For a given data set, the equation of the least squares regression line will always pass through the point [tex]\((\bar{x}, \bar{y})\),[/tex] where [tex]\(\bar{x}\)[/tex] is the mean of the x-values and[tex]\(\bar{y}\)[/tex] is the mean of the y-values.
Explanation:The least squares regression line minimizes the sum of squared differences between the observed y-values and the values predicted by the line. The equation of the line is given byy = mx + b, where m is the slope and bis the y-intercept. The slopem and y-intercept b are determined by formulas involving the means[tex](\(\bar{x}\)[/tex] and [tex]\(\bar{y}\))[/tex]and other statistical measures from the data set.
The specific formulas for the least squares regression line are:
[tex]\[ m = \frac{\sum_{i=1}^{n} (x_i - \bar{x})(y_i - \bar{y})}{\sum_{i=1}^{n} (x_i - \bar{x})^2} \]\[ b = \bar{y} - m\bar{x} \][/tex]
It can be observed from the formulas that when [tex]\(x = \bar{x}\)[/tex], the corresponding y value is[tex]\(\bar{y}\)[/tex]. Therefore, the least squares regression line passes through the point[tex]\((\bar{x}, \bar{y})\)[/tex]. This point represents the centroid of the data set and ensures that the line adequately represents the overall trend of the data.
Question:
It seems there might be some repetition or an incomplete question in your request. Could you please provide more details or clarify your question so that I can assist you accurately? If you have a specific question related to the least squares regression line or any other topic, feel free to provide more context, and I'll do my best to help you.
Everett and marie are going to make fruit bars for their family reunion they want to make 4 times the amount the recipe makes if the recipe calls for 2/3 cup of oil, how much oil will they need?
Jim and Stephanie just got married and are thinking about changing their health care insurance plans to be more affordable. Currently, both Jim and Stephanie are insured through their own employers. Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries. Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary. Insurance Jim's Employer Beneficiary Monthly Premium Employer Contribution Jim $378 42% Additional (each) $345 23% Stephanie's Employer Beneficiary Monthly Premium Employer Contribution Stephanie $298 35% (+10% for each additional beneficiary) Additional (each) $349 30% Which would be the most economical way for the couple to purchase health insurance? a. They should both add each other to their plans. b. Stephanie should add Jim to her health care plan. c. Jim should add Stephanie to his health care plan. d. They should each purchase a plan from their own employer. Please select the best answer from the choices provided A B C D
Answer:
Option B is correct.
Stephanie should add Jim to her health care plan.
Step-by-step explanation:
Let's take the options one by one.
Option 1
If Jim's employers insure him and his wife.
Jim’s employer pays 42% of his $378 monthly premium. His insurance plan will also pay for 23% of the $345 premium for additional beneficiaries.
It means Jim will pay (0.58 of $378) for himself plus (0.73 of $345) for his wife.
Amount Jim pays = (0.58 × 378) + (0.73 × 345) = $471.09
Option 2
If Stephanie's employers insure both of them.
Stephanie’s employer pays 35% of her $298 monthly premium but offers to pay an extra 10% of her premium for each beneficiary Stephanie adds to her plan. Her employer would then pay 30% of the $349 premium for each additional beneficiary.
It means Stephanie would pay (0.65 of $298) she'll pay for herself plus (0.70 of $349) she'll pay for her husband minus (10% of $298) that her company wants to pay out of the insurance fee of any of her additional beneficiary.
Amount Stephanie will pay = (0.65 × 298) + (0.70 × 349) - (0.10 × 298) = $408.2
Option 3
If each of them does an insurance plan with their respective employers
Jim’s employer pays 42% of his $378 monthly premium.
Stephanie’s employer pays 35% of her $298 monthly premium
Jim would pay (0.58 × $378) for himself = $219.24
Stephanie would pay (0.65 × $298) for herself = $193.7
Total they would pay in this option = $219.24 + $193.7 = $412.94
Of all the three options, the option that minimizes their expenses is when Stephanie insures herself and Jim with her employers for a total cost of $408.2 compared to a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they respectively insure each other with their respective employers.
Hope this Helps!!!
Insurance is termed as the process of safeguarding against financial loss. It's a type of risk management that's used mostly to protect against the danger of a speculative or unpredictable loss.
An insurer, an insurance company, an insurance carrier, an underwriter is a business that sells insurance.
The correct answer is option B. Stephanie should add Jim to her health care plan.
The evaluation of each and every option is as follows:
Option 1
If Jim and his wife are covered by Jim's employer's insurance.
Jim's $378 monthly premium is covered by his company to the tune of 42 percent. Additional beneficiaries will be covered by 23 percent of his insurance plan's $345 cost.
Jim will have to pay 0.58 of $378 for himself and 0.73 of $345 for his wife.
Jim's payment = = $471.09
Option 2
If both of them are protected by Stephanie's company's insurance.
Stephanie's company pays 35% of her $298 monthly premium, but she has the choice of paying a further 10% of her discount for each beneficiary she adds to her plan. For each new beneficiary, her employer would pay 30% of the $349 payment.
Stephanie would pay (0.65 of $298) for herself plus (0.70 of $349) for her husband, minus (10 percent of $298) that her firm wants to pay out of any of her extra recipients' insurance payments.
Stephanie will pay $408.2 by multiplying (0.65 298) by (0.70 349) by (0.10 298).
Option 3
If they both join an insurance plan via their companies, Jim's employer will cover 42 percent of his $378 monthly payment.
Stephanie's $298 monthly charge is compensated by the business to the tune of 35%.
For himself, Jim would pay [tex](0.58 \times \$378)[/tex]= $219.24
Stephanie would pay (0.65 $298) for herself = $193.7 The total cost of this option would be $219.24 + $193.7 = $412.94.
Stephanie ensures herself and Jim with her employers for a total cost of $408.2, against a total cost of $471.09 if Jim insures the two of them with his employers or $412.94 if they insure each other with their respective jobs.
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Subtract -7a^2+3a-9−7a
2
+3a−9minus, 7, a, squared, plus, 3, a, minus, 9 from 5a^2-6a-45a
2
−6a−45, a, squared, minus, 6, a, minus, 4.
When subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45, subtract each corresponding term: a^2 terms, a terms and constant terms. The result is 12a^2 - 9a - 36.
Explanation:To subtract one polynomial from another, we simply subtract the corresponding terms. In the given problem, we are subtracting -7a^2 + 3a - 9 from 5a^2 - 6a - 45. Let's subtract term by term:
Subtract the a^2 terms: 5a^2 - (-7a^2) = 12a^2.Next, subtract the a terms: -6a - 3a = -9a.Lastly, subtract the constants: -45 - (-9) = -36.So, the result of the subtraction is 12a^2 - 9a - 36.
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19. Which of the following is not a solution to the system of inequalities
A. (1-, -1)
B. (0, 1)
C. ( -3, 3)
D. (-3, 2)
Answer: The answer should be C!
Step-by-step explanation:
I took the quiz
The pair of coordinates which is not a solution to the system of inequalities is; Choice C: (-3, 3).
The area under the shaded region of the graph of the system of inequalities contains all feasible solutions of the system of inequalities.
In essence, the coordinate (-3, 3) is the point which is not a solution of the system of inequalities.
This is so because it doesn't fall under the shaded area.
This is due to the broken horizontal line; y < 3.
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HELP ASAP!! The time taken for a journey on a motorway varies inversely as the average speed for the journey. The journey takes 1.5 h when the average speed is 54 miles per hour. Identify the time taken in hours for this journey when the average speed is 45 miles per hour.
Answer: it will take 1.8 hours
Step-by-step explanation:
The time taken for a journey on a motorway varies inversely as the average speed for the journey. Let t represent taken for the journey. Let s represent the average speed. If we introduce a constant of varistion, k, the expression becomes
t = k/s
The journey takes 1.5 h when the average speed is 54 miles per hour. This means that
1.5 = k/54
k = 54 × 1.5 = 81
The equation becomes
t = 81/s
Therefore, when the average speed is 45 miles per hour, the time taken would be
t = 81/45
t = 1.8
24p
8
–
36p
6
+
36p
2
Answer:
24p8 - 36p6 + 36p2 = 48p
Step-by-step explanation:
I hope this helps!
An aircraft departs an airport in the mountain standard time zone at 1515 MST for a 2-hour 30-minute flight to an airport located in the Pacific standard time zone. What is the estimated time of arrival at the destination airport
The flight departing at 3:15 PM MST, after 2 hours and 30 minutes, arrives at an estimated time of 4:45 PM PST considering that PST is one hour behind MST.
Explanation:The subject of this question revolves around time conversion between different standard global time zones. The departure time is 15:15 or 3:15 PM Mountain Standard Time (MST). A flight taking 2 hours and 30 minutes is added onto this original departure time. Therefore, in MST, the arrival time would be 17:45 or 5:45 PM MST. However, we must consider the time difference to Pacific Standard Time (PST) which is one hour behind MST. This means, to reflect PST, we subtract one hour from the MST arrival time, giving us an estimated arrival time of 16:45 or 4:45 PM PST.
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Use the given information to find the exact value of each of the following. a. sine 2 theta b. cosine 2 theta c. tangent 2 theta sine theta equals five sixths comma theta lies in quadrant II
Answer:
(a) [tex]sin 2\theta = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=[/tex][tex]\frac{5\sqrt{7} }{11}[/tex]
Step-by-step explanation:
If [tex]sin \theta =\frac{5}{6} , 90\leq \theta\leq 180[/tex]
Using Pythagoras,
Opposite=5, Hypotenuse =6, Adjacent=?
[tex]6^2=5^2+Adj^2\\Adj^2=36-25=11\\Adjacent=\sqrt{11}[/tex]
In the Second Quadrant,
[tex]sin \theta =\frac{5}{6} , cos \theta =-\frac{\sqrt{11} }{6}, Tan \theta =-\frac{5 }{\sqrt{11}}[/tex]
(a) [tex]sin 2\theta=2sin\theta cos\theta=2 X \frac{5}{6} X -\frac{\sqrt{11} }{6} = -\frac{5\sqrt{11} }{18}[/tex]
(b)[tex]cos 2\theta= cos^2\theta-sin^2\theta=(-\frac{\sqrt{11} }{6})^2-(\frac{5}{6})^2= -\frac{7}{18}[/tex]
(c)[tex]tan 2\theta=\frac{2tan\theta}{1-tan^2\theta}[/tex]
[tex]tan 2\theta=\frac{2(-\frac{5 }{\sqrt{11}})}{1-(-\frac{5 }{\sqrt{11}})^2} =\dfrac{-\frac{10 }{\sqrt{11}}}{1-\frac{25}{11}} =\dfrac{-\frac{10 }{\sqrt{11}}}{-\frac{14}{11} }=\frac{5\sqrt{7} }{11}[/tex]
33. The following statement calls a function named half, which returns a value that is half that of the argument passed to it. Assume that result and number have both been defined to be double variables. Write the half function. result = half(number);
Answer:
Step-by-step explanation:
#using java
Double result;
public Double half(Double number){
return number/2;
}
result=half(number);
Final answer:
The function named 'half' is demonstrated using C++ code, where it takes a double as an argument and returns its half. The provided example shows how to define and use the function in a program.
Explanation:
The student's question involves writing a function in a programming language that effectively halves the value of the passed argument. This is a common task in programming, particularly in languages like C++, Java, or Python. Let's consider a simple function in C++ for illustrative purposes.
Example of a half function in C++:
double half(double number) {
return number / 2.0;
}
This function, half, takes a double (a data type that stores floating-point numbers) as an argument and returns a value that is half of the argument's value. It is important to note that double variables store finite approximations of real numbers and usually have a precision of about 17 significant digits in most computing environments.
To use this function, you would write the following code in your main program:
double number = 10.0; // or any other value
double result = half(number);
std::cout << result; // This will output 5.0
Understanding the code:
When invoked, the function will return half of the input value, effectively operating as number / 2.0.
A teacher writes the name of each of her 25 students on a slip of paper and places the papers in a box. To call on a student, she draws a slip of paper form the box. Each paper is equally likely to be drawn, and the papers are replaced in the box after each draw.
If the class contains 11 boys and 14 girls, what is the probability of calling on a girl?
a.
0.0016
c.
0.56
b.
0.36
d.
Answer:
0.56
Step-by-step explanation:
There are 14 girls, and a total of 25 students. So the probability of selecting a girl is P = 14/25 = 0.56.
The probability of calling on a girl will be 0.56. The correct option is C.
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that an event is impossible, and 1 indicates that an event is certain.
The probability of calling on a girl can be calculated by dividing the number of girls by the total number of students in the class:
Probability of calling on a girl = Number of girls / Total number of students
Number of girls = 14
Total number of students = 11 + 14 = 25
Therefore, the probability of calling on a girl is:
Probability of calling on a girl = 14 / 25 = 0.56
So, the correct answer is (c) 0.56.
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40. What is the system of inequalities associated with the following graph?
Answer:
The bottom answer
Step-by-step explanation:
The Cole family owns an above-ground circular swimming pool that has walls made of aluminum. Find the length of aluminum surrounding the pool if the radius is 14 feet.
Answer:
Therefore the length of aluminum surrounding the pool is 88 feet.
Step-by-step explanation:
Circle:
The line is drawn from the center to the arc is the radius of the circle.The value of diameter of a circle is 2 times of the value of radius.The formula of area of a circle = [tex]\pi r^2[/tex] The formula of circumference of a circle [tex]= 2\pi r[/tex].Given that the circular swimming pool has walls made of aluminum.
To find out the length of the of aluminum, we need to find out the circumference of the pool.
The radius of the circular pool is = 14 feet.
Therefore the circumference of the pool is =[tex]2\pi r^2[/tex]
[tex]=2\times \frac{22}{7} \times 14[/tex] feet
=88 feet
Therefore the length of aluminum surrounding the pool is 88 feet.
0. An airplane rises vertically 1000 feet over a horizontal distance of 1 mile. What is the
angle of elevation of the airplane's path? (***you need to know how many feet are in 1
mile)
TAN
Answer:
10.7°
Step-by-step explanation:
1 mile = 5280 feet
Tan(X) = 1000/5280 = 25/132
X = (tan^-1)(25/132)
X = 10.72444854
Answer:
Step-by-step explanation:
The movement of the forms a right angle triangle with the ground. The vertical distance which the plane moves represents the opposite side of the right angle triangle. The horizontal distance covered by the plane represents the adjacent side of the right angle triangle.
1 mile = 5280 feet
To determine the angle of elevation, θ, we would apply
the tangent trigonometric ratio.
Tan θ, = opposite side/adjacent side. Therefore,
Tan θ = 1000/5280 = 0.189
θ = Tan^-1(0.189)
θ = 10.7°
The output of a plant is 4335 pounds of ball bearings per week (five days). If each ball bearing weighs 0.0113 g, how many ball bearings does the plant make in a single day
Answer:
The plant makes 34,802,178 ball bearings in a single day
Step-by-step explanation:
The total output of a plant in a 5-day week is 4335 pounds
Each ball bearing weighs 0.0113g
We are to calculate the number of ball bearings made per day
First, we ensure both mass are in the same unit
Now 1 pound =453.5924 grams
4335 pounds=453.5924 X 4335 =1966323.054 grams
Number of bearings made in a week therefore
= 1966323.054 /0.0113=174010889.7
≈174010890 (to the nearest whole number)
Since there are 5 days in a week of production,
Daily Production=174010890/5
=34802178
The plant makes 34,802,178 ball bearings in a single da
The solution set for -18 < 5x - 3 is _____.
-3 < x
3 < x
-3 > x
3 > x
Answer:
[tex]x > - 3[/tex]
Step-by-step explanation:
[tex] - 18 < 5x - 3 \\ \Leftrightarrow 5x > - 15 \\ \Leftrightarrow x > - 3[/tex]
PLEASE HELP!!! NEED HELP ASAP !!! WILL MARK BRAINLIEST !!!
What is the area of a circle whose radius is 6ft? (Use Π)
Question 4 options:
6 Π ft2
9 Π ft2
36 Π ft2
72 Π ft2
Answer:
36 π square feet
Step-by-step explanation:
so the formula for area of a circle is πr^2
so the radius is 6, which we can just plug in
π(6)^2
36π
so option 3
Simplify. Identify any x-values for which the expression is undefined. HELP ASAP!!
The required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Given expression.
= x ² + 8x + 12 / x² - 2x -8
= (x + 6)(x + 2) / (x + 2)(x - 4)
Since, if we put x = -2 and x = 4, the expression will we undefined.
And,
= x + 6 / x -4
Thus, the required simplified expression is x +6 / x - 4, and the expression is not defined for x ≠ -2, 4. Option B is correct.
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The vertex of this parabola is at (-5, -2). When the x-value is -4, the
y-value is 2. What is the coefficient of the squared expression in the parabola's equation?
A 1
B 4
C -1
D 5
Answer:
The answer to your question is letter A
Step-by-step explanation:
Data
Vertex = (-5, -2)
Point = (-4, 2)
This is a vertical parabola the opens upwards.
The equation is
(x - h)² = 4p(y - k)
Substitution
(-4 + 5)² = 4p (2 + 2)
Simplification
1² = 4p(4)
1 = 16p
p = 1/16
Equation of the parabola
(x + 5)² = 4/16(y + 2)
x² + 10x + 25 = 1/4y + 1/2
Conclusion
The coefficient of the squared expression is 1
The variable z is directly proportional to x. When x is 10, z has the value 140.
What is the value of z when x = 20?
Answer: z = 280
Step-by-step explanation:
If two variables are directly proportional, it means that an increase in the value of one variable causes an increase in the value of the other variable. Also, a decrease in the value of one variable causes an decrease in the value of the other variable.
The variable z is directly proportional to x. If we introduce a constant of variation, the expression would be
z = kx
When x is 10, z has the value 140. It means that
140 = 10k
k = 140/10
k = 14
The equation becomes
z = 14x
the value of z when x = 20 is
z = 14 × 20
z = 280
Taylerbarne can you help me learn to find percentages. Please ASAP!
Sure, what do you need help finding?
Answer:
to find a percentage of a number u multiply/divide 100
Replace ∗ with a monomial so that the result is an identity:
1. (2a + ∗)(2a - ∗) = 4a^2–b^2
2. (∗− 3x )(∗ +3x) = 16y^2–9x^2
3. 100m^4–4n^6 = (10m^2−∗)(∗ +10m^2)
4. m^4–225c^10 = (m^2−∗)(∗ +m^2).
Answer:
Each of these is based on the principle of difference of two squares where:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Step-by-step explanation:
1.[tex](2a + *)(2a - *) = 4a^2-b^2[/tex]
[tex]4a^2-b^2=(2a)^2-b^2=(2a+b)(2a-b)[/tex]
2. [tex](*- 3x )(*+3x) = 16y^2-9x^2[/tex]
[tex]16y^2-9x^2=(4y)^2-(3x)^2=(4-3x)(4+3x)[/tex]
3. [tex]100m^4-4n^6 = (10m^2-*)(*+10m^2)[/tex]
[tex]100m^4-4n^6 = (10m^2-(2n^3)^2)= (10m^2-2n^3)(2n^3+10m^2)[/tex]
4. [tex]m^4-225c^{10} = (m^2-*)(* +m^2)[/tex]
[tex]m^4-225c^{10} =(m^2)^2-(15c^5)^2= (m^2-15c^5)(15c^5 +m^2)[/tex]
A ladder leans against a side of a building, making a 63-degree angle with the ground, and reaching over a fence that is 6 feet from the building. The ladder barely touches the top of the fence, which is 8 feet tall. Find the length of the ladder.
Answer:
22.19 feet
Step-by-step explanation:
You want the length of a ladder that makes a 63° angle with the ground and reaches over an 8 ft fence to a building 6 ft beyond.
Trig functionsThe relevant trig relations are ...
Sin = Opposite/Hypotenuse ⇒ Hypotenuse = Opposite/Sin
Cos = Adjacent/Hypotenuse ⇒ Hypotenuse = Adjacent/Cos
ApplicationUsing these relations, we can find the lengths of the segments of the ladder between the ground and the fence, and between the fence and the building.
Referring to the attached diagram, we have ...
CE = 8/sin(63°) ≈ 8.9786
FC = 6/cos(63°) ≈ 13.2161
Then the total length of the ladder is ...
FE = CE +FC
FE = 8.9786 +13.2161 = 22.1947
The length of the ladder is about 22.19 feet.
The formula A=6 2/3 relates the surface area A, in square units, of a cube to the volume V, in cubic units. What is the volume, in cubic inches, of a cube with surface area 486 in2
Answer:
This is the volume of cube V = 729 [tex]in^{3}[/tex]
Step-by-step explanation:
Surface area of cube = 486 [tex]in^{2}[/tex]
Surface area of the cube is given by A = 6 × [tex]a^{2}[/tex]
⇒ 6 × [tex]a^{2}[/tex] = 486
⇒ [tex]a^{2}[/tex] = 81
⇒ a = 9 in
This is the value of side of the cube. so volume of the cube is given by
⇒ V = [tex]a^{3}[/tex]
Put the value of a in above formula w get,
⇒ V = [tex]9^{3}[/tex]
⇒ V = 729 [tex]in^{3}[/tex]
This is the volume of cube
To find the volume of a cube with a surface area of 486 in², calculate the side length using the formula A=6s², leading to a side length of 9 inches, and then calculate the volume as V=s³, resulting in 729 cubic inches.
The volume of a cube with a given surface area using the formula A=6s², where A is the surface area and s is the side length of the cube. First, find the side length by dividing the given surface area by 6, then take the square root. After finding the side length, calculate the volume using the formula V=s³.
Given the surface area A=486 in², the side length s can be found as follows:
Calculate the side length: s = √(A/6) = √(486/6) = √81 = 9 inches.Calculate the volume: V = s³ = 9³ = 729 cubic inches.Vicky has 2 jobs offers for teaching. She just finished her Master’s Degree in mathematics education.
A. She can work at Southside High School as a teacher with a base salary of $43,600 per year. She will also coach JV softball which will add another $900 to her annual salary. The contract suggests the school will be expecting her 190 days but she will be provided with 10 sick days. So, she must actually work a minimum of 180 days (any less and her salary will be reduced). Each day will consist of 8 working hours. With this school she will be provided with free life insurance for $15,000 of coverage. Her health & dental or medical premiums are $78/month. Finally, the school system would require her to automatically invest 5% of his her monthly income for retirement.
B. She can work at Central Tech College as a math instructor. She will be paid $900 for each credit hour she teaches. During the course of her first year of teaching, she would teach a total of 50 credit hours. The college expects she will work a minimum of 170 days (any less and the salary would be reduced) and 8 hours each day. At the college she will have to pay $3 per month for a life insurance policy of $25,000. Her health & dental or medical premiums are $85 per month. Finally, the company would require her to automatically invest $200 per month for retirement.
What is Vicky's Gross Monthly Income for the job at Southside High School?
Answer:
I have a feeling its B
Step-by-step explanation:
Vicky's Gross Monthly Income for the job at Southside High School is $3708.33.
What is Gross Income?Gross income of an individual is the income he/she receives before deduction and taxes.
Given that,
Base salary per year = $43,600
Income for coaching JC softball = $900
Free life insurance coverage = $15,000
Health & dental or medical premiums = $78/month
Gross income is the income an employee receives before all the deductions.
Insurance premiums are deducted from the base salary. So it is not included in gross income.
Annual Gross income = $43,600 + $900 = $44,500
Monthly Gross Income = $44,500 / 12 = $3708.33
Hence the monthly gross income is $3708.33.
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If you are given the graph of h(x)=log6x, how could you graph m(x)=log6(x+3)?
Translate each point of the graph of h(x) 3 units up.
Translate each point of the graph of h(x) 3 units down.
Translate each point of the graph of h(x) 3 units right.
Translate each point of the graph of h(x) 3 units left.
Answer: last option.
Step-by-step explanation:
There are several transformations for a function f(x). Some of them are shown below:
1. If [tex]f(x)+k[/tex], then the function is translated "k" units up.
2. If [tex]f(x)-k[/tex], then the function is translated "k" units down.
3. If [tex]f(x+k)[/tex], then the function is translated "k" units left.
4. If [tex]f(x-k)[/tex], then the function is translated "k" units right.
In this case you have the following function:
[tex]h(x)=log_6x[/tex]
And the function m(x) is obtained by transformating the function h(x). This function is:
[tex]m(x)=log_6(x+3)[/tex]
Then, based on the transformatios shown before, you can identify that:
[tex]m(x)=h(x+3)[/tex]
Therefore, you can determine that you could graph the function [tex]m(x)=log_6(x+3)[/tex] by translating each point of the graph of the function h(x) 3 units left.
will give brainliest if correct!!1
Triangle PQR is formed by the three squares A, B, and C: A right triangle PQR is shown. On the side PQ of this triangle is a square. Inside the square is written Square A, Area equal to 9 square units. On the side QR of this triangle is another square. Inside the square is written Square B, Area equal to 16 square units. On the side PR of this triangle is another square. Inside the square is written Square C, Area equal to 25 square units. Which statement best explains the relationship between the sides of triangle PQR?
Answer:
PR² = PQ² + QR²
Step-by-step explanation:
Since the triangle PQR is a right triangle, according Pythagorean theorem:
The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.So:
PR² = PQ² + QR²as
25 = 9 + 16Answer:
PR² = PQ² + QR²
Step-by-step explanation:
Branson and his sister Beatrice combined their allowance of $7 each, so they could buy a movie for $12. They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. How many containers of fruit salad did they each get?
Answer:
Step-by-step explanation:
Branson and his sister Beatrice combined their allowance of $7 each. This means that the total amount they had is 7 + 7 = $14
They bought a movie for $12. The amount that they have left is
14 - 12 = $2
They bought $1 containers of fruit salad with the remaining money and split the containers evenly between them. This means that the number of containers that they bought is
2/1 = 2
If they split the containers evenly between themselves, then each person would get
2/2 = 1 container of fruit salad
Which ordered pair is the solution to the system of linear equations y = negative 7 x + 2 and y = 9 x minus 14? (negative 5, 1) (1, negative 5) (5, negative 1) (Negative 1, 5)
Answer:
B. [tex](1,-5)[/tex]
Step-by-step explanation:
We have been given a system of equations. We are asked to choose the ordered par that is the solution to the given system.
[tex]y=-7x+2...(1)[/tex]
[tex]y=9x-14...(2)[/tex]
To solve our given system, we will equate both equations as:
[tex]9x-14=-7x+2[/tex]
Combine like terms:
[tex]9x+7x-14+14=-7x+7x+2+14[/tex]
[tex]16x=16[/tex]
[tex]x=\frac{16}{16}=1[/tex]
Upon substituting [tex]x=1[/tex] in equation (1), we will get:
[tex]y=-7(1)+2\\\\y=-7+2\\\\y=-5[/tex]
Therefore, the ordered pair [tex](1,-5)[/tex] is the solution of the given system and option B is the correct choice.
Answer:
mmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm its b
Step-by-step explanation:
please look at this multiple choice. thanks!!!!
Step-by-step explanation:
[tex]y = - 2x + 3[/tex]
The slope of the above line = -2
slope of the line perpendicular to the above line = 1/2
If it passes through point (4,-3) , it's equation
[tex] \frac{y - ( - 3)}{x - 4} = \frac{1}{2} [/tex]
[tex] \frac{y + 3}{x - 4} = \frac{1}{2} [/tex]
[tex]2(y + 3) = x - 4[/tex]
[tex]2y + 6 = x - 4[/tex]
[tex]x - 4 - 2y - 6 = 0[/tex]
[tex]x - 2y - 10 = 0[/tex]
A = 1, B = -2 and C = -10
A+B+C= 1+(-2)+(-10)
= 1-2-10
= 1-12
= -11
Answer:
A = 1, B = -2 and C = -10
Step-by-step explanation:
William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles write an expression using parentheses to show how many marbles each boy will get.
Answer:
Each boy will get 25 marbles.
Step-by-step explanation:
Given:
William has 3 jars of marbles to share equally with his brother the first jar holds 12 marbles the second jar holds 21 marbles the last jar holds 17 marbles.
Now, to write an expression using parentheses to find number of marbles each boy get.
Let the number of marbles each boy get be [tex]x.[/tex]
Total number of boys = 2.
Number of marbles first jar holds = 12.
Second jar holds = 21.
And third jar holds = 17.
As given, William shares marbles equally with his brother.
Now, we write the expression to find the number of marbles each boy get:
[tex]x=\frac{(12+21+17)}{2}[/tex]
[tex]x=\frac{12}{2} +\frac{21}{2} +\frac{17}{2}[/tex]
[tex]x=6+10.5+8.5[/tex]
[tex]x=25.[/tex]
Therefore, each boy will get 25 marbles.