One table at a bake sale has 75 oatmeal cookies. Another table has 60 lemon cupcakes. Which table allows for more rectangular arrangements when all the cookies and cupcakes are displayed?

Answers

Answer 1

Answer:

75 = 3·5², so has 6 divisors. 6 rectangles are possible if you make the distinction between 1×75 and 75×1.

60 = 2²·3·5, so has 12 divisors. 12 rectangles are possible under the same conditions.

The cupcake table can be arranged more ways.

_____

When 1 is added to each exponent of the prime factors, the product of those sums is the number of divisors. For 75: (1+1)(1+2) = 6; for 60: (1+2)(1+1)(1+1) = 12.

Answer 2

Answer:

Arrangement is simply the order, which items are displayed or presented.

The table of 60 lemon cupcakes allow more rectangular arrangements

The given parameters are:

$\mathbf{Oatmeal = 75}$

$\mathbf{Lemon = 60}$

The rectangular arrangement (R) is calculated as follows:

$\mathbf{R = (Area)/(n)}$

Where n represents the number of items, and Area represents the area of the rectangular table

For the oatmeal, we have:

$\mathbf{R_1 = (Area)/(75)}$

$\mathbf{R_1 = 0.0133Area}$

For the lemon, we have:

$\mathbf{R_2 = (Area)/(60)}$

$\mathbf{R_2 = 0.0167Area}$

By comparison, 0.0167Area is greater than 0.0133Area

Hence, the table of 60 lemon cupcakes allow more rectangular arrangement

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If the population of a particular country is growing at 1.5 % compounded continuously, how long will it take the population to triple?
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In a recent Super Bowl, a TV network predicted that 31 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 120 people who saw the commercials and found that 40 of them said they would watch one of the television shows. Suppose you have the following null and alternative hypotheses for a test you are running:1. H0: p = 0.53 Ha: p ≠ 0.532. H0: p = 0.53 Ha: p ≠ 0.53Calculate the test statistic, rounded to 3 decimal places.

A certain genetic condition affects 8% of the population in a city of 10,000. Suppose there is a test for the condition that has an error rate of 1% (i.e., 1% false negatives and 1% false positives). Consider the values that would complete the table below.

Has condition Does not have condition totals

Test positive

Test negative

Totals

What is the probability (as a percentage) that a person has the condition if he or she tests positive? (Round your answer to one decimal place.)

Answers

Solution:

Population in the city= 10,000

As genetic condition affects 8% of the population.

8 % of 10,000

$=(8)/(100)* 10,000=800$

As, it is also given that, there is an error rate of 1% for condition (i.e., 1% false negatives and 1% false positives).

So, 1% false negatives means out of 800 tested who are found affected , means there are chances that 1% who was found affected are not affected at all.

So, 1% of 800 $=(1)/(100)* 800=8$

Also, 1% false positives means out of 10,000 tested,[10,000-800= 9200] who are found not affected , means there are chances that 1% who was found not affected can be affected also.

So, 1% of 9200 $=(1)/(100)* 9200=92$

1. Has condition Does not have condition totals = 800

2. Test positive =92

3. Test negative =8

4. Total =800 +92 +8=900

5. Probability (as a percentage) that a person has the condition if he or she tests positive= As 8% are found positive among 10,000 means 9200 are not found affected.But there are chances that out of 9200 , 1% may be affected

$=\frac{\text{1 percent of 9200}}{9200}\n\n ((1)/(100)* 9200)/(9200)=(92)/(9200)\n\n =0.01$

that is Probability equal to 0.01 or 1%.

A family buys 8 tickets to a show. They also pay a $5parking fee. They spend $61 to see the show.
What is the solution to the story?

13.80
10.60
07.00
8.25

Answers

Answer:

C. $7.00

Step-by-step explanation:

8 times 7 is 56 + 5 = 61

Choose the statement below that describes the relationship between a circles diameter and circumference. A. Circumference times diameter is always π. B. Diameter divided by circumference is always π. C. Circumference divided by diameter is always π. D. There is no relationship between circumference and diameter.

Answers

Answer:

Step-by-step explanation:

The y-intercept of a parabola is 1, and its vertex is at (1,0). What function does the graph represent?OA. Rx) = (x - 1)2
OB. Rx) = (x + 1)2
OC. Rx) = -1(x - 1)
OD. Rx) = -1(x + 1)2
Reset
Next

Answers

Considering it's y-intercept and vertex, the equation of the parabola is given by:

$y = (x - 1)^2$

What is the equation of a parabola given it’s vertex?

The equation of a quadratic function, of vertex (h,k), is given by:

$y = a(x - h)^2 + k$

In which a is the leading coefficient.

In this problem, the vertex is (1,0), hence h = 1, k = 0 and:

$y = a(x - 1)^2$

The y-intercept is of 1, hence, when x = 0, y = 1, so:

$y = a(x - 1)^2$

$1 = a(0 - 1)^2$

$a = 1$

Hence, the equation is:

$y = (x - 1)^2$

More can be learned about the equation of a parabola at brainly.com/question/24737967

Answer:

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (1, 0) , thus

y = a(x - 1)² + 0

To find a substitute the coordinates of the y- intercept (0, 1) into the equation

1 = a(- 1)² = a , thus

a = 1

y = (x - 1)² → A

Gloria earned a total of $810 over the summer. She earned $162 babysitting and the restfrom mowing lawns. Which bar model and solution represent x, the amount of money Gloria
earned mowing lawns?

Answers

Let x represent the amount of money Gloria earned mowing lawns.

We have been given that Gloria earned a total of $810 over the summer. She earned $162 babysitting and the rest from mowing lawns.

The total amount earned by Gloria would be amount earned from baby sitting and lawn mowing that is $x+162$ .

Now we will equate total earnings of Gloria by 810 as:

$x+162=810$

$x+162-162=810-162$

$x=648$

Therefore, Gloria earned $648 from mowing lawns.

Answer:

Gloria earned $648 from mowing lawns

Step-by-step explanation:

As sample size increases, which of the following is true for a t-distribution-Distribution will get taller and SD will increase
-distribution sill get taller and SD will decrease
-distribution will get shorter and SD will decrease
Distribution will get shorter and SD will increase

Answers

Answer:

Distribution will get taller and SD will decrease.

Step-by-step explanation:

Sample Size and Standard Deviation:

In a t-distribution, sample size and standard deviation are inversely related.

A larger sample size results in decreased standard deviation and a smaller sample size will result in increased standard deviation.

Sample Size and Shape of t-distribution:

As we increase the sample size, the corresponding degree of freedom increases which causes the t-distribution to like normal distribution. With a considerably larger sample size, the t-distribution and normal distribution are almost identical.

Degree of freedom = n - 1

Where n is the sample size.

The shape of the t-distribution becomes more taller and less spread out as the sample size is increased

Refer to the attached graphs, where the shape of a t-distribution is shown with respect to degrees of freedom and also t-distribution is compared with normal distribution.

We can clearly notice that as the degree of freedom increases, the shape of the t-distribution becomes taller and narrower which means more data at the center rather than at the tails.

Also notice that as the degree of freedom increases, the shape of the t-distribution approaches normal distribution.

Final answer:

In a t-distribution, as the sample size increases, the distribution becomes 'shorter', and the standard deviation decreases following the law of large numbers. The increased sample size reduces variability and introduces less deviation from the mean.

Explanation:

As the sample size increases for a t-distribution, the distribution tends to approach a normal distribution shape, which means the distribution will get 'shorter'. Additionally, the standard deviation (SD) would generally decrease as the sample size increases. This is due to the fact that when sample size increases, a smaller variability is introduced, hence less deviation from the mean.

To illustrate, imagine rolling a dice. If you roll it a few times, you may end up with quite a bit of variation. If you roll it a hundred times, however, the numbers should average out closer to the expected value (3.5 for a six-sided dice), and the standard deviation (a measure of variability) would decrease.

In conclusion, when the sample size increases, a t-distribution will get 'shorter' and SD will decrease. This concept is often referred as the law of large numbers.

Learn more about t-distribution here:

brainly.com/question/32675925

#SPJ6

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