A rectangular piece of metal is 20 in longer than it is wide. Squares with sides 4 in long are cut from the four corners and the flaps are folded upward to form an open box. If the volume of the box is 1200 in3,
what were the original dimensions of the piece of metal?

Answer:

3876

Step-by-step explanation:

Given the following :

Fraternity members = 20

They are to attend 5 different parties in groups of 4

Meaning a group = 4 persons

Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).

Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.

Group members are in 4's

19C4

From: nCr = n! /(n-r)! r!

19C4 = 19! / (19 - 4)! 4!

= 19! / 15! 4!

= (19 * 18 * 17 * 16) / (4 * 3 * 2)

= 93024 / 24

= 3876

Answer:

120

Step-by-step explanation:

Your description is a little different from below picture, but the logic is the same. The 1 in the tens position represents 10x12 = 120, hence 120 should be subtracted and leaves you with 67 to continue.

Answer:

187

Step-by-step explanation:

12 in not the divisor of 8587 in the dividend with 7 hundreds and 1 tens. 8400 you subtracted from 8587 to give 187.

Answer:

the answer is 69

Step-by-step explanation:

you find the square root of 4761

Answer:

its 69

Step-by-step explanation:

Answer:

1 MILE

Step-by-step explanation:

Answer:

4k=16

k=4

Step-by-step explanation:

please give 5 star i need it

Answer:

Smaller integer = -6

Larger integer = -5

Step-by-step explanation:

Let the two consecutive integers = [tex]x[/tex] and ([tex]x+1[/tex])

As per the given statement,

Larger i.e. ([tex]x+1[/tex]) is 7 greater than twice ([tex]2\times x[/tex]) the smaller integer.

To find:

The value of integers = ?

Solution:

First of all, let us learn about integers.

The integers are of the form (put in increasing order):

[tex]-\infty, ...., -3, -2,-1, 0, 1, 2, 3, ...., \infty[/tex]

and -1 > -2

So the consecutive integers are 1 greater than the smaller.

Therefore, the two integers can be [tex]x, x+1[/tex]

Now, writing the given condition in the form of an equation:

[tex]x+1=2x+7\\\Rightarrow 1-7=2x-x\\\Rightarrow -6=x\\\Rightarrow \bold{x=-6}[/tex]

So, the smaller integer = -6

Larger integer = -6+1 = -5

Answer:

6 hours?

Step-by-step explanation:

12:00    0 hour(s)

1:00       1 hour(s)

2:00      2 hour(s)

3:00      3 hour(s)

4:00      4 hour(s)

5:00      5 hour(s)

6:00      6 hour(s)

Answer:

The box should have base 16ft by 16ft and height 8ft Therefore,dimensions are 16 ft by 16 ft by 8 ft

Step-by-step explanation:

We were given the volume of the tank as, 2048 cubic feet.

Form minimum weight, the surface area must be minimum.

Let the height be h and the lengths be x

the volume will be: V=x²h then substitute the value of volume, we have

2048=hx²

hence

h=2048/x²

Since the amount of material used is directly proportional to the surface area, then the material needs to be minimized by minimizing the surface area.

The surface area of the box described is

A=x²+4xh

Then substitute h into the Area equation we have

A= x² + 4x(2048/x²)

A= x² + 8192/x

We want to minimize

A

dA/dx = -8192/x² + 2 x= 0 for max or min

when dA/dx=0

dA/dx= 2x-8192/x²=0

2x=8192/x²

Hence

2x³=8192

x³=4096

x=₃√(4096)

X=16ft

Then h=2048/x²

h=2048/16²

h=8ft

The box should have base 16ft by 16ft and height 8ft

Hence the dimensions are 16 ft by 16 ft by 8 ft

Answer:

Step-by-step explanation:

Since the function is a linear function

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question the equation is

y = 4x + 6

Comparing with the general form of equation above the slope of the function is

Hope this helps you

Answer:

2 Values

Step-by-step explanation:

For a five-year moving average, two values will be lost at the beginning and end of the time series.

This is because we add the first five elements and divide it by 5 to get the five year moving average. But the middle value of 5 is 2.5 which is greater than 2 so the result is placed against the third value. In this way the first two and last 2 values are lost.

For understanding let us compute the 5 year moving average as

a1= 1/5( y1+ y2+y3+ y4+y5)

a2= 1/5 ( y2+y3+ y4+y5+ y6)

a3 = 1/5(y3+ y4+y5+ y6+ y7)

a4= 1/5(y4+y5+ y6+ y7+ y8)

a5= 1/5(y5+ y6+ y7+y8+y9)

The average so obtained are placed opposite the middle year of each group.

So the values at the y1,y2 ,at the beginnign and at the end y8 and y9 are lost.

Answer:

yes

Step-by-step explanation:

this is correct because if you multipy them both by 4 you get those answers .

4 x 4 = 16

5 x 4 = 20

The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.

A ratio is a group of sequentially ordered numbers a and b expressed as a/b, where b is never equal to zero. When two objects are equal, a statement is said to be proportional.

The equivalent is the expression that is in different forms but is equal to the same value.

The two ratios are given below.

4:5 and 16:20

Convert the ratios into their simplified form. Then the ratios are given as,

4:5 and 16:20

4:5 and 4:5

The ratios 4:5 and 16:20 are equivalent to each other. Yes, the ratios are equal to 4: 5.

More about the ratio and the proportion link is given below.

https://brainly.com/question/14335762

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Answer:

D

Step-by-step explanation:

first of all we need to solve the inequalities

[tex]3-x\geq 2\\\\3-x+x\geq 2+x\\\\3\geq2+x \\\\3-2\geq 2-2+x\\\\1\geq x\\\\x\leq 1[/tex] (-∞,1] or ]-∞,1]

the second inequality is

[tex]4x+2\geq 10\\\\4x+2-2\geq 10-2\\\\4x\geq 8\\\\\frac{4x}{4}\geq \frac{8}{4} \\\\x\geq 2[/tex] [2,∞) or [2,∞[

so the answer is D

Answer: D

Step-by-step explanation:

To graph the inequalities on the number line, let's first solve them.

3-x≥2                                [subtract both sides by 3]

-x≥-1                                [divide both sides by -1, remember to flip inequalities]

x≤1

---------------------------------------------------------------------------------------------

4x+2≥10                           [subtract both sides by 2]

4x≥8                                 [divide both sides by 4]

x≥2

---------------------------------------------------------------------------------------------

Now, we have our inequalities, x≤1 and x≥2. Notice that both inequalities are greater/less than or equal to. The "or equal to" part means that x is equal to 1 and 2. Therefore, when graphed, it is a closed circle. This let's us automatically eliminate B and C because they have open circles.

For x≤1, we know that x is going to be 1 and below, meaning it starts at 1 and travels left where it gets smaller and smaller. This tells us that the answer is D, but let's check to be sure.

For x≥2, we know that x is going to be greater than 2. This let's us know that the arrow will be pointing to the right, where the numbers are getting bigger and bigger. Knowing this, we can confirm that D is the correct answer.

Answer:

function

Step-by-step explanation:

A function is a rule that pairs each element in one set with exactly one element from a second set.​

A function is a rule that pairs each element in one set with exactly one element from a second set.​

A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.

Function is a relation.

Let a set A = {1, 2, 3, ........} and set B = {1, 4, 9, .....}

Let f(x) = x² be the function.

f(1) = 1 , so 1 is mapped to 1

f(2) = 4, so 2 is mapped to 4.

...............

It goes on like this.

No element would map to more than one element.

1 will only map to 1, not to 4, 9, .......

Similarly, 2 will map to 4 only, not any other element.

But more than one element in set A can be mapped to same element in set B.

Suppose A = {......, -2, -1, 0, 1, 2, .......} and B = {1, 4, 9, .....}

We have f(1) = f(-1) = 1

Also, f(2) = f(-2) = 4

But this is a function.

Hence the rule is that pairs each element in one set with exactly one element from a second set.​

Learn more about Functions here :

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Answer:

H₀ should be rejected, yogurt cups are under-filling, the manager has to check the process

Step-by-step explanation:

Normal distribution and n < 30. We must use t-student test.

a) If it is required to test   H₀    μ >= 6     Hₐ   μ < 6  is a one tail test (left-tail)

At  α = 5 %     α = 0,05    and   n = 16  then degree of freedom is n -1

df = 15  find   t(c) = - 1,753

μ = 5,85     and  s  = 0,2      ( sample mean and standard deviation respectevily)

T compute   t(s)

t(s)  =  ( μ  -  μ₀ ) / s/√n

t(s)  =  ( 5,85 - 6 ) /0,2/√16

t(s)  =  - 0,15*4/0,2

t(s)  =  - 3

t(s) < t(c)       -3 < - 1,753

Then t(s) is in the rejection region we reject H₀. There is enough evidence to claim the yogurt cups are under-filling.

Manager has to check on the process

Answer:

C

Step-by-step explanation:

In the pattern, there are some similarities with the first three circles.

1. The number is on the blue half.

2. The halves switch spots, red-blue, blue-red, red-blue.

So, the next one should have the number on the blue half and the next pattern should be red-blue, blue-red, red-blue, and blue-red.

Which one has both the number on the blue half and the pattern blue-red?

C

Hoped this helped.

Answer:

2 1/3

Step-by-step explanation:

i know because i did the test in k 12

An absolute value of |x| {modulus of x} is the value of a real number x. The absolute value of ||2 1/3|| is 2 1/3.

An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.

The absolute value of ||2 1/3|| is,

||2 1/3||

= |2 1/3|

= 2 1/3

Hence, The absolute value of ||2 1/3|| is 2 1/3.

Learn more about Absolute value here:

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Answer:

Prove that (A-B) U (B-A) =(A U B) - (A intersection B). 2. See answers ... izvoru47 and 170 more users found this answer helpful

Answer:

B.) 2x2 + 8x – 24 = 0

Step-by-step explanation:

For x= 2 and x= -6

Let's determine the equation of the solutions.

(X-2)(x+6)=0

X²+6x -2x -12= 0

X² +4x -12= 0

So the above is the real equation to the solution of x= 2 and x= -6

But in the options, we don't have something like that.

But let's try and multiply the solution will a positive or negative integer.

Lets start with +2

2(X² +4x -12= 0)

2x² + 8x -24 = 0

Yeah, option B is the answer

Answer:  The answer is:  " x = 2.833333333333...." .

___________________________

             or:  write as:  " 2 [tex]\frac{5}{6}[/tex] " .  

___________________________

Step-by-step explanation:

___________________________

Set up a ratio:

Note:  Segment FH =  (x + 35)

         Segment JL = 20 ;

         Segment FH ~ Segment JL ;

___________________________

Note:  Segment GH = (x - 4) ;

         Segment  KL  =  5 ;

         Segment GH ~ Segment KL .

___________________________

So, ( x + 3.5) : 20 :: (x-4) : 5 ;

Write this ratio in fraction format:

___________________________

→  [tex]\frac{(x+3.5) }{20 } = \frac{(x-4) }{5}[/tex]  ;

Now; "cross-factor multiply" :

→  [tex]\frac{a}{b} = \frac{c}{d }[/tex]  ;  → [tex]ad = bc[/tex] ; { [tex]{ a\neq0 ; b\neq0 ; c\neq0 ; d\neq0[/tex] .}.

___________________________

So:

  5(x + 3.5)  =  20(x - 4) ;  

___________________________

→ To simplify, start by divide each side of the equation by "5" ;

___________________________

  →   {5(x + 3.5) } / 5  =  { 20(x - 4)  } / 5 ;

to get:

      →  (x + 3.5)  =  4(x - 4) ;

___________________________

Now, on the right-hand side of the equation;

  let us expand the expression;

___________________________

We have the expression:  " 4(x - 4) " ;

 To expand:

Note the "distributive property of multiplication:

     →   a(b + c)  = ab + ac ;

Likewise:

     →   4(x - 4)  = 4x  - 16 ;

___________________________

Now, we can rewrite our equation:

___________________________

     →   " x + 3.5  =  4x - 15 "  ;

Now, we can subtract "x" from each side of the question;

     & add "15" to each side of the equation; as folllows:

___________________________

     →     x + 3.5  =  4x - 15 ;

          - x + 15   =  - x  +15

___________________________

to get:        8.5  =  3x ;  

                   ↔  3x  = 8.5 ;

Now, divide each side of the equation by "3" ;

       to isolate "x" on one side of the equation;

       & to solve for "x" ;  as follows:

                     →  3x / 3 = 8.5 / 3 ;

             to get:   x  = 8.5 /3  

                              = 2.83333333333 ;  

                         or; write as:  " 2 [tex]\frac{5}{6}[/tex] ."

___________________________

Hope this is helpful to you!  Best wishes!

___________________________

Answer:

There is sufficient evidence to support the claim that the mean temperature is different from 42 deg

Step-by-step explanation:

From the given information, we are being told that:

The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 42°F

i. e  mean  μ = 42

The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect.

Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

From above;

The null and the alternative hypothesis can be computed as:

[tex]\mathbf{H_o : \mu = 42} \\ \\ \mathbf {H_1 : \mu \neq 42}[/tex]

Here , the hypothesis test of the claim is the alternative hypothesis.

The conclusion based on the decision rule:  is to reject the null hypothesis

∴

The conclusion in non technical terms is that :

There is sufficient evidence to support the claim that the mean temperature is different from 42 deg

Answer:bruh

Step-by-step explanation:u really need that easy ahh question?

Answer:

x = -13

Step-by-step explanation:

3(x + 7) = -18

Divide both sides by 3.

x + 7 = -6

Subtract 7 from both sides.

x = -13

Answer:

12 cells every hour.

Step-by-step explanation:

You would do 2 x 6

(the 2 is the cells per hour, and the 6 is the amount of hours)

Answer:

6w + 18z

Step-by-step explanation:

distribute the 2

2 x 3w = 6w

2 x 9z = 18 z

6w + 18z

Answer:

6w+18z

Step-by-step explanation:

Answer:

Pythagoras

Step-by-step explanation:

Pythagoras

Answer:

12

Step-by-step explanation:

The formula for RANGE of a given set if data = Maximum value - Minimum value.

In the above question, we are given a group of ACT scores

21, 22, 23, 25, 26, 33.

Maximum value = 33

Minimum value = 21

Range = 33 - 21

= 12

Therefore, the range for this distribution of scores is 12

Answer:

10/3

Step-by-step explanation:

Step 1: Subtract 4 from both sides.

3

x

+

4

−

4

=

14

−

4

3

x

=

10

Step 2: Divide both sides by 3.

3

x

3

=

10

3

Answer:

16 miles long to work it would be 0 miles shorter

Step-by-step explanation:

8+8 is 16

if the road was just one street it would still be the same distance

I hope this helps. THIS MIGHT BE WRONG though if someone say something else, take a good look at their answer too because the way I did it, seems like it's a little too simple.

Answer:   The distance will be about 11 miles . 2) The man's one way-trip will be 5 miles shorter.

Step-by-step explanation:

If the man  drove east by 8 miles and  North by 8 miles and we want to determine the distance that is directly  from east to north then we will use the Pythagorean Theorem  solve for that distance.

Now since we are solving for the distance directly from his home to work we will be looking for the hypotenuse in this case.

a^2 + b^2 =c^2  where c is the hypotenuse

8^2 + 8^2 =c^2

64 +64 = c^2  

c= [tex]\sqrt{128}[/tex]  

c =  11.31

  In this case the distance from his home directly to his work will be about 11 miles.

2.   To find out how much shorter the man will travel ,add the east and north distance and subtract 11.31 from it.

8 + 8 = 16

16  - 11.31 = 4.69

Answer: 0.49

Step-by-step explanation:

given data:

no of computer services firms =200

no of firms under $1million = 102

no of firms between $1million to $20million = 61

no of firms $20million and above = 37

solution:

probability that a firm selected has 1$million or above.

P ( x ≥ $1million )

= 61/200 + 37/200

= 49/100

= 0.49

the probability of selecting with $1million or more in income taxes is 0.49%

Answer:

There is no sufficient evidence to support the executive claim

Step-by-step explanation:

From the question we are told that

     The  population proportion is  [tex]p = 0.48[/tex]

      The  sample proportion is  [tex]\r p = 0.45[/tex]

       The sample  size is  [tex]n = 300[/tex]

       The  level of significance is [tex]\alpha = 0.02[/tex]

The null hypothesis is  [tex]H_o : p= 0.48[/tex]

The  alternative hypothesis is  [tex]H_a : p \ne 0.48[/tex]

   Generally the test statistics is mathematically evaluated as

           [tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1 - p )}{n} } }[/tex]

=>        [tex]t = \frac{0.45 - 0.48 }{ \sqrt{ \frac{0.48 (1 - 0.48 )}{300} } }[/tex]

=>       [tex]t = -1.04[/tex]

The  p-value is mathematically represented as

     [tex]p-value = 2P(z > |-1.04|)[/tex]

Form the z-table  

                 [tex]P(z > |-1.04|) = 0.15[/tex]

=>   [tex]p-value = 2 * 0.15[/tex]

=>   [tex]p-value = 0.3[/tex]

Given that  [tex]p-value > \alpha[/tex]  we fail to reject the null hypothesis

   Hence we can conclude that there is no sufficient evidence to support the executive claim