find the sum of the first 25 terms. 2,8,14,20

Answers

Answer 1

This is an arithmetic sequence as each term has a common difference to the previous term. Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number.

We know that a=2 and d=(20-14)=(14-8)=(8-2)=6 so

a(25)=2+6(25-1)

a(25)=146

The sum of an arithmetic sequence is the average of the first and last terms times the number of terms, in this case:

s(25)=25(2+146)/2

s(25)=1850

And if you care to remember the arithmetic sum formula it is:

s(n)=(2an+dn^2-dn)/2, using a=2, d=6, and n=25 we get:

s(25)=(4(25)+6(25^2)-6(25))/2

s(25)=1850

Answer 2

Answer:

1850

Step-by-step explanation:

Related Questions

Sales tax on an item is directly proportional to the cost of the item purchased. If the tax on a $500 item is $30, what is the sales tax on a $900 item?

Answers

30 / 500 = x / 900....$ 30 tax / 500 item = $ x tax on 900 item
cross multiply
(500)(x) = (900)(30)
500x = 27000
x = 27000/500
x = 54 <===

Answer: $54

Step-by-step explanation:

The equation to show the direct variation in two quantities x and y is given by :-

[tex]\dfrac{x_1}{y_1}=\dfrac{x_2}{y_2}[/tex]

The tax on a $500 item is $30.

Let 'x' be the sales tax on a $900 item.

Then , we have the following equation:-

[tex]\dfrac{x}{900}=\dfrac{30}{500}\\\\\Rightarrow\ x=\dfrac{900\times30}{500}\\\\\Rightarrow\ x=54[/tex]

Hence, the sales tax on a $900 item = $54

How many millimeters are there in 5 meters?

Answers

1 meter = 1000 mm

so 5 meters = 5 x 1000 = 5,000 millimeters

There are 5000 milimeters in 5 meters because the prefix milli stands for 1000.

Regroup to express the number in a different way , please help

Answers

25.3 = 1 ten + 15 ones + 3 tenths

hope it helps

You have just purchased a 10-year, $1,000 par value bond. the coupon rate on this bond is 8 percent annually, with interest being paid each 6 months. if you expect to earn a 10 percent simple rate of return on this bond, how much did you pay for it?

Answers

V = I (PVIFA kd, n) + MV (PVIF kd, n)

I=(1000×0.08)/2=40

(PVIFA kd, n)=((1−(1+0.1÷2)^(−2×10))
÷(0.1÷2))

Mv =1000

(PVIF kd, n) =1÷(1+0.1÷2)^(2×10))

So the answer is
V=40×((1−(1+0.1÷2)^(−2×10))
÷(0.1÷2))+(1,000÷(1+0.1÷2)^(2×10))
=875.38...answer

A cold front moved in last weekend. In eight hours overnight, the temperature outside dropped from 14 degrees to -10. What was the average temperature change for each hour ?

Answers

[tex]\bf slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby \begin{array}{llll} average\ rate\\ of\ change \end{array}\\\\ -------------------------------\\\\ \begin{cases} x_1=0\\ x_2=8 \end{cases}\implies \cfrac{f(8)-f(0)}{8-0}\implies \cfrac{14-(-10)}{8-0}\implies \cfrac{14+10}{8}\implies \cfrac{3^o}{1hr}[/tex]

Evaluate the limit, if it exists. (if an answer does not exist, enter dne.)lim h → 0 (x + h)3 − x3h

Answers

Presumably, the limit is

[tex]\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h[/tex]

Now, if you're familiar with the definition of the derivatives, you'll notice that this is the limit form of the derivative of the function [tex]f(x)=x^3[/tex], which you may also know to be [tex]3x^2[/tex]. But let's assume you don't know that just yet, and that it's actually the result you intend to find.

Expand the numerator:

[tex]\dfrac{(x+h)^3-x^3}h=\dfrac{(x^3+3x^2h+3xh^2+h^3)-x^3}h=\dfrac{3x^2h+3xh+h^3}h[/tex]

Now, when [tex]h\neq0[/tex], we can divide through by the lowest power of [tex]h[/tex]. We can do this because we're considering the limit as [tex]h[/tex] is *approaching* 0, and not when it actually takes on the value of [tex]h=0[/tex].

[tex]\dfrac{(x+h)^3-x^3}h=3x^2+3xh+h^2[/tex]

Now, as [tex]h\to0[/tex], we can see only the leading term remains, so that

[tex]\displaystyle\lim_{h\to0}\frac{(x+h)^3-x^3}h=3x^2[/tex]

as expected.

Final answer:

To evaluate the limit of (x + h)³ - x³h as h approaches 0, we can expand the expression using the binomial theorem and simplify. The resulting expression can be factored to show that as h approaches 0, the entire expression becomes 0. Therefore, the limit is 0.

Explanation:

To evaluate the given limit, we can start by expanding the expression (x + h)³ using the binomial theorem. This gives us (x³ + 3x²h + 3xh² + h³) - x³h. Simplifying further, we can cancel out the x³ terms and obtain 3x²h + 3xh² + h³ - x³h. Now, we can factor out h from the expression to get h(3x² + 3xh + h² - x³). As h approaches 0, the entire expression becomes 0, since h is being multiplied by a polynomial that does not contain h. Therefore, the limit is 0.

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The first card selected from a standard 52-card deck was a king. if it is not returned to the deck, what is the probability that a king will be drawn on the second selection?

Answers

there would be 3 kings left and 51 cards left

so it would be a 3/51 which reduces to 1/17 probability

Final answer:

The probability of drawing a king from a 52-card deck on the second draw, given that a king was drawn on the first draw and was not replaced, is 1 in 17.

Explanation:

The question pertains to the concept of probability, specifically with regards to sampling without replacement in a 52-card deck. First, let's identify the elements: there are 4 kings in a 52-card deck. When one king is drawn and not replaced, there are now 51 cards left with 3 kings.

The probability of drawing a king on the second draw, with the first king not replaced, is the number of favorable outcomes (drawing a king) divided by the total number of outcomes (total cards left). Hence, the probability is 3/51 = 1/17.

This means that there is 1 chance in 17 of drawing a king on the second draw if a king has been drawn on the first draw and not replaced.

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Three counters are used for a board game.If the counters are tossed,how many ways can at least one counter with Side A occur?

Answers

We use the equation for repeated trials written below:

Probability = n!/r!(n-r)! * p^(n-r) * q^r

The p is the probability of getting a side A in one toss. Since a counter has only two side, p = 0.5. The q is the probability of not getting side A in one toss, which is also q = 0.5. Now, r is the number of success per n trials. There are 3 tosses so, n=3. The question is getting "at least 1" counter. So, r=1, r=2 and r=3.

Probability for r=1: 3!/1!(3-1)! * (0.5)^(3-1) * (0.5)^1= 0.375
Probability for r=2: 3!/2!(3-2)! * (0.5)^(3-2) * (0.5)^2= 0.375
Probability for r=1: 3!/3!(3-3)! * (0.5)^(3-3) * (0.5)^3= 0.125

Total probability = 0.375 + 0.375 + 0.125 = 0.875

Linda deposits $500 into an account that pays simple interest at a rate of 4% per year. How much interest will she be paid in the first 4 years?

Answers

Assuming that she deposits $500 and forgets about it, here is what she would get after 4 years:

Year 1 - $500 * 1.04 = $520
Year 2 - $520 * 1.04 = $540.80
Year 3 - $540.80 * 1.04 = $562.432
Year 4 - $562.432 * 1.04 = $584.92928

Aftere four years. Linda would be paid $84.93

richerd works at an ice cream shop. regular cones get two scopes of ice cream and large cones get three scoops. One hot saturday richard scooped 234 regular cones and 156 large cones one scoop of ice cream is 3 ounces a tub of ice cream is 10 pounds how many tubs of ice cream did richerd use to make the cones?

Answers

234 x 2 = 468 scoops

156 x 3 = 468 scoops

468 + 468 = 936 total scoops

936 x 3 = 2808 ounces

16 ounces = 1 pound

2808/16 = 175.5 pounds

175.5/10 = 17.55 tubs

round answer as needed

the base of this solid crate has an area of 6 square centimeters the height of the crate is 4 meters what is the volume of the crate

Answers

[tex]Area Of Cuboid = length*width*height[/tex]

The length * width is the area of the base, so:

[tex]Area Of Cuboid = base*height = 6 * 4 = 24 meters^3[/tex]

Answer:

2 × 10³ cm³

Step-by-step explanation:

Given data

Area of the base: 6 cm²Height of the crate: 4 m = 4 × 10² cm

Considering the crate is a cuboid, its volume (V) is:

V = length × width × height

Since

area of the base = length × width

We get

V = area of the base × height

V = 6 cm² × 4 × 10² cm

V = 2.4 × 10³ cm³ ≈ 2 × 10³ cm³ (we round off to 1 significant figure)

One school survey showed that 3 out of 5 students own a pet. Another survey showed that 6 out of 11 students owned a pet. Are these results equivalent? Explain your reasoning.

Answers

no they are not because 3/5 is not equal to 6/11. if they were equal, it would be 6/10

3/5 own a pet means that (0.6) or 60% own a pet
6/11 own a pet means that (0.545) or 54.5% own a pet

Conclusion, in the 1st class more people 60% own a pet whereas in the second class only 54.5% have a pet

Round to the nearest while decimal 6.7

Answers

If you meant "[tex]whole [/tex]" instead of "[tex]while [/tex]"

Then, [tex]six [/tex] is rounded [tex]1ten[/tex] & [tex]seven[/tex] is rounded to [tex]ten [/tex]

Your answer: [tex]7[/tex]

[tex]good\\luck \\ on \\ your \\ assignment \\ \\ \\ \\ enjoy \\ your \\ day \\ \\ \\ \\ \\ \\ MeIsKaitlyn :)[/tex]

Find the value of y, rounded to the nearest tenth. Please help me, I'd appreciate it!!

Answers

If a secant and a tangent of a circle are drawn from a point outside the circle, then the product of the lengths of the secant and its external segment equals the square of the length of the tangent segment.

y² = 7(15+7)
y² = 7*22
y² = 154
y = √154
y = 12.4 ← to the nearest tenth

Help!
During exercise, the recommended maximum heart rate in beats per minute is modeled by the formula, M = 176 – 0.8A, where M is the maximum heart rate and A is the person’s age. Solve the formula for A. At what age would you have a recommended maximum heart rate in beats per minute of 140?

A) 40 years
B) 50 years
C) 25 years D)
45 years

Answers

D) 45

140= 176-0.8A
+.8A. +0.8A
140 + .8A = 176
-140. -140
.8A= 36
/.8. /.8
A = 45

Express the volume of a cone, V, as a function of its radius, r, if the radius is 1/5 of the height.

Answers

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ------\\ r=\frac{h}{5}\implies 5r=h \end{cases}\implies V=\cfrac{\pi r^25r}{3} \implies V=\cfrac{5\pi r^3}{3}[/tex]

A rectangular garden has a length of 12 feet. You need 36 feet of fencing to enclose the garden. What is the width of the garden.

Answers

The width of the garden would be 6 since it is looking for perimeter. I set an equation to find it:
Equation and steps:
12+12+x+x=36 x= width of the garden
24+2x=36
2x=12
x=6

The width of the rectangular garden is 6 feet with a perimeter of 36 feet.

What are the area and perimeter of a rectangle?

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Given, A rectangular garden has a length of 12 feet.

Assuming the width of the garden to be x feet.

We know the perimeter of a rectangle is 2(length + width).

∴ 2(12 + x) = 36.

24 + 2x = 36.

2x = 12.

x = 6 Or the width is 6 feet.

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A farmer is going to plant carrots on 5 3/14 acres, corn on 4 23/42 acres and peppers on 2 5/21 acres. If each acre requires 6 bags of fertilizer, how many bags of fertilizer does the farmer need to plant all the acres?

Answers

hmm we do the same as before, you convert the mixed fractions to "improper fractions" by simply making the numerator the product and sum like you saw it

so

[tex]\bf 5\frac{3}{14}\implies \cfrac{5\cdot 14+3}{14}\implies \cfrac{73}{14} \\\\\\ 4\frac{23}{42}\implies \cfrac{4\cdot 42+23}{42}\implies \cfrac{191}{42} \\\\\\ 2\frac{5}{21}\implies \cfrac{2\cdot 21+5}{21}\implies \cfrac{47}{21}\\\\ -------------------------------\\\\ \cfrac{73}{14}+\cfrac{191}{42}+\cfrac{47}{21}\impliedby \textit{our LCD is just 42}\implies \cfrac{3\cdot 73+1\cdot 191+2\cdot 47}{42} \\\\\\ \cfrac{219+191+94}{42}\implies \cfrac{504}{42}\implies \cfrac{12}{1}\implies 12[/tex]

now, that's how many acres the farmer has in total
now, if each acre takes 6 bags of fertilizer, well, you surely know how much that is.

What is the limit for lim x -> 2 int x

Answers

we are asked in the problem to determine the limit of integral of x dx as x approaches to 2. In this case, the first step to do is to integrate first the function. The integral of x dx by the power rule is equal to x^(n+1)/n+1. In this case, since n is equal to 1 from the given, then integral of x dx is equal to x^2/2. To evaluate the limit of x as x approaches to 2, we just have to substitute x by 2, that is
2^2 / 2 equal to 2. Hence the answer to this problem is equal to 2.

222+203 is rounded up to what?

Answers

[tex]222: 220 \\ 203 = 200 \\ \\ 222 + 203 = 425 \\ 220 + 200 = 420 \\ \\ \\ \\ Good \\ luck \\ on \\ your \\ assignment \\ \\ enjoy \\ your \\ day \\ \\ \\ MeIsKaitlyn :)[/tex]

[tex]Remember [/tex]↓

[tex]1-5[/tex] would rounded [tex]downward [/tex]
[tex]6-9[/tex] would be rounded [tex]upward [/tex]

A total of 504 tickets were sold for the school play. They were either adult tickets or student tickets. There were 54 more student tickets sold than adult tickets. How many adult tickets were sold?

Answers

a + s = 504
s = a + 54

a + (a + 54) = 504
2a + 54 = 504
2a = 504 - 54
2a = 450
a = 450/2
a = 225 <=== adults

a + s = 504
225 + s = 504
s = 504 - 225
s = 279 <=== students

Final answer:

Using algebra, we find that 225 adult tickets were sold out of a total of 504 tickets.

Explanation:

Let's denote the number of adult tickets as x. Since there were 54 more student tickets sold than adult tickets, we can represent the number of student tickets as x + 54. The total number of tickets sold is 504, so we set up the equation x + (x + 54) = 504.

Combining like terms, we get 2x + 54 = 504. Subtracting 54 from both sides gives us 2x = 450. Finally, dividing both sides by 2 gives us x = 225.

Therefore, 225 adult tickets were sold.

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Simplify the expression. 33 • 32 + 12 ÷ 4

Answers

Final answer:

The expression 33 • 32 + 12 ÷ 4 simplifies to 1059.

Explanation:

To simplify the expression 33 • 32 + 12 ÷ 4, we follow the order of operations - performing multiplication and division before addition.

Multiply 33 and 32 to get 1056.Divide 12 by 4 to get 3.

Now we can add the results: 1056 + 3 = 1059.

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Suppose y varies directly with x, and y = 8 when x = –6. What direct variation equation relates x and y? What is the value of y when x = –2?

Answers

B -4/3=-1.33 and 8/3=2.6666

Answer:

Direct variation states that the relationship between two variables in which one is a constant multiple of the other one.

In other words, when one variable changes the other one changes in proportion to the first.

i.e, if y is directly proportional to x then, the equal will be of the form is, y= kx where k is the constant of variation.

Given: y varies directly with x, and y = 8 when x = –6

By definition of direct variation,

y = kx

Substitute the values of x = -6 and y=8 to solve for k;

8 = -6k

Divide both sides by -6 we get;

[tex]k = -\frac{8}{6} = -\frac{4}{3}[/tex]

Now, to find the value of y when x = 2 we have;

[tex]y = -\frac{4}{3}x[/tex]

Substitute the given value of x =-2 we have;

[tex]y = -\frac{4}{3} \cdot -2 = \frac{8}{3}[/tex]

Therefore, the direct variation related x and y is, [tex]y = -\frac{4}{3}x[/tex]

and the value of [tex]y =\frac{8}{3}[/tex] when x = -2

I really suck at math. please help =)

Answers

check the picture below.

A marina is in the shape of a coordinate grid. Boat A is docked at (4.2, −2) and Boat B is docked at (−5.2, −2). The boats are ____ units apart. A) 6.2 B) 7.2 C) 9.4 D) 13.4

Answers

The distance between any two points is:

d^2=(x2-x1)^2+(y2-y1)^2

d^2=(4.2--5.2)^2+(-2--2)^2

d^2=(9.4)^2

d=9.4

Answer:

Your answer will be D.

Step-by-step explanation:

I did it on the test and got it correct.

The Kwon family has a rainwater catchment system they use to water their garden. After 3 days without rain, the depth of water in the tank is 63 inches. After 5 days, the depth is 57 inches. What will the depth of water in the tank be after 17 days?

Answers

f(d) = 72 - 3d

if d = 3
f(d) = 72 -3d = 72 - 3(3) = 72 - 9 = 63 inches

if d = 5
f(d) = 72 -3d = 72 - 3(5) = 72 - 15 = 57 inches

so
if d = 17
f(d) = 72 -3d = 72 - 3(17) = 72 - 51 = 21 inches

answer
the depth of water in the tank will be 21 inches after 17 days

63-57 = 6 inches in 2 days

6/2 = 3 inches per day

17-5 = 12

12*3 =36 inches in 12 days

57-36 = 21 inches after 17 days

What percent of 28.8 is 3.6?

Answers

divide them:

3.6/28.8 = 0.125

0.125 = 12.5%

the length of the hypotenuse is:

6.
12.
36.
[tex]6 \sqrt{3[/tex]

Answers

cos 60° = 1/2
1/2 = 6/x
1/2x=6
x = 6X 2 = 12
The length of the hypothenuse is 12

True or False: The sample size you need to estimate the population distribution should always be at least 10% of the population size.

Answers

Final answer:

False. The sample size needed to estimate the population distribution should not always be at least 10% of the population size.

Explanation:

False. The statement that the sample size needed to estimate the population distribution should always be at least 10% of the population size is not true. The size of the sample needed depends on various factors such as the original population, the level of confidence desired, and the margin of error allowed. For example, if the population is large and diverse, a smaller sample may still provide a reliable estimate of the population distribution. It is important to consider statistical concepts such as normal distribution and sampling techniques when determining the appropriate sample size.

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Tommy has a piece of toast that has butter on one side, and he dropped it twice. Both times, it landed with the butter side up. If he drops it two more times, what is the probability that it will have landed butter side up a total of three times?

Answers

Answer: The required probability is 50%.

Step-by-step explanation: Given that Tommy has a piece of toast that has butter on one side.

The first two times dropped the piece, it landed with the butter side up.

We are to find the probability that the piece will have landed butter side up a total of three times, if he drops it two more times.

For the butter side to be landed up three times, one of the last two drops must land butter side up.

Let, 'S' denotes the sample space for the experiment of dropping the piece for the last two times, then

n(S) = 2.

Let, 'B' be the event of getting one of the last two drops landed butter side up, then

n(B) = 1.

Therefore, the probability of getting one of the last two drops landed butter side up will be

[tex]P(B)=\dfrac{n(B)}{n(S)}=\dfrac{1}{2}=50\%.[/tex]

Thus, there is 50% probability of landing butter side up a total of three times.

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