ANSWER:
$ 117.51
STEP-BY-STEP EXPLANATION:
The commissions are divided into two payments, the first payment of the first $ 1500 with a commission of 3.16% and a second payment with a commission of 11% of all the remaining money of the first $ 1500.
Therefore, we calculate it as follows:
[tex]\begin{gathered} p_T=p_1+p_2 \\ p_1=1500\cdot\frac{3.16}{100}=47.4 \\ p_2=(2137.38-1500)\cdot\frac{11}{100}=637.38\cdot0.11=70.11 \\ p_T=47.4+70.11 \\ p_T=117.51 \end{gathered}[/tex]The total commission is $ 117.51
Find the ordered pairs for the x- and y-intercepts of the equation 8x - 2y = 16 and select the appropriate option below. The x-intercept is (-2, 0), the y-intercept is (0, 8). The x-intercept is (0, 2), the y-intercept is (-8, 0). The x-intercept is (2, 0), the y-intercept is (0, -8). The x-intercept is (0, -2), the y-intercept is (8, 0).
The given equation is
[tex]8x-2y=16[/tex]To find the x-intercept, we make y = 0.
[tex]\begin{gathered} 8x-2\cdot0=16 \\ 8x-0=16 \\ 8x=16 \\ x=\frac{16}{8} \\ x=2 \end{gathered}[/tex]Hence, the x-intercept is (2,0).To find the y-intercept, we make x = 0.
[tex]\begin{gathered} 8\cdot0-2y=16 \\ 0-2y=16 \\ -2y=16 \\ y=-\frac{16}{2} \\ y=-8 \end{gathered}[/tex]Hence, the y-intercept is (0,-8).3. For the sequence defined by tn = 3n + 8,find each indicated term.a) t1b) t7c) t14
The sequence is given by .
[tex]t_n=3n+8[/tex]a. The indicated term
[tex]t_1=3(1)+8[/tex][tex]t_1=3+8[/tex][tex]t_1=11[/tex]b. The indicated term
[tex]t_7=3(7)+8[/tex][tex]t_7=29[/tex]c. The indicated term
[tex]t_{14}=3(14)+8[/tex][tex]t_{14}=42+8[/tex][tex]t_{14}=50[/tex]
16) A bottle of high blood pressure medication contains 90 tablets. Each tablet contains 150 mg of the active ingredient. How many grams of the active ingredient are in the entire bottle? Hint: 1 gram = 1,000 mg
One tablet contains 150 mg of the active ingredient. Then, 90 tablets contain
[tex]90\text{ tablets }\cdot\frac{150\text{ mg}}{1\text{ tablet}}=13500mg_{}[/tex]1 gram is equivalent to 1,000 mg, then 13500 mg is equivalent to
[tex]13500\text{ mg}\cdot\frac{1\text{ gram}}{1000\text{ mg}}=13.5\text{ grams}[/tex]There are 13.5 grams of the active ingredient in the entire bottle
Give the domain of definition of the function and find the asymptotes to the following function y = arctan 1/x - x
we have the function
[tex]y=arctan(\frac{1}{x}-x)[/tex]using a graphing tool
see the attached figure below
The domain is all real numbers except for x=0
The range is the interval (-pi/2, pi/2)
there are horizontal asymptotes at
y=pi/2 and y=-pi/2
solve the equation: y+2.4=15.6
Use the properties of equalities to solve the given equation:
[tex]y+2.4=15.6[/tex]Substract 2.4 from both sides of the equation:
[tex]\begin{gathered} y+2.4-2.4=15.6-2.4 \\ \Rightarrow y=13.2 \end{gathered}[/tex]Therefore, the solution to the equation is:
[tex]y=13.2[/tex]у 10 8 P 4 2 0 2 6 8 10 Which ordered pair represents the location of point P on the coordinate plane? a (5,6) b (6,5) (6,7) d (7,6)
The ordered pair that represents the location of point P is (6,5)
Explanation:
In order to determine the position of point P, we will need to trace its position to the x axis and also trace its position to the y axis.
Tracing its position to the x axis, we find it corresponds to 6 units
Tracing its position to the y axis, we find it corresponds to 5 units.
This because each line represents 1 units. After the 4 units, the next line is 5 units.
Using the coordinates (x,y):
The ordered pair that represents the location of point P is (6,5)
jodie has 2 1/2 cases of soda to split between 5 families. what fraction of a case does each family receive?
We have in total 2 1/2 so we need to divide this in 5 equal parts
First we will convert our mixed number into a fraction
[tex]2\frac{1}{2}=\frac{4}{2}+\frac{1}{2}=\frac{5}{2}[/tex]Then we divide between 5
[tex]\frac{5}{2}÷\frac{5}{1}=\frac{5\ast1}{2\ast5}=\frac{1}{2}[/tex]ANSWER
1/2 case
Find the equation (in terms of x) of the line through the points (-4,-5) and (1,5)
Solution:
Step 1: Find the slope of the line:
Given the points (X1, Y1)=(-4,-5) and (X2, Y2)= (1,5), we have that the slope of the line that passes through the points (-4,-5) and (1,5) is:
[tex]m=\frac{Y2-Y1}{X2-X1}=\frac{5+5}{1+4}=\frac{10}{5}=2[/tex]Step 2: Write the provisional equation of the given line. If the slope of the line is m=2, we get that the provisional equation of this line is:
[tex]y\text{ =2x+b}[/tex]Step 3: Find the y-intercept b. Take any point (x,y) on the line and replace its coordinates into the above equation and then solve for b. For example, take the point (x,y)=(1,5), then we obtain:
[tex]5\text{ =2(1)+b}[/tex]this is equivalent to:
[tex]5\text{ =2+b}[/tex]solving for b, we get:
[tex]b\text{ = 5-2 = 3}[/tex]that is:
[tex]b\text{ = 3}[/tex]Step 4: Write the equation of the line. If the given line has slope m=2 and y-intercept b = 3, then its equation would be:
[tex]y\text{ =2x+}3[/tex]and in terms of x, this is equivalent to:
[tex]f(x)=2x+3[/tex]So that, we can conclude that the correct answer is:
[tex]f(x)=2x+3[/tex]Write 5e slopes as a fraction or improper fraction using a slash
Given:
Given a graph of the function.
[tex]\begin{gathered} (x1,y1)=(0,3) \\ (x2,y2)=(-5,0) \end{gathered}[/tex]Required:
To find the slope.
Explanation:
The slope is
[tex]\begin{gathered} m=\frac{y2-y1}{x2-x1} \\ \\ =\frac{0-3}{-5-0} \\ \\ =\frac{-3}{-5} \\ \\ =\frac{3}{5} \end{gathered}[/tex]The y-intercept is at (0,3).
Final Answer:
The slope is : 3/5.
y-intercept : (0,3)
2. What is the equation of the line that passes through (5, 2) and isperpendicular to y =10x + 7?AC.y10x +yX+1021y = 10x - 4810B.-+52+52D.
Step 1
Given; What is the equation of the line that passes through (5, 2) and is
perpendicular to y =
10x + 7?
Step 2
The slope of the given line is;
[tex]\begin{gathered} m=10 \\ since,\text{ when we compare y=mx+b} \\ m=10 \end{gathered}[/tex]Slope of perpendicular lines have the following relationship;
[tex]\begin{gathered} m_1=-\frac{1}{m_2} \\ 10=-\frac{1}{m_2} \\ m_2=-\frac{1}{10} \end{gathered}[/tex]Therefore the required equation will be in the form of;
[tex]\begin{gathered} y=-\frac{1}{10}x+b \\ y=2 \\ x=5 \end{gathered}[/tex]Find b, the y-intercept
[tex]\begin{gathered} 2=-\frac{1}{10}(5)+b \\ 2=-\frac{1}{2}+b \\ 4=-1+2b \\ 2b=5 \\ b=\frac{5}{2} \end{gathered}[/tex]Thus the answer will be; Option B
[tex]\begin{gathered} y=-\frac{1}{10}x+\frac{5}{2} \\ \\ \\ \\ \end{gathered}[/tex]
Translate the figure 1 unit left and 3 units down.Plot all of the points of the translated figure.You may click a plotted point to delete it.-10--54 - -3 4 5 6 7
The coordinates of the quadrilateral after translation will be : A'( 0 , 6 ) , B'( 6 , 4) , C'( 0 , 1 ) and D'( 4 , -2 )
The given quadrilateral in the graph has the coordinates:
A(1,8) , B(7,7) , C(1,4) , D(5,4)
When this figure is translated 1 unit to the left and 3 units downwards we get :
A ( 1 , 8 ) → A'( 0 , 5 )
B ( 7 , 7 ) → B'( 6 , 4 )
C ( 1 , 4 ) → C'( 0 , 1 )
D ( 5 , 4 ) → D'( 4 , 1 )
Hence the translated figure will have the coordinates:
A'( 0 , 6 ) , B'( 6 , 4) , C'( 0 , 1 ) and D'( 4 , -2 ) .
In Euclidean geometry, a translation or transformation is still a geometric change that entails shifting every point in a figure, shape, or space uniformly in one direction.
Moving the origin of the coordinate system or adding a constant vector to each point are other ways to conceptualize translation.
to learn more about translation visit:
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Question 9 of 10What is the length of AB?O A. 3B. 6O c. 9O D. 12
Answer:
Step-by-step explanation:
c. it is the answer
CM Bookmarks Geometry Unit 11 Test Area of Plane Figures E CALCULATOR • colo a a noosa 12. Find the area of the shaded region of the figure
It is a trapezoid
[tex]\begin{gathered} \text{ Area = h}\frac{B\text{ + b}}{2} \\ \text{Area = 4}\cdot\text{ }\frac{16\text{ + 6}}{2} \\ \text{Area = 4}\cdot\frac{22}{2} \\ \text{Area = }\frac{88}{2} \\ \text{Area = 44 mm}^2 \end{gathered}[/tex]
I need help with this math question all parts pleasePart 2: find y-interceptPart 3: find the zerosPart 4: Graph k(x)
Given the following function:
[tex]k(x)=x^3-5x^2[/tex]We will find the end behavior of the function.
the given function has a degree = 3 (odd)
And the leading coefficient is positive
the end behavior will be as follows:
[tex]\begin{gathered} x\to-\infty\Rightarrow k(x)\to-\infty \\ x\to\infty\Rightarrow k(x)\to\infty \end{gathered}[/tex]So, the answer will be:
The end behavior of the function is down to the left and up to the right.
===============================================================
Part (2), we will find the y-intercepts
The y-intercept is the value of y when x = 0
So, we will substitute x = 0 and then solve y
[tex]y=0^3-5(0^2)=0[/tex]So, the answer will be:
y-intercept = (0, 0)
================================================================
Part 3: we will find the zeros of k(x)
The zeros of the function are the values of x which make k(x) = 0
So, we will write the equation k(x) = 0 and then solve it for x.
[tex]\begin{gathered} x^3-5x^2=0 \\ x^2(x-5)=0 \\ x^2=0\to x=0 \\ x-5=0\to x=5 \end{gathered}[/tex]So, the answer will be:
Zeros of k: 0,5
===============================================================
Part 4: we will find the graph of k(x)
From the previous parts, we can conclude that
The graph of the function will be as shown in option D
Solve the following system using the substitution method. Enter your answer as an ordered pair in the form (x,y).3x - 2y = -95x + 10y = - 5
Given,
[tex]\begin{gathered} 3x-2y=-9\ldots\ldots\ldots(1) \\ 5x+10y=-5\ldots\ldots\text{.}(2) \end{gathered}[/tex]Multiply 1st equation by 5.
[tex]\begin{gathered} 5(3x-2y=-9) \\ 15x-10y=-45\ldots\ldots\text{.}(3) \end{gathered}[/tex]Solve equations (2) and (3)
[tex]\begin{gathered} 20x=-50 \\ x=\frac{-5}{2} \end{gathered}[/tex]Put x =-5/2 in equation (1)
[tex]\begin{gathered} 3x-2y=-9 \\ 3\times\frac{-5}{2}-2y=-9 \\ \frac{-15}{2}-2y=-9 \\ -2y=-9+\frac{15}{2} \end{gathered}[/tex]Further solved as,
[tex]\begin{gathered} -2y=\frac{-45+15}{5} \\ -2y=\frac{-30}{5} \\ -2y=-6 \\ y=3 \end{gathered}[/tex]Therefore, the value of x and y is -5/2 and 3.
2. Given that the indicated lines in figure 10.30(a) are parallel, determine the unknown angles without actually measuring them. Explain your reasoning briefly.
The opposie angles are equal
c is opposite to a, so
[tex]c=a=34^o[/tex]The angle p is opposite to that of n, so
[tex]p=118^o[/tex]The total angle of rotation in a line is 180°. so,
[tex]o=180-118=62[/tex]This o is the oppsite to m, and hence m=o.
similarly,
[tex]d=180-34=146[/tex]And hence, b=d=146
A right triangle has a hypotenuse of 18 feet and a side length opposite of 12 feet . What is the measure of angle A the nearest degree ?
can you PLEASE help me
In this problem we know that
Applying the exterior angle theorem
10x+30=58+(7x-1)
solve for x
10x-7x=57-30
3x=27
x=9Find m
mm
Find mmm
Write an expression in simplest form that represents the income from w women and m men getting a haircut and shampoo. Women: haircut $45 shampoo $12. Men: haircut $15 shampoo $7
Write an expression in simplest form that represents the income from w women and m men getting a haircut and shampoo. Women: haircut $45 shampoo $12. Men: haircut $15 shampoo $7
the income is equal to
45w+12w+15m+7m
combine like terms
57w+22m
total income=57w+22mwhere
w is the number of women
m is the number of men
the image is downloading nowabout 15%is too slowlyDo you can write the question?Study PathsTestPlacement Test Williston State College 2018 Study PathTestInit: GeometryogressQuestion ID: 1191695The movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answerFind the circumference of a circle with a diameter of 13 meters. Use 3.14 as an approximation for E. Round your answer to thenearest whole meter. Enter only the numberThe solution isSubmitPassDon't know answerSave and close
Explanation:
The question wants us to obtain the circumference of the circle given that the diameter of the circle is 13 meters.
To do so, we will use the formula:
[tex]\begin{gathered} Circumference=\pi D \\ Where \\ \pi=3.14 \\ D=diameter=13\text{ meters} \end{gathered}[/tex]Therefore, the circumference will be
[tex]Circumference=3.14\times13=40.82\text{ }meters[/tex]Rounding off to the nearest whole number, we will have 41 meters
see image for question
The angle of rotation = 19.35°
Explanations:The diameter of the ferris wheel = 225 feet
Radius, r = diameter/2
r = 225/2
r = 112.5 feet
The passenger travels 38 feet when the wheel stops
This is the arc length
Arc length = 38 feet
Using the formula for the length of an arc
[tex]\text{Arc length = }\frac{\theta}{360}\times2\text{ }\pi\text{ r}[/tex][tex]\begin{gathered} 38\text{ = }\frac{\theta}{360}\times2\times\frac{22}{7}\times112.5 \\ \theta\text{ = }\frac{38\times360\times7}{2\times22\times112.5} \\ \theta\text{ = }\frac{95760}{4950} \\ \theta\text{ = }19.35^0 \end{gathered}[/tex]The angle of rotation = 19.35°
Male and females high school students reported how many hours they worked each week in summer jobs . The data represented in the following box plots
Answer:
The correct answer is c.
Step-by-step explanation:
Boys:
Range from 0 to 15 hours worked.
The third quartile, which is shown by the line in the box, is of 10 hours.
Females:
More bunched together, ranging from 15 to 20 hours worked, with a median, shown by a line on the middle of the box, of 17.5.
However, the line for females begins at around 1 hour, far from the median, which means that there is a significant outlier at the low end for females.
The correct answer is c.
Usually it takes Mrs. Manny 5.2 hours to grade her students' assignments. Thisweekend, her daughter Lexi is home and has offered to help. If it would take Lexi 6.4hours to grade the papers alone, how long will it take the two to finish the task of grading,working together?
Mrs. Manny needs 5.2 hours to grade her students' assignments. It would take Lexi 6.4 hours to grade the assignments alone.
In one hour, Mrs. Manny completes 1 / 5.2 = 0.1923 of the work.
In one hour, Lexi completes 1 / 6.4 = 0.15625 of the work
Together, they complete 0.1923 + 0.15625 = 0.34856 of the work.
The full work would take them 1 / 0.34856 = 2.87 hours.
It would take 2.87 hours for them to finish the task together.
Question Joan invested $1,420 at the start of the year and found she had $1,621.40 at the end of the year. What is the annual effective yield of her investment? Input your answer as a percentage rounded to two decimal.
Money invested = $1420
Final money = $1621.4
Effective yield = [ 1 + i/n]^n - 1
i = nominal rate let's consider 10%
n = number of payments 12 payments because it is in a year
Effective yield = [1 + 0.1/12]^12 - 1
= [ 1 + 0.00833]^12 - 1
= [1.0083]^12 - 1
= 1.1 - 1
Effective yield = 0.10 %
About 13 out of 20 homes have a personalcomputer. On a street with 60 homes, howmany would you expect to have a personalcomputer?
Answer:
On a street with 60 homes, the number of homes expected to have a personal computer is;
[tex]39\text{ }[/tex]Expected
Given that;
About 13 out of 20 homes have a personal computer.
It means that;
[tex]\frac{13}{20}\text{ PC/home}[/tex]Out of 60 homes, the expected number of homes with PC is;
[tex]\begin{gathered} n=\frac{13}{20}\times60 \\ n=39 \end{gathered}[/tex]Therefore, On a street with 60 homes, the number of homes expected to have a personal computer is;
[tex]39\text{ }[/tex]Jenny has a deck of 52 alphabet cards (26 uppercase and 26 lower case). Jenny selects one card.What is the probability that she selects a vowel?
We know that we have five vowels in the alphabet. Since the deck has uppercase and lower case cards this means that it has a total of 10 vowels.
The probability is given by the quotient between the number of favorable outcomes and the number of total outcomes; then in this case we have:
[tex]P=\frac{10}{52}=\frac{5}{26}[/tex]Therefore the probability of selecting a vowel is 5/26
it's a graph, I need help with the first one to understand how to do the rest. Please draw it clearly and understandably.
1) In this inequality 3x ≥ 9 we have to find a set of values for x.
3x ≥ 9 Divide both sides by 3
x ≥3
2) We can express this set of solutions in the number line as well. Since is greater than or equal to we'll use a closed dot. To include this 3.
3) Hence the graph above represents that every value greater than and the 3 satisfies the restraint x ≥3.
John makes 15 goals for every 25 shots he attempts. How many
goals can you expect John to miss if he shoots 75 shots in a
season?
Answer:
45 goals
Step-by-step explanation:
g = # of goals
s = # of shots
15g = 25s
45g = 75s
25 x 3 = 75
15 x 3 = 45
Answer:
30 missed shoots expected================
Ratio of goals per shoots:
g : s = 15 : 25If the number of shoots is 75, then number of goals is proportional:
g : 75 = 15 : 25g = 75 × 15 : 25g = 45Number of missed shoots:
75 - 45 = 30i need help please with m and b#1 and graph
ANSWER
• m = 2
,• b = -5
EXPLANATION
This equation is written in slope-intercept form,
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
In this case, the slope is m = 2 and the y-intercept is b = -5. This tells us that the line intersects the y-axis at y = -5, so that is our first point. Then, we can find the next point using the slope,
[tex]m=2=\frac{\Delta y}{\Delta x}[/tex]The next point is 1 unit to the right of the y-intercept, and 2 units up,
To draw a line we only need two points, so we have to draw a line passing through these two points.
About how far does the flag have to travel to complete full rotation?1. 37.68 ft2. 75.36 ft3. 150.72 ft4. 452.16 ftPlease explain if possible!
Due to the circular shape, one complete rotation of the flag is equal to the circumference of a circle with radius 12 ft.
Then, use the following formula for the cirumference:
C = 2π·r
where r is the radius. In this case, r = 12 ft and π = 3.14. Replace the previous values into the formula for C:
C = 2(3.14)(12 ft)
C = 75.36 ft
Hence, the flag has to travel 75.36 ft to complete a full rotation