Find where the function f(x) = 33° - 873 – 210.x2 + 4 is increasing and where it is decreasing -6 -4 4 6 8 2000- -4000 -6000 -8000 a f'(x) = 123 - 242 - 420x = 12x(1 - + To use the VD Test, we have to know where f'() > 0 and where f'(x) < 0. This depends on the signs of the three factors of f'(-), namely, 127, 1- and + We divide the real line into intervals whose endpoints are the critical numbers (smallest). O, and (largest) and arrange our work in a chart. A plus sign indicates that the given expression is positive, and a negative sign indicates that it is negative. The last column of the chart gives the conclusion based on the V/D Test. For instance, f'(=) < 0 for 0 << < 7. so fis Settano on (0,7). (It would also be true to say that f is decreasing on the closed interval (0, 713 Interval 12r 2-7 +5 f'(2) - 5 decreasing on (- 0,-5) -5 <<0 Select on ( - 5,0) 0

In about 2.8 hours, the prices of each stock will be the same

An equation is a mathematical statement that indicates that two expressions are the same by joining them with an 'equals to' sign.

The initial price of the Stock A at 9 A.M. = $14.55

The rate at which the price of the stock is increasing = $0.12

The price of the Stock B at noon = $15.30

The rate of decrease of the price every hour = $0.15

The equation of the price of Stock A is; P = 14.55 + 0.12 × x

The equation of the price of Stock B is; P = 15.30 - 0.15 × x

When the prices of the stock are the same, the price equations for the two Stocks are equated to get the following;

14.55 + 0.12 × x = 15.30 - 0.15 × x

0.12 × x + 0.15 × x = 15.30 - 14.55 = 0.75

0.27·x = 0.75

x = 0.75 ÷ 0.27 = 2.\(\overline 7\) ≈ 2.8

The time it takes for the price of the stocks to be the same is approximately 2.8 hours

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The p-value of the test statistic will be equal to -1.5.

A statistic employed in statistical hypothesis testing is known as a test statistic. A hypothesis test is often defined in terms of a test statistic, which can be thought of as a numerical summary of a data set that distils the information into a single value that can be used to conduct the test.

The formula for test statistics:

Test statistic = z =

A sample of patients n = 160

Patients insured =x =80

P = x/n

P = 80/ 160

P = 1/2

P = 0.5

P₀ = 56/100

P₀ = 0.56

Putting the values we get:

\(Z =\dfrac{P-P_o}{\sqrt{\dfrac{P_o-(1-P_o)}{n}}}\)

\(Z =\dfrac{0.5-0.56}{\sqrt{\dfrac{0.56-(1-0.56)}{150}}}\)

Z=  -0.06/0.04

Z = - 1.5

Therefore, the p-value of the test statistic will be equal to -1.5.

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To solve this second-order linear homogeneous differential equation, we first find the characteristic equation:

r^2 + 4 = 0

This has roots r = ±2i, so the general solution to the homogeneous equation is:

y_h(t) = c_1 cos(2t) + c_2 sin(2t)

Next, we need to find a particular solution to the non-homogeneous equation. Since the right-hand side of the equation is a polynomial times an exponential, we can try a particular solution of the form:

y_p(t) = (At^2 + Bt + C)e^t

Taking the first and second derivatives of y_p(t), we get:

y_p'(t) = (2At + B + At^2 + 2At + 2B + C)e^t

y_p''(t) = (4A + 2At)e^t + (2At + 2B)e^t + (At^2 + 4At + 2B + C)e^t

Substituting these into the differential equation and simplifying, we get:

(4A + 2At)e^t + (2At + 2B)e^t + (At^2 + 4At + 2B + C)e^t - 4(At^2 + Bt + C)e^t = t^2/2

Simplifying further and collecting like terms:

(e^t)(At^2 + (2A - 4B)t + (4A + 2B - 4C)) = t^2/2

Since the left-hand side is a quadratic polynomial in t, we can equate its coefficients to those of the right-hand side to get a system of equations:

A = 1/8

2A - 4B = 0

4A + 2B - 4C = 0

Solving this system of equations, we get:

A = 1/8, B = 1/16, C = 5/64

Therefore, the particular solution is:

y_p(t) = (t^2/8 + t/16 + 5/64)e^t

The general solution to the non-homogeneous equation is then:

y(t) = y_h(t) + y_p(t) = c_1 cos(2t) + c_2 sin(2t) + (t^2/8 + t/16 + 5/64)e^t

Using the initial conditions y(0) = 0 and y'(0) = 1, we can find the constants c_1 and c_2:

y(0) = 0 = c_1 + 5/64

c_1 = -5/64

y'(t) = -2c_1 sin(2t) + 2c_2 cos(2t) + (t/4 + 5/64)e^t + (t^2/8 + t/16 + 5/64)e^t

y'(0) = 1 = 2c_2 + 5/64

c_2 = 27/128

Therefore, the solution to the initial value problem is:

y(t) = (-5/64) cos(2t) + (27/128) sin(2t) + (t^2/8 + t/16 + 5/64)e^t

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if angle m∠2 = 120°, then m∠7 is 120°.

An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

Supplementary angles are those angles that sum up to 180 degrees.

Given that  m∠2 = 120°.

We have to find the  m∠7.

m∠2  and m∠4 are supplementary angles.

120+m∠4=180

m∠4=60 degrees.

m∠4 is corresponding angle of m∠8.

m∠8 and m∠7 are again supplementary angles.

60+m∠7=180

m∠7=120 degrees.

Hence, if angle m∠2 = 120°, then m∠7 is 120°.

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Answer:

x=0.125

Step-by-step explanation:

4/32=0.125

Answer:

110.1

Step-by-step explanation:

Answer:

110.4

Step-by-step explanation:

180°-69.6°=110.4°

Answer:

(-6,0)

Step-by-step explanation:

Answer:

(-1,-6)

Step-by-step explanation: edmentum

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

carnival game:

spinner: 1 to 8

Step 02:

simple probability:

p = favorable outcomes / total outcomes

1. probability of an event:

a. p (odds):

p (odds) = 4 / 8 = 1 / 2

b. p (evens):

p (evens) = 4 / 8 = 1 / 2

c. p (3):

p (3) = 1 / 8

d. p (4 or 6):

p (4 or 6) = 2 / 8 = 1 / 4

e. p (7'):

p (7') = 7 / 8

f. p (1):

p (1) = 1 / 8

That is the full solution.

Answer: -25

Step-by-step explanation:

4 - 2(-3) - 5 (7)

4 + 6 - 35

10 - 35

The probability that a student who can drive is a college student is 0.2771 or 27.7%

It will be sooved using Baye's theorem -

P(college) = P(C) / 1/5 = 0.2

P(high school students) = P(H) = 4/5 = 0.8

P(college drives) = 0.23

P(high school drives) = 0.15

We have to find, probability that a student who drives is a college student.

That is, we have to find P(C/D).

P(C/D) = P(C ∩ S)/P(S)

Since P(C ∩ S) is an independent event.

P(C ∩ S) = P(C) × P(S)

P(C ∩ S) = 0.2 × 0.23

= 0.046

Using bayes's theorem, we will get

P(C/D) = 0.2771 or 27.7%

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Answer:

A (7,2)

Solution is in the photo :)

Steps to solve:

4x + 1/3y^2 when x = 2 and y = 3

~Substitute

4(2) + 1/3(3)^2

~Simplify

8 + 1/3(9)

~Simplify

8 + 3

~Add

11

Best of Luck!

The sum of two terms are:

The sum of two numbers is one that tells you to find the sum of two or more numbers, and as such, you have to add the numbers altogether.

t₅, ₃ =  5 + 3

= 8

t₁₁, ₂ = 11 + 2

= 13

t₁₅,₁₃ =  15 + 13

= 28.

Hence the correct sum of two terms are:

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Answer:

The answer is the first choice

Step-by-step explanation:

That is because the answer to the question is 256 and the first choice is equivalant to that

The absolute value of the Pearson correlation coefficient indicates the strength or consistency of the relationship between two variables.

Therefore, the Pearson correlation coefficient with the greatest strength or consistency of relationship is the one with the highest absolute value.

In this case, the answer is:

a. â€"0.90

because it has the highest absolute value (|â€"0.90| = 0.90) among the options given. This indicates a very strong negative relationship between the two variables being compared.

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Answer:

Triangle A - Equilateral

Triangle B - Scalene

Triangle C - Scalene

Step-by-step explanation:

Equilateral triangles are where all the sides are equal, because triangle A has 3 equal lengths of 16, we know it is an equilateral.

Scalene triangles are where no sides match, and because triangle B and C have all different lengths, we know these are scalene.

None of the triangles in these examples are isosceles because isosceles triangles have 2 of the same lengths, and one different.

Before doing the answer , we should know some properties of triangles ;

Now , Checking for Triangle A :-

As , it's all sides are of equal length 16 , So option 3) Equilateral ✓

Now , Checking for Triangle B :-

As , it's all sides are of different length , So option 1) Scalene ✓

Now , Checking for Triangle C :-

As , it's all sides are of different length , So option 1) Scalene ✓

Answer:

216 pancakes every 9 hours

Step-by-step explanation:

9/3 = 3

72 x 3 = 216

Answer:

44. 7in

45. 35in

Step-by-step explanation:

44.

\(24^{2} + x^{2} = 25^{2} \\576 + x^{2} = 625\\576 - 625 = -x^{2} \\\sqrt{49} = x\\x = 7\)

45.

\(15^{2} + x^{2} = 25^{2} \\225 + x^{2} = 625\\225 - 625 = -x^{2} \\-400 = -x^{2} \\\sqrt{400} = x\\x = 20\)

\(25in*15in = 35in^{2}\)

Answer:

Step-by-step explanation:

Consider the property of the 30x60x90 degree right triangle.

It has side with ratio:

According to the picture we have:

Answer:

x = 9

Step-by-step explanation:

To solve for x, you must isolate the variable.

First, start by adding 2 to BOTH sides to eliminate the 2.

3=1/3x. then divide each side by 1/3

3÷1/3 = x

3/1 × 3/1 = x

9 = x

the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.

The Θ-intercepts of a graph of a function f are the values of Θ where the graph intersects the Θ-axis, i.e., where f(Θ) = 0.

In the case of f(Θ) = tan(Θ), we know that the function has vertical asymptotes at Θ = π/2, 3π/2, etc., where the function is undefined. Therefore, the graph of f will intersect the Θ-axis at these values of Θ, since the function is negative for Θ between π/2 and 3π/2 and positive for Θ outside of that interval.

Thus, the Θ-intercepts of the graph of f are π/2 and 3π/2. We know this because these are the values of Θ where f(Θ) = 0 and where the graph intersects the Θ-axis.

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Answer:

8.7cm

Step-by-step explanation:

From the question, we know that:

10 km = 2 cm(on the map)

43.5 km = x cm

Cross Multiply

10 × x cm = 43.5km × 2

x cm = 43.5 km × 2/10

x cm = 8.7 cm

The length in centimetres of Galveston Island on Quincy's map is 8.7cm

The quotient between the two polynomials is:

q(x) = 2x² + x - 1

We want to take the quotient between the polynomials:

2x³ - 9x² - 6x + 5 and (x -5)

first, notice that x = 5 is a zero of the first polynomial:

2*5³ - 9*5² - 6*5 + 5 = 0

So (x - 5) is a factor, then we can write:

2x³ - 9x² - 6x + 5 = q(x)*(x - 5)

Where q(x) is the quotient, and it must be a polynomial of degree 2, then we can write:

q(x) = ax² + bx + c

Replacing that we can write:

2x³ - 9x² - 6x + 5 = (ax² + bx + c)*(x - 5)

Expanding the right side:

2x³ - 9x² - 6x + 5 = ax³ + bx² + cx - 5ax² - 5bx - 5c

2x³ - 9x² - 6x + 5 =  ax³ + (b - 5a)x² + (c - 5b)x - 5c

Now we can write 4 equations (one for each term of the polynomials)

2 = a

-9 = (b - 5a)

-6 = (c - 5b)

5 = -5c

With the first equation we can see that a = 2.

With the fourt equation we can see that:

5 = -5c

5/-5 = c

-1 = c

Finally, we can use any of the other two equations to find the value of b.

-9 = b - 5a

-9 = b - 5*2

-9 = b - 10

-9 + 10 = b

1 = b

Then the quotient is:

q(x) = 2x² + x - 1

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Answer:sorry i don’t know

Sorry

Step-by-step explanation:

Answer:

#1:

Formula- length x width

Plug in values- 6 x 12

Area- 72 ft

#2:

Formula: base x height

Plug in Values: 3.7 x 12

Area: 44.4 m

#3:

Formula: base x height

Plug in Values: 2.2 x 8

Area: 17.6 cm

#4:

Formula: length x width

Plug in Values: 15 x 2.5 (2 1/2)

Area: 37.5 in

Answer:

4/9

Step-by-step explanation:

sorry if wrong i don't know how to explain it also

Answer:

Convert 1 1/2 to an improper fraction.

3/2⋅2

Cancel the common factor of 2.

3

Stephanie would not be able to rescind the contract because she made a unilateral mistake, and it was not a bilateral mistake.

In contract law, a unilateral mistake occurs when one party to a contract is mistaken about a material fact related to the agreement. However, the general rule is that unilateral mistakes do not provide grounds for rescission of a contract. The reason for this is that contract law places a higher emphasis on the principle of enforceability and preventing one party from unilaterally avoiding their obligations based on their own mistake.

In this case, Stephanie's mistaken belief that the painting was directly painted by Van Gogh, rather than his student, constitutes a unilateral mistake. It is important to note that the art expert's opinion, though incorrect, did not induce Stephanie's mistake or misrepresent the nature of the painting. Stephanie made the decision to sell the painting to Charlie based on her own belief and understanding of its value.

Option d is the correct choice: No, because Stephanie made the mistake, and it was not a bilateral mistake. Stephanie's mistake was unilateral, meaning it was her own error in judgment. A bilateral mistake, on the other hand, occurs when both parties to a contract share a common misunderstanding or mistake about a material fact. In such cases, the contract may be voidable by either party since there was no true "meeting of the minds."

Moreover, the exchange of consideration further strengthens Charlie's position as a bona fide purchaser. Charlie purchased the painting for $15,000.00, and consideration is a fundamental element in the formation of a contract. Once consideration is exchanged, it signifies that the parties have entered into a binding agreement, and it may limit the grounds for rescission.

In conclusion, based on the unilateral nature of Stephanie's mistake and the presence of consideration, Stephanie would not be able to rescind the contract. Therefore, option d is the correct choice.

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To find the relationship between the volume of a prism and a pyramid with congruent bases and equal heights, we need to consider their formulas.  
The volume of a pyramid is given by the formula V = (1/3)Bh,

where B represents the area of the base and h represents the height. Since the bases of the prism and pyramid are congruent and their heights are equal, we can write the equation:

Volume of Prism = 2 × Volume of Pyramid Using the formulas mentioned earlier, we can substitute the expressions for the volumes:

Bh = 2 × (1/3)Bh
Simplifying this equation, we can cancel out the B's:

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The statement "a prism and a pyramid have congruent bases and equal heights, and the volume of the prism is twice the volume of the pyramid" is FALSE.

To understand why, let's consider a simple example. Imagine we have a triangular prism and a triangular pyramid with congruent bases and equal heights. The base of both shapes is a triangle, and their heights are the same.

The volume of a prism can be calculated by multiplying the area of its base by its height. Similarly, the volume of a pyramid can be calculated by multiplying the area of its base by one-third of its height.

Since the prism and the pyramid have congruent bases and equal heights, the only difference in the volume calculation is the factor of 1/3 for the pyramid.

This means that the volume of the pyramid is one-third the volume of the prism, not half. Therefore, the statement that the volume of the prism is twice the volume of the pyramid is false.

Therefore, the statement is incorrect, and the volume of the prism is not twice the volume of the pyramid, but rather three times as much.

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Answer:

Option B is the correct option.

Step-by-step explanation:

\( \mathrm{ - \frac{4}{5} \div 2}\)

\( \mathrm{dividing \: a \: negative \: and \: a \: positive \: equals \: a \: negative \:. \: ( - ) \div ( + ) = ( - )}\)

\( \mathrm{ - \frac{4}{5} \div 2}\)

\( \mathrm{dividing \: is \: equivalent \: to \: multiplying \: with \: the \: reciprocal}\)

\( \mathrm{ - \frac{4}{5} \times \frac{1}{2} }\)

\( \mathrm{reduce \: the \: numbers \: with \: G.C.F \: 2}\)

\( \mathrm{ - \frac{2}{5} }\)

Hope I helped!

Best regards!

The quotient of  -4 /5 divide 2 would be equal to -2/5 in simplified form.

Quotients are the number that is obtained by dividing one number by another number. We can use the fact that division can be taken as multiplication but with the denominator's multiplicative inverse.

We have been given that  -4 /5 divide 2

Thus, we have to divide the terms as;

-4 /5   ÷ 2

Therefore,  -4 /5 x 1/ 2

-2/5

Hence, the quotient of  -4 /5 divide 2 would be equal to -2/5 in simplified form.

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Answer:

Rewriting our equation with parts separated

=1+3/4−2−7/10=1+3/4−2−7/10

Solving the whole number parts

1−2=−11−2=−1

Solving the fraction parts

3/4−7/10=?

Find the LCD of 3/4 and 7/10 and rewrite to solve with the equivalent fractions.

LCD = 20

15/20−14/20=1/20 15/20−14/20=1/20

Combining the whole and fraction parts

−1+1/20=−19/20

Answer:

I believe it is true, false, true, true.

Step-by-step explanation:

there are no green marbles, there are way more yellow marbles then even blue and red combined, you could get a blue one being the odds 5/16, and there are only 2 red marbles so it is unlikely that you choose red. I hope this helps!

Answer:

true false true true

Step-by-step explanation:

there is no green marbles

you are most likely to get a yellow

blue marble is gonna be selected

there's only 2 red marbles low chance of getting choose.