If today is Friday, tomorrow will be Saturday
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Answer:

(x+5)(x-3) / (x+5)(x+1)

Step-by-step explanation:

A removeable discontinuity is always found in the denominator of a rational function and is one that can be reduced away with an identical term in the numerator.  It is still, however, a problem because it causes the denominator to equal 0 if filled in with the necessary value of x.  In my function above, the terms (x + 5) in the numerator and denominator can cancel each other out, leaving a hole in your graph at -5 since x doesn't exist at -5, but the x + 1 doesn't have anything to cancel out with, so this will present as a vertical asymptote in your graph at x = -1, a nonremoveable discontinuity.

The question is incomplete. The complete question is :

Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision.

[tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]

Solution :

Given :

Function : [tex]$\{ x^5, x^5-1,3 \} \text{ on } (- \infty, \infty)$[/tex]

We have to determine whether the given function is linear dependent or linearly independent for the interval [tex]$(-\infty, \infty)$[/tex].

The given function are linearly dependent because for the constants, [tex]c_1[/tex] and [tex]c_2[/tex], the equation is :

[tex]$c_1x^5 + c_23 = x^5-1$[/tex]  has the solution [tex]$c_1 = 1$[/tex] and [tex]$c_2 = -\frac{1}{3}$[/tex]

Therefore,

[tex]$1x^5 + \left(-\frac{1}{3}\right)3 = x^5-1$[/tex]

9514 1404 393

Answer:

  LCD = 18

Step-by-step explanation:

6 and 9 have a common factor of 3, so the LCD is ...

  (6×9)/3 = 18

Then the fractions can be written as ...

  3/6 = 9/18

  2/9 = 4/18

Answer:

-18

Step-by-step explanation:

b = -6

c = 3

-4c + b = ?

Plug in the value of each variable into the equation

-4c + b = ?

= -4(3) + (-6)

= -12 - 6

= -18

Answer:

reflected across the y axis: (5,2)

reflected across the x axis: (-2,5)

Answer:

Answer: (5,2) when reflected off the y-axis. (-5,-2) when reflected off the x-axis

Answer:

mark me as brinalist if answers are correct

Answer:

30° and -1/2. This is pretty easy to do on a piece of paper but I recommend googling "unit circle" and clicking images, it tells you everything you need to know.

Step-by-step explanation:

Answer:

[tex]c = \frac{1}{12}[/tex]

The mean of the distribution is 0.25.

The variance of the distribution is of 0.6875.

Step-by-step explanation:

Probability density function:

For it to be a probability function, the sum of the probabilities must be 1. The probabilities are 3c, 3c and 6c, so:

[tex]3c + 3c + 6c = 1[/tex]

[tex]12c = 1[/tex]

[tex]c = \frac{1}{12}[/tex]

So the probability distribution is:

[tex]P(X = -1) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]

[tex]P(X = 0) = 3c = 3\frac{1}{12} = \frac{1}{4} = 0.25[/tex]

[tex]P(X = 1) = 6c = 6\frac{1}{12} = \frac{1}{2} = 0.5[/tex]

Mean:

Sum of each outcome multiplied by its probability. So

[tex]E(X) = -1(0.25) + 0(0.25) + 1(0.5) = -0.25 + 0.5 = 0.25[/tex]

The mean of the distribution is 0.25.

Variance:

Sum of the difference squared between each value and the mean, multiplied by its probability. So

[tex]V^2(X) = 0.25(-1-0.25)^2 + 0.25(0 - 0.25)^2 + 0.5(1 - 0.25)^2 = 0.6875[/tex]

The variance of the distribution is of 0.6875.

9514 1404 393

Answer:

  2/7

Step-by-step explanation:

Any unit fraction with a denominator between 3 and 4 will be between 1/3 and 1/4. For example, ...

  1/3.5 = 2/7 . . . . is between 1/3 and 1/4

__

You can also go at this considering decimal equivalents.

  1/4 = 0.25

  1/3 = 0.333... (repeating)

So, decimal numbers like 0.26, 0.295, 0.3330 are all values that are between 1/4 and 1/3.

Answer:

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A statistician calculates that 7% of Americans are vegetarians.

This means that [tex]p = 0.07[/tex]

Sample of 403 Americans

This means that [tex]n = 403[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.07[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.07*0.93}{403}} = 0.0127[/tex]

What is the probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%?

Proportion below 7 - 3 = 4% or above 7 + 3 = 10%. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them, and multiply by 2.

Probability the proportion is below 4%

p-value of Z when X = 0.04.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.04 - 0.07}{0.0127}[/tex]

[tex]Z = -2.36[/tex]

[tex]Z = -2.36[/tex] has a p-value of 0.0091

2*0.0091 = 0.0182

0.0182 = 1.82% probability that the proportion of vegetarians in a sample of 403 Americans would differ from the population proportion by more than 3%.

Answer:

irrational numbers

Step-by-step explanation:

An irrational number is a number that cannot be expressed as a fraction p/q for any integers p and q.

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I believe your answer is:

Irrational Number

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Answer:

Step-by-step explanation:

volume of cone=1/3 πr²h

=1/3×π×5²×11

=275/3 ×3.14

≈287.33 in³

Answer:

30 additional teachers will have to be hired to reduce the ratio to 1:20.

Step-by-step explanation:

Given that Jefferson School has 1800 students, and the teacher-pupil ratio is 1:30, to determine how many additional teachers will have to be hired to reduce the ratio to 1:20, the following calculation must be performed:

30 = 1800

1 = X

1800/30 = X

60 = X

20 = 1800

1 = X

1800/20 = X

90 = X

90 - 60 = 30

Therefore, 30 additional teachers will have to be hired to reduce the ratio to 1:20.

The value of the expression for the given values of x, y and z is B. -5.

Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.

Given expression is,

x²z² - y²(x + z)

We have certain values for x, y and z.

x = 2, y = -3 and z = -1.

Substituting the values,

(2²)(-1²) - (-3²) (2 + -1) = (4 × 1) - (9 × 1)

                                 = 4 - 9

                                 = -5

Hence the value of the expression is -5.

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Answer:

[tex]\sqrt{49}[/tex]

Step-by-step explanation:

Define a rational number by a number able to expressed a fraction where the denominator is not 0 or 1.

Non-terminating (never-ending) decimals cannot be expressed as a fraction and therefore are irrational. However, recall that [tex]\sqrt{49}=7[/tex], which can be expressed as a fraction (e.g. [tex]\frac{14}{2}[/tex], etc). Thus, the answer is [tex]\boxed{\sqrt{49}}[/tex].

Answer:

34m = c

Step-by-step explanation:

For every month (m) you pay 34 dollars. However many months youu use that service time 34 equals your total cost (c).

Answer:

[tex]let \: cost \: be \: { \bf{c}} \: and \: months \: be \: { \bf{n}} \\ { \bf{c \: \alpha \: n}} \\ { \bf{c = kn}} \\ 34 = (k \times 1) \\ k = 34 \: dollars \\ \\ { \boxed{ \bf{c = 34n}}}[/tex]

Answer:

80 students

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

60% of 500 = 300

72% of 500 = 360

40% of 500 = 200

28% of 500 = 140

300+360 = 660

660 - 2x = 500

660 - 500 = 2x

160 = 2x

2x = 160

x = 80

Answer:

We know that every number can be written as a product of prime numbers.

The method to find the factorized form of a number depends on the number, we just try to find the different factors by dividing by them, for example for the number 1000 we have:

1000 is an even number, then we can divide it by 2 (2 is a prime number)

1000 = 2*500   (so we already found a prime factor)

500 is also an even number, so we can divide it by 2

1000 = 2*500 = 2*2*250  (we found another prime factor)

dividing by 2 again we get:

1000 = 2*2*250 = 2*2*2*125

1000 = (2*2*2)*125

now we just need to factorize 125

we know that 125 is a multiple of 5, such that:

125 = 5*25 = 5*5*5

(5 is a prime number, so it is completely factorized).

Then the factorization of 1000 is:

1000 = (2*2*2)*(5*5*5) = 2^3*5^3

Now with another example, 1422

1422 is an even number, so we again start using the factor 2:

1422 = 2 = 711

then:

1422 = 2*711

we already found a factor.

711 is a multiple of 3 (the sum of its digits is a multiple of 3), then:

711/3 = 237

We can write our number as:

1422 = 2*3*237

237 is also a multiple of 3

237/3 = 79

then:

1422 = 2*3*3*79

and 79 is a prime number, so we already have 1422 completely factorized.

Answer:

24

Step-by-step explanation:

18 times 5 is 90 so that means that the given numbers have to add up to 90 (including x)

so,

6+10+20+30=66

90-66=24

I hope this helps!

Answer:

[tex]x = 24[/tex]

Step-by-step explanation:

[tex]6 + 10 + x + 20 + 30 = 18[/tex]

There are 5 numbers that we must add to average out to get 18 so let set this equation up

[tex] \frac{6 + 10 + x + 20 + 30}{5} = 18[/tex]

[tex]6 + 10 + x + 20 + 30 = 90[/tex]

[tex]x = 24[/tex]

Answer:

median

Step-by-step explanation:

Q is at the midpoint of RS and so PQ is a median

A median is a segment from a vertex to the midpoint of the opposite side.

We want to define what type of line is PQ (the line that passes through points P and Q) by looking at the given image, one can easily see that the line PQ is a median, now let's explain why.

First, let's analyze the image:

In the image, we can see that P is one vertex of the triangle, and Q is the midpoint of the segment RS (you can see that RQ = 4 and QS = 4) , where R and S are the other two vertexes of the triangle.

Particularly, we can define a median of a triangle as the line that passes through the midpoint of one side of the triangle and by the vertex that does not belong to that side.

With that definition, we can see that PQ is a median because Q is the midpoint of one side of the triangle and P is the vertex that does not belong to that side.

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Answer:

The two equivalent expressions are 6(x − y) and 6x − 6y.

Step-by-step explanation:

Answer:

The statement is false

Step-by-step explanation:

Given

See comment for complete statement

Required

Is the statement true or false

From central limit theorem, we understand that a distribution is approximately normal if the distribution takes a sample considered to be large enough from the population.

Also, the mean and the standard deviation are known.

However, the given statement implies that the distribution will be normal depending on an underlying distribution; this is false.

Answer:

Step-by-step explanation:

Answer:

[tex]y=(x-7)^2-1[/tex]

Step-by-step explanation:

We want to convert the equation:

[tex]\displaystyle y=x^2-14x+48[/tex]

Into vertex form, given by:

[tex]\displaystyle y=a(x-h)^2+k[/tex]

Where a is the leading coefficient and (h, k) is the vertex.

There are two methods of doing this. We can either: (1) use the vertex formulas or (2) complete the square.

Method 1) Vertex Formulas

Let's use the vertex formulas. First, note that the leading coefficient a of our equation is 1.

Recall that the vertex is given by:

[tex]\displaystyle \text{Vertex}=\left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]

In this case, a = 1, b = -14, and c = 48. Find the x-coordinate of the vertex:

[tex]\displaystyle x=-\frac{(-14)}{2(1)}=7[/tex]

To find the y-coordinate, substitute this value back into the equation. Hence:

[tex]y=(7)^2-14(7)+48=-1[/tex]

Therefore, our vertex (h, k) is (7, -1), where h = 7 and k = -1.

And since we already determined a = 1, our equation in vertex form is:

[tex]\displaystyle y=(x-7)^2-1[/tex]

Method 2) Completing the Square

We can also complete the square to acquire the vertex form. We have:

[tex]y=x^2-14x+48[/tex]

Factor out the leading coefficient from the first two terms. Since the leading coefficient is one in this case, we do not need to do anything significant:

[tex]y=(x^2-14x)+48[/tex]

Now, we half b and square it. The value of b in this case is -14. Half of -14 is -7 and its square is 49.

We will add this value inside the parentheses. Since we added 49 inside the parentheses, we will also subtract 49 outside to retain the equality of the equation. Hence:

[tex]y=(x^2-14x+49)+48-49[/tex]

Factor using the perfect square trinomial and simplify:

[tex]y=(x-7)^2-1[/tex]

We acquire the same solution as before, with the vertex being (7, -1).

Answer:

Area of ellipse=[tex]\pi ab[/tex]

Step-by-step explanation:

We are given that

[tex]x=acos\theta[/tex]

[tex]y=bsin\theta[/tex]

[tex]0\leq\theta\leq 2\pi[/tex]

We have to find the area enclose by it.

[tex]x/a=cos\theta, y/b=sin\theta[/tex]

[tex]sin^2\theta+cos^2\theta=x^2/a^2+y^2/b^2[/tex]

Using the formula

[tex]sin^2x+cos^2x=1[/tex]

[tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex]

This is the equation of ellipse.

Area of ellipse

=[tex]4\int_{0}^{a}\frac{b}{a}\sqrt{a^2-x^2}dx[/tex]

When x=0,[tex]\theta=\pi/2[/tex]

When x=a, [tex]\theta=0[/tex]

Using the formula

Area of ellipse

=[tex]\frac{4b}{a}\int_{\pi/2}^{0}\sqrt{a^2-a^2cos^2\theta}(-asin\theta)d\theta[/tex]

Area of ellipse=[tex]-4ba\int_{\pi/2}^{0}\sqrt{1-cos^2\theta}(sin\theta)d\theta[/tex]

Area of ellipse=[tex]-4ba\int_{\pi/2}^{0} sin^2\theta d\theta[/tex]

Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(2sin^2\theta)d\theta[/tex]

Area of ellipse=[tex]-2ba\int_{\pi/2}^{0}(1-cos2\theta)d\theta[/tex]

Using the formula

[tex]1-cos2\theta=2sin^2\theta[/tex]

Area of ellipse=[tex]-2ba[\theta-1/2sin(2\theta)]^{0}_{\pi/2}[/tex]

Area of ellipse[tex]=-2ba(-\pi/2-0)[/tex]

Area of ellipse=[tex]\pi ab[/tex]

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I believe your answer is:  

Quadrant III

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Answer:

32

Step-by-step explanation:

18 : 6 = 3

therefore, x : 3 has to equal 3.

X : 3 = 3

X = 3 × 3

X = 9

To verify:

18 : 6 = 9 : 3

3 = 3

It's true that X = 9, so now just replace the X with 9 in the next equation

5 + 3(9) = 32

Answer:

32

Step-by-step explanation:

18 :  6 = x : 3

Product of means  =  Product of extremes

6 * x = 3*18

     x = [tex]\frac{3*18}{6}[/tex]

     x = 3*3

x = 9

Now plugin x = 9 in the expression

5 + 3x = 5 + 3*9

          = 5 + 27

          = 32

Answer:

45 miles per hour

Step-by-step explanation:

d=distance in miles

r=rate miles/hr

t = time in hours

t = 352/(r+3)

330/r = 352/(r+3)

352r = 330r + 990

22r = 990

r = 45

Explanation:

Divide 126 over 3. This is because any equilateral triangle has all three sides the same length

126/3 = 42

Each side is 42 mm long

So its perimeter is 3*42 = 126 mm

Side note: if your teacher says a triangle is equiangular, then it's automatically equilateral as well (and vice versa).

The length of one of its sides of an equilateral triangle is  42 mm.

In geometry, an equilateral triangle exists as a triangle that contains all its sides equivalent in length. Since the three sides stand equivalent therefore the three angles, opposite to the equivalent sides, stand equivalent in measure. Thus, it stands also named an equiangular triangle, where each angle measure 60 degrees.

The perimeter of an equilateral triangle exists 126 mm.

The equilateral triangle contains all three sides of the same length

126/3 = 42

Each side stands 42 mm long

So its perimeter stands 3 [tex]*[/tex] 42 = 126 mm

Therefore, the length of one of its sides = 42 mm.

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Explanation:

It might help to draw out the picture as shown below. The pool itself (just the water only) is the inner rectangle. The outer rectangle is the pool plus the border of those 1 by 1 tiles.

The pool is a rectangle 90 feet by 80 feet. If we add on the tiles, then we get a larger rectangle that is 90+2 = 92 feet by 80+2 = 82 feet.

We add on 2 since we're adding two copies of "1" on either side of each dimension.

The larger rectangle's area is 92*82 = 7544 square feet

The smaller rectangle's area is 90*80 = 7200 square feet

The difference in areas is 7544-7200 = 344 square feet.

Each 1 by 1 tile is of area 1*1 = 1 sq foot, meaning that 344 tiles will get us the 344 square foot border around the pool.