A cooler has a 60-L capacity. Its internal length is 60 cm and its internal width is 35 cm. Determine the internal height and the internal surface area of the cooler.

Hint 1 cm=1 ml

Answer:The equation of a line is written as ​y=mx​+​b​, where the constant ​m​ is the slope of the line, and the ​b​ is the ​y​-intercept.

Step-by-step explanation:

The sum of the terms of the given sequence will be 648.

An arithmetic sequence or arithmetic progression is a sequence in which each term is created or obtained by adding or subtracting a common number to its preceding term or value.

The given sequence is representing an arithmetic sequence.

Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6

3 - (-3) = 3 + 3 = 6

Since last term of the sequence is 81.

By the explicit formula of an arithmetic sequence, we can find the number of terms of this sequence.

[tex]\rm T_n= a+(n-1)d\\\\[/tex]

Where a = first term of the sequence, d = common difference.

Substitute all the values in the formula

[tex]\rm T_n= a+(n-1)d\\\\ 81 = -9 + 6(n - 1)\\\\ 81+9 =6(n-1)\\\\90=6(n-1)\\\\ n-1=\dfrac{90}{6}\\\\n-1=15\\\\n = 15+1\\\\n=16[/tex]

Now we know the sum of an arithmetic sequence is represented by

[tex]\rm S_{16}=\dfrac{16}{2}[-9+(16-1)6]\\\\S_{16}=8 [-9+15\times 6]\\\\S_{16}=8 [-9+90}\\\\S_{16} = 8 \times 81\\\\S_{16}=648[/tex]

Hence, the sum of the terms of the given sequence will be 648.

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Answer:

60 degrees

Step-by-step explanation:

It measures 60 degrees

Tip: the wider the angle, the bigger the degree.

Hope this helps!

Answer:

so

Step-by-step explanation:

it is 5 pounds your welcome

The bigger measurement is 5 lbs.

Measurement is the method of comparing the properties of a quantity or object using a standard quantity.

Measurement is essential to determine the quantity of any object.

Given two measurements.

75 ounces and 5 lbs.

We have the conversion formula,

1 lbs = 16 ounces

5 lbs = 5 × 16 = 80 ounces

80 ounces is greater than 75 ounces

5 lbs is greater than 75 ounces.

Hence the measurement which is bigger is 5 lbs.

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Step-by-step explanation:

the height from the right angle in a right-angled triangle is the square root of the product of the segments of the Hypotenuse the height is splitting it into.

so,

x = sqrt(7×9) = sqrt(63) = 3×sqrt(7)

Answer:

The y axis is a vertical line

Step-by-step explanation:

Y axis is up

Answer:

There are 10,560 yards in 3 mile or miles in 3 yard. Both yards and miles are units of length in the US customary and imperial systems of measurement.

Answer:

(For the first two questions I do believe that you will need a protractor to calculate the angles.)

15) [tex]-(\frac{7\pi }{18} )\\[/tex] measures out to -70° in order to display that the angle would be in quadrant IV (the bottom right quadrant.)

The first image attached shows where the angle should be located.

16) [tex]\frac{\pi }{3}[/tex] is equal to 60° (the line you draw will be in quadrant 1 (the top right quadrant))

17) 350° is [tex]\frac{35\pi }{18}[/tex] or 6.11 (the answer depends on the format the professor wants.)

18) 240° is [tex]-(\frac{4\pi }{3})[/tex] radians or -4.19 (I am rounding to the nearest hundredths place the unsimplified answer is −4.18879020...)

Answer:

9.42 years (= 113 months)

Step-by-step explanation:

Use the compound rate interest formula:

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where:

Given:

[tex]\implies 7850=5000(1+\frac{0.048}{12})^{12t}[/tex]

[tex]\implies 7850=5000(1.004)^{12t}[/tex]

[tex]\implies \dfrac{7850}{5000}=(1.004)^{12t}[/tex]

[tex]\implies 1.57=(1.004)^{12t}[/tex]

Take natural logs:

[tex]\implies \ln1.57=\ln(1.004)^{12t}[/tex]

[tex]\implies \ln1.57=12t\ln(1.004)[/tex]

[tex]\implies t=\dfrac{\ln 1.57}{12 \ln1.004}[/tex]

[tex]\implies t=9.42\textsf{ years (nearest hundredth)}[/tex]

[tex]\implies t=113 \textsf{ months}[/tex]

D.

[tex]22 - 8 \sqrt{5} [/tex]

Answer:

150 people

Step-by-step explanation:

20/50 = 40%
So 40% are wearing hats and 60% aren't

0.6=60%

250x0.6= 150

Answer:

B

Step-by-step explanation:

(4 , 9) and (0, 5)

4 is x1, 9 is y1, 0 is x2, 5 is y2

formula:

slope = y2 - y1/ (underline is fraction line btw ;) )

             x2 - x1

5 - 9

0 - 4

So the answer is B

Answer:

y - int = 7

Step-by-step explanation:

y = -3/4x + 7

Answer:

i think the intercept is (0,7) im not sure, sorry if its not.

Step-by-step explanation:

Answer:

51

Step-by-step explanation:

3n means 3 × n

substitute n = 17 into the expression

3n = 3 × 17 = 51

Answer:

Step-by-step explanation:

[tex]Cos3A= Sin2A ........ (i)\\\\Cos3A= Cos (90-2A)\\\\3A= 90-2A\\\\5A= 90\\\\A= 18\\\\[/tex]

Now,

Putting the value of A to find the value,

[tex]From (i)\\Cos(3x18) = Sin (2x18)\\Cos54= Sin36\\0.5877= 0.5877 \\LHS=RHSProved .[/tex]

Answer:

Cos3A= Sin2A ........ (i)

Cos3A= Cos (90-2A)

3A= 90-2A

5A= 90

A= 18

from (i)

Cos(3×18) = Sin (2×18)

Cos54= Sin36

0.5877= 0.5877 proved .

Step-by-step explanation:

Answer:

C. 22/5

Step-by-step explanation:

4x5=20

20+2=22

Answer:

C. 22/5

When making an improper fraction you must first multiply the denominator with the whole number in this case that would be 4 and 5

4*5=20

Then just add the numerator

20+2=22

And bring it back over the denominator

22/5

There you go your improper fraction.

Step-by-step explanation:

Answer: 3.33

Step-by-step explanation:

6x-2= 20

    +2= +2

Add two to both sides

6x=22

÷ 6= ÷6

Divide both sides by 6

x= 3.33 OR x= 22/6 simplified = 11/3

What you do to one side you do to the other to make the equation balanced.

Answer:

Step-by-step explanation:

6x - 2 = 20

Add 2 to both sides

6x - 2 + 2 = 20 + 2

          6x = 22

Divide both sides by 6

         [tex]\dfrac{6x}{6}=\dfrac{22}{6}\\\\\\x =\dfrac{11}{3}\\\\\\x = 3\dfrac{2}{3}[/tex]

Answer:

a.) y= 75x+25

b.) y= 25x+225

c.) Their account balances will be the same in 4 months and they'll have $325.

Step-by-step explanation:

For A and B: The variable is x which is the amount of months then add the initial amounts without a variable and equal it to y which is the amount in all.

For Rowan, they are saving $75 per month. This is where our variable goes and then we add the intial $25 dollars. The equation is y= 75x+25.

For Reem, they are saving $25 per month. This is where our variable goes and then we add the intial $225 dollars. The equation is y= 25x+225

C. You have to set the equations equal to each other and then solve for x.

75x+25 = 25x+225

Subtract 25 from each side

75x=25x+200

Subtract 25x from each side

50x=200

Divide each side by 50

X=4

For the amount they'll have, just plug 4 into one of the equations.

Rowan : y=75(4)+25

y=325

Reem: y=25(4)+225

y=325

gallon = pint *0.125

gallon = pint / 8
0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+0.125+

0.125+0.125+0.125+0.125+0.125 = 2

16 would be the answer I believe, maybe I'm wrong, double check.

Answer:

5 1/3 pints

Step-by-step explanation:

1 pint is 1/8gal and u need to find how many pints in 2/3 gal so it'll be 2/3 ÷ 1/8 which is 5 1/3

Answer: 3.5 ft cubed.

Step-by-step explanation:

width*length*height Multiply all the numbers to find the volume.

It will be easier to change the fractions to decimals first.

Answer:

nonlinear increasing

Step-by-step explanation:

Answer:

Step-by-step explanation:

Area = s^2 =

New Area = (S- 6)(S+6) = S^2 -36, Choice (A)

Hope that helps!

Answer:

22 years

Step-by-step explanation:

suppose his present age is x years

After 2 years, father's age (x+24+2) years and son will be (x+2). now x = 22 years is the answer if u solve it.

The present age of the son is 22 years .

Let us assume that the present age of the son is x years . Therefore according to question, we can say that the present age of his father will be x + 24 years. Then after two years, the age of the man will be twice the age of his son , i.e:

[tex] \quad\dashrightarrow\quad \sf {(x + 24) + 2 = 2 ( x + 2 ) }[/tex]

[tex] \quad\dashrightarrow\quad \sf { x + 26 = 2x + 4}[/tex]

[tex] \quad\dashrightarrow\quad \sf {2x -x = 26 - 4 }[/tex]

[tex] \quad\dashrightarrow\quad \underline{\sf {x = 22 }}[/tex]

Hence, the present age of the son is 22 years.

We are given with a limit and we need to find it's value so let's start !!!!

[tex]{\quad \qquad \blacktriangleright \blacktriangleright \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}}[/tex]

But , before starting , let's recall an identity which is the main key to answer this question

Consider The limit ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}}[/tex]

Now as directly putting the limit will lead to indeterminate form 0/0. So , Rationalizing the numerator i.e multiplying both numerator and denominator by the conjugate of numerator

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}\times \dfrac{\sqrt{x}+\sqrt{3\sqrt{x}-2}}{\sqrt{x}+\sqrt{3\sqrt{x}-2}}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-\sqrt{3\sqrt{x}-2})(\sqrt{x}+\sqrt{3\sqrt{x}-2})}{(x^{2}-4^{2})(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Using the above algebraic identity ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x})^{2}-(\sqrt{3\sqrt{x}-2})^{2}}{(x-4)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-(3\sqrt{x}-2)}{(x-4)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}+2}{\{(\sqrt{x})^{2}-2^{2}\}(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}-2}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , here we need to eliminate (√x-2) from the denominator somehow , or the limit will again be indeterminate ,so if you think carefully as I thought after seeing the question i.e what if we add 4 and subtract 4 in numerator ? So let's try !

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{x-3\sqrt{x}-2+4-4}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(x-4)+2+4-3\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , using the same above identity ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)+6-3\sqrt{x}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)+3(2-\sqrt{x})}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , take minus sign common in numerator from 2nd term , so that we can take (√x-2) common from both terms

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)(\sqrt{x}+2)-3(\sqrt{x}-2)}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , take (√x-2) common in numerator ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-2)\{(\sqrt{x}+2)-3\}}{(\sqrt{x}-2)(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Cancelling the radical that makes our limit again and again indeterminate ;

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{\cancel{(\sqrt{x}-2)}\{(\sqrt{x}+2)-3\}}{\cancel{(\sqrt{x}-2)}(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}+2-3)}{(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

[tex]{:\implies \quad \displaystyle \sf \lim_{x\to 4}\dfrac{(\sqrt{x}-1)}{(\sqrt{x}+2)(x+4)(\sqrt{x}+\sqrt{3\sqrt{x}-2})}}[/tex]

Now , putting the limit ;

[tex]{:\implies \quad \sf \dfrac{\sqrt{4}-1}{(\sqrt{4}+2)(4+4)(\sqrt{4}+\sqrt{3\sqrt{4}-2})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{2-1}{(2+2)(4+4)(2+\sqrt{3\times 2-2})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+\sqrt{6-2})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+\sqrt{4})}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(2+2)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{(4)(8)(4)}}[/tex]

[tex]{:\implies \quad \sf \dfrac{1}{128}}[/tex]

[tex]{:\implies \quad \bf \therefore \underline{\underline{\displaystyle \bf \lim_{x\to 4}\dfrac{\sqrt{x}-\sqrt{3\sqrt{x}-2}}{x^{2}-16}=\dfrac{1}{128}}}}[/tex]

We can transform the limand into a proper rational expression by substitution.

Let y = √x. Then as x approaches 4, y will approach √4 = 2. So

[tex]\displaystyle \lim_{x\to4}\frac{\sqrt x - \sqrt{3 \sqrt x - 2}}{x^2 - 16} = \lim_{y\to2} \frac{y - \sqrt{3y-2}}{y^4 - 16}[/tex]

Now let z = √(3y - 2). Then as y approaches 2, z will approach √(3•2 - 2) = 2 as well. It follows that y = (z² + 2)/3, so that

[tex]\displaystyle \lim_{y\to2} \frac{y - \sqrt{3y-2}}{y^4-16} = \lim_{z\to2} \frac{\frac{z^2+2}3 - z}{\frac{(z^2+2)^4}{81}-16} \\\\ = \lim_{z\to2} \frac{27(z^2+2)-81z}{(z^2+2)^4 - 1296} \\\\ = 27 \lim_{z\to2} \frac{z^2 - 3z + 2}{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280}[/tex]

Plugging z = 2 into the denominator returns a value of 0, which means z - 2 divides z⁸ + 8z⁶ + 24z⁴ + 32z² - 1280 exactly. Polynomial division shows that

[tex]\dfrac{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280}{z-2} \\\\ = z^7+2z^6+12z^5+24z^4+72z^3+144z^2+320z+640[/tex]

and it's easy to see that the numerator is also divisible by z - 2, since

[tex]z^2 - 3z + 2 = (z - 1) (z - 2)[/tex]

So, we can eliminate the factor of z - 2 and we're left with

[tex]\displaystyle 27 \lim_{z\to2} \frac{z^2 - 3z + 2}{z^8 + 8z^6 + 24z^4 + 32z^2 - 1280} = 27 \lim_{z\to2}\frac{z-1}{z^7+\cdots+640}[/tex]

The remaining limand is continuous at z = 2, so we can evaluate the limit by direct substitution:

[tex]\displaystyle 27 \lim_{z\to2}\frac{z-1}{z^7+\cdots+640} = \frac{27}{3456} = \boxed{\frac1{128}}[/tex]

Answer:

$320

Step-by-step explanation:

If $38.40 is 12%, then 1% is 38.40 ÷ 12.

⇒ 1% = 38.40 ÷ 12 = $3.20

Simply multiply 3.2 by 100 to get 100%:

⇒ 3.2 x 100 = $320

Answer:

Set up an equation using the key terms:

We can consider 60% in our equation to be 60/100 which we later on simplify.

We contemplate that "-Of a blank number(of what number)" means the multiplication of an unknown value, "x".

The resulting of 51 will be what the equation will equal.

Form the equation;

Solve for x:-

60/100x = 51

60/100 can simplify to 0.6 so it will now be,

0.6x = 51

Isolate x by dividing by 0.6 from both sides because the inverse operation of multiplication is division(since 0.6 is being multiplied by x).

÷0.6  ÷0.6

x = 85, therefore 60% of 85 is 51.

Answer:

the perimeter is 58 inches

Step-by-step explanation:

15+8+9+14+12= 58