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3 years ago

I will give branliest if you answer all four questions!

Mathematics

2 answers:

dem82 [27]3 years ago

5 0

Answer:

3- 0

there's 8 rows, and 48 tiles, 48/8=6, so there's no purple tiles needed

4- 240

36 students + 4 adults = 40, 40 people times 6 full buses = 240 people in total

5- 12

72 flags divided by 6 flags in each row = 12 rows

6- 10, 24, 38

composite numbers are like the opposite of prime numbers, you can divide them by more than just themselves and 1

hope this helps :)

Gennadij [26K]3 years ago

4 0

3.) 24 (im not exactly sure)

4.) 240

5.) 12

6.) 10, 24, 38

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A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce

NemiM [27]

Answer:

0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 12 ounces and a standard deviation of 0.2 ounces.

This means that $\mu = 12, \sigma = 0.2$

Sample of 9:

This means that $n = 9, s = \frac{0.2}{\sqrt{9}}$

Find the probability that the mean of the sample will be less than 12.1 ounces.

This is the pvalue of Z when X = 12.1. So

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{12.1 - 12}{\frac{0.2}{\sqrt{9}}}$

$Z = 1.5$

$Z = 1.5$ has a pvalue of 0.9332

0.9332 = 93.32% probability that the mean of the sample will be less than 12.1 ounces.

6 0

3 years ago

H=7 + 29t-16t^2 find all values of t for which the balls height is 19ft

NikAS [45]

$\bf \qquad \textit{initial velocity}\\\\
\begin{array}{llll}
\qquad \textit{in feet}\\\\
h(t) = -16t^2+v_ot+h_o
\end{array} 
\quad 
\begin{cases}
v_o=\textit{initial velocity of the object}\\
h_o=\textit{initial height of the object}\\
h=\textit{height of the object at "t" seconds}
\end{cases}\\\\
-------------------------------\\\\$

$\bf h(t)=7+29t-16t^2\qquad h(t)=19\implies 19=7+29t-16t^2
\\\\\\
16t^2-29t+12=0\impliedby \textit{now, let's use the quadratic formula}
\\\\\\
t=\cfrac{-(-29)\pm\sqrt{(-29)^2-4(16)(12)}}{2(16)}\implies t=\cfrac{29\pm\sqrt{841-768}}{32}
\\\\\\
t=\cfrac{29\pm\sqrt{73}}{32}\implies t\approx 
\begin{cases}
1.17\\
0.64
\end{cases}$

so hmm check the picture below, thus the ball hits 19 feet of height twice, once on the way up, and once on the way down, at about 0.64 seconds and at 1.17 seconds.