Peggy invests $8, 400 at 6 1/2% interest for 10 years compounded semiannually. Find the amount of money in the account at the end of the term.

The solution set of the given homogeneous system in parametric vector form is x₁ = 5 = x₂ , x₃ = 1.

What is parametric vector form?

The identity matrix's two columns, which stand in for the two leading coefficients in the row echelon form of the original matrix, are added to create the parametric vector.

We are given set of equations as:

x₁ + 2x₂ - 15x₃ = 0

2x₁ + x₂ - 15x₃ = 0

-x₁ + x₂ = 0

Now, representing this in the matrix form, we get

[tex]\left[\begin{array}{cccc}1&2&-15&0\\2&1&-15&0\\-1&1&0&0\end{array}\right][/tex]

Now, we will reduce the matrix i.e. in row echelon form using elementary operations

From this, we get

[tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&-5&0\\0&0&0&0\end{array}\right][/tex]

So, we get that x₃ is the free variable.

Now, representing this in the parametric vector form, we get

x₁ - 5x₃ = 0

x₂ - 5x₃ = 0

x₃ = x₃

From this, we get

x₁ = 5x₃

x₂ = 5x₃

x₃ = x₃

So, we now get

x = [tex]\left[\begin{array}{c}x_{1} &x_{2} &x_{3} \end{array}\right][/tex]

This is equal to

x = [tex]\left[\begin{array}{c}5x_{3} &5x_{3} &x_{3} \end{array}\right][/tex]

Thus,

x = [tex]\left[\begin{array}{c}5 &5 &1 \end{array}\right][/tex]

Hence, the solution is x₁ = 5 = x₂ , x₃ = 1.

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Factors are the numbers that divide the supplied number exactly and are multiplied by another number to get specific numbers.

A prime factor is any semi natural integer that is able to divided only by itself and by 1. Actually, a few of the initial number theory are 2, 3, 5, 7, 11, and so forth. a sum that has multiplied to yield a new sum. For illustrate, if we divide 15 by 3 and 5, we get 3 5 = 15. components: All prime but non-composite components are referred to here as prime factors. 2, 3, and 5 are a some of the major determinants of 30. It is essential to list 2 twice as 2 2 3 (or 22 3) in order to factorise 12 since only 2 and 3 represent prime factors of 12. 2 + 3 can really be added to make 12.

given

As contrast to multiples, which are multiplied by another number to produce particular numbers, factors are the numbers that split the supplied number exactly.

Factors are the objects that numbers can be multiplied by one another to produce another number (e.g., 1, 2, 3, and 6 are factors of 6). When you multiply a number by an integer, you obtain multiples (e.g., 20 is a multiple of 4).

e.g., 1, 2, 3, and 6 are factors of 6

e.g., 20 is a multiple of 4

Factors are the numbers that divide the supplied number exactly and are multiplied by another number to get specific numbers.

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The percentage Tallulah have to put down in order to pay for the car is given by the equation A = 15 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

Given data ,

Let the percentage Tallulah have to put down in order to pay be A

Now , the equation will be

The price of the car = $ 18,500

The amount of money Tallulah can get from the bank = $ 15,725

So , the remaining amount = price of the car - amount of money Tallulah can get from the bank

Substituting the values in the equation , we get

The remaining amount = 18,500 - 15,725

The remaining amount = $ 2,775

Now , $ 2,775 = A % of price of the car

So , 2,775 = ( A/100 ) x 18,500

On simplifying the equation , we get

Divide by 18,500 on both sides of the equation , we get

A/100 = 0.15

Multiply by 100 on both sides of the equation , we get

A = 15 %

Hence , the percentage is 15 %

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The discount can be found by subtracting the sale price from the original price:

$25.40 - $16.51 = $8.89

So the discount was $8.89.

To find the percent discount, we can divide the discount by the original price and multiply by 100:

$8.89 / $25.40 * 100% = 35%

Therefore, the percent discount from the coupon was 35%.

Answer:

x=4.875

Step-by-step explanation:

19.5=4x

19.5/4=4.875

x=4.875

Check:

4.875×4=19.5

The given diagram in the image is dilated by a scale factor of 1.5.

The scale factor is defined as the proportion of the new image's size to that of the previous image. Dilation is the process of increasing an object's size without altering its shape. Depending on the scale factor, the object's size may increase or decrease

The coordinate point of the image is at 2. After dilation, the point will reach the coordinate at 5.

The scale factor of the point will be calculated as:-

Scale factor = 9 / 6

Scale factor = 1.5

Therefore, the scale factor for the given diagram in the image is 1.5.

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Answer: 6x=90

Step-by-step explanation:

We know that one angle in a right triangle is 90 degrees and the sum of all the angles is 180, so we can start by subtracting 90 from 180. We are left with 90 and now we have angle ratios which represent fractional quantities. We know that one of these quantities is 5 and the other is 1. Their sum is 6 and equals 90. So the proportion would be 6x = 90. The larger angle is 75 degrees and the smaller one is 15.

Answer: 16 cats

Step-by-step explanation: how many times does 5 go into 20?? 4 times (5x4) so you multiply 4 by 4

Answer:

The average weight of a 3-pound human brain in ounces is approximately 48 ounces.

Answer:

Mean = $54.875 ($54.88 to nearest cent because $54.875 is impossible)

Median = $32

Mode = $32

Step-by-step explanation:

Mean = all numbers added together / amount of numbers in dataset

$32 + $87 + $67 + $32 + $32 + $87 + $77 + $25 = $439

$439/8= $54.875 = $54.88 to the nearest cent.

Median =

1. Order the numbers. Here's how it's ordered: $25,$32,$32,$32,$67,$77,$87

2. Calculate the middle position with the formula [tex](n+1)/2[/tex] where n is the amount of numbers in dataset (for odd datasets) or find the two middle values (for even datasets.) In this case, it is an odd dataset, so we use the formula.

(7+1)/2 = 4

In the 4th position, the number is $32, so the median is $32.

Mode = The numbers that comes up most often.

In this case, $32 comes up 4 times, which is the most, so the mode is $32.

Brainliest please!

1) The perimeter of the composite figure is 31.9

2) The area of the composite figure is 64.25

What is perimeter?

The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.

There are 2 shapes: half circle and right triangle

diameter of half circle ,d=10

radius, r=d/2 = 10/2 = 5

Perimeter of half circle = π r = 3.14 * 5 = 15.7

In the right triangle,

base = 5, line perpendicular to  base = 10

hypotenuse² = squares of  other 2 sides  added

                       = 5² + 10²

                       = 25 +100

                       = 125

hypotenuse = ± √125 = ±11.18

consider positive for length

hypotenuse = 11.18

The perimeter of the composite figure

= Perimeter of half circle +base of  right triangle + hypotenuse of  right triangle

=15.7 + 5 +  11.18

= 31.9

Area of  half circle = 0.5*π *r² = 0.5*3.14*5² = 39.25

Area of  right triangle = 0.5*base * height

                                     = 0.5*5*10

                                     =  25

The area of the composite figure

=Area of  half circle + Area of  right triangle

=  39.25 +   25

= 64.25

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Answer:

1/2x + 6

4

-2x + 5

Step-by-step explanation:

Find the slope (rise over run) and the y intercept for each function.

Answer:

The difference between the vertical intercept is a ratio of 20$ so the difference in intercepts is about 2.50$ or 20 spaces.

Hope this helps

The expression that is not equivalent is 23 + (-27) + 16 + 32. Option C

PEDMAS is described as a mathematical acronym that represents the arithmetic operations in the other of their usage in calculation.

They are;

From the information given, we have that;

23 + ( − 27 ) − 16 − ( − 32 )

expand the parentheses, we get;

23 - 27 - 16 + 32

Add the values

23 - 27 - 16

Now, subtract the values

-20

Hence, the value is -20

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The complete question

Which of the following is not equivalent to 23 + ( − 27 ) − 16 − ( − 32 )

Range = 7. IQR = 4.5. Variance: 8.67, Std Dev: 2.96 when researcher organized diet groups on weight loss weighed five clients after several weeks on the program.

The range of the weight-loss scores can be calculated by subtracting the smallest value from the largest value. In this case, the range would be

13 - 6 = 7.

The inter-quartile range (IQR) is calculated as the difference between the 75th percentile and the 25th percentile of the data.

IQR: 11.25 - 6.75 = 4.5

To calculate the variance, first find the mean weight-loss score by summing all the scores and dividing by the number of clients: (13 + 12 + 6 + 9 + 9 + 10) / 6 = 9.17. Next, subtract the mean from each score and square the result for each client:

[tex](13 - 9.17)^2 = 3.69\\(12 - 9.17)^2 = 1.69\\(6 - 9.17)^2 = 16.0\\(9 - 9.17)^2 = 0.02\\(9 - 9.17)^2 = 0.02\\(10 - 9.17)^2 = 0.69[/tex]

Next, sum the squared deviations and divide by the number of clients minus one (n-1):

(3.69 + 1.69 + 16.0 + 0.02 + 0.02 + 0.69) / (6-1) = 4.83

The variance is 4.83 and the standard deviation is the square root of the variance: [tex]\sqrt{(4.83)} = 2.19.[/tex]

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Since both the coordinates of (-2,-3) are negative the point lies in option B: quadrant iii.

What is a quadrant?

A quadrant is an area or section of a cartesian plane that results from the intersection of two axes. It is used to establish a point's location in a plane.

Consider the point A = (x,y) given in the coordinate system, where x and y are arbitrary numbers.

If x and y are positive numbers then point A is in the first quadrant.

If x is negative number and y is positive then point A is in the second quadrant.

If x and y are negative numbers then point A is in the third quadrant.

If x  is positive number and y is negative then point A is in the fourth quadrant.

Now the given point is (-2,-3).

The first coordinate of this point is a negative number, and the second is also negative.

So, the point lies in third quadrant.

Therefore, (-2,-3) is in 3rd quadrant.

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The Standard deviation of data(5, 13, 9, 10, 5, 12) that represents orders filled per day is 3.4

The sample standard deviation formula looks like this:

s = √Σ(X-x)² / √n-1

Where….

s = sample standard deviation

Σ = sum of…

X = each value

x = sample mean

n = number of values in the sample

We have,

Number of values in the sample, n = 6

sample mean, x = 5+13+9+10+5+2 / 6 = 9

So sample standard deviation, S = √Σ(X-x)² / √n-1

s = √58/√5

s = 7.6/2.2

s = 3.4

Therefore sample standard deviation of data that represents orders filled per day is 3.4

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$89.1 is the amount paid by Beau to buy skateboard.

percentage, a relative value indicating hundredth parts of any quantity.

Given that Beau buys a skateboard with a price tag of $82.50

The tax rate is 8%

Let us find what 8% of 82.50

Convert 8% to decimal value

8/100=0.08

0.08×82.5=$6.6

Now let us find the amount he paid including tax

$82.50+$6.6

$89.1

Hence, $89.1 is the amount paid by Beau to buy skateboard.

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The scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1: 168 and 1: 1080 respectively.

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

For the ratio 1 in : 14 feet, we convert to the same unit in inches:

1 foot = 12 inches

14 feet = 12 × 14 inches

14 feet = 168 inches

1 in = 168 in

1 : 168

For the ratio 1 in : 30 yards, we convert to the same unit in inches:

1 yard = 36 inches

30 yards = 36 × 30 inches

30 yards = 1080 inches

1 in = 1080 in

1 : 1080

Therefore, the scale factor for the ratios of 1 in : 14 feet and 1 in : 30 yards without units are 1 : 168 and 1 : 1080 respectively.

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Answer:

Step-by-step explanation:

4:05pm go back 4hours and it’s 12:05, then go back another 2 hours, 10:05, then go back another 20mins and it’s 9:45am

The value of y is 13√2 (optionB)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

Sin(tetha) = opp/hyp

cos (tetha) = adj/hyp

tan(tetha) = opp/adj

therefore cos 45 = 13/y

1/√2 = 13/y

y = 13√2

therefore the value of y is 13√2

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The approximate area between the x-axis and the function, f(x) = x² + 3, obtained by finding the sum of the of the four rectangles is Area ≈ 9.75

The area between the x-axis and the graph under a function can be referred to as the area under a curve of the function, which can be found using definite integrals.

The area between the x-axis and the function f(x) = x² + 3 over the interval [0, 2], can be found by finding the area of the rectangular bars, A, in the figure as follows;

The values at the endpoints of the rectangles are; 0.5, 1, 1.5, and 2

Therefore;

f(0.5) = 0.5² + 3 = 3.25

f(1) = 1² + 3 = 4

f(1.5) = 1.5² + 3 = 5.25

f(2) = 2² + 3 = 7

Therefore; A = 0.5 × f(0.5) + 0.5 × f(1) + 0.5 × f(1.5) + 0.5 × f(2)

Plugging in the values of the function, we get;

Area ≈ 0.5 × 3.25 + 0.5 × 4 + 0.5  × 5.25 + 0.5 × 7 = 9.75

The approximate area between the x-axis and the graph of f(x) = x² + 3 over the interval [0, 2] is about 9.75 square units

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For the statement "Integer x divisible by 6" the option C is correct.

Either statements are NOT sufficient, but BOTH together are sufficient.

What is integer?

The Latin term "Integer," which implies entire or intact, is where the word "integer" first appeared. Zero, positive numbers, and negative numbers make up the particular set of numbers known as integers.

(1) x + 3 is divisible by 3

This means that x is a multiple of 3.

Hence x + 3 is a multiple of 3.

But x could be 0, 3, 6. If x = 3, x is not divisible by 6.

Otherwise it is.

So, this statement is insufficient.

(2) x + 3 is an odd number

This means that x is an even number.

X can be 6, or 10.

So, this statement is insufficient.

Together -

From (1) it is known that x is a multiple of 3.

Hence X can be 0,3,6,9,12,15,18,21,24,27,30.

From (2) it is known that x is even.

Hence X can be 0,6,12,18,24,30.

Therefore, x is divisible by 6.

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The time it takes for the balance of the account to reach $23,100 is given as follows:

21 years.

An exponential function is defined as follows:

y = ab^(x/n).

In which the parameters are defined as follows:

In the context of this problem, the parameter values are given as follows:

a = 8700, b = 2, n = 15.

Hence the function for the balance after x years is given as follows:

y = 8700(2)^(x/15).

Then the time needed for a balance of $23,100 is given as follows:

23100 = 8700(2)^(x/15).

2^(x/15) = 23100/8700

x/15 = log2(23100/8700)

x/15 = 1.41

x = 15 x 1.41

x = 21 years.

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Answer:

  the required equation is x² -10x +18 = 0

Step-by-step explanation:

Given side x and diagonal 8 cm of a rectangle with perimeter 20 cm, you want to show that the value of x satisfies an equation of the form ...

  x² +ax +b = 0 . . . . . where a and b are integers.

The perimeter is the sum of the side lengths. It can be expressed by the formula ...

  P = 2(L +W)

Solving for W gives ...

  W = P/2 -L

For the given rectangle, the width is ...

  W = 20/2 -x = 10 -x

The length of the diagonal is related to the length and width of the rectangle by the Pythagorean theorem.

  c² = a² +b²

  8² = x² +(10 -x)² = 2x² -20x +100

  32 = x² -10x +50 . . . . . . . . divide by 2

  x² -10x +18 = 0 . . . . . . . . . . subtract 32

This shows that x must satisfy a quadratic of the form x² +ax +b = 0, where a=-10, and b=18, both integers.

__

Additional comment

The vertex form of the equation is ...

  (x -5)² -7 = 0

This has solutions ...

  x = 5 ±√7 ≈ {2.354, 7.646} . . . . centimeters

Answer:

Step-by-step explanation:

Compound ratio of 2:3 and 9:7 is

2x9=18

3x7=21

Answer: 18:21