A bond with a face value of $5,000 has a current yield of 7% and a coupon rate of 8%, what is the bonds yield?

Answer:

8 sec^2 x + 4 tan^2 x − 12 = 0     →     sec^2x = tan^2x + 1

8 [ tan^2x + 1] + 4tan^2x - 12  = 0

8tan^2x + 8 + 4tan^2x - 12  = 0

12tan^2x - 4   = 0     divide through by 4

3tan^2x - 1  = 0

3tan^2x  =  1  

tan^2x  = 1/3      take the square root of both sides

tanx = ±1 / √

The value of the function is -9

Functions are simply defined as mathematical expressions, rules, laws o theorem that compares or explains the relationship between two variables.

These variables are known as;

Based on the information given, we have that;

To determine the value of the function,  (f +g)(-3), we have to add the functions for both f(x) and g(x)

We have;

(f +g)(x) = 2x - 1 + (-4x -2)

expand the bracket

(f +g)(x) = 2x - 1 - 4x - 2

Now, substitute the value of x as -3, we have;

(f +g)(-3) = 2(-3) - 1 - 4(-3) - 2

expand the bracket

(f +g)(-3) = -6 -1 + 12 - 2

Add or subtract the values

(f +g)(-3) = -9

Hence, the value is -9

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Answer:

A

Step-by-step explanation:

The multiplicative inverse property states that any number multiplied by its multiplicative inverse (also called reciprocal) results in 1.

the area of the pie that Carol will bake will be equal to 249.51 inches².

We are given the circumference of the pie as = 56 inches.

As pie is in the shape of a circle, we will use the formula for circumference to find the radius of the circle.

2 π r = 56 inches

2 × 22 / 7 × r = 56

r = 56 × 7 / ( 22 × 2)

r = 8.91 inches.

Area of circle is given by:

π r²

Substituting the values in the formula, we get that

A = 22 / 7 (8.91)²

A = 249.51 inches²

Therefore, we get that, the area of the pie that Carol will bake will be equal to 249.51 inches².

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Answer:

Varies

Step-by-step explanation:

If bill were to put 4 bananas and only 1 apple there would be more banana's then apples, but if he put more apples then bananas then it would be the greater then bananas

If the cafeteria ordered 400 paper plates. They used 226 at breakfast. They bought 100 more. Then, they used some plates for lunch. Now there are 78 plates. The number of  plates that was used at lunch is 196.

Given :

Paper plates ordered = 400 plates

Plates used for breakfast = 226

Additional plate bought = 100

Plate used for lunch = ?

Hence,

Let calculate the plate left after breakfast

Number of plates = Paper plates ordered - Plates used for breakfast

Number of plates = 400 plates - 226 plates

Number of plates = 174 plates

Now let determine the plates that were used for lunch

Pates used for lunch :

Pates used for lunch = (174 + 100) -78

Pates used for lunch = 274 -78

Pates used for lunch = 196 plates

Therefore we can conclude that the number of  plates that was used at lunch is 196 plates .

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After evaluating the limit we have came to find that the limit of      [tex]\lim_{x\rightarrow \Pi }cos(x)[/tex] as x approaches π is –1

As an input or as an index approaches a specific value in mathematics, a limit is the value that the function, sequence, or index approaches. The definitions of continuity, derivatives, and integrals all require limits, which are fundamental to calculus and mathematical analysis.

In addition to having a connection to the category theory concepts of limit and direct limit, the idea of a limit of a sequence is further generalized to include the idea of a limit of a topological network.

A limit of a function is typically expressed in formulas as

[tex]{\displaystyle \lim _{x\to c}f(x)=L,}[/tex]

To find the limit

⇒ [tex]\lim_{x\rightarrow \Pi }cos(x)[/tex]

Evalúe π as x

= cos (π)

= cos 180°

= cos(180° – 0°)

= – cos 0°

= – (1)

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A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. The square number will be [tex]\frac{625}{28561}[/tex].

A square is a common polygon with four equal sides and angles that are each 90 degrees in length.

A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width.

Many objects can be found in your surroundings that have a square shape. The chessboard, craft sheets, bread slice, picture frame, pizza box, wall clock, etc. are typical instances of this shape.

Specifications of a Square

[tex](\frac{25}{169})^{2} = \frac{625}{28561}[/tex]

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Answer:

(√25/69)^2

Step-by-step expla$nation:

You might see this as cheating but technically it is the correct answer :)

Hope this helps ^^

btw is this RSM?

The volume of the solution  A that we require in the fusion reaction is 3.9x10^-7 L

The term fusion has to do with a kind of nuclear reaction in which there is the combination of two light nuclei to have a heavier nucleus. This is the kind of process by which energy is produced in the sun.

Given that;

If we conduct fusion of hydrogen in 1 liter of solution A, the energy that i obtained is 7.6x10^10 J. Then the energy that any one of the homes could use is  3x10^4 J.

Let x be the volume of the solution A that we need. It the follows that;

x * 7.6x10^10 J = 3x10^4 J

x =  3.9x10^-7 L

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Missing parts;

if you could generate energy by fusing the hydrogen in solution a, how much of the solution would you need to generate the electrical energy used daily in a certain home? energy released by fusion of hydrogen in 1 liter of solution A = 7.6*10^10 Electrical energy used daily in a certain family home = 3*10^4

The cost of 3 pounds =$2.40

For the cost of 1 pound, divide the cost of three pounds noodles with 3.

The student is not correct ,

The cost of unit pound is $0.8

Simple interest typically favors consumers who pay their bills or loans on time or early each month because it is frequently calculated on a daily basis. The loan's simple interest rate is 4.5%.

Simple interest typically favors consumers who pay their bills or loans on time or early each month because it is frequently calculated on a daily basis.

In the aforementioned student loan example, if you paid a $300 payment on May 1st, $238.36 would be applied to the principle. On April 20, if you made the same payment, $258.91 would be applied to the principal. Your main balance will decrease more quickly and the loan will be paid off faster than anticipated if you can make an early payment every month.

On the other hand, if you pay the loan back late, you pay more in interest than if you pay it on time. If your payment is due on May 1 and you make it on May 16 (using the same car loan example), you will be charged interest for 45 days at a cost of $92.46. Consequently, only $207.54 of your $300 payment is applied to the principal. If you frequently make late payments over the course of a loan, your final payment will be more than anticipated because the principal did not decrease at the anticipated rate.

Principal amount,

P=$5000

Future value,

A=$5900

Time,

t=4years

Let us determine the loan's simple interest rate:

A=P(1+rt)

5900=5000(1+r*4)

5900=5000(1+4r)

5900=5000*1+5000*4r

5900=5000+20000r

5900−5000=20000r

900=20000r

20000r=900

r=900/20000

r=9/200

r=0.045

r=0.045/100%

r=4.5%

Therefore, the loan's simple interest rate is 4.5%.

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The angle x in the parallel line is 123 degrees.

In the diagram, l₁ and l₂ are parallel.

l₃ and l₄ are perpendicular to each other.

Since l₁ and l₂ are parallel lines, the line l₃ is a transversal that cut across the parallel lines.

Angle relationship are formed such as corresponding angles, alternate angles, vertically opposite angle etc.

Therefore,

57 + x  = 180°

x = 180 - 57

Therefore,

x = 123 degrees.

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ANSWER:

The probability is 0.018

STEP-BY-STEP EXPLANATION:

That 5% are defective means that 5 out of 100 tires are defective.

If 5 tires are selected, the probability that they are exactly defective is calculated as follows

Now, resolving

replacing:

Point C represents √11 on number line

A number line is a visual depiction of numbers on a straight line in mathematics. A number line's numerals are arranged in a sequential manner at equal intervals along its length. It is often displayed horizontally and can extend indefinitely in any direction. A number line is exactly what it sounds like—a horizontal, straight line with numbers spaced evenly apart throughout its length. Since it's not a ruler, the distance between each number is irrelevant; instead, the numbers on the line specify how it should be used.

Given Data

Number:

√11

√11 = 3.31

Point C represents √11 on number line.

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Answer:

X = 1/5

Step-by-step explanation:

16 - 10X = 14

10X = 2

X = 0.2

Answer

x=0.2

-16+10x=-14

10x=-14+16

10x=2

10x÷10=2÷10

x=0.2

The answer is 0.00650508866

Answer:

Here is the answer: sin(3π/2) = -1

So 3π/2 is the correct choice.

Answer:

327 x 564

1648+2092+1685

190068

Step-by-step explanation:

im pretty sure that this is right. and the bold letter are the missing ones

It is known that:

Therefore, 40 quarts in gallons is:

So to fill 40 quart bottles, atleast 10 gallons of oil will be needed.

Hence the tank of 12 gallons should be used since it has more than 10 gallons of oil.

The two gallon one does not have enough oil.

Option B that means the second option is correct.

"The 2 gallon tank is not enough ,but the 12 gallon tank is enough".

Answer: [tex]y=-((x-2)/\sqrt{2} )^{2} +4[/tex]

Step-by-step explanation:

This equation has it's parabola starting at (2,4)

So, we know that our equation will include (x-2) and +4

Next, we see the parabola is upside down, so we need a -

Next, we see the equation is wider than normal, so we need to divide x by something.

at x = -2, a normal graph would go through (0,0) , but this one goes through  (0,2)

at x = -2, [tex]2^{2} =4[/tex]

but we see at x = -2, [tex]x^{2} =2[/tex]

[tex]x=\sqrt{2}[/tex]

a) 10.7

b) ΔABE~ΔACD | Angle Angle Similarity

1) Analyzing that triangle, and considering they are similar we can write out the following to find x

a) If they are similar their corresponding sides are proportional, therefore we can write a pair of ratios.

The smallest hypotenuse over the largest hypotenuse as well as there is a proportionality between those two corresponding legs 8 and 18.

b) In the last statement of that proof table, we can tell that the last line is well written as:

ΔABE~ΔACD | Angle Angle Similarity

The Angle Angle Similarity states that:

Note that in that table there are two instances in which there is a reference to two congruent angles.

1) In this problem, we need to isolate the variables on the left side.

Notice that in two steps we can solve the problem.

2) Thus the answer is

Answer: 3*3*3*3*3*3

Step-by-step explanation:

The value of 9³ = 3ˣ and x = 6

9³ = 3 x 3 x 3 x 3 x 3 x 3

9³ = 3⁶

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number be A

The number A = 9³

The value of A = 729

Now , the number 9³ can be expressed as the power of 3

So , the equation will be

9³ = ( 3² )³

    = 3³ˣ²

    = 3⁶

    = 729

Therefore , the value of 9³ = 3⁶

Hence , The value of 9³ = 3ˣ and x = 6

9³ = 3 x 3 x 3 x 3 x 3 x 3

9³ = 3⁶

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The x and y intercepts of the given graph of the function are 3/2 and -1 respectively.

Intercepts of the line

The point where the line or curve crosses the axis of the graph is called intercept. If a point crosses the x-axis, then it is called the x-intercept. If a point crosses the y-axis, then it is called the y-intercept.

Given equation of the line:

y = (2/3)x - 1

To find the y -intercept, putting x = 0, we get,

y = (2/3)*0 - 1

y = 0 - 1

y = -1

Hence, the y - intercept is -1.

To find the x -intercept, putting y = 0, we get,

0 = (2/3)x - 1

1 = (2/3)x

x = 3/2

Hence, the x - intercept is 3/2.

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Answer:

|AC| = 132 cm  (nearest centimetre)

Step-by-step explanation:

Pythagoras Theorem

Pythagoras Theorem explains the relationship between the three sides of a right triangle. The formula is:

[tex]\large\boxed{c^2=a^2+b^2}[/tex]

where:

From inspection of the given right triangle:

Substitute the given values into the formula and solve for AC:

[tex]\begin{aligned}c^2 & = a^2+b^2 &\\\\\implies AC^2&=AB^2+BC^2\\ AC^2&=45^2+124^2\\ AC^2&=2025+15376 \\ AC^2&=17401\\\sqrt{ AC^2}&=\sqrt{ 17401}\\ AC&=131.91285\\AC&=132\; \sf cm \; (nearest\;centimetre)\end{aligned}[/tex]

Therefore, |AC| is 132 cm to the nearest centimetre.

Answer:

y = ± 13

Step-by-step explanation:

If y² = 169 then y = √169

√169 is either +13 or -13

This is usually written using the plus/minus sign

√169 = ± 13

The result of the addition of complex numbers 3+i and 2 - 3i will be 5-2i as the rule says "to add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts.".

Every complex number can be expressed in the form a + bi, where a and b are real numbers. A complex number is an element of a number system that extends the real numbers with a specific element denoted I also known as the imaginary unit, and satisfying the equation i² = -1.

The complex plane in mathematics is the plane made up of complex numbers, with real and imaginary numbers making up the x-axis (also known as the real axis) and the y-axis (also known as the imaginary axis) of the Cartesian coordinate system.

Here,

To add the complex numbers,

To add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts.

(3+i)+(2-3i)=5-2i

According to the rule, "to add or subtract two complex numbers, just add or subtract the corresponding real and imaginary parts," the sum of the complex numbers 3+i and 2 - 3i will be 5-2i.

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