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Q
The value of y varies directly as x and y = 9 when x = 6. What is the value of y when x = 15?

Answer:

[tex]x \le 5[/tex]

Step-by-step explanation:

Given

Shape: Cube

Dimensions: x, 3x and 2x

[tex]Volume < 900[/tex]

Required

Show that [tex]x \le 5[/tex]

First, calculate the volume

[tex]Volume = x * 3x * 2x[/tex]

[tex]Volume = 6x^3[/tex]

[tex]Volume < 900[/tex] becomes

[tex]6x^3 < 900[/tex]

Divide both sides by 9

[tex]x^3 < 150[/tex]

For [tex]x^3 < 150[/tex], the value of x as to be: 1, 2, 3, 4 or 5

Hence:

[tex]x \le 5[/tex]

Answer:

78

Step-by-step explanation:

Answer:

(4,5)

Step-by-step explanation:

Answer:

4x + 8

Step-by-step explanation:

Answer:

1/36 = 0.0278 = 2.78% probability that you guess the summer's top two must see movies if you randomly guess

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the movies are chosen is not important, which means that we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Desired outcomes:

Top two movies, so only one outcome, which means that [tex]D = 1[/tex]

Total outcomes:

Two movies from a set of 1. So

[tex]T = C_{9,2} = \frac{9!}{2!(9-2)!} = 36[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{1}{36} = 0.0278[/tex]

1/36 = 0.0278 = 2.78% probability that you guess the summer's top two must see movies if you randomly guess

Answer:

1.39%

Step-by-step explanation:

This is a permutation problem because order matters.

There are 9! ways to rank the summer's must-see movies.

There are (9−2)!=7! ways to choose two movies as the top two must-see movies.

P = 7!/9! = 1/72 = 0.0139

To express our answer as a percent, we multiply by 100:

0.0139 x 100 = 1.39%

Answer:

m∡A = 100°

m∡B = 50°

m∡C = 30°

Step-by-step explanation:

let 'x' = m∡B;  50°

let '2x' = m∡A;   100°

let 'x-20' = m∡C;   30°

x + 2x + x - 20 = 180

4x - 20 = 180

4x = 200

x = 50

Answer:

x=21

Step-by-step explanation:

69+90= 159

180-159=21

9514 1404 393

Answer:

  29

Step-by-step explanation:

Let w represent the number of wins. Then the number of losses is w-18. The total number of games played is ...

  wins + losses = 40

  w + (w-18) = 40

  2w = 58

  w = 29

The Rangers won 29 games.

Answer:

hi

Step-by-step explanation:

Daniel bought 1 pound of jelly beans and 2 pounds of chocolates for $2.00. ... for $1.50. How much would he have to pay on his next trip to the candy store if he bought 1 pound of each of the 4 kinds ... How many are there? Assign ... Multiply each equation by a factor, so that all equations will have the same total price: 3(1j +.

Answer:

20%

Step-by-step explanation:

Not sure if this is exactly correct, but let's say we start with 1 unit. If it increased by 25%, we get:

1 × 1.25 = 1.25 units.

Now, to get back to 1 unit, we need to find:

1.25 × ?  = 1

? = [tex]\frac{1}{1.25}[/tex] = 0.80

So, 100% - 80 % = 20%

A 20% decrease.

Not completely sure though.

Answer:

perimeter of square = 4×side.

36cm=4×side.

36/4=side.

9cm=side

Answer:

28

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

30% of 40 is 12, 40-12=28, the answer is 28.

Given:

A plane is normal to the vector = -2i+5j+k

It contains the point (-10,7,5).​

To find:

The component equation of the plane.

Solution:

The equation of plane is

[tex]a(x-x_0)+b(y-y_0)+c(z-z_0)=0[/tex]

Where, [tex](x_0,y_0,z_0)[/tex] is the point on the plane and [tex]\left< a,b,c\right>[/tex] is normal vector.

Normal vector is -2i+5j+k and plane passes through (-10,7,5). So, the equation of the plane is

[tex]-2(x-(-10))+5(y-7)+1(z-5)=0[/tex]

[tex]-2(x+10)+5y-35+z-5=0[/tex]

[tex]-2x-20+5y-35+z-5=0[/tex]

[tex]-2x+5y+z-60=0[/tex]

[tex]-2x+5y+z=60[/tex]

Therefore, the equation of the plane is [tex]-2x+5y+z=60[/tex].

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the straight lines.

y-y1 = m(x-x1) + C

====> y - 1 = 3(x - 2)

====> y-1 = 3x -6

====> y = 3x - 5

hence the equation is y = 3x - 5

Answer: 14

Step-by-step explanation

Do the prime factorization & it will give you 14

Answer:

8:6 and 16:12

Step-by-step explanation:

Answer:

137.67

Step-by-step explanation:

hello !

first, we find the midpoint of each interval in the score column (you can look for it by adding the two numbers and then dividing it by 2). then, we multiply the midpoint to the frequency:

1 - 7 is 4 = 4 * 17 = 68

8 - 10 is 9 = 9 * 15 = 135

11 - 15 is 13 = 13 * 13 = 169

16 - 20 is 18 = 18 * 6 = 108

23 - 35 is 29 = 29 * 6 = 174

36 - 50 is 43 = 43 * 4 = 172

now, we look for the mean, which we get by adding the sums and dividing the total with 6.

[tex]\frac{68+135+169+108+174+172}{6} = 137.6666667[/tex] or, when rounded to two decimal places, is equal to 137.67.

Answer:

y = 5x + (anything except negative 10)

For example:

y = 5x + 5

Step-by-step explanation:

A parallel equation is any equation with the same slope, but a different y intercept. As long as your y intercept isn't - 10, your answer will be parallel.

Answer:

a. [tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]

b. [tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]

c. 3.717 kg

Step-by-step explanation:

a) Write the differential equation that represents the problem.

Let A(t) be the amount of dissolved oxygen in the tank at any time, t.

The net flow rate dA(t)/dt = mass flow in - mass flow out

Since 10 g/l of oxygen flows in at a rate of 5 l/min, the mass flow in is 10 g/l × 5 l/min = 50 g/min

Since A(t) is the amount of oxygen present in the tank at time, t, and the volume of the tank is 400 liters. The concentration of oxygen in the tank is thus A(t)/400 g/l.

Also, water is being pumped out at a rate of 7 l/min. So, the mass flow out is thus concentration × flow rate out = A(t)/400 g/l × 7 l/min = 7A(t)/400 g/min

So, dA(t)/dt = mass flow in - mass flow out

dA(t)/dt = 50 - 7A(t)/400 with A(0) = 400 l × 1 g/l = 400 g since the tank initially contains 1 g/l of dissolved oxygen and has a volume of 400 l

So, the differential equation is

dA(t)/dt = 50 - 7A(t)/400  where A(0) = 400 g

[tex]dA(t)/dt = 50 - \frac{7A(t)}{400} where A(0) = 400[/tex]

b) Solve the differential equation

To solve the equation, we use separation of variables, so

dA(t)/dt = 50 - 7A(t)/400  where A(0) = 400 g

dA(t)/(50 - 7A(t)/400) = dt

Integrating both sides, we have

∫dA(t)/(50 - 7A(t)/400) = ∫dt

-7/400 ÷ -7/400∫dA(t)/(50 - 7A(t)/400) = ∫dt

1/ (-7/400)∫-7/400dA(t)/(50 - 7A(t)/400) = ∫dt

(-400/7)㏑(50 - 7A(t)/400) = t + C

㏑(50 - 7A(t)/400) = -7t/400 + (-7/400)C

㏑(50 - 7A(t)/400) = -7t/400 + C'     (C' = (-7/400)C)

taking exponents of both sides, we have

50 - 7A(t)/400 = exp[(-7t/400) + C']

50 - 7A(t)/400 = exp(-7t/400)expC'

[tex]50 - \frac{7A(t)}{400} = e^{-7t/400}e^{C'} \\50 - \frac{7A(t)}{400} = Ae^{-7t/400} A = e^{C'}\\ \frac{7A(t)}{400} = 50 - Ae^{-7t/400} \\A(t) = \frac{400}{7} X 50 - \frac{400}{7} Ae^{-7t/400} \\A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400}[/tex]

when t = 0 , A(0) = 400. So,

[tex]A(t) = \frac{20000}{7} - \frac{400}{7} Ae^{-7t/400} \\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{-7(0)/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0/400}\\A(0) = \frac{20000}{7} - \frac{400}{7} Ae^{0}\\A(0) = \frac{20000}{7} - \frac{400}{7} A\\400 = \frac{20000}{7} - \frac{400}{7} A\\\frac{400}{7} A = 400 - \frac{20000}{7}\\\frac{400}{7} A = \frac{2800}{7} - \frac{20000}{7}\\\frac{400}{7} A = -\frac{17200}{7}\\\\A = -\frac{17200}{7} X \frac{7}{400} \\A = -43[/tex]

So,

[tex]A(t) = \frac{20000}{7} - \frac{400}{7} X -43e^{-7t/400} \\A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}[/tex]

c) At 1 p.m., what is the amount of dissolve oxygen in the fish tank.

At 1 p.m, t = 60 min

So, the amount of dissolved oxygen in the fish tank is A(60)

So,

[tex]A(t) = \frac{20000}{7} + \frac{17200}{7}e^{-7t/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-7X60/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-420/400}\\A(60) = \frac{20000}{7} + \frac{17200}{7}e^{-1.05}\\A(60) = \frac{20000}{7} + \frac{17200}{7} X 0.3499\\A(60) = \frac{20000}{7} + \frac{6018.93}{7} \\A(60) = \frac{26018.93}{7} \\A(60) = 3716.99 g[/tex]

A(60) ≅ 3717 g

A(60) ≅ 3.717 kg

Answer:

P = 150 - 25w

Step-by-step explanation:

Amount borrowed = $150

Repayment amount = $25 each week

P = amount Nancy owes

w = number of weeks

Amount Nancy owes = amount borrowed - repayment plan per week

P = 150 - 25w

During the first week of repayment: when w = 1

P = 150 - 25w

P = 150 - 25(1)

= 150 - 25

= 125

P = $125

Answer:

D

Step-by-step explanation:

Because, the biologist wants to find the difference between the population of trouts from two watershed,

A biologist wants to compare the proportions of rainbow trout infected with whirling disease (an illness of trout and salmon caused by a microscopic parasite) coming from two separate watersheds.

The biologist will collect a random sample of trout and record the proportion infected in the sample The biologist intends to estimate the difference for all trout in the two watersheds

According to the given question, the most appropriate method for the biologist will be -A two-sample z-interval for a difference in population proportions

Because,Biologist wants to compare the proportions of rainbow trout infected with whirling disease and find the difference between the population of the trouts from two watershed .

Therefore , Statement D is the Correct

Learn more about Similar questions here : https://brainly.com/question/1904003

Answer:

a/..the first is 3/8

b/ 84/280

Answer:

a) 3/8

b) 3/10

Step-by-step explanation:

multiply the numerators and the denominators and then simplify.

a) is just 3*1 divided by 4*2, no simplification possible

b) is 4*21 divided by 7*40 is 84/280 and simplifies to 3/10 (divide by 28)

Answer:

Y<2x

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

the answer is a

Answer:sorry I don’t speak proeze najsztbsza but do you know the way

Step-by-step explanation:

Answer:

Step-by-step explanation:

Credit card interest is what are you are charged when you don't pay your credit card bill in full each month. It works as a daily rate calculated by dividing your annual percentage rate by 365, and then multiplying your current balance by the daily rate. That amount is then added to your bill.