What is the prime factorization of 24?
A 1.24
B. 2.12
C. 3.8
D. 2.2.6
E 2.2.2.3

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

The sequence is will always have even numbers, is hence proved.

Given, the quadratic sequence is: 44:52:64:80

Sequences with a term are known as quadratic sequences. They can be distinguished by the fact that the first differences between terms are not equal but the second differences between terms are. Utilizing the term sum in an arithmetic progression formula, the sum of even numbers formula is achieved. The equation is Sum of Even Numbers Formula = n(n+1), where n is the total number of terms in the series.

The formula is: Tₙ = 2n² ₊ 2n  ₊ 40

take 2 common

Tₙ = 2(n² ₊ n  ₊ 20)

in other words n² ₊ n  ₊ 20  = y

therefore , Tₙ = 2y

which by definition makes Tₙ an even number at all times.

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Answer:

65,937.5

Step-by-step explanation:

Answer:

$65,937.5

Step-by-step explanation:

5.5%× 62500= $3,437.5

$62,500+ $3,437.5= $65,937.5

Half of a number n

n/2

How far is n/2 from 14

l 14 - n/2 l

At most 5 units ( less or equal)

l 14 - n/2 l ≤ 5

Solve;

14 - n/2 ≤ 5

14-5 ≤ n/2

9 ≤ n/2

9*2 ≤ n

18 ≤ n

-(14-n/2) ≤ 5

-14+n/2 ≤ 5

n/2 ≤ 5+14

n/2 ≤ 19

n ≤ 19*2

n ≤ 38

Solution:

18 ≤ n ≤ 38

we have the expression

2log3x+5log3y-2-7log3z

so

applying properties of logarithms

we have that

2log3x=3x^2

5log3y=3y^5

2=log3 (3^2)

7log3z=3z^7

Part 2

In this case we have

log3(x^2g^5) -log3(9z^7)

Answer:

$3500

Step-by-step explanation:

25/100 = 0.25

0.25 x 14000 = $3500

Answer:

Step-by-step explanation:

Sengun had 14000

25%of 14000 he spend

=25/100×14000

=3500

He spend 3500

Answer:

138 "8/9"

Step-by-step explanation:

Answer:

x ≥ 5

Step-by-step explanation:

  5 + 2(2x - 3) ≥ 3x + 4

Expand brackets:

⇒ 5 + 4x - 6 ≥ 3x + 4

Combine like terms:

⇒ 4x - 1 ≥ 3x + 4

Subtract 3x from both sides:

⇒ x - 1 ≥ 4

Add 1 to both sides:

⇒ x ≥ 5

Answer:  x>=5

Step-by-step explanation:

Simplify the expression

5+2\cdot\left(2x-3\right)>=3x+4

5+2\cdot2x+2\cdot-3>=3x+4

5+4x-6>=3x+4

4x+\left(5-6\right)>=3x+4

4x-1>=3x+4

Group all r terms on the left side of the inequality

x-1>=4

x-1+1>=4+1

x>=4+1

x>=5

Answer:

64cm³

Step-by-step explanation:

( 4 x 4 x 4) cm x cm x cm

The image of point P under a 90-degree counter Clockwise rotation about the origin is (-6, -4).

To find the image of point P = (-4, 6) after a 90-degree counterclockwise rotation about the origin, we can use the following formula:

(x', y') = (xcosθ - ysinθ, xsinθ + ycosθ)

where (x, y) are the coordinates of the original point, θ is the angle of rotation, and (x', y') are the coordinates of the rotated point.

In this case, θ = 90 degrees, so we have:

(x', y') = (-4cos90 - 6sin90, -4sin90 + 6cos90)

        = (-6, -4)

Therefore, the image of point P under a 90-degree counterclockwise rotation about the origin is (-6, -4).

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Given:

Answer:

Below

Step-by-step explanation:

A cube has SIX sides of equal area

  each side has area = L x W       and L and W are the same = 4.5 m

      so:   Area =   six   X   ( 4.5  X 4.5)  =   6 * 4.5 * 4.5 = 121.5 m^2

Answer:

Hope the picture will help you...

1. Initial prediction for the data set with smaller Mean Absolute Deviation was Period A. Prediction was wrong.

2. The Mean Absolute Deviation for Period A is 1.8 and Period B, 1.1

This means that period B has a smaller Mean absolute deviation.

We start by finding the mean for each set;

Period A: Mean = (1×92 + 1×94 + 3×95 + 1×96 + 2×97 + 1×99 + 1×100)/10

= 960/10

= 96

Period B: Mean = (1×94 + 3×95 + 1×96 + 4×97 + 1×98)/10

= 961/10

= 96.1

Period A:

Mean Absolute Deviation = ((92-96) + (94-96) + 3(95-96) + (96-96) + 2(97-96) + (99-96) + (100-96))/10

Mean Absolute Deviation = (4 + 2 + 3 + 0 + 2 + 3 + 4)/10

Mean Absolute Deviation = 1.8

Period B:

Mean Absolute Deviation = ((94-96.1) + 3(95-96.1) + (96-96.1) + 4(97-96.1) + (98-96.1))/10

Mean Absolute Deviation = (2.1 + 3.3 + 0.1 + 3.6 + 1.9)/10

Mean Absolute Deviation = 1.1

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Step-by-step explanation:

Answer:

5x+50

Step-by-step explanation:

you have one x. An x plus fifty. And 3 mire x's. So 5 x's and a 50.

Answer:

My bad, the answer is -0.335

Step-by-step explanation:

r = (nΣxy - ΣxΣy) / sqrt([nΣx^2 - (Σx)2][nΣy2 - (Σy)^2])

Using the data provided in the table, we can calculate r as follows:

n = 8 Σx = 84 Σy = 96 Σxy = 0.017 Σx^2 = 1438 Σy^2 = 7396

r = (8 * 0.017 - 84 * 96) / sqrt([(8 * 1438 - 84^2)(8 * 7396 - 96^2)])

r ≈ -0.335

Therefore, the value of the linear correlation coefficient r is approximately -0.335.

Answer:

A

Step-by-step explanation:

The slope intercept form of a line is written as

y = mx + c

Where

m represents slope

c represents y intercept

The x intercept is the value of x when y = 0

When y = 0 and x = - 8, then

0 = - 8 * m - 5

0 = - 8m - 5

8m = - 5

m = - 5/8

The equation in slope intercept form is

y = - 5x/8 - 5

The equation in standard form is expressed as

Ax + By = C

We would convert the slope intercept form to this form. It becomes

5x/8 + y = - 5

Where

A = 5/8

B = 1

C = - 5

The linear speed of the vehicle In miles per hour is 19.04 miles per hour

Angular speed is the time rate at which an object rotates, or revolves, about an axis, or at which the angular displacement between two bodies changes. In the figure, this displacement is represented by the angle θ between a line on one body and a line on the other.

The relationship between angular and linear speed is v = wr

where w= angular speed

v = linear speed

and r is the radius

1 inch = 1.578×10^-5

r = 32/2 = 16 inches = 16×1.578×10^-5

= 25.25×10^-5 = 2.5×10^-4miles

1 revolution = 2π = 6.28

800 revolution = 6.28× 800 = 5024

1 minutes = 1/60

800rev/minutes = 5024×60= 301440 rad/hour

v = wr

v = 301440 × 1.578 × 10^-5 = 4.76 miles per hour

therefore the linear speed of the car is 4.76miles/ hour × 4 = 19.04 miles per hour

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The population of the country will be 796 million approximately in the year 2022.

To find when the population of the country will be 796 million, we can set the equation equal to 796 and solve for t:

\(A = 433.4e^{(0.032t)}\\796 = 433.4e^{(0.032t)}\)

Divide both sides by 433.4:

\(e^{(0.032t)} = 1.836\)

Take the natural logarithm of both sides:

\(ln(e^{(0.032t)}) = ln(1.836)\)

0.032t = 0.605

Divide both sides by 0.032:

t = 18.91

Therefore, the population of the country will be 796 million approximately 19 years after 2003. To find the year, we add 19 to 2003:

2003 + 19 = 2022

Therefore, the population of the country will be 796 million approximately in the year 2022.

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\((a)\\\\m=6.1\times 10^{-5},~~ t=1.7 \times 10^{-6} \\G = \sqrt{\dfrac{m}{t^2}} = \sqrt{\dfrac{6.1\times 10^{-5}}{\left(1.7 \times 10^{-6}\right)^2} } ~=4590\\\\\\(b)\\\\m=6.1\times 10^{-5}(1+ 8\%) = 6.1\times 10^{-5}(1+0.08) = 0.0000648\\\\t=1.7\times 10^{-6}(1+ 5\%)= 1.7\times 10^{-6}(1+0.05) =0.000001785\\\\\\G=\sqrt{\dfrac{m}{t^2}} = \sqrt{\dfrac{0.0000648}{(0.000001785)^2}}=4510\)

Answer:

[ D ] 140

Step-by-step explanation

4 x 265 = 1060

1060 - 1200 = -140

the answer is 140  i hope this helped <3

Answer:

All conjecture postulates and theorems prove a logical argument.

This is my opinion

Step-by-step explanation:

Theorems are the basics of mathematics.

They are verified multiple times in past.

They are certified by all famous mathematicians of world.

Some famous theorems are

Answer:

\(\sqrt{210/16}\)  

Step-by-step explanation:

By saying reach the ground, it means the altitude w\(\sqrt{}\)ill be zero, so the equation will be: 210 - 16t^2 = 0

210 = 16t^2, t = \(\sqrt{210/16}\)  

Answer:

1) 2/x³ the secound option

2)1/x²⁴ the secound option

I think

Inverse of function f(x) = 7x + 6 is

Given,

f(x) = 7x + 6

Now,

Put y in place of f(x)

y = 7x + 6

Now interchange the variables,

x = 7y + 6

Solve for variable y,

y = x/7 - 6/7

Replace y with f-¹(x),

f-¹(x) = x/7 - 6/7

Thus the inverse of the function is obtained to be x/7 - 6/7 .

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Answer:

9-6r

Step-by-step explanation:

9(1−r)+3r

Use the distributive property to multiply 9 by 1−r.

9−9r+3r

Combine −9r and 3r to get −6r.

Answer: 9−6r

Answer:

-6r + 9

Step-by-step explanation:

9( 1 - r ) + 3r

9 - 9r + 3r

9 - 6r

So, the answer is -6r + 9

Answer:

They have to be similar because careful inspection will show all of their angles (the two triangles) are equal.

One can start with the fact that the two triangles have a common angle.

CAll it x.

x * 40 + q = 180

x + 50 + r = 180

q and r must equal 50 and 40 to satisfy the sum of the interior angles must sum to 180.

Answer:

the answer is B

Step-by-step explanation:

the inequality is say any number bigger or equal to -5

so -5, -4.5, -3 is the answer.