An investment firm recommends that a client invest in bonds rated AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 6%, and on B bonds 11%. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond under the following conditions?
A. The total investment is $26,000, and the investor wants an annual return of $1,620 on the three investments.
B. The values in part A are changed to $38,000 and $2,360, respectively
A. The client should invest $(?) in AAA bonds, $(?)in A bonds, and $(?)in B bonds.

Answers

Answer 1

Part A.

1) Variables:

X: amount invested in AAA bonds

Y: amount invested in A bonds

Z: amount invested in B bonds.

2) Return:

4%* X + 6% * Y + 11% * Z = 1620

3) Investment:

X + Y + Z = 26,000

4) Ratio between AAA and B bonds.

X = 2*Z

5) Solution of the system of equations:

Replace X with 2Z in the two first equations:

2Z * 4% + Y * 6% + Z * 11% = 1620

=> 0.08Z + 0.06Y + 0.11Z = 1620

=> 0.19Z + 0.06Y = 1620

2Z + Y + Z = 26,000

=> 3Z + Y = 26,000 => Y = 26,000 - 3Z

Replace Y with 26,000 - 3Z

0.19Z + 0.06(26,000 - 3Z) = 1620

0.19Z + 1560 - 0.18Z = 1620

0.01Z = 1620 - 1560

0.01Z = 60

Z = 60 / 0.01 = 6000

=> X = 2*6000 = 12,000

=> Y = 26,000 - 12,000 - 6,000 = 8,000

Answer: 12,000 in bonds AAA, 8,000 in bonds A, and 6000 in bonds B.

Part B.

2) Return:

0.04X + 0.06 Y + 0.11Z = 2360

3) Investment:

X + Y + Z = 38,000

4) Ratio between AAA and B bonds.

X = 2Z

5) Solution of the system of equations:

Replace X with 2Z in the two first equations:

=> 0.08Z + 0.06Y + 0.11Z = 2360

=> 0.19Z + 0.06Y = 2360

2Z + Y + Z = 38,000

=> 3Z + Y = 38,000 => Y = 38,000 - 3Z

Replace Y with 38,000 - 3Z

0.19Z + 0.06(38,000 - 3Z) = 2360

0.19Z + 2280 - 0.18Z = 2360

0.01Z = 2360 - 2280

0.01Z = 80

Z = 80 / 0.01 = 8000

=> X = 2*8000 = 16,000

=> Y = 38,000 - 16,000 - 8000 = 14,000

Answer: 16,000 in AAA bonds, 14,000 in A bonds, and 8,000 in B bonds.

Related Questions

Find the volume v of the described solid s. the base of s is an elliptical region with boundary curve 16x^22 + 9y^2 = 144. cross-sections perpendicular to the x-axis are isosceles right triangles with hypotenuse in the base.

Answers

Where are your answer choices

A surveyor took the following measurements from two irregularly shaped pieces of land. Some of the lengths and angle measures are missing. Find all missing lengths and angle measures. Round lengths to the nearest tenth and angle measures to the nearest minute

Answers

Part A:

To find angle D, we make use of the rule of Sines because we know the measure of the side opposite angle D and we also know the meansure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle D as follows:

[tex] \frac{62}{\sin{D}} = \frac{51}{\sin{53^o}} \\ \\ \Rightarrow \sin{D}= \frac{62\sin{53^o}}{51}} \\ \\ = \frac{49.5154}{51} =0.9709 \\ \\ \Rightarrow D=\sin^{-1}{0.9709} \\ \\ =76.14^o=76^o8'[/tex]

Therefore, angle D is 76°8'

Part B:

To find angle E, recall that the sum of the angles in a triangle is 180°.

Thus, 53° + 76°8' + E = 180°

E = 180° - 53° - 76°8' = 50°52'

Therefore, angle E is 50°52'

Part C:

To find the measure of side e, we apply the cosine rule as follows:

[tex]e^2=51^2+62^2-2(51)(62)\cos{50^o52'} \\ \\ =2,601+3,844-2,098.85=3,991.25 \\ \\ \Rightarrow e=\sqrt{3,991.25}=63.18[/tex]

Therefore, the measure of side e is 63.2

Part D

To find angle G, we make use of the rule of Sines because we know the measure of the side opposite angle G and we also know the measure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle G as follows:

[tex]\frac{80}{\sin{G}} = \frac{62}{\sin{49^o}} \\ \\ \Rightarrow \sin{G}= \frac{80\sin{49^o}}{62} \\ \\ = \frac{60.3768}{62} =0.9738 \\ \\ \Rightarrow G =\sin^{-1}{0.9738}=76.86^o=76^o52'[/tex]

Therefore, angle G is 76°52'

Part E:

To find angle H, recall that the sum of the angles in a triangle is 180°.

Thus, 49° + 76°52' + H = 180°

H = 180° - 49° - 76°52' = 54°14'

Therefore, angle H is 54°14'

Part F:

To find the measure of side a, we apply the cosine rule as follows:

[tex]a^2=80^2+62^2-2(80)(62)\cos{54^o14'} \\ \\ =6,400+3,844-5,798.10=4,445.90 \\ \\ \Rightarrow a=\sqrt{4,445.90}=66.68[/tex]

Therefore, the measure of side a is 66.7

Part G:

To find angle A, we make use of the rule of Sines because we know the measure of the side opposite angle A and we also know the measure another angle of the triangle with the measure of the side opposite the angle.

Thus, we find angle A as follows:

[tex]\frac{66.7}{\sin{A}} = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow \sin{A}= \frac{66.7\sin{25^o54'}}{30} \\ \\ = \frac{29.1347}{30} =0.9712 \\ \\ \Rightarrow A =\sin^{-1}{0.9712}=76.21^o=76^o12'[/tex]

Therefore, angle A is 76°12'

Part H:

To find angle B, recall that the sum of the angles in a triangle is 180°.

Thus, 25°54' + 76°12' + B = 180°

B = 180° - 25°54' - 76°12' = 77°53'

Therefore, angle B is 77°53'

Part I:

To find the measure of side b, we make use of the rule of sines

Thus, we find side b as follows:

[tex]\frac{b}{\sin{77^o53'}} = \frac{30}{\sin{25^o54'}} \\ \\ \Rightarrow b= \frac{30\sin{77^o53'}}{\sin{25^o54'}} \\ \\ = \frac{29.3317}{0.4368} =67.15[/tex]

Therefore, the measure of side b is 67.2

Final answer:

To find the width of the river, use trigonometry and the tangent function. The width of the river is approximately 67.1 meters.

Explanation:

To find the width of the river, we can use trigonometry. The surveyor measured an angle of 35° from the baseline to the tree on the opposite bank. We know the distance along the river is 100 m. Let's denote the width of the river as 'x'.

We can use the tangent function to solve for 'x'. The tangent of the angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is 'x' (the width of the river) and the adjacent side is 100 m (the distance along the river).

So, the equation becomes:

tan(35°) = x/100

To find the value of 'x', we can multiply both sides by 100:

x = 100 * tan(35°)

Using a calculator, we can find that x is approximately 67.1 m. Therefore, the width of the river is approximately 67.1 meters.

Name the triangle with the following characteristics. Sides: 5 cm, 5 cm, 7 cm.
A. scalene triangle B. acute triangle C. isosceles triangle D. right triangle

HELP ASAP

Answers

i belive it might be a right triangle

Isosceles triangle since two sides are equal

Cell phones can weigh as little as 2 ounces. How many pounds can the cell phone weigh?

Answers

16 ounces in a pound.

2/16= .125

.125 pounds

Final answer:

A cell phone weighing 2 ounces translates to 0.125 pounds, since there are 16 ounces in one pound.

Explanation:

Cell phones can weigh as little as 2 ounces. The first step in determining how much a cell phone can weigh in pounds is to know the conversion factor between ounces and pounds. Since there are 16 ounces in one pound, you can divide the weight of the cell phone in ounces by 16 to convert it to pounds. For a cell phone that weighs 2 ounces:

Divide the weight in ounces by 16 to convert to pounds: 2 ounces ÷ 16 = 0.125 pounds.

Therefore, a cell phone that weighs 2 ounces is equivalent to 0.125 pounds.

The Fenton College Cougars made 40 field goals in a recent basketball game some 2 pointers and the rest 3 pointers. Altogether the 40 baskets counted for 89 points. how many of each type of field goal was made?

Answers

x = 2 pointers, y = 3 pointers

x + y = 40.....x = 40 - y
2x + 3y = 89

2(40 - y) + 3y = 89
80 - 2y + 3y = 89
-2y + 3y = 89 - 80
y = 9 <=== there were 9 three-point shots

x = 40 - y
x = 40 - 9
x = 31 <=== there were 31 two-point shots

write in logarithmic form
6^2=36

Answers

log 6 (36)=2
The 6 is gonna be on the bottom of the g.

Final answer:

The conversion of the expression 6^2=36 into logarithmic form results in log6(36) = 2. This method involves identifying the base (6), the exponent (2), and the result (36) in the original exponential equation.

Explanation:

In mathematics, you can interchange between an exponential form and a logarithmic form. Your given expression is 6^2=36, which is in exponential form.

To change this into logarithmic form, identify the base (which is 6 in this case), the exponent (which is 2), and the result (which is 36). The logarithmic form of the equation would then be 'log base 6 of 36 is 2'.

So, written in the usual mathematical notation, your answer would be log6(36) = 2. Here, 'log' stands for logarithm; the number following 'log' (6 in this case) is the base, the term within parentheses (36 in this case) is the number we're taking log of, and '2' is the value of the logarithm.

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which is another way to write this number? (3 x 1,000) + (3 x 10) (3 x 1/100) + (3 x 1/1000)

Answers

Final answer:

The equivalent expression to (3 x 1,000) + (3 x 10) + (3 x 1/100) + (3 x 1/1000) is 3030.033. This result doesn't require simplification through Exponential or Scientific notation since it's not an especially large or small value.

Explanation:

The student's question is asking for an alternative way to write the number produced by the mathematical operation: (3 x 1,000) + (3 x 10) + (3 x 1/100) + (3 x 1/1000). This is a combination of addition and multiplication involving decimal places. It can also be expressed in exponential notation:

First simplify and solve the individual operations: (3 x 1,000) = 3000, (3 x 10) = 30, (3 x 1/100) = 0.03, and (3 x 1/1000) = 0.003.Next, add your results: 3000 + 30 + 0.03 + 0.003 = 3030.033.

So, another way to write the stated combination of multiplication and addition operations is 3030.033. The Exponential notation might not be an ideal replacement in this specific case since the result is not a large or small number which normally requires this notation. Scientific notation, (which uses powers of ten to express larger or smaller numbers), could most effectively be implemented if our final result was a very large or very small number.

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Area of 100 3/4 feet x 75 1/2 feet?

Answers

100 3/4 x 75 1/2
25 x 3 x 75 1/2. (Divided by 4 to 100 and 4 to get 25)

25 x 3 x 75 1/2 ( multiple everything on top)

5625/2 ( then divided normally)

2812.5 or 2812 1/2

Choose the best answer. Which of the following is not a type of savings account? A.passbook account
B.statement account
C.club account
D.automatic account

Answers

Hello!

I believe the best answer to this question would be D. Club account, because there was something called "Christmas club account" during the Great Depression. Now, it's a savings program, so you could save that it's technically not a savings account.

I really hope this helped you! :)

Answer with explanation:

Saving Account →A savings account is a type of bank account in which you can keep extra money possessed by you in an institution, which is most safest place,The money you get as an interest is proportional to amount of money deposited in that institution.

A. Passbook Account : A Passbook Savings account is also a saving account,in which you get interest for your deposit and also get a passbook for easy record keeping.

B.Statement account : It is also a saving account,in which you get statement for your credit and debit in your account.

C. Club Account: In this type of Saving account, you deposit money for your future investment or for any future purpose by a group.You have to deposit and withdraw money within a certain time frame.

D. Automatic account: In this type of account , money is transferred to it's customers automatically in their accounts by a certain process. It is not a saving Account.

Option 4→: Automatic Account : is the type of account which is not a saving Account.

w varies jointly as x and y and inversely as the square of z. If w=280 when x=30, y=12, and z=3, find w when x=20, y=10 and z=2

Answers

[tex]\bf \qquad \qquad \textit{double proportional variation}\\\\ \begin{array}{llll} \textit{\underline{y} varies directly with \underline{x}}\\ \textit{and inversely with \underline{z}} \end{array}\implies y=\cfrac{kx}{z}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------[/tex]

[tex]\bf \begin{array}{llll} \textit{"\underline{w} varies jointly as \underline{x} and \underline{y}}\\ \textit{and inversely as the square of \underline{z}"} \end{array}\implies w=\cfrac{kxy}{z^2} \\\\\\ \textit{we also know that } \begin{cases} w=280\\ x=30\\ y=12\\ z=3 \end{cases}\implies 280=\cfrac{k(30)(12)}{3^2}[/tex]

[tex]\bf 280=\cfrac{360k}{9}\implies \cfrac{280\cdot 9}{360}=k\implies 7=k \\\\\\ therefore\qquad \boxed{w=\cfrac{7xy}{z^2}} \\\\\\ if~ \begin{cases} x=20\\ y=10\\ z=2 \end{cases}~\textit{what is \underline{w}?}\qquad w=\cfrac{7(20)(10)}{2^2}[/tex]

When finding the length of the hypotenuse of a right triangle why might you approximate the answer

Answers

You would approximate because the hypotenuse might not be a perfect square.

Sample Response:: If the square root is not a perfect square, then an approximation of the root often makes more sense in the context of the problem. For real-world problems, you would want an approximation, so you have an estimate of the length you are looking at.

For each lettered part, a through c, examine the two given sets of numbers. without doing any calculations, decide which set has the larger standard deviation and explain why. then check by finding the standard deviations by hand. set 1 set 2

a.4, 7, 7, 7, 10 4, 6, 7, 8, 10

b.100, 140, 150, 160, 200 10, 50, 60, 70, 110

c.10, 16, 18, 20, 22, 28 48, 56, 58, 60, 62, 70

Answers

a. Set 2 has larger standard deviation.

b. Set 1 and set 2 have same standard deviation.

c. Set 2 has larger standard deviation.

a. Set 1: 4, 7, 7, 7, 10

Set 2: 4, 6, 7, 8, 10

It seems like Set 2 might have a larger standard deviation because the numbers are more spread out from the mean (which appears to be around 7).

The set 3 has larger standard deviation.

For Set 1:

Mean = (4 + 7 + 7 + 7 + 10) / 5

= 7

Standard Deviation = ([tex]\sqrt{\frac{(4-7)^2 + (7-7)^2 + (7-7)^2 + (7-7)^2 + (10-7)^2)}{5}[/tex]]

= 1.89

For Set 2:

Mean = (4 + 6 + 7 + 8 + 10) / 5

Standard Deviation = ([tex]\sqrt{\frac{(4-7)^2 + (6-7)^2 + (7-7)^2 + (8-7)^2 + (10-7)^2)}{5}[/tex]]

= 2

Hence, set 2 has larger standard deviation.

b. Set 1: 100, 140, 150, 160, 200

Set 2: 10, 50, 60, 70, 110

Here, Set 1 seems to have same standard deviation as set 2.

For set 1:

Mean = (100 + 140 + 150 + 160 + 200) / 5 = 150

Standard Deviation =[tex]\sqrt{\frac{(100-150)^2 + (140-150)^2 + (150-150)^2 + (160-150)^2 + (200-150)^2)}{5}}[/tex]

= 32.24

For set 2:

Mean = (10 + 50 + 60 + 70 + 110) / 5

= 60

Standard Deviation = [tex]\sqrt{\frac{(10-60)^2 + (50-60)^2 + (60-60)^2 + (70-60)^2 + (110-60)^2)}{5}}[/tex]

=32.24

Hence, set 1 and set 2 have same standard deviation.

c. Set 1: 10, 16, 18, 20, 22, 28

Set 2: 48, 56, 58, 60, 62, 70

Set 2 generally has larger values, suggesting that it could have a larger standard deviation because the mean is larger for set 2.

For Set 1:

Mean = (10 + 16 + 18 + 20 + 22 + 28) / 6

= 19

Standard Deviation = [tex]\sqrt{\frac{(10-19)^2 + (16-19)^2 + (18-19)^2 + (20-19)^2 + (22-19)^2 + (28-19)^2)}{6}}[/tex]

= 5.50

For Set 2:

Mean = (48 + 56 + 58 + 60 + 62 + 70) / 6

= 58.33

Standard Deviation = [tex]\sqrt{\frac{(48-58.33)^2 + (56-58.33)^2 + (58-58.33)^2 + (60-58.33)^2 + (62-58.33)^2 + (70-58.33)^2)}{6}}[/tex]

=6.641

Hence, the second set have the larger standard deviation.

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An audio cable is 15.7dm long. How long is the cable in meters?

Answers

The answer should be 1.57m

Each morning librarians place 560 books on a book shelf in the school library. Each student that visits library that day takes exactly 3 books from this shelf. Let s be the number of students which visit library on a particular day. Let b be the number of books left on the shelf at the end of that day. a How does the number of books left on the shelf depend on number of students visiting library? Find formula for the function b(s).

Answers

b(s) = -3s + 560 <== here is ur function

How does the number of books left on the shelf depend on the number of students visiting the library ?

well..if each person takes out 3 books....lets say 10 people came into the library....that would mean (3 * 10) = 30 books would be checked out...but if only 5 people came, then (3 * 5) = 15 books would be checked out. I dont know how else to explain it. The more people that visit, the more books will be checked out.

The relationship between the books and the students is an illustration of a linear function

The formula for the function is: [tex]b(s) = 560 - 3s[/tex]

From the question, we have:

[tex]b = 560[/tex] --- number of books in the morning

[tex]r = 3[/tex] ---- the number of books per students

So, the number of books as a function of number of students is:

[tex]b(s) = b - r \times s[/tex]

Substitute known values

[tex]b(s) = 560 - 3 \times s[/tex]

[tex]b(s) = 560 - 3s[/tex]

Hence, the formula for the function is:

[tex]b(s) = 560 - 3s[/tex]

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Is 7.38 a mixed decimal

Answers

yes, all mixed decimal has a decimal with an integer.

7.38 is the mixed decimal tho.

The top of a 22-foot ladder rests against the top of an 18-foot wall. If the base of the ladder is on the same ground level as that of wall, what angle does the ladder form with the ground? Express your solution to the nearest degree.

Answers

use the sine ratio here:- sin = opposite / hypotenuse so
sin A = 18/22

A = 54.9 degrees

55 to nearest degree

Answer:

Step-by-step explanation:

Given that The top of a 22-foot ladder rests against the top of an 18-foot wall.

The ladder, the wall and the floor together make a right angled triangle with hypotenuse as ladder.

Thus we have a right triangle with hypotenuse = 22 ft

and the side of the wall = 18

The required angle is the angle the ladder form with the ground.

Hence we have if x is the angle

[tex]sin x =\frac{Opposite}{Hypotenuse} =\frac{18}{22}[/tex]

From this we can find the angle X

X = sin inverse of 18/22

X=54.9

Round it off to X=55 degrees

Red and grey bricks were used to build a decorative wall. There were 140 bricks used in all. How many red bricks were used?

Answers

if your using variables, it could be with greater than or equal to signs involved such as: 150 ≤ r The variable "r" standing for the number of red bricks :) hope this is what you were looking for

Final answer:

To find the number of red bricks used to build the decorative wall, we can set up a system of equations. By solving the equations, we find that all 140 bricks used were red bricks.

Explanation:

To find the number of red bricks used, we can set up a system of equations.

Let r represent the number of red bricks and g represent the number of grey bricks.

We know that there were 140 bricks used in total, so we can write the equation: r + g = 140.

Since we specifically want to find the number of red bricks, we can write the equation: r = 140 - g.

By substituting this expression for r in the first equation, we get: 140 - g + g = 140.

Simplifying the equation, we find that 140 - g + g = 140 - g + g = 140.

Therefore, 140 - g = 140, and solving for g, we find that g = 0.

This means that no grey bricks were used and all 140 bricks used were red bricks.

Suppose θ is an angle in the fourth quadrant with cosθ=x/4. Find expressions for the other five trig functions in terms of x?

Answers

[tex]\bf sin(\theta)=\cfrac{opposite}{hypotenuse} \qquad cos(\theta)=\cfrac{adjacent}{hypotenuse} \quad % tangent tan(\theta)=\cfrac{opposite}{adjacent} \\\\\\ % cotangent cot(\theta)=\cfrac{adjacent}{opposite} \qquad % cosecant csc(\theta)=\cfrac{hypotenuse}{opposite} \quad % secant sec(\theta)=\cfrac{hypotenuse}{adjacent}\\\\ -------------------------------[/tex]

now, we know the angle is in the IV quadrant, that means, the cosine is positive and the sine is negative, or "x" is positive whilst "y" is negative.

[tex]\bf cos(\theta )=\cfrac{\stackrel{adjacent}{x}}{\stackrel{hypotenuse}{4}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{4^2-x^2}=b\implies \stackrel{IV~quadrant}{-\sqrt{16-x^2}=b}\\\\ -------------------------------[/tex]

[tex]\bf sin(\theta)=\cfrac{-\sqrt{16-x^2}}{4} \qquad cos(\theta)=\cfrac{x}{4} \qquad % tangent tan(\theta)=\cfrac{-\sqrt{16-x^2}}{x} \\\\\\ % cotangent cot(\theta)=\cfrac{x}{-\sqrt{16-x^2}} \qquad % cosecant csc(\theta)=\cfrac{4}{-\sqrt{16-x^2}} \qquad % secant sec(\theta)=\cfrac{4}{x}[/tex]

now, for the cotangent and the cosecant, let's rationalize the denominator,

[tex]\bf cot(\theta)=\cfrac{x}{-\sqrt{16-x^2}}\cdot \cfrac{\sqrt{16-x^2}}{\sqrt{16-x^2}}\implies cot(\theta)=-\cfrac{x\sqrt{16-x^2}}{16-x^2} \\\\\\ csc(\theta)=\cfrac{4}{-\sqrt{16-x^2}}\cdot \cfrac{\sqrt{16-x^2}}{\sqrt{16-x^2}}\implies csc(\theta)=-\cfrac{4\sqrt{16-x^2}}{16-x^2}[/tex]

Which of these is equivalent to 3-23-2?

Answers

Answer:

-22

Step-by-step explanation:

This is a case of directed numbers. The numbers 23 and 2 carry negative signs like this:

- 23

- 2

Therefore, adding these negative numbers gives -23 - 2 = -25

Adding the sum to 3 gives: 3 - 25 = -22

The depths of water, at the edge of a pier, at different times of day, are represented by the table below. Which of the following functions best models the depths of the water?

Answers

The best answer is C) y=4.75 * cos(0.52x - 2.08) + 7.65

Unfortunately, the two only ways to solve this problem are to either graph all the options or plug in time values for x and see which agrees the most with the tide chart. Both are time-consuming, but I chose to graph each one with a graphing application.
Plugging in a few values for x confirms that C is the best function.
12pm (x=0)
y = 4.75 * cos(0 - 2.08) + 7.65
y = 5.334
2pm (x=2)
y= 6.5
4pm (x=4)
y=12.4
It is not a perfect representation, but the shape of the graph and closeness to the points given is the best of the four options provided.

Find three points that solve the equation , -5x-3y=-7

Answers

To find three points, we can literally plug x values in a solve for y. To make this a little easier, we can solve for y to start. First, we can add 5x to both sides (addition property of equality) to get 7+5x=-3y. Next, we can divide both sides by -3 to get
[tex]- \frac{7+5x}{-3} =y[/tex]

To make this really simple, we can make 7+5x equal to factors of -3. For example, -3*2=-6. If we have 7+5x=-6, we can subtract 7 to both sides to get -13=5x. Next, we can divide both sides by 5 to get x=-13/5. Since 7+5x=-6, we can plug that into
[tex]- \frac{7+5x}{-3} =y[/tex]
to get (-6)/(-3)=2=y. I challenge you to find the other two points on your own - good luck!

What's the Estimate of 615-342

Answers

Final answer:

To estimate the difference between 615 and 342, round each number to the nearest ten or hundred and subtract. Rounding to the nearest hundred gives an estimate of 300, while rounding to the nearest ten gives an estimate of 280.

Explanation:

To estimate the difference between 615 and 342, you can round each number to the nearest ten or hundred and then subtract the rounded numbers. Here's the step-by-step process:

Round 615 to the nearest hundred, which gives you 600.Round 342 to the nearest hundred, which gives you 300.Subtract the rounded numbers: 600 - 300 = 300.

This gives an estimate of the difference between 615 and 342 as 300.

If you prefer to round to the nearest ten instead, you'd get:

Round 615 to the nearest ten, which gives you 620.Round 342 to the nearest ten, which gives you 340.Subtract the rounded numbers: 620 - 340 = 280.

In this case, the estimate would be 280. You can choose the level of precision you want in your estimate based on how you round the numbers.

which types of angels are not congruent?

Answers

same side exterior angles are not congruent

What is the differentiation of f(x) =2x^4/5?

Answers

[tex]\bf f(x)=\cfrac{2x^4}{5}\implies f(x)=\cfrac{2}{5}x^4\implies \cfrac{df}{dx}=\cfrac{2}{5}\cdot 4x^3\implies \cfrac{df}{dx}=\cfrac{8x^3}{5}[/tex]

notice, the 2/5 is just a "scalar" value, so you can just get the derivative of the variable part and slap the scalar as its factor.

Take apart an addend to solve 35+27

Answers

Using take apert, we have

35 + 27

= 32 + 3 + 27

= 32 + 30

= 62

Can someone help me if anyone know. Please, thanks

Answers

6 and 8/15 inches. Take the 1/5 and 1/3 and find a common denominator. Then Subtract the smaller number from the bigger number. Bam

I simplified the numbers. Then the subtract his height at birth from his height when he was a year old.

what is the exact of the expressions square root of 180 - square root of 125 + square root of 5

Answers

[tex]\bf \sqrt{180}-\sqrt{125}+\sqrt{5}\qquad \begin{cases} 180=2\cdot 2\cdot 3\cdot 3\cdot 5\\ \qquad 2^2\cdot 3^2\cdot 5\\ \qquad (2\cdot 3)^2\cdot 5\\ \qquad 6^2\cdot 5\\ 125=5\cdot 5\cdot 5\\ \qquad 5^2\cdot 5 \end{cases} \\\\\\ \sqrt{6^2\cdot 5}-\sqrt{5^2\cdot 5}+\sqrt{5}\implies 6\sqrt{5}-5\sqrt{5}+\sqrt{5}\implies 2\sqrt{5}[/tex]

The exact value of the expression √180 - √125 + √5 simplifies to 2√5, by combining like terms after simplifying each square root separately.

The exact value of the expression [tex]\sqrt{180}[/tex] - [tex]\sqrt{125}[/tex] + [tex]\sqrt{5}[/tex] can be calculated by simplifying each square root separately. Firstly, the [tex]\sqrt{180}[/tex] can be simplified to 6√5, because 180 = 36 × 5, and 36 is a perfect square whose square root is 6. Similarly, the [tex]\sqrt{125}[/tex] simplifies to 5√5, since 125 = 25 × 5 and the [tex]\sqrt{25}[/tex] is 5. The [tex]\sqrt{5}[/tex] remains as it is because it cannot be simplified further.

The expression then becomes 6√5 - 5√5 + √5. Now, we combine like terms. Since all terms involve the [tex]\sqrt{5}[/tex], we can combine them as follows: (6 - 5 + 1)√5, which simplifies to 2√5. Therefore, the exact value of the expression is 2√5.

What is a transformation and 3 types of transformations.

Answers

a transformation happen when the shape changes.
There are four transformations
translation
rotation
reflection
dilation

translation, rotation and reflection do not change the shape or the size of the shape and are known as rigid motions

A transformation is the movement or change in size of a shape on a graph.

The four types:
Dilation: Change of size.
Rotation: A clockwise turn in each of the four quadrants in a graph.
Translation: Simply relocating the shape.
Reflection: Mirroring the shape across either the y or x axis.

Hope that helps!

What is the value of the 4 in 24,659

Answers

4000

Place values are according to the digits...

So...
20000+4000+600+50+9=24,659

The value of 4 in the given number is 4000.

The given number is 24,659.

What is the place value?

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

In the given number 24,659, 4 is in thousands place.

So, the value of 4 is 4000

Therefore, the value of 4 in the given number is 4000.

To learn more about the place value visit:

https://brainly.com/question/21467438.

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a child is to receive a dose of 0.5 teaspoon of cough medicine every 4 hours. if the bottle contains 60 doses, how many days will the medicine last?

Answers

The medicine would last 20 days.

I hoped this helped! :)

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