As per the given condition for the system of equation, the two numbers are equal to 4 and 3.
As given in the question,
To begin with the solution, let the two unknown numbers be x and y. Now, translating the two mathematical statements into system of equations,
When three times the first of two numbers decreased by the second number equals 9.
3 x - y = 9 ____(1)
Twice the first number increased by the second number equals 11,
2 x + y = 11 ____(2)
By solving resultant system of equations we get,
3 x - y = 9
2 x + y = 11
5x = 20 (by adding the two equations)
=> x = 4
Substituting the value of x in second equation,
y = 11 - 2x
= 11 - 2(4)
= 11 - 8 = 3
Therefore, as per given condition for the system of equation, the two numbers are equal to 4 and 3.
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Given the pay rate and hours worked, determine the gross earnings, federal taxes (assuming 15% of gross earnings),
state taxes (assuming 5% of gross earnings), local taxes (assuming 2% of gross earnings), social security deduction
(assuming 7.65% of gross earnings), total deductions, and net pay.
pay rate= $8.50
hours worked = 38
1. Gross Earnings
2. Federal Taxes
3. State Taxes
4. Local Taxes
5. Social Security Deduction
6. Total Deductions
7. Net Pay
$6.46
$227.23
$16.15
$48.45
$323.00
$24.71
$95.77
Gross Earning is $323
Total deduction is $95.77 and Net pay is $227.23
In light of the hourly rate and salary (8.50, 38.0)
$8.50 an hour is the pay rate.
worked 38.0 hours in total.
38 hours total compensation (Gross Earning)=38×8.5 =$323
Now, we can see the total tax deduction.
Federal taxes (assumed to be 15% of gross income)
Therefore, Federal taxes = 0.15 x 323 = $48.45
State taxes (assuming 5% of gross earnings)
Therefore, State taxes = 0.05 x 323 = $16.15
Local taxes (assuming 2% of gross earnings)
Therefore, Local taxes = 0.02 x 323 = $6.46
Social security deduction (assuming 7.65% of gross earnings)
Therefore, Social security deduction = 0.0765 x 323 = $24.71
Total deduction = Federal taxes + State taxes + Local taxes + Social security deduction
Total deduction = 48.45+16.15+6.46+24.71 = $95.77
Net Pay = Gross Earning - Total deduction
Net Pay = $323 - $95.77 = $227.23
Thus, Gross Earning is $323, Total deduction is $95.77 and Net pay is $227.23
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if 1kg=2,2ib(pounds),convert 300g into pounds
1 kg = 1000g
Hence,
[tex]1000g\equiv2.2\text{ pounds}[/tex]This implies that,
[tex]1g\equiv\frac{2.2}{1000}[/tex][tex]300g\equiv\frac{2.2}{1000}\times300=\frac{6.6}{10}=0.66\text{ pounds}[/tex]line m || line n m<4 = 72°
what is the measure of angle 5?
Answer: [tex]108^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle 4[/tex] and [tex]\angle 5[/tex] are supplementary since they are consecutive interior angles.
The diagram shows two quadrilaterals graphed on a coordinate plane. 4 5 6 7 8 Which transformation on quadrilateral 1 can be used to verify that is similar to quadrilateral
dilation, k=0.5
Explanation
Step 1
as we can see, the quadrilaterals have different size. it means we can discard a traslation
Step 2
now, we can see both quadrilateral have similar shape, so we can check for a dilation.
A dilation is a type of transformation that changes the size of the image. The scale factor measures how much larger or smaller the image is
[tex]A(x,y)\rightarrow Dilation\rightarrow A^{\prime}(kx,ky)[/tex]in this case, quadrilateral 1 is bigger than quadrilateral 2, it means it suffered a compresion, so k is smaller than 1
[tex]A(x,y)\rightarrow A^{\prime}(kx,ky)\text{ for k}<1[/tex]we can find k,
let
A=a point of the quadrilateral
[tex]\begin{gathered} A(-6,0)\rightarrow A^{\prime}(-6k,0k)\rightarrow A^{\prime}(-3,0) \\ so \\ -6k=-3 \\ k=\frac{-3}{-6} \\ k=\frac{1}{2} \end{gathered}[/tex]I hope this helps you
In the figure shown, &, //&₂. If m26=146°, what is the measure of 21 in degrees?
Answer:
angle 1 = 34 degrees
Step-by-step explanation:
Angle 2 and angle 6 are corresponding, therefore they are congruent and have a measure of 146 degrees.
angle 1 and angle 2 form supplementary angles so:
angle 1 = 180-angle 2
angle 1 = 180 - 146
angle 1 = 34 degrees
Given that tan x= - 10 and sin x is positive, determine sin(2x), cos(2x) and tan(2x) . Write the exact answer. Do not round
Answer:
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Given that tanx and sinx is negative, determine sin(2x), cos(2x), and tan(2x) Write the exact answer. Do not round: Answer Keyboard sin(Zx) cos(2x) Submit Ar
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in this question we have to find the value of sine two X cost two X. And turn to work given 10 X. is equal to minus 11 and syntax is yeah negative 10 X. And cynics both are negative together. In Yeah. Quarante food All right. Mhm signed two X. is equal to to 10 X. Yeah. Yeah upon one plus tell a square X is equal to to into minus 11 upon one plus -11 to the power to is equal to -22 upon one plus 1 21 is equal to -22 upon 1 22 is equal to minus 11 upon 61 Cost two X is equal to 1 -1 tennis square X upon one plus tennis square is equal to one -11 to the power to upon one plus -11 to the power to is equal to one 1 21. Plus upon one plus 1 21 is equal to minus 1 20 upon 1 22 is equal to minus 60 appalled 61. Yes tend to X. Is equal to signed two x upon cost two X is equal to minus 11 upon 61. A phone minus 16.61 is equal to 11 upon 16. Okay that Kind two X is equal to minus 11 upon 61 Cost two X is equal to minus 60. .61 tend to work is equal to 11 upon 60. My answer to the question.
. Which of the following expressions is a factor of the
expression x² - 6x + 8?
F. x-3
G. x-4
H. x-5
J. x-6
K. x-8
The correct answer is [G] x-4
x-4 is the expressions is a factor of the expression x² - 6x + 8.
What is a factor?The positive integers that can divide a number evenly are known as the factors in mathematics. Let's say we multiply two numbers to produce a result. The product's factors are the number that is multiplied. Each number has a self-referential element. There are several examples of factors in everyday life, such putting candies in a box, arranging numbers in a certain pattern, giving chocolates to kids, etc. We must apply the multiplication or division method in order to determine a number's factors.
The numbers that can divide a number exactly are called factors. There is therefore no residual after division. The numbers you multiply together to obtain another number are called factors. A factor is therefore another number's divisor.
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Data on annual tuition and average mid-career salary of graduates of a certain degree program are collected from a number of universities and colleges. The result of the data collection is the linear model
y
=
0.83
x
+
106
,
where
x
=
annual tuition and
y
=
average mid-career salary of graduates, both in thousands of dollars. This model is accurate for annual tuition values between 10 thousand and 40 thousand dollars.
What is the slope of this linear model?
According to this model, what is the average salary for a graduate of a college or university where the annual tuition is $25,000?
$
The slope of the model is 0.83 and a graduate is expected to have an average salary of $20856
How to determine the slope of the model?The equation of the linear model is given as
y = 0.83x + 106
A linear equation is represented as
y = mx + c
Where m represents the slope
This means that when the equations y = mx + c and y = 0.83x + 106 are compared, we have:
m = 0.83
This means that the slope of the equation y = 0.83x + 106 is 0.83
Hence, the slope of the equation is 0.83
How to determine the average salary for a graduate?
Here, we have
Annual tuition = $25,000
This means that
x = 25,000
So, we have
y = 0.83 x 25000 + 106
Evaluate
y = 20856
Hence, the average salary for a graduate is $20856
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What is the slope of a line perpendicular to the line whose equation is 4x-3y=-3 simple answer
Answer:
3=-4x+3y or -4x+3y=3
Step-by-step explanation:
it perpendicular
The sum of two integers is 236. If one of the integers is-122, determine the other.
Answer: 114.
Step-by-step explanation: This would be an equation to set up. We have all three parts of the equation: The sum of the two numbers (236), one of the integers (122), and then an unknown number, (let's call it x). Since 236 is the total, 122 is one of the numbers, we need to look for the unknown number, x. Then we would set it up as 122+x=236. Subtract 122 to both sides, to get 114.
A telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 25% of her calls, there is no answer or the line is busy. She sells subscriptions to 9% of the remaining calls. For what proportion of calls does she make a sale?
If a telemarketer calls people and tries to sell them a subscription to a daily newspaper. On 25 % of her calls, there is no answer or the line is busy. She sells subscriptions to 9 % of the remaining calls. The proportion of calls she make a sale is: 189/ 25.
ProportionGiven data ;
Calls without answer or line busy = 25%
Subscription sold out of remaining calls = 9%
Now let determine the proportion of calls she make a sale :
Proportion = 9 % × ( 100 % - 25 %)
Proportion = 9 % × 75 %
Proportion = 7.56 %
Since we were told the proportion of calls she make a sale we would have to convert the percentage into fraction :
Proportion :
Proportion = 7.56 %
Proportion = 189 / 25
Therefore we can conclude that the proportion is 189 / 25.
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While on a holiday in Montego Bay, Jamaica, Marilyn shops for souvenirs for friends. She
has budgeted C$120 for souvenirs.
a) How much does she have in Jamaican dollars to spend on souvenirs?
She spend J$10039.48 in Jamaican currency on souvenirs.
What is currency?The term "money" in mathematics refers to a form of payment, such as bills, coins, and demand deposits, that is used to purchase goods and services. Money is used to pay for the worth or price of an item or service. The US dollar is the country's recognized unit of exchange. A currency is the standardization of money, including banknotes and coins, that is used or in circulation as a means of exchange. A currency can also be defined more broadly as a system of money that has been used often over time within a particular setting, particularly by residents of a country state.
Given Data
While on a holiday in Montego Bay, Jamaica, Marilyn shops for souvenirs for friends. She has budgeted C$120 for souvenirs.
She spend a certain amount in Jamaican currency is:
CD$120(83.6623)
J$10039.48
She spend J$10039.48 in Jamaican currency on souvenirs.
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Will equation 2/5 + 3 squared be rational or irrational? Why?
The short answer is [tex]\frac{2}{5}+3^2[/tex] will be considered rational.
Why you ask? Continue reading below for a deeper explanation.
_____________________________________________________
| Rational and Irrational Numbers |"What Are They?" - Descriptions and Examples
Rational Numbers are numbers in which can be expressed as an integer or the quotient of an integer divided by a nonzero integer. For example, the number can be represented in the form of [tex]\frac{p}{q}[/tex] , where P and Q are integers and Q ≠ 0.
Example ( [tex]\frac{1}{3}, \frac{2}{4}, \frac{1}{5}, ...[/tex]are all considered rational.Irrational Numbers on the other hand cannot be written in the form of simple fractions. In other words, it is a real number the isn't able to be made by dividing two integers.
Example ([tex]\sqrt{2}, \sqrt{3} , \sqrt{5},...[/tex] are all considered irrational._____________________________________________________
Hope this helps! If I missed anything, feel free to ask any further questions you may have regarding the topic below in the comments and I'll see what else I can do to assist you further. However, if this did help, feel free to lmk. Thank you for your time and I wish you the best of luck on the rest of your studies!
A school district has the following high school committee officers.• Committee A: Amber, Calipso, Juan• Committee B: Megan, Amber, Sam
For the given high school committee officers.
We need to find the sharing between the committee officers.
AS shown:
Amber is a common between A and B
Calipso is a common between A and C
Juan is a common between A and D
Sam is a common between B and C
So, the figure represents the situation will be option A
The length of a rectangle is four times its width.
If the perimeter of the rectangle is 60 ft , find its area.
A rectangle has a perimeter of 60 feet. The rectangle's length is four times its width. The area of rectangle is 144 square feet.
Given that,
A rectangle has a perimeter of 60 feet.
The rectangle's length is four times its width.
We have to find the area of rectangle.
Let us take length as x
The width will be 4x
The perimeter =2(4x+x)
2(4x+x)=60
4x+x=60/2
5x=30
x=30/5
x=6
The length will be 6.
The width will be 4×6=24.
The area of rectangle is length×width
=6×24
=144 square feet.
Therefore, the area of rectangle is 144 square feet.
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Rai compares the fee structure for two different art classes.
Which equation can be used to solve for the number of classes, c, for which Class A and Class B cost the same?
Class A
No registration fee
$40 per class Class B
$60 registration fee
$25 per class
CLEAR CHECK
40=25+60c
40c=25+60c
40c+60=25c
40c=25c+60
The equation that can be used to solve for the number of classes, c, for which Class A and Class B cost the same is D. 40c = 25c+60
How to illustrate the equation?From the information, Rai compares the fee structure for two different art classes.
For class A, it should be noted that the expression will be 40c.
For class B, it should be noted that the expression will be 60 + 25c where c is the number of classes
Therefore, equating both equations will be:
40c=25c+60
In conclusion, the correct option is D.
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Below is the graph of f’(×), the derivative of f(x), and has x-intercepts at x =-3, x = 1, and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5.Which of the following statement is false?
Answer:
Option 1:
Explanation:
In order for f(x) to be concave up in an interval, the graph of the derivative would have to be increasing in that interval.
In the given graph, from x=-1.5 to x=1.5, the graph of the derivative is decreasing, therefore, the statement that "f is concave up from x=-1.5 to x=1.5" is false.
Next, for f to have an inflection point at any x-value the slope of the derivative, f'(x) must change signs at that x-value. Therefore, the statement "f has an inflection point at x=1.5" is true.
Finally, for f(x) to have a relative minimum at x=2, the value of the derivative must be 0, which is as seen on the graph.
Therefore, the first option is False.
Can you please help me with this with question
The standard normal distribution or standardized normal distribution is a singular normal distribution. Its variable, Z is the product of a transformation or change of variable of the variable X. This transformation is called typing:
[tex]Z=\frac{X-\mu}{\sigma}[/tex]From our exercise, the values of
[tex]\begin{gathered} \mu=0 \\ \sigma=1 \end{gathered}[/tex][tex]\begin{gathered} Z=\frac{X-0}{1} \\ Z=X \end{gathered}[/tex][tex]\begin{gathered} X=0.9265 \\ Z=0.9265 \end{gathered}[/tex]Now we look up this value of z in our table so we can find the probability at this point. the first digits that is 0.9 tells us in which row we are going to search and the third 0.02 in which column
[tex]0.92\to0.8212[/tex]The probability calculated with the z score is 0.82()82%Answer:
i really dont understand u gotta take better pictures
Step-by-step explanation:
Mai, Bill, and Dante have a total of $105 in their wallets. Dante has 3 times what Mai has. Bill has $10 more than Mai. How much does each have?
Answer:
Mai 19
Bill 29
Dante 57
Step-by-step explanation:
assume
mai = X
Bill = Y
Dante = Z
X + Y + Z = 105
Z = 3X
Y = 10 + X
then
X + Y + Z = X + 3X + 10 + X
5X + 10 = 105
5X = 95
X = 19
Y = 29
Z = 57
Many people use mobile apps and online software to manage and create personalized budgets. Suppose your task is to develop an online tool for personal budgeting. What information would be included or entered? What types of features would the tool have?
The information that would be included or entered into the application or online tool for personal budgeting should include but not be limited to:
ExpensesExpense CategoriesAuto Expense summationExpense forecastingExpense reporting etc.IncomeIncome categoriesAuto Income summationIncome forecastingIncome reporting etc.The features that the tool will have are:
Item-by-item analysisCalendar Reporting AnalysisEmail and Password for login and User RegistrationCloud functionality so that you are able to back up and retrieve information.Learn more about Budgeting:
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Devon owns a house cleaning company and has to give price quotes to potential customers. He figures out his price by assuming a $25 base charge and then adding $8 for each bathroom and $4 for each other room.
If he uses P to represent the price, B for bathroom, and R for other rooms, which of the following represents his price quote formula?
A P = 25 + 12(BR)
B P = 25 + 8B + 4R
C P = 25(4R + 8B)
D P = (4)(8)(R + B) + 25
Answer:
B P = 25 + 8B + 4R
Step-by-step explanation:
The price quote, P, will be equal to the total amount of charges. It’s given that there is a $25 base charge, so we can begin by writing the price quote as P = $25. To this base charge of $25, $8 per each bathroom, represented by the variable B, is added; our price quote is now P = $25 + $8B. Lastly, $4 per each other room, R, is added, and the actual price quote is P = $25 + $8B + $4R, or P = 25 + 8B + 4R.
Find the distance to the oil platform from each end of the beach. Enter both values.
Answer:
3671.8, 3576.4
Step-by-step explanation:
The third angle of the triangle is 19°.
Let the first length be a. Then,
[tex] \frac{a}{\sin 85^{\circ}}=\frac{1200}{\sin 19^{\circ}} \\ \\ a=\frac{1200\sin 85^{\circ}}{\sin 19^{\circ}} \approx 3671.8[/tex]
Let the second length be b.
[tex] \frac{b}{\sin 76^{\circ}}=\frac{1200}{\sin 19^{\circ}} \\ \\ b=\frac{1200\sin 76^{\circ}}{\sin 19^{\circ}} \approx 3576.4[/tex]
D) Simplify the expression.
7/12- 11/12 + 5/12=
Answer: 1/12
step by step equation:
Find the number of zeros at the end of (51! −50!).
choose the fraction that has not been reduced to simplest form 19/3810/1921/3415/18
19/38 and 15/18
Explanation:
19/38 can be reduced as there is a factor other than 1 that can divide without a remainder. Factor is 19
It can still be reduced because 19*2 = 38
19/38 = 1/2
10/19 cannot be reduced as there is no factor other than one to divide without a remainder
21/34 cannot be reduced as there is no factor other than one to divide without a remainder
15/18 can be reduced as there is a factor other than 1 that can divide without a remainder.
The factor is 3
15/18 = 5/6
Fraction that has not been reduced to simplest form are 19/38 and 15/18
Hi, can you help me to solve this exercise please. If MK=6 ft, find the length “MKL to the nearest Tenth!
To find the arc length we need to know the angle subtended by the arc.
From the diagram we notice that angle MNK is of 180°.
We also notice that:
[tex]\begin{gathered} m\angle JNK+m\angle KNL=90 \\ 52+m\angle KNL=90 \\ m\angle KNL=90-52 \\ m\angle KNL=38 \end{gathered}[/tex]Then the angle subtended by the arc MKL is 218°.
Now that we know this we need to remember that the arc length is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]in this case the radius is 3 ft (The radius is half the diameter) then we have that:
[tex]\begin{gathered} s=2\pi(3)(\frac{218}{360}) \\ s=11.4 \end{gathered}[/tex]Therefore the arc length is 11.4 ft.
A science experiment has a catapult launch a ball. The result of the experiment is shown in the table. experiment is shown in the table.
a. What is the average distance of the 5 attempts? Show your work.
B. How far does the ball have to travel on the sixth attempt so that the average of all 6 of the attempts is 50.9 meters? Explain
please help!!
The data on the attempts and distances of the science experiment on the launch of a ball by a catapult, presented in a tabular form gives the following;
a. The five attempts have an average distance of 50.58
b. The distance the sixth ball has to travel so as to give an average distance traveled of 50.9 meters is 52.5 meters
What is an average of a data set?An average is a descriptive statistics that tends to describe the values in a dataset. An average or the mean of a dataset is obtained by summing the data values and dividing the result by the number of data points
Please find attached, the Attempt to Distance table obtained from a similar question online
a. The formula for average, [tex] \bar{x} [/tex] of a set of data or observations is presented as follows;
[tex] \displaystyle{\bar x = \frac{Sum \: of \: observations}{Number \: of \: observations}} [/tex]
Mathematically, we have;
[tex] \displaystyle{\bar x = \frac{\sum x}{N}} [/tex]
Which gives from the attached table;
[tex]\displaystyle{\sum {x} =50.7+49.4 +52.3 + 48.9 + 51.6 = 252.9}[/tex]
N = 5
Which gives;
[tex] \displaystyle{\bar x = \frac{252.9}{5} = 50.58}[/tex]
The average distance of the 5 attempts is 50.58 metersb. The distance, d, the ball has to travel on the sixth attempt to get an average of 50.9 meters is found as follows;
The new total number of attempts, N = 6
Which gives;
[tex] \displaystyle{\bar x = 50.9 = \frac{d + 252.9}{6} }[/tex]
6 × 50.9 = d + 252.9
Therefore;
d = 6 × 50.9 - 252.9 = 52.5
The distance the ball has to travel in the sixth attempt to have an overall average of 50.9 meters is 52.5 metersLearn more about the average of a dataset here:
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Your teacher wants to put a garden in her backyard with a fence around it. The width needs to be the same size as the shed which is 8ft. If she bought 50 feet of fence and wants the largest garden she can make, what should the length of the garden be? Justify your thinking.
Th length of the garden when the teacher bought 50 feet of fence is 17 feet.
How to calculate the value?From the information, the width needs to be the same size as the shed which is 8ft and she bought 50 feet of fence and wants the largest garden she can make,
It should be noted that perimeter is calculated as:
= 2(Length + Width)
In this case, the perimeter is 50 feet.
2(Length + Width) = 50
2(Length + 8) = 50
2L + 16 = 50
2L = 50 - 16
2L =34
Divide
L = 34/3
L = 17 feet.
The length is 17 feet.
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The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random
variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl
in 10 births is a significantly low number of girls.
Use the range rule of thumb to identify a range of values that are not significant.
The maximum value in this range is ___
Number ofGirls x
0
1
2
3
4
5
6
8
9
10
P(x)
0.004
0.015
0.036
0.116
0.201
0.245
0.196
0.115
0.041
0.012
0.019
The maximum value in this range is 8.3 girls. The range of a set of numbers is the difference between its highest and lowest values. To find it, subtract the lowest number from the highest in the distribution.
What is maximum value?The maximum value of a function is the point on a graph where the function reaches its highest point, or vertex. In this image, for example, the maximum value of the function is y equals 5. To find the maximum, we must locate the point on the graph where it changes from increasing to decreasing. We look at the second derivative and see when the value changes from positive to negative to determine the rate at which the graph shifts from increasing to decreasing. The min is simply the smallest observation, while the max is the largest. Obviously, determining the min and max is easier if the data is ordered from lowest to highest. So, for our data, the minimum is 13 and the maximum is 110To learn more about maximum value, refer to:
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a recipe calls for 15 oz of flour for every 8 fl oz of milk
if you use 15 fl oz of milk, how much flour should you use
Work Shown:
(15 oz of flour)/(8 fl oz of milk) = (x oz of flour)/(15 fl oz of milk)
15/8 = x/15
15*15 = 8*x
225 = 8x
8x = 225
x = 225/8
x = 28.125