Express ln 32-ln 8 as a single logarithm

Answer:

5/9

Step-by-step explanation:

Let the denominator be k and thus numerator be 4 less than k or k - 4.

Fraction = (k - 4)/k

If 5 is added to both:

=> (k-4 + 5)/(k + 5) = 5/7

=> 7(k + 1) = 5(k + 5)

=> 7k + 7 = 5k + 25

=> 2k = 18

=> k = 9

Thus,

Fraction is (k-4)/k = (9-4)/9 = 5/9

Answer:

[tex] x = - 3 \frac{4}{15}[/tex]

Step-by-step explanation:

[tex]2x - \frac{1}{3} + 3 = x - \frac{3}{5} [/tex]

[tex] = > 2x - \frac{ 1 +9 }{3} = x - \frac{3}{5} [/tex]

[tex] = > 2x + \frac{8}{3} = x - \frac{3}{5} [/tex]

[tex] = > 2x - x = - \frac{3}{5} - \frac{8}{3} [/tex]

[tex] = > x = - \frac{9 - 40}{15} [/tex]

[tex] = > x = - \frac{49}{15} [/tex]

[tex] = > x = - 3 \frac{4}{15} (ans)[/tex]

Answer:

x = - [tex]\frac{49}{15}[/tex]

Step-by-step explanation:

Given

2x - [tex]\frac{1}{3}[/tex] + 3 = x - [tex]\frac{3}{5}[/tex]

Multiply through by 15 ( the LCM of 3 and 5 ) to clear the fractions

30x - 5 + 45 = 15x - 9 , that is

30x + 40 = 15x - 9 ( subtract 15x from both sides )

15x + 40 = - 9 ( subtract 40 from both sides )

15x = - 49 ( divide both sides by 15 )

x = - [tex]\frac{49}{15}[/tex]

Your answer would be A because the radius of the circle is half of its diameter.

Hope this helps <3 :)

Answer:

17.6

Step-by-step explanation:

If you add all of the digets up you get: 86

86 divided by the quanity of numbers is: 17.6

Answer:

Steve needs to sell 34 items.

Step-by-step explanation:

S= 5x+50

220=5x+50

-50       -50

170= 5x

/5       /5

34 =  x

Check:

220= 5(34)+50

220=170+50

220=220

Answer:

9

Step-by-step explanation:

V=pi (r squared) (h/3)

75pi = 25pi (h/3)

Divide both sides by 25 pi

3= h/3

Multiply both sides by 3

h=9

Answer:

Vertical angles: <3 and <8, <2 and <5, <1 and <6, <4 and <7 (choose one pair, these are all right)

Linear: <1 and <5, <2 and <6, <3 and <7, <4 and <8, there are more (choose one pair, all these are right)

Congruent: Choose one of the vertical angle pairs I listed above

Step-by-step explanation:

Vertical angles are diagonally across for each other and equal the same angle. You would get a better explanation if you looked up pictures.  

Linear angles are two angles on a straight line that are divided by another line. Again, you would get a better explanation by looking at a visual

Congruent angles are equal to each other, and because there are no angle measures here, you would go with a vertical angle pair.

Answer:

Step-by-step explanation:

Vertical angles: <3 and <8, <2 and <5, <1 and <6, <4 and <7 (choose one pair, these are all right)

Linear: <1 and <5, <2 and <6, <3 and <7, <4 and <8, there are more (choose one pair, all these are right)

Congruent: Choose one of the vertical angle pairs I listed above

Answer:

131.2

Step-by-step explanation:

x/55=31/14

x=31/13*55

x=131.153846154

Answer:

ABC= 60 XYZ=540

Step-by-step explanation:

The area of a triangle is 1/2*base*height so for ABC we need to find the height first. To do this we use pythag theorem, and create the equation 13^2=5^2+height^2 rearranging this we can figure out that sqrt(height)=13^2-5^2. For the base we do 2*5 since there are two congruent line segments both equal to 5. Using this we can do 1/2*12*10=area of ABC

For XYZ we can do 1/2*30*36=area of XYZ, we can do 2*15 since there are 2 congruent 15 length line segments at the base.

Answer:

Yes

Step-by-step explanation:

In [tex]a^2+bx+c[/tex], b is the middle term.

Answer:

2 1/2

Step-by-step explanation:

The heaviest bag weighs 4 pounds, and the lightest bag weighs 1 1/2.

4 can be converted to 8/2 and 1 1/2 can be converted to 3/2.

8/2-3/2=5/2.

5/2 converts to 2 and 1/2 or 2.5

The heaviest bags weigh than one of the lightest bags by 2.5 pounds.

A number expressed as a quotient, in which a numerator is divided by a denominator.

The heaviest bag weighs 4 pounds,

and the lightest one weighs 3/2 pounds

The difference between the heaviest and lightest one is:

= 4-3/2

= 8/2-3/2

=5/2 pounds

= 2.5 pounds

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Answer:

a

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

All you have to do is count the number of squares it is from the point to the y axis horizontally. And count from there onwards. When you get further in Maths, you will realise there are much easier ways but this is the most basic.

Answer:

the answer is (-3,0) or 4

Step-by-step explanation:

Answer:

x = 6

Step-by-step explanation:

Tip: You want to isolate the x-variable on one side of the equation to find its value.

1) First, get rid of the radical signs on both sides of the equation by squaring both sides. This should leave you with 5x-7 = 3x+5.

2) Get the x-variables on one side by subtracting 3x from both sides, so the equation should be 2x-7=5.

3) Solve for x by adding 7 to both sides, so that your equation looks like this: 2x = 12.

4) Divide both sides by 2 and you will get x = 6. You can verify 6 as the x-value by plugging 6 back into the original equation.

I hope that helps! :)

Answer:

x=6

Step-by-step explanation:

Answer:

x = 62°

Step-by-step explanation:

the top-most angle in the top isosceles triangle must be 73° also

the third angle of the top isosceles triangle is (180 - 73 + 73) which is 34°

the left portion of the right angle must be 56°

you can find by using this equation:  x + x + 56 = 180

2x = 124

x = 62

Answer:

78.4 miles

Step-by-step explanation:

Since there are 14 days in two weeks, you multiply 5.6 miles times 14 days to get 78.4 miles in total since 5.6 is how much he ran every DAY

Answer:

division

Step-by-step explanation:

you need to get the x by its self because right now x is being multiplied by 3 tou divide it out

Answer:

Division

Step-by-step explanation:

you will divide both sides by 3..“the number that is disturbing x”

Answer: 208 in^2

Step-by-step explanation:

find the surface area of the square base

8(8)=64

find the surface area of the 4 triangular lateral faces

SA=4(bh÷2)

4(8 x 9 ÷2)

4(36)=144

add the surface area of the square base and lateral faces

64+144=208

Answer:

a. 20

b. 6

c. y=2/9x

Step-by-step explanation:

Answer:

width = 9 cm

Step-by-step explanation:

the area of a 12cm square is 144

16w = 144

x = 9

Answer:

14/48 Feet

Step-by-step explanation:

First, you multiply 7/8x2/3 which equals 14/24, which makes the base of the prisim 14/24 feet. Then you need to multiply 14/24 ( the base) by 1/2 (the height). 14/24x1/2= 14/48.

The final answer is 14/48.

Answer:

a b and d

Step-by-step explanation:

Answer:

0.205 ; 0.117 ; 0.999

Step-by-step explanation:

Using binomial probability distribution :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

Probability of success, p = 0.5

P(x = 4) = 10C4 * 0.5^4 * 0.5^6

P(X = 4) = 0.205078125

B.) 3 heads and 7 tails

P(X = 7) = 10C7 * 0.5^7 * 0.5^3

P(X = 7) = 120 * 0.0009765625

P(X = 7) = 0.117

P(atleast one head)

P(x greater than equal to 1) = p(x =1) +... P(x = 10)

Using a binomial probability calculator :

P(x greater than equal to 1) = 0.999

Answer:

99.7% of the boys are between 54 and 84 inches tall.

Step-by-step explanation:

The heights 54 and 84 inches are 3 standard deviations away from the mean. Thus, 99.7% of the boys are between 54 and 84 inches tall.

The percentage of the boys are between 54 and 84 inches tall is 99.7%

What is percentage?

Percentage a relative value indicating hundredth parts of any quantity.

What is empirical rule?

The empirical rule or  the three-sigma rule , is a statistical rule which states that for a normal distribution, almost all observed data will fall within three standard deviations of the mean.

The empirical rule predicts that 68% of observations falls within the first standard deviation (µ ± σ), 95% within the first two standard deviations (µ ± 2σ), and 99.7% within the first three standard deviations (µ ± 3σ).

From question mean(μ) = 69 in. and  standard deviation(σ)= 5 in.

(µ ± σ) = (69 ± 5)

           =64 - 74

           =68%

(µ ± 2σ) =(69 ± 10)

            =59 -79

            =95%

(µ ± 3σ) =(69 ± 15)

             =54 -84

             = 99.7%

Thus the percentage of the boys are between 54 and 84 inches tall is 99.7%

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Answer 50% or .5 there are 2 things

Answer:

1. m∠CUK = 70°

2. m∠K = 112°

Step-by-step explanation:

1. The given parameters of the parallelogram LUCK are;

∠C = 68°

∠LUK = 42°

From the diagram of parallelogram LUCK obtained from an online source, we have;

Given that LUCK = A parallelogram, we have;

The same side interior angles ∠C and ∠U are supplementary angles

Therefore;

∠C + ∠U = 180°

∠U = 180° - ∠ C

∴ ∠U = 180° - 68° = 112°

∠U = 112°

By angle addition property, ∠U = ∠LUK + ∠CUK

∴ m∠CUK = ∠U - ∠LUK

By plugging in the value of ∠LUK = 42°, and ∠U = 112°, we have;

m∠CUK = ∠U - ∠LUK = 112° - 42° = 70°

m∠CUK = 70°

2. By angle addition property, we have;

∠K = ∠LKU + ∠CKU

∠LKU and ∠CUK are alternate interior angles

∴ ∠LKU = ∠CUK = 70°

Similarly, ∠CKU and ∠LUK are alternate interior angles

∠CKU = ∠LUK = 42°

m∠K = ∠LKU + ∠CKU = 70° + 42° = 112°

m∠K = 112°.

Answer:

88

Step-by-step explanation:

11*4 = 44

4*4 = 16

11-4 = 7

7*4 = 28

44+16+28 = 88

Answer:aw ehtI Belive its 7 i could be wrong though

Step-by-step explanation:

the way you would solve this is u would arange the numbers like small to greatest then count how many there are and there happends to be 15 then you find the middle.

HOPE THIS HELPS