A 60-inch pipe is cut into two pieces. One piece is five times the length of the other. Find the length of the shorter piece
Answers
The length of the shorter piece is 10 inches.
To solve this problem, we need to use algebra to set up an equation that represents the information we know about the two pieces of the pipe. We know that the longer piece is five times the length of the shorter piece, so we can call the length of the shorter piece "x" and the length of the longer piece "5x".
To solve this problem, let's call the length of the shorter piece "x". We know that the longer piece is five times the length of the shorter piece, so we can call the length of the longer piece "5x".
We also know that the two pieces add up to the total length of the pipe, which is 60 inches. So we can write an equation:
x + 5x = 60
Simplifying this equation, we get:
6x = 60
Dividing both sides by 6, we get:
x = 10
In summary, we can find the length of the shorter piece of a 60-inch pipe that is cut into two pieces by setting up an equation that represents the information we know about the lengths of the two pieces, simplifying that equation, and then solving for the unknown variable (in this case, the length of the shorter piece).
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Related Questions
i need help asap!!!!
Answers
Answer:
it's A
Step-by-step explanation:
just did it made 80
Answer:
heyy hello how r u? I hope u r fine
бр - 5 =13
need help !
Answers
Answer:
\(p=3\)
Step-by-step explanation:
\(6p-5=13\)
\(+5\) \(+5\)
\(6p=18\)
\(/6\) \(/6\)
\(p=3\)
378 mL converted to liters?
help please
Answers
Answer:
the answer is 0.378 ml
.......
Answer: 0.378 liters
========================================================
Explanation:
To go from mL to liters, we divide by 1000
This is because there are 1000 milliliters in 1 liter.
----------
You can write it like this
\(378 \text{ mL} = 378 \text{ mL } \times \frac{1 \text{ L}}{1000 \text{ mL}} = \frac{378}{1000} \text{ L} = 0.378 \text{ L}\)
Note how the mL units cancel when we divide.
give the possible lengths of the legs of a right triangle with a hypotenuse of the square root of 265
Answers
To find the possible lengths of the legs of a right triangle with a hypotenuse of √265, solve the equation a^2 + b^2 = 265 for positive integer pairs (a, b).
To determine the possible lengths of the legs (a, b) of a right triangle with a hypotenuse of √265, we apply the Pythagorean theorem, which states that a^2 + b^2 = c^2, where c represents the hypotenuse. In this case, we have a^2 + b^2 = 265.
To find valid solutions, we search for positive integer pairs (a, b) that satisfy this equation. By trying different values of a and solving for b using the equation, we can identify potential combinations of leg lengths.
It is important to note that there may be multiple valid solutions, as there are various pairs of positive integers that fulfill the Pythagorean theorem for this specific hypotenuse length.
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The ____ sequence begins with two ones, and then each new term is formed by adding the two terms before it: 1, 1, 2, 3, 5, 8, 13, 21,...
Answers
Answer:
Fibonacci
Step-by-step explanation:
the Fibonacci sequence
Check whether the given value is a solution to the equation. 1/3 (x+4)=20 when x = 48
Answers
Answer:
the answer may be made up to 17
the nurse is caring for a child who weighs 44 lb (20 kg). the health care provider has prescribed amoxicillin 50 mg/kg/day in equally divided doses every 6 hours. how many milligrams will the nurse administer for the 0600 dose? record your answer using a whole number.
Answers
Answer:
100 mg / dose
Step-by-step explanation:
We need to use conversion factors to get out answer, starting with 20kg. 20 kg * 50mg/kg/day = 400mg / day.
400 mg / day * 1 day / 24h * 6 h / 1 dose = 100 mg / dose.
the manager of a paint supply store wants to determine if the mean amount of paint contained in 1- gallon cans purchased from a nationally known manufacturer is actually more than 1-gallon. it is known that for this manufacturer the population standard deviation of the amount of paint is equal to 0.01 gallons. a random sample of 55.0 cans is selected, and the mean amount of paint per 1-gallon can is 0.987 gallons. use a significance level of 0.05. is (are) the critical region(s) for this test in the left tail, right tail, or both tail(s)?
Answers
In this case, the critical region will be in the right tail.
To answer this question, you need to conduct a hypothesis test to determine whether the mean amount of paint in 1-gallon cans from this manufacturer is significantly different from 1 gallon. The null hypothesis for this test is that the mean amount of paint in 1-gallon cans from this manufacturer is equal to 1 gallon, and the alternative hypothesis is that it is greater than 1 gallon.
To determine the critical region(s) for this test, you need to decide on the significance level, which is given as 0.05. This means that you will reject the null hypothesis if the test statistic falls in the critical region with a probability of less than 0.05.
In this case, since the alternative hypothesis is that the mean amount of paint in 1-gallon cans is greater than 1 gallon, the critical region will be in the right tail. This means that you will reject the null hypothesis if the test statistic falls in the right tail with a probability of less than 0.05.
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If $432 invested today yields $450 in a year's time, what is the discount factor? A) 0.10. B) 0.96. C) 1.96. D) 1.92. B) 0.96.
Answers
The discount factor of an investment with initial investment of $432 and future vaue of $450 in a year's time is 0.96 (B).
We can find the discount factor of the investment by taking the present value ($432) divided by the future value ($450) after one year. Using the present value formula, we know that:
PV = FV / (1 + r)ⁿ
where:
PV = investment present value
FV = investment future value
r = discount factor
n = time period
Based on the given data, we have:
PV = $432
FV = $450
n = 1 r?
We use the present value formula to find the discount factor:
PV = FV / (1 + r)ⁿ
$432 = $450 / (1 + r)
1 + r = 1.96
r = 0.96
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Consider the function F(x, y) = e^-x^2/5 - y^2/5 and the point P(- 2, - 2). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P b. Find a vector that points in a direction of no change in the function at P. a. The direction of steepest ascent is (Squareroot 2/2, Squareroot 2/2) The direction of steepest descent is (-Squareroot 2/2, -Squareroot 2/2) Which of the following vectors points in a direction of no change of the function at P(- 2, - 2)? (0, 1) (-1, -1) (1, 0) (1, -1)
Answers
a. The unit vectors that give the direction of steepest ascent and steepest descent at P is (√2/2, √2/2) and (-√2/2, -√2/2), respectively.
b. A vector that points in a direction of no change in the function at P is (1, 0). The correct answer is C.
a. To find the unit vectors that give the direction of steepest ascent and steepest descent at point P(-2, -2), we need to find the gradient of the function F(x, y) at that point.
So,
\(F(x, y) = (-2x/5)e^{(-x^{2/5} - y^{2/5})} i - (2y/5)e^{(-x^{2/5} - y^{2/5})} j\)
At P(-2, -2), we have:
\(F(-2, -2) = (8/5)e^{(-8/5)} i + (8/5)e^{(-8/5)} j\)
Now, we need to normalize this vector to find the unit vectors in the direction of steepest ascent and steepest descent:
The direction of steepest ascent is given by:
u = (∇F(-2, -2)) / ||∇F(-2, -2)||
=\([(8/5)e^{-8/5} i + (8/5)e^{-8/5} j] / (8/5)e^{-8/5}\sqrt{2}\)
= (1/√2) i + (1/√2) j
= (√2/2, √2/2)
Similarly, the direction of steepest descent is given by:
v = -u = (-√2/2, -√2/2)
b. Now, to find a vector that points in a direction of no change in the function at P(-2, -2), we need to find a vector that is orthogonal to the gradient vector ∇F(-2, -2).
So, we can take the cross product of ∇F(-2, -2) with the z-axis (which is orthogonal to the xy-plane), to get a vector that is orthogonal to both.
Let k be the unit vector in the z-direction (i.e., k = (0, 0, 1)).
Then, the vector that points in a direction of no change in the function at P(-2, -2) is given by:
w = ∇F(-2, -2) x k
= \([(8/5)e^{(-8/5)} i + (8/5)e^{(-8/5)} j]\) x k
= \((8/5)e^{(-8/5)} (-j)\)x (i)
= \((8/5)e^{(-8/5)}\) k
= (0, 0, (8/5)e\(^{-8/5}\)
Therefore, the answer is (0, 0, (8/5)e\(^{-8/5}\)), which is option (c) (1, 0).
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x over 8 = 3 solve for x
Answers
Answer:
x = 24
Step-by-step explanation:
\(\frac{x}{8}\) = 3 ( multiply both sides by 8 to clear the fraction )
x = 8 × 3 = 24
Answer: 24
Step-by-step explanation:
x/8 = 3
x = 3x8
x = 24
What’s the value for 2.3 + 4.09 =n
Answers
n = 6.39
Explanation:
2.3 + 4.09 = n
6.39 = n
Swap the sides of the equation
n = 6.39
alice has a total of 12 dimes and nickles. she has 2 more nickles than dimes. which equation represents the given problem situation
Answers
Answer:
A
Step-by-step explanation:
She has 2 more nickels then dimes not 2 times more therefore answers B and D are incorrect. C is incorrect because it has that there are 2 more dimes than nickels. A is correct because it says that there are c dimes, and then c +2 nickels.
What is
4y+6x=18
3y-2x=33
Answers
Answer:
x = -3 and y = 9
Step-by-step explanation:
Solving system of linear equations by elimination method:4y + 6x = 18 -----------------(I)
3y - 2x = 33 -----------------(II)
Multiply equation (II) by 3.
(I) 4y + 6x = 18
(II)*3 9y - 6x = 99 {Now add the equations}
13y = 117
Divide both sides by 13,
y = 117 ÷ 13
\(\boxed{\bf y = 9}\)
Substitute y = 9 in equation (I) and obtain the value of 'x',
4*9 + 6x = 18
36 + 6x = 18
Subtract 36 from both sides,
6x = 18 - 36
6x = -18
Divide both sides by 6
x = -18 ÷ 6
\(\boxed{\bf x = -3}\)
\( \\ 4y + 6x = 18 \\ \\ 6x= 18 - 4y \\ = x = 3 - \frac{2}{3 }y \\ x = - \frac{2}{3} y+ 3\)
how do you do this question? 再20至30之间，有多少个质数？A .2 B.4 C.6 D.8
Answers
Answer:
有两个，是23 和29
所以是 A
A twelve-sided die has sides numbered 1 through 12. The die is rolled once. Find each probability.: P(odd or a multiple of 4)
Answers
The probability of getting an odd number or a multiple of 4 is 3/4.
Given that, a twelve-sided die has sides numbered 1 through 12. we need to find the probability of getting a number odd or a multiple of 4.
Probability = favorable outcomes / total number of outcomes
For odd numbers =
Favorable outcomes = 1, 3, 5, 7, 9, 11 = 6
P(odd number) = 6/12 = 1/2
For multiple of 4 =
Favorable outcomes = 4, 8, 12 = 3
P(multiple of 4) = 3/12 = 1/4
P(odd or a multiple of 4) = 1/2 + 1/4 = 3/4
Hence, the probability of getting an odd number or a multiple of 4 is 3/4.
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What is the definition of a pandemic? How does a pandemic differ from an endemic or epidemic? What is the life cycle of the HIV virus once it enters the body? How does the genetic code of the virus change? How does HIV affect the body? How do people become infected with HIV? How does AIDS develop from an HIV infection? What are the current infection rates of HIV across the globe? Where is HIV/AIDS most prevalent? What treatments are currently available for HIV/AIDS? Do some regions of the world have better access to treatments than others? What is the average life expectancy for someone with HIV? Does life expectancy differ around the globe?
Answers
Answer:
HIV (human immunodeficiency virus) is a virus that attacks the body’s immune system. If HIV is not treated, it can lead to AIDS (acquired immunodeficiency syndrome). Learning the basics about HIV can keep you healthy and prevent HIV transmission. You can also download materials to share or watch videos on basic information about HIV.
What is HIV?
HIV Overview
HIV (human immunodeficiency virus) is a virus that attacks the body’s immune system. If HIV is not treated, it can lead to AIDS (acquired immunodeficiency syndrome).
There is currently no effective cure. Once people get HIV, they have it for life.
But with proper medical care, HIV can be controlled. People with HIV who get effective HIV treatment can live long, healthy lives and protect their partners.
Where did HIV come from?
History of HIV
HIV infection in humans came from a type of chimpanzee in Central Africa.
The chimpanzee version of the virus (called simian immunodeficiency virus, or SIV) was probably passed to humans when humans hunted these chimpanzees for meat and came in contact with their infected blood.
Studies show that HIV may have jumped from chimpanzees to humans as far back as the late 1800s.
Over decades, HIV slowly spread across Africa and later into other parts of the world. We know that the virus has existed in the United States since at least the mid to late 1970s.
To learn more about the history of HIV in the United States and CDC’s response to the epidemic, see CDC’s HIV and AIDS Timeline.
Step-by-step explanation:
Someone plz help it’s due in 3 minutes
Answers
Answer:
Yes
Step-by-step explanation:
Because as you look closer to this question, you will notice, their the same questions but the denominator is just switched around.
Hope this helped!
Answer:
Both products are equals
Step-by-step explanation:
The rule:
(a/b) × (c/d) = (a*c) / (b*d)
then:
According to the rule, numerators are multiplied by numerators and denominators by denominators. In this exercise the numerators are the same as the denominators, so the result of both products is the same.
Which term is a constant numerical value in w/4+12.5-7z????
help me i need help with what I’m doing!
Answers
Explanation:
The w/4 term is the same as (1/4)w or 0.25w since 1/4 = 0.25
Because a variable is attached to this term, it is not constant. The same can be said about the -7z term as well.
The 12.5 is constant. It never changes. It will always be 12.5 no matter what the other variable terms change to.
For example, if w = 12, then the term w/4 becomes 12/4 = 3. Or if w = 24, then w/4 = 24/4 = 6 is the new value. This shows that term changing depending on the input variable.
find the greatest common factor 35a^7b^4c^2 and -7a^3bc^2d
Answers
Answer:
35742
Step-by-step explanation:
an you guys help me with this one too
Answers
Amanda and Diana given right solution set.
The solution set of given graph of inequality is,
x < 4.
Now, The solution of given created inequality,
Amanda:- -3x + 5 > -7
=> -3x> -7 -5
=> - 3x > -12
=> 3x < 12
=> x < 4
So, it is correct
Briana:- 1/2 (2x - 4)> 2
=> 2x - 4 > 4
=> 2x > 8
=> x > 4
It is wrong
Courtney:- -7x+8 > -3x + 24
=> -7x + 3x > 24 - 8
=> -4x > 16
=> 4x < -16
=> x < -4
It is wrong
Diana:- 9x -6 < 3x + 18
=> 9x - 3x < 18 + 6
=> 6x < 24
=> x < 4
So, it is right
Hence, Amanda and Diana given right solution set.
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true or false: the points (6, 13), and (21, 33) and (99, 137) all lie on the same line. th equation of the lines is y + /3x + 5. explain or show your reasoning.
Answers
Answer:
point A (6,13) lies on the equation. True
given point B(21,33) lies on the equation. True
given point C (99, 137) lies on the equation. True
The equation that was given was y = 4/3x + 5
Now,check the given equation for the given points.
1) A (6,13)
Substitute x = 6 in the given equation y = 4/3x +5
y = 4/3(6) + 5 = 4(2) + 5 = 8+5 = 13
y=13
the given point A (6,13) lies on the equation.
2) B (21,33)
Substitute x = 21 in the given equation y=4/3x+5
y=4/3(21) + 5 = 4(7) + 5=28+5=33
y = 33
the given point B(21,33) lies on the equation.
3) C (99, 137)
Substitute x = 99 in the given equation y = 4/3x + 5
y=4/3(99) + 5 = 4(33) + 5 = 132 + 5 = 137
y = 137
the given point C (99, 137) lies on the equation.
There is your answer
Find the average rate of change in the simplest form
Answers
Slope = -5
American jurists ____ and ____ defined law in a functional sense as predictions of the way that a court will decide specific legal questions.
Answers
American jurists (fill in the names) defined law as predictions of how a court will decide specific legal questions, based on a functional perspective.
American jurists Oliver Wendell Holmes Jr. and Benjamin Cardozo are known for their functionalist approach to defining law. They viewed law not merely as a set of abstract principles or rules, but as a prediction of how courts will decide specific legal questions in practice. According to their perspective, the law should be seen as a dynamic and evolving system that adapts to societal changes and reflects the judgments and decisions of the judiciary. By emphasizing the functional aspect of law, Holmes and Cardozo recognized the importance of considering how legal principles are actually applied and interpreted in real-world scenarios. Their approach acknowledges that the interpretation and application of law by judges can vary and evolve over time, depending on factors such as legal precedent, social context, and the specific facts of the cases before them.
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Safiya travels at an average speed of 40 mph for 30 miles.
Without stopping, Safiya then travels 50 miles in 1.5 hours.
Find her average speed for the entire journey to 2 dp.
Pls help
Answers
Average speed is 35.56 mph.
Calculating average speed involves dividing the whole distance travelled by the total time it took to cover that distance. Speed is the rate of movement of something at a specific time. Average speed refers to the average speed during the course of a journey.
We have to find the average speed of the whole journey.
First we have to find total distance for whole journey and then total time for whole journey.
Total distance for whole journey = 30 miles + 50 miles = 80 miles
Time for 30 miles = distance/speed = 30/40 = 3/4 hrs = 0.75 hrs
Total time = 1.5 + 0.75 hrs = 2.25 hrs
Average speed = total distance/ total time
= 80/2.25
= 35.56 mph.
The average speed is 35.56 mph.
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the instructions on the bag of concrete mix say to add 2 gallons of water to each 8 pound bag of concreate mix. how much concreate mix is used per gallon of water?
A. 2 pounds
B. 4 pounds
C. 6 pounds
D. 10 pounds
E. 16 pounds
Answers
if m, p, and t are distinct positive prime numbers, then m3pt has how many different positive divisors greater than 1 ?
Answers
There are 15 different positive divisors (greater than 1) for the number m³pt. Here m, p, and t are distinct prime numbers. This is obtained by the prime factorization method.
How to find the number of positive factors for a number?The following are the steps to find the number of positive factors of a number:
Step 1: Find the L.C.M of the number by using the prime factorization method. For example: consider the number 24. Then, its prime factorization is as follows:
24 = 2 × 2 × 2 × 3
Step 2: Same bases should be added in powers. So, the factors we can write as
24 = 2³ × 3¹
Step 3: To find the number of positive factors of the number, the exponents of the prime factors is multiplied by adding 1.
I,e., N = (3 + 1)(1 + 1) = 4 × 2 = 8.
So, there are 8 factors for the number 32. They are 1, 2, 3, 4, 6, 8, 12, and 24.
Calculation:It is given that, m, p, and t are distinct positive prime numbers.
Then, the number of positive divisors greater than 1 for the number m³pt are
m³× p × t
Since m, p, and t are prime factors, we can multiply their power by adding 1 to them. I.e.,
N = (3 + 1) (1 + 1) (1 + 1) = 4 × 2 × 2 = 16
So, there are a total of 16 factors for the given number (including 1). So, the number of factors greater than 1 is 16 - 1 = 15.
Therefore, there are 15 different positive divisors greater than 1 for the number having prime factors as m³pt.
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Convert 32/9 to a mixed number
Answers
Answer:
Step-by-step explanation:
Marcie cooked dinner for herself. The original recipe has a serving size of 3 and requires three and three sevenths pounds of chicken. How many pounds of chicken will be needed for a single serving?
one and one seventh pounds
nine and three sevenths pounds
two over 49 pounds
three sevenths pounds
Answers
Using proportions, the number of pounds that will be needed for a single serving is: one and three seventh pounds.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
The number of pounds for 3 people is given by:
\(3 \frac{3}{7} = 3 + \frac{3}{7} = \frac{24}{7}\)
Hence, for one person, the number of pounds can be divided by three(multiplied by 1/3), hence:
\(\frac{24}{7} \times \frac{1}{3} = \frac{24}{21}\)
24 divided by 21 has a quotient of 1 and remainder of 3, hence as a mixed number, the amount is:
one and three seventh pounds.
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Answer:
Step-by-step explanation:
the awnser is cerrot.
can someone help me with this?
Answers
Answer:
The roots of the equation
\(x^{3}-10x^{2}+31 x-30 = 0\)
correspond to the x-intercepts of the function graph
Step-by-step explanation:
The roots of the equation
\(x^{3}-10x^{2}+31 x-30 = 0\)
are x = 2, x = 3, x = 5
which are located at points (2, 0), (3, 0), (5,0)
These points are the x-intercepts of the graph of the equation
So the x-intercepts of the equation are the roots of the equation
I have graphed this using Geogebra which I am familiar with. You should probably use Desmos as per the instructions
