Jerimiah can type 300 words in 1/5 of an hour. How many words can he type in 2/3 of an hour

Answer:

7.5 -ln(0.25)

Step-by-step explanation:

We can first graph this function. Looking at the graph, we can separate this into two ranges -- from x=0.25 to x=1 and from x=1 to x=4.

From x=0.25 to x=1, we want to find the area above y=1/x and below y=4. To do this, we can take the integral of y=4 from x=0.25 to x=1 to encompass the whole area under y=4 from that range. Then, we subtract the area under y=1/x as we don't need that (we only want what's above it). Therefore, we have

[tex]\int\limits^{1}_{0.25}{4} \, dx - \int\limits^{1}_{0.25} {1/x} \, dx \\= 4(1) - 4 (0.25) - (ln(1) - ln(0.25))\\= 4 - 1 - ln(1) + ln(0.25)\\= 3 - ln(1) + ln(0.25)[/tex]

Next, we know that ln(x/y) = ln(x) - ln(y), so ln(0.25) - ln(1) = ln(0.25/1) = ln(0.25), so we have

3 - ln(0.25)

For x=1 to x=4, we want to find the area above y=x and below y=4. We can apply a similar strategy, subtracting the area below y=x from the area below y=4 to get

[tex]\int\limits^{4}_{1}{4} \, dx - \int\limits^{4}_{1} {x} \, dx \\ \\= 4(4) - 4(1) - (4^{2} /2 - 1^2/2)\\= 16 - 4 - 8 + 0.5\\= 4.5[/tex]

Add these two areas up to get

3-ln(0.25) + 4.5 = 7.5 -ln(0.25)

Answer:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}} \frac{x\ln x}{\tan x}=-\infty\implies \text{B. Nonexistent (best answer)}[/tex]

Step-by-step explanation:

Recall L'Hopital's rule:

[tex]\displaystyle \lim_{x\rightarrow c}\frac{f(x)}{g(x)}=\lim_{x\rightarrow c}\frac{f'(x)}{g'(x)}[/tex]

First derivative of [tex]x\ln x[/tex]:

Recall the product rule:

[tex](f\cdot g)'=f'\cdot g+g'\cdot f[/tex]

[tex]\displaystyle \frac{d}{dx} (x\ln x)=\frac{d}{dx}(x)\cdot \ln (x)+\frac{d}{dx}(\ln x)\cdot x[/tex]

Note that:

[tex]\displaystyle \frac{d}{dx}(x)=1,\\\frac{d}{dx}(\ln (x))=\frac{1}{x}[/tex]

Simplifying, we get:

[tex]\displaystyle \frac{d}{dx} (x\ln x)=1\cdot \ln x+\frac{1}{x}\cdot x,\\\frac{d}{dx}(x\ln x)=\ln x+1[/tex]

First derivative of [tex]\tan x[/tex]:

[tex]\displaystyle \frac{d}{dx}(\tan x)=\sec^2 x[/tex]

Therefore, we have:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}[/tex]

By definition, [tex]\cos x=\frac{1}{\sec x}[/tex]. Therefore,

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=\lim_{x\rightarrow 0^{+}}\frac{\ln x+1}{\sec^2{x}}=\lim_{x\rightarrow 0^{+}}\cos^2x(\ln x+1)[/tex]

Note:

[tex]\displaystyle \lim_{x\rightarrow 0^{+}}\cos^2x=1,\\\lim_{x\rightarrow 0^{+}}\ln x+1=-\infty[/tex]

Substitute:

[tex]\displaystyle \lim_{x \rightarrow0^{+}} \cos^2x(\ln x+1)=1\cdot (-\infty)=-\infty[/tex]

Therefore, we have:

[tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty \text{}[/tex], which best corresponds with [tex]\boxed{\text{B. Nonexistent}}[/tex]

*Commentary:

Technically speaking, a limit exists only if it is equal to a real number. By proper definition, infinity is not a number. With that being said, you will see limits expressed as infinity or negative infinity.

Here's what I will say about this specific problem.

The problem is stipulating that we approach [tex]x[/tex] from the right side. Because of this condition, it may be unorthodox to say this limit doesn't exist. However, if the problem just asked for [tex]\displaystyle \lim_{x\rightarrow 0}\frac{x\ln x}{\tan x}[/tex], it is common and preferred to say this limit does not exist, since [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{x\ln x}{\tan x}\neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}[/tex].

For example, [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}=\text{DNE}[/tex], because [tex]\displaystyle \lim_{x\rightarrow 0}\frac{1}{x}[/tex] diverges. In other words, [tex]\displaystyle \lim_{x\rightarrow 0^{-}}\frac{1}{x}=-\infty \neq \displaystyle \lim_{x\rightarrow 0^{+}}\frac{1}{x}=\infty[/tex].

But again, the problem is asking for the limit as [tex]x[/tex] approaches from the right, in which case [tex]\displaystyle \lim _{x\rightarrow 0^{+}}\frac{x\ln x}{\tan x}=-\infty }[/tex]. It's really a pedagogical choice whether to say a limit equal to infinity or negative infinity exists or not since infinity implies there is no limit, so saying the limit of something is infinity becomes an oxymoron. In this case, the person who wrote the answer choices chose to express a limit of infinity as nonexistent, but it is worth mentioning that someone else solving this problem might express [tex]-\infty[/tex] as the answer, and they would be just as, if not more, correct.

Without resorting to L'Hopital's rule, recall that

[tex]\displaystyle \lim_{x\to0}\frac{\sin(ax)}{ax} = 1[/tex]

for a ≠ 0. Then

[tex]\displaystyle \lim_{x\to0^+} \frac{x \ln(x)}{\tan(x)} = \lim_{x\to0^+}\frac x{\sin(x)} \times \lim_{x\to0^+}\cos(x) \times \lim_{x\to0^+}\ln(x)[/tex]

The first two limits exist and are equal to 1, but the last limit is -∞.

Answer:

Step-by-step explanation:

(4c1×6c4)+(4c2×6c3)+(4c3×6c2)+(4c4×6c1)

(4×15) +(6×20) +(4×15) +(1×6)

60+120+60+6

246 ways

Answer:

4 2/4 2/3 3/4 5/8

Step-by-step explanation:

Answer:

9-2b

Step-by-step explanation:

Set up equation:

[tex]9 - 8b + 6b[/tex]

Add like terms

[tex]9 - 2b[/tex]

Answer: -5^3

Step-by-step explanation:

Answer:3

Step-by-step explanation:

-3x+2=-7

subtract 2 from both sides

-3x+2-2-(-7-2

simplify the arithmetic

-3x=-7-2

simplify the arithmetic aging

-3x=-9

=3

Answer:

[tex] \sqrt{5} \times \sqrt{10} \\ = \sqrt{5} \times \sqrt{2 \times 5} \\ = \sqrt{5} \times \sqrt{2} \times \sqrt{5} \\ = 5 \sqrt{2} \\ thank \: you[/tex]

Hence commission will be 7%

[tex]\\ \rm\longmapsto 23458\times \dfrac{7}{100}[/tex]

[tex]\\ \rm\longmapsto \dfrac{164206}{100}[/tex]

[tex]\\ \rm\longmapsto 1642.06[/tex]

Vito Avido's commission on $23,458 in sales is $1466.06.

Here, we have to calculate Vito Avido's commission on $23,458 in sales, we'll break down the sales amount into different ranges and apply the respective commission rates for each range.

For the first $5,000 of sales: 5% commission

Commission = 5% of $5,000 = 0.05 * $5,000 = $250

For the next $15,000 of sales: 6.5% commission

Commission = 6.5% of $15,000 = 0.065 * $15,000 = $975

For the remaining amount over $20,000: 7% commission

Sales above $20,000 = $23,458 - $20,000 = $3,458

Commission = 7% of $3,458 = 0.07 * $3,458 = $241.06

Now, add up the commissions from each range:

Total Commission = $250 + $975 + $241.06 = $1466.06

Vito Avido's commission on $23,458 in sales is $1466.06.

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Answer:

20.

Step-by-step explanation:

when you add how far Kyle's already traveled you get sixty, the rest of the lecture explains the rest, leaving you with 20 seconds. Lol.

Answer:

4.5m

Step-by-step explanation:

The formula for triangle is

1/2 x base x height = area

1/2 x 3 x h = 6.75m

h = 6.75 ÷3÷1/2

h = 4.5m

Answer:

dccxxydffffyyyrtttttttyhg

Answer

4

Step by step explanation

2/3=x/10-x

cross multiply

2(10-x)=3x

20-2x=3x

20=3x+2x

20=5x

x=4

Answer:

is this u want?

Step-by-step explanation:

if no so sorry..

Answer:

x = -2, y = 2

Step-by-step explanation:

-7x + 7y = 28

7y = 28 + 7x

y = 4 + x ----(1)

-8x+4y=24 -----(2)

sub (1) into (2)

-8x+4(4+x)=24

-8x+16+4x = 24

-8x+4x = 24-16

-4x = 8

x = -2

sub x = -2 into (1)

y=4+(-2) = 2

Answer:

1) 2x - y + 6 = 0

2) x - y + 4 = 0

Step-by-step explanation:

1) -8x + 4y = 24

= -8x + 4y - 24 = 24 - 24

= -8x + 4y - 24 = 0

= (-8x + 4y - 24) ÷ 4 = 0 ÷ 4

= -8x ÷ 4 + 4y ÷ 4 - 24 ÷ 4 = 0

= -2x + 4y ÷ 4 - 24 ÷ 4 = 0

= -2x + y - 24 ÷ 4 = 0

= -2x + y - 6 = 0

= 2x - y + 6 = 0

2) -7x + 7y = 28

= -7x + 7y - 28 = 28 - 28

= -7x + 7y - 28 = 0

= (-7x + 7y - 28) ÷ 7 = 0 ÷ 7

= -7x ÷ 7 + 7y ÷ 7 - 28 ÷ 7 = 0 ÷ 7

= -7x ÷ 7 + 7y ÷ 7 - 28 ÷ 7 = 0

= -x + 7y ÷ 7 - 28 ÷ 7 = 0

= -x + y - 28 ÷ 7 = 0

= -x + y - 4 = 0

= x - y + 4 = 0

(A)

Step-by-step explanation:

The meal cost $45.25 so 20% of this for tip is

($45.25)(0.20) = $9.05. Since the tip is split between 4 friends, divide this tip by 4 and each one paid ($9.05/4) = $2.26.

Answer:

[tex]thank \: you[/tex]

The number of candies left in the bag is given by the equation n = 40 candies

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as n

Now , the value of A is

The number of candies which were eaten = 80 candies

The fraction of candies that were eaten = 2/3

So , ( 2/3 ) of the total = 80

( 2/3 )A = 80

Multiply by 3 on both sides , we get

2A = 240

Divide by 2 on both sides , we get

A = 120 candies

Now , the number of candies that were left n = total number of candies - number of candies that were eaten

On simplifying the equation , we get

The number of candies that were left n = 120 - 80

The number of candies that were left n = 40 candies

Hence , the number of candies that are left is 40 candies

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Answer:

1/2 plus 5/6 would equal 8/6 cause six is the lowest denominator so then you times 8/6 by 3 and the 2/9 by 2 and that would give you 24/18 and 4/18 and you subtract them together to 20/18 or 1  2/18

Step-by-step explanation:

1/2 plus 5/6 would equal 8/6 cause six is the lowest denominator so then you times 8/6 by 3 and the 2/9 by 2 and that would give you 24/18 and 4/18 and you subtract them together to 20/18 or 1  2/18

1/2 = 3/6

5/6 + 3/6 = 8/6

8/6 x 3 = 24/18

2/9 x 2 = 4/18

24/ 18 - 4/18 = 20/18 or 1 and 2/18

Answer:

1/2 x > 20

Step-by-step explanation:

Let x be the unknown number

1/2 x > 20

Answer:

100,000 x $15 = 1.5 million US$

Answer:

z = 40 + 26.00x + 15.00y

Coefficients: 26.00, 15.00

Constant: 40

Variables: z, x, y

Step-by-step explanation:

Let x be the number of canoe rentals and y be the number of bicycle rentals.

(The family can hold only one annual pass, so we don't need a variable for that. Rather, we'll use a "constant." But the number of bicycle/canoe rentals can change!)

Let z be how much the family spends in a year.

The family spends $26 for each canoe rental, so

26.00x for x canoe rentals

Similarly, 15.00y for y canoe rentals

So z = 40 + 26.00x + 15.00y

The coefficients are the 26.00 and the 15.00. Coefficients are the numbers attached to the variables.

The constant is 40. A constant is a number by itself.

The variables are z, x, and y. Variables are our unknowns.

Answer: 7 bags.

Step-by-step explanation:

Since the baker needs 56 apples, he needs to buy enough apples to fulfill his recipe. Since each bag contains 8 apples, he must divide 56/8, in this case yielding 7.

Answer:

7 bags

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Answer:

[tex] \frac{3}{50} [/tex]

Step-by-step explanation:

[tex] \frac{1}{5} \times \frac{3}{10} [/tex]

➡️ [tex] \frac{1 \times 3}{5 \times 10} [/tex]

➡️ [tex] = \frac{3}{50} [/tex] ✅

Answer:

x=-5,6

Step-by-step explanation:

SEE THE IMAGE FOR SOLUTION

HOPE IT HELPS

HAVE A GREAT DAY

Step-by-step explanation:

Let [tex]P_1(-1, -8)\:\text{and}\:P_2(-4, -9)[/tex]

The slope of the line through these two points is

[tex]m = \dfrac{y_2 - y_1}{x_2 - x_1} = \dfrac{(-9 + 8)}{(-4 + 1)} = \dfrac{1}{3}[/tex]

So the slope-intercept form of the line passing through the two points is

[tex]y = mx + b = \frac{1}{3}x + b[/tex]

To find b, we use either point into our equation. Let's use (-1, -8):

[tex]-8 = \frac{1}{3}(-1) + b \Rightarrow b = -\dfrac{23}{3}[/tex]

Therefore, the slope-intercept form of the equation for the line is

[tex]y = \dfrac{1}{3}x - \dfrac{23}{3}[/tex]

The standard form of the equation can be written as

[tex]x + 3y + 23 = 0[/tex]

Answer:

tea

Step-by-step explanation:

just cuz lol

Answer:

Gin

Step-by-step explanation:

9a^2 - 9

Uejdjeujdksjdndkdkdk

Answer:

[tex]a=-4[/tex]

Step-by-step explanation:

Since [tex]f(x)=\frac{3x+8}{2x-a}[/tex], we have

[tex]2=f(0)=\frac{3(0)+8}{2(0)-a}=-\frac8a[/tex]

Taking the reciprocal gives

[tex]-\frac a8=\frac12[/tex]

Then multiplying by [tex]-8[/tex] gives

[tex]a=\frac12(-8)=-4[/tex]