Malcom Davis earnings is an illustration of equations and proportions.
The equation is: [tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]The gross income must be $300000, for Dave to earn the same amount with either plan.His earning is $3333.33 when the plans are the same.Let the profit be P, and the gross income be G.
So, we have:
[tex]\mathbf{P= G - 100000}[/tex]
(a) The equations
For plan A, we have:
[tex]\mathbf{A = \frac{1}{90}G}[/tex] ----1/90 of the company's gross income
For plan B, we have:
[tex]\mathbf{B = \frac{1}{60}P}[/tex] ----1/90 of the company's profit
When both are the same, we have:
[tex]\mathbf{A= B}[/tex]
This gives
[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}P}[/tex]
Substitute [tex]\mathbf{P= G - 100000}[/tex]
[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]
Hence, the equation is: [tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]
(b) Solve the equation in (a), and intepret
[tex]\mathbf{\frac{1}{90}G= \frac{1}{60}(G- 100000)}[/tex]
Cross multiply
[tex]\mathbf{60G = 90G - 9000 000}[/tex]
Collect like terms
[tex]\mathbf{90G - 60G = 9000 000}[/tex]
[tex]\mathbf{30G = 9000 000}[/tex]
Divide both sides by 30
[tex]\mathbf{G = 3000 00}[/tex]
The gross income must be $300000, for Dave to earn the same amount with either plan.
(c) His earnings based on (c)
We have:
[tex]\mathbf{A = \frac{1}{90}G}[/tex]
Substitute [tex]\mathbf{G = 3000 00}[/tex]
[tex]\mathbf{A = \frac{1}{90} \times 300000}[/tex]
[tex]\mathbf{A = 3333.33}[/tex]
His earning is $3333.33 when the plans are the same
(d) If the gross income in less than (b)
If the gross income is less than $300,000, then plan A would better for Malcom Davis, because his earnings in plan A would be greater than plan B
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I need help finding what x is
Step-by-step explanation:
using Trigonometry,
sin40°=CB/x
x=CB/sin40°.
hope this helps you.
Answer x=1
Step-by-step explanation;
sin 90 =x
1=x
sorry im not sure of the answer
Jessica is stacking items on a shelf she has large books that weigh 5 pounds each and medium books that weigh 3 pounds each. The shelf should hold at most 50 pounds.
Let x represent the number of large books.
Let y represent the number of medium books.
Which inequality represents the situation?
a.) 5x + 3y < 50 b.) 5x +3y ≤ 50 c.) 5x + 3y ≥ 50 d.) 5x + 3y > 50
Answer:
b) 5x +3y ≤ 50
Step-by-step explanation:
What is the value of Y when X=-3 ?
Answer:
2
Step-by-step explanation:
the line is at 2 for Y
PLEASE HELP THIS IS GOING TO BE MY FIRST GRADE!!!!!!
The rate of change is 3/4.
Explanation:
The rise is 3 and the run is 4.
The slope, or rate of change, is rise/run.
3 in
3 in
Perimeter:
Area:
Step-by-step explanation:
The area = 3 × 3 = 9
The perimeter = 2(3 +3) = 12
please give me a brainliest answer
Answer:
A= a^2, which is 9.
P= 4a, which is 12.
Graham drove 42 1/3 miles in 1 1/3 hours. What is the unit rate for miles per hour? Use pencil and paper. Describe a situation in which the unit rate would be easier to work with than the given rate.
Answer:
Step-by-step explanation:
42+(1/3)
42*(3/3)+(1/3)
(126/3) + 1/3
126/3 + 1/3 = 127/3 miles
4/3 hours
(127/3)/4/3)
(127/3)*(3/4)
= 127/4 or 31.75 miles/hour
It would have been nicer if we were told Graham's distance after 1 hour (when he had travelled 31.75 miles).
2(x + 4) – 3(x – 6) + 5(x + 1) Simplified completely.
Answer:
4x+31
Step-by-step explanation:
2(x + 4) – 3(x – 6) + 5(x + 1)
Distribute
2x+8 -3x+18 +5x +5
Combine like terms
2x-3x+5x +8+18+5
4x+31
maths giving 10 point asap 1 question only
Answer:
Price of shirt=RM9.8
Step-by-step explanation:
Shirt=x Trouser=y
x+y=RM20
5x+y=RM59.20
y=20-x
5x+20-x=59.20
4x=39.20
x=9.8
y=20-9.8
y=10.2
402/3333 simplified please
Answer:
134/1111
Step-by-step explanation:
Answer:
Reduce the expression, if possible, by cancelling the common factors.
Exact form: [tex]\frac{134}{1111}[/tex]
Decimal form: 0.1206... (repeating)
Pleasehelp!!!!!!!!!! I'll mark Brainliest!!!!!!!!!!!!!!!!
Explain if possible!
A physicist working in a large laboratory has found that light particles traveling in a particle accelerator increase velocity in a manner that can be described by the linear function -4x+y=15, where x is time and y is velocity ion kilometers per hour. Use this function to determine when a certain particle will reach 30 km/hr.
Answer:
it will take the certain particle 15/4 (unit of time) to reach 30 km/hr
Input 30 as for y and solve the equation.
Step-by-step explanation:
Since y is kilometers per hour and the question is asking for how long it takes for a certain particle to reach 30 km/hr, you input 30 for y and solve for x.
-4x + y = 15
-4x + (30) = 15
subtract 30 from both sides
-4x = -15
divide -4 from both sides
x = 15/4
it will take the certain particle 15/4 (unit of time) to reach 30 km/hr
A lead cylinder has a mass of 618.7 grams and a density of 2.70 g/mL. Calculate the volume, in mL, and round your answer to the correct number of sig figs.
Answer:
1670.49 mLStep-by-step explanation:
Volume = mass * density
Substitute values and calculate:
V = 618.7 * 2.7 = 1670.49 mL(a) A square has a perimeter of 8 cm. What is the length of each side?
Answer: 2
Step-by-step explanation:
Perimeter is all the sides added up together so a square has 4 sides. 8/4= 2
Realiza los siguientes problemas de Tanto Por Ciento.
1. Se desplaza un camión consumiendo el 60% de su combustible, si el tanque
lleno tiene 45 litros de gasolina ¿Cuántos litros ha consumido?
2. En un gimnasio una persona se pesa y tiene 78 kilogramos de peso, si el peso ideal (100%) para una persona de su edad es de 62 kilogramos ¿Cuales el porcentaje de peso que tiene la persona?
3. Un cohete lunar ha consumido el 20% de su tiempo de vida útil, el cual es de 15 años (100%) ¿Cuânto tiempo de vida útil ha consumido el cohete lunar?
4. El volcán de Pacaya incremento su altitud en 25 metros en su ultima erupción de ceniza, si el volcán mide 2,552 metro ¿Qué porcentaje de altura incremento?
5. Beni tiene el 40% de la edad de su hermano Aarón que tiene 24 años ¿Que edad tiene Beni?
Answer:
1. 27 liters
2. 125.8%
3. 3 years
4. 0.98%
5. 9.6 years
Step-by-step explanation:
1. (60%)(45) = 27 liters
2. Percentage of weight relative to ideal weight = (100%)(78/62) = 125.8%, rounded to nearest 10th of a percent.
3. (20%)(15) = 3 years
4. Assume that the beginning height is 2552 meters and the height increases 25 meters. Then, the percentage increase = (100%)(25/2552) = 0.98%, rounded to the nearest 100th of a percent.
5. Beni's age = (40%)(24) = 9.6 years
Which of the following are roots of the polynomial function below?
Check all that apply.
F(x) = x3 - 3x2 + 2
Answer:
A
Step-by-step explanation:
The answer is A
The roots of the given quadratic equation are -
x = 2 and x = 1.
What is function?A function is a relation between a dependent and independent variable. We can write the examples of functions as -
y = f(x) = ax + b
y = f(x, y, z) = ax + by + cz
Given is a quadratic function f(x) defined as -
f(x) = x³ - 3x² + 2
The given quadratic function f(x) is -
f(x) = x³ - 3x² + 2
We can write the roots of the equation as -
x = {3 ± √(9 - 8)}/2
x = {3 + √(9 - 8)}/2 and {3 - √(9 - 8)}/2
x = (3 + 1)/2 and x = (3 - 1)/2
x = 2 and x = 1
Therefore, the roots of the given quadratic equation are -
x = 2 and x = 1.
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[50 pts] Zeke is a cook at Maxine’s Café after school and earns $12.75 per hour. Zeke worked a lot hours this week and charged $17.90 in meals. After paying for meals, Zeke’s earnings were less than $240. Which inequalities can be used to find h, the maximum number of hours that Zeke could have worked this week? (choose 2)
A 240 > 12.75h + 17.90
B 240 > 12.75h – 17.90
C 12.75h – 17.90 < 240
D 12.75h – 17.90 < 240
E 17.90 – 12.75h < 240
Answer:
240 > 12.75h – 17.9012.75h – 17.90 < 240Step-by-step explanation:
Zeke's earnings are:
12.75h - 17.90This amount is less than 240.
This can be shown as:
12.75h - 17.90 < 240 or240 > 12.75h - 17.90The matching choices are B, C and D (note C and D are given same, must be a typo)
Answer:
C 12.75h – 17.90 < 240
Step-by-step explanation:
Expand the following
Answer:
A) 3x +15
B) 8x -2
C) 20x + 10
D) 4x - 8y
Step-by-step explanation:
A) 3x+3 x 5 = 3x + 15
B) 2 x 4x -2 = 8x -2
C) 5 x 4x +5 x 2 = 20x + 10
D) 4x -4 x 2y = 4x - 8y
(Hope this helps can I pls have brainlist (crown)☺️)
HELP PLEASEEEE!!!
Which of the following inequalities matches the graph? у 10 8. दा 4 x 2. 6 8 10 --10-8-6-4-2 -2 - -8 -10 | OX-7 Oxs-7 Oy=-7 Oyz-7
Answer:
45
Step-by-step explanation:
The graph given is of inequality x ≤ -7.
What is an inequality?In Algebra, inequality is a mathematical statement that shows the relation between two expressions using the inequality symbol.
Given is a graph of an inequality, we need to determine the inequality,
So, the graph is cutting the x-axis at -7 and all the numbers less than -7 is covered by the graph,
so the inequality will be x ≤ -7
Hence, the graph given is of inequality x ≤ -7.
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Molly has 3 pounds of blueberries. She is freezing the berries into 1 half pound portions. How many smaller portions of blueberries will Molly make
Answer:
6 smaller portions
Step-by-step explanation:
1 pound (lb) = 16 ounces (oz)
3 lbs = 48 oz
1/2lb = 8oz
48oz (total)/8oz (amount in each portion) = 6 portions
----
an
- 11 + 5(n-1)
Answer:
-3.2
Step-by-step explanation:
Fine a number such that half of the number is 4 more than 6.
Answer:
20
Step-by-step explanation:
20 / 2 = 10
10 - 4 = 6
Find the next three terms of the arithmetic sequence.
10, 13, 16, 19
Answer:
22, 25, 28
Step-by-step explanation:
10 + 3 = 13
13 + 3 = 16
16 + 3 = 19
19 + 3 = 22
22 + 3 = 25
25 + 3 = 28.
all numbers go up by three points
write an equation of the line that passes through the point P(2, 5 ) that is parallel to y=4x+1
I need help, I'm stuck
1: 12 * [tex]10^{9}[/tex]
We can easily tell this is the answer here as 12 is larger than 4. They are both being multiplied by the same power of 10, so we can ignore that part and still tell which is larger.
2: 3 * [tex]10^{12}[/tex]
Same here, we can easily tell this is the answer here as 3 is larger than 1.5. They are both being multiplied by the same power of 10, so we can ignore that part and still tell which is larger.
3: 6 * [tex]10^{5}[/tex]
This one is slightly more complicated than the other two, but still not to difficult when you know what you're doing.
A tip: 10 to the fourth power ([tex]10^{4}[/tex]) is 10,000. Aka, a 1 with four zeros!
For the first one, 20 has a zero, so we can take it and put it onto the 10th power. We know have:
2 * [tex]10^{5}[/tex] and 6 * [tex]10^{5}[/tex]
Using the same method as #1 and #2, we can tell that 6 * [tex]10^{5}[/tex] is the answer here!
I hope this helps, have a nice day :D
I need help with this assignment. Help please
The answer came as 2257 as listed above
WILL GIVE BRAINLIEST!!
Hooke’s Law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 180 newtons stretches a spring 5 cm, how much will a force of 270 newtons stretch the same spring?
Answer:
Simple springs obey Hooke's Law. Hooke's Law states that the force on a spring is proportional to it's displacement from it's resting length:
F = -k*x
Where F is the force, x is how far the string is stretched or compressed, and k is a proportionality constant called the spring constant. The negative sign is because the spring resists stretching.
In this case, we can solve for k using the first case:
(100N) = -k * (5cm)
k = ???
And plug that answer in to find x in the second case:
(360N) = -k * x
This is a "Hooke's Law" problem: the restoring force required to compress or stretch a spring is proportional to the distance the spring is deformed. You can figure solve it by setting up a proportion equation and then using the algebraic tool of cross multiplication to solve for the unkown "stretch".
1) set up the proportion equation
100 = 360
5 x
2) cross multiply to get a linear equation
100x = 5*360
3) solve for x
100x = 1800
x = 18
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Answer:
The law: F=kx
Therefore,
180N = k * 5cm
k = 180÷5= 36N per cm
Using the known constant with the law,
270=36*x
x= 270 ÷ 36 = 7.5cm
How do you shift exponential functions?
Answer:
Shift the graph of f(x)=bx f ( x ) = b x left c units if c is positive and right c units if c is negative. Shift the graph of f(x)=bx f ( x ) = b x up d units if d is positive and down d units if d is negative.
A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y=2.5x+3
represents the cost y of bowling x games. Interpret the parameters of the function.
represents the shoe rental charge.
represents the price per game.
The number that represents the shoe rental charge is 3.
The number that represents the price per game is 2.5.
The equation provided is a linear equation. A linear equation is made up of one varaible that has a power of one.
y= 2.5x + 3
In the given equation, 2.5 represent the additional fee for each game played. This number increases with each game played.
When:
1 game is played, the additional fee is 2.5 x 1 = 2.50.10 games are played, the additional fee is 2.5 x 10 = 25.3 is the flat fee to rent the shoes. It is a constant cost that does not change with the total games played.
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8x divided by 13x
how do you do this plis give answer
Answer:
8/13
Step-by-step explanation:
8x
------
13x
The x in the numerator and denominator cancel
8/13
A bag has 4 red balls ,3 green balls and 5 blue balls. What is the probability of getting a red ball randomly
1-100%. You'll never know until you try it yourself.
i’ll mark brainliest!! i will give a lot of points
Answer:
Step-by-step explanation:
You have 2 points given. Take them seriously. They represent actual numbers that don't need to be rounded.
The two points are (2,-2) and (-3,-6)
Now construct a line in point intercept form from these two points.
y2 = -2y1 = -6x2 = 2x1 = -3m = (y2 - y1)/(x2 - x1)
m = (-2 - - 6)/(2 - - 3)
m = 4/5
So far what you know is
y = 0.8 x + b
Use either one of the two points to get b (the y intercept)
x = 2
y = - 2
-2 = 0.8*2 + b
-2 = 1.6 + b Subtract 1.6 from both sides
-3.6 = b
y = 0.8x - 3.6
3