A large rectangular parking lot is 2/3 km long and 1/2 km wide. What's the area of the raking lot?

Answer:

[tex]\large\boxed{N-T=-a^2+a-11}[/tex]

Step-by-step explanation:

[tex]T=-2a^2+a+6\\N=-3a^2+2a-5\\\\N-T=?\\\\\text{Substitute:}\\\\N-T=(-3a^2+2a-5)-(-2a^2+a+6)\\\\N-T=-3a^2+2a-5-(-2a^2)-a-6\\\\N-T=-3a^2+2a-5+2a^2-a-6\qquad\text{combine like terms}\\\\N-T=(-3a^2+2a^2)+(2a-a)+(-5-6)\\\\N-T=-a^2+a-11[/tex]

The difference between the functions is [tex]-a^2+a-11[/tex]

Given the following expression:

[tex]T=-2a^2+a+6\\N=-3a^2+2a-5[/tex]

We are to take the difference between N and T and this is as shown:

[tex]N - T= -3a^2+2a-5-(-2a^2+a+6)\\Expand\\N - T= -3a^2+2a-5+2a^2-a-6\\\\Collect \ the \ like \ terms\\N-T=-3a^2+2a^2+2a-a-5-6\\N-T=-a^2+a-11[/tex]

Hence the difference between the functions is [tex]-a^2+a-11[/tex]

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Assume the car starts at the origin, so that its initial position is [tex]x(0)=0[/tex]. The car's displacement at any time [tex]t[/tex] over the 20 second interval is

[tex]\displaystyle x(0)+\int_0^t(44+2.2u)\,\mathrm du=0+\left(44u+1.1u^2\right)\bigg|_{u=0}^{u=t}=44t+1.1t^2[/tex]

so that after 20 seconds the car has moved 1320 ft.

###

Without using calculus, recall that under constant acceleration, the average velocity of the car over the 20 second interval satisfies

[tex]v_{\rm avg}=\dfrac{v_f+v_i}2[/tex]

and that, by definition, we have

[tex]v_{\rm avg}=\dfrac{\Delta x}{\Delta t}[/tex]

where [tex]v_f[/tex] and [tex]v_i[/tex] are the final/initial speeds of the car and [tex]\Delta x[/tex] is the displacement it undergoes. It starts with a speed of 44 ft/s and ends with a speed of 88 ft/s, so we have

[tex]\dfrac{88\frac{\rm ft}{\rm s}+44\frac{\rm ft}{\rm s}}2=\dfrac{\Delta x}{20\,\rm s}\implies\Delta x=1320\,\mathrm{ft}[/tex]

same as before.

To find the distance traveled by the car during the 20 seconds, we integrate the velocity function and solve for the distance using the given values. The car travels a distance of 1320 feet.

To find the distance traveled by the car during the 20 seconds, we need to calculate the area under the velocity-time graph. The velocity function given is v(t)=44+2.2t. To find the distance, we integrate the velocity function from 0 to 20 seconds:

d = ∫(44+2.2t) dt

Applying integration, we get: d = 44t + 1.1t^2

Substituting the values t=0 and t=20 into the equation, we can find the distance traveled by the car:

d = 44(20) + 1.1(20)^2

Solving this equation, we get d = 880 + 440

So, the car has traveled a distance of 1320 feet during the 20 seconds.

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Answer:

$14.21

Step-by-step explanation:

Hello, I think I can help yo with this

if the lamp is on sale for 25% it means you have to pay the 75% of the original cost, you can find that 75% or to find the 25 % and the subtract that value from the original cost, it is the same anyway

Step 1

if

$18.95 ⇔100%

x$?       ⇔75%

[tex]\frac{18.95}{100}=\frac{x}{75}[/tex]

Step 2

solve for x

[tex]\frac{75*18.95}{100}=x\\x=\frac{1421.51}{100}\\ x=14.21\\\\[/tex]

the new price is $14.21

have a great day.

Answer:

Step-by-step explanation:

10x10 squared

=10x100

=1000

Answer 10000

Step-by-step explanation:

10x10=100

100x100=10000

The difference between the greatest and least areas is 72 square inches.

What is perimeter of a rectangle?

Let L be the length and w be the width of the rectangle.

Perimeter = 2l + 2w = 48

Since each side is a whole number, list pairs of whole numbers that satisfy the equation.

Potential pairs (length, width) are:

(23, 1)

(22, 2)

(21, 3)

(20, 4)

(19, 5)

Let's calculate the areas for the pairs mentioned:

Area = l*w

(23, 1)) A = 23* 1 = 23

(22, 2) A = 22 *2 = 44

(21, 3) A = 21 *3 = 63

(20, 4) A = 20 *4 = 80

(19, 5) A = 19 *5 = 95

The greatest area is 95 square inches, and the least area is 23 square inches.

The difference between the greatest and least areas is 95 - 23 = 72 square inches. Therefore, the answer is 72.

Answer:

m = 15.

Step-by-step explanation:

∛(3375) =  15.

You can use a calculator to do this. Some calculators have a direct key giving you a cube root or  you can use the power key + 1/3 .

Note:   ∛(3375) = 3375^(1/3).

Answer:

-5

Step-by-step explanation:

Edge 2020

Hello!

The answer is:

B. [tex]9x^{2}-16y^{2}[/tex]

To find the equivalent expression we need to apply the distributive property, so:

[tex](3x-4y)(3x+4y)=9x^{2}+12xy-12yx-16y^{2}\\\\9x^{2}+12xy-12yx-16y^{2}=9x^{2}+12xy-12xy-16y^{2}=9x^{2}-16y^{2}[/tex]

So, the correct option will be B. [tex]9x^{2}-16y^{2}[/tex]

Have a nice day!

Answer:

  tn = 243·(1/3)^(n-1)

Step-by-step explanation:

The recursive formula tells you the first term (243) and the common ratio (1/3). You can put these numbers into the general formula for the n-th term of a geometric sequence:

  an = a1·r^(n-1) . . . . . where a1 is the first term and r is the common ratio

You want the n-th term of your sequence to be called tn, so ...

  tn = 243·(1/3)^(n-1)

First, lets start with the formula for the volume of a cone

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

Then lets find the diameter so we can get the radius...

Since we have circumference, all we need to do is use this formula-

[tex] c \div \pi[/tex]

C being circumference, the PI being the 3.14, we plug it in to the formula as the number we have to get the diameter...

[tex]{75.36} \div 3.14[/tex]

And it comes out to...

24.

Now we need to divide it by two to get the radius, and we come up with 12.

Now that we have our radius, we can finally plug in all of the numbers into our original formula...

[tex] \frac{1}{3} (3.14 \times \: {12}^{2} ) \times 18[/tex]

The answer of the entire problem turns out to be... Drum roll please...

2712.96 cubic centimeters.

angle GAL would be the same as MLA

Answer:

y = 1 for the line.

Step-by-step explanation:

All values under y = 1. Surprisingly 1^0 is still 1. So just fill the table in with 1s under y.

I've drawn the line in desmos for you. I'm not sure whether you can extend the question enough to graph a line segment containing these 5 points (which is what I have done) or if you should just submit a graph with 4 points on. If it does not cost you anything to submit it twice, I would try the line first and the points alone the second time.

Answer:12 yards

Step-by-step explanation: 22-10=12

Answer:

[tex]\large\boxed{1.\ f(1)=135}\\\boxed{2.\ f(6)=115}\\\boxed{3.\ f(26)=25}\\\boxed{4.\ f(n)=139-4n}[/tex]

Step-by-step explanation:

[tex]f(1)=135\\f(2)=135-4=131\\f(3)=131-4=127\\f(4)=127-4=123\\f(5)=123-4=119\\\vdots\\\\\text{It's an arithmetic sequence with firs term = 135 and the common}\\\text{difference d = -4.}\\\text{The formula of arithmetic sequence: }\\\\f(n)=f(1)+(n-1)d\\\\\text{We have}\ f(1)=135\ \text{and}\ =-4.\ \text{Substitute:}\\\\f(n)=135+(n-1)(-4)=135+(n)(-4)+(-1)(-4)\\=135-4n+4=139-4n\\\\\boxed{f(n)=139-4n}[/tex]

[tex]\text{Put n = 6, n=26 to the formula:}\\\\f(6)=139-4(6)=139-24=115\\\\f(26)=139-4(26)=139-104=25[/tex]

Answer:

2/3

Step-by-step explanation:

5 black

3 green (not black)

3 blue (not black)

4 yellow (not black)

there are 5 black and 10 not black out of a total of 15 marbles.

there are 10/15 that are not black.  Reduced 2/3.

The probability of not drawing a black marble is 2/3, calculated by subtracting the number of black marbles from the total number of marbles in the bag and dividing the result by the total number of marbles.

The question asks to find the probability of not drawing a black marble. To solve this, we first determine the total number of marbles and then subtract the number of black marbles to find the number of marbles that are not black. In this case:

Next, we calculate the probability using the formula:

Probability (not black) = Number of marbles that are not black / Total number of marbles

Plugging in the numbers:

Probability (not black) = 10 / 15 = 2/3

Therefore, the probability of not drawing a black marble is 2/3.

Answer:

Similarity means that two figures are the same shape, but not necessarily the same size, color or orientation, congruent means two figures are the same in every form.

Step-by-step explanation:

In my understanding, The Property of Rigid motion holds two points:

- The relative distance between two points stays the same,

- The relative position of the points stays the same

This includes, translations, reflections, and rotation but not to dilutions since it breaks these rules. The relative distance between points gets smaller after dilution.

Final answer:

The range of Set A is 5 and Set B is 16. The mean of Set A is 15.2 and Set B is 12. Set B has a larger range but a smaller mean compared to Set A.

Explanation:

The range of a data set is calculated by subtracting the smallest value from the largest value. For Set A, the range is 18 - 13 = 5. For Set B, the range is 20 - 4 = 16.

The mean of a data set is calculated by summing all the values and dividing by the number of values. For Set A, the mean is (13 + 15 + 16 + 18 + 14) / 5 = 76 / 5 = 15.2. For Set B, the mean is (4 + 10 + 8 + 18 + 20) / 5 = 60 / 5 = 12.

Comparing the two data sets, we can see that Set B has a larger range than Set A, indicating greater variability in the data. However, Set B has a smaller mean than Set A, indicating that the values in Set B are generally lower than those in Set A.

Answer:

x = 15.

Step-by-step explanation:

Given : Two similar triangle .

To find : What is the value of x in the diagram.

Solution : We have given that

Two triangle with corresponding sides .

By the similar triangle property

The ratio of the two corresponding sides  are equal.

[tex]\frac{x}{25} = \frac{9}{15}[/tex].

On cross multiplication

x = [tex]\frac{9* 25}{15}[/tex].

x =  [tex]\frac{225}{15}[/tex].

x =  [tex]\frac{45}{3}[/tex].

x = 15.

Therefore,  x = 15.

The value of x in the diagram is 15. Option A

Similar triangles have the same shape but different sizes. In similar triangles, corresponding angles are equal.

Corresponding sides of similar triangles are in the same ratio.

The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides.

Then, we have that;

x/25 = 9/15

cross multiply the  values, we have;

x = 9(25)/15

Multiply the values

x = 225/15

Divide the values

x = 15

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It would be 30.8 hope this helps

Answer:

C

Step-by-step explanation:

We will graph [tex]3^{-x}[/tex]  and  [tex]6^{-x}[/tex]  and find WHERE in the x-axis,  [tex]3^{-x}[/tex]  is greater than  [tex]6^{-x}[/tex].

Attached is the graph of both the functions. RED color graph is of  [tex]3^{-x}[/tex]  and BLUE color graph is of  [tex]6^{-x}[/tex].

So, WHICH WHERE IN X-AXIS IS THE RED GRAPH "ABOVE" THE BLUE GRAPH?

We can clearly see that this occurs when x > 0.

Hence, C is the correct answer.

Answer:

C edge

Step-by-step explanation:

Answer:

[tex]y = 2 - \frac{1}{32}x\text{ or } y=2-0.03125x[/tex]

Step-by-step explanation:

Here x represents the number of student and y represents the amount of juice remain after x students are served,

Given,

The total number of cup = 32,

And, the amount of juice in 32 cups = 2 gallon,

⇒ The amount in 1 cup = [tex]\frac{2}{32}[/tex] = [tex]\frac{1}{16}[/tex] gallons,

Number of cups served to a student = [tex]\frac{1}{2}[/tex] cup.

⇒ The amount of juice served to a student = [tex]\frac{1}{32}[/tex] gallon.

⇒ The amount of juice served to x students = [tex]\frac{x}{32}[/tex] gallon

Thus, the remaining amount of juice = The amount of juice in 32 cups - served amount

⇒ [tex]y = 2 - \frac{1}{32}x\text{ or } y=2-0.03125x[/tex]

Which is the required equation.

Answer:  [tex]266,407.057\ km[/tex]

Step-by-step explanation:

The formula used to calculate the circumference of a circle is:

[tex]C=2\pi r[/tex]

The radius of the circle is r.

In the diagram you can observe that the radius of the satellite's orbit (r2) is the sum of the radius of the Earth (r1) and the distance from the Earth's surface to the satellite's orbit:

[tex]r2=r1+36,000\ km\\r2=6,400\ km+36,000\ km\\r2=42,400\ km[/tex]

Then, the circumference of the satellite's orbit is:

[tex]C=2\pi (42,400\ km)\\C=266,407.057\ km[/tex]

The circumference of the satellite's orbit is calculated by adding Earth's radius to the satellite's distance from Earth's surface to determine the orbit radius. The circumference is then found by using the formula for the circumference of a circle, 2πr, giving approximately 266,433 kilometers.

To find the circumference of the satellite's orbit, we need to first calculate the total distance from the center of Earth to the satellite. This is the sum of the Earth's radius (6400 kilometers) and the satellite's distance from the Earth's surface (36000 kilometers), which totals 42400 kilometers.

Once we have the radius of the orbit, we can calculate the circumference using the formula for the circumference of a circle, which is 2πr (two times Pi times the radius). Using this formula, the circumference of the satellite's orbit is approximately 266,433 kilometers.

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Answer:

im pretty sure its d) 0.25

Step-by-step explanation:

To find the experimental probability of each, divide the number for each color by 500. Then, multiply it by 20, to find the amount expected out of 20.

Answer:

look in picture below :)

Answer:

[tex]x=20.6\ in[/tex]

Step-by-step explanation:

we know that

Applying the Pythagoras Theorem

[tex]41.2^{2} =35.7^{2} +x^{2}[/tex]

solver for x

[tex]x^{2}=41.2^{2}-35.7^{2}[/tex]

[tex]x^{2}=422.95[/tex]

[tex]x=20.6\ in[/tex]

Answer:

Option b

Step-by-step explanation:

To solve this problem use the law of the sines.

We have 2 angles of the triangle and one of the sides.

[tex]a = 4.6\\B = 19\°\\A = 92\°\\C = 180 -A - B\\C = 180 - 92 - 19\\C = 69\°[/tex]

The law of the sines is:

[tex]\frac{sin(A)}{a} = \frac{sin(B)}{b} = \frac{sin(C)}{c}[/tex]

Then:

[tex]\frac{sin(92)}{4.6} = \frac{sin(19)}{b}\\\\b = \frac{sin(19)}{\frac{sin(92)}{4.6}}\\\\b = 1.5[/tex]

[tex]\frac{sin(B)}{b} = \frac{sin(C)}{c}\\\\\frac{sin(19)}{1.5} = \frac{sin(69)}{c}\\\\c = \frac{sin(69)}{\frac{sin(19)}{1.5}}\\\\c = 4.30[/tex]

Final answer:

To compare Plan A's increase of 200 homes per year and Plan B's 10% increase per year for a town's housing development, Plan A adds homes linearly, while Plan B's growth is exponential, potentially leading to a larger increase and more significant infrastructure needs over time.

Explanation:

To compare the two growth plans for the town's development—which are Plan A, an increase of 200 homes per year, and Plan B, a 10% increase each year—we need to analyze the two scenarios mathematically.

Under Plan A, the town will add a fixed number of homes each year, that is, 200 homes. After one year, the total will be 1200 homes, after two years 1400 homes, and this pattern will continue linearly.

Plan B's 10% annual increase results in exponential growth. Starting with 1000 homes, in the first year, there will be 1000 + (10% of 1000) = 1100 homes. The second year, the growth will be based on the new total, so it will be 1100 + (10% of 1100) = 1210 homes, and this pattern will continue to result in an increasingly larger number of homes added each year.

In terms of the community's development, Plan A adds homes predictably and steadily, while Plan B accelerates growth over time. This could lead to a boom in construction and investment depending on the current needs and infrastructure of the town.

Plan B's compound growth could lead to a much larger number of homes in the long run, but might require more significant investment in infrastructure and services as the growth compounds.

Answer:

the mean (average) will change

Step-by-step explanation:

Answer:

the rangue

Step-by-step explanation:

False. That does not satify the equation

Answer:

False

Step-by-step explanation:

The given inequality  is [tex]-3 \:<\:x\:<\:14[/tex].

Since both boundaries of the inequalities are not inclusive , we use the parenthesis for open interval."()".

We write the given inequality in interval notation as;

[tex](-3,14)[/tex].

The correct choice is false

Answer:

Step-by-step explanation:

[tex]3\sqrt2\cos\theta+2=-1\\\\\text{Method 1}\\\\\text{Put}\ \theta=\dfrac{\pi}{4}\ \text{to the equation and check the equality:}\\\\\cos\dfrac{\pi}{4}=\dfrac{\sqrt2}{2}\\\\L_s=3\sqrt2\cos\dfrac{\pi}{4}+2=3\sqrt2\left(\dfrac{\sqrt2}{2}\right)+2=\dfrac{(3\sqrt2)(\sqrt2)}{2}+2\\\\=\dfrac{(3)(2)}{2}+2=3+2=5\\\\R_s=-1\\\\L_s\neq R_s\\\\\boxed{FALSE}[/tex]

[tex]\text{Method 2}\\\\\text{Solve the equation:}\\\\3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\\\\3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\\\\\cos\theta=-\dfrac{3}{3\sqrt2}\\\\\cos\theta=-\dfrac{1}{\sqrt2}\cdot\dfrac{\sqrt2}{\sqrt2}\\\\\cos\theta=-\dfrac{\sqrt2}{2}\to\theta=\dfrac{3\pi}{4}+2k\pi\ \vee\ \theta=-\dfrac{3\pi}{4}+2k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\text{It's not equal to}\ \dfrac{\pi}{4}\ \text{for any value of }\ k.[/tex]