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kolezko [41]
3 years ago
10

A mortgage firm estimates the true mean current debt of local homeowners, using the current outstanding balance of a random samp

le of 35 homeowners. They find a 95% confidence interval for the true mean current debt to be ($56,000, $120,000). Which of the following would correctly produce a confidence interval with a smaller margin of error than this 95% confidence interval?
Using the balances of older homeowners because they will have paid off more of their mortgage
Using the balances of 50 homeowners rather than 35, because using more data gives a smaller margin of error
Using the balances of only fifteen homeowners rather than 35, because there is likely to be less variation in fifteen balances than 35
Using 99% confidence, because then its more likely that the true mean is contained in the confidence interval
Mathematics
1 answer:
AVprozaik [17]3 years ago
6 0

Answer:

Option B.

Step-by-step explanation:

As we know that

Margin of error = Z * standard error

Here , the only way to decrease the value of margin of error is to decrease either the value of z or value of standard error as both are directly proportional to margin of error.

Z-value can be decreased by using lower confidence intervals. Standard error can be decreased by increasing sample size (as given in option B)

The answer is option B as it is using sample size of 50 instead of 35 thus decreasing standard error and ultimately decreasing margin of error.

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The owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway. If s
navik [9.2K]

Answer:

Step-by-step explanation:

Given that the owner of a motel has 2900 m of fencing and wants to enclose a rectangular plot of land that borders a straight highway.

Fencing is used for 2times length and 1 width if highway side is taken as width

So we have 2l+w = 2900

Or w = 2900-2l

Area of the rectangular region = lw

A(l) = l(2900-2l) = 2900l-2l^2\\

Use derivative test to find the maximum

A'(l) = 2900-4l\\A"(l) = -4

So maximum when I derivative =0

i.e when l =\frac{2900}{4} =725

Largest area = A(725)

= 725(2900-2*725)\\= 1051250

1051250 sqm is area maximum

3 0
3 years ago
MCR3U1 Culminating 2021.pdf
11111nata11111 [884]

Answer:

(a) y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is 607,325

(ii) The population after 24 hours is 1,828,643

(c) The rate of increase of the population as a percentage per hour is 7.132%

(d) The doubling time of the population is approximately, 10.06 hours

Step-by-step explanation:

(a) The initial population of the bacteria, y₁ = a = 350,000

The time the colony grows, t = 12 hours

The final population of bacteria in the colony, y₂ = 800,000

The exponential growth model, can be written as follows;

y = a \cdot (1 + r)^t

Plugging in the values, we get;

800,000 = 350,000 \times (1 + r)^{12}

Therefore;

(1 + r)¹² = 800,000/350,000 = 16/7

12·㏑(1 + r) = ㏑(16/7)

㏑(1 + r) = (㏑(16/7))/12

r = e^((㏑(16/7))/12) - 1 ≈ 0.07132

The  model is therefore;

y = 350,000 \times (1 + 0.07132)^t

(b) (i) The population after 8 hours is given as follows;

y = 350,000 × (1 + 0.07132)⁸ ≈ 607,325.82

By rounding down, we have;

The population after 8 hours, y = 607,325

(ii) The population after 24 hours is given as follows;

y = 350,000 × (1 + 0.07132)²⁴ ≈ 1,828,643.92571

By rounding down, we have;

The population after 24 hours, y = 1,828,643

(c) The rate of increase of the population as a percentage per hour =  r × 100

∴   The rate of increase of the population as a percentage = 0.07132 × 100 = 7.132%

(d) The doubling time of the population is the time it takes the population to double, which is given as follows;

Initial population = y

Final population = 2·y

The doubling time of the population is therefore;

2 \cdot y = y \times (1 + 0.07132)^t

Therefore, we have;

2·y/y =2 = (1 + 0.07132)^t

t = ln2/(ln(1 + 0.07132)) ≈ 10.06

The doubling time of the population is approximately, 10.06 hours.

8 0
3 years ago
5x3 + 9x² - 13x - 2<br>As x approaches --, f(x) approaches<br>As x approaches +o, f(x) approaches​
Solnce55 [7]

9514 1404 393

Answer:

  (x, y) → (-∞, -∞), (+∞, +∞)

Step-by-step explanation:

The expression is of odd degree with a positive leading coefficient. It will have a generally upward slope (/). That is, the sign of f(x) will match the sign of x for large-magnitude values of x:

  x → -∞, f(x) → -∞

  x → ∞, f(x) → ∞

3 0
3 years ago
What is the cost of 4 pounds of apples, if 3 pounds of apples cost $5.28 and the unit price for each pound of apples is the same
Ne4ueva [31]

Answer:

B. $7.04

Step-by-step explanation:

5.28 / 3 = 1.76

1.76 x 4 = 7.04

6 0
3 years ago
Wendy’s offers eight different condiments (mustard, catsup, onion, mayonnaise, pickle, lettuce, tomato, and relish) on hamburger
julsineya [31]

Answer:

Check the explanation

Step-by-step explanation:

Conclusion: young people like condiments.

First, let's convert things into percentages, since the number in each age category is different. There are 143 in "Under 18", 233 in "18 to 40", 161 in "40 to 60", and 122 in "over 60".

Of the under 18s: 71 of 143 = 49.7% order three or more.

Of the 18-40s: 87 of 233 = 37.3% order three or more.

Of the 40-60s: 47 of 161 = 29.2% order three or more.

Of the 60 and ups: 28 of 122 = 23.0% order three or more.

The older you are, the less likely you are to order lots of condiments.

4 0
3 years ago
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