I need to know the answers to number 7, 8, 9, 10

Rewriting the equations in matrix form, we get:

[1 78/1399 | 1]

[50 1 | 1149/1399]

What is square matrix?

A square matrix is a matrix that has the same number of rows and columns. That is, a matrix A is square if A has dimensions n x n, where n is a positive integer.

To create an augmented matrix, we need to represent the system of equations in matrix form. Let x be the number of months it will take Chris to pay off the total purchase price of the mattress using monthly payments and savings. Then the system of equations is:

1399/18 + 78x = 1399

50x + 250 = 1399

The first equation represents the fact that the total price of the mattress must be paid off in 18 months using monthly payments, and the second equation represents the fact that Chris sets aside $50 each month in savings to put towards the purchase.

Rewriting the equations in matrix form, we get:

[1 78/1399 | 1]

[50 1 | 1149/1399]

This is the augmented matrix for the system of equations, where the leftmost columns represent the coefficients of the variables (1 for x in the first equation, 50 for x in the second equation, and 78/1399 for the monthly payment in the first equation), and the rightmost column represents the constants on the right-hand side of each equation.

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      Column 1  Column 2  Column 3

Row 1--   50          -1               -250

Row 2--   78           1             1,399

I got it right on my test.

Your Welcome:)

Answer:

13

Step-by-step explanation:

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

The principle of mathematical induction is a proof technique used to prove a statement that holds for all positive integers.

It consists of two steps:

Base case: Show that the statement is true for the smallest possible value of the positive integer, usually n = 1.

Inductive step: Assume that the statement is true for an arbitrary positive integer k, and then use this assumption to show that the statement must also be true for k + 1.

Here we have

The following recursive function computes the number of comparisons used in the worst case of merge sort.

M (1) = 0

M (2k) = 2M (2k−1) + 2k for all k > 0

To prove that M(2k) = k × 2k for all k ∈ N using mathematical induction, we will first show that the base case holds:

Base case: When k = 1,

we have M(2) = 2M(1) + 2¹ = 2(0) + 2 = 2, and k × 2k = 1 × 2¹ = 2.

Therefore, the base case holds.

Inductive hypothesis:

Assume that M(2k) = k × 2k holds for some positive integer k.

Inductive step:

We need to show that M(2k+1) = (k+1) × 2k+1.

Using the recursive definition of M, we have:

M(2k+1) = 2M(2k) + 2(2k+1)

= 2(k × 2k) + 2(2k+1) (using the inductive hypothesis)

= 2k(2k+2) + 2(2k+1)

= 2k(2(k+1)) + 2(2k+1)

= 2(k+1) × 2k + 2(2k+1)

= (k+1) × 2(2k+1)

Therefore, the inductive step holds.

Hence,

By the principle of mathematical induction, we have shown that

M(2k) = k  2k for all k ∈ N.

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Answer:

0.077

Step-by-step explanation:

Mathematically, the quantity of wire Liam needs for the top of the 8 sculptures he is making is 5¹/₃ yards.

The quantity of wire Liam needs for the top of the sculptures that he makes is determined using mathematical operations.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The total quantity of wire used = 10²/₃ yards.

The quantity of wire needed for each base = ²/₃ yards

The quantity of wire needed for each top = ²/₃ yards

The number of sculptures Liam is making = 8

²/₃ yards + ²/₃ yards = 1¹/₃ yards

8 x 1¹/₃ yards = 10²/₃ yards

8 x ²/₃ yards = 5¹/₃ yards

5¹/₃ yards x 2 = 10²/₃ yards

Therefore, the quantity of wire needed for the top will be 5¹/₃ yards.

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Answer: x = -1 and x = 9

Step-by-step explanation:

Lets solve this equation step by step

1. Simplify both sides of the equation

x^2 - 8x + 16 = 25

2. Subtract 25 from both sides

x^2 - 8x + 16 - 25 = 25 - 25

3. Factor the left side of the equation

(x + 1) (x - 9) = 0

4. Set the factors equal to zero

x + 1 = 0 or x - 9 = 0

Thus your answers are x = -1 and x = 9

You can check by inputting the values into the original equation

(-1 - 4)^2 = 25 and (9 - 4)^2 = 25

Answer: He could be 47 or 46

Step-by-step explanation: I need the exact date of the time he was born (just the month and the day) to tell you how old he really is, but with the information given, he could be 47 or 46.

He would be 47 years                       [tex]1945\\-\\1898\\=\\47\\[/tex]

The length of side AB is given as follows:

[tex]AB = \frac{6}{\sqrt{3}}[/tex]

The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:

For the angle of 30º, we have that:

Hence the length of side AB is obtained as follows:

tan(30º) = AB/6

AB = 6 x tan(30º)

[tex]AB = 6 \times \frac{1}{\sqrt{3}}[/tex]

[tex]AB = \frac{6}{\sqrt{3}}[/tex]

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The value of the side AB is calculated as: AB = 6/√3

There are different trigonometric ratios used in right angle triangles which are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Looking at the given triangle, the value of AB can be gotten via the trigonometric ratio tan x. Thus:

AB = 6 * tan 30

AB = 6 * 1/√3

AB = 6/√3

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Answer:

The answer is x<8

Step-by-step explanation:

x/2<4

x<8

We can show by the uniqueness theorem that the linear transformation, Y = aX + b, is also a normal random variable because the resultant probaility density fnction of Y equals: f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)).

To show that the linear transformation, Y = aX + b is a normal random variable, we need to demonstrate that it satisfies the properties of a normal distribution. This means that it should have a bell-shaped probability density function, mean, and variance.

We can prove that it meets the mean condition this way:

E(Y) = E(aX + b) = aE(X) + b = aμX + b

Next, we can prove that it meets the variance condition thus:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σX^2

Lastly, the probability density function is given as f(y) = (1/√(2πa^2σX^2)) * exp(-(y-aμX-b)^2/(2a^2σX^2)). This proves that the conditions for a normal random variable is met.

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The side length of the the rectangular garden are 20 feet by 5 feet.

Let

s = side length of the square garden

l = length of the rectangular garden

w = width of the rectangular garden

From the problem statement,

area of the square garden = area of the rectangular garden

Since the area of a square is just the side length squared, we can write:

s² = l * w

We also know that the length of the rectangular garden is 10 feet longer than the side of the square garden, and that the width of the rectangular garden is 5 feet shorter than the side of the square garden. We can express them as:

l = s + 10

w = s - 5

Now we can substitute these expressions for l and w into our first equation:

s² = (s + 10) * (s - 5)

Expanding the right-hand side, we get:

s² = s² + 5s - 50

0 = 5s - 50

5s = 50

Dividing both sides by 5, we get:

s = 10

Since the side length of the square garden is 10 feet.

We can use this to find the dimensions of the rectangular garden:

l = s + 10 = 10 + 10 = 20

w = s - 5 = 10 - 5 = 5

So the dimensions of the rectangular garden are 20 feet by 5 feet.

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After solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers.

The inverse additives of the equivalent positive numbers are the negative numbers.

The boldface Z is a common mathematical symbol for the set of integers.

Numbers that are negative: -1, -2, -3, -4, -5, and so on indefinitely.

Non-negative integers include 0 and all whole numbers that are positive, such as 6, 7, 8, 9, 10, and so forth.

Positive integers include 1, 2, 3, 4, 5, and on indefinitely.

So, we have the expression:

= 2 - 0.4 ÷ 0.2

Now, evaluate using the BODMAS rule as follows:

= 2 - 0.4 ÷ 0.2

= 2 - 2

= 0

Therefore, after solving the given expression 2 - 0.4 ÷ 0.2 the resultant answer is an integer which is 0.

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Answer:

Domain: [tex]x\geq 0[/tex]

Range: [tex]y\leq 0[/tex]

Step-by-step explanation:

Recall that the domain of a function is the values that x can be, while the range of a function is the values that y can be.

Let's take a look at one part of the function: [tex]\sqrt{x}[/tex].

The square root of any positive number does exist. It may not be rational, but it exists. The square root of zero also exists -- it's zero.

However, the square root of a negative number will never exist - it's imaginary. So, x cannot be negative as long as it is under the radical.

The domain is: [tex]x\geq 0[/tex]

Now, to find the range, let's look at the coefficient: -3.

A negative number times a negative number is positive. A negative number times a positive number is negative.

However, x can never be negative, so no matter what real value you plug in for x, you will always be multiplying -3 by a positive number (or zero).

Since zero times any number is zero, and a positive number times a negative number is a negative number, y will always be either equal to zero or negative.

So, the range is: [tex]y\leq 0[/tex]

Answer: To calculate how many times Francisco will earn interest after keeping the money in the account for 5 years, we need to determine the number of quarters in 5 years.

Since there are 4 quarters in a year, the total number of quarters in 5 years is:

4 quarters/year x 5 years = 20 quarters

Therefore, Francisco will earn interest 20 times over the 5-year period.

To calculate the value of his account in 5 years, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time the money is invested (in years)

In this case, P = $5,000, r = 0.03, n = 4 (since the interest is compounded quarterly), and t = 5. Substituting these values into the formula, we get:

A = $5,000(1 + 0.03/4)^(4x5)

A = $5,000(1.0075)^20

A = $5,866.02

Therefore, the value of Francisco's account in 5 years, if he does not make any additional deposits or withdrawals, will be $5,866.02.

Step-by-step explanation:

the equation rearranged to solve for B is: B = 1/2 * (-S + Ph)

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It typically contains one or more variables and can be solved to find the value(s) of the variable(s) that make the equation true.

In the given question,

To solve for the area of the base (B), we need to isolate it on one side of the equation.

First, we can simplify the equation by distributing the 2 to the terms inside the parentheses:

S = 2B + Ph

S = 2B + P * h

Next, we can move the term containing B to the other side of the equation by subtracting 2B from both sides:

S - 2B = P * h

Then, we can isolate B by dividing both sides of the equation by 2:

(S - 2B) / 2 = P * h / 2

Simplifying the right side of the equation:

(S - 2B) / 2 = Ph/2

Finally, we can isolate B by subtracting S/2 and dividing by -1:

(S/2 - Ph/2) = B

Therefore, the equation rearranged to solve for B is:

B = 1/2 * (-S + Ph)

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Answer:

Step-by-step explanation:

2.1 so a

A.y-intercept: 4

axis of symmetry: x=2

x-coordinate of the vertex: 2

B.x f(x)

  0   4

  1   1

  2   0

  3     1

  4   4

C. 5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

An intercept refers to the point(s) at which a curve or line intersects an axis. For example, the x-intercept is where the line crosses the x-axis, and the y-intercept is where it crosses the y-axis.

A vertex is a point where two or more lines or curves meet. In the context of a parabolic curve, the vertex is the point at which the curve changes direction.

According to the given information:

A. The y-intercept occurs when x=0. Therefore, f(0) = 0² - 4(0) + 4 = 4. So the y-intercept is (0, 4).

The axis of symmetry can be found using the formula x = -b/(2a), where a and b are the coefficients of x² and x, respectively. In this case, a = 1 and b = -4, so x = -(-4)/(2*1) = 2. Therefore, the equation of the axis of symmetry is x = 2.

To find the vertex, we use the fact that the vertex occurs at the axis of symmetry. So when x=2, f(x) = 2² - 4(2) + 4 = -4. Therefore, the vertex is at (2, -4).

B. We can use the vertex to make a table of values:

x f(x)

0 4

1 1

2 0

3 1

4 4

C. We can use the table of values to plot the points and sketch the graph of the function. The graph of the function is a parabola that opens upward, since the coefficient of x² is positive.

  5 |           .  

      |        .    

      |     .        

      |  .            

      |.                

  0 |_____________

      0  1  2  3  4

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The number of price increases that would be needed to cause zero profit as shown on the graph, is C) 87.

The point on the graph that would show the number of price increases necessary for the company to record zero profit would be the point on the x - axis where the line crosses the x-axis. This is because this would show the 0 profit mark.

This point on the graph is shown to be 87. This means that if the company increases the price of the wood chairs they sell, 87 times, they will experience zero profit.

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Increased land prices and acreage on the Great Plains could be seen as negative owing to  potential ecological impact, as a disruption for Traditional communities and unsustainable resource use.

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So, the answer as a fraction is 16/36.

A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. It is written as one number (the numerator) placed above another number (the denominator) and separated by a horizontal line. For example, 3/4 is a fraction where 3 is the numerator and 4 is the denominator. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up the whole. Fractions can also be written in decimal or percentage form. Fractions are commonly used in everyday life, such as in cooking recipes, measurements, and financial calculations.

There are 6 purple marbles and 10 blue marbles, so there are 6 + 10 = 16 marbles that are either blue or purple.

The total number of marbles in the bag is 9 + 6 + 4 + 10 + 7 = 36.

Therefore, the probability of selecting a blue or purple marble is 16/36.

So, the answer as a fraction is 16/36

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The four points on the graph of f(x) = √x-4  including the left most point are: (4,0), (5,1), (8,2), and (20,4).

To find points on the graph of f(x) = √x-4, we can choose values of x and find the corresponding values of y.

The leftmost point on the graph is when x is the smallest possible value, which is x = 4 (since we can't take the square root of a negative number). At x = 4, f(x) = √0 = 0, so the leftmost point is (4,0).

To find three additional points, we can choose values of x that are greater than 4 and find the corresponding values of y:

When x = 5: f(5) = √1 = 1, so the point is (5,1)

When x = 8: f(8) = √4 = 2, so the point is (8,2)

When x = 20: f(20) = √16 = 4, so the point is approximately (20.4)

So, four points on the graph of f(x) = √x-4 are: (4,0), (5,1), (8,2), and (20,4).

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[tex]~\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\\\\ x^{-2}\implies \cfrac{1}{x^2}\hspace{5em} {\Large \begin{array}{llll} \ne \end{array}}\hspace{5em}-x^2[/tex]

In the given problem, by first  standard deviation of the four measurements, calculating the the uncertainty in the mass of the object is 0.004582g.

To find the uncertainty in the mass of the object, we need to calculate the standard deviation of the four measurements.

First, we calculate the mean of the four measurements:

mean = (2.744g + 2.756g + 2.751g + 2.758g) / 4 = 2.75225g

Next, we calculate the variance of the measurements:

variance = [(2.744g - 2.75225g)^2 + (2.756g - 2.75225g)^2 + (2.751g - 2.75225g)^2 + (2.758g - 2.75225g)^2] / 3

       = 0.000021g^2

The variance is the average of the squared deviations from the mean, divided by the number of measurements minus 1. Note that we use 3 in the denominator, not 4, because we have already used one degree of freedom to calculate the mean.

Finally, we take the square root of the variance to obtain the standard deviation:

standard deviation = sqrt(variance) = 0.004582g

Therefore, the uncertainty in the mass of the object is 0.004582g. We can report the mass as: mass = 2.75225g ± 0.004582g

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Answer:

To approximate the location of the square root of 14 on a number line, we can first find the two integers that √14 is between. We know that:

3^2 = 9 < 14 < 16 = 4^2

So √14 is between 3 and 4. We can divide the distance between 3 and 4 into equal parts and estimate the location of √14 based on where it falls in that interval.

Dividing the interval into 10 equal parts, we get:

3.0 - 3.1 - 3.2 - 3.3 - 3.4 - 3.5 - 3.6 - 3.7 - 3.8 - 3.9 - 4.0

Since √14 is closer to 3 than to 4, we can estimate its location as being closer to 3.4 than to 3.5. Therefore, a good approximation for the location of √14 on the number line is 3.7.

Answer:

i think its 11.2

Step-by-step explanation: