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leonid [27]
3 years ago
15

Given the sequence 7, 12, 17, 22, ...

Mathematics
1 answer:
abruzzese [7]3 years ago
7 0

Answer:

option D is true.

Step-by-step explanation:

Given the sequence

7, 12, 17, 22, ...

An arithmetic sequence has a constant difference 'd' and is defined by

a_n=a_1+\left(n-1\right)d

Computing the differences of all the adjacent terms

12-7=5,\:\quad \:17-12=5,\:\quad \:22-17=5

The difference between all the adjacent terms is the same

so

d=5

as

a_1=7

Thus, the nth term of the arithmetic sequence will be:

a_n=5\left(n-1\right)+7

a_n=5n+2

Therefore, option D is true.

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It takes Ben 2 days to write reports, and it takes Kate 3 days to write reports. Bens rate, in reports per day, is how much grea
sergejj [24]

Answer:

Ben's rate is \dfrac{1}{6} greater than Kate's rate.

Step-by-step explanation:

1. If it takes Ben 2 days to write reports, then his rate is \dfrac{1}{2} of reports per day.

2. If it takes Kate 3 days to write reports, then her rate is \dfrac{1}{3} of reports per day.

3. Ben's rate is

\dfrac{1}{2}-\dfrac{1}{3}=\dfrac{3-2}{6}=\dfrac{1}{6}

greater than Kate's rate.

4 0
3 years ago
Two 5-year girls, Alyse and Jocelyn, have been training to run a 1-mile race. Alyse's 1 mile time A is approximately Normally di
tatyana61 [14]

Answer:

1.7 × 10⁻⁴

Step-by-step explanation:

The question relates to a two sample z-test for the comparison between the means of the two samples  

The null hypothesis is H₀:  μ₁ ≤ μ₂

The alternative hypothesis is Hₐ: μ₁ > μ₂

z=\dfrac{(\bar{x}_1-\bar{x}_2)-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}

Where;

\bar {x}_1 = 13.5

\bar {x}_2 = 12

σ₁ = 2.5

σ₂ = 1.5

We set our α level at 0.05

Therefore, our critical z = ± 1.96

For n₁ = n₂ = 23, we have;

z=\dfrac{(13.5-12)-(0)}{\sqrt{\dfrac{2.5^{2} }{23}-\dfrac{1.5^{2}}{23}}} = 3.5969

We reject the null hypothesis at α = 0.05, as our z-value, 3.5969 is larger than the critical z, 1.96 or mathematically, since 3.5969 > 1.96

Therefore, there is enough statistical evidence to suggest that Alyse time is larger than Jocelyn in a 1 mile race on a randomly select day and the probability that Alyse has a larger time than Jocelyn is 0.99983

Therefore;

The probability that Alyse has a smaller time than Jocelyn is 1 - 0.99983 = 0.00017 = 1.7 × 10⁻⁴.

8 0
3 years ago
-5.6+(-9.72) what does this equal?
nevsk [136]

So I'm not totally sure but I got -15.32

So sorry if it's wrong!!

4 0
3 years ago
If a quadratic function has x-intercepts at (-7,0) and 10,0), where would
madam [21]

Answer:

x = 1.5

Step-by-step explanation:

Since the axis of symmetry is between the 2 x intercepts, we can find it by finding the average of the x-coordinates of the 2 points.

(-7 + 10) / 2

3/2

= 1.5

So, the axis of symmetry is at x = 1.5

8 0
3 years ago
an official playing field (including end zone) for the indoor football league has a length 39 yd longer than its width. the peri
ch4aika [34]

Answer:

42

Step-by-step explanation:

39+39 = 78

162 - 78 = 2 lengths =84

84/2 = 42

5 0
3 years ago
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