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2 years ago

Draw or write to explain why 1 hundred 4 tens and 14 tens name the same amount

Mathematics

2 answers:

mihalych1998 [28]2 years ago

7 0

1 hundred can also be 10 tens so when you add 10 tens and 4 tens you 14 tens and that is the same thing as 14 tens

IrinaVladis [17]2 years ago

4 0

Write the number 55 in another way

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If Julie needs 3 1/4 cups of oatmeal, how many 1/4 cups oatmeal will shw use?

lyudmila [28]

If Julie needs 3 ¼ cups of oatmeal How many ¼ cups will she uses, Solution: The # of cups she will use = 3 ¼ divide by ¼ 13/4/1/4 = 13/4*4/1 =13 cups

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2 years ago

Read 2 more answers

Compute P(x) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate thi

stich3 [128]

Answer:

The answers to the questions are;

A) P(X) where x = 12 is equal to 3.55 ×10⁻²

B) P(x) using the normal distribution is given by the probability distribution function and is equal to 3.453 ×10⁻²

C) The calculated probabilities of P(x=12) using the binomial probability formula and the probability distribution function differ by 9.7×10⁻⁴

D) The normal distribution be used to approximate this probability because a. because np(1-p) %u2265 ⇒ np(1-p) ≥ 10

E) c. the value of fi represents the expected proportion of observation less than or equal to the ith data value.

Step-by-step explanation:

To solve the question, we note that

n = 58

p = 0.3

x = 12

Here we have n·p = 17.4 and n·q = 40.6 both ≥ 5 that is the normal distribution can be used to estimate the probability

A) We are to use the binomial probability formula to find P(X)

Where x = 12, we have P(12) = ₅₈C₁₂×0.3¹²×0.7⁴⁶

= 891794789340×0.000000531441×7.49×10⁻⁸ = 3.55 ×10⁻²

B) Using the standard distribution table we have

the z score for x = 12 given as $z = \frac{x-\mu}{\sigma}$ = -1.55

From the normal distribution table, we have the probability that value is below 12 = .06057 while the normal probability distribution function which gives the probability of a number being 12 is given by

$\frac{1}{\sigma\sqrt{2 \pi } } e^{\frac{-(x-\mu)^2}{2\sigma^2} }$

where:

σ = Standard deviation = $\sqrt{npq} = \sqrt{np(1-p)} = \sqrt{58*0.3*(1-0.3)} = 3.48999$

μ = Sample mean = n·p = 58×0.3 =17.4

Therefore the probability density function is $\frac{1}{3.49\sqrt{2 \pi } } e^{\frac{-(12-17.4)^2}{2*3.49^2} } = 3.453*10^{-2}$

C) The probabilities differ by 3.55 ×10⁻² - 3.453 ×10⁻² = 9.7×10⁻⁴

D) The normal distribution be used to approximate this probability because n·p and n·p·(n-p) ≥ 5

E) f $_i$ represents the area under the curve towards left of the ith data observed in a normally distributed population.

Therefore, the value of fi represents the expected proportion of observation less than or equal to the ith data value

5 0

2 years ago

It takes Lucas 3 hours to cycle from his home to his friends village but if travels 5 mph slower, it will take him 1.5 hours lon

Alika [10]

The distance from friend's village to Lucas's house is 45 miles

Step-by-step explanation:

Lets assume the distance from Lucas home to friend's village is x miles

The time taken to cycle from Lucas home to friend's village is 3 hrs....t₁

The time taken if travelling at a 5 mph reduced speed is 1.5 hrs longer......t₂

t₂=4.5 hrs

t₁= 3 hrs

Speed for cycle in first instance, where t₁=3 hrs and distance is x miles

s₁=d/t = x/3 mph

Speed for cycle if travelling at a slower speed,

$s=\frac{x}{3}-5$

Time taken in the second instance when travelling at a slower speed

= $\frac{x}{\frac{x}{3}-5 }=4.5\\ \\\frac{3x}{x-15} =4.5\\\\\\3x=4.5(x-15)\\\\3x=4.5x-67.5\\\\\\67.5=4.5x-3x\\\\\\67.5=1.5x\\\\\\67.5/1.5=x\\\\\\45=x$