Solve for n. (7^2)^4 = n^8

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

mars1129 [50]

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.

6 0

3 years ago

A hyena can run one over four mile in 22.5 seconds. Which of the following correctly shows this rate as miles per hour?

UNO [17]

Wouldnt you divide ? so itll be 5.62

8 0

3 years ago

What system the system that is made up of the heart,blood, and blood vessels is called the ____ this is for sceince but i cant f

Fiesta28 [93]

Answer:

Cardiovascular system

Step-by-step explanation:

8 0

2 years ago

Suppose that two openings on an appellate court bench are to be filled from current municipal court judges. The municipal court

Ksju [112]

Answer:

$(a)\dfrac{92}{117}$

$(b)\dfrac{8}{39}$

$(c)\dfrac{25}{117}$

Step-by-step explanation:

Number of Men, n(M)=24

Number of Women, n(W)=3

Total Sample, n(S)=24+3=27

Since you cannot appoint the same person twice, the probabilities are <u>without replacement.</u>

(a)Probability that both appointees are men.

$P(MM)=\dfrac{24}{27}X \dfrac{23}{26}=\dfrac{552}{702}\\=\dfrac{92}{117}$

(b)Probability that one man and one woman are appointed.

To find the probability that one man and one woman are appointed, this could happen in two ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.

P(One man and one woman are appointed) $=P(MW)+P(WM)$

$=(\dfrac{24}{27}X \dfrac{3}{26})+(\dfrac{3}{27}X \dfrac{24}{26})\\=\dfrac{72}{702}+\dfrac{72}{702}\\=\dfrac{144}{702}\\=\dfrac{8}{39}$

(c)Probability that at least one woman is appointed.

The probability that at least one woman is appointed can occur in three ways.

A man is appointed first and a woman is appointed next.
A woman is appointed first and a man is appointed next.
Two women are appointed

P(at least one woman is appointed) $=P(MW)+P(WM)+P(WW)$

$P(WW)=\dfrac{3}{27}X \dfrac{2}{26}=\dfrac{6}{702}$

In Part B, $P(MW)+P(WM)=\frac{8}{39}$

Therefore:

$P(MW)+P(WM)+P(WW)=\dfrac{8}{39}+\dfrac{6}{702}\\$P(at least one woman is appointed)=\dfrac{25}{117}$

5 0

3 years ago

at the snack shack, students attending the football game can buy sodas for $1 and slices of pizza for $3. At fridays game, the s

hram777 [196]

Answer:

126-pizza

124- soda

Step-by-step explanation:

4 0

3 years ago