The machine lays cable at a rate of 25 meters per minute. This is calculated by dividing 125 meters by 5 minutes.
To determine how quickly the machine can lay underground cable, we need to calculate the rate of cable it places per minute. We start by noting that the machine can lay 125 meters of cable in 5 minutes.
We calculate the rate as follows:
Divide the total length of cable by the total time: 125 meters / 5 minutes = 25 meters per minute.This means the machine lays cable at a rate of 25 meters per minute.
Complete Question: A machine laying underground cable can place 125 meters of cable in 5 minutes. What is the rate per minute?
evaluate each expression if y=2 Question 8y to the power of -4
Determine the domain of the function f(x)=1/3x^2+10x+8
Estimated the sum
97,991 + 102,489
_ + _ = _
Sergei says that 10%10% of a number will always be less than 20%20% of any other number. Complete one inequality to support Sergei's claim and one to show that he is incorrect
Answer:
Step-by-step explanation:
The temperature is changing every day by negative 7 over 18 degrees Fahrenheit. What will be the change in the temperature after 3 days? 21 over 6 degrees Fahrenheit negative 21 over 6 degrees Fahrenheit negative 7 over 6 degrees Fahrenheit 7 over 6 degrees Fahrenh
-7
6
taking teeeeesststt not sure id corryect
how much water will it take to simmer 1 3/4 quarts of barley using a water to barley ratio of 4 to 1
Answer:
The water will be 4 times more as compared to the original.
Step-by-step explanation:
A money market fund advertises a simple interest rate of 88%. Find the total amount received on an investment of $4000 for 15 months.A money market fund advertises a simple interest rate of 88%. Find the total amount received on an investment of $4000 for 15 months. The total amount received on an investment of $4000 for 15 months is $ . (Do not round until the final answer. Then round to the nearest cent as needed.)
Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5 . . . ? Check all that apply.
f(n) = –6.5n + 14.5f(n) = –1.5n + 9.5f(n) = 6.5n + 1.5f(1) = 8, f(n + 1) = f(n) – 6.5f(1) = 8, f(n + 1) = f(n) – 1.5f(1) = 8, f(n + 1) = f(n) + 6.5
Answer:
f(n)= -6.5n +14.5
f(1)= 8, f(n+1) = f(n) - 6.5
Step-by-step explanation:
the arithmetic sequence 8, 1.5, –5, –11.5 . . .
First term is 8
Now we find difference between the terms
1.5 - 8= -6.5
-5-1.5= -6.5
difference is -6.5
The formula is f(n)= a1 + (n-1)d
where a1 is the first term and d is the difference
f(n)= 8 + (n-1)(-6.5)
f(n)= 8 -6.5n+6.5
f(n)= -6.5n +14.5
To get recursive formula we use
f(n+1) = f(n)+ difference
f(1)= 8, f(n+1) = f(n) - 6.5
The functions that represent the arithmetic sequence is given by:
f(n) = –6.5n + 14.5
f(n+1) f(n) – 6.5, f(1) = 8
------------------
In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d, and the nth term is given by:
[tex]f(n) = a_1 + (n-1)d[/tex]
In which [tex]a_1[/tex] is the first term.The sequence can also be represented by a recursive sequence, given by:
[tex]f(1) = a_1[/tex]
[tex]f(n+1) = f(n) - d[/tex]
In this sequence:
The first term is [tex]a_1 = -[/tex]The common difference is [tex]d = 1.5 - 8 = -6.5[/tex].Thus, the possible representations are:
[tex]f(n) = a_1 + (n-1)d[/tex]
[tex]f(n) = 8 - 6.5(n-1)[/tex]
[tex]f(n) = 8 - 6.5n + 6.5[/tex]
[tex]f(n) = -6.5n + 14.5[/tex]
And
[tex]f(1) = a_1[/tex]
[tex]f(n+1) = f(n) - d[/tex]
[tex]f(1) = 8[/tex]
[tex]f(n+1) = f(n) - 6.5[/tex]
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In calculating one variable statistics you find the standard deviation to be equal to zero
A standard deviation of zero in a data set signifies that all data points are identical, with no variation among them.
When calculating one variable statistics, if you find that the standard deviation is equal to zero, it means that all of the data points in the set have the same value. There is no spread or variability within the data, as standard deviation measures how much each number in a set differs from the mean of the data set. Since all numbers are the same, they all equal the mean, resulting in zero deviation.
A veterinarian estimated the weight of a puppy to be 9kg. The actual weight of the puppy was 9.5kg Find the absolute error and the percent error of the veterinarian's estimate. If necessary, round your answers to the nearest tenth.
Answer:
That huy is wrong... the answer is negetive! People
Step-by-step explanation:
The absolute error of the veterinarian's estimate is 0.5 kg, and the percent error is approximately 5.3% when rounded to the nearest tenth.
The question given asks us to find the absolute error and the percent error of a veterinarian's estimate of a puppy's weight. To calculate the absolute error, we take the actual weight of the puppy (9.5 kg) and subtract the veterinarian's estimate (9 kg), which gives us an absolute error of 0.5 kg. To find the percent error, we divide the absolute error by the actual weight and multiply by 100, resulting in a percent error of about 5.3% when rounded to the nearest tenth.
Here is the step-by-step breakdown:
Calculate absolute error: Actual weight - Estimated weight = 9.5kg - 9kg = 0.5kgCalculate percent error: (Absolute error / Actual weight) * 100 = (0.5kg / 9.5kg) * 100 ≈ 5.263%. Round this to the nearest tenth: 5.3%The owners of a business must spend less than $140 on supplies. They have already spent $60. Now they want to buy chairs that cost $20 each. Let x represent the number of chairs they can buy. Select True or False for each statement.
They can buy any number of chairs fewer than 4
They can buy any number of chairs fewer than 8
If owners of a business must spend less than $140 on supplies. They have already spent $60. Now they want to buy chairs that cost $20 each. Let x represent the number of chairs they can buy. Then they can buy any number of chairs fewer than 4.
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
Given,
owners of a business must spend less than $140 on supplies.
They have already spent $60.
They want to buy chairs that cost $20 each.
Let x represent the number of chairs they can buy.
60+20x<140
Now solve for x
20x<140-60
20x<80
Divide both sides by 20
x<80/20
x<4
Hence they can buy any number of chairs fewer than 4
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Find the average value of the function f(x) = 9 sin2(x) cos3(x) on the interval [−π, π].
The average value of f(x) = 9 sin²(x) cos³(x) over the interval [-π, π] is 0.
Explanation:Integrate and Divide: To find the average value of a function f(x) over an interval [a, b], we calculate the definite integral of f(x) over the interval and divide by the interval's width:
Average value = (1/(b-a)) * ∫a^b f(x) dx
In this case, a = -π and b = π, so b - a = 2π.
Integrate f(x): Unfortunately, integrating f(x) = 9 sin²(x) cos³(x) directly is quite complex. However, we can use the trigonometric identity sin²x = (1 - cos²x) to rewrite the function:
f(x) = 9 sin²(x) cos³(x) = 9 (1 - cos²x) cos³(x)
Integrating this form of f(x) is more manageable, although it still involves integration by parts due to the product of three terms.
Zero Integral: After integrating and simplifying, the definite integral of f(x) over [-π, π] evaluates to 0.
Average Value: Dividing the integral by the interval's width (2π) confirms the average value of f(x) on [-π, π] is 0:
Average value = (1/2π) * 0 = 0
Therefore, the average value of f(x) = 9 sin²(x) cos³(x) on the interval [-π, π] is 0, despite the function's non-zero values within the interval.
your bakery is in a large shopping center. The entrie shopping center is 4,500 square feet. Your bakery takes up only 1/10 of that space.How many square feet is your bakery
The bakery takes up 1/10 of the total shopping center space. Since the shopping center is 4,500 square feet, the bakery is 450 square feet.
To determine the size of the bakery in square feet, we need to calculate 1/10th of the total shopping center's area. The shopping center is 4,500 square feet in total. So, the calculation would be:
Divide the total area by 10 to find 1/10 of the area.Multiply that number by 1 to get the exact area for the bakery.Here's the step-by-step calculation:
4,500 square feet / 10 = 450 square feetTherefore, the bakery takes up 450 square feet of space within the shopping center.
The library is 0.96 mile away from Theo’s home. Write this distance as a fraction in simplest from.
Which graph represents the solution set of the system of inequalities?
Find the extreme values of f on the region described by the inequality. f(x, y) = 2x2 + 3y2 − 4x − 2, x2 + y2 ≤ 16
The minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].
[tex]f(x,y)=2x^2+3y^2-4x-2, g(x,y)=x^2+y^2-16.[/tex]
[tex]f_x (x,y)=4x+0-4-0=4(x-1)[/tex]
[tex]f_y (x,y)=0+6y-0-0=6y[/tex]
[tex]4(x-1)=0, x=1[/tex]
[tex]6y=0, y=0.[/tex]
So, critical points of [tex]f(x,y)[/tex] is [tex](1,0)[/tex].
Put this in [tex]g(x,y)=x^2+y^2-16[/tex].
[tex]g(1,0)=1^2+0^2-16=-15<0[/tex].
So, critical point is in the interior point of the given region.
[tex]g_x (x,y)=2x+0-0=2x[/tex]
[tex]g_y (x,y)=0+2y-0=2y[/tex]
Let there is a parameter [tex]\lambda[/tex] such that [tex]f_x = \lambda g_x[/tex] and [tex]f_y = \lambda g_y[/tex].
[tex]4(x-1)=\lambda (2x)[/tex] and [tex]6y=\lambda (2y)[/tex]
So, [tex]2(x-1)=x\lambda[/tex] and [tex]\lambda=3[/tex]
So, [tex]2(x-1)=3x[/tex]
So, [tex]-2=x[/tex]
Put [tex]x=-2[/tex] in [tex]x^2+y^2=16[/tex], to determine the value of [tex]y[/tex].
[tex](-2)^2+y^2=16[/tex]
[tex]y^2=12[/tex]
[tex]y=\pm 2\sqrt{3}[/tex]
So, the obtained possible extrema are [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].
Now, find [tex]f(x,y)[/tex] at [tex](1,0), (-2, -2\sqrt{3}),[/tex] and [tex](-2, 2\sqrt{3})[/tex].
[tex]f(1,0)=2(1)^2+3(0)^2-4(1)-2[/tex]
[tex]=2-4-2[/tex]
[tex]=-4[/tex]
[tex]f(-2,-2\sqrt{3})=2(-2)^2+3(-2\sqrt{3})^2-4(-2)-2[/tex]
[tex]=8+36+8-2[/tex]
[tex]=50[/tex]
[tex]f(-2,2\sqrt{3})=2(-2)^2+3(2\sqrt{3})^2-4(-2)-2[/tex]
[tex]=8+36+8-2[/tex]
[tex]=50[/tex]
So, the minimum value of the function [tex]f(x,y)[/tex] is [tex]-4[/tex] at the point [tex](1,0)[/tex] and the maximum value of the function [tex]f(x,y)[/tex] is [tex]50[/tex] at the points [tex](-2, -2\sqrt{3}), (-2, 2\sqrt{3})[/tex].
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The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. how long do the longest 10% of calls last?
To solve this problem, we use the formula:
z = (x – u) / s
where z is the z score value which can be obtained from the tables, x is the sample value, u is the mean = 6.3 min, and s is the std dev = 2.2 min
at P value = 0.90, the z = 1.28, finding for x:
x = z s + u
x = 1.28 * 2.2 + 6.3
x = 9.116
at P value = 1.0, the z = 3.49, finding for x:
x = z s + u
x = 3.49 * 2.2 + 6.3
x = 13.978 ~ 14
Therefore the longest 10% calls last about 9.1 minutes to 14 minutes
Family spends 67.50 for 23 gallons of gasoline. If they need to go 350 miles how much money is spent on gas per gallon
A family has two cars. During one particular week, the first car consumed 30 gallons of gas and the second consumed 40 gallons of gas. The two cars drove a combined total of 1800 miles, and the sum of their fuel efficiencies was 50 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Number 26 on a b and c pls I need the answer
Write the whole number 10 as an equivalent fraction with 9 as the denominator
which regular polygon has a minimum rotation of 45 to carry the polygon onto itself
Help asap pleaaaaaaaaase
pls help i have a math question and I can`t figure out the answer
The student's questions relate to high school-level mathematics, such as using a graphing calculator for probability distribution calculations, the practice of mental arithmetic, and understanding significant figures and rounding. Some problems also touch on algebraic thinking and the application of mathematics in real-world contexts.
Explanation:The student is asking several questions that pertain to solving mathematical problems and making calculations, which fall within the subject of Mathematics. It's apparent that the questions involve using a graphing calculator, understanding probability distributions, mental arithmetic, and solving equations. This level of mathematics typically corresponds to High School curriculum.
For instance, the student mentions using a graphing calculator to find a probability with a binomial distribution (binompdf), which indicates a familiarity with statistical functions and probability theory. The second part of the series includes an arithmetic puzzle meant to encourage mental math skills by breaking down a problem into more manageable parts. Another problem gives insight into significant figures and decimal places, suggesting the topic of precision and rounding in measurements or calculated results.
Additional parts of the problems focus on making estimates and using ratios for time calculations, implying topics potentially from an algebra or pre-calculus course, with a touch on the real-world application of mathematics and the flexibility and multiple methods within the mathematical process.
Ciprofloxacin (Cipro) oral suspension is available as a 250mg/5mL concentration. The physician orders a dose of 150mg. How many milliliters of suspension will have to be given for each dose?
A consumer group claims that the mean annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. A random sample of 120 people in the U.S. has a sample mean annual consumption of high fructose corn syrup of 49.5 pounds. Assume the population standard deviation is 3.6 pounds. evidence to support the group’s claim? 1). State the hypothesis: H0 : Ha : 2). Specify the level of significance 3). Sketch the sampling distribution 4). Calculate the test statistic At = 0.05, is there enough 5). Find the P-value and shade this in the distribution in (3): 6). Decision (using the P-value): 7). Write a statement to interpret the decision in the context of the original claim 2
common denominator of
8\15 and 5\9
A box without a lid is constructed from a 26 inch by 26 inch piece of cardboard by cutting x x in. squares from each corner and folding up the sides. a) Determine the volume of the box as a function of the variable x x .
The base of a pyramid has n sides.
Write an EXPRESSION for the number of faces of the pyramid.
Answer: The expression for number of faces of a pyramid =1+n
Step-by-step explanation:
A Pyramid is a polyhedron or a three dimensional shape having a polygon base and all lateral faces are triangles .
Its base describe the number of other faces of it.
For example a triangular pyramid has a triangular base which gives rise to 3 lateral faces , and a rectangular pyramid has a rectangular base which give rise to 4 lateral faces and so on.....
So the total number of faces in a pyramid = base + lateral faces
If a pyramid has n sides therefore it give rise to n lateral faces such that
The total number of faces in a pyramid= 1+n .
The total number of faces of the pyramid is [tex]n+1[/tex].
A pyramid is a three-dimensional structure whose lateral sides converge to a single step at the summit, roughly forming a pyramid in the geometric sense. A pyramid's base can be trilateral, quadrilateral, or any other polygon shape.
For a pyramid having triangular base then, the total number of faces will be [tex]3+1=4[/tex].
In a similar way, if a pyramid has four sides at the base then, the total number of faces will be [tex]4+1=5[/tex].
Hence, in the given question the pyramid has [tex]n[/tex] sides at the base so, the total number of faces of the pyramid is [tex](n+1)[/tex].
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What is the nth term for 1 13 33 61 97 141