Which equivalent expression will be generated by applying the Distributive Property and combining like terms in the expression 11 + 4(x + 2y + 4)?

Answer:

25 cm hope whoever gets to see this has a great day :D

The equation of the circle that you are looking for is x^2 + y^2 = 100.

You can find this by using the base formula for a circle:

(x - x1)^2 + (y - y1)^2 = r^2

In which x1 is the x-coordinate of the origin, y1 is the y-coordinate of the origin, and r is the radius. So we put in the values we know and simplify.

(x -0)^2 + (y - 0)^2 = 10^2

x^2 + y^2 = 100

The equation of a circle centered at the origin such that the length of its radius is 10 units will be x² + y² = 100.

Circle is a round plane figure whose boundary (the circumference) consists of points equidistant from a fixed point (the center).

Given is a circle is centered at the origin, and the length of its radius is 10 units.

The equation of the circle whose center is at origin is given by -

x² + y² = r²

We have radius [r] = 10 units

Therefore, we can write the equation of the circle as -

x² + y² = 10 x 10

x² + y² = 100

Therefore, the equation of a circle centered at the origin such that the length of its radius is 10 units will be x² + y² = 100.

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Answer: a. [tex]\dfrac{1}{6}[/tex]

Step-by-step explanation:

Given : Events X and Y are independent.

The probability of X occurring is [tex]\dfrac{1}{3}[/tex].

The probability of Y occurring is [tex]\dfrac{1}{2}[/tex].

Since both events are independent, then we have

[tex]\text{P(X and Y)}=\text{P(X)}\times \text{P(Y)}\\\\\Rightarrow\ \text{P(X and Y)}=\dfrac{1}{2}\times\dfrac{1}{3}=\dfrac{1}{6}[/tex]

Hence, [tex]\text{P(X and Y)}=\dfrac{1}{6}[/tex]

Thus , (a.) is the correct option.

Final answer:

The original fraction, based on the provided conditions, is found to be 3/8 by setting up an equation relative to the changes described and solving for the unknown numerator and denominator.

Explanation:

The question involves solving for the numerator and denominator of a fraction based on provided conditions. Let's denote the denominator as x and the numerator as x - 5, since the numerator is 5 less than the denominator. According to the given conditions, when the numerator is multiplied by 2 and the denominator is increased by 16, the fraction becomes smaller by 1/3 of its original value.

Original fraction: [tex]\(\frac{x - 5}{x}\)[/tex]. After the modifications: [tex]\(\frac{2(x - 5)}{x + 16}\)[/tex]. The condition that the fraction becomes smaller by 1/3 of its original value leads to the equation: [tex]\(\frac{x - 5}{x} - \frac{1}{3} \cdot \frac{x - 5}{x} = \frac{2(x - 5)}{x + 16}\)[/tex].

Simplifying this equation, we first express the reduced original fraction as [tex]\(\frac{2(x - 5)}{3x}\)[/tex]. Then, setting it equal to the modified fraction, we get[tex]\(\frac{2(x - 5)}{3x} = \frac{2(x - 5)}{x + 16}\)[/tex]. Canceling out [tex]\(2(x - 5)\)[/tex] from both sides and solving for x, we find that x = 8. Therefore, the original denominator is 8, and the numerator is 3, making the original fraction 3/8.

Answer:

D. -1

Step-by-step explanation:

All the variable terms are on the left, so subtract the constant on the left (5) from the equation and collect terms.

... 4t = -4 . . . . . . . variable term on one side; constant term on the other

Divide by the coefficient of t.

... t = -1

Answer:

3 ways

Explanation:

We know that a parabola has a second degree equation), while a line has a first degree equation.

To get the points of intersection, we will need to solve both simultaneously.

Solving them, we can reach a maximum of two solutions, however, other scenarios are also possible.

Possible scenarios:

1- no intersection occurs as shown in the first attachment

2- one intersection occurs as shown in the second attachment

3- two intersections occur as shown in the third attachment

Based on the above, there are three ways where the line and parabola can intersect

Hope this helps :)

Answer:

0,1,2

Step-by-step explanation:

When both variables are standardized, the correlation coefficient remains the same. Scaling the variable by a constant factor doesn't change the relationship or correlation strength.

When both variables are standardized, the correlation coefficient between the standardized variables will always be the same as the correlation coefficient between the original variables. The standardization process does not change the relationship between the variables, but rather scales them to have a mean of 0 and a standard deviation of 1. Therefore, the correlation coefficient remains unchanged.

If median family income had been measured in thousands of dollars instead of dollars, the correlation would not change. Scaling the variable by a constant factor, such as thousands, would only change the units of measurement, but not the relationship between the variables or the strength of the correlation.

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The last two numbers of the given sequence are respectively gotten to be; 83 and 77

From the sequence, we see that;

From 98 to 97, there is a decrease of 1

From 97 to 95, there is a decrease of 2

From 95 to 92, there is a decrease of 3

From 92 to 88, there is a decrease of 4

The sequence pattern of decrease is seen to be: 1, 2, 3, 4

Thus, by inference we can say that the next decrease is 5. Thus,

Next number in sequence = 88 - 5 = 83

The number after that will be; 83 - 6 = 77

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Answer:

The first graph, so A is the answer

Step-by-step explanation:

Answer:

  24

Step-by-step explanation:

The given age relationships can be used to reason about their ages.

__

When Holly was 4 times Spencer's age, the difference in their ages was 4-1=3 times Spencer's age. That is, Spencer was 51/3 = 17 years old, and Holly was 68.

That was 7 years ago, so Spencer is now 17+7 = 24 years old.

Answer:

All of them will double at the same time.

Step-by-step explanation:

The rule of 72 wa created to have an estimate of how long will an account that pays interests will take to double its value, in this case, as they all have the same interest rate, and the rule of 72 depends only on the interests that the account pays, there will be no difference between the doubling time of the accounts since eventhough they all have different amounts of money, having the same interest rate, will make them grow at the same rate.

The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences. Then the probability is given as,

P = (Favorable event) / (Total event)

A school radio station polled 500 students to find out what kind of music they appreciate. According to the study, 207 people prefer rock, 172 prefer country, and 126 choose jazz. Furthermore, 33 like rock and country, 27 prefer rock and jazz, 32 prefer country and jazz, and 13 prefer all three forms of music.

The number of favorable events is given as,

Favorable events = 33 + 27 + 32 + 17

Favorable events = 105

Then the probability is given as,

P = 105 / 500

P = 0.21

P = 21%

The probability that a randomly chosen student like at least two of the three styles of music will be 0.21.

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