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Taya2010 [7]
3 years ago
5

1. 1.267 expanded and word form 2. 2,456.98 expanded and word form 3. 34,568.2​

Mathematics
1 answer:
blagie [28]3 years ago
3 0

1 One and two hundred sixty-eight thousandths

2 two thousand 4 hundred fifty-six and ninety-eight hundredths

3 thirty-four thousand five hundred sixty-eight and two tenths

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What does 4.23×9 equal
nata0808 [166]
<span>4.23 times 9 equals 38.07 :)</span>
8 0
3 years ago
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7.109) The leading brand of dishwasher detergent has a 30% market share. A sample of 25 dishwasher detergent customers was taken
Rina8888 [55]

Answer:

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they choose the leading brand, or they do not. The probability of a customer choosing the leading brand is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

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 combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

The leading brand of dishwasher detergent has a 30% market share.

This means that p = 0.3

A sample of 25 dishwasher detergent customers was taken.

This means that n = 25

a. What is the probability that 10 or fewer customers choose the leading brand?

This is:

P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

In which

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

P(X = 0) = C_{25,0}.(0.3)^{0}.(0.7)^{25} = 0.0001

P(X = 1) = C_{25,1}.(0.3)^{1}.(0.7)^{24} = 0.0014

P(X = 2) = C_{25,2}.(0.3)^{2}.(0.7)^{23} = 0.0074

P(X = 3) = C_{25,3}.(0.3)^{3}.(0.7)^{22} = 0.0243

P(X = 4) = C_{25,4}.(0.3)^{4}.(0.7)^{21} = 0.0572

P(X = 5) = C_{25,5}.(0.3)^{5}.(0.7)^{20} = 0.1030

P(X = 6) = C_{25,6}.(0.3)^{6}.(0.7)^{19} = 0.1472

P(X = 7) = C_{25,7}.(0.3)^{7}.(0.7)^{18} = 0.1712

P(X = 8) = C_{25,8}.(0.3)^{8}.(0.7)^{17} = 0.1651

P(X = 9) = C_{25,9}.(0.3)^{9}.(0.7)^{16} = 0.1336

P(X = 10) = C_{25,10}.(0.3)^{10}.(0.7)^{15} = 0.0916

Then

P(X \leq 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0001 + 0.0014 + 0.0074 + 0.0243 + 0.0572 + 0.1030 + 0.1472 + 0.1712 + 0.1651 + 0.1336 + 0.0916 = 0.9021

0.9021 = 90.21% probability that 10 or fewer customers choose the leading brand

3 0
2 years ago
Given the sequence 1/2 ; 4 ; 1/4 ; 7 ; 1/8 ; 10;.. calculate the sum of 50 terms
miv72 [106K]

<u>Hint </u><u>:</u><u>-</u>

  • Break the given sequence into two parts .
  • Notice the terms at gap of one term beginning from the first term .They are like \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} . Next term is obtained by multiplying half to the previous term .
  • Notice the terms beginning from 2nd term , 4,7,10,13 . Next term is obtained by adding 3 to the previous term .

<u>Solution</u><u> </u><u>:</u><u>-</u><u> </u>

We need to find out the sum of 50 terms of the given sequence . After splitting the given sequence ,

\implies S_1 = \dfrac{1}{2},\dfrac{1}{4},\dfrac{1}{8} .

We can see that this is in <u>Geometric</u><u> </u><u>Progression </u> where 1/2 is the common ratio . Calculating the sum of 25 terms , we have ,

\implies S_1 = a\dfrac{1-r^n}{1-r} \\\\\implies S_1 = \dfrac{1}{2}\left[ \dfrac{1-\bigg(\dfrac{1}{2}\bigg)^{25}}{1-\dfrac{1}{2}}\right]

Notice the term \dfrac{1}{2^{25}} will be too small , so we can neglect it and take its approximation as 0 .

\implies S_1\approx \cancel{ \dfrac{1}{2} } \left[ \dfrac{1-0}{\cancel{\dfrac{1}{2} }}\right]

\\\implies \boxed{ S_1 \approx 1 }

\rule{200}2

Now the second sequence is in Arithmetic Progression , with common difference = 3 .

\implies S_2=\dfrac{n}{2}[2a + (n-1)d]

Substitute ,

\implies S_2=\dfrac{25}{2}[2(4) + (25-1)3] =\boxed{ 908}

Hence sum = 908 + 1 = 909

7 0
2 years ago
Factor the polynomial 8x² - 24x – 224 completely. A- 4(x + 4)(x-7) B- (4x + 16X(12x – 14) C- 8(x + 4)(x - 7) ht D- 2(4x + 16)(x
alisha [4.7K]

Answer:

The correct answer would be...

c. 8(x + 4)(x - 7)

Hope this helps!

8 0
3 years ago
BRAINLIEST FOR CORRECT ANSWER, IM FAILING SCHOOL AND NEED HELP ASAP. EVEN OFFICIAL HELP COUNTS
Delvig [45]

Answer:

x=76

Step-by-step explanation:

The two marked angles are alternate angles, which means they're equal.

8 0
3 years ago
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