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Gre4nikov [31]
3 years ago
11

In remodeling a kitchen, a builder decides to place a splash-guard behind the sink consisting of eight 6-inch-square ceramic til

es decorated with different botanical herbs. The tiles will be installed in a custom-made wooden panel. The tile supplier has 12 different herb designs to choose from, and the builder selects 8 of these 12 at random. Suppose the order in which the tiles are arranged on the splash-guard does not matter. Fill in the blanks. (Give your answers to four decimal places.)
Two of the 12 herb tiles contain a blue tint that matches the kitchen color scheme. The probability that these 2 tiles will be included in the splash-guard is __.

The family actually grows 5 of the 12 herbs in a backyard garden. The probability that all 5 of these will be included on the splash-guard is _
Mathematics
1 answer:
oksano4ka [1.4K]3 years ago
6 0

Answer:

(a) 0.4242

(b) 0.0707

Step-by-step explanation:

The total number of ways of selecting 8 herbs from 12 is

\binom{12}{8}=495

(a) If 2 herbs are selected, then there are 8 - 2 = 6 herbs to be selected from 12 - 8 = 10. The number of ways of the selection is then

\binom{10}{6}= 210

Note that this is the number of ways that both are included. We would have multiplied by 2! if any of them were to be included.

The probability = \dfrac{210}{495}=0.4242

(b) If 5 herbs are selected, then there are 8 - 5 = 3 herbs to be selected from 12 - 5 = 7. The number of ways of the selection is then

\binom{7}{3}= 35

This is the number of ways that both are included. We would have multiplied by 5! if any of them were to be included. In that case, our probability will exceed 1; this implies that certainly, at least, one of them is included.

The probability = \dfrac{35}{495}=0.0707

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A random sample of 20 houses selected from a city showed that the mean size of these houses is 1880 square feet with a standard
azamat

Answer:

Option C

Step-by-step explanation:

Given that for a  random sample of 20 houses selected from a city showed that the mean size of these houses is 1880 square feet with a standard deviation of 320 square feet.

X, the sizes of houses is Normal

Hence sample mean will be normal with

Mean = 1880

and std dev = \frac{320}{\sqrt{20} } \\=71.5542

For 90% confidence interval critical value for t with degree of freedom 19 is

1.328

Confidence interval upper bound

= mean + margin of error

= 1880+1.328*71.55\\=1975

Option C is right

3 0
3 years ago
What is the measure of angle J in the triangle below? <br> A. 99<br> B. 42 <br> C. 9<br> D. 48
Leya [2.2K]
For this use the law of sines:
\sin( \alpha ) \div a = \sin( \beta ) \div b \\ \sin( \alpha ) \div 11 = \sin(103) \div 16
\frac{ \sin( \alpha ) }{11} = \frac{0.97}{16}
cross-multiply:
16×sin (J) = 11×0.97
sin(J) = 10.72/16
sin(J) = 0.67
hit the "arcsin" button on your calculator:
{ \sin}^{ - 1} (0.67) = 42.06 = 42.1 \: deg
therefore answer B. 42 is the correct answer!!
4 0
3 years ago
does anyone have Skype or Outlook and do you want to join a Skype if you have Skype if you have Outlook email me
MaRussiya [10]

Answer:

not today

Step-by-step explanation:

sorry

3 0
3 years ago
Read 2 more answers
Simplify.
irina1246 [14]
We have,
(2y)^3 × y^-1

Simplify the term (2y)^3

= 8y^3 × y^-1

Now, multiply the terms with the same base y by adding their exponents.

Note: Using exponent product rule x^y × x^z = x^(y+z)

= 8y^{3+(-1)}
= 8y^(3-1)
= 8y^(3-1)
= 8y^2
3 0
3 years ago
If the wwight of a package is multiplied by 7/10 the result is 65.8 find the weight of the package
ANTONII [103]

Answer:

The answer is 94

Step-by-step explanation:

divide 7/10 because thats the fraction = 0.7

divide 65.8 by 0.7

to get 94

to check

multiply 94 by 0.7


8 0
3 years ago
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