If the area of the square above is 144 what is the value of x

Answer:

initial population : 89

after 9 years : 676

Step-by-step explanation:

no need for panic. this is just plain calculator mechanics. yes, we need to do some more complicated typing and use e, but it is still only typing.

the initial population is P(0). or t = 0.

simply when there were 0 years since the fish were added.

that is simple.

we get (as -0.42×0 = 0)

800 / (1 + 8e⁰) = 800 / (1+8×1) = 800 / 9 ≈ 89

now, after 9 years we have to calculate P(9). or t=9.

let's pre-calculate : -0.42×9 = -3.78

e to the power of -3.78 = 0.022822691...

8 times this is 0.182581531...

and plus 1 is 1.182581531...

800 / 1.182581531... = 676.486127 ≈ 676

The number that is in "proper" scientific notation is A. 2.31 * 10^-4

A number is written in scientific notation when a number between 1 and 10 is multiplied by a power of 10.  When a number is too big or too small to be conveniently stated in decimal form, or if doing so would involve writing out an exceptionally long string of digits, it can be expressed using scientific notation. It is also known as standard form in the scientific form, standard index form, and standard form.

The number on the left in scientific notation always consists of a single digit, a decimal point, and the appropriate (see important figures) number of digits after the decimal.

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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] ✅

9514 1404 393

Answer:

  295 mg

Step-by-step explanation:

The proportion can be written ...

  dose/(96 lb) = (200 mg)/(65 lb)

  dose = (96/65)(200 mg) ≈ 295.4 mg . . . . . multiply by 96 lb, cancel lb units

The doctor might recommend 295 mg for a 96-pound patient.

Answer:

600

Step-by-step explanation:

if SP>CP,  

It is profit [SP - CP = Profit]

if CP>SP,  

It is loss  [CP - SP = Loss]

Here in the question CP>SP so,  

loss = CP - SP  

      =2500 - 1900  

      = 600

Answer:

24

Step-by-step explanation:

C.P=2500

S.P=1900

Here,

Cp>Sp

So,

Loss= cp-sp

---------- ×100%

cp

=2500-1900

----------------- ×100%

2500

= 600

------- ×100 %

2500

= 24.

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 -∞.

9514 1404 393

Answer:

  a(n) = 1/2(-8)^(n-1)

Step-by-step explanation:

The general term of a geometric sequence is ...

  a(n) = a(1)×r^(n-1)

where a(1) is the first term, and r is the common ratio.

Here, the first term is a(1) = 1/2. The common ratio is the ratio of any two sequential terms: r = 32/-4 = -8. Then the explicit formula is ...

  a(n) = 1/2(-8)^(n-1)

Answer:

30 tsp of sugar

Step-by-step explanation:

If 20 is 2 parts of the 5 parts  then 1 part is 10

 10x3 =30

   30 to 20    =  3 to2

Step-by-step explanation:

[tex] \frac{58}{165}[/tex]

[tex] \frac{79}{225} [/tex]

[tex] \frac{13}{37} [/tex]

[tex] \frac{8}{45} [/tex]

[tex] \frac{17}{99} [/tex]

The answer is in the picture shown here

Graphs can be created by inputting data in MS Excel and choosing a chart type that represents the type of data to display

Please find attached the required graph of the function of the Incidence of mumps (cases per 100,000 people)

The known data for the incidence of mumps is presented in the following table;

[tex]\begin{array}{|c|cc|}Year&&Incidence \ of \ Mumps \ per \ 100,000 \ People\\1984&&1\\1985&&1\\1987&&5.5\\1988&&2\\1989&&2.5\\1999&&0.1\\2004&&0.1\end{array}[/tex]

The data from the above table can be entered in MS Excel and a graph can be plotted as follows;

Please find attached the required graph created with MS Excel

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Answer:

C

Step-by-step explanation:

The volume of a box (rectangular prism) is given by:

[tex]\displaystyle V = \ell wh[/tex]

We are given that the desired volume is 540 cubic inches. The width is three inches longer than the length and the height is four inches longer than the length. Substitute:

[tex]\displaystyle (540) = \ell(\ell + 3)(\ell + 4)[/tex]

Solve for the length. Expand:

[tex]\displaystyle \begin{aligned} 540 &= \ell (\ell^2 + 7\ell +12) \\ 540&= \ell ^3 + 7\ell^2 +12\ell \\ \ell^3 + 7\ell ^2 +12\ell -540 &= 0\end{aligned}[/tex]

We cannot solve by grouping, so we can consider using the Rational Root Theorem. Our possible roots are:

±1, ±2, ±3, ±4, ±5, ±6, ±9, ±10, ±12, ±15, ±18, ±20, ±27, ±30, ±36, ±45, ±54, ±60, ±90, ±108, ±135, ±180, ±270, and/or ±540.

(If you are allowed a graphing calculator, this is not necessary.)

Testing values, we see that:

[tex]\displaystyle (6)^3 +7(6)^2 + 12(6) -540 \stackrel{\checkmark}{=} 0[/tex]

Hence, one factor is (x - 6).

By synthetic division (shown below), we can see that:

[tex]\displaystyle \ell^3 + 7\ell^2 +12\ell -540 =(\ell -6)(\ell ^2 + 13\ell +90)[/tex]

The second factor has no real solutions. Hence, our only solution is that l = 6.

In conclusion, our answer is C.

Answer:

6 inches

Step-by-step explanation:

I just took the test

Answer:

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

Step-by-step explanation:

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

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:

D

Step-by-step explanation:

f(1)=(3+2)/(0)=5/0 which means f(1) doesn't exist

Step-by-step explanation:

[tex] \frac{x + 1}{5} + \frac{x + 1}{6} +\frac{x + 1}{7} +\frac{x + 1}{8} +\frac{x + 1}{9} +\frac{x + 1}{10 } = 0[/tex]

[tex](x + 1)( \frac{1}{5} + ... + \frac{1}{10} ) = 0[/tex]

Since the second factor is non-zero, the only possible condition for the equation to hold is,

[tex]x + 1 = 0[/tex]

[tex]x = - 1[/tex]

As x increases, y increases

The rate of change for y as a function of x is 1.4

therefore the function is growth function

For all values of x, the function value y increases

The y-intercept of the graph is the function value y 1

When x = 6, the function value y = 7.5

For an exponential function, the rate of change is b, in the equation

= f(x) = abˣ

From the graph, points (0, 1), and (2, 2) will be used for the calculation

Exponential function is represented by f(x) = abˣ

for x = 0, f(x) = 1

1 = a * b^0

a = 1

for x = 2, f(x) = 2

2 = 1 * b^2

2 = b^2

b = √2 = 1.414

for increasing rate, b = 1 + r

1.41 = 1 + r, r = 41%

When x = 6

= 1 * 1.4^6

= 7.5

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Answer:

maybe but (-4,2) only because the -4 is in the x place (x,y)

Step-by-step explanation:

Ordered pair usually refers to a set of two numbers used to locate a point in a coordinate plane. When an ordered pair refers to the location of a point in the coordinate plane, they are called the coordinates of the point.

Answer:

[tex]3x - \frac{29}{5} = - 4 \\ 3x = - 4 + \frac{29}{5} \\ 3x = \frac{ - 20 + 29}{5} \\ \\ 3x = \frac{9}{5} \\ x = \frac{9}{5} \div 3 \\ x = \frac{9}{5} \times \frac{1}{3} \\ x = \frac{3}{5} [/tex]

I hope I helped you^_^

Answer:

p = k(d)/u^2

Step-by-step explanation:

BRAINLIEST, PLEASE!

Answer:

90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

10 x 9 = 90 which is what the question asked but. re worded

[tex] \large \mathfrak{Solution : }[/tex]

Answer:

19500

Step-by-step explanation:

30/100 X 15000 = 4500

15000 + 4500 = 19500

Answer:

A = $19,965.00

A = P + I where

P (principal) = $15,000.00

I (interest) = $4,965.00

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 10/100

r = 0.1 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 15,000.00(1 + 0.1/1)(1)(3)

A = 15,000.00(1 + 0.1)(3)

A = $19,965.00

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $15,000.00 at a rate of 10% per year compounded 1 times per year over 3 years is $19,965.00.

Answer:

28

Step-by-step explanation:

6+8+6+8

6+8=14x2=28

Answer:

28

Step-by-step explanation:

P = 2(l+ w)

2(6+ 8) =

2(14)=

28

Hope this helps.

Answer:

1 5/16

Step-by-step explanation:

(-1/4 - 1/2) ÷ (-4/7)

Parentheses first

Get a common denominator

(-1/4 - 1/2 *2/2)

(-1/4 - 2/4)

-3/4

Replace in the equation

(-3/4 ) ÷ (-4/7)

Copy dot flip

-3/4 * -7/4

21/16

1 5/16

[tex]\\ \rm\Rrightarrow \left(\dfrac{-1}{4}-\dfrac{1}{2}\right)\div \dfrac{-4}{7}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{-1-2}{4}\times\dfrac{-7}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{-3}{4}\times \dfrac{-7}{4}[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{21}{16}[/tex]

[tex]\\ \rm\Rrightarrow 1\dfrac{5}{16}[/tex]

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:

15

Step-by-step explanation:

You have to calculate the boys name using ratio expression.

3/5 × 25

= 15

Answer:

x = 3^2

Step-by-step explanation:

2x^2 = 18

x^2 = 18 / 2

x^2 = 9

x = √9

= 3