Mr. Vella can build a brick wall in 4 days. His apprentice can build the same wall in 6 days. After working alone for 3 days, Mr. Vella became ill and left the job for his apprentice to complete. How many days did it take the apprentice to finish the wall?
Apprentice will take [tex]1\frac{1}{2}[/tex] days to finish the wall.
What is work?" Work is defined as when force is applied to move an object in the direction of displacement."
According to the question,
Number of days taken by Vella to build a brick = 4 days
Work done by Vella in 1 day = [tex]\frac{1}{4}[/tex]
Work done by Vella in 3 days = [tex]\frac{3}{4}[/tex]
Number of days taken by apprentice to build same brick = 6 days
Total days taken by apprentice to complete 3/4 of work = [tex]\frac{3}{4} of 6[/tex]
= [tex]\frac{3}{4}[/tex] × 6
=[tex]\frac{9}{2}[/tex]
= [tex]4\frac{1}{2}[/tex] days
Number of days apprentice take to finish the wall is = 6 - [tex]4\frac{1}{2}[/tex]
= [tex]1\frac{1}{2}[/tex]
Hence, apprentice will take [tex]1\frac{1}{2}[/tex] days to finish the wall.
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Complete the coordinate proof of the theorem.
The sum of three consecutive odd integers is 75. find the numbers
Earns 8.50 an hour . Works 45 hours.
Steve had 7 more than twice as many quarters as dimes. if the total value of her coins was $10.15, how many of each kind of coin did she have?
How are these shortcuts (SSS, SAS, ASA, and AAS) similar to or different from those for proving triangle congruence?
Which value of x is the solution of the equation
2( x-4) + 7= 3?
1. 1
2.2
3 . 6
4 . 0
The solution to the equation 2(x - 4) + 7 = 3 is x = 2, after simplifying and solving for x.
Explanation:The student has asked which value of x is the solution of the equation 2(x - 4) + 7 = 3. To find the solution, we first simplify and solve for x:
2(x - 4) + 7 = 32(x - 4) = 3 - 72(x - 4) = -4x - 4 = -2x = -2 + 4x = 2Therefore, the correct solution for x is 2.
Fill in the blanks to write an equation in slope-intercept form representing the function shown in the table.
48.5 out of 50 as a percentage
48.5 out of 50 as a percentage, is 97%.
48.5 out of 50 as a percentage can be calculated by dividing 48.5 by 50 and then multiplying by 100 to get the percentage.
Divide 48.5 by 50: 48.5 / 50 = 0.97
Multiply by 100 to get the percentage: 0.97 * 100 = 97%
Merry and pippin were working on a project in carpentry class. they needed to cut 4 lengths of 1 5/8 feet from a board. how long must the board be to allow this?
A company makes storage tanks in the shape of a cylinder of height H and radius R. The standard model the company sells has a height of 20 cm in the radius of 20 cm. Customers may also request tanks that have a smaller radius. For each centimeter a tank’s radius decreases, however it’s height must increase by 5 cm.
The volume of a cylinder Jeckel storage tank is represented by the formula V= 3.14 (radius)^2 (height). X represent the number of centimeters by which the radius is decreased due to a customer’s request. Write a function V(x) to represent the volume of a tank a customer a request as a function of X.
We are given the formula for volume V:
V = 3.14 r^2 h
where r is radius and h is height
The standard height and radius is both 20 cm each, therefore we can write it as:
V = 3.14 (20)^2 (20)
It is stated that the radius can be modified, for every 1 cm change in tanks radius, the height must increase by 5 cm, therefore:
V = 3.14 (20 – x)^2 (20 + 5x)
or in general form:
V = 3.14 (r – x)^2 (h + 5x)
Harper has $15.00 to spend at the grocery store. She is going to buy bags of fruit that cost $4.75 each and one box of crackers that cost $3.50. Model the problem algebraically and determine the maximum number of bags of fruit,b, Harper can buy.
One box of crackers costs $1.75. The crackers are advertised as “3 boxes for $5.25.” Which proportion can be used to represent the cost of the crackers?
Which linear inequality is represented by the graph?
A.y ≥1/3 x – 4
B.y ≤1/3 x – 4
C.y ≤1/3 x + 4
D.y ≥1/3 x + 4
Answer:
the answer is actually D
Step-by-step explanation:
got it on edg
A sample of n = 25 individuals is selected from a population with µ = 60 and sigma = 10 and a treatment is administered to the sample. after treatment, the sample mean is m = 63. what is the value of cohen's d for this sample?
The information regarding the sampling shows that the value of cohen's d for this sample is 0.3.
How to calculate the sampleFrom the information given, the sample of n = 25 individuals is selected from a population with µ = 60 and sigma = 10 and a treatment is administered to the sample. after treatment, and the sample mean is m = 63.
Therefore, the value of cohen's d for this sample will be:
= (M - µ) / 10
= (63 - 60) / 10
= 0.3
In conclusion, the correct option is 0.3.
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Final answer:
Cohen's d for the given sample is 0.3, calculated by subtracting the population mean from the sample mean and dividing by the population standard deviation.
Explanation:
The student's question is regarding the calculation of Cohen's d for a sample after treatment. Cohen's d is a measure of effect size used to indicate the standardized difference between two means. In this case, the following formula can be used: Cohen's d = (M - μ) / σ, where M is the sample mean after treatment, μ is the population mean, and σ is the population standard deviation.
Given that M = 63, μ = 60, and σ = 10, the calculation of Cohen's d is as follows:
Cohen's d = (63 - 60) / 10 = 3 / 10 = 0.3.
Therefore, the value of Cohen's d for this sample is 0.3, which is considered a small effect size according to Cohen's standards.
There are 13 animals in the barn. Some are chickens and some are pig's. There are 40legs in all. How many of each animal are there?
Answer:
7 pigs6 chickensStep-by-step explanation:
If all were chickens, there would be 26 legs. There are 14 legs more than that. Each pig contributes 2 additional legs, so there must be 14/2 = 7 pigs. The remaining 6 animals are chickens.
___
Check
7×4 + 6×2 = 28 +12 = 40 . . . . total legs
Answer:
easy! 27
Step-by-step explanation:
13- 40 = 27
or 13 + 27 =40
just add up 13 and 27 you'll get 40 in all
edit; btw I'm not the brightest
AD¯¯¯¯¯ , BD¯¯¯¯¯ , and CD¯¯¯¯¯ are angle bisectors of the sides of △ABC . BE=12 m and BD=20 m
A credit card issuer offers an APR of 19.94% and compounds interest monthly. Find the effective interest rate and explain which the card issuer is mostly likely to advertise, its APR or its effective interest rate?
((1+0.1994/12)^12)-1 = 21.87% effective rate
it would advertise the APR because it is lower
What are the roots of the equation? 5 x 3+45x2+70x=0
Final answer:
The roots of the equation 5x³ + 45x² + 70x = 0 are -7 and -2.
Explanation:
This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 5, b = 45, and c = 70. To find the roots of the equation, we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Plugging in the values, we get:
x = (-45 ± √(45² - 4(5)(70))) / (2(5))
Simplifying further gives us:
x = (-45 ± √(2025 - 1400)) / 10
And finally, calculating the square root and applying the ± gives us the two roots:
x = (-45 ± √625) / 10
x = (-45 ± 25) / 10
which can be further simplified to:
x = -7 or x = -2
Which linear inequality is represented by the graph?
y > 2x + 2
y ≥ x + 1
y > 2x + 1
y ≥ x + 2
Step 1
Find the slope of the line
Let
[tex]A(0,1)\\B(2,5)[/tex]
the slope is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{5-1}{2-0}[/tex]
[tex]m=\frac{4}{2}[/tex]
[tex]m=2[/tex]
Find the equation of the line
we know that
the equation of the line into slope-intercept form is
[tex]y=mx+b[/tex]
where
m is the slope
b is the y-intercept
in this problem we have
[tex]m=2[/tex]
[tex]b=1[/tex] ------> the y-intercept is the point A
substitute
[tex]y=2x+1[/tex]
Step 2
Find the equation of the inequality
we know that
the solution is the shaded area above the dotted line
so
above dotted line---------> represent the symbol ([tex]>[/tex])
the inequality is
[tex]y>2x+1[/tex]
therefore
the answer is
[tex]y>2x+1[/tex]
The correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].
Further explanation:
The linear equation of the line is [tex]y=mx+b[/tex] where, [tex]m[/tex] is the slope of the line and [tex]c[/tex] is the [tex]y[/tex]-intercept of the line.
Suppose the line passes through the two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex].
Therefore, the slope of the line can be calculated as follows:
[tex]\boxed{m=\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}}[/tex]
The symbol [tex]>[/tex] represents the solution set lies above the dotted line and the symbol [tex]<[/tex] represents the solution set below the dotted line.
Given:
The linear inequalities are given as follows:
[tex]\boxed{\begin{aligned}y&>2x+2\\ y&\geq x+1\\ y&>2x+1\\ y&\geq x+2\end{aligned}}[/tex]
Calculation:
First we will find the equation of the line.
The line cuts the [tex]y[/tex]-axis on the coordinate [tex](0,1)[/tex] as shown in the Figure 1 (attached in the end).
Therefore, the [tex]y[/tex]-intercept is [tex]1[/tex].
Kindly refer the Figure attached to the question.
From the figure 1 (attached in the end) we can see that the line passes through the points [tex](-2,-3)\text{ and }(1,3)[/tex].
The slope of the line can be calculated as follows:
[tex]\begin{aligned}m&=\dfrac{3-(-3)}{1-(-2)}\\&=\dfrac{6}{3}\\&=2\end{aligned}[/tex]
Therefore, the value of [tex]m[/tex] is [tex]m=2[/tex] and the value of [tex]b[/tex] is [tex]b=1[/tex].
Substitute [tex]2[/tex] for [tex]m[/tex] and [tex]1[/tex] for [tex]b[/tex] in the equation of the line [tex]y=mx+b[/tex].
Second we will find the equation of the inequality.
The shaded region is shown in Figure 1 above the dotted line .
Therefore, the solution set of the line lie above the dotted line and it will represented by the symbol [tex]>[/tex].
Thus, the inequality [tex]y>2x+1[/tex] satisfies the given graph.
Therefore, the correct option is [tex]\boxed{\bf option (c)}[/tex] i.e., [tex]\boxed{y>2x+1}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Linear inequalities
Keywords: Linear equations, linear inequality, equation, line, slope, intercept, dotted line , coordinate, shaded region, solutions set, graph, curve.
A spinner is divided into 4 equal sections the probability of landing on A is 1/4 Norma spins the spinner 16 times how many times can she expect the spinner to land on A
Final answer:
Norma can expect the spinner to land on section A 4 times after spinning it 16 times, based on the probability of [tex]\frac{1}{4}[/tex].
Explanation:
The question asks about the expected number of times Norma can anticipate the spinner to land on section A after spinning it 16 times, given that the probability of landing on A is [tex]\frac{1}{4}[/tex]. To find this, we use the concept of expected value, which in this context is the probability of an event happening multiplied by the number of trials. Since the probability of landing on A is [tex]\frac{1}{4}[/tex] and there are 16 spins, the expected number of times landing on A is calculated as [tex]\frac{1}{4}[/tex] multiplied by 16.
Expected number of landings on A = Probability of landing on A × Number of spins = [tex]\frac{1}{4}[/tex] × 16 = 4.
Therefore, Norma can expect the spinner to land on section A four times after spinning it 16 times.
Did the Native Americans The pilgrims encountered lived in tipis and traveled on horseback?
Answer:
They were nomadic and moved from place to place.
Step-by-step explanation:
Match the expression with its name. 9x4 – 3x + 4
Answer:
Fourth-degree trinomial
Step-by-step explanation:
9x^4 – 3x + 4 is a trinomial expression because it has three parts: 9x^4, –3x and 4, and is a fourth-degree expression because four is the highest exponent applied to the variable x (the other exponents are one and zero).
What is the least common multiple of 3, 4a, 5b, and 6ab?
Final answer:
The least common multiple (LCM) of 3, 4a, 5b, and 6ab is 60ab, calculated by prime factorizing each term and identifying the highest power of each prime factor.
Explanation:
The least common multiple (LCM) of 3, 4a, 5b, and 6ab is calculated by finding the LCM of the individual components.
Prime factorize each term: 3 = 3, 4a = 2*2*a, 5b = 5*b, 6ab = 2*3*a*b.
Identify the highest power of each prime factor: LCM = 2*2*3*5*a*b = 60ab.
what are the x intercepts for 5/x + 1/3x = 4x/3
Amanda apent 2$ more than Barry on school supplies together they spent
34 How much money did each spend
A company makes computer chips from square wafers of silicon. It wants to keep the side length of a wafer very close to 12 mm and it wants to know how the area A(x) of a wafer changes when the side length x changes. Find A'(12)
The value of the derivatives is A'(12) = 24.
We have,
To find the derivative of the area function A(x) with respect to x, we can differentiate the equation for the area of a square:
A(x) = x^2
Using the power rule, we differentiate A(x) with respect to x:
A'(x) = 2x
To find A'(12), we substitute x = 12 into the derivative equation:
A'(12) = 2 * 12 = 24
Therefore,
The value of the derivatives is A'(12) = 24.
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Final answer:
To find A'(12), the rate at which the area A(x) changes when the side length x changes, take the derivative of A(x), which is 2x, and evaluate it at x = 12. The derivative of A(x) is 2x, so A'(12) = 2(12) = 24.
Explanation:
To find the rate at which the area A(x) changes with respect to a change in x, we need to take the derivative of A(x) with respect to x. In this case, A(x) represents the area of a square wafer of silicon with a side length x. The derivative with respect to x is A'(x), which represents the rate of change of the area.
We want to find A'(12), which means we want to find the rate of change of the area when the side length is 12 mm. To do this, we need to take the derivative of A(x) and then evaluate it at x = 12.
Since the side length of the wafer is very close to 12 mm, we can assume x = 12.
Let's find the derivative of A(x):
A(x) = x^2
A'(x) = 2x
Now we can evaluate A'(12):
A'(12) = 2(12) = 24
Which of the following prefixes would be best to use when measuring your own mass? need help.
Milli
Centi
Deci
Kilo
Add: 4/100 + 2/10 = A) 6/10 B) 6/100 C) 24/100 D) 42/100
the perimeter of the rectangle shown is 76 cm. it is rotated about line b.
which best describes the resulting three-dimensional figure?
•a cone with a base radius of 26cm
•a cone with a base radius of 14cm
•a cylinder with a base radius of 26cm
•a cylinder with a base radius of 14cm
If a rectangle is rotated about the line b, then the three-dimensional figure formed is cylinder with a circle base.
One side of the rectangle has lenght of 24 cm. Let the second side has length of x cm. The perimeter of the rectangle is 76 cm, then
24 + x + 24 + x = 76,
2x + 48 = 76,
2x= 76 - 48,
2x= 28,
x = 14 cm.
Then the three-dimensional figure is a cylinder with a base radius of 14 cm.
Answer: correct choice is D
Answer: •a cylinder with a base radius of 14cm
Step-by-step explanation:
From the given picture it can be seen that the side of rectangle is adjacent to line B is the longer side.
If the rectangle is rotated about line b, then it will create a cylinder such that
the radius of the cylinder= smaller(width) side of the rectangle
The measure of the longer side (length) of rectangle= 24 cm
Perimeter of rectangle=[tex]2[length+width][/tex]
[tex]\\\Rightarrow\ 76=2[24+w]\\\Rightarrow\ 24+w=38\\\Rightarrow\ w=14[/tex]
hence, the measure of smaller side is 14 cm.
Therefore, the base radius =14 cm