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SashulF [63]
2 years ago
10

Specify the set of all integers that are congruent to 5 (mod 7) using (a) the roster method and (b) set-builder notation

Mathematics
1 answer:
IrinaVladis [17]2 years ago
4 0

Answer:

(a) A = {... -23, -16, -9, -2, 5, 12, 19, 26, ....}

(b) A = {x\in Z: x = 5 - 7t,\ t\in Z}

Solution:

For two integers x and y to be congruent, we know that:

If 't' divides y - x, we say that x is congruent to y modulo t, written x ≡ y mod t.

Now,

In roster form, we include each element in the representation of the set.

In set-builder form, we use mathematical notation and properties of the elements of the set.

Now,

As per the question;

(a) To represent all the integers congruent to  5 (mod 7) by roaster method of a set A (say):

where

x\in Z such that

x ≡ 5 (mod 7)

Then

A = {... -23, -16, -9, -2, 5, 12, 19, 26, ....}

(b) In set builder form,

A = {x\in Z: x = 5 - 7t,\ t\in Z}

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Hayley has $155 in savings, and her brother Hank has $230. Hayley is saving $10 each week, and her brother is spending $15 each
Sindrei [870]

Answer:

After 3 weeks they both will have the same amount in their savings account.

Step-by-step explanation:

Given:

Amount saved by Haley = $155

Amount saved by Hank = $230

Amount saving each week by Haley = $10

Amount spending each week by Hank = $15

We need to find Number of weeks when both both will have same amount in savings account.

Solution:

Let Number of week be 'x'.

Total Amount of Haley can be calculated by Amount saved by Haley plus Amount saving each week by Haley multiplied by number of weeks.

framing in equation form we get;

Total Amount of Haley = 155+10x

Also;

Total Amount of Hank can be calculated by Amount saved by Hank minus Amount spending each week by Hank multiplied by number of weeks.

framing in equation form we get;

Total Amount of Hank = 230-15x

Now we need to find the number of weeks when both will have same amount.

To find the same we will have to make both the equation equal.

So we can say.

155+10x=230-15x

On Solving above equation we get;

We will combine the like terms together;

10x+15x =230-155\\\\25x = 75

Now Dividing both side by 25 using Division property of equality we get;

\frac{25x}{25} = \frac{75}{25}\\\\x=3 \ weeks

Hence, After 3 weeks they both will have the same amount in their savings account.

4 0
2 years ago
A 64-ounce container of sports juice costs $6.50. A 48-ounce container of the same juice costs $4.25. Which juice container is t
larisa86 [58]

Answer:

The juice container that is a better buy is the 48 ounce container because the price per ounce is lower.

Step-by-step explanation:

In order to determine the juice container that is the better buy, you have to find the one that has a lower cost per ounce by dividing the price of each juice container by the number of ounces it has:

64-ounce container: 6.50/64=0.10

48-ounce container: 4.25/48=0.08

According to this, the answer is that the juice container that is a better buy is the 48 ounce container because the price per ounce is lower.

6 0
3 years ago
Change the decimal into a %:0.7
Tomtit [17]
Simply multiply 0.7 by 100. 0.7 x 100= 70%. The answer is 70%
8 0
3 years ago
Read 2 more answers
Help please if you can
enot [183]

Answer: mutiply x by itself to get y

Step-by-step explanation:

6 0
3 years ago
he amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.3 minutes and s
sp2606 [1]

Complete question:

He amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.3 minutes and standard deviation 1.4 minutes. Suppose that a random sample of n equals 47 customers is observed. Find the probability that the average time waiting in line for these customers is

a) less than 8 minutes

b) between 8 and 9 minutes

c) less than 7.5 minutes

Answer:

a) 0.0708

b) 0.9291

c) 0.0000

Step-by-step explanation:

Given:

n = 47

u = 8.3 mins

s.d = 1.4 mins

a) Less than 8 minutes:

P(X

P(X' < 8) = P(Z< - 1.47)

Using the normal distribution table:

NORMSDIST(-1.47)

= 0.0708

b) between 8 and 9 minutes:

P(8< X' <9) =[\frac{8-8.3}{1.4/ \sqrt{47}}< \frac{X'-u}{s.d/ \sqrt{n}} < \frac{9-8.3}{1.4/ \sqrt{47}}]

= P(-1.47 <Z< 6.366)

= P( Z< 6.366) - P(Z< -1.47)

Using normal distribution table,

NORMSDIST(6.366)-NORMSDIST(-1.47)

0.9999 - 0.0708

= 0.9291

c) Less than 7.5 minutes:

P(X'<7.5) = P [Z< \frac{7.5-8.3}{1.4/ \sqrt{47}}]

P(X' < 7.5) = P(Z< -3.92)

NORMSDIST (-3.92)

= 0.0000

3 0
2 years ago
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