I have $20 in my investment account if i save $5 each week how much money will I have in the account after 9 weeks? solve using an algebraic equation

Answer:

(1) 56 miles/hour

Step-by-step explanation:

We need to find the average rate of change from t = 2 to t = 9.

At t = 2 hours, d = 106 miles.

At t = 9 hours, d = 498 miles.

The average rate of change in function f(x) from x = a to x = b is

[f(b) - f(a)]/(b - a)

average rate of change from t = 2 to t = 9 =

(498 - 106)/(9 - 2) = 392/7 = 56

Answer: (1) 56 miles/hour

Answer:  What an entrepreneur really is, though, is someone who runs their own business and takes a risk to do it.

Step-by-step explanation:

Answer:

1/21

Step-by-step explanation:

Answer:

option c .

Step-by-step explanation:

Given exponential equation is ,

\(\longrightarrow 2^{7-2x}= \dfrac{1}{4}\)

As we know that 4 = 2² , so ;

\(\longrightarrow 2^{7-2x}= \dfrac{1}{2^2}\)

Recall that ,\( a^{-m}=\dfrac{1}{a^m}\) .So ;

\(\longrightarrow 2^{7-2x}= 2^{-2} \)

Since the bases are equal we can compare the powers as ,

\(\longrightarrow 7-2x = -2\)

Subtracting 7 on both sides,

\(\longrightarrow -2x = -9\)

Divide both sides by -2,

\(\longrightarrow x =\dfrac{-9}{-2}\)

Simplify,

\(\longrightarrow \underline{\underline{ x = 4.5 }} \)

Hence the correct option is C .

Answer:

Step-by-step explanation:

To solve this question, we can use either of the 2 below given methods:

1. Rule of Exponents:

\(2 ^ { 7-2x } = \frac{ 1 }{ 4 }\\\rightarrow 2 ^ { 7-2x } = \frac{ 1 }{ 2^{2} }\)

Now, by using the law → \(x^{-y} = \frac{1}{x^{y}}\)...

\(2 ^ { 7-2x } = \frac{ 1 }{ 2^{2} }\\2 ^ { 7-2x } = 2^{-2}\)

Now, let's take the exponential values as the base values are equal.

\(7 - 2x = - 2\\- 2x = - 2 + (-7)\\- 2x = - 9\\\boxed{x = \frac{9}{2} = 4.5}\)

2. Logarithms:

\(2 ^ { 7-2x } = \frac{ 1 }{ 4 }\\\rightarrow2^{-2x+7}=\frac{1}{4}\)

Now, take the logarithm of both the sides of the equation.

\(\log(2^{-2x+7})=\log(\frac{1}{4})\)

We know that, the logarithm of a number raised to an exponential power is power times the logarithm of the number. So,

\(\log(2^{-2x+7})=\log(\frac{1}{4}) \\ \rightarrow \left(-2x+7\right)\log(2)=\log(\frac{1}{4})\)

Now, divide both the sides of the equstion by log (2).

\(-2x+7=\frac{\log(\frac{1}{4})}{\log(2)}\)

According to the change of base formula, \(\frac{\log(x)}{\log(y)}\) = \(\log_{y}(x)\). Then,

\(-2x+7=\log_{2}\left(\frac{1}{4}\right)\)

By subtracting 7 from both the sides of the equation & then simplifing it further....

\(-2x=-2-7 \\-2x = - 9\\\boxed{x = \frac{9}{2} = 4.5}\)

_____________

Hope it helps!

\(\mathfrak{Lucazz}\)

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Polar coordinates describe the position of a point P in the plane by its separation from the origin, r, and the angle formed between the positive x-axis and the line segment leading to P.

To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

Polar coordinates can also be extended into three dimensions using the coordinates (ρ, φ, θ), where ρ is the distance from the pole, φ is the angle from the z-axis ( called the co-latitude or zenith and measured from 0 to 180° ) and θ is the angle from the x-axis ( as in the polar coordinates ).

Given data ,

Let the polar curve be represented as A

Now , the polar coordinates is given as

r = -4 sin ( 3θ )

And , To graph the polar curve, we make use of the following representations:

r represents the y-axis

θ represents the x-axis

So , on simplifying , we get

The graph which represents the polar curve r = -4 sin ( 3θ ) is plotted

Hence , the polar curve is r = -4 sin ( 3θ )

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Answer:

D

Step-by-step explanation:

The point estimate of the population mean  is 22 and margin of error for the confidence interval is 3.

1. Point estimate

Point estimate = Upper bound+ Lower bound/2

Point estimate = (25+19) /2

Point estimate = 44/2

Point estimate = 22

2. Margin error

Margin error = Upper bound  - Lower bound/2

Margin error = ( 25-19) /2

Margin error = 6 /2

Margin error = 3

Therefore the point estimate is 22.

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Answer:

a. is false

Step-by-step explanation:

4 liters= 1.057 gal

1.057 is greater than 1

Hope this helps :)

The graph of the function f(x) = 4(2/3)^x is added as an attachment

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

f(x)=4⋅(

2

3

​)

x

Express the equation properly

So, we have

f(x) = 4(2/3)^x

The above expression is a an equation of a exponential function

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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By logarithm properties, the logarithmic equation 2 · ㏒ₐ (5 · x³) - (1 / 2) · ㏒ₐ (2 · x + 3) is equivalent to ㏒ₐ [(25 · x⁶) / √(2 · x + 3)]. (Correct choice: A)

In this problems we have a logarithmic equation that must be simplified by means of logarithm properties, all of them described below:

Logarithm of a product of two numbers

㏒ₙ (a · b) = ㏒ₙ a + ㏒ₙ b

Logarithm of a division of two numbers

㏒ₙ (a / b) = ㏒ₙ a - ㏒ₙ b

Logarithm of a power of a number

㏒ₙ aˣ = x · ㏒ₙ a

Now we proceed to reduce the logarithmic equation into a single expression:

2 · ㏒ₐ (5 · x³) - (1 / 2) · ㏒ₐ (2 · x + 3)

㏒ₐ (5 · x³)² - ㏒ₐ √(2 · x + 3)

㏒ₐ (25 · x⁶) - ㏒ₐ √(2 · x + 3)

㏒ₐ [(25 · x⁶) / √(2 · x + 3)]

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Answer:

The tightened spot is 10 feet away from the foot of the pole.

Step-by-step explanation:

1. Draw the diagram. Notice that the shape of the electric pole and its supporting wire creates a right triangle.

2. We know 2 side lengths already (26ft, 24ft), and we need to find 1 more side length. Therefore, to find the 3rd side length of a right-triangle, utilize Pythagoras' Theorem.

⭐What is the Pythagoras' Theorem?

3. Substitute the values of the side lengths into the equation, and solve for the unknown side length.

Let B= the distance from the tightened spot to the foot of the pole.

\((C)^2 = (A)^2 + (B)^2\)

\(26^2 = 24^2 + B^2\)

\(676 = 576 + B^2\)

\(100 = B^2\)

\(\sqrt{100} = \sqrt{(B)^2}\)

\(10 = B\)

∴ The tightened spot is 10 feet away from the foot of the pole.

Diagram:

Answer:

The ratios are not equal, so this is not a dilation.

Step-by-step explanation:

4/3 is the first ratio

3/4 is the second ratio

Since these ratios are not equal there is not a dilation.

Answer:

Below.

Step-by-step explanation:

3 to the 4th is 3x3x3x3 or 81. 5x5=25

81+25=106.

Answer:

( h + 5 )^2 + ( y - 8 ) ^2 = 49

Step-by-step explanation:

Equation of a circle:

( x - h )^2 + ( y - k )^2 = r^2

Where ( h , k ) = center and r = radius

We are given that the circle has a center at ( -5 , 8 ) meaning that h = -5 and k = 8

We are also given that the circle has a radius of 7 meaning that r = 7

Now that we have identified each variable we plug the values into the equation

( h - (-5)^2 + ( y - 8 )^2 = 7^2

Our final step is to simplify

we get that the equation of the circle is

( h + 5 )^2 + ( y - 8 ) ^2 = 49

By the way ^ means exponent

Answer:

30units

Step-by-step explanation:

Hope this answers helps you

The value of x is (-∞, -5) ∪ (1, ∞).

Given is a polynomial, \(x^4+2x^3-12x^2+14x-5 > 0\),

Solving for x,

Factors =

\(x^4+2x^3-12x^2+14x-5\\ \\= \quad \left(x-1\right)^3\left(x+5\right)\)

Therefore,

\(\left(x-1\right)^3\left(x+5\right) > 0\)

\(x < -5\quad \mathrm{or}\quad \:x > 1\)

Hence the value of x is (-∞, -5) ∪ (1, ∞).

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Answer:

2 brown

Step-by-step explanation:

The only time you can be so sure you've chosen 2 brown socks is when there are no more white socks and black socks. This means that to be 100% sure that you have chosen 2 brown socks you have to choose the 12 white socks and the 18 black socks and only then can you choose 2 brown socks without looking. Therefore, the total number of socks to choose from is:

Total number of socks = 12 white socks + 18 black socks + 2 brown socks

Total number of socks = 32 socks

A total picking of 32 socks is necessary to be sure without looking that 2 brown have already been chosen that way.

The least number of socks must choose, must choose without looking, to be certain that you have chosen two socks of the same color is 4.

The least number is "the smallest or lowest number or degree".

According to the question,

A drawer contains 12 identical white socks, 18 identical black socks, and 14 identical brown socks.

In order to find the least number of socks you must choose, without looking, to be certain that you have chosen two socks of the same color.

Since, we have only 3 different colors to get pair of one color we need to take 4 socks so that last one must matches color of socks what we have already have in our hand.

Hence, it clearly shows the least number of socks must choose, without looking, to be certain that you have chosen two socks of the same color is 4.  

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Answer:

C. a quadratic function with a negative value of a

Step-by-step explanation:

It is likely that a quadratic function with a negative value of a would be the best model for this data, as it would represent a parabolic shape that can accommodate a downward trend, followed by an upward trend, in the stock price. The value of "a" determines the direction of the parabola, with a negative value resulting in a downward-facing parabola, which is appropriate for a stock price that starts low and increases over time. This type of function would provide a good fit for the data, especially if there are fluctuations or ups and downs in the stock price over time.

Answer:

0..................

Answer:

0

Step-by-step explanation:

9514 1404 393

Answer:

  y -2 = 2(x -30)

Step-by-step explanation:

The point-slope equation is ...

  y -k = m(x -h) . . . . . line through (h, k) with slope m

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

  m = (-28 -2)/(15 -30) = -30/-15 = 2

Using this slope and the first point, the equation of the line is ...

  y -2 = 2(x -30)

The inequality represented by the graph is given as follows:

y > 3x - 4.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The graph crosses the y-axis at y = -4, hence the intercept b is given as follows:

b = -4.

When x increases by 1, y increases by 3, hence the slope m is given as follows:

m = 3.

Hence the equation of the line is:

y = 3x - 4.

The inequality is composed by the values to the right (greater) of the line, and has an open interval due to the dashed line, hence:

y > 3x - 4.

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The system of linear equations that can be solved from the matrices is given as follows:

Considering that the row [3, -6] is common to matrices Ax and Ay, the matrix A is given as follows:

A = [-5 4; -8 1]

Hence the multiplication of matrices representing the system is given as follows:

[-5 4; -8 1][x; y] = [3; -6]

Applying the multiplication of matrices, the system of equations is given as follows:

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Answer: (0,3)

x=0 ; y=3

Step-by-step explanation:

To solve the system of equations:

2x + 4y = 12

3x + y = 3

We can use the method of substitution or elimination. Here we will use the substitution method:

From Equation 2, we can isolate y:

y = 3 - 3x

We can substitute this expression for y into Equation 1:

2x + 4(3 - 3x) = 12

Simplifying and solving for x:

2x + 12 - 12x = 12

-10x = 0

x = 0

Now that we have found the value of x, we can substitute it back into either Equation 1 or Equation 2 to solve for y. Here we will use Equation 2:

3(0) + y = 3

y = 3

Therefore, the solution to the system of equations is (x, y) = (0, 3).

This means that the point (0, 3) is the intersection point of the two lines represented by the given equations. To verify this, we can substitute the values of x and y into both equations and see if they are true.

The correct statements regarding the scatter plot are given as follows:

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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Nathaniel drinks 3 glasses of water in one hour.

To find out how many glasses of water Nathaniel drinks in one hour, we need to calculate his drinking rate per hour.

In 2 2/5 hours, Nathaniel drinks 4/5 of a 10-ounce glass of water.

Let's convert the mixed number of hours to an improper fraction:

\(2\frac{2}{5} = \frac{(5 \times2 + 2)}{5}\)

\(=\frac{12}{5}\)

Now, we can set up a proportion to find his drinking rate per hour.

We know that \(\frac{12}{5}\) hours corresponds to \(\frac{4}{5}\) of a glass of water.

Let's assign "x" as the number of glasses he drinks in one hour.

The proportion is then

\(\frac{(\frac{12}{5} hours) }{(x glasses) } =\frac{(\frac{4}{5} glass)}{(1 hour)}\)

Cross-multiplying gives us

\((\frac{12}{5} )\times1=\frac{4}{5}\times(x)\)

Simplifying, we get

\(\frac{12}{5} =\frac{4}{5}\times x\)

Dividing both sides by \(\frac{4}{5}\), we find x:

\(x=\frac{(\frac{12}{5} )}{\frac{4}{5} }\)

\(x=\frac{12}{4}\)

\(x = 3.\)

Therefore, Nathaniel drinks 3 glasses of water in one hour.

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Answer:

2ap + aq - bq -2bp = (a - b)(2p + q)

Step-by-step explanation:

(2ap + aq) - (bq -2bp)

a(2p +q) -b(q + 2p)    [ taking a common from the first, and b from the second]

(2p + q) [a - b]           [takin (2p + q)]

(2p + q)(a - b)

The completely factored form of the expression 2ap + aq - bq - 2bp is

(a - b)(2p + q).

In order to completely factorize the given expression, we need to look for common factors and apply factorization techniques.

Given expression: 2ap + aq - bq - 2bp

Step 1: Look for common factors.

Notice that 'a' is common in the first two terms, and '-b' is common in the last two terms.

Step 2: Factor out the common terms.

We can factor 'a' from the first two terms: a(2p + q)

And factor '-b' from the last two terms: -b(q + 2p)

Step 3: Rearrange the expression.

Now we have: a(2p + q) - b(q + 2p)

Step 4: Factor by grouping.

We can see that (2p + q) is common in both terms, so we can factor it out: (2p + q)(a - b)

Step 5: Final result.

Thus, the completely factored form of the given expression is

(a - b)(2p + q).

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The value of x in this problem, considering the intersecting chords, is given as follows:

x = 10.

A chord of a circle is a straight line segment that connects two points on the circle, that is, it is a line segment whose endpoints are on the circumference of a circle.

When two chords intersect each other, then the products of the measures of the segments of the chords are equal.

Hence the value of x is obtained as follows:

12x = 15 x 8

12x = 120

x = 10.

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We can expect a student to guess 17 correct answers on a test with 68 four-choice multiple choice questions with probability 0.25.

Since the probability of guessing the correct answer to a four-choice multiple choice question is 0.25, the probability of guessing an incorrect answer is 1 - 0.25 = 0.75.

We can model the number of correct guesses as a binomial distribution with n = 68 (the number of trials) and p = 0.25 (the probability of success, i.e., guessing correctly).

The expected value of a binomial distribution is given by the formula:

E(X) = n * p

So, in this case, the expected number of correct answers that a student should guess on the test is:

E(X) = 68 * 0.25 = 17

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Answer:

Step-by-step explanation:

The closer together the points are to a line that can be drawn, the stronger the association.

1.  weak is B, the points are all over the place and a clear line can't even be drawn

2.  moderate is A, if you drew a line between the points, a line can be drawn and they points are somewhat close to the line

3. strong is C because you can draw a line through points are they are pretty closely clustered near the line.

Answer:

184233

Step-by-step explanation:

651∑n=1 88+0.6(n-1)

651∑n=1 88 + 651∑n=1 0.6(n-1)

(651)(88) + 0.6(651∑n=1 (n-1))

57288 + 0.6((651∑n=1 (n))-(651∑n=1 (-1))

57288 + 0.6((651)(652)/2+(651)(-1))

57288 + 0.6(212226-651)

57288 + 0.6(211575)

57288 + 126945

184233