y varies directly as the square of R. If y is 7 when R is 3​, find y when R is 15 . ​a) Write the variation. ​b) Find y when R is 15.

[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:

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)  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:

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

Using concepts of circles, it is found that the angle measure of each slice is of 72º.

--------------------------------------------

--------------------------------------------

5 equal slices, thus:

[tex]\frac{360}{5} = 72[/tex]

The angle measure of each slice is of 72º.

A similar problem is given at https://brainly.com/question/16746988

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:

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:

Total amount in dollars= $64614.00

Step-by-step explanation:

Initial starting salary is $40000.

Rate of increase is 3%

Number of years is 16 years

The salary is compounded yearly.

Amount A after 16 years is given as

A= p (1+r/n)^ (nt)

A=40000(1+0.03/16)^(16*16)

A= 40000(1.001875)^(256)

A=40000(1.61534824)

A= 64613.92959

Total amount in dollars= $64614.00

Answer: the answer is $806275

Step-by-step explanation:

A p e x

Answer:

$16.43.

Step-by-step explanation:

At the grocery store, you spent $485.72. With 2% cashback, you would get 485.72 * 0.02 = 9.7144 dollars worth of cashback.

At other places, you spend $671.28. With 1% cashback, you would get 671.28 * 0.01 = 6.7128 dollars worth of cashback.

9.7144 + 6.7128 = 16.4272, which is about $16.43 of cashback.

Hope this helps!

The amount of cashback that you earned will be $16.42.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

Suppose you earn 2% cash back at grocery stores and 1% on all other purchases. If you spent $485.72 at the grocery store and $671.28 on all other purchases.

The total cashback is calculated as,

⇒ 0.02 x $485.72 + 0.01 x $671.28

⇒ $9.71 + $6.71

⇒ $16.42

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ3

Step-by-step explanation:

42 is your answer according to bodmas

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:

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]

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:

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:

(-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) 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:

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:

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:

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:

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

Answer:

b

Step-by-step explanation:

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

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:

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:

4/ (10+r) * r/ (10+r)

Step-by-step explanation:

four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles

P( blue) = blue marbles / total marbles

             = 4/ (10+r)

Then replace

P( r) = red marbles / total marbles

             = r/ (10+r)

P( blue replace ,red) =P ( blue ) * P(red)

                                    =  4/ (10+r) * r/ (10+r)

                                    = 4r / ( 10+r) ^2

Answer:

C. 4/10+r (r/10+r)

Step-by-step explanation:

EDG20

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:

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:

Kindly check explanation

Step-by-step explanation: Jullian's claim that the distance she drives to work is exactly 11.7miles is incorrect because, in other to record or get the exact result of a certain calculation such as Jullian's Distance, the value of the distance obtained will not be approximated or rounded. In this scenario, Distance was to the nearest tenth of a mile, thereby altering the true outcome of the calculation.

The word exact means that what is stated is very precise and does not fall below or above in any respect. However, a number whose accuracy is to the nearest tenth of a mile, violates this assertion.