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Suppose you buy a $1000 bond with a 4.3% coupon that matures in 30 years.
1. First, how much do you earn off your bond every 6 months?
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68% of states have an infant mortality rate between 5.36 and 8.60 percent.

In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within an interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively.

In this problem, we have that:

Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births)?

\(\sf 5.36 = 6.98 - 1\times1.62\)

So, 5.36 is one standard deviation below the mean.

\(\sf 8.60 = 6.98 + 1\times1.62\)

So 8.60 is one standard deviation above the mean.

Therefore, by the Empirical Rule, 68% of states have an infant mortality rate between 5.36 and 8.60 percent.

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Answer:

210

Step-by-step explanation:

10 choose 4. 10 letters choose 4. Using the combination formula. C(n,r)

Answer:

C

Step-by-step explanation:

The width of the screen is approximately 15.65 or √(245) inches. The correct answer would be an option (C).

Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.

The height of the screen (AB) is 14 inches, and the diagonal distance (AC) is 21 inches.

AB² + BC² = AC²

We can use these values to solve for the width of the screen (x):

x² = 21² - 14²

x²  = 441 - 196

x²  = 245

To solve for x, we can take the square root of both sides of the equation:

x = √(245)

x ≈ 15.65

Thus, the width of the screen is about 15.65 or √(245) inches.

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The measure of <1 is 31°.

Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.

In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;

<2 = 31° (given)

So that;

<1 = <2 = 31°

Thus,

<1 = 31°

Therefore, it can be concluded that the measure of <1 is 31°.

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Answer: h = 22.5

Step-by-step explanation:

Total angle area of a 12 sided polygon is 1800

1. One angle would be 1800/12= 150

2. Add 30 one each side to cancel out and only leave 8h.

3. To get rid of the 8 we divide the the other side by 8.

The answer is 22.5

Answer: D 22.5 i got it right on the exam

Step-by-step explanation:

In order to find the height of 2 different 3-D shapes, we must identify which dimension represents the height for each individual shape and then add them together.

The first thing is that we must identify which dimension represents the height for each individual shape, for instance, if one shape is a rectangular prism, its height would be the length of one of its sides.

After we identified the height for each shape, you can add them together to get the total height of the composite figure, but, we must understand that this method assumes that the two shapes are stacked vertically on top of each other with their bases aligned.

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Answer:

1/4+1/3+1/8

=17/24

Step-by-step explanation:

1-17/24

=7/24

7/24×240

=70

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

Both the numerator and denominator were multiplied by 4

Answer:

find a number that is divisible by both the denominator and the numerator

Step-by-step explanation:

divide 4/12 by 4, so you get 1/3

Answer:

b,d,c

Step-by-step explanation:

y = 1 4 x calculates the number of eggs, y, for x crepes. The constant of proportionality is 1 4 . Ella needs 15 eggs to make 60 crepes. y = kx, where k is the constant of proportionality → y = 5 eggs 20 crepes x → y = 1 4 x; thus, k = 1 4 y = 1 4 (60) = 15 eggs

For 60 creps, 15 eggs will be needed.

Given is that the number of eggs used in the recipe is proportional to the number of crepes being made. The recipe calls for 5 eggs per 20 crepes. Sixty crepes will be served

Now, for 20 creps, 5 eggs are needed.

Then for 1 crep, (5/20) eggs are needed.

For 60 creps, (5/20) x 60 = 15 eggs will be needed.

Therefore, For 60 creps, 15 eggs will be needed.

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Answer:

Yes, Dayson can completely cover the package with wrapping paper.

Step-by-step explanation:

Given: The rectangular prism is 50 centimeters by 20 centimeters by 18 centimeters.

Area of wrapping paper is 1 square meter.

To find: whether he can completely cover the package with wrapping paper

Solution:

Total surface area of the rectangular prism = 2(lb + bh +hl)

where l denotes length, b denotes breadth and h denotes height

Total surface area of the rectangular prism = \(2\left [ (50)(20)+(20)(18)+(18)(50) \right ]\)

\(=2\left ( 1000+360+900 \right )\\=2(2260)\\=4520\,\,cm^2\)

As \(1\,m^2=10000\,cm^2\),

Total surface area of the rectangular prism = \(4520\,cm^2=0.4520\,m^2\)

As Dayson has \(1\,m^2> 0.4520\,m^2\) of wrapping paper, he can completely cover the package with wrapping paper.

The capacity of the mug is 1.2. The capacity of the mug can be found by using the equation C = (3/4) ÷ (5/8).

It is the maximum amount of output that can be produced in a given period of time. Capacity is usually expressed in terms of units per unit of time, such as gallons per minute or passengers per hour.

In this equation, 3/4 represents the amount of water in the mug, and 5/8 represents the amount the mug is full.

Let the capacity of the mug be x.

Given,

Mug is 5/8 full and contains 3/4 of water

So, 5/8 of the mug is filled with water

Therefore,

5/8 of x = 3/4

(5/8 )x = (3/4)

x = (3/4) × (8/5)

x = (24/20)

x = 1.2

Therefore, the capacity of the mug is 1.2.

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The sentences in this paragraph best support the idea that the printing press was an important invention A. They provide examples showing the impact of the printing press on varied groups of people.

With the greater availability of books, people were spurred to develop necessary skills in reading, thus resulting in higher literacy rates and a enhanced societal benefit.

Subsequently, due to simpler, more exact shares of data through printing, scientific progress was greatly boosted. Moreover, churches had the chance to further propagate their supernatural ideas with the aid of the printing press.

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

Subtract 9, then divide by 2

If x equals the affected number, the expression would be: \(\frac{x-9}{2} \)

Step-by-step explanation:

Difference means subtraction

Half a number means to divide by two, or multiply by \(\frac{1}{2} \)

Answer:

They should interview 1620 adults now.

Step-by-step explanation:

Margin of error of a confidence interval:

The margin of error of a confidence interval has the following format:

\(M = z\frac{\sigma}{\sqrt{n}}\)

In which z is related to the confidence level, \(\sigma\) is the standard deviation of the population and n is the size of the sample.

In this question:

z wont change, neither will \(\sigma\)

We want to increase n as such the margin of error is reduced to one third.

We have that the margin of error is inversely proportional to the square root of the size of the sample, which means that for the margin of error to be reduced to one third, the sample size has to be multiplied by \(3^2 = 9\). So

180*9 = 1620

They should interview 1620 adults now.

Answer:

355.94 cm squared

Step-by-step explanation:

Area of rectangle = 4 cm * 6 cm = 24 square cm

Radius (r) of circle = 11 cm

\(Area \: of \: circle = \pi {r}^{2} \\ \\ = 3.14 \times (11)^{2} \\ \\ = 3.14 \times 121 \\ \\ = 379.94 \: {cm}^{2} \\ \\ area \: of \: shaded \: region \\ \\ = 379.94 - 24 \\ \\ = 355.94 \: {cm}^{2} \\ \)

Answer: 355.94 cm squared

Step-by-step explanation:

= 3.14 x (11)²

= 3.14 x 121

= 379.94 - 24

= 355.94 centimeters squared

Answer:

Third option, last one

Step-by-step explanation:

Let's solve for x first.

|2x| - 12 = -2

|2x| = 10

2x = 10 or -2x = 10

x = 5 or x = -5

The number line that represents this is the last one.

Answer:

Step-by-step explanation:

Given the trigonometric equation;

cos x =-0.4226

To get the value of x within the range 0° < x < 360°, we need to take the arc cosine of the value as shown;

x = arccos -0.4226

x = 114.99°

x ≈ 115°

Since x is positive in the 4th quadrant, the value of x can also be 360 - \(\theta\)

where \(\theta = 115^{o}\)

x2 = 360°-115°

x2 = 245°

The value of x within the interval are 115° and 245°

Answer:

The value of x within the interval are 115° and 245°

Step-by-step explanation:

The rear windshield wiper of a car rotated 120 degrees, as shown in the figure. The area cleared by the wiper blade is approximately 205.875 square inches.

The problem states that a car’s rear windshield wiper rotates 120 degrees, as shown in the figure. Our aim is to find the area cleared by the wiper.

The wiper's arm is represented by a line segment and has a length of 14 inches.

The wiper's blade is perpendicular to the arm and has a length of 25 inches.

Angular degree measure indicates how far around a central point an object has traveled, relative to a complete circle. A full circle is 360 degrees, and 120 degrees is a third of that.

As a result, the area cleared by the wiper blade is the sector of a circle with radius 25 inches and central angle 120 degrees.

The formula for calculating the area of a sector of a circle is: A = (θ/360)πr², where A is the area of the sector, θ is the central angle of the sector, π is the mathematical constant pi (3.14), and r is the radius of the circle.

In this situation, the sector's central angle θ is 120 degrees, the radius r is 25 inches, and π is a constant of 3.14.A = (120/360) x 3.14 x 25²= 0.33 x 3.14 x 625= 205.875 square inches, rounded to the nearest thousandth.

Therefore, the area cleared by the wiper blade is approximately 205.875 square inches.

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Answer: 5

Step-by-step explanation:

First of all, keep in mind that absolute value of any real number (positive and negative) is always positive because it stands for the distance from zero, and distance will never be negative.

         i.e. |x|=x, |-x|=x

-------------------------------------------

 |-9|-|-4|

=9-4

=5

Hope this helps!! :)

Answer:

\(\huge \boxed{5}\)

Step-by-step explanation:

\(|-9|-|-4|\)

Apply rule : \(|-a|=a\)

\(9-4\)

Subtract.

\(=5\)

The given expression is equivalent to -2x² - 3x - 5.

In order to solve the given expression first we should transform the given equation into the form of a polynomial. A polynomial may be represented in the form of y = ax² + bx + c where a, b and c are coefficients, y is the dependent variable and x is the independent variable.

Now, we assume that y = -4x² + (2x-5) (1 + x).

Now we simplify the above expression by multiplying and taking the like terms together.

y = -4x² + 2x + 2x² - 5 - 5x

y = -4x² + 2x² + 2x - 5x - 5

y = -2x² - 3x - 5

Thus, the given expression can be written is the simplified form as y = -2x² - 3x - 5.

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The variable x can infinite many values as Michelle walks from her house to the bus stop

The distance is given as:

Distance = 300 yards

This means that

x = 0 to 300

Distance is a continuous variable.

This is so because it can assume any positive real value

This means that the value of x is any value from 0 to 300

Hence, the variable x can infinite many values as Michelle walks from her house to the bus stop

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Answer: D

Step-by-step explanation:

Remember the formula -

\(A = \pi\) × \(r^{2}\)

π = 3.14

\(r^{2}\) = 7

7² = 49

3.14 x 49 = 153.94

A = π · r² = π · 72 ≈ 153.93804

153.93804 ⇒ 154 (rounded)

Your answer is D.

1. The slopes of perpendicular lines are  a negative reciprocal

2. Parallel lines have the same slope.

3. The shortest distance from any point to a line is a straight line

The slope of two perpendicular lines is such that the slope of one line is equal to the reciprocal of the negative slope of the other.

if two lines of slope m and m' are perpendicular their slopes is written as

m = -1/m'

Parallel lines grow vertically and flow horizontally at the same rate. they have the same slope, they never cross.

if two lines of slope m and m' are perpendicular their slopes is written as

m = m'

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The set of capacity measures related to cubic meter are ordered from the greatest to the least:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

In this problem we need to order a group of capacity measures in cubic meters and its related units from the greateast to the least. To make this we need to understand the following relations:

Now we proceed to order the following set of information:

First, write the set of measures:

5 dam³, 530 m³, 5.480 m³, 5.5 dam³, 5 dam³, 61 m³

Second, convert all measures in cubic decameters into cubic meters:

5.000 m³, 530 m³, 5.480 m³, 5.500 m³, 5.000 m³, 61 m³

Third, order all the set from the greatest to the least:

5.500 m³, 5.480 m³, 5.000 m³, 5.000 m³, 530 m³, 61 m³

Fourth, rewrite the set of measures in its original units:

5.5 dam³, 5.480 m³, 5 dam³, 5 dam³, 530 m³, 61 m³

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The largest size of a team according to the task content is; 20 kids.

It follows from the task content that the population is; 20 students in Mrs. Tanya's class and 24 kids in Mrs. Olga's class.

However, since, the team forming condition states that students be placed on teams of equal size with students from only their own class.

It therefore follows that the largest size of a team is 20 as only 20 students are in Mrs. Tanya's class hence leaving 4 kids in Mrs. Olga's class without a team.

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