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Savatey [412]
3 years ago
7

What is the fifth term in the arithmetic sequence defined by the explicit formula an=6n−4?

Mathematics
2 answers:
Vesna [10]3 years ago
5 0
The correct answer is 26.i took the test
Juli2301 [7.4K]3 years ago
4 0
<span>In an explicit formula, n represents any term number and a(n) represents the value of the n-th term. Therefore, in order to find the fifth term, we simply solve for a(n) when n = 5. Plugging that value into the equation gives us a(5)=6(5)-4, or a(5) = 26. The fifth term is of the sequence is 26.</span>
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An orbiting satellite has seven solar cells, which function independently of each other. During a mission, each cell fails with
Makovka662 [10]
The due date is 2pm, dolololo
4 0
3 years ago
The prices of three t-shirts styles are $24, $30 and $36. the probability of choosing a $24 t-shirt is 1/6. the probability of c
Slav-nsk [51]

\text{Answer} : \text{The expected value of a t-shirt is \$31.}

Explanation:

Since we have given that

The prices of three t-shirts styles  i.e $24, $30, $36 with their probability is given by

\frac{1}{6}, \frac{1}{2},\frac{1}{3}

As we know that,

E(X)= \sum_{1}^{3}x_iP(x_i)

\text{where} x_i \text{ is the prices of t- shirts styles}

Now,

x_1= \$24 , x_2=\$30 , x_3=$36

and

P(x_1)=\frac{1}{6},P(x_2)=\frac{1}{2}, P(x_3)=\frac{1}{3}

So,

E(X)= 24\times \frac{1}{6}+30\times\frac{1}{2}+36\times \frac{1}{3}\\=4+15+12\\=31

So, the expected value of a t-shirt = $31.

4 0
3 years ago
The cross country coach later determine that the length of the football field is 120 yards. All students must run five laps. Usi
Sedaia [141]

Answer:

25.2

Step-by-step explanation:

3 0
2 years ago
Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).
aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0
3 years ago
Please explain how you got your answers! (: Solve the problem by using the counting principle.
Natasha2012 [34]
A. The number of fabric-pattern-color combinations is 4 * 13 * 9 = 468

B. P(1st choice) = no of novels / total books = 3/6 = 1/2
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    P(both novels) = 1/2 * 2/5 = 1/5          (without replacement assumed)

C. P(1st choice) = no of biographies / total books = 2/6 = 1/3
    P(2nd choice) = no of remaining biographies/ total remaining books =        1/5
    P(both biographies) = 1/3 * 1/5 = 1/15          (without replacement                assumed)

D. P(1st choice) = no of history books / total books = 1/6
    P(2nd choice) = no of novels/ total remaining books = 3/5
    P(a history, then a novel) = 1/6 * 3/5 = 1/10          (without replacement assumed)
7 0
3 years ago
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