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faust18 [17]
3 years ago
8

The sum of the first 150 negative integers is represented using the expression What is the sum of the first 150 negative integer

s? A. –22,650 B. –22,350 C. –11,325 D. –11,175

Mathematics
2 answers:
Rasek [7]3 years ago
8 0

Answer:

C

Step-by-step explanation:

E2020

Kamila [148]3 years ago
7 0

Answer:

C. -11,325

Step-by-step explanation:

  • To know the answer, is convenient to replace some values of "n" in the sum \sum_{(n=1)}^{150}[-1-(n-1)].
  • The result would appear after adding up every value of the expression \sum_{(n=1)}^{150}[-1-(n-1)] when n=1,2,3.....,150.
  • When n=1, the expression takes the value of (-1): [-1-(1-1)]= (-1)-0=-1.
  • When n=2, the expression takes the value of (-2): [-1-(2-1)]=-1-1=-2.
  • Following this way, for every n, we will obtain -n, then, the sum will be: -1-2-3-4-5-6-...-150. This sum can actually be expressed as \sum_{n=1}^{150}(-n), which is the result of solving the initial expression of the sum -1-(n-1)=-1-n+1=-n.
  • Finally, the sum of n=-1 to n=-150 equals -11,325.
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A new youth sports center is being built in a safe harbor. The perimeter of the rectangular playing field is 510 yards. The leng
podryga [215]

Answer:

<h2>L=203 yards</h2><h2>W=52 yards</h2>

Step-by-step explanation:

Step one:

given data

perimeter= 510 yards

let the width be x, width=x

length= (4x-5)-----quadruple mean 4 times

Step two:

the expression for perimeter is

P=2L+2W

510=2(4x-5)+2x

510=8x-10+2x

510+10=8x+2x

520=10x

divide both sides by 10

x=520/10

x=52

the width is 52 yards

the lenght is  (4x-5)

L=4(52)-5

L=208-5

L=203 yards

4 0
2 years ago
A total of $98,000 is to be​ invested, some in bonds and some in certificates of deposit​ (CDs). If the amount invested in bonds
mamaluj [8]
B= 2000 + CD
98000 = B + CD
substitute b in
98000 = 2000 + CD + CD
add variables
98000 = 2000 + 2CD
subtract 2000 from each side
96000 = 2CD
divide each side by 2
48000 = CD
7 0
3 years ago
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IRINA_888 [86]
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7 0
3 years ago
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A pyramid with a square base has how many faces?
mylen [45]

Answer:

It has 5 Faces. The 4 Side Faces are Triangles. The Base is a Square. It has 5 Vertices (corner points)


Step-by-step explanation:


3 0
3 years ago
A random sample of 100 automobile owners in thestate of Virginia shows that an automobile is driven onaverage 23,500 kilometers
Anastaziya [24]

Answer:

a) 22497.7 < μ< 24502.3

b)  With 99% confidence the possible error will not exceed 1002.3

Step-by-step explanation:

Given that:

Mean (μ) = 23500 kilometers per year

Standard deviation (σ) = 3900 kilometers

Confidence level (c) = 99% = 0.99

number of samples (n) = 100

a) α = 1 - c = 1 - 0.99 = 0.01

\frac{\alpha }{2} =\frac{0.01}{2}=0.005\\ z_{\frac{\alpha }{2}}=z_{0.005}=2.57

Using normal distribution table, z_{0.005 is the z value of 1 - 0.005 = 0.995 of the area to the right which is 2.57.

The margin of error (e) is given as:

e= z_{0.005}\frac{\sigma}{\sqrt{n} }  = 2.57*\frac{3900}{\sqrt{100} } =1002.3

The 99% confidence interval = (μ - e, μ + e) = (23500 - 1002.3, 23500 + 1002.3) =  (22497.7, 24502.3)

Confidence interval = 22497.7 < μ< 24502.3

b) With 99% confidence the possible error will not exceed 1002.3

5 0
3 years ago
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