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4 years ago

Which statement(s) is (are) correct?

Mathematics

1 answer:

Anna71 [15]4 years ago

6 0

Answer:

statements 3 and 4 are correct.

Step-by-step explanation:

(1)

The probability of choosing cured pasta and bear= probability that the card is king.

Hence, The probability of choosing cured pasta and bear= $\dfrac{4}{52}=\dfrac{1}{13}$

Probability of choosing baked cucumber and lime mutton=probability that the card is 3.

as there are 4 cards that are '3'.

Hence Probability of choosing baked cucumber and lime mutton= $\dfrac{4}{52}=\dfrac{1}{13}$

as both the probabilities are equal.

Hence statement 1 is incorrect.

(2)

The probability of choosing gooseberry & passion fruit cheesecake= Probability taht the card is ace.

as there are 4 cards which are ace out of 52 cards.

Hence, The probability of choosing gooseberry & passion fruit cheesecake= $\dfrac{4}{52}=\dfrac{1}{13}$

probability of choosing poached fennel & lemon alligator=Probability that the card is a face card.

As there are 12 face cards out of 52 cards.

Hence, probability of choosing poached fennel & lemon alligator= $\dfrac{12}{52}=\dfrac{3}{13}$

Hence, the probability of choosing gooseberry and passion fruit cheesecake is smaller than the probability of choosing poached fennel & lemon alligator.

Hence statement 2 is false.

(3)

The probability of choosing a praline wafer=probability that the card is a diamond.

as there are 13 diamond cards out of 52 cards.

The probability of choosing a praline wafer= $\dfrac{13}{52}=\dfrac{1}{4}$

the probability of choosing poached fennel & lemon alligator=Probability that the card is a face card.

As there are 12 face cards out of 52 cards.

Hence, probability of choosing poached fennel & lemon alligator= $\dfrac{12}{52}=\dfrac{3}{13}$

Hence, The probability of choosing a praline wafer is greater than the probability of choosing poached fennel & lemon alligator.

Hence statement 3 is correct.

(4)

The probability of choosing pressure-cooked mushroom & garlic chicken =probability that the card is red.

As there are 26 red cards out of 52 cards.

Hence,

The probability of choosing pressure-cooked mushroom & garlic chicken = $\dfrac{26}{52}=\dfrac{1}{2}$

probability of choosing an oven-baked apple & lavender calzone =probability that the card is black.

As there are 26 red cards out of 52 cards.

Hence, probability of choosing an oven-baked apple & lavender calzone= $\dfrac{26}{52}=\dfrac{1}{2}$

Hence, The probability of choosing pressure-cooked mushroom & garlic chicken and the probability of choosing an oven-baked apple & lavender calzone are the same.

Hence statement 4 is true.

(5)

The probability of choosing pressure-cooked mushroom & garlic chicken =probability that the card is red.

As there are 26 red cards out of 52 cards.

Hence,

The probability of choosing pressure-cooked mushroom & garlic chicken = $\dfrac{26}{52}=\dfrac{1}{2}$

the probability of choosing a praline wafer=probability that the card is a diamond.

as there are 13 diamond cards out of 52 cards.

The probability of choosing a praline wafer= $\dfrac{13}{52}=\dfrac{1}{4}$

Hence, the probability of choosing pressure-cooked mushroom & garlic chicken and the probability of choosing a praline wafer are not same.

Hence, statement 5 is not correct.

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(a) Context or story

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There are 8 bits in a byte; How many bits are there, in $32\frac 14$ bytes

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3 years ago

Find the nature of the root

GREYUIT [131]

Answer:

1) Real and same.

2) Real and distinct

3) Real and distinct

4) Real and distinct

5) Real and distinct

6) Real and distinct

7) Real and distinct

8) Real and distinct

Step-by-step explanation:

If a quadratic equation is in the form of ax² + bx + c = 0, then Discriminant of the equation D = b² - 4ac, which governs the nature of roots the equation has.

If D > 0, then there will be two different real roots.

If D = 0, then two same and real roots.

If D < 0, then two distinct but imaginary roots.

Now, 1) x² + 6x + 9 = 0 has D = 6² - 4 × 9 × 1 = 0. So, there will be two same and real roots.

2) 5x² - x = 4x² + 2

⇒ x² - x - 2 = 0

It has D = (-1)² - 4 × 1 × (-2) = 9. Therefore, the roots will be two distinct and real.

3) $\frac{2}{x} + \frac{3}{x} = x - 4$

⇒ 5 = x² - 4x

⇒ x² - 4x - 5 = 0.

So, D = (-4)² - 4 × (1) × (- 5) = 36. So, the equation has two real and distinct rools.

4) x(x - 5) = 4(5 - x)

⇒ x² - x - 20 = 0

Hence, D = (-1)² - 4 × 1 × (-20) = 81

So, the roots will be real and distinct.

5) x² + 7x + 1 = 0 has D = 7² - 4 × 1 × 1 = 45

So, the roots will be real and distinct.

6) 2x² + 9x + 3 = 0, has D = 9² - 4 × 2 × 3 = 57.

Hence, the roots will be real and distinct.

7) 5x² - 6 = 13x

⇒ 5x² - 13x - 6 = 0

So, D = (-13)² - 4 × 5 × (-6) = 289

So, the roots will be real and distinct.

8) x² - x = 3(x + 7)

⇒ x² - 4x - 21 = 0

It has D = (-4)² - 4 × 1 × (-21) = 100

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3 years ago

A rectangular prism has a volume of 600 cubic inches.

choli [55]

Answer:

The length is 12 inches.

Step-by-step explanation:

The volume of a rectangular prism is given by:

V=LBH

It was given that; the rectangular prism has a volume of 600 cubic inches.

The height of the prism is 5 inches and the width is 10 inches.

We want to find the length of the rectangular prism.

We substitute V=600, H=5,and W=10 into the formula:

600=5×10×L

600=20L

$L = \frac{600}{50}$

$L = 12in$

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