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3 years ago

1)What are the first five terms of the sequence given by the formula an=4n+1 ?

2 answers:

5 0

We are asked to determine the first five terms of the sequence given by the formula an=4n+1, if n is equal to 1 to 5, then an is equal to 5, 9, 13, 17, 21. Answer is A. In 2, given the sequence 8,6,4,2 then the expression is a1=8, an = an-1-2

koban [17]3 years ago

4 0

Answer:1) c. 5,9,13,17,21

2) a. a1=8, an=an-1 -2

Step-by-step explanation: 1) an=4n+1

⇒ a1=4×1+1=5

a2=4×2+1=9

a3=4×3+1=13

a4=4×4+1=17

a5=4×5+1=21

2) clearly a1=8 and then the terms of series are decreasing by 2

so, an=an-1 -2

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Determine the area enclosed by y=2x+3, the x-axis and the ordinates x=3 and x=4

jok3333 [9.3K]

Answer:

$\displaystyle \int\limits^4_3 {2x + 3} \, dx = 10$

General Formulas and Concepts:
Calculus

Integration

Integrals

Integration Rule [Reverse Power Rule]: $\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C$

Integration Rule [Fundamental Theorem of Calculus 1]: $\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)$

Integration Property [Multiplied Constant]: $\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx$

Integration Property [Addition/Subtraction]: $\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx$

Area of a Region Formula: $\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx$

Step-by-step explanation:

Step 1: Define

Identify.

y = 2x + 3

x-interval [3, 4]

x-axis

See attachment for graph.

Step 2: Find Area

Substitute in variables [Area of a Region Formula]: $\displaystyle A = \int\limits^4_3 {2x + 3} \, dx$
[Integral] Rewrite [Integration Property - Addition/Subtraction]: $\displaystyle A = \int\limits^4_3 {2x} \, dx + \int\limits^4_3 {3} \, dx$
[Integrals] Rewrite [Integration Property - Multiplied Constant]: $\displaystyle A = 2 \int\limits^4_3 {x} \, dx + 3 \int\limits^4_3 {} \, dx$
[Integrals] Integrate [Integration Rule - Reverse Power Rule]: $\displaystyle A = 2 \bigg( \frac{x^2}{2} \bigg) \bigg| \limits^4_3 + 3(x) \bigg| \limits^4_3$
[Integrals] Integrate [Integration Rule - FTC 1]: $\displaystyle A = 2 \bigg( \frac{7}{2} \bigg) + 3(1)$
Simplify: $\displaystyle A = 10$

∴ the area bounded by the region y = 2x + 3, x-axis, and the coordinates x = 3 and x = 4 is equal to 10.

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Learn more about integration: brainly.com/question/26401241

Learn more about calculus: brainly.com/question/20197752

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

3 0

2 years ago

32 percent of the customers of a fast food chain order the Whopper, French fries and a drink. A random sample of 10 cash registe

weqwewe [10]

Answer: 0.0023

Step-by-step explanation:

Let X be the binomial variable that represents the number of receipts will show that the above three food items were ordered.

probability of success p = 32% = 0.32

Sample size : n= 10

Binomial probability function :

$P(X=x)= \ ^nC_xp^x(1-p)^{n-x}$

Now, the probability that eight receipts will show that the above three food items were ordered :

$P(X=8)=\ ^{10}C_8(0.32)^8(1-0.32)^2\\\\=\dfrac{10!}{8!2!}(0.32)^8(0.68)^2\\\\=5\times9(0.0000508414176684)\\\\=0.00228786379508\approx0.0023$

hence, the required probability = 0.0023

8 0

3 years ago

What is 1.8 added 8 times? (IF YOU CAN PLS DO IT IN EXPLANATION) and this is about decimals and pls do it in grade five type, bc

Salsk061 [2.6K]

Answer:

14.4

Step-by-step explanation:

1.8 added 8 times = 1.8 * 8

1.8 * 8

use distributive property

1.8 = 1 + 0.8

1.8 * 8 = (1+0.8) * 8

= 1*8 + 0.8*8

anything multiplied by 1 equals itself

1*8 + 0.8*8 = 8 + 0.8 * 8

0.8 = 8/10

0.8 * 8 = (8/10) * 8

= 64/10

= 6.4

8 + 0.8 * 8 = 8 + 6.4 = 14.4 as our answer

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2 years ago

Someone please help me on this math problem!

Galina-37 [17]

Look at the picture.

Therefore we have the equation:

10y - 29 = 7y + 19 add 29 to both sides

10y = 7y + 48 subtract 7y from both sides

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3x = 5x = -28 subtract 5x from both sides

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3 years ago

The weight of baby goats is believed to be Normally distributed, with a mean of 5.75 pounds. The average weight of a random samp

Julli [10]

Answer:

The standard error of the mean is 0.0783.

Step-by-step explanation:

The Central Limit Theorem helps us find the standard error of the mean:

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ .