You deposit $6000 in a savings account that earns 4.5% annual interest compounded mon
a. Write a functions that represents the balance (in dollars) of your savings account after t years.

b. What is the balance of the account after 6 years to the nearest cent?

Answer:

24

Step-by-step explanation:

Okay, let's solve this step-by-step:

1) We are given: a = -8, b = 2, c = 7, d = 11

2) We are asked to solve the matrix equation: [[x + y, z], [z - x, w - y]] = [[a, b], [c, d]]

3) Matching up the elements in the matrices:

x + y = a = -8 (1)

z = b = 2 (2)

z - x = c = 7 (3)

w - y = d = 11 (4)

4) Solving the equations:

From (1): x + y = -8 => x = -8 - y

Substitute in (3): z - (-8 - y) = 7 => z - (-8) = 7 + y => z = 15 + y

Substitute (2) into the above: 2 = 15 + y => y = 13

Substitute y = 13 into (1): -8 - 13 = -21 = x

Substitute x = -21 and y = 13 into (4): w - 13 = 11 => w = 11 + 13 = 24

Therefore, the values are:

x = -21

y = 13

z = 15

w = 24

So the final value of w is:

w = 24

Answer:

x = 21/ 2

Step-by-step explanation:

Solve for  x  by simplifying both sides of the equation, then isolating the variable.

~Hoped this helped~

The values of the missing angles and sides after dilation are:

m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

m∠C'B'D = 180° - m∠B'C'D' - m∠B'D'C'

m∠B'C'D = m∠BCD, m∠B'D'C' = m∠BDC  (dilation)

m∠C'B'D = 180° - 34° - 51° = 95°

Thus, by way of scale factor we can say that:

BC/B'C' = BD/B'D' = 36/18 = 2

B'D' = ¹/₂BD = ¹/₂ * 22 = 11

ΔC'P'Q ∼ ΔCPQ

Thus:

C'Q'/CQ = C'D'/CD = D'Q'/DQ

CQ = 2C'Q' = 2 * 3 = 6

Therefore, m∠C'B'D' = 95°,  CQ = 6 and  B'D' = 11.

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Answer:

number (c)

Step-by-step explanation:

I am not sure about this

Answer:

(5x + 8y)(5x - 8y)

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a^2 - b^2 = (a + b)(a - b) where a = 5x and b = 8y.

~Hoped this helped~

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

\(\displaystyle h'(0) = -5\)

Step-by-step explanation:

We are given the function:

\(\displaystyle h(x) = 3f(x) -2g(x) - 5\cos x - 3\)

And that f'(0) = 3 and g'(0) = 7.

And we want to determine the value of h'(0).

Find h'(x). We can take the derivative of both sides:

\(\displaystyle h'(x) = \frac{d}{dx}\left[ 3f(x) - 2g(x) - 5\cos x - 3\right]\)

Expand and simplify:

\(\begin{aligned}\displaystyle h'(x) & = \frac{d}{dx}\left[ 3f(x) - 2g(x) - 5\cos x - 3\right] \\ \\ & = \frac{d}{dx}[3f(x)] + \frac{d}{dx}[-2g(x)] + \frac{d}{dx}[-5\cos x] + \frac{d}{dx}[-3]\\ \\ & = 3f'(x) -2g'(x) +5\sin x\end{aligned}\)

Therefore:

\(\displaystyle h'(0) = 3f'(0) -2 g'(0) + 5 \sin (0)\)

Substitute and evaluate:

\(\displaystyle \begin{aligned} h'(0) & = 3(3) - 2(7) + 5(0) \\ \\ & = (9) - (14) + (0) \\ \\ & = -5\end{aligned}\)

In conclusion:

\(\displaystyle h'(0) = -5\)

m∠E = tan-1(3/4.6)

Explanation

Answer:

Step-by-step explanation:

we can write -9 instead of x and y=1 instead of 1

so we write solution again

-9a+1b=-31

-9a-1b=-41

-18a=-72

a=4

we should write 4 instead of a

-9(4)+1b=-31

-36+b=-31

b=5

a=4

The critical value for the 0.05 level of significance is k = 21.

To find the critical value, we can use the binomial distribution. The binomial distribution models the number of successes in n independent Bernoulli trials, each with probability p of success. In this case, the number of successes is the number of dog owners who say Woof Chow is their regular brand, and the number of trials is n = 100. The null hypothesis is that the true market share of Woof Chow is 25%, and the alternative hypothesis is that it is not 25%.

We can use the binomial cumulative distribution function (CDF) to find the critical value. The CDF gives the probability of getting k or fewer successes in n trials, given a probability of success p. The critical value is the smallest value of k such that the CDF at k is greater than or equal to 1 - alpha, where alpha is the level of significance. In this case, alpha = 0.05.

So, we want to find the smallest k such that:

P(X <= k) >= 1 - 0.05

where X is a random variable representing the number of dog owners who say Woof Chow is their regular brand. We can use a binomial calculator or a software package to calculate the binomial CDF, or we can use a table of critical values for the binomial distribution.

The critical value for the 0.05 level of significance is k = 21. This means that if the true market share of Woof Chow is 25%, then the probability of getting 23 or more dog owners who say Woof Chow is their regular brand is less than 0.05. Since the observed number of dog owners who say Woof Chow is their regular brand is 23, which is greater than 21, we can reject the null hypothesis that the true market share is 25%.

This means that based on the survey results, we cannot conclude that Woof Chow has a market share of 25%. The survey results suggest that Woof Chow may have a market share that is greater than 25%.

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The function (g+h)(n-4) is the sum of the function g(n-4) and h(n-4) will be written as (g+h)(n-4) = n² - 7n + 9.

A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.

The functions are given below.

g(n) = n² + 4n

h(n) = - 3n - 3

The function (g+h)(n) is calculated as,

(g+h)(n) = g(n) + h(n)

(g+h)(n) = n² + 4n - 3n - 3

(g+h)(n) = n² + n - 3

Put n = n - 4, then we have

(g+h)(n-4) = (n - 4)² + (n - 4) - 3

(g+h)(n-4) = n² + 16 - 8n + n - 4 - 3

(g+h)(n-4) = n² - 7n + 9

The function (g+h)(n-4) will be (g+h)(n-4) = n² - 7n + 9.

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We are 90% confident that the true population mean of yards per carry for all running backs is between 4.17 and 5.05 yards per carry, based on our sample of 25 running backs.

To construct the 90% confidence interval, we first find the sample mean and the standard error of the mean. The sample mean is the average yards per carry of the 25 running backs, which we can find by adding up all the yards per carry and dividing by 25:

x = (1.5 + 4.8 + 3.1 + 3.5 + 3.5 + 6.7 + 6.2 + 4.9 + 5.1 + 1.9 + 1.6 + 4.3 + 5.7 + 6.3 + 5.6 + 4.5 + 6.9 + 3.7 + 7.2 + 5.6 + 2.5 + 6.8 + 4.8 + 5.9 + 3.6) / 25 = 4.61

The standard error of the mean (SEM) is the standard deviation of the sampling distribution of the mean, which can be found using the formula:

SEM = σ/ √(n) = 1.27 / √(25) = 0.254

Next, we need to find the critical value for a 90% confidence interval using the normal distribution. This can be found using a standard normal distribution table or a calculator, and we get a critical value of 1.645.

Finally, we can construct the 90% confidence interval using the formula:

CI = x ± zSEM = 4.61 ± 1.6450.254 = (4.17, 5.05)

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Complete Question:

Use the standard normal distribution or the​ t-distribution to construct a 90 ​% confidence interval for the population mean. Justify your decision. If neither distribution can be​ used, explain why. Interpret the results. In a recent​ season, the population standard deviation of the yards per carry for all running backs was 1.27 . The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 1.5 4.8 3.1 3.5 3.5 6.7 6.2 4.9 5.1 1.9 1.6 4.3 5.7 6.3 5.6 4.5 6.9 3.7 7.2 5.6 2.5 6.8 4.8 5.9 3.6

Which distribution should be used to construct the confidence​interval?

A. Use a normal distribution because n less than 30 ​, the miles per gallon are normally distributed and the sigma is unknown.

B. Use a normal distribution because sigma is known and the data are normally distributed.

C. Use a​ t-distribution because n is less than 30 and sigma is known.

D. Use a​ t-distribution because n is less than 30 and sigma is unknown.

E. Cannot use the standard normal distribution or the​t-distribution because sigma is​ unknown, n less than 30 ​, and the yards are not normally distributed.

The equation of the line can be written  as, y = 9x/4 - 53/4.

Given :

9x -4y = 7 points given : (5, -2)

Writing the equation in the standard form of y=mx+b, we get:

4y = 9x -7

y = (9x/4)  - (7/4)

Thus, the slope of the given line is the coefficient of x which is equal to 9/4.

Let the equation of the line parallel to the given line be y=m1x+b1

Here m1 = 9/4

y = (9x/4) +b1

The line passes through (5,-2), hence the point satisfies the equation. Replacing the x and y coordinates with 5 and -2 respectively,

-2 = 45/4 + b1

-b1 = 45/4 +2

-b1 = 53/4

b1 = -53/4

Hence the equation of the line can be written as,

y = 9x/4 - 53/4.

The slope-intercept form of a  line is one of the most common forms used to represent the equation of a line. The slope-intercept formula can be used to find the equation of a line  given the slope of the  line and the y-intercept (the y-coordinate of the point where the line intersects the y-axis). The equation of a line is an equation that is satisfied by each point  on that line. There are several methods to find this equation of a  line given as

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The number of ways can this test batch be chosen is 2380 ways  of combination.

Give an example of permutation and combination?

Calculation of the number of ways:

Since As part of a quality-control program, 4 batteries from a box of 17 is chosen at random for testing.

Here we used the combination

So,

        = 17!/4!(17 - 4 )!

         = 17!/4! * 13!

          = 17 * 16 * 15 * 14 * 13/4! * 3!

          = 2380 ways

Therefore, The number of ways can this test batch be chosen is 2380 ways.

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Answer:

a. 473.15

b. C=K-273.15

C. 26.85

Answer:20

Step-by-step explanation:

80 times .25 or 1/4 is 20

Answer:20

Step-by-step explanation:

So, 25% is 1/4 of 100, so if you divide 80 by 4 you get 20, which is 25% of 80.

Another way to do this is on a calculator, do 80 x 25 / 100, this works with finding the percentage of anything!

The intersection point is (4,-3) which is the solution of given linear equations.

What is a linear equation, exactly?

A linear equation is an equation that describes a straight line in a two-dimensional plane or a plane in higher dimensions. In its most basic form, a linear equation takes the form: y = mx + b,  where y and x are variables, m is the slope of the line, and b is the y-intercept. The slope of a line represents how steep it is, and it is calculated as the change in y divided by the change in x between any two points on the line.

Now

For equation y=-(1/2)x-1

For  x        y is

      1         -3/2

      2        -2

      3         -5/2

      4          -3

and for equation y=(1/4)x-4

For   x         y  is

       1         -15/4

      2        -7/4

      3         -13/4

      4          -3

Hence,

           After making graph the intersection point is (4,-3) which is the solution of given equations.

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Right question:-

Create a graph to solve these linear equations y=-1/2x-1 and y=1/4x-4.

Answer:

x=8

7x=56

Step-by-step explanation:

Answer:

75 EUR

Step-by-step explanation:

1.00 (EUR 60) + .25 (EUR 15)

60 EUR * 1.25 = 75 EUR

Answer:

45

Step-by-step explanation:

\(60 \times 25 \div 100 = 15 \\ 60 - 15 = 45\)

The values of the missing sides are;

a.  x = 35. 6 degrees

b. x = 15

c. x = 22. 7 ft

d. x = 31. 7 degrees

To determine the values, we have;

a. Using the tangent identity;

tan x = 5/7

Divide the values

tan x = 0. 7143

x = 35. 6 degrees

b. Using the Pythagorean theorem

x² = 9² + 12²

find the square

x² = 225

x = 15

c. Using the sine identity

sin 29= 11/x

cross multiply the values

x = 11/0. 4848

x = 22. 7 ft

d. sin x = 3.1/5.9

sin x = 0. 5254

x = 31. 7 degrees

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If teacher is distributing sheets in a class, then the equation which is used to find number of students in class is (d) 2x+8 = 3x - 11​.

A "Linear-Equation" is a mathematical equation that represents a straight line in a coordinate plane. It is of form : y = mx + b

where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept (the point at which the line crosses the y-axis).

Let number of students in class be denotes as "x",

If each student get 2 sheets, then 8 sheets are remaining, it is mathematically represented as : 2x + 8 ,

If each student get 3 sheets each, then there would be 11 sheets less, and this is represented as : 3x - 11,

So, the equation which is used to find number of students in class is 2x+8=3x-11,

Therefore, the correct option is (d).

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The given question is incomplete, the complete question is

If a teacher were to distribute sheets of paper so that each student got two sheets, there would be 8 sheets remaining. However, if three sheets were given to each student, the teacher would be 11 sheets short. Which equation could be used to find how many students are in the class?

(a) 2(x - 8) = 3(x + 11)

(b) 2(x + 8) = 3(x - 11)

(c) 2x-8 = 3x + 11

(d) 2x+8 = 3x - 11​

Answer:

K= 15

Step-by-step explanation:

K/-3 +3 = -2

Simplify by subtracting 3 on each side:

K/-3 = -2-3

K/-3 = -5

Simplify further by multiplying each side by -3:

K= -5*-3

K = 15

In a 3 x 3 between subjects factorial design, there are four sources of variance.

A 3 x 3 between subjects factorial design involves two independent variables, each with three levels, and participants are randomly assigned to different combinations of these levels. In this design, the four sources of variance are as follows:

Main Effect of Variable A: This source of variance represents the overall effect of the levels of the first independent variable. It assesses whether there are significant differences between the means of the three groups created by varying levels of Variable A.

Main Effect of Variable B: This source of variance represents the overall effect of the levels of the second independent variable. It examines whether there are significant differences between the means of the three groups created by varying levels of Variable B.

Interaction Effect: This source of variance assesses whether there is an interaction between the two independent variables. It examines whether the effect of one independent variable on the dependent variable differs across the levels of the other independent variable.

It evaluates whether the combined effect of the independent variables is greater (or lesser) than the sum of their individual effects.

Error Variance: This source of variance represents the variability in the dependent variable that cannot be accounted for by the independent variables. It includes random error, individual differences, and any other uncontrolled factors that may influence the outcome.

Therefore, in a 3 x 3 between subjects factorial design, there are four sources of variance: the main effects of Variable A and Variable B, the interaction effect between the two variables, and the error variance.

Each of these sources contributes to understanding the overall pattern of results and the relationships between the variables in the design.

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Answer:

The angles are supplementary.

x = 31

Step-by-step explanation:

The way the two angles lay together and make a straight line shows that they are supplementary. Supplementary means that they add up to 180°

Use this idea to write an equation.

2x + 3x + 25 = 180

combine like terms

5x + 25 = 180

subtract 25

5x = 155

divide by 5

x = 31

Answer:

x = 31

Step-by-step explanation:

(3x + 25) and 2x are a linear pair and are supplementary, that is

3x + 25 + 2x = 180

5x + 25 = 180 ( subtract 25 from both sides )

5x = 155 ( divide both sides by 5 )

x = 31

Answer:

Question 1 is C

Step-by-step explanation:

Answer:

a: top right 1 top left 2 bottom left 3 bottom right 4

c: axis going horizontal is the x axis and the axis going vertical is the y axis

d: origin is the very middle and it is (0,0)

Step-by-step explanation:

Answer:

Answer = B.19.25

Step-by-step explanation:

(4x-6)=71

4x=71+6

4x=77

x=77÷4

x=19.25

Answer:

if Maria sells 6 she will make 12 add base wage she earned 15. if eve sells 1 she will also make a profit of 15