The restaurant salesman will pay a commission of $1,052
How to calculate the amount of commission that will be paid ?Commission is the amount of money that is paid to a worker when a work is completed.
The commission rate of the total sales is 4%
= 4/100
= 0.04
The total sales for the week is $26,300
The commission that will be paid can be calculated as follows
= 26,300 × 0.04
= 1.052
Hence the amount of commission that will be paid is $1,052
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The table below shows the average annual cost of health insurance for a single individual, from 1999 to 2019, according to the Kaiser Family Foundation.YearCost1999$2,1962000$2,4712001$2,6892002$3,0832003$3,3832004$3,6952005$4,0242006$4,2422007$4,4792008$4,7042009$4,8242010$5,0492011$5,4292012$5,6152013$5,8842014$6,0252015$6,2512016$6,1962017$6,4352017$6,8962019$7,186(a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).Pt = (b) Using this linear model, predict the cost of insurance in 2030.$ (c) = According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year (d) Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of P0 and d to the nearest dollar.Pt= (e) Using the regression model, predict the cost of insurance in 2030.$ (f) According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).During the year
Part (a) Using only the data from the first and last years, build a linear model to describe the cost of individual health insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0).
we have the ordered pairs
(1999, 2,196) -------> (0,2,196)
(2019,7,186) -------> (20,7,196)
Find out the slope
where
t -----> is the number of years since 1999
P ----> the cost
m=(7,196-2,196)/(20-0)
m=5,000/20
m=250
Find the equation of the linear model in slope-intercept form
P=mt+b
we have
m=250
point (0,2,196)
substitute and solve for b
2,196=250(0)+b
b=2,196
therefore
P=250t+2,196
Part b
Using this linear model, predict the cost of insurance in 2030
For t=2030=2030-1999=31 years
substitute
P=250(31)+2,196
P=$9,946
Part c
According to this model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute in the linear model
12,000=250t+2,196
250t=12,000-2,196
250t=9,804
t=39 years
therefore
1999+39=year 2038
Part d
Using a calculator or spreadsheet program, build a linear regression model to describe the cost of individual insurance from 1999 onward. Use t to represent years after 1999 (treating 1999 as year 0), and round the values of
P0 and d to the nearest dollar
using a regression calculator
the equation is
ŷ = 239.15065X + 2406.39827
y=239x+2,406
Part e
Using the regression model, predict the cost of insurance in 2030
For t=2030-1999=31 years
P=239(31)+2,406
P=$9,815
Part f
According to the regression model, when do you expect the cost of individual insurance to reach $12,000? Give your answer as a calendar year (ex: 2020).
For P=$12,000
substitute
12,000=239x+2,406
239x=12,000-2,406
239x=9,594
t=40 years
year=1999+40=2039
Shannon started a savings account by putting
in $25. On the 1st week she deposited $15
and plans to continue depositing $15 each
week.
Given the graph, description or sequence values create an explicit equation
A circle passes through (-2, 6) , (2, 8) , and (5, -1) Using the general form of a circle and the points above, fill in missing numbers to create the system of equations. (-2, 6) creates D + E + 1F = (2, 8) creates D + E + 1F = (5, -1) creates D + E + 1F = Solve the system of equations that you created, and write the equation for the circle by filling in the values for D, E, and F.
The equation of the circle passing through points (-2, 6) , (2, 8) , and (5, -1) is given as follows:
(x - 2)² + (y - 3)² = 25.
Equation of a circleThe equation of a circle with center (x*, y*) and radius r is given according to the following rule:
(x - x*)² + (y - y*)² = r².
The circle passes through point (-2,6), hence the first equation of the system is given as follows:
(-2 - x*) + (6 - y*)² = r².
r² = x*² + 4x* + 4 + y*² - 12y* + 36.
The circle also passes through point (2,8), hence the second equation of the system is given as follows:
(2 - x*) + (8 - y*)² = r².
r² = x*² - 4x* + 4 + y*² - 16y* + 64.
The final point is point (5,-1), meaning that the third equation is:
(5 - x*) + (-1 - y*)² = r².
r² = x*² - 10x* + 25 + y*² + 2y* + 1.
The system of equations to find the coordinates of the center and the radius is given as follows:
x*² + y*² + 4x* - 12y* + 40 - r² = 0.x*² + y*² - 4x* - 16y* + 68 - r² = 0.x*² + y*² - 10x* + 2y* + 26 - r² = 0.The solution to the system is given as follows:
x* = 2, y* = 3, r² = 25.
Hence the equation of the circle is:
(x - 2)² + (y - 3)² = 25.
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Use the information provided to answer questions 2 - 5. Leah would like to earn at least $ 120 per month. She babysits for $ 5 per hour and works at an ice cream shop for $ 8 per hour. Leah cannot work more than a total of 20 hours per month. Let x represent the number of hours Leah babysits and let y represent the number of hours Leah works at the ice cream shop.
Leah would like to earn at least $120 per month. This expression means she ould like to earn $120 as a minimum and possible higher than that. In other words, she wants to earn either 120 or above that. If the number of hours she babysits is x, and the number of hours worked at the ice cream shop is y, then her earnings as per x and y woud be;
[tex]\begin{gathered} 5x+8y\ge120---(1) \\ x+y\leq20---(2) \\ Solve\text{ these on a graph and you'll have;} \end{gathered}[/tex]The red graph represents x + y =<20
The blue graph represents 5x +8y =>120
Observe that the region where the blue and red are "mixed" together represent the solution region.
Option A (4, 15)
Option B (5, 12) and
Option C (10, 9) are possible solutions
A ride sharing company offers two options: riding in small cars that can carry up to 3 passengers each, or riding in large vans that can carry up to 6 passengers each. A group of 27 people is going to use the ride sharing service to take a trip. The trip in a small car costs $10 and the trip in a large van costs $15. The group ends up spending $80 total.What do x and y represent?
Answer:
x = no of people in a small car
y = number of people in a van
Explanation:
The relevant information in the problem is that the total number of people is 27 and that the small car costs $10 and the large van $15.
If we call x the number of people in a small car, and y the number in the large van then the following equations can be obtained
[tex]\begin{gathered} x+y=27 \\ 10x+15y=80 \end{gathered}[/tex]The first equation simply says that the total number of people is 27 and the second equation says that the total cost of the trip is $80.
Hence,
x = no of people in a small car
y = number of people in a van
Past due I don't really understand, what's the answer??
Answer:
$50.16
Step-by-step explanation:
id.k if it's actually right but i believe the tip would be $8.36 if it's 20% so adding it together is $50.16
Simplify: 2.4 x 10−4 0.00024 0.000024 −0.000024 −2.4000
Answer:
0.00067
Step-by-step explanation:
You always want the period to the right of the first number meaning you’ll start from there counting backwards because it is negative.
In 3 hours, 5 people can paint a hall with the area of 750 ft 2. How long would it take for 2 people to paint the hall with the same rate of speed?
ANSWER:
STEP-BY-STEP EXPLANATION:
In this case, we can make a proportion, since we know the time when there are 5 people, we need to know the time when there are two people
[tex]\frac{5}{3}=\frac{2}{x}[/tex]solving for x:
[tex]undefined[/tex]I need help figuring out the answer, I’m very much confused
My first step is to draw a picture
We know that the length is 2 times the width
L = 2w
We are given a width of 4.6 yards
L = 2(4.6) = 9.2 yards
We can find the area by using the formula
A = l*w
A = 9.2 * 4.6
A =42.32 yd^2
A secant line intersects the curve g(x)=-x² +8 at x = 1 and x = 1+h. What expression is equal to the slope of this secant?
The slope of the line secant to the curve g(x) = - x² + 8 is equal to m = - (2 + h).
How to derive the equation of the slope of a line secant to a curve
A secant line is a line that passes through a curve in two places, the formula for the slope of the secant line is described below:
m = [f(a + h) - f(a)] / [(a + h) - a]
m = [f(a + h) - f(a)] / h
If we know that f(x) = - x² + 8 and a = 1, then the equation for the slope of the secant line is:
m = {[- (1 + h)² + 8] - (-1² + 8)} / h
m = (- 1² - 2 · h - h² + 8 + 1² - 8) / h
m = (- 2 · h - h²) / h
m = - 2 - h
m = - (2 + h)
The slope of the line is equal to m = - (2 + h).
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Which angle pair is NOT an example of Corresponding Angles?
angle 2 and angle 10
angle 1 and angle 11
angle 13 and angle 15
angle 8 and angle 16
Answer:
Step-by-step explanation:
So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!
a list of 1111 positive integers has a mean of 1010, a median of 99 and a unique mode of 88 what is the largest possible value of an integer in the list?
The largest possible value in the list is 35.
What is mean, median and mode?
Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.
Given: There is a list of 11 positive integers.
Has a mean of 10, a median of 9 and a unique mode of 8.
Since the mode (8) is less than the median (9), the mode can only appear (at most) 5 times since the mode is the 6th number in the list (assuming the list has been sorted in ascending order).
If so, the first five numbers can be 8, the following four numbers can be 9, and the next greatest number can be 10, which means the largest number must be 110 - (8 x 5 + 4 x 9 + 10) = 110 - 86 = 24.
The largest number must be 110 - 77 = 33 if the mode repeats just twice, in which case we can let the first ten numbers be 1, 2, 3, 8, 8, 9, 10, 11, and 13, totaling 77.
The biggest number in this scenario is 110 - 75 = 35 if the mode repeats itself three times. Alternatively, we can let the first ten numbers be 1, 1, 8, 8, 8, 9, 10, 10, and 11 totaling 75.
Therefore, the largest possible value of an integer in the list is, 35.
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solve 2/3x + 4 = 5/6x by eliminating the fraction.
The value of x in the given equation is 24.
Given equation:
(2/3)x + 4 = (5/6)x
We have to find the value of x by eliminating the fraction.
Fraction
Fraction is termed as a portion or section of any quantity. It is denoted by using ‘/’ symbol, such as a/b. For example, in 2/4 is a fraction where the upper part denotes the numerator and the lower part is the denominator.
LCM (3,6) = 6
Multiplying the whole equation by 6, we get:-
(2/3)x*6 + 4*6 = (5/6)x*6
4x + 24 = 5x
5x - 4x = 24
x = 24
Hence, the value of x is 24.
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Convert 450 liters into fluid ounces. Round your answer to the nearest whole number.
Answer:15216.31 Fluid Ounces
Step-by-step explanation:
which classification describes the following system of equations x=5 y=6 -x-y+z=0
?
A. inconsistent and dependent
B. consistent and dependent
C. consistent and independent
D. inconsistent and independent
The system of equations has one solution, so it is consistent and independent, the correct option is C.
What is the classification of the system of equations?
Here we have the system of equations:
x = 5
y = 6
-x - y + z = 0
By replacing the first and second equations into the third one, we get:
-5 - 6 + z = 0
-11 + z = 0
z = 11
So the solution is (5, 6, 11)
So it is consistent, and it is independent as clearly, the equations are linearly independent (system of 3 equations with 3 variables having only one solution).
Then the correct option is C.
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Solve the trig equation on the interval [tex]0 \leqslant theta \: \ \textless \ 2\pi[/tex][tex]3 sec \: \: theta \: - 2 \sqrt{3 } = 0[/tex]
Answer:
pi/6 and 11pi/6
Explanation
Given the trigonometry equation:
[tex]\begin{gathered} 3\text{sec}\theta\text{ - 2}\sqrt[]{3}=0 \\ \end{gathered}[/tex]Add 2\sqrt[3] to both sides as shown;
[tex]\begin{gathered} 3\sec \theta-2\sqrt[]{3}=0+2\sqrt[]{3} \\ 3\sec \theta\text{ = 2}\sqrt[]{3} \\ \sec \text{ }\theta\text{ = }\frac{2\sqrt[]{3}}{3} \\ \frac{1}{\cos \theta}=\frac{2\sqrt[]{3}}{3} \\ \cos \theta\text{ =}\frac{3}{2\sqrt[]{3}} \\ \cos \text{ }\theta\text{ = }\frac{3\sqrt[]{3}}{2\cdot3} \\ \cos \text{ }\theta\text{ = }\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]Take the cos inverse of both sides
[tex]\begin{gathered} \cos ^{-1}(\cos \theta)=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=cos^{-1}\frac{\sqrt[]{3}}{2} \\ \theta=30^0 \end{gathered}[/tex]Since theta is between 0 and 2pi
theta = 360 - 30
theta = 330^0
Convert to radians
180^0 = pi rad
30^0 = x
180x = 30pi
x = 30pi/180
x = pi/6
Similarly;
180^0 = pi rad
330^0 = x
180x = 330pi
x = 330pi/180
x = 11pi/6
Hence the value of thets between 0 and 2pi are pi/6 and 11pi/6
Hi! So I am stuck on three problems right now, can you Please help me?number 1, says "What is the cosine ratio of
The cosine ratio is given by the following formula:
[tex]\cos (Z)=\frac{\text{adjacent leg}}{hypotenuse}[/tex]The adjacent leg of angle Z is side ZY=12 and the hypotenuse of the triangle is the side XZ=20, thus the cosine ratio of Z is:
[tex]\cos (Z)=\frac{12}{20}[/tex]what is the correct ascending order for these numbers1.525/848%
Given the set of numbers:
[tex]\text{ 1.52, 5/8 and 48\%}[/tex]To be able to determine their correct ascending order, we must first make all the numbers into similar forms.
Let's convert a
In the diagram shown, lines MN and PQ intersect at R. If ZNRS is a right angle and the measure of ZMRQ is 1420, then what is the measure of ZPRS? Show or explain how you arrive at your answer.
The measure of the angle PRS is given as follows:
m<PRS = 45º.
Measure of angle PRSAs stated in this problem, these following angles are given:
<MRQ = 142º.m<NRS = 90º.MRQ and and QRN form a ray, hence they are supplementary angles.
For supplementary angles, the sum of the measures is of 180º, hence the measure x of angle QRN is calculated as follows:
142 + x = 180
x = 180 - 142
x = 38º.
The entire diagram forms an angle of 360º, hence:
142 + 38 + 90 + m<MRS = 360º.
270 + m<MRS = 360º
m<MRS = 90º.
The segment PR bisects the angle MRS, dividing into two angles of 90º/2 = 45º, as a bisection of an angle basically splits the angle in half hence these following measures are identified:
The diagram is given by the image at the end of the answer.
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At a restaurant, Elena wants to leave a tip that is 15% of the bill B plus $1. Which linear model best describes the total T?
Answer:
The total T can be described as
[tex]T = (B+(B*.15))+1[/tex]
A farm is being divided so that each section of land has equal access
to the canal running through the property for watering crops. If the road on the
opposite side of the property runs parallel to the canal, explain how this can be
done.
The best way to divide the land having canal and road parallel, is divide land with the line perpendicular to the road and canal.
What is parallel and perpendicular?
In simple geometry, two geometric objects cross at a right angle (90 degrees or /2 radians) if they are perpendicular to one another. The perpendicular symbol,⟂, can be used to graphically depict the condition of perpendicularity. It can be defined between two planes, between two lines (or line segments), and between two lines.
In geometry, parallel lines are coplanar, straight lines that never intersect. Any parallel planes in the same three-dimensional space are those that never intersect. Parallel curves are those that have a predetermined minimum separation between them and do not touch or intersect.
We need to give equal access of canal to each section of land so, the best way to divide land is divide land perpendicularly to canal and the road.
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Solve 4(3m + 1) − 2m = −16. m = −0.83 m equals negative 20 over 12 m equals negative 17 over 10 m = −2.
The solution to the equation given as 4(3m + 1) − 2m = −16 is m = -2
How to determine the solution to the equation?The equation is given as
4(3m + 1) − 2m = −16
Open the brackets in the above equation
So, we have
12m + 4 − 2m = −16
Collect the like terms in the above equation
So, we have the following equation
12m − 2m = −16 -4
Evaluate the like terms in the above equation
So, we have the following equation
10m = −20
Divide both sides by 10
m = -2
Hence, the soluton is m = -2
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12 is 150% of what number
To get 150% of a given number x, we multiply it by 1.5
This way, we'll have that:
[tex]1.5x=12[/tex]Solving for x,
[tex]1.5x=12\rightarrow x=\frac{12}{1.5}\rightarrow x=8[/tex]Therefore, we can conclude that 12 is 150% of 8
The question is in the image. Answer question 13 only.
We need to convert 40 degrees to radians:
Then, we need to use the next equation:
[tex]40\ast\frac{\pi}{180}[/tex]Solve it:
[tex]40\ast\frac{\pi}{180}=\frac{2}{9}\pi[/tex]Hence, 40 degrees is equal to 2/9π radians.
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
Drag the choices into the boxes to correctly complete the statements.
Considering the equation of a circle, it is found that:
The equation of the circle that represents the dartboard is [tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex], where the origin is the lower left corner of the room and the unit of the radius is in inches;The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given as follows:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
In the context of this problem, we have that:
The radius of the circle is of 9 inches, as the diameter is of 18 inches and the radius is half the diameter.The height is of 5 feet 8 inches = 5 feet and 2/3 feet = 17/3 feet, which is the y-coordinate of the center.The bull's-eye is 12 feet from a wall to its left, hence the x-coordinate of the center is of 12.Hence the equation of the circle is given by:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 = 81[/tex]
Brian's dart lands at the following position:
(11.5, 5)
All the points that land on the dartboard respect the following equation:
[tex](x - 12)^2 + \left(y - \frac{17}{3}\right)^2 \leq 81[/tex]
For the coordinate where the dart landed, we have that:
(11.5 - 12)² + (5 - 17/3)² = 0.7 < 81, meaning that Brian's dart lands on the dartboard.
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gmm
2
#x²
13
O
1
2
ABC
3
5x+2
3x + 40
Find the measure of angle 2.
label optional
1
2 3 4
5 6 78 9
XY Z<
7
VI
Xi
+
8
=
V
Answer: [tex]\angle 2=83^{\circ}[/tex]
Step-by-step explanation:
By the alternate interior angles theorem,
[tex]5x+2=3x+40\\\\2x=38\\\\x=19[/tex]
This means that [tex]5x+2=3x+40=97[/tex].
Since [tex]\angle 2[/tex] and the [tex]97^{\circ}[/tex] form a linear pair, they add to 180 degrees. So, [tex]\angle 2=83^{\circ}[/tex]
535(-8) ??? What is the answer
Answer: the answer is -4280
Step-by-step explanation:
The relationship between time and the number of laps is not proportional across all swimmers. which two swimmers swam at the same rate (had time and laps in the same proportion)?
Answer: Undefined
Step-by-step explanation:
There is not enough information to complete the task.
Answer:
Jonathan and Seth
Step-by-step explanation:
multiple the laps by 2 youll get the minutes
Evaluate: -6 × (-4)
= Enter your next step here
() TO
Answer:
24
Step-by-step explanation:
-6*(-4)
The negative signs cancel:
6*4
24
The sum of the angle measures of a polygon with s sides is 2,340 degrees. Find s.thank you ! :)
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The sum of interior angles of a polygon is:
[tex]\begin{gathered} (s\text{ -2 \rparen x 180}^0=\text{ 2340}^0\text{ , where s = number of sides} \\ Divide\text{ both sides by 180}^0,\text{ we have that:} \\ s\text{ - 2 = 13} \\ s\text{ = 13 + 2} \\ s\text{ = 15} \\ \end{gathered}[/tex]CONCLUSION:
The final answer is:
[tex]s\text{ = 15}[/tex]