Every cereal box has a gift inside, but you cannot tell from the outside what the gift is. The store manager assures you that 18 of the 52 boxes on the shelf have the secret decoder ring. The other 34 boxes on the shelf have a different gift inside. If you randomly select two boxes of cereal from the shelf to purchase, what is the probability that BOTH of them have the secret decoder ring?

Answer:

D

Step-by-step explanation:

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.

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]

Answer:

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

Answer:

.

Step-by-step explanation:

$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.

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

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

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%

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]

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

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.

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

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]

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!!!

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

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

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.

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

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.

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.

Answer:

236,000

Step-by-step explanation:

When rounding to thousands, if the hundred is 500 or over, you round up. If it is less, round down.

Answer:

Hey! The answer is 236,000.... steps will be below!

Step-by-step explanation:

Since there is 5,674 it is more closer to 6,000 than 5,000

So we change the number to 236,000

ANSWER TO YOUR QUESTION: 236,000

Hope this helps! :)

⭐️Have a wonderful day!⭐️

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

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.

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)

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).

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

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

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!

Answer:

In order to solve this problem, we need to know the volume of a sphere.

The volume of a sphere is (4/3)pir^3

In this case our r value, or radius, is 30cm.

If we plug in 30cm to the equation like so:

(4/3)pi(30)^3

The answer is 113097 cm^3 of air

Hope you understand

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°