Let x and y be real numbers satisfying 2/x=y/3=x/y Determine the value of x^3

Answer:

Hey there!

Pythagorean Theorem:

[tex]a^2+b^2=c^2\\[/tex]

Let 6 be a, and 11 be b.

[tex]6^2+11^2=c^2\\[/tex]

[tex]36+121=c^2\\[/tex]

[tex]157=c^2[/tex]

[tex]\sqrt{157} =c[/tex]

Hope this helps :)

Answer:

[tex]12.529[/tex]

Step-by-step explanation:

[tex] {a}^{2} + {b}^{2} = {c}^{2} \\ {6}^{2} + {11}^{2} = {c}^{2} \\ 36 + 121 = {c}^{2} \\ 157 = {c}^{2} \\ \sqrt{157} = {c}^{2} \\ c = 12.529[/tex]

[tex]hope \: it \: helps \: < 3[/tex]

Answer:

-8 i + 19 j , 105.07°

Step-by-step explanation:

Solution:

- Define two unit vectors ( i and j ) along x-axis and y-axis respectively.

- To draw vectors ( v and w ). We will move along x and y axes corresponding to the magnitudes of unit vectors ( i and j ) relative to the origin.

  Vector: v = 2i + 5j

Vector: w = 4i - 3j

- The algebraic manipulation of complex numbers is done by performing operations on the like unit vectors.

                      [tex]2*v - 3*w = 2* ( 2i + 5j ) - 3*(4i - 3j )\\\\2*v - 3*w = ( 4i + 10j ) + ( -12i + 9j )\\\\2*v - 3*w = ( 4 - 12 ) i + ( 10 + 9 ) j\\\\2*v - 3*w = ( -8 ) i + ( 19 ) j\\[/tex]

- To determine the angle ( θ ) between two vectors ( v and w ). We will use the " dot product" formulation as follows:

                     v . w = | v | * | w | * cos ( θ )

                     v . w = < 2 , 5 > . < 4 , -3 > = 8 - 15 = -7

                     [tex]| v | = \sqrt{2^2 + 5^2} = \sqrt{29} \\\\| w | = \sqrt{4^2 + 3^2} = 5\\\\[/tex]

- Plug the respective values into the dot-product formulation:

                     cos ( θ ) = [tex]\frac{-7}{5\sqrt{29} }[/tex]

                      θ = 105.07°

Answer: 1. [tex]-\dfrac{5}{6}[/tex]  2. [tex]-\dfrac{1}{3}[/tex] . 3. [tex]-3[/tex]

Step-by-step explanation:

Formula: Slope[tex]=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

1. (-2,2) (3,-3)

Slope [tex]=\dfrac{-3-2}{3-(-2)}[/tex]

[tex]=\dfrac{-5}{3+2}\\\\=\dfrac{-5}{6}[/tex]

Hence, slope of line passing through  (-2,2) (3,-3) is [tex]-\dfrac{5}{6}[/tex] .

2. (-5,1) (4,-2)

Slope [tex]=\dfrac{-2-1}{4-(-5)}[/tex]

[tex]=\dfrac{-3}{4+5}\\\\=\dfrac{-3}{9}\\\\=-\dfrac{1}{3}[/tex]

Hence, slope of line passing through  (-2,2) and (3,-3) is [tex]-\dfrac{1}{3}[/tex] .

3. (-1,5) (2,-4)

Slope [tex]=\dfrac{-4-5}{2-(-1)}[/tex]

[tex]=\dfrac{-9}{2+1}\\\\=\dfrac{-9}{3}\\\\=-3[/tex]

Hence, slope of line passing through (-1,5) and (2,-4) is -3.

Hey there! I'm happy to help!

If we add Machine 1's 459 satisfactory pistons and 51 unsatisfactory pistons, we get 510 total pistons.

If we add Machine 2's 360 satisfactory pistons and 40 unsatisfactory pistons, we get 400 total pistons.

First, we want to find the probability of choosing an unsatisfactory piston from Machine 1.

We see that 51/510 (unsatisfactory pistons out of total pistons) simplifies to equal 1/10, so there is a 1/10 chance of getting an unsatisfactory piston from Machine 1.

For Machine 2, there are 360 satisfactory and 400 total. This gives us 360/400, which simplifies to 9/10.

Now, we multiply our two probabilities together to find the probability that they both happen.

1/10×9/10=9/100

Therefore, the probability that a piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 9/100 or 9%.

Have a wonderful day! :D

Answer:

a

  [tex]z_t = -1.645[/tex]

b

 We should reject the Upper  [tex]H_o[/tex]

Step-by-step explanation:

From the question we are told that

   The test statistics is     [tex]t_s = -3.43[/tex]

     The probability is   [tex]p < 0.39[/tex]

      The level of significance is [tex]\alpha = 0.05[/tex]

Now looking at the probability we can deduce that this is a left tailed test

The  second step to take is to obtain the critical value of [tex]\alpha[/tex] from the critical value table  

    The value  is  

               [tex]t_ {\alpha } = 1.645[/tex]

Now  since this  test is  a  left tailed test  the critical value will be

               [tex]z_t = -1.645[/tex]

This because we are considering the left tail of the normal distribution curve

 Now  since the test statistics falls within the  critical values the Null hypothesis is been rejected

Answer:

Answer y=7

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The equation of the hyperbola can be written as ...

  ((x -h)/a)² -((y -k)/b)² = 1

This has asymptotes ...

  (x -h)/a ± (y -k)/b = 0

Solving for y, we have ...

  y = ±(b/a)(x -h) +k

Filling in the given values a=6, b=8, h=1, k=2, we have ...

  y = ±8/6(x -1) +2

  [tex]y=\dfrac{\pm4x\mp4+6}{3}\\\\\boxed{y=\dfrac{4x+2}{3}\ \text{and }y=\dfrac{10-4x}{3}}[/tex]

Answer:

A. y = 4x+2/3 and y = 10-4x/3

Step-by-step explanation:

this is the correct answer for the question on edmentum and Plato

Answer:

calls first evening = 26

calls second evening  = 80

calls third evening = 20

Step-by-step explanation:

Let x = calls third evening

x+6 = calls first evening

4x = calls second evening

x+6 + 4x + x = total calls = 126

Combine like terms

6x+6 = 126

Subtract 6 from each side

6x =120

Divide by 6

6x/6 =120/6

x = 20

x+6 = calls first evening = 20+6 = 26

4x = calls second evening = 4*20 = 80

Let x = calls third evening = 20

Answer:

k = [tex]\frac{980a}{b}[/tex]

Step-by-step explanation:

Fisherman noticed a stretch in the spring = 'b' centimetres

Weight of the fish = a kilograms

If force applied on a spring scale makes a stretch in the spring then Hook's law for the force applied is,

F = kΔx

Where k = spring constant

Δx = stretch in the spring

F = weight applied

F = mg

Here 'm' = mass of the fish

g = gravitational constant

F = a(9.8)

  = 9.8a

Δx = b centimetres = 0.01b meters

Therefore, 9.8a = k(0.01b)

k = [tex]\frac{9.8a}{0.01b}[/tex]

k = [tex]\frac{980a}{b}[/tex]

Therefore, spring constant of the spring will be determined by the expression, k = [tex]\frac{980a}{b}[/tex]

Answer:

37

Step-by-step explanation:

To find the fifth term , we have to take the value of n as 5

So, F(5)= 6.5 (5) +4.5

= 32.5 + 4.5

= 37

Answer:

Perimeter = 19.42 in and area = 26.13 in^2.

Step-by-step explanation:

The perimeter = 2 * 5 + length of the semicircle

= 10 * 3.14 * 3

= 19.42 in.

Total area = area of the semicircle + area of the triangle

= 1/2 * 3.14 * 3^2 + 3 * 4

= 26.13 in^2.

Answer:

Step-by-step explanation:

The derivative of your function is ...

  y' = dy/dx = 2e^(2x) +6

At x=0, the value is ...

  y'(0) = 2e^0 +6 = 8

  dy = 8·dx

__

  Δy = y'(0)·Δx

  Δy = 8(.03)

  Δy = 0.24

Answer:

work is shown and pictured

Answer:

answer 1 /9x^3

Step-by-step explanation:

9ײ/81×⁵​

change the expression to indices form

3^2 x^2 /3^4 x^5

1 /3^2 x^3

1 /9x^3

Answer:

Number : 41

Step-by-step explanation:

Say that this number is x. The sum of this number ( x ) and 9 subtracted from 60 will be 10. Therefore we can create the following equation to solve for x,

60 - (x + 9) = 10,

60 - x - 9 = 10,

51 - x = 10,

- x = 10 - 51 = - 41,

x = 41

This number will be 41

Answer:

D (13,5)

Step-by-step explanation:

X 2 3 4 5

Y 2 5 9 13

So the ordered pairs are (2,2),(3,5), (4,9), (5,13)

and the ordered pairs for the inverse are

(2,2),(5,3), (9,4), (13,5)

from which D (13,5) is found among the options.

Answer:

b

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

The n th term of a GP is

[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]

where a is the first term and r the common ratio

Given a₂ = 6 and a₅ = 48, then

ar = 6 → (1)

a[tex]r^{4}[/tex] = 48 → (2)

Divide (2) by (1)

[tex]\frac{ar^4}{ar}[/tex] = [tex]\frac{48}{6}[/tex] , that is

r³ = 8 ( take the cube root of both sides )

r = [tex]\sqrt[3]{8}[/tex] = 2

Substitute r = 2 into (1)

2a = 6 ( divide both sides by 2 )

a = 3

Thus

3, 6, 12, 24 ← are the first 4 terms

3 + 6 + 12 + 24 = 45 ← sum of first 4 terms

Answer:

1800

Step-by-step explanation:

Hello,

First of all we need to find the prime factorisation of the numbers.

18 = 2 * 3 * 3

40 = 2 * 2 * 2 * 5

75 = 3 * 5 * 5

It means that the LCM should have 5 * 5 , 2 * 2 * 2 and 3 * 3

Then LCM = 3 * 3 * 2 * 2 * 2 * 5 * 5 = 1800

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

1800

Step-by-step explanation:

→ First of all we need to find the prime factorisation of the numbers.

18 = 2 × 3 × 3 or 2 × 3²

40 = 2 × 2 × 2 × 5 or 2³ × 5

75 = 3 × 5 × 5 or 5² × 3

→ Now find the number that appear twice or more and write them down

3 and 3 from 18

2, 2 and 2 from 40

5 and 5 from 75

→ Now multiply all of these numbers together

3 × 3 × 2 × 2 × 2 × 5 × 5 = 3² × 2³ × 5² = 1800

Hi there! :)

Answer:

w = 7 cm.

Step-by-step explanation:

Given:

P = 56

Use the formula P = 2l + 2w to solve for the perimeter of the rectangle.

Let w = width, and

3w = length

Plug these into the equation:

56 = 2(3w) + 2(w)

56 = 6w + 2w

Combine like terms:

56 = 8w

Divide both sides by 8:

w = 7 cm.

The width of rectangle is 7 cm.

Answer:

The answer is 15.6/31 or 1/2

Step-by-step explanation:

The data in the question is sufficient to find an answer for it.

1. I look at the temperature and rainfall chart for Brighton, United Kingdom.

2. Check for rainy season and dry season.

3. The rainy season lasts approximately 5 months while the dry season (which still has some rainfall) lasts approximately 7 months. All together, 12 months of the calendar year.

4. July happens to fall within the dry season. The temperature and rainfall statistics are observed.

The number of rainfall days is 15.6 and we know there are 31 days in July.

If the approximate number of days it rains in Brighton, in July, is 15.6 then the probability of rainfall in the month is 15.6/31 which is = 0.503 or 0.5

Therefore, there's a 50% chance of having rainfall in Brighton, on any day in the month of July.

In fraction, 0.5 = 1/2

Answer: 0.476

Step-by-step explanation:

Let A = Event of choosing an even number ball.

B = Event of choosing an 8 .

Given, A lottery game has balls numbered 1 through 21.

Sample space: S= {1,2,3,4,5,6,7,8,...., 21}

n(S) = 21

Then, A= {2,4,6,8, 10,...(20)}

i.e. n(A)= 10

B= {8}

n(B) = 1

A∪B = {2,4,6,8, 10,...(20)} = A

n(A∪B)=10

Now, the probability of selecting an even numbered ball or an 8 is

[tex]P(A\cup B)=\dfrac{n(A\cup B)}{n(S)}[/tex]

[tex]=\dfrac{10}{21}\approx0.476[/tex]

Hence, the required probability =0.476

Answer:

6.96x10^-3

Step-by-step explanation:

0.00696

We move the decimal point to between 6 and 9

since the number with the decimal point should be between 0 and 9.

Then we count the numbers.

6.96x10^-3.

Hope this helps. ❤❤❤

Answer: 6.96 * 10^(-3)

Step-by-step explanation:

In scientific notation, you multiply a number that has a value in the ones place and no value in the tens place by 10 raised to an exponent.

Hope it helps <3

Answer:

The  probability is  [tex]P[ D n R] = 0.196[/tex]

Step-by-step explanation:

  From the question we are told that

     The number of Democrats is  [tex]D = 8[/tex]

       The number of republicans is  [tex]R = 8[/tex]

The  number of ways of selecting selecting two Democrats and four Republicans.

         [tex]N = \left {D} \atop {}} \right. C_2 * \left {R} \atop {}} \right. C_1[/tex]

Where C represents combination

substituting values

           [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1[/tex]

           [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(8-2)! 2!} * \frac{8! }{(8-4)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8!}{(6)! 2!} * \frac{8! }{(6)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 * 6!}{(6)! 2!} * \frac{8*7 *6! }{(6)! 1 !}[/tex]

=>        [tex]N = \left {8} \atop {}} \right. C_2 * \left {8} \atop {}} \right. C_1 = \frac{8 * 7 }{ 2*1 } * \frac{8*7 }{ 1 *1 }[/tex]

=>      [tex]N = 1568[/tex]

The total number of ways of selecting the committee of six people is  

          [tex]Z = \left {D+R} \atop {}} \right. C_6[/tex]

substituting values

           [tex]Z = \left {8+8} \atop {}} \right. C_6[/tex]

            [tex]Z= \left {16} \atop {}} \right. C_6[/tex]

substituting values

             [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16! }{(16-6) ! 6!}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 * 10! }{10 ! 6!}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = \frac{16 *15 *14 * 13 * 12 * 11 }{6* 5 * 4 * 3 * 2 * 1}[/tex]

           [tex]Z= \left {16} \atop {}} \right. C_6 = 8008[/tex]

The probability of selecting two Democrats and four Republicans  is  mathematically  represented as

           [tex]P[ D n R] = \frac{N}{Z}[/tex]

substituting values

           [tex]P[ D n R] = \frac{1568}{8008}[/tex]

            [tex]P[ D n R] = 0.196[/tex]

Answer:

[tex]\boxed{15 \ dime \ and \ 10 \ nickel \ coins}[/tex]

Step-by-step explanation:

1 dime = 10 cents

1 nickel = 5 cents

So,

If there are 15 dimes

=> 15 dimes = 15*10 cents

=> 15 dimes = 150 cents

=> 15 dimes = $1.5

Rest is $0.5

So, for $0.5 we have 10 nickels coins

=> 10 nickels = 10*5

=> 10 nickels = 50 cents

=> 10 nickel coins = $0.5

Together it makes $2.00

Answer:

The lower bound = 35.443

The upper bound = 71.697

The error bound = 18.127

Step-by-step explanation:

We are given that a survey of the average amount of cents off that coupons gives was done by randomly surveying one coupon per page from the coupon sections of a recent San Jose Mercury News.

The following data were collected (X): 20cents; 70cents; 50cents; 65cents; 30cents; 55cents; 40cents; 40cents; 30cents; 55cents; 150 cents; 40cents; 65cents; 40cents.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

                              P.Q.  =  [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex]  ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean worth of coupons = [tex]\frac{\sum X}{n}[/tex] = [tex]\frac{750}{14}[/tex] = 53.57 cents

            s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = 31.40 cents

            n = sample size = 14

            [tex]\mu[/tex] = population mean worth of coupons

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics as we don't know about population standard deviation.

So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;

P(-2.16 < [tex]t_1_3[/tex] < 2.16) = 0.95  {As the critical value of t at 13 degrees of

                                             freedom are -2.16 & 2.16 with P = 2.5%}  

P(-2.16 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.16) = 0.95

P( [tex]-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}{[/tex] < [tex]2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

P( [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95

95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.16 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.16 \times {\frac{s}{\sqrt{n} } }[/tex] ]

 = [ [tex]53.57-2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] , [tex]53.57+2.16 \times {\frac{31.40}{\sqrt{14} } }[/tex] ]

 = [35.443, 71.697]

Therefore, a 95% confidence interval for the population mean worth of coupons is [35.443, 71.697].

Answer:

A) Fail to Reject the Null Hypothesis

Step-by-step explanation:

Given that:

A local Internet provider wants to test the claim that the average time a family spends online on a Saturday is at least 7 hours.

sample size = 30

sample mean [tex]\bar x[/tex] = 6

standard deviation [tex]\sigma[/tex] = 1.5

level of significance ∝ = 0.05

The null hypothesis and the alternative hypothesis can be computed as:

[tex]\mathbf{ H_o: \mu \leq 7}[/tex]

[tex]\mathbf{ H_i: \mu \geq 7}[/tex]

The test statistic  can be computed as:

[tex]z = \dfrac{\bar x - \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]z = \dfrac{6 -7} {\dfrac{1.5}{\sqrt {30}}}[/tex]

[tex]z = \dfrac{-1} {\dfrac{1.5}{5.477}}}[/tex]

[tex]z = \dfrac{-5.477} {1.5}[/tex]

z = -3.65

Given that ;

level of significance of 0.05;

z = -3.65

degree of freedom = 30 -  1 = 29

The p-value = P([tex]t_{29}[/tex] > - 3.65)

= 0.9998

Decision Rule: Reject [tex]H_o[/tex] if p-value is less than the level of significance

But since the p -value is greater than the level of significance, we conclude that There is no enough evidence to support the  Internet provider  claim, Therefore;

Fail to Reject the Null Hypothesis

Step-by-step explanation:

Hello there!

Its simple,

Given that, Ade had 23 hand bags.

selling price of each bag=$409

total sold bags= 22.

now, total amount he got was = no.of sold bag×sp of each bag.

so, total amount = 22×$409

=$8998.

Therefore, he has $ 8998 now.

Hope it helps...

Answer:

y=1/5x+11/5

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula  y-y^1=m(x-x^1) to find line parallel to -x+5y=1

Hope this helps

Answer: y = 1/5x+ 2.2

Step-by-step explanation:

First, change the expression into y-intercept form

-x+5y=1

5y=x+1

y=1/5x+1/5

For a line to be parallel to another line, it must have the same slope.  Thus, the slope must be 1/5x.  Then, to find the y-intercept simply do:

y = 1/5x+b, where x = -1 and y = 2

2=1/5(-1)+b

2 = -1/5+b

b = 2 1/5.

Thus, the equation y = 1/5x+ 2.2

Hope it helps <3

Answer:

2π radians

Step-by-step explanation:

Answer:

Option B

Step-by-step explanation:

The margin of error describes how many percentage points the results will differ from the real population value, thus 'the margin of error for a 95% confidence interval is given as plus or minus 7 milligrams per deciliter of blood (mg/dl)' can be interpreted as 'The study used a method that gives a results within 7 mg/dl of the truth about the population in 95% of all samples.'