What is the quotient of 5 7 ÷ 5 14 ?

Answer:

[tex]\displaystyle \log_3 5=\frac{\ln 5}{\ln 3}[/tex]

Step-by-step explanation:

We want to write:

[tex]\log_3 5[/tex]

Using natural logarithms.

We can use the following property of logarithms:

[tex]\displaystyle \log_b a=\frac{\log_c a}{\log_c b}[/tex]

Hence, if we let c be equal to e:

[tex]\displaystyle \log_b a= \frac{\log _e a}{\log _e b} = \frac{\ln a}{\ln b}[/tex]

Then by letting a = 5 and b = 3:

[tex]\displaystyle \log_3 5=\frac{\ln 5}{\ln 3}[/tex]

Answer:

y = P • (1+r)^t

Balance after 2 years: $3307.5

Step-by-step explanation:

To answer this question, we will use standard equation that calculates bank interests:

A = P(1+(r/n))^(n•t)

It might seem complicated, but let's explain:

A - amount of money after the time period

P - principal amount, the amount of money you started with

r - interest rate, in decimal numbers

n - number of times interest is being calculated per year

t - number of years

Since here, interest is annual, n = 1, so our equation is:

A = P(1+r)^t

P = $3000

r = 5% = 0.05

t = 2 years

A = 3000(1+0.05)^2

A = 3000•(1.05)^2

A = $3307.5

The better deal

Would be the lowest cost per ounce.

Divide total cost by total ounces and compare them.

7.20/60 = 0.12 per ounce.

8.25/75 = 0.11 per ounce.

75 ounces for 8.25 is the better deal

Answer:

59

Step-by-step explanation:

The total amount of angles in a triangle with equal 180 degress

Answer:

Step-by-step explanation:

83° + 38° + x° = 180°

121 + x = 180

x = 59

Answer:

[tex]P(64<x<76)=0.68[/tex]

Step-by-step explanation:

Given that, the mean, [tex]\mu[/tex], and the standard deviation, [tex]\sigma[/tex], of normally distributed exam score are :

[tex]\mu=70[/tex]

[tex]\sigma=6[/tex]

Let [tex]x[/tex] represent the score on a randomly selected exam from this set

The z-score, for the randomly selected exam score x:

For 64<x<76, the range of z-score is

[tex]\frac{64-70}{6}<z<\frac{76-70}{6}= -1<z<1[/tex]

Now, from the z-score table, the value for z=-1 is the probability for x<64.

As the value for z=-1 is 0.15866, so

P(x<64)=0.15866.

Similarly, the value for z=0.67 is 0.84134, so

P(x<76)=0.84134

So, [tex]P(64<x<76)= P(x<76)-P(x<64) \\\\[/tex]

[tex]\Rightarrow P(64<x<76)=0.84134-0.15866=0.68268.[/tex]

Hence, [tex]P(64<x<76)=0.68[/tex]

Answer:

0.68

Step-by-step explanation:

khan

Answer:

[tex]48m^2-72mn[/tex]

Step-by-step explanation:

We need to solve [tex](8m-3n)^2 - (4m+3n)^2[/tex]

We know that,

[tex](a+b)^2=a^2+b^2+2ab\\\\(a-b)^2=a^2+b^2-2ab[/tex]

Using the above formula,

[tex](8m-3n)^2 - (4m+3n)^2=(8m)^2+(3n)^2-2(8m)(3n)-[(4m)^2+(3n)^2+2(4m)(3n)]\\\\=64m^2+9n^2-48mn-(16m^2+9n^2+24mn)\\\\=64m^2+9n^2-48mn-16m^2-9n^2-24mn\\\\=48m^2-48mn-24mn\\\\=48m^2-72mn[/tex]

So, the final answer is [tex]48m^2-72mn[/tex].

Answer:

hmmmmmmmmmm thats a tuff one

Answer:

-99

Step-by-step explanation:

First, let's find an equation to use to make things easier.

So, as we can see, the numbers go down 3 every time and we start at 27, so, the first term is 27, that means that we need to find the number before 27, so we add 3 to 27 to get 30.

We can put the equation using y = mx + b, since that is the most appropriate formula to use.

y = -3x + 30

y = -3(1) + 30

y = -3 + 30

y = 27

y = -3x + 30

y = -3(2) + 30

y = -6 + 30

y = 24

So, this is a good equation to use. Now, we substitute 43 as x

y = -3x + 30

y = -3(43) + 30

y = -129 + 30

y = -99

Answer:

the answer Is 277.2

Step-by-step explanation:

V=277.2

Answer:

I believe it would be 16

Step-by-step explanation:

8 is half of 16 and if she had 8 dollars after spending half her allowance, she would've had 16 as her allowance

Final answer: Her allowance would be 16 dollars

Answer:

Step-by-step explanation:

The prime factor of the product 75:

Factors of 75

1,3, 5, 15, 25, 75

or for the prime factorization of 75

3 x 5 x 5, which can also be written 75 = 3 x 5².

Hope this help :)

Answer:

3 × 5 × 5

I hope this helps!

I hope it is helpful for you ....

Answer:

x=3

Step-by-step explanation:

15-7x=5x-21

12x=36

x=3

Answer:

Used for Linear Graphs

Step-by-step explanation:

Y=mx = b

m represents the slope/gradient of the graph

b represents the y intercept

Slope is the change in y over the change in x

Slope = (9 - -6)/( -8 -1)

Slope = 15/-9

Slope = -15/9

Simlipy:

Slope = -5/3

Answer:

Step-by-step explanation:

Slop = (y2 - y1)/(x2-x1)

= {9 -(-6)}/{(-8)-1}

= 15/-9

= -1.66

Answer:

f(-1) = -6

Step-by-step explanation:

[tex]f(x) = (x+2)^{2}-6[/tex] for [tex]x\neq -1[/tex]

[tex]f(x) = -6[/tex] for x = -1

f(-1) means x=-1, so we can't use the first expression.

Answer:

36 : 4

Step-by-step explanation:

40 divided into ratio 9:1 is like 40 / (9 + 1) multiplied to both sides of 9:1

40 / (9 + 1) = 4, and if you multiply both sides by 4, you get 36 : 4

Answer:

I think the answer is 36

Step-by-step explanation:

You add 9 and 1 to get 10 and then you divide 40 by 10 and get 4 and then you multiple 9 and 4 to get 36.

Answer:

Y = -3/4  + 7

Step-by-step explanation:

7 is the y intercept

-3/4 is the slope

Answer:

y=5/2+3

Step-by-step explanation:

Answer:

[tex]f\left(2,3,1\right)=\bold{14}[/tex]

Step-by-step explanation:

Given the function:

[tex]f\left(x,y,z\right)=\frac{x^3-2.5y^2+\frac{z}{2}}{z\left(x-y\right)}[/tex]

To find:

The value of [tex]f(2, 3, 1)[/tex] = ?

Solution:

[tex]f(2, 3, 1)[/tex] means the values of [tex]x, y\ and\ z[/tex] as:

[tex]x=2\\y=3\\z=1[/tex]

Let us put the given values in the given function and let us solve for it:

[tex]\Rightarrow f\left(2,3,1\right)=\dfrac{2^3-2.5\times 3^2+\frac{1}{2}}{1\left(2-3\right)}\\\\\Rightarrow f\left(2,3,1\right)=\dfrac{8-2.5\times 9+0.5}{1\left(-1\right)}\\\\\Rightarrow f\left(2,3,1\right)=\dfrac{8-22.5+0.5}{-1}\\\\\Rightarrow f\left(2,3,1\right)=\dfrac{-14}{-1}\\\\\Rightarrow f\left(2,3,1\right)=\bold{14}[/tex]

Therefore, the answer is:

[tex]f\left(2,3,1\right)=\bold{14}[/tex]

Answer:

niwebfasfbjsdfb

Step-by-step explanation:

jsdfhsdbfjhadsjbdsfhb

Answer:

Step-by-step explanation:

y-2=3(x-5)

y-2=3x-15

Slope intercept form is y=3x-13

y-12= -2(x-3)

y-12= -2x+6

Slope intercept form is y= -2x+18

Answer:

x = 58

[tex] m\angle 4 = 116\degree [/tex]

Step-by-step explanation:

[tex] m\angle 2 = m\angle 6..... (1)\\(alternate \: \angle s) \\\\

m\angle 5 + m\angle 6 = 180\degree \\(linear \: pair\: \angle s) \\\\

\therefore m\angle 6 = 180\degree-m\angle 5..... (2)\\\\[/tex]

From equations (1) & (2)

[tex] m\angle 2 =180\degree-m\angle 5\\\\

\therefore (2x)\degree =180\degree-(x+6)\degree \\\\

\therefore (2x)\degree +(x+6)\degree =180\degree\\\\

\therefore (2x+x+6) \degree =180\degree\\\\

\therefore (3x+6) \degree =180\degree\\\\

3x + 6 = 180\\\\

3x = 180-6\\\\

3x = 174\\\\

x = \frac{174}{3} \\\\

\huge \purple {\boxed {x = 58}} \\\\

\because m\angle 4 = m\angle 2\\(corresponding \: \angle s) \\\\

\therefore m\angle 4 = (2x)\degree \\\\

\therefore m\angle 4 = (2\times 58)\degree \\\\

\huge \orange {\boxed {\therefore m\angle 4 = 116\degree}} [/tex]

Answer: Angle X

Reason: For any triangle, the largest angle is always opposite the longest side.

∠X is the largest measure on the triangle XYZ.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

The angle opposite to the largest side is the largest measure.

So,

XY = 6 and opposite angle = ∠Z

YZ = 9 and opposite angle = ∠X

XZ = 8 and opposite angle = ∠Y

We see that,

YZ > XZ > XY

So,

∠X > ∠Y > ∠Z

Thus,

∠X is the largest measure on the triangle XYZ.

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Answer:

1.2

Step-by-step explanation:

The cost per pound is $2.3.

Given that Bo is buying candy by the pound. For every 10 pounds, he pays $23.

We need to find the cost per pound,

So, we see that,

For 10 pounds he is paying $23,

We need to find the unit rate, so divide both by 10,

10/10 pound = $23/10

1 pound = $2.3

Hence the cost per pound is $2.3.

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The correct equation of the line that is perpendicular to 2x - 5y = 5 and passes through the point (2, -9) is y = (-5/2)x - 4.

Here,

Let's go through the steps again and find the correct equation for the line that is perpendicular to 2x - 5y = 5 and passes through the point (2, -9).

Step 1: Convert the given equation into slope-intercept form.

2x - 5y = 5

Subtract 2x from both sides:

-5y = -2x + 5

Now, divide everything by -5 to isolate y:

y = (2/5)x - 1

So, the slope of the given line is 2/5.

Step 2: Find the slope of the line perpendicular to the given line.

For two lines to be perpendicular, their slopes must be negative reciprocals of each other.

The negative reciprocal of 2/5 is -5/2.

Step 3: Write the equation of the line using the point-slope form.

Now that we have the slope (-5/2) and a point (2, -9), we can use the point-slope form of the linear equation:

[tex]y - y_1 = m(x - x_1)[/tex]

where m is the slope, and [tex](x_1, y_1)[/tex]is the given point.

Substitute m = -5/2 and [tex](x_1, y_1)[/tex] = (2, -9):

y - (-9) = (-5/2)(x - 2)

Simplify:

y + 9 = (-5/2)x + 5

Now, isolate y by subtracting 9 from both sides:

y = (-5/2)x + 5 - 9

y = (-5/2)x - 4

So, the correct equation of the line that is perpendicular to 2x - 5y = 5 and passes through the point (2, -9) is y = (-5/2)x - 4.

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Given:

Total number of cars = 36

Each car has 2 red stickers and one blue sticker.

To find:

The expression that represents the total number of stickers on the 36 cars.

Solution:

Total number of cars = 36

Each car has 2 red stickers and one blue sticker. So,

Total number of stickers on each car = (2+1)

Total number of stickers on 36 car = 36(2+1)

                                                           = 36(3)

                                                           = 108

Therefore, the required expression for the total number of stickers on the 36 cars is 36(2+1) and the total number of stickers is 108.

Answer:

a=5

Step-by-step explanation:

18-2a=8

-18     -18

-2a=-10

/-2  /-2

a=5

9514 1404 393

Answer:

  16b = 96

Step-by-step explanation:

There are many aspects of "this situation" for which we could write equations. Perhaps the one that is of interest is ...

  b bags of 16 treats each will total 96 treats

  16b = 96

Answer:

false

Step-by-step explanation: