Find interval of increase and decrease of f(x) = 8 sin(x) + cot(x), −π ≤ x ≤ π

Answer:

Step-by-step explanation:

Given:

x = 2cost,

t = (1/2)arccosx

y = 2sint

dy/dx = dy/dt . dt/dx

dy/dt = 2cost

dt/dx = -1/√(1 - x²)

dy/dx = -2cost/√(1 - x²)

Differentiate again to obtain d²y/dx²

d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)

At t = π/4, we have

(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)

Answer:

The  95% confidence interval is  [tex]0.503 < p < 0.535[/tex]

The  interpretation is that there is 95% confidence that the true population proportion lie within the confidence interval

Step-by-step explanation:

From the question we are told that

    The  sample size is n  =  1003

     The number that indicated television are a luxury is  k  =  521

Generally the sample mean is mathematically represented as

           [tex]\r p = \frac{k}{n}[/tex]

          [tex]\r p = \frac{521}{1003}[/tex]

         [tex]\r p = 0.519[/tex]

Given the confidence level is  95% then the level of significance is mathematically evaluated as

       [tex]\alpha = 100 - 95[/tex]

       [tex]\alpha = 5\%[/tex]

       [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

          [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The  margin of error is mathematically represented as

           [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]

=>       [tex]E = 1.96 * \sqrt{ \frac{ 0.519 (1- 0.519 )}{1003} }[/tex]

=>       [tex]E = 0.016[/tex]

The  95%  confidence interval is mathematically represented as

       [tex]\r p -E < p < \r p +E[/tex]

=>   [tex]0.519 - 0.016 < p < 0.519 + 0.016[/tex]

=>    [tex]0.503 < p < 0.535[/tex]

Answer:

51.

Step-by-step explanation:

f(x) = x^2 + 2x + 3 and g(x) = x + 4.

f(g(x)) = (x + 4)^2 + 2(x + 4) + 3

= x^2 + 4x + 4x + 16 + 2x + 8 + 3

= x^2 + 8x + 16 + 2x + 11

= x^2 + 10x + 27.

x = 2.

f(g(2)) = 2^2 + 10 * 2 + 27

= 4 + 20 + 27

= 31 + 20

= 51.

Hope this helps!

Answer:

Solution : Third Option

Step-by-step explanation:

The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.

[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]

Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.

Therefore, the third option is a solution to the system.

Answer:

D. 800,000

Step-by-step explanation:

It is D because you find the hundred thousand place which is the 8, the you go to the number next door which is 3, if the 3 is 5 or greater the 8 will become a 9 or if it is not then it will stay the same. And everything to the left stays the same, everything to the right turns into zeros.

(2x+1)(x-3)

y(x-3) .... let y = 2x+1

y*x+y(-3) .... distribute

xy - 3y

x( y ) - 3( y )

x( 2x+1 ) - 3( 2x+1) ... replace y with 2x+1

2x^2 + x - 6x - 3 ..... distribute

2x^2 - 5x - 3

Answer is choice A

Answer:

His earnings for the period= $123

Step-by-step explanation:

Kevin's total payroll deductions are 30% of his earnings. His deductions add up to $369 for a two week period.

If 30% of his earnings = $369

His earnings = x

30/100 * x= 369

X= 369*100/30

X= 123*10

X=$ 1230

His earnings for the period= $123

Answer:

84 beads

Step-by-step explanation:

She had 98 beads and lost all but fourteen. So it would be 98 - 14 which would get you 84 beads that the girl has lost

Answer:

58

Step-by-step explanation:

By the property of intersecting secants outside of a circle, we have:

x° = 1/2( 141° - 25°) = 1/2 * 116° = 58°

Therefore, x = 58

Answer:

∠A and ∠G is the pair of vertical angles.

Step-by-step explanation:

From the figure attached,

Two lines 'm' and 'n' are two parallel lines. These lines intersect a horizontal line 'l'.

Since, "Pair of opposite angles formed at the point of intersection are the vertical angles and equal in measure."

Therefore, Opposite angles ∠A ≅ ∠G, ∠B ≅ ∠H, ∠C ≅ ∠E and ∠D ≅ ∠F are the vertical angles.

From the given options,

∠A and ∠G is the pair representing the pair of vertical angles and thus congruent.

Answer:

a

Step-by-step explanation:

Answer:

One - way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Step-by-step explanation:

ANOVA is a statistical technique designed to test mean of one or more quantitative populations.  In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA. It is a statistical technique designed to test mean of one or more quantitative populations. In two-way ANOVA it equals the block mean. Column block means square is three-way ANOVA.

One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

It should be the statistical technique that are made for testing the mean for one or more than one quantitative population. In two-way ANOVA it should be equivalent to the block mean. Here the column block represent the square be the three-way ANOVA.

Therefore, One-way ANOVA, the smaller the between treatment

The smaller the value of F statistic will give us significant evidence.

Learn more about evidence here: https://brainly.com/question/6764645?referrer=searchResults

Answer:

1. elements it contains =  (1,3)

2.  elements it contains = 35

3.  elements it contains = 8

4.  elements it contains = 17

Step-by-step explanation:

A. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 4; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols.

The red die shows 1 and the numbers add to 4.

How many elements does it contain?

B. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 3; B: the numbers add to 2; C: at least one of the numbers is 1; and D: the numbers do not add to 10. Express the given event in symbols. HINT [See Example 5.]

The numbers do not add to 2.

How many elements does it contain?

C. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 1; B: the numbers add to 2; C: at least one of the numbers is 3; and D: the numbers do not add to 11. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 11 or the red die shows a 1.

How many elements does it contain?

D. Suppose two dice (one red, one green) are rolled. Consider the following events. A: the red die shows 4; B: the numbers add to 5; C: at least one of the numbers is 1; and D: the numbers do not add to 9. Express the given event in symbols. HINT [See Example 5.]

Either the numbers add to 5, or they add to 9, or at least one of them is 1.

How many elements does it contain?

NB. Attached is the solution to the problems stated above

Answer:

88%.

Step-by-step explanation:

Multiply the fraction by 100:

(22/25) * 100

= 22 * 4

= 88%.

Answer:

(3x+2)^2

Step-by-step explanation:

Answer: 0.8749

Step-by-step explanation:

Given, The time, X minutes, taken by Tim to install a satellite dish is assumed to be a normal random variable with mean 127 and standard deviation 20.

Let x be the time taken by Tim to install a satellite dish.

Then, the probability that Tim will takes less than 150 minutes to install a satellite dish.

[tex]P(x<150)=P(\dfrac{x-\text{Mean}}{\text{Standard deviation}}<\dfrac{150-127}{20})\\\\=P(z<1.15)\ \ \ [z=\dfrac{x-\text{Mean}}{\text{Standard deviation}}]\\\\=0.8749\ [\text{By z-table}][/tex]

hence, the required probability is 0.8749.

Answer:

3.75

Step-by-step explanation:

[tex]v = lbh \\ 2.5 \times 1.5 \times 1 \\ = 3.75[/tex]

The volume of the rectangular prism will be 3.75 cubic meters.

Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as

V = L x W x H

A box is 1 m high, 2.5 m long, and 1.5 m wide.

Then the volume of the rectangular prism will be

V = L x W x H

V = 1 x 2.5 x 1.5

V = 3.75 cubic meters

Thus, the volume of the rectangular prism will be 3.75 cubic meters.

More about the volume of the rectangular prism link is given below.

https://brainly.com/question/21334693

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Answer:

90% confidence interval for the difference between the two population means

( -23.4166 , -6.5834)

Step-by-step explanation:

Step(i):-

Given first sample size n₁ = 100

Given mean of the first sample x₁⁻ = 178

Standard deviation of the sample S₁ = 35

Given second sample size n₂= 100

Given mean of the second sample x₂⁻ = 193

Standard deviation of the sample S₂ = 37

Step(ii):-

Standard error of two population means

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{s^{2} _{1} }{n_{1} }+\frac{s^{2} _{2} }{n_{2} } }[/tex]

       [tex]se(x^{-} _{1} -x^{-} _{2} ) = \sqrt{\frac{(35)^{2} }{100 }+\frac{(37)^{2} }{100 } }[/tex]

        [tex]se(x^{-} _{1} -x^{-} _{2} ) = 5.093[/tex]

Degrees of freedom

ν  = n₁ +n₂ -2 = 100 +100 -2 = 198

t₀.₁₀ = 1.6526

Step(iii):-

90% confidence interval for the difference between the two population means

[tex](x^{-} _{1} - x^{-} _{2} - t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2}) , x^{-} _{1} - x^{-} _{2} + t_{\frac{\alpha }{2} } Se (x^{-} _{1} - x^{-} _{2})[/tex]

(178-193 - 1.6526 (5.093) , 178-193 + 1.6526 (5.093)

(-15-8.4166 , -15 + 8.4166)

( -23.4166 , -6.5834)

Answer:

hello attached is the missing part of your question and the answer of the question asked

answer : 0.2951

Step-by-step explanation:

Given data:

number of persons allowed in the elevator = 15

weight limit of elevator = 2500 pounds

average weight of individuals = 152 pounds

standard deviation = 26 pounds

probability that an individual selected weighs more than 166 pounds

std = 26 ,  number of persons(x) = 15, average weight of individuals(u) = 152 pounds

p( x > 166 ) = p( x-u / std,  166 - u/ std )

                  = p (  z > [tex]\frac{166-152}{26}[/tex] )

                  = 1 - p( z < 0.5385 )

p( x > 166 ) = 1 - 0.70488 = 0.2951

Answer:

[tex]f(x) = x^{4}[/tex], [tex]g(x) = x-1[/tex]

Step-by-step explanation:

Let be [tex]F(x) = f\circ g (x) = (x-1)^{4}[/tex], then expression for [tex]f(x)[/tex] and [tex]g(x)[/tex] are, respectively:

[tex]f(x) = x^{4}[/tex] and [tex]g(x) = x-1[/tex]

Answer:

Height (z)= 4+(5/3)(z)

Where z is the number of weeks

1). Slope = 4

2). Height= 5.67 inches

3).Height (z)= 4+(5/3)(z)

4).Height= 30.67 inches

Step-by-step explanation:

At week four

10.67= x+4y

Week 7

15.67= x+7y

Solving both equation simultaneously

3y= 5

Y= 5/3

15.67= x+7y

15.67= x+7(5/3)

15.67-35/3= x

15.67-11.67= x

4= x

The modeled equation is

Height (z)= 4+5/3(z)

Where z is the number of weeks

Slope of the function as compared to y= mx+c is 4

The first week of it's plantation

Height (z)= 4+5/3(z)

Height (1)= 4+5/3(1)

Height= 5.67 inches

After 16 weeks

Height (z)= 4+(5/3)(z)

Height (16)= 4+(5/3)(16)

Height= 30.67 inches

Answer:

(B) [tex]\sqrt{221}[/tex] yards

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean Theorem to find the length of x.

The Pythagorean Theorem states that [tex]a^2 + b^2 = c^2[/tex], where a and b are our legs and c is the hypotenuse.

We need to find c, and we already know a and b, so let's substitute.

[tex]10^2 + 11^2 = c^2\\\\100+121=c^2\\\\221=c^2\\\\c=\sqrt{221}[/tex]

Hope this helped!

Answer:

c/sin C = b/sin C

Step-by-step explanation:

Look at the statement in the previous step and the reason in this step.

c sin B = b sin C

Divide both sides by sin B sin C:

(c sin B)/(sin B sin C) = (b sin C)/(sin B sin C)

c/sin C = b/sin B

Answer:

0.71419 &0.71421 are the correct.

Answer:

0.065617 ft

Step-by-step explanation:

Answer:

0.0656168 feet.

Step-by-step explanation:

Answer:

Drag the ruler over each side of the triangle to find its length.

The length of AB is

✔ 5

.

The length of BC is

✔ 4

.

Drag the protractor over each angle to find its measure.

The measure of angle C is

✔ 90°

.

The measure of angle B is

✔ 36.9°

.

Step-by-step explanation:

The length of sides AB and BC of the triangle will be 5 units and 4 units. And the measure of angle C and angle B of the triangle will be 90° and 37°.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Drag the ruler over each side of the triangle to find its length.

The length of side AB of the triangle is 5 units.

The length of side BC of the triangle is 4 units.

Drag the protractor over each angle to find its measure.

The measure of angle C of the triangle is 90°.

The measure of angle B of the triangle is 37°.

The length of sides AB and BC of the triangle will be 5 units and 4 units.

And the measure of angle C and angle B of the triangle will be 90° and 37°.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

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▹ Answer

80

▹ Step-by-Step Explanation

(2²)³ + (2³)² ÷ 4

Rewrite:

2⁶ + 2⁶ ÷ 2²

Divide:

2⁶ + 2⁴

Factor:

(2² + 1) * 2⁴

Evaluate:

(4 + 1) * 2⁴

Calculate:

5 * 16

= 80

Hope this helps!

CloutAnswers ❁

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Answer:

False

Step-by-step explanation:

Here, we want to check the validity of the given statement. The statement is false.

Under the empirical rule, following a normal distribution, 99.7% of observed data lies within 3 standard deviations from the mean while 95% of observed data lies within 2 standard deviation from the mean and 68% of observed data lies within 1 standard deviation of the mean.

Please check attachment for diagrammatic representation of the empirical rule.

Responder:

2

Explicación paso a paso:

El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).

Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.

Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;

= | 13-11 |

= | 2 |

Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.

Por tanto, el valor absoluto de la expresión es 2

Answer:

$3 per pineapple

Step-by-step explanation:

Hey there!

If 2 pineapples are $6,

6 / 2 = 3

So 1 pineapple is $3.

Hope this helps :)

Answer:

3 dollars for 1 pineapple

Step-by-step explanation:

well 2 pinapples is 6 bucks. so 2x=6, and to get x, just divide each side by 2. 6/2=3.