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Mrrafil [7]
3 years ago
8

During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the

machine recommends that the temperature of the machine part remain below 141°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by
T = 0.005x² + 0.45x + 125.
Will the temperature of the part ever reach or exceed 141F? Use the discriminant of a quadratic equation to decide.
A. yes
B. no
Mathematics
1 answer:
mars1129 [50]3 years ago
6 0

Answer:

Yes, it will reach or exceed 141 degree F

Step-by-step explanation:

Given equation that shows the temperature T in degrees Fahrenheit x minutes after the machine is put into operation is,

T = 0.005x^2 + 0.45x + 125

Suppose T = 141°F,

\implies 141 = 0.005x^2 + 0.45x + 125

\implies 0.005x^2 + 0.45x + 125 - 141 =0

\implies 0.005x^2 + 0.45x - 16=0

Since, a quadratic equation ax^2 + bx + c =0 has,

Real roots,

If Discriminant, D = b^2 - 4ac \geq 0

Imaginary roots,

If D < 0,

Since, 0.45^2 - 4\times 0.005\times -16 = 0.2025 + 32 > 0

Thus, roots of -0.005x² + 0.45x + 125 are real.

Hence, the temperature can reach or exceed 141 degree F.

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A woman is randomly selected from the 18-24 age group. For women of this group, systolic blood pressures (in mm Hg) are normally
dybincka [34]

Answer:

0.0274

Step-by-step explanation:

The mean is \mu =114.8 and the standard deviation is \sigma =13.1.

Calculate

Z=\dfrac{X-\mu}{\sigma}

for X=140:

Z=\dfrac{140-114.8}{13.1}\approx 1.9237.

If X\sim N(114.8,\ 13.1), then Z\sim N(0,1)

and

Pr(X>140)=Pr(Z>1.9237).

Use table for normal distribution probabilities to get that

Pr(Z>1.9237)=1-Pr(Z\le 1.9237)=1-0.9726=0.0274.

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3 years ago
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Given:

The descriptions and equations. The equations are

y=4x

y=x+4

To find:

The correct description for each equation and match them.

Solution:

We know that, "+" is used for more and "×" is used for times.

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Additive: x is 4 more than y.

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y=4x

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4 0
3 years ago
What statement about a rhombus is never true?
Alekssandra [29.7K]
It can never be a square.
7 0
3 years ago
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a bucket contains 3 1/2 gallon of water. If Marie adds 5 gallons more, how many gallons of water will there be in all?​
Klio2033 [76]

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2 years ago
If jill and katie share 42 chocolates in the ratio of 3:4 then how may chocolates does jill get?
nasty-shy [4]

Answer:

jil got 18 chocolates

Step-by-step explanation:

let the ratio constants be x,

so, jil has 3x chocolates

katie has 4x chocolates

and we know total chocolates = 42

then,

=》3x + 4x = 42

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=》x = 42 ÷ 7

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so, jil got 3x = (3 × 6) = 18 chocolates

katie got 4x = (4 × 6) = 24 chocolates

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