Evan invested $800 in an account that pays 3.25% interest compounded annually.
Assuming no deposits or withdrawals are made, find how much money Evan would
have in the account 12 years after his initial investment. Round to the nearest tenth
(if necessary).

The average rate of change of the function over the interval is -6

From the question, we have the following parameters that can be used in our computation:

The graph

The interval is given as

From x = 2 to x = 4

The function is a quadratic function

This means that it does not have a constant average rate of change

So, we have

f(2) = -3

f(4) = -15

Next, we have

Rate = (-15 + 3)/(4 - 2)

Evaluate

Rate = -6

Hence, the rate is -6

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Answer:

Step-by-step explanation:

tail is 20 millimeters

body is 3*20=60

60+20=80

80 millimeters, divide by ten for centimeters,

answer: 8 centimeters

Answer:

0.039

Step-by-step explanation:

Expanded Notation Form:

0.039 =

 0  

+   0.0

+   0.03

+   0.009

Expanded Factors Form:

   0.039 =

 0 × 1  

+ 0 ×   0.1

+ 3 ×   0.01

+ 9 ×   0.001

Expanded Exponential Form:

 0.039 =

0 × 100

+ 0 × 10-1

+ 3 × 10-2

+ 9 × 10-3

Those are the way you can express .039 in different expanded forms

Hope this helps

Step-by-step explanation:

42 5/9 + 7 1/12 = 49 23/36 metres

it is to be added because one ant is at the top and the other is deep below

The properties that we can use in order to solve this equation are:

- Reflexive

- Addition

- Subtraction

- Multiplication

- Division

- Distributive

From S1 to S2, the property we applied is the R1 = Subtraction property of equality, because both sides of the equation were subtracted by 32.

From S2 to S3, the property we applied is the R2 = Distributive property of equality, because we expanded the product of 9 by the term (x - 2).

From S3 to S4, we can divide both sides by 9, so we will be using R3 = Division property of equality, and the result would be S4 = x - 2 = 43/9

Then, from S4 to S5, using the addition property of the equality, we added 2 to both sides of the equation, so the result is x = 61/9.

For R5, we can write the Reflexive property of equality, because we are just stating the value of x

The value of f(-0.01) is approximately 0.99005.

To evaluate f(-0.01), we substitute -0.01 into the function f(x) = (1+x)^(1/x). Thus, we have f(-0.01) = (1+(-0.01))^(1/(-0.01)).

Using a calculator, we simplify this expression to f(-0.01) = 0.99005. Therefore, the value of f(-0.01) rounded to five decimal places is approximately 0.99005.

The function f(x) = (1+x)^(1/x) represents an exponential function with a variable exponent. In this case, we are evaluating the function at x = -0.01.

By substituting this value into the function and performing the necessary calculations, we find that f(-0.01) is approximately 0.99005. This means that when x is equal to -0.01, the function value is approximately 0.99005.

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Answer:

Andrés

Step-by-step explanation:

Andrés porque el 10% es .10 = 10 centavos

Answer:

a.  2p + 2d + 1c + 1p + 1c + 2p + 1d

b. 5p + 3d + 2c

c. In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

Step-by-step explanation:

a.
From the cute diagram we see that the family bought

2 pizzas + 2 drinks + 1 cone + 1 pizza + 1 cone + 2 pizzas + 1 drink

Using the variables provided, this becomes

2p + 2d + 1c + 1p + 1c + 2p + 1d

b.
Combining like terms the total purchase is:
(2p + 1p + 2p) + (2d + 1d) + (1c + 1c)

Adding the coefficients of each grouped term we get

(5p) + (3d) + (2c)

Opening the brackets, this becomes
5p + 3d + 2c

c.
In an algebraic expression each term can only be combined with another like term. For example x terms can be combined only with x terms, y terms can be combined only with y terms etc.

This is similar to the above example in which pizza(p) can only be combined with pizza(p), drinks (d) can only be combined with drinks(d) and cone(c) can only be combined with cone(c)

Answer:

Step-by-step explanation:

what is the sloution to this question x- 16=-8

x - 16 = -8

x = -8 + 16

x = 8

----------------

check

8 - 16 = -8

-8 = -8

the answer is good

The result of this equation is x = 8

-

To solve this equation - we will:

\( \\ \large \sf x- 16=-8\)

\( \large \sf x=-8 + 16\)

\( \green{ \boxed{ \large \sf x=8}}\)

So, the answer of this equation is x = 8

Answer: All real numbers

Step-by-step explanation:

Let's find the critical points of the inequality.

2y2+1=

−9

5

y−6

2y2+1−(

−9

5

y−6)=

−9

5

y−6−(

−9

5

y−6)(Subtract (-9)/5y-6 from both sides)

2y2+

9

5

y+7=0

For this equation: a=2, b=1.8, c=7

2y2+1.8y+7=0

y=

−b±√b2−4ac

2a

(Use quadratic formula with a=2, b=1.8, c=7)

y=

−(1.8)±√(1.8)2−4(2)(7)

2(2)

y=

−1.8±√−52.76

4

First we are going to see if the relationship is proportional or not.

Let us calculate 2 ratios with two pairs to see if there is a constant of proportionality

10/1 = 10

8/2= 4

Since the ratios are not the same this relationship is not proportional.

From the information we can deduce that each minute the distance is reduced 2 blocks. Then, at the beginning Caleb was 12 blocks from home and he is walking at a rate of -2 blocks per minute.

- Since the relationship is not proportional we can not write an equation of the form y=k*x.

Answer:

38 = 2 × 19

95 = 5 × 19

GCF of 38 and 95: 19

Answer:

19

Step-by-step explanation:

You can also use GCF calculators.

The solution set of f(x) > 0 is x ∈ (-2, 8).

To find the solution set of f(x) > 0, we need to first determine the critical values of x where f(x) changes sign.

Let's start by finding the domain of the function:

x² - 6x - 16 ≠ 0

We can solve for x by using the quadratic formula:

x = [6 ± √(6² + 4(16))]/2 = [6 ± √52]/2 = 3 ± √13

So the domain of f(x) is (-∞, 3 - √13) U (3 + √13, ∞).

Now let's factor the numerator and denominator of f(x):

f(x) = (x + 10)/[(x - 8)(x + 2)]

The critical points occur where the numerator or denominator of f(x) changes sign.

The numerator changes sign at x = -10, and the denominator changes sign at x = -2 and x = 8.

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hi brainly user! ૮₍ ˃ ⤙ ˂ ₎ა

⊱┈────────────────────────┈⊰

\(\large \bold {ANSWER}\)

\(\large \bold {SOLUTION}\)

Well, the first thing we have to do is see if we have any repeated letters and count how many letters the word has.

The word has 10 letters, the letters "i" is repeated once. So we need to exclude the repetitions.

\(10 - 2 = 8\)

Once this is done, we will use the combinatorial analysis, we will use this formula:

\({C}^{p}_{n} = \frac{n!}{p!(n- p)!}\)

The n is the number of letters and the o will be the number of elements we want to know how many groups are possible. Which will be the 4. The symbol of ! means factorial.

\(\begin{gathered}{C}^{4}_{8} = \frac{8!}{4!(8 - 4)!} \\ \\ {C}^{4}_{8} = \frac{8 \times 7 \times 6 \times 5 \times \not4 !}{4! \times \not4!} \\ \\ {C}^{4}_{10} = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} \\ \\ {C}^{4}_{10} = \frac{1680}{24} = 70\end{gathered}\)

Answer:

B. (1,4)

Step-by-step explanation:

hope this helps! Have a good day!

Answer:

b, I’m taking the test right now

Step-by-step explanation:

Answer:

14cm

Step-by-step explanation:

Volume of the pyramid = Base area × height/3

V = BH/3

Base area = 14×width

Height= 9cm

Volume = 168cm³

Substitute into the formula

168 = 4w×9/3

36w = 168×3

36w = 504

w = 14cm

Hence the width of the pyramid is 14cm

The probability that the random sample of 100 male students has a mean gpa greater than 3. 42 is 0.9452.

A statistic known as the standard deviation is used to describe how volatile or dispersed a group of numerical values is. While a big standard deviation denotes that the values are scattered across a wider range, a low standard deviation indicates that the values tend to be close to the set mean.

From the given information, a scores random sample of 100 male students is selected and the GPA for each student is calculated which follows approximately normal with a mean of 3.5 and standard deviation of 0.5. That is,

µ = 3. 5 and σ = 0. 5

and the random sample of 100 male students has a mean GPA 3.42 is considered.

The z-score value is,

Z=( 3.42-3.5)/ (0.5/√100)

Z= -0.08/0.05

Z=-1.6

The value of z-score is obtained by taking the difference of x and µ. Then the resulting value is divided with the standard deviation by sample size.

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is obtained below:

The required probability is,

P(X>3.42)=P(z>-1.6)

= 1- P(Z≤-1.6)

From the “standard normal table”, the area to the left of Z=-1.6 is 0.0548.

P(X>3.42)= 1- P(Z≤-1.6)

=1-0.0548

=0.9452

The probability that the random sample of 100 male students has a mean GPA greater than 3.42 is 0.9452.

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This function represents a downward-opening parabola with a vertical shift of 6 units upward.

The given function is Ƒ(t) = –1/(2t²) + 2t + 6.

This is a quadratic function in terms of t. The general form of a quadratic function is f(t) = at² + bt + c, where a, b, and c are constants.

Comparing the given function Ƒ(t) = –1/(2t²) + 2t + 6 with the general form, we can see that a = -1/2, b = 2, and c = 6.

So, the function Ƒ(t) can be written as:

Ƒ(t) = (-1/2)t² + 2t + 6

This function represents a downward-opening parabola with a vertical shift of 6 units upward.

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Part a

The domain is the set of x-values, which is \((-\infty, \infty)\)

Part b

The range is the set of y-values, which is \((-\infty, -2]\)

Part c

The x-intercepts is when y=0, which there are none of.

Part d

The y-intercept is when x=0, which is at (0, -2).

Intersection of B'∩C = {k, y}

To find the intersection of B' and C, we need to first find the complement of set B (B') and then find the intersection between B' and C.

1. Complement of set B (B'):

The complement of set B (B') consists of all elements in the universal set U that are not in set B. From the given information, set B is defined as {k, s, y}', which means it contains all elements in U except for k, s, and y. Therefore, the complement of set B is {f, m, x, z}.

2. Intersection between B' and C:

Now, we need to find the intersection between B' (complement of B) and set C. From the given information, set C is defined as {s, z}. To find the intersection, we need to identify the common elements between B' and C.

The elements present in both B' and C are k and y. Therefore, the intersection of B' and C is {k, y}.

So, the answer to (b) is B'∩C = {k, y}.

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Evaluating the function in the values of the domain we will get some coordinate pairs. The graph of these is in the image at the end.

Here we have the function:

3x - y = 1

And we want to graph this in the domain (-3, -1, 0, 4)

To do so, we need to evaluate the function (the values of x) in the values of the domain.

Solving the equation for y we get:

y = 3x - 1

Now, when x = -3

y = 3*-3 - 1 = -10

when x = -1

y = 3*-1 - 1 = -4

when x = 0

y = 3*0 - 1 = -1

When x = 4

y = 3*4 - 1 = 11

So we have the points (-3, -10), (-1, -4),  (0, -1), (4, 11)

The graph of these points is on the image below.

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Answer:

Step-by-step explanation:

A short web search will turn up the authors of the given titles:

  The Old Man and the Sea - Hemingway

  Huckleberry Finn - Twain

  Moby D.ick - Melville

  1984 - Orwell

  Crime and Punishment - Dostoevsky

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Answer:

the third option

Step-by-step explanation:

it starts a 0 so theres nothing to be added. rise over run is the slope and it rises 1 and goes over 3

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.

1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.

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Answer: The answer is D. the last option

Step-by-step explanation:

The correct answer is option d) The graph is the radical function, y = √x shifted right 1 unit and up 4 units.

The original function is y = √(x - 1) + 4, which represents a radical function.

This function involves taking the square root of the quantity (x - 1) and then adding 4 to the result.

By shifting the function right 1 unit, we are replacing x with (x - 1). This means that the graph will be shifted horizontally by 1 unit to the right compared to the standard square root function.

By shifting the function up 4 units, we are adding 4 to the output of the square root function.

This means that the graph will be shifted vertically by 4 units compared to the standard square root function.

Therefore, the graph of the function y = √(x - 1) + 4 is the radical function y = √x shifted right 1 unit and up 4 units.

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Answer:

Option A , should not be rejected

Step-by-step explanation:

From the question we are told that:

Sample 1 \(n=25\)

Standard deviation 1 \(\sigma_1=30\)

Sample 2 \(n=16\)

Standard deviation 2 \(\sigma_2=20\)

Level of  confidence \(\alpha=95\%=>0.95\)

Generally The Hypothesis are given as

 \(H_0:\sigma_1^2=\sigma_1^2\)

 \(H_1:\sigma_1^2\neq \sigma_1^2\)

Generally the equation for test Statistics is mathematically given by

 \(T=\frac{\sigma_1^2}{\sigma_2^2}\)

 \(T=\frac{30^2}{20^2}\)

 \(T=2.25\)

Therefore

Critical Value

 \(X=(\alpha,df_1)\)

 \(X'=(\alpha,df_2)\)

Where

 \(df=n-1\)

Therefore

 \(X=(0.95,24)\)

 \(X'=(0.95,15)\)

From Table

 \(T_{Critical}=T_x,T_{x'}\)

 \(T_{Critical}=0.41,2.701\)

Therefore

 \(T_x<T<T_{x'}\)

Hence,We fail to reject the Null Hypothesis \(H_0\)

Option A , should not be rejected