Given that -5 is a zero of the function f(x) = x^3 + x^2 - 14x + 30 find the remaining zeros

End behavior refers to graph of a polynomial function at the extreme ends, as the values approach positive or negative infinity. In other words, it says the behavior of the graph as the x-values get very large or very small.

To find the end behavior of a polynomial function, you can look at the degree (or highest power) of the polynomial, as well as the sign of the leading coefficient. The degree of a polynomial is the highest power of x in the polynomial, and the leading coefficient is the coefficient of the term with the highest power of x.

Here are some guidelines for finding the end behavior based on the degree and leading coefficient of the polynomial:

For example, consider the polynomial function f(x) = -3x^4 + 2x^3 + 5x - 1. The degree of the polynomial is 4, and the leading coefficient is -3. Since the degree is even and the leading coefficient is negative, we know that the end behavior will be the same on both sides of the graph, and the graph will approach negative infinity on both ends.

By knowing the end behavior, we can sketch the general shape of the graph of a polynomial function, without having to plot many points. This can be helpful when analyzing or comparing polynomial functions.

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\(\large \mathfrak{Solution : }\)

let's find the value of added tax :

The value of added tax (VAT) = ₹ 3277.5

Answer:

73.3 years

Step-by-step explanation:

Use the Compound Amount formula:

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

Here A = 3P, r = 0.015, n = 12, and so we have:

3 = (1 + 0.015/12)^(12*t).  Find t (in years)

3 = (1.00125)^(12*t)

Take the log of both sides.  We get:

log 3 = (12*t)(log 1.00125), or  0.47712 = (12*t)(5.425*10^(-4)

                                                 0.47712

Solving this for t, we get   t = ---------------------------  =  73.3 years

                                                 (12)(5.425*10^(-4))

Answer:

true

Step-by-step explanation:

Answer:

4/-15 is the slope

Step-by-step explanation:

Answer:

25 minutes

Step-by-step explanation:

they started at a quarter past 11, which is 11:15

they then played for 45 minutes, which would be until 12:00

you also know that they stopped playing at 10 minutes past 1, at 1:10.

before 1:10, they had been playing for 45 minutes, which means they started playing for the second time at 12:25.

all that's left is the time between 12:00 and 12:25, which is 25 minutes, so they spent 25 minutes stopping for a drink and a cookie.

The formula for y in terms of x is y = 8/x^3 and x is 1/2 when y = 64

The variation statement is given as

y is inversely proportional to the cube of x

This means that

y = k/x^3

Where k represents the constant of variation

Using the points on the table, we have

(x, y) = (1, 8)

This gives

8 = k/1^3

Evaluate

k = 8

So, we have

y = 8/x^3

Here, we have

y = 64 and y = 8/x^3

This gives

8/x^3 = 64

So, we have

x^3 = 1/8

Take the cube roots

x = 1/2

Hence, the value of x is 1/2

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The value of the test statistic is 6.51.

The test statistic for this problem can be calculated using the formula:

z = (p - P) / √(P * (1 - P) / n)

Where p is the sample proportion (0.67 in this case), P is the hypothesized population proportion (we don't know this value, so we assume it to be 0.5 for a two-tailed test), n is the sample size (380), and z is the standard normal distribution value corresponding to the level of significance.

Plugging in the values, we get:

z = (0.67 - 0.5) / √(0.5 * (1 - 0.5) / 380) = 6.51

So the value of the test statistic is 6.51.

The test statistic is a measure of how far the sample proportion deviates from the hypothesized population proportion under the null hypothesis. In this case, we assume that the population proportion is 0.5 (since we have no reason to believe otherwise), and we calculate the probability of observing a sample proportion of 0.67 or greater assuming this null hypothesis is true.

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Thus, the cost of the triangular lot land is approximately $81,940 found using Heron's formula.

To determine the cost of the triangular lot, you first need to calculate its area and then convert it to acres.

Given the three sides of the triangle (470 yards, 860 yards, and 1130 yards), you can use Heron's formula to find the area.

Heron's formula for the area of a triangle with sides a, b, and c is:
Area = √(s * (s - a) * (s - b) * (s - c))

where s is the semi-perimeter, calculated as:
s = (a + b + c) / 2

In this case, a = 470 yards, b = 860 yards, and c = 1130 yards.

Therefore, the semi-perimeter, s, is:

s = (470 + 860 + 1130) / 2 = 1230 yards

Now, plug the values into Heron's formula to calculate the area:

Area = √(1230 * (1230 - 470) * (1230 - 860) * (1230 - 1130))
Area ≈ 198,342.77 square yards

To convert square yards to acres, use the conversion factor:

1 acre = 4,840 square yards
So, the area in acres is:

198,342.77 square yards * (1 acre / 4,840 square yards) ≈ 40.97 acres

Finally, multiply the area in acres by the price per acre to find the cost:
Cost = 40.97 acres * $2000 per acre ≈ $81,940

The cost of the land is approximately $81,940.

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i)

The graph is attached  as an image.

ii.)  We notice that all the lines have the same slope of 2 which shows a consistent rate of change

A graph is described as as the pictorial representation of that represents any given data in a chronological manner that is ascending to descending type.

1. y =2x+8

x = 1

Y = 2(1)+8

Y= 2+8

Y = 10

2. y =2x + 2

x=2

Y= 2(2) +2

=4+2

Y=6

3. y= 2x – 3

x = 3

Y = 2(3) -3

Y= 6-3

Y=3

4. y = 2x -6

x=4

Y = 2(4) -6

Y= 8-6

Y=2

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Answer:

Step-by-step explanation:

(a + 2)/(a ^ 2 + a) - 3/(a - 2)​

The LCD is (a^2 + a)(a - 2) so we have

[(a + 2) - 3(a^2 + a)] /  (a^2 + a)(a - 2)

= (-3a^2 - 3a + a + 2) / (a^2 + a)(a - 2)

= -3a^2 - 2a + 2 / (a^2 + a)(a - 2)

Both angles AOB and COD are measured in the counterclockwise direction from the positive x-axis, we can say that angle AOB = angle COD.

To prove that AOAB is equal to AOCD, we need to show that angle AOAB is equal to angle AOCD.

Given that AOD and BOC are straight lines, we can see that angle AOD and angle BOC are supplementary angles, which means they add up to 180 degrees.

Since angle BOC is given as 70 degrees, angle AOD must be 180 - 70 = 110 degrees.

Now, let's consider triangle AOB. We have angle AOB, which is a right angle (90 degrees), and angle ABO, which is 70 degrees.

Since the sum of the angles in a triangle is 180 degrees, we can find angle AOB by subtracting the sum of angles ABO and BAO from 180 degrees:

AOB = 180 - (70 + 90)

   = 180 - 160

   = 20 degrees

Now, let's consider triangle COD. We have angle COD, which is a right angle (90 degrees), and angle CDO, which is 110 degrees.

Using the same logic as before, we can find angle COD by subtracting the sum of angles CDO and DCO from 180 degrees:

COD = 180 - (110 + 90)

   = 180 - 200

   = -20 degrees

Since both angles AOB and COD are measured in the counterclockwise direction from the positive x-axis, we can say that angle AOB = angle COD.

Therefore, we have proven that AOAB = AOCD.

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The new coordinates are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

A 180 degrees rotation denoted by R(180, 0) is a rotation that has the same effect as the 180 degrees counterclockwise of a figure.

And it has the algebraic rule of its rotation to be changed from (x, y) to (-x, -y) i.e  (x, y) ⇒ (-x, -y)

The coordinates of the parallelogram are given as

M(1, 7), N(8, 5), O(4, 2), and P(-3, 4)

The rotation is given as 180° rotation

As mentioned above,

We have (x, y) ⇒ (-x, -y)

Substitute M(1, 7), N(8, 5), O(4, 2), and P(-3, 4) in (x, y) ⇒ (-x, -y)

So, we have

M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

Hence, the coordinates of the image are M'(-1, -7), N'(-8, -5), O'(-4, -2), and P'(3, -4)

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The average Jeremy can create 24 different outfits for school by combining 1 pair of pants, 1 shirt, 1 tie, and 1 jacket.

Jeremy can mix and match his items to create different outfits for school. Since he owns 4 pairs of pants, 3 shirts, 3 ties, and 2 jackets, he can create 24 different outfit combinations. For each outfit, he must wear 1 pair of pants, 1 shirt, 1 tie, and 1 jacket. He can mix and match any of the items he owns to create a variety of looks. For example, he could wear a blue shirt, grey pants, and a striped tie with a black jacket. Or, he could wear a white shirt, black pants, a polka-dotted tie, and a brown jacket. By combining his items in different ways, he can create 24 different outfits for school.

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Answer:

y = x+1/3

Step-by-step explanation:

y = x+1/3 is adding 1/3 to the value of x

This is not a constant of proportionality, which is in the form\

y=kx

y = 1/3x

y = x/3 or multiplying by 3 on each side

3y =x

Answer:

the last option

Step-by-step explanation:

slope: 4/1

y-intercept: 12

hopefully this helps :)

Answer:

the answer will be this

Answer:

+4

Step-by-step explanation:

-5 - (-9)

-5 + 9

4

Answer:

4

Hope this helped and if I'm wrong sorry

Answer:

f−1(x)=x−3

Step-by-step explanation:

Using the values of the 5th and 95th percentiles of these variables, the bootstrap method may be used to generate the 90% confidence interval for the population standard deviation.

So, a random sample with replacement from the original sample must be taken thousands of times in order to determine the 90% confidence interval for the population standard deviation.

Therefore, using the values of the 5th and 95th percentiles of these variables, the bootstrap method may be used to generate the 90% confidence interval for the population standard deviation.

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Answer:

x=-9

Step-by-step explanation:

The interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.

The answer to this question is option D, which is μ - σ to Q3. To understand why this is the correct answer, we need to first understand what each of the intervals represents. Q1 and Q3 are the first and third quartiles of the data set, respectively. μ is the mean of the data set, and σ is the standard deviation.

When we look at the interval μ - σ to Q3, we can see that it includes the upper quartile and some of the data points to the left of it. This means that the area under the normal curve within this interval will be relatively small compared to the other options.

On the other hand, option B includes the mean and a larger range of data points, which would result in a larger area under the curve. Option C includes Q1 and a larger range of data points, which would also result in a larger area. Option A includes both Q1 and Q3, which cover the majority of the data set and would therefore have the largest area under the curve.

In summary, the interval μ - σ to Q3 corresponds to the smallest area under a normal curve because it includes only a small portion of the data set.
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1)  the three transformations are a reflection across the x-axis, a horizontal shift 3 units to the left, and a vertical stretching by a factor of 2.

2) The Firework is 500 feet  the ground at two different times: t = 15/4 (or 3.75) seconds and t = 8 seconds.

Q1: To determine the three transformations that will produce the graph of y = -2(x+3)^2 from the original function g(x) = x^2, we can analyze the given equation:

1. Reflection: The negative sign in front of the 2 in y = -2(x+3)^2 indicates a vertical reflection of the graph. This means that the graph will be reflected across the x-axis.

2. Vertical Translation: The term (x+3) in y = -2(x+3)^2 represents a horizontal shift of the graph. Since it is inside the parentheses, we shift the graph 3 units to the left. This means the vertex of the parabola will now occur at x = -3.

3. Vertical Scaling: The coefficient -2 in y = -2(x+3)^2 represents a vertical scaling of the graph. It indicates that the graph will be stretched vertically by a factor of 2.

In summary, the three transformations are a reflection across the x-axis, a horizontal shift 3 units to the left, and a vertical stretching by a factor of 2.

Q2: To find the time(s) at which the firework reaches a height of 500 feet, we can set the equation h(t) = -16t^2 + 180t + 20 equal to 500 and solve for t:

-16t^2 + 180t + 20 = 500

Rearranging the equation, we get:

-16t^2 + 180t - 480 = 0

Dividing the entire equation by -4, we obtain:

4t^2 - 45t + 120 = 0

Next, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use factoring:

(4t - 15)(t - 8) = 0

Setting each factor equal to zero, we have:

4t - 15 = 0    or    t - 8 = 0

Solving for t in each equation, we get:

t = 15/4    or    t = 8

Therefore, the firework is 500 feet above the ground at two different times: t = 15/4 (or 3.75) seconds and t = 8 seconds.

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Answer:

\( m \angle \: 3 = 94 \degree\)

Step-by-step explanation:

\(m \angle \: 3 + 86 \degree = 180 \degree \\(linear \: pair \: \angle s) \\ \\ m \angle \: 3 = 180 \degree - 86 \degree \\ \\ m \angle \: 3 = 94 \degree \\ \\ \)

It is shown that \(P(X $\geq$ 2\alpha \beta) $\leq$ (2/e)^\alpha\) is for a gamma distribution with parameters α and β

To show that \(P(X $\geq$ 2\alpha \beta) $\leq$ (2/e)^\alpha\) for a gamma distribution with parameters α and β, we can start by using the cumulative distribution function (CDF) for the gamma distribution:

Where Γ(α, x) is the upper incomplete gamma function and Γ(α) is the gamma function. Note that the CDF is defined for x ≥ 0 since the gamma distribution is a continuous probability distribution with support on the non-negative real numbers.

Now, we can use the fact that the complement of the event X ≥ 2αβ is X < 2αβ and substitute this into the CDF:

Simplifying this expression, we get:

Now, we can use the upper bound on the incomplete gamma function given by the following inequality:

for all α > 0 and z > 0. This is known as the Bohr-Mollerup theorem and can be shown using the properties of the gamma function.

Using this inequality, we get:

Now, we can use the fact that Γ(α) = (α - 1)! for integer α to simplify the expression:

To proceed further, we need to choose a suitable value of β. We can do this by minimizing the upper bound, which is achieved when β = 1 / (2α). Substituting this value of β, we get:

Where the last step follows from the fact that e < 3.

Therefore, we have shown that:

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The probability If no letter can be used twice, 32292000 ways different pass word options are there .

What is probability?

 Mathematical branch known as probability deals with determining the possibility of an event occurring. Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given event will occur.

Here a password contains 4 letters followed by 2 numbers.

Total number of alphabets = 26

If without repetition the words can be arranged as,

=> 26*25*24*23

Total numbers = 0 to 9 = 10

if without repetition the numbers can be arranged as ,

=> 10 * 9

If no letter can be used twice, number of  different pass word options are,

=> 26*25*24*23*10*9=32292000

Therefore there are 32292000 ways different password options available.

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Answer:

the circumference of this circle is approximately 25.12 cm with π as 3.14.

Step-by-step explanation:

circumference of a circle is technically a perimeter of a circle.

we find the circumference of a circle by using the following formula :

c = 2πr                                   or                                 c = πd

r represents the radius                                             d represents the diameter

since 4 yds here is a radius, we use the left formula i placed above. then, we substitute the numbers in. pi represents 3.14 as said in your question. even if you use 22/7, you will still get around the same result.

c = 2πr

c = 2(3.14)4

c = 6.28(4)

c = 25.12 yds

therefore, the circumference of this circle is approximately 25.12 yds.

Expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16

What do you mean by One-to-One Correspondence?

the capability of relating one object to another. For each number spoken aloud, the learner should be able to count or move one object while saying "1,2,3,4". She has not learned one-to-one correspondence if she accidentally counts an object twice or skips one of the things while counting. Before starting Giggle Facts, students must be able to match one object to each number counted.

Remind your kids that a double fact is a mathematical expression that has the same addend twice, such as 3 + 3 = 6 or 8 + 8 = 16. Give children the chance to practise combining groups of the same number using manipulatives or other classroom supplies.

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Answer:

A double expression

Step-by-step explanation:

Answer:

It's 1/36

Hope this is the correct ans