Solve for x:
4(x + 2) = 3(x - 2)

Answer:

Step-by-step explanation: My variables are

d=big number q=small number

My equations are 6=3q2d+3=qI

will solve for q in first equation 6/3 = 3q/32=q

Now I will pluck back in to get d2d+3=(2)   -3   -32d=-12d/2=-½d=-1/4 So the solution is(-1/4, .2)

The graph of y = 3(x + 1) is a vertical stretch of the graph of y = x + 1 by a factor of 3 and a translation of 1 unit to the left.

To see why, let's rewrite y = 3(x + 1) as y = 3x + 3. This equation has the same slope as y = x + 1, which is 1. However, the y-intercept is different. For y = x + 1, the y-intercept is (0, 1), while for y = 3x + 3, the y-intercept is (0, 3). This means that the graph of y = 3x + 3 is shifted vertically upward by 2 units compared to the graph of y = x + 1.

Next, let's look at how the graph of y = 3x + 3 is stretched vertically compared to the graph of y = x + 1. The factor of 3 in front of the parentheses in y = 3(x + 1) means that the y-coordinate of each point on the graph of y = x + 1 is multiplied by 3. This stretches the graph vertically by a factor of 3.

So, in summary, the graph of y = 3(x + 1) is the graph of y = x + 1 shifted 1 unit to the left and stretched vertically by a factor of 3.

Answer:

Hope I helped!~

Step-by-step explanation:

To find the equation of the line, we can use the slope-intercept form of the equation:

y = mx + b

where m is the slope of the line and b is the y-intercept.

Using the two data points given, we can calculate the slope:

m = (11.25 - 8.35) / (1995 - 1993) = 1.95

To find the y-intercept, we can use one of the data points:

8.35 = 1.95(1993) + b

b = -3884.65

So the equation of the line is:

y = 1.95x - 3884.65

To predict the price of a box of two pieces on July 1, 1999, we can substitute x = 6 (since 1999 is 6 years after 1993) into the equation:

y = 1.95(6) - 3884.65

y = 11.7 - 3884.65

y = -3872.95

This gives us a negative price, which obviously does not make sense. It is likely that the price of a box of two pieces was not linearly increasing during this time period, or that there were other factors influencing the price. Therefore, we cannot use this equation to accurately predict the price of a box of two pieces on July 1, 1999.

Answer:

(5, 2 )

Step-by-step explanation:

5x + 2y = 29 → (1)

x + 4y = 13 → (2)

multiplying (1) by - 2 and adding to (2) will eliminate y

- 10x - 4y = - 58 → (3)

add (2) and (3) term by term to eliminate y

- 9x + 0 = - 45

- 9x = - 45 ( divide both sides by - 9 )

x = 5

substitute x = 5 into either of the 2 equations and solve for y

substituting into (2)

5 + 4y = 13 ( subtract 5 from both sides )

4y = 8 ( divide both sides by 4 )

y = 2

solution is (5, 2 )

Answer:

$2,250 in interest

Step-by-step explanation:

The simple interest formula applicable here is

i = prt, where p is the principal (initial value), r is the interest rate as a decimal fraction, and t is the number of years elapsed.

Here we have i = $15,000(0.0375)(4) = $2,250 in interest

A fraction is the numerator divided by the denominator best describes a fraction.

Given,

- A fraction is the denominator divided by the numerator.

- A fraction is the numerator divided by the denominator.

- A fraction is the numerator multiplied by the denominator.

- A fraction is the denominator multiplied by the numerator.

We need to find which option best describes a fraction.

A fraction has two parts: Numerator and Denominator.

It is in the form of Numerator / Denominator.

We have,

- A fraction is the denominator divided by the numerator.

It is written as denominator / Numerator.

- A fraction is the numerator divided by the denominator.

It is written as Numerator / Denominator

- A fraction is the numerator multiplied by the denominator.

It is written as Numerator x Denominator.

- A fraction is the denominator multiplied by the numerator.

It can be written as Denominator x Numerator.

We see that the option "a fraction is a numerator divided by the denominator" is the correct answer.

Thus A fraction is the numerator divided by the denominator best describes a fraction.

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Answer:

9-6r

Step-by-step explanation:

9(1−r)+3r

Use the distributive property to multiply 9 by 1−r.

9−9r+3r

Combine −9r and 3r to get −6r.

Answer: 9−6r

Answer:

-6r + 9

Step-by-step explanation:

9( 1 - r ) + 3r

9 - 9r + 3r

9 - 6r

So, the answer is -6r + 9

Answer:

A. It was decreasing by -138,629.44 barrels

B. 26 years of time

Step-by-step explanation:

Due to the length of this question solution, I was unable to type it. The answer is contained in the attachment.

A. At 1200000

Bt = 1200000

-1/6ln2 x 1200000

Solve this using a calculator

= -138,629.4361

So the amount of oil is decreasing by -138,629.44 barrels

Violin to Celio.

Violin : Celio

Violin = 6

Celio = 5

6:5

D. 6/5

61 gallons are needed to cover the whole area.

The area that needs to be covered is the ring with an inner radius of 9 yards and an outher radius of 14 yards, so the area is:

A = 3.14*( (14yd)² - (9yd)²)

A = 361.1 yd²

and each gallon covers 6 yd², so you need x gallons, such that:

x*6 = 361.1

x = 361.1/6

x = 60.2

rounding to the next whole, we get 61.

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The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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The motivations for producers and consumers in the black market are largely driven by financial incentives and a desire to avoid legal consequences.

The black market refers to the illegal trade of goods and services that are not permitted by law, such as drugs, counterfeit items, and stolen goods. Producers and consumers in the black market are motivated by a variety of factors, including:

High profits, Producers in the black market can earn higher profits than they would in legal markets due to the lack of regulation and taxes.

Escaping legal consequences: Producers and consumers may participate in the black market to avoid legal consequences, such as fines or imprisonment, for engaging in illegal activities.

Limited availability, Some goods and services are only available on the black market due to legal restrictions or limited supply.

Low prices, Consumers in the black market can often purchase goods and services at lower prices than in legal markets due to the lack of taxes and regulations.

Desire for anonymity, The black market can provide anonymity for both producers and consumers, allowing them to engage in illegal activities without fear of detection or retribution.

However, participating in the black market also comes with significant risks, including the possibility of arrest, fines, and even violence.

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The area of the shaded region is  104 cm²

First, we need to know that the area of a circle is calculated using the formula;

A = πr²

Such that the parameters of the formula are;

First, let us find the area of the small circle

Area = 3.14 × 4²

Find the square value and multiply, we have;

Area = 50.24cm²

Area of the large circle = 3.14 × 7²

Find the square value and multiply

Area = 153. 86cm²

Area of the shaded region = Area of large circle - area of small circle

= 153.86 - 50.24

= 104 cm²

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Answer:

b/3 = c - 6

Step-by-step explanation:

A number b divided by 3 is 6 less than a number c

b/3 = c - 6

Answer:

---------------

Let the numbers be s and l.

We are given that:

Set up equations:

Eliminate l:

Solve for s:

Find l:

Answer: Liquid B is warmer.

Step-by-step explanation:

The data that we have is:

Temperature A = -105.4° C

Temperature B = -10.83° C

We want to know which liquid is warmer, this is equivalent to see which temperature is bigger, Ta or Tb.

Now, you can see that temperature A is larger in module, but this is a negative number.

When we work with negative numbers, the bigger ones are the ones closer to zero. This means that for example, -1 is larger than - 150.

From this, we can conclude that Liquid B is warmer.

Another way to see it is with a change of units.

If we have A degrees Celcius, and we want to to transform it into Kelvins, we must add 273.15°.

Then we have:

Ta = (-105.4° + 273.15°) K = 167.75 K

Tb = (-10.83 ´273.15°) = 262.35 K

where you can see that liquid B has a larger temperature.

Answer:

Liq A= -105.4ºC < LiqB= -10.83ºC

Step-by-step explanation:

Hello!

The easiest and quickest way to compare two negative values and determine which one is greater is by sorting them in a number line. (Check attachment)

You can also compare the absolute value of the temperature measurements. |10.83| < |105.4|. As the negative value decrease, the absolute value increases.

So the temperature of Liquid B > Temperature of liquid A.

I hope this helps!

Answer:

1.)-4

2.) 2/5

3.) -1/3

4.)2

Step-by-step explanation:

y2-y1

---------

x2-x1

The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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Answer:

25%

Step-by-step explanation:

Answer:

The time used for the show itself is 45 minutes.

Step-by-step explanation:

25% of 60 minutes were used for the credits. We can see how long the credits last by dividing 60 by 4.

60 ÷ 4 = 15

We know that 15 minutes were used for the credits. That leaves 45 minutes

(60 - 15 = 45) for the program itself!

The rates and the car value are 86.3% and 7679.66 respecyivelt

A) The annual rate

The function is represented as

y = ab^x

Where

a = 45000 i.e. value in 1991

So, we have

y = 45000b^x

In 2000, we have

45000b^9 = 12000

This gives

b^9 = 0.266

Solving for b, we have

9ln(b) = ln(0.266)

So, we have

ln(b) = ln(0.266)/9

This gives

b = e^(ln(0.266)/9)

Evaluate

b = 0.863

B) To convert the rate to a percentage, we multiply by 100 and add the percent symbol:

b = 0.863

So, we have

b = 86.3%

C) If the car value continues to drop by the same percentage, we can use the formula:

Value = 45000* (0.863)^12

Evaluate

Value = 7679.66

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A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

In prοbability,  experiment refers tο prοcess that generates οutcοme οr event, which cannοt be predicted with certainty. An experiment in prοbability may invοlve flipping  cοin, rοlling  die, drawing  card frοm deck, οr any οther randοm prοcess.

Part A:

The tοtal number οf cards in  hat is:

12 (red) + 17 (blue) + 14 (purple) + 7 (yellοw) = 50 cards

theοretical prοbability οf drawing purple card frοm hat is are:

P(purple) = number οf purple cards / tοtal number οf cards

P(purple) = 14 / 50

P(purple) = 0.28 οr 28%

Part B:

theοretical prοbability οf drawing purple card frοm  hat are 0.28 οr 28%.

The experimental prοbability οf drawing a purple card is:

P(exp) = number οf times a purple card is drawn / tοtal number οf trials

P(exp) = 324 / 1080

P(exp) = 0.3 οr 30%

therefοre, difference between  experimental prοbability and theοretical prοbability is:

P(exp) - P(theοretical) = 0.3 - 0.28

P(exp) - P(theοretical) = 0.02 οr 2%

Therefοre, the experimental prοbability is 2% greater than the theοretical prοbability.

A. The theοretical prοbability οf drawing a purple card frοm the hat is 0.28 οr 28%.

B. The experimental prοbability οf drawing a purple card is 2% greater than the theοretical prοbability.

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Answer:

x=55

Step-by-step explanation:

since it’s a right angle do 90*-35*=55*
Hope this helps! ;-)

A. Right triangles.

B. Height of 16cm with bases 20cm

C. 320

D.?

you can start by dividing the total length of the road by the distance that can be repaired per week:

13 km ÷ 3 1/2 km/week = 3.71 weeks

Rounding up, it will take 4 weeks to repair the entire 13 km stretch of road.

The interval where function f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

We have,

The function f(x) crosses the x-axis at (-3, 0), (-1.1, 0), and (0.9, 0), it means that f(x) is negative for x values less than -3, between -1.1 and 0.9, and greater than 0.

Therefore, we can say that:

f(x) < 0 for x < -3 and -1.1 < x < 0.9

And,

The function f(x) has a minimum value of (0, -3) and a maximum value of (-2.4, 17).

This means that f(x) is positive for x values greater than -2.4. Therefore, we can say that:

f(x) > 0 for x > -2.4

Now,

Combining these inequalities, we can say that f(x) is negative over the intervals (-∞, -3) and (-1.1, 0.9), and positive over the interval (-2.4, ∞).

So,

The interval where f(x) is negative and greater than 0 is:

(-∞, -3) U (-1.1, 0)

Thus,

The interval where f(x) is negative and greater than 0 is (-∞, -3) U (-1.1, 0)

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The correlation coefficient is,

This is the interpretation of the correlation coefficient,

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The probability that a randomly selected integer from the first 100 positive integers is divisible by 3 or 5 is 47/100. The events of choosing an integer divisible by 3 and choosing an integer divisible by 5 are not independent.

To find the probability that a randomly selected integer from the first 100 positive integers is divisible by 3 or 5, we need to count the number of integers in this range that are divisible by 3 or 5, or both.

There are 33 integers in the range from 1 to 100 that are divisible by 3: 3, 6, 9, ..., 99. Similarly, there are 20 integers in this range that are divisible by 5: 5, 10, 15, ..., 100. However, some of these integers are divisible by both 3 and 5, which means we have counted them twice. To find the total number of integers that are divisible by 3 or 5, we need to subtract the number of integers that are divisible by both 3 and 5 (which are the multiples of 15):

33 + 20 - 6 = 47

So, there are 47 integers out of the first 100 positive integers that are divisible by 3 or 5.

To find out whether the two events of choosing an integer divisible by 3 and choosing an integer divisible by 5 are independent, we need to check whether the probability of one event changes if the other event has already occurred.

Let A be the event of choosing an integer divisible by 3, and B be the event of choosing an integer divisible by 5. We can find the probabilities of these events as follows:

P(A) = 33/100

P(B) = 20/100

To check for independence, we need to compare the probability of A given that B has occurred (i.e., the probability of choosing an integer divisible by 3, given that we know it is also divisible by 5) with the probability of A without any information about B:

P(A|B) = P(A and B) / P(B)

Since the multiples of 15 are the only integers that are divisible by both 3 and 5, we have:

P(A and B) = P(15) / 100 = 1/20

So,

P(A|B) = (1/20) / (20/100) = 1/4

This means that if we know an integer is divisible by 5, the probability that it is also divisible by 3 is 1/4.

Now, let's compare this with the probability of A without any information about B:

P(A) = 33/100

Since P(A|B) ≠ P(A), we can conclude that the events of choosing an integer divisible by 3 and choosing an integer divisible by 5 from the first 100 positive integers are not independent.

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Answer:

The low tide level is 0, integer as 0

Step-by-step explanation:

The tide is at the numberline point 0, making it at integer 0.

Please let me know if I need to change the answer via comments (pls don't report me)

Answer:

D 40 and 50

Step-by-step explanation:

Complimentary angles are equal to 90

Answer: D, 40 and 50

Steps:

1. Since complementary angles equal 90 degrees, 4r + 5r = 90

2. 4r + 5r is 9r

3. This makes the equation, 9r=90

4. Divide both sides by 9, and then you get r=10

5. Substitute r=10 into 4r and 5r

6. This should make 4(10) and 5(10)

7. Multiply and then get 40 and 50