find L.C.M. of:

a) 3 x (x + 1) (x-1) and 2x² (x-1) (x+3).
​

Answer:

Step-by-step explanation:

The last one: 79, 79, 79, 79, 79, 79, 79, 79, 79, 79 because there isn't any difference in the numbers.

S.D.: 0

The expected enrolment in 7 years is  1845.

The formula for calculating future value of the number of students is an exponential equation with this form:

FV = P (1 + r) ^n

1500 x (1.03)^7 = 1845

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Answer: Choice D) set of even integers

=======================================================

Explanation:

U = universal set = {all positive integers} = {1, 2, 3, 4, 5, ...}

A = {stuff in set U that is odd} = {1, 3, 5, 7, 9, ...}

[tex]A^c[/tex] = {stuff in set U but NOT from set A} = {2, 4, 6, 8, ...}

[tex]A^c[/tex] = {set of even numbers from set U}

In set theory, the complement is simply the complete opposite. If the number 7 is found in set A for instance, then 7 is not going to live in the complement [tex]A^c[/tex]

The opposite of the odd numbers is the set of even numbers.

Therefore, we go for choice D as our final answer.

Side note: if we union set A with its complement [tex]A^c[/tex] then we get the universal set as a result. [tex]A \cup A^c = \text{universal set} = \text{set of all positive integers}[/tex]

The solution is Option D.

Ac =  {x|x ∈ U and is an even positive integer} where Ac represents the complement of set A

What is union and intersection of sets?

The union of two sets A and B is the set of all those elements which are either in A or in B, i.e. A ∪ B, whereas the intersection of two sets A and B is the set of all elements which are common. The intersection of these two sets is denoted by A ∩ B

The union of two sets is a new set that contains all of the elements that are in at least one of the two sets

The intersection of two sets is a new set that contains all of the elements that are in both sets

Given data ,

Let the set U be = {all positive integers}

So , the values of set U = { 1 , 2 , 3 , 4 , 5 .. }

And , let the set A = {x|x ∈ U and x is an odd positive integer}

So , the value of set A = { 1 , 3 , 5 , 7 , ... }

And , the complement of set  A is Ac

The value of set Ac is all the even positive odd integers

So , the value of set Ac = { 2 , 4 , 6 , 8 .. }

Therefore , the value of set Ac = { 2 , 4 , 6 , 8 .. }

Hence , the set Ac = {x|x ∈ U and is an even positive integer}

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Answer:

Step-by-step explanation:

Comment

Either you know the answer to this or you don't. There is no point in eliminating the wrong answers until you get to the right one. It is better to get to the right one immediately.

A rhombus and its diagonals have many interesting properties.  This one is one of those properties. The diagonals are not the same length. The diagonals bisect each other at right angles.

Answer: B

Answer:

-1

Step-by-step explanation:

3-1=2

2-1=1

Answer:

[tex]-\dfrac{69}{14}[/tex]

Step-by-step explanation:

Substitute the given values of the variables into the given expression:

[tex]\implies \dfrac{60 \left(\dfrac{1}{3}\right)\left(-\dfrac{1}{5}\right)\left(\dfrac{1}{4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When multiplying fractions, simply multiply the numerators and the denominators:

[tex]\implies \dfrac{60 \left(\dfrac{1 \cdot -1 \cdot 1}{3\cdot 5 \cdot 4}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{60 \left(-\dfrac{1}{60}\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{4}\right)}{\left(\dfrac{1}{3}-\dfrac{1}{5}\right)\left(\dfrac{1}{3}+\dfrac{1}{4}\right)}[/tex]

When adding or subtracting fractions, make the denominators the same:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20}{60}-\dfrac{12}{60}+\dfrac{15}{60}\right)}{\left(\dfrac{5}{15}-\dfrac{3}{15}\right)\left(\dfrac{4}{12}+\dfrac{3}{12}\right)}[/tex]

Now add the numerators and put that over the denominator:

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{20-12+15}{60}\right)}{\left(\dfrac{5-3}{15}\right)\left(\dfrac{4+3}{12}\right)}[/tex]

[tex]\implies \dfrac{\left(-1\right)\left(\dfrac{23}{60}\right)}{\left(\dfrac{2}{15}\right)\left(\dfrac{7}{12}\right)}[/tex]

Again, multiply the fractions:

[tex]\implies \dfrac{\left(-1 \cdot \dfrac{23}{60}\right)}{\left(\dfrac{2 \cdot 7}{15 \cdot 12}\right)}[/tex]

[tex]\implies \dfrac{-\dfrac{23}{60}}{\dfrac{14}{180}}[/tex]

To divide the fractions, turn the second fraction upside down, then multiply it by the first fraction:

[tex]\implies -\dfrac{23}{60} \cdot \dfrac{180}{14}[/tex]

[tex]\implies -\dfrac{4140}{840}[/tex]

Finally, simplify:

[tex]\implies -\dfrac{4140 \div 60}{840 \div 60}[/tex]

[tex]\implies -\dfrac{69}{14}[/tex]

Answer:

1/12  mile per minute

Step-by-step explanation:

1/4 mile in 3 minutes

 then miles per minute   is   1/4 mile / 3 min = 1/12  mile/min

a short sale is when a house is sold for less than what the mortgage is.

answer: B. for less than the mortgage owed on it

Answer:

Step-by-step explanation:

Based on the given mean absolute deviations, the sample mean absolute deviation will be 2 and the population mean absolute deviation will be 3.8.

= Sum of sample mean absolute deviation / Number

= (0 + 0.5 + 4.5 + 0.5 + 0 + 4 + 4.5 + 4 + 0) / 9

= 2

First find the population mean:

= (10 + 11 + 19) / 3

= 13.3

Population mean absolute deviation:
= 1/3 x ( (10 - 13.67) + (11 - 13.3) + (19 - 13.3))

= 3.8

We can therefore see that the sample mean deviations is a biased estimate of the population mean absolute deviation.

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The total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

The table is in the picture, please refer to the picture.

Tony needs to purchase 3,600 oz of vegetable oil for his catering business.

Lowest unit price = 26 cents per ounce

Total price at this rate = 3600×26 = 93600 cents = $936

The highest unit price = 34 cents per ounce

Total price at this rate = 3600×34 = 122400 cents = $1224

Total saving he purchases the container that has the lowest unit price:

= 1224 - 936

= $288

Thus, the total amount at the lowest price is $936, the total amount at the highest price is $1224, and the amount saved is $288.

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The number of cubes needed to fill the rectangular prism 4608 cubes.

volume of rectangular prism = lwh

where

Therefore,

volume of the rectangular prism = 8 × 4 × 9 / 4 = 72 inches³

volume of the cube = l³

where

Therefore,

volume = (1 / 4)³

volume of the cube = 1  / 64 inches³

Therefore,

The number of cubes needed to fill the rectangular prism = 72 ÷ 1 / 64

The number of cubes needed to fill the rectangular prism = 72 × 64 = 4608

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When Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

One fourth of the part of a circle is said to be the quadrant of the circle.

Given the angle Ф lies in quadrant IV.

As we know, cos Ф is positive only in first and fourth quadrant i.e when Ф lies in 0<Ф<90 and 270<Ф<360.

cosФ range from [-1,1]

So, cos Ф is positive when Ф lies in 1st and 4th quadrant.

&  cos Ф is negative when Ф lies in 2nd and 3rd quadrant.

If cos ∅ lies in the quadrant IV, anything between [0, 1] can be the value of cos ∅.

Hence, when Ф lies in quadrant IV the value of cos Ф lies in [0, 1].

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The series diverges. You Consider concluding this because the series is in arithmetic progression.

An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.

The explicit formula for any arithmetic series is given by the formula,

[tex]a_n = a_1 + (n-1)d[/tex]

where d is the difference and a₁ is the first term of the sequence.

The given series of numbers 1/4+3/2+11/4+4+21/4+.... is an arithmetic series because the difference between any two consecutive terms is 5/4. Therefore, the blanks can be filled as,

The series diverges. You Consider conclude this because the series is in arithmetic progression.

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Answer:

w = -1/5

OR

w = -3

Step-by-step explanation:

Given equation:

−16w-3 = 5w²

Solution:

Subtracting 5w^2 from both sides,we get

Factor the LHS of this equation using middle term factor:

Now,

Solving for equation 1:

Solving for equation 2:

[tex] - 16w - 3 = 5 {w}^{2} \\ \\ 0 = 5 {w}^{2} + 16w + 3 \\ \\ 5 {w}^{2} + 16w + 3 = 0 \\ \\ 5 {w}^{2} + w + 15w + 3 = 0 \\ \\ (5 {w}^{2} + w) + (15w + 3) = 0 \\ \\ w(5w + 1) + 3(5w + 1) = 0 \\ \\ (w + 3)(5w + 1) = 0. [/tex]

The value of w is -3 and -1/5 .

Reason:

sorry but here is no options so I am giving you a example so that you can understand by your own!

Answer;

5r+3

2x-6

X4+10

4y-1

Step by step answer;

So the method of identifying the Monomail is if you see a variable in a constant so it is a Monomail !

In the given graph point B is a relative maximum with the coordinates (0, 2).

The given function is [tex]y=x^{4}-2x^{2} +1[/tex].

In the given graph, we need to find which point is a relative maximum.

The function's graph makes it simple to spot relative maxima. It is the pivotal point in the function's graph. Relative maxima are locations where the function's graph shifts from increasing to decreasing. A point called Relative Maximum is higher than the points to its left and to its right.

In the graph, the maximum point is (0, 2).

Therefore, in the given graph point B is a relative maximum with the coordinates (0, 2).

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Answer:

10

Step-by-step explanation:

use PEMDAS

PEMDAS order is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

2[32 — (4 − 1)³] =

2[32 — (3)³] =

2[32 — 27] =

2[5] =

10

khanacademy

The error happens in the last line.

The relevant log rule is ln(A) - ln(B) = ln(A/B)

The issue is that the 0 isn't ln(0), so that 0 cannot be thrown into the natural log like that.

What we can do is this set of steps

ln(3x) - 0

ln(3x) - ln(1)

ln(3x/1) ... applying the log rule mentioned

ln(3x)

But these steps are a needlessly overcomplicating things. We can simply go from ln(3x)-0 to ln(3x) in one step. Subtracting off zero doesn't change ln(3x) at all.

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

Let's continue the steps to solve for x.

ln(x^2) = ln(3x)

x^2 = 3x

x^2-3x = 0

x(x-3) = 0

x = 0 or x-3 = 0

x = 0 or x = 3

Those are the two possible solutions.

However, x = 0 isn't valid because it's not in the domain of ln(x^2). In other words, ln(0) isn't defined. The domain of y = ln(x) is x > 0

This means that x = 3 is the only solution.

The figures show that the number of births for Florida and Michigan reduced

From the data sourced, the number of births in Florida in 2010 was 214519 while in 2011, it was 213237. For Michigan, there was decrease from 114717 to 114159.

When a person born during 2011 in the United States is chosen randomly, the person is more likely to have been born in Florida.

The probability that a randomly selected us resident in 2011 was living in Florida will be:

= 18,801,310/308,745,538

= 0.061

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Answer:.20

Step-by-step explanation:

According to what are written in the table the probability for x=-10 is .20

Answer:

principal = $400

Step-by-step explanation:

amount(a)=principal(p) + interest(y).........(1)

Interest(y)=principal(p) x rate(r) x time(t)....(2)

In (1), p= a - y...........(3)

putting (3) in (2),

y = (a - y) x r% x t

y = (432 - y) x 8% x 1

y = 3456%-8y%

y + 0.08y = 3456%

1.08y = 34.56

y = 32

but a - y = p

432 - 32 = p

p = 400

principal = $400

Answer:

[tex]\textsf{B.}\quad -2(\sqrt{2}-1)[/tex]

Step-by-step explanation:

Given integral:

[tex]\displaystyle \int^{\pi}_{\frac{\pi}{2}}\dfrac{\cos \theta}{\sqrt{1+ \sin \theta}}\:\:d\theta[/tex]

Solve by using Integration by Substitution

Substitute u for one of the functions of [tex]\theta[/tex] to give a function that's easier to integrate.

[tex]\textsf{Let }u=1+\sin \theta[/tex]

Find the derivative of u and rewrite it so that [tex]d \theta[/tex] is on its own:

[tex]\implies \dfrac{du}{d \theta}=\cos \theta[/tex]

[tex]\implies d \theta=\dfrac{1}{\cos \theta}\:du[/tex]

Use the substitution to change the limits of the integral from [tex]\theta[/tex]-values to u-values:

[tex]\textsf{When }\theta=\pi \implies u=1[/tex]

[tex]\textsf{When }\theta=\dfrac{\pi}{2} \implies u=2[/tex]

Substitute everything into the original integral and solve:

[tex]\begin{aligned}\displaystyle \int^{\pi}_{\frac{\pi}{2}}\dfrac{\cos \theta}{\sqrt{1+ \sin \theta}}\:\:d\theta & =\int^{1}_2}\dfrac{\cos \theta}{\sqrt{u}}\:\cdot \dfrac{1}{\cos \theta}\:\:du\\\\& =\int^{1}_{2}\dfrac{1}{\sqrt{u}} \:\:du \\\\& =\int^{1}_{2} u^{-\frac{1}{2}}\:\:du \\\\& = \left[ 2u^{\frac{1}{2}} \right]^{1}_{2}\\\\& = \left(2(1)^{\frac{1}{2}}\right)-\left(2(2)^{\frac{1}{2}}\right)\\\\& = 2-2\sqrt{2}\\\\& = -2(\sqrt{2}-1)\end{aligned}[/tex]

Answer:

Step-by-step explanation:

tan 45=1

[tex]tan 2\alpha =\frac{2tan\alpha}{1-tan^2\alpha } \\put~\alpha =22.5\\2\alpha =2 \times 22.5=45\\tan~2\alpha =tan~45=1\\1=\frac{2tan \alpha }{1-tan^2\alpha} \\1-tan^2\alpha =2 tan\alpha \\ tan^2\alpha +2tan \alpha -1=0\\tan\alpha =\frac{-2 \pm\sqrt{4+4} }{2} \\=-1\pm\sqrt{2} \\\alpha =22.5\\so ~tan~\alpha ~is~positive.\\so ~tan~\alpha =\sqrt{2} -1[/tex]

Answer:

     [tex]\frac{15*7^{x} }{7^{x} +9}[/tex]

Step-by-step explanation:

→ Substitute f(x) into g(x)

     [tex]\frac{15*7^{x} }{7^{x} +9}[/tex]