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2 months ago

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Question

A line of best fit predicts that when x equals 35, y will equal 34.785, but actually equals 37. What is the residual in this case?

Solution 1

We know that

Residual Value = Observed Valueâ€“ Predicted Value

in this problem

Observed Value=37

Predicted Value=34.785

Residual ValueÂ = 37-34.785------> 2.215

positive values for the residual (on the y-axis) mean that the prediction was too low

**the answer is**

**2.215**

Residual Value = Observed Valueâ€“ Predicted Value

in this problem

Observed Value=37

Predicted Value=34.785

Residual ValueÂ = 37-34.785------> 2.215

positive values for the residual (on the y-axis) mean that the prediction was too low

Question

What is the equation of the axis of symmetry of the graph of y + 3x â€“ 6 = â€“3(x â€“ 2)squared + 4?

Solution 1

**Answer:**

x = 3/2

**Step-by-step explanation:**

That is quite long and drawn out, so we have to get it down to a single quadratic equation, set equal to 0.

Begin by expanding the right side to get

then multiplying in the -3 to get

Now we will combine all the like terms and get everything on one side of the equals sign, and set it equal to 0:

In order to find the equation of the axis of symmetry we have to put it into vertex form, which is accomplished by completing the square on this quadratic.

In order to complete the square, the leading coefficient has to be a +1. Â Ours is a -3, so we will factor that out. Â First, though, now that it is set to equal 0, we will move the constant, -2, over to the other side, isolating the x terms.

Now we can factor out the -3:

The rules for completing the square are as follows:

Take half the linear term, square it, and add it to both sides. Â Our linear term is 3. Â Half of 3 is 3/2, and squaring that gives you 9/4. Â We add into the parenthesis on the left a 9/4, but don't forget about that -3 hanging around out front that refuses to be ignored. Â We didn't add in just a 9/4, we added in (-3)(9/4) = -27/4:

In the process of completing the square we created a perfect square binomial on the left. Â Stating that binomial and simplifying the addition on the right gives us:

We can determine the axis of symmetry at this point. Â Because this is a positive x-squared polynomial, the axis of symmetry is in the form of (x = ) and what it equals is the h coordinate of the vertex. Â Our h coordinate is 3/2; therefore, the axis of symmetry has the equation x = 3/2

Question

How many radii does a circle have? Explain.

Solution 1

Radii is defined as the line joining the centre of the circle to a point on the circumference

as there are infinite points on a circle

therefore there are infinite number of radii and hence there is no fixed number.

as there are infinite points on a circle

therefore there are infinite number of radii and hence there is no fixed number.

Question

Multiply 12.57 by 4.11. Round your answer to the nearest hundredth. a. 51.25
b. 51.66
c. 49.45
d. 52.66

Solution 1

When you are going to multiply 12.57 by 4.11, the result would be 51.6627.

To round off the result to the nearest hundredth, it would become 51.66.

According to the rules of rounding off a number, if the number after the rounded off digit is more than or equal to 5, you have to add 1 to the rounded off digit. But if it is less than 5, then the rounded off digit would be still the same. In this case, the rounded off digit which is 6 would still be the same since the number after that is 2 which is less than 5.Â

So, the answer is letter B which is 51.66

To round off the result to the nearest hundredth, it would become 51.66.

According to the rules of rounding off a number, if the number after the rounded off digit is more than or equal to 5, you have to add 1 to the rounded off digit. But if it is less than 5, then the rounded off digit would be still the same. In this case, the rounded off digit which is 6 would still be the same since the number after that is 2 which is less than 5.Â

So, the answer is letter B which is 51.66

Solution 2

Answer: 51.66

Step-by-step explanation:

Question

Jeremy, Sue, and Holly are siblings. Sue was born three years before Holly, and Jeremy was born five years before Sue. The product of Sue's age and Jeremy's age is at most 150. If x represents the age of Holly, which inequality can be used to find the age of each sibling?

Solution 1

**Answer:**

Inequality to find the age of siblings is **xÂ²+ 11x + 24 â‰¤ 150.**

**Step-by-step explanation:**

Let the age of Holly is x years. Now from the statements of the question we will form the equations.

Sue was born three years before Holly.

Sue = Holly + 3 = x + 3------(1)

Jeremy = Sue + 5

From equation (1)

Jeremy = (x + 3) + 5 = x + 8------(2)

Now statement says the product of Sue's age and Jeremy's age is at most 150.

Sue Ã— Jeremy â‰¤ 150

(x + 3)(x + 8) â‰¤ 150

**xÂ² + 11x + 24 â‰¤ 150**

Therefore inequality **xÂ² + 11x + 24 â‰¤ 150 **can be used to find the age of each sibling.

Solution 2

**Answer: x^2+11x+24 </= 150**

Question

Find the amount in a continuously compiunded account for the following condition. Principal, $4000; Annual interest rate, 5.1%; time, 2 years

Solution 1

A = P*e^(rt)

Here,

A = $4000*e^(0.051*2) = $4000*e^1.02 = $4000(2.773) = $11092.78Â

Note:Â This seems very high to me.

Here,

A = $4000*e^(0.051*2) = $4000*e^1.02 = $4000(2.773) = $11092.78Â

Note:Â This seems very high to me.

Question

An 8-oz bottle of ketchup costs $1.39. If the unit rate stays the same, how much should a 14-oz bottle cost?

Solution 1

First, you need to find how much an ounce costs. To do that, you have to divide 1.39 by 8. Then you get about 0.17. Now, you multiply 0.17 by 14, and get the answerÂ of 2.38. Therefore, a 14-oz bottle of ketchup costs $2.38.

Solution 2

Cost forÂ 8-oz bottle = $ 1.39

Cost for 1-oz bottle = 8/1.39

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1.75 ( approx )

Cost for 14-oz bottle of ketchup = 14* cost of 1-oz bottle

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 14* 1.75

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =**$ 24.5**

Cost for 14-oz of ketchup bottle is**$ 24.5**

Cost for 1-oz bottle = 8/1.39

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 1.75 ( approx )

Cost for 14-oz bottle of ketchup = 14* cost of 1-oz bottle

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 14* 1.75

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â =

Cost for 14-oz of ketchup bottle is

Question

What is the fraction 18/24 reduced to its lowest terms? A. 18/24
B. 24/18
C. 3/4
D. 9/12

Solution 1

C. 3/4

To simplify, you find the greatest common multiple of 18 and 24, which is 6. As a result, you divide 18 and 24 by 6. 18 divided by 6 is 3, and 24 divided by 6 is 4. Then you get 3/4 as an answer.

To simplify, you find the greatest common multiple of 18 and 24, which is 6. As a result, you divide 18 and 24 by 6. 18 divided by 6 is 3, and 24 divided by 6 is 4. Then you get 3/4 as an answer.

Question

suppose you deposit 1,000 ina savings account that pays interest at an annual rate of 5%. if no money is added or withdrawn from the account answer the following questions. How much money will be in the account after 3 years? How much will be in the account after 18 years? How many years will it take for the account to contain 1,500? How many years will it take for the account to contain 2,000?

Solution 1

After three years:Â $1000(1+0.05)^3 = $1157.63

Time req'd for amount to reach $1500 from $1000:

1500=1000(1+0.05)^t, or 1.5=1.05^t

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ln 1.5

ln 1.5 = t ln 1.05, so that t = ------------ = 8.31 years, or 8 yr 3 3/4 months

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ln 1.05

Time req'd for amount to reach $1500 from $1000:

1500=1000(1+0.05)^t, or 1.5=1.05^t

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ln 1.5

ln 1.5 = t ln 1.05, so that t = ------------ = 8.31 years, or 8 yr 3 3/4 months

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â ln 1.05

Question

Regression equation: y = 3.915(1.106)x the pond can hold 400 water lilies. by what day will the pond be full? write and solve an equation. the pond will be full by the end of day

Solution 1

**Answer:**

46 days

**Step-by-step explanation:**

**Given : **Regression equation:

Where,

Â y = amount of water lilies the pond hold

3.915 = represents the initial population.

1.106 = represents the increase in population at time x.

x = is a variable of time.

The pond can hold 400 water lilies â‡’ **y=400**

**Putting values in equation **we get,

**Taking log both side **

**By logarithm property **-

Approx.** x=46 **

**Therefore,** 46th day the pond be full.

Solution 2

46 Days

It said I have to have at least 20 characters to explain it well so here.

I hope you have a good day

It said I have to have at least 20 characters to explain it well so here.

I hope you have a good day

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