Even if the Extreme Value Theorem does not apply to this functions, does it have an absolute maximum and/or an absolutè minimum on the interval (-2,2]? What are those values, if they exist. 2013 x < 1 f(x) - 3 ex? -1 +2 x>1 (The second inequality should be x>1)

Answer:

Train P : \(t_{P} =\frac{330}{55}=6\ \text{hours}\)

Train Q : \(t_{Q} =\frac{330}{55}+\frac{1}{2}=6\ \text{hours}\ 30\ \text{minutes}\)

Step-by-step explanation:

The formula to compute the distance traveled by a train is:

\(d=s\times t\)

Here,

d = distance traveled

s = speed of the train

t = time taken

From the provided information:

Train P :

d = 330 km

s = x km/h

Then time taken is:

\(t=\frac{d}{s}=\frac{330}{x}\)

Train Q :

d = 330 km

s = (x - 5) km/h

\(t=\frac{330}{x}+\frac{1}{2}\)

Both the trains traveled the same distance.

\(x\times \frac{330}{x}=(x-5)\times [\frac{330}{x}+\frac{1}{2}]\\\\330=\frac{330(x-5)}{x}+\frac{x-5}{2}\\\\330\times 2x=[660(x-5)+x(x-5)]\\\\660x=660x-3300+x^{2}-5x\\\\x^{2}-5x-3300=0\\\\x^{2}+60x-55x-3300=0\\\\x(x+60)-55(x+60)=0\\\\(x-55)(x+60)=0\\\\x=55\)

Compute the time taken by the two trains as follows:

Train P : \(t_{P} =\frac{330}{55}=6\ \text{hours}\)

Train Q : \(t_{Q} =\frac{330}{55}+\frac{1}{2}=6\ \text{hours}\ 30\ \text{minutes}\)

Answer:

\(a_5=-12\)

Step-by-step explanation:

Given that,

The first term of the sequence, a = 8

Common difference, d = -5

We need to find the fifth term of the sequence.

The nth term of the sequence is given by :

\(a_n=a+(n-1)d\)

Put n = 5, a = 8 and d = -5 in the above formula

\(a_5=8+(5-1)(-5)\\\\=8+4(-5)\\\\=8-20\\\\=-12\)

So, the fifth term of the sequence is -12.

The confidence interval estimate is (6.41, 7.11) of the population mean rating for Miami

The question includes a sample of the data.

The sample size, n = 50

The sample mean:

x= ∑X /n

= 6.76

The sample standard deviation;

s= √∑(X-x)²/(n-1)

=2.55

The confidence level =0.95

The significance level , α = 0.05

The sample mean, X

= 6.76

The sample standard deviation, s = 2.55

The sample size , n= 50

Degree of freedoms :

Df = n-1

=49

Using the t-distribution table, the critical value of t is:

t critical = t α/2, df

= t 0.025,49

= 0.098

95% confidence interval :

μ =  X ± t.s/√n

 t.s /

= 6.76  2.01  2.55 / √50

= 6.76  0.7249

Therefore, The confidence interval is ( 6.41, 7.11)

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Answer: 155

35+90=125

180-125=55

55+60=115

180-115=65

65+90=155

x=155

Answer:

See below

Step-by-step explanation:

Answer:

60 degrees

Step-by-step explanation:

If each side of the triangle WRD is 3 inches long, then WRD is an equilateral triangle, meaning all angles are the same size. Since there are 180 degrees in a triangle, 180/3 = 60 degrees.

a. The table value of z 0.99 is given as 2.58.

b. we use σ = 2.30 minutes.

c. The value of Z is given as 0.609.

d. The confidence interval is (23.391, 24.609) minutes.

a) To find the z-score for a 0.99 confidence interval, we need to find the z-score that leaves 0.5% (since it's two-tailed, we split the 1% or 0.01 of the data that's not within the confidence interval into two) in each tail. The z-score for 0.995 (0.5% in the upper tail) is approximately 2.58 in standard normal distribution tables. So, Z_0.99 is 2.58.

b) Therefore, we use σ = 2.30 minutes.

c) The standard error of the mean (SE) is given by σ/√n, where n is the sample size.

Here, σ = 2.30 minutes and n = 95.

Therefore, SE = σ/√n

= 2.30/√95

= 0.236 minutes.

Multiply this by the z-score to find Z * σ/√n.

Therefore, Z * σ/√n = 2.58 * 0.236 ≈ 0.609.

d) The 0.99 confidence interval for μ

Here, x is the sample mean which is 24 minutes.

So the confidence interval is approximately

= (24 - 0.609, 24 + 0.609)  

= (23.391, 24.609) minutes.

This is the range of values we are 99% confident that the true population mean (μ) falls in.

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Answer: 7 Pack

Step-by-step explanation: Divide each price by the number of shirts :)

Check the picture below.

Answer: Linear.

Step-by-step explanation:

      A linear function forms a straight line when it is graphed.

      A nonlinear function will be curved in some way when graphed.

      We can graph the given points to find the answer to this question. See attached for this graph. These points create the function y = 3x + 2, which is a linear function.

Answer:conjectured that F(n)≈0.72∗n∗f(n). Following that clue, we can find the following identity holds for all cases we tested by trial and error.

F(n)=nf(n)−(n−2)f(n−2)+(n−4)f(n−4)−(n−6)f(n−6)+⋯

where the sequence of summands goes on as long as the summand makes sense.

Step-by-step explanation:

Answer: 8r+5t

Step-by-step explanation:

8t + 6r - 3t + 2r

8t-3t= 5t

6r+2r=8r

= 8r+5t

Answer:

The answer would be 8r + 5t

70 + 60 + 8x + 2 = 180

132+8x= 180

8x= 180-132

8x=48

x= 6

plug in x

8(6)+2 = 50

Answer:

x = 6

Step-by-step explanation:

The sum of interior angles in a triangle is equal to 180°.

To find the value of x, we can use the following equation:

70 + 60 + 8x + 2 = 180

132 + 8x = 180

8x = 48

x = 6

Answer:

the price with the offer is going to be 1.59$

Step-by-step explanation:

\( \frac{x}{5.30} = \frac{70}{100} \)

\(100(x) = 70(5.30)\)

\(100(x) = 371\)

\( \frac{100(x)}{100} = \frac{371}{100} \)

\(x = 3.71\)

\(70\% \: \: \: of \: \: \: 5.30 \: \: \: is \: \: \: 3.71\)

\(5.30 - 3.71 = 1.59\)

Answer

C

Area of a circle is pi r to the power of 2.

so the radius is 6

so pi(6)^2= 36pi

The cost of cementing the walls of the cuboidal well is Rs 3640.

A three-dimensional solid form with six rectangular sides is called a cuboid. It also goes by the name rectangular prism. The shapes and sizes of the faces on either side of each other are identical.

A cuboid's surface area is the sum of all of its faces. We can determine the area of each face and put them together to determine the cuboid's surface area.

Given that, the cost of cementing the walls of the well at the rate Rs 52 per square m.

Thus,

Area of one rectangular face = length x height = 2 x 10 = 20m².

Area of the other rectangular face = width x height = 1.5 x 10 = 15m².

Total surface area of the walls = 2(20) + 2(15) = 70m².

Now, the cost of cementing the walls of the well at the rate of Rs 52 per m² is:

Cost = 70m x Rs 52 = Rs 3640

Hence, the cost of cementing the walls of the well is Rs 3640.

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Answer:

75p²

Step-by-step explanation:

Given data

We are given the expression

(196p²– 121p²)

We can see the p is common in both terms

=p²(196-121)​

=p²(75)

=75p²

Hence the factorized form is 75p²

The probability of rolling a sum of 7 or more is 7/12.Therefore, the correct answer is 7/12.

When rolling two dice, the probability of rolling a sum of 7 or more can be calculated by determining the favorable outcomes and dividing by the total possible outcomes.

There are 36 possible outcomes when rolling two dice (6 sides on each die, so 6 x 6 = 36). The combinations that result in a sum of 7 or more are: (1,6), (2,5), (2,6), (3,4), (3,5), (3,6), (4,3), (4,4), (4,5), (4,6), (5,2), (5,3), (5,4), (5,5), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6) There are 21 favorable outcomes.

So the probability is 21/36, which simplifies to 7/12.

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The given measurement in scientific notation as \(6\times10^9\). Therefore, option D is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as \(1.56\times10^7\).

The given distance is 6,000,000,000 miles.

There are 9 zeros in the given number

So, scientific notation is \(6\times10^9\)

Therefore, the number in scientific notation is \(6\times10^9\).

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To form two pairs of perpendicular lines that intersect at the point (-3, -7), we can consider the slope-intercept form of linear equations. One pair of perpendicular lines can be y = mx - 7 and y = (-1/m)x - 7, where m is any non-zero real number. Another pair can be y = 7x - 52 and y = (-1/7)x - 7.

To create perpendicular lines, we need to find pairs of lines that have negative reciprocal slopes. We can start with a general equation in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
For the first pair, we can choose y = mx - 7 as the equation of one line. To make it perpendicular, we take the negative reciprocal of the slope, resulting in y = (-1/m)x - 7.
For the second pair, we can choose y = 7x - 52 as the equation of one line. To make it perpendicular, we take the negative reciprocal of the slope, resulting in y = (-1/7)x - 7.
Both pairs of equations form perpendicular lines that intersect at the point (-3, -7). The choice of m can be any non-zero real number, providing different examples of perpendicular lines that meet at the given point.

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The simplified form of the expression \((8a^{-3} )^{-\frac{2}{3} }\) is \(\frac{a^{2} }{4}\)

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, the expression to simplify is as follows:

\((8a^{-3} )^{-\frac{2}{3} }\)

using the law of indices,

\((a^{b} )^{c} = a^{bc}\)

Therefore,

8 = 2³

Hence,

\((2^{3} a^{-3} )^{-\frac{2}{3} }\)

using the aforementioned law of indices,

\((2^{3} a^{-3} )^{-\frac{2}{3} } = 2^{-2} .a^{2}\)

Hence,

\(2^{-2} .a^{2} = \frac{a^{2} }{2^{2} } =\frac{a^{2} }{4}\)

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Answer:

2

Step-by-step explanation:

-2+4=2

81 can be used as a model for (2+6)×3÷2-3 to the 2nd power.

Generally, The expression (2+6)×3÷2-3 can be simplified using the order of operations (also known as PEMDAS) as follows:

Perform the addition inside the parentheses: 2 + 6 = 8.

Perform the multiplication: 8 × 3 = 24.

Perform the division: 24 ÷ 2 = 12.

Perform the subtraction: 12 - 3 = 9.

So, the simplified expression is 9.

To find a model for (2+6)×3÷2-3 to the 2nd power, we can simply square the simplified expression:

(2+6)×3÷2-3 to the 2nd power = 9^2 = 81.

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Answer:

a) \(32\)

b) \(25\)

d) \(30\)

Step-by-step explanation:

\((2 \times 2 \times 2 \times 2 \times 2 \times)\)

\(32\)

\((5 \times 5 × 5)\)

\(125\)

\( \sqrt{ {30}^{2} } \)

\(30\)

The critical numbers of f are x = -5 and x = 5.

(A) To find the derivative f'(x), we differentiate f(x) = x³ - 75x - 2 with respect to x:
f'(x) = 3x² - 75

(B) There are no partition numbers for f' as partition numbers are related to integer partitions, which are not applicable in this context.

(C) To find the critical numbers of f, we set f'(x) equal to 0 and solve for x:
3x² - 75 = 0
x² = 25
x = ±5

So the critical numbers of f are x = -5 and x = 5.

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The equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t is x - 5y - 2z = 30

The plane is passing through point P₀(-1, -7, 2)

And the parametric equation of the line is:

x = -1+t , y= -7-5t , z= -2t

L: (-1, -7, -2) + t(1, -5, -2)

The required plane passes through P₀ and perpendicular to line L.

The direction vector of L is V = <1, -5, -2>.

The equation of a plane with normal vector <1, -5, -2> passing through a given point P(x₁, y₁, z₁) is

1(x - x₁) - 5(y - y₁) - 2(z - z₁) = 0

The equation of plane P passing through point P₀ (-1, -7, 2) is:

1(x - (-1)) - 5(y - (-7)) - 2(z - 2) = 0

(x + 1) - 5(y + 7) - 2(z - 2) = 0

x - 5y-2z + 1 - 35 + 4 = 0

x - 5y - 2z = 30 is the required equation of the plane

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The complete question is:

Find the equation for the plane through P₀ (-1, -7, 2) perpendicular to the following line. x = -1+t , y= -7-5t , z= -2t

Answer:

Option D

Step-by-step explanation:

Option A

x² - 3x² + 2x² = 0

Therefore, the given polynomial has no roots.

Option B

x² + 2x + 8

By quadratic formula,

x = \(\frac{-2\pm \sqrt{4-32} }{2}\)

  = \(\frac{-2\pm \sqrt{-28} }{2}\)

Therefore, roots are imaginary and for a polynomial with degree 1 or more than 1, both the roots can't be imaginary.

So the polynomial can't have exactly two roots.

Option C

99x³ - 33x + 1

Since the polynomial is of degree 3, so it will have three roots.

Therefore, the polynomial will not have exactly 2 roots.

Option D

√2x - 3x² + 7√2

By quadratic formula,

x = \(\frac{-\sqrt{2}\pm\sqrt{(\sqrt{2})^2-4(-3)(7\sqrt{2} )}}{2(-3)}\)

x = \(\frac{-\sqrt{2}\pm\sqrt{2+84\sqrt{2} )}}{(-6)}\)

There are exactly two real roots.

Therefore Option D is the answer.

Option E

4x + 11x - 111

Since this polynomial is of a degree 1.

There will be only one root.

= 7.211102550928

The distance is 7.21 units.

Answer:

Points R(4,1) S(7,3) T(6,4) after translation

R(4-3, 1) S(7-3, 3) T(6-3, 4)

R'(1, 1) S'(4, 3) T'(3, 4)

Points R'(1, 1) S'(4, 3) T'(3, 4) after reflection

R''(1, -3) S''(4, -5) T''(3, -6)

Step-by-step explanation:

Answer:Step-by-step explanation:Points R(4,1) S(7,3) T(6,4) after translation R(4-3, 1) S(7-3, 3) T(6-3, 4) R'(1, 1) S'(4, 3) T'(3, 4) Points R'(1, 1) ...