Is 100 a good estimate for the difference of 712 and 589? If it is, explain why it is a good estimate. If it is not, explain why it is a bad estimate.

Answer:

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

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Answer:

b . sphere

Step-by-step explanation:

Answer:

x = 32

but

I would say anything from 30 to 33

but truly i have no clue about the range

Step-by-step explanation:

3x-9=87 (because 180 -93 =87)

3x = 96

x = 32

Answer:

it is 32

Step-by-step explanation:

Answer:

26.75 units²

Step-by-step explanation:

Cube Area: A = l²

Triangle Area: A = 1/2bh

Step 1: Find area of biggest triangle

A = 1/2(3.5)(2 + 2 + 5)

A = 1.75(9)

A = 15.75

Step 2: Find area of 2nd biggest triangle

A = 1/2(5)(2)

A = 1/2(10)

A = 5

Step 3: Find area of smallest triangle

A = 1/2(2)(2)

A = 1/2(4)

A = 2

Step 4: Find area of cube

A = 2²

A = 4

Step 5: Add all the values together

A = 15.75 + 5 + 2 + 4

A = 20.75 + 2 + 4

A = 22.75 + 4

A = 26.75

Answer:

Step-by-step explanation:

1. 4/4+4-4=1

2. 4/4+4/4=2

3. 4+4/4-4=3

4. 4 × (4 − 4) + 4=4

5. (4 × 4 + 4) / 4=5

6. 44 / 4 − 4=6

7. 4+4-4/4=7

8. 4+4+4-4=8

9. 4+4+4/9=9

10. 44 / 4.4=10

Answer:

1 = (4 x 4)/(4 x 4) or  (4 + 4)/(4 + 4) or  (4 / 4) x (4 / 4) or  (4 / 4)/(4 / 4)  

2= (4 x 4)/(4 + 4) or 4 / ((4+4)/4)

3= (4 + 4 + 4)/4 or (4 x 4 - 4)/4

4 = 4 - (4 - 4)/4

5 = (4 x 4 + 4)/4

6 = 4 + (4 + 4)/4

7 = 4 - (4/4) + 4

8 = 4 + (4 x 4)/4

9 = 4 + 4 + (4/4)

10 - I tried the best. You might need ! or sqrt operator to get 4.

Updated:

I forgot we could use 4, 44, 444, or 4444, so that 10 could be expressed as:

10 = (44 - 4)/4

Answer:

c = 468 / 13

Step-by-step explanation:

If c is the number of cans of soda in each case, we know that the number of cans in 13 cases is 13 * c = 13c, and since the number of cans in 13 cases is 468 and we know that "is" denotes that we need to use the "=" sign, the equation is 13c = 468. To get rid of the 13, we need to divide both sides of the equation by 13 because division is the opposite of multiplication, therefore the answer is c = 468 / 13.

Answer:

468/13 = c

Step-by-step explanation: Further explanation :

[tex]13 \:cases = 468\:cans\\1 \:case\:\:\:\:= c\: cans\\Cross\:Multiply \\\\13x = 468\\\\\frac{13x}{13} = \frac{468}{13} \\\\c = 36\: cans[/tex]

Answer:

[tex]\huge \boxed{x=3}[/tex]

Step-by-step explanation:

[tex]6(x+2)=30[/tex]

[tex]\sf Divide \ both \ sides \ by \ 6.[/tex]

[tex]x+2=5[/tex]

[tex]\sf Subtract \ 2 \ from \ both \ sides.[/tex]

[tex]x=3[/tex]

Answer:

3

Step-by-step explanation:

30 = 6(x+2)

30/6 = 5

5 = x+2

5-2 = 3

3=x

This is a pretty simple question and I tried to make it as simple as possible when explaining it.

Answer:

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Solution Set : { x = 123, y = 246, z = 11 }

Step-by-step explanation:

Let's say that x represents the number of car wash tickets, y represents the number of silly sting fight tickets, and z represents the number of dance tickets. We know that the total tickets = 380, so therefore,

x + y + z = 380,

And the car wash tickets were $5 each, the silly sting fight tickets were $3 each and the dance tickets were $10 each, the total cost being $1460.

5x + 3y + 10z = 1460

The silly string tickets were sold for twice as much as the car wash tickets.

y = 2x

Therefore, if we allign the co - efficients of the following system of equations, we get it's respective matrix.

System of Equations :

[tex]\begin{bmatrix}x+y+z=380\\ 5x+3y+10z=1460\\ y=2x\end{bmatrix}[/tex]

Matrix :

[tex]\begin{bmatrix}1&1&1&|&380\\ 5&3&10&|&1460\\ -2&1&0&|&0\end{bmatrix}[/tex]

Let's reduce this matrix to row - echelon form, receiving the number of car wash tickets, silly sting fight tickets, and dance tickets,

[tex]\begin{bmatrix}5&3&10&1460\\ 1&1&1&380\\ -2&1&0&0\end{bmatrix}[/tex] - Swap Matrix Rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ -2&1&0&0\end{bmatrix}[/tex] - Cancel leading Co - efficient in second row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{2}{5}&-1&88\\ 0&\frac{11}{5}&4&584\end{bmatrix}[/tex] - Cancel leading Co - efficient in third row

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&\frac{2}{5}&-1&88\end{bmatrix}[/tex] - Swap second and third rows

[tex]\begin{bmatrix}5&3&10&1460\\ 0&\frac{11}{5}&4&584\\ 0&0&-\frac{19}{11}&-\frac{200}{11}\end{bmatrix}[/tex] - Cancel leading co - efficient in row three

And we can continue, canceling the leading co - efficient in each row until this matrix remains,

[tex]\begin{bmatrix}1&0&0&|&\frac{2340}{19}\\ 0&1&0&|&\frac{4680}{19}\\ 0&0&1&|&\frac{200}{19}\end{bmatrix}[/tex]

x = 2340 / 19 = ( About ) 123 car wash tickets sold, y= 4680 / 19 =( About ) 246 silly string fight tickets sold, z = 200 / 19 = ( About ) 11 tickets sold

Answer:

69

Step-by-step explanation:

The order of operations is PEMDAS; parentheses, exponents, multiplication and division, and finally addition and subtraction.

We know that x is the first row, and if there are 30 spots in the first row, then x=30. Using this information, all we have to do now is plug in 30 for x and solve.

[tex]\frac{5(x)}{2} -6[/tex]

[tex]\frac{5(30)}{2}-6[/tex]

[tex]\frac{150}{2}-6[/tex]

[tex]75-6[/tex]

[tex]69[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 5

▹ Step-by-Step Explanation

The x-axis and y-axis are labeled on the graph. The x-axis is the horizontal axis. Between 4 and 6, there is a missing number. That number should be 5, leaving us with an x-value of 5 for Point A.

Hope this helps!

CloutAnswers ❁

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Answer:

The x value is 5

Step-by-step explanation:

The x value is the value going across

Starting where the two axis meet, we go 5 units to the right

That is the x value

Answer:

x=11

Step-by-step explanation:

Answer:

x = 11

Step-by-step explanation:

6x - 10 = 4(x+3)

6x - 10 = 4*x + 4*3

6x - 10 = 4x + 12

6x - 4x = 12 + 10

2x = 22

x = 22/2

x = 11

check:

6*11 - 10 = 4(11+3)

66 - 10 = 4*14 = 56

Answer:

x=9; one ticket is $9

Step-by-step explanation:

4x+12=48

4x=48-12

4x=36

x=36/4

x=9

Answer:

The correct answer is A

Step-by-step explanation:

Answer:

(-8, -2)

Step-by-step explanation:

y-x = 6

y + x = -10

Add the two equations together to eliminate x

y-x = 6

y + x = -10

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

2y = -4

Divide by 2

2y/2 = -4/2

y = -2

Now find x

y+x = -10

-2+x = -10

x = -8

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

Answer:

Show that the statement is true for n=1

Step-by-step explanation:

Hey,

Show that the statement is true for n=1

You can check my other answer there which explains a little bit more the ideas.

https://brainly.com/question/17162256

thank you

Answer: There are 15 friends.

Step-by-step explanation:

We know that there is N friends (N is the number that we are looking for)

Each friend weights 1/20 ton.

Now, the weight of the N friends together is N times 1/20 ton.

Then we have:

N*(1/20) ton = 3/4 ton

We solve this for N.

First multiply both sides by 20.

20*N*(1/20) = N = 20*(3/4) = 60/4 = 15

Answer:

I can find the total number of people by dividing the total weight by the weight of one person.

Step-by-step explanation:

Answer:

a) 40 dollars

b) 480 dollars

Step-by-step explanation:

Given the average property tax on a three bedroom home in a certain community modelled by the equation T(x) =20x²+40x+600, the rate at which the property tax is increasing with respect to time in 2008 can be derived by solving for the function T'(x) at x=0

T'(x) = 2(20)x¹ + 40x° + 0

T'(x) = 40x+40

At x = 0,

T'(0) = 40(0)+40

T'(0) = 40

Hence the property tax was increasing at a rate of 40dollars with respect to the initial year (2008).

b) There are 4 years between 2008 and 2012. To know how much that the tax change between the years 2008 and 2012, we will find T(4) - T(0)

Given T(x) =20x²+40x+600

T(4) =20(4)²+40(4)+600

T(4) = 320+160+600

T(4) = 1080 dollars

Also T(0) =20(0)²+40(0)+600

T(0) = 0+0+600

T(0)= 600 dollars

T(4) - T(0) = 1080 - 600

T(4) - T(0) = 480 dollars

Hence, the tax has changed by $480 between 2008 and 2012

The area is given by the integral

[tex]\displaystyle A=2\pi\int_Cx(t)\,\mathrm ds[/tex]

where C is the curve and [tex]dS[/tex] is the line element,

[tex]\mathrm ds=\sqrt{\left(\dfrac{\mathrm dx}{\mathrm dt}\right)^2+\left(\dfrac{\mathrm dy}{\mathrm dt}\right)^2}\,\mathrm dt[/tex]

We have

[tex]x(t)=t+\sqrt 2\implies\dfrac{\mathrm dx}{\mathrm dt}=1[/tex]

[tex]y(t)=\dfrac{t^2}2+\sqrt 2\,t+1\implies\dfrac{\mathrm dy}{\mathrm dt}=t+\sqrt 2[/tex]

[tex]\implies\mathrm ds=\sqrt{1^2+(t+\sqrt2)^2}\,\mathrm dt=\sqrt{t^2+2\sqrt2\,t+3}\,\mathrm dt[/tex]

So the area is

[tex]\displaystyle A=2\pi\int_{-\sqrt2}^{\sqrt2}(t+\sqrt 2)\sqrt{t^2+2\sqrt 2\,t+3}\,\mathrm dt[/tex]

Substitute [tex]u=t^2+2\sqrt2\,t+3[/tex] and [tex]\mathrm du=(2t+2\sqrt 2)\,\mathrm dt[/tex]:

[tex]\displaystyle A=\pi\int_1^9\sqrt u\,\mathrm du=\frac{2\pi}3u^{3/2}\bigg|_1^9=\frac{52\pi}3[/tex]

Work Shown:

T = average Celsius temperature two Sundays ago

8% = 8/100 = 0.08

8% of T = 0.08T

L = average Celsius temperature last sunday

L = 8% higher than T

L = T + (8% of T)

L = T + 0.08T

L = 1.00T + 0.08T

L = (1.00 + 0.08)T

L = 1.08T

The 1.08 refers to the idea that L is 108% of T

Answer:

b and d

Step-by-step explanation:

khan

Step-by-step explanation:

42 is your answer according to bodmas

Answer:

197 = 10(31-1) + a

197 = 300 + a

-103 = a

Answer:

The value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]

The property to be used is : [tex]x^a{\cdot} x^b=x^{a+b}[/tex]

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

[tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}[/tex]

So, the value of [tex]4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}[/tex]  is  [tex]4^{\dfrac{8}{15}}[/tex] .

Answer:

(a) After t years, the height is

18t² + 3t + 10

(b) The shrubs are847 cm tall when they are sold.

Step-by-step explanation:

Given growth rate

dh/dt = 1.8t + 3

dh = (18t + 3)dt

Integrating this, we have

h = 18t² + 3t + C

When t = 0, h = 10cm

Then

10 = C

So

(a) h = 18t² + 3t + 10

(b) Because they are sold after every 9 years, then at t = 9

h = 18(9)² + 3(9) + 10

= 810 + 27 + 10

= 847 cm

Answer:

The portfolio beta is  [tex]\alpha = 1.354[/tex]

Step-by-step explanation:

From the question we are told that

      The  first investment is [tex]i_1 = \$ 25,000[/tex]

       The  first  beta is  [tex]k = 0.8[/tex]

      The second investment is  [tex]i_2 = \$ 40,000[/tex]

       The  second  beta is  [tex]w = 1.7[/tex]

Generally the portfolio beta is mathematically represented as

           [tex]\alpha = \frac{ i_1 * k + i_2 * w }{ i_1 + i_2}[/tex]

substituting values

          [tex]\alpha = \frac{ (25000 * 0.8) + ( 40000* 1.7 ) }{40000 + 25000}[/tex]

          [tex]\alpha = 1.354[/tex]

Answer:

There is a positive correlation between X and Y.

Step-by-step explanation:

The estimated regression equation is:

[tex]\hat Y=20X+200[/tex]

The general form of a regression equation is:

[tex]\hat Y=b_{yx}X+a[/tex]

Here, [tex]b_{yx}[/tex] is the slope of a line of Y on X.

The formula of slope is:

[tex]b_{yx}=r(X,Y)\cdot \frac{\sigma_{y}}{\sigma_{x}}[/tex]

Here r (X, Y) is the correlation coefficient between X and Y.

The correlation coefficient is directly related to the slope.

And since the standard deviations are always positive, the sign of the slope is dependent upon the sign of the correlation coefficient.

Here the slope is positive.

This implies that the correlation coefficient must have been a positive values.

Thus, it can be concluded that there is a positive correlation between X and Y.

Answer:

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Step-by-step explanation:

Given

[tex]Sections = 10[/tex]

[tex]n(Gray) = 5[/tex]

[tex]n(Blue) = 5[/tex]

Required

Determine P(Gray and Blue)

Using probability formula;

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

Calculating P(Gray)

[tex]P(Gray) = \frac{n(Gray)}{Sections}[/tex]

[tex]P(Gray) = \frac{5}{10}[/tex]

[tex]P(Gray) = \frac{1}{2}[/tex]

Calculating P(Gray)

[tex]P(Blue) = \frac{n(Blue)}{Sections}[/tex]

[tex]P(Blue) = \frac{5}{10}[/tex]

[tex]P(Blue) = \frac{1}{2}[/tex]

Substitute these values on the given formula

[tex]P(Gray\ and\ Blue) = P(Gray) * P(Blue)[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{2} * \frac{1}{2}[/tex]

[tex]P(Gray\ and\ Blue) = \frac{1}{4}[/tex]

Answer:

C). $3523.83

Step-by-step explanation:

loan of principles p= $9,300,

at rate R= 12 1 /8 % interest

Rate R = 12.125%

for duration year T = 37.5 months

T= 37.5/12 = 3.125 years

Interest I=PRT/100

Interest I =( 9300*12.125*3.125)/100

Interest I = (352382.8125)/100

Interest I = 3523.83

Interest I= $3523.83

Answer:

x=9.6

Step-by-step explanation:

The dot in the middle represents the center of the circle, so therefore, the line that is represented by 16 is the radius. Since that is the radius, the side that is the hypotenuse of the small triangle is also 16, since they have the same distance.

The line represented by 25.6 with x as its bisector shows that when we divide it by 2, the other side of the triangle besides the hypotenuse is 12.8.

Now that we have the two sides of the triangle, we can find the last side (represented by x). Use pythagorean theorem:

[tex]a^2 +b^2=c^2\\x^2+(12.8)^2=16^2\\x^2+163.84=256\\x^2=92.16\\x=9.6[/tex]