All categories

2 years ago

Find the 89th term of the arithmetic sequence -16 -3 10

Mathematics

1 answer:

Alekssandra [29.7K]2 years ago

8 0

Answer:

$a_{89}=1128$

Step-by-step explanation:

The given arithmetic progression is -16, -3, 10,...

We observe that the first term of this progression is $a_1=-16$ .

The constant difference is

$d=-3--16\\d=-3+16=13$

The 89th term of an arithmetic sequence is given by:

$a_{89}=a_1+88d$

We substitute the first term and the common difference to obtain:

$a_{89}=-16+88(13)$

We simplify to get:

$a_{89}=-16+1144$

This simplifies to:

$a_{89}=1128$

You might be interested in

Eliza's backpack weighs 18 and StartFraction 7 over 9 EndFraction pounds with her math book in it. Without her math book, her ba

kati45 [8]

Answer:

$Math\ Book = 3\frac{65}{72}\ kg$

Step-by-step explanation:

Given

$Backpack = 18\frac{7}{9}kg$ --- with math book

$Backpack = 14\frac{7}{8}kg$ --- without math book

Required

Determine the weight of her math book

To do this, we simply calculate the difference in the weights given.

Math Book= Backpack(with math book) - Backpack (without math book)

$Math\ Book = 18\frac{7}{9} - 14\frac{7}{8}$

$Math\ Book = \frac{169}{9} - \frac{119}{8}$

Take LCM

$Math\ Book = \frac{8 * 169 - 9 * 119}{72}$

$Math\ Book = \frac{1352 - 1071}{72}$

$Math\ Book = \frac{281}{72}$

$Math\ Book = 3\frac{65}{72}\ kg$

7 0

1 year ago

Exercise 6.22 provides data on sleep deprivation rates of Californians and Oregonians. The proportion of California residents wh

kherson [118]

Answer:

a. The alternative hypothesis H₀: p'₁ ≠ p'₂ is accepted

b. Type I error

Step-by-step explanation:

Proportion of California residents who reported insufficient rest = 8.0%

Proportion of Oregon residents who reported insufficient rest = 8.8%

p'₁ = 0.08 * 11545 =923.6

p'₂ = 0.088 * 4691=412.81

σ₁ = $\sqrt{n*p_1*q_1} = \sqrt{n*p_1*(1-p_1)}$ = $\sqrt{11545*0.08*(1-0.08)}$ = 29.15

σ₂ = $\sqrt{n*p_2*q_2} = \sqrt{n*p_2*(1-p_2)}$ = $\sqrt{4691*0.088*(1-0.088)}$ = 19.40

Samples size of California residents n₁ = 11,545

Samples size of Oregon residents n₂ = 4,691

Hypothesis can be constructed thus

Let our null hypothesis be H ₀: p'₁ = p'₂

and alternative hypothesis H ₐ: p'₁ ≠ p'₂

Then we have

$z =\frac{(p'_1 -p'_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma^2_1}{n_1}+\frac{\sigma^2_2}{n_2} } }$

The test statistics can be computed by

t₀ = $\sqrt{\frac{n_1n_2(n_1+n_2-2)}{n_1+n_2} } *\frac{p_1'-p_2'}{\sqrt{(n_1-1)\sigma_1^2+(n_2-1)\sigma_2^2} }$ = 1104.83

c from tables is P(T ≤ c) = 1 - α where α = 5% and c = 1.65

since t₀ ≥ c then then the hypothesis is rejected which means the alternative hypothesis is rejected

b. Type I error, rejecting a true hypothesis

5 0

1 year ago

261, 256, 251, ... Find the 46th term

slava [35]

Answer:

46th term is 36.

Step-by-step explanation:

we need to subtract like this..

251-5=246,246-5=241.likewise the 46th term is 36

5 0

1 year ago

Read 2 more answers

A school teacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the s

marin [14]

Answer:

H0 ; μ ≤ 4 pCi/L

Ha ; μ > 4 pCi/L

The null hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is less than or equal to the safe level of 4pCi/L

H0 ; μ ≤ 4 pCi/L

The alternative hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.

Ha ; μ > 4 pCi/L

Step-by-step explanation:

The null hypothesis (H0) tries to show that no significant variation exists between variables or that a single variable is no different than its mean. While an alternative Hypothesis (Ha) attempt to prove that a new theory is true rather than the old one. That a variable is significantly different from the mean.

The null hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is less than or equal to the safe level of 4pCi/L

H0 ; μ ≤ 4 pCi/L

The alternative hypothesis is that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L.

Ha ; μ > 4 pCi/L

7 0

2 years ago

Help please!!! What is P(0.6 ≤ z ≤ 2.12)? 16% 26% 73% 98%

Lelu [443]

26% is the answer to your question

5 0

1 year ago

Read 2 more answers