Need help ASAP!! Struggling with these word problems... D:
You invest in AAA-rated bonds, A-rated bonds, and B-rated bonds. The average yields are 4.5% on AAA bonds, 5% on A bonds, and 9% on B bonds. You invest twice as much in B bonds as in A bonds. Let x, y, and z represent the amounts invested in AAA, A, and B bonds, respectively.


x + y + z = (total investment)
0.045x + 0.05y + 0.09z = (annual return)
2y − z = 0
Use the inverse of the coefficient matrix of this system to find the amount invested in each type of bond for the given total investment and annual return. (Round your answers to the nearest cent.)
Total Investment Annual Return
$10,300 $620

Answer:

1 solution, x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

We can factor [tex]4x^2 - 4x + 1[/tex] first:

[tex](2x-1)(2x-1)[/tex]

= [tex](2x-1)^2[/tex]

To find the solution, we can do:

[tex]2x-1=0[/tex]

Let's find x now:

2x = 1

x = [tex]\frac{1}{2}[/tex]

Therefore, there is 1 solution and it is x = [tex]\frac{1}{2}[/tex]

54% of the students did not wear hats on the field trip.

What is percentage ?

Percentage is a way of expressing a quantity as a fraction of 100. It is often denoted by the symbol "%". For example, if you say that something has a percentage of 50%, it means that 50 out of every 100 parts of that thing belong to the quantity being measured.

According to given condition :

To find out what percentage of people did not wear hats, we first need to find out how many of the 50 students did not wear hats.

If 23 students wore hats, then the number of students who did not wear hats is:

50 - 23 = 27

So 27 students did not wear hats. To express this as a percentage, we divide the number of students who did not wear hats by the total number of students and then multiply by 100:

(27/50) x 100 = 54%

Therefore, 54% of the students did not wear hats on the field trip.

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In order for the expected value and standard deviation to be well-defined, we must have p > 0. If p = 0, then the geometric distribution is degenerate and always takes the value 0. If p = 1, then the geometric distribution is also degenerate and always takes the value 1.

To find the expected value and standard deviation of a geometric random variable, we first need to understand what a geometric random variable is.

A geometric random variable is a discrete random variable that represents the number of independent Bernoulli trials (i.e., trials that have only two possible outcomes) needed to obtain the first success. The probability of success on each trial is denoted by p, and the probability of failure (i.e., not obtaining a success) is denoted by q = 1 - p.

The expected value (also known as the mean) of a geometric random variable is given by E(X) = 1/p. This means that on average, we expect to perform 1/p independent Bernoulli trials before we obtain the first success.

To find the standard deviation of a geometric random variable, we use the formula:

SD(X) = [tex]\sqrt {[ (1 - p) / p^2 ][/tex]

This formula is derived using the variance formula, which is

Var(X) = [tex](1 - p) / p^2[/tex]. The standard deviation is then the square root of the variance.

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Counter example:

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Conclusion: the difference between two positive numbers can also be a negative number.

What is meant by negative numbers?

Given are given a set of difference of positive numbers.

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

The conclusion for this difference is given as the difference between two positive numbers is always positive.

We are asked to give a counter example.

Now a counterexample means an example that makes the given conclusion invalid.

So the counterexample of given example would be to prove the difference between positive numbers can also be a negative number.

For example,

3 - 7 = -4

5 - 8 = -3

8 -9 = -1

Therefore using the same numbers but subtracting the larger numbers from smaller number, we proved that the difference between positive numbers can also be a negative number.

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The number 41 is a prime number because it can be divided only by the number one and itself to yield remainder zero.

A prime number is defined as the number which is an integer, greater than one and has the ability to divide only by one and the number itself. The division here indicates that remainder should be zero.

Now, we see that 41 is an integer and it is greater than one. Additionally, it can not be divided by other numbers expect one and itself. These reasons make 41 a prime number.

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According to the Centers for Disease Control and Prevention (CDC) growth charts, the average height for a 14-year-old guy in the United States is about 5 feet, 5 inches (165 cm). Some 14-year-old guys may be taller or shorter than the average.

Height is a measure of the distance between the base of an object and its highest point. Human height is commonly described as the vertical distance between the bottom of the feet and the top of the head. Height is generally measured in centimetres or feet and inches. Height is an important physical feature that can be influenced by both inherited and environmental factors such as nutrition and physical activity.

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The surface area of a square base pyramid is 696.96 cm².

The surface area of the cone is 353.43 mm².

The surface area of a square base pyramid is calculated by applying the following formula as shown below;

SA = 2bs + b²

where;

let the half of the base = x

Apply Pythagoras theorem to determine the value of x using the given heights of the right triangles

x = √ ( 17² - 15.4² )

x = 7.2 cm

The base of the pyramid = 2x = 2 (7.2 cm ) = 14.4 cm

SA = 2 x 14.4 x 17  +  ( 14.4)²

SA = 696.96 cm²

The surface area of the cone is calculated as follows;

SA = πrs + πr²

where;

The slant height of the cone is calculated as follows;

s = √ (4.5²  +  20² )

s = 20.5 mm

SA = π x 4.5 x 20.5   +   π(4.5²)

SA = 353.43 mm²

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Multiply each row of the first matrices of 3 x 3 order by the column of another matrix of 3 x 3 order, then add the result.

Therefore, to multiply  3 x 3 order matrices multiply each row of first matrix with each column of the second matrix.

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Answer: 20

Step-by-step explanation:

a + b = 60.

a - 6 = 5b - 30 or a = 5b - 24

a = 60 - b

60 - b = 5 b - 24

84 = 6b

b = 14

a = 46

Mother is 46 and daughter is 14 now. After 6 years, daughter will be 20.

Hope this helped you, And if possible, could I have brainliest?

I also answered first! :D (Please don't copy what I said for the people that are going to answer this question, thank you!) :D

The magnitude and direction of the vector is 7.3 units and 15.9° north of east respectively.

option B.

To find the magnitude and direction of MN, we can use the distance formula and trigonometry.

The distance formula is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Using the coordinates of M(-3,-2) and N(4,0), we get:

d = √((4 - (-3))² + (0 - (-2))²)

d = √(49 + 4)

d = √(53)

d ≈ 7.3 units

To find the direction, we can use trigonometry. We can first find the angle between the line and the positive x-axis using:

tan θ = (y₂ - y₁)/(x₂ - x₁)

tan θ = (0 - (-2))/(4 - (-3))

tan θ = 2/7

θ = arc tan (2/7) =  15.9°

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Answer:

A + B must lie between 90 and 450 degrees.

Explanation:

Since sin A and cos B are both negative, A and B must lie in the third quadrant or the fourth quadrant. In the third quadrant, sin A and cos B are both negative, while in the fourth quadrant, sin A is negative and cos B is positive.

Let's consider the case where A and B are both in the third quadrant. In this case, both A and B are between 180 and 270 degrees. Since A + B is the sum of two angles in this range, it follows that A + B must be between 360 and 450 degrees.

Now let's consider the case where A is in the fourth quadrant and B is in the third quadrant. In this case, A is between 270 and 360 degrees, while B is between 180 and 270 degrees. Since sin A is negative and cos B is positive, it follows that cos A and sin B are both negative. Using the identities sin(180 - x) = sin x and cos(180 - x) = -cos x, we can write:

sin A + cos B = sin(180 - (180 - A) - B) + cos(180 - (180 - A) - B)

= sin(180 - A) - cos(180 - B)

= -sin A - cos B

Therefore, A + B is the difference of two angles in the third quadrant, and it must be between 90 and 180 degrees.

Putting the two cases together, we see that A + B must lie between 90 and 450 degrees.

The required values are;

q = 09.2 and p = 0.4.

And P(X > 2) = 0.3

The possibility of an event in time is known as probability in mathematics. How frequently does the incidence occur over the course of a specific time period, in plain English?

Given:

A die labeled 1, 2. 3, and 4 is rolled.

The total probability is 1.

∑P (X = x) = 1>

Which is,

p + 0.3 + q + 0.1 = 1  

p + q = 0.6  {equation 1}

And E(X) = 2  {equation 2}

(1 x p) + (2 x 0.3) + (3 x q) + (4 x 0.1) = 2   {equation 3}

p + 0.6 + 3q + 0.4 = 2   {equation 4}

p + 3q = 1    {equation 5}.

Solving 3 and 5,

we get,

q = 09.2 and p = 0.4.

And P(X > 2) = 0.2 + 0.1 = 0.3.

Therefore, P(X > 2) = 0.3.

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The rectangular form of 6{(cos225°) +i(sin225°) }is -3√2-3i√2.The shape that complex numbers typically take is referred to as rectangle form: z = a + bi.

Polar notation depicts a complex number in terms of the lengths of the vector and the angular direction from the starting point. In rectangle notation, a complex number is represented by its vertical and horizontal dimensions. The system is referred to be rectangular because the angles made by the axes at the origin and the measurements at point p are both 90 degrees. As a result, the measurement results in a rectangle with sides Xp and Yp.

To determine  rectangular form, we obtain,

Let Z=6{(cos225°) +i(sin225°)}

Now, cos225°=-cos( 180°+45°)= -cos45°= -[tex]\frac{1}{√2}[/tex]

sin225°=-[tex]\frac{1}{√2}[/tex]

S0, 6{(cos225°) +i(sin225°)}= 6 ( -[tex]\frac{1}{√2}[/tex])+6i(-[tex]\frac{1}{√2}[/tex])=-3√2-3i√2.

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Answer:

A

Step-by-step explanation:

right on edge

The length of 75cm converting to inches is 29.53 inches.

The inch is a unit of length commonly used in the United States, the United Kingdom, and some other countries. It can be calculated by using the conversion factor of 1 inch being equal to 2.54 centimeters.

Understanding conversions between different units of measurement is crucial in various fields such as science, engineering, and mathematics. Therefore, to convert centimeters to inches, we need to divide the number of centimeters by 2.54.

In this case, 75 cm divided by 2.54 results in 29.53 inches.

The length of 75 cm is equivalent to approximately 29.53 inches.

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To find a point of inflection, take the second derivative of the function, set it equal to zero and solve for x, and verify the point by checking the sign of the second derivative on either side of the point.

Follow these steps to locate a point of inflection:

It is a point of inflection if the curve shifts from concave up to concave down at the point. It is also a point of inflection if it transitions from concave down to concave up.

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By knowing the conversion factors, we can easily and accurately convert measurements to any unit we desire. In this case, 300m is equal to 984.252 feet.

Measurement conversions are an important aspect of mathematical calculations. They help us convert units of measurement to another, making it easier to compare and understand quantities. In this case, we will look at how to convert 300m to feet.

To convert 300m to feet, we need to know the conversion factor between the two units of measurement. One meter is equal to 3.28084 feet. Therefore, to convert 300m to feet, we need to multiply 300 by the conversion factor.

300m * 3.28084 = 984.252 feet

Therefore, 300m is equivalent to 984.252 feet.

It's important to note that when converting between units of measurement, it's important to use the correct conversion factor to ensure accurate results. Additionally, being familiar with common conversion factors can save time and make calculations easier.

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250 grams is approximately equal to 0.5511 pounds  ( rounded to four decimal places )

The conversion factor to convert grams to pounds is 0.00220462

1 gram = 0.00220462 pounds

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

The mass in pounds = The mass in grams × conversion factor

Substitute the values in the equation

1 gram = 0.00220462 pounds

250 grams =  250 × 0.00220462

Multiply the numbers

= 0.5511 pounds  ( rounded to four decimal places )

Therefore, 250 grams is 0.5511 pounds

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The distance between points A and B is 11785.2 ft.

In mathematics, an algebraic expression is an expression built up from constant algebraic numbers, variables, and the algebraic operations.

Given is that the plane maintains a constant altitude of 6350 feet. Mei Mei initially measures an angle of elevation of 17° to the plane at point A. At some later time, she measures an angle of elevation of 36° to the plane at point B.

We can write -

tan (17°) = 6350/AC

tan (36°) = 6350/BC

Now, we can write -

AC = 6350/tan (17°)                                ... { 1 }

AC = 20483.9 ft

&

BC = 6350/tan (36°)                              ... { 2 }

BC = 8698.7 ft

We can write -

AB = AC - BC                                        ... { 3 }

AB =  20483.9 - 8698.7

AB = 11785.2 ft

Therefore, the distance between points A and B is 11785.2 ft.

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Answer:

10<=x <= 20

Step-by-step explanation:

Sorry but <= means less that or equal to.

The distance between the two points, we can use the trigonometric equation distance = altitude/tan(angle of depression). Using this equation, we can calculate the distance to be approximately  6,665.93 ft.

Pilot is at point A. The angles of depression to mileposts B and C are 32 degrees and 56 degrees, respectively. We are asked to find the distance between B and C.

Let AB = x, BC = y, and AD = CD = h = 25,000 ft.

tan(32°) = h/AB

tan(56°) = h/AC = h/(AB + BC)

We can use the first equation to solve for AB:

AB = h/tan(32°) = 25,000/tan(32°) ≈ 44,908.55 ft

We can use the second equation to solve for AC:

tan(56°) = h/(AB + BC)

tan(56°) = 25,000/(AB + BC)

AB + BC = 25,000/tan(56°)

BC = 25,000/tan(56°) - AB ≈ 38,242.62 ft

Therefore, the distance between the two mileposts is:

BC ≈ 38,242.62 - 44,908.55 ≈ 6,665.93 ft

So the distance between the two mileposts is approximately 6,665.93 ft.

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187 centimeter is approximately equal to 6.1351 feet

To convert 185cm to feet, we can use the following formula:

1 cm = 0.0328 feet

The conversion is the process of changing the unit of one quantity to another units  

The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing

Therefore,

The distance in feet = conversion factor × The distance in centimeter

Substitute the values in the equation

187 cm = 187 x 0.0328

Multiply the numbers

= 6.1351 feet ( rounded to four decimal places )

Therefore, 187 cm is 6.13517 feet.

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Answer:

3906250

Step-by-step explanation:

They are multiplying each one by 5 to get the next number in the sequence so we just have to do it for each one until we get to the 10th sequence

1) 10 =

10

2) 10 x 5 =

50

3) 50 x 5=

250

4) 250 x 5=

1250

5) 1250 x 5=

6250

6) 6250 x 5=

31250

7) 31250 x 5=

156250

8) 156250 x 5=

781250

9) 781250 x 5=

3906250

10) 3906250

The solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

An equation is a mathematical statement that shows that two expressions are equal. It is usually written as an expression on the left-hand side (LHS) and an expression on the right-hand side (RHS) separated by an equal sign (=).

The expressions on both sides of the equation can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. The variables in an equation represent unknown values that can vary, while the constants are fixed values that do not change.

Equations are used to represent mathematical relationships or describe real-world situations. They can be used to solve problems, make predictions, and test hypotheses.

To solve an equation, one must find the value of the variable that makes the LHS equal to the RHS. This is done by performing mathematical operations on both sides of the equation to isolate the variable. The goal is to get the variable by itself on one side of the equation, with a specific value on the other side.

Equations can be simple or complex, linear or nonlinear, and can involve one or more variables. Examples of equations include:

2x + 5 = 13

y = 3x^2 - 2x + 7

4a + 2b - 3c = 10

Equations are used in many areas of mathematics and science, including physics, chemistry, and engineering, among others.

Substitute the value of y in the second equation with the expression for y from the first equation:

2x + 3(4x-22) = 4

Simplify and solve for x:

2x + 12x - 66 = 4

14x = 70

x = 5

Substitute the value of x in the first equation to solve for y:

y = 4(5) - 22

y = -2

Therefore, the solution to the system of equations is x = 5 and y = -2, or (5,-2) in coordinate form.

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The converted value in the standard form using grams to pounds representing the mass is given by 400 grams = (0.881849 ) pounds.

Standard form  to relates these two given quantities of mass grams and pounds is equal to  :

One gram is equivalent 0.00220462 pounds.

Now, substitutes the standard relation between the grams and the pounds to calculate the required value,

1 gram = 0.00220462 pounds

⇒ 400 grams = ( 400 ) × ( 0.00220462 ) pounds

⇒ 400 grams = ( 0.881849 ) pounds

Therefore, the converted value of 400 grams into the pounds as per standard norms is written as  ( 0.881849 ) pounds.

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Answer:

a = √c² - b²

Step-by-step explanation:

The process...

Shae's monthly payment will be approximately $114.63.

First we can use the formula for the present value of an annuity:

P = (r * A) / (1 - (1 + r)^(-n))

where

First, we need to convert the annual percentage rate (APR) to a monthly rate, which is done by dividing it by 12:

r = 13.5% / 12 = 0.01125

Next, we can plug in the values and solve for A:

2400 = (0.01125 * A) / (1 - (1 + 0.01125)^(-24))

Simplifying this equation, we get:

A = (0.01125 * 2400) / (1 - (1 + 0.01125)^(-24)) = 114.63

Therefore, Shae's monthly payment will be approximately $114.63.

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Dallas and San Antonio, Texas are separated by approximately 240 miles (386 kilometres) by road. The predicted journey time is around 4 hours, although this may vary based on traffic and other conditions.

Dallas is located in Texas, in the country's southern central area. It is the ninth-largest city in the United States and the third-largest in Texas in terms of population. Dallas is part of the Dallas-Fort Worth metropolitan area, which is one of the largest in the United States. Dallas, in North Texas, is surrounded by a variety of suburban towns. Dallas and San Antonio are approximately 240 miles apart.

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Answer and Step-by-step explanation:

To graph the equation with a slope of -2 and a y-intercept of 6, we can use the slope-intercept form of the equation of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

Substituting in the given values, we get:

y = -2x + 6

To graph this line, we can start by plotting the y-intercept, which is the point (0, 6). Then, we can use the slope to find additional points on the line. The slope of -2 means that for every increase of 1 in the x-direction, the y-value decreases by 2. So, we can plot another point by starting at the y-intercept and moving down 2 units and to the right 1 unit. This gives us the point (1, 4). We can continue this pattern to plot more points and draw the line.

Here's what the graph looks like:

Step-by-step explanation:

We are given the slope -2 and the y intercept -6. So we can create a linear equation using this data:

[tex]y=-2x+6[/tex]

Now all we have to do is graph it.

(graph below)