If (x + 1)(x-3) = 5, then which of the following statements is true?

Ox+1=0 orx-3=0
Ox+1=5 orx-3=5
Ox-4-0 orx+2=0

Answer:

a

Step-by-step explanation:

the answer is a. 6 faces 12 edges and 8 vertices

Answer:

I beleive it is the first option

Step-by-step explanation:

Answer:

equation of line

(-2,7) as (x,y)

-2 as x point

7 as y point

slope of line = -4

its formula

y- y1=s(x - x1)

y - 7 = -4(x - (-2)

y - 7 = -4(x + 2)

y - 7 = -4x - 8

y + 4x = -8 + 7

y + 4x = -1

Using linear approximation, we estimate that √65.3 ≈ 47.822, rounded to four decimal places.

To use linear approximation, we need to find the equation of the tangent line to the function f(x) at x=64. Then, we can use this tangent line to approximate the value of f(x) near x=64.

First, let's find the equation of the tangent line to f(x) at x=64. The slope of the tangent line is given by the derivative of f(x) at x=64:

f'(x) = √3/2x^(1/2)

f'(64) = √3/2(64)^(1/2) = √3/2 * 8 = 4√3

Equation of tangent line f(x) at x=64:

y - f(64) = f'(64)(x - 64)

y - 64√3 = 4√3(x - 64)

y = 4√3x - 128√3

Now, we can use this tangent line to approximate f(x) near x=64. We want to estimate √65.3, which is close to x=64. Let's substitute x=65.3 into the equation of the tangent line:

y = 4√3(65.3) - 128√3 ≈ 47.822

Therefore, using linear approximation, we estimate that √65.3 ≈ 47.822, rounded to four decimal places.

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Answer:

19;30

Step-by-step explanation:

Adding them together is the total

Answer:

a) y = 0

Step-by-step explanation:

Given equation,

→ 3y - 7(y + 5) = y - 35

Now the value of y will be,

→ 3y - 7(y + 5) = y - 35

→ 3y - 7y - 35 = y - 35

→ -4y - y = -35 + 35

→ -5y = 0

→ y = 0/-5

→ [ y = 0 ]

Hence, the value of y is 0.

The values of h'(5) are:

a. 4.36

b. -55.80

c. -8.51

To find h'(5) for each function, we need to apply the chain rule. Let's calculate the derivative of each function and evaluate it at x = 5.

\((a) h(x) = (4f(x) - 5e^{x/9})^2\)

Using the chain rule, we have:

\(h'(x) = 2(4f(x) - 5e^{x/9}(4f'(x) - 5e^{x/9})\)

Substituting x = 5 and the given values:

\(h'(5) = 2(4f(5) - 5e^{5/9})(4f'(5) - 5e^{5/9})\)

Substituting f(5) = 3 and f'(5) = -2:

\(h'(5) = 2(4(3) - 5e^{5/9})(4(-2) - 5e^{5/9})\)

= 4.36

(b) h(x) = 60ln(f(x)) / (x² + 4)

Using the quotient rule, we have:

h'(x) = [(60 / f(x))(f'(x))(x² + 4) - 60ln(f(x))(2x)] / (x² + 4)²

Substituting x = 5 and the given values:

h'(5) = [(60 / f(5))(f'(5))(5² + 4) - 60ln(f(5))(2(5))] / (5² + 4)²

Substituting f(5) = 3 and f'(5) = -2:

h'(5) = [(60 / 3)(-2))(5² + 4) - 60ln(3)(2(5))] / (5² + 4)²

h'(5) = -55.80

(c) \(h(x) = e^{f(x)}\times cos(5\pix)\)

Using the chain rule and product rule, we have:

\(h'(x) = (e^{f(x)})(f'(x)) \times cos(5\pi x) - (e^{f(x)})\times sin(5\pix) \times (5\pi)\)

Substituting x = 5 and the given values:

\(h'(5) = (e^{f(5)})(f'(5))\timescos(5\pi(5)) - (e^{f(5)})\times sin(5\pi (5))\times(5\pi)\)

Substituting f(5) = 3 and f'(5) = -2:

\(h'(5) = (e^3)(-2) \times cos(25\pi) - (e^3) \times sin(25\pi) \times (5\pi)\)

h'(5) = -8.51

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If inlet pipe can fill empty pool in 9 hours, and a drain can empty pool in 15 hours, then it take the pipe 22.5 hours to fill pool if drain is left open.

Let us assume that the pool has a volume of 1 unit.

The inlet pipe can fill pool in 9 hours, so it can fill 1/9 of the pool in one hour.

The drain pipe can empty  pool in 15 hours, so it can empty 1/15 of pool in one hour.

Let time taken for pool to be filled when inlet pipe and drain pipe are working simultaneously be = x hours,

This means that pool is getting filled at  "1/x" per hour.

So, Net amount of water added to pool per hour is :

⇒ (1/x) = (1/9) - (1/15),

⇒ (1/x) = 2/45,

⇒ x = 45/2 = 22.5,

Therefore, the time taken to fill up a unit volume of water when both pipes are open is 22.5 hours.

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The amount of cream in the coffee cup and the amount of coffee in the pitcher of cream remain the same.

When a spoonful of cream is taken from the pitcher and put into the coffee cup, the amount of cream in the pitcher decreases and the amount of cream in the coffee cup increases.

However, when a spoonful of the mixture is put back into the pitcher, the amount of cream in the pitcher increases again and the amount of cream in the coffee cup decreases.

Since the amount of coffee in the pitcher and the cup remains constant throughout this process, there is no net increase or decrease in the amount of coffee or cream in either container.

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f(x)>=-7

Functions:

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics.

If a variable y is so related to a variable x that whenever a numerical value is assigned to x, there is a rule according to which a unique value of f(x)is determined, then f(x) is said to be a function of the independent variable x

Given :

f(x) = -3|x+1|-4

using the table of values for g(x) = |x|

Solution :

f(x) = -3|x+1|-4

f(x) = -3|g(x)+1|-4

f(x) = -3||x|+1|-4

which means |x| is always positive |x|>0

f(x) = -3||x|+1|-4

f(x) = -3x-3-4

f(x) = -3x-7

f(x)>=-7

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t distributions tend to be flatter and more spread out than the normal distribution.

This is due to the fact that in the formula, the denominator is s rather than σ.

The distribution of the sample mean is normal if some samples are taken from a normal population with known variance. However, if the population variance is unknown, the distribution is not normal but Student-t with long tails. This means that sample means tend to be extreme when the population variance is unknown. Using the normal distribution instead of the t distribution to test the hypothesis increases the chance of error.

Note that there is a different t-distribution for each sample size. That is, the class of distributions. When talking about a particular t-distribution, we need to specify the degrees of freedom. The degrees of freedom for this t-statistic is given by the sample standard deviation s in the denominator of Equation 1. The spread is larger than the standard normal distribution. This is because the denominator of equation (1) is s, not σ. Because s is a random variable that changes from sample to sample, t becomes more volatile and more spread out.

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The largest possible rank of A is 5, which is the number of rows in the matrix. This occurs when all rows are linearly independent, meaning that no row can be written as a linear combination of the others. In this case, the columns of A would also be linearly independent, and the matrix would be said to have full rank.


The smallest possible rank of A is 0, which would occur if A is the zero matrix (i.e., all entries are zero). In this case, the columns of A would be linearly dependent, since any linear combination of them would also be zero.

The largest possible nullity of A is 8 - 5 = 3, which is the difference between the number of columns and the rank of A. This occurs when there are 3 linearly dependent columns in A, which means that there are 3 free variables in the equation Ax = 0.

The smallest possible nullity of A is 0, which would occur if A has full rank (i.e., all columns are linearly independent). In this case, the only solution to Ax = 0 is x = 0, and the nullspace is just the zero vector.
The matrix A is a 5x8 matrix, meaning it has 5 rows and 8 columns. The rank of a matrix refers to the number of linearly independent rows or columns in the matrix. The nullity of a matrix refers to the dimension of its null space.

1. The largest rank of A: Since there are 5 rows in matrix A, the largest rank it could have is 5.

2. The smallest rank of A: If all rows are linearly dependent, the smallest rank of A would be 0.

3. The largest nullity of A: According to the Rank-Nullity Theorem, rank(A) + nullity(A) = n (number of columns). If the rank is at its smallest (0), the largest nullity would be equal to the number of columns, which is 8.

4. The smallest nullity of A: If the rank is at its largest (5), the smallest nullity would be n - rank(A) = 8 - 5 = 3.

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Exponential smoothing is a popular forecasting technique used to predict future trends in time-series data. It works by assigning weights to historical data points, with more recent data points receiving higher weights. The level of smoothing is controlled by a smoothing parameter called alpha, which ranges between 0 and 1. As alpha increases, the influence of older data points decreases, and the model becomes more reactive to recent changes in the data.

When alpha is high, the exponential smoothing model group of answer choices tends to produce sluggish forecasts. This is because the model gives more weight to recent data points, which can cause it to overreact to short-term fluctuations in the data. As a result, the model may miss important trends or patterns in the data that would have been captured by a more balanced weighting scheme.

On the other hand, when alpha is low, the model tends to be more stable and less reactive to short-term changes in the data. This can be useful for predicting long-term trends or for smoothing out noisy data sets.

In summary, the choice of alpha in an exponential smoothing model depends on the characteristics of the data and the goals of the forecast. A high alpha value may be appropriate for short-term forecasting or for data sets with high volatility, while a low alpha value may be more suitable for long-term forecasting or for data sets with low volatility.

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Answer:

4(x + 12) = 4x + 48

Step-by-step explanation:

Answer:

2(2x + 6)

Step-by-step explanation:

Answer:

$951.50

Step-by-step explanation:

Answer:

y = 1/5x

Step-by-step explanation:

Answer:

4 (5c - 2d)

Step-by-step explanation:

We factorise .

4×5c - 4×2d

20c -8d

Hope it helped.

In 1940, John Atanasoff, a physicist from Iowa State University, wanted to solve a 29 x 29 linear system of equations. To solve this system using Gaussian elimination, it would have required approximately 29^3/3 = 24389 arithmetic operations.

In 1940, John Atanasoff developed the Atanasoff-Berry Computer (ABC), which was the first electronic computer. Atanasoff wanted to use the ABC to solve a 29 x 29 linear system of equations.

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Answer:

X = 56 degrees (rounded)

Step-by-step explanation:

in this case we are given the hypotenuse and adjacent measurments, this means we need to us cos to find the angel

\( \cos(x) = \frac{5}{9}\)

\(x = \cos^{ - 1} ( \frac{5}{9} ) \)

\(x = 56.2510114\)

Answer:

I think so but I'm not 100% sure

For the given statement option C  increase, wider and decrease , narrower is correct.

What is confidence interval?

A confidence interval is computed at a designated confidence level; the  95% confidence level is most common, but other levels, such as 90% or  99%, are sometimes used.

When constructing a confidence interval, if the level of confidence increases, the margin of error must Increase and the confidence interval will be Wider.

Hence  Increase; wider is the correct answer.

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The sample space is the set of all possible outcomes that can result from a random experiment. In this case, the random experiment is drawing one card from a deck of ten cards. We need to find the size of the sample space.The total number of cards is 10. Therefore, the size of the sample space is 10 (since there are 10 possible outcomes).The probability of drawing a blue card is the number of favorable outcomes divided by the number of possible outcomes. Since there are 3 blue cards in the deck, the number of favorable outcomes is 3. The number of possible outcomes is 10. Hence, the probability of drawing a blue card is:P(B) = favorable outcomes / possible outcomesP(B) = 3/10P(B) = 0.3Similarly, the probability of drawing an odd-numbered card is the number of favorable outcomes divided by the number of possible outcomes. Since there are 4 odd-numbered cards (1, 3, 5, 7), the number of favorable outcomes is 4. The number of possible outcomes is 10. Hence, the probability of drawing an odd-numbered card is:P(O) = favorable outcomes / possible outcomesP(O) = 4/10P(O) = 0.4

The are 10 elements on the sample space and the probability of drawing a blue card is 0.3.

There are 10 cards in total, so the sample space consists of 10 possible outcomes. Therefore, the number of elements in the sample space is 10.

Now let's calculate the probability of drawing a blue card (B). Since there are 3 blue cards out of 10 total cards, the probability of drawing a blue card is:

P(B) = Number of favorable outcomes / Total number of possible outcomes

= 3 / 10

= 0.3

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There are 16 people who share the worm.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this illustration, Vince brought 6 boxes of worms to use as bait while fishing with his friends if each person uses exactly 3 8ths of a box of worms

The number of people who shared the works will be:

= Number of worms / Amount collected by each person

= 6 ÷ 3/8

= 6 × 8/3

= 16

In conclusion, 16 people shared it.

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Answer:

D) 18!

Step-by-step explanation:

HAHAHAHAHH BESTIEE

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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We have the next information

48000 represent the 100%

8640 represent the ?

ANSWER

8640 represent the 18%

A statistically significant negative correlation coefficient of r = -0.91 was obtained from a sample of n = 30. This indicates a strong and significant negative relationship between the variables.

The researcher conducted a correlation analysis and found a correlation coefficient (r) of -0.91, which indicates a strong negative relationship between the variables under investigation. The negative sign indicates that as one variable increases, the other variable tends to decrease, and vice versa.

The statistical significance of the correlation coefficient is crucial in determining whether the observed relationship is likely to be due to chance or if it truly exists in the population. In this case, the report should highlight that the obtained correlation coefficient is statistically significant.

To establish statistical significance, the researcher likely conducted a hypothesis test, such as a t-test or a permutation test, to determine the probability of obtaining a correlation coefficient as extreme as -0.91 under the null hypothesis of no correlation. Since the obtained correlation coefficient is statistically significant, it suggests that the observed negative relationship is unlikely to be a result of chance and provides evidence for a genuine association between the variables in the population from which the sample was drawn.

Reporting this finding is important for conveying the strength and significance of the negative relationship to the readers, providing valuable insights for further analysis and interpretation of the variables under investigation.

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well, clearly is 4 :).

now, if we take 25 to be the 100%, what is 4 off of it in percentage?

\(\begin{array}{ccll} amount&\%\\ \cline{1-2} 25 & 100\\ 4& x \end{array} \implies \cfrac{25}{4}~~=~~\cfrac{100}{x} \implies 25x=400\implies x=\cfrac{400}{25}\implies x=16\)

Therefore, the measure of the central angle whose radii define the given arc is approximately 83.077 degrees.

The length of an arc on a circle is given by the formula:

Arc Length = (Central Angle / 360°) * Circumference

In this case, we know the arc length is 6π centimeters, and the radius of the circle is 13 centimeters. The circumference of the circle can be calculated using the formula:

Circumference = 2π * Radius

Substituting the radius value, we get:

Circumference = 2π * 13

= 26π

Now we can use the arc length formula to find the central angle:

6π = (Central Angle / 360°) * 26π

Dividing both sides of the equation by 26π:

6π / 26π = Central Angle / 360°

Simplifying:

6 / 26 = Central Angle / 360°

Cross-multiplying:

360° * 6 = 26 * Central Angle

2160° = 26 * Central Angle

Dividing both sides by 26:

2160° / 26 = Central Angle

Approximately:

Central Angle ≈ 83.077°

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Answer:

90(8) + 2(38) = 270 + 76 = 346p

Step-by-step explanation: