What is the sum of the series? ​ ∑ i=1 5 4i ​ Enter your answer in the box.

Answer:

3 3/4 miles

Step-by-step explanation:

Mr. Connors' pattern is to drive 1 3/12 fewer miles each day. The third day after Tuesday (on Friday), he wll drive 3×(1 1/4) = 3 3/4 fewer miles than on Tuesday.

Final answer:

Mr. Connors will drive 1/12 mile fewer on Friday compared to Tuesday.

Explanation:

To find how many fewer miles Mr. Connors will drive on Friday compared to Tuesday, we need to calculate the difference in the distances driven.

On Tuesday, he drove 77 1/12 miles.

On Friday, he will continue the pattern of subtracting a fraction from the distance driven each day. Therefore, we can subtract the same fraction (1/12) from the distance driven on Friday.

So, the difference in miles driven between Friday and Tuesday will be 77 1/12 - (77 1/12 - 1/12), which simplifies to 1/12 mile.

Therefore, Mr. Connors will drive 1/12 mile fewer on Friday compared to Tuesday.

Answer:

Approximate Total area that will be watered is 5887.5 feet²

Step-by-step explanation:

Radius of the Circular area that sprinkler cover , r = 25 feet

Number of sprinkler = 3

Area covered by 1 sprinkler = Area of circle

                                          = πr²

                                          = 3.14 × (25)²

                                          = 3.14 × 625

                                          = 1962.5 feet²

Area covered by 3 sprinkler = 3 × 1962.5 = 5887.5 feet²

Therefore, Approximate Total area that will be watered is 5887.5 feet²

The approximate total area that will be watered will be 5887.5 feet². Square centimeters and other similar units are used to measure area.

The space filled by a flat form or the surface of an item is known as the area.

The number of unit squares that cover the surface of a closed-form is the figure's area.

The given data in the problem is;

r is the radius of the Circular area that sprinkler cover = 25 feet

n is the number of sprinklers = 3

The sprinkler executes a circular motion ;

Area covered by sprinkler = Area of the circle

The area covered by sprinklers is found as;

[tex]A_S = \pi r^2 \\\\ A_S = 3.14 \times (25)^2 \\\\\ A_S = 3.14 \times 625 \\\\ A_S= 1962.5 \ feet^2[/tex]

The area covered by the three sprinklers will be;

[tex]\rm A_S = 3 \times 196.25 \\\\ \rm A_S =5887.5 \ feet^2[/tex]

Hence approximate total area that will be watered will be 5887.5 feet².

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Given the sum of the sequence and the first term, we rearrange the formula for the sum to solve for 'd', the common difference. This will allow us to calculate the term at any given point in the arithmetic sequence.

In an arithmetic sequence, the nth term can be represented by the formula a + (n-1)d where 'a' is the first term, 'n' is the number of terms and 'd' is the common difference between the terms.

The sum, 's', of the first 'n' terms in an arithmetic sequence is given by the formula s = n/2 * (2a + (n - 1)d).

Given the sum, 's', and the first term in the sequence, 'a', we can rearrange the sum formula to find 'd', the common difference, which will then allow us to find any term in the sequence.

We have s16 = -288 and a1 = -21. So, our problem reduces to solve for 'd' in s = n/2 * (2a + (n - 1)d) The solution with most relevance to the student's question will be the calculated 'd' value.

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Answer:

Approximately 391 minutes taken by 20 people to paint 20 walls.                    

Step-by-step explanation:

Given : It takes 48 minutes for 7 people to paint 7 walls.

To find : How many minutes does it take 20 people to paint 20 walls?

Solution :

7 people to paint 7 walls in 48 minutes.

So, 1 people to paint 7 walls in [tex]\frac{48}{7}[/tex] minutes.

and 1 people to paint 1 walls in [tex]\frac{48}{7\times 7}[/tex] minutes.

Now, We have to find minutes does it take 20 people to paint 20 walls.

20 walls will be painted in [tex]\frac{48\times 20}{7\times 7}[/tex] minutes.

20 people to paint 20 walls in [tex]\frac{48\times 20\times 20}{7\times 7}[/tex] minutes.

i.e. [tex]\frac{48\times 20\times 20}{7\times 7}=\frac{19200}{49}=391.83[/tex]

Therefore, Approximately 391 minutes taken by 20 people to paint 20 walls.

The cost function is an illustration of linear functions

From the question, we have:

[tex]G = 4.50[/tex] --- cost per game

[tex]R = 3.75[/tex] --- cost per shoe rent

Since the cost is a function of number of games, it means that;

The cost of shoe rent is a fixed cost

Let x represents the number of games.

So, the cost function is:

[tex]C(x) = R + G \times x[/tex]

This gives

[tex]C(x) = 3.75 + 4.50 \times x[/tex]

[tex]C(x) = 3.75 + 4.50x[/tex]

Substitute 3 for x; to evaluate the function for 3 games

[tex]C(3) = 3.75 + 4.50 \times 3[/tex]

[tex]C(3) = 3.75 + 13.50[/tex]

[tex]C(3) = 17.25[/tex]

Hence, the cost for three games is $17.25

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The numbers are consecutive, meaning they are in arithmetic progression.

Sum of Arithmetic Progression = (n/2)[2a + (n- 1)d]

Where, n = total number of numbers and d = common difference between two successive numbers

Therefore n = 4 and d = 1 ( as the numbers are consecutive )

now (4/2)(2a + (4 - 1)1) = 2

i.e. 2(2a + 3) = 2

i.e. 4a + 6 = 2

i.e. 4a = - 4

i.e. a = - 1

Therefore nos are -1, -1+1 , -1+1+1 , -1+1+1+1

i.e. -1, 0 , 1 , 2

Hope this helps..!!

Thank you :)

Answer:

The thirtieth term of sequence is 52

Step-by-step explanation:

Given the A.P series

-6, -4, -2, 0, ...

we have to find the thirtieth term of the following sequence.

The A.P is -6, -4, -2, 0, ...

which implies

Common difference, d=-4-(-6)=-4+6=2

First term=a=-6

n=30

[tex]a_n=a+(n-1)d[/tex]

[tex]a_{30}=a+29d[/tex]

[tex]a_{30}=-6+29(2)=-6+58=52[/tex]

hence, the thirtieth term of sequence is 52

Answer:

Jessica patio is made up of two rectangles.

Dimension of one rectangle which is in the shape of cuboid = 7 ft x 4 ft x 5 ft,

Dimension of Second rectangle which is also in the shape of cuboid =10 ft x 8 ft x 6 ft

→Total Area of Patio=Total  Surface Area of Cuboid having Dimension 7 ft x 4 ft x 5 ft,+ Total  Surface Area of Cuboid having Dimension 10 ft x 8 ft x 6 ft

= 2 ×[7×4+4×5+5×7]+2×[10×8+8×6+10×6]

=2×[28+20+35]+2×[80+48+60]

=2×83 +2×188

=166+376

=542 square feet

Upper face of larger cuboid is partially covered , with smaller cuboid.

Area of Lower face of smaller cuboid =7 ×4=28 square feet

Total Area of patio = 542- (Area of lower face of smaller cuboid)

  = 542 - 28

  =514 square feet

Initial price of car = $x

After one year the price of car = $0.88x

to find the change in price we subtract the price after one year from initial price.

It means change in price = (x-0.88x)= 0.12x

By this we can easily see that , price dropped by 0.12

Or we can say that price dropped by 12%

So option C is the correct answer

C) 12% decrease

1.) The center is at (-2,-5).

3.) The con vertices  are at (-2,-4) and (-2,-6).

4.) The distance between the center and each focus is 2√6 units.

Statements 1,3 and 4 about the ellipse are true. Ellipse is the result of carving a cone with an oblique plane that does not intersect the base.

The asymmetrical oval shape is drawn by a spot advancing along a plane so that the sum of its distance from foci is kept the same known as an ellipse.

1.) The center is at (-2,-5).

3.) The cone vertices are at (-2,-4) and (-2,-6).

4.) The distance between the center and each focus is 2√6 units.

Hence statements 1,3 and 4 about the ellipse are true.

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These are called "Equivalent Fractions."

Equivalent fractions may look different from each other, but all equivalent fractions have he same value.

Answer:

the answer is 14 speed limit signs

Step-by-step explanation:

The equilibrium rate of return is 8.3%.

The equilibrium rate of return of a security is the sum of the real risk-free rate, the inflation risk premium, the default risk premium, the liquidity risk premium, and the maturity risk premium.

In this case, the equilibrium rate of return is:

3.5% + 1.75% + 2% + 0.25% + 0.85% = 8.3%

So the answer is 8.3%.

Here is a breakdown of the calculation:

The real risk-free rate is the rate of return that investors would expect to earn on an investment with no risk of default or inflation.

The inflation risk premium is the additional return that investors demand to compensate them for the risk of inflation.

The default risk premium is the additional return that investors demand to compensate them for the risk of default on a security.

The liquidity risk premium is the additional return that investors demand to compensate them for the difficulty of selling a security quickly and easily.

The maturity risk premium is the additional return that investors demand to compensate them for the risk that the value of a security will decline as it approaches maturity.

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Answer:

There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).

Step-by-step explanation:

We use the combination formula because the order does not matter.

For example, John, Laura,... is the same way as Laura, then John, then ...

Combinations formula

[tex]C_{n,x}[/tex] is the number of different combinatios of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this problem, we have that:

Combinations of 4 students from a set of 10. So

[tex]C_{10,4} = \frac{10!}{4!(10-4)!} = 210[/tex]

There are 210 ways in which you can pick 4 students from 10 students (6 men, 4 women).

In the given data set, the standard deviation is the more appropriate measure of variation as it takes all the scores into account and provides a better insight into the data compared to the range.

In the given data set, both range and standard deviation can be used to measure the variation. However, the standard deviation might be a better measure in this instance. The standard deviation provides a numerical measure of the overall amount of variation in the data set. It indicates how far the values are from their average, or mean. In contrast, the range only provides the difference between the highest and lowest values, potentially overlooking the distribution of all the values.

When calculating the standard deviation for your dataset, it becomes evident that most scores are concentrated around the 90s, but there's one score dramatically lower at 60. This single score skews the data set and increases the standard deviation, indicating a larger spread around the mean than what might first be observed. As such, the standard deviation gives us a more detailed understanding of the spread within this set of quiz scores, making it the more useful measure in this case compared to the range.

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When making enough BLT sandwiches to use 2 full heads of lettuce, Omar will be using 2.5 pounds of bacon and will end up making a total of 40 BLT sandwiches.

The subject of this question is Mathematics, specifically ratios and proportions. Given that Omar uses one full head of lettuce for every 5 tomatoes, for 2 heads of lettuce, he will use 10 tomatoes (2*5). Since he uses 1/2 pound of bacon for every 2 tomatoes, then for 10 tomatoes, he will need 2.5 pounds of bacon (10/2*0.5). Finally, since it takes 1/4 pound of bacon to make 4 sandwiches, with 2.5 pounds of bacon he will make 40 sandwiches (2.5/0.25*4). Therefore, Omar will use 2.5 pounds of bacon and make a total of 40 BLT sandwiches.

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