The expression that equals to 9[tex]\sqrt[3]{10}[/tex] is 5[tex]\sqrt[3]{10}[/tex] + 4[tex]\sqrt[3]{10}[/tex] so option 2 is correct.
Given expression:
Second option:
= 5[tex]\sqrt[3]{10}[/tex] + 4[tex]\sqrt[3]{10}[/tex]
Take cube root 10 as common
= [tex]\sqrt[3]{10}[/tex](5+4)
= ∛10(9)
= ∛10*9
= 9∛10.
which is equal to given expression.
Therefore the expression that equals to 9[tex]\sqrt[3]{10}[/tex] is 5[tex]\sqrt[3]{10}[/tex] + 4[tex]\sqrt[3]{10}[/tex] so option 2 is correct.
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How do you find the cubic polynomial if sum of the zeros and product of the zeros is given?.
The cubic polynomial can be computed using the following formula if the zeros of a cubic polynomial's product and sum are known: (x - sum of zeros) (x² + product of zeros) is a cubic polynomial.
A three-degree polynomial is referred to as a cubic polynomial. The cubic polynomial can be computed using the following formula if the zeros of a cubic polynomial's product and sum are known:
cubic function = (x - sum of zeros)
(x² + zero product)
For instance, the cubic polynomial is (x + 1)(x2 - 4) if the product of the zeros is 4 and the total of the zeros is -1.
The cubic polynomial is illustrative of:
ax³ + bx² + cx + d = 0
In the general case, where a, b, c, and d are constants.
The product of the zeros is given by: d/a ,
The zeros' sum is given by : - b/a.
These numbers are substituted into the cubic polynomial's general equation to produce the following result:
ax³ + bx² + cx + d = a(x³ + (-b/a)x² + (d/a)x)
= a(x³ - bx + d)
Therefore, if the product and sum of the zeros are known, the cubic polynomial may be obtained.
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What are the main advantages of using a random forest versus a single decision tree?.
The main advantages of using a random forest versus a single decision tree is that Random forest algorithm avoids and prevents overfitting by using multiple trees.
Random forest replaces the data used to build the tree and also the explanatory variables are bootstrapped so that partition is not done on the same important variable whereas decision trees do not follow this algorithm. Bootstrapping reduces bias and variance both which makes the model more robust and accurate.
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FILL IN THE BLANK. A gate has a standard key pad with the digits 0 through 9. How many possible code combinations are there if the code is 4 digits long.
There are____ different code combinations.
A gate has a standard key pad with the digits 0 through 9. How many possible code combinations are there if the code is 4 digits long.
There are 10,000 different code combinations.
We have given that,
A gate has standard key pad with digits 0-9 ..
we have to make a 4 digit code with 10 possible digits (0-9) and first one cannot be zero .
but digits can't be repeat.
put down 5 blank spaces on paper and then put the number of combinations in each space.
the first digit can not be 0, so there are 9 possible combinations (1-9).
The second digit cannot be the same as the first digit, but it can be 0, so there are 9 combinations.
The third digit cannot be either the first or the second digit and thus there are 8 combinations.
The fourth digit has 7 combinations.
numbers of combinations you should have
9×9×8×7 = 4536
hence, total possible combination are 4536.
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You are at a restaurant and your bill comes to $29.38. You need to add the sales tax which is 6% and a tip of 20%. You have one $20 bill, two $10 bills, one $5 bill, five $1 bills, and five pennies. How much is your total bill including tax? How much should you give the server so you do not get back any pennies? Make sure you show all your work.
Answer: The amount of money needed to be given to the server is $30 and 23 cents.
Since tax is 6%, hence:
Total bill including tax = $28.52 + 6% of $28.52 = $30.23
The amount of money needed to be given to the server is $30 and 23 cents.
Therefore the denominations needed for this is one $20 bill, two $10 bills and 23 pennies.
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Step-by-step explanation:
What 3 things should be done to properly maintain the AED and its supplies?.
To maintain AED and its supplies;-
Check the AED's power by turning it on and ensuring it does so without any issues.Verify that the AED has the additional rescue items, such as gloves, a razor, and a breathing mask.Look for cracks, wear, and other signs of deterioration on the actual gadget.Given,
AED;-
When a person is having a sudden cardiac arrest, an AED, or automated external defibrillator, is used to assist them. It is an advanced but simple to use medical equipment that can analyze the heart's rhythm and, if necessary, provide an electrical shock, or defibrillation, to aid in the heart's re-establishment of an efficient rhythm.
Here,
To maintain AED and its supplies;-
Check the AED's power by turning it on and ensuring it does so without any issues.Verify that the AED has the additional rescue items, such as gloves, a razor, and a breathing mask.Look for cracks, wear, and other signs of deterioration on the actual gadget.Learn more about AED here;
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Cortez Manufacturing intends to increase capacity by overcoming a bottleneck operation by adding new equipment. Two vendors have presented proposals. The fixed costs are $50,000 for proposal A and $80,000 for proposal B. The variable cost is $14.00 for A and $10.00 for B. The revenue generated by each unit is $22.00. a) The break-even point in units for the proposal by Vendor A = units (round your response to the nearest whole number). b) The break-even point in units for the proposal by Vendor B = units (round your response to the nearest whole number).
(a) The break-even point in units for the proposal by Vendor A = 6250 units
(b) The break-even point in units for the proposal by Vendor B = 6667 units.
In the question ,
it is given that ,
the fixed cost for proposal A [tex]=[/tex] $50000
the fixed cost for proposal B is = $80000
the variable cost for proposal A is = $14
the variable cost for proposal B is = $10
the revenue generated by each unit is = $22
So , the break even points for both the proposal can be calculated using the formula ,
break even point = (fixed cost)/(contribution margin)
Substituting the values from above ,
we get ,
Break even point for proposal A is
break even point [tex]=[/tex] 50000/(22 - 14)
= 50000/8
= 6250
Break even point for proposal B is
break even point [tex]=[/tex] 80000/(22 - 10)
= 80000/12
= 6667
Therefore , break even point for proposal A is 6250 units and for proposal B is 6667 units .
The given question is incomplete , the complete question is
Cortez Manufacturing intends to increase capacity by overcoming a bottleneck operation by adding new equipment. Two vendors have presented proposals. The fixed costs are $50,000 for proposal A and $80,000 for proposal B. The variable cost is $14.00 for A and $10.00 for B. The revenue generated by each unit is $22.00.
(a) The break-even point in units for the proposal by Vendor A = units (b) The break-even point in units for the proposal by Vendor B = units.
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what fraction is greater than 3/4 5/8 10/12 7/16 10/20
The fraction that is greater than 3/4 is B. 10/12
How to calculate the value?It should be noted that a fraction has a numerator and denominator and is expressed as a/b..
It should be noted that 5/8 in percentage will be:
= 5/8 × 100
= 62.5%
10/12 will be:
= 10/12 × 100
= 83.3%
7/16 will be:
= 7/16 × 100
= 700/16
= 43.75%
Therefore, the fraction greater is 10/12.
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What is the mean of this set of data if the outlier is removed?
Thank you for helping.
Answer:
4.65[tex]m^{2}[/tex]
Step-by-step explanation:
the outlier is 28.4
add up all the numbers
3.7+5.2+3.8+5.5+4.2+5.5 = 27.9
divide by 6 (because there are 6 numbers)
27.9/6=4.65
Laurie has a signed contract with I- Mobile where she will pay a $25 fee each month plus $2 per phone call.
The equation represents the total cost for one month as y= 25 + 2x.In January she did 15 calls. In March, she owes $35.The graph of the function has been drawn below.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
A)
Total cost = fixed cost + 2 x number of calls
y = 25 + 2x
B)
In January y = 55
55 = 25 + 2x
x = 15
C)
In march x = 5
y = 25 + 2 x 5 = 35
D) The graph has been drawn below.
Hence "The equation represents the total cost for one month as y= 25 + 2x.In January she did 15 calls. In March, she owes $35.The graph of the function has been drawn below".
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The measure of angle NCB is 113°.
What is the measure of angle BCG?
Answer:87 degrees
Step-by-step explanation:
113 degrees-26degrees= 87degrees.
Fatima is taking a test that is 45 minutes long.
She finishes the test at 10:50 a.m.
What time did she start the test?
Answer:10:05
Step-by-step explanation:
subtract 45 from 50!
Answer:
She started the test at 10:05 am
Step-by-step explanation:
Take the end time and subtract the time of the test
10:50-45 = 10:05
She started the test at 10:05 am
how much fuel will you need to travel 75 sm if your airplane burns 3 gallons of fuel/hr. and your groundspeed is 45 mph?
Using Simple Speed formula,
To travel the distance of 75m with an airplane will need five gallons of fuel .
We have given that,
An airplane, fuel burn speed = 3 gallons of fuel per hour
ground speed of airplane = 45mph
distance = 75m
Speed = distance /time = 45 mph
=> 45 m distnce in one hour
fuel consumption of airplane = 3gallons/h
from above discussion we get,
fuel consumption for 45 m is equal to 3 gallons .
we have to calculate the quantity of fuel need to travel 75 m .
Now, 45 m distnce implies 3 gallons fuel consumption
1 m distance implies 3/45 gallons of fuel consumption
fuel consumption for 75 m =( 3/45)×75 = 5 gallons
Hence, 5 gallons fuel we need to travel 75 m .
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given a non-negative integer numrows, generate the first numrows of pascal's triangle. in pascal's triangle, each number is the sum of the two numbers directly above it
For the non negative number, the first number of rows of pascal's triangle is attached below.
Non negative number:
Non negative number means the number which is either zero or a positive number.
Given,
Here we have a non-negative integer number of rows, And we have to generate the first number of rows of pascal's triangle And in pascal's triangle, each number is the sum of the two numbers directly above it.
Before make the pascal's triangle,
We know that the given condition is each number is the sum of the two numbers directly above it.
Based on these condition, we have plotted the following pascal's triangle.
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unit test, part 2: exponential and logarithmic functions 1.the population of a town was 5655 in 2010. the population grows at a rate of 1.4% annually. (a)use the exponential growth model to write an equation that estimates the population t years after 2010. (a)estimate the population of the town in 2022. show your work.
(a) The equation that estimates the population t years after 2010 is
P(t) = 5655(1.014)^t.
(b) Population of the town in 2022 is 6,681.
We have given that the population of a town was 5655 in 2010.
And the population grow at a rate of 1.4% annually.
(a) We have to find equation that estimates the population t years after 2010.
We know the formula for exponential growth,
P(t) = P₀(1 + r)^t
where P₀ is the initial population,
r is the relative growth rate,
t is the time unit.
Putting the values in above equation we get,
P(t) = 5655(1 + 0.014)^t
P(t) = 5655(1.014)^t
(b) Now we have to find population of the town in 2022.
Here t = 2022 - 2010 = 12
Therefore equation of growth will become,
P(12) = 5655(1.014)^12
P(12) = 6681
Hence the population of the town in 2022 is 6,681.
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under what kind of sampling procedure must the researcher adhere closely to precise selection procedures to ensure that the results are projectable to the population under study?
Probability sampling procedure is the way researcher adhere closely to precise selection procedures to ensure that the results are projectable to the population under study.
What is Probability Sampling ?
Using this methodology based on probability theory, probability sampling is the strategy in which the research fellows selects samples from the larger population. A participant must be chosen at random if they are to be used as a probability as a sample.
As in this question researcher must follow Probability sampling, a participant must be chosen at random if they are used as a probability as the sample.
So, the required answer will be Probability sampling, as it helps researcher to precise selection procedures.
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How many solutions does this linear system have Y =- 1 2x 4 x 2y =- 8?.
The linear system of equation y = -12x and 4x+2y= -8 has only one solution at 0.4,-4.8) .
The linear equation is y = -12x and 4x+2y = -8
Now we solve the equations by substitution:
Using the value of y from the first equation and substituting in the second equation we get:
4x+2y = -8
or, 4x + 2(-12x)= -8
or, 4x -24x = -8
or, -20 x = -8
or, x = 0.4
At x=0.4 , y = -4.8
Hence solution is (0.4,-4.8) which represents the point of intersection of the two lines.
The collection of variable values in a linear equation that yields every feasible solution is referred to as the "solution of a linear equation." Unknown variables are used as one or more variables in linear equations to model real-world issues.
The solutions are the points at which the lines or planes used to describe the linear equations intersect or meet. The set of values for each variable in a system of linear equations is known as the solution set.
Disclaimer: the complete question is :
How many solutions does this linear system have y = -12x and 4x+2y= -8 have?
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What is the slope of a line perpendicular to the line whose equation is 3x+3y=183x+3y=18.
The slope of a line perpendicular to the line whose equation is 3x+3y=18 is 1.
Given:
3x+3y=18
3y = 18 - 3x
3y = -3x + 18
divide by 3 on both sides
3y/3 = -3x/3 + 18/3
y = -3x/3 + 18/3
y = -1*x + 6
compare with y = mx+c
m = -1
slope of perpendicular line = -1/m
= -1/-1
= 1/1
= 1
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e : f = 2 : 3 and f : g = 7 : 8 Work out e : g Give your answer in its simplest form.
Walter ued hi bank' ATM to withdraw $150. Thi wa the ixth time he ued the ATM in June. Hi bank doe not charge for the firt five ATM ue each month. After that, the fee i $1. 50 for each ue. What i the total he hould ubtract from hi balance including fee?
By using addition, it can be calculated that
Amount of money Walter should subtract from his bank account =
$(150 + 1.5) = $151.5
What is addition?
Suppose there are many numbers and the sum of the numbers have to be calculated. To find the sum of all the numbers, addition is used
This is a problem on addition
Walter used his bank's ATM to withdraw $150.
This was the sixth time he used the ATM in June.
His bank does not charge for the first five ATM use each month. After that, the fees is $1. 50 for each use.
Amount of money Walter should subtract from his bank account =
$(150 + 1.5) = $151.5
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160138 to the nearest 1000
The nearest 1000 is 160000.
Answer:
Step-by-step explanation:
The 160138 to the nearest 1000 is 160000
what is the answer?
Step-by-step explanation:
1)
to finish the work in 30 days, 9 workers are needed.
that means one worker can do 1/9 of the work in 30 days, and therefore 1/9 / 30 = 1/270 of the work in one day.
that means we need 270 workdays to finish the work.
to get the work done in 18 days we need therefore
270/18 = 15 workers
2)
you mention only 3 things (emergency, Tracey insurance and mutual fund) but the ratio covers 4.
what is missing ?
without that information this cannot be solved.
but this is what you do, when you find the 4th thing :
the ratio 9 : 5 : 4 : 7 tells us that the whole (P5000) is split into 9+5+4+7 = 25 parts.
each part is therefore worth 5000/25 = P200.
so, whatever is represented by 9 parts gets 9×200 = P1800.
whatever is represented by 5 parts gets 5×200 = P1000.
whatever is represented by 4 parts gets 4×200 = P800.
and whatever is represented by 7 parts gets 7×200 = P1400.
According to Levinson, which of the following ages most closely corresponds to the point in adulthood when a person enters the phase of Becoming One's Own Man (BOOM)?
38
22
50
44
Answer: 38
Age 38 most closely resembles the stage of adulthood known as "Becoming One's Own Man," (BOOM) according to Levinson. As a result, choice (A) is the best way to respond.
What is the men's boom phase?
Becoming One's Own Man, or BOOM is the name of Levinson's model's fourth stage. The man currently feels confined by the power brokers in their world. The person desires greater autonomy, dominance, and vocal authenticity.
Before the novice stage of adulthood ends, this transition gives people the chance to fix the problems with the first life structure they've created and make it closer in line with their young ideals and Dream.
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Lois and Alexander bought petrol from different petrol stations. a) Was Lois's petrol or Alexander's petrol better value for money? b) How much would 30 litres of petrol cost from the cheaper petrol station? Give your answer in pounds (£). Lois £17.40 for 12 litres of petrol Alexander £22.80 for 19 litres of petrol
Alexander's petrol better value for money and 30 litres of petrol cost from the cheaper petrol station is £36.
Given:
Lois £17.40 for 12 litres of petrol Alexander £22.80 for 19 litres of petrol.
a)
Lios money for 1 liter is:
= 17.40/12
= 1740/100/12
= 1740*1/100*12
= £1.45
Alexander money for 1 liter is:
= 22.80/19
= £1.2
From this alexander petrol better value for money.
b)
= 30 liters*alexander petrol cost for 1 liter
= 30*1.2
= £36.
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What is a group of cubicles called?.
A cubicle-filled office may also be referred to as a "sea of cubicles," "cube farm," or "pods" such as a 4-pod or 8-pod of cubes.
In the given question we have to explain about a group of cubicles.
A cubicle-filled office may also be referred to as a "sea of cubicles," "cube farm," or "pods" such as a 4-pod or 8-pod of cubes.
A cubicle is a type of office workspace that is partially enclosed and divided from adjacent workspaces by partitions that are typically 5 to 6 feet (1.5 to 1.8 metres) tall. Its objective is to shield managers and office workers from the sights and sounds of an open workspace so they can focus with fewer interruptions. Walls, work areas, compartments, cabinets, and bookcases are just a few of the modular components that make up cubicles, which can be arranged anyway the user sees fit.
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7) Solve using a proportion. Round to the nearest tenth.
A machine bearing weighs just 1 kilogram. If 7 bearings weigh 15.4 pounds, how many pounds
would 12 bearings weigh?
The number of pounds would 12 bearings weigh are 26.39615 pounds.
What is meant by ratio?A ratio in mathematics represents the number of times one number contains another. For instance, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the lemon-to-orange ratio is 6:8 (or 3:4), while the orange-to-fruit ratio is 8:14. (or 4:7).
Ratios are mathematical expressions that compare two numbers by dividing them. If you want to compare one data point (A) to another (B), your formula is A/B.
Machine Weigh
1 ---------------> 1 kg=2.20462 pounds
7 ----------------> 15.4 pounds
12 ----------------> ?
If 6 machine -------- 13.19538
5 machine ------- ?
x=(5×13.19538)/6
x=10.00615
∴ 12 machines bearings=15.4+10.99615pounds
=26.39615 pounds
The number of pounds would 12 bearings weigh are 26.39615 pounds
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What is the output of the function when the input is −3?
The output of the function when input is -3 is 3.
How to find the output of a function?A function relates each element of a set with exactly one element of another set (possibly the same set).
In a simpler term function relates input and output.
The inputs or the independent variables are on the x axis while the output or dependent variable of a function is on the y-axis.
Therefore, let's trace the y output value for an input value of -3.
Therefore, the output function when input is -3 is 3.
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Which ordered pair is a solution to the system of inequalities y >- 2 x/y 4?.
Point (-3,5) is a solution to the system of inequalities
What is inequality?
An inequality in mathematics depicts the connection between two values in an algebraic statement that are not equal. One of the two variables on the two sides of the inequality may be greater than, greater than or equal to, less than, or less than or equal to another value, according to inequality signals.
For this case, what we must do is find a point that meets both inequalities.
y> -2
x + y <4
We have then:
For (0,4):
First inequation:
4> -2 (correct)
Second inequality:
0 + 4 <4 (incorrect)
For (1,4):
First inequation:
4> -2 (correct)
Second inequality:
1 + 4 <4 (incorrect)
For (-3,5):
First inequation:
5> -2 (correct)
Second inequality:
-3 + 5 <4 (correct)
Point (-3,5) is system solution
For (-2,-3):
First inequation:
-3> -2 (incorrect)
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Which graph represents the function f x equals four over X?.
Answer:
You can see the graph in the picture attached.
Which equation represents a line that has a slope of 1/3 and passes through point 2 1?.
Equation which represents a line that has a slope of 1/3 and passes through the point (-2,1) is:
[tex]y=\frac{1}{3} x+\frac{5}{3}[/tex]
What is the Equation of a Line?
The slope of the line and a point on the line can be used to create the equation of a line. To better comprehend how the equation for a line is formed, let's learn more about the line's slope and the necessary point on the line. The slope of the line, which can be stated as a numeric integer, fraction, or tangent of the angle it forms with the positive x-axis, is the line's inclination with respect to the positive x-axis. The coordinate system's point with the x coordinate and the y coordinate is referred to as the point.
Let the equation of line be y=mx+c
Where m is the slope and c is the y-intercept
⇒ m=1/3
and The line passes through (-2,1)
Putting it in the equation
[tex]\begin{aligned}&1=\frac{1}{3} \times-2+c \\&c=1+\frac{2}{3} \\&c=\frac{5}{3}\end{aligned}[/tex]
Hence,
An equation that represents a line that has a slope of 1/3 and passes through the point (-2,1) is: [tex]y=\frac{1}{3} x+\frac{5}{3}[/tex]
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Find a 3 digit postive interger,the sum of the digits is 14, the tens digit is two more than the ones digit, and if the digits are reversed, the number is unchanged
Three digit number:
ABC
"if the digits are reversed, the number is unchanged":
A=C, so our number is ABA
"the sum of the digits is 14":
A + B + A = 14 or 2A + B = 14
"the tens digit is two more than the ones digit":
B = A + 2
We have two equations:
2A + B = 14
B = A + 2
Using substitution, we have:
2A + A+2 = 14
3A + 2 = 14
3A = 12
A = 4
Going back to B = A + 2:
B = 4 + 2
B = 6
The number, ABA is 464.
