After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:

Answer:

56

Step-by-step explanation:

98 gallons of a 20 percent salt solution results in 20/100 * 98 = 19.6 gallons of salt.

Let's say we need x gallons of the 42% salt solution.

To make sure that the resulting mixture has 28% salt, we need to have the total salt divided by the total amount of gallons.

We have 98 total gallons in the first solution, and x total gallons in the second solution. We have 19.6 gallons of salt in the first solution and 42% of x gallons in the second solution:

[tex]19.6+\frac{42}{100}(x)=\frac{28}{100}(98+x)[/tex]

Expanding, we have

[tex]19.6+\frac{42}{100}x=27.44+\frac{28}{100}x[/tex]

Subtracting 19.6 and subtracting 28/100x from both sides equals

[tex]\frac{14}{100}x=7.84[/tex]

Multiplying both sides by 100:

[tex]14x=784[/tex]

Dividing both sides by 14:

[tex]x=56[/tex]

Answer:

To solve for a, you will need to get that variable alone on one side. First you will multiply each side by variable b. This will give you the equation pb = 3a + 4. Next you subtract 4 from each side. This puts it at pb - 4 = 3a. After that you’ll divide both sides by 3 and get a alone. This gives you (pb - 4)/3 = a or, if you switch it around, a = (pb - 4)/3. This is the simplest form when solving for a in this equation.

Answer:

Hello,

All my sentences will be written in mathematical language.

Step-by-step explanation:

[tex]p=\dfrac{3a+4}{b} \\\\p*b=3a+4 \ :\ \forall\ x,y,z\in\mathbb{R},z\neq 0:x=y\Longleftrightarrow\ x*z=y*z\\\\p*b-4=3a \ :\forall\ x,y,z\in\mathbb{R} :x=y\Longleftrightarrow\ x+z=y+z\\\\\dfrac{p*b-4}{3} =a \ :\forall\ x,y,z\in\mathbb{R},z\neq 0:x=y\Longleftrightarrow\ x*z=y*z\\\\a=\dfrac{p*b-4}{3} \ :\forall\ x,y\in\mathbb{R}:x=y\Longleftrightarrow\ y=x[/tex]

Answer:

Step-by-step explanation:

They travel 500 - 300 = 200 miles in 2 hours so their combined speed is

100 mph.

If their respective speed are x and y mph then we have the system

x + y = 100

x - y = 20

Adding the 2 equations

2x = 120

x = 60

and y = 40.

The other solution is that y = 60 mph and x = 40 mph.

Answer:

100 inches^3

Step-by-step explanation:

The volume of the back rectangle is

V = l*w*h

V = 8*5*1 = 40 inches ^3

The volume of the front rectangle is

V = 6*2*5 = 60 inches^3

Add the volumes

40+60 = 100 inches^3

Answer:

7 and above

Step-by-step explanation:

Go and 7 draw a dot and a arrow to the right

Answer:

Step-by-step explanation:

Answer:

this question is inappropriate

Answer:

Step 1: Set the expression inside the square root greater than or equal to zero. Step 2: Solve the equation found in step 1. In this case, we divided by a negative number, so had to reverse the direction of the inequality symbol. Step 3: Write the answer using interval notation.

Answer:

bzbdvdbdyrhevgdhs sdd

Step-by-step explanation:

ushebdvrudvd very

zhrjdvfjvrhfbrjrbr

hhrbdbdbfbfhfhthr

rhdjdbbffbdbbdve

9514 1404 393

Answer:

  1.767 gal/min

Step-by-step explanation:

The flow rate in gallons per minute is found by dividing gallons by minutes.

  (10.6 gal)/(6 min) ≈ 1.767 gal/min

Answer:

5/0 is not a rational number

Step-by-step explanation:

you cant divide by 0

Answer:

last option

Step-by-step explanation:

(x-h)²+(y-k)²=r²

(x--7)²+(y-4)²=5²

(x+7)²+(y-4)²=25

The equation of the circle is (x + 7)² + (y - 4)² = 25.

Option D is the correct answer.

A circle is a two-dimensional figure with a radius and circumference of 2pir.

The area of a circle is πr².

We have,

The equation of a circle with center (h,k) and radius r.

(x - h)² + (y - k)² = r²

Substituting the given values, we get:

(x - (-7))² + (y - 4)² = 5²

Simplifying the equation:

(x + 7)² + (y - 4)² = 25

Therefore,

The equation of the circle is (x + 7)² + (y - 4)² = 25

Learn more about Circle here:

https://brainly.com/question/11833983

#SPJ3

Answer:

56.7

Step-by-step explanation:

We know

mean = sum / count, with count being the amount of papers corrected in this case. We want to find the sum of all the papers as well as the count to figure out the mean of all papers.

For Tony's papers,

mean = sum / count

50 = sum / 40

multiply both sides by 40 to isolate the sum

sum = 50 * 40 = 2000

For Alice's papers,

mean = sum / count

70 = sum / 20

multiply both sides by 20 to isolate the sum

70 * 20 = sum = 1400

The total sum of all 60 papers is equal to the sum of 40 papers + the sum of the remaining 20 papers, or 2000 + 1400 = 3400. The mean of the 60 papers is therefore

mean = sum / count

mean = 3400/60 ≈ 56.7

Answer:

18 dimes and 1 nickle

Step-by-step explanation:

This is because 18 time 10 is 180 and one of 5 add it and this is $1.85

Remeber a dollar is 100 cents

Answer:

83.33 milliliters

Step by step explanation:

2L = 2000 ml   Change the liters to milliliters first

2000 ml : 24 hours

x ml : 1 hour

Next you cross multiply : 2000 × 1 hour = 2000 and 24 × x = 24x

Then you divide:

[tex]\frac{24x}{24} : \frac{2000}{24}[/tex]

x : 83.3333333...

When this is rounded off it is equal to 83.33

HOPE THIS HELPED

hopefully this answer can help you to answer the next question. can you choose this answer as the brainliest answer and give five stars

Answer:

x = π/4.

Step-by-step explanation:

3sin(2x) = 2sin(2x) + 1

3sin(2x) - 2sin(2x) = 1

1sin(2x) = 1

sin(2x) = 1

When a variable n = π/2, sin(π/2) = 1 [refer to the unit circle].

2x = π/2

x = π/4.

Hope this helps!

Answer:

Step-by-step explanation:

Total amount = 200 mg + (13 days)×(180 mg)/day = 2620 mg

One 35 mL bottle contains (35 mL)×(10 mg)/mL) = 350 mg of medication.

(2620 mg)×(1 bottle)/(350 mg) ≈ 7.5 bottles

8 bottles are needed.

Answer: x= 11

Step-by-step explanation:

To answer the question, we first need to know how many miles he/she/it can drive in one hour (to make it simpler. Doing a bunch of calculations involving decimals and other stuff can be very confusing)

335 divided by 5 is 67

Therefore in one hour Ivan can drive 67 miles. We want to know the TIME it takes for Ivan to drive 737 miles and the formula for time is Distance / Speed.

The distance is 737 miles

The speed is 67 miles/hour

737 divided by 67 is 11

Therefore Ivan takes 11 hours to drive 737 hours

Answer:

Step-by-step explanation:

perimeter=2(l+w)=2(17+14)=2(31)=62 m

cost of fencing=62×25=1550 Rs.

Answer:

30

Step-by-step explanation:

5x3=p

px2 = a

5x3 = 15 x 2 = 30

Answer:

5 times 3 times 2=30

Step-by-step explanation:

5×3=15×2=30

Answer:

3.143

Step-by-step explanation:

Since you're rounded it to the third decimal, you look at the fourth one. And since the fourth one is 8, ur going round 2, which is the third decimal to 3.

Answer:

The answer is below

Step-by-step explanation:

In this question, to round three decimal place, we need to count three numbers after the dot.

Here..

the three numbers are 142

so after that we round it, so first of all we ignore 1 and, and focus on the number 2 and 4.

and if the number is below 5, it is rounded to the last number, but if the number is 5 or more than it, then we round it to the next number.

For example

142 - here we have 2, which is below 5, so we round it to '140'

where as if we have..

147 - here we have 7, which is above 7, so we round it to '150'

____________________________________________________________

So in this problem we round 142, so the number 2 is below 5 so it is round to 140

therefore the answer is - 3.14

Answer:

16, 16(sqrt3)

Step-by-step explanation:

30-60-90 triangles follow a rule where the hypotenuse is 2 times the shortest leg, and the longer leg is sqrt3 times the shorter leg.

So, the sides are x, 2x, and (sqrt3)x.

If 2x = 32, then x = 16.

Therefore the two legs are 16 and 16(sqrt3)

you can search up 30-60-90 triangle for more information

Step-by-step explanation:

Recall that 1 dozen = 12 so 4 dozen cookies has a total of 48 cookies. We are going to use the following ratios to solve the problem:

[tex]\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right)[/tex] and [tex]\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right)[/tex]

a) [tex]12\:\text{eggs}×\left(\dfrac{48\:\text{cookies}}{3\:\text{eggs}}\right) = 192\:\text{cookies}[/tex]

b) 18 dozen cookies = 216 cookies

[tex]216\:\text{cookies}×\left(\dfrac{3\:\text{eggs}}{48\:\text{cookies}}\right) = 13.5\:\text{eggs}[/tex]

Answer:

yes, the volume = 16 ft^3

Answer:

-6

Step-by-step explanation:

27-3/2x=36

53-3x=72

3x=-18

x=-6

Answer:

slope= 3/1

y-intercept (0,2)

y= 3/1 b + 2