MATHEMATICS COLLEGE

23.5 in expanded form164.38 in expanded form
209.106 in expanded form

can you help me

Answers

Answer 1

Answer:

Answer:

+ 3

+ 0.5

100

+ 60

+ 4

+ 0.3

+ 0.08

200

+ 0

+ 9

+ 0.1

+ 0.00

+ 0.006

Step-by-step explanation:

Hope this helps :D

Answer 2

Answer:

23.5 in expanded form is: 20 + 3 + 0.5

164.38 in expanded form is: 100 + 60 + 4 + 0.3 + 0.08

209.106 in expanded form is: 200 + 0 + 9 + 0.1 + 0.00 + 0.006

Step-by-step explanation:

Show the value of each digit when writing in expanded form. Use plus signs (+) between the values. Knowing the definition of expanded notation can help. Expanded notation means:

"Writing a number to show the value of each digit. It is shown as a sum of each digit multiplied by its matching place value (ones, tens, hundreds, etc.)."

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What times what equals -20 and those same numbers added together equals 8

Multiply.(3x+4)(2x−1)

Express the answer in standard form.

Enter your answer in the box.

Answers

(3x+4)(2x−1)

FOIL (first outer inner last)

3x*2x + 3x*(-1) + 4*2x+4*(-1)

6x^2 -3x+8x -4

6x^2 +5x-4

(3x + 4)(2x - 1) distributive

= (3x)(2x) + (3x)(-1) + (4)(2x) + (4)(-1) = 6x² - 3x + 8x - 4

combine like terms

= 6x² + 5x - 4

Answer: (3x + 4)(2x - 1) = 6x² + 5x - 4

For the equation y = 2x2 - 5x + 18, choose the correct
application of the quadratic formula.

Answers

Answer:

Option (2)

Step-by-step explanation:

For a quadratic equation,

ax² + bx + c = 0

roots of this equation can be determined by using quadratic formula,

x = $(-b\pm√(b^2-4ac))/(2a)$

Comparing this quadratic equation with the given equation,

y = 2x² - 5x + 18 = 0

a = 2

b = (-5)

c = 18

By substituting these values in the given formula,

x = $(5\pm√((-5)^2-4(2)(18)) )/(2(2))$

Therefore, Option (2) will be the answer.

Hey !! Can anyone help me with this question please and thank you !

Answers

Answer:

x = 22

Step-by-step explanation:

6x+3 = 7x - 19

22 = x

good day

A typical person has an average heart rate of 70.0 70.0 beats/min. Calculate the given questions. How many beats does she have in 6.0 6.0 years? How many beats in 6.00 6.00 years? And finally, how many beats in 6.000 6.000 years? Pay close attention to significant figures in this question.

Answers

Answer:

a) 2.2 × 10⁸ beats

b) 2.20 × 10⁸ beats

c) 2.207 × 10⁸ beats

Step-by-step explanation:

Data provided in the question:

Average heart rate of a typical person = 70.0 beats/min

Now,

In the given cases, the significance is on the significant figures after the decimal

Therefore,

the answer is will be provided accordingly

Now,

a) Time = 6.0 years

[since 1 significant figure after decimal. answer will be give in 1 significant figure after decimal ]

time in minutes = 6.0 × 365 × 24 × 60

= 3.1 × 10⁶ minutes

Total beats = Average heart rate × Time

= 70 × 3.1 × 10⁶

= 2.2 × 10⁸ beats

b) Time = 6.00 years

[since 2 significant figure after decimal. answer will be give in 2 significant figure after decimal ]

time in minutes = 6.00 × 365 × 24 × 60

= 3.15 × 10⁶ minutes

Total beats = Average heart rate × Time

= 70 × 3.15 × 10⁶

= 2.20 × 10⁸ beats

c) Time = 6.000 years

[since 3 significant figure after decimal. answer will be give in 3 significant figure after decimal ]

time in minutes = 6.000 × 365 × 24 × 60

= 3.154 × 10⁶ minutes

Total beats = Average heart rate × Time

= 70 × 3.154 × 10⁶

= 2.207 × 10⁸ beats

PLEASE HELP ME ASAPP if can of not then just leave it

Answers

Answer:

Step-by-step explanation:

A manufacturing company regularly conducts quality control checks at specified periods on the products it manufactures. Historically, the failure rate for LED light bulbs that the company manufactures is 5%. Suppose a random sample of 10 LED light bulbs is selected. What is the probability that a) None of the LED light bulbs are defective? b) Exactly one of the LED light bulbs is defective? c) Two or fewer of the LED light bulbs are defective? d) Three or more of the LED light bulbs are not defective?

Answers

Answer:

a) There is a 59.87% probability that none of the LED light bulbs are defective.

b) There is a 31.51% probability that exactly one of the light bulbs is defective.

c) There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) There is a 100% probability that three or more of the LED light bulbs are not defective.

Step-by-step explanation:

For each light bulb, there are only two possible outcomes. Either it fails, or it does not. This means that 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 combinatios of x objects from a set of n elements, given by the following formula.

$C_(n,x) = (n!)/(x!(n-x)!)$

And p is the probability of X happening.

In this problem we have that:

$n = 10, p = 0.05$

a) None of the LED light bulbs are defective?

This is P(X = 0).

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

$P(X = 0) = C_(10,0)*(0.05)^(0)*(0.95)^(10) = 0.5987$

There is a 59.87% probability that none of the LED light bulbs are defective.

b) Exactly one of the LED light bulbs is defective?

This is P(X = 1).

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

$P(X = 1) = C_(10,1)*(0.05)^(1)*(0.95)^(9) = 0.3151$

There is a 31.51% probability that exactly one of the light bulbs is defective.

c) Two or fewer of the LED light bulbs are defective?

This is

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = 2) = C_(10,2)*(0.05)^(2)*(0.95)^(8) = 0.0746$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.5987 + 0.3151 + 0.0746 0.9884$

There is a 98.84% probability that two or fewer of the LED light bulbs are defective.

d) Three or more of the LED light bulbs are not defective?

Now we use p = 0.95.

Either two or fewer are not defective, or three or more are not defective. The sum of these probabilities is decimal 1.

$P(X \leq 2) + P(X \geq 3) = 1$

$P(X \geq 3) = 1 - P(X \leq 2)$

In which

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)$

$P(X = 0) = C_(10,0)*(0.95)^(0)*(0.05)^(10)\cong 0$

$P(X = 1) = C_(10,1)*(0.95)^(1)*(0.05)^(9) \cong 0$

$P(X = 2) = C_(10,1)*(0.95)^(2)*(0.05)^(8) \cong 0$

$P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0$

$P(X \geq 3) = 1 - P(X \leq 2) = 1$

There is a 100% probability that three or more of the LED light bulbs are not defective.

Final answer:

The question relates to binomial distribution in probability theory. The probabilities calculated include those of none, one, two or less, and three or more LED bulbs being defective out of a random sample of 10.

Explanation:

This question relates to the binomial probability distribution. A binomial distribution is applicable because there are exactly two outcomes in each trial (either the LED bulb is defective or it's not) and the probability of a success remains consistent.

a) In this scenario, 'none of the bulbs being defective' means 10 successes. The formula for probability in a binomial distribution is p(x) = C(n, x) * [p^x] * [(1-p)^(n-x)]. Plugging in the values, we find p(10) = C(10, 10) * [0.95^10] * [0.05^0] = 0.5987 or 59.87%.

b) 'Exactly one of the bulbs being defective' implies 9 successes and 1 failure. Following the same formula, we get p(9) = C(10, 9) * [0.95^9] * [0.05^1] = 0.3151 or 31.51%.

c) 'Two or less bulbs being defective' means 8, 9 or 10 successes. We add the probabilities calculated in (a) and (b) with that of 8 successes to get this probability. Therefore, p(8 or 9 or 10) = p(8) + p(9) + p(10) = 0.95.

d) 'Three or more bulbs are not defective' means anywhere from 3 to 10 successes. As the failure rate is low, it's easier to calculate the case for 0, 1 and 2 successes and subtract it from 1 to find this probability. This gives us p(>=3) = 1 - p(2) - p(1) - p(0) = 0.98.