A sporting goods manufacturer produces skateboards and in-line skates. Its dealers demand at least 30 skateboards per day and 20 pairs of in-line skates per day. The factory can make at most 60 skateboards and 40 pairs of in-line skates per day. The total number of skateboards and pairs of in-line skates cannot exceed 90. The profit of each skateboard is $12 and the profit on each pair of in-line skates is $19. What is the maximum profit the company can make given these constraints?

$1100
$1100

$1200
$1200

$1360
$1360

$2200
$2200

The perimeter of the given figure for the given values is equal to 24units.

As given in the question,

Given values of the figure,

AB = 8 cm, BC = 3 cm, CD = 1 cm, DE = 2 cm, EF = 3 cm, and FG = 1 cm

HG = AB - (EF + CD)

      = 8- (3 +1)

      = 4 units

AH = (BC-DE)+FG

     = (3-2)+1

     =2units

Perimeter of the given figure

= AB + BC+ CD+ DE+ EF+ FG+ GH+ HA

= 8+ 3+ 1+ 2+ 3+ 1+ 4+ 2

=24 units

Therefore, the perimeter of the given figure for the given values is equal to 24units.

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The value of the greatest integer is equal to 1.

We are given that:

The sum of an integer and 7 times the next consecutive odd integer is 6

Consecutive numbers are the numbers that follow each other continuously in the order from smallest to largest. For example 34 and 35.

Let the first number be x.

Second number = x + 2 ( as we need an odd integer)

ATQ:

x + 7( x + 2) = 6

x + 7 x + 14 = 6

8 x = 6 - 14

8 x = - 8

x = - 1

x + 2 = - 1 + 2

= 1

Therefore, the value of the greatest integer is equal to 1.

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the answer is 1.
i just did this question on delta

Answer:

D [tex] \frac{1}{3} x - \frac{2}{3} [/tex]

Step-by-step explanation:

[tex] f(x) = 3x + 2[/tex]

[tex] {f}^{ - 1} (x) = \frac{x}{3} - \frac{2}{3} ⟹ \frac{1}{3} x - \frac{2}{3} [/tex]

(a) 45 tens is equal to 450. :- True

(b) 12.3 is equal to 123 ones. :- True

(c) 80 tens is greater than 6 hundreds. :- True

(d) 43,200 is less than 50 thousands. :- True

(e) 60 hundreds = 6,000 :- True

Consider the first statement,

45 tens are equal to 450

So, 45 tens mean 45 times 10 is written as:

45 × 10 = 450

Hence, it's true.

Consider the second statement,

12.3 is equal to 123 ones.

Now, 123 ones is equal to 123 times 1.

123 × 1 = 123

Hence, the statement is true.

Consider the third statement,

80 tens is greater than 6 hundreds.

Now 80 tens = 80 × 10 = 800

Now, 6 hundreds = 6 × 100 = 600

Now, 800 > 600

Hence, the statement is true.

Consider the fourth statement.

43,200 is less than 50 thousands.

Now, 50 thousands = 50 × 1000 = 50,000

We know,

50,000 > 43,200

Therefore, the statement is true.

Consider the fifth statement,

60 hundreds = 6000

Now, 60 hundreds = 60 × 100 = 6000

Therefore, the statement is true.

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The graph of the parabola is given at the end of the answer.

The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the range and the symmetry line, the vertex of the function is at (-1,-4) and:

h = -1, k = -4.

Hence:

y = a(x + 1)² - 4.

It has a y-intercept of -3, that is, when x = 0, y = -3, hence we use it to find a as follows.

-3 = a - 4

a = 1.

Hence the function is:

y = (x + 1)² - 4.

The graph of this function is given at the end of the answer.

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Answer:

Volume of sphere = 4.187x³

Step-by-step explanation:

[tex]\textsf {Volume of a sphere = $\dfrac{4}{3} \pi {r^2 }$}[/tex]

Here r = x

[tex]\textsf {Volume = $\dfrac{4}{3} \pi {x^2 }$}[/tex]

[tex]\textsf {Volume of cuboid = $4x^3$}\\[/tex]

[tex]\textsf {volume of sphere = $\dfrac{4}{3}\pi \cdot x^3$}[/tex]

[tex]\textsf {Since $\pi \approx 3.14$, this is} \approx \dfrac{4\cdot (3.14)}{3} x= 4.187x[/tex]

So volume of sphere of radius x = 4.187x³  is greater than cuboid volume of 4x³

[tex]s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} [/tex]

The shaded region represents 1.5 grids

[tex]1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} [/tex]

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

Answer:

perpendicular slope = - [tex]\frac{4}{3}[/tex]

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

- 3x + 4y = 7 ( add 3x to both sides )

4y = 3x + 7 ( divide through by 4 )

y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{7}{4}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{3}{4}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{3}{4} }[/tex] = - [tex]\frac{4}{3}[/tex]

Answer:

  zero real solutions

Step-by-step explanation:

You want the number of real roots of 3x² -5x +4 = 0 and determined by using the discriminant.

The discriminant of a quadratic equation ax²+bx+c=0 is ...

  d = b² -4ac

When d < 0, both roots are complex. When d = 0, there is one (repeated) real root. The number of real solutions is 2 when d > 0.

For this equation, a=3, b=-5, c=4, so the discriminant is ...

  d = b² -4ac = (-5)² -4(3)(4) = 25 -48 = -23

This means both roots are complex. There are no real solutions.

__

Additional comment

As confirmation, we can look at the graph. It does not cross the x-axis, so there are no (real) values of x that make the value of the quadratic be zero.

Answer:

−55x+750=0

Step-by-step explanation:

Answer:

I'll answer the question in the picture first.

log(6) = 1.788

log(8) = 2.079

ln(6) = 1.792

ln(8)= 2.08

How to use a scientific calculator?

There are many different types of scientific calculators, so it is difficult to give a single answer to this question. However, most scientific calculators have a variety of buttons that perform different functions. Typically, there are buttons for the four basic operations ( addition, subtraction, multiplication, and division), as well as buttons for more complex functions such as square roots and exponential operations. To use a scientific calculator, simply press the buttons corresponding to the operations you want to perform.

Step-by-step explanation:

Answer:

y = x - 11

Step-by-step explanation:

5y + 22 = 5x - 33

5y = 5x - 33 - 22

5y = 5x - 55

y = x - 11

Answer:

40

Step-by-step explanation:

Answer:

6+8x=

16.8

x=

Step-by-step explanation:

Answer:

x = 30°

Step-by-step explanation:

If l and m are parallel lines, then corresponding angles should be congruent.

  3x - 20 = 2x + 10

Add 20 to both sides,    

          3x = 2x + 10 + 20

         3x  = 2x + 30

Subtract 2x from both sides,

     3x - 2x = 30

                x = 30

Answer: Domain: -2<=x<=2

Range: -2<=y<=2

Not a function

Step-by-step explanation:

Domain: x goes from -2 to 2

-2<=x<=2

Range: y goes from -2 to 2

-2<=y<=2

Not a function since there are several y-coordinates that have the same x-coordinate, so the graph doesn't pass the vertical line test. Example: (0, -2) and (0, 2).

The last year's salary is found as 33078.43.

Divide the value by the total value as well as multiply the result by 100 to get the percentage. (amount/total amount), the formula for determining the percentage is 100%.

A percentage is defined as a portion of the whole expressed in the form of 100. There are two ways to calculate a percentage:

As per the given question;

The salary for the current year is given as  37,740.

There is the increase in 2%.

Let the last year's salary be x.

Then 2% of x will be;

x + 2%of x = 37,740

x + 2x/100 = 37,740

x + 0.02x = 37,740

1.02x = 37,740

x =  37,740/1.02

x = 33500

Therefore, the value of last year's salary is was 33,500.

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Answer:

[tex]x = 2[/tex]

[tex]y = 5[/tex]

Step-by-step explanation:

The graph is in the attached image above

Answer:

=======================

Given equations:

Solve by graphing, graph each line and find the point the lines intersect, this point is the solution.

See the attached, the solution is (2, 5)

The money James needs to invest as his principal in order to achieve this goal is $ 5, 197. 67

The formula for simple interest is expressed as;

Simple Interest, I = PRT/100

Where:

Substitute the values

8388 = P × 7. 34 × 22/ 100

cross multiply

161. 48 P = 838800

Make 'P' the subject of formula

P = 838800/ 161. 38

Divide through

P = $ 5, 197. 67

Thus, the money James needs to invest as his principal in order to achieve this goal is $ 5, 197. 67

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Answer:

9

Step-by-step explanation:

Answer:

Step-by-step

Answer:

x + 7

___________________________________________________
What are variables?

A variable is a quantity that may change within the context of a mathematical problem or experiment. Typically, we use a single letter to represent a variable. The letters x, y, and z are common symbols used for variables!

How do we describe variables in word form?

When we describe an expression in words that includes a variable, we're describing an algebraic expression (an expression with a variable).

In this case "The sum of a number" has no definite correlation to a number, therefore, it is automatically considered a variable.

Then, since it says "The sum" we know we are adding. Adding what? We are adding an unknown term to the number 7.

Henceforth, the answer is x + 7.
___________________________________________________
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To make lines u and v parallel, the indicated angle must be 108°.

So, if two parallel lines n and m intersect, then all the angles generated in line m must be exactly the same as the angles generated in line n.

According to the second (and previously used) criterion, we must have:

When we solve that, we get:

Therefore, to make lines u and v parallel, the indicated angle must be 108°.

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The 58 m/s initial velocity of the arrow with height, y = 58•t - 0.83•t², gives;

(1) 55.925 m/s

(2) 56.257 m/s

(3) 56.3317 m/s

(4) 56.33917 m/s

(b) 56.34 m/s

Initial velocity of the arrow = 58 m/s

Height of the arrow is; y = 58•t - 0.83•t²

The above kinematic equation can be analyzed as follows;

(1) The height at t = 1 is found as follows;

y = 58 × 1 - 0.83 × 1² = 57.17

Height at t = 1.5 s. is y = 58×1.5 - 0.83×1.5² = 85.1325

Which gives;

Average velocity = (85.1325-57.17)/(1.5-1) = 55.925

The average velocity in the interval [1, 1.5] is therefore;

(2) [1, 1.1]

Height at t = 1.1 s. is y = 58×1.1 - 0.83×1.1² = 62.7957

Which gives;

Average velocity = (62.7957-57.17)/(1.1-1) = 56.257

(3) [1, 1.01]

Height at t = 1.01 s. is y = 58×1.01 - 0.83×1.01² = 57.733317

Which gives;

Average velocity = (57.733317-57.17)/(1.01-1) = 56.3317

The average velocity is 56.33 m/s

(4) [1, 1.001]

Height at t = 1.01 s. is y = 58×1.001 - 0.83×1.001² = 57.22633917

Which gives;

Average velocity = (57.22633917-57.17)/(1.001-1) = 56.33917

(b) The equation for the instantaneous velocity is found as follows;

v = dy/dt = 58 - 2×0.83•t

After 1 second, we have;

t = 1

v = 58 - 2×0.83 × 1 = 56.34

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The value of y is 48

y= kx

let's solve for k which is the constant

y= 8 , x= 4

k= 8/4

k= 2

Next is to calculate the value of y when x is 24

y = 2 × 24

y= 48

Hence the value of y is 48

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The bucket and the jar together will hold (c + d) litres of water.

A linear equation in 2 variables [x and y] is any equation with the form:

ax + by = c and at least one of a or b being non-zero.

This is known as the equation's General Form.

For the given question;

The water hold by bucket = c litres.

The water hold by jar = d litres.

Thus, the water hold by both bucket and jar is is linear equation with two variable c and d.

Total water =  c + d

By, varying any value the total amount of the water will also get change.

Thus, total water hold by jar and bucket is (c + d) litres.

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Answer:625

Step-by-step explanation:(2+3)^4

5^4

Answer:

12:15 or a quarter past 12

Step-by-step explanation:

Math.

The correct answer is:   " 12:15 a.m."

Step-by-step explanation:

1 hour = 60 minutes {"exact equivalent."}

 ⇒ p.m.  =  afternoon or evening;

 {Note: "p.m." stands for: post meridiem —in Latin terminology.}.

____

7 hours + 5 hours = 12 hours;  12 hours + [tex]\frac{1}{4}[/tex] hours  = 12[tex]\frac{1}{4}[/tex] hours.  

____

1) 1st hour:    7 pm - 8 pm

2) 2nd hour:  8 pm - 9 pm

3) 3rd hour:   9 pm - 10 pm

4) 4th hour:   10 pm - 11 pm

5) 5th hour:  11 pm - 12 am ;

Note:  After 5 [five] hours past 7:00 pm;

The determined time, at this stage of solving this problem, is: 12am ; {commonly known as midnight ; based on the "am/pm" time schedule.

 {Note: "a.m." stands for:  ante meridiem— in Latin terminology.}

Then: we add:  " [tex]\frac{1}{4}[/tex] " hour to: 12 am.
____
[tex]\frac{1}{4}[/tex] hr = 0.25 hr.

{ [tex](\frac{1}{4} hr )* \frac{60minutes}{hr} =?[/tex] } ;

→  The units of "hr" [for: "hour(s)"]; cancel out ; since: "[ (hr ÷ hr) = 1 ] ".

and we have:  [tex]\frac{1}{4}* 60= 60/4 =[/tex] [tex]15 min.[/tex]

____

So:  12am + 15 minutes;  which is: 12:15 a.m. → the correct answer.

Hope this is helpful to you!  
     Best wishes in your academic endeavors!
____

Answer:

Step-by-step explanation

it is true