Suppoe on January​ 15, ​, the U. S. Treaury iued a​ five-year inflation-indexed note with a coupon of. On the date of​ iue, the conumer price index​ (CPI) wa. By January​ 15, ​, the CPI had increaed to. What principal and coupon payment wa made on January​ 15, ​?

The measure of each exterior angle of a regular polygon of 12 sides is 75°. A regular polygon is a polygon with equal sides and angles.

The measure of each exterior angle of a regular polygon of 12 sides is 60o. A regular polygon is a polygon with equal sides and angles. The total number of sides of the polygon is denoted by n, and the measure of each exterior angle is denoted by x.The measure of each angle of a regular polygon can be determined using the formula x = (360°/n). In this case, n = 12. Therefore, x = (360°/12) = 30°. This is the measure of each interior angle.To calculate the measure of each exterior angle, we must add the measure of an interior angle to 180°. This is because an exterior angle is always 180° more than an interior angle in a regular polygon. Therefore, the measure of each exterior angle is 30° + 180° = 210°. Since a circle is 360°, 210° must be converted to its equivalent angle in a circle. This is done by subtracting 210° from 360°, which gives us 150°. Finally, we divide 150° by 2 to get the measure of each exterior angle: 150° / 2 = 75°.Therefore, the measure of each exterior angle of a regular polygon of 12 sides is 75°.

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Answer:

Step-by-step explanation:

where is the full question????

The perimeter be 410 then the maximum area be \($A=\left(\frac{410-3 x}{2}\right) * x$$\).

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

Let the perimeter be p = 410

The perimeter of the fence is:

p = 2(x + y + 5 + y) + x

p = 2x + 2y + 10 + 2y + x

Collect like terms

p = 2x + x + 2y + 2y + 10

p = 3x + 4y + 10

Where, p = 410, then

3x + 4y + 10 = 410

\($$\begin{aligned}& 4 y=410-10-3 x \\& 4 y=400-3 x\end{aligned}$$\)

simplifying the equation, we get

\($y=\frac{400-3 x}{4}$$\)

The area (A) of the fence is:

\($$\begin{aligned}& A=(y+y+5) * x \\& A=(2 y+5) * x\end{aligned}$$\)

Substitute: \($y=\frac{400-3 x}{4}$\)

\($$\begin{aligned}& A=\left(2 * \frac{400-3 x}{4}+5\right) * x \\& A=\left(\frac{400-3 x}{2}+5\right) * x\end{aligned}$$\)

simplifying the equation, we get

\($A=\left(\frac{400-3 x+10}{2}\right) * x$$\)

\($A=\left(\frac{410-3 x}{2}\right) * x$$\)

\($A=\frac{410 x-3 x^2}{2}$$\)

A = 205x - 1.5 x²

Differentiate both sides, we get

A' = 205-3 x

simplifying the equation, we get

205 - 3x = 0

3x = 205

Therefore, the maximum area be \($A=\left(\frac{410-3 x}{2}\right) * x$$\).

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Answer:

A = s^2

Step-by-step explanation:

The area of a square can be found by multiplying the side by its side.

A = side x side = s^2

So if the side of a square is 3, to find the are you would multiply 3 times 3. Giving you an area of 9.

Answer:

B

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

The slope is \(-\frac{3}{4}\)

Step-by-step explanation:

To find the slope, you take 2 points and use rise/run. I used (0,1) and (4,-2) because they look like they are being touched by the line. So by looking at the graph, I have to look at how I can get from (0,1) to (4,-2). So from (0,1), I go down 3 units which makes my number -3, over the run which is 4 units to the right, which makes it positive. so I went down 3 and then went right 4, making this    \(-\frac{3}{4}\). You could also use point-slope which means \(\frac{y2-y1}{x2-x1}\) or \(\frac{-2-1}{4-0}\) which equals the same thing

Inferential statistics involves using sample data to make inferences, predictions, or generalizations about a larger population, providing valuable insights and conclusions based on statistical analysis.

The term "inferential statistics" is associated with the task of making inferences or drawing conclusions about a population based on sample data.

In other words, it involves using sample data to make generalizations or predictions about a larger population.

Inferential statistics is concerned with analyzing and interpreting data in a way that allows us to make inferences about the population from which the data is collected.

It goes beyond simply describing the sample and aims to make broader statements or predictions about the population as a whole.

This branch of statistics utilizes various techniques and methodologies to draw conclusions from the sample data, such as hypothesis testing, confidence intervals, and regression analysis.

These techniques involve making assumptions about the underlying population and using statistical tools to estimate parameters, test hypotheses, or predict outcomes.

The goal of inferential statistics is to provide insights into the larger population based on a representative sample.

It allows researchers and analysts to generalize their findings beyond the specific sample and make informed decisions or predictions about the population as a whole.

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Answer:

3

Step-by-step explanation:

1,14

Answer:

88 yards

Step-by-step explanation:

To find the width we'll use this formula 2(length) + 2(width) = perimeter

With the given information, our equation is this:

2(98) + 2(width) = 372

196 + 2(width) = 372

- 196                 - 196

2(width) = 176

2(width)/2 = 176/2

width = 88

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

The perimeter of a rectangle is given as:

Perimeter = 2 ( length + width )

The width of the rectangle is 88 yards.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

The perimeter of a rectangle = 372 yards.

Length of the field = 98 yards.

The perimeter of a rectangle is given as:

Perimeter = 2 ( length + width )

372 = 2 (98 + width)

186 = 98 + width

width = 186 - 98

width = 88 yards

Thus,

The width of the rectangle is 88 yards.

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It is proved that [ [A, B]², C] = 0 for any 2 × 2 real matrices A, B, and C.

To prove or disprove the statement [ [A, B]², C] = 0, where A, B, and C are 2 × 2 real matrices, we need to evaluate the commutator [ [A, B]², C] and check if it equals zero.

First, let's calculate [A, B]:

[A, B] = A * B - B * A

Next, we calculate [ [A, B]², C]:

[ [A, B]², C] = [ (A * B - B * A)², C]

               = (A * B - B * A)² * C - C * (A * B - B * A)²

Expanding the square terms:

= (A * B - - B * A * A *

          B * C B * A) * (A * B - B * A) * C - C * (A * B - B * A) * (A * B - B * A)

= A * B * A * B * C - A * B * A * B * C - B * A * B * A * C + B * A * B * A * C

              - A * B * B * A * C + B * A * A * B * C + A * B * B * A * C

= 0

Therefore, we have proved that [ [A, B]², C] = 0 for any 2 × 2 real matrices A, B, and C.

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The Complete Question is:

We define the commutator, denoted by [ X , Y ], of two square matrices X and Y to be [ X , Y ] = X Y − Y X. Let A, B, and C be 2 × 2 real matrices. Prove or disprove: [ [A, B]², C] = 0

It will take 120 minutes for smaller hose to fill the complete swimming pool on its own.

Let us represent the complete swimming pool as 1. Now, total time required to fill the swimming pool is 40 hours. So, amount of swimming pool filled in 1 minute = 1/40

Similarly, amount fo swimming pool filled by larger hose in 1 minute = 1/60

Now for the smaller hose, the amount of swimming pool filled in 1 minute = 1/40 - 1/60

The amount of swimming pool filled in 1 minute = (60 - 40)/2400

The amount of swimming pool filled in 1 minute = 20/2400

The amount of swimming pool filled in 1 minute = 1/120

Total time taken to fill swimming pool = 1 ÷ (1/120)

Total time taken to fill swimming pool = 120 minutes

Thus, 120 minutes are required.

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Answer: About $118.66

Step-by-step explanation:

53.4/0.45 is 118.66

Answer:

A. -146

Step-by-step explanation

46th term = -11 + ( 46 -1) (-3)

= -11 + (45)(-3)

=-11 -135

= - 146

Answer:

decay factor is 0.43

Step-by-step explanation:

1-0.57=0.43

Answer:

2/3

Step-by-step explanation:

Simplify

\(26=6\cdot \left(5-a\right)\\26=6\cdot 5+6\cdot -a\\26=30+6\cdot -a\\26=30+\left(6\cdot -1\right)a\\26=30-6a\\30-6a=26\)

Group constants

\(30-6a=26\\30-6a-30=26-30\\-6a+30-30=26-30\\-6a=26-30\\-6a=-4\\\)

Isolate the term, a

\(-6a=-4\\\frac{-6a}{-6}=\frac{-4}{-6}\\\frac{6a}{6}=\frac{-4}{-6}\\a=\frac{-4}{-6}\\\\\frac{-a}{-b} = \frac{a}{b}\\\\a=\frac{4}{6}\\a=\frac{2\cdot 2}{3\cdot 2}\\a=\frac{2}{3}\)

The values of t that place 85% of the area in the middle of the distribution are between -3.379 and 3.379.

To find the values of t that place 85% of the area in the middle of the distribution, we need to find the t-scores that correspond to the 7.5th and 92.5th percentiles of the t-distribution with 46 degrees of freedom.

We can use a t-table or a statistical software to find these values. Using a t-table, we can look up the critical t-values for the two tails of the distribution that include 7.5% and 92.5% of the area.

For a two-tailed test at the 5% significance level with 46 degrees of freedom, the critical t-value is approximately 2.013.

To find the t-scores for the 7.5th and 92.5th percentiles, we need to multiply the critical t-value by the corresponding t-multiplier for the degrees of freedom. For 46 degrees of freedom, the t-multiplier is approximately 1.678.

Thus, the t-score that corresponds to the 7.5th percentile is -2.013 x 1.678 = -3.379, and the t-score that corresponds to the 92.5th percentile is 2.013 x 1.678 = 3.379.

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The given question is incomplete, the complete question is:

Consider a t distribution with 46 degrees of freedom. What values of t place 85% of the area in the middle of the distribution?

Step-by-step explanation:

x^4-9x^2-8x^2+72

x^2(x^2-9)-8(x^2-9)

(x^2-8)(x^2-9)

(x^2-8)(x+3)(x-3)

Answer:

The discount was \(47\frac{6}{7}\)%

Step-by-step explanation:

In order to find out the discount will have to do the following.

First find out what part of the origin price was taken of, so we create a fraction with the denominator being the original price and the numerator being the difference between the original price and the discount price. So we do.....

\(\frac{28.00-14.60}{28.00} = \frac{2800 - 1460}{2800} = \frac{1340}{2800} = \frac{67}{140}\)

Now we have to find a fraction with the same value but with the denominator being a 100, so we do.....

\(\frac{67 / 1.4}{140/1.4}= \frac{47\frac{6}{7} }{100}\)

From this we know that the the discount in percentages will be equal to \(47\frac{6}{7}\)%

Answer:

52.1428571429

Step-by-step explanation:

14.60 × 100 = 1460

1460 ÷ 28 = 52.1428571429

When the probability of paying the claim is 5%, the chance the insurance company must pay for (a) exactly two claims is 31.51%, (b) two or more claims is 8.62%, and (c) four or fewer claims is 98.22%.

To calculate the probability of these scenarios, we will use the binomial probability formula:

P(x) = C(n, x) * p^x * (1-p)^(n-x),

where n is the number of trials (projects), x is the number of successes (claims), p is the probability of success (5%), and C(n, x) is the number of combinations of n items taken x at a time.

a) For exactly two claims:

P(2) = C(10, 2) * (0.05)^2 * (0.95)^8

P(2) ≈ 0.3151

So, the chance the insurance company must pay for exactly two claims is approximately 31.51%.

b) For two or more claims:

P(2 or more) = 1 - P(0) - P(1)

P(0) = C(10, 0) * (0.05)^0 * (0.95)^10 ≈ 0.5987

P(1) = C(10, 1) * (0.05)^1 * (0.95)^9 ≈ 0.3151

P(2 or more) ≈ 1 - 0.5987 - 0.3151 ≈ 0.0862

So, the chance the insurance company must pay for two or more claims is approximately 8.62%.

c) For four or fewer claims:

P(4 or fewer) = P(0) + P(1) + P(2) + P(3) + P(4)

P(3) = C(10, 3) * (0.05)^3 * (0.95)^7 ≈ 0.0573

P(4) = C(10, 4) * (0.05)^4 * (0.95)^6 ≈ 0.0111

P(4 or fewer) ≈ 0.5987 + 0.3151 + 0.0573 + 0.0111 ≈ 0.9822

So, the chance the insurance company must pay for four or fewer claims is approximately 98.22%.

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Answer:

30

Step-by-step explanation:

49 - 31 = 18

12 + 18 = 30

There are 191 different patterns of mail delivery possible for the 19 houses on the northern side of the street, satisfying the given conditions.

To determine the number of different patterns of mail delivery in this scenario, we can use a combinatorial approach.

Let's consider the possible patterns based on the number of houses in a row that receive mail on the same day: If no houses in a row receive mail on the same day: In this case, all 19 houses would receive mail on different days. We have a single pattern for this scenario.

If one house in a row receives mail on the same day: We have 19 houses, and we can choose one house in a row that receives mail on the same day in 19 different ways. The remaining 18 houses would receive mail on different days. So, we have 19 possible patterns for this scenario.

If two houses in a row receive mail on the same day: We have 19 houses, and we can choose two houses in a row that receive mail on the same day in C(19, 2) = 19! / (2! * (19-2)!) = 171 different ways. The remaining 17 houses would receive mail on different days. So, we have 171 possible patterns for this scenario.

Therefore, the total number of different patterns of mail delivery in this scenario is: 1 (no houses in a row) + 19 (one house in a row) + 171 (two houses in a row) = 191 different patterns.

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Farmer need 750.5 feet fencing for his triangular field.

"Triangle is  two dimensional geometrical shape with three sides and three vertices. Sum of all the angles of a triangle is equals to 180°.

Formula used

Cosine rule

As per the diagram,

cosθ = (b² +c² -a²) / 2bc

cos 70° = 0.3420

According to the question,

Let AB = c , AC = b  are given sides of measure 120 feet and 325 feet respectively.

and BC = a

Angle between given sides be θ = 70°

Substitute the value in the formula we get,

cos70° = [ (325)² +(120)² - a²] / 2(120)(325)

⇒ 0.3420 = [ 120025 - a²] / 78000

⇒ 120025 -a² = 26676

⇒ a² = 93349

⇒ a = 305.5

Total fencing required for  triangular field = AB + BC +CA

                                                                      = 120 + 325 + 305.5

                                                                      = 750.5 feet

Hence, farmer need 750.5 feet fencing for his triangular field.

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Answer:

x = 5

Step-by-step explanation:

2x-1+9x+3=57

2x+9x=57+1-3

11x=55

x= 55/11

x= 5

Answer:

x = 5

Step-by-step explanation:

Simplifying 2x + -1 + 9x + 3 = 57

Reorder the terms: -1 + 3 + 2x + 9x = 57

Combine like terms: -1 + 3 = 2 2 + 2x + 9x = 57

Combine like terms: 2x + 9x = 11x 2 + 11x = 57

Solving 2 + 11x = 57

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation. 2 + -2 + 11x = 57 + -2

Combine like terms: 2 + -2 = 0 0 + 11x = 57 + -2 11x = 57 + -2

Combine like terms: 57 + -2 = 55 11x = 55

Divide each side by '11'. x = 5

Simplifying x = 5

♡ hope it helps♡

Answer:

answer is B. :)

The graph of the given f(x) shows that: on a coordinate plane, an exponential decay function decreases from quadrant 2 into quadrant 1 and approaches y = 0. It crosses the y-axis at (0, 4) and goes through (2, 1).

The graph of a function is a visual representation of the function for which the slope, the x-intercept, and the y-intercept can be shown or determined from the graph.

Given that:

The domain of the function are values of f(x) for which f(x) ranges from:

The graph of the function as shown in the image attached shows that the graph decrease from the 2nd quadrant into the 1st quadrant and approaches = 0. It crosses the y-axis at (0, 4) and goes through (2, 1).

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\( \frac{24}{13} = \frac{x}{39} \)

We move 39 to multiply 24/13.

\( \frac{24}{13} (39) = x \\ 24(3) = x \\ 72 = x\)

Substitute x = 72 in the equation.

\( \frac{24}{13} = \frac{72}{39} \\ \frac{24}{13} = \frac{24}{13} \)

The equation is true for x = 72.

\( \large \boxed {x = 72}\)

The area of each of the semicircle is approximately:

a. 9.82 in.²       b. 16.08 in.²

A semicircle is half of a full circle. Therefore, the formula to find the area of a semicircle would be:

Area = 1/2(πr²), where r is the radius of the semicircle.

a. The parameters given are:

Diameter = 5 in.

Radius (r) = 5/2 = 2.5 in.

Area of the semicircle = 1/2(π * 2.5²) ≈ 9.82 in.²

b. The parameters given are:

Diameter = 6.4 in.

Radius (r) = 6.4/2 = 3.2 in.

Area of the semicircle = 1/2(π * 3.2²) ≈ 16.08 in.²

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Answer:

y = 8/5 x + 24

Explanation:

To get an equatio for the best line of fit, we will have to loacte two coordinate points on the line first. Using the coordinate points (10, 40) and (35, 80)

The general equation of a line is expressed as y = mx+b

m is the slope

b is the y intercept

Get the slope m

m = y2-y1/x2-x1

m = 80-40/35-10

m = 40/25

m = 8/5

Get the y-intercept

Substitute m = 8/5 and the point (10,40) into the equation y = mx+b

40 = 8/5(10) + b

40 = 16+b

b = 40 - 16

b = 24

Get the required equation using y = mx+b

y = 8/5 x + 24

This gives the required equation

Marcia states that some numbers have an odd number of factors so Marcia is correct

Factors

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers  are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors multiplication and division.

Odd Number and Even Number

Odd numbers are those numbers that cannot be divided into two equal parts, whereas even numbers are those numbers that can be divided into two equal parts. Examples of odd numbers are 3, 5, 7, 9, 11, 13, 15 Examples of even numbers are 2, 4, 6, 8, 10, 12, 14

Rob states that all numbers have an even number of factors.

Marcia states that some numbers have an odd number of factors.

Consider the number 36. It is given that,

1 × 36 = 36

2 × 18 = 36

3 × 12 = 36

4 × 9 = 36

6 × 6 = 36

The repeated factor is counted only once. So, the factors of 36 are given by 1, 2, 3, 4, 6, 9, 12, 18, and 36.

This tells us that 36 has 9 factors and has an odd number of factor. Then Marcia is correct

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H(t) = -16t^2 +704t = -16(t^2 -44t)

Putting in vertex form: -16(t^2 -44t +484) + 704

h(t) = -16(t-22)^2 + 704

It takes 22 seconds to reach the maximum height, which is the vertex of the parabola at (22,704)

please mark me as the BRAINLIEST.....

Answer:

Step-by-step explanation:

Given function:

Maximum value is obtained at vertex. Using vertex formula to find the value of t at maximum height: x = -b/2a of a  quadratic formula ax² + bx + c