The inequality that relates the number of hours to the weekly sales is:
[tex]450 + 0.20x \ge 35y[/tex]
The complete question implies that we define an inequality that represents the relationship between the number of hours worked in a week and the weekly sales
We make use of the following representation:
[tex]x \to[/tex] weekly sales from cars.
[tex]y \to[/tex] hours worked in a week
His weekly salary is then calculated as:
Salary (S) = Earnings per week + Commission * Sales from car
So, we have:
[tex]S = 450 + 20\% * x[/tex]
Express percentage as decimal
[tex]S = 450 + 0.20* x[/tex]
[tex]S = 450 + 0.20x[/tex]
Assume he works for y hours in a week.
His hourly rate is:
[tex]Hourly = \frac{S}{y}[/tex] --- i.e. weekly salary divided by number of hours
[tex]Hourly = \frac{450 + 0.20x}{y}[/tex]
For this rate to be at least [tex]\$35[/tex], the following condition must be true
[tex]Hourly \ge 35[/tex] --- i.e. is hourly rate must be greater than or equal 35
So, we have:
[tex]\frac{450 + 0.20x}{y} \ge 35[/tex]
Multiply both sides by y
[tex]450 + 0.20x \ge 35y[/tex]
Learn more about inequality:
https://brainly.com/question/20383699
(4,-5) with slope of 2
that's a point slope form so
y +5 = 2(x -4)
james cuts his neighbor's lawn the first is 1000 m long and 100 m wide what is the area
Answer:
100,000 m²
Step-by-step explanation:
the area = l x w = 1000 x 100 = 100,000 m²
Una empresa que trabaja en un mercado de competencia perfecta tiene una función de costos totales CT=Q^3-45Q^2+600Q+1.200 Las funciones de oferta y demanda de este mercado son: Qo=5P-300 y Qd=2.860-8P. Recuerde que la condición para maximizar beneficios dice que la empresa habrá de producir una cantidad tal que haga igualar sus costos marginales con el precio de equilibrio de mercado.
Answer:
La cantidad producida para maximizar las ganancias es de 915 unidades
Step-by-step explanation:
Pregunta: Calcule cuánto producirá para maximizar las ganancias.
La función de costo dada se presenta de la siguiente manera;
CT = Q³ - 45 · Q² + 600 · Q + 1200
La función de suministro es Qo = 5 · P - 300
La función de demanda es Qd = 2860 - 8 · P
A precio de equilibrio, tenemos;
Qo = Qd
Por lo tanto;
5 · P - 300 = 2860 - 8 · P
13 · P = 2.860 + 300 = 3.160
P = 3160/13
Por lo tanto;
Q = 2860 - 8 × (3160/13) = 11900/13 ≈ 915,38
La cantidad producida que maximiza las ganancias es de aproximadamente 915 unidades.
El costo total CT = 915³ - 45 × 915² + 600 × 915 + 1200 = 728,935,950
The data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 40 inches. Is the result close to the actual weight of 372 pounds? Use a significance level of 0.05.
Answer:
y = 16.3216X - 330.3904
322 pounds;
Result is significant
Step-by-step explanation:
Given the data:
Chest size, x : 41,54,44,55,39,51
Weight, Y : 328,528,418,580,296,503
Using technology, the prediction model obtained by fitting the data is :
y = 16.3216X - 330.3904
Where, x = chest size ; y = weight
The best predicted weight of a bear with chest size of 40 is
Put x = 40 in the equation :
y = 16.3216(40) - 330.3904
Y = 322.4736
Y = 322 pounds
At α = 0.05
The regression Coefficient, R value obtained is 0.986 ; using this to obtain the Pvalue ;
df = n - 1
Pvalue(0.986, 5) = 0.00198
Since, Pvalue < α ; result is significant at α = 0.05
is 23/17 a rational number?
Answer:
rational number
Step-by-step explanation:
a rational number can be written as a/b where a and b are integers
23/17 = a/b where a = 23 and b = 17
This is a rational number
Determine the equation of a perpendicular line to x=-2
Answer:
+1/2
Step-by-step explanation:
its the negative reciprocal
15) The sum of one-fourth, one-ninth and one- third of a number is 25. Find the number.
Answer:
Step-by-step explanation:
(1/4 + 1/9 + 1/3)x = 25.
x = 36
Answer:
Let the number be x
(1/4 + 1/9 + 1/3) * x = 25
25/36 * x = 25
25x = 25*36
x = 25*36/25
x = 36
Step-by-step explanation:
A 10-foot ladder rests against a vertical wall. Let x be the distance from the bottom of the ladder to the wall and y be the distance from the floor to the top of the ladder. If the bottom of the ladder slides away from the wall, how fast does the top of the ladder fall down the wall with respect to x
Answer:
The rate of change of the top of the ladder with respect to x is -x/y
Step-by-step explanation:
The given parameters are;
The length of the ladder = 10 ft.
The horizontal distance of the bottom of the ladder from the wall = x
The distance of the top of the ladder from the floor = y
By Pythagoras's theorem, we have;
10 = y² + x²
Therefore, we have;
x² = 10 - y²
d(x²)/dx = 2·x = d(10 - y²)/dx = -2·y·dy/dx
∴ 2·x = -2·y·dy/dx
dy/dx = 2·x/(-2·y) = -x/y
Therefore, the rate of change of the top of the ladder with respect to x, dy/dx = -x/y.
Let g(x) = f (x+1) - 2, find when g(x) = 12
I don't know how to evaluate this since I have both g(x) and an f(x).
Answer:
f(x +1 ) =14
Step-by-step explanation:
12= f(x +1) -2
f(x +1) = 12 +2
f (x+1 ) = 12
You draw a red marble out of a bag and give it your friend. You draw another marble out of the bag. Are the events independent? Explain.
No; the red marble was not replaced, so it has an effect on drawing a second marble.
Yes; you may not get a red marble again.
No; you do not know which marble you will draw next.
Yes; the red marble was kept out, so you can not draw it again.
Answer:
the red marble was kept out so you can not draw it again
Answer:
Yes; you may not get a red marble again.
Step-by-step explanation:
there is a chance to get a red marble but it is not high
What is the sum of the interior angles of the octagon below?
Select one:
a. 360°
b.720°
C. 1,080
d. 800
Answer:
Option C, 1,080
Step-by-step explanation:
sum of the interior angles of the octagon,
(8-2)×180
= 6×180
= 1080
Answered by GAUTHMATH
Create an equation in slope-intercept form for the line that passes through (3, 6) and (6, 10).
Answer: y = 4/3x + 2
Step-by-step explanation:
Use the slope form of y2 - y1/ x2 - x1 and substitute in the values from the coordinates. In this case, it would be 10-6/6-3, which gives you 4/3. Thus, that would be the slope(m). Then take a pair of coordinates (x,y) and substitute in the equation y = mx + b.
If you take the first coordinate (3,6): 6 = 3(4/3) + b
6 = 4 + b
b = 2
If you take the second coordinate (6, 10) : 10 = 6(4/3) + b
10 = 8 + b
b = 2
Then, substitute m and b into the equation (y = mx + b) to get your answer.
mutual sold an item for sh.3250 after allowing his customers a 12% discount on the marked price.if he had sold the article without giving a discount,he would have made a profit of 25%.calculate the percentage profit he made by selling the article at a discount?
Answer:
lol Step-by-step explanation:
Find the area of the shaded regions:
Answer:
84.78
Step-by-step explanation:
Used calculator and formula
Which lists all of the shapes that are in a two-dimensional net of a square pyramid? 6 squares 4 triangles 1 square and 3 triangles 1 square and 4 triangles
Answer:
4 triangles and 1 square
Step-by-step explanation:
Required
The shapes in two-dimensional net of a square pyramid
To do this, I will attach an attachment of a 2D net of a square pyramid (see attachment)
From the attachment, we can see that:
The 2d shape of the pyramid is made of 4 triangles and 1 square
Answer:
D
Step-by-step explanation:
1. Write three different solutions of 4x - 2y = 8. plzz answer fast
Answer:
y=-4+2x
x=(4+y)/2
2x-y=4
How many solutions exist for the mixed-degree system graphed below?
Answer:
The answer is one.
Find the interior angle sum for the following polygon
Find the volume of each figure. Round your answers to the nearest tenth, if necessary.
Answer:
201.1 km^3
Step-by-step explanation:
The volume of a cylinder is V=πr2h. In this problem, our radius is 8, and our heigh is 4. Plugging in our values we get:
V=π(8)(2)(4)=64π, which is approximately 201.1.
Hope this helped,
~cloud
Answer:
804.2 km^3
Step-by-step explanation:
Volume of cylinder = πr^2h
π(8)^2(4)
= 804.247719319
Rounded of to nearest 10th = 804.2 km^3
Answered by G a u t h m a t h
PLEASE HELP! DUE TODAY :))
Step-by-step explanation:
do like the picture I sent
Single adults: According to a Pew Research Center analysis of census data, in 2012, 20% of American adults ages 25 and older had never been married. Suppose that we select random samples from this population of American adults ages 25 and older. For each sample we then calculate the proportion that had never been married.
For which of the following sample sizes will the sampling distribution be approximately normal?
Wang, W., and Parker, K. (2014). Record Share of Americans Have Never Been Married. Pew Research Center. http://www.pewsocialtrends.org/2014/09/24/record-share-of-americans-have-never-married/
A) 25
B) 50
C) 75
Answer:
B. 50
Step-by-step explanation:
Central limit theorem is used to calculate the sampling distribution of the given case. The number of adults who are 25 years of age or above and not married is 20% of the samples selected. The standard deviation is 0.06 while the sample size should be 50 to conclude the results.
find k so that x^2+2x+k is a factor of 2x^4+x^3-14x^2+5x+6. also find all the zeroes of the two polynomial
Compute the quotient and remainder,
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x+k} \\\\ = 2x^2 - 3x - (8+2k) + \dfrac{(21+7k)x+(6+8k+2k^2)}{x^2+2x+k}[/tex]
The remainder upon dividing [tex]2x^4+x^3-14x^2+5x+6[/tex] by [tex]x^2+2x+k[/tex] should leave no remainder, which means
[tex]21+7k = 0 \implies 21 = -7k \implies k=-3[/tex]
and
[tex]6+8k+2k^2 = 0 \implies 2(k+3)(k+1)=0 \implies k=-3\text{ or }k=-1[/tex]
Only k = -3 makes both remainder terms vanish.
Then the previous result reduces to
[tex]\dfrac{2x^4+x^3-14x^2+5x+6}{x^2+2x-3} = 2x^2 - 3x - 2[/tex]
so that
[tex]2x^4+x^3-14x^2+5x+6 = (x^2+2x-3) (2x^2 - 3x - 2) \\\\ 2x^4+x^3-14x^2+5x+6 = (x+3)(x-1)(2x + 1)(x-2)[/tex]
and so the zeroes of the quartic polynomial are x = -3, x = 1, x = -1/2, and x = 2.
Find the shortest side of a triangle whose perimeter is 64 if the ratio of two of its sides is 4:3 and the third side is 20 less than the sum if the other two
Answer:
The shortest side of the triangle is 18
Step-by-step explanation:
Let the sides the triangle be x, y and z.
From the question, the perimeter of the rectangle is 64, that is
x + y + z = 64 ...... (1)
Also, the ratio of two of its sides is 4:3, that is x:y = 4:3, then we can write that x/y = 4/3 ⇒ 3x = 4y ...... (2)
The third side, z, is 20 less than the sum of the other two, that is
z + 20 = x + y ...... (3)
Substitute equation (3) into (1)
Then,
z + 20 + z = 64
2z +20 = 64
2z = 64 - 20
2z = 44
z = 44/2 k
z = 22
From equation (3)
z + 20 = x + y
Then, k
22 + 20 = x +y
42 = x + y
x = 42 - y ...... (4)
Substitute this into equation 2
3x = 4y
3(42-y) = 4y
126 - 3y = 4y
4y + 3y = 126
7y = 126
y = 126/7
y = 18
Substitute this into equation (4)
x = 42 - y
x = 42 - 18
x = 24
∴ x = 24, y = 18 and z = 22
Hence, the shortest side of the triangle is 18.
Find cos A and cot B exactly if a=15 and b=11 , what will Cos A be and Cot B be?
Answer:
D. <15/√346>
Have a nice day! :)
What is 200% of 20? Thanks!
Answer:
40
Step-by-step explanation:
200% x 20
200/100 x 20
(200 ÷ 100) x 20
200 x 20 ÷ 100
4,000 ÷ 100 = 40
kPLEASE SOMEONE SOLVE B) I ALREADY KNOW 1. A) Is 75.875m^2
The answer to part A is correct. You basically have to find the area of that L shape, and subtract off the area of the shaded trapezoid.
To get part B, you need to find the perimeter. This is because the trim runs along the bottom edge of the wall. Refer to the diagram below. Adding up the exterior sides gets us:
12+12+4+8+8+4 = 48
So she needs 48 meters of trim.
I'm not sure what your teacher means by "what assumptions do you make". If your teacher is referring to something like making room for a door, then we'll have to subtract some value from that 48. The problem with this though is that we don't have any clue how wide the door is. So you'll have to ask your teacher for clarification.
Luckily, this value 48 is an overestimate of the amount of trim Jennifer needs to buy. In my opinion, it's better to overestimate than underestimate, which saves from having to make another trip to the hardware store.
58×62 without actual multiplication
Answer:
3596
Step-by-step explanation:
Use long multiplication to evaluate.
Answer:
3596
Step-by-step explanation:
(58*10) = 580
580*6 = 3480
58 * 2 = 116
3480 + 116 = 3596
what is the mass of raisins in a package
Answer:
Step-by-step explanation:
12
Find the value of y. Round
the nearest tenth.
Answer: 178.3
Step-by-step explanation:
Use cos to find the value of x: cos(27)=350/x
You will find x = 392.81
Using this value, find sin(27): Sin(27)=y/392.81
You will find y=178.33
Rounding to the nearest tenth, you get 178.3
Find the value of x. PLEASE HELP ASAP!
A.4
B. 16
С. 5
D. 12
Answer: x>12
so i think x is 16.
