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frosja888 [35]
3 years ago
12

The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for th

e nth term of this sequence? 1. an = 8n + 10 2. an = 8n − 14 3. an = 16n + 10 4. an = 16n − 38

Mathematics
2 answers:
Lynna [10]3 years ago
8 0
The fourth term in an arithmetic sequence is 18 and the seventh term is 42. if the first term is a1, which is an equation for the nth term of this sequence?
1. an = 8n + 10
☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆☆ 2. an = 8n − 14
3. an = 16n + 10
4. an = 16n − 38

Ilia_Sergeevich [38]3 years ago
6 0

Answer:

Option 2nd is correct

a_n =8n-14

Step-by-step explanation:

The nth term for the arithmetic equation is give by:

a_n = a_1+(n-1)d             ....[A]

where,

a_1 is the first term

d is the common difference and

n is the number of term.

As per the statement:

The fourth term in an arithmetic sequence is 18 and the seventh term is 42

⇒a_4 = 18 and a_7 = 42

then by above definition we have;

a_1+3d = 18             .....[1]

a_1+6d = 42            .....[2]

Subtract equation [1] from [2] we have;

3d = 24

Divide both sides by 3 we have;

d = 8

Substitute in [1] we have;

a_1+24 = 18

Subtract 24 from both sides we have;

a_1=-6

We have to find the equation for the nth term of this sequence

Substitute the given values in [A] we have;

a_n = -6+(n-1)\cdot 8

⇒a_n = -6+8n-8

⇒a_n =8n-14

Therefore, an equation for the nth term of this sequence is, a_n =8n-14

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The triangular pyramid shown is made up of four congruent triangles. The length of the base is 8 inches, and the height of the b
Aneli [31]

Answer:

(B) Talia is correct. The lateral area can be found by approximating one large triangle, which can be found using the expression 4 (one-half (8) (6.9))

Step-by-step explanation:

Base of the Pyramid = 8 Inches

Height of the Triangular Face = 6.9 Inches

In any solid shape, the Lateral surface area is the sum of all sides except its top and bottom bases.

Since the four triangles are congruent:

Lateral Surface Area = 4 X Area of One Triangle

Area of a Triangle = \frac{1}{2}$ X Base X Height

Area of one Triangular Face = \dfrac{1}{2}(8)(6.9)

Therefore:

Lateral Surface Area = 4\left(\dfrac{1}{2}(8)(6.9)\right)

Therefore, Talia is correct.

8 0
3 years ago
An international phone call costs $12.61 for 32 minutes minutes. How many cents per minute?
lilavasa [31]
32/12.61=2.537668517
8 0
3 years ago
Read 2 more answers
We wish to construct a 90% confidence interval on the mean of a population known to be normally distributed based on a sample of
sergiy2304 [10]

Answer:

Margin of error = 0.773

Step-by-step explanation:

We are given the following information in the question.

Sample size, n = 20

Sample mean = 8

Sample standard deviation = 2

90% Confidence interval

\bar{x} \pm t_{critical}\displaystyle\frac{s}{\sqrt{n}}  

Putting the values, we get,  

t_{critical}\text{ at degree of freedom 19 and}~\alpha_{0.10} = \pm 1.729  

Margin of error:

t_{critical}\displaystyle\frac{s}{\sqrt{n}}  

Putting the values, we get,  

1.729(\frac{2}{\sqrt{20}} ) = 0.773  

7 0
3 years ago
The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let n rep
tia_tia [17]

Answer:

B. 5 ≤ n≤ 8

f. 10 ≤ S ≤ 16

C. c=2n

d. S = c

Step-by-step explanation:

Jada is making lemonade for a get together with her friends. She expects a total of 5 to 8 people to be there (including herself).?

She plans to prepare 2 cups of lemonade for each person. The lemonade recipe calls for 4 scoops of lemonade powder for each quart of water. Each quart is equivalent to 4 cups. Let n represent the number of people at the get together, c the number of cups of water, S the number of scoops of lemonade powder. Select all the mathematical statements that repsent the quantities and constraints in the situation.

A. 5<n<8

B. 5≤ n≤8

C. c=2n

d. S = c

e. 10<c<16

f. 10≤S≤16

Let

n = number of people at the get together,

c = number of cups of water,

S = number of scoops of lemonade powder.

She expects a total of 5 to 8 people to be there (including herself).

B. 5 ≤ n ≤ 8

She plans to prepare 2 cups of lemonade for each person.

With minimum of 5 people and maximum of 8 people

2 × 5 = 10

2 × 8 = 16

f. 10≤S≤16

The number of cups of water is twice the number of people at the party

C. c=2n

Number of scoops of lemonade powder is equivalent to number of cups of water

d. S = c

4 0
2 years ago
3c + 5d = 7d – 6c, solve for d
liubo4ka [24]

Answer:

-3c+12d

Step-by-step explanation:

3 0
3 years ago
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