An employee receives a 3% raise once per year. If the employee's initial salary is $65,800.00, what will the employee's salary be after 7 years?

Answer:

p = 17.125

Step-by-step explanation:

Answer:

Given

f

(

x

)

=

4

⋅

7

x

For

x

=

−

1

we have

f

(

−

1

)

=

4

⋅

7

−

1

=

4

7

using

a

−

n

=

1

a

n

For x=2, we have

f

(

2

)

=

4

⋅

7

2

=

196

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

\(f(x) = 4. {7}^{x} \\ \\ plug \: x = - 1 \\ \\ f( - 1) = 4. {7}^{ - 1} \\ \\ f( - 1) = \frac{4}{7} \\ \\plug \: x = 2 \\ \\ f( 2) = 4. {7}^{ 2} \\ \\ f( 2) = 4 \times 49 \\ \\f( 2) = 196 \\ \\\)

Answer:

\(\begin{equation*}% \mbox{\large\( % - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)

Step-by-step explanation:

sin²(x) = 1 - cos²(x)

So the expression sin²(x) + 7cosx +7 becomes

1 - cos²(x) + 7cos(x) + 7

Group like terms

\(\begin{equation*}% \mbox{\large\( %=-\cos ^2\left(x\right)+7\cos \left(x\right)+1+7 %\)} %\end{equation*}\)

\(\begin{equation*}% \mbox{\large\( %=-\cos ^2\left(x\right)+7\cos \left(x\right)+8 %\)} %\end{equation*}\)\(\begin{equation*}% \mbox{\large\( %=-\cos ^2\left(x\right)+7\cos \left(x\right)+1+7 %\)} %\end{equation*}\)\(\begin{equation*}% \mbox{\large\( %=7\cos \left(x\right)-\cos ^2\left(x\right)+8\)} %\end{equation}\)

\(\begin{equation*}% \mbox{\large\( %=-\left(\cos ^2\left(x\right)-7\cos \left(x\right)-8\right)\)} %\end{equation}\)

Let's deal with the expression in parenthesis
\(\begin{equation}% \mbox{\large\( %=\cos ^2\left(x\right)-7\cos \left(x\right)-8\)} %\end{equation}\)\(\begin{equation*}% \mbox{\large\( %=\cos ^2\left(x\right)-7\cos \left(x\right)-8)} %\end{equation}\)

\(\begin{equation*}% \mbox{\large\( %\cos^2(x) - 7\cos(x)-8\)} %\end{equation*}\\\\\)

This is of the form \(\begin{equation*}% \mbox{\large\( %ax^2 + bx + c\)} %\end{equation*}\)

with a = 1, b = -7 and c = -8

To factor this find two values u and v such that

\(\begin{equation*}% \mbox{\large\( %u\cdot v = -8, v + v = -7\)} %\end{equation*}\)

If we choose u = 1 and v = -8 we can satisfy the above relationship since
u · v = 1 (-8) = -8 and u + v = 1 +(-8) = -7

\(\displaysize {\textrm{Group\:into\:}\left(ax^2+ux\right)+\left(vx+c\right)}\)
\(\begin{equation*}% \mbox{\large\( %\left(\cos ^2\left(x\right)+\cos \left(x\right)\right)+\left(-8\cos \left(x\right)-8\right)\)} %\end{equation*}\)

\(\textrm{Factor\:out}\:\cos \left(x\right)\:\mathrm{from}\:\cos ^2\left(x\right)+\cos \left(x\right)\)

\(\begin{equation*}% \mbox{\large\( %=\cos \left(x\right)\left(\cos \left(x\right)+1\right)\)} %\end{equation*}\)

\(\textrm{Factor\:out}\:-8\:\mathrm{from}\:-8\cos \left(x\right)-8:\)

\(=-8\left(\cos \left(x\right)+1\right)\)

So
\(\begin{equation*}% \mbox{\large\( %\left(\cos ^2\left(x\right)+\cos \left(x\right)\right)+\left(-8\cos \left(x\right)-8\right)\)} %\end{equation*}\)

=  \(\begin{equation*}% \mbox{\large\( %\cos \left(x\right)\left(\cos \left(x\right)+1\right)-8\left(\cos \left(x\right)+1\right)\)} %\end{equation*}\)

\(\textrm{Factor\:out\:common\:term\:}\cos \left(x\right)+1\)
\(\begin{equation*}% \mbox{\large\( %=\left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)

Since this was the term in the parenthesis with a leading negative sign, add the negative sign to get

\(\begin{equation*}% \mbox{\large\( %1-\cos ^2\left(x\right)+7\cos \left(x\right)+7\)} %\end{equation*}\) \(\begin{equation*}% \mbox{\large\( %= - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)\(\begin{equation*}% \mbox{\large\( %= - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\\\)

Answer: \(\begin{equation*}% \mbox{\large\( % - \left(\cos \left(x\right)+1\right)\left(\cos \left(x\right)-8\right)\)} %\end{equation*}\)

Answer: Skewed left, no outlier

Step-by-step explanation: You use the IQR and quartile 1&3 to find the number that defines an outlier. And for this one there are none

Answer:

The correct answer is a.

Step-by-step explanation:

The sequence is: 2 3 E 4 5 I 6 8 We can notice that there are numbers and letters alternating in the sequence. The numbers are increasing, and the letters seem to be vowels in alphabetical order. So, the next value should be a letter (vowel) after I, which is O. The correct answer is a.

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

Answer:

The correct option is d

Step-by-step explanation:

From the question we are told that

    The sample size is  n = 64

    The mean is  \(\= x = 320\)

    The standard deviation is \(\sigma = 120\)

Generally the standard error of the mean is mathematically represented as  

       \(\sigma_x = \frac{\sigma}{ \sqrt{n} }\)

=>    \(\sigma_x = \frac{120}{ \sqrt{64} }\)

=>    \(\sigma_x =15\)

Answer:

But the 2lbs.

Step-by-step explanation:

Divide $9.19 by 2 and you get 4.595 which would be the cheapest option out of the 3 because the 1lb is $7.05 and the 3lb is $5.13.

You're welcome.

Answer:

$0.40

I had the same question and it was $0.40

Answer:

$0.55

Got it on the test, hope this helps :)

Answer: -56/55

Step-by-step explanation:

2 4/5x = -11/4

14/5x = -11/4

Cross multiply:

-55x = 14 * 4 = 56

x = -56/55

Answer:

A and E

Step-by-step explanation:

x²+3x-28=0

x²+7x-4x-28=0

x(x+7)-4(x+7)=0

(x-4)(x+7)=0

x=4, x= -7

Please give brainliest if it helps

Solving a system of equations we can see that each pound of trail mix costs $3.50, and each pound of jelly beans costs $1.50

Let's define the variables:

Then we can write a system of equations so we will get:

5x + 3y = 22

2x + 12y = 25

To solve this, we can subtract 4 times the first equation fom the second one:

2x + 12y - 4(5x + 3y) = 25 - 4*22

2x + 12y - 20x - 12y = -63

-18x = -63

x = -63/-18

x = 3.5

That is the cost of each pound of trail mix, and replacing that in one of the equations:

2*3.5 + 12y = 25

y = (25 - 2*3.5)/12

y = 1.5

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Given:

Discount offered = $57

Original price of paint = $100

Let x represent the percentage discount.

Thus, we have:

x% of $100 = $57

Solving further, we have:

Therefore, the percentage discount is 57%

ANSWER:

57%

The rental car is getting approximately 37.56 miles per gallon.

To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:

1 km/l ≈ 2.82475 mpg

Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:

13.3 km/l x 2.82475 mpg ≈ 37.56 mpg

So, your rental car is getting approximately 37.56 miles per gallon.

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The True- False of given statements of Solutions of Equations are justified.

1.13 False. The solution set to a system of three equations in three unknowns can be a point, a line, or a plane. It depends on the system of equations and how they intersect in three-dimensional space.

1.14 False. A system of linear equations can have infinitely many solutions, one solution, or no solutions. It depends on the coefficients of the equations and the rank of the coefficient matrix.

1.15 False. The solution set to a consistent rank 2 linear system in four unknowns would be a plane in four-dimensional space, not a line.

1.16 False. A system of four equations in four unknowns may not have a solution, or it may have infinitely many solutions or one solution. It depends on the coefficients of the equations and the rank of the coefficient matrix.

1.17 False. A system of four equations in four unknowns can have infinitely many solutions or one solution, but it cannot have at most one solution.

1.18 True. The rank of a system is always less than or equal to the number of equations in the system.

1.19 (a) False. If (i) has exactly one solution, it does not necessarily mean that (ii) will have exactly one solution. It depends on the coefficients of the equations in (ii).

(b) False. If the solution set of (i) is a line, it does not necessarily mean that the same is true for (ii). It depends on the coefficients of the equations in (ii).

(c) True. If (i) has no solutions, then the same is true for (ii), since (ii) is equivalent to (i).

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Answer:

cos θ = -5/13

Step-by-step explanation:

sin θ = -12/13

Use Pythagorean identity.

sin²θ + cos²θ = 1

(-12/13)² + cos²θ = 1

144/169 + cos²θ = 1

cos²θ = 25/169

cos θ = ±5/13

θ is in the 3rd quadrant, so cos θ < 0.

cos θ = -5/13

The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

In the context of this problem, the variables x and y are given as follows:

The equation for the constant is given as follows:

k = y/x.

Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.

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The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.

The standard equation of a line is ax + by + c = 0.

Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.

In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.

It is given that,

The equation of the given line is 3x + 4y = 24

Rewriting the given equation into the general form,

3x + 4y - 24 =0

On comparing with ax + by + c = 0,

a = 3, b = 4 and c = -24

So,

The x-intercept of the line (-c/a) = -(-24)/3 = 8 and

The y-intercept of the line (-c/b) = -(-24)/4 = 6

Therefore, the required x and y intercepts are 8 and 6 respectively.

(The graph showing the intercepts of the given line is shown below)

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The utility can be used to quantify and compare preferences in decision-making scenarios where performance is not measured by monetary value.

The utility can be used as a measure of preference or satisfaction in decision-making situations where performance is not directly measured by monetary value. Utility refers to the subjective value or desirability that an individual assigns to different outcomes or options.

In such cases, utility can be quantified using a utility function, which maps the outcomes or attributes of the decision problem to a numerical representation of the individual's preferences. This function allows for the comparison and evaluation of different options based on their utility values.

For example, consider a decision involving healthcare treatments. The performance of different treatments may not be easily measured in monetary terms, but individuals may have preferences based on factors such as effectiveness, side effects, or quality of life impact.

Utility can be used to capture these preferences and make a decision that maximizes the overall satisfaction or well-being of the individual.

To use utility in decision-making, it is necessary to understand and quantify individual preferences through techniques like surveys, interviews, or experimental methods. By assigning utility values to different outcomes or attributes, decision-makers can then compare options and select the one that maximizes utility.

However, it's important to note that utility is subjective and varies among individuals. Different people may have different utility functions and weigh attributes differently. Therefore, utility-based decision-making requires taking into account the preferences of the specific individual or group involved.

In summary, utility can be employed in decision-making scenarios where performance is not directly measured in monetary terms. It quantifies subjective preferences and allows for the comparison and selection of options based on the utility values assigned to different outcomes or attributes.

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The given information does not provide any clear indication for determining the position that should be taken on 3/01 and 3/02. Without additional information, it is not possible to make a decision. The table only displays the closing prices of the July GBP Futures Contract on different days, and it is unclear what trading strategy or what scenario is being considered. Additional information about the goals and objectives, the market conditions, and other relevant factors would be necessary to make a decision about trading positions.

Answer

0.00336

Step-by-step explanation:

Given :

P(Brown), P(Br) = 0.4

P(Blue) = P(b= 0.35

P(green,) = P(g) = 0.12

P(gray), P(Gr) = 0.07

If 3 individuals are selected, the probability that one has brown eye, 1 has Grey and one has green.

Since the probabilities are independent :

P(Br) * P(Gr) * P( g)

0.3 * 0.07 * 0.12

= 0.00336

Answer:300

Step-by-step explanation:25 cents each quarter so the equation would be 12 times 25.

Answer: 300 cents

Step-by-step explanation: 12 quarters saved, 1 quarter = 25 cents, 12 x 25 = 300

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

c) 144

Step-by-step explanation:

Since A is between Y and Z,

\(YZ = YA + AZ\)

\(116 = 22 + 16x\\16x = 116 - 22\\16x = 144\\x = 9\)

however, the question asks for \(the length of AZ\), not the value of x.

Thus,

\(AZ = 16x\)

\(AZ = 16\\\) × \(9\)

\(AZ = 144\)

\(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\) is the possible root

What is a root ?

Mathematicians refer to a number as having a root if it can be multiplied by itself to give the original number. The square root of 49, for instance, is 7, as 77=49. 7 is referred to as the square root of 49 in this instance because it takes 49 to multiply 7 by itself twice. Considering that 333=27, the cube root of 27 is 3.

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfill the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.

3x^4 -10x^3 -9x^2 + 40x - 12

=\(\left(3x-1\right)\frac{3x^4-10x^3-9x^2+40x-12}{3x-1}\)

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

= \(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\)

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Answer:

25/9

Step-by-step explanation:

3 1/3 ÷ 1 1/5

3 1/3 = 10/3

1 1/5 = 6/5

10/3 ÷ 6/5 = 10/3 x 5/6 = 50/18 = 25/9

So, the answer is 25/9

The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)

An expression is defined as a mathematical statement consisting of variables , constants and mathematical operators.

The expression given is

28w⁴x²y⁷+12w⁹x⁸

Factors of the given expression will be the common terms in both the terms

w⁴x² is common in the variable term

The HCF of 28 and 12 is 4

4w⁴x² (7y⁷ + 3w⁵x⁶)

The expression after factorisation is 4w⁴x² (7y⁷ + 3w⁵x⁶)

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Answer:

21

Step-by-step explanation:

you do 7x3

Answer:

5 out of 70

Step-by-step explanation:

all you have to do is figure all of the multiple of 12 in 70 which is 12, 24, 36, 48, and 60 so that's 5 numbers out of the 70

A) The variable is n, which represents the number of the figure in the pattern.

B) Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                      1

2                      3

3                      6

4                     10

5                     15

6                     21

7                    28

8                    36

C) The equation to represent the nth term of the sequence is n(n+1)/2.

D) If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12.

E) It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

Here is a more detailed explanation of how to answer each question:

A) Identify and label the variable

The variable is n, which represents the number of the figure in the pattern. For example, the first figure is figure 1, the second figure is figure 2, and so on.

B) Make a table for up to 8-figure patterns

Here is a table for up to 8-figure patterns:

Figure Number of Cheerios

1                        1

2                        3

3                        6

4                        10

5                        15

6                        21

7                        28

8                        36

C) Write an equation to represent the nth term of the sequence

The equation to represent the nth term of the sequence is n(n+1)/2. This equation can be derived by looking at the table of values. For example, the number of Cheerios in the first figure is 1, which is equal to 1(1+1)/2. The number of Cheerios in the second figure is 3, which is equal to 2(2+1)/2. And so on.

D) If the pattern continues, what figure number will have 20 whole Cheerios in it?

If the pattern continues, the figure number that will have 20 whole Cheerios in it is 12. This can be found by solving the equation n(n+1)/2 = 20. The solution is n = 12.

E) Is it reasonable to think this pattern would continue forever? If not, explain.

It is not reasonable to think this pattern would continue forever. The number of Cheerios in each figure is increasing by 2 each time. This means that the number of Cheerios in the figure will eventually exceed the number of Cheerios in a box.

F) Based on the information provided, what is the largest figure number we can have using a full box of Cheerios?

Based on the information provided, the largest figure number we can have using a full box of Cheerios is 107. This is because there are 108 Cheerios in a box, and the number of Cheerios in each figure is increasing by 2 each time.

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