What is the L.C.M of 4,10​

If [tex]251_x\equiv100_{10}[/tex], then this translates to the equation

[tex]251_x = 2x^2 + 5x + 1 = 100[/tex]

Solve for [tex]x[/tex].

[tex]2x^2 + 5x = 99[/tex]

[tex]2\left(x^2 + \dfrac52 x\right) = 99[/tex]

[tex]2 \left(x^2 + \dfrac52 x + \dfrac{25}{16}\right) - \dfrac{25}8 = 99[/tex]

[tex]2 \left(x + \dfrac54\right)^2 = \dfrac{817}8[/tex]

[tex]\left(x + \dfrac54\right)^2 = \dfrac{817}{16}[/tex]

[tex]x + \dfrac54 = \pm \dfrac{\sqrt{817}}4[/tex]

[tex]x = \dfrac{-5\pm\sqrt{817}}4[/tex]

though it is a bit unusual (but not entirely out of the question) to have an irrational base number system.

In case you meant [tex]100_2[/tex] on the right side, then [tex]100_2 = 2^2 = 4_{10}[/tex], so that

[tex]2x^2 + 5x + 1 = 4 \\\\ 2x^2 + 5x - 3 = 0 \\\\ (x+3) (2x-1) = 0 \\\\ x=-3 \text{ or } x = \dfrac12[/tex]

which at first glance seem like more reasonable choices of base.

In the context of probability, an experiment is a process:

First, he has to decide on a pair of shirts and he has 7 different colors to choices.

A value between 0 and 1, inclusive, describes the relative possibility (chance or likelihood) that an event will occur.

For each of those choices he has a choice of 7 different shirts, so that gives him 3 times 7 = 21 different shirts.

For each of those 21 possibilities, he has 21 times 3 = 63 different outfits, and some of them may be acceptable to wear in public.

It is simply,3*3*7=64 ways.

The number of favorable outcomes is divided by the number of possible outcomes.

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The question was incomplete. Below you will find the missing content.

In the figure below, BL, AM, and CK are medians of △ABC. If KC = 108 and OC = 2n + 10, then n=

The picture is attached below.

The value of n is 31.

The median is the line connecting the vertex and its midpoint on the opposite side of the triangle.

The intersection of all 3 medians of the triangle is called the centroid.

As we know centroid divides the median in the ratio of 2:1.

In the given picture,

Medians of triangle △ABC are AM, BL, and CK.

So the centroid of the triangle is O.

Given that KC= 108

As the centroid O divides the line KC in 2:1.

Let OC=2x

KO= X

As KC= KO+OC

⇒ 108= x+2x

⇒ 3x=108

⇒ x=108/3

⇒ x=36

Then OC= 2x= 2*36= 72

As given in the question OC= 2n+10

putting the value of OC in above equation

⇒ 72= 2n+10

⇒ 2n= 72-10

⇒ 2n=62

⇒ n=62/2

⇒n=31

Therefore the value of n is 31.

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The solutions of the inequality x>-2 is 0, 4 2/5, 1.999, 347.595

Given the inequality is x>-2

Solution of the inequality is greater than -2

0, 4 2/5, 1.999, 347.595 are the solutions of given inequality.

Hence, the solutions of the inequality x>-2 is 0, 4 2/5, 1.999, 347.595

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The required volume of the prism is 48 cubic centimeters

The formula for calculating the volume of a prism is expressed as:

V = lwh

where l is the side length

w is the width

h is the height

Given the following

l =  2 cm.

Height 2cm

Width 12 cm

Substitute

V = 2(2)(12)

V = 48 cubic centimeters

Hence the required volume of the prism is 48 cubic centimeters

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The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600

An equation is an expression that shows the relationship between two or more numbers and variables.

Let y represent the bacteria population at time t. a represent the initial population at t = 0. Since the doubling period of a bacteria population is 10 minutes, hence:

[tex]y=a(2)^\frac{t}{10}[/tex]

At time t = 110 minutes, the bacterial population was 800. Hence:

[tex]800=a(2)^\frac{110}{10} \\\\a = 0.39[/tex]

At 4 hours (240 minutes):

[tex]y=0.39(2)^\frac{240}{10} =6553600[/tex]

The initial population at time t = 0 was 0.39 while the size of the bacteria population after 4 hours was 6553600

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Answer: 390 m².

Step-by-step explanation:

[tex]Surface \ area = 11*13+11*12+11*5+2*\frac{12*5}{2}=11*(13+12)+11*5+12*5=\\ =11*25+5*(11+12)=275+5*23=275+115=390\ (m^2).[/tex]

Answer:

The mean is ^6

Step-by-step explanation: To figure out the mean, add up the numbers, 7+3+5+2+9+10=36 then divide it by how many numbers you have 36/6=6

Answer:

The correct answer is 6

Step-by-step explanation:

x/10=3/5

then cross multiply

it will now give

5x=30

x=6

Answer:

6

Step-by-step explanation:

the sequence increases by 1,2,3,4,5,6 each time, thus it is 6

Adam's weekly money deposit is a linear relation with a slope of $6 per week.

A) Money deposited by Adam each week is $6.

B) The answer can be determined by observing the graph provided to us, in which the point representing 1 week on the x-axis is intersected by the point representing $6 on the y-axis. This helps us determine that Adam's weekly deposit is $6.

C) An alternative strategy of calculating the slope can be used.

The slope can be calculated in the following way:

m = (y₂ - y₁)/(x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.

Thus slope of this line can be calculated as,

m = (12 - 6)/(2 - 1) = 6/1 = 6 {Since, the line passes through the points (2, 12) and (1, 6)}.

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The algebraic expression is 2/3(2y + y)

The length of the 2/3 feet long

It is broken into two parts x and y

If x is twice the length of y, we have

x = 2y

The algebraic expression is 2/3/x + y , if x = 2y

We have that,

2/3(2y + y)

Thus, the algebraic expression is 2/3(2y + y)

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Answer:

34%

Step-by-step explanation:

hope I helped

have a nice day

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

If a pupil scored 17/50 on a test, then what percentage is this?

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

First let's turn 17/50 into a decimal.

[tex]\bf{17/50=0.34}[/tex]

Now move the decimal point two places to the right to convert to percentages.

[tex]\bf{34\%}[/tex] .Uh-oh, better luck next time, student!

[tex]\cline{1-2}[/tex]

[tex]\bf{Result:}[/tex]

          [tex]\bf{=34\%}[/tex]

[tex]\LARGE\boxed{\bf{aesthetic\not1\theta\ell}}[/tex]

Answer:

[tex]\huge\boxed{\sf 46.2\%}[/tex]

Step-by-step explanation:

Prediction = 19 throws

Actual = 13 throws

[tex]\displaystyle =\frac{Predication -Actual}{Actual} \times 100 \%\\\\= \frac{19-13}{13} \times 100 \%\\\\= \frac{6}{13} \times 100 \%\\\\= 0.462 \times 100 \%\\\\= 46.2\%\\\\\rule[225]{225}{2}[/tex]

Answer:

$20.55

Step-by-step explanation:

2.5 x 6.1 + 0.5 x 10.6 = 15.25 + 5.3 = 20.55

Answer:

12.0 to 3 dig digs You must include the 0 to get 3 significant figures.

Step-by-step explanation:

Comment

This is a Pythagorean Problem. Use the formula

c ^2 = a^2 + b^2

Givens

a = 8 - 7 = 1 cm

b = 12 cm

c = ?

solution

c^2 = 1^2 + 12^2  

c^2 = 1 + 144

c^2 = 145                 Take the square root of both sides

√c^2 = √145  

c = 12.04

c = 12.0 to 3 sig digs.

The appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].

Given the equation and interval.

tanθ = -3, [ π/2 < θ < π ]

First, we use the definition of tangent to determine the known sides of the unit circle right triangle.

Note that; the quadrant determines the sign of each values.

tanθ = opposite / hypotenuse

We can use Pythagoras theorem to find the hypotenuse of the unit circle right triangle as the opposite and adjacent sides are known.

Hypotenuse = √( opposite² + adjacent² )

Hence, we have;

Hypotenuse = √( [3]² + [-1]² )

Hypotenuse = √( 9 + 1 )

Hypotenuse = √10

1) To find sinθ

sinθ = opposite / hypotenuse

sinθ = 3/√10

We simplify

sinθ = 3/√10 × √10/√10

sinθ = 3√10 / 10

[tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex]

2) cosθ

cosθ = adjacent / hypotenuse

cosθ = -1 / √10

Simplify

cosθ = -1 / √10 × √10/√10

cosθ = -√10 / 10

[tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex]

3) cotθ

cotθ = adjacent / opposite

cotθ = -1 / 3

[tex]cot\theta= -\frac{1}{3}[/tex]

4) secθ

secθ = hypotenuse / adjacent

secθ = √10 / -1

[tex]sec\theta=-\sqrt{10}[/tex]

5) cscθ

cscθ = hypotenuse / opposite

cscθ = √10 / 3

[tex]csc\theta= \frac{\sqrt{10} }{3}[/tex]

Therefore, the appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].

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Using proportions, it is found that:

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The unit price is given by the cost divided by the number of ounces, and the better deal is given by the deal with the lowest unit price.

Hence, for the 11.3 ounce package:

u = 3.68/11.3 = $0.33 per ounce.

For the 29.3 ounce package:

u = 8.98/29.3 = $0.31 per ounce.

Due to the lower unit cost, the 29.3 ounce package is the better deal.

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Answer:

12.75

Step-by-step explanation:

Turn 12 ¾ = to a decimal

¾ = 0.75

12 + 0.75

12.75

Using translation concepts, the transformations are given as follows:

a) The function is horizontally compressed by a factor of 3 and shifted down one unit.

b) The function is shifted right 3 units and vertically stretched by a factor of 2.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

Item a:

The transformations are:

Item b:

The transformations are:

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Answer:

24 Inches

Step-by-step explanation:

Its 24 Inches away from the centre lol

Answer:

Step-by-step explanation:

Directions

Givens

AC = 13 inches                   Given

CB = 24 inches                  Given

CE = 12 inches                    Construction and property of a midpoint.

So what we have now is a right triangle (ACE) with the right angle at E.

What we seek is AE

Formula

AC^2 = CE^2 + AE^2

13^2 = 12^2 + AE^2

169 = 144 + AE^2                     Subtract 144 from both sides.

169 - 144 = 144-144 + AE^2     Combine

25 = AE^2                                Take the square root of both sides

√25 = √AE^2

5 = AE

Answer

The 24 inch chord is 5 inches from the center of the circle.

Yes at 0.05 significance level we can conclude that mean income of those selecting plan B is bigger.

Given mean yearly income for sample of 40 subscribers is $57000 with standard deviation of $9200, mean yearly income for sample of 30 subscribers with standard deviation of $7100.

First we have been given significance level (α) of 0.05. So (1-α)=1-0.05=0.95 and we have to find Z score for this significance level. (1+0.95)/2=0.425

Z=1.44

Now we have to calculate margin of error which will be calculated as under:

[tex]M_{A} =Z*st/\sqrt{n}[/tex]

=[tex]1.44*9200/\sqrt{40}[/tex]

=1.44*9200/6.32

=1869.10

[tex]M_{B}=Z*st/\sqrt{n}[/tex]

=[tex]1.44*7100/\sqrt{30}[/tex]

=1.44*7100/3.47=2096.2

We know that margin of error shows the difference between real and calculated values. So if we increase mean of both plans by margin of error of respective plans then mean of plan A becomes=57000+1869.10=58869.10 and mean of plan B becomes =61000+2096.2=630622.2. We can clearly notice that mean of plan B is greater.

Hence it is reasonable to say that the mean of plan B is greater at the significance level of 0.05.

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The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix. The correct option is C.

A parabola is a U-shaped figure, all the point on the parabola is equidistant from the focus, and a line called Directrix.

The Parabola is a locus of points equidistant from a single point called focus and a line called Directrix.

Therefore, The correct option is C.

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There is only 2 outliers in a scatter plot. And the graph is attached below

A scatter plot is shown. In the form of (x, y) coordinates. The ordered pairs 0, 2 and 1, 3 and 1, 9 and 1.2, 4 and 1.9, 4 and 2.6, 4.2 and 3, 5 and 4, 5 and 4, 6 and 4.8, 6.1 and 5, 7 and 5, 7.9 and 6.9, 7.1 and 6, 8 and 7, 3.8 and 7, 8.2 and 7, 9.1 and 7.1, 9.8 and 8, 10 and 10, 7.

Coordinate, is represented as the values on x axis and y axis of graph

Clearly every preceding coordinate is close to each other and follow a close patter of line or continuous curve. except only two points are far from the curve are (1, 9)  and (10, 7).

Thus, The required outliers is given by (1, 9) (10, 7)

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The exponential function to model the quail population is 910*(1.2)^t

Concept: An exponential function is a mathematical function denoted f(x)=\exp or e^{x}. Unless otherwise stated, the term generally refers to a positive function of a real variable, although it may be extended to complex numbers or generalized to other mathematical objects such as matrices or Lie algebras.

Given data

Initial population= 910 quail

Rate= 20%

Now using the model below:

A= P(1+r)^t

r= 0.2

A= 910(1+0.2)^t

A= 910*(1.2)^t

Hence the expression to model the population is  910*(1.2)^t

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4 times as likely is Phillip to get exactly three heads than exactly two heads

A chance that something might exist, happen, or be true : the state or fact of being possible is called possibilities.

Possibility is the universal set whereas probability is the subset. Possibility is surer to occur than probability. Possibility has its opposite in the word impossibility whereas probability has its opposite in the word improbability.

We can find;

P (three heads) =  C(8,3)(2/3)^3(1/3)^5  = 448 / 6561

P (two heads) = C(8,2)(2/3)^2(1/3)^6  = 112 / 6561

So......     448 / 112   =  4 times more likely to get 3 heads than 2 heads

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The factorized expression of -x - 10 is -(x + 10)

The expression is given as:

-x - 10

Factor out -1 from the expression

-1(x + 10)

Rewrite as:

-(x + 10)

Hence, the factorized expression of -x - 10 is -(x + 10)

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Answer:

x=1

Step-by-step explanation:

It's pretty obvious to see that x equals 1 after you subtract 3 from both sides, but this question specifies using change base, so:

log(b)a means log base b with a as the contents
1.
4^x+3-3=7-3

4^x=4

log(4)4^x=log(4)4    (both logs are base 4 in this case to free the x)

x=log(4)4

x=log(10)4/log(10)4   (both logs are base 10 in this case)

x=1

Change base is definitely unnecessary in this problem

The image of the figure under reflections in line m and then line t is shown below.

A spatial transformation is each mapping of feature shapes to itself, and it maintains some spatial correlation between figures.

Reflection does not change the size and shape of the geometry.

The image of the figure under reflections in line m and then line t.

The reflection of the rectangle DEFG will be given in the figure.

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The average commute distance of all 50,000 heads of households in the town is estimated as 8.7, and this estimate is likely to be off by 0.28 or so.

The population mean = 8.7

population standard deviation = s/√n

s = 9

n = 1000

= 9/√1000

= 0.28

The conclusion is that the estimate is 8.7 and it is off by 0.28.

CI = bar X ± Z∝/2(s/√n)

= 8.7±1.645(0.28)

= 8.7 ± 0. 47

Confidence interval = 8.23, 9.17

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