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3 years ago

Given that the point (4,10) is a max on the quadratic function, explain whether these statements are true or false:

Mathematics

1 answer:

11Alexandr11 [23.1K]3 years ago

7 0

Answer:

(a) TRUE; (b) FALSE; (c) TRUE

Step-by-step explanation:

a. The instantaneous rate of change at 4 is 0. TRUE.

The function is f(x) = a(x-4)^2 - 10; the derivative of this function is f '(x) = 2a(x-4), which must equal zero (0) at the vertex / max (4,10). Zero slope at the vertex corresponds with instantaneous rate of change zero at that point.

b. f(6)>f(4). FALSE.

Using the function given in (a), above, f(x) = a(x-4)^2 - 10. Since (4,10) is the max of this function, f is increasing on (-infinity, 4) and decreasing on (4, infinity). Thus, f(6) is smaller than f(4).

c. There is only one possible value for x that has an instantaneous rate of change = 0. TRUE

The inst. rate of change takes on the value 0 only at (4,10), since (4,10) is the vertex of this downward-opening parabolic graph.

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Each algorithm is applied to a group of 52 sample problems. The new algorithm completes the sample problems with a mean time of

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Answer:

Therefore we fail to reject the Null hypothesis $H_0$

Because the is no sufficient evidence to support the claim of the alternative hypothesis $H_a$

Step-by-step explanation:

From the question we are told that

Sample size $n_1 =52$

Mean time 1 $\=x_1=24.04\ hours$

Mean time 2 $\=x_2=24.52\ hours$

Standard deviation $\partial _1=5.769$

Standard deviation $\partial _2=5.556$

Level of significance 0.05

The null hypothesis is $H_o: \mu_1=\mu_2$

Alternative hypothesis $H_a: \mu_1$

Generally the test statistics is mathematically represented as

$Z= \frac{\=x_1-\=x_2}{\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}}$

$Z= \frac{24.04-24.52}{\sqrt{\frac{5.769^2}{52}+\frac{5.5562^2}{52}}}$

$Z= -0.4321583379$

$Z= -0.43$

From Table the Z-critical value at $\alpha =0.05\ is\ -1.6449$

Therefore

Zcal> Zcritical

(-0.43)=(-1.645)

Generally we fail to reject the null hypothesis $H_0$ at $\alpha = 0.05$

Therefore we fail to reject the $H_0$

Because the is no sufficient evidence to support the claim of $H_a$

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Answer:

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Step-by-step explanation:

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$\large\underline{\underline{\red{\rm\blue{\longmapsto} Step-by-step\: Explanation:-}}}$

Given that , a dealer bought an article for Rs 1500 and sold it at a profit of 20% .

So , here ,

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Profit on the article = 20% .

Since the article is sold at profit , the Selling price of the article will equal to Cost price + 20% of cost price .

Firstly let's Calculate 20% of 1500 .

= 20% of Rs 1500 .

= 20/100 × Rs 1500 .

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Hence we can find now Selling price as ,

$\boxed{\green{\bf Selling\: Price=Cost\:Price+Profit}}$

⇒ SP = CP + Profit .

⇒ SP = Rs ( 1500 + 300 ).

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