Therefore , the solution of the given problem of unitary method comes out to be option C The lengths of side an are 2.5 inches, side b is 5 inches, and side c is 13 inches.
What is a unitary method?
Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.
Here,
We may calculate the side lengths of the physical object using the following formulae given the scale factor of 2:1:
Drawing to scale: Side a: 11 inches
8 inches on side B.
3 inches on side C.
real thing
11 inches by two equals 22 inches on side a.
Side B: 8 inches times two equals 16 inches
3 inches by 2 equals 6 inches on side C.
B. Side a: 26 inches in the scale drawing.
20 inches on side B.
10 inches on side C.
real thing
Side a: 2 times 26 inches equals 52 inches.
Side B: 20 inches times two equals 40 inches
20 inches are equal to 10 inches on side C.
C. Side a: 2.5 inches in the scale drawing.
5 inches on side B.
6.5 inches on side C.
real thing
2.5 x 2 = 5 inches on side a.
Side B: 5 inches times two equals 10 inches
6.5 inches by two equals 13 inches on side C.
So, the appropriate response is:
C. The lengths of side an are 2.5 inches, side b is 5 inches, and side c is 13 inches.
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Two real numbers are defined as: a=0444444444444 b=0.354355435554 Determine whether each number is rational or irrational. Is the product of a and b rational or irrational? Justify your answers. Enter your answers and your justifications in the box provided.
The a is rational , b is irrational and product of a and b is rational.
The number a=0.444444444444 is rational
Because it can be expressed as the ratio of two integers.
a = 4/9
The number b=0.354355435554 is irrational
Because it cannot be expressed as the ratio of two integers.
It has an infinite non-repeating decimal expansion.
To determine whether the product of a and b is rational or irrational, we can simply multiply them together:
a × b = (4/9) × 0.354355435554
= 0.158919191574
This product is a rational number, because it can be expressed as the ratio of two integers.
Hence, a is rational , b is irrational and product of a and b is rational.
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Share oranges among three boys so that the first gets twice more oranges than the second and the second gets twice the third's amount of the third. What is each boy's share? l
The calculated value of each boy's share is shown below
Let's call the amount of oranges the third boy gets "x".
According to the problem, the second boy gets twice the amount of oranges as the third boy, so he gets 2x oranges.
And the first boy gets twice more oranges than the second boy, so he gets 2(2x) = 4x oranges.
So the total number of oranges is x + 2x + 4x = 7x, and we need to divide this equally among the three boys.
Therefore, the first boy gets 4/7 of the total oranges, which is 4x/3, the second boy gets 2/7 of the total oranges, which is 2x/3 and the third boy gets 1/7 of the total oranges, which is x/3.
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9. A classroom table has a mass of 24 kg. Pulling with a force of 36 N, a student moves the table to the other side of the classroom. How much did the table accelerate? Record your answer and fill in the bubbles. Be sure to use the correct place value.
The acceleration of this classroom table is equal to 1.5 meter per seconds square.
How to calculate the acceleration of this classroom table?From Newton's Second Law of Motion, the force exerted on the classroom table is modeled or represented by this mathematical equation (formula):
F = ma
Where:
F represent the force.m represent the mass.a represent the acceleration.By making "acceleration" the subject of formula, we have the following:
Acceleration, a = force/mass
Acceleration, a = 36/24
Acceleration, a = 1.5 meter per seconds square.
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A population has a mean μ=135 and a standard deviation Ï=28. Find the mean and standard deviation of the sampling distribution of sample means with sample size n=57.
A population has a mean μ=135 and a standard deviation Ï=28.
The mean of the sampling distribution of sample means is equal to the population mean, that is 135.
The standard deviation of the sampling distribution of sample means can be calculated by using the formula
SE = Ï /[tex]\sqrt{n}[/tex]
Where Ï is the population standard deviation and n is the sample size.
By putting the given values we get
SE = 28 / [tex]\sqrt{57}[/tex] = 3.7
Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.
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A piece of metal with a mass of 611 g is placed into a graduated cylinder that contains25.1 mL of water, raising the water level to 56.7 mL. What is the density of the metal?A) 2.70 g/cm3 B) 7.13 g/cm3 C) 8.96 g/cm3 D) 10.5 g/cm3 E) 19.3g/cm3
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
The given mass of the metal is 611 g and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal volume can be evaluated by subtracting the initial volume from the final volume of water released by the metal.
Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL
Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³
The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.
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Q3. (Calculator)
Abox contains only red, blue and green pens.
The ratio of red pens to blue pens is 5:9.
The ratio of blue pens to green pens is 1:4.
Calculate the percentage of pens that are blue.
The percentage of pens that are blue =18%
Let's assume that r represents the red pens, b represents the blue pens and g represents the green pens.
From the statements we can observe that the blue appears in both ratio.
The ratios are,
r:b=5:9 and b:g=1:4
Consider ratio b:g,
b:g
= 1:4
= (1×9) : (4×9)
=9:36
i.e., b:g = 9:36 and r:b = 5:9
So, we can conclude that, b=9, g=36, r=5
so, the total number of pens would be,
n = b + g + r
n = 9 + 36 + 5
n = 50
Now we need to find the percentage of pens that are blue.
Using percentage formula,
p = (b/n) × 100
p = (9/50) × 100
p = 18%
Hence, the percentage of blue pens are 18%.
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dont understand what m supposed to do at the radius = diameter/2 part
Step-by-step explanation:
Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle
PLEASE HELP!!!
A principal of $4200 is invested at %8 interest, compounded annually. How much will the investment be worth after 12 years?
Answer:
$10,244.14 after 12 years
Step-by-step explanation:
To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(n*t)
A = the final amount of the investment
P = the principal amount ($4200 in this case)
r = the annual interest rate (8% or 0.08 as a decimal)
n = the number of times the interest is compounded per year (once annually in this case)
t = the number of years the money is invested (12 years in this case)
Substituting the given values into the formula, we get:
A = 4200(1 + 0.08/1)^(1*12)
A = 4200(1.08)^12
A = 4200(2.44140625)
A = $10,244.14 (rounded to the nearest cent)
Change the subject of each formula to the letter given in brackets.
Here he formula for v is:
v = √(2gh)
What is meant by the term formula?
A formula is a mathematical relationship or rule that is expressed using symbols and mathematical operations. It is used to represent a relationship between quantities or to calculate a value based on given variables or inputs. Formulas are often used in various branches of mathematics, science, and engineering.
According to the given information
To change the subject of the formula mgh = (1/2)mv² to v, we need to isolate v on one side of the equation.
First, we can multiply both sides of the equation by 2 to eliminate the fraction:
2mgh = mv²
Next, we can divide both sides of the equation by m:
(2mgh) / m = v²
Simplifying the left side, we get:
2gh = v²
Finally, we can take the square root of both sides of the equation to solve for v:
v = √(2gh)
Therefore, the formula for v is:
v = √(2gh)
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(Part 2 of 2) Please help there is not much time left (Look at photo)
The rate of change for the function f(x) is 9.5 over the interval.
How I calculated the rate of change for f(x):
f(2) = 12, f(6) = 50
slope = (50 - 12) / (6 - 2) = 9.5
The rate of change for the function g(x) is -2 over the interval.
How I calculated the rate of change for g(x):
g(2) = -10, g(6) = -18
slope = (-18 - (-10)) / (6 - 2) = -2
What is the rate of change of the function?To find the rate of change for a function over an interval, we need to calculate the slope of the secant line that connects the two endpoints of the interval.
The slope of a line can be found using the formula:
slope = (y2 - y1) / (x2 - x1)
For the quadratic function f(x) = (x + 1)² + 8, we can find the values of f(2) and f(6) by substituting x = 2 and x = 6 into the function:
f(2) = (2 + 1)² + 8 = 12
f(6) = (6 + 1)² + 8 = 50
Therefore, the rate of change for f(x) over the interval 2 ≤ x ≤ 6 is:
slope = (f(6) - f(2)) / (6 - 2) = (50 - 12) / 4 = 9.5
So the answer is: The rate of change for f(x) is 9.5 over the interval.
To find the rate of change for the linear function g(x) = -2x - 6, we can use the same formula:
g(2) = -2(2) - 6 = -10
g(6) = -2(6) - 6 = -18
Therefore, the rate of change for g(x) over the interval 2 ≤ x ≤ 6 is:
slope = (g(6) - g(2)) / (6 - 2) = (-18 - (-10)) / 4
slope = -2
So the answer is: The rate of change for g(x) is -2 over the interval.
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A rectangle is seven times as long as it’s width. One way to write an expression to find the perimeter would be m+7m+m+7m. Write the expression in two other ways.
Step-by-step explanation:
Perimeter = 2 m + 2 * 7m
Perimeter = 2 ( m + 7m)
Perimeter = 2m + 14m
Perimeter = 16 m Pick any of them
WHAT IS THE RANGE OF THIS PIECEWISE FUNCTION?
The given piecewise function has a range of:
Range = {46, 48, 50, 52, 54, 56}.
What is range of a function?The range of a function is the set of all possible output values, or the set of all y-coordinates that correspond to the x-coordinates in the domain of the function.
It is, in other words, the entire set of values that the function is capable of returning as its result.
From the given piecewise function, we can see that the y-coordinates of the function are limited to the values 46, 48, 50, 52, 54, and 56.
These values correspond to the y-intercepts of each of the line segments in the graph.
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If Joanne has three hours and 45 minutes before swim practice, she wants to go to the store which will take 220 minutes. She also wants to take her brother to the park for 230 minutes which activity does Joanne have time to do before practice
What is the total surface area of the square pyramid?
The surface area of the square pyramid is 384 cm squared.
How to find the surface area of a square base pyramid?The surface area of the square base pyramid can be found as follows:
surface area of the square base pyramid = base area + 2al
where
a = side length of the basel = height of the pyramidTherefore,
base area = 12 × 12
base area = 144 cm²
Hence,
surface area of the square base pyramid = 144 + 2 × 12 × 10
surface area of the square base pyramid = 144 + 240
surface area of the square base pyramid = 384 cm²
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What is the surface area of this composite solid? Show your work.
According to the above, we have to add the surface area of each face. So, the surface area of this solid would be 127.
What is the surface area of the composite solid?To calculate the surface area of the composite solid we have to perform the following procedure:
Sides (a) area
4 * 3 = 1212 * 2 = 24Sides (b) area
7 * 3 = 2121 * 3 = 63Face (c) area
3 * 4 / 2 = 66 * 2 = 12Base area
4 * 7 = 28
Total surface area
To calculate the total surface area we have to add the value of each face as shown below:
28 + 12 + 63 + 24 = 127According to the above, the surface area of this solid would be 127.
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Can I get the answer?
The meaning of the y - intercept in the context of the problem of the snow level in Moose Wyoming is the level of snow at the beginning of the time period in question.
What is the y - intercept ?The y-intercept of the function y = 2x + 14 is the value of y when x = 0. Substituting x = 0 into the equation, we get:
y = 2(0) + 14
y = 14
Therefore, the y-intercept is 14.
In terms of the problem, this means that at midnight (when x = 0), there is already 14 inches of snow on the ground in Moose, Wyoming. The y-intercept represents the initial or starting value of the snow level function, which in this case is the amount of snow already on the ground at the start of the time period being modeled.
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How many planes of symmetry does a right pyramid with an isosceles triangle base have?
Answer: The amount of planes of symmetry a right pyramid with an isosceles triangle base has four.
Hope this helps!
Dave is buying popcorn and sodas for his son and his five friends that he brings to the movies (Six kids total). The needs to buy at least one of the two items for each of the six. Popcorn costs $2. 50 per bag and sodas cost $4. 00 each. Dave can spend at most $40. Lets represent the number of sodas he buys and p represent the number of bags of popcorn he buys
The system of equations that models this scenario is:
p + s ≥ 62.50p + 4.00s ≤ 40How can it be modeled using a system of equations?Let p be the number of bags of popcorn.
Let s be the number of sodas Dave buys.
Since Dave needs to buy at least one of each item for all six kids, we have:
p + s = 6 -----(1)
Given:
The cost of a bag of popcorn is $2.50.
The cost of a soda is $4.00.
The total cost of Dave's purchase can be expressed as:
2.50p + 4.00s = C -----(2) where the C is the total cost of Dave's purchase.
Since Dave can spend at most $40, we have:
2.50p + 4.00s ≤ 40 -----(3).
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A. Find the average rate of change over the interval (-1, 2] for each function. Show all steps and work for credit.
B. Which function has the greatest average rate of change over the interval [1, 2]
the average rate of change over the interval (-1, 2] in the given function is 1.17.all three functions have the same average rate of change over the interval [1, 2], which is 2
what is function and average rate?A function is a mathematical rule that takes an input and produces an output. The average rate of change of a function over an interval is the average amount the output changes per unit change in the input over that interval.
According to given informationFor the function f(x) = 2x + 3:
Let x1 = -1 and x2 = 2
f(x1) = 2(-1) + 3 = 1
f(x2) = 2(2) + 3 = 7
The average rate of change is:
[f(x2) - f(x1)] / [x2 - x1] = [7 - 1] / [2 - (-1)] = 6 / 3 = 2
Therefore, the average rate of change of f(x) over the interval (-1, 2] is 2.
For the function g(x) = x^2 - 1:
Let x1 = -1 and x2 = 2
g(x1) = (-1)^2 - 1 = 0
g(x2) = 2^2 - 1 = 3
The average rate of change is:
[g(x2) - g(x1)] / [x2 - x1] = [3 - 0] / [2 - (-1)] = 3 / 3 = 1
Therefore, the average rate of change of g(x) over the interval (-1, 2] is 1.
For the function h(x) = 2^x + 1:
Let x1 = -1 and x2 = 2
h(x1) = 2^(-1) + 1 = 1.5
h(x2) = 2^2 + 1 = 5
The average rate of change is:
[h(x2) - h(x1)] / [x2 - x1] = [5 - 1.5] / [2 - (-1)] = 3.5 / 3 = 1.17 (rounded to 2 decimal places)
Therefore, the average rate of change of h(x) over the interval (-1, 2] is approximately 1.17.
b)To determine which function has the greatest average rate of change over the interval [1, 2], we need to calculate the average rate of change for each function over that interval and compare the results.
Let's assume the functions are f(x), g(x), and h(x).
The average rate of change for f(x) over the interval [1, 2] is:
[f(2) - f(1)] / [2 - 1] = (2(2) + 3 - 2(1) - 3) / 1 = 2
The average rate of change for g(x) over the interval [1, 2] is:
[g(2) - g(1)] / [2 - 1] = (2^2 - 1 - 1^2 + 1) / 1 = 2
The average rate of change for h(x) over the interval [1, 2] is:
[h(2) - h(1)] / [2 - 1] = (2^2 + 1 - 2^1 - 1) / 1 = 2
Therefore, all three functions have the same average rate of change over the interval [1, 2], which is 2.
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Think of a number. The L C M of this number and 42 is 126. If the number lies between 60 and 70, what is the number
The LCM of 63 and 42 is 126 where 63 is the required number lying in between 60 and 70.
Let the missing number be x.
The number x lies in between 60 and 70.
The LCM ( Least Common Multiple) refers to the least value that is divisible by any two (or more) numbers.
Here LCM of x and 42 is 126.
Simplifying 126 we can write it as,
126 = 2*3*21
Thus, one of the number having 126 is as multiple is 42 (as already given).
The other number, that is x, having 126 as multiple lying between 60 and 70 is,
x = 3*21 = 63
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please solve and explain
LaTisha's calculation of the distance for the brake anchor placement is incorrect because she didn't take into account the height at which the cable is attached to the starting tree.
What is the correct distance ?The bungee cord is attached 16 feet above the ground, which will also contribute to the length of the cable needed to reach the ending tree.
To correctly calculate the distance, we can use the Pythagorean theorem, considering the height (16 feet) and the length of the stretched bungee cord (24 feet + 18 feet = 42 feet). Let's denote the horizontal distance from the base of the ending tree to the brake anchor as 'd'. We have:
d² + 16² = 42²
Now, we can solve for d:
d² + 256 = 1764
d² = 1508
d = √1508 = 38.8 feet (rounded to one decimal place)
The brake anchor should be placed approximately 38.8 feet from the base of the ending tree.
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(I NEED THIS ASAP)
2. Write a rule that
describes this transformation.
Answer:
the y is always gonna be a difrent like a negative and a postive
Step-by-step explanation:
the y on the left if it's a positive the y on the right Is nightie ect
can someone js help me w these questions
Answer:
a=60 (12*5=60)
b=7 (45/9=5 5+2=7)
c=62
d=25 (11*5=55 55-30=25)
what is the value of f(16)
Step-by-step explanation:
Put '16' where 'x' is and compute
3/4 ( 16 ) + 7 = f(16) = 19
At a company a copy machine prints 175 pages in 5 minutes. if the number of pages printed is proportional to the time in minutes what is the unite rate
Answer:
The unit rate is 35 pages per minute.
Step-by-step explanation:
Divide 175 by 5, or 175/5 to get the unit rate, which is 35.
please help asap!! i need the help
Answer:
Step-by-step explanation:
angle L is 106 degrees
x= 2
angle LMK is 37 degrees
its equal, you can check by adding up all the angles to 360 degrees
please help me IXL have to achieve a smart score of 80 part 1
The equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.
What is a linear equationA linear equation is an algebraic equation that represents a straight line on a graph. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.
given the slope m = -3/5 and y intercept b = 6, we can write the equation as;
y = (-3/5)x + 6
y = -3x/5 + 6.
Therefore, the equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.
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HELPP
Find the area of this shape:
Answer:
67 [tex]ft^{2}[/tex]
Step-by-step explanation:
Divide the shape into more recognizable shapes.
5*7 = 35
7*4 = 28
35+28
67
Is 409  greater or less than 1.008
Answer:
409 > 1.008
Step-by-step explanation:
409 is greater than 1.008
Select the acceptable conclusions to a hypothesis test. a The value of the test statistic lies in the nonrejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. b The value of the test statistic does not lie in the rejection region. Therefore, we accept the null hypothesis. c The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true. d The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true. e The value of the test statistic does not lie in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is true. f The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
The acceptable conclusions to a hypothesis test are option a, c, d, f.
What is hypothesis test?
Hypothesis Testing is a way of statistical analysis in which a person can put his assumptions about a population parameter to the test. It usually used to estimate the relationship between two statistical variables.
By the property of hypothesis test the following can be stated.
⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.
⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.
⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.
Hence the correct options are a, c, d, f.
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