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3 years ago

HURRY!! select ALL the correct answers

Mathematics

1 answer:

Rainbow [258]3 years ago

8 0

Answer:

2nd, 3rd and 5th options are correct.

Step by step explanation:

We are asked to find which of the given operations involving complex numbers have solutions represented by point A on the graph.

We can see that point A lies on (1,-2i). Let us see which of our given expressions give us coordinates of point A.

1. $(4+i)+3(1+i)$

$4+i+3+3i$

$4+3+i+3i$

$7+4i$

We can see that our 1st option is incorrect.

2. $(4+i)-3(1+i)$

$4+i-3-3i$

$4-3-3i+i$

$1-2i$

We can see that our 2nd option is correct.

3. $(4+i)+(-3-3i)$

$4+i-3-3i$

$4-3+i-3i$

$1-2i$

We can see that our 3rd option is correct.

4. $(4+i)+(3-3i)$

$4+i+3-3i$

$4+3+i-3i$

$7-2i$

Upon simplifying our expression we got $7-2i$ which is not equal to coordinates of point A. Therefore, 4th option is incorrect.

5. $(4+i)-(3+3i)$

$4+i-3-3i$

$4-3+i-3i$

$1-2i$

Upon simplifying our expression we got coordinates of point A. Therefore, 5th option is correct indeed.

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Assume the annual day care cost per child is normally distributed with a mean of $9000 and a standard deviation of $1000. What

Tpy6a [65]

Answer:

65.54% (nearest hundredth)

Step-by-step explanation:

Given:

$\sf \mu=9000$

$\sf \sigma=1000$

$\sf X \sim N(\mu, \sigma^2)\implies X \sim N(9000,1000^2)$

P(X > 8600) = 1 - P(X ≤ 8600)

= 1 - 0.3445782584

= 0.6554217416

= 65.54%

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2 years ago

Diego drank x ounces of juice. Lin drank 1/8 less than that.

Varvara68 [4.7K]

Answer:

Step-by-step explanation:

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3 years ago

A scientist has a sample of bacteria that initially contains 10 million microbes. They observe the sample and finds that the num

sergiy2304 [10]

Answer:

M(t) = 6.7 * 10⁷ (67 million)

Minutes (t) =55

Step-by-step explanation:

1. Write an exponential equation that represents M, the total number of bacterial microbes in millions, as a function of t, the number of minutes the sample has been observed.

For answering this question, we will use the following formula:

M(t) = B₀ * g ^(t/m), where:

•M(t) represents the total number of bacterial microbes in millions.

• B₀ represents the initial population of bacteria in millions.

• g represents the growth factor.

• t represents the total number of minutes we will observe the bacteria growing.

• m represents the time in minutes it takes to the growth factor g to occur.

2. Then, determine how much time, to the nearest minute, will pass until there are 67 million bacterial microbes.

M(t) = B₀ * g ^(t/m)

Replacing with the values we know:

6.7 * 10⁷ = 10⁷ * 2 ^(t/20)

6.7 = 2 ^(t/20) (Dividing by 10⁷ at both sides)

ln 6.7 = ln 2 ^(t/20)

ln 6.7 = t/20 ln 2

ln 6.7/ ln 2 = t/20

t = ln 6.7/ln 2 * 20

t = 2.74 * 20

t = 54.88

t ≅ 55 (rounding to the nearest minute)

3 0

2 years ago

A rectangle has a length that is three feet more than twice it's width. The perimeter of the rectangle is 78 feet. State the val

ivann1987 [24]

Let the width of the rectangle be 'w'

According to the question length of the rectangle (l) is three feet more than twice it's width;

$\longrightarrow$ l = (2w + 3) ft

Perimeter of rectangle = 78 ft

Formula of perimeter of rectangle = 2(Length + Width)

So,

$\rm \implies 2(Length + Width) = 78 \\ \\ \rm \implies 2(2w + 3 + w) = 78 \\ \\ \rm \implies 2(3w + 3) = 78 \\ \\ \rm \implies 2 \times 3(w + 1) = 78 \\ \\ \rm \implies 6(w + 1) = 78 \\ \\ \rm \implies w + 1 = \dfrac{78}{6} \\ \\ \rm \implies w + 1 = 13 \\ \\ \rm \implies w = 13 - 1 \\ \\ \rm \implies w = 12 \: ft$

$\therefore$ Width of the rectangle (w) = 12 ft

3 0

3 years ago

The length of Marianna's dress measures 1 1/4 yards. She hems the dress, makint it 3/8 yard shorter. How long is her dress now?

ser-zykov [4K]

Answer:

7/8 yards

Step-by-step explanation:

1 1/4- 3/8

first change 1 1/4 to an improper fraction: 5/4

next, find common denominator which is 8

5/4=10/8

10/8-3/8=7/8

6 0

3 years ago