When patey pontoons issued 6% bonds on january 1, 2016, with a face amount of $600,000, the market yield for bonds of similar risk and maturity was 7%. the bonds mature december 31, 2019 (4 years). interest is paid semiannually on june 30 and december 31?

Since slope, m, is defined as the rise/run; then m = 9/12 

simplify m = 3/4  

Answer:

The given data is

Pr(xi)=0.3*0.70

The expected value =0.90

Where as we calculated the probability=0.96

As 0.96>0.9

So he should pass the ball as probability is greater.

Final answer:

The volume of the ellipsoid x²+y²+9z²=64 is 1024π/3 cubic units.

Explanation:

To find the volume of the ellipsoid given by the equation x²+y²+9z²=64, we can use the formula for the volume of an ellipsoid, which is V = (4/3)πa×b×c, where a, b, and c are the semi-axes of the ellipsoid. In our case, the ellipsoid can be rewritten to show its semi-axes clearly by dividing the equation by 64, which gives us (x²/64) + (y²/64) + (z²/(64/9)) = 1, indicating that our semi-axes are a = b = 8 and c = 8/3. Plugging these values into our volume formula gives us V = (4/3)π×8×8×(8/3), which simplifies to V = 1024π/3 cubic units.

Answer:

10s

100s

Step-by-step explanation:

One of the 6s are in the 10th digit position

the other one is in the 100th digit position

No. We can use the pythagorean theorem to prove this.The equation being a2 + b2 = c2. We then use two of  the least of the three numbers, which are 4 and 5, to substitute for “a” and “b”. We get a value for “c” which is 6.4, rounded off to the nearest tenth. This value is greater than 6. Note that this is a very logical way of solving the problem since a greater number for “a” and “b” would lead a greater value for “c”

Answer: The z-score of the value 9 rounded to the nearest tenth = 1.4

Step-by-step explanation:

Given: Mean [tex]\mu=8[/tex]

Standard deviation [tex]\sigma=0.7[/tex]

The given random value x= 9

Now, the formula to calculate the z score is given by:-

[tex]z=\dfrac{x-\mu}{\sigma}\\\\\Rightarrow\ z=\dfrac{9-8}{0.7}\\\\\Rightarrow\ z=1.42857142857\approx1.4[/tex]

Hence, the z-score of the value 9 rounded to the nearest tenth = 1.4

64 fewer cheeseburgers were sold than hamburgers. The total number of hamburgers sold on Friday was 250.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that,

Total number of hamburgers and cheeseburgers sold on Friday: 436.

The number of cheeseburgers sold was 64 fewer than the number of hamburgers.

The objective is to find the number of hamburgers sold on Friday.

To find out how many hamburgers were sold on Friday,

Set up a system of equations.

Let's denote the number of hamburgers as 'H' and the number of cheeseburgers as 'C'.

From the given information,

The total number of hamburgers and cheeseburgers sold is 436,

So write the equation,

H + C = 436.

Since there were 64 fewer cheeseburgers sold than hamburgers,

Which can be written as C = H - 64.

Now substitute the second equation into the first equation and solve for H:

H + (H - 64) = 436

Combine like terms,

2H - 64 = 436

Add 64 to both sides,

2H = 500.

Divide both sides by 2,

H = 250.

Hence,

250 hamburgers were sold on Friday.

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Answer:

B-60

Step-by-step explanation:

The  area of the trapezoid is 60 square units

The formula for finding the area of a trapezoid is expressed as:

A = 0.5(a+b)h

Given the following parameters

a = AD = √4² + 6²

AD = √16+36
AD = √52

For the length of BC
a = AD = √6² +10²

AD = √36+100
AD = √136
Calculate the height of the trapezium (10, 6) and (8, 12)

H = √6² +2²

H =  √40

Substitute

A = 1/2(7.21+11.66)*6.33

A = 60 square units

Hence the  area of the trapezoid is 60 square units

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Answer:

Quotient of 22x²y²÷11x²y² is:

2

Step-by-step explanation:

If a number p is divided by b then,

if p could be written as p=qb+r then q is the quotient and r is the remainder

Here, p=22x²y²

and b=11x²y²

22x²y²= 2(11x²y²)+0

⇒ q=2 and r=0

⇒ quotient=2

Hence, quotient of 22x²y²÷11x²y² is:

2

Answer:

It is 4.

Step-by-step explanation:

It said so in my classes.

To find the 95% confidence interval for the average number of words typed, use the formula: sample mean ± (critical value) * (standard deviation / square root of sample size).

To find the 95% confidence interval for the average number of words typed by all graduates of the secretarial school, we can use the formula:

Confidence Interval = sample mean ± (critical value) * (standard deviation / square root of sample size)

Plugging in the given values, we have:

Confidence Interval = 79.3 ± (1.96) * (7.8 / √12)

Simplifying, the 95% confidence interval is approximately 75.6 to 83.0 words per minute.

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Answer: The correct option is A., i.e, Slope of Function B = 2 x Slope of Function A.

Explanation:

The given function is,

[tex]f(x)=x-9[/tex]

It can be written as,

[tex]y=x-9[/tex]

It is the slope intercept form like y=mx+c, where m is the slope. On comparing the f(x) with the slope intercept form, we get the slope of f(x) is 1.

The graph of function g(x) passing through the point (-1,-3) and (2,3).

If a line passing through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the slope of line is,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{3-(-3)}{2-(-1)}=\frac{3+3}{2+1}= \frac{6}{3} =2[/tex]

The slope of g(x) is 2.

Since slope of f(x) is 1 and the slope of g(x) is 2, so we can say that the slope of function B is twice of slope of function A.

Slope of Function B = 2 x Slope of Function A

Therefore, the first option is correct.

The answer is A... yeet                                      

here is the solution.

 Round the answer as needed.

To estimate the sum of 503 and 69, one could round the numbers to the nearest tens or hundreds and then add the rounded numbers together. For example, rounding to the nearest tens would result in the equation 500 + 70 = 570.

The question asks for a method to write an equation that would allow them to estimate the sum of 503 and 69. This is more related to the concept of rounding numbers. We can estimate this sum by rounding these numbers to the nearest tens or hundreds, and then adding those rounded numbers together.

For example, if you round to the nearest tens, 503 can be rounded down to 500 and 69 can be rounded up to 70. Adding these rounded numbers together gives 500 + 70 = 570. Therefore, one possible equation could be: 500 + 70 = 570, which is a fairly close estimate of the original sum, 503 + 69.

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The equation of the parabola with the given dimensions and vertex at the origin is y = -4x^2.

Finding the Equation of a Parabola

To find the equation of a parabola with a vertex at the origin and given dimensions, we can use the standard form of a parabolic equation, which is y = ax^2. In this case, since the parabola opens downward and the vertex is at the origin (0,0), the equation will have the form y = -ax^2. The value of 'a' can be determined using the dimensions provided for the parabola, which are a width of 42 feet (meaning that the points (21,0) and (-21,0) are on the parabola) and a height of 84 feet (the y-coordinate at the vertex).

Since the point (21, 0) lies on the parabola, substituting it into the equation y=-ax^2 gives us 0 = -a(21)^2, which leads us to find that a = -84/(21)^2. Substituting the value of 'a' back into the equation gives us the final equation of the parabola: y = -84/(21)^2
x^2.

The equation of the parabola is: [tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex] .

To find the equation of the parabola with its vertex at the origin, we can use the standard form of a parabolic equation, which is [tex]\( y = ax^2 \).[/tex]

Given that the parabola opens downwards, we know that  a  must be negative. To determine the value of ( a ), we need to find a point on the parabola.

We're given the dimensions of the arch: 84 feet high and 42 feet wide at the base. Since the arch is symmetrical, the highest point is at the midpoint of the base, which is ( x = 0 ). At this point,( y = 84 ).

So, substituting the coordinates of this point into the equation, we get:

[tex]\[ 84 = a \times 0^2 \][/tex]

This simplifies to ( 84 = 0 ), which doesn't give us any useful information. Instead, we need to consider another point on the parabola.

Since the arch is symmetric, we can choose a point where ( x = 21 ) (half of the width of the base), and ( y = 0 ).

Substituting these coordinates into the equation, we get:

[tex]\[ 0 = a \times (21)^2 \][/tex]

0 = 441a

Dividing both sides by 441, we find ( a = 0 ). However, this seems incorrect, as it would mean the arch is just a straight line, which it isn't. This suggests that our choice of coordinates may not be correct.

Let's reconsider. The midpoint of the base is  x = 0, but the highest point might not be there. Instead, let's choose a point where ( x = 0 ) and ( y = 42 ), as this is the highest point of the arch.

Substituting these coordinates into the equation, we get:

[tex]\[ 42 = a \times 0^2 \][/tex]

42 = 0

This also doesn't give us useful information. It seems we might have approached this problem incorrectly. Let's try a different strategy.

Since we know the arch is a parabolic shape, and the parabola opens downwards, we can write its equation in the form:

[tex]\[ y = ax^2 + c \][/tex]

To find the values of  a  and  c , we need two points on the parabola. We already have one: the highest point of the arch, which is at  x = 0 and (y = 42 ).

Now, we need to find another point. Since the arch is symmetric, we can use any point along the base. Let's choose the point where x = 21 , which is half of the width of the base. At this point,  y = 0 .

Substituting these points into the equation, we get:

[tex]\[ 42 = a \times 0^2 + c \][/tex]

[tex]\[ 0 = a \times 21^2 + c \][/tex]

The first equation simplifies to ( c = 42 ).

Substituting this value of ( c ) into the second equation, we get:

[tex]\[ 0 = a \times 21^2 + 42 \][/tex]

Solving for  a :

[tex]\[ a \times 441 = -42 \][/tex]

[tex]\[ a = \frac{-42}{441} \][/tex]

[tex]\[ a = -\frac{2}{21} \][/tex]

So, the equation of the parabola is:

[tex]\[ y = -\frac{2}{21}x^2 + 42 \][/tex]

The fraction 2/100000 written in form of a decimal is 0.00002

Given the fraction 2/100000, we are to express this fraction as a decimal

The fraction can also be expressed as;

2/100000 = 2  * 1/00000

2/100000 = 2 * 0.00001

2/100000 = 0.00002

Hence the fraction 2/100000 written in form of a decimal is 0.00002

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