The problem primarily involves the calculation and understanding of the concepts of perimeter and area in Mathematics. Given the length is 3 ft longer than the width, and the perimeter of the rectangle is 26 feet, first, we find that the width is 5 feet and the length is 8 feet. The area is thus, 40 square feet.
Explanation:To solve this problem, we need to understand the formula for the perimeter of a rectangle, which is 2l + 2w, where 'l' stands for length and 'w' for width. Also, the area of a rectangle is calculated by l*w. The problem states that the length is 3 ft longer than the width and that the perimeter is 26 feet. Firstly, we can express the length as 'w + 3' and substitute into the perimeter formula:
2(w + 3) + 2w = 26
After simplifying, we get the width equals to 5 feet. Substituting 5 for width, we get the length as 8 feet, because length is 3 feet longer than the width. Then, the area of the rectangle can be calculated by multiplying the width by the length:
Area = l * w = 8 ft * 5 ft = 40 square feet
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Jana is doing an experiment. She is on a dock that is 10 feet above the surface of the water. Jana drops the weighed end of a fishing line 35 feet below the surface of the water. She reels out the line 29 feet, and then reels it back in 7 feet. What is the final distance between Jana and the end of the finishing line?
Which of the following is true?
1.75 > 1½
0.25 ≠ ¼
0.2185 = ⅓
1.436 < 25⁄2
After converting all values to decimal form for consistent comparison, the statements '1.75 > 1½' and '1.436 < 25⁄2' are true, while the statements '0.25 ≠ ¼' and '0.2185 = ⅓' are false.
Explanation:The question is asking to compare different given values, either greater than (>), not equal to (≠), or less than (<). To do this accurately, we need to convert all numbers to a common form. In this case, it is easiest to consider everything as decimal values:
1.75 is indeed greater than 1½ (which is 1.5 in decimal), so 1.75 > 1½ is true.0.25 is equal to ¼ (which is also 0.25 in decimal), therefore 0.25 ≠ ¼ is false. 0.2185 is not equal to ⅓. ⅓ in decimal is approximately 0.333, so 0.2185 = ⅓ is false. 1.436 is less than 25/2 (which is 12.5 in decimal form), so 1.436 < 25⁄2 is true. Learn more about Decimal Comparison here:https://brainly.com/question/12970629
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Tom"s and Tim's ages add up to 21 years. In 3 years, Tom will be twice Tim's age. How old are they now?
Find f`(x) for the following function. Then find f(5),f(0),f(-9).
f(x)=2x+1 (simplify)
A lawn is in the shape of a trapezoid with a height of 40 feet and bases of 60 feet and 140 feet. How many bags of fertilizer must be purchased to cover the lawn if each bag covers 1800 square feet?
Finley makes 1 batch of her favorite shade of orange paint by mixing 5 liters of yellow paint with 3 liters of red paint. How many batches of orange paint can Finley make if she has 15 liters of red paint?
The length of a ribbon is 3/4 meter. Sun Yi needs pieces measuring 1/3 meter for an art project. What is the greatest number of pieces measuring 1/3 meter that can be cut from the ribbon? How much ribbon will be left after Sun Yi cuts the ribbon?
Sales at a local ice cream shop went 80% in 5 years. If 12,000 ice cream cones were sold in the current year find the number of ice cream cones sound in 5 years
For the initial value problem y' −xy = x, y(0) = 1. write down the first four nonzero terms of the series
6.24 divided by 200 equals what
How much money should be invested at 5% interest, compounded quarterly, so that 7 years later the investment will be worth $5000? This amount is called the present value of $5000 at 5% interest.
PLEASE HELP!!!!!! DUE TODAY!!!!!! PLEASEEEEEEEE!!!!!!!!
Ke Shawn is placing a right triangle in the coordinate plane. He knows that the longer leg is twice the length of the shorter leg. He places the longer leg on the x-axis.
What coordinates should he assign to the third vertex of the triangle?
Enter your answer in the boxes.
Answer: (2a,0) is the answer. But you already know.
Step-by-step explanation:
What is the conversion factor to convert cups to liters?
Answer:
0.2365882365 L/cup
Step-by-step explanation:
The conversion factor can be found from the size of a cup in relation to a gallon, and the size of a cubic inch in relation to a liter.
[tex]1\,\text{cup}=8\,\text{fl oz}\times\dfrac{231\,in^{3}}{128\,\text{fl oz}}\times\left(\dfrac{0.254\,\text{dm}}{1\,\text{in}}\right)^{3}\times\dfrac{1\,L}{1\,dm^{3}}\\\\=\dfrac{8\cdot 231\cdot 0.254^{3}}{128}\,L=0.2365882365\,L[/tex]
what is the mean of this data if necessary round your answer to the nearest tenth. please help with my homework
identify the product and it in scientific notation. 4.7 x(6.02 x 10^23)
the product of [tex]\( 4.7 \times (6.02 \times 10^{23}) \) is \( 2.8294 \times 10^{24} \).[/tex]
Sure, let's identify the product and express it in scientific notation.
[tex]\( 4.7 \times (6.02 \times 10^{23}) \)[/tex]
To find the product, we simply multiply the two numbers:
[tex]\( 4.7 \times 6.02 \times 10^{23} \)[/tex]
First, we multiply 4.7 by 6.02:
[tex]\( 4.7 \times 6.02 = 28.294 \)[/tex]
Next, we multiply this result by [tex]\( 10^{23} \):[/tex]
[tex]\( 28.294 \times 10^{23} \)[/tex]
Now, to express this product in scientific notation, we need to adjust the decimal point so that the number is between 1 and 10:
[tex]\( 2.8294 \times 10^{24} \)[/tex]
Therefore, the product of [tex]\( 4.7 \times (6.02 \times 10^{23}) \) is \( 2.8294 \times 10^{24} \).[/tex]
1. First, we multiplied 4.7 by 6.02 to get 28.294.
2. Then, we multiplied this result by [tex]\( 10^{23} \)[/tex] to shift the decimal point 23 places to the right, resulting in[tex]\( 2.8294 \times 10^{24} \)[/tex] in scientific notation.
This method helps in handling large numbers efficiently, especially when dealing with calculations involving scientific notation and significant figures.
complete question
identify the product and it in scientific notation. 4.7 x(6.02 x 10^23)
The height of Niagara falls is 182.How many yards high is Niagara falls
To convert the height of Niagara Falls from meters to yards, we multiply the given height of 182 meters by the conversion factor of 1.09361 yards per meter, which gives us approximately 199.18 yards.
Explanation:The height of Niagara Falls is provided in this question as 182. However, no units are given so let's assume this is in meters as that's a common unit for height. The conversion factor from meters to yards is approximately 1 meter = 1.09361 yards. Therefore, we multiply the given height in meters by this conversion factor to get the height in yards.
First, identify the height given in the question- here it is 182.Next, apply the conversion factor: 182 meters * 1.09361 yards/meter.Doing this multiplication gives us approximately 199.18 yards.So, Niagara Falls is approximately 199.18 yards high when converted from meters.
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Suppose x follows a continuous uniform distribution from 1 to 5. determine the conditional probability p(x >2.5 | x ≤ 4).
Final answer:
The conditional probability P(x > 2.5 | x ≤ 4) for a variable x following a uniform distribution from 1 to 5 is calculated using the conditional probability formula, resulting in a probability of 0.5.
Explanation:
The question asks to determine the conditional probability P(x > 2.5 | x ≤ 4) when x follows a continuous uniform distribution from 1 to 5. The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of A and B both happening, and P(B) is the probability of B happening.
Here, event A is 'x > 2.5' and event B is 'x ≤ 4'. The probability of x being greater than 2.5 and less than or equal to 4, P(A ∩ B), is the length of the interval from 2.5 to 4, which is 1.5 units. Since x is uniformly distributed, this translates to a probability of 1.5/(5-1), because the total length of the distribution is 4 units. Event B 'x ≤ 4' has a probability of 3/(5-1) since the interval from 1 to 4 is 3 units long.
Hence, the conditional probability is P(A|B) = (1.5/4) / (3/4) = 1.5/3 = 0.5.
How do I Factor 125x^3 -64
The answer is not (5x+4)(5x-4) or (5x-4)(25x^2 +15x+16)
The correct factorization would be (5x - 4)(25x^2 + 20x + 16).
The law of factoring cubes states that we use the following formula when we have two cubes being subtracted by one another.
(a - b)(a^2 + ab + b^2)
If we take the cube root of 125x^3 we get 5x, which will be our a value. If we take the cube root of 64, we get 4, which will be our b value. Then we plug in to the formula.
(5x - 4)((5x)^2 + (5x)(4) + 4^2)
(5x - 4)(25x^2 + 20x + 16)
I think the problem with your second answer is that you just did not properly multiply the 5x and the 4 to get 20x (instead you got 15x).
7,209,000 in the year 2050 and that this will be 24% of the population. What is the total population?
PLZ HELP IM FAILING!!!!!! The linear equation y−3=4(x+5)y−3=4(x+5) y minus 3 equals . 4 open x plus 5 close is in what form.
You took 500 calls in 30 days that means I took a average of
Answer:
17 calls
Step-by-step explanation:
You took 500 calls in 30 days.
We have to calculate the average calls per day.
Average calls = [tex]\frac{\text{Total calls}}{\text{total days}}[/tex]
= [tex]\frac{500}{30}[/tex]
= 16.7 ≈ 17 calls per day
That means i took an average 17 calls per day.
A 16 oz package of brown rice cost 79cents and 32oz package of white rice costs $3.49 which package is a better deal
0.79 / 16 oz = 0.049 ( price for 1 oz of brown rice)
3.49 / 32 = 0.109 ( price for 1 oz of white rice)
the price per oz of brown rice is cheaper then 1 oz of white rice so the brown rice is the better deal
The 16 oz package of brown rice is a better deal because it has a lower price per ounce compared to the 32 oz package of white rice.
Explanation:To determine which package of rice is a better deal, we calculate the price per ounce for each package. The 16 oz package of brown rice costs 79 cents, so the price per ounce of brown rice is 79 cents ÷ 16 oz = 4.9375 cents per ounce. The 32 oz package of white rice costs $3.49, therefore the price per ounce of white rice is $3.49 ÷ 32 oz = 10.90625 cents per ounce.
By comparing the price per ounce, we can see that the price per ounce for the brown rice is less than the price per ounce for the white rice. Therefore, the 16 oz package of brown rice is the better deal.
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A school uses merit based pay for teachers. Each teacher would be given a score between 1 (Far Below Expectations) and 5 (Exceeds expectations) in the following categories. The weight of each category is included.
Content Knowledge (20%)
Lesson plans (15%)
Instruction delivery (20%)
Classroom management (15%)
Student Performance (20%)
Supplementary Responsibilities (10%)
A teacher received the following scores. What was his weighted average?
Content Knowledge = 4
Lesson plans = 3
Instruction delivery = 3
Classroom management = 5
Student Performance = 4
Supplementary Responsibilities = 2
The teacher's weighted mean is ______________.
4*0.20 = 0.8
3 *0.15 = 0.45
3*0.20 = 0.6
5 *0.15 = 0.75
4 *.20 = 0.8
2 *0.10 =0.2
0.8 + 0.45 + 0.6 +0.75 +0.8 +0.2 = 3.6
weighted mean = 3.6
The teacher's weighted mean is 3.6 out of 5.
To calculate the weighted average, you'll multiply each score by its corresponding weight, then sum up the results.
Here are the scores and their respective weights:
- Content Knowledge: 4 (score) * 0.2 (weight) = 0.8
- Lesson Plans: 3 * 0.15 = 0.45
- Instruction Delivery: 3 * 0.20 = 0.6
- Classroom Management: 5 * 0.15 = 0.75
- Student Performance: 4 * 0.20 = 0.8
- Supplementary Responsibilities: 2 * 0.10 = 0.2
Now, sum up these weighted scores:
0.8 + 0.45 + 0.6 + 0.75 + 0.8 + 0.2 = 3.6
So, the teacher's weighted mean is 3.6.
A suit is on sale for $154. If the original price of the suit was $440, what percent was discounted for the sale?
What is the value of 2x to the 4th degree + 5x when x=6
Rose bought 7/20 kilogram of ginger candy and 0.4 kilogram of cinnamon candy. Which did she buy more of? Explain how you know.
Answer:
Rose bought cinnamon candy more of.
Step-by-step explanation:
Rose bought ginger candy = [tex]\frac{7}{20}[/tex] kilogram
= 0.35 Kilogram
She bought cinnamon candy = 0.4 kilogram
As we know 1 kilogram = 1000 grams
0.35 kilogram = 1000 × 0.35 = 350 grams ginger candy
0.4 kilograms = 1000 × 0.4 = 400 grams cinnamon candy
Therefore, She bought cinnamon candy more.
A data set a has a mean of 7,a median 5,and a mode of 8.wich of the the numbers 7,5,and 8 must be in the data set?
How do i solve this equation and how did you do it
Suppose that f(x+h)−f(x)= −6hx2−7hx−6h2x−7h2+2h3.
Find f′(x).
f′(x)=
Final answer:
To find f'(x), simplify the given expression by canceling the common factor of h, then take the limit as h approaches zero. The resulting derivative is f'(x) = -6x² -7x.
Explanation:
To find the derivative of function f(x), denoted as f'(x), we use the definition of the derivative and the given equation f(x+h) - f(x) = -6hx2 - 7hx - 6h2x - 7h2 + 2h3. The definition of the derivative is the limit of the average rate of change as the interval approaches zero, formally:
f'(x) = lim (h -> 0) [f(x+h) - f(x)] / h
In the given difference quotient, every term includes an h, allowing us to simplify by cancelling an h from each term before taking the limit as h approaches zero. This gives us:
f'(x) = lim (h -> 0) [-6x² - 7x - 6h2 - 7h + 2h2]
When h approaches zero, the terms containing h also approach zero. Thus, we are left with:
f'(x) = -6x² - 7x
How can you check to see if this equation is correct? 12+39=49
Answer:
By solving it.
Step-by-step explanation:
In order to see if the equation is correct, you just have to perform the operations in both sides of the inequality and then check if those are equal, that means that the equation is correct, for example if both sides of the equation give as a result 10 then the equation is correct, now let´s do it with the problem:
12+39=49
51=39
Since 51 is not equal to 39 that means that the equation is not correct.