Each of three identical jewelry boxes has two drawers. Each drawer of the first box contains a gold coin. Each drawer of the second box contains a silver coin. In the third box, one drawer has a gold coin and the other drawer a silver coin. If a box and drawer are selected at random, and the selected drawer has a silver coin, what is the probability that the other drawer has a gold coin

Answer:

-8, -6, -4, -2, ...

Step-by-step explanation:

-8, -6, -4, -2, ...  is an arithmetic sequence:  each new term is obtained by adding 2 to the previous term.

Answer:

-8, -6, -4, -2

Step-by-step explanation:

"An arithmetic sequence is a list of numbers with a definite pattern. If you take any number in the sequence then subtract it by the previous one, and the result is always the same or constant then it is an arithmetic sequence."

Answer:

34

Step-by-step explanation:

= 26 + 8

= 34

Answer:

486

Step-by-step explanation:

Hello!

To find the surface area of a cube we use the equation

[tex]S = 6a^{2}[/tex]

S is the surface area

a is the side length

Put what we know into the equation

[tex]S = 6*9^{2}[/tex]

Solve

S = 6 * 81

S = 486

Hope this Helps!

Answer:486[tex]ft^{2}[/tex]

Step-by-step explanation:

surface area= 6[tex]l^{2}[/tex]

l=9

sa=6 ([tex]9^{2}[/tex])= 6 x 81=486[tex]ft^{2}[/tex]

Answer:

17 miles

Step-by-step explanation:

4+5+5+3=17

Answer:

Y=2(1)+4

Y=2+4

Y=6

Step-by-step explanation:

Please follow me

Answer:

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Answer:

0.90415

Step-by-step explanation:

Given the following :

Arrival rate = mean(μ) = 24

Probability that at most 30 customers arrive in the next hour:

The poisson distribution formula :

P(x, μ) = [(e^-μ) * (μ^x)] / x!

Where :

e = euler's constant

P(x ⩽ 30) = p(0) + p(1) + p(2) +.... + p(30)

Using the online poisson probability distribution calculator :

P(x ⩽ 30, 24) = 0.90415

Therefore there is about 90.4% probability that at most 30 customers will arrive in the next hour.

Answer:

[tex] \frac{1}{3} [/tex]Rational number as denominator is not equal to zero and numerator is a integer.

Rational numbers. denoted by [tex] \mathbb Q[/tex]

1/3 is clearly not a natural number or integer.

it is a fraction, =0.333 , it fits the definition of rational number ([tex] \frac pq [/tex]).

Answer:

19 purses

Step-by-step explanation:

Set up an inequality where x represents the number of purses:

127 [tex]\geq[/tex] 7x

Solve for x by dividing each side by 7:

18.14 [tex]\geq[/tex] x

Round up to 19 because purses have to be whole

So, 19 purses have to be sold.

Answer:

(i) 0.32          (ii) 0.85

(iii) 0.3412    (iv) 0.20

(v) 0.29         (vi) 0.12

Step-by-step explanation:

The data provided is as follows:

   Race                    Smoker (S)         Nonsmoker (N)             Row Total

 White(W)                    290                       560                           850

  Black(B)                     30                        120                           150

Column Total                320                       680                        1,000

(i)

Compute the value of P (S) as follows:

[tex]P(S)=\frac{n(S)}{N}=\frac{320}{1000}=0.32[/tex]

P (S) = 0.32.

(ii)

Compute the value of P (W) as follows:

[tex]P(W)=\frac{n(W)}{T}=\frac{850}{1000}=0.85[/tex]

P (W) = 0.85.

(iii)

Compute the value of P (S|W) as follows:

[tex]P(S|W)=\frac{n(S\cap W)}{n(W)}=\frac{290}{850}=0.3412[/tex]

P (S|W) = 0.3412.

(iv)

Compute the value of P (S|B) as follows:

[tex]P(S|B)=\frac{n(S\cap B)}{n(B)}=\frac{30}{150}=0.20[/tex]

P (S|W) = 0.20.

(v)

Compute the value of P (S∩W) as follows:

[tex]P(S\cap W)=\frac{n(S\cap W)}{T}=\frac{290}{1000}=0.29[/tex]

P (S∩W) = 0.29.

(vi)

Compute the value of P (N∩B) as follows:

[tex]P(N\cap B)=\frac{n(N\cap B)}{T}=\frac{120}{1000}=0.12[/tex]

P (S∩W) = 0.12.

Hector outperformed the challenge rate as he exercised 2.88 hours a week.

It is best to convert the mixed fraction to decimals for easier calculation.

The students are encouraged to exercise 2¹/₂ hours per week. In decimals this is:

= 2 + ¹/₂

= 2 + 0.5

= 2.5 hours per week

In the 4 week period, Hector exercised 11¹/₂ hours which is:

= 11 + ¹/₂

= 11 + 0.5

= 11.5 hours

The number of hours he exercised per week is:

= Number of hours in total / Number of weeks

= 11.5 / 4

= 2.88 hours per week

When compared to the fitness challenge rate, we can conclude that Hector outperformed the challenge rate

Find out more at https://brainly.com/question/17951676.

Answer:

The answer is 2 7/8

Answer:

7

Step-by-step explanation:

First plug in the variable amounts so the expression now looks like this:

(3 × 4 - 12) + 1/2(4 × 6 - 10)

Now, start by solving the multiplication parts first, so it now looks like this:

(12 - 12) + 1/2(24 - 10)

Now, apply the rules of order of operation, so start by solving what's in parenthesis. It should now look like this: (0) + 1/2(14)

Next, solve the multiplication part, so it now looks like this: 0 + 7

Solve that and the answer is 7.

Answer:

x>125

Step-by-step explanation:

Answer:

x > 125

Step-by-step explanation:

I hope this helps!

Answer:

2/3×3/5=2/3. 3/4×1/6=1/8

2/3-1/8=11/40

Answer:

Step-by-step explanation:

[tex]( \frac{2}{3} \times \frac{3}{5} ) - ( \frac{3}{4} \times \frac{1}{6} )[/tex]

Reduce the numbers with Greatest common factor 3

⇒[tex] \mathsf{(2 \times \frac{1}{5} ) - ( \frac{1}{4} \times \frac{1}{2} )}[/tex]

Calculate the product

⇒[tex] \mathsf{( \frac{2}{5} )- ( \frac{1}{4} \times \frac{1}{2}) }[/tex]

Subtract the fractions

⇒[tex] \mathsf{ \frac{2 \times 8 - 1 \times 5}{40} }[/tex]

⇒[tex] \mathsf{ \frac{16 - 5}{40} }[/tex]

⇒[tex] \mathsf{ \frac{11}{40} }[/tex]

Hope I helped!

Best regards!

Answer:

(A) The probability that a male spent less than $210 online before deciding to visit a store is 0.0668.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is 0.0655.

(C) Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Step-by-step explanation:

We are given that the reports indicate that men spend an average of $240 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $20.

Let X = the spending limit

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

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

where, [tex]\mu[/tex] = mean spending limit = $240

           [tex]\sigma[/tex] = standard deviation = $20

So, X ~ Normal([tex]\mu=\$240,\sigma^{2} =\$20^{2}[/tex])

(A) The probability that a male spent less than $210 online before deciding to visit a store is given by = P(X < $210)

     P(X < $210) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$210-\$240}{\$20}[/tex] ) = P(Z < -1.50) = 1 - P(Z [tex]\leq[/tex] 1.50)

                                                            = 1 - 0.9332 = 0.0668

The above probability is calculated by looking at the value of x = 1.50 in the z table which has an area of 0.9332.

(B) The probability that a male spent between $270 and $300 online before deciding to visit a store is given by = P($270 < X < $300)

     P($270 < X < $300) = P(X < $300) - P(X [tex]\leq[/tex] $270)

     P(X < $300) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{\$300-\$240}{\$20}[/tex] ) = P(Z < 3) = 0.9987

     P(X [tex]\leq[/tex] $270) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{\$270-\$240}{\$20}[/tex] ) = P(Z [tex]\leq[/tex] 1.50) = 0.9332

The above probability is calculated by looking at the value of x = 3 and x = 1.50 in the z table which has an area of 0.9987 and 0.9332 respectively.

Therefore, P($270 < X < $300) = 0.9987 - 0.9332 = 0.0655.

(C) Now, we have to find ninety percent of the amounts spent online by a male before deciding to visit a store is less than what value, that is;

         P(X < x) = 0.90     {where x is the required value}

         P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90

         P(Z < [tex]\frac{x-\$240}{\$20}[/tex] ) = 0.90

In the z table, the critical value of z that represents the bottom 90% of the area is given as 1.2816, i.e;

                     [tex]\frac{x-\$240}{\$20}=1.2816[/tex]

                     [tex]x-240=1.2816\times 20[/tex]

                     [tex]x=240 + 25.632[/tex]

                     x = 265.632

Hence, Ninety percent of the amounts spent online by a male before deciding to visit a store is less than $265.632.

Answer: 72576m7

Step-by-step explanation:

2m x 8m x 6m x 9m x 7m x 6m x 2m

All together equals my answer 72576m7

Hope this helps!

Answer:

m<A = 133 degrees

m<B = 17 degrees

m<C = 30 degrees

Step-by-step explanation:

In a triangle, all the angles add up to 180 degrees.

So, adding all the angles gets us,

39x + 24

This equals 180 degrees so,

39x + 24 = 180

Subtract 24 from both sides,

39x + 24 - 24 = 180 - 24

39x = 156

Divide both sides by 39

x = 4

Now we have x = 4, we use this to plug in each equation of the angles.

m<A = 40(4) - 27 = 160 - 27 = 133

m<B = 25 - 2(4) = 25 - 8 = 17

m<C = 26 + 4 = 30

Answer:

Explained below.

Step-by-step explanation:

In this case we need to test whether the extra carbonation of cola results in a higher average compression strength.

(a)

The hypothesis for the test can be defined as follows:

H₀: The extra carbonation of cola does not results in a higher average compression strength, i.e. μ₁ - μ₂ = 0.

Hₐ: The extra carbonation of cola results in a higher average compression strength, i.e. μ₁ - μ₂ < 0.

(c)

Since the population standard deviations are not provided, we would use the t-test for difference between means.

The test statistic is:

[tex]t=\frac{\bar x_{1}-\bar x_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}[/tex]

  [tex]=\frac{537-559}{\sqrt{\frac{22^{2}}{10}+\frac{17^{2}}{10}}}\\\\=\frac{-22}{8.792}\\\\=-2.502[/tex]

The test statistic value is -2.502.

(c)

Compute the p-value as follows:

[tex]p-value=P(t_{16}<-2.052)=0.012[/tex]

*Use a t-table.

The p-value of the test is 0.012.

(d)

The significance level of the test is, c

p-value = 0.012 < α = 0.05.

The null hypothesis will be rejected.

Conclusion:

The data suggest that the extra carbonation of cola results in a higher average compression strength.

(e)

The assumption necessary for the analysis is:

The distributions of compression strengths are approximately normal.

The correct option is (A).

Answer:

C. 360/900 = 0.40

Step-by-step explanation:

The number of the males that are using cellphone and the females who are using cell phones are in total 410. The total people surveyed are 900 people. There are total 480 males and rest 420 are females. Among the 420 females there are 290 females who use cellphones. The probability for males can be given by 360/900.

Answer:

[tex]\dfrac{-14}{9}[/tex].

Step-by-step explanation:

The given number is [tex]-1.\overline{5}[/tex].

We need to find a rational number in fraction form that is equivalent to given number.

Let [tex]x=-1.\overline{5}[/tex]

[tex]x=-1.555...[/tex]     ...(1)

Multiply both sides by 10.

[tex]10x=-15.555...[/tex]  ...(2)

Subtracting (1) from (2), we get

[tex]10x-x=-15.555...-(-1.555...)[/tex]

[tex]9x=-14[/tex]

Divide both sides by 9.

[tex]x=\dfrac{-14}{9}[/tex]

Therefore, the required rational number is [tex]\dfrac{-14}{9}[/tex].

Answer: 139/7

Step-by-step explanation:

Answer:

139/7

Step-by-step explanation:

182/10 = 18.2 < 18 7/11

219/12 = 18 + 3/12 = 18 1/4  < 18 7/11

139/7 = 19 + 4/7 > 18 7/11

179/10 = 17.9 < 18 7/11

Answer:

Step-by-step explanation:

(1-CotA)² + (tanA-1)² = 4csc2A(csc2A-1)

To prove this equation we will take the expression given in left hand side and will convert it into the expression given in right hand side of the equation.

L.H.S. = (1-CotA)² + (tanA-1)²

          = 1 + Cot²A - 2CotA + 1 + tan²A - 2tanA

          = cosec²A - 2CotA + Sec²A - 2tanA

[Since, (1 + Cot²A = cosec²A) and (1 + tan²A = Sec²A)]

          = (cosec²A + Sec²A) - 2(CotA + tanA)

          = [tex](\frac{1}{\text{SinA}})^{2}+(\frac{1}{CosA} )^{2}-2\text{(tanA}+\frac{1}{\text{tanA}})}[/tex]

          = [tex]\frac{1}{(\text{SinA.CosA})^2}-2(\frac{tan^2A+1}{tanA} )[/tex]

          = [tex]\frac{4}{\text{(Sin2A})^{2}}-4(\frac{1}{\text{Sin2A}} )[/tex]

[Since 2SinA.CosA = Sin2A and [tex]\frac{2(\text{tanA})}{1+\text{tan}^{2}A}=\text{Sin2A}[/tex]]

          = 4Cosec²2A - 4Cosec2A

          = 4Cosec2A(Cosec2A - 1)

          = R.H.S. (Right hand side)

Hence the equation is proved.

Answer: 3

Step-by-step explanation:

first, we know that:

1 + 2 + 3 + 4 +5 +6 = 21

Now, which two numbers we should take out in order to have 15?

we can remove the 2 and the 4, or the 1 and the 5.

so here we have two possibilities, 2 and 4 are opposite, or 1 and 5 are opposite (they are located in opposite faces of the die)

in the other arrange, we have that removing two numbers we should get 12.

in order to reach 12, we should remove two numbers that add 9 together.

those can be 4 and 5, or 6 and 3.

Now, notice that in the first restriction we have that:

Or 2 and 4 are opposite,

or 1 and 5 are opposite.

So 4 and 5 can never be opposite, so we should have that 6 and 3 are opposite.

Then we can affirm that the value that appears in the face opposite to the 6, is the 3.

Answer:

2 ( x+4) ( x+1)

Step-by-step explanation:

2x^2+10x+8

Factor out 2

2 ( x^2 +5x+4)

What two numbers  multiply to 4 and add to 5

4*1 = 4

4+1 = 5

2 ( x+4) ( x+1)

[tex] \large{ \underline{ \underline{ \bf{ \pink{To \: factorise}}}}}[/tex]

By middle term factorisation,

⇛ 2x² + 2x + 8x + 8

⇛ 2x(x + 1) + 8(x + 1)

⇛ (2x + 8)(x + 1)

⇛ 2(x + 4)(x + 1)

☃️ Now you can break it down and check which are the factors of the polynomial according to options.

━━━━━━━━━━━━━━━━━━━━

Answer:

The expression = [tex] \frac{40}{y - 16} [/tex]

Value of the expression = 4 (when y is 20)

Step-by-step explanation:

Quotient simply means the result you get when you divide two numbers. Thus, dividend (the numerator) ÷ divisor (the denominator) = quotient.

From the information given to us here,

the dividend = 40

the divisor = y - 16

The quotient = [tex] \frac{40}{y - 16} [/tex]

There, the expression would be [tex] \frac{40}{y - 16} [/tex]

Find the value of the expression when y = 20.

Plug in 20 for y in the expression and evaluate.

[tex] \frac{40}{y - 16} [/tex]

[tex] = \frac{40}{20 - 16} [/tex]

[tex] = \frac{40}{4} = 10 [/tex]

The value of the expression, when y is 20, is 4.

Answer:

x = 38.7

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan theta = opp / adj

tan x = 8/10

taking the inverse tan of each side

x = tan ^-1 (8/10)

x=38.65980825

To the nearest tenth

x = 38.7

Answer:

box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35

Step-by-step explanation:

The scores of the students represented on the dot plot are:

1 dot => 24

3 dots => 26, 26, 26

3 dots => 27, 27, 27

5 dots => 28, 28, 28, 28, 28

3 dots => 30, 30, 30

3 dots => 32, 32, 32

1 dot => 35

Quickly, we can ascertain 3 values from these data points of which we can use to find out which box plot represents the dot plot data.

The minimum score = 24

The maximum score = 35

The median score is the 10th value, which is the middle value of the data point = 28

Therefore, we can conclude that: "box plot titled ACT Score with a minimum of 24, quartile 1 of 27, median of 28, quartile 3 of 30, and maximum of 35".

Answer:

If a number is an integer, then it is irrational.  ⇒ false statement

Step-by-step explanation:

Let's check:

If a number is an integer, then it is irrational.

- incorrect, as all integers are rational

If a number is a natural number, then it is rational.

- correct, natural numbers are subset of rational numbers

If a number is a fraction, then it is rational.

- correct, they can be shown as p/q

If a number is a whole number, then it is rational.

- correct, whole numbers are subset of rational numbers

The statement "If a number is an integer, then it is irrational" is false.

The statement "If a number is an integer, then it is irrational" is false. This is because not all integers are irrational.

The other statements are all true:

"If a number is a natural number, then it is rational." This is true because all natural numbers are integers, and all integers are rational.

"If a number is a fraction, then it is rational." This is true because a fraction is a number of the form p/q, where p and q are integers and q is not equal to 0. Any number of this form is rational.

"If a number is a whole number, then it is rational." This is true because all whole numbers are integers, and all integers are rational.

Therefore, the false statement is the first one: "If a number is an integer, then it is irrational."

Below is a table summarizing the statements:

Statement                                                                  Truth value    

If a number is an integer, then it is irrational               False

If a number is a natural number, then it is rational     True

If a number is a fraction, then it is rational                  True

If a number is a whole number, then it is rational      True

Learn more about rational numbers on:

brainly.com/question/22221295

#SPJ6

Answer:

option a

Step-by-step explanation:

give person above brainliest :)

Answer:

The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Step-by-step explanation:

Let the random variable X represent the amount of gas in Sarah's car.

It is provided that [tex]X\sim Unif(1, 16)[/tex].

The amount of gas in a car is a continuous variable.

So, the random variable X follows a continuous uniform distribution.

Then the probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]

For a continuous probability distribution the probability at an exact point is 0.

So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:

P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)

              = P (6.5 < X < 7.5)

              [tex]=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067[/tex]

Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.