A toy manufacturer makes a toy truck, a toy car, and a toy boat. The production spreadsheet is:
Toy Time to Produce Cost to Produce Profit for Each Truck 10 minutes $1.00 $1.00 Car 12 minutes $0.75 $1.50 Boat 8 minutes $0.80 $0.60
After accounting for breaks, a worker actually works 400 minutes each day. The manufacturer needs each worker to generate a potential profit of $35 each day. Write a system of inequalities that expresses these constraints.

Answers

Answer 1

Let x be the number of toy truck, y is the number of toy car, and z is the number of toy boat.

The constraint for the time
[tex]10x+12y+8z\le 400[/tex]

The constraint for the profit
[tex]x+1.50y+0.6z\ge 35[/tex]

Answer 2

Answer:

[tex]\left\{\begin{array}{l}10x+12y+8z\le 400\\x+1.5y+0.6z\ge 35\end{array}\right.[/tex]

Step-by-step explanation:

Let x be the number of toy trucks, y be the number of toy cars and z be the number of toy boats a worker makes each day.

1. If a worker spends 10 minutes to make one toy truck, then he spends 10x minutes to make x toy trucks. If a worker spends 12 minutes to make one toy car, then he spends 12y minutes to make y toy cars. If a worker spends 8 minutes to make one toy boat, then he spends 8z minutes to make z toy boats. In total he can spend at most 400 minutes each day, then

[tex]10x+12y+8z\le 400.[/tex]

2. If a worker generates profit of $1.00 per one toy truck, then he generates profit of $x per x toy trucks. If a worker generates profit of $1.50 per one toy car, then he generates profit of $1.50y per y toy cars. If a worker generates profit of $0.60 per one toy boat, then he generates profit of $0.60z per z toy boats. The manufacturer needs each worker to generate a potential profit of $35 each day, then

[tex]x+1.5y+0.6z\ge 35.[/tex]

Thus, the system of two inequalities is

[tex]\left\{\begin{array}{l}10x+12y+8z\le 400\\x+1.5y+0.6z\ge 35\end{array}\right.[/tex]

Related Questions

Any answers please??

Answers

Your answer is going to be (4,4).
X-axis= (x,y) --->(x,-y)
Y-axis= (x,y) --->(-x,y)

X-axis= (-4,4) --->(-4,-4)
Y-axis= (-4,-4) --->(4,-4)
X-axis= (4,-4) --->(4,4)

Hope this Helps! :)

If sin x =1/2 what
is cos x

Answers

[tex]\sin^2x+\cos^2x=1\to\cos^2x=1-\sin^2x\to\cos x=\sqrt{1-\sin^2x}\\\\\sin x=\dfrac{1}{2}\\\\\text{substitute}\\\\\cos x=\sqrt{1-\left(\dfrac{1}{2}\right)^2}=\sqrt{1-\dfrac{1}{4}}=\sqrt{\dfrac{3}{4}}=\dfrac{\sqrt3}{\sqrt4}=\dfrac{\sqrt3}{2}[/tex]

For $360, a rock-climbing gym offers a yearly membership where members can climb as many days as they want and pay $4 per day for equipment rental. Nonmembers pay $10 per day to use the gym and $6 per day for equipment rental. Find the total number of visits when the cost for a member and nonmember will be the same.

Answers

If after x day of their visit, non-member and member pays the same

360+4x=16x
360=12x
x=30

After 30 days they visit, they will spend the same amount.

Final answer:

The cost for a member and a nonmember of a rock-climbing gym will be the same at 30 visits.

Explanation:

To find the total number of visits when the cost for a member and a nonmember will be the same, we need to set up an equation based on the problem statement, which we can then solve.

For the member, the cost is the $360 yearly fee plus $4 per visit (for equipment rental) - so if 'x' represents the number of visits, the total cost for a member would be $360 + 4x.

For a nonmember, the cost is $10 per visit (for gym use) plus $6 per visit (for equipment rental) - so the total cost for a nonmember is $16x.

So, to find the number of visits 'x' where both costs are equal, we need to solve this equation: $360 + 4x = $16x.

Solving the equation gives us $360 = 12x, which simplifies to x = 30.

So, the cost for a member and a nonmember would be the same at 30 visits.

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Help please? what is the length of side x?
Triangle AAS use sine rule

Answers

check the picture below.

make sure your calculator is in Degree mode.

Zekia divides of 6 cups of fruit juice equally among 8 friends two of her friends don't drink the juice how much juice is leftover

Answers

6 cups divided by 8 friends is 0.75 cup per friend
if 6 friends drink and 2 dont, then the amount of juice saved is
0.75 cup/friend * 2 friends = 1.5 cup

1.5 cup of juice is left over

Final answer:

Since Zekia has 6 cups of fruit juice to divide among 8 friends, with 2 not drinking, there will be no juice leftover because each of the 6 drinking friends will receive 1 cup each.

Explanation:

Zekia has 6 cups of fruit juice that she wants to divide equally among her 8 friends, but 2 friends don't drink any. Initially, we would divide 6 cups by 8 to find out how much each friend gets. However, since 2 friends aren't drinking, only 6 friends will be actually consuming the juice.

First, let's calculate the amount of juice each of the 6 friends would receive:

Total juice = 6 cups

Number of friends drinking = 8 - 2 = 6

Juice per friend = Total juice ÷ Number of friends drinking = 6 cups ÷ 6 = 1 cup

So, each of the 6 friends will get 1 cup of juice. Since all 6 cups of juice are consumed, there is no juice leftover.

To the nearest hundredth, what is the area of a circle with a radius of 3 units

Answers

28.27 square units (APEX)

Answer:

28.27

Step-by-step explanation:

gl on test

A pet store is selling a new dog collar for $12.00. If there is a sales tax of 10 percent, what is the actual cost of the collar

Answers

Price of the collar = $12.00

Sales Tax = 10% x $12 = 0.1 x 12 = $1.20

Total Cost = $12.00 + $1.20 = $13.20

Answer: $13.20

Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 $1.75 for the first 1 5 15 of a mile and $ 0.25 $0.25 for each additional 1 5 15 of a mile. if the distance from one of the convention hotels to the airport is 5.8 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?

Answers

the correct question is
Recently, the texas junior college teachers association annual conference was held in austin. at the time a taxi ride in austin was $ 1.75 for the first 1/5 of a mile and $ 0.25 for each additional 1/5 of a mile. if the distance from one of the convention hotels to the airport is 5.8 miles, how much will it cost to take a taxi from that hotel to the airport?

we know that
(1/5) miles is equal to 0.20 miles
so

for the first 0.20 miles----------> $1.75
Remaining Distance = 5.8 - 0.2 miles = 5.6 miles
5.6/(0.2) =28 (this is the number of (1/5)th of a mile after the 1st (1/5)th
Each of these costs 0.25 dollars
28*0.25 = 7 dollars

total cost=$1.75+$7------> $8.75

the answer is
$8.75

To calculate the total taxi fare in Austin, first calculate the initial fee for the first 1/15 mile and then the cost for each additional 1/15 mile. For 5.8 miles, the total cost amounts to $23.25, comprising a $1.75 initial fare and $21.50 for the subsequent distance.

Let's break down the cost of a taxi ride based on the given pricing structure. To find the total cost of a taxi ride for a given distance, we need to calculate the cost for the first 1/5 mile and the additional cost for the remaining distance.

The initial cost for the first 1/5 mile is given as $1.75.

We know the total distance is 5.8 miles. Since the first 1/5 mile is included in the initial cost, the distance to be charged in increments of 1/5 mile is:

[tex]\[ 5.8 - \frac{1}{5} = 5.8 - 0.2 = 5.6 \, \text{miles} \][/tex]

To find the number of 1/5 mile increments in 5.6 miles, divide by 0.2:

[tex]\[ \frac{5.6}{0.2} = 28 \][/tex]

Thus, there are 28 additional 1/5 mile increments.

Each additional 1/5 mile increment costs $0.25. Thus, the total cost for the additional distance is:

[tex]\[ 28 \times 0.25 = 7.00 \][/tex]

The total cost is the initial cost plus the cost for the additional distance:

[tex]\[ 1.75 + 7.00 = 8.75 \][/tex]

Thus, the total cost to take a taxi from the hotel to the airport, given a distance of 5.8 miles, is $8.75.

PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ HELPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP

Find the value of x and y.

Answers

[tex]180^o-112^o=68^o[/tex]

[tex]\left\{\begin{array}{ccc}2x+3y=68&|\cdot(-15)\\30x+11y=112\end{array}\right\\\underline{+\left\{\begin{array}{ccc}-30x-45y=-1020\\30x+11y=112\end{array}\right}\\.\ \ \ \ \ \ \ -34y=-908\ \ \ |:(-34)\\\\.\ \ \ \ \ \ \ \ \ \ \ y=\dfrac{908}{34}\to y=\dfrac{454}{17}\\\\2x+3\cdot\dfrac{454}{17}=68\ \ \ \ |\cdot17\\\\34x+1362=1156\ \ \ \ |-1362\\34x=-206\ \ \ \ |:34\\\\x=-\dfrac{206}{34}\to x=-\dfrac{103}{17}\\\\ \left\{\begin{array}{ccc}x=-\dfrac{103}{17}\\\\y=\dfrac{454}{17}\end{array}\right[/tex]

Which ordered pairs are in the solution set of the system of linear inequalities? y > -1/2x y <1/2 x + 1

Answers

Look at the picture.

[tex]y=-\dfrac{1}{2}x\\\\for\ x=0\to y=-\dfrac{1}{2}\cdot0=0\to(0;\ 0)\\\\for\ x=2\to y=-\dfrac{1}{2}\cdot2=-1\to(2;\ -1)\\\\\\y=\dfrac{1}{2}x+1\\\\for\ x=-2\to y=\dfrac{1}{2}\cdot(-2)+1=-1+1=0\to(-2;\ 0)\\\\for\ x=0\to y=\dfrac{1}{2}\cdot0+1=1\to(0;\ 1)[/tex]

Answer: Every points on orange area.

Answer: is c on edge (5,-2) , (3,1) ,(4,2)

What is the slope-intercept form equation of the line that passes through (3, 4) and (5, 16)?

Answers

Answer:
y = 6x - 14

Explanation:
The general formula of the linear line is:
y = mx + c
where:
m is the slope and c is the y-intercept

1- getting the slope:
slope is calculated as follows:
m = [tex] \frac{y2-y1}{x2-x1} [/tex] = [tex] \frac{16-4}{5-3} = 6[/tex]

The equation of the line now is:
y = 6x + c

2- getting the y-intercept:
To get the y-intercept, we will use any of the given points, substitute in the equation and solve for c.
I will use the point (3,4) as follows:
y = 6x + c
4 = 6(3) + c
4 = 18 + c
c = -14

Based on the above calculations, the equation of the line is:
y = 6x - 14

Hope this helps :)

What is the radian measure of a 150° angle?

Answers

well, since we know that in π radians there are 180°, then how many radians in 150°?

[tex]\bf \begin{array}{ccll} radians&de grees\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \pi &180\\ x&150 \end{array}\implies \cfrac{\pi }{x}=\cfrac{180}{150}\implies \cfrac{\pi \cdot 150}{180}\implies \stackrel{simplified}{\cfrac{5\pi }{6}}[/tex]

The radian measure of a 150° angle is (5/6) π rad, found by multiplying 150° by the conversion factor π/180.

To find the radian measure of a 150° angle, we use the relationship between degrees and radians. Recall that a full circle in degrees is 360° and in radians is 2π rad. Therefore, we can say that 360° equals 2π radians. To convert degrees to radians, we multiply the degree measure by the fraction π/180.

For a 150° angle, the calculation would be:
150° multiplied by the conversion factor π/180
150° * (π/180) = (150/180) * π = (5/6) * π rad

Thus, the radian measure of a 150° angle is (5/6) π rad.

By dividing the number of houses in antonio's subdivision by 4 and adding 15, you can find the number of houses in hector's subdivision. if hector has 47 houses in his subdivision, how many houses are in antonio's subdivision?

Answers

let
x--------> the number of houses in antonio's subdivision
y-------> the number of houses in hector's subdivision

we know that
(x/4)+15=y----> equation 1
y=47-----> equation 2

substitute equation 2 in equation 1
(x/4)+15=47-----> multiply by 4----> x+60=188-----> x=128

the answer is
the number of houses in antonio's subdivision are 128

Show work please (6th grade math)

Answers

A rate is a special ratio in which the two terms are in different units. A rate is a little bit different than the ratio, it is a special ratio. For this case, the rate would have units of miles per minutes. We calculate as follows:
rate = 36 miles / 45 min = 0.8 miles per mindistance traveled = 0.8 miles per min ( 60 min ) = 48 miles
Hope this answers the question. Have a nice day.

The answer is 48 miles.

To find how long the bus travels in 60 minutes, we need to find a ratio of how long the bus travels every 15 minutes.

We do this by dividing 45 minutes by 3. We now have 15 minutes.
You then divide the miles by 3 as well. 36 divided by 3 is 12.

A bus travels 12 miles every 15 minutes.

Now, this still isn't the answer. We need to find how many miles the bus travels in 60 minutes.

To find this, we need to find how many 15 minute intervals are in 60 minutes. To do this, we divide 60 by 15 to get 4. We use this 4 to multiply it by 12 to find the total number of miles in 60 minutes.

12 times 4 is 48 miles.

Therefore, the bus travels 48 miles in 60 minutes.

answer this question please and right

Answers

Formula : (x - x1)² + (y - y1)² = r²

Given center of the circle at (-10,6) and radius 4,

(x + 10)² + (y - 6)² = 4²

(x + 10)² + (y - 6)² = 16

Answer: (x + 10)² + (y - 6)² = 16

Use the formula (x - x1)² + (y - y1)² = r².

Center of circle: (-10, 6)
Radius: 4

(x - -10)² + (y - 6)² = 4²
Equation: (x + 10)² + (y - 6)² = 16

What is the square root of 325 rounded to two decimal places?

Answers

The square root of 325 is 18.03

help pls!!! 10 points!!!

Answers

1) The angle bisector divides makes the segments on one side proportional to the corresponding segments on the other side.
3/4 = x/7.5
x = (3/4)*7.5 = 5.625

2) There are a number of ways to compute the area of the figure. I choose to divide it into a rectangle 8 units wide by 6 units high and two triangles. One triangle is 3 units wide and 2 high, the other is 6 units wide and 1 high. Then the total area is
(8*6)+(1/2)*(3*2 +6*1)
= 48 +6
= 54 units²

given function f(x)=x^2-x+8, find each of the following. f(9) f(-6) f(0)

Answers

[tex]f(x)=x^2-x+8[/tex]

f(9) - substract x = 9 to the equation of the function:

[tex]f(9)=9^2-9+8=81-9+8=80\\\\f(-6)=(-6)^2-(-6)+8=36+6+8=50\\\\f(0)=0^2-0+8=8[/tex]

License plates are made using 2 letters followed by 3 digits. how many plates can be made ifrepetition of letters and digits is allowed

Answers

26×26×10×10×10= 676 000

20 PTS AND I'LL MARK BRAINLIEST

∠1 and ∠2 are a linear pair, and ∠2 and ∠3 are vertical angles. m∠2=(5+4y)∘ and m∠3=(6y−25)∘ . What is m∠1 ?

Answers

Since m∠2 and m∠3 are vertical angles, they are congruent. Knowing this, we can form this equation:
5+4y=6y-25 (We'll add the degrees symbol later)
5 = 2y - 25
30 = 2y
y = 15°
We can plug the y-value into the value for m∠2.
5 + 4(15) = 65°

Now, we can easily find m∠1, since they are a linear pair.
m∠1 + m∠2 = 180
m∠1 + 65 = 180
m∠1 = 115°.
m∠1 equals 115°.

Hope this helps!

In a poll of students at basketball champoin 82% of the students say that basketball is better than fottball.

Answers

69 for sure. Too easy give me something harder

Find the following measure for this figure.
Volume =
18 cubic units
24 cubic units
36 cubic units

Answers

The figure on the picture is parallelepiped (or right rectangular prism), whose volume is icalculated as V=lwh, where l measures the length, w measures the width and measures the altitude of parallelepiped.

In your case, l=4 units, w=2 units, h=3 units and V=4×2×3=24 cubic units.

Answer:

So the answer is 24 cubic units

Step-by-step explanation:

l=4 units,

w=2 units,

h=3 units and

V=4×2×3=24 cubic units.

The height of a triangle is 8 inches more than its base. the area of the triangle is 104.5 square inches. find the base and height.

Answers

let
b------> the base of the triangle
h------> the height of the triangle

we know that
area of the triangle=b*h/2
h=b+8-----> equation 1
area=104.5 in²
104.5=b*h/2-----> 209=b*h-----> equation 2

substitute equation 1 in equation 2
209=b*[b+8]----> 209=b²+8b-----> b²+8b-209=0

using a graph tool---> to resolve the second order equation
see the attache figure

the solution is
b=11 in
h=b+8----> h=19 in

the answer is
the base is 11 in and the height is 19 in

Find all solutions to the equation sin2x+sinx-2cosx-1=0 in the interval [0, 2pi)

Answers

The solutions appear to be {π/2, 2π/3, 4π/3}.

_____
Replacing sin(2x) with 2sin(x)cos(x), you have
2sin(x)cos(x) +sin(x) -2cos(x) -1 = 0
sin(x)(2cos(x) +1) -(2cos(x) +1) = 0 . . . . factor by grouping
(sin(x) -1)(2cos(x) +1) = 0

This has solutions
sin(x) = 1
x = π/2
and
2cos(x) = -1
cos(x) = -1/2
x = {2π/3, 4π/3}

What is the equation of this circle in general form? x² + y² + 2x + 6y + 4 = 0 x2+y2−2x−6y−26=0 x2+y2−2x−6y+4=0 x2+y2+2x+6y−26=0 a circle on a coordinate plane centered at begin ordered pair 1 comma 3 end ordered pair. the horizontal x-axis ranges from negative 10 to 10 increments of 1. the vertical y-axis ranges from negative 10 to 10 in increments of 1. the circle passes through begin ordered pair negative 5 comma 3 end ordered pair, begin ordered pair 1 comma 9 end ordered pair, begin ordered pair 7 comma 3 end ordered pair, and begin ordered pair 1 comma negative 3 end ordered pair?

Answers

A circle on a coordinate plane is centered at the beginning ordered (1, 3). The equation of the circle is x²+y²-2x-6y-26=0

What is the equation of the circle with radius r units, centered at (x,y)?

If a circle O has radius of r units length and that it has got its center positioned at (h, k) point of the coordinate plane, then, its equation is given as:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

A circle on a coordinate plane is centered at the beginning ordered (1, 3).

The horizontal x-axis ranges from negative 10 to 10 increments of 1. and the vertical y-axis ranges from negative 10 to 10 in increments of 1.

The equation of the circle is

[tex]x^2+y^2-2x-6y-26=0[/tex]

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does anyone know what the measuure of Ф should be . is so i will mark brainliest.

Answers

Since the triangles are congruent, they should have similar angle measures:

A triangle's angles measure 180°, so we just have to subtract the other two angle measures:

180 - 50 - 70 = Ф
60 = Ф

Triangle rst is circumscribed about the circle below. What is the perimeter of the triangle?

Answers

I have attached the diagram that is related to this question.

Answer:
perimeter of the triangle = 24 units

Explanation:
Using the grid, we can note that:
RS = 6 units
ST = 8 units

We know that the triangle inscribed in a circle is a right-angled triangle. Therefore, we can use the Pythagorean theorem to get the third side as follows:
(RT)² = (RS)² + (ST)²
(RT)² = (6)² + (8)²
(RT)² = 100
RT = 10 units

Now, we can get the perimeter as follows:
perimeter = RS + ST + RT
perimeter = 6 + 8 + 10
perimeter = 24 units

Hope this helps :)

Not sure what the answer is but this guy didnt attach the dang picture so here.

Which expression is equivalent to 3(4m − 5)?

Answers

Hello!

your answer is:
using the distributive property of multiplication, the equivalent expression is:
12m-15

I hope this helps, and have a nice day!

The equivalent expression for the given expression is 12m-15.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

The given expression is 3(4m-5).

Using distributive property A(B+C)=AB+AC, we get

3×4m-3×5

= 12m-15

Therefore, the equivalent expression for the given expression is 12m-15.

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What is the value, after 7 years...

Answers

$13946.1651 is the final answer:)

Answer:

13946

Step-by-step explanation:

3 problems, 50 points

Answers

1is 6/13 2is5/x-m h

1. m=9

2.vertical: x=4, horizontal y=1

3.So if y = 3 and x = 5 then we have
3= y(1/6)
Solve for y
y= 24

Therefore the equation should be
y = 24/x

So when x = 3
y = 24/3
y = 8
hope this helps and sorry if I'm wrong

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What are the answers?? I need help!! Complete the area model to identify the factored form of the quadratic expression it represents. A)(x + 2)(x + 5) B)(x 2)(x + 5) C)(x + 2)(x 5) D)(x 2)(x 5) find the measure of the angle You are building a rectangular deck. The area of the deck should be 250ft. You want the length of the deck to be 5 ft longer than twice its width. What should the dimensions of the deck be? The outer edge of the dime is about 55mm. What is the approximate length of the radius? SOME ONE PLEASE HELP Choose the correct simplification of the expression (7m3 n)2. A.14m5n3 B.14m6n2 C.49m5n3 D. 49m6n2 Geometry question, will give brainiest For a popular Broadway musical, theater box office all $356 apiece 275, tickets and $60 apiece, and 369 tickets and $45 apiece. How much money did the box office ticket Take in? Damage to the enteric nervous system that innervates the digestive organs could affect: What is the solution to the equation 1/square root of 8 = 4^(m + 2)? m = 15/4 m = 11/4 m = 5/4 m = 9/4 Which pair of points forms a vertical line segment that is 4 units long? In ABC, A is a right angle, and mB = 45. What is the length of BC? If the answer is not an integer, leave it in simplest radical form. The diagram is not drawn to scale. explain why many compounds that contain one or more hydrogen atoms are not classified as arrhenius acids Chalk and talc are insoluble. what do you think thus term means In a broad sense, the boys epiphany in Araby reveals thea.futility of human pursuits.c.pervasiveness of self-deception.b.indifference of society to individuals.d.pointlessness of religious ceremony. A plane can travel 640 miles against the wind in the same time it can travel 800 miles with the wind. If the plane can fly 180 mph in calm air, what is the speed of the wind? If x represents the speed of the wind, which expression represents the time it takes for the plane to travel the 640 miles against the wind? Read the sentence. Even though the musicians were not in an orchestra, their music was often referred to as symphonic. What does symphonic mean? A. no sounds used; silent B. many sounds used together C. few sounds used D. many sounds used separately 4 of 10 During the Han Dynasty of China, Emperor Wudi decided China should be a Confucian state and not a Taoist state. This dramatically changed the way government operated. What was one result of the change to Confucianism? What is an interest group? (10) describe three different types of interest groups active in american politics. (15) what are some of the similarities these different types share in terms of organization and recruitment? In the wake of the Soviet launch of Sputnik, Congress passed this law in 1958 that increased funding to all levels of education in the United States.