All categories

3 years ago

A)the eight term of arthematic sequence is 28, the common difference is 6 calculate the first term of sequence.

Mathematics

1 answer:

Vinil7 [7]3 years ago

4 0

Solution

Part A

The general form of the n-th term = a + (n-1)d

Here we are given the 8th term A8 = 28 , common difference (d) = 6

A8 = a + (n - 1) 6

28 = a + (8- 1)6

28 = a + 7*6

28 = a + 42

a = 28 - 42

a = -14

Part B

n-th term is 760. a = -14 and d = 6.

Plugging in the values in the general form, we get

760 = -14 + (n -1)6

760 = -14 + 6n - 6

760 = -20 + 6n

6n = 760 + 20

6n = 780

Dividing both sides by 6, we get

n = 780/6 = 130

The value of n is 130

You might be interested in

What is blank/11 = 12/44 equivalent fractions

nordsb [41]

Answer:

3/11

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Match the compound inequalities

kondor19780726 [428]

I one is 8x<24 and -8≤2x-4

Hence x <24/8 =3 and -4≤2x: divide by positive 2 to get -2≤x

Hence solution is -2≤x<3

Therefore c is the correct matching for 1.

2) 5x-2>13 or -4x≥8

i.e. 5x>15 or x≤8/(-4) = -2 (since dividing by negative inequality reverses)

Or x>3 or x ≤-2

Hence solution is two regions to the right of 3 excluding 3 and left of -2 including -2.

Graph b is the correct match.

3) -25≤9x+2<20

Subtract 2

-27≤9x<18: Now divide by positive 9

-3≤x<2

Hence graph is the region between -3 and 2 including only -3.

Graph a is correct matching for question 3.

5 0

4 years ago

Please help please need help ASAP

Anuta_ua [19.1K]

The altitude of a triangle is a line segment through a vertex and perpendicular to a line containing the side opposite the vertex.

Answer: $\overline{A F}$

6 0

3 years ago

Consider the following hypothesis test. H0: μ ≥ 55 Ha: μ < 55 A sample of 36 is used. Identify the p-value and state your con

Ket [755]

Answer:

Step-by-step explanation:

Given that:

$H_o: \mu \ge 55 \ \\ \\ H_1 : \mu < 55$

(a) For x = 54 and s = 5.3

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{54-55}{\dfrac{5.3}{\sqrt{36}} }$

$Z = \dfrac{-1}{\dfrac{5.3}{6} }$

Z = -1.132

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-1.132,35,1) = 0.1326

Decision: p-value is greater than significance level; do not reject $\mathbf{H_o}$

$Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \$ $\mu < 55$

For x = 53 and s = 4.6

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{53-55}{\dfrac{4.6}{\sqrt{36}} }$

$Z = \dfrac{-2}{\dfrac{4.6}{6} }$

Z = -2.6087

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(-2.6087,35,1) =0.0066

Decision: p-value is < significance level; we reject the null hypothesis.

$Conclusion: \ There \ is \ sufficient \ evidence \ to \ conclude \ that$ $\mu < 55$

For x = 56 and s = 5.0

The test statistics can be computed as:

$Z = \dfrac{\overline x - \mu}{\dfrac{s}{\sqrt{n}} }$

$Z = \dfrac{56-55}{\dfrac{5.0}{\sqrt{36}} }$

Z = 1.2

degree of freedom = n - 1

= 36 - 1

= 35

Using the Excel Formula:

P-Value = T.DIST(1.2,35,1) = 0.88009

Decision: p-value is greater than significance level; do not reject $\mathbf{H_o}$

$Conclusion: \ There \ is \ insufficient \ evidence \ to \ conclude \ that \$ $\mu < 55$

6 0

3 years ago

Which of the following are techniques used in geometric constructions with

Alisiya [41]

Answer= A
Explication

6 0

3 years ago

Read 2 more answers