Solve the equation for solutions in the interval [0, 2 π). Use algebraic methods and give exact values. Support your solution graphically. cos2x = 0

Complete question :

The development of AstroWorld ("The Amusement Park of the Future") on the outskirts of a city will increase the city's population at the rate given below in people/year t yr after the start of construction. 5,700√t + 11,000 The population before construction is 67,000. Determine the projected population 16 yr after the construction of the park has begun. people

Answer:

486,200

Step-by-step explanation:

Given that the rate of change in population is represented by the function:

f(t) = 5,700√t + 11,000

To get the original function, we take the integral of the rate function because the rate of change is obtained by taking the derivate of the original equation

f(t) = 5,700t^1/2 + 11,000

Taking the integral of f with respect to t:

∫(5,700t^1/2 + 11,000)

[5700t^(1/2 + 1)] / (1/2 + 1) + 11000t + C

[(5700t^3/2)/ 3/2] + 11000t + C

Where C = constant

If population before construction = 67000

Then C = 67000

t = time = 16 years

Substitute values into the original change equation:

[(5700(16)^3/2)/ 3/2] + 11000t + 67000

[(5700 * 64) / 1.5] + 11000(16) + 67000

243200 + 176000 + 67000

= 486,200

Answer:

4.2

Step-by-step explanation:

f varies inversly with L can be translated matimatically as:

● f = k/L

It takes 7 pounds of pressure to break a 3 feet long board.

Replace f by 7 and L by 3.

● 7 = k/3 => k=7×3=21

■■■■■■■■■■■■■■■■■■■■■■■■■■

Let's find tge length of a board that takes 5 pounds of pressure to be broken.

● 5 = k/L

● 5 = 21/L

● L = 21/5 = 4.2

So the board is 4.2 feet long

Hey there! I'm happy to help!

When graphing a system of equations, the solution is the point where the two lines meet. We see that they intersect at (-2,4).

Therefore, the solution to the system of equations is (-2,4).

Have a wonderful day! :D

Answer:

A

Step-by-step explanation:

edge 2020 Dec 9

Answer:

(1+y^2) /2y

Step-by-step explanation:

arithmetic mean is the average of x and y

(x+y)/2

Using the equation

xy = 1

and solving for x

x = 1/y

Replacing x in the first equation

(1/y + y) /2

Multiply by y/y

(1/y + y) /2 * y/y

(1/y + y)*y /2y

(1+y^2) /2y

Answer:

The equation 1+0=1

Step-by-step explanation:

Other options are not eligible because

1 option -Natural numbers cannot be closed under subtraction

2 option-The equation is not having proper rational numbers, they are decimals

3 option-Whole numbers cannot be closed under subtraction

Thank you!

Answer:

[tex]\huge\boxed{r<8}[/tex]

Step-by-step explanation:

[tex]5 > r - 3[/tex]

Adding 3 to both sides

[tex]5 + 3 > r[/tex]

[tex]8 > r\\OR \\r < 8[/tex]

Answer: D. r<8

Step-by-step explanation:

[tex]5>r-3[/tex]

add 3 to both sides

[tex]r-3+3<5+3[/tex]

[tex]5+3=8[/tex]

simplify

[tex]r<8[/tex]

Answer:

4

Step-by-step explanation:

Plug in 3 as x in the expression:

10 - 2x

10 - 2(3)

10 - 6

= 4

Answer:

4

Step-by-step explanation:

10 - 2x

Let x =3

10 -2(3)

10 -6

4

Answer:

B is the correct answer.

Step-by-step explanation:

-2x+3y+z=-6

z=6

-2x+3y+6=-6

-2x+3y=-12

-2(3)+3(2)

-6+6=0 A is incorrect

-2(3)+3(-2)=-12

-6-6=-12

B is the correct answer.

I am not going to show C or D, because you have the right answer. Hope this helps you. Thank you.

Answer:

1/3

Step-by-step explanation:

there are twelve marbles total. there are 4 blue marbles.

4/12 = 1/3

Answer:

  36

Step-by-step explanation:

Each cut creates a triangular face where the corner used to be. That face adds three edges to the figure. The 8 cuts add a total of 8×3 = 24 edges to the 12 edges the prism already had.

The new figure has 12+24 = 36 edges.

Step-by-step explanation:

It is given that, a projectile is fired vertically upward from a height of 300  feet above the ground, with an initial velocity of 900 ft/s.

The general equation with which a projectile are modled by the function is given by :

[tex]h(t)=-16t^2+v_ot+y_o[/tex]

y₀ is the initial height above the ground

v₀ = initial velocity

So,

[tex]h(t)=-16t^2+900t+300[/tex]

This is the quadratic equation that models the projectile height in feet above the ground after t seconds.

Answer:

the standard deviation of the sample is less than  0.1

Step-by-step explanation:

Given that :

The sample size n = 100 units

The average proportion of non-conforming windshield wipers is found to be 0.042 which is the defective rate P-bar

The standard deviation of the machine([tex]S_p[/tex]) can be calculated  by using the formula:

[tex]S_p =\dfrac{ \sqrt{ \overline P \times (1 - \overline P)} }{n}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.042 \times (1 -0.042)} }{100}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.042 \times (0.958)} }{100}[/tex]

[tex]S_p =\dfrac{ \sqrt{0.040236} }{100}[/tex]

[tex]S_p =\dfrac{ 0.2005891323 }{100}[/tex]

[tex]S_p =0.002[/tex]

Thus , the standard deviation of the sample is less than  0.1

Answer:

B

Step-by-step explanation:

Calculate the ratio of corresponding sides, image to preimage, that is

scale factor = [tex]\frac{DE}{AC}[/tex] = [tex]\frac{12.09}{16.12}[/tex] = 0.75 → B

The scale factor of the dilation will be 1.33. Then the correct option is A.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

In the diagram, ∆ABC and ∆DBE are similar.

Then the scale factor of the dilation that will map the preimage ΔABC onto the image ΔDBE will be

⇒ 16.12 / 12.09

⇒ 1.33

Then the correct option is A.

More about the dilation link is given below.

https://brainly.com/question/2856466

#SPJ2

Answer:

b

Step-by-step explanation:

it makes the most senses the lower the discount the higher the chance

Answer:

If something is guaranteed, it has a probability of 100%, or 1.

Step-by-step explanation:

A standard deck has 52 cards. Of these, half are red cards (diamonds and hearts) and half are black cards (clovers and spades)

Half of the deck is 26 cards (52 ÷ 2 = 26), so you have 26 red and 26 black cards.

What this means in our context is, if we draw 27 cards, even if we drew all 26 black cards, we would still have 1 red card.

So the probability is 100%, or 1, of drawing a red card when we pick 27 cards from a deck, no matter how it's shuffled

The probability of getting a red card is 1.

No matter how you shuffle the cards, the no of cards will remain the same.

Therefore, it will not affect the probability.

Probability is simply how likely something is to happen. Whenever we're unsure about the outcome of an event, we can talk about the probabilities of certain outcomes—how likely they are. The analysis of events governed by probability is called statistics.

Learn more about probability here: https://brainly.com/question/251701

#SPJ2

Hey there! I'm happy to help!

We know that the ice cream store makes 144 quarts in eight hours. What about in one hour? Let's divide this by eight to find out.

144/8=18

So, they make 18 quarts every hour. We want to figure out how many can be made in 12 hours. So, we just multiply 18 by 12!

18(12)=216

Therefore, 216 quarts of ice cream could be made in 12 hours.

Have a wonderful day! :D

The ice cream store will make 216 quarts of ice cream in 12 hours.

Division is breaking a number up into an equal number of parts.

Given that, An ice cream store makes 144 quarts of ice cream in 8 hours.

Since, they make 144 quarts of ice cream in 8 hours

Therefore, in 1 hour they will make = 144/8 = 18 quarts

So, in 12 hours = 18x12 = 216 quarts.

Hence, The ice cream store will make 216 quarts of ice cream in 12 hours.

For more references on divisions, click;

https://brainly.com/question/21416852

#SPJ2

Complete Question

It has been found that 26% of men 20 years and older suffer from hypertension (high blood pressure) and 31.5% of women are hypertensive. A random sample 150 of each gender was selected from recent hospital records, and the following results were obtained.

Men. 43 patients had high blood pressure

Woman. 52 patients had high blood pressure.

Answer:

The  95% confidence interval is  

      [tex]- 0.1651 < p_m - p_f <0.0451[/tex]

This mean that there is a 95 % confidence that the difference between the true proportions of male and  female that are hypertensive  is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive        

Step-by-step explanation:

From the question we are told that

    The  sample size for male is  [tex]n_1 = 150[/tex]

    The  number of male that are hypertensive is  [tex]m = 42[/tex]

    The  sample size of female is  [tex]n_2 = 150[/tex]

     The  number of female that are hypertensive is [tex]q = 52[/tex]

The proportion of male that are hypertensive is mathematically represented as

         [tex]\r p_m = \frac{43}{150}[/tex]

         [tex]\r p_m = 0.287[/tex]          

The proportion of female that are hypertensive is mathematically represented as

       [tex]p_f = \frac{52}{150}[/tex]

      [tex]p_f = 0.347[/tex]

From the question we are told that confidence level is 95%, hence the level of significance is mathematically represented 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]

Generally the margin of error is mathematically represented as

          [tex]E = Z_{\frac{\alpha }{2} } * \sqrt{\frac{ \r p_m (1- \r p_m )}{n_1} + \frac{ \r p_f (1- \r p_f )}{n_2} }[/tex]

substituting value

         [tex]E = 1.96 * \sqrt{\frac{ 0.287 (1- 0.287 )}{150} + \frac{ 0.347 (1- 0.347 )}{150} }[/tex]

         [tex]E = 0.1051[/tex]

The  95% confidence interval is mathematically represented as  

           [tex](\r p_m - \r p_f ) - E < p_m - p_f < (\r p_m - \r p_f ) + E[/tex]

substituting values

          [tex]( 0.287 - 0.347 ) - 0.1051 < p_m - p_f <( 0.287 - 0.347 ) + 0.1051[/tex]    

           [tex]- 0.1651 < p_m - p_f <0.0451[/tex]

This mean that there is a 95 % confidence that the difference between the true proportion is within this interval and given that the interval contains zero then there is no statistically significant difference between the genders that are hypertensive.

Answer:

distance covered in 5 seconds

= 1.4283 *10^10 feet

Step-by-step explanation:

A racecar is traveling at a constant speed of 150 miles per hour.

One mile = 5280 feet

150 miles= 5290*150

150 miles= 793500 feet

A racecar is traveling at a constant speed of 793500 feet per hour.

Converting 793500 feet per hour to feet per seconds .

793500 feet per hour

= 793500*60*60 feet per seconds

=2856600000 feet per second

In 5 seconds , distance covered

= 2856600000 *5

distance covered in 5 seconds

= 1.4283 *10^10 feet

Answer:

The  confidence interval is  [tex]0.304 < p < 0.324[/tex]

Step-by-step explanation:

From the question we are told

      The sample proportion [tex]\r p = 0.314[/tex]

      The margin of error  is [tex]E = 0.01[/tex]

The confidence interval for  p is mathematically represented as

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

=>    [tex]0.314 - 0.01 < p < 0.314 + 0.01[/tex]

=>   [tex]0.304 < p < 0.324[/tex]

Answer:

[tex]\huge\boxed{n\leq\dfrac{2-2c}{p}\ \text{for}\ p<0}\\\boxed{n\geq\dfrac{2-2c}{p}\ \text{for}\ p>0}[/tex]

Step-by-step explanation:

[tex]-np-4\leq2(c-3)\qquad\text{use the distributive property}\\\\-np-4\leq2c-6\qquad\text{add 4 to both sides}\\\\-np\leq2c-2\qquad\text{change the signs}\\\\np\geq2-2c\qquad\text{divide both sides by}\ p\neq0\\\\\text{If}\ p<0,\ \text{then flip the sign of inequality}\\\boxed{n\leq\dfrac{2-2c}{p}}\\\text{If}\ p>0 ,\ \text{then}\\\boxed{n\geq\dfrac{2-2c}{p}}[/tex]

Answer:

Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Step-by-step explanation:

We are given that a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

Let [tex]\mu[/tex] = mean number of clicks per day.

So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 200 clicks a day

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 200 clicks a day

Here, the null hypothesis states that the mean number of clicks per day is 200 clicks a day.

On the other hand, the alternate hypothesis states that the mean number of clicks per day is different than 200 clicks a day.

Hence, this is the correct null and alternative hypotheses.

Answer: Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Step-by-step explanation:

Let [tex]\mu[/tex] be the mean number of clicks per day.

Given, a website developer wished to analyze the clicks per day on their newly updated website.

The website developer wants to know if the number of clicks per day is different than 200 clicks a day, on average.

i.e. he wants to check either [tex]\mu=200\text{ or }\mu\neq 200[/tex]

Since a null hypothesis is a hypothesis believes that there is no difference between the two variables whereas an alternative hypothesis believes that there is a statistically significant difference between two variables.

So,  Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Hence, the required null and alternative hypotheses.

Null Hypothesis [tex]H_0:\mu=200[/tex]

Alternate Hypothesis[tex]H_a:\mu\neq200[/tex]

Answer:

135.06 feet

Step-by-step explanation:

Since the side of the building makes a right triangle with the ground and you know one side length and the degree angle between you and the top of the building we can use trigonometric function to find the height of the building. So since we know one side other than the hypotenuse we can use tangent to solve. Tangent is the opposite side over the adjacent side of the known angle.

opposite side = x

adjacent side = 150 feet

angle = 42°

tan(42°) = x/150 feet

150 feet * tan(42°) = x

x = 135.06 feet

First pair of equations :

[tex]\dfrac{1}{2}x+y=15\ ..(i)\\\\-x-\dfrac{1}{3}y=-6\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]x+2y=30\ ..(iii)[/tex]

By Elimination Method, Add (i) and (ii) (term with x eliminate), we get

[tex]2y-\dfrac{1}{3}y=30-6\\\\\Rightarrow\ \dfrac{5}{3}y=24\\\\\Rightarrow\ y=\dfrac{24\times3}{5}=14.4[/tex]

put y= 14.4 in (iii), we get

[tex]x+2(14.4)=30\Rightarrow\ x=30-28.8=1.2[/tex]

hence, x=1.2 and y =14.4

Second pair of equations :

[tex]\dfrac{5}{6}x+\dfrac13y=0\ ..(i)\\\\ \dfrac12x-\dfrac{2}{3}y=3\ ..(ii)[/tex]

Multiply 2 to equation (i), we get

[tex]\dfrac{5}{3}x+\dfrac{2}{3}y=0\ ..(iii)[/tex]

Elimination Method, Add (i) and (ii) (term with y eliminate) , we get

[tex]\dfrac53x+\dfrac12x=3\Rightarrow\ \dfrac{10+3}{6}x=3\\\\\Rightarrow\ \dfrac{13}{6}x=3\\\\\Rightarrow\ x=\dfrac{18}{13}[/tex]

put [tex]x=\dfrac{18}{13}[/tex]   in (i), we get

[tex]\dfrac{5}{6}(\dfrac{18}{13})+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{15}{13}+\dfrac{1}{3}y=0\\\\\Rightarrow\ \dfrac{1}{3}y=-\dfrac{15}{13}\\\\\Rightarrow\ y=-\dfrac{45}{13}[/tex]

hence, [tex]x=\dfrac{18}{13}[/tex]   and [tex]y=\dfrac{-45}{13}[/tex] .

Answer:

a

   The  null hypothesis is  [tex]H_o : \mu = 35 .1 \ million \ shares[/tex]

    The  alternative hypothesis  [tex]H_a : \mu \ne 35.1\ million \ shares[/tex]

b

 The   95% confidence interval is  [tex]27.475 < \mu < 37.925[/tex]

Step-by-step explanation:

From the question the we are told that

      The  population mean is  [tex]\mu = 35.1 \ million \ shares[/tex]

      The  sample size is  n = 30

       The  sample mean is  [tex]\= x = 32.7 \ million\ shares[/tex]

       The standard deviation is  [tex]\sigma = 14.6 \ million\ shares[/tex]

Given that the confidence level is  [tex]95\%[/tex] then the level of significance is mathematically represented 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]

Generally the margin of error is mathematically represented as

                 [tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma }{\sqrt{n} }[/tex]

substituting values

                [tex]E = 1.96 * \frac{ 14.6 }{\sqrt{30} }[/tex]

                [tex]E = 5.225[/tex]

The 95% confidence interval confidence interval is mathematically represented as

              [tex]\= x -E < \mu < \= x +E[/tex]

substituting values

               [tex]32.7 - 5.225 < \mu < 32.7 + 5.225[/tex]

                [tex]27.475 < \mu < 37.925[/tex]

Answer:

The answer is "Analysis the information by chart and number processes".

Step-by-step explanation:

They already have articulated a query and also gathered information unless you are searching only at the distribution of your results. Those who are ready to analyze your results for all are there.

Answer:

The test statistic is [tex]t = 2.79[/tex]

Step-by-step explanation:

From the question we are told that

    The population mean is [tex]\mu = 59.3[/tex]

    The sample size is  [tex]n = 79[/tex]

    The  sample mean is  [tex]\= x = 62.4[/tex]

    The  standard deviation is  [tex]\sigma = 9.86[/tex]

Generally the test statistics is mathematically represented as

            [tex]t = \frac{\= x - \mu }{ \frac{ \sigma}{ \sqrt{n} } }[/tex]

substituting values

          [tex]t = \frac{ 62.2 - 59.3 }{ \frac{ 9.86}{ \sqrt{ 79} } }[/tex]

          [tex]t = 2.79[/tex]

Answer:

"Teens and Distracted Driving: Texting, Talking and Other Uses of the Cell Phone Behind the Wheel"

a. The inference made involves estimation.  The question provided that the statements were made on the basis of the resulting data and not on the basis of some hypothesis testing.

This implies that some statistics were calculated from sample data to approximate the population parameter, as shown in the statements.  The statements were not an attempt to establish the statistical significance of some claims.

b. The population of interest is American teenagers between 12-17.

Step-by-step explanation:

An inference from data is a statistical estimation by which some statistics are calculated based on the sample data of 800 teens between the ages of 12 and 17.  The statistics serve as an approximation to the population parameter.

Inference based on hypothesis testing establishes if a claim has statistical significance by providing  statistical evidence in favor of the claim or against it.

Answer:

A

Step-by-step explanation:

Hey there! I'm happy to help!

To find the volume of a cube, you simply cube the side length (multiply it by itself three times). This is because all of the sides of a cube are the same and if you multiply the length by the width by the height it is the same number multiplied by itself three times.

We already know that the volume is 91.125 cubic inches. To find the side length, we simply do the cube root on our calculator, which tells us what number we cube to get 91.125.

∛91.125=4.5

Therefore, the side length of the sandbox is 4.5 inches.

I hope that this helps! Have a wonderful day! :D