Critique Reasoning An office manager has $10,000 to spend on new equipment. He planned to purchase 300 lamps for $72 each. He completed the calculations at the right and concluded that there would be plenty of money left to buy additional equipment. 4. What does the office manager do to support his thinking?​

Answers:

1 yard by 72 yards

4 yards by 18 yards

6 yards by 12 yards

8 yards by 9 yards

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Explanation:

Let's list out all the ways to multiply to 72 using two values

1*72

2*36

3*24

4*18

6*12

8*9

Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.

We're left with this list

1*72

4*18

6*12

8*9

which represent the possible dimensions of this rectangle.

Keep in mind that 1 is not prime.

Cost for each pound of chocolate chips is equal to $3.5.

Cost for each pound of walnuts is equal to $1.75

In order to solve this word problem, we would assign variables to the cost for each pound of chocolate chips and each pound of walnuts respectively, and then translate the word problem into algebraic equation as follows:

For 3 pounds of chocolate chips and 2 pounds of walnuts, we have:

3c + 2w = 14              .....equation 1.

For 5 pounds of chocolate chips and 6 pounds of walnuts, we have:

5c + 6w = 28      .....equation 2.

Solving the system of equations by using the elimination method, we have:

3 × (3c + 2w = 14) = 9c + 6w = 42

                                5c + 6w = 28_

4c = 14

c = 14/4

c = $3.5

For the cost for each pound of walnuts, we have:

3c + 2w = 14

3(3.5) + 2w = 14

10.5 + 2w = 14

2w = 14 - 10.5

2w = 3.5

w = 3.5/2

w = $1.75.

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After dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),

C' = (8 , 12),  D' = (-4 , 16).

As given in the question,

From the given graph of quadrilateral  the vertices of the given image is given by :

A and D are second quadrant , C is first quadrant and B is in fourth quadrant.

Each unit on both the axis represents 1 unit only.

Coordinates of each vertices are:

A = (-3 , 1) , B = (4 , -3) ,C = (2 , 3), D = (-1 , 4)

Now for dilation scale factor is equal to 4

Image vertices for a dilation with center (0 , 0) multiply the vertices by scale factor 4.

Required image vertices are given by:

A' = (-12 , 4),

B' = (16 , -12)

C' = (8 , 12)

D' = (-4 , 16)

Therefore, after dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4),  B' =(16 , -12),

C' = (8 , 12),  D' = (-4 , 16).

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Answer:71/40 or 1 31/40 or 1.775  

Step-by-step explanation:1 31/40 is the mixed number

Part a

The equation for the way Michelle is paid is

Total weekly payment y = 495.50 + 0.105x

Part b

The total payment in a  month = $4021.625

She makes a 10.5% commission on every kayak she sells

Consider the total value of kayaks she sold = x

The rate of commission = 10.5%

The amount of commission = x × (10.5/100)

= 0.105x

The weekly fixed payment = $495.50

Total weekly payment y = 495.50 + 0.105x

Part b

The total value of the kayaks she sold = $19425

Total number of weeks in a month = 4

Then the total payment in a month = (4 × 495.50) + (0.105×19425)

= 1982 + 2039.625

= $4021.625

Hence,

part a

The equation for the way Michelle is paid is

Total weekly payment y = 495.50 + 0.105x

Part b

The total payment in a  month = $4021.625

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Answer:

Step-by-step explanation:

Ok:

1. Anything times zero always equals zero.

So: 55555555555555555555555555555555555555555555555555555555555555555555555555x0=

Answer:0

By the principle of mathematical induction, it has been proved that

[tex]p^3 + 11p[/tex] is divisible by 6

What is Principle of mathematical induction?

Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers

The given expression is [tex]p^3 + 11p[/tex]

For p = 1

[tex](1)^3 + 11 \times 1\\12[/tex]

which is a multiple of 6

Let it be true for p = m

[tex]m^3 + 11m[/tex] is a multiple of 6

[tex]m^3 + 11m = 6k[/tex], where k is any integer

For p = m + 1

[tex](m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12[/tex]

Now,

[tex]m^3 + 11m[/tex] is divisible by 6

We know that the product of two consecutive integers are divisible by 6

[tex]3m(m+1)[/tex] is divisible by 6

12 is divisible by 6

[tex](m+1)^3 + 11(m+1)[/tex] is divisible by 6

So it is true for p = m + 1

By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers

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According to the product rule of logarithms, the given equation is written as,  log₄(x² + 13x + 40) = 1

Product rule of logarithm

Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.  

And it is the first law and it can be represented as;

logₐ(x) + logₐ(y) = logₐ(xy)

Given,

Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1

And we have to rewrite the equation.

Here we have the logarithmic equation,

=> log₄(x+8) + log₄(x+5) = 1

By using the product property of logarithms, 

We have to rewrite the equation as,

=> log₄(x+8)(x+5) = 1

Now, we have to expand (x+8)(x+3) using the FOIL Method.

Then we get,

=> log₄(x² + 5x + 8x + 40) = 1

=> log₄(x² + 13x + 40) = 1

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The probability that the person obtains a note with C written in it is of:

0.1538 = 15.38%.

The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

The total number of notes in this problem is composed as follows:

Hence the total number is of:

Total = 7 x 4 + 8 x 3 = 52 notes.

The desired number of outcomes is the number of notes with C, hence:

Desired = 8 notes.

Thus the probability is calculated as follows:

Probability = Desired/Total = 8/52 = 0.1538 = 15.38%.

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Answer:

Step-by-step explanation:

1) first we find the x and y intercepts. Remember the intercepts are where x=0 and y=0

2) To find the x-intercept, substitute y = 0 and solve for x.

given equation:  x +2y= -4

then substitute y=0    so

x+ 2(0) = -4    -> any number multiplied by 0 it will always equal zero

then,  it will be  x=-4

the coordinates will be (-4,0)

3) To find the y-intercept, substitute x =0 and solve for y.

given equation:  x +2y= -4

then substitute x=0    so

(0)+ 2y = -4    -> x disappears since is zero

then,  it will be  2y=-4

then we multiply by 2 :

2y/2 = -4/2

y=-2

the coordinates for the y-intercept will be (0,-2)

The equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and  22.2 – 4x = 1.9, so options A and E are correct.

A formula known as an equation uses the equals sign to denote the equality of two expressions.

Given:

The Balance on the gift card =  $22.20,

The no of patches bought = 4,

The left balance on the card =  $1.90.

The equation for the statement in the question is,

The no of patches bought × The price of patches  + The left balance on the card = The Balance on the gift card

Let x be the price of one batch

Substitute the values,

4x + 1.9 = 22.20 or 22.2 – 4x = 1.9

Therefore, the equations you use to find the price of one tire patch are   4x + 1.9 = 22.20 and  22.2 – 4x = 1.9.

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                  The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]

Cone:

        A cone is a three-dimensional geometric shape that tapers smoothly from a flat base.

Given,

        The height of a cone is two times its base diameter.

         we have to find the volume of cone in terms of base radius.

let us assume the base radius of cone is equal to r units

                    so diameter(d) of cone will be, d= 2r units

so,

     height(h) of cone will be equal to, h = 2d units

                                                           h = 2x2r units

                                                           h = 4r  units

We know,

              Volume of the cone(V) = [tex]\pi r^{2} h/3[/tex]

                Where,

                             r = radius of base

                            h = height of cone

                            π = 22/7

Thus by using formula,

                                   Volume of cone(V) = [tex]\pi r^{2} h/3[/tex]

                                                                 = 22/7 * [tex]r^{2}[/tex] * 4r/3

                                                                 = 88[tex]r^{3}[/tex]/21

                                                                 = [tex]\frac{88r^{3} }{21}[/tex]

  Hence,

              The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]

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The absolute value function is represented by f(x) = |x+3| and the

x-intercept of the function is -3.

The function is represented as absolute value of 3 more than x.

hence the function 3 more than x is given by

f(x)=x+3

Now for absolute function:

f(x)=|x+3|

The graph of the function will have no negative value for f(x).

The graph will pass through the point (0,3) which is the y-intercept.

The x-intercept is at (-3,0) .

The domain of the function is all real vales of x.

The range of the function is (0,∞)

The parent function is given by y=|x| .

An procedure that establishes the absolute value of a number or variable is known as a modulus function. It produces the variable count's size.

It is also known as an absolute value function. No matter what input was given to this function, a positive result is always the result.

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The graph of the equation y = 3x + 2 + 3 is shown below .

In the question ,

it is given that ,

the equation of the line is y [tex]=[/tex] 3x [tex]+[/tex] 2 [tex]+[/tex] 3 ,

we need to draw the graph of it .

Do draw the graph we need at least two points .

for the first point

put x = 0

we get ,

y = 3(0) + 2 + 3

y = 0 + 2 + 3

y = 2 + 3

y = 5

the first point is (0,5)

for the second point put y = 0,

we get ,

0 = 3x + 2 + 3

3x = - 2 - 3

3x = -5

x = -5/3 ,

So , the second point is (-5/3 , 0)

the graph of the given equation is shown below .

Therefore , The graph of the equation y [tex]=[/tex] 3x + 2 [tex]+[/tex] 3 is shown below .

The given question is incomplete , the complete question is

What is the graph of the equation y = 3x + 2 + 3 ?

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Answer:

I think its 108 each Box is going to cost 108

The mid point of the line segment with the end coordinates of:

(0, 2) and (8,8) is (4,5).

For the given question;

The given coordinates are-

(x1, y1) = (0, 2)

(x2, y2) =  (8,8)

The mid point is found by the formula;

x = (x1 + x2 )/2

y = (y1 + y2)/2

Put teh values,

x = (0 + 8)/2

x = 4

y = (2 + 8)/2

y = 5

Thus, the mid point of the line segment with the end coordinates of:

(0, 2) and (8,8) is (4,5).

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Answer:

The answer to this problem is 0.0013.

Probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.

As given in the question,

Number of blue tickets in a box is equal to 25

Number of red tickets in a box is equal to 20

Total number of tickets in a box = 25 + 20

                                                     =  45

Drawing a ticket one at a time and not replaced

Probability of drawing a ticket first is red and second drawn is blue

= ( 20 / 45 ) × ( 25 / 44 )

= ( 500 / 1980 )

= 0.2525..

= 0.253

Therefore, probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.

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Answer:

x would be 3 by 2

I am 90% sure but I hope this helps!

After the firm work year reduced to 48 weeks at the same rate, the architect annual pay decrease to 43,392 dollars.

An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects

The company cuts the work year to 48 weeks but keeps the same rate of pay.  The amount the architect should expect his annual pay to decrease can be calculated as follows:

Let's find the rate.

Therefore,

52 weeks = 47008

1 week = ?

cross multiply

rate = 47008 / 52

rate = 904 dollars per weeks

He collects the same rate after the company cuts the work year to 48 weeks.

Therefore,

annual pay of the architect after the cut = 48 × 904

annual pay of the architect after the cut = 43,392 dollars

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Step-by-step explanation:

let angles of a triangle a=86

b= 180-3z , c= 180-4z

a+b+c = 180 {angle sum property}

86 +180+180-3z-4z=180

446 -7z = 180

-7z = -266

[tex]z = \frac{ - 266}{ - 7} = 38[/tex]

so other angle are

3z = 3 x 38 = 114

4z = 4 x 38 = 152

The set of side measurements that could be used to form a triangle are 8, 14, 20.

The concept that will be used is the concept of triangle inequality theorem.

To know if the given 3 side lengths are a triangle, then the use of the  triangle inequality theorem comes into play.

This rule tells us that when we sum 2 sides of a triangle  the value must be greater than the third side.

Then this rule can be applied as

The first option; 8, 14, 20

a+b>c  = 8+14>20

a+c>b  =  8+20>14

b+c>a   = 20+14>8

Therefore, first option is correct.

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Answer:

3

Step-by-step explanation:

When you substitute 0 in for x in the equation. You are left with f(0) = 3.

The total amount Frank pays back to the bank = $210642.72

Assuming the given interest rate- that is the simple interest rate.

so the future value A for the simple interest rate is given by,

A = P(1 + rt)

here, P = $56022

r = 0.04

t = 69

Substitute these values in above formula.

A = 56022 (1 + 0.04 * 69)

A = 56022 * 3.76

A = $210642.72

Therefore, the total amount Frank pays back to the bank = $210642.72

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Juan have earned of interest after 36 months at the rate of 7.5% interest per year.

Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. The formula of simple interest is as follows:

S.I = p×r×t

Where p is principle value, r is rate and t is time in years.

Here, the principle amount is $7,850 and rate is 7.5% i.e  [tex]\frac{7.5}{100}=0.075[/tex] and time is 36 months i.e 3 years.

Now, putting the values,

SI = 7850×0.075×3

= $ 1766

Therefore, the interest Juan have earned in 36 months is $1,766.

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Step-by-step explanation:

In general equation, y = mx+c, c represents y-intercept.

So, y-4 = 6x+42

y = 6x+46

So, y intercept will be 46

Answer:

Step-by-step explanation:

no idea

The number of oranges with first women are 200 and the number of oranges with other women are 100.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, 2 market women shared 300 oranges.

The share of first woman is twice the other.

Let the number of oranges with other women be x.

Then, the number of oranges with first women will be 2x.

Now, x+2x=300

3x=300

x=100

So, 2x=200

Therefore, the number of oranges with first women are 200 and the number of oranges with other women are 100.

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The weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.

A percentage is a minimum number or ratio that is measured by a fraction of 100.

Given that An investment portfolio is;

Investment Amount   Invested    ROR

Savings Account  $3,200     2.1%

Municipal Bond  $4,900       4.5%

Preferred Stock   $940         10.5%    

Common Stock A       $1,675     -3.5%

The weighted dollar amount of the savings account is;

= 2.1% of $3200

=  ( 2.1 / 100)  × $3200

= ($6720) /100

= $ 67.20

Therefore, the weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.

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