verify sin4x - sin2x = cos4x-cos2x

Verify Sin4x - Sin2x = Cos4x-cos2x

Answers

Answer 1

Answer:

sin⁴x - sin²x = cos⁴x - cos²x

Solve the right hand side of the equation

That's

sin⁴x - sin²x

From trigonometric identities

sin²x = 1 - cos²x

So we have

sin⁴x - ( 1 - cos²x)

sin⁴x - 1 + cos²x

sin⁴x = ( sin²x)(sin²x)

That is

( sin²x)(sin²x)

So we have

( 1 - cos²x)(1 - cos²x) - 1 + cos²x

Expand

1 - cos²x - cos²x + cos⁴x - 1 + cos²x

1 - 2cos²x + cos⁴x - 1 + cos²x

Group like terms

That's

cos⁴x - 2cos²x + cos²x + 1 - 1

Simplify

We have the final answer as

cos⁴x - cos²x

So we have

cos⁴x - cos²x = cos⁴x - cos²x

Since the right hand side is equal to the left hand side the identity is true

Hope this helps you


Related Questions

What is the solution of log3(3x+2)= log3 (4x-6)?

Answers

Answer:

x=8 i got it right on my homework on khan academy

Step-by-step explanation:

Answer: Using logarithms to solve you will get x = 8

There is a stack of 10 cards, each given a different number from 1 to 10. Suppose we select a card randomly from the stack, replace it, and then randomly select another card. What is the probability that the first card is an odd number and the second card is greater than 7

Answers

Answer:  3/20

====================================================

Explanation:

Here's our sample space

{1,2,3,4,5,6,7,8,9,10}

This is the set of all possible outcomes.

We see that {1,3,5,7,9} are odd. We have 5 odd numbers out of 10 total. The probability of getting an odd number is therefore 5/10 = 1/2. Let A = 1/2 as we'll use it later.

After we select the first card and put it back (or replace it with a copy), the stack of cards is the same as before we made that first selection. So the sample space hasn't changed. The set of values greater than 7 is {8,9,10}. We have 3 items in here out of 10 total. The probability of getting a value larger than 7 is 3/10. Let B = 3/10.

Multiply the values of A and B to get the answer

A*B = (1/2)*(3/10) = 3/20

This represents the probability of getting an odd number on the first selection, and a second card that is larger than 7. This only applies if a replacement is made on the first card. Otherwise, 3/10 would be different.

Write the equation of the line in slope intercept form that passes through the points (4,-2) and (2,-1)

Answers

Answer:

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

Step-by-step explanation:

Let's move from (2, -1) to (4, -2) and measure the changes in x and y.  x increases by 2 units from 2 to 4, and y decreases by 1 unit from -1 to -2.  Thus, the slope of the line connecting the two points is m = rise / run =

-1

--- = (-1/2).

2

Using the point-slope formula, we get:

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

Please help!! Which inequality is graphed on the coordinate plane?

Answers

Answer:

The correct answer that corresponds with that graph is B: y ≤-3x+2.

Step-by-step explanation:

1) First we need to figure out what kind of symbol the line is, greater or less than equations (< , >) then the line are dotted,and if its greater than or equal to or less than or equal to equations ( ≤, ≥) since the line are solid.

2) Now we need to figure out which side should be shaded, if the symbol is a less than or a less than or equal to then the shaded side should be on the left, if the symbol is a greater than or a greater than or equal then the shaded side should be on the right.

In this case we have a solid line and a shaded left side which mean the symbol that been used here is a less than or equal to symbol ( ).

So our answer is B: y ≤-3x+2.

Remember:

- greater or less than equations (< , >) = dotted line

- greater than or equal to or less than or equal to equations ( ≤, ≥) = solid line

- less than or a less than or equal to = shaded left side

- greater than or greater than or equal to = shaded right side

Solve the equation for x 5x-(4x-1)=2 A 1/9 B -1 C -1/9 D 1

Answers

Answer:

D

Step-by-step explanation:

Find y................

Answers

Answer:

[tex] y = 3 [/tex]

Step-by-step explanation:

Given the above right angled triangle, we would use a trigonometric ratio formula to find y.

Given angle = 30°

Hypotenuse = 6

Opposite side = y

Solve for y using the trigonometric ratio formula as follows:

[tex] sin(X) = \frac{opposite}{hypotenuse} [/tex]

[tex] sin(30) = \frac{y}{6} [/tex]

Multiply both sides by 6

[tex] sin(30)*6 = \frac{y}{6}*6 [/tex]

[tex] 0.5*6 = y [/tex]

[tex] 3 = y [/tex]

[tex] y = 3 [/tex]

State the degrees of freedom error in each of the following tests. (a) A consultant measures job satisfaction in a sample of 14 supervisors, 14 managers, and 14 executives at a local firm. (b) A researcher tests how nervous public speakers get in front of a small, medium, or large audience. Ten participants are randomly assigned to each group. (c) A high school counselor has 8 students in each of five classes rate how much they like their teacher.

Answers

Answer:

.

Step-by-step explanation:

The equation of the line of best fit is y=15.621x+8.83 Based on the line of best fit, Approximately how many pages are predicted To be in a book with eight chapters

Answers

Answer:

[tex] y = 15.621x +8.83[/tex]

We assume that y represent the number of pages predicted and x the number of chapters.

And we want to find the predicted value for a book of x =8 chapters. S replacing we got:

[tex] y = 15.621*8 + 8.83= 133.798[/tex]

And we can conclude that approximately we would have between 133 and 134 pages for a book of 8 chapters

Step-by-step explanation:

For this case we have the following model given:

[tex] y = 15.621x +8.83[/tex]

We assume that y represent the number of pages predicted and x the number of chapters.

And we want to find the predicted value for a book of x =8 chapters. S replacing we got:

[tex] y = 15.621*8 + 8.83= 133.798[/tex]

And we can conclude that approximately we would have between 133 and 134 pages for a book of 8 chapters

i
dont
get
this
help
rn

Answers

Answer:

6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.

Step-by-step explanation:

Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.

Use identities to find values of the sine and cosine functions of the function for the angle measure
a. theta, given that cos2theta=28/53 and 0theta < theta < 90degrees
b. 2theta, given sin theta= - sqrt 7 over 5 and cos theta > 0
c. 2x, given tan x=2 and cos x<0

Answers

Answer:

Step-by-step explanation:

a) Given cos2theta=28/53 and 0degrees< theta < 90degrees

From cos2theta=28/53

[tex]2\theta = cos^{-1}\frac{28}{53}[/tex]

[tex]2\theta = cos^{-1}0.5283\\ \\2\theta = 58.12\\\\Dividing\ both \ sides\ by \ 2\\\\\frac{2\theta}{2} = \frac{58.12}{2}\\ \\\theta = 29.06^0[/tex]

b) Given

[tex]sin\theta = \frac{-\sqrt{7} }{5} \\\\\theta = sin^{-1} \frac{-\sqrt{7} }{5}\\\\\\\theta = sin^{-1} \frac{-2.6458}{5}\\\\\theta = sin^{-1} -0.5292\\\\\theta = -31.95^0[/tex]

If cos theta [tex]\gneq[/tex] 0, this means we need to look for the quadrant where sin is negative and cos is positive. That will be the fourth quadrant. In the fourth quadrant, theta = 360 - 31.95° = 328.05°

2theta = 2 * 328.05

2theta = 656.1°

c) Given tan x=2 and cos x<0, lets find the angle of x first.

If tan x = 2

x = tan^-1 2

x = 63.4°

Sine cos is less than 0, then we need to find the angle of x where tan is positive and cos is negative. That will be the third quadrant. In the third quadrant, ew value of x = 180+63.4

x = 243.4°

Since we are to find 2x,

2x = 2(243.4)

2x = 486.8°

A certain article indicates that in a sample of 1,000 dog owners, 680 said that they take more pictures of their dog than of their significant others or friends, and 490 said that they are more likely to complain to their dog than to a friend. Suppose that it is reasonable to consider this sample as representative of the population of dog owners.
(a) Construct a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends. (Use a table or technology. Round your answers to three decimal places.)
(______),(_________)
(b) Construct a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend. (Use a table or technology. Round your answers to three decimal places.)
(_______),(_______)

Answers

Answer: a) a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).

b) a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).

Step-by-step explanation:

Confidence interval for a population proportion is given by:-

[tex]\hat{p}\pm z(\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}})[/tex]

, where [tex]\hat{p}[/tex] = sample proportion , n= sample size, z= critical z-value.

As per given,

a) n=1000

Sample proportion of dog owners say they take more pictures of their dog than of their significant others or friends =[tex]\hat{p}=\dfrac{680}{1000}=0.68[/tex]

critical value for 90% confidence = 1.645  [By table]

A 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends.

[tex]0.68\pm (1.645)\sqrt{\dfrac{0.68(1-0.68)}{1000}}\\\\\approx0.68\pm0.024=(0.68-0.024,0.68+0.024)=(0.656,0.704)[/tex]

Hence, a 90% confidence interval for the proportion of dog owners who take more pictures of their dog than of their significant others or friends is (0.656,0.704).

b) Sample proportion of dog owners say they are more likely to complain to their dog than to a friend =[tex]\hat{p}=\dfrac{490}{1000}=0.49[/tex]

critical value for 95% confidence = 1.96  [By table]

A 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend:

[tex]0.49\pm (1.96)\sqrt{\dfrac{0.49(1-0.49)}{1000}}\\\\\approx0.49\pm0.031=(0.49-0.031,0.49+0.031)=(0.459,0.521)[/tex]

Hence, a 95% confidence interval for the proportion of dog owners who are more likely to complain to their dog than to a friend is (0.459,0.521).

Linda, Reuben, and Manuel have a total of $70 in their wallets. Reuben has $10 more than Linda. Manuel has 2 times what Linda has. How much does each have? Amount in Linda's wallet: $ Amount in Reuben's wallet: $ Amount in Manuel's wallet:

Answers

Answer:

Linda has $15Reuben has $25Manuel has $30

Step-by-step explanation:

Together, they have 4 times what Linda has, plus $10. So, Linda has 1/4 of $60 = $15.

  Linda has $15

  Reuben has $25 . . . . . . $10 more than Linda

  Manuel has $30 . . . . . . twice what Linda has

A magazine article states that the mean weight of one-year-old boys is the same as that of one-year-old girls. Does the confidence interval contradict this statement? The confidence interval this statement

Answers

Answer:

Yes, the confidence interval contradict this statement.

Step-by-step explanation:

The complete question is attached below.

The data provided is:

[tex]n_{1}=318\\n_{2}=297\\\bar x_{1}=25\\\bar x_{2}=24.1\\s_{1}=3.6\\s_{2}=3.8[/tex]

Since the population standard deviations are not provided, we will use the t-confidence interval,

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]

Compute the pooled standard deviation as follows:

[tex]s_{p}=\sqrt{\frac{(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}=\sqrt{\frac{(318-1)(3.6)^{2}+(297-1)(3.8)^{2}}{318+297-2}}=2.9723[/tex]

The critical value is:

[tex]t_{\alpha/2, (n_{1}+n_{2}-2)}=t_{0.05/2, (318+297-2)}=t_{0.025, 613}=1.962[/tex]

*Use a t-table.

The 95% confidence interval is:

[tex]CI=(\bar x_{1}-\bar x_{2})\pm t_{\alpha/2, (n_{1}+n_{2}-2)}\cdot s_{p}\cdot\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}[/tex]

     [tex]=(25-24.1)\pm 1.962\times 2.9723\times \sqrt{\frac{1}{318}+\frac{1}{297}}\\\\=0.90\pm 0.471\\\\=(0.429, 1.371)\\\\\approx (0.43, 1.37)[/tex]

The 95% confidence interval for the difference between the mean weights is (0.43, 1.37).

To test the magazine's claim the hypothesis can be defined as follows:

H₀: There is no difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}=0[/tex].

Hₐ: There is a significant difference between the mean weight of 1-year old boys and girls, i.e. [tex]\mu_{1}-\mu_{2}\neq 0[/tex].

Decision rule:

If the confidence interval does not consists of the null value, i.e. 0, the null hypothesis will be rejected.

The 95% confidence interval for the difference between the mean weights does not consists the value 0.

Thus, the null hypothesis will be rejected.

Conclusion:

There is a significant difference between the mean weight of 1-year old boys and 1-year old girls.

HELP number 12 pls i do nor have long more​

Answers

Answer:

Dian has $250 originally.

Step-by-step explanation:

Let the total money Dian has originally = $S

Dian gave [tex]\frac{2}{5}[/tex] of her total money to Justin,

Money given to Justin = [tex]\frac{2}{5}(\text{S})[/tex]

Money left with Dian = S - [tex]\frac{2}{5}(\text{S})[/tex]

                                   = [tex]\frac{\text{5S-2S}}{5}[/tex]

                                   = [tex]\frac{3S}{5}[/tex]

Since Dian has $150 left then the equation will be,

[tex]\frac{3S}{5}=150[/tex]

S = [tex]\frac{150\times 5}{3}[/tex]

S = $250

Therefore, Dian has $250 originally.

If Joe drives 50 mph for 0.5 hours and then 60 mph for 1.5 hours, then how far did he drive?

Answers

Answer:

115 mi

Step-by-step explanation:

speed = distance/time

distance = speed * time

0.5 hours at 50 mph

distance = 50 mph * 0.5 h = 25 mi

1.5 hours at 60 mph

distance = 60 mph * 1.5 h = 90 mi

total distance = 25 mi + 90 mi = 115 mi

If the triangle on the grid below is translated by using the rule (x, y) right-arrow (x + 5, y minus 2), what will be the coordinates of B prime?

Answers

Answer:

Option (2)

Step-by-step explanation:

If a point having coordinates (x, y) is translated by 'h' units right and 'k' units down,

New coordinates of the point will be,

(x, y) → [(x + h), (y - k)]

Coordinates of the vertices of the given triangle ABC are,

A(-1, 0), B(-5, 0) and C(-1, 2)

If this triangle is shifted 5 units right and 2 units down then the coordinates of point B will be,

B(-5, 0) → B'[(-5 + 5), (0 -2)]

             → B'(0, -2)

Therefore, coordinates of vertex B' will be (0, -2).

Option (2) will be the answer.

Answer:

(0,-2) is Correct

Have a Blessed day!

Lacey's mom makes her a birthday cake in the shape of an "L" . Lacey loves frosting, so her mom covers the entire outside of the cake in frosting, even the bottom of the cake. How much space does Lacey's mom cover in frosting? cm2\text{cm}^2cm2start text, c, m, end text, squared

Answers

Answer:

1360cm²

Step-by-step explanation:

Since the shape of the cake is in L shape, we can divide the cake in to rectangles..

The amount of space covered by the frosting = The sum of the areas of the sides that we can find in this L shaped cake diagram.

The sides of this cake, are shaped like a rectangle.

Hence, Area of a Rectangle = Length × Width

a) Side 1 = Rectangle on the left

Area of a Rectangle = Length × Breadth

Length = 30cm

Breadth =10cm

Area = 30 × 10 = 300cm²

Since we have another side with this measurement/ dimensions also,

Side 2 = 300cm²

Side 3 = The front face of the cube by the right

Area of a Rectangle = Length × Breadth

Length = 22cm - 10cm = 12cm

Breadth =10cm

Area = 12 × 10 = 120cm²

Likewise, we have the another side with the same dimensions as well

Hence, Side 4 = 120cm²

Side 5

30 × 5 = 150cm²

Side 6

10 × 5 = 50cm²

Side 7

20 × 5 = 100cm²

Side 8

22cm × 5 cm = 110cm²

Side 9

10cm × 5cm = 50cm²

Side 10

12cm × 5cm = 60cm²

The amount of space covered by the frosting = Area of Sides( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)

= (300 + 300 + 120 + 120 + 150 + 50 + 100 + 110 + 50 + 60) cm²

= 1360cm²

How many solutions does the following equation have? 14(z+3)=14z+21

Answers

Answer:

No solutions

Step-by-step explanation:

14(z + 3) = 14z + 21

Expand brackets.

14z + 42 = 14z + 21

Subtract 14z on both sides.

42 = 21

There are no solutions.

Answer:

No solution

Step-by-step explanation:

First, We have to simplify the right side.

Distribute 14, 14z+42.

Now the equation stands as 14z+42=14z+21

Subtract 14z from both sides,

this makes it 42=21.

We know when the solution is #=#, our answer is no solution.

Eighty percent of the light aircraft that disappear while in flight in a certain country are subsequently discovered. Of the aircraft that are discovered, 63% have an emergency locator, whereas 89% of the aircraft not discovered do not have such a locator. Suppose a light aircraft has disappeared. (Round your answers to three decimal places.) (a) If it has an emergency locator, what is the probability that it will not be discovered? (b) If it does not have an emergency locator, what is the probability that it will be discovered?

Answers

Answer:

a) P(B'|A) = 0.042

b) P(B|A') = 0.625

Step-by-step explanation:

Given that:

80% of the light aircraft that disappear while in flight in a certain country are subsequently discovered

Of the aircraft that are discovered, 63% have an emergency locator,

whereas 89% of the aircraft not discovered do not have such a locator.

From the given information; it is suitable we define the events in order to calculate the probabilities.

So, Let :

A = Locator

B = Discovered

A' = No Locator

B' = No Discovered

So; P(B) = 0.8

P(B') = 1 - P(B)

P(B') = 1- 0.8

P(B') = 0.2

P(A|B) = 0.63

P(A'|B) = 1 - P(A|B)

P(A'|B) = 1- 0.63

P(A'|B) = 0.37

P(A'|B') = 0.89

P(A|B') = 1 - P(A'|B')

P(A|B') = 1 - 0.89

P(A|B') = 0.11

Also;

P(B ∩ A) = P(A|B) P(B)

P(B ∩ A) = 0.63 × 0.8

P(B ∩ A) = 0.504

P(B ∩ A') =  P(A'|B) P(B)

P(B ∩ A') = 0.37 × 0.8

P(B ∩ A') = 0.296

P(B' ∩ A) = P(A|B') P(B')

P(B' ∩ A) = 0.11 × 0.2

P(B' ∩ A) = 0.022

P(B' ∩ A') =  P(A'|B') P(B')

P(B' ∩ A') = 0.89 × 0.2

P(B' ∩ A') = 0.178

Similarly:

P(A) = P(B  ∩  A ) + P(B'  ∩  A)

P(A) = 0.504 + 0.022

P(A) = 0.526

P(A') = 1 - P(A)

P(A') = 1 - 0.526

P(A') =  0.474

The probability that it will not be discovered given that it has an emergency locator is,

P(B'|A) =  P(B' ∩ A)/P(A)

P(B'|A) = 0.022/0.526

P(B'|A) = 0.042

(b) If it does not have an emergency locator, what is the probability that it will be discovered?

The probability that it will be discovered given that it does not have an emergency locator is:

P(B|A') = P(B ∩ A')/P(A')

P(B|A') = 0.296/0.474

P(B|A') = 0.625

From which sphere of earth did this food did this food originate

Answers

Answer:

I'm not entirely sure what you are asking, could you comment on this answer the full question so I can edit this question to provide you an answer?

Answer: biosphere

Step-by-step explanation:

I am not sure what picture you are looking at but if it is 3 barbeque chicken legs in one image than this is your answer. The reason being that chickens can only be found on land and the land is considered part of the biosphere because bio = life

What are some key words used to note addition operations?

Answers

Answer:

The correct answer is

For addition, Caulleen used the words total, sum, altogether, and increase. But we could also have used the words combine, plus, more than, or even just the word "and". For subtraction, Caulleen used the words, fewer than, decrease, take away, and subtract. We also could have used less than, minus, and difference.

Step-by-step explanation:

hope this helps u!!!

-15≤-3c plz helpppppppppp

Answers

Answer:

5 ≥ c

Step-by-step explanation:

-15≤-3c

Divide each side by -3, remembering to flip the inequality

-15/-3 ≤ -3c/-3

5 ≥ c

Answer:

c ≤ 5

Step-by-step explanation:

Since you have to divide both sides of the equation by a negative number, you have to flip the equality sign.

-15 ≤ -3c

(-15)/(-3) ≤ (-3c)/-3

5 ≥ c

c ≤ 5

Suppose the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.68 and standard deviation 0.92.
A. If a random sample of 25 specimens is selected, what is theprobability that the sample average sediment density is at most3.00? Between 2.68 and 3.00
B. How large a sample size would be required to ensure thatthe first probability in part (a) is at least .99 ?

Answers

Answer:

The sample size must be 45 large enough that would ensure that the first probability in part (a) is at least 0.99.

Step-by-step explanation:

We are given that the sediment density (g/cm) of a randomly selected specimen from a certain region is normally distributed with mean 2.68 and standard deviation 0.92.

Let [tex]\bar X[/tex] = sample  average sediment density

The z-score probability distribution for the sample mean is given by;

                             Z  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 2.68

           [tex]\sigma[/tex] = population standard deviation = 0.92

           n = sample of specimens = 25

(a) The probability that the sample average sediment density is at most 3.00 is given by = P([tex]\bar X[/tex] [tex]\leq[/tex] 3.00)

   

   P([tex]\bar X[/tex] [tex]\leq[/tex] 3.00) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{3.00-2.68}{\frac{0.92}{\sqrt{25} } }[/tex] ) = P(Z [tex]\leq[/tex] 1.74) = 0.9591

The above probability is calculated by looking at the value of x = 1.74 in the z table which has an area of 0.9591.

Also, the probability that the sample average sediment density is between 2.68 and 3.00 is given by = P(2.68 < [tex]\bar X[/tex] < 3.00)

P(2.68 < [tex]\bar X[/tex] < 3.00) = P([tex]\bar X[/tex] < 3.00) - P([tex]\bar X[/tex] [tex]\leq[/tex] 2.68)

 

   P([tex]\bar X[/tex] < 3.00) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\frac{3.00-2.68}{\frac{0.92}{\sqrt{25} } }[/tex] ) = P(Z < 1.74) = 0.9591

   P([tex]\bar X[/tex] [tex]\leq[/tex] 2.68) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{2.68-2.68}{\frac{0.92}{\sqrt{25} } }[/tex] ) = P(Z [tex]\leq[/tex] 0) = 0.50

The above probability is calculated by looking at the value of x = 1.74 and x = 0 in the z table which has an area of 0.9591 and 0.50.

Therefore, P(2.68 < [tex]\bar X[/tex] < 3.00) = 0.9591 - 0.50 = 0.4591.

(b) Now, we have to find a sample size that would ensure that the first probability in part (a) is at least 0.99, that is;

      P([tex]\bar X[/tex] [tex]\leq[/tex] 3.00) [tex]\geq[/tex] 0.99

      P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\leq[/tex] [tex]\frac{3.00-2.68}{\frac{0.92}{\sqrt{n} } }[/tex] ) [tex]\geq[/tex] 0.99

      P(Z [tex]\leq[/tex] [tex]\frac{3.00-2.68}{\frac{0.92}{\sqrt{n} } }[/tex] ) [tex]\geq[/tex] 0.99

Now, in the z table; the critical value of x which has an area of at least 0.99 is given by 2.3263, that is;

                 [tex]\frac{3.00-2.68}{\frac{0.92}{\sqrt{n} } }=2.3263[/tex]

                 [tex]\sqrt{n} } }=\frac{ 2.3263\times 0.92}{0.32}[/tex]

                  [tex]\sqrt{n} } }=6.69[/tex]

                    n = 44.76 ≈ 45          {By squaring both sides}

Hence, the sample size must be 45 large enough that would ensure that the first probability in part (a) is at least 0.99.

How would 2X - 2Y - 6 = 0 be
written in slope-intercept form?

A. 2X - 2Y = 6
B. -2Y = 2X = 6
C. Y=X - 3
D. Y = -2X - 3
E. Y = x + 3

Answers

Answer:

D. Y= -2x - 3

Step-by-step explanation:

The reason the answer is D is because it is the reverse form of standard. D shows that the form of slope-intercept for is y=mx + b.

Answer:

C. Y=X - 3

Step-by-step explanation:

[tex]2X - 2Y - 6 = 0\\\mathbf{y=mx+b}\:\mathrm{is\:the\:slope\:intercept\:form\:of\:a\:line\:where}\: \mathbf{m}\:\mathrm{is\:the\:slope\:and}\:\mathbf{b}\:\mathrm{is\:the}\:\mathbf{y}\:\mathrm{intercept}\\\mathrm{For\:a\:line\:in\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is}\:\mathbf{m}\:\mathrm{and}\:\mathbf{y}\:\mathrm{intercept\:is}\:\mathbf{b}\\\\Y=X-3[/tex]

The letters G, E, N, I, D, S are placed in a bag. What is the probability that the letters are randomly pulled from the bag in the order that spells DESIGN?

Answers

Answer as a fraction = 1/5040

Answer in decimal form (approximate) = 0.000198

Answer in percentage form (approximate) = 0.0198%

=========================================================

Explanation:

There is only one ordering of the letters to get DESIGN out of 5040 different permutations. The 5040 comes from the fact that 7*6*5*4*3*2*1 = 5040. In shorthand notation, use factorials to say 7! = 5040. Notice how we started with 7 and counted down until reaching 1, multiplying all along the way. You could use the nPr permutation formula to get the same result of 5040 (use n = 7 and r = 7).

So because we have 1 way to order the letters (getting DESIGN) out of 5040 ways total, this means the probability is the fraction 1/5040. Use your calculator to find that 1/5040 = 0.000198 approximately. Move the decimal over 2 spots to the right to convert 0.000198 to 0.0198%

A copy machine makes 153 copies in 4 minutes 15 seconds how many copies does it make per minute

Answers

Answer:

36 copies.

Step-by-step explanation:

4mins 15 seconds is the same as 4+1/4 minsutes. Since 1 minute is less than 4+1/4minutes and 4+1/4 minutes produces 153 copies. 1 minute will produce less.

(1÷4+1/4)×153

= 36 copies.

36

Change the time into seconds so they’ll be in the same unit, (4*60) + 15= 255. Do cross multiplication,
153. 255
? 60
(153*60) / 255= 36

Find dw/ds using the appropriate Chain Rule for w=y^3-4x^2y where x=e^s and y=e^t, and evaluate the partial derivative at s=-3 and t=5 . Round your answer to two decimal places.

Answers

Answer:

-2.95

Step-by-step explanation:

Given the functions w=y^3-4x^2y where x=e^s and y=e^t, to get dw/ds, we will use the chain rule for composite functions as shown;

dw/ds = dw/dx*dx/ds + dw/dy*dy/ds

dw/dx = -8xy

dx/ds = e^s

dw/dy = 3y²-4x²

dy/ds = 0 (since there are no s variable in the function)

Substituting the differentials into the formula above;

dw/ds = -8xy(e^s) + 3y²-4x²(0)

dw/ds = -8xy(e^s)

Substituting s = -3 and t = 5 into the resulting function;

dw/ds = -8(e^s)(e^t)(e^s)

dw/ds = -8(e^2s)(e^t)

dw/ds =  -8(e^-6)(e^5)

dw/ds = -8*0.00248*148.413

dw/ds = -2.945 ≈ --2.95 (to 2 dp)

i will give brainliest and 50 points pls help ASP

pls can u show how to work this out thx !!! : )​
its a simultaneous equation

Answers

Answer:

x = 3

y = -2

Step-by-step explanation:

Given:

8x - 3y = 30 ..................(1)

3x + y = 7 .......................(2)

Eliminate y by adding (1)+3*(2)

8x-3y + 3*( 3x+y) = 30 + 3*7

8x + 9x -3y + 3y = 51

17x = 51

x = 3  .....................(3)

substitute (3) in (2)

3(3) + y = 7

y = 7-9 = -2

y = -2 ....................(4)

Answer:

Step-by-step explanation:

[tex]8x-3y=30\\y=7-3x\\\\8x-3(7-3x)=30\\8x-21+9x=30\\17x=51\\x=3\\\\y=7-3(3)\\y=7-9\\y=-2[/tex]

Select the correct answer. Sarah wants to print copies of her artwork. At the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies. How much would it cost Sarah to make 100 copies? A. $15 B. $20 C. $25 D. $30

Answers

$1 = 5copies means

$5 = 25 copies obviously

then

$x = 100 copies

100 / 5 = $x

so she needs

$20

The cost of printing 100 copies of artwork is $20.

What is a unitary method?

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Suppose 2 pens cost $10, So the cost of 1 pen is (10/2) = $5.

From this unitary cost of pens, we can determine the cost of any no. of pens by multiplying the unit cost by the no. of pens.

Given, The cost of printing 5 artworks is $1.

∴ The cost of printing 100 copies is $(100/5),

= $20.

learn more about the unitary method here :

https://brainly.com/question/22056199

#SPJ2

Write a system of equations in x and y describing the situation. Do not solve the system.
Keiko has a total of $5500, which she has invested in two accounts. The larger account is $700 greater than the smaller account. (Let x be the amount of money in the
larger account and y be the amount of money in the smaller account.)
Choose a system of equations describing the situation,
X+ y + 5500 = 0
x+y=5500
X= y + 700
X-y+ 700 = 0
O
2x = 5500
2x + 2y = 5500
x-y=700
x- y = 700​

Answers

X=y+700
X is larger acct
Y is smaller acct
Larger acct equals amount in smaller account plus $700.
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