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4. Suppose y varies inversely with the x, and y = -1 when = 3. What inverse variation equation relates x and y?

a. y = 3/x
b. b. y = -3x
c. y = 3x
d. y = -3/x

5. Suppose y varies inversely with x and y = 68 when x = 1/17. What is the value of x when y = 16?

a. 64
b. 32
c. 1/4
d. 1/16

6. Suppose y varies inversely with x, and y = 5 when x = 15. What is the value of y when x = 25
a. 3
b. 5
c. 25
d. 15

Answer:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Step-by-step explanation:

We need to find 9 rational number between [tex]\dfrac{8}{7}\ \text{and}\ \dfrac{17}{10}[/tex]

We make the denominators of both fractions same. So,

[tex]\dfrac{8}{7}\times \dfrac{10}{10}=\dfrac{80}{70}[/tex]

and

[tex]\dfrac{17}{10}\times \dfrac{7}{7}=\dfrac{119}{70}[/tex]

The rational number are:

[tex]\dfrac{81}{70},\dfrac{82}{70},\dfrac{83}{70},\dfrac{84}{70},\dfrac{85}{70},\dfrac{86}{70},\dfrac{87}{70},\dfrac{88}{70},\dfrac{89}{70}[/tex]

Answer:

18

Step-by-step explanation:

Supplementary angles means sum of angles is 180.

4x + 4 + 6x - 4 = 180

4x + 6x + 4 - 4 = 180

10x = 180

x = 180 / 10

x = 18

Answer:

x=18 degree

Step-by-step explanation:

If they are supplementary angles, then their sum = 180 degree

4x+4 + 6x-4 =180

4x+6x + 4-4 = 180

10x = 180

x=180/10

x=18

9514 1404 393

Answer:

  (f-g)(x) = 4x^3 +7x^2 -6x +1

Step-by-step explanation:

(f -g)(x) = f(x) -g(x)

  = (4x^3 +7x^2 -2x -1) -(4x -2)

  = 4x^3 +7x^2 +(-2-4)x +(-1+2)

(f -g)(x) = 4x^3 +7x^2 -6x +1

Pentagon has sum of 540°

Answer:

Option A

Step-by-step explanation:

Histogram shows the range of data on the x-axis while the frequency of occurrence is on the y-axis.

We have the following ranges from the Histogram ;

0 to 11

11 to 22

22 to 33

33 to 44

44 to 55

55 to 66

66 to 77

77 to 88

88 to 99

99 to 110

From the given set of data, the frequency according to the range is as follows;

0 to 11; 4

11 to 22; 8

22 to 33; 7

33 to 44; 6

44 to 55; 4

55 to 66; 2

66 to 77; 2

77 to 88; 1

88 to 99; 0

99 to 110; 1

The only Histogram that corresponds to these frequency is option A

Answer:

5v2 – 125 = 0

5(v2−25)=0

v2−25=0

a couple more steps and the answer is...

v=-5

Answer:

1) C

2) D

3) A

4) B

hope it helps

Answer:

52/3

Step-by-step explanation:

Use basic Thales therom,

[tex]\frac{3x}{4x}=\frac{3x+7}{5x-8}\\\\\frac{3}{4}=\frac{3x+7}{5x-8}\\[/tex]

Cross multiply,

3*(5x-8)=4*(3x+7)

3*5x - 3*8 = 4*3x + 4*7

15x - 24 = 12x +28

Add 24 to both sides

15x = 12x + 28 + 24

15x = 12x + 52

Subtract 12x from both sides

15x-12x =52

3x = 52

Divide both sides by 3

x = 52/3

Answer:

The angle between them is 60 degrees

Step-by-step explanation:

Given

[tex]a = 2i + j -3k[/tex]

[tex]b = 3i - 2j -k[/tex]

Required

The angle between them

The cosine of the angle between them is:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

First, calculate a.b

[tex]a \cdot b =(2i + j -3k) \cdot (3i - 2j -k)[/tex]

Multiply the coefficients of like terms

[tex]a \cdot b =2 * 3 - 1 * 2 - 3 * -1[/tex]

[tex]a \cdot b =7[/tex]

Next, calculate |a| and |b|

[tex]|a| = \sqrt{2^2 + 1^2 + (-3)^2[/tex]

[tex]|a| = \sqrt{14[/tex]

[tex]|b| = \sqrt{3^2 + (-2)^2 + (-1)^2}[/tex]

[tex]|b| = \sqrt{14}[/tex]

Recall that:

[tex]\cos(\theta) = \frac{a\cdot b}{|a|\cdot |b|}[/tex]

This gives:

[tex]\cos(\theta) = \frac{7}{\sqrt{14} * \sqrt{14}}[/tex]

[tex]\cos(\theta) = \frac{7}{14}[/tex]

[tex]\cos(\theta) = 0.5[/tex]

Take arccos of both sides

[tex]\theta =\cos^{-1}(0.5)[/tex]

[tex]\theta =60^o[/tex]

9514 1404 393

Answer:

  6

Step-by-step explanation:

Work backward.

If he has 24 after adding 6, he had 18 before that addition.

If he had 18 after tripling his collection, he had 18/3 = 6 cards to start with.

__

Note that this is the same process you would use if you started with an equation.

  3c +6 = 24 . . . . where c is the number of cards Johnny started with

  3c = 24 -6 = 18 . . . . . subtract 6 from the final number

  c = 18/3 = 6 . . . . . . . . divide the tripled value by 3 to see the original value

Johnny started with 6 cards.

Answer:

The probability that the company will receive 7 property damage claims on a randomly selected day is 0.137

Step-by-step explanation:

Given,

[tex]\lambda=6[/tex],

The probability mass function of Poisson distribution is used for evaluating the probability of the company will receive 7 property damages claims on any selected day is,

[tex]\begin{aligned}P(X=K)&=e^{-6} \times \dfrac{6^7}{7!}\\&=0.002478\times\dfrac{279936}{5040}\\&=\dfrac{693.89136}{5040}\\P(X=7)&=0.1365927874\\P(X=7)&=0.137\; (\rm{rounded \;off})\end{aligned}[/tex]

To learn more about this, please refer to the below link:

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Answer:

4r + 4(r + 3) = 68

r = 7 miles per hour

r + 3 = 10 miles per hour

Step-by-step explanation:

distance = rate * time

a)

4r + 4(r + 3) = 68

Distribute

4r + 4r + 12 = 68

8r + 12 = 68

8r = 56

r = 7 miles per hour

r + 3 = 10 miles per hour

Answer:

A 1/2

Step-by-step explanation:

Ratio of short length to hypotenuse

= cos60

= 1/2

Answer:

[tex]Var = 1.9[/tex]

Step-by-step explanation:

Given

[tex]p = \frac{1}{20}[/tex]  i.e. 1 per 20cc of water

[tex]n = 40[/tex] -- sample size

Required

The variance

This is calculated using:

[tex]Var = np(1 - p)[/tex]

So, we have:

[tex]Var = 40 * \frac{1}{20} * (1 - \frac{1}{20})[/tex]

[tex]Var = 40 * \frac{1}{20} * \frac{19}{20}[/tex]

[tex]Var = 2 * \frac{19}{20}[/tex]

[tex]Var = \frac{38}{20}[/tex]

[tex]Var = 1.9[/tex]

Answer:

11 + 10i

Step-by-step explanation:

Just treat i like any other variable, and combine like terms. Hope that helps!

Answer:

[tex](a)\ P(White) = \frac{1}{2}[/tex]

(b) 10 additional white balls

(c) 10 additional black balls

Step-by-step explanation:

Given

[tex]White = 5[/tex]

[tex]Black =3[/tex]

[tex]Red = 2[/tex]

Solving (a): P(White)

This is calculated as:

[tex]P(White) = \frac{White}{Total}[/tex]

[tex]P(White) = \frac{5}{5+3+2}[/tex]

[tex]P(White) = \frac{5}{10}[/tex]

[tex]P(White) = \frac{1}{2}[/tex]

Solving (b): Additional white balls, if [tex]P(White) = \frac{3}{4}[/tex]

Let the additional white balls be x

So:

[tex]P(White) = \frac{White+x}{Total+x}[/tex]

This gives:

[tex]\frac{3}{4} = \frac{5+x}{10+x}[/tex]

Cross multiply

[tex]30+3x = 20 + 4x[/tex]

Collect like terms

[tex]4x - 3x = 30 - 20[/tex]

[tex]x = 10[/tex]

Hence, 10 additional white balls must be added

Solving (c): Additional black balls, if [tex]P(White) = \frac{1}{4}[/tex]

Let the additional black balls be x

So:

[tex]P(White) = \frac{White}{Total+x}[/tex]

So, we have:

[tex]\frac{1}{4} = \frac{5}{10+x}[/tex]

Cross multiply

[tex]10+x = 5 * 4[/tex]

[tex]10+x = 20[/tex]

Collect like terms

[tex]x = 20 -10[/tex]

[tex]x = 10[/tex]

Hence, 10 additional black balls must be added

Answer:

p and q are two numbers.whrite down an expression of

Answer:

x > 2, x < -8

Interval notation:

( -infinity, -8) U (2, infinity)

Step-by-step explanation:

x(x+6) > 16

distribute x into x+6, multiply

x^2 + 6x > 16

bring 16 to left side, subtract

x^2 + 6x - 16 > 0

factors of -16 that add to +6 is -2 and +8

(x - 2)(x + 8) > 0

solve for x:

x < -8,  x > 2

Interval notation:

( -infinity, -8) U (2, infinity)

Answer:

45°

Step-by-step explanation:

<lmk=90°

angles in a triangle add up to 180

45+90+<o=180

<o=180-135

<o=45

Answer:

∠ O = 45°

Step-by-step explanation:

The angle between the tangent and the radius at the point of contact is 90°

The sum of the 3 angles in Δ OML is 180° , then

∠ O = 180° - (90 + 45)° = 180° - 135° = 45°

Answer:

100

Step-by-step explanation:

f(1) = 1

f(2) = -10×f(1) = -10 × 1 = -10

f(3) = -10×f(2) = -10 × -10 × f(1) = -10 × -10 × 1 = 100

f(n) = -10 to the power of n-1

Answer:

c - 100

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

Metro and Medec

METRO

Post-merger Financial Position, using the pooling of interest method:

Pre-merger Financial Positions:

                           Metro (RM ‘000)

Assets  

Current assets                          120

Fixed assets                             830

Total assets                             950

Liabilities and Equities  

Current liabilities                      40

Long term debt                      200

Common stock (RM1 par)      480

Capital surplus                       120

Retained earnings                  110

Total liabilities and equity    950

Earnings available to

common stockholders            230

Common Dividends                  150

Addition to Retained Earnings  80

Step-by-step explanation:

Pre-merger Financial Positions:

                           Metro (RM ‘000)    Medec(RM ‘000)

Assets  

Current assets                          50                     70

Fixed assets                           650                    180

Total assets                            700                   250

Liabilities and Equities  

Current liabilities                      30                     10

Long term debt                       140                    60

Common stock (RM1 par)      400                    80

Capital surplus                         50                    70

Retained earnings                   80                    30

Total liabilities and equity     700                 250

Earnings available to

common stockholders            100                  130

Common Dividends                  50                  100

Addition to Retained Earnings 50                   30

Exchange ratio = 1:2

9514 1404 393

Answer:

  (c)

Step-by-step explanation:

  [tex]\displaystyle\sqrt[3]{xy^5}\sqrt[3]{x^7y^{17}}=\sqrt[3]{x^{1+7}y^{5+17}}=\sqrt[3]{x^6x^2y^{21}y}=\sqrt[3]{x^6y^{21}}\sqrt[3]{x^2y}\\\\=\boxed{x^2y^7\sqrt[3]{x^2y}}[/tex]

Answer:

??????

Step-by-step explanation:

Answer:

Ok so on a clock there is 12 numbers where 12 is on top so at 12 am and 12 pm noon and midnight you will be at the top of the clock

Hope This Helps!!!

During the ride on the London Eye, you will be at the same height as the top of the Elizabeth Tower at approximately 21 minutes and 43.16 seconds after the start of the ride.

To determine the time(s) during the ride on the London Eye when you are at the same height as the top of the Elizabeth Tower (commonly known as Big Ben), we need to consider the height of the London Eye and its rotational motion.

Given that the Elizabeth Tower is 320 feet tall, we need to find the position of the London Eye when its height aligns with the top of the tower.

The London Eye has a height of 443 feet, and it completes one full rotation in approximately 30 minutes (or 1800 seconds). This means that it moves at a constant angular velocity of 360 degrees per 1800 seconds.

To find the time(s) when the heights align, we can set up a proportion:

(Height of the Elizabeth Tower) / (Height of the London Eye) = (Angle covered by the London Eye) / 360 degrees

Substituting the given values:

320 / 443 = (Time to align) / 1800

Simplifying the equation:

(Time to align) = (320 / 443) * 1800

Calculating the value:

(Time to align) ≈ 1303.16 seconds

Converting the time to minutes and seconds:

(Time to align) ≈ 21 minutes and 43.16 seconds

Therefore, during the ride on the London Eye, you will be at the same height as the top of the Elizabeth Tower at approximately 21 minutes and 43.16 seconds after the start of the ride.

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Answer:

71

Step-by-step explanation:

The measure of angle WXY will be thee ame as the measure of the intercepted arc, 109°.

W and Y are both tangent to the circle; this means angle XWZ and angle XYZ are both 90°.

Every quadrilateral has a total measure of 360°; to find the measure of WZY, we subtract:

360-90-90-109 = 71°

The measure of angle WZY (∠WZY) is; 71°

From the attached image, we can say that the measure of ∠WXY will be the same as the measure of the intercepted arc, 109°.

Now, W and Y are both tangent to the circle and this means that ∠XWZ and ∠XYZ are both equal to 90°.

Now, every quadrilateral has a total internal sum of angles as 360°.

Thus,  ∠WZY is gotten from;

∠WZY = 360 - (90 + 90 + 109)

∠WZY = 71°

Read more about angles in cyclic quadrilaterals at; https://brainly.com/question/24368895

Answer:

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Step-by-step explanation:

thankyou and have nice day