How many 1020 flats can fit on a 10’*6’table

Answer:

Final answer is approx x=-0.66.

Step-by-step explanation:

Given equation is [tex]5^{-2x-1}=4^{4x+3} [/tex].

Now we need to solve equation [tex]5^{-2x-1}=4^{4x+3} [/tex] and round to the nearest hundredth.

[tex]5^{-2x-1}=4^{4x+3} [/tex]

[tex]\log(5^{-2x-1})=\log(4^{4x+3}) [/tex]

[tex](-2x-1)\log(5)=(4x+3)\log(4) [/tex]

[tex]-2x \log(5)- \log(5)=4x \log(4)+3 \log(4) [/tex]

[tex]-2x \log(5) -4x \log(4)=3 \log(4) +\log(5)[/tex]

[tex]x=\frac{\left(3\log(4)+\log(5)\right)}{\left(-2\log(5)-4\log(4)\right)}[/tex]

Now use calculator to calculate log values, we get:

[tex]x=-0.65817959094[/tex]

Round to the nearest hundredth.

Hence final answer is approx x=-0.66.

Answer:

Step-by-step explanation:

see attached

Answer: [tex]\bold{a)\ P(t)=P_o\cdot e^{t\cdot ln(2.7)}}[/tex]

               b) 5314

               c) ln 2.7

               d) 4.6 hrs

Step-by-step explanation:

[tex]P(t) = P_o\cdot e^{kt}\\\\\bullet \text{P(t) is the number of bacteria after t hours} \\\bullet P_o\text{ is the initial number of bacteria}\\\bullet \text{k is the rate of growth}\\\bullet \text{t is the time (in hours)}\\\\\\270=100\cdot e^{k(1)}\\2.7=e^k\\ln\ 2.7=\ln e^k\\\boxed{ln\ 2.7=k}\\\\\text{So the equation to find the number of bacteria is: }\boxed{P(t)=P_o\cdot e^{t\cdot ln(2.7)}}\\\\\\P(4)=100\cdot e^{4\cdot ln(2.7)}\\.\qquad =\boxed{5314}[/tex]

[tex]10,000=100\cdot e^{t\cdot ln(2.7)}\\100=e^{t\cdot ln(2.7)}\\ln\ 100=ln\ e^{t\cdot ln(2.7)}\\ln\ 100=t\cdot ln(2.7)\\\dfrac{ln\ 100}{ln\ 2.7}=t\\\\\boxed{4.6=t}[/tex]

Final answer:

The question involves solving an exponential growth problem, often modeled by the equation P(t) = P0ekt, to determine the bacterial population at specific times and the growth rate after 4 hours, as well as the time it takes to reach a certain population size.

Explanation:

The student's question falls into the realm of differential equations and specifically pertains to exponential growth in the context of a bacteria population. When dealing with bacterial growth, the formula used is P(t) = P0ekt, where P0 is the initial population, e is the base of the natural logarithm, k is the rate constant, and t is the time in hours.

To find the expression for P(t), we first need to determine the value of k using the information that after one hour the population has increased from 100 to 270 cells. We can then use this value to determine P(4), the population after 4 hours, and P'(4), the rate of growth after 4 hours. Finally, to find when the population reaches 10,000 cells we solve P(t) = 10,000.

Here are the steps we follow:

Answer:

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Step-by-step explanation:

Answer:

1/100

Step-by-step explanation:

Answer:

The answer in the procedure

Step-by-step explanation:

step 1

Find the volume of the cylinder

The volume of the cylinder is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=10\ cm[/tex]

[tex]h=9\ cm[/tex]

substitute

[tex]V=\pi (10)^{2}(9)=900\pi\ cm^{2}[/tex]  

step 2

Find the volume of the cone

The volume of the cone is equal to

[tex]V=(1/3)\pi r^{2} h[/tex]

we have

[tex]r=10\ cm[/tex]

[tex]h=9\ cm[/tex]

substitute

[tex]V=(1/3)\pi (10)^{2}(9)=300\pi\ cm^{2}[/tex]  

therefore

we have

[tex]Vcylinder=900\pi\ cm^{2}[/tex]  

[tex]Vcone=300\pi\ cm^{2}[/tex]  

so

[tex]Vcylinder=3Vcone[/tex]  

Answer:

Circle table

Step-by-step explanation:

More people will fit around the circle table then the rectangle table. You can find the distance around using the circumference.

C = πr² = π(4)²=16π = 50.24 feet

The perimeter of a rectangle table is P = 2l+2w = 2(10) + 2(5) = 30 feet.

With more than 20 feet more, the circle table will fit more.

Answer:

A square that has sides of 4.5 units, or a rectangle that is 1 unit wide and 8 units long.

Step-by-step explanation:

First, you need to find the perimeter in the first place. Since there are two sides of the same number, you would double each number.

2 would become 4

6 would become 12

Add 4+12=18

So, our rectangle has to have a perimeter of 18 units. Because a square is a rectangle, you can divide 18 and 4, since a square has 4 sides. You get 4.5. Each side can be 4.5 units.

Or, you can have a rectangle. What I thought first was a length of 9, but I knew that wouldn't work. I drew a rectangle and tried 8. If I put it on the top and bottom, which you need to to find the perimeter, it was only 16. Then I knew I could use 1 as a side length. If you added the sides, it would equal 2, and when you add 16 and 2, it's 18. So, you can use a rectangle that has a length of 8 units and a width of 1 unit.

The price increased so it would be a positive net change.

Subtract the new price from the original price:

45.83 - 30.46 = 15.37

The net change was C. $15.37

Answer:

C) 15,37

Step-by-step explanation:

You can to obtain the net change in the stock price with a substract:

Vt = [Pf - Pi]

Vt = [$45.83 - 30.46]

Vt = 15.37

Its a positive variation

Best regards

D) 408 in^2 is your answer.

The surface area of the pyramid is approximately 345 square inches.

The base of the pyramid is a polygon, and in this case, it is a square since it has 12-inch sides. The formula to find the area of a square is side length squared. Therefore, the area of the square base can be calculated as follows:

Area of base = side length * side length = 12 in * 12 in = 144 square inches.

Since we have the slant height of the pyramid (11 inches) and the base side length (12 inches), we can find the height of the triangle (distance from the base to the apex) using the Pythagorean theorem.

Let 'h' be the height of the triangle:

h² + (1/2 * base)² = slant²

h² + (1/2 * 12)² = 11²

h² + 36 = 121

h² = 121 - 36

h² = 85

h = √85 ≈ 9.22 inches (rounded to two decimal places).

Now that we have the height of the triangular face, we can calculate its area using the formula:

Area of triangle = (1/2 * base * height)

= (1/2 * 12 in * 9.22 in) ≈ 55.32 square inches

Find the Total Surface Area

To find the total surface area of the pyramid, we add the area of the base and the four triangular lateral faces:

Total Surface Area = Area of base + 4 * Area of triangle

Total Surface Area = 144 square inches + 4 * 55.32 square inches

Total Surface Area ≈ 345.28 square inches

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Answer:

C

Step-by-step explanation:

Use the Heron's formula for the area of the triangle:

[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]

where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]

Since [tex]a=2,\ b=7,\ c=8,[/tex] then

[tex]p=\dfrac{2+7+8}{2}=8.5.[/tex]

Hence,

[tex]A=\sqrt{8.5(8.5-2)(8.5-7)(8.5-8)}=\sqrt{8.5\cdot 6.5\cdot 1.5\cdot 0.5}=\\ \\=\sqrt{41.4375}\approx 6.4\ un^2.[/tex]

Answer:

Area Δ = 6.4 units² ⇒ the answer is (c)

Step-by-step explanation:

* Use the formula of the area:

∵ Area of the triangle = 1/2 (a)(b) sin(C)

∵ We have the length of the 3 sides

∴ Use cos Rule to find the angle C

∵ cos(C) = (a² + b² - c²)/2ab

∵ a = 2 , b = 7 , c = 8

∴ cos(C) = (2² + 7² - 8²)/2(2)(7) = 4 + 49 - 64/28 = -11/28

∴ m∠C = 113.1°

∴ Area Δ = (1/2)(2)(7)sin(113.1) = 6.4 units²

Answer:

13.43

Step-by-step explanation:

Law of Sines

x/sin50 = 12/sin42

solve for x and don't forget to put calculator into degree mode

Answer:

[tex]AB\approx13.7cm[/tex] to the nearest  tenth.

Step-by-step explanation:

We know two angles and a given side, we can use the sine rule to find the required length.

[tex]\frac{AB}{\sin(50\degree)}=\frac{12}{\sin(42\degree)}[/tex]

We solve for the AB by multiplying both sides by [tex]\sin(50\degree)[/tex].

This implies that;

[tex]AB=\frac{12}{\sin(42\degree)}\times \sin(50\degree)[/tex]

[tex]AB=13.738[/tex]

[tex]AB\approx13.7cm[/tex] to the nearest  tenth.

Answer:

NO = 4.5

MO = 3.5

LN = sqrt(44)

Step-by-step explanation:

Since the value of the base of the triangles is 8, and the value of NO is 4.5, the value of MO is MN - NO, which is 8 - 4.5, which comes out to 3.5.

Then, we apply the quadratic formula to triangle MLO to find that the middle line value is sqrt(23.75). Then we use the quadratic formula on traingle OLN to find the LN is sqrt(44).

Answer:

2/5 of the students

Step-by-step explanation:

Let the total number of students be x. Two-Thirds of the students plan to do some volunteering. Two-Thirds in fraction can be written as 2/3. So the portion of the students which plan to do some volunteering is:

[tex]\frac{2x}{3}[/tex]

From these students, 3/5 plan to volunteer at community center. So the students who plan to volunteer at community center will be:

[tex]\frac{2x}{3} \times \frac{3}{5}\\\\  = \frac{2x}{5}[/tex]

This means, among x students, 2/5 of the students plan to volunteer at the community center this summer.

Answer: There is exactly 1 million in 1 kilogram

Step-by-step explanation:

Answer:

ello mate

Step-by-step explanation:

Answer:

144

Step-by-step explanation:

Height and Length are A and Hypotenuse is Asqrt(2)

Set hyp = 24 and solve for a.

a = 24/sqrt(2)

Area of Tri = 1/2*(A^2)

Answer:

144

Step-by-step explanation:

➷ It would help if you drew it out as a triangle

You will notice that you need to use tan

tan70 = 39/x

x = 39/tan70

x = 14.194

The correct option would be 14.2 ft

You will need to use tan

tan51 = 6/x

x = 6/tan51

x = 4.8587

The correct option would be 4.9m

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

↬ ʜᴀɴɴᴀʜ ♡

Answer:

Step-by-step explanation:

How long it takes to reach the ground is a y-dimension thing, and horizontal displacement is an x-dimension thing.  So let's set up a table with the info we have in each dimension:

                           x                             y

V₀                     10.0 m/s               10.0 m/s

Δx                        ?                       -122.5 m

a                       0 m/s/s                -9.8 m/s/s

v                       10.0 m/s                    ?

t                           ?                             ?

That seems like an awful lot of question marks, doesn't it?

The first question asks us for the time, t, it takes for the pathetic and greatly disliked Justin Bieber to hit the ground.  We will use the equation:

Δx = V₀t + 1/2at²

Filling in our values using the y-dimension stuff only:

[tex]-122.5 = 10.0t+\frac{1}{2}(-9.8)t^2[/tex] which simplifies to

[tex]-122.5=10.0t-4.9t^2[/tex]

Hmmm...this is beginning to resemble a parabolic equation you probably already studied in Algebra 2!

We can solve for t by getting everything on one side and setting the equation equal to 0.  We set it equal to 0 since the height on the ground is 0:

[tex]-4.9t^2+10.0t+122.5=0[/tex]

When you factor that for the 2 values of t, you get

t = -4.1 and 6.1

Of course, since time can't EVER be negative, we use a t value of 6.1.  That's how long it takes to hit the ground.  That t value can now be filled into the t values in our table above.  We need that t value for the next part that asks us the horizontal displacement, Δx.  This is x-dimension stuff now.  Using the same equation:

Δx =[tex]10.0(6.1)+\frac{1}{2}(0)(6.1)^2[/tex]

Of course since the acceleration in the x-dimension is always 0, the whole portion of the equation after the equals sign is eliminated, leaving us with

Δx = 10.0(6.1)

Δx = 61 m

Poor Justin, upon his demise, hits the ground.  Therefore, his final velocity is 0, since his body met the ground and stopped dead.

Answer:

81 : 8

Step-by-step explanation:

Cube 1 has side lengths of 3, so it's volume is 3³ = 81

Cube 2 has side lengths of 2, so it's volume is 2³ = 8

So the ration of volume of the larger cube to the smaller cube is 81 : 8

Answer:

$1280.59

53 years

Step-by-step explanation:

To find how much we will get in 5 years, we use the formula:

[tex]A=Pe^{rt}[/tex]

P = $1200

r = 1.3% or 0.013

t = 5

Now that we have our values, let's plug them into the formula.

[tex]A=1200e^{0.013(5)}[/tex]

[tex]A=1200e^{0.065}[/tex]

[tex]A=1280.59[/tex]

We will have $1280.59 after 5 years.

Now to find how long it will take for our investment to double.

t = ln(A/P)/r

A = 2400

P = 1200

r = 1.3 or 0.013

Let's plug it in.

t = ln(2400/1200)/0.013

t = ln(2)/0.013

t = 53.32 or 53 years

Assuming that N is the midpoint of QR, its coordinates are the average of the coordinates of Q and R. So, we have

[tex] N = \left(\dfrac{0+2c}{2},\dfrac{2b+0}{2}\right)=(c,b)[/tex]

Check the picture below.

Answer:

The correct option is A.

Step-by-step explanation:

A  relation is called a function if for each values of x, there exist a unique value of y.

A graph show a function if it passes the vertical line test. It means the function intersect each vertical at most once.

From the given graph it is clear that the graph passes the vertical line test because the the function intersect each vertical at most once and for each values of x, there exist a unique value of y.

Hence the correct option is A.

Answer:

The measures would be 30, 60, and 90 degrees.

Step-by-step explanation:

60 is 30 more than 30, and 90 is the sum of 30 and 60. Also the sum of the measures of triangle is always 180, and 30 + 60 + 90 = 180.

If One angle of a triangle is 30 degrees more than the smallest angle. The largest angle is the sum of the other angles. Then 30, 60 and 90 are

measures of all three angles.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given,

One angle of a triangle is 30 degrees more than the smallest angle.

x=30+y

The largest angle is the sum of the other angles

z=x+y

By angle sum property the sum of three angles is 180 degrees

x+y+z=180

30+y+y+z=180

30+y+y+30+y+y=180

60+4y=180

Subtract 60 from both sides

4y=120

Divide 4 on both sides

y=30

Now substitute y value in x

x=60

z=90

Hence the measure of all three angles are 30,60 and 90 degrees.

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[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{cos^2(\theta )-cos^4(\theta )}{tan(\theta )}\implies \cfrac{cos^2(\theta )[1-cos^2(\theta )]}{\frac{sin(\theta )}{cos(\theta )}}\implies \cfrac{cos^2(\theta )[sin^2(\theta )]}{\frac{sin(\theta )}{cos(\theta )}} \\\\\\ \cfrac{cos^2(\theta )[sin^2(\theta )]}{1} \cdot \cfrac{cos(\theta )}{sin(\theta )}\implies cos^3(\theta )sin(\theta )[/tex]

Answer:

48°

Step-by-step explanation:

The sum of the three angles of a right triangle is 180°.

If one angle is 90° and another is 42°, then

90° + 42° + x = 180°

    132°    + x = 180°

                  x = 180° - 132° = 48°

The third angle is 48°.

Set the two equations to equal each other and solve:

3x-2 = x+2

Subtract x from each side:

2x -2 = 2

Add 2 to each side:

2x = 4

Divide both sides by 2:

x = 4/2 = 2

Now replace x with 2 in one of the equations and solve for y:

y = 3x -2 = 3(2) - 2 = 6-2 = 4

X = 2, Y = 4

(2,4)

Answer:

$97.38

Step-by-step explanation:

Subtract the finance charge and new purchases from the previous balance.

    102.35 - 1.24 - 15.73 = 85.38

Add the payment/credit

85.38 + 12 = 97.38

Answer:

$107.32

Step-by-step explanation:

New balance = previous balance + finance charge + purchases - payments

Previous balance = $102.35

Finance charge = $1.24

Purchases = $15.73

Payments = $12.00

New balance

Fill in the given information and do the arithmetic.

... New balance = previous balance + finance charge + purchases - payments

... New balance = $102.35 + $1.24 + $15.73 - $12.00

... New balance = $107.32

Answer:

2.5

Step-by-step explanation:

so LM is 3 right, right?

so PQ is 6

what they did to get that is they doubled 3 so 3x2=6

so if we divide 5 by 2 we get 2.5 because 2.5+2.5= 5

and that is how i got 2.5

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Answer:

x < -12

Step-by-step explanation:

-1/2x > 6

Multiply by -2 to isolate x

Remember that when multiplying by a negative, we flip the inequality

-2 * -1/2x < 6*-2

x < -12