Which of the following is equivalent to 18 minus StartRoot negative 25 EndRoot?

C. y= -28/x

y=k/x

cross multiply

k= y×x

k = -2×14

k = -28

y = -28/x [ equation connecting x and y]

The equation that connects x and y si y = –28∕x.

The correct option is (C)

The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant. The proportionality constant's value is determined by the proportion between the two specified quantities.

For example,  The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.

We have given that

y ∝ 1∕x

To remove proportional sign we use proportionality constant

y=k/x

Now, cross multiply

k= y×x

k = -2×14

k = -28

y = -28/x

Hence, the equation is y = -28/x .

Learn more about proportionality here:

https://brainly.com/question/8598338

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Answer:

B. 3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Step-by-step explanation:

A B

Bread $3.19 $3.49

Milk $4.59 $4.39

Sue paid $137.24 in supermarket A

Sue paid $140.04 in supermarket B

Let

Price of bread A=$3.19

Price of bread B=$3.49

Price of milk A=$4.59

Price of milk B=$4.39

Quantity of Bread=b

Quantity of Milk=m

Pb=price of bread

Pm=price of milk

Qb=Quantity of bread

Qm=Quantity of milk

For each supermarket

Supermarket A Equation

PbQb + PmQm =$137.24

3.19b+ 4.59m = 137.24

Supermarket B Equation

PbQb + PmQm=$140.04

3.49b + 4.39m = $140.04

Combining both equations

3.19b + 4.59m = 137.24

3.49b + 4.39m = $140.04

Answer:

Surface area of the reflective glass is 543234.4 square feet.

Step-by-step explanation:

Given that: height = 311 feet, sides of square base = 619 feet.

To determine the slant height, we have;

[tex]l^{2}[/tex] = [tex]311^{2}[/tex] + [tex]309.5^{2}[/tex]

   = 96721 + 95790.25

   = 192511.25

⇒ l = [tex]\sqrt{192511.25}[/tex]

      = 438.761

The slant height, l is 438.8 feet.

Considering one reflecting surface of the pyramid, its area = [tex]\frac{1}{2}[/tex] × base × height

  area =  [tex]\frac{1}{2}[/tex] × 619 × 438.8

          = 135808.6

          = 135808.6 square feet

Since the pyramid has four reflective surfaces,

surface area of the reflective glass = 4 × 135808.6

                                                          = 543234.4 square feet

Answer:

The percent of households with rates from $100 to $115. is      [tex]P(100 < x < 115) =[/tex]94.1%

Step-by-step explanation:

From  the question we are told that  

   The  mean rate is [tex]\mu =[/tex]$ 106.50  per month

    The standard deviation is  [tex]\sigma =[/tex]$3.85

Let the lower rate be  [tex]a =[/tex]$100

Let the higher rate  be  [tex]b =[/tex]$ 115

Assumed from the question  that the data set is normally

The  estimate of the percent of households with rates from $100 to $115. is mathematically represented as

         [tex]P(a < x < b) = P[ \frac{a -\mu}{\sigma } } < \frac{x- \mu}{\sigma} < \frac{b - \mu }{\sigma } ][/tex]

here x is a random value rate  which lies between the higher rate and the lower rate so

     [tex]P(100 < x < 115) = P[ \frac{100 -106.50}{3.85} } < \frac{x- \mu}{\sigma} < \frac{115 - 106.50 }{3.85 } ][/tex]

      [tex]P(100 < x < 115) = P[ -1.688< \frac{x- \mu}{\sigma} < 2.208 ][/tex]

Where  

      [tex]z = \frac{x- \mu}{\sigma}[/tex]

Where z is the standardized value of  x

So

     [tex]P(100 < x < 115) = P[ -1.688< z < 2.208 ][/tex]

     [tex]P(100 < x < 115) = P(z< 2.208 ) - P(z< -1.69 )[/tex]

Now  from the z table we obtain that

      [tex]P(100 < x < 115) = 0.9864 - 0.0455[/tex]

     [tex]P(100 < x < 115) = 0.941[/tex]

    [tex]P(100 < x < 115) =[/tex]94.1%

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: 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:

The answer is "20".

Step-by-step explanation:

It is also known as the group of the study, that targets the population, which helps to find the survey, which is the sampled population. It is measured by an ideal world, which will be the same, and they're always unique.  

Answer:

184, 185, 186

Step-by-step explanation:

If the first number is x, the other numbers are x + 1 and x + 2, therefore we can write:

x + x + 1 + x + 2 = 555

3x + 3 = 555

3x = 552

x = 184 so the other numbers are 185 and 186.

Answer:

Aquarium dimensions:

x = 3,106 m

h = 6,22 m

C(min) = 1277,62 $

Step-by-step explanation: (INCOMPLETE QUESTION)

We have to assume:

The shape of the aquarium  (square base)

Let´s call "x" the side of the base, then h ( the heigh)

V(a) = x²*h          h = V(a)/x²      

Cost of Aquarium   C(a) = cost of the base (in stones) + 4* cost of one side (in glass)

C(a) = Area of the base *120 + 4*Area of one side*30

Area of the base is x²

Area of one side  is   x*h   or  x*V(a)/x²  

Area of one side is V(a)/x

C(x) = 120*x² + 4*30*60/x

C(x) = 120*x² +  7200/x

Taking derivatives on both sides of the equation we get

C´(x) = 2*120*x  - 7200/x²

C´(x) = 0 means    240 *x  - 7200/x² = 0

240*x³ - 7200 = 0

x³ = 7200/240

x = 3,106 m   and  h = 60 /x²     h =   6,22 m

and C (min) = 120*(3,106)³ - 7200 / 3,106

C(min) =  3595,72 - 2318,1

C(min) = 1277,62

Answer:

Savita will have more bags

Step-by-step explanation:

Savita: 250 cherries, 8 cherries per bag

Gail: 350 cherries, 12 cherries per bag

Savita: 250/8 = 31.25 bags

Gail: 350/12 = 29.17 bags

Savita will have more bags since 31.25 > 29.17

Answer:

Savita will have more bags

Step-by-step explanation:

Savita has 250 cherries and 8 cherries per bag

Gail has 350 cherries and 12 cherries per bag

Savita

=250/8 = 31.25 bags

Gail

=350/12 = 29.17 bags

therefore Savita will have more bags since 31.25 is more than Gail with 29.17 bags

Answer:

The temperature droped from 17 5/8° C to - 8 1/2° C = 26 1/8° C, simply add the 2 mixed fractions together and you'll get the temperture change.

Step-by-step explanation:

Convert to a mixed number:

209/8

Divide 209 by 8:

8 | 2 | 0 | 9

8 goes into 20 at most 2 times:

| | 2 | |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

8 goes into 49 at most 6 times:

| | 2 | 6 |  

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 |  

Read off the results. The quotient is the number at the top and the remainder is the number at the bottom:

| | 2 | 6 | (quotient)

8 | 2 | 0 | 9 |  

- | 1 | 6 | |  

| | 4 | 9 |  

| - | 4 | 8 |  

| | | 1 | (remainder)

The quotient of 209/8 is 26 with remainder 1, so:

Answer: 26 1/8° C

Answer:

Step-by-step explanation:

cool

Answer:

retype that im not understanding .

Step-by-step explanation:

Step-by-step explanation:

a = 14.56231 cm

b(width) = 9 cm

a+b = 23.56231 cm

A(area) = 343.1215 cm

Sorry if this doesnt help

Answer:

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Step-by-step explanation:

In a golden rectangle, the width is a and the length is a + b.

The proportion of the lengths of the sides is:

(a + b)/a = a/b

Here, the width is 9 cm, so we have a = 9 cm.

(9 + b)/9 = 9/b

(9 + b)b = 81

b^2 + 9b - 81 = 0

b = (-9 +/- sqrt(9^2 - 4(1)(-81))/(2*1)

b = (-9 +/- sqrt(81 + 324)/2

b = (-9 +/- sqrt(405)/2

b = -9/2 +/- 9sqrt(5)/2

Length = a + b = 9 - 9/2 +/- 9sqrt(5)/2

Length = a + b = 9/2 +/- 9sqrt(5)/2

Since the length of a side of a rectangle cannot be negative, we discard the negative answer.

length = [9/2 + (9/2)sqrt(5)] cm

length = 14.56 cm

Answer and Step-by-step explanation:

1. Data provided

[tex]\frac{d^2y}{dx^2} + 4y = x - x^2 + 20\\\\ \frac{d^2y}{dx^2} + 4y = - x^2 + x + 20[/tex]

Now as a non homogeneous part which is

[tex]- x^2 + x + 20[/tex] let us assume the computation is

[tex]y_p(x) = Ax^2 + Bx + C[/tex]

2. Data provided

[tex]\frac{ d^2y}{dx^2} + \frac{6dy}{dx} + 8y = e^{2x}[/tex]

As a non homogeneous part is [tex]e^2x[/tex] , let us assume the computation is

[tex]y_p(x) = Ae^{2x}[/tex]

3. Data provided

[tex]y'' + 4y' + 20y = -3sin2x[/tex]

As a non homogeneous part −3sin(2x), let us assume the computation is

[tex]y_p(x) = Acos(2x) + Bsin(2x)[/tex]

4. Data provided

[tex]y'' - 2y' - 15y = 3xcos(2x)[/tex]

As a non homogeneous part  3xcos(2x), let us assume the computation is

[tex]y_p(x) = (Ax+B)cos2x+(Cx+D)sin2x[/tex]

Answer:

11% of the Total the entire voting population

Step-by-step explanation:

Let's bear in mind that the total number of sample candidates is equal to 600.

But out of 600 only 66 preffered candidate A.

The proportion of sampled people to that prefer candidate A to the total number of people is 66/600

= 11/100

In percentage

=11/100 *100/1 =1100/100

=11% of the entire voting population

Answer:

it took 7 hours for the bread to drop at a constent rate

Step-by-step explanation:

Answer:

The hypothesis test is right-tailed.

Step-by-step explanation:

We are given that we want to test the claim that the majority of adults are in favor of raising the voting age to 21.

Let p = proportion of adults who are in favor of raising the voting age to 21

So, Null Hypothesis, [tex]H_0[/tex] : p [tex]\leq[/tex] 50%

Alternate Hypothesis, [tex]H_A[/tex] : p > 50%

As we know that the majority is there when we have more 50% chance of happening of that event.

Here, the null hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is less or equal to 50%.

On the other hand, the alternate hypothesis states that the proportion of adults who are in favor of raising the voting age to 21 is more than 50%.

This shows that our hypothesis test is right-tailed because in the alternate hypothesis, the greater than sign is included.

*see the attachment below for the missing figure

Answer:

[tex] sin B = \frac{24}{25} [/tex]

Step-by-step explanation:

Given a right angled triangle, ∆ABC

AB = 25

BC = 7

AC = 24

<ACB = 90°

Required:

Value of Sin B

Solution:

Using trigonometric ratio formula,

[tex] sin B = \frac{opposite}{hypotenuse} [/tex]

Opposite = AC = 24 (the side opposite to <B)

Hypotenuse = AB = 25 (the longest side facing the right angle)

[tex] sin B = \frac{24}{25} [/tex]

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:

13=x

Step-by-step explanation:

Since BE is a bisector

ABE = EBC

2x+20 = 4x-6

Subtract 2x from each side

2x+20-2x =4x-6-2x

20 = 2x-6

Add 6 from each side

20+6 = 2x-6+6

26 = 2x

Divide each side by 2

26/2 = 2x/2

13=x

Answer:

x = 13

Step-by-step explanation:

The angle bisector theorem means that m<ABE = m<EBC. Now that we know they are equal, we can set the equations to each other and solve for x.

2x + 20 = 4x - 6

26 = 2x

13 = x

So the value of x is 13.

Cheers.

Answer:

The height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Step-by-step explanation:

It is given that,

Distance between a person and an elephant is 15 ft

The angle of elevation of the elephant is 30 degrees.

We need to find the height of the elephant. For this let us consider that height is h. So,

[tex]\tan\theta=\dfrac{P}{B}\\\\\tan(30)=\dfrac{h}{15}\\\\h=15\times \tan(30)\\\\h=\dfrac{15}{\sqrt3}\ ft[/tex]

So, the height of the elephant is [tex]\dfrac{15}{\sqrt3}\ ft[/tex].      

Answer:

196 ft

6 seconds

Step-by-step explanation:

Solution:-

We have a quadratic time dependent model of the ball trajectory which is thrown from the top of a 96-foot building as follows:

                     [tex]y(t) = -16t^2 + 80t + 96[/tex]

The height of the ball is modeled by the distance y ( t ) which changes with time ( t ) following a parabolic trajectory. To determine the maximum height of the ball we will utilize the concepts from " parabolas ".

The vertex of a parabola of the form ( given below ) is defined as:

                     [tex]f ( t ) = at^2 + bt + c[/tex]

                    Vertex: [tex]t = \frac{-b}{2a}[/tex]

- The modelling constants are: a = -16 , b = 80.

                   [tex]t = \frac{-80}{-32} = 2.5 s[/tex]

- Now evaluate the given function " y ( t ) " for the vertex coordinate t = 2.5 s. As follows:

                    [tex]y ( 2.5 ) = -16 ( 2.5 )^2 + 80*(2.5) + 96\\\\y ( 2.5 ) = 196 ft\\[/tex]

Answer: The maximum height of the ball is 196 ft at t = 2.5 seconds.

- The amount of time taken by the ball to hit the ground can be determined by solving the given quadratic function of ball's height ( y ( t ) ) for the reference ground value "0". We can express the quadratic equation as follows:

                    [tex]y ( t ) = -16t^2 + 80t + 96 = 0\\\\-16t^2 + 80t + 96 = 0[/tex]

Use the quadratic formula and solve for time ( t ) as follows:

                    [tex]t = \frac{-b +/- \sqrt{b^2 - 4 ac} }{2a} \\\\t = \frac{-80 +/- \sqrt{80^2 - 4 (-16)(96)} }{-32} \\\\t = \frac{-80 +/- 112 }{-32} = 2.5 +/- (-3.5 )\\\\t = -1, 6[/tex]

Answer: The value of t = -1 is ignored because it lies outside the domain. The ball hits the ground at time t = 6 seconds.

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:

D.

m = 2 = figures/month

b = 20 = # of action figures

Answer:

[tex]B(a)=\frac{a}{5} -7[/tex]

Step-by-step explanation:

The input it taken as the unknown base value, while the output here is the area of the trapezoid. b is therefore the base value, and A( b ) is the area of the trapezoid. Let's formulate the equation for the area of the trapezoid, and isolate the area of the trapezoid. To find the inverse of this function, switch y ( this is A( b ) ) and b, solving for y once more, y ➡ y ⁻ ¹.

y = height [tex]*[/tex] ( ( unknown base value ( b ) + 7 ) / 2 ),

y = 10 [tex]*[/tex] ( ( b + 7 ) / 2 )

Now switch the positions of y and b -

b = 10 [tex]*[/tex] ( ( y + 7 ) / 2 ) or [tex]b=\frac{\left(y+7\right)\cdot \:10}{2}[/tex] - now that we are going to take the inverse ( y ⁻ ¹ ) or B( a ), b will now be changed to a,

[tex]y+7=\frac{a}{5}[/tex],

[tex]y^{-1}=\frac{a}{5}-7 = B(a)[/tex]

Therefore the equation that represents the inverse function will be the following : B(a) = a / 5 - 7

Answer:

We should reject H0

At the 5% significance level, there is sufficient evidence to conclude that the die is not fair.

Step-by-step explanation:

Null hypothesis is a statement that is to be tested against the alternative hypothesis and then decision is taken whether to accept or reject the null hypothesis. The critical value is 15.091 and  test statistic is 11.070. The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value Test statistics is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. In the given case p-value is less than critical value then we should reject the null hypothesis.

Answer:

1

Cans              4cans                  8 cans                   12 cans

Cost                $2.25                   $4.5                      $6.75

2

Ice Cream   180 q       360 q      540 q       720q        900q           1080 q

Hours       2 hours     4 hours    6 hours    8 hours   10 hours      12 hours

***q = quarts

3

Distance        650 miles           1300 miles           1950 miles

Hours              3 hours                 6 hours                9 hours

Answer:

Question 1 - 8 cans = $4.50, 12 cans = $10.13

Question 2 - 4 hours = 360 quarts, 6 hours = 540 quarts, 8 hours = 720 quarts, 12 hours = 1,170

Question 3 - 1,950 miles in 9 hours

Hope this helps :)

Answer:

I always factor out the -1 so my leading coefficient is 1

Step-by-step explanation:

-x^2 + 10x -24

I always factor out the -1 so my leading coefficient is 1

-1 ( x^2 -10x +24)

Then what 2 terms multiply to 24 and add to -10

-6*-4 = 24

-6+-4 = -10

-1( x-6)(x-4)

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