope = 2

Y - intercept = 3

y = -3x + 3

Gradient / slope = -3

Y - intercept = 3

Answer:

$240.87 is how much you made. Hope this helps and I wish you luck.

Answer:

X − 4.2

Step-by-step explanation:

Answer:

x - 4.2

Step-by-step explanation:

x + 1 - 1 = x

so x - 4.2 is the simplest i believe <3

These are sequence that increases in an exponential manner. The value of the log function is 55

These are sequence that increases in an exponential manner. The nth term of the sequence is expressed as:

Tn = ar^n-1

Given the following

Substitute

Tn = x = 8(2)^52
x = 8(2)^52

Take the log of the result to have:

\(log_28(2)^{52} = log_22^{55}\\ log_22^{55} = 55log_22=55\)

Hence the value of the log function is 55

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The number 9 x 10^7 is 30,000 times greater than the number 3 x 10³.

To obtain how many times a number a is greater than a number b, we have to obtain the ratio, which is the division of the number a by the number b.

The numbers in this problem are given as follows:

The division of these two numbers is given as follows:

(9 x 10^7)/(3 x 10³).

The division of the two coefficients is given as follows:

9/3 = 3.

For the powers of 10, we have the division of two terms with the same base and different exponents, hence we keep the base and subtracted the exponents, as follows:

10^7/10³ = 10^(7 - 3) = 10^4 = 10,000.

Hence the complete quotient is given as follows:

3 x 10,000 = 30,000.

Which is how many times the number 9 x 10^7 is greater than the number 3 x 10³.

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Answer:

2,375 m

Step-by-step explanation:

The computation of the distance from his walk to the bus stop is given below:

Let us assume he walks be x

So the bus trip be 4x

4x + 500m

From Home to school, it would be 10km

As we know

1km = 1000m

So for 10km it would be  = 10,000 m

4x + 500 m = 10,000 m

4x = 10,000 m - 500 m

4x = 9,500 m

x = 2,375 m

Answer:

Angie

Step-by-step explanation:

When it is negative it basically means you owe that amount and Angie owes the most

Answer:

Angie because the bigger a negative number it the less in value it is.

Step-by-step explanation:

a) Randomization ,Independence and Normality is required for constructing a confidence interval.

b) The standard error is \[0.014\].

(a) Conditions required for constructing a confidence interval are as follows:

Randomization: We must use simple random sampling or any other sampling technique that ensures that each sample of the given size is equally likely to be selected.

Independence: Sampling is done without replacement when the sample size is less than 10% of the population size. When the sample size is larger than 10% of the population size, the sampling distribution is assumed to be approximately normal.

Normality: The sampling distribution is approximately normal when the population distribution is normal or the sample size is sufficiently large (n > 30).

(b) Standard error is calculated as:

$$SE = \sqrt{\frac{p(1-p)}{n}}$$

Where:p = 64/752 = 0.08511 - p = 0.085

n = 752 SE = \[\sqrt{\frac{0.085(1-0.085)}{752}}\]

SE = \[0.014\]

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For a Poisson process with rate λ, the interarrival times between events are exponentially distributed with parameter μ = 1/λ. So, the time between the (n-1)-th and n-th event, denoted as Tn, follows an exponential distribution with parameter μ = 1/3 minutes.

Since Sn is the sum of the first n interarrival times, we have:

Sn = T1 + T2 + ... + Tn

The sum of n exponential random variables with parameter μ is a gamma random variable with shape parameter n and scale parameter μ. Therefore, Sn follows a gamma distribution with shape parameter n and scale parameter μ.

In this case, n = 10 and μ = 1/3. So, E[S10] can be calculated as:

E[S10] = n * μ = 10 * (1/3)

= 10/3 minutes.

Therefore, E[S10] = 10/3 minutes.

b. E[S4|N(1) = 3]:

Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, the time of the 4th event, S4, will be the sum of the first 3 interarrival times plus the time between the 3rd and 4th event.

Using the same reasoning as in part a, we know that the sum of the first 3 interarrival times follows a gamma distribution with shape parameter 3 and scale parameter 1/3. The time between the 3rd and 4th event, denoted as T4, follows an exponential distribution with parameter 1/3.

So, S4 = T1 + T2 + T3 + T4.

Since T1, T2, T3 are independent of T4, we can calculate E[S4|N(1) = 3] as:

E[S4|N(1) = 3] = E[T1 + T2 + T3 + T4]

= E[T1 + T2 + T3] + E[T4]

= (3/3) + (1/3)

= 4/3 minutes.

Therefore, E[S4|N(1) = 3] = 4/3 minutes.

c. Var(S10):

The variance of Sn, Var(Sn), for a Poisson process with rate λ, is given by:

Var(Sn) = n * σ^2,

where σ^2 is the variance of the interarrival times.

In this case, n = 10 and the interarrival times are exponentially distributed with parameter μ = 1/3. The variance of an exponential distribution is \(\mu^2\)So, \(\sigma^2 = \left(\frac{1}{3}\right)^2\)

= 1/9.

Substituting the values into the formula, we have:

Var(S10) = 10 * (1/9)

= 10/9.

Therefore, Var(S10) = 10/9.

d. E[N(4) − N(2)|N(1) = 3]:

Given that N(1) = 3, we know that there are 3 events in the first minute. Therefore, at time t = 2 minutes, there will be 3 - 1 = 2 events that have already occurred.

Now, we need to find the expected value of the difference in the number of events between time t = 4 minutes and t = 2 minutes, given that there were 3 events at t = 1 minute.

Since the number of events in a Poisson process follows a Poisson distribution with rate λt, where t is

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Answer:

i think you need apply the compound interest

Answer:

90 degrees

Step-by-step explanation:

The final answers are as follows: Function f(x) is even.

Function g(x) is odd.

Function h(x) is neither even nor odd

To determine if a function is even, we check if f(x) = f(-x) for all x in the domain. Let's evaluate f(x) and f(-x) for the given function:

f(x) = \(x^{2}\) + 2\(x^{4}\)

f(-x) = \(-x^{2}\) + 2\(-x^{4}\)

Since f(x) = f(-x), the function is even.

Function: g(x) = \(x^{3}\) - x

To determine if a function is odd, we check if f(x) = -f(-x) for all x in the domain. Let's evaluate g(x) and -g(-x) for the given function:

g(x) = \(x^{3}\) - x

-g(-x) = -\(x^{3}\) - (-x) = -\(x^{3}\) + x

Since g(x) = -g(-x), the function is odd.

Function: h(x) = 2x + \(x^{2}\)

To determine if a function is even or odd, we need to satisfy the conditions mentioned above. Let's evaluate h(x) and h(-x) for the given function:

h(x) = 2x + \(x^{2}\)

h(-x) = 2(-x) + -\(x^{2}\) = -2x + \(x^{2}\)

Since h(x) is not equal to h(-x) or -h(-x), the function is neither even nor odd.

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The approximate probability that one of the 1000 books published this week will contain almost 3 pages with errors is 0.414 or 41.4%. Note that this is an approximation because the Poisson distribution assumes independence between the trials, but errors may be correlated within a book or across books.

To solve this problem, we can use the Poisson distribution, which approximates the probability of rare events occurring over a large number of trials. In this case, the rare event is a page containing an error, and the large number of trials is the 1000 books published.
The average number of pages with errors per book is p * number of pages = 0.005 * 500 = 2.5. Using the Poisson distribution, we can find the probability of having almost 3 pages with errors in one book:
P(X = 3) = (e^(-2.5) * 2.5^3) / 3! = 0.143
This is the probability of having exactly 3 pages with errors. To find the probability of having almost 3 pages (i.e., 2 or 3 pages), we can sum the probabilities of having 2 and 3 pages:
P(X = 2) = (e^(-2.5) * 2.5^2) / 2! = 0.271
P(almost 3 pages) = P(X = 2) + P(X = 3) = 0.271 + 0.143 = 0.414
Therefore, the approximate probability that one of the 1000 books published this week will contain almost 3 pages with errors is 0.414 or 41.4%. Note that this is an approximation because the Poisson distribution assumes independence between the trials, but errors may be correlated within a book or across books.

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Answer:

2.7027027027027027

Step-by-step explanation:

1,000 grams make a kilogram

Answer:

Top left

Step-by-step explanation:

Look at the numbers it's going through. The x axis is the one going side to side, y is up and down

Answer:

Sorry, but I can't see this well! I am on lapton, and it is impossible to tilt the whole thing over.

Answer: A: 145 degrees

Step-by-step explanation:

If two random variables, Y1 and Y2, are independent, the condition that needs to be satisfied is that the joint probability distribution of Y1 and Y2 factors into the product of their individual probability distributions.

Mathematically, for independent random variables Y1 and Y2, the condition can be expressed as:

P(Y1 = y1, Y2 = y2) = P(Y1 = y1) * P(Y2 = y2)

This means that the probability of both events Y1 = y1 and Y2 = y2 occurring together is equal to the product of the probabilities of each event occurring individually.

In simpler terms, knowing the outcome or value of one random variable does not provide any information about the outcome or value of the other random variable if they are independent. They do not influence each other's probability distributions.

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Answer:

.

Step-by-step explanation:

Answer:

-3 , -2 , -0.8 , 0.8 , 7

hope this helps...

Answer:

i really dk

Step-by-step explanation:

im only 5......

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Answer: y = -0.5x + 1

It can be evaluated using the limit comparison test or by integrating 1/\(x^3\) directly to get -1/2\(x^2\) evaluated from 1 to infinity, Therefore, the integral converges to 1/2.

The integral can be written as:

∫₁^∞ 1/x³ dx

To determine whether the integral converges or diverges, we can use the p-test for integrals. The p-test states that:

If p > 1, then the integral ∫₁^∞ 1/xᵖ dx converges.

If p ≤ 1, then the integral ∫₁^∞ 1/xᵖ dx diverges.

In this case, p = 3, which is greater than 1. Therefore, the integral converges.

To evaluate the integral, we can use the formula for the integral of xⁿ:

∫ xⁿ dx = x (n+1)/(n+1) + C

Using this formula, we get:

∫₁^∞ 1/x³ dx = lim┬(t→∞)⁡(∫₁^t 1/x³ dx)

             = lim┬(t→∞)⁡[ -1/(2x²) ] from 1 to t

             = lim┬(t→∞)⁡( -1/(2t²) + 1/2 )

             = 1/2

Therefore, the integral converges to 1/2.

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To determine if this integral converges or diverges, we can use the p-test. According to the p-test, if the integral of the form ∫1∞ 1/x^p dx is less than 1, then the integral converges. If the integral is equal to or greater than 1, then the integral diverges.

In this case, p=3, so we have ∫1∞ 1/x^3 dx = lim t→∞ ∫1t 1/x^3 dx.

Evaluating the integral, we get ∫1t 1/x^3 dx = [-1/(2x^2)]1t = -1/(2t^2) + 1/2.

Taking the limit as t approaches infinity, we get lim t→∞ [-1/(2t^2) + 1/2] = 1/2.

Since 1/2 is less than 1, we can conclude that the given improper integral converges.

Therefore, the value of the integral is ∫1∞ 1/x^3 dx = 1/2.
To determine whether the improper integral converges or diverges, we need to evaluate the integral and see if it results in a finite value. Here's the given integral:

∫(1 to ∞) (1/x^3) dx

1. First, let's set the limit to evaluate the improper integral:

lim (b→∞) ∫(1 to b) (1/x^3) dx

2. Next, find the antiderivative of 1/x^3:

The antiderivative of 1/x^3 is -1/2x^2.

3. Evaluate the antiderivative at the limits of integration:

[-1/2x^2] (1 to b)

4. Substitute the limits:

(-1/2b^2) - (-1/2(1)^2) = -1/2b^2 + 1/2

5. Evaluate the limit as b approaches infinity:

lim (b→∞) (-1/2b^2 + 1/2)

As b approaches infinity, the term -1/2b^2 approaches 0, since the denominator grows without bound. Therefore, the limit is:

0 + 1/2 = 1/2

Since the limit is a finite value (1/2), the improper integral converges. Thus, the integral evaluates to:

∫(1 to ∞) (1/x^3) dx = 1/2

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Answer:

(0,6)

Step-by-step explanation:

The y intercept is where the line crosses the y axis or the coordinate where x = 0.

Here, when x is equal to 0, y is equal to 6 meaning that the y intercept is at (0,6)

1) The value of k in the polynomial division is: 4

2) The sum of all even integers from 10 to 500 is: 62220

When dividing polynomials, we know that if (x - a) is the root of a polynomial, then when we put a into the polynomial, the result will be zero.

Thus:

If kx³ – (k + 3)x² + 13 is divided by x – 4, and the remainder is 157, i means that:

k(4)³ – (k + 3)(4)² + 13 = 157

64k - 16k - 48 + 13 - 157 = 0

48k = 192

k = 192/48

k = 4

2) The series would look like this:

12, 14,16,........498

We know that:

aₙ = a + (n - 1)d

498 = 12 + (n - 1)2

498 - 12 = (n - 1)2

486/2 = n-1

243+1 = n

n = 244

Sₙ = ¹/₂n(a + l)

Sₙ = ¹/₂(244)(12 + 498)

= 122(510)

= 62220

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Answer: -1/4

Step-by-step explanation:

1-3= -2

-2/8 simplifies to -1/4  

The likelihood of single adolescent mothers breastfeeding their newborn infants is not statistically significant based on the given p-value of 0.18.

In statistical analysis, p-value measures the strength of evidence against the null hypothesis. A p-value less than 0.05 is typically considered statistically significant, indicating strong evidence against the null hypothesis. Conversely, a p-value greater than 0.05 suggests that there is not enough evidence to reject the null hypothesis.

In this case, the p-value of 0.18 indicates that there is a 18% chance that the observed results occurred by chance alone, assuming the null hypothesis is true. Since this p-value is greater than the commonly used threshold of 0.05, it suggests that there is not enough evidence to conclude a significant association between single adolescent mothers and breastfeeding rates of their newborn infants.

Based on the p-value of 0.18, there is no strong statistical evidence to suggest a significant association between being a single adolescent mother and the likelihood of breastfeeding their newborn infant. However, it is important to consider other factors and conduct further research to gain a comprehensive understanding of the relationship between these variables.

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