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3 years ago

X² - kx+4-0If the equation hasequal roots, thenb²-4ac=0where a=1, b = -k and c=4

Mathematics

1 answer:

olga55 [171]3 years ago

3 0

Answer:

k = ± 4

Step-by-step explanation:

Given

x² - kx + 4 = 0 ← in standard form

with a = 1, b = - k, c = 4

The equation has equal roots, thus the discriminant

b² - 4ac = 0, that is

(- k)² - (4 × 1 × 4) = 0

k² - 16 = 0 ( add 16 to both sides )

k² = 16 ( take the square root of both sides )

k = ± $\sqrt{16}$ = ± 4

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151 3/16 divided by 10 1/4

anyanavicka [17]

Answer: 59/4 or 14 3/4

Step-by-step explanation:

151 3 /16 ÷ 10 1 /4

2419 /16 ÷ 41 /4

2419/16 × 4/41

2419 × 4 /16 × 41

9676 /656

Divide both sides by 164

9676 ÷ 164 / 656 ÷ 164

59 /4 = 14 3 /4

4 0

2 years ago

The National Vaccine Information Center estimates that 90% of Americans have had chickenpox by the time they reach adulthood.32

drek231 [11]

Answer:

0.59% probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.

Step-by-step explanation:

For each person, there are only two possible outcomes. Either they have had chickenpox, or they have not. The probability of a person having had chickenpox is independent from other people. So we use the binomial probability distribution to solve this problem.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

90% of Americans have had chickenpox by the time they reach adulthood.

This means that $p = 0.9$

Suppose we take a random sample of 100 American adults. Is the use of the binomial distribution appropriate for calculating the probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood

This is $P(X = 97)$ when $n = 100$ . So

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 97) = C_{100,97}.(0.9)^{97}.(0.1)^{3} = 0.0059$

0.59% probability that exactly 97 out of 100 randomly sampled American adults had chickenpox during childhood.

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3 years ago

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3 years ago

Honey's blueberry muffin recipe calls for 3 1/4 pounds of blueberries and 2 1/2 cups of muffin mix. How many cups of muffin mix

astra-53 [7]

For this case we convert the mixed numbers to improper fractions: $3 \frac {1} {4} = \frac {4 * 3 + 1} {4} = \frac {12 + 1} {4} = \frac {13} {4}\\2 \frac {1} {2} = \frac {2 * 2 + 1} {2} = \frac {4 + 1} {2} = \frac {5} {2}$

Now, we propose a rule of three:

$\frac {13} {4}$ pounds of blueberries -------------> $\frac {5} {2}$ cups of muffin mix

7 pounds of blueberries -----------------------------> x

Where the variable "x" represents the number of cups of muffin mix that Honey should use.

$x = \frac {7 * \frac {5} {2}} {\frac {13} {4}}\\x = \frac {\frac {35} {2}} {\frac {13} {4}}\\x = \frac {35 * 4} {2 * 13}\\x = \frac {140} {26}\\x = \frac {70} {13}\\x = 5.38$

So approximately Honey should use $5 \frac {5} {13}$ cups of muffin mix

Answer:

Approximately Honey should use $5 \frac {5} {13}$ cups of muffin mix

7 0

2 years ago

I need help on this question plz

podryga [215]

It’s 4, because ththey go by fours because of the way they go up.

7 0

3 years ago

X² - kx+4-0If the equation hasequal roots, thenb²-4ac=0where a=1, b = -k and c=4​

X² - kx+4-0If the equation hasequal roots, thenb²-4ac=0where a=1, b = -k and c=4