5. A function is defined by f(x) = ax^3 + bx^2 + cx + d. Find the values of a, b, c, d, if f(x) has a local maximum at its y intercept of 4 and a point of inflection at (-1/2, -9/2). Keep your work organized and be sure to show all steps.

Answer:

\(-\frac{3}{4}\)

Step-by-step explanation:

Slope

(2, 5) and (14, -4)

_______________

When we solve for slope within two points, we have to follow the formula of slope.

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

X and Y - The first and second number in both points

1 and 2 - The first or second number within one point

Substitute :

\(\frac{-4-5}{14-2}\)

\(\frac{-9}{12}\)

Simplify :

\(-\frac{3}{4}\)

Answer:

Rewritten in slope-intercept form

y = mx + b

The answer is

m = -3/4

To determine the distance traveled by Katie at different marks, we can use the formula Distance = Rate × Time.

To determine how far Katie has traveled at each mark, we can use the formula:
Distance = Rate × Time

So, the elements in the range of the function that would be used to determine how far Katie has traveled at each mark are 384 miles, 416 miles, and 448 miles.

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Answer:

8 students

Step-by-step explanation:

there are 80 students

difference between bus% and car%

=10%

80students×10%

=8

Answer:8 more students than in car

Step-by-step explanation:

Answer:

648

Step-by-step explanation:

\(3^4 \cdot 2^3 = 3 \cdot 3 \cdot 3 \cdot 3 \cdot 2 \cdot 2 \cdot 2 = 81 \cdot 8 = 648\)

Answer:

648

Step-by-step explanation:

Step 1:

First, make an equation:

3⁴ · 2³

Step 2:

Then, simplify both factors:

3⁴ = 81

2³ = 8

Step 3:

Finally, multiply the numbers together:

81 · 8

And you will get 648.

\(\huge\boxed{Hi\:there!}\)

\(\huge\sf{3x=9^2}\)

\(\huge\sf{3x=81}\)

\(\huge\sf{Divide\:both\:sides\:by\:3\:to\:isolate\:x:}\)

\(\huge\sf{x=27}\)

\(\huge\boxed{Hence,\:x=27.}\)

\(\huge\sf\underline{Hope\:it\:helps}\)

\(\boxed{CheerfulGirlie\:here\:to\:help}\)

Find the value of x

3x = 9²

x = 27

=> 3x = 9²

=> 3x = 81 [9² = 9×9 = 81]

=> x = 81/3

=> x = 27

The given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

To show continuity, we need to verify that the partial derivatives of ψ and φ with respect to x and y are equal. Let's calculate these partial derivatives:

∂ψ/∂x = 2y

∂ψ/∂y = 2x

∂φ/∂x = 2x

∂φ/∂y = -2y

From the above calculations, we can see that the partial derivatives of ψ and φ with respect to x and y are equal. Therefore, the condition for continuity, which requires the equality of partial derivatives, is satisfied.

To show irrotational flow, we need to verify that the curl of the velocity vector is zero. The velocity vector can be obtained from the stream function ψ and velocity potential φ as follows:

V = ∇φ x ∇ψ

Taking the curl of V:

∇ x V = ∇ x (∇φ x ∇ψ)

Using vector calculus identities and simplifying the expression, we find:

∇ x V = 0

Since the curl of the velocity vector is zero, the condition for irrotational flow is satisfied.

Therefore, based on the calculations and verifications, we can conclude that the given functions ψ = 2xy and φ = x^2 - y^2 satisfy the conditions for continuity and irrotational flow.

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Answer:

7 miles

Step-by-step explanation:

The final answer rounded to 1 decimal place is 0.1.

To find the probability P(4 ≤ X ≤ 6) for a normally distributed random variable X with mean μ = 10 and standard deviation σ = 6, you'll need to use the Z-score formula to standardize the values and then look up the probabilities in a standard normal table or use a calculator with a built-in normal distribution function.

The Z-score formula is: Z = (X - μ) / σ

For the lower limit, X = 4:
Z1 = (4 - 10) / 6 = -1

For the upper limit, X = 6:
Z2 = (6 - 10) / 6 = -0.67 (rounded to 2 decimal places)

Now, use a standard normal table or calculator to find the probabilities associated with these Z-scores.

P(Z ≤ -1) = 0.1587
P(Z ≤ -0.67) = 0.2514

To find P(4 ≤ X ≤ 6), subtract the lower probability from the upper probability:

P(4 ≤ X ≤ 6) = P(Z ≤ -0.67) - P(Z ≤ -1) = 0.2514 - 0.1587 = 0.0927

Therefore, rounded to one decimal place, the probability is 0.1.

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Answer:

58

Step-by-step explanation:

i think

Answer:

Step-by-step explanation:

-2.8, -13/9, .25, 2/3, 1 7/8, 2.16

Answer:

The operation used is the Subtraction operation

39 bags of marshmallows

Step-by-step explanation:

The operation we would be using here is the Subtraction operation.

Total number of bags if Marshmallows bought = 48 bags

Number of people present = Taylor + 10 friends = 11 people

Amount of Marshmallows left = 9 bags

Hence, the number of bags of marshmallows that Taylor and her friends went through is calculated as:

48 bags of marshmallows - 9 bags of marshmallows

= 39 bags of marshmallows

Due to its smaller range than Group A, Group B has a lower overall variability and a higher median than Group A.

Probability refers to the likelihood that an event will occur.

In real life, we frequently have to make predictions about the future.

We might or might not be aware of how an event will turn out.

When this occurs, we proclaim that there is a possibility that the event will occur.

In conclusion, probability has a wide range of amazing uses in both business and this rapidly developing area of artificial intelligence.

The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes.

According to our question-

The median is the line in the center of the box, and as you can see from the number line, b's median is higher.

Because the outliers are the small marks at the end and b's marks are closer together, the entire line of b is then shorter and has less variability.

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Because of its more modest reach than Gathering A, Gathering B has a lower generally speaking changeability and a higher middle than Gathering A.

The probability of an event occurring is referred to as probability. We frequently have to make predictions about the future in real life. We may or may not be aware of the outcome of an event.

At the point when this happens, we broadcast that there is plausible that the occasion will happen. In conclusion, probability can be put to great use in business as well as in this rapidly expanding field of artificial intelligence.

By simply dividing the total number of outcomes by the favorable number of possibilities, the probability of an event can be calculated using the probability formula.

Our question says that the line in the middle of the box is the median, and the number line shows that b's median is higher.

The entire line of b is then shorter and has less variability because the outliers are the tiny marks at the end and b's marks are closer together.

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Answer:

How Do You Find the X- and Y-Intercepts of a Line in Slope-Intercept Form? To find the x-intercept of a given linear equation, plug in 0 for 'y' and solve for 'x'. To find the y-intercept, plug 0 in for 'x' and solve for 'y'.

Answer:

1200

Step-by-step explanation:

12 multiplied by 2 is 24.

24 divided by 2 is 12.

12 times 100 is 12 plus 2 zeros, or 1200.

{(5, 2), (4, 2), (3, 2), (2, 2), (1, 2)}, {(−8, −3), (−6, −5), (−4, −2), (−2, −7), (−1, −4)} and {(−6, 4), (−3, −1), (0, 5), (1, −1), (2, 3)} are the sets of ordered pairs considered as a function.

{(−4, −2), (−1, −1), (3, 2), (3, 5), (7, 10)} is not a function.

In mathematics, ordered pair is a pair of numbers that are written in a specific order. They are generally written in (x, y) form. For example (3, 5) is an ordered pair.

The function can also be represented by a set of ordered pairs. A function Is a set of ordered pairs in which no two different ordered pairs have the same value of x coordinate.

Option (a) : {(5, 2),(4, 2),(3, 2),(2, 2),(1, 2)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (b) : {(-4, -2),(-1, -1),(3, 2),(3, 5),(7, 10)}

Two ordered pairs have the same value of x coordinate (3, 2) and (3, 5).

So, it can not be considered a function.

Option (c) : {(-8, -3),(-6, -5),(-4, -2),(-2, -7),(-1, -4)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Option (d) : {(-6, 4),(-3, -1),(0, 5),(1, -1),(2, 3)}

No two ordered pairs have the same value of the x coordinate.

So it is a function.

Therefore, Options (a), (c), and (d) are the functions.

Option (b) is not a function.

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Answer:

I believe that the answer is c or -9

Step-by-step explanation:

The figure in the question shows QRST and Q'R'S'T', having the positions

of the lettering flipped over a line parallel to side RS.

Reasons:

From the attached figure, likely to be that of the question we have that, a reflection of the sides RS and QT, across a line parallel to the side RS and equidistant to the side RS on rectangle QRST and R'S' on rectangle Q'R'S'T', maps the RS to R'S', QT to Q'T', QR to Q'R', and TS to T'S'.

Therefore;

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The likely question options are;

Reflection

Translation

Rotation

Stretch

Mean of x for sample size is [28.34, 32.66]

The closest option is (c) 30.5.

The mean of the sample means will be the same as the population mean, which is 30.5.

The standard error of the mean, which is the standard deviation of the sampling distribution of the mean, can be calculated as:

SE = σ / sqrt(n)

where σ is the population standard deviation and n is the sample size.

SE = 3.5 / sqrt(10) = 1.108

The mean of x for sample size of 10 can be calculated as:

x = μ ± z*(SE)

where μ is the population mean, z is the z-score corresponding to the desired level of confidence (we'll assume 95% here), and SE is the standard error of the mean.

Using a z-score of 1.96 for a 95% confidence interval, we have:

x = 30.5 ± 1.96*(1.108) = [28.34, 32.66]

Therefore, the closest option is (c) 30.5.

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The MATLAB code to solve the partial fraction expansion for the given system, So the answer is: c_t = ilaplace(C, s, t);

Matlab          Code

[ syms s t

X = 10 / (s*(s-2)*(s+3));

[r, p, k] = residue(10, [1, -2, 3]);

C = r(1)/ (s-p(1)) + r(2) / (s-p(2)) + r(3) / (s-p(3));

c_t = ilaplace(C, s, t);

disp('Solution for c(t):');

disp(c_t);

]

In the above code, we first define the transfer function X (C(s)) using the symbolic variable 's'. Then, we use the 'residue' function to obtain the partial fraction expansion, with the numerator '10' and the denominator '[1, -2, 3]'. The outputs 'r', 'p', and 'k' represent the residues, poles, and direct term (if any).

Next, we construct the partial fraction expansion 'C(s)' using the obtained residues and poles. Finally, we use the ' ilaplace' function to perform the inverse Laplace transform and obtain the solution for c(t). The result is displayed using 'disp'.

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Step-by-step explanation:

where is the figure??!!!

Answer:

Step-by-step explanation:

It's the median.............. Ur welcome ;)

Answer:

5,400,300...........

5004300

........

......

....

...

..

.

Answer:

Step-by-step explanation:

=5^-3 X 2^-1

= 1/5³ X 1/2

=1/(5³X 2)

=1/250 (Answer)

OR

=0•004 (Answer)

Answer:

1/250 or 0.004.

Step-by-step explanation:

5^-3 x 2^-1

= 1/5^3 * 1/2

= 1/125 * 1/2

= 1/250.

Answer:

0.51

Step-by-step explanation:

The probability of the horse finishing in second place is approximately 0.29.

To convert the odds given as "29 to 71" into a probability value, we can divide the number of favorable outcomes (29) by the total number of possible outcomes (29 + 71 = 100).

The probability is calculated as:

Probability = Number of favorable outcomes / Total number of possible outcomes.

In this case, the probability is 29/100, which is equal to 0.29.

To convert odds to probability, we divide the number of favorable outcomes (29) by the total number of outcomes (29 + 71 = 100). The probability of the horse finishing in second place is 29/100, which simplifies to 0.29 or 29%.

This means there is a 29% chance or likelihood of the horse finishing in second place based on the given odds.

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Answer:

C) \(f(x)=-3x^4-6x^3-2x^2+x+3\)

Step-by-step explanation:

As the graph of the function has 3 turning points, then it cannot be options B or D because the function would've had 2 turning points at most.

Also, since the graph of the function opens downward, the leading coefficient must be negative, so C must be the correct answer.

9514 1404 393

Answer:

  8. p(t) = 5(2^t)

  9. 20, 40, 80

  10. doubles every year

  11. multiplies by 4

  12. no, it will soon exceed available habitat

Step-by-step explanation:

8. From the graph, a = p(0) = 5, and b = p(1)/p(0) = 10/5 = 2.

The function is ...

  p(t) = 5(2^t)

__

9. You can read the values from the graph: 2 years: 20; 3 years: 40; 4 years: 80.

If you insist on evaluating the function, you have ...

  p(2) = 5(2^2) = 5·4 = 20

  p(3) = 5(2^3) = 5·8 = 40

  p(4) = 5(2^4) = 5·16 = 80

__

10. The population doubles each year.

__

11. In 2 years, the population doubles twice, so is multiplied by 4.

__

12. No. Exponential functions don't last long in the real world. Eventually, required resources run out. In 15 years, there would be 163,840 snakes; in 20 years, there would be 5.2 million snakes; in 40 years, there would be 5.5 trillion snakes, about 44 snakes for every acre of land on earth (including polar areas).

\(\sf\:f(x) = \begin{cases}9 & \text{if } x < -4 \\ -x+5 & \text{if } -4 \leq x < 4 \\ -2 & \text{if } x = 4 \\ 5 & \text{if } x > 4 \\ \end{cases} \\\)

To sketch the graph of this function, we plot the points and lines as follows:

\(\sf\:\begin{align}(-\infty, -4) & : \text{Line segment with a constant value of } 9 \\ [-4, 4) & : \text{Line segment with a slope of -1 and y-intercept of 5} \\ (4, \infty) & : \text{Horizontal line with a constant value of } 5 \\ x = 4 & : \text{Point at } (4, -2) \\ \end{align} \\\)

1. \(\sf\:\lim_{{x \to -4^-}} f(x) \\\): The limit as x approaches -4 from the left side. Since the function is continuous at -4, the limit exists and is equal to the value of the function at that point. So, \(\sf\:\lim_{{x \to -4^-}} f(x) = f(-4) = 9 \\\).

2. \(\sf\:\lim_{{x \to -4^+}} f(x) \\\): The limit as x approaches -4 from the right side. Again, since the function is continuous at -4 , the limit exists and is equal to the value of the function at that point. So, \(\sf\:\lim_{{x \to -4^+}} f(x) = f(-4) = 9 \\\).

3. \(\sf\:\lim_{{x \to -4}} f(x) \\\): The limit as x approaches -4. Since the left and right limits both exist and are equal, the overall limit exists and is equal to the common value. So, \(\sf\:\lim_{{x \to -4}} f(x) = \lim_{{x \to -4^-}} f(x) = \lim_{{x \to -4^+}} f(x) = 9 \\\).

4. \(\sf\:\lim_{{x \to 4}} f(x) \\\): The limit as x approaches 4. Since the function has a discontinuity at \(\sf\:x = 4 \\\) (a jump from \(\sf\:-x + 5 \\\) to (-2), the limit does not exist. So, \(\sf\:\lim_{{x \to 4}} f(x) \\\) is DNE.

5. \(\sf\:\lim_{{x \to 4^+}} f(x) \\\): The limit as x approaches 4 from the right side. Since the function is continuous at 4, the limit exists and is equal to the value of the function at that point. So, \(\sf\:\lim_{{x \to 4^+}} f(x) = f(4) = -2 \\\).

6. \(\sf\:\lim_{{x \to 4^+}} (x + 4) f(x) \\\): The limit as x approaches 4 from the right side, multiplied by \(\sf\:(x + 4) \\\). Since the function is continuous at 4, we can evaluate this limit by substituting

\(\sf\:x = 4. So, \lim_{{x \to 4^+}} (x + 4) f(x) = (4 + 4) f(4) = 8 \cdot (-2) = -16 \\\).

That's it!

Answer:

43.4 yd

Step-by-step explanation:

\(45^{2}\)-\(12^{2}\)

2025-144=1881

\(\sqrt{1881}\)

43.37049

43.4