The length of the wall is : 26 ft.
and width of the wall is: 9 ft.
What is area of a rectangle?
The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.
The area of a rectangle is: Area= length × width
Solution:
area = 234
length = ?
width = ?
Given, length is 8 ft greater than twice the width.
Now, l = 2w ₊ 8
l × w = 234 (given)
Substitute for l
(2w ₊ 8)w = 234
multiply
2w² ₊ 8w = 234
2w² ₊ 8w ₋ 234 = 0
Now divide by 2 to eliminate the coefficients of w.
w² ₊ 4w ₋ 117=0
get the factors for the above equation.
We get the factors as: 9 and ₋13,( ₋13 is not applicable as width cannot be negative)
Hence we get the width as 9, now substitute it in:
l = 2w ₊ 8
l = 2(9) ₊ 8
l = 26 ft,
Hence the length and width of the rectangle is 26 ft and 9 ft respectively.
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A repeated-measures study using a sample of n = 20 participants would produce a t statistic with df of what?
The t-statistic for a repeated-measures study with a sample of n = 20 participants would have df=19.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Now, For determine the degrees of freedom (df) for a repeated-measures study with a sample size of n = 20, we can use the formula:
⇒ df = n - 1
However, in a repeated-measures study, we are comparing two sets of measurements from the same participants.
This means that the difference scores between the two sets of measurements will be used to compute the t-statistic.
Now, For a paired t-test with a sample size of n=20, we would have;
⇒ n - 1 = 19
⇒ n = 20 degrees of freedom.
Therefore, the t-statistic for a repeated-measures study with a sample of n = 20 participants would have df=19.
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Suppose an Egyptian mummy is discovered in which the amount of carbon 14 is present is only about one third the amount found in living human beings. About how long did the egyptian die
Answer: 9035
Step-by-step explanation:
A pizza shop offers nine toppings. No topping is used more than once. What is the probability that the toppings on a tree topping pizza are pepperoni, onions, and mushrooms?
Final answer:
The probability of selecting pepperoni, onions, and mushrooms from nine toppings for a pizza is 1/84, using the combination formula to calculate the total number of three-topping combinations.
Explanation:
To find the probability that a pizza has pepperoni, onions, and mushrooms as the toppings, we first have to determine the total number of ways we can select any three toppings from nine. This is given by the combination formula C(n, k) = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose.
In this case, n is 9 and k is 3. Thus, the total number of ways to choose any three toppings from nine is C(9, 3).
Since there is only one way to specifically get pepperoni, onions, and mushrooms together, the probability P is 1 divided by the total number of three-topping combinations, which simplifies to P = 1 / C(9, 3).
Therefore, P = 1 / (9! / (3!(9-3)!)) = 1 / (9! / (3!6!)) = 1 / (84) = 1/84. Thus, the probability is 1/84.
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 80 mm? Evaluate your answer numerically.
The diameter is 80 mm, the volume of the sphere is increasing at a rate of approximately 40211.2 mm³/s.
To find how fast the volume of the sphere is increasing, we can use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Where V is the volume of the sphere and r is the radius.
Differentiating both sides of the equation with respect to time t, we get:
[tex]\[ \frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt} \][/tex]
Given:
- [tex]\( \frac{dr}{dt} = 2 \)[/tex] mm/s (rate at which the radius is increasing)
- [tex]\( r = \frac{d}{2} = \frac{80}{2} = 40 \)[/tex] mm (radius when the diameter is 80 mm)
Substitute these values into the formula:
[tex]\[ \frac{dV}{dt} = 4\pi (40)^2 (2) \][/tex]
[tex]\[ \frac{dV}{dt} = 4\pi (1600) (2) \][/tex]
[tex]\[ \frac{dV}{dt} = 12800\pi \][/tex]
Now, let's evaluate this numerically:
[tex]\[ \frac{dV}{dt} ≈ 12800 \times 3.14 \][/tex]
[tex]\[ \frac{dV}{dt} ≈ 40211.2 \text{ mm}^3/\text{s} \][/tex]
Therefore, when the diameter is 80 mm, the volume of the sphere is increasing at a rate of approximately 40211.2 mm³/s.
Find two consecutive positive integers such that the sum of their squares is 421 .
Bao and Calvin use 6 lemons to make ever 4auarts of lemonade. They want to make 12 quarts of lemonade. How many lemons do they need?
A beluga whale is 5 yards and 3 inches long, and a gray whale is 15 yards and 5 inches long. What is the difference in length between the two whales?
Answer:
Difference in length between two whales is 362 inches or 10 yards and 2 inches.
Step-by-step explanation:
Lets convert the values to inches:
1 yard = 36 inches
Length of a beluga whale in inches:
5 yards = [tex]5*36[/tex] inches = [tex]180[/tex] inches
Therefore total length of a beluga whale = 180 inches + 3 inches
=183 inches
Length of a gray whale in inches:
15 yards = [tex]15*36[/tex] inches = [tex]540[/tex] inches
Therefore total length of a beluga whale = 540 inches + 5 inches
=545 inches
Difference in length between two whales = 545 inches - 183 inches
= 362 inches
To represent this in yards and inches we can divide the value by 36.
[tex]\frac{362}{36} =10.06[/tex] yards
=10 yards and 2 inches
Difference in length between two whales is 10 yards and 2 inches.
Your friend has a fabulous recipe for salsa, and he wants to start packing it up and selling it. He can rent the back room of a local restaurant any time he wants, complete with their equipment, for $100 per time. It costs him $2 a jar for the materials (ingredients for the salsa, jars, labels, cartons) and labor (you and a couple of friends of his) for each jar he makes. He can sell 12,000 jars of salsa each year (I told you it was a fabulous recipe!), with a constant demand (that is, it's not seasonal; it doesn't vary from week to week or month to month). It costs him $1 a year per jar to store the salsa in the warehouse he ships from. He wants to find the number of jars he should produce in each run in order to minimize his production and storage costs, assuming he'll produce 12,000 jars of salsa each year.
Your friend wants to find the number of jars he should produce in each run in order to minimize his production and storage costs, assuming he'll produce 12,000 jars of salsa each year.
The EOQ formula takes into account the demand, setup cost, and holding cost per unit is 154.91 by calculating the EOQ, that identify the batch size that results in the most cost-efficient production and storage.
Given that:
demand is 12,000 jars, setup cost is $100 per run, and holding cost per unit is $1 per jar per year.To determine the number of jars to produce in each run, uses the Economic Order Quantity (EOQ) formula.
The Economic Order Quantity (EOQ) formula is given by:
EOQ =[tex]\sqrt{[/tex][(2 * Demand * Setup cost) / Holding cost per unit].
By substituting these values into the formula:
EQR = [tex]\sqrt{\frac{2\times1200\times10}{1} }[/tex]
On multiplying gives:
EQR = [tex]\sqrt{{24000}}[/tex]\
Take square root on both sides:
EQR = 154.91
The EOQ formula takes into account the demand, setup cost, and holding cost per unit is 154.91 by calculating the EOQ, that can identify the batch size that results in the most cost-efficient production and storage.
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