Ryan sold half of his comic books and
then bought eleven more. He now has 38.
With how many did he begin?

Answer:

[tex]\dfrac{-1}{6}[/tex]

Step-by-step explanation:

Given the limit of a function expressed as [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3}[/tex], to evaluate the following steps must be carried out.

Step 1: substitute x = 0 into the function

[tex]= \dfrac{sin(0)-tan(0)}{0^3}\\= \frac{0}{0} (indeterminate)[/tex]

Step 2: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the function

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ sin(x)-tan(x)]}{\frac{d}{dx} (x^3)}\\= \lim_{ x\to \ 0} \dfrac{cos(x)-sec^2(x)}{3x^2}\\[/tex]

Step 3: substitute x = 0 into the resulting function

[tex]= \dfrac{cos(0)-sec^2(0)}{3(0)^2}\\= \frac{1-1}{0}\\= \frac{0}{0} (ind)[/tex]

Step 4: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 2

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ cos(x)-sec^2(x)]}{\frac{d}{dx} (3x^2)}\\= \lim_{ x\to \ 0} \dfrac{-sin(x)-2sec^2(x)tan(x)}{6x}\\[/tex]

[tex]= \dfrac{-sin(0)-2sec^2(0)tan(0)}{6(0)}\\= \frac{0}{0} (ind)[/tex]

Step 6: Apply  L'Hôpital's rule, by differentiating the numerator and denominator of the resulting function in step 4

[tex]= \lim_{ x\to \ 0} \dfrac{\frac{d}{dx}[ -sin(x)-2sec^2(x)tan(x)]}{\frac{d}{dx} (6x)}\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^2(x)sec^2(x)+2sec^2(x)tan(x)tan(x)]}{6}\\\\= \lim_{ x\to \ 0} \dfrac{[ -cos(x)-2(sec^4(x)+2sec^2(x)tan^2(x)]}{6}\\[/tex]

Step 7: substitute x = 0 into the resulting function in step 6

[tex]= \dfrac{[ -cos(0)-2(sec^4(0)+2sec^2(0)tan^2(0)]}{6}\\\\= \dfrac{-1-2(0)}{6} \\= \dfrac{-1}{6}[/tex]

Hence the limit of the function [tex]\lim_{ x\to \ 0} \dfrac{sin(x)-tan(x)}{x^3} \ is \ \dfrac{-1}{6}[/tex].

Answer: Choice C

[tex](xy)^{1/2}[/tex] which is equivalent to [tex]\sqrt{xy}[/tex]

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

Explanation:

The exponent for the y term inside the parenthesis is 1/6 and then that expression is raised to the 3rd power. The exponents multiply to (1/6)*3 = 3/6 = 1/2

This means [tex]\left(y^{1/6}\right)^3 = y^{1/2}[/tex]

Having an exponent of 1/2 is the same as applying the square root, so,

[tex]\sqrt{x} = x^{1/2}[/tex]

Meaning,

[tex]y^{1/2}\sqrt{x} = y^{1/2}x^{1/2} = (xy)^{1/2} = \sqrt{xy}[/tex]

Answer:

Step-by-step explanation:

80/100 = 8/10= 4/5

Answer: 943,212

Step-by-step explanation:

Suppose that you want to know the value of a given digit in a given number, where the digit is x.

Now, you should count the position of this digit, starting at the decimal point and counting to the left.

This position, a number n, will give the value of our digit as:

Value = x*10^(n-1)

in the number 893,417 the digit 9 is in the fifth place (counting from right to left).

Then the value of this 9 is:

9*10^(5 - 1) = 90,000

Now, if we want something ten times larger than this, we have:

N = 10*90,000 = 900,000

Now the 9 is in the sixth place, then we must find a number with a 9 in the sixth place, for example, 943,212.

Image of the correlation between Risk-Taking (R) and Relationship Happiness (HAPPY) is missing, so i have attached it.

Answer:

Option 1 - The relationship is non - significant

Step-by-step explanation:

From the image attached, we can see that under the correlations table;

For correlation between relationship happiness and risk taking;

σ(sigma) = 0.053

Similarly, for correlation between risk taking and relationship happiness;

σ(sigma) = 0.053

.

Now,σ(sigma) = 0.053 is more than the standard alpha level of 5%(0.05). Thus, we fail to reject the null hypothesis since it is non - significant.

Answer:

6

Step-by-step explanation:

Answer:

T=112.5+0.50*b (since there was not a given number of beads)

Answer:

  161.5 miles

Step-by-step explanation:

19 inches is 9.5 times 2 inches. So, the actual distance is 9.5 times 17 miles:

  9.5 × 17 miles = 161.5 miles

Answer:

$187.5

Step-by-step explanation:

25 times 7.5 is 187.7

Answer:

Liquid

Step-by-step explanation:

solids :have definite shape and definite volume.

Liquids :have definite volume and shape of the container.(or no definite shape)

Gas: has no definite volume and no definite shape.

Answer:

1/3

Step-by-step explanation:

hope this helps  

Answer:

It is 3/8

Step-by-step explanation:

I got it right on Edge 2021.

Answer:

153/40

Step-by-step explanation:

The first step to finding the fraction is to get rid of the decimal points as fractions do not have decimals. To do this we can multiply it by 1000 which gives us 3825. To have this equal to the original number we add ÷1000 on the denominator which gives us 3825/1000 which is a fraction still equal to the original number (3825÷1000=3.825). Which can further be simplified to 153/40 (both numbers divisible by 25). This is the simplest fraction which can express the number 3.825 (153/40=3.825).

Hope this helped!

Answer:

If this was all the fruit, 3 and 7/12

Step-by-step explanation:

1/4 and 1/3 LCM is 12

1/4=3/12

1/3=4/12

2+1=3

3/12+4/12=7/12

3+7/12= 3 7/12

Answer:

If x= - 2. then 6x - 2 = -14

If x = 6, then 6x - 2 = 34

If x= - 5. then 6x-2= -32

Step-by-step explanation:

You have to substitute the value of x in the expression.

If x = -2,

6x-2 = 6*(-2) - 2 = -12-2 = -14

I'm going to assume you're asking where the point is located on a coordinate plane.

We have x = 0 and y = -4.

So, we start at (0, 0) and move down 4 units.

Best of Luck!

Answer:

56

Step-by-step explanation:

The sum of two even consecutive integers is 114.

Let's let the first even integer be 2n, where n is some integer: it doesn't matter what n is, but if we multiply n by 2, we are certainly getting an even number. This is because any integer multiplied by 2 is even.

So, this means that the second number is 2n+2.

Their sum is 114. In other words:

[tex](2n)+(2n+2)=114[/tex]

Solve for n.

Combine like terms:

[tex]4n+2=114[/tex]

Subtract 2 from both sides:

[tex]4n=112[/tex]

Divide both sides by 4:

[tex]n=28[/tex]

So, n is 28.

This means that the first number is 28(2) or 56.

And the second number is 58.

So, the smallest integer is 56.

And we're done!

Answer:

X=7

Step-by-step explanation:

(2) means time 2 so use 5 times 2 and get 10 and take away 3 you get 7 and 7 is X

to prove I am right use 7x5-3/2=16-3x2=10

hey bro I was joking at first

Answer:

f(2) = 5(2) -3

         10 - 3

f(2) = 7

The formula for the slope is [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{20-10}{2-1}[/tex]

[tex]m=\frac{10}{1}[/tex]

[tex]m=10[/tex]

Hope this helps.

頑張って!

Answer:

The answer is 10 minutes per mile!

Step-by-step explanation:

I hope this helped! :)

Answer: Because the a-value is negative.

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k    where

Given: g(x) = - (x + 1)² - 3

                    ↓

                 a= -1

Since the a-value is negative, the parabola will be reflected over the x-axis which will change the curve from (U-shaped) to (∩-shaped).

Answer:

1

Step-by-step explanation:

Anything to the power is 0 is equal to 1.

Answer:

the answer is 1

Step-by-step explanation:

Answer:

11 25/64 in ^3

Step-by-step explanation:

Volume of a cube is given by

V = s^3

s = 2 1/4 = 9/4

V = (9/4) ^3

  = 729/64

  =11 25/64 in ^3

Answer:

28. m<A=20°, m<B=70°

32. m<A=103°, m<B=77°

Step-by-step explanation:

complementary angle=a+b=90°

supplementary angle=a+b=180°

28. A+B=90°

      5x+17x+2=90°

      22x+2=90°

      22x=90-2

      22x=88

        22x/22=88/22

      x=88/22=4

m<A=5x=5*4=20°

m<B=17x+2=17*4+2=68+2=70°

         Check

A+B=90°

20+70=90°

90°=90°

32. A+B=180°

     x+11+x-15=180°

     2x-4=180°

     2x=180+4

     2x=184

     2x/2=184/2

     x=184/2

     x=92

m<A=x+11=92+11=103°

m<B=x-15=92-15=77°

     Check

A+B=180°

103+77=180°

180°=180°

Answer:

Perimeter = 14.0942 ft       (aprox)

Step-by-step explanation:

1 ft = 12 inches

1 inch = 1/12 = 0.08333 ft

4 inch = 4*0.08333 = 0.3333 ft

then:

there are:

        perimeter = 2π r

         π = 3.1416

         r = radius

         perimeter = 2*3.1416*0.3333ft

         perimeter = 2.0942 ft       (aprox)

       perimeter = 4*3ft

        perimeter = 12ft

Total perimeter:

2.0942ft +´12ft = 14.0942 ft

Answer:

Fraction of the number that received an A= = 27/50

Step-by-step explanation:

In a class of 50 statistics​ students, 27

students received an A.

Total number of students=50

Number that received an A= 27

Fraction of the number that received an A= Number that received an A/Total number of students

Fraction of the number that received an A= = 27/50

Answer:

Number of mugs in cartoon = 24 / 25

Step-by-step explanation:

Given:

Pints of cartoon = 4/5

Pints of mugs = 5/6

Find:

Number of mugs in cartoon

Computation:

Number of mugs in cartoon = Pints of cartoon / Pints of mugs

Number of mugs in cartoon = (4/5) / (5/6)

Number of mugs in cartoon = 24 / 25