Express the given logarithm in terms of common logarithms. Then approximate its value to four decimal places.


log2 11

Answer:

48

Step-by-step explanation:

Here are two methods for finding the answer.

Method A.

In 1 foot, there are 4 1/4-foot pieces.

In 12 feet, there are 12 times as many as in 1 foot.

12 * 4 = 48

Method B.

Divide 12 ft by 1/4 ft.

12/(1/4) = 12 * 4/1 = 12 * 4 = 48

Answer: 48

48 cut from a 12 foot board.

Bed cradles and foot boards are devices that attach to your bed. They keep sheets and blankets from touching and rubbing your legs or feet. Foot boards will also keep your feet in proper position while you are in bed.

In 1 foot, there are 4 1/4-foot pieces.

In 12 feet, there are 12 times as many as in 1 foot.

12 ×4 = 48

Divide 12 ft by 1/4 ft.

12/(1/4) = 12 ×4/1

= 12 × 4 = 48

1/4 foot pieces can you cut from a 12 foot board = 48

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Answer:

[tex]\large\boxed{Q1.\ \left\{\begin{array}{ccc}y\leq-2x-1\\y\leq x+5\end{array}\right}\\\boxed{Q2.\ 6\leq y-3\leq8}\\\boxed{Q3.\ y\leq x-4}[/tex]

Step-by-step explanation:

<, > - dotted line

≤, ≥ - solid line

<, ≤ - shaded above the line

>, ≥ - shaded below the line

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

The slope intercept form of a line: y = mx + b

m - slope

b - y-intercept (0, b)

If m > 0, then the function is increasing

If m < 0, then the function is decreasing

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

y = -2x - 1 → m = -2 < 0 and b = -1

decreasing function, y-intercept -1 → (0, -1)

y = x + 5 → m = 1 > 0 and b = 5

increasing function, y-intercept 5 → (0, 5)

y = 2x - 1 → m = 2 > 0, and b = -1

increasing function, y-intercept -1 → (0, -1)

y = -x + 5 → m = -1 < 0 and b = 5

decreasing function, y-intercept 5 → (0, 5)

From the picture we have

(1) increasing function and y-intercept 5 → y = x + 5

shaded below the solid line → y ≤ x + 5

(2) decreasing function and y-intercept -1 → y = -2x - 1

shaded below the solid line → y ≤ -2x - 1

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

[tex]9\leq y\leq11[/tex]            subtract 3 from both sides

[tex]9-3\leq y-3\leq11-3\\\\6\leq y-3\leq8[/tex]

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

solid line (≤ or ≥)

shaded below the line (≤ or <)

y ≤ x - 4

Find the volume of what the full rectangle would be then find the area of the missing piece and subtract:

10 x 12 x = 960 cm^3

4 x 5 x 8 = 160 cm^3

960 - 160 = 800 cm^3

Answer:

y=$2.95x+$479.4

Step-by-step explanation:

Let

x----> the number of movie rentals

y ----> the cost for movie rentals

we know that

The expression that represent the monthly cost is equal to

y=$2.95x+$39.95

1 year has 12 months

so

The expression that represent the yearly cost is equal to

y=$2.95x+$39.95*(12)

y=$2.95x+$479.4

Answer:

A

Step-by-step explanation:

Answer:

A.) The are of the circle depends on the square of the radius

Step-by-step explanation:

To find the area, use the formula A= pi r^2

A= pi(18^2)= 1017.88

so A and B are not correct

Pi is a constant and is never changing.

Central Angle doesn't apply to this problem

so the correct answer is the first choice

The following statements are correct with reference to the circle given -

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a circle with the radius 18 cm.

The area of the circle is given by -

A = πr²

A = 18 x 18 x π

A = 324π

Therefore, we can conclude that the following statements are correct with reference to the circle given -

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Answer:

C

Step-by-step explanation:

The equation represents speed as a function of time. The point (3,120) implies that the car with a speed of 40 miles per hour, travelled a total of 120 miles in a time span of 3 hours.

In this scenario, the equation ys = 40x relates the speed of the car (40 miles per hour) to the time travelled (x in hours). The 'y' in the equation represents the distance travelled by the car. So, when interpreting the point (3,120) on the graph for this equation, '3' refers to time (hours) and '120' refers to distance travelled (miles).

Thus, the point (3,120) on the graph signifies that the car travelled 120 miles in 3 hours, so the correct answer is C. The car traveled 120 miles In 3 hours.

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Answer: a^2+b^2=c^2

Step-by-step explanation: (18^2=14^2+c^2)=324=196+c^2

324-196=128 and the square root of 128 is 8 radical 2 or in decimal form 11.31

Answer:

11.3137085 ft

Step-by-step explanation:

The length (l) of the ladder is 18ft

The height (h) of the ladder from the ground is 14 ft

The distance (x) of the foot of the ladder to the bottom of the house is:

Applying the Pythagorean theorem:

x² = l² - h²

x = [tex]\sqrt{l^2 - h^2}[/tex]

x = [tex]\sqrt{18^2 - 14^2}[/tex] = 11.3137085 ft

Answer: [tex]f(2)=44[/tex]

Step-by-step explanation:

Given the polynomial [tex]f(x) =3x^3+5x^2+x-2[/tex], you can evaluate it for the given value of the variable "x" by substituting the value [tex]x=2[/tex] into the polynomial.

Therefore, when [tex]x=2[/tex],  you get the following result:

[tex]f(x) =3x^3+5x^2+x-2 \\\\f(2) =3(2)^3+5(2)^2+(2)-2\\\\f(2)=3(8)+5(4)+2-2\\\\f(2)=24+20\\\\f(2)=44[/tex]

Answer:

x > -1/2

Step-by-step explanation:

Step 1: Use the Distributive Property

-2x - 1 < 0

Step 2: Isolate x

-2x < 1

Step 3: Simplify

x > -1/2

Note that when dividing by a negative in an inequality, reverse the inequality symbol.

Answer:

I dont know the answer

Step-by-step explanation:

But you can find the answer by figuring out what a domain and a range iss and chose which one is a domain and a range you can find what a domain and a range is on google

-The domain has all possible values of S so is the amount of sugar transported.

-The range has all possible values of C so is the cost to transport sugar

Answer:

[tex]\large\boxed{-\dfrac{8}{\sqrt{63}}}[/tex]

Step-by-step explanation:

[tex]\csc\theta=\dfrac{1}{\sin\theta}\\\\\cos\theta=-\dfrac{1}{8}\qquad\text{use}\ \sin^2\theta+\cos^2\theta=1\\\\\sin^2\theta+\left(-\dfrac{1}{8}\right)^2=1\\\\\sin^2\theta+\dfrac{1}{64}=1\qquad\text{subtract}\ \dfrac{1}{64}\ \text{from both sides}\\\\\sin^2\theta=\dfrac{64}{64}-\dfrac{1}{64}\\\\\sin^2\theta=\dfrac{63}{64}\to\sin\theta=\pm\sqrt{\dfrac{63}{64}}\\\\180^o<\theta<270^o\to III\ quadrant,\ \sin\theta<0.\\\\\text{Therefore}\ \sin\theta=-\sqrt{\dfrac{63}{64}}=-\dfrac{\sqrt{63}}{\sqrt{64}}=-\dfrac{\sqrt{63}}{8}.[/tex]

[tex]\csc\theta=\dfrac{1}{-\frac{\sqrt{63}}{8}}=-\dfrac{8}{\sqrt{63}}[/tex]

Answer:

6y - 3y - 7 = -2 +3

Simplify both sides:

3y -7 = 1

Add 7 to both sides:

3y = 8

Divide both sides by 3:

y = 8/3 = 2 2/3

There is only one solution.

Answer:

See the procedure

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

a,b,c the lengths side of triangle

c is the greater side

The perimeter is equal to

P=a+b+c

P=36 cm

If c=18 cm

then

a+b=18

Applying the Triangle Inequality Theorem

a+b > c

18 > 18  ----> is not true

therefore

Principal Aranda is incorrect

The larger side cannot measure 18 cm

The largest side must be less than 18 cm

Answer:

(fog)(2)=2

Step-by-step explanation:

Given

f(x)= -2x+8

and

g(x)= √(x+7)

For finding (fog)(2), we have to find (fog)(x) first

In order to find (fog)(x) we will put the value of g(x) in f(x) in place of x.

(fog)(x)= -2g(x)+8

Putting the value of g(x)  

(fog)(x)= -2√(x+7)+8

We have to find (fog)(2), so we have to put at the place of x in the composition

(fog)(x)= -2√(2+7)+8

(fog)(x)= -2√9+8

= -2(3)+8

= -6+8

=2

So,

(fog)(2)=2   ..

Answer:

- 10

Step-by-step explanation:

Given

3(x - 4) ≥ 5x + 2 ← distribute left side

3x - 12 ≥ 5x + 2 ( subtract 3x from both sides )

- 12 ≥ 2x + 2 ( subtract 2 from both sides )

- 14 ≥ 2x ( divide both sides by 2 )

- 7 ≥ x ⇒ x ≤ - 7

The only value from the list that is in the solution set is

x = - 10

The value of x is -10

The correct option is (A)

Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols. In elementary algebra, those symbols (today written as Latin and Greek letters) represent quantities without fixed values, known as variables.

Given expression:

3(x - 4) ≥ 5x + 2

Using distributive law,

3x - 12 ≥ 5x + 2

- 12 ≥ 2x + 2 ( subtract 2 from both sides )

- 14 ≥ 2x ( divide both sides by 2 )

- 7 ≥ x

x ≤ - 7

Hence, x is less than and equal -7 so the only solution is -10

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Answer:

C

Step-by-step explanation:

Because if you have 75 baskets of 30 then you have to multiply 75x30 it is the same thing with 50x45. Hope this helps

Answer:C) 75x30) +(50x45)

Step-by-step explanation: 75 * 30 for the 30 apples in each basket and 50 * 45 for the 45 in each and put them into their own equation with parenthesees. Then add to find the total

[tex]\bf \begin{array}{ccll} book&days\\ \cline{1-2}\\ \frac{3}{4}&2\\\\ x&4\frac{1}{3} \end{array}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{4\frac{1}{3}}\implies \cfrac{~~\frac{3}{4}~~}{x}=\cfrac{~~2~~}{\frac{13}{3}} \implies \cfrac{~~\frac{3}{4}~~}{\frac{x}{1}}=\cfrac{~~\frac{2}{1}~~}{\frac{13}{3}}[/tex]

[tex]\bf \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{2}{1}\cdot \cfrac{3}{13}\implies \cfrac{3}{4x}=\cfrac{6}{13}\implies 39=24x\implies \cfrac{39}{24}=x\implies \cfrac{13}{8}=x \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 1\frac{5}{8}=x~\hfill[/tex]

40% of the figure is shaded.

The image depicts many grids. These small squares has 10 rows and 10 columns. So, the total number of squares are:

10 x 10=100 squares.

Out of 100 squares, 4 rows and their 10 columns are shaded. So,

4*10=40 squares

So, 40 squares are shaded. To find the percentage we can use the formula:

Shaded/ Total Squares x 100

= 40/100 x 100

= 40%

Therefore, 40 percent of the figure is shaded.

To find what percent of a figure is shaded, calculate the shaded area divided by the total area and multiply by 100. In probability distributions, shading indicates the probability that a variable falls within a specific range, such as the 80th or 90th percentile of a distribution.

To determine what percent of the figure is shaded, one must first understand the concept of percentage calculations. The percentage is computed by dividing the part (shaded area) by the total area, then multiplying by 100. In the case of probability distributions, the shaded area represents a probability, such as the probability of a variable falling between two values, or the specific percentile of a distribution.

For example, if we have a graph with a horizontal axis for X, and we need to shade the region corresponding to a certain probability or percentile, we need to identify the region under the curve that equates to that percentage. This could involve calculating the area between two x-values or finding a value that corresponds to a given area under the curve, such as the 80th percentile or 90th percentile. To express the result as a percentage, multiply the probability by 100.

Sometimes, the question may provide specific conditions, such as indicating that the shaded area under one curve is equal to the area of another shape, like a rectangle or another curve. In this case, we can assume the two percentages are equal and express the probability of one as the same percentage as the other.

Answer:

[tex]a_t=ar^{t-1}[/tex]

t=6 months

Step-by-step explanation:

We are given that the number of people playing a new phone app game triples every month

When the app first launch , the number of people started playing the  game  right away=800

According to question

The number of peoples are currently playing the game=194,400

We solve by using the formula of  geometric series because we get a geometric series pattern

The number of people playing the game when app game launch=800

The number of people playing game after one month=2400

800,2400,7200,........,194,400

[tex]a_1=800,a_2=2400,a_3=7200,a_t=194,400[/tex]

We are finding common ratio

[tex]\frac{a_2}{a_1}=\frac{2400}{800}=3[/tex]

[tex]\frac{a_3}{a_2}=\frac{7200}{2400}=3[/tex]

Hence, the common ratio is 3 therefor nth term of  G.P

[tex]a_t=ar^{t-1}[/tex]

a=800,r=3,[tex]a_t=194,400[/tex]

Substitute the values then we get

[tex]194,400=800(3)^{t-1}[/tex]

[tex]\frac[194400}{800}=(3)^{t-1}[/tex]

[tex]243=3^{t-1}[/tex]

[tex]3^5=3^{t-1}[/tex]

When base are same on both side then the power are equals

Therefore, t-1=5

t=5+1=6

Hence, when there are 194,400 people currently playing the game then

the number of months ,t=6 that have passed since the app launched.

Answer:

800(3)^t = 194,400; t = 5 months

Step-by-step explanation:

Answer:

The answer is 11 100%FOR SURE BELIEVE ME!!!

Step-by-step explanation:

A,B= (2*11)=22-3= 19

B,C= (11+1)=12

A,C= 19+12= 31

PLZZ MARK BRAINLIST PLLZZZZ THANK YOU

Answer:

AB

Reflexive Property

BE

SSS

Definition of perpendicular

Step-by-step explanation:

Answer:

This question is based on concept of geometry. Therefore, the answers are as follows:

1) AB         2) Reflexive property           3) BE          4) SSS

5) definition of perpendicularity.

Given that:

ABCD is a square.

In this question, we have to fill the blanks and complete the sentence where it is looking like incomplete.

According to question,

Therefore, at first It is given that, if we consider triangle AEB and Triangle AED, we observe that side AB side is congruent to side AD.

(2) We know that, side AE is congruent to side AE by using the Reflexive property because sides of a square are congruent.

(3) Finally, we know that side DE is congruent to side BE because the diagonals of a square bisect each other.

(4)Therefor triangle AEB is congruent to triangle AED by SSS congruency.

(5) We see that angle AED and angle AEB are a linear pair, and congruent  by CPCT , the angle AED and AEB are a linear pair and the measure of these angle will be 90 because ABCD is a square and thus diagonal AC is perpendicular to diagonal BD by the definition of perpendicularity.

Therefore, the answers are as follows:

1)AB

2)Reflexive property  

3)BE  

4)SSS

5) definition of perpendicularity.

Step-by-step explanation:

The answer is:

The third option,

c) [tex]h(x)=2.25x-22[/tex]

We are given the functions E(x) and K(x), since they both are function of the same variable, we need to calculate the difference between them.

From the statement we know the functions:

[tex]f(x)=9.75x+62[/tex]

and

[tex]g(x)=7.5x+84[/tex]

So, calculating the difference the functions we have:

[tex]h(x)=f(x)-g(x)[/tex]

[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]

[tex]h(x)=(9.75x+62)-(7.5x+84)[/tex]

[tex]h(x)=9.75x-7.5x+62-84[/tex]

[tex]h(x)=2.25x-22[/tex]

Hence, the answer is the third option,

c) [tex]h(x)=2.25x-22[/tex]

Have a nice day!

Answer: Option C

[tex]h(x)=2.25x-22[/tex]

Step-by-step explanation:

To find the function h(x) that models the difference between Hector's and Cari's gains, subtract the functions f(x) with g(x)

That is to say:

[tex]h (x) = f (x) -g (x)[/tex]

We know that

[tex]f (x) = 9.75x + 62\\\\g (x) = 7.5x + 84[/tex]

Then we can find the function h(x)

[tex]h(x) = 9.75x + 62 - (7.5x + 84)\\\\h(x) = 9.75x + 62 -7.5x -84[/tex]

[tex]h(x)=2.25x-22[/tex]

I ussually think of them as arrows telling me where to go.

if it is >   you go ----->

if it is < you go <------

Answer:

[tex]\large\boxed{-\dfrac{1}{3}-\dfrac{\sqrt{14}}{3}i,\ -\dfrac{1}{3}+\dfrac{\sqrt{14}}{3}i}[/tex]

Step-by-step explanation:

Use

[tex]ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]3x^2+2x+5=0\\\\a=3,\ b=2,\ c=5\\\\b^2-4ac=2^2-4(3)(5)=4-60=-56\\\\\sqrt{b^2-4ac}=\sqrt{-56}=\sqrt{(4)(-14)}=\sqrt4\cdot\sqrt{-14}=2\sqrt{-14}[/tex]

Use

[tex]i=\sqrt{-1}[/tex]

[tex]\sqrt{-14}=\sqrt{(-1)(14)}=\sqrt{-1}\cdot\sqrt{14}=i\sqrt{14}[/tex]

Therefore:

[tex]x=\dfrac{-2\pm 2i\sqrt{14}}{2(3)}=-\dfrac{2}{6}\pm\dfrac{2i\sqrt{14}}{6}=-\dfrac{1}{3}\pm \dfrac{\sqrt{14}}{3}i[/tex]

The complex solution of the given quadratic equation 3x^2+2x+5=0 is x = (1/6)[ -2 ± i√56].

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax2 + bx + c = 0, where x is the variable, and a must not be zero.

For example, 3x² + 6x + 8 = 0 here x has the highest term as 2 and the coefficient of x² is not zero.

As per the given quadratic equation, 3x^2+2x+5=0

x = [-2 ±√(4 - 4 x 3 x 5)]/(2 x 3)

x = (1/6)[ -2 ± i√56]

Hence "The complex solutions of the given quadratic equation 3x^2+2x+5=0 is x = (1/6)[ -2 ± i√56]".

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Quotient means divide so 7 divided by 1/5 is 35

answer:35

reason: because all you are doing is dividing 7 and 1/5

Answer:

-8.5

Step-by-step explanation:

-4x+8=42

42-8=34

34/-4=8.5

Answer:

x = -8.5

Step-by-step explanation:

minus 8 on both sides and the eight should cancle on the left side

42 minus 8 is 34

then you divide negative 4 on both sides

Answer:

well this old so like yeah u prob know by now...

Step-by-step explanation:

The sister is 4n yrs old.

That is because 4 times n is 4n.

Answer:

[tex]n\le 5[/tex]

Step-by-step explanation:

Let n be the number of tickets Makaya has to buy.

If the cost of one ticket is $1.5, then the cost of n tickets is $1.5n.

Makayla has $8 to buy tickets at the school fair, thus

[tex]1.5n\le 8\\ \\n\le \dfrac{8}{1.5}\\ \\n\le \dfrac{80}{15}\\ \\n\le \dfrac{16}{3}\\ \\n\le 5\dfrac{2}{3}[/tex]

The maximum number of tickets Makaya can buy is 5, so

[tex]n\le 5[/tex]

Answer:

31.5 litres

Step-by-step explanation:

If Mel uses all 30 litres of yellow paint, then:

5 / 2 = 30 / x

5x = 60

x = 12

Mel would need 12 litres of blue paint, but she only has 9 litres.  So the amount of yellow paint she needs is:

5 / 2 = x / 9

2x = 45

x = 22.5

Mel will use 22.5 litres of yellow paint with 9 litres of blue paint to make a total of 31.5 litres of green paint.

She can make a maximum of 28 litres of green paint.

To find the maximum amount of green paint Mel can make with her yellow and blue paint, we must use the ratio of 5:2 (yellow to blue) given for mixing the green paint.

Firstly, calculate the number of batches of green paint that can be made with the available yellow paint:

Mel has 30 litres of yellow paint and needs 5 litres per batch of green paint, so she can make 30 ÷ 5 = 6 batches from the yellow paint.

Next, calculate the number of batches that can be made with the blue paint:

Mel has 9 litres of blue paint and needs 2 litres per batch of green paint, so she can make 9 ÷ 2 = 4.5 batches from the blue paint.

However, since we cannot have half a batch, the maximum number of full batches Mel can produce from the blue paint is 4.

The limiting reactant here is the blue paint since it allows fewer batches to be made. Therefore, Mel can only make 4 full batches of green paint.

To find the total amount of the green paint from the batches:

Combine the ratios, which add up to 7 parts (5 parts yellow and 2 parts blue).

Multiply the number of batches by the sum of the parts: 4 batches × 7 parts per batch = 28 litres of green paint.

Thus, the maximum amount of green paint Mel can make is 28 litres.