For the data in the table, does y vary directly with x? If it does, write an equation for the direct variationx y
10 12
15 18
20 24

Answers

Answer 1

Answer: Say that:

$\left( { x }_( 1 ),{ y }_( 1 ) \right) =\left( 10,12 \right) \n \n \left( { x }_( 2 ),{ y }_( 2 ) \right) =\left( 15,18 \right) \n \n \therefore \quad \frac { \delta y }{ \delta x } =\frac { { y }_( 2 )-{ y }_( 1 ) }{ { x }_( 2 )-{ x }_( 1 ) } =\frac { 18-12 }{ 15-10 } =\frac { 6 }{ 5 } \n \n$

If this is the case,

$y=\frac { 6 }{ 5 } x$

Another way to solve the problem,

$y\propto x\n \n \therefore \quad y=kx$

When x=10, y=12, so...

$12=k\cdot 10\n \n k=\frac { 12 }{ 10 } =\frac { 6 }{ 5 } \n \n \therefore \quad y=\frac { 6 }{ 5 } x$

Answer 2

Answer:

Answer:

y=1.2x

Step-by-step explanation:

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Each week Marissa withdraws the same amount from her bank account the equation A=1550-90w represent the relationship between the amount of money remaining in her account ,A,in dollars , and the number of weeks of withdraws ,W. For how many weeks has Marissa made withdraws when the amount remaining in the account is $110??A)14B)16C)17D)18
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If 3t − 7 = 5t , then 6t = how do you solve this

Answers

$3t-7=5t \ \ \ |\hbox{subtract 3t} \n -7=5t-3t \n -7=2t \ \ \ |\hbox{multiply by 3} \n \boxed{6t=-21}}$

$3t-7=5t\n5t-3t=-7\n2t=-7|\cdot3\n\boxed{6t=-21}$

How do I complete each pattern, Example 1 block, 3 blocks,6 blocks

Answers

Well,

This could be an arithmetic sequence.
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
15 + 6 = 21
...

This could also be a geometric sequence.
1*3=3
3*2=6
6*1=6
6*0=0
0*-1=0
0*(anything)=0
...

Pablo and his wife are each starting a saving plan. Pablo will initially set aside $50 and then add $40.75 every week to the savings. The amount A (in dollars) saved this way is given by the function A=50+40.75N, where N is the number of weeks he has been saving. His wife will not set an initial amount aside but will add $60.75 to the savings every week. The amount B (in dollars) saved using this plan is given by the function B=60.75N. Let I be total amount (in dollars) saved using both plans combined. Write an equation relating I to N. Simplify your answer as much as possible.

Answers

Answer:

The equation relating the total amount saved (I) to the number of weeks (N) for both Pablo and his wife is I = 50 + 101.5N.

Step-by-step explanation:

To find the equation relating the total amount saved (I) to the number of weeks (N) for both Pablo and his wife, we need to add the amounts saved by each person.

For Pablo, the amount saved (A) is given by the function A = 50 + 40.75N, where N is the number of weeks. This means that after 1 week, Pablo will have saved $50 + $40.75, after 2 weeks, he will have saved $50 + 2($40.75), and so on.

For his wife, the amount saved (B) is given by the function B = 60.75N. This means that after 1 week, his wife will have saved $60.75, after 2 weeks, she will have saved 2($60.75), and so on.

To find the total amount saved (I) by both of them combined, we need to add the amounts saved by Pablo and his wife:

I = A + B

Substituting the given functions:

I = (50 + 40.75N) + (60.75N)

Simplifying, we combine like terms:

I = 50 + 40.75N + 60.75N

I = 50 + (40.75 + 60.75)N

I = 50 + 101.5N

So, the equation relating the total amount saved (I) to the number of weeks (N) for both Pablo and his wife is I = 50 + 101.5N.

The distribution of the weights of a sample of 1,500 cargo containers is symmetric and bellshaped. According to the Empirical Rule, what percent of the weights will lie: a. According to the Empirical Rule, what percent of the weights will lie between formula73.mml b. According to the Empirical Rule, what percent of the weights will lie betweenformula75.mml and student submitted image, transcription available below+1s c. Below formula75.mml-1s

Answers

Answer:

Step-by-step explanation:

According to the Empirical Rule, for a symmetric and bell-shaped distribution:

a. Approximately 68% of the weights will lie between formula73.mml. This means that about 34% of the weights will lie to the left of formula73.mml, and about 34% of the weights will lie to the right of formula73.mml.

b. Approximately 95% of the weights will lie between formula75.mml and formula75.mml +1s. This means that about 47.5% of the weights will lie to the left of formula75.mml +1s, and about 47.5% of the weights will lie to the right of formula75.mml.

c. Approximately 68% of the weights will lie below formula75.mml-1s. This means that about 34% of the weights will lie to the left of formula75.mml-1s.

These percentages are approximate values based on the Empirical Rule and provide a general understanding of the distribution of the weights in a symmetric and bell-shaped distribution.

The smith is generate one and a half times as much as their neighbors, the joneses. Together, the two households produce 15 bags of trash each month. How much trash does each household generate ?

Answers

Answer:

The Smith generates 6 bags of trash per month, and the Joneses generates 6 bags of trash per month.

Step-by-step explanation:

We know that

The Smith generates one and a half times trash as much as the Joneses.
Both families generate 15 bags of trash per month.

To solve this problem, we need to transform each statement in a equation.

$S=1(1)/(2)J$

Where $S$ represents the Smith, and $J$ represents the Joneses.

This expressions expresses the one and a half difference between the two families.

If both families produce 15 bags of trash, the equation would be

$S+J=15$

Now, we replace the first equation into the second one and solve for $J$

$1(1)/(2)J+J=15\n1.5J+J=15\n2.5J=15\nJ=(15)/(2.5)=6$

Then, we replace this value into one equation to find the other variable

$S+J=15\nS+6=15\nS=15-6\nS=9$

Therefore, the Smith generates 6 bags of trash per month, and the Joneses generates 6 bags of trash per month.

Smith = 1.5Jones
S=1.5J
S + J = 15
1.5J + J = 15
2.5J = 15
J = 6
S = 9

The videography team entered a contest and won amonetary prize of $1,350.
Which expression represents how much each person
would get if there were people on the team?
1350
х
1350 + x
1350
5
1350 - X