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Vikentia [17]
3 years ago
6

Solve for x: 11x-10=-6x^2

Mathematics
1 answer:
Orlov [11]3 years ago
5 0

Answer:

<h2>x = -5/2 , x = 2/3</h2>

Step-by-step explanation:

11x - 10 = -6x^2

-6x^2 = 11x - 10

-6x^2 + 10 = 11x - 10 + 10

-6x^2 + 10 = 11x

-6x^2 + 10 -11x   = 11x - 11x

-6x^2 - 11x + 10 = 0

<h3><em /></h3><h3><em>Solve with the quadratic formula.</em></h3>

<em>*I will only solve for the first x</em>

<em />

<em>- 11 + root 361 / 12 </em>

<em>= -11 + 19  / 12</em>

<em>= - 30/12</em>

<em>= -5/2</em>

<em />

<em />

<em />

<em />

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5 0
3 years ago
In a recent survey of college professors, it was found that the average amount of money spent on entertainment each week was nor
Alenkinab [10]

Answer:

0.0918

Step-by-step explanation:

We know that the average amount of money spent on entertainment is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.

The mean and standard deviation of average spending of sample size 25 are

μxbar=μ=95.25

σxbar=σ/√n=27.32/√25=27.32/5=5.464.

So, the average spending of a sample of 25 randomly-selected professors is normally distributed with mean=μ=95.25 and standard deviation=σ=27.32.

The z-score associated with average spending $102.5

Z=[Xbar-μxbar]/σxbar

Z=[102.5-95.25]/5.464

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Z=1.3269=1.33

We have to find P(Xbar>102.5).

P(Xbar>102.5)=P(Z>1.33)

P(Xbar>102.5)=P(0<Z<∞)-P(0<Z<1.33)

P(Xbar>102.5)=0.5-0.4082

P(Xbar>102.5)=0.0918.

Thus, the probability that the average spending of a sample of 25 randomly-selected professors will exceed $102.5 is 0.0918.

5 0
3 years ago
Sierra applies a coat of epoxy paint to the four sides and floor of a rectangular swimming pool. The pool is 4 feet deep, 18 fee
Brilliant_brown [7]

Answer:

4 gallons of paint

Step-by-step explanation:

We solve using the formula for surface area of rectangular prism.

A=2(wl+hl+hw)

Where:

w = Width

h = Height

l = Length

The pool is 4 feet deep, 18 feet long, and 12 feet wide.

Hence,

=2 × (12 × 18 + 4 × 18 + 4 ×12)

=672 square feet

One gallon of paint covers 155 square feet.

Hence,

155 square feet = 1 gallon of paint

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Cross Multiply

155 square feet × x = 672 square feet × 1 gallon of paint

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x = 4.335483871 gallons of paint

Therefore, based on the calculation above, approximately to the nearest whole number, Sierra uses 4 gallons of paint

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3 years ago
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