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2 months ago

Guest #9962

2 months ago

Trip upstream took 90v−390v−3 hours and trip downstream took 90v+390v+3 hours. Also given that the difference in times was 1212 hours --> 90v−3−90v+3=1290v−3−90v+3=12;

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

90v−3−90v+3=1290v−3−90v+3=12 --> 90(v+3)−90(v−3)v2−9=1290(v+3)−90(v−3)v2−9=12 --> 90∗6v2−9=1290∗6v2−9=12 --> v2=90∗6∗2+9v2=90∗6∗2+9 --> v2=9∗(10∗6∗2+1)v2=9∗(10∗6∗2+1) --> v2=9∗121v2=9∗121 --> v=3∗11=33v=3∗11=33;

Trip downstream took 90v+3=9033+3=2.590v+3=9033+3=2.5 hours.

Question

Air is escaping from a spherical balloon at the rate of 4cc/min. how fast is the surface area of the balloon shrinking when the radius is 24 cm? (a sphere of radius r has volume 4 3 πr3 and surface area 4πr2 .)

Solution 1

The volume of the ball is given by:

V = (4/3) πr ^ 3

Deriving we have:

V '= (3) (4/3) (π) (r ^ 2) (r')

Clearing r 'we have:

r '= V' / ((3) (4/3) (π) (r ^ 2))

Substituting values:

r '= 4 / ((3) (4/3) (π) ((24) ^ 2))

r '= 0.000552621 c / min

Then, the surface area is:

A = 4πr2

Deriving we have:

A '= 8πrr'

Substituting values:

A '= 8π (24) (0.000552621)

A '= 0.33 cm ^ 2 / min

**Answer:**

**The surface area of the balloon is shrinking at:**

**A '= 0.33 cm ^ 2 / min**

V = (4/3) πr ^ 3

Deriving we have:

V '= (3) (4/3) (π) (r ^ 2) (r')

Clearing r 'we have:

r '= V' / ((3) (4/3) (π) (r ^ 2))

Substituting values:

r '= 4 / ((3) (4/3) (π) ((24) ^ 2))

r '= 0.000552621 c / min

Then, the surface area is:

A = 4πr2

Deriving we have:

A '= 8πrr'

Substituting values:

A '= 8π (24) (0.000552621)

A '= 0.33 cm ^ 2 / min

Question

How much would it be to get 67.1 to 73.3?

Solution 1

6.2.. 73.3 - 67.1 = 6.1...

Question

A sample of 16 from a population produced a mean of 85.4 and a standard deviation of 14.8. a sample of 18 from another population produced a mean of 74.9 and a standard deviation of 16.0. assume that the two populations are normally distributed and the standard deviations of the two populations are equal. the null hypothesis is that the two population means are equal, while the alternative hypothesis is that the mean of the first population is different than the mean of the second population. the significance level is 1%.

Solution 1

**Solution: **The test statistic under the null hypothesis is:

Where:

Now, to find the critical values, we need to use the t distribution table at 0.01 significance level for and is given below:

Since the t statistic is less than the t critical value, we therefore fail to reject the null hypothesis and conclude that the two population means are equal.

Question

You travel 5 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 6 miles upstream at a speed of 0.6r miles per hour. Finally, you turn around and return to your original starting point at a speed of r+1 miles per hour.

Solution 1

Kyle, d = rt, right? This means that t = d/r. If we call the rate of the current c, then her rate upstream is hindered by the current and is 3 - c. Downstream is 3 + c. The total time is 6 hours... 5/(3 - c) + 5/(3 + c) = 6 Once we put everything over the same denominator, we don't need it anymore. 5(3 + c) + 5(3 - c) = 6(3 - c)(3 + c) 15 + 5c + 15 - 5c = 54 - 6c2

30 = 54 - 6c26c2 = 24c2 = 4c = 2 2 mph

30 = 54 - 6c26c2 = 24c2 = 4c = 2 2 mph

Question

What is the decimal equivalent of 37%

Solution 1

0. 37 is the answer

Solution 2

37 divided by 100 equals 0.37

Question

A boy flies a kite with a 100-foot-long string. The angle of elevation of the string is 48°. Find the vertical distance between the kite and the point at which the boy is holding the string.

Solution 1

The vertical distance will be given by:

sinθ=opposite/hypotenuse

where:

θ=48°

opposite=h

hypotenuse=100 ft

thus

sin 48=h/100

hence

h=100 sin48

h=74.315 ft

Answer: 74.315 ft

sinθ=opposite/hypotenuse

where:

θ=48°

opposite=h

hypotenuse=100 ft

thus

sin 48=h/100

hence

h=100 sin48

h=74.315 ft

Answer: 74.315 ft

Question

Today Jan put a necklace on layaway by making a down payment of $75 and agreeing to pay $15 per month, starting next month, for 18 months. When will Jan receive the necklace?

Solution 1

**Answer:**

The answer is 18 months.

**Step-by-step explanation:**

Today Jan put a necklace on layaway by making a down payment of $75 and agreeing to pay $15 per month, starting next month, for 18 months.

So, she will receive the necklace in 18 months.

**Layaway is a system of paying a deposit for your product to secure it for later purchase. When all your payments are done, the product is given to you.**

Solution 2

Jan will receive her necklace in the fifth month.

She will start with a balance of $75, and we will take away $15 for each month

Month. 1. 2. 3. 4. 5.

Owed. 60. 45. 30. 15. 0

After

Each

Month

She will start with a balance of $75, and we will take away $15 for each month

Month. 1. 2. 3. 4. 5.

Owed. 60. 45. 30. 15. 0

After

Each

Month

Question

Add. Express your answer in lowest terms. 8 3/10 + 7 2/15

Solution 1

Question

In a right rectangles pyramid with base edges a= 18 cm and b= 10 cm the slant height toward a is k= 13 cm while the slant height towards b is l= 15 cm. What is the surface area of the pyramid

Solution 1

To find the surface area of this pier amid, you will find the area of the base and the areas of all for triangular lateral faces. Add these together for the total surface area in the end.

Base : 18 x 10 = 180 cm²

1st set of lateral faces:

A = 1/2 x b x h

1/2 x 13 x 18

A = 117 cm² x 2

234 cm²

2nd set of lateral faces:

1/2 x 10 x 15

A = 75 cm² x 2

150 cm²

150 cm² +234 cm² +180 cm²

The surface area of the pyramid is 564 cm².

Base : 18 x 10 = 180 cm²

1st set of lateral faces:

A = 1/2 x b x h

1/2 x 13 x 18

A = 117 cm² x 2

234 cm²

2nd set of lateral faces:

1/2 x 10 x 15

A = 75 cm² x 2

150 cm²

150 cm² +234 cm² +180 cm²

The surface area of the pyramid is 564 cm².

Question

At bonnie's bagels, you can choose from five different types of bagels, four different spreads, and four different toppings. how many different bagel combinations are possible?

Solution 1

Times all the numbers together. 5 bagels x 4 spreads x 4 toppings= 80

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