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andrew-mc [135]
3 years ago
5

What is the sum of the arithmetic series

Mathematics
1 answer:
docker41 [41]3 years ago
6 0

Answer:

S_ {12} = 192

Step-by-step explanation:

The nth term of the given arithmetic sequence is

U_n = 3 + 2n

The first term of this series is:

U_1 = 3 + 2(1) = 5

The last term of this series is when

n = 12

U_ {12}= 3 + 2(12)

U_ {12}= 3 + 24 = 27

The sum of the first n terms of an arithmetic series when the first an last term is known is given by:

S_n =  \frac{n}{2}(a + l)

Where a=5 is the first term and l=27 is the last term.

S_ {12} =  \frac{12}{2}(5 + 27)

S_ {12} =6(32) =19 2

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Delicious77 [7]

Answer:

x = 51^o

Step-by-step explanation:

Given

Intersecting lines

Required

Find x

To do this, we make use of:

x + 23^o + 2x + 4^o = 180^o --- angle on a straight line

Collect like terms

x  + 2x = 180^o - 4^o - 23^o

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5 0
3 years ago
The mean hours of sleep that students get per night is 7 hours, the standard deviation of hours of sleep is 1.7 hours, and the d
densk [106]

Answer:

c. 3.6 and 10.4 hrs

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean 7, standard deviation 1.7.

For about 95% of students, nightly amount of sleep is between

7 - 2*1.7 = 7 - 3.4 = 3.6 hours

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So the correct answer is:

c. 3.6 and 10.4 hrs

5 0
3 years ago
Write an equation for a quadratic function that has x intercepts (-3, 0) and (5, 0)
Blizzard [7]

Answer:

One possible equation is f(x) = (x + 3)\, (x - 5), which is equivalent to f(x) = x^{2} - 2\, x - 15.

Step-by-step explanation:

The factor theorem states that if x = x_{0}  (where x_{0} is a constant) is a root of a function, (x - x_{0}) would be a factor of that function.

The question states that (-3,\, 0) and (5,\, 0) are x-intercepts of this function. In other words, x = -3 and x = 5 would both set the value of this quadratic function to 0. Thus, x = -3\! and x = 5\! would be two roots of this function.

By the factor theorem, (x - (-3)) and (x - 5) would be two factors of this function.

Because the function in this question is quadratic, (x - (-3)) and (x - 5) would be the only two factors of this function. In other words, for some constant a (a \ne 0):

f(x) = a\, (x - (-3))\, (x - 5).

Simplify to obtain:

f(x) = a\, (x + 3)\, (x - 5).

Expand this expression to obtain:

f(x) = a\, (x^{2} - 2\, x - 15).

(Quadratic functions are polynomials of degree two. If this function has any factor other than (x - (-3)) and (x - 5), expanding the expression would give a polynomial of degree at least three- not quadratic.)

Every non-zero value of a corresponds to a distinct quadratic function with x-intercepts (-3,\, 0) and (5,\, 0). For example, with a = 1:

f(x) = (x + 3)\, (x - 5), or equivalently,

f(x) = x^{2} - 2\, x - 15.

6 0
2 years ago
Help !!! i dont understand !
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3 years ago
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Inga [223]

Answer:

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2. Compare all of the unit rate values (Savannah: $9.50 per hour, Greg: $9 per hour, and Kevin: $8.25 per hour).

4 0
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