Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.
As given in the question,
Macro earns commission rate of 6% for the first $6500
And 9% on sales over $6500
Out of $10,500
For first $6500 Commission =(6500 × 6)/ 100
= $390
For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100
= $360
Total graduated commission on sales of $10,500 = $( 390 + 360)
= $750
Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.
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Can someone PLEASE give me the solution to this question, my exams in 2 days.
Answer:
see explanation
Step-by-step explanation:
the shaded area is calculated as
outer circle area - inner circle area
since CAB is a tangent to the inner circle at A then OAB = 90° and
Δ OAB is right
using Pythagoras' identity in the right triangle to express R in terms of r and d , then
R² = d² + r²
------------------------------------------
A( outer Δ ) = πR² = π(d² + r² ) = πd² + πr²
A ( inner Δ ) = πr²
Then
shaded area = πd² + πr² - πr² = πd²
The table shows the numbers y of students absent from school x days after a flu outbreak.
Write a function that models the data.
Use the model to approximate the number of students absent 10 days after the outbreak.
A scatter plot can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.
What is a quadratic function?A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is given by;
ax² + bx + c = 0
By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the quadratic function is given by:
y = -0.4908x² + 5.8845x + 1.3572
For the number of students that are absent 10 days after the outbreak, we have:
y = -0.4908(10)² + 5.8845(10) + 1.3572
y = -0.4908(100) + 58.845 + 1.3572
y = -49.08 + 58.845 + 1.3572
Number of students, y = 11.12 ≈ 11 students.
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does anybody know this? i’ve been struggling for hours
12 lies between 9 and 16 so √12 lies between 3 and 4.
Perfect square-: Those whole numbers in which we can pair the factors are known as perfect square.
We can write the number 40 as 2 × 2 × 2 × 5. This is not a perfect square because we cannot pair the factors.
Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.
We write 40−−√ to be the square root of 40, and can investigate between which two whole numbers it lies.
Consider the table of perfect squares below:
Whole number 1 2 3 4 5 6 7 8 9 10 11 12
Whole number squared 1 4 9 16 25 36 49 64 81 100 121 144
The number 40 lies between 36 and 49 hence 40−−√ lies between 6 and 7.
Similarly, 12 lies between 9 and 16 so √12 lies between 3 and 4.
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The temperature dropped from 27 degrees to -4 degrees in one day. Write and solve an expression to represent the
change in degrees. also with give branly to who answers first
Answer:
See explanation
Step-by-step explanation:
d=degree change
d=-4-27
d=-31 degrees
List all pairs of congruent angles, and write a proportion that relates the corresponding sides for each pair of similar polygons.
J K L M ≅ TSRQ
Pairs of congruent angles are: ∠J ≅ ∠T; ∠K ≅ ∠S; ∠L ≅ ∠R; ∠M ≅ ∠Q
A proportion of their corresponding sides is: JK/TS = KL/SR = LM/RQ = JM/TQ
What are Similar Polygons?When two polygons are similar to each other, they have the same shape but different sizes. Therefore, they will have pairs of angles that are congruent to each other and pairs of corresponding sides that have ratios that are the same, which means they have the same proportion.
Given polygons JKLM and TSRQ, the corresponding congruent angles are:
∠J ≅ ∠T
∠K ≅ ∠S
∠L ≅ ∠R
∠M ≅ ∠Q
A proportion of their corresponding sides would be:
JK/TS = KL/SR = LM/RQ = JM/TQ
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Can someone help plss
Answer:
Make y the subject of the formula which will give the answer below
y=1/3x-3
select C
How do you know the difference between a odd, even, and neither graph?
Answer: Even functions
Symmetric about the yy-axis
When you plug -x−x into the function, it will simplify to be the same as the original function. This means that it doesn’t matter whether you plug in xx or -x−x, your output will be the same. So
f(-x)=f(x)f(−x)=f(x)
Below are graphs that are even and symmetric about the yy-axis.
even functions are symmetric about the y-axis
Odd functions
Symmetric about the origin
When you plug -x−x into the function, it will simplify to be negative of the original function, or the original function multiplied by -1−1. This means that when you plug -x−x into the function, you’ll get the same output as you do when you plug in xx, except it will be negative (or have the opposite sign as the original output). So
f(-x)=-f(x)f(−x)=−f(x)
Below are graphs that are odd and symmetric about the origin. Be sure to visually compare quadrants that are diagonal from each other (quadrants 1 and 3, and quadrants 2 and 4).
odd functions are symmetric about the origin
Neither even nor odd
Not symmetric about the yy-axis, and not symmetric about the origin
The function has no symmetry. It’s possible that a graph could be symmetric to the xx-axis, but then it wouldn’t pass the Vertical Line Test and therefore wouldn’t be a function.
functions that are neither even nor odd
hope this helps!!
Think About the Process The length of cell A is 2x107 m. The length of cell B is 0.00000001 m. What is the ratio of cell A's length to cell B's length? Use pencil and paper. Is it easier to find the
ratio when the numbers are expressed in scientific notation or in standard form? Explain your reasoning
The ratio of cell A's length to cell B's length is [tex]2\times10^{15} :1[/tex]
In mathematics, a ratio is a comparison of two or more numbers, indicating their magnitude relative to each other. A ratio compares two quantities by division. The dividend or divisor is called the antecedent and the divisor or divisor is called the sequence.Scientific notation is a form of representing very large or very small numbers in a simpler form.It is given that length of cell A is [tex]2\times10^7m[/tex] which is in scientific notation and length of cell B is 0.00000001 m which is in standard form.
On converting length of B in scientific notation , we get
[tex]0.00000001 =1.0\times10^{-8}m[/tex]
The ratio of length A to length B is given by
[tex]\frac{2\times10^7}{1.0\times10^{-8}} =\frac{2\times10^{15}}{1}[/tex]
which can be written as [tex]2\times10^{15} :1[/tex]
Yes, finding ratios is easier when numbers are represented in scientific notation. This is because scientific notation is a mathematical methodology used to describe very large or very small numbers in a compact and simple form, raised to powers of ten.
Hence , it is easier to calculate or solve mathematical operations using numbers in scientific notation.
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Tiffany has taken out a loan with a stated interest rate of 8.145%. how much greater will tiffany’s effective interest rate be if the interest is compounded weekly than if it is compounded semiannually? a. 0.3340 percentage points b. 0.1659 percentage points c. 0.1681 percentage points d. 0.1234 percentage points please select the best answer from the choices provided a b c d
Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually.
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
Given,
The interest rate i= 8.145%
Number of weeks in an year n= 52
We know,
Effective interest rate =[tex](1+\frac{i}{n})^{n}-1[/tex]
Substitute the values
[tex]R_{1}=(1+\frac{0.08145}{52})^{52}-1\\ R_{1}= 0.084789[/tex]
Case 2
Compounded semiannually
[tex]R_{2}=(1+\frac{0.08145}{2})^{2}-1\\ R_{2}=0.083108[/tex]
The difference is
[tex]R_{1}-R_{2}= 0.084789-0.083185[/tex]
=0.001604
=0.1604%
Hence, the Tiffany's effective interest is compounded weekly is 0.1604% greater than the compounded semiannually
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Which of the following is equal to 7 1/3
A. √7
B. √7.3
C. 73
D. 3√7
Given E(-2,4), F(-7,-4), G(-5,2),E(−2,4),F(−7,−4),G(−5,2), and H(x, -6). Find x such that EF∥GH.
Two lines are said to be parallel when slopes are same. If EF∥GH and E(−2,4),F(−7,−4),G(−5,2), and H(x, -6) then x is -3.
What are Parallel lines?Parallel lines are straight lines that never meet each other no matter how long we extend them.
Given;
G(-5,2),E(−2,4),F(−7,−4),G(−5,2), and H(x, -6).
Two lines are said to be parallel when slopes are same.
The equation of line passing through two points is y-y1=m(x-x1)
where m is the slope
The equation of line EF is
y-4=8/5(x+2)
Here slope is 8/5.
The equation of line GH is
y-2=-8/(x-2)(x+5)....*
As the two lines are parallel, the slopes must be equal.
In * the slope should be 8/5,so
x-2=-5
x=-3
Therefore the value of x is -3.
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4. The store offers a similar deal if you purchase the $139.95 workouts but with a 20% off discount
instead of 15% for purchases over $1000. The home gym she'd really like, the Shredmaster 5000,
costs $1199 before-tax. Write a new function, g(x) for this second deal and calculate the
before-tax cost of the Shredmaster 5000.
the price of the Shredmaster 5000 will be $ 959.2 and the function is g (x) = 0.8 x for x > 1000.
If the purchase is made for $ 1000 and above. the discount = 20 %
Now the cost of Shredmaster 5000 = $ 1199
Now, the price after the discount will be
Price = 1199 - 20 % of 1199
Price = 1199 - 20 / 100 × 1199
Price = 1199 - 0.20 × 1199
Price = 1199 - 239.8
Price = $ 959.2
The function will be:
g (x) = x - 0.2 x
g (x) = 0.8 x for x > 1000.
Therefore, the price of the Shredmaster 5000 will be $ 959.2 and the function is g (x) = 0.8 x for x > 1000.
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a board measures 212 inches. how many feet is this? [ ? ] ft. give your rounded answer with one decimal place.
Answer:17.67
Step-by-step explanation:
Which of the following could be the same graph as y=-2x+5
The equation shows that the slope of the line is -2 and the y-intercept is 4 that is the line will pass through the point (0, 5)
Graphing linear equationThe standard linear equation is expressed as y = mx + b where;
m is the slopeb is the y-interceptGiven the linear equation y=-2x+5
The equation shows that the slope of the line is -2 and the y-intercept is 5 that is the line will pass through the point (0, 5)
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Find the coordinates of the missing endpoint if M is the midpoint of Ab B(-7 , 16) and M (-2 , 8)
If M is the midpoint of AB , B(-7,16) and M(-2,8) then coordinates of the missing endpoint A are (3,0).
As given in the question,
M is the midpoint of AB
Let coordinates of A(x₁ ,y₁) , B(x₂ ,y₂) and M(x ,y)
So,
x = (x₁ + x₂)/2
⇒-2 = (x₁ + (-7))/2
⇒ x₁ = 7-4
⇒x₁ =3
y = (y₁+ y₂)/2
⇒8 = (y₁ +16)/2
⇒ y₁ = 16-16
⇒ y₁ =0
Therefore, if M is the midpoint of AB , B(-7,16) and M(-2,8) then coordinates of the missing endpoint A are (3,0).
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The shape of a dome can be
modeled by the equation h =
- 2d^2 + 100 where h is the height
(in feet) of the dome from the
floor d feet from its center. How
far from the center of the dome
is the height 50 feet?
Answer:
5 feet
Step-by-step explanation:
We are told that the height of the dome can be modelled by the equation:
[tex]\boxed{h = -2d^2 + 100}[/tex]
The question is essentially asking us: for what value of d will the value of h be 50 feet?
To solve this, we have to substitute h in the equation with 50 and then solve for d.
∴ [tex]50 = -2d^2 + 100[/tex]
⇒ [tex]50 + 2d^2 + 100[/tex]
⇒ [tex]2d^2 = 100 - 50[/tex]
⇒ [tex]d^2 = \frac{100 - 50}{2}[/tex]
⇒ [tex]d^2 = 25[/tex]
⇒ [tex]d = \sqrt{25}[/tex]
⇒ [tex]d = \bf 5[/tex]
This means that 5 feet from the center of the dome, the height of the dome is 50 feet.
The options are
A. (6, 3)
B. (1, -4)
C. (2, 1)
D. (0, 3)
Answer:
Correct answer is D.
Step-by-step explanation:
A. 6 = 3-3 ×
B. 1 = -4-3 ×
C. 2 = 1-3 ×
D. 0 = 3-3 ✓
A house cost $150,000 and you give 10%. The amount of mortgage is. a. 135,000
B.130,000 C.125,000 D.145, 000
Answer:
Your answer is C.125,000
Step-by-step explanation:
. What is a solution of x² + 6x = -5?
Ox=-6
Ox=-1
Ox=1
Ox=6
Answer:
x = -1
Step-by-step explanation:
x² + 6x = -5
x² + 6x -( -5) = 0
Use the quadratic formulaEvaluate the exponentMultiply the numberSubtract the numberEvaluate the square rootMultiply the numberx = (-x + 4)/2
Separate the equationsTo solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
x = (-6 + 4)/2
x = (-6 - 4)/2
Rearrange and isolate the variable to find each solutionx = -1
lol last one before i have to watch another lesson love yall
Hey there!
4a + 1 + a + 3
= 4a + 1 + 1a + 3
COMBINE the LIKE TERMS:
= (4a + 1a) + (1 + 3)
= (4a + a) + (1 + 3)
= 4a + a + 1 + 3
= 5a + 4
Therefore, your answer should be:
5a + 4
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
this is a pond in the shape of a prism it is completely full of water Collin uses a pump to empty the pond the level goes down by 20cm in the first 30 mins work out how many minutes Colin has to wait until the pond is completely empty
To empty the tank in the shape of prism completely, Colin has to wait 150 minutes for the water of the pond to at zero level.
What is the prism volume formula?
V=Bh, where B is the base area and h is the height, is the formula for a prism's volume. The prism has a rectangular base. The rectangle measures 9 cm in length and 7 cm in breadth. A rectangle's area A is equal to its length l and width w.Given :
A pond in the shape of a prism.
Colin uses a pump to empty the pond. The level goes down by 20 cm in the first 30 minutes.
Solution :
We know that the volume of the prism is given by,
Volume = ( Base area ) × height
Base area = 1/2 ( 1.4 + 0.6 ) × 2 ⇒2 m²
Volume = 2 × 1 = 2m³
Given that the level of pond goes down by 20 cm in the first 30 minutes. Therefore, the volume becomes,
Volume = 2 × 0.8 = 1.6m³
Now, the rate of emptying the tank is,
[tex]= \frac{2 - 16}{30} = \frac{1}{75}[/tex] m³/min
time = volume / rate
= [tex]\frac{2}{\frac{1}{75} }[/tex] = 150
Therefore, Colin has to wait 150 minutes for the pond to completely empty
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does x+6=x have one solution, no solution, or infinite solutions?
Answer:
infinite solution
Step-by-step explanation:
because thats the right answers
The temperature on Wednesday at 5:00 p.m. was 15°F. In the following 12 hours, the temperature dropped 22°F. The temperature on Thursday at 5:00 p.m. was 27°F.
Part A: What was the temperature on Thursday at 5:00 a.m.? Explain or show how you got your answer.
The temperature on Thursday at 5:00 a.m. was
The temperature required on Thursday at 5:00 a.m. was observed as -7°F
given,
The temperature on Wednesday at 5:00 p.m. = 15°F
the temperature dropped 22°F in the following 12hours
The temperature on Thursday at 5:00 p.m. was 27°F.
the temperature on Thursday at 5:00 a.m. is calculated with a vertical number line.
number line - A number line is defined as the number marked on the line calibrated into an equal number of units.
For example -1, 0, 1, and so on.
Thus, the temperature on Thursday at 5:00 a.m. is
=15° - 22°
= -7°
The temperature required on Thursday at 5:00 a.m. was observed as -7°F
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Write the additive inverse of -7.
worth 20 points
Answer:
7
Step-by-step explanation:
a=additive inverse of -7
-7+a=0
-7+7+a=0+7 ==> add 7 on both sides to isolate 'a'
a=7
given y left parenthesis z right parenthesis equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction determine the final value
The simplification of the given algebraic expression is;
yz = (z + 1)/z(z - 1)
How to simplify algebraic expressions?We are given y left parenthesis z right parenthesis which is expressed as; yz
Now, we are given the algebraic expression that yz equals space fraction numerator z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction
z squared minus 1 over denominator z left parenthesis z minus 1 right parenthesis squared end fraction is expressed as; (z² - 1)/z(z - 1)²
Thus, our main expression is;
yz = (z² - 1)/z(z - 1)²
Factorizing the numerator and denominator gives;
yz = (z + 1)(z - 1)/z(z - 1)(z - 1)
(z - 1) is common to both numerator and denominator and as such, we now have;
yz = (z + 1)/z(z - 1)
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while standing in front of the school, jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.
The method used to collect data for the given scenario is: observational study.
What is observational study?Observational study refers to a study design in which subjects are watched or specific outcomes are gauged. No effort is taken to influence the result (for example, no treatment is given).Now,
In the given scenario, Jace is taking records by observing all the students who are walking or riding the bike or taking the bus and are being driven, all by himself.He is taking notes and writing each and every student's respective mode of transportation.Hence, the method used to collect data is observation, i.e., observational study is being made here.
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(COMPLETE QUESTION:
Use the drop-down menus to identify the method used to collect data for each scenario.
While standing in front of the school, Jace recorded the number of students who walked, rode their bikes, took the bus, and were driven there.)
Please help! radicals.
(Check picture)
Answer:
10√2
Step-by-step explanation:
You want the simplified form of the radical expression 2√200 -10√2.
SimplificationRadicals are simplified by removing perfect squares from under the radical. Radicals with the same radicand are "like terms" and can be combined.
[tex]2\sqrt{200}-10\sqrt{2}=2\sqrt{10^2\cdot2}-10\sqrt{2}\\\\=2\cdot10\sqrt{2}-10\sqrt{2}=(20-10)\sqrt{2}=\boxed{10\sqrt{2}}[/tex]
Answer:
[tex]10 \sqrt{2} [/tex]
Step-by-step explanation:
Simplify.
[tex]2 \sqrt{200} \\ = 2 \sqrt{100 \times 2 } \: \: \: \: \\ = 2 \sqrt{100} \times \sqrt{2} \\ = 2 \times 10 \times \sqrt{2} \\ = 20 \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
Now let us solve the given expression.
[tex]2 \sqrt{200} - 10 \sqrt{2} \\ 20 \sqrt{2} - 10 \sqrt{2} \\ 10 \sqrt{2} [/tex]
6. Write the following numbers in expanded exponential form:
a) 74009234 =
Answer:
74,009,234= 7^6+ 9^3+2^2+3^1+4^0
Step-by-step explanation:
PLEASE HELP!!!! I WILL MARK BRAINLIEST!!!
Find a quadratic equation that models the decline in physical recorded music revenue (not digital).Let x=number of years since 2000 and y be the physical recorded music revenue in millions of dollars.
PLEASE HELP!!!! I WILL MARK BRAINLIEST!!!
The rate of decrease in the revenue reduces each year, resulting in an
approximate quadratic equation model that is concave upwards.
The variables are;
x = Number of years since 2,000
y = Revenue for physically recorded music in millions of dollars
Find out -
To model the decline using a quadratic equation.
The general form of the quadratic equation is; y = a·x² + b·x + c
When y = 5547, x = 8
We get;
5547 = a·8² + b·8 + c = 64·a + 8·b + c
5547 = 64·a + 8·b + c...(1)
When y = 3113, x = 11
We get;
3113 = a·11² + b·11 + c = 121·a + 11·b + c
3113 = 121·a + 11·b + c...(2)
When y = 2056, x = 14
We get;
2056 = a·14² + b·14 + c = 196·a + 14·b + c
2056 = 196·a + 14·b + c...(3)
Subtracting equation (2) from equation (1) gives;
5547 - 3113 = 64·a + 8·b + c - (121·a + 11·b + c) = -57·a - 3·b
2434 = -57·a - 3·b...(4)
Subtracting equation (3) from equation (2) gives;
3113 - 2056 = 121·a + 11·b + c - (196·a + 14·b + c) = -75·a - 3·b
1057 = -75·a - 3·b...(5)
Subtracting equation (5) from equation (4) gives;
2434 - 1057 = -57·a - 3·b - (-75·a - 3·b) = 18·a
1377 = 18·a
a = 76.5
From, equation (4), 2434 = -57·a - 3·b, we have;
2434 = -57 × 76.5 - 3·b
Therefore;
b = -2264.8
From equation (1), we get;
5547 = 64 × 76.5 + 8×(-2264.8) + c
Therefore;
c = 5547 - (64 × 76.5 + 8×(-2264.8)) = 18769.
c = 18769.
Therefore, the quadratic model is;
Verifying, we have in year 2012, x = 12
y = 76.5×12² - 2264.8×12 + 18769. = 2607.74
Thus ,the completed table and comparison of the predicted physical revenue and actual values is presented in the attachment;
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What the mean of 120, 60 , 0 , 30 , 15 , 0 , 0 , 10 , 20
-------------------------------------------------------------------------------------------------------------
Answer: [tex]\textsf{28 1/3}[/tex]
-------------------------------------------------------------------------------------------------------------
Given: [tex]\textsf{We are given 9 numbers}[/tex]
Find: [tex]\textsf{Determine the mean of the numbers}[/tex]
Solution: In order to determine the mean of the numbers the first step that we need to do is to add up all of the numbers. After adding up all of the numbers we divide it by the amount of numbers that were provided to us.
Add up the numbers
[tex]\textsf{120 + 60 + 0 + 30 + 15 + 0 + 0 + 10 + 20}[/tex][tex]\textsf{255}[/tex]Divide it by the amount of numbers provided
[tex]\textsf{255 / 9}[/tex][tex]\textsf{((28 * 9) + 3) / 9}[/tex][tex]\textsf{28 (3/9)}[/tex][tex]\textsf{28 1/3}[/tex]Therefore, the mean of the numbers provided is [tex]\textsf{28 1/3}[/tex]