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Aliun [14]
3 years ago
13

Find the nth term of 14,23,32,41

Mathematics
1 answer:
german3 years ago
8 0

\\$Let a_n$ be the following sequence: 14, 23, 32, 41, ...\\a_1 = 14 \ \ \ a_2 = 23 \ \ \ a_3 = 32 \ \ \ a_4 = 41\\$Observe that $ a_2 - a_1 = a_3 - a_2 = a_4 - a_3 = 9 =>$ a_n - $Arithmetic progression$=> a_n = 14 + 9(n-1)

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Find the distance of a line given the following points. R(3, 1), W(-1, -2)
olga_2 [115]

Answer:

5 units

Step-by-step explanation:

±√(- 2 - 1)^2 + (- 1 - 3)^2 = ±5 (rej - 5 since distance > 0)

Apply distance formula

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7 0
2 years ago
Lilia scores 15 points fewer than Bob, who scores 35 points. Carol scores half as many points as Lilia. How many points does Car
nignag [31]

Answer:

10  points the explantion is below

Step-by-step explanation:

Bob scored 35 points and Lilla scores 15 less so you start with 35 - 15. Then you want to divide 20 by 2 because Carol scored half as much as Lilla. Your equation is ( 35-15) / 2 = 10

3 0
3 years ago
Help!<br><br> If a sphere has a radius of 8mm, what is its volume? (Show work)
babymother [125]
The formula for the volume of a sphere is V = (4/3) * π * r³. Knowing this, we can plug in the radius:

V = \frac{4}{3} \pi *8^{3} \\ V = \frac{4}{3} \pi*512 \\ V = 2144.66

The sphere's volume is approximately 2144.66 mm^3.
7 0
3 years ago
A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At a
zubka84 [21]

Answer:

Z = -1.333

P-value  = 0.09176

Decision Rule: Reject H_o if ∝  is greater than the P-value

Conclusion: Since P-value is >  the level of significance ∝, we fail to reject the null hypothesis, therefore there is insufficient evidence to conclude that at least half of all voters prefer the Democrat.

Step-by-step explanation:

Given that:

The sample size of the poll = 1068

The proportion of voters that preferred Democratic candidate is \hat p = 0.48

To test the claim that at least half of all voters prefer the Democrat, i.e 1/2 = 0.5

The null hypothesis and the alternative hypothesis can be computed as:

H_o : p \geq 0.50

H_1 : p < 0.50

Using the Z test statistics which can be expressed by the formula:

Z = \dfrac{\hat p - p}{\dfrac{\sqrt{p(1-p) }}{n}}}

Z = \dfrac{0.48 - 0.5}{\dfrac{\sqrt{0.5(1-0.5) }}{1068}}}

Z = \dfrac{-0.02}{\sqrt{\dfrac{{0.5(0.5) }}{1068}}}

Z = \dfrac{-0.02}{\sqrt{\dfrac{{0.25}}{1068}}}

Z = \dfrac{-0.02}{0.015}

Z = -1.333

P-value = P(Z< -1.33)

From z tables,

P-value  = 0.09176

The level of significance ∝ = 0.05

Decision Rule: Reject H_o if ∝  is greater than the P-value

Conclusion: Since P-value is >  the level of significance ∝, we fail to reject the null hypothesis, therefore there is insufficient evidence to conclude that at least half of all voters prefer the Democrat.

5 0
3 years ago
#5 In *triangle* ABC, AB = 9 and BC = 15. What is the range the possible lengths for CA?<br> Why?
Naddika [18.5K]
CA must be in the range [15 - 9, 15 + 9] = [6, 24]
For the line segments to form a triangle the length of CA cannot be less the the difference between the other sides or greater than their sum.
At either extreme the three points A, B and C will be co-linear thus forming a triangle with area of zero
5 0
2 years ago
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