757.923 expanded form

Find the values of x and y if (-x + 5, 1) = (-y, 2x - 5y).

MrMuchimi

Answer:

x = 8, y = 3

Step-by-step explanation:

Equating corresponding x and y coordinates , then

- y = - x + 5 ( multiply through by - 1 )

y = x - 5 → (1)

2x - 5y = 1 → (2)

Substitute y = x - 5 into (2)

2x - 5(x - 5) = 1 ← distribute and simplify left side

2x - 5x + 25 = 1

- 3x + 25 = 1 ( subtract 25 from both sides )

- 3x = - 24 ( divide both sides by - 3 )

x = 8

Substitute x = 8 into (1) for corresponding value of y

y = 8 - 5 = 3

7 0

3 years ago

1. A man has 5 grandchildren, 4 girls and 1 boy. He thinks this is unusual. If the probability that any child born

mojhsa [17]

Answer:

6.25%

Step-by-step explanation:

To know the final probability that this has happened, we must multiply the probability of each event, they tell us that the probability that it is a girl is 1/2 and this happened 4 times, therefore:

(1/2) ^ 4 = 0.0625

that is, the probability that 4 girls are born is 6.25%

an unusual probability is considered when it is less than 5%, therefore, although it approaches this figure, it is not unusual

4 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

Can u please help me with 27

Pachacha [2.7K]

The answer would be 237.375. To get this answer, you will first use the formula given for each unit. First, you will do the first unit by putting 8 to the third power, or basically 8x8x8. After you get the product 512, you will then do the next unit. Do that one by doing 6.5 to the third power, or as followed, 6.5x6.5x6.5. Once you get the product 274.625, you will then subtract that from 512. You will then receive the answer 237.375.

5 0

3 years ago

What does it mean in Maths when it says translate triangle p by the vector.(2 -7)

laila [671]

Answer:

Step-by-step explanation:

A Translation Vector is a vector that gives the length and direction of a particular translation

6 0

3 years ago