A duck has 1,100 feathers. It went for a swim in a pond and lost 2/100 of its feathers. How many feathers did it lose?

[tex]\displaystyle \int\sec x\:dx = \ln |\sec x + \tan x| + C[/tex]

Step-by-step explanation:

[tex]\displaystyle \int\sec x\:dx=\int\sec x\left(\frac{\sec x+ \tan x}{\sec x + \tan x}\right)dx[/tex]

[tex]\displaystyle = \int \left(\dfrac{\sec x\tan x + \sec^2x}{\sec x + \tan x} \right)dx[/tex]

Let [tex]u = \sec x + \tan x[/tex]

[tex]\:\:\:\:\:\:du = (\sec x\tan x + \sec^2x)dx[/tex]

where

[tex]d(\sec x) = \sec x\tan x\:dx[/tex]

[tex]d(\tan x) = \sec^2x\:dx[/tex]

[tex]\displaystyle \Rightarrow \int \left(\frac{\sec x\tan x + \sec^2x}{\sec x + \tan x}\right)\:dx = \int \dfrac{du}{u}[/tex]

[tex]= \ln |u| + C = \ln |\sec x + \tan x| + C[/tex]

Answer:

1.6 Bitcoins

Step-by-step explanation:

Given data

We have the rate as

$1 USD to 0.004

Hence $400 will buy x bitcoins

Cross multiply to find the value of x

1*x= 400*0.004

x=1.6

Hence $400 will get you 1.6 Bitcoins

Answer:

[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]

Step-by-step explanation:

Given

[tex]9 < x < 10[/tex] --- interval

Required

The probability density of the volume of the cube

The volume of a cube is:

[tex]v = x^3[/tex]

For a uniform distribution, we have:

[tex]x \to U(a,b)[/tex]

and

[tex]f(x) = \left \{ {{\frac{1}{b-a}\ a \le x \le b} \atop {0\ elsewhere}} \right.[/tex]

[tex]9 < x < 10[/tex] implies that:

[tex](a,b) = (9,10)[/tex]

So, we have:

[tex]f(x) = \left \{ {{\frac{1}{10-9}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]

Solve

[tex]f(x) = \left \{ {{\frac{1}{1}\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]

[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex]

Recall that:

[tex]v = x^3[/tex]

Make x the subject

[tex]x = v^\frac{1}{3}[/tex]

So, the cumulative density is:

[tex]F(x) = P(x < v^\frac{1}{3})[/tex]

[tex]f(x) = \left \{ {{1\ 9 \le x \le 10} \atop {0\ elsewhere}} \right.[/tex] becomes

[tex]f(x) = \left \{ {{1\ 9 \le x \le v^\frac{1}{3} - 9} \atop {0\ elsewhere}} \right.[/tex]

The CDF is:

[tex]F(x) = \int\limits^{v^\frac{1}{3}}_9 1\ dx[/tex]

Integrate

[tex]F(x) = [v]\limits^{v^\frac{1}{3}}_9[/tex]

Expand

[tex]F(x) = v^\frac{1}{3} - 9[/tex]

The density function of the volume F(v) is:

[tex]F(v) = F'(x)[/tex]

Differentiate F(x) to give:

[tex]F(x) = v^\frac{1}{3} - 9[/tex]

[tex]F'(x) = \frac{1}{3}v^{\frac{1}{3}-1}[/tex]

[tex]F'(x) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]

[tex]F(v) = \frac{1}{3}v^{-\frac{2}{3}}[/tex]

So:

[tex]f(v) = \left \{ {{\frac{1}{3}v^{-\frac{2}{3}}\ 9^3 \le v \le 10^3} \atop {0, elsewhere}} \right.[/tex]

Answer:

Step-by-step explanation:

Substituting y = 4x+1 into 2y = -x-1 gives the equation

2(4x+1) = -x-1

Solve the equation:

8x+2 = -x-1

9x = -3

x = -⅓

Substituting y = 4x+1 into 2y = -x-1 will produce the equation 2(4x+1) = -x-1

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. Based on the degree, there are four different main types of equations. Equations that are linear, quadratic, cubic, and polynomial

Given,  the equation y = 4x + 1 and another equation 2y = -x – 1.

Substituting equation 1 into equation 2 we will get

2(4x+1) = -x-1

Solve the equation:

8x+2 = -x-1

9x = -3

x = -⅓

Therefore, The equation 2(4x+1) = -x-1 is created when y = 4x+1 is substituted into 2y = -x-1.

Learn more about equations here:

https://brainly.com/question/16255566

#SPJ2

Answer:

x is 1. i looked it up so that's all you need

Step-by-step explanation:

D. RAMONA SAVED THE MOST IN 2006

D. Ramona saved the most in 2006

Answer:

x=2

y=3

Step-by-step explanation:

y=−2x+7

y=5x−7

Set the two equations equal since they are both equal to y

−2x+7 =5x−7

Add 2x to each side

-2x+7+2x = 5x-7+2x

7 = 7x-7

Add 7 to each side

7+7 = 7x-7+7

14 =7x

Divide by 7

14/7 = 7x/7

2 =x

Now find 7

y = 5x-7

y = 5(2) -7

y = 10-7

y = 3

Given that y=y=y,

→ -2x+7 = 5x-7

Let's find the value,

→ -2x+7 = 5x-7

→ 7 = 5x+2x-7

→ 7 = 7x-7

→ 7+7=7x

→ 14 = 7x

→ x = 14/7

→ [x = 2]

Then we can find 7,

→ y = 5x-7

→ y = 5(2) -7 y = 10-7

→ [y = 3]

This is required answer.

Answer:

3.564 m^2

Step-by-step explanation:

The area of the original garden is

A = 5.4 * 1.5 = 8.1

The new garden is

5.4*1.2 = 6.48 by 1.5*1.2 =1.8

The area is

A = 6.48*1.8=11.664

The increase in area is

11.664-8.1=3.564

The given information is,

To find the increase in area of the garden.

Formula we use,

→ Area = Length × Width

Area of the real garden is,

→ 5.4 × 1.5

→ 8.1 m

The new garden will be,

→ 5.4 × 1.2 = 6.48 m

→ 1.5 × 1.2 = 1.8 m

The area of the new garden is,

→ 6.48 × 1.8

→ 11.664

Then the increase in area of the garden,

→ 11.664 - 8.1

→ 3.564 m²

Hence, 3.564 m² is the increase in area.

Answer:

0.706....

Step-by-step explanation:

Answer:

The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).

Step-by-step explanation:

Before building the confidence interval, we need to understand the Central Limit Theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A BYU-Idaho professor took a survey of his classes and found that 82 out of 90 people who had served a mission had personally met a member of the quorum of the twelve apostles.

This means that:

[tex]p_S = \frac{82}{90} = 0.9111[/tex]

[tex]s_S = \sqrt{\frac{0.9111*0.0888}{90}} = 0.045[/tex]

Of the non-returned missionaries that were surveyed 86 of 110 had personally met a member of the quorum of the twelve apostles.

This means that:

[tex]p_N = \frac{86}{110} = 0.7818[/tex]

[tex]s_N = \sqrt{\frac{0.7818*0.2182}{110}} = 0.0394[/tex]

Distribution of the difference:

[tex]p = p_S - p_N = 0.9111 - 0.7818 = 0.1293[/tex]

[tex]s = \sqrt{s_S^2+s_N^2} = \sqrt{0.045^2+0.0394^2} = 0.0598[/tex]

Calculate a 99% confidence interval for the difference in the two proportions.

The confidence interval is:

[tex]p \pm zs[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower bound of the interval is:

[tex]p - zs = 0.1293 - 2.575*0.0598 = -0.0247[/tex]

[tex]p + zs = 0.1293 + 2.575*0.0598 = 0.2833[/tex]

The 99% confidence interval for the difference in the two proportions is (-0.0247, 0.2833).

Answer:

The greatest possible value of xy is 165.

Step-by-step explanation:

The three modes are 5, 12, and 150 since they occur the most times and they tie one another in being the most frequent (each occurring 3 times).

Only the 7 and 8 occur once each, and aren't modes. Everything else is a mode. It's possible to have more than one mode and often we represent this as a set. So we'd say the mode is {5, 12, 150} where the order doesn't matter.

Answer:

555.56

Step-by-step explanation:

Purpose of the study:  To determine if women are better drivers than men.

Survey or Opinion population:  1,000

You are experimenting on 9 out of a thousand opinions.

5 of these opinions are that women are better drivers

4 of these opinions are that women are not better drivers

You want to know the sample (full sample size is 9) proportion for women as better drivers; using the large sample method. This method is also called the asymptotic method.

This involves approximating the desired statistic, with just a small fraction of the population; in this case, 9/1000.

This approximation will get more and more accurate as sample size increases and you know that a larger sample size gives a better representation and interpretation of the population preference!

So using ratio, the sample proportion for women as the better drivers is given by:

5/9 x 1000   = 555.56 opinions

Hello!

1) 6/10 × 10/6 × 5/9 = 1/10 × 10 × 5/9 = 1 × 5/9 = 5/9 or 0,5

2) 6/10 × 4/3 × 10/20 = 6 × 4/3 × 1/20 = 2 × 4 × 1/20 = 2 × 1/5 = 2/5 or 0,4

Good luck! :)

Answer:

1) 5/9

2) 2/5

Explanation:

1) 6/10 × 10/6 × 5/9=

Multiply all the denominators and all the numerators then simplify= 300/540 = 5/9

2)  6/10 × 4/3 × 10/20=

Multiply all the denominators and all the numerators then simplify= 240/600 = 2/5

Answer:

   =(s^2 - t^2)/4

Step-by-step explanation:

a + b = s and a - b = t,

Add the two equations together

a + b = s

a - b = t

----------------

2a = s+t

a = (s+t)/2

Subtract the two equations

a + b = s

- a + b = -t

-------------------

2b =(s-t)

b = (s-t)/2

We want to find ab

ab = (s+t)/2 *  (s-t)/2

FOIL

    =(s^2 - t^2)/4

Answer:

A, B, and E apply

Step-by-step explanation:

One thing we can do is to make everything in the same format, under one square root, with no non-square roots.

First, we can say that 6 is equal to √36 as 6² =36, and 6 ≥ 0. Therefore, 6√3 = √36 * √3 = √108

For A, √3 * √36 = √108, so this applies

For B, √18 * √6 = √108, so this applies

For C, 108² = √something bigger than 108 = √11664, so this does not apply

For D, √54 ≠ √108, so this does not apply

For E, √108 = √108, so this applies

For F, √3 * √6 = √18, so this does not apply

Answer:

2 = x          -7 = x

Step-by-step explanation:

f(x) = (x - 2)(x + 7)

y  = (x - 2)(x + 7)

Set y = 0

0 = (x - 2)(x + 7)

Using the zero product property

0 = x-2    0 = x+7

2 = x          -7 = x

Answer:

Zeros happen when f(x) = 0. There are two zeros in the given function:

Therefore solve both equations above and you'll get:

Answer:

It took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.

Step-by-step explanation:

Given that Chau took 5 3/8 hours to clean the bedroom, and then he took a 1/2 to clean the den, to determine how much total time did he take to clean two rooms the following calculation must be performed:

5 + 3/8 + 1/2 = X

5 + 0.375 + 0.5 = X

5.875 = X

0.875 = 7/8

60/8 x 7 = 52.5

Therefore, it took Chau 5 hours, 52 minutes, and 30 seconds to clean both rooms.

Answer:

The product of a constant factor of four and a factor with the sum of two terms

Step-by-step explanation:

4(y + 6)

This is two terms, a constant 4 and a term with y+6

We a multiplying so we have a product

Answer:

A

Step-by-step explanation:

I believe A is the best answer because 4 is the constant factor with the sum of y + 6. I just think it best rrepresents the equation! :)

Answer:

Proportions and percent

Answer:

Assessing the association between supplemental vitamin A exposure and mortality and morbidity for measles:

Regarding the relative risk, the correct statement is:

a. Exposure to vitamin A appears to protect against morbidity and mortality for measles.

Step-by-step explanation:

Relative risk for incidence of measles = 0.75

Relative risk for measles mortality = 0.5

Relative risk for mortality and morbidity for measles = 0.375 (0.75 * 0.5)

The combined relative risk is less than 50%

The association is weak because RR is less than 1.

Therefore, there is no association between supplemental vitamin A exposure and mortality and morbidity for measles.

Answer:

the percentage increase is 35%

Answer:  Choice B)  [tex]\sqrt{2}[/tex]

Work Shown:

[tex]\sec^2(\theta) = \tan^2(\theta) + 1\\\\\sec^2(\theta) = (\tan(\theta))^2 + 1\\\\\sec^2(\theta) = (-1)^2 + 1\\\\\sec^2(\theta) = 2\\\\\sec(\theta) = \sqrt{2}\\\\[/tex]

Note: secant is positive in quadrant Q4, when theta is between 3pi/2 radians and 2pi radians (270 degrees and 360 degrees). So that's why we don't consider the minus form of the plus minus.

Answer:

-5

2

-125

-3

Step-by-step explanation:

5 + A = 0

Subtract 5 from both sides.

A = -5

-8/4 - B = -4

-2 - B = -4

B + 2 = 4

B = 2

C ÷ 25 = -5

C = -125

D × 13 = -39

D × 13/13 = -39/13

D = -3

Answer:

The probability would be 1/8.

Step-by-step explanation:

The probability of the spinner landing on an odd number is 1/2, and the probability of the spinner landing on a number greater than 8 is 1/4. So we multiply those two probabilites to get our answer 1/8.

Step-by-step explanation:

[tex]a_3 [/tex] = - 4

[tex]a_3 [/tex] = a* + (3- 1) d*

- 4 = a + 2d . . . . . . . . .(i)

[tex]a_8 [/tex] = - 29

[tex]a_8 [/tex] = a + ( 8 - 1) d

- 29 = a + 7d . . . . . . . . (ii)

subtracting equations (i) and (ii)

25 = 5d

d = -5

placing d = -5 in equation (i)

a - 10 = -4

a = 6

For an arithmetic Progtession

[tex]a_n [/tex] = a + (n - 1)d

[tex]a_n [/tex] = 6 + (n- 1)-5

[tex]a_n [/tex] = 6 - 5n + 5

[tex] \underline {a_n = 11 - 5n }[/tex]

[tex]\\[/tex]

*[tex] \boxed{ \mathfrak { a \:stands\: for\: first\: term } } [/tex]

*[tex] \boxed{ \mathfrak { d \:stands\: for\: common \: difference } } [/tex]

Answer:

General rule » -5n+11

Step-by-step explanation:

a3 = a+2d = -4 .......(1)

a8=a+7d = -29..........(2)

(2)-(1) » 5d= -25

d = -25/5

. = -5

substitute d = -5 in ( 1)

» a-2×-5= -4

a-10 = -4

a = -4 +10

= 6

General rule » a +(n-1)d

» 6 +(n-1)×-5

» 6-5n+5

» -5n+11

Answer:

10 + 8 + 10 + 10 + 10 + 10 + 8 + 8 + 6 + 6

Answer:

Step-by-step explanation:

Let many universities and colleges have conducted supplemental instruction(SI) programs. In that a student facilitator he meets the students group regularly who are enrolled in the course to promote discussion of course material and enhance subject mastery.

Here the students in a large statistics group are classified into two groups:

1). Control group: This group will not participate in SI and

2). Treatment group: This group will participate in SI.

a)Suppose they are samples from an existing population, Then it would be the population of students who are taking the course in question and who had supplemental instruction. And this would be same as the sample. Here we can guess that this is a conceptual population - The students who might take the class and get SI.

b)Some students might be more motivated, and they might spend the extra time in the SI sessions and do better. Here they have done better anyway because of their motivation. There is other possibility that some students have weak background and know it and take the exam, But still do not do as well as the others. Here we cannot separate out the effect of the SI from a lot of possibilities if you allow students to choose.

The random assignment guarantees ‘Unbiased’ results - good students and bad are just as likely to get the SI or control.

c)There wouldn't be any basis for comparison otherwise.