For a free lunch giveaway, a restaurant draws 1 card from a bowl of business cards. Val puts in 5 cards. The bowl has 50 cards. What is the probability that Val will win?

[tex] \Large{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]

Let one of those even numbers be x, Then other even number would be x + 2.

According to question,

⇛ Their reciprocal add upto 3/4

So, we can write it as,

⇛ 1/x + 1/x + 2 = 3/4

⇛ x + 2 + x / x(x + 2) = 3/4

⇛ 2x + 2 / x² + 2x = 3/4

Cross multiplying,

⇛ 3(x² + 2x) = 4(2x + 2)

⇛ 3x² + 6x = 8x + 8

⇛ 3x² - 2x - 8 = 0

⇛ 3x² - 6x + 4x - 8 = 0

⇛ 3x(x - 2) + 4(x - 2) = 0

⇛ (3x + 4)(x - 2) = 0

Then, x = -4/3 or 2

☃️ It can't be -4/3 because it is fraction and negative number. So, x = 2

Then, x + 2 = 4

✤ So, The even numbers are 2 and 4.

━━━━━━━━━━━━━━━━━━━━

Answer: 6

Step-by-step explanation:

Answer:

[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Step-by-step explanation:

The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]

where:

Base stands for the larger base (in our case the dimension "B" in the attached image)

base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)

and

height stands for the distance between bases (in our case the dimension "h" in the attached image.

Therefore the formula for the area of the grassy section becomes:

[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]

Answer:

1/2 (b+b) h

here is the actual picture

Answer:

D

Step-by-step explanation:

Let the number of rows be x

And the numbers of holes in each be y

xy = 32

x and y must be factors of 32

From options stated

4 is the only factor of 32

Hence option D is correct

Answer:

The mean commute time in the U.S. is less than half an hour.

Step-by-step explanation:

In this case we need to test whether the mean commute time in the U.S. is less than half an hour.

The information provided is:

 [tex]n=45\\\bar x=25.5\\s=19.1\\\alpha =0.05[/tex]

(a)

The hypothesis for the test can be defined as follows:

H₀: The mean commute time in the U.S. is not less than half an hour, i.e. μ ≥ 30.

Hₐ: The mean commute time in the U.S. is less than half an hour, i.e. μ < 30.

(b)

As the population standard deviation is not known we will use a t-test for single mean.

Compute the test statistic value as follows:

 [tex]t=\frac{\bar x-\mu}{s/\sqrt{n}}=\frac{25.2-30}{19.1/\sqrt{45}}=-1.58[/tex]

Thus, the test statistic value is -1.58.

(c)

Compute the p-value of the test as follows:

[tex]p-value=P(t_{(n-1)}<-1.58)=P(t_{(45-1)}<-1.58)=0.061[/tex]  

*Use a t-table.

The p-value of the test is 0.061.

Decision rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected and vice-versa.

p-value = 0.061> α = 0.05

The null hypothesis will not be rejected at 5% level of significance.

Thus, concluding that the mean commute time in the U.S. is less than half an hour.

Answer:

The probability that at least, one of the four children the couple has is a boy is 0.8.

Step-by-step explanation:

Given that boys and girls are equally likely, we want to find the probability of having at least, one boy, from four children..

Note that it is possible to have the following for 4 children:

1. 4 boys, 0 girls

2. 3 boys, 1 girl

3. 2 boys, 2 girls

4. 1 boy, 3 girls

5. 0 boys, 4 girls.

To have at least, one boy, out of the 5 options, only 4 is possible.

1. 4 boys, 0 girls.........YES

2. 3 boys, 1 girl ...........YES

3. 2 boys, 2 girls.........YES

4. 1 boy, 3 girls.............YES

5. 0 boys, 4 girls..........NO

The probability is therefore,

(Probability of event = 4) ÷ (Total possible outcome = 5)

P = 4/5 = 0.8

Answer:

7161

Step-by-step explanation:

7 + 7(2) + 7(2)² + ... + 7(2)⁹

= ∑₁¹⁰ 7(2)ⁿ⁻¹

= 7 (1 − 2¹⁰) / (1 − 2)

= 7161

Answer: Will continue to rise

Step-by-step explanation:

Looking at the graph one notices that after a slight dip in the unemployment rate from August 2010 to January 2011, the unemployment rate began to rise and by November 2011 was still rising.

The arrow on the graph serves to indicate the direction the unemployment rate is going and as it is pointing upwards, this means that the Unemployment rate will continue to rise.

This was down to the fact that in 2011 the US was still yet to recover from the Great Recession of 2008 - 2009.

Answer:

EDGE 2021

Step-by-step explanation:

1) 4%

2) Increase

Answer:

(-1,0) and (0,-8)

Step-by-step explanation:

Hey there!

Well first we’ll graph -8x - y = 8,

Look at the image below

By lookig at the image below we can tell the 2 points are at,

(-1,0) and (0,-8)

Hope this helps :)

Answer:  A)  g(x) = 3x - 14

Step-by-step explanation:

Solve the equation for y and replace y with g(x):

y - 3x = -14

y        = 3x - 14

  g(x) = 3x - 14

Answer:

37 hours

Step-by-step explanation:

4.5 + 8.75 + 9.5 + 10 + 4.25 = 37 hours

Answer:

37 hours

Step-by-step explanation:

4.5 hours = 4 hrs and 30 mins

8.75 hrs = 8 hrs and 45 mins

9.5 hrs = 9 hrs and 30 mins

10 hrs = 10 hrs and 0 min

4.25 hrs = 4 hrs and 15 mins

(30 + 45 + 30 + 15) mins = 2 hrs

Therefore, total hours Sam worked = (4 + 8 + 9 + 10 + 4 + 2) hrs = 37 hours

Answer:

The probability is  [tex]P( \= X \ge 70 ) = 0.07311[/tex]

Step-by-step explanation:

From the question we are told that

    The  population mean is  [tex]\mu = 68[/tex]

      The standard deviation is  [tex]\sigma = \sqrt{36} = 6[/tex]

      The  sample size is  [tex]n = 19[/tex]

Generally the standard error of the mean is mathematically represented as  

            [tex]\sigma_{\= x } = \frac{\sigma }{\sqrt{n} }[/tex]

=>         [tex]\sigma_{\= x } = \frac{6 }{\sqrt{19} }[/tex]

=>         [tex]\sigma_{\= x } = 1.3765[/tex]

Generally the probability that their average score will be at least 70 is mathematically represented as

            [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(\frac{ \= X - \mu }{\sigma_{\= x}} < \frac{70 - 68}{ 1.3765} )[/tex]

Generally [tex]\frac{ \= X - \mu }{\sigma_{\= x}} = z(The \ z-score \ of \ \= X )[/tex]

So

          [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - P(Z <1.453 )[/tex]

From the z-table

            [tex]P(Z <1.453 ) = 0.92689[/tex]

=>          [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 1 - 0.92689[/tex]

=>         [tex]P( \= X \ge 70 ) = 1 - P( \= X < 70 ) = 0.07311[/tex]

=>          [tex]P( \= X \ge 70 ) = 0.07311[/tex]

Answer: 1860480

Step-by-step explanation:

Initially, there are 20 balls where 5 must be chosen in order.

The number of possible outcomes may be calculated using the concept of permutations.

The formula for permutations is:

nPr =n!/(n−r)!

where n represents the number of items and r represents the number of items to be selected.

The number of ways of selecting 5 balls in order out of 20 is:

20P5 = 20!/15!

= 1860480

To conclude, there are 1860480 possible outcomes.

Answer:

1365

Step-by-step explanation:

We figure out combinations using this formula:    n!

                                                                              r!(n-r)!

n=15

r=4

So n!= 15x14x13x12x11x0x9x8x7x6x5x4x3x2x1

r! = 4x3x2x1 times 15-4!, which is 11! = 11x10x9x8x7x6x5x4x3x2x1

Put this together and you have 15x14x13x12/4x3x2x1=

There are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.

Combinations are the procedures used in mathematics to pick k things from n different items without replacement.

The following formula computes the combinations of k items from n:

(n, k) = n! / k!×(n-k)!

The number of ways to award the 4 door prizes to 4 guests out of a group of 15 guests is a combinatorial problem that can be calculated using the formula.

Here, n = 15 (the total number of guests) and k = 4 (the number of prizes to be awarded).

So, the number of ways to award the prizes is:

C(15, 4) = 15! / (4! (15 - 4)!)

= 15! / (4! 11!)

= 15 x 14 x 13 x 12 / (4 x 3 x 2 x 1)

= 1365.

Therefore, there are 1365 different ways to award the 4 door prizes to 4 guests from a group of 15 guests.

Learn more about permutation here:

brainly.com/question/1216161

#SPJ6

Answer:

49

Step-by-step explanation:

With these types of problems, you have to subtract the outer and inner values and then divide by 2. So, (125-27)/2 = 49. Hope this helps!

Answer:

x = 5

Step-by-step explanation:

Angle Bisector Theorem: When a ray bisects an angle, we get 2 congruent smaller angles

Step 1: Set equation equal to each other (Angle Bisector Theorem)

5x + 3 = 7x - 7

Step 2: Subtract 5x on both sides

3 = 2x - 7

Step 3: Isolate x term (Add 7 to both sides)

10 = 2x

Step 4: Isolate x (Divide both sides by 2)

x = 5

Answer:

210.33 cm^2

Step-by-step explanation:

We know that 6 equilateral triangles makes one hexagon.

Also, an equilateral triangle has all its sides equal.

If the tile of each side of the triangular tile measure 9 cm, then the height of the triangular tiles can be gotten using Pythagoras's Theorem.

The triangle formed by each tile can be split along its height, into two right angle triangles with base (adjacent) 4.5 cm and slant side (hypotenuse) of 9 cm. The height  (opposite) is calculated as,

From Pythagoras's theorem,

[tex]hyp^{2} = adj^{2} + opp^{2}[/tex]

substituting, we have

[tex]9^{2} = 4.5^{2} + opp^{2}[/tex]

81 = 20.25 + [tex]opp^{2}[/tex]

[tex]opp^{2}[/tex] = 81 - 20.25 = 60.75

opp = [tex]\sqrt{60.75}[/tex] = 7.79 cm  this is the height of the right angle triangle, and also the height of the equilateral triangular tiles.

The area of a triangle = [tex]\frac{1}{2} bh[/tex]

where b is the base = 9 cm

h is the height = 7.79 cm

substituting, we have

area = [tex]\frac{1}{2}[/tex] x 9 x 7.79 = 35.055 cm^2

Area of the hexagon that will be formed = 6 x area of the triangular tiles

==> 6 x 35.055 cm^2 = 210.33 cm^2

Answer:

Height = 4 feet

Step-by-step explanation:

To determine how tall I can be we take the difference between the shadow cast by the 32-feet tree and the distance away from the tree

But the tree is 32 feet tall but on shadow it's 160

So lemme determine how long I'll be in my shadow first

Distance away from tree= 140 feet

Length of shadow cast by tree

= 160 feet

Length of shadow= 160-140

Length if shadow= 20 feet

My height= x

X/20= 32/160

X= 20*32/260

X = 4 feet

Height = 4 feet

Answer:

a) y = 4

b) RS = 26, ST = 19, RT = 45

Step-by-step explanation:

From the line given, the following vector equation is true, RS + ST = RT since R, S and T lies in the same straight line.

Given RS = 6y + 2, ST = 3y + 7, and RT = 14y - 11

On substituting this values into the equation above we will have;

6y+2+(3y+7) = 14y-11

6y+2+3y+7 = 14y-11

Collect the like terms

6y+3y-14y = -11-7-2

9y-14y = -20

-5y = -20

y = 20/5

y = 4

Since RS = 6y + 2

RS = 6(4)+2

RS = 24+2

RS = 26

ST = 3y + 7

ST = 3(4)+7

ST = 12+7

ST = 19

Also, RT = 14y - 11

RT = 14(4)-11

RT = 56-11

RT = 45

Answer:

b

Step-by-step explanation:

The value of a is negative, so the vertex is a minimum.

Answer:

17

Step-by-step explanation:

We are adding the previous two terms

1+5 = 6

5+6 = 11

6+11 = 17

11+17 = 28

The missing term is 17

Answer:a

a

   [tex]336.04 < \mu < 443.96[/tex]

b

  The  margin of error will increase

c

The  margin of error will decreases

d

The 99% confidence interval is  [tex]0.4107 < p < 0.4293[/tex]

Step-by-step explanation:

From the question we are  told that

   The sample size  [tex]n = 19[/tex]

    The sample mean is  [tex]\= x = \$\ 390[/tex]

    The  standard deviation is  [tex]\sigma = \$ \ 120[/tex]

Given that the confidence level is  95% 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

    So  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

The  margin of error is mathematically represented as

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

=>    [tex]E = 1.96 * \frac{120}{\sqrt{19} }[/tex]

=>   [tex]E = 53.96[/tex]

The 95% confidence interval is  

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

=>   [tex]390 - 53.96 < \mu < 390 - 53.96[/tex]

=>  [tex]336.04 < \mu < 443.96[/tex]

When the confidence level increases the [tex]Z_{\frac{\alpha }{2} }[/tex] also increases which increases the margin of error hence the confidence level becomes wider

Generally the sample size mathematically varies with margin of error as follows

         [tex]n \ \ \alpha \ \ \frac{1}{E^2 }[/tex]

So if the sample size increases the margin of error decrease

The  sample proportion is mathematically represented as

       [tex]\r p = \frac{210}{500}[/tex]

       [tex]\r p = 0.42[/tex]

Given that the confidence level is 0.99 the level of significance is  [tex]\alpha = 0.01[/tex]

The critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table is  

      [tex]Z_{\frac{\alpha }{2} } = 2.58[/tex]

  Generally the margin of error is mathematically represented as

       [tex]E = Z_{\frac{\alpha }{2} }* \sqrt{ \frac{\r p (1- \r p )}{n} }[/tex]

=>   [tex]E = 0.42 * \sqrt{ \frac{0.42 (1- 0.42 )}{ 500} }[/tex]

=>     [tex]E = 0.0093[/tex]

The 99% confidence interval  is

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

     [tex]0.42 - 0.0093 < p < 0.42 + 0.0093[/tex]

     [tex]0.4107 < p < 0.4293[/tex]

Answer:

x³ - 5x² - x + 5

Step-by-step explanation:

(x+1)(x-1)(x-5) = 0

fisrt step:

(x+1)(x-1) = x*x + x*-1 + 1*x + 1*-1 = x² - x + x - 1 = x² - 1

then:

(x+1)(x-1)(x-5) = (x²-1)(x-5)

(x²-1)(x-5) = x²*x + x²*-5 -1*x -1*-5 = x³ - 5x² - x + 5

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you

Answer:

Ordering a soft drink is independent of ordering a square pizza.

Step-by-step explanation:

20% more customers order a soft drink than pizza, therefore they cannot be intertwined.

Given: P(A)=0.5 & P(B)=.7

P(A∩B) =  P(A) × P(B)

=  0.5 × .7

=  0.35

P(A∪B) =  P(A) + P(B) - P(A∩B)

=  0.5 + .7 - 0.35

=  0.85

P(AΔB) =  P(A) + P(B) - 2P(A∩B)

=  0.5 + .7 - 2×0.35

=  0.5

P(A') =  1 - P(A)

=  1 - 0.5

=  0.5

P(B') =  1 - P(B)

=  1 - .7

=  0.3

P((A∪B)') =  1 - P(A∪B)

=  1 - 0.85

=  0.15

Yes ordering a soft drink is independent of ordering a square pizza.

We have given 50 percent of the customers at Pizza Palooza order a square pizza, 70 percent order a soft drink, and 35 percent order both a square pizza and a soft drink.

Let A: denote pizza

     B: Soft drink

Then,

P(A)=0.5 and P(B)=0.7

And P(A∩B) =  P(A) × P(B)

=  0.5 × 0.7

=  0.35

We know P(A∪B) =  P(A) + P(B) - P(A∩B)

=  0.5 + 0.7 - 0.35

=  0.85

P(AΔB) =  P(A) + P(B) - 2P(A∩B)

=  0.5 + 0.7 - 2×0.35

=  0.5

Also we know P(A') =  1 - P(A)

=  1 - 0.5

=  0.5

And P(B') =  1 - P(B)  

=  1 -0.7

=  0.3

And P((A∪B)') =  1 - P(A∪B)

=  1 - 0.85

=  0.15

Learn more:https://brainly.in/question/16017018

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

42 is your answer according to bodmas

Answer:

16 + 8b ≥ 50

4500

Step-by-step explanation:

He needs at least 50 rooms and has already reserved 16

They are in groups of 8

16 + 8b ≥ 50

Subtract 16 from each side

16+8b-16 ≥ 50 -16

8b≥ 34

Divide by 6

8b/8 ≥ 34/8

b≥ 4.25

We need to round up since we need at least 50

b = 5 since we want the least amount of rooms

Each block is 900

5*900 = 4500 more that he will have to spend