32. A student is in the process of solving an equation. The original equation and the first step are shown
below.

Using compound interest and continuous compounding, it is found that it would take 2.61 years longer for Carter's money to triple.

The amount of money earned, in compound interest, after t years, is given by:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

In which:

For Carter, we have that the rate of interest and the number of compoundings are, respectively, r = 0.04875 and n = 12. The time to triple is t for which A(t) = 3P, hence:

[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]

[tex]3P = P\left(1 + \frac{0.04875}{12}\right)^{12t}[/tex]

[tex](1.0040625)^{12t} = 3[/tex]

[tex]\log{(1.0040625)^{12t}} = \log{3}[/tex]

[tex]12t\log{(1.0040625)} = \log{3}[/tex]

[tex]t = \frac{\log{3}}{12\log{(1.0040625)}}[/tex]

t = 22.58.

The amount of money is given by:

[tex]A(t) = Pe^{kt}[/tex]

For Jack, we have that the rate of interest is of k = 0.055, hence:

[tex]A(t) = Pe^{kt}[/tex]

[tex]3P = Pe^{0.055t}[/tex]

[tex]e^{0.055t} = 3[/tex]

[tex]\ln{e^{0.055t}} = \ln{3}[/tex]

[tex]0.055t = \ln{3}[/tex]

[tex]t = \frac{\ln{3}}{0.055}[/tex]

t = 19.97.

The difference is given by:

22.58 - 19.97 = 2.61

It would take 2.61 years longer for Carter's money to triple.

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A cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.

A cube is a three-dimensional shape that has equal length, width, and height.

We are given that the height of a cube is 1 unit. Since the length, width, and height of a cube are always equal, therefore:

Length of the cube =1 unit

Width of the cube = 1 unit.

In summary, a cube that has a height of 1 unit, will also have length and width that are both 1 unit in length.

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Answer:

correct answer is

A = 32

B= 24

To know how many calories has Sabir burned in his workout, first identify the calories he burnt every day, and then add them.

The total of calories burnt is equal to adding the calories burnt everyday:

Due to this, the steps recommended are:

Here is a hypothetical example:

Note: This question is incomplete because the chart is not given;  due to this, the answer is based on general knowledge.

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Answer:

C

Step-by-step explanation:

d / rate = time

d / 90  + d/60  = 6 hours

(2d+ 3d)/180 = 6

5d = 1080

d = 216 miles

The distance from NYC to Boston is 216 miles.

We have a guy named Steve travels from NYC to Boston at 90 mph and returns to NYC at 60 mph taking 6 hours total for the round-trip without stopping.

We have to determine distance between NYC and Boston.

The distance covered by the body will be -

d = v x t

According to question, we have -

Assume that the distance travelled by Steve from NYC to Boston be x.

Then, total distance covered for the round trip = 2x.

From NYC to Boston -

Suppose that in going from NYC to Boston, Steve takes t hours. Then

x =  90 x t            (1)

From Boston to NYC -

Steve will take (6 - t) hours to travel the distance. Then -

x = 60 x (6 - t)         (2)

Now, Equating the equations (1) and (2), we get -

90 x t = 60 x (6 - t)

1.5t = 6 - t

1.5t + t = 6

2.5 t = 6

t = [tex]\frac{12}{5}[/tex] = 2.4 hours

Therefore -

x = 90 x 2.4 = 216 miles

Hence, the distance from NYC to Boston is 216 miles.

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Answer:

[tex]y = 0.835193[/tex] (use the '≈' )

Step-by-step explanation:

[tex]y^3+2y^2+12y+16=28[/tex] (original equation)

[tex]y^3+2y^2+12y+16 - 28 =28 -28[/tex] (subtract 28 from both sides)

[tex]y^3+2y^2+12y-12=0[/tex] (new equation)

then use the cubic formula (i don't really know how to explain the process through a screen. I'm sorry! Hopefully, this helps enough though)

Answer:69/56 that is your answer did it help

Answer:

152 ft²

Step-by-step explanation:

First, we can work out the area of the triangles using the formula 1/2 × base × height. 1/2 × 6 × 4 = 12 ft². This is the area of one triangle so we can multiply this by 2 to get the area of both triangles - 24ft².

Next, we can work out the area of the rectangular sides by multiplying the length and width together. 8 × 5 = 40ft². Again, this is the area of one rectangle so we can multiply this by 2 to get the area of both rectangles - 80ft².

Then, we can work out the area of the base by multiplying the length and width together. 8 × 6 = 48ft².

Finally, we can add all the areas together to find the total surface area of the tent. 24 + 80 + 48 = 152 ft².

Hope this helps!

Mean is average 11 x 2 = 22

The two cards need to equal 22 when added together.

the difference is 6:

6/2 = 3

11-3 = 8

11+ 3 = 14

14 +8 = 22

the two numbers are 8 and 14

Answer:

#1: 4) D

#2: 1) 34.89 = 3 × C

#3: 4) 6y + 18

Step-by-step explanation:

#1

Using the distributive property:

3 × 5z = 15z

3 × -3 = -9

The correct expression is 15z - 9. Hence, D is the right option.

#2

You need to find the cost of each box.

3 × C = 34.89

34.89 ÷ 3 = 11.63

3 × 11.63 = 34.89

Hence, 1) is the right option.

#3

Using the distributive property:

6 × y = 6y

6 × 3 = 18

The expression is 6y + 18. Hence, 4) is the right option.

hope this helps!! p.s. i really need brainliest :)

Answer:

Using a graduated ruler, draw a line segment AB of length 10 cm.

Draw 2 arcs of radius more than half of AB with A as the center, one above AB and one below AB.

With the same radius, similarly, draw 2 arcs with B as the center.

Answer:

1,253 in³

Step-by-step explanation:

The container can be split into two rectangular prisms. Adding their volumes together will give us the volume of the container.

The formula for the volume of a rectangular prism is length×width×height or base×height

Let's substitute!

(l×w×h)+(l×w×h)

=(7×5×5)+(11×14×7)

=175+1078

=1,253 in³

Hope this helps!

Answer:

30 .24 m/hr

Step-by-step explanation:

2 hours and 5 minutes  = 2  + 5/60  hours = 2 5/60 hrs

63 miles / (2  5/60) = 30.24 m/hr

Step-by-step explanation:

To find the average speed, we must know this formula :

[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = \dfrac{Distance \: Travelled}{Total \: Time \: Taken}}} \\ \\ [/tex]

Now, substituting the given values in the formula :

[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = \dfrac{63 \: miles}{2.083 \: hr}}} \\ \\ [/tex]

[tex] \\ {\longrightarrow\sf \qquad{Average \: speed = 30.24 \: mph}} \\ \\[/tex]

Therefore,

Answer:

Step-by-step explanation:

The slope-intercept formula can be used to find the equation of the line.

Slope-intercept formula:

[tex]\Longrightarrow:\sf{y=mx+b}}[/tex]

y=-3x+14

I hope this helps you! Let me know if my answer is wrong or not.

The gym option costs less per class for six classes(Option B), and the gym option costs less per class for seven (Option D).

You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

Here we're specified that:

For high school classes:

For local gym:

For 6 classes:

High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 6 = $(20+60) = $80

(since $20 dollar is one time cost, and $10 was price for each class)

Similarly, joining local gym's $50 cost is one time, and rest of $5 is price for each class.

Local gym : $50 + $(5+5+5+5+5+5) = $20 + $5 × 6 = $(20+30) = $50

For 7 classes:

High school : $20 + $(10 + 10 + 10 + 10 + 10 + 10 + 10) = $20 + $10 × 7 = $(20+70) = $90

Local gym : $50 + $(5+5+5+5+5+5+5) = $20 + $5 × 7 = $(20+35) = $55

Thus, the statements which are true about the average cost for the two options is given by: Option B: The gym option costs less per class for six classes., Option D: The gym option costs less per class for seven classes.

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Answer:

There are 9 ounces of peanuts

Make the ounces of cashews equal to three, and this works! Don’t know the math otherwise :|

Answer: Below

Step-by-step explanation:

Looking at the numbers, they already seem to be multiples of fours. If we try to scale four up, 12 is the next biggest factor.
84 = 12 * 7
48 = 12 * 4
7 + 4 = 13
12 * 13 = 84 * 48
12 * 13 = 132

Answer:

x=15

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

The legs and x and 20 and the hypotenuse is 25

20 ^2+x^2 = 25^2

400 + x^2 = 625

Subtract 400 from each side

x^2 = 625-400

x^2 = 225

Take the square root of each side

sqrt(x^2) = sqrt(225)

x = 15

Answer:

parallelogram

Step-by-step explanation:

Parallelograms have two pairs of parallel sides and no right angles.

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♫[/tex]

As we can see, the probability of this event is 2/7 = 0.28 (approx), so it's even less than 50%, hence we can conclude that the given event is less likely to happen.

The Correct choice is B

The less likely would be the best description of the likelihood of the event.

The correct option is B.

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?

The probability of the event is 2/7.

To describe the likelihood of the event,

we can convert the fraction to a decimal:

2/7 = 0.2857...

Since the decimal is between 0 and 0.5, we can say that the event is "less likely" to occur.

Therefore, the best answer is B. Less likely.

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Answer:

70 fl oz

Step-by-step explanation:

Find how much is added to the punch bowl.

2 containers and each holds 6 fluid ounces.

2 x 6 = 12

Now find the total amount of liquid by adding the original amount and the amount added.

58 + 12 = 70

The name of the shape depicted in the graph below is rose, so the answer is A.

A rose is a flat curve resembling a symbolic image of a flower. Geometrically, it is the algebraic or transcendent curve whose graph is characterized by a series of windings around a central point.

In the best known cases, these windings produce figures in the shape of a rose window, from which its name derives from.

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The speed of the raft if the speed of the patrol-boat was 12 km/hour, and it caught the raft in 5 hours 20 min later is 2.857 km/hours.

What is the speed of a body?

The speed of a body is the rate at which it covers the total distance is in the time taken. The speed of the body is given as,

[tex]S=\frac{D}{T}[/tex]

Here, (d) is the distance travelled by the body, and (t) is time taken by the body to cover that distance.

A raft was sent away from point A downstream. A patrol-boat left A 5 hour and 20 min later and caught up with the raft 20 km away from point A.

Total time the patrol boat took in hours is,

[tex]T = 5 + \frac{20}{60}[/tex]

T=5+0.3333

T=5.3333 hours

The speed of the patrol boat is 12 km/hour, and it caught up with the raft 20 km away from point A. Thus, the time taken with this speed to cover 20 km distance is,

[tex]T=\frac{20}{12}[/tex]

T=1.6667 Hours

Thus, the total time is,

T=5.3333+1.6667

T=7 Hours

Now as the raft travel 20 km in 7 hours. Therefore, find the speed of raft by putting the values in above formula as,

[tex]S=\frac{20}{7}[/tex]

S=2.857 kmph

Answer:

The car travelled 73 miles

The boat travelled 53 miles

The car arrived 17.7 minutes before the boat

Step-by-step explanation:

The total distance the car travelled from Point A to Point B = 28+45 = 73 miles

The total distance the boat travelled is given by the displacement; Using Pythagorean theorem = 53miles.

Time taken by the car = Distance/Speed = 73/40 = 1.825 hrs or 109.5 minutes

Time taken by the boat = Distance/speed = 53/25 = 2.12 hrs or 127.2 minutes.

The time taken by the car is the shortest, therefore it arrives first before the boat.

(◔‿◔)

The probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes is 0.16 or 16%.

Normally distributed data is the distribution of probability which is symmetric about the mean.

The mean of the data is the average value of the given data.

The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

The times of the runners in a marathon are normally distributed, with

Refere the probabiliity table attached below. The probability of Z being inside the 1 Standard daviation of mean is 0.84.

The probability of runner selected with time less than or equal to 3 hours and 20 minutes,

[tex]P=1-0.84\\P=0.16[/tex]

Thus, the probability that a randomly selected runner has a time less than or equal to 3 hours and 20 minutes is 0.16 or 16%.

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