Rewrite the following using exponents.
5*5*5*5*5*5
O
25
(5) * (6)
056

Answer:

EF = 15 units

Step-by-step explanation:

Calculate the distance using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = E (5, - 3) and (x₂, y₂ ) = F (- 4, 9)

EF = [tex]\sqrt{-4-5)^2+(9-(-3))^2}[/tex]

     = [tex]\sqrt{(-9)^2+(9+3)^2}[/tex]

      = [tex]\sqrt{81+12^2}[/tex]

      = [tex]\sqrt{81+144}[/tex]

      = [tex]\sqrt{225}[/tex]

      = 15

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{0.001}[/tex]

[tex]\\ \sf\longmapsto 10x=\dfrac{1}{\dfrac{1}{1000}}[/tex]

[tex]\\ \sf\longmapsto 10x=1000[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{1000}{10}[/tex]

[tex]\\ \sf\longmapsto x=100[/tex]

Answer:

∠ A ≈ 79.0°

Step-by-step explanation:

Using the Cosine rule to find the angle

cosA = [tex]\frac{b^2+c^2-a^2}{2bc}[/tex]

        = [tex]\frac{15^2+29^2-30^2}{2(15)(29)}[/tex]

        = [tex]\frac{225+841-900}{870}[/tex]

        = [tex]\frac{166}{870}[/tex] , then

A = [tex]cos^{-1}[/tex] ([tex]\frac{166}{870}[/tex] ) ≈ 79.0° ( to the nearest tenth )

Answer:

A=1024 yd.^2

Step-by-step explanation:

A=s^2

Substitute,

A=32^2

So,

A=1024 yd.^2

Answer:

1024 yd²

Step-by-step explanation:

Since it's a square, the side lengths will all be the same length. Due to this, you can square the given value to find the area.

A(Square) = 32² = 1024

Answer:

B

Step-by-step explanation:

Two friends + Bud = 3 people

7/10 = 70%, or less than a full cake

D is more than a full cake so this cannot be the answer.

C is 3/4 which 75% for each person, but there is only 70% to begin with so this is impossible.

B is 1/4 for each person also known as 25% for each person. 25% × 3 people = 75% which is slightly over how much cake Bud has (70%).

A is 1/2 for each person, but there isn't enough cake to go around to give each person a half piece.

The soundest solution would be B. Since the problem calls for estimations, B gives about 25% to each person, totaling to 75% after 3 people. Although we only have 70%, we are only estimating. A 5% difference is a good estimate.

Answer:

16 once is the better one.

Answer: 12-ounce bag is better by $0.02 per ounce

Concept:

When coming across questions that ask for a comparison between prices, we should make the final unit [price per object].

In finding [price per object], simply do [Total price / number of objects].

Solve:

A 12-ounce bag of rice costs $4.08

Total price / number of objects = 4.08 / 12 = $0.34 per ounce

A 16-ounce bag of rice costs $5.76

Total price / number of objects = 5.76 / 16 = $0.36 per ounce

$0.36 - $0.34 = $0.02

$0.34 < $0.36, therefore, 12-ounce bag is better by $0.02 per ounce.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

15

Step-by-step explanation:

Answer:

To Find F(3) you just have to replace x=3 so:

F(3)= -3^3 + 4×3^2 -2×3 = -27 +4×9 - 6 = -33 + 36 = 3

Answer: $ 39.60

Step-by-step explanation:

36 + (36*0.10) = 39.60

Answer: 1,526.04 yd³ (this is what i got on my calculator others may vary use any rounding you need)

VOLUME of CONE is: V= Pir² h / 3

Pi= 3.14

r= 9

h= 18

V= (3.14) x (9)² x (18)

9²= 81

3.14 x 81= 254.34 x 18= 4,578.12

4,578.12 / 3= 1,526.04 <-- answer

Answer:

9

Step-by-step explanation:

use Tangent-chord formula for finding the arc knowing E

x=1/2n

4x+19=1/2n

n=8x+38

both arcs = 360

28x-2+8x+38=360

x=9

Answer:

Yeah, x varies directly with (6 - y)

Step-by-step explanation:

[tex]x = 6 - y \\ x = k(6 - y) \\ x \: \alpha \: (6 - y)[/tex]

9514 1404 393

Answer:

Step-by-step explanation:

Their age total is 15+10=25, so Ram will get 15/25 = 0.6 of the total. Kalpana will get the remaining 0.4 of the total.

  Ram receives 0.6 × ₹2000 = ₹1200

  Kalpana receives 0.4 × ₹2000 = ₹800

Answer:

width: 3

Step-by-step explanation:

Given a length l and a width w, we can say that the perimeter is equal to

2 * l + 2 * w. Then, we also know that the perimeter is 27 plus its width, so

2 * l + 2 * w = 27 + w

and the length is 4 times its width, so length = 4 * width = l = 4 * w

We therefore have the two equations

2 * l + 2 * w = 27 + w

l = 4 * w

What we can do is plug 4* w for l in the first equation and solve from there. We thus have

2 * ( 4 * w) + 2 * w = 27 + w

8 * w + 2 * w = 27 + w

10 * w = 27 + w

subtract w from both sides to isolate the w and its coefficient

9 * w = 27

divide both sides by 9 to isolate w

w = 3

l = 4 * w = 12

Therefore, the width is 3 and the length is 12

Answer:

A = 2025 ft^2

Step-by-step explanation:

The area of a square is given by

A = s^2 where s is the side length

A = 45^2

A = 2025 ft^2

Answer:

Step-by-step explanation:

The area of any square is s^2

s in this case is 45

Area = s^2

Area = 45 * 45

Area = 2025 m^2

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

Just a correction, the characteristic roots of the equation are [tex]y = 7[/tex] and [tex]y = -\frac{1}{2}[/tex], thus, we should test for:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

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

Question a:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]y^{\prime\prime} = 49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}[/tex]

[tex]2y^{\prime\prime} - 13y^{\prime} - 7y = 0[/tex]

[tex]2(49Ae^{-7x} + \frac{1}{4}Be^{-\frac{x}{2}}) - 13(7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}) - 7(Ae^{7x} + Be^{-\frac{x}{2}}) = 0[/tex]

[tex]98Ae^{-7x} + \frac{1}{2}Be^{\frac{x}{2}} - 91Ae^{-7x} + \frac{13}{2}e^{-\frac{x}{2}} - 7Ae^{7x} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]98Ae^{-7x} - 91Ae^{-7x} - 7Be^{-\frac{x}{2}} + \frac{1}{2}Be^{\frac{x}{2}}  + \frac{13}{2}e^{-\frac{x}{2}} - 7Be^{-\frac{x}{2}} = 0[/tex]

[tex]0A + 0B = 0[/tex]

[tex]0 = 0[/tex], thus, we found the identity, and for each constant A and B, the following is a solution.

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

Question b:

[tex]y = Ae^{7x} + Be^{-\frac{x}{2}}[/tex]

[tex]A + B = 3 \rightarrow B = 3 - A[/tex]

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

[tex]y^{\prime} = 7Ae^{-7x} - \frac{1}{2}Be^{-\frac{x}{2}}[/tex]

[tex]7A - \frac{1}{2}B = -5[/tex]

Using [tex]B = 3 - A[/tex]

[tex]7A - \frac{3}{2} + \frac{A}{2} = -5[/tex]

[tex]\frac{14A}{2} + \frac{A}{2} = -\frac{10}{2} + \frac{3}{2}[/tex]

[tex]\frac{15A}{2} = -\frac{7}{2}[/tex]

[tex]15A = -7[/tex]

[tex]A = -\frac{7}{15}[/tex]

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

Then, B is given by:

[tex]B = 3 - A = 3 - (-\frac{7}{15}) = \frac{45}{15} + \frac{7}{15} = \frac{52}{15}[/tex]

Thus, the values are: [tex]A = -\frac{7}{15}, B = \frac{52}{15}[/tex]

A similar problem is given at https://brainly.com/question/2456414

Answer:

Step-by-step explanation:

Answer:

first choice..

first choice

Answer:

FIRST CHOISE FIRST CHOISE

Step-by-step explanation:

Let y = x + 22 and dy = dx, so the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{25}^{31} \frac{\mathrm dy}{(y-1)\sqrt{y}}[/tex]

Now let z = √y, so that z ² = y. Then 2z dz = dy, and the integral becomes

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_{\sqrt{25}}^{\sqrt{31}} \frac{2z}{(z^2-1)z} \\\\ = \int_5^{\sqrt{31}} \frac{2}{z^2-1}\,\mathrm dz[/tex]

Expand the integrand into partial fractions:

[tex]\dfrac{2}{z^2-1} = \dfrac1{z-1}-\dfrac1{z+1}[/tex]

Then we have

[tex]\displaystyle \int_3^9 \frac{\mathrm dx}{(x+21)\sqrt{x+22}} = \int_5^{\sqrt{31}}\left(\frac1{z-1}-\frac1{z+1}\right)\,\mathrm dz \\\\ = \left(\ln|z-1|-\ln|z+1|\right)\bigg|_5^{\sqrt{31}} \\\\ =\left[\ln\left|\frac{z-1}{z+1}\right|\right]\bigg|_5^{\sqrt{31}} \\\\ =\ln\left(\frac{\sqrt{31}-1}{\sqrt{31}+1}\right) - \ln\left(\frac{4}{6}\right) \\\\ =\ln\left(32-2\sqrt{31}\right) - \ln\left(\frac23\right) \\\\ =\boxed{\ln\left(48-3\sqrt{31}\right)}[/tex]

This is of Both

Range = Highest - Lowest data

Range = 45 - 10

Range = 35

Only A

Range = 45 - 10

Range = 35

Only B

Range = 40 - 15

Range = 25

Must click thanks and mark brainliest

We want to make a system of linear equations that would allow us to find the measure of the angles (we only want to find the system, not solving it)

Here we will find that we do not have a system of linear equations, we have:

s + t = 90°

t < 2*s

Here we have two complementary angles s and t.

Remember that two angles are complementary if their sum is equal to 90°, then we can write:

s + t = 90°

We also know that "t is less than twice s"

this can be written as:

t < 2*s

Notice that the above one is not an equation, is an inequality.

Then the system that we should use to

s + t = 90°

t < 2*s

If we want to force our system to be a system of linear equations, we can write:

s + t = 90°

t = 2*s

But naturally;

s + t = 90°

t < 2*s

has more solutions than:

s + t = 90°

t = 2*s

So we should not replace the inequality with an equation.

If you want to learn more, you can read:

https://brainly.com/question/9446123

9514 1404 393

Answer:

  2^6 = 64

Step-by-step explanation:

Each hour the initial value (1) is multiplied by 2 (again). So the number of times 2 multiplies the initial value is the number of passing hours (t).

The number of cells after t hours is ...

  c(t) = 1×2^t = 2^t

After 6 hours, this is

  c(6) = 2^6 = 64 . . . . cells after 6 hours

_____

Additional comment

As you know, multiplication simplifies repeated addition.

  x + x + x = 3x

In a similar way, exponentiation simplifies repeated multiplication.

 x·x·x = x³ . . . . (written as x^3 in plain text)

In this problem, we're repeatedly multiplying by 2. After we do that t times, the initial value is multiplied by 2^t.

Answer:

what is this sy man i dnt get it

Step-by-step explanation:

Answer:

Kevin travels for 2 hours at 60 mph and 3.5 hours at 55 mph

Step-by-step explanation:

Let's say that Kevin spends x hours going 60 mph and y hours going 55 mph. We can say that the sum of the two parts is 5.5, so x+y = 5.5 . Next, he goes 60 miles per hour for the first part of the trip, so for each hour he goes 60 mph, he travels 60 miles. We can then denote 60 * x as the distance traveled during the first part of his trip as he goes 60 mph for x hours. Similarly, 55 * y denotes the distance Kevin travels during the second part of his trip. His total distance is thus 60 * x + 55 * y = 312.5 miles

We have

x + y = 5.5

60 * x + 55 * y = 312.5

One way we can solve this is to solve for y in the first equation and plug that into the second. Subtracting x from both sides in the first equation, we get

y = 5.5 - x

Plugging that into the second equation, we get

60 * x + 55 * (5.5-x) = 312.5

60 * x + 55 * 5.5 - 55x = 312.5

5x  +302.5 = 312.5

subtract 302.5 from both sides to isolate the x and its coefficient

5x = 10

divide both sides by 5 to solve for x

x = 2

y = 5.5 - x = 5.5 - 2 = 3.5

Therefore, Kevin travels for 2 hours at 60 mph and 3.5 hours at 55 mph

Answer:

A square is a retangle

Step-by-step explanation:

Because a squre is a rectangle

Answer:

totally 16 numbers can be formed

It is hard and the condition of repeat of number should be clear if you have formula ( it is obvious to have) you can use that.

Answer:

c.145.3 to 154.7.

Step-by-step explanation:

We have to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a p-value of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

Now, find the margin of error M as such

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.645\frac{20}{\sqrt{50}} = 4.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 150 - 4.7 = 145.3.

The upper end of the interval is the sample mean added to M. So it is 150 + 4.7 = 154.7.

Thus the correct answer is given by option c.

Answer:

114 cm²

Step-by-step explanation:

Surface area of the rectangular prism,

2(wl+hl+hw)

=2×(3×8+3×8+3×3)

=2×(24+24+9)

=2×(57)

=114 cm²