What is the volume of the sphere? Round the answer to the nearest cubic unit. Diameter: 22 cm

1) 507 cm^3
2) 1,394 cm^3
3) 5,575 cm^3
4) 16,725 cm^3

To solve for New Mexico's population density, we represent the given condition in a mathematical equation: '1 + 16x = y', where 'x' is the population density of New Mexico and 'y' is the Texas population density. We solve for 'x' by rearranging the equation to: 'x = (y - 1) / 16'. The specific population density of New Mexico can be calculated when the density of Texas is known.

The seemingly complicated question is basically one about algebra. It can be expressed as: '1 + 16x = y', where 'x' is the population density of New Mexico and 'y' is the population density of Texas. To find 'x' (New Mexico's population density) given the value for 'y', we need to rearrange the equation by subtracting 1 from both sides to get '16x = y - 1', and then divide both sides by 16 to solve for 'x': 'x = (y - 1) / 16'.

Without specific population density values for Texas ('y'), we cannot compute an actual numeric value for New Mexico's population density. However, we can use this equation to perform the necessary calculations once we know the population density (per square mile, for instance) of Texas.

This focuses on math skills including algebra and application of formulas, important aspects of high school math curriculum.

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Answer:

C. [tex]72+78+70+x\geq 289[/tex]

Step-by-step explanation:

Let x represent the number of points John needs to pass the class.

We have been that John  must have at least 289 test points to pass his math class. He already has test scores of 72, 78, and 70.

After scoring x points on John's total score would be [tex]72+78+70+x[/tex].

Since John needs at least 289 test points to pass his math class, so the total number of points should be greater than or equal to 289.

We can represent this information in an inequality as:

[tex]72+78+70+x\geq 289[/tex]

Therefore, the inequality [tex]72+78+70+x\geq 289[/tex] represents the number of more points John needs to pass the class.

there are 10 numbers ( 0-9)

there are 26 letters ( A-Z)

10 x 26 x 26 x 10 x 10 x 10 x 10 =67,600,000 possible combinations

it is a linear equation

 if you take the negative of x and subtract 1 you get Y

 so the answer is A

The LCM of P and Q is found by taking the highest powers of the common prime factors from both numbers, which results in LCM(P, Q) = 37 x 73 x 112.

To find the Least Common Multiple (LCM) of P and Q when given as products of prime factors, we look for the highest powers of the prime factors that appear in either P or Q. In this case:

For prime factor 3, the highest power in P and Q is 37. For prime factor 11, the highest power is 112 (from P). Since prime factor 7 only appears in Q, we include it in its highest power, which is 73. Combining these, the LCM of P and Q as the product of prime factors is:

LCM(P, Q) = 37 x 73 x 112

To solve this problem, all you have to do is to subtract 360 degrees (equivalent to 1 rotation) from the given angle until the answer is less than 360 degrees.

1st subtraction: 750 – 360 = 390 degrees

2nd subtraction: 390 – 360 = 30 degrees

Therefore the positive angle less than one rotation that is coterminal with 750 degrees is 30 degrees.

Answer:

[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Solution to the problem

We assume that the die is fair and the probability of obatin a one is 1/6.

Let X the random variable of interest, on this case we now that:

[tex]X \sim Binom(n=12, p=1/6)[/tex]

And we want to find this probability:

[tex] P(X=12)[/tex]

And if we replace we got:

[tex]P(X=12)=(12C12)(\frac{1}{6})^12 (1-\frac{1}{6})^{12-12}=4.59x10^{-10}[/tex]

If two triangles are similar then the corresponding sides are in proportion. Thus,

AB / AU = BC / UV = AC / AV

AB / (20x+108) = 703 / 444

Where AB is equivalent to:

AB = AU + UB

AB = 20x + 108 + 273

AB = 20x + 381

Therefore going back to the first equation:

(20x + 381) / (20x + 108) = 703/444

444 (20x + 381) = 703 (20x + 108)

8880x + 169164 = 14060x + 75924

14060x - 8880x = 169164 – 75924

5180 x = 93240

x = 93240 / 5180

x = 18

Answer:

  x = 18

Step-by-step explanation:

You want the value of x, given similar triangles ABC and AUV with ...

Corresponding sides, or their parts, of similar triangles are proportional. In this geometry, this means ...

  [tex]\dfrac{AU}{UB}=\dfrac{AV}{VC}[/tex]

We know that VC = AC -AV = 589 -372 = 217, so we can write the proportion as ...

  [tex]\dfrac{20x +108}{273}=\dfrac{372}{217}= \dfrac{12}{7}\\\\7(20x+108)=273(12)\qquad\text{multiply by $273\cdot12$}\\\\140x = 2520\qquad\text{subtract 756}\\\\x=\dfrac{2520}{140}=18[/tex]

The value of x is 18.

7% = 0.07

 since it is growing add that to 1 = 1.07

 now that is to the power of length of time 1.07^7

now multiply

524 x 1.07^7 = 841.429 ( round answer as needed)

Solutions:

As given in the question ,  patients who had a poor hospital experience, 23% had post-surgical complications.

Option (C) appears the right choice from my point of view which is c) Most patients who have a poor hospital experience also have post-surgical complications.

The reason being , that the patients who suffer from these complications have    experienced badly  in the last hospital where they were diagnosed or cured.

Answer:

a) Some patients who have a poor hospital experience also have post-surgical complications.  

Step-by-step explanation:

Given is :

Last year, the results of the surveys showed that of the patients who had a poor hospital experience, 23% had post-surgical complications.

The conclusion that can be drawn from this study is - Some patients who have a poor hospital experience also have post-surgical complications.  

If we turn the percentage in figures, we can see that almost 2.3 person or 2 patients out of 10 patients have a poor hospital experience and also have post-surgical complications.  

So, this is a low value that is why the correct answer is Some patients who have a poor hospital experience also have post-surgical complications.  

Answer:

[tex]a = 100 * 4^{d}[/tex]

In a 1 week there would be 1,638,400 bacteria

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.

Since the amount of bacteria are quadrupling every day this means that the bacteria are compounding, meaning that every time they quadruple the next day the new amount is quadrupled. Thus growing exponentially every time.

So to solve this we would need to create an exponential equation that calculates the amount of bacteria after a certain amount of days, like so...

[tex]a = 100 * 4^{d}[/tex]

If we want to calculate the number of bacteria after 1 week , we would substitute d for 7 and solve for a.

[tex]a = 100 * 4^{7}[/tex]

[tex]a = 100 * 16,384[/tex]

[tex]a = 1,638,400[/tex]

In a 1 week there would be 1,638,400 bacteria

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

The problem states that the paths of the two planes form a right triangle, therefore this means that the distance between the two is the hypotenuse. Given that information, we can use the hypotenuse formula for finding the distance formula:

c^2 = a^2 + b^2             ---> 1

Where c is the hypotenuse, in this case the distance between the two planes.

First let us find the value of a. We know that one plane is 150 miles from point P and this distance is decreasing by a rate of 450 miles per hour, therefore a is:

a = 150 – 450 t              ---> 2

We also know that the other plane is 200 miles away and this distance decreases by a rate of 450 miles per hour also, therefore b is:

b = 200 – 450 t              ---> 3

Substituting equations 2 and 3 to 1:

c^2 = (150 - 450 t)^2 + (200 – 450 t)^2

c^2 = 22500 – 135000t + 202500t^2 + 40000 – 180000t +  + 202500t^2

c^2 = 405,000 t^2 – 315,000 t + 62,500               (ANSWER)

Final answer:

To find the imagined number, we need to follow the given steps: add a zero to the original number, subtract it from 143, and set the result equal to the tripled imagined number.

Explanation:

To find the imagined number in this question, we need to follow the given steps. Let's assume the original number is x. Adding a zero to the right of it gives us 10x. Subtracting this result from 143 gives us 143 - 10x. According to the question, this result is equal to the tripled imagined number, so we have 143 - 10x = 3x. To solve for x, we can rearrange the equation as 143 = 13x, and then divide both sides by 13. Therefore, the imagined number, x, is 11.

Answer:x equals 12

Step-by-step explanation:

4x+40=100-x

add x to both sides

5x+40=100

Subtract 40 on both sides

5x=60

divide both sides by 5

x=12

The number is 12 from the obtained equation.

Given that, When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the unknown number be x.

4 times a number is increased by 40

=4x+40

100 is decreased by the number

= 100-x

So, equation is 4x+40=100-x

4x+x=100-40

⇒ 5x = 60

⇒ x=12

Therefore, the number is 12 from the obtained equation.

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Answer:  The required slpe-intercept form of the given inequality is

[tex]y\leq 0\times x+24.[/tex]

Step-by-step explanation:  We are given to write the following inequality in the slope-intercept form :

[tex]-6+2y\leq 42~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We know that

the slope intercept form of a straight line with slope m and y-intercept c is given by

[tex]y=mx+c.[/tex]

Writing equation (i) in slope-intercept form, we have

[tex]-6+2y\leq 42\\\\\Rightarrow 2y\leq 42+6\\\\\Rightarrow 2y\leq 48\\\\\Rightarrow y\leq 24\\\\\Rightarrow y\leq 0\times x+24,[/tex]

where slope, m = 0  and  y-intercept, c = 24.

Thus, the required slpe-intercept form of the given inequality is

[tex]y\leq 0\times x+24.[/tex]

The domain of the (goh)(x) will be [6, ∞).

The domain means all the possible values of x and the range means all the possible values of y.

The functions are given below.

g(x) = √(x - 4) and h(x) = 2x - 8

Then the function f of g (x) will be

(goh)(x) = g(h(x))

(goh)(x) = √((2x - 8) - 4)

(goh)(x) = √(2x - 12)

Then the domain of the (goh)(x) will be

We know that the value under the square root should be greater than zero.

2x - 12 ≥ 0

2x ≥ 12

x ≥ 6

The domain of the (goh)(x) will be [6, ∞).

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x+2 cancels out and leaves 8x/x-5

Also, Answer A and B are the same

Answer: a=100 and b=5

Step-by-step explanation:

Given: A school typically sells 500 yearbooks each year for $50 each.

The economics class discovers that they can sell 100 more yearbooks for every $5 decrease in price.

Let x represents the number of $5 decreases in price.

Then the new price (in dollars)=50-5x

Total yearbook sold=500+100x

If the revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook.

Then the revenue function will be [tex]R(X)=(500+100x)(50-5x)[/tex]

On comparing this with the given revenue expression we get

a=100 and b=5.

In this exercise we have to calculate the values ​​of A and B, so we have to:

[tex]A=100\\B=5[/tex]

Since the equation is:

[tex]R(X)=(500+ax)(50-bx)[/tex]

And the following information was given:

So knowing that by increasing 100 more books sold this is equal to A and the decrease in value is going to be equal to b.

[tex]R(X)=(500+100x)(50-5x)[/tex]

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