1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
vlada-n [284]
2 years ago
6

4) The quantities x and y are in proportion x 4 30 8 __b__ a) b) c) y 6 45 __a__ 15 Find the value of a and b. Find the constant

of variation. Is it direct variation or inverse variation?
Mathematics
1 answer:
Ivan2 years ago
3 0

Question:

The quantities x and y are in proportion

x      y

4      6

30   45

8      b

a      15

(a) Find the values of a and b.

(b) Find the constant of variation. Is it direct variation or inverse variation?

Answer:

a = 10 and b = 12

Constant of variation is 1.5

Direct Variation

Step-by-step explanation:

Solving (a): The values of a and b

First, we determine the equation that relates x and y

From the table, we have:

(x_1,y_1) = (4,6)

(x_2,y_2) = (30,45)

The slope (m) is:

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{45 - 6}{30 -4}

m = \frac{39}{26}

m = 1.5

The equation is then calculated using:

y - y_1 = m(x - x_1)

This gives:

y - 6 = 1.5(x - 4)

y - 6 = 1.5x - 6

y = 1.5x

Solving for the value of b

From the table: x = 8, y = b

Substitute these values in y = 1.5x

b = 1.5 * 8

b = 12

Solving for the value of a

From the table: x = a, y = 15

Substitute these values in y = 1.5x

15 = 1.5 * a

Solve for a

a = \frac{15}{1.5}

a = 10

Solving (b): The constant of variation.

This has been solved in (a) above as:

m = 1.5

Direct or Inverse?

From the given table, we notice that y increases as x increases and y decreases as x decreases.

<em>This shows direct variation</em>

You might be interested in
Given that f(x) = 2x + 1 and g(x) = the quantity of 3x minus 1, divided by 2, solve for g(f(3)). 5 7 9 10
AlladinOne [14]

The correct answer is 10.

In order to evaluate any composite function, you need to first put the value in for the inside function. In this case f(x) is on the inside along with the number 3. So, we input 3 in for x in f(x).

f(x) = 2x + 1

f(3) = 2(3) + 1

f(3) = 6 + 1

f(3) = 7

Now that we have the value of f(3), we can stick the answer in for the outside function, which is g(x).

g(x) = (3x - 1)/2

g(7) = (3(7) - 1)/ 2

g(7) = (21 - 1)/2

g(7) = 20/2

g(f(3)) = 10

5 0
3 years ago
What is 5r^2 = 80<br><br> It says solve each equation with the quadratic formula.
katovenus [111]
5r^2 = 80 \ \ /:5\\ \\r^2=\frac{80}{5}\\ \\r^2=16\\ \\r^2-16=0\\ \\ r^2 - 4^2 =0 \\ \\(r-4)(r+4)=0

r-4=0 \ \ \vee \ \ r+4 =0 \\ \\r=4 \ \ \vee \ \ r = -4 \\ \\ \\ a^2-b^2 = (a- b)(a+b)


5 0
3 years ago
A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40
bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. How large was the sample used in this survey?

We have that s = 25, \sigma = 400. We want to find n, so:

s = \frac{\sigma}{\sqrt{n}}

25 = \frac{400}{\sqrt{n}}

25\sqrt{n} = 400

\sqrt{n} = \frac{400}{25}

\sqrt{n} = 16

(\sqrt{n})^2 = 16^2[tex][tex]n = 256

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

3 0
3 years ago
A playstation 5 is $900 and costs $50 per game. A xbox is $400 and costs $60 per game. How many games will it take for both cons
belka [17]

Answer:

It would take a PlayStation 5 and 2 games to equal an Xbox and 10 games.

Step-by-step explanation:

I made a list that increase in the increments of the game price.

Something like this:

900—400~consoles alone

950—460~1 game

1000–520~2 games

1050—580~3 games

1100—640~4 games

1150—700~5 games

1200—760~6 games

1250—820~7 games

1300—880~8 games

1350—940~9 games

1400—1000~10 games

Left side is PlayStation 5 and right side is Xbox. The first row is the price of the consoles alone and then each row after that is the price of the console with an additional game. As you can see, the third row down on the left, the PlayStation 5 with 2 games is $1,000. If you look at the eleventh row on the right, you can see that Xbox with 10 games is also $1,000

3 0
2 years ago
Which equation is true for the value x = 15?
boyakko [2]
The third one because 2(15+5)=2(20)=40
4 0
3 years ago
Other questions:
  • If f(x)=-x+3 find f(-3)
    7·2 answers
  • Sam recorded how many punded he gained each month for four months and recorded the results as: 1/8, 0.75, 2/5, 5,6. list the amo
    10·1 answer
  • Solve each system of equations by adding, subtracting, or multiplying.
    15·1 answer
  • Solve please very ez​
    13·2 answers
  • If a 40 foot tree cast a 16 foot shadow, what is the length of the shadow cast by a 27 foot tree?
    11·2 answers
  • Help what is 4(3q+10)=6(2q-9)
    13·2 answers
  • Which numbers are rational? the dots, . . ., indecate tue pattern that continues.
    5·1 answer
  • -7+ 3x-2(3x+4)= 5(2x-3) + 4 (3x - 1) - 4.
    15·1 answer
  • 18-3(4.5-5) ÷ 10-2(3·2-16) =
    13·1 answer
  • Does anybody know how to find area of a triangle?
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!