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LiRa [457]
3 years ago
13

Alex and Freddy collect stamps. The number of stamps in Alex’s collection to the number of stamps in Freddy’s collection is in t

he ratio of 3:5. How much more stamps does Freddy have if together they have 136 stamps?
Please explain how you got the answer. Thanks.
Mathematics
1 answer:
vazorg [7]3 years ago
5 0

Remark

The trick here is to realize that you have to find the number both have in order to find the difference. That means you take (effectively) 3/8 and 5/8 to find out how much each of them has. The 8 stands for the 136

Step One

Find the number of stamps Alex has. Remember his ratio is the smaller so he will have 3/8

Alex = 3/8 * 136

Alex = 408/8 = 51

Step 2

Find the number that Freddy has.

The total is 136

<u>Formula</u>

Freddy = Total - Alex

Freddy = 136 - 51

Freddy = 85

<u>Check</u>

Let us see if 5/8 * 136 = 85

5*136/8 = 680 / 8 = 85 So your answers are correct.

Difference

Difference = 85 - 51 = 34 which is how many more stamps Freddy has than Alex.

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What ratios are equal to 10:15​
Zielflug [23.3K]

Answer:

It is 2/3

Step-by-step explanation:

Divide 10 and 15 by 5 to get 2:3

7 0
3 years ago
A state legislator wants to determine whether his voters' performance rating (0 - 100) has changed from last year to this year.
ra1l [238]

Answer:

Step 1 of 4

Point estimate for the population mean of the paired differences = -8.2

Step 2 of 4

Sample standard deviation of the paired differences = 16.116244

Step 3 of 4

Margin of Error = ±9.326419

Step 4 of 4

90% Confidence interval = (-17.5, 1.1)

Step-by-step explanation:

The ratings from last year and this year are given in table as

Rating (last year) | x1 | 87 67 68 75 59 60 50 41 75 72

Rating (this year) | x2| 85 52 51 53 50 52 80 44 48 57

Difference | x2 - x1 | -2 -15 -17 -22 -9 -8 30 3 -27 -15

Step 1 of 4

Mean = (Σx)/N = (-82/10) = -8.2 to 1 d.p.

Step 2 of 4

Standard deviation for the sample

= √{[Σ(x - xbar)²]/(N-1)} = 16.116244392951 = 16.116244 to 6 d.p.

Step 3 of 4

Confidence Interval for the population mean is basically an interval of range of values where the true population mean can be found with a certain level of confidence.

Mathematically,

Confidence Interval = (Sample mean) ± (Margin of error)

Sample Mean = -8.2

Margin of Error is the width of the confidence interval about the mean.

It is given mathematically as,

Margin of Error = (Critical value) × (standard Error of the mean)

Critical value will be obtained using the t-distribution. This is because there is no information provided for the population standard deviation.

To find the critical value from the t-tables, we first find the degree of freedom and the significance level.

Degree of freedom = df = n - 1 = 10 - 1 = 9.

Significance level for 90% confidence interval

= (100% - 90%)/2 = 5% = 0.05

t (0.05, 9) = 1.83 (from the t-tables)

Standard error of the mean = σₓ = (σ/√n)

σ = standard deviation of the sample = 16.116244

n = sample size = 10

σₓ = (16.116244/√10) = 5.0964038367

Margin of Error = (Critical value) × (standard Error of the mean) = 1.83 × 5.0964038367 = 9.3264190212 = 9.326419 to 6 d.p.

Step 4 of 4

90% Confidence Interval = (Sample mean) ± (Margin of Error)

CI = -8.2 ± (9.326419)

90% CI = (-17.5264190212, 1.1264190212)

90% Confidence interval = (-17.5, 1.1)

Hope this Helps!!!

4 0
3 years ago
Denise has 6 hours to spend training for an upcoming race. She completes her training by running full speed the distance of the
VMariaS [17]
  To solve this problem,you need to use the formula d = rd (distance = rates x time)She runs at a speed of 7 mph and walks at a speed of 3 mph. Her distance running is d = 7trwhere tr is the time she spends running Her distance walking isd = 3twwhere tw is the time she spends walking The distances are the same so7tr = 3tw We also know that the total time is 4 hourstr + tw = 4tr = 4-tw Substitute this value of tr in the first equation7tr = 3tw7(4-tw) = 3tw28-7tw = 3tw28 = 10tw2.8 = tw Denise will spend 2.8 hours (2 hours, 48 minutes) walking back and 1.2 hours (1 hour, 12 minutes running.

Hope I helped :)
5 0
3 years ago
What is tan K? help pleasee
alina1380 [7]

8/15

Hope this helps!

5 0
3 years ago
Read 2 more answers
Please Help! My question is in the picture.
Varvara68 [4.7K]
First we need to determine the type of progression in the question.
That's geometric progression. Because the pattern from one sequence to the others are about multiplying.

Second, determine the ratio of the progression
r = a₂/a₁
r = a₂ ÷ a₁
r = 1/2 ÷ 2
r = 1/2 × 1/2
r = 1/4

Third, determine the formula to know the recursive rule
a₂ = a × 1/4
a₂ = 1/4 × a
a_{n} =   \frac{1}{4} a_{(n-1)}

Fourth, determine a₁. a₁ is the first term of the progression
a₁ = 2

Final answer:
Recursive rule
a_{n} = \frac{1}{4} a_{(n-1)}
a₁ = 2

4 0
3 years ago
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