Hector invests $800 in an account that earns 6.96% annual interest compounded semiannually. Rebecca invests $1,000 in an account that earns 5.44% annual interest compounded monthly. Find when the value of Rebecca's investment equals the value of Hector's investment and find the common value of the investments at that time. If necessary, enter the year to the nearest tenth and the value to the nearest cent. The value of Rebecca's investment equals the value of Hector's investment after approximately ________ years to the nearest tenth. The common value of the investments is approximately $_________ .

Answer:

equal to: =

Step-by-step explanation:

1 gallon has 4 quarts and half a gallon has two quarts, all together there is 6 quarts in 1 1/2 gallons

1 1/2 gallons is equal to 6 quarts.

1 1/2 gallons is equivalent to 6 quarts. Since the two quantities are equal, 1 1/2 gallons is not greater than 6 quarts. This can be shown by converting the gallons to quarts.

1 gallon is equal to 4 quarts, so 1 1/2 gallons is equal to 6 quarts (1.5 x 4 = 6). Therefore, 1 1/2 gallons is not greater than 6 quarts.

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Answer:

1:12

Step-by-step explanation:

Answer:

1.666666

Step-by-step explanation:

Answer:

One and two thirds or 1 2/3

Step-by-step explanation:

2/6*5=10/6=1 4/6= 1 2/3

Answer:

Givens

[tex]m \angle BAC=63\°[/tex]

[tex]m(BE)=96\°[/tex]

[tex]DE[/tex] is secant.

[tex]DG[/tex] is tangent.

Remember that the arc subtended by a central angle is equal to it. That means

[tex]m(BC)=m\angle BAC = 63\°[/tex]

Now, by sum of arcs, we know

[tex]m(EBC)=m(EB)+m(BC)=96\° +63\°=159\°[/tex]

By definition, the total arc of a circle is 360°, so

[tex]m(EFC)=360\°-m(EBC)=360\° - 159\°=201\°[/tex]

We know that the external angle formed by a secant and a tanget is one half of the difference between the intercepted arcs, so

[tex]\angle D=\frac{1}{2}(m(EFC)-m(BC))=\frac{1}{2} (201\° - 63\°)=\frac{1}{2} (138\°)=69\°[/tex]

So, the angle D is 69°.

Answer: False.

Step-by-step explanation:

There does not exist a "quarter circle" as a circle with a radius of 4 units, the only notable circle that does exist is the unit circle, that is the circle where the radius is equal to 1, represented by the equatin x^2 + y^2 = 1

The term "quarter circle" actually does refer to a fourth part of a circle, not to a circle of radius 4.

So the statement is false

Answer:

-85/8

Step-by-step explanation:

- 10 5/8  is a mixed fraction

- 10 and  5/8 =  -85/8

The mixed number -10 5/8 is equivalent to the improper fraction -85/8, which is found by converting the mixed number to an improper fraction and then applying the negative sign.

When converting a mixed number with a negative sign, you first convert the fractional part and then apply the negative sign. The mixed number -10 5/8 can be converted to an improper fraction by multiplying the whole number 10 by the denominator 8, adding the numerator 5, and then placing the result over the same denominator. Finally, place a negative sign in front.

The calculation would be as follows:

Therefore, the expression equivalent to -10 5/8 is -85/8.

Answer

Step-by-step explanation:The fine schedule for overdue books at the county library is modeled by the values in the table.

Library Fines for Overdue Books

Days overdue

Amount of fine

0

0 ¢

2

5 ¢

4

10 ¢

6

15 ¢

8

20 ¢

10

25 ¢

Which equation best models the fine schedule for overdue books?

y = five-halves x, where x is the cost in cents for a book that is y days overdue

y = five-halves x, where y is the cost in cents for a book that is x days overdue

y = 5 x, where x is the cost in cents for a book that is y days overdue

y = 5 x, where y is the cost in cents for a book that is x days overdue

After 4 hours: 60 ng/mL, After 8 hours: 30 ng/mL, After 12 hours: 15 ng/mL, After 16 hours: 7.5 ng/mL.

The half-life of a drug is the time it takes for the concentration of the drug in the body to reduce by half. In this case, the half-life of the drug is 4 hours. When a patient discontinues taking the medication, the concentration of the drug decreases exponentially over time.

The initial concentration is given as 120 ng/mL. After the first 4 hours, which is one half-life, the concentration reduces to 60 ng/mL. Subsequent half-lives continue to halve the concentration. After 8 hours, it becomes 30 ng/mL, after 12 hours it's 15 ng/mL, after 16 hours it's 7.5 ng/mL.

This exponential decrease reflects the nature of drug elimination from the body, with each half-life reducing the concentration by half. The rounded values in the table represent the decreasing drug concentrations at different time intervals after the patient stops taking the medication.

Answer:

d. sin 80.

Step-by-step explanation:

Use the identity cos x = sin (90-x).

So cos 10 = sin(90 - 10)

= sin 80.

Cos 10 when written in terms of sine would be d. sin 80.

The relationship between cosine and sine for complementary angles can be expressed as:

cos ( θ ) = sin ( 90 ° - θ )

This relation arises from the definition of cosine and sine in a right triangle. They are complementary functions. The cosine of an angle in a right triangle is the sine of its complement, and vice versa.

Given this relationship, we can express cos(10°) as:

cos ( 10 ° ) = sin ( 90 ° - 10 ° ) = sin ( 80 ° )

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Answer:

a

Step-by-step explanation:

both sides are going up by 2 .

so the number after 6 in the x column would have to be 8 because in the y column it went up by two.

then for the missing number in the y column we see that the x value went up from 8 to 10. that means that the y column value went up by 2. so you get 23

Answer:

Volume of the cube is [tex]64x^9[/tex].

Step-by-step explanation:

Given:

Volume of the cube [tex]V = L^3[/tex]

where [tex]L[/tex] ⇒ side length

side length [tex]L =4x^3[/tex]

We need to find the Volume of the cube.

Solution:

Now we know that;

Volume of the cube [tex]V = L^3[/tex]

But side length [tex]L =4x^3[/tex]

So we will substitute the value of L in above equation we get;

Volume of the cube [tex]V = L^3=(4x^3)^3[/tex]

Now by using Law of indices which states [tex](a^m)^n=a^{mn}[/tex]

So we can say that;

Volume of the cube [tex]V = L^3=(4x^3)^3=4^3x^{3\times3}=64x^9[/tex]

Hence Volume of the cube is [tex]64x^9[/tex].

Answer:

(-2,-3)

Step-by-step explanation:

The first step is to find the equations of the two lines. For the first line, the slope is 3/2, while the y intercept is 0. This gives it an equation of y=3/2x. For the second line, it has a slope of -3/2, and a y intercept of -6. This gives it an equation of y=-3/2x-6. Setting these two equations equal to each other, you get

3/2x=-3/2x-6

3x=-6

x=-2

y=-3

(-2,-3) Hope this helps!

Jill owns approximately 60,000 acres of land.

Let's first find out how many trees Jill has per acre based on the information given.

Jill has 150 peach trees on 1/2 of her land, which means she has 300 peach trees on her entire land. If there are 5 trees for every 1,000 square feet of land, we can calculate the total square feet of land that Jill owns:

[tex]\[ \text{Total trees} = \text{Trees per acre} \times \text{Total acres} \]\[ 300 = \frac{5}{1000} \times \text{Total acres} \][/tex]

Solving for the total acres:

[tex]\[ \text{Total acres} = \frac{300}{\frac{5}{1000}} \]\[ \text{Total acres} = \frac{300 \times 1000}{5} \]\[ \text{Total acres} = \frac{300000}{5} \]\[ \text{Total acres} = 60000 \][/tex]

Now, we can convert the total acres from square feet to acres using the conversion factor given:

[tex]\[ \text{Total acres in square feet} = 60000 \times 43560 \]\[ \text{Total acres} = \frac{60000 \times 43560}{43560} \]\[ \text{Total acres} = 60000 \][/tex]

So, Jill owns approximately 60,000 acres of land.

Jill owns approximately 1.38 acres of land.

To find out how many acres of land Jill owns, we first need to determine the total number of peach trees on all her land.

Since she counts 150 peach trees on half of her land, we can assume there are 300 peach trees in total (since half of her land has 150 trees and the other half will also have 150 trees).

Now, if there are 5 trees for every 1,000 square feet of land, we can set up a proportion to find out how many square feet of land these 300 trees occupy:

[tex]\( \frac{5 \text{ trees}}{1000 \text{ square feet}} = \frac{300 \text{ trees}}{x \text{ square feet}} \)[/tex]

Cross-multiplying, we get:

[tex]\( 5x = 300,000 \)[/tex]

Dividing both sides by 5:

[tex]\( x = 60,000 \)[/tex]

So, Jill's 300 peach trees occupy 60,000 square feet of land.

To convert this to acres, we use the conversion factor provided: [tex]1 acre = 43,560 square feet.[/tex]

[tex]\( \text{Number of acres} = \frac{60000}{43560} \)[/tex]

[tex]\( \text{Number of acres} = 1.38 \)[/tex]

Complete correct question:

Jill counts 150 peach trees on 1/2 of the land she owns. She determines that there are 5 trees for every 1,000 square feet of land. About how many acres of land does Jill own? [tex]1 acre= 43,560 square feet.[/tex]

Answer:

-5

Step-by-step explanation:

To solve for z, divide both sides of this equation by -0.25:

        1.25

z = ----------- = -5

       -0.25

Answer:

The correct answer is -5.

Step-by-step explanation:

To find my answer, I divided both sides by -0.25.

-0.25z = 1.25

-0.25z ÷ -0.25 = 1.25 ÷ (-0.25)

z = -5

Hope this helps,

❤Nicki❤

Answer:

13

Step-by-step explanation:

Answer and Step-by-step explanation:

First, you want to graph the line of x = -1. This line is simply a vertical line running through (-1, 0).

The coordinates of each of the points are:

G(5, 9)

F(8, 9)

D(5, 6)

E(8, 6)

When we reflect point G over the line x = -1, we will get a point with the same y-coordinate, but with a different x-coordinate. Since 5 is 6 units away from -1, when you reflect G, the new x-coordinate will be -1 - 6 = -7. So, the new point for G is (-7, 9).

By similar reasoning for all the other points, we have:

F'(-10, 9)

D'(-7, 6)

E'(-10, 6)

Finally, just graph the points G'(-7, 9), F'(-10, 9), D'(-7, 6), and E'(-10, 6), and that's your new shape.

Hope this helps!

Answer:

D': (-7,6)

E': (-10,6)

F': (-10,9)

G': (-7,9)

Step-by-step explanation:

D: (5,6)

E: (8,6)

F: (8,9)

G: (5,9)

After reflection in x = -1

D': (-1-6,6)

E': (-1-9,6)

F': (-1-9,9)

G': (-1-6,9)

D': (-7,6)

E': (-10,6)

F': (-10,9)

G': (-7,9)

Answer:

Use what you used for the first one and you should get the right answer.

Step-by-step explanation:

Answer:

  [tex]\dfrac{y^2+3y}{y^2-6y+9}[/tex]

Step-by-step explanation:

When we write this using appropriate math symbols, it is easier to see the solution. To evaluate this, we multiply by the inverse of the denominator fraction.

  [tex]\dfrac{2y}{y - 3}\div \dfrac{ 4 y - 12}{2 y + 6}=\dfrac{2y}{y-3}\cdot\dfrac{2y+6}{4y-12}\\\\=\dfrac{4y(y+3)}{4(y-3)^2}}=\boxed{\dfrac{y^2+3y}{y^2-6y+9}}[/tex]

Answer:

d

Step-by-step explanation:

9514 1404 393

Answer:

  Sally's work: StartFraction b Over 12 EndFraction = 16. B = 192

Step-by-step explanation:

Of the offered choices, the only one that is solved correctly is Sally's work.

Here are the solutions for the equations the students wrote:

  [tex]\dfrac{12}{b}=16\ \rightarrow\ 12=16b\ \rightarrow\ \dfrac{12}{16}=b=0.75\\\\\dfrac{b}{12}=16\ \rightarrow\ b=12\cdot16=192[/tex]

_____

Comment on the wrong answers

The "solution" value of 1.3 appears to be a rounded version of 16/12, a value that will not show up as a solution to any of the equations written.

Comment on dimensional analysis

The dimensions of "16" are "cases." The dimensions of "12" are "bottles per case", or bottles/case. Multiplying this by the number of cases, gives the number of bottles. This is where I'd start:

  (bottles/case)×(cases) = bottles    ⇒    12×16 = b

The ratios the students wrote had units of ...

  b/12 = (bottles)/(bottles/case) = cases = 16

and (incorrectly) ...

  12/b = (bottles/case)/(bottles) = 1/cases = 16 . . . . wrong

It can be useful to consider what the numbers represent. That can help avoid math mistakes.

a bought 16 cases of water bottles. There were 12 water bottles in each case. Four students wrote and solved equations to find b, the number of bottles that Clara bought. Which student wrote and solved the equation correctly?

Maya’s work:

StartFraction b Over 12 EndFraction = 16. b = 1.3

Larissa’s work:

12 b = 16. b = 1.3

Sally’s work:

StartFraction b Over 12 EndFraction = 16. b = 192.

Anika’s work:

StartFraction 12 Over b EndFraction = 16. b = 192.

Step-by-step explanation:

Answer:Yes

Step-by-step explanation:A=16 B=30 C=34

16*16= 256 30*30=900 34*34=1156

256+900=1156

Answer:

let's check first is it Right Triangle because we can do it using Pythagorean theorem:

let's sides 16 and 30 be legs, and 34 hypotenuse

1156=1156...so, this is true and your triangle IS Right Triangle

but, it is also a scalene triangle with a right angle

Step-by-step explanation:

The requried volume of the cylinder is approximately 1017.9 cubic meters.

The volume of a cylinder can be calculated using the formula:

Volume = π * (diameter/2)² * height

where π (pi) is a mathematical constant approximately equal to 3.14159, diameter is the base diameter of the cylinder, and height is the height of the cylinder.

In this case, the height is 9m and the base diameter is 12m. We need to first calculate the radius, which is half of the diameter:

Radius = diameter/2 = 12m/2 = 6m

Now we can substitute the values into the formula and calculate the volume:

Volume = π * (6m)² * 9m

Volume ≈ 1017.88 cubic meters

Rounding to the nearest tenth place, the volume of the cylinder is approximately 1017.9 cubic meters.

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Final answer:

The volume of a cylinder with a height of 9m and a base diameter of 12m is approximately 9160.9 cubic meters when rounded to the nearest tenth.

Explanation:

The student is asking for the volume of a cylinder with a given height and base diameter, which is a common problem in mathematics related to geometry and measurements. To find the volume, we use the formula for the volume of a cylinder V = πr²h, where V is the volume, r is the radius of the base, and h is the height of the cylinder. Given that the diameter is 12 meters, the radius (r) is half of that, which is 6 meters. We then substitute these values into the formula:

V = π(6m)²(9m)

V = 3.1416 × 36m² × 9m

V = 3.1416 × 324m² × 9m

V = π × 2916m³

V = 9160.88m³

After calculating, we round the volume to the nearest tenths place, obtaining V ≈ 9160.9m³.

Answer:uh look up a video?

Step-by-step explanation:

Answer:

$9

Step-by-step explanation:

set up a proportion where 20% is represented as 20/100 and set it equal to 1.80/x

cross multiply and you should get 180=20x

divide by 20 to solve for x

you then get 9, which is the amount you were looking for

Answer:

c

Step-by-step explanation:

Answer:

Question

Select the correct answer. Which expression is equivalent to x + y + x + y + 3(y + 5)? A. 2x + 5y + 5 B. 2x + y + 30 C. 2x + 5y + 15 D. 2x + 3y + 10 Reset          Answer C.

Step-by-step explanation:

Answer:

$7.58

Step-by-step explanation:

Think about it, (S+C), each flavor costs $3.97 per carton, and there's 2 cartons. $3.79 x 2 = $7.58

Answer:Stan used 19/40 of a gallon of gasoline.

Step-by-step explanation:

At first, Stan's lawn mower had 1/8 of a gallon of gasoline in the tank. When it got finished, he put 6/10 of a gallon of gasoline in the tank. It means that the number of gallons of gasoline that he has already put in the tank is

1/8 + 6/10 = 29/40 of a gallon.

After he mowed, 1/4 of a gallon was left in the tank. Therefore, the total amount of gasoline Stan used is

29/40 - 1/4 = 19/40 of a gallon

Final answer:

Stan used a total of 0.475 gallons of gasoline for mowing, calculated by adding the initial and added amounts of gasoline and then subtracting what was left after mowing.

Explanation:

To calculate the total amount of gasoline Stan used, we will first need to know the total gasoline added to the mower and then subtract the amount left after mowing.

Firstly, Stan started with ⅛ of a gallon (which is the same as 0.125 gallons) and added ⅔ of a gallon (0.6 gallons) to the tank. To find out how much gas was in the tank after refilling, we add these two amounts together:

0.125 + 0.6 = 0.725 gallons (total gas in the tank after refilling).

Once Stan finished mowing, he had ¼ of a gallon left in the tank. We need to subtract this amount from the total gas in the tank after refilling to find out the amount of gas used:

0.725 - 0.25 = 0.475 gallons (total gas used by Stan while mowing).

Therefore, Stan used a total of 0.475 gallons of gasoline for mowing.

Answer:

24 candies originally

Step-by-step explanation:

Add the 4 to how many you had left, then think about that number, 16, and what goes into 16 evenly 2 times? 8 and originally she gave away 1/3 of the box and if you were to add another 8 to the box it would be 24 divided by 1/3, -,-4,= 12.

Answer:

I believe it is about 47.63 meters squared

Leave a comment if you'd like a step-by-step explanation