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3 years ago

Suppose that y varies directly with x and y=10 when x=20. What is y when x=15

Mathematics

1 answer:

Likurg_2 [28]3 years ago

4 0

Answer:

y=kx

subst y=10 and x=20 into the above

10=k20

k=10/20

k=1/2

therefore relationship: y=1/2x

subst x=15 into the relationship

y=1/2(15)

y=7,5

Step by step explanation:

Step 1: when they say y varies directly with x they mean y is proportional to x
step 2: so y=kx where k is the constant
step 3: is to substitute y=10 and x=20 into the above equation y=kx
step 4: you will end up with 10=k20 then divide both sides by 20 so that k becomes the subject of the formula 
step 5: your answer from the above will be k=10/20 so the relationship is y is directly proportional to 1/2 x what you did here is that you substituted k for 1/2 in the equation in step 3
step 6: is to finally substitute x=15 into the equation y=1/2x to finally get your answer y=7,5.

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A 12-sided die is rolled. The set of equally likely outcomes is {1,2,3,4,5,6,7,8,9,10,11,12). Find the probability of rolling a

levacccp [35]

Answer:

$P(x>12) = 0$

Step-by-step explanation:

Given

$x = \{1,2,3,4,5,6,7,8,9,10,11,12\}$ --- outcomes

$n(x) = 12$ -- sample size

Required

$P(x > 12)$

This is calculated as:

$P(x > 12) = \frac{n(x > 12)}{n(x)}$

$n(x>12) = 0$ because none of the outcomes is greater than 12:

So:

$P(x > 12) =\frac{0}{12}$

$P(x>12) = 0$

6 0

3 years ago

4x + 10 = 2x - 14 Find the value of x.

Gre4nikov [31]

Answer:

x= -12

Step-by-step explanation:

Simplifying

4x + 10 = 2x + -14

Reorder the terms:

10 + 4x = 2x + -14

Reorder the terms:

10 + 4x = -14 + 2x

Solving

10 + 4x = -14 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.

10 + 4x + -2x = -14 + 2x + -2x

Combine like terms: 4x + -2x = 2x

10 + 2x = -14 + 2x + -2x

Combine like terms: 2x + -2x = 0

10 + 2x = -14 + 0

10 + 2x = -14

Add '-10' to each side of the equation.

10 + -10 + 2x = -14 + -10

Combine like terms: 10 + -10 = 0

0 + 2x = -14 + -10

2x = -14 + -10

Combine like terms: -14 + -10 = -24

2x = -24

Divide each side by '2'.

x = -12

Simplifying

x = -12

3 0

3 years ago

Read 2 more answers

Hello! Can someone help with this question?

IgorC [24]

Hello! :)

$\large\boxed{\text{70 seconds}}$

Use a proportion to find how many seconds are needed to fold 5 shirts.

We are given that he takes 28 seconds to fold 2 shirts:

28 sec : 2 shirts

We are not given the amount of time needed for 5 shirts, which we need to solve:

x seconds : 5 shirts

Express in a fraction:

$\frac{2 shirts}{28 seconds} = \frac{5 shirts}{xseconds}$

Cross multiply and simplify:

$2 * x = 5 * 28\\\\2x = 140\\\\x = 70 sec$

Therefore, he needs 70 seconds to fold 5 shirts.

5 0

3 years ago

Which graph models the solution set of 50x + 150y>1500?

hodyreva [135]

Answer:

see attached diagram

Step-by-step explanation:

First, draw the dashed line 50x+150y=1500 (dashed because the inequality is without notion "or equal to"). You can do it finding x and y intercepts.

When x=0, then 150y=1500, y=10.

When y=0, then 50x=1500, x=30.

Connect points (0,10) and (30,0) to get needed dashed line.

Then determine which region (semiplane) you have to choose. Note that origin's coordinates (0,0) do not satisfy the inequality 50x + 150y>1500, because

$50\cdot 0+150\cdot 0=0$