Please help me with number 9

Prime factorization of 1408

V125BC [204]

Answer:

There are 7 copies of 2 and 1 copy of 11 in the product:

1408 = 2^7×11

Step-by-step explanation:

Factor the following integer:

1408

The last digit of 1408 is 8, which means it is even. Therefore 1408 is divisible by 2:

1408 = 2 704:

1408 = 2×704

The last digit of 704 is 4, which means it is even. Therefore 704 is divisible by 2:

704 = 2 352:

1408 = 2×2×352

The last digit of 352 is 2, which means it is even. Therefore 352 is divisible by 2:

352 = 2 176:

1408 = 2×2×2×176

The last digit of 176 is 6, which means it is even. Therefore 176 is divisible by 2:

176 = 2 88:

1408 = 2×2×2×2×88

The last digit of 88 is 8, which means it is even. Therefore 88 is divisible by 2:

88 = 2 44:

1408 = 2×2×2×2×2×44

The last digit of 44 is 4, which means it is even. Therefore 44 is divisible by 2:

44 = 2 22:

1408 = 2×2×2×2×2×2×22

The last digit of 22 is 2, which means it is even. Therefore 22 is divisible by 2:

22 = 2 11:

1408 = 2×2×2×2×2×2×2×11

11 is not divisible by 2 since 11 is odd and 2 is even:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2)

The sum of the digits of 11 is 1 + 1 = 2, which is not divisible by 3. This means 11 is not divisible by 3:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2 or 3)

The last digit of 11 is not 5 or 0, which means 11 is not divisible by 5:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3 or 5)

Divide 7 into 11:

| | 1 | (quotient)

7 | 1 | 1 |

- | | 7 |

| | 4 | (remainder)

11 is not divisible by 7:

1408 = 2×2×2×2×2×2×2×11 (11 is not divisible by 2, 3, 5 or 7)

No primes less than 11 divide into it. Therefore 11 is prime:

1408 = 2×2×2×2×2×2×2×11

There are 7 copies of 2 and 1 copy of 11 in the product:

Answer: 1408 = 2^7×11

8 0

3 years ago

A survey of 700 adults from a certain region asked, "What do you buy from your mobile device?" The results indicated that 59%

Kryger [21]

Answer:

a) the test statistic z = 1.891

the null hypothesis accepted at 95% level of significance

b) the critical values of 95% level of significance is zα =1.96

c) 95% of confidence intervals are (0.523 ,0.596)

Step-by-step explanation:

A survey of 700 adults from a certain region

Given sample sizes $n_{1} = 400 and n_{2} = 300$

Proportion of mean $p_{1} = \frac{236}{400} = 0.59 and p_{2} = \frac{156}{300} = 0.52$

Null hypothesis H0 : assume that there is no significant difference between males and women reported they buy clothing from their mobile device

p1 = p2

Alternative hypothesis H1:- p1 ≠ p2

a) The test statistic is

$Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} )} } }$

where $p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1}+n_{2}}= \frac{400X0.59+300X0.52}{700}$

on calculation we get p = 0.56

now q =1-p = 1-0.56=0.44

$Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} }+\frac{1}{n_{2} )} } }\\ =\frac{0.56-0.52}{\sqrt{0.56X0.44}(\frac{1}{400}+\frac{1}{300} }$

after calculation we get z = 1.891

b) The critical value at 95% confidence interval zα = 1.96 (from z-table)

The calculated z- value < the tabulated value

therefore the null hypothesis accepted

conclusion:-

assume that there is no significant difference between males and women reported they buy clothing from their mobile device

p1 = p2

c) 95% confidence intervals

The confidence intervals are P± 1.96(√PQ/n)

we know that = $p = \frac{n_{1}p_{1} +n_{2}p_{2} }{n_{1}+n_{2}}= \frac{400X0.59+300X0.52}{700}$

after calculation we get P = 0.56 and Q =1-P =0.44

Confidence intervals are ( P- 1.96(√PQ/n), P+ 1.96(√PQ/n))

now substitute values , we get

( 0.56- 1.96(√0.56X0.44/700), 0.56+ 1.96(0.56X0.44/700))

on simplification we get (0.523 ,0.596)

Therefore the population proportion (0.56) lies in between the 95% of confidence intervals (0.523 ,0.596)

3 0

3 years ago

Draw rectangles to show 3 1/2

Nataliya [291]

Just draw three rectangles and a half of one

5 0

3 years ago

1. The graph below shows the past 9 months of sales for the Carver Cars company. у Carver Cars Sales Car Sales (in dollars) 200,

motikmotik

Answer:

$170,000 D. $800,000

Step-by-step explanation:

$170,000 D. $800,000

5 0

3 years ago

Find the missing number for 1/3 = 3:

RSB [31]

1/3=3:9
since 1×3=3
3×3=9

7 0

3 years ago