A person invests $1,450 in an account that earns 6% annual interest compounded continuously. Find when the value of the investment reaches $2,500. If necessary round to the nearest tenth. The Investment will reach a value of $2.500 in approximately ____ years.

Answer:

The volume is equal to [tex]112\frac{1}{2}\ cm^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

[tex]V=LWH[/tex]

we have

[tex]L=4\frac{1}{2}\ cm=\frac{4*2+1}{2}=\frac{9}{2}\ cm[/tex]

[tex]W=5\ cm[/tex]

[tex]H=5\ cm[/tex]

substitute the values

[tex]V=(\frac{9}{2})(5)(5)[/tex]

[tex]V=112.5\ cm^{3}[/tex]

Convert to mixed number

[tex]112.5\ cm^{3}=112\frac{1}{2}\ cm^{3}[/tex]

Answer:

D

Step-by-step explanation:

Answer:

$20

Step-by-step explanation:

4×5=$20

this is random do not look

let's recall that in an isosceles triangle, the twin sides make twin angles at the bottom/base, so on the triangle on the left-side, if the "vertex" atop has an angle of 116°, then the twin sides below are simply 180° - 116 = 64, split that in half and that's 32° each.

The same is true for the isosceles triangle on the right side.  Also recall that a flat-line is always 180°, 32 + 72 + 76 = 180.

Check the picture below.

Answer:

  152 in³

Step-by-step explanation:

Each cube's volume is the cube of its edge length, so the total volume is ...

  (5 in)³ + (3 in)³ = 125 in³ +27 in³ = 152 in³

the answer is the second one

Answer:

The answer is b!!

Independent, means the first event won't affect the second event.

The independent events would be :

A, B, E, F

let's notice something on this hyperbola, the fraction that is positive, is the fraction with the "y" variable, that simply means that the hyperbola is opening vertically, namely runs over the y-axis or it has a vertical traverse axis, which means, that, the foci will be a certain "c" distance from the center over the y-axis, well, with that mouthful, let's proceed.

[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\cfrac{(y-3)^2}{1}-\cfrac{(x+2)^2}{4}=1\implies \cfrac{[y-3]^2}{1^2}-\cfrac{[x-(-2)]^2}{2^2}=1~~ \begin{cases} h=-2\\ k=3\\ a=1\\ b=2 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ c=\sqrt{a^2+b^2}\implies c=\sqrt{1+4}\implies c=\sqrt{5} \\\\\\ \stackrel{\textit{so then the foci are at}}{(-2~~,~~3\pm \sqrt{5})}\qquad \qquad \qquad \stackrel{\textit{and its vertices are at }}{(-2~~,~~3\pm 1)}\implies \begin{cases} (-2,4)\\ (-2,2) \end{cases}[/tex]

now let's check for the asymptotes.

[tex]\bf y=3\pm \cfrac{1}{2}[x-(-2)]\implies y=3\pm \cfrac{1}{2}(x+2) \\\\[-0.35em] ~\dotfill\\\\ y=3+ \cfrac{1}{2}(x+2)\implies y=3+\cfrac{x+2}{2}\implies y=\cfrac{6+x+2}{2} \\\\\\ y=\cfrac{x+8}{2}\implies y=\cfrac{1}{2}x+4 \\\\[-0.35em] ~\dotfill\\\\ y=3- \cfrac{1}{2}(x+2)\implies y=3-\cfrac{(x+2)}{2}\implies y=\cfrac{6-(x+2)}{2} \\\\\\ y=\cfrac{6-x-2}{2}\implies y=\cfrac{-x+4}{2}\implies y=-\cfrac{1}{2}x+2[/tex]

Answer:

1 9

2 11

3 13

4 15.

Step-by-step explanation:

When x = 1 y = 2(1) + 7 = 9.

x = 2, y = 2(2)+7 = 11

x = 3, y = 2(3) + 7 = 13

x = 4, y = 2(4) + 7 = 15.

Multiply corresponding components, then add the products:

[tex]v\cdot w=3(-4)+(-8)(-2)+(-3)(-6)=22[/tex]

The resultant of the dot product of two vectors is:

                     [tex]v\cdot w=22[/tex]

We are asked to find the dot product of the two vectors v and w.

The vectors are given by:

r = <8, 8, -6>; v = <3, -8, -3>; w = <-4, -2, -6>

This means that  in the vector form they could be written as follows:

[tex]r=8\hat i+8\hat j -6\hat k\\\\v=3\hat i-8\hat j -3\hat k\\\\w=-4\hat i-2\hat j -6\hat k[/tex]

Hence, the dot product of two vectors is the sum of the product of the entries corresponding to each direction component.

i.e. the x-component get multiplied to each other, y-component get multiplied to each other and so happens with z.

Hence, the dot product of v and w is calculated as:

[tex]v\cdot w=3\times (-4)-8\times (-2)-3\times (-6)\\\\i.e.\\\\v\cdot w=-12+16+18\\\\i.e.\\\\v\cdot w=22[/tex]

Answer:

  c.  5, 8, 17, 44

Step-by-step explanation:

Put the given number into the formula and do the arithmetic:

  3·4 -7 = 5 . . . . . matches answer choice C only

___

You know the correct answer at this point. You can check the other numbers if you wish:

  3·5 -7 = 8

  3·8 -7 = 17

  3·17 -7 = 44

Answer:

  82

Step-by-step explanation:

The sum resolves to ...

  13 + 18 + 23 + 28 = 82

_____

for n=2, the term is 5·2 +3 = 10+3 = 13

The coefficient of n is 5, so you know the next term will be 5 more than this:

for n=3, the term is 5·3 +3 = 15+3 = 18

Additional terms are each 5 more than the one before. Since there are so few terms, you can add them up directly as quickly as you can use any other formula. For a longer series, you might find the average term (here, 41/2), then multiply by the number of terms (here, 4). The result is the sum of the series:

  4·(41/2) = 82

Answer:

A

Step-by-step explanation:

We can use a simple formula to solve for SST. The formula is:

[tex]SST=\frac{SSE}{1-R^2}[/tex]

Where

the coefficient of determination is  [tex]R^2[/tex]

Now, we are given  [tex]R^2[/tex]  is 0.25 and SSE is 12 (not SEA, it's SSE). we simply put it into the formula and solve for SST:

[tex]\\SST=\frac{12}{1-0.25}\\SST =16[/tex]

correct answer choice is A

Answer:

The side length of the original patio was [tex]12\ ft[/tex]

Step-by-step explanation:

Let

x----> the side length of the original square patio

we know that

[tex]441=(x+9)^{2}\\ \\x^{2} +18x+81=441\\ \\ x^{2} +18x- 360=0[/tex]

Solve the quadratic equation by graphing

The solution is [tex]x=12\ ft[/tex]

see the attached figure

Answer:

for study island it is 11 feet

Step-by-step explanation:

Answer:

It is a right triangle.

Step-by-step explanation:

By the  Inverse Pythagoras Theorem if 39^2 = 36^2 + 15^2  then it is a right triangle.

39^2 = 1521

36^2 + 15^2 = 1296 + 225 = 1521.

So it is a right triangle.

Based on the converse of the Pythagorean Theorem, the triangle with the following side lengths is a right triangle.

What is the Converse of the Pythagorean Theorem?

The converse of the Pythagorean Theorem states that a triangle is a right triangle if the sum of the squares of two of its legs are equal to the square of the length of the longest side (hypotenuse).

The longest side in the triangle is 39 in. Therefore:

39² = 36² + 15²

1,521 = 1,521

Based on this, we can conclude that the triangle given is a right triangle.

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Answer:

15/8.

Step-by-step explanation:

Tan A = opposite / adjacent side

= 15/8.

The value of tan A is 15/8.

Given: Right angled triangle

AB = 8

AC = 17

BC = 15

We have to find tan A.

We know,

tan A = Opposite side / Adjacent side

In the given right angle triangle:

Opposite side = BC

Adjacent side = AB

⇒ tan A = BC/AB

⇒ tan A = 15/8

Therefore, the value of tan A is 15/8.

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Answer:

A, B, C

Step-by-step explanation:

Answer: try question cove but brainly is good so keep using it

]

You can think of an inverse function as a function that “unwraps” x from whatever operations are attached to it. In the case of F(x) = √x, we can ”unwrap” x by squaring it. This narrows our options down to either A or D. Keep in mind that since there are no real number solutions to the square root of a negative number, we need to limit our domain to non-negative values. In other words, x ≥ 0. With that restriction, our answer is A.

The answer is:

The inverse of the given function is:

A. [tex]f(x)^{-1}=x^{2}[/tex]

Where,

[tex]x\geq 0[/tex]

Inversing a function involves inversing the function variables. If we want to inverse a function, we need to rewrite the variable "x" with "y" and rewrite the variable "y" with "x", and then, isolate the variable "y".

Also, the domain of the original function will be the range of its inverse function, and the range of the original function, will be the domain of the its inverse function.

We are given the function:

[tex]f(x)=\sqrt{x}[/tex]

[tex]f(x)=y=\sqrt{x}[/tex]

So, inversing we have:

[tex]y=\sqrt{x}[/tex]

[tex]x=\sqrt{y}[/tex]

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

So, we have that the given function is only "part" of its inverse function, since negative square roots does not exist, it means that the domain of the given function starts from the number 0 taking only positive numbers.

Hence, we have that the answer is:

A. [tex]F(x)=x^{2}[/tex]

Where,

[tex]x\geq 0[/tex]

Have a nice day!

Answer:

[tex]\$10,665.64[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]V=P(1-r)^{x}[/tex]  

where  

V is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is Number of Time Periods  

in this problem we have  

[tex]P=\$19,900\\r=7.5\%=0.075\\x=8\ years[/tex]

substitute the values in the formula

[tex]V=\$19,900(1-0.075)^{8}=\$10,665.64[/tex]  

Answer: The answer is 10665.64

Step-by-step explanation:

Exponential Functions:

y=ab^x

A= starting value = 19900

r=rate = 7.5%=0.075

Exponential Decay:

b=1-r=1-0.075=0.925  

Write Exponential Function:

y=19900(0.925)^x

Plug in time for x:

y=19900(0.925)^8

y= 10665.6404317  

Evaluate

y≈10665.64

Answer:

Step-by-step explanation:

105 years old. Since if he 35 the mother is 105>>------->(35 x 3= 105)

85 years old. 25•3=75 the difference between 75 and 25 is 50, which means she is 50 years older than him. 35+50=85.

ANSWER

[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]

EXPLANATION

We want to find the coordinates of the point W(x,y) which divides V(-3,3) and X(9,13) in the ratio m:n=3:4.

The x-coordinate of this point is given by:

[tex]x= \frac{mx_2+nx_1}{m + n} [/tex]

[tex]x= \frac{3(9)+4( - 3)}{4 + 3} [/tex]

[tex]x= \frac{21 - 12}{4 + 3} [/tex]

[tex]x= \frac{9}{7} [/tex]

The y-coordinates is given by;

[tex]y= \frac{my_2+ny_1}{m + n} [/tex]

[tex]y= \frac{3(13)+4( 3)}{4 + 3}[/tex]

[tex]y= \frac{39+12}{4 + 3}[/tex]

[tex]y= \frac{51}{7}[/tex]

Hence

[tex]W(\frac{9}{7},\frac{51}{7} )[/tex]

The compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.

If n is the number of times the interest is compounded each year and r is the yearly rate of compound interest, the final amount after 't' years is:

[tex]a = p(1 + \dfrac{r}{n})^{nt}[/tex]

The function b(x) is expressed as follows:

[tex]\rm b(x) = 33741(1+\frac{0.028}{1} )^x\\\\[/tex]

Where ;

Rate(r)=2.8 percent

Total after x years(b)

Initial amount ( P)= 33741

x represents the number of years since 2015.

Hence, the compounding tuition fee function's complete expression is,b(x)=33741(1.028)ˣ.

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For this case we will indicate expressions equivalent to 6 ^ {16}:

We can write the following:

[tex]6 ^ {16} = 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6\\6 ^ {16} = (6 ^ 8) ^ 2\\6 ^ {16} = 6 ^ {\frac {32} {2}}[/tex]

Answer:

The equivalent expressions are shown in the previous part.

Answer:

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

At the northside store there are 12 females with college degrees

At the southside store there are 18 females with college degrees

The total number of females at the two stores with college degrees is

12+18 = 30

Answer:

[tex]\large\boxed{x=7}[/tex]

Step-by-step explanation:

[tex]5^{x+2}=5^9\iff x+2=9\qquad\text{subtract 2 from both sides}\\\\x+2-2=9-2\\\\x=7[/tex]

The value of x if 5ˣ⁺²=5⁹ is 7. Therefore, the correct answer is option C.

The given equation is 5ˣ⁺²=5⁹.

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.

We know that, when the bases are equal their exponents are equal.

x+2=9

x=9-2

x=7

Therefore, the correct answer is option C.

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Answer:

"a period change"

Step-by-step explanation:

Simple ways of understanding transformations are:

Phase shift: 2 graphs would be shifted version of each other, all other things constant.

Period change: the 2 graphs would have different cycles, one would be compressed/stretched version of the other, all other things constant

Amplitude Change: The height/crest of the graphs would vary, that is the amplitude. All other things constant.

Addition of Negative constant: this would shift the 1 graph downwards with respect to the other graph, it is a vertical shift. All other things constant.

Now carefully looking at the 2 graphs given, we can see that the cycles are different. One is a more "relaxed", or "stretched" version of the other. This means, the period is changed.

2nd answer choice is right.

I think it's C. Trout increased its predicted average population.

Answer:

b

Step-by-step explanation:

because it increases the most

Answer:

The answer is B

Step-by-step explanation:

Answer:

54.5 amps to the nearest tenth.

Step-by-step explanation:

V = IR  where V = volts, I = current and R = resistance.

12 = I * 0.22

I = 12/0.22

I = 54.5 Amps.

When the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.

The question regarding how many amps will be drawn from the 12-volt battery when a car engine with a resistance of 0.22 ohms is started can be solved using Ohm's Law. Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. The formula is given by I = V / R.

Therefore, the current drawn from the battery can be calculated as follows:

So, when the key is turned and the engine starts, the battery will supply approximately 54.55 amps to the engine.

Answer:

B

Step-by-step explanation: