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21 day ago

7

Pat had 9 flowerpots, and she wants to plant a different type of flower in each one. There are 11 types of flowers available at

the garden shop. In how many different ways can she choose the flower

2 answers:

PIT_PIT [9.1K]21 day ago

7 0

<span>In this situation, a combination approach will be applied since the sequence is irrelevant and each flower can only be chosen once. Given that there are 11 flowers and 9 flowerpots available, the number of potential combinations can be represented as 11C9 or computed as 11! / {9! (11-9)!}. Thus, the total number of distinct combinations amounts to 55.</span>

tester [8.8K]21 day ago

3 0

Answer:

The result is 55

Step-by-step explanation:

The sequence is irrelevant, so it simply amounts to 55.

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According to Consumer Digest (July/August 1996), the probable location of personal computers (PC) in the home is as follows: Adu

PIT_PIT [9117]

Answer:

a) 0.32

b) 0.68

c) Office or den

Step-by-step explanation:

a) The likelihood that a personal computer is located in a bedroom can be calculated by adding the probabilities of it being in an adult bedroom, child bedroom, or another bedroom:

$P(B) =P(adult)+P(child)+P(other)\\P(B) = 0.03+0.15+0.14\\P(B) =0.32$

b) The probability of a PC not being located in a bedroom is found by calculating 100% minus the probability of it being in a bedroom:

$P(Not\ B) = 1- P(B)\\P(Not\ B) =1-0.32\\P(Not\ B) =0.68$

c) The expected location for finding a personal computer in a randomly selected household is derived from the room most likely to contain a PC according to Consumer Digest. The Office or den ranks as the most likely place with a probability of 0.40.

A PC would most likely be found in the Office or den.

6 0

22 days ago

Tran has a credit card with a spending limit of $2000 and an APR (annual percentage rate) of 12%. During the first month, Tran c

babunello [8412]

Detailed explanation:

Information provided:

Tran possesses a credit card that allows up to $2000 in spending with an APR of 12%.

In the initial month, Tran incurred charges of $450 and settled $150 within that billing period.

The formula to determine the interest that will accrue for Tran in the first month is (0.012)(300)

Here, 0.01 signifies the monthly interest rate.

The 300 reflects the outstanding balance, as Tran charged $450 but only paid back $150.

5 0

6 days ago

The number of "destination weddings" has skyrocketed in recent years. For example, many couples are opting to have their wedding

zzz [9080]

Answer:

Based on the findings, we infer that the average cost of a wedding is lower than the $30,000 that was initially suggested.

Step-by-step explanation:

The following data set is provided: (in thousands)

29100, 28500, 28800, 29400, 29800, 29800, 30100, 30600

Formula:

$\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}$

where $x_i$ denotes data points, $\bar{x}$ represents the mean, and n indicates the number of samples.

$Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}$

$Mean =\displaystyle\frac{236100}{8} = 29512.5$

The sum of squares of the differences equals 3408750

$S.D = \sqrt{\frac{3408750}{7}} = 697.82$

The population mean, μ = $30,000

The sample mean, $\bar{x}$ = $29512.5

Sample size, n = 8

Alpha, α = 0.05

Sample standard deviation, s = $697.82

Initially, we formulate the null hypothesis and the alternative hypothesis.

$H_{0}: \mu = 30000\text{ dollars}\\H_A: \mu < 30000\text{ dollars}$ A one-tailed t-test will be conducted for this analysis.

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

<pinserting the="" values="" we="" derive="">

$t_{stat} = \displaystyle\frac{29512.5 - 30000}{\frac{697.82}{\sqrt{8}} } = -1.975$

<pnow>

$t_{critical} \text{ at 0.05 level of significance, 7 degree of freedom } = -1.894$

<pgiven the="" situation="">

$t_{stat} < t_{critical}$

<pwe do="" not="" accept="" the="" null="" hypothesis="" and="" reject="" it.="">

Thus, we conclude that the average wedding cost is indeed less than the advertised $30,000.

</pwe></pgiven></pnow></pinserting>

8 0

21 day ago

Of the 2000 students attending, every 5th student going into the basketball game is asked if the school should spend more money

babunello [8412]

The students likely won't care much about the spending because they aren't using their own money.

8 0

19 days ago

Three ships, A, B, and C, are anchored in the atlantic ocean. The distance from A to B is 36.318 miles, from B to C is 37.674 mi

Leona [9271]

Let's sketch the triangle.

The sides are a= 37.674 miles

b= 11.164 miles

c= 36.318 miles

We'll apply the cosine rule for angle calculations

(since the sine law cannot be employed without knowing any angle measurements).

The cosine law is given by

$c^{2} = a^{2} +b^{2} -2ab cos C$

Substituting the values results in

$(36.318)^{2} = (37.674)^{2} + (11.164)^{2} - 2(37.674)(11.164). Cos C$

$1318.997 = 1419.33 + 124.634 - 841.184. Cos C$

$1318.997 = 1543.964 - 841.184. Cos C$

$841.184. Cos C = 1543.964-1318.997$

$841.184. Cos C = 224.967$

$Cos C = \frac{224.967}{841.184}$

$cos C = 0.267$

C = 74.48°

We can find angle A using the sine law

$\frac{a}{SinA} = \frac{c}{Sin C}$

$\frac{37.674}{Sin A} = \frac{36.318}{Sin 74.48}$

$Sin A = \frac{37.674. sin 74.48}{36.318}$

$Sin A = \frac{37.674 X 0.963}{36.318}$

$Sin A = 0.998$

A= $sin^{-1} (0.998)$

A = 87.38°

The third angle B can be determined by calculating 180° minus the sum of angles A and C

$B = 180-(74.48 + 87.38)$

B = 180 - 161.86

B = 18.14°

Thus, we have calculated all three angles (as shown in the attached figure).

7 0

28 days ago