The length of a rectangle is 3 mm greater than the width. the area is 154 mm squared. find the length and the width.

Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.

What is Scientific notation ?

Scientific notation is the way to express the large value in short form. The number in scientific notation have two parts. The digits (decimal point will place after first digit) × 10 ( the power which put the decimal point where it should be).

Here it is given that The distance between the earth and the sun is approximately 93 million miles and 1 million miles equals 1,00,000 miles.

Now, writing 93 millions Scientific notation by writing 1,00,000 in power of 10 and 93 as 9.3 x 10 :

93 million miles = 9.3 x 10 x 1,00,000

                          = 9.3 x 10^7

Therefore, Scientific notation of distance between the earth and the sun is approximately 9.3 x 10^7 miles.

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The distance between the Earth and the Sun (93 million miles) in scientific notation is [tex]9.3 *10^7 miles[/tex].

To write the distance between the Earth and the Sun (93 million miles) in scientific notation, follow these steps:

First, write 93 million as a standard numeral: 93,000,000.

Next, identify how many places to move the decimal point to get a number between 1 and 10. For 93,000,000, the decimal point moves 7 places to the left.

After moving the decimal point in 93,000,000.00 by 7 places, you get 9.3, which is between 1 and 10. This is known as mantissa.

Mantissa = 9.3

Write the number as a coefficient multiplied by 10 raised to the number of places the decimal was moved. This is called the exponent term. Exponent term = [tex]10^7[/tex].

Scientific notation of a number = Mantissa*Exponent term

So, 93,000,000 = [tex]9.3 *10^7[/tex].

Therefore, the distance between the Earth and the Sun in proper scientific notation is [tex]9.3 *10^7 miles[/tex].

Final answer:

The greatest common factor (GCF) of the numbers 12, 28, and 24 is found by identifying the smallest powers of their common prime factors, which are 2 and 3. Multiplying these together, 2 squared times 3, gives us the GCF of 12.

Explanation:

To find the greatest common factor (GCF) of the numbers 12, 28, and 24, we break each number down into its prime factors:

28 = 2 x 2 x 7

The smallest power of 3 that is common is just 3.

Therefore, the GCF of 12, 28 and 24 is 22 x 3 = 4 x 3 = 12.

In a circle, the point of symmetry is the centerpoint; any straight line that passes through this point is a line of symmetry. The standard form of equation of a circle is given as:

(x – h)^2 + (y – k )^2 = r^2

Where,

h = x coordinate of the center

k = y coordinate of the center

In the problem statement, we are given that the equation of the circle is:

(x – 5)^2 + (y + 4)^2 = 25

So identifying the variables from the standard form of equation of a circle:

h = 5

k = - 4

Therefore the point of symmetry is (5, -4).

Answer:

i) t = 5

ii) a = 3√7

iii)  x =3√13

Step-by-step explanation:

We have right triangles.

Know the two sides of the triangle and need to find the third missing side.

In order to find the third side of the right triangle, we use pythagoras theorem.

It is,

(Hypotenuse)² = (base)² + (height)²

i)

13² = 12² + t²

169 = 144 + t²

t² = 25

t = 5.

ii)

12² = 9² + a²

144 = 81 + a²

144 - 81 = a²

a² = 63

a = √63

iii)

x² = 9² + 6²

x² = 81 + 36

x² = 117

x = √117

x = 3√13

The inheritance problem deals with distributing Rs. 300,000 among 4 sons and 3 daughters after a Rs. 80,000 debt is paid. Using algebra and ratios, it is determined that each daughter receives Rs. 20,000 while each son receives Rs. 40,000.

The situation given is that a person dies leaving behind an inheritance of Rs. 300,000, which must be divided among 4 sons and 3 daughters such that each son receives double what each daughter gets. Additionally, a debt of Rs. 80,000 is to be taken out of the inheritance before distribution.

First, we need to consider the debt. Subtracting the debt from the total inheritance, we have:

Total inheritance after debt = Rs. 300,000 - Rs. 80,000 = Rs. 220,000

Now, let's assume each daughter gets x amount. Therefore, each son gets 2x the amount. We can set up the equation accounting for all sons and daughters:

3x (daughters' shares) + 4(2x) (sons' shares) = Rs. 220,000

Simplifying:

3x + 8x = Rs. 220,000

11x = Rs. 220,000

x = Rs. 20,000 (share of each daughter)

Consequently, the share of each son will be double that of a daughter, which is:

2x = 2(Rs. 20,000) = Rs. 40,000 (share of each son)

The correct option is that a score of 79 on a psychology test is relatively better than a score of 48 on an economics test.

To determine which score is relatively better, we can calculate the z-scores for each test score. The z-score tells us how many standard deviations away from the mean a particular score is.

For the psychology test, the mean is 85 and the standard deviation is 5. The score is 79. The z-score can be calculated using the formula:

[tex]\[ z = \frac{X - \mu}{\sigma} \][/tex]

where [tex]\( X \)[/tex] is the score,[tex]\( \mu \)[/tex] is the mean, and [tex]\( \sigma \)[/tex] is the standard deviation.

For the psychology test:

[tex]\[ z_{psychology} = \frac{79 - 85}{5} = \frac{-6}{5} = -1.2 \][/tex]

For the economics test, the mean is 52 and the standard deviation is 3. The score is 48. Using the same formula:

[tex]\[ z_{economics} = \frac{48 - 52}{3} = \frac{-4}{3} \approx -1.33 \][/tex]

Now, comparing the z-scores:

- The z-score for the psychology test is -1.2, which means the score is 1.2 standard deviations below the mean.

- The z-score for the economics test is approximately -1.33, which means the score is about 1.33 standard deviations below the mean.

Since a lower (more negative) z-score indicates a worse relative performance, the score of 79 on the psychology test is relatively better than the score of 48 on the economics test, because -1.2 is greater than -1.33. This means that the psychology test score is closer to its mean relative to its standard deviation than the economics test score is to its mean relative to its standard deviation.

Using the friction equation mg sin A = μmg cos A and the given coefficient of friction (μ) of 0.17, the angle at which a waxed wood block begins to slide on wet snow is calculated to be approximately 9.6°.

To find the angle at which a waxed wood block on an inclined plane of wet snow begins to slide, we can use the equation mg sin A = μmg cos A, where A is the angle of inclination, m is the mass of the block, g is the acceleration due to gravity, and μ is the coefficient of friction. Since the mass (m) and gravity (g) are both common factors on each side of the equation, they can be canceled out, leaving us with tan A = μ, where tan A is the tangent of the angle A, and μ is the coefficient of friction (0.17 in this case). Solving for A gives us A = arctan(μ). So, A = arctan(0.17), which calculates to approximately 9.6°. This is the angle at which the block begins to slide.

Answer:

We have to find a graph which represents a  reflection of f(x) = 1/10 (10)x across the y-axis.

As we know that on reflecting the graph across the y-axis the x-coordinate of the point changes to opposite sign nut with same magnitude and the y-coordinate remains same.

Hence, the function f(x) is transformed to:

[tex]f(x)=\dfrac{1}{10}\times 10^{-x}[/tex]

The graph of the function passes through the point (0,0.1) and is a strictly decreasing function.

and the end behavior of the graph is that:

when x→∞    f(x)→ 0

when x→ -∞    f(x) → ∞

In this scenario involving an elevator's movement, the negative velocity indicates downward motion and corresponds to the slope in the equation of a line. By applying the slope and initial conditions, we calculated that Monica was initially 470 feet above the ground, which is the y-intercept in the slope-intercept form.

The student's question involves understanding the implications of negative velocity in a real-world situation involving an elevator, calculating an initial position based on this velocity and elapsed time, and tying these concepts to algebraic representations in slope-intercept form.

We know from physics class that the formula for distance of a linear motion is given as:

d = v t

Where,

d = distance travelled

v = average velocity

t = time it took to reach the destination

Since the distance going to the office and back is just similar, therefore we can simply equate the two:

v1 t1 = v2 t2

Where 1 signifies going to the office and 2 signifies going back from the office. Therefore this yields to:

v1 * 5 hours = 65 mph * 4 hours

v1 = 52 mph

Answer: The average speed going to the office is 52 mph.

The average speed of Jill's trip to the ferry office was 52 mph, calculated by dividing the distance of 260 miles by the time of 5 hours.

To find the average speed of the trip there, we need to know the distance Jill traveled to the ferry office. Since she averaged 65 mph on the return trip which took 4 hours, the distance is calculated as speed x time, which equals 260 miles (65 mph x 4 hours).

The distance to the ferry office is the same as the distance back, so Jill also traveled 260 miles on the trip there. Given that the trip there took 5 hours, we can find the average speed by dividing the distance by the time. The average speed is 260 miles / 5 hours, which equals 52 mph.

The solution is, the volume of the square pyramid is 605 cm^3.

and, the surface area of the cylinder in terms of pi is 522 pi in^2.

In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.

here, we have,

we know that,

volume of pyramid is:

V = 1/3 B h

here, we have,

B = 11*11

  = 121

h = 15

so, we get,

V = 605 cm^3

again, we have,

surface area of the cylinder :

s = 2πr( r + h)

here, we have,

r = 9

h = 20

so, we get,

s = 522 pi in^2

Hence, The solution is, the volume of the square pyramid is 605 cm^3.

and, the surface area of the cylinder in terms of pi is 522 pi in^2.

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The volume of the square pyramid is A) 126 cm³ and the surface area of the cylinder is B) 522π in².

The volume of a square pyramid is expressed as:

Volume = l² × h/3

The surface area of a cylinder is expressed as:

Surface area = 2πrh + 2πr²

From the diagram:

For the square pyramid:

Length l = cm

Height h = 15cm

Volume =?

Volume = l² × h/3

Plug in the values:

Volume = 11² × 15/3

Volume = 121 × 5

Volume = 605 cm³

Option C) 605 cm³ is the correct answer.

Next, we find the surface area of the cylinder:

Radius r = 9 in

Height h = 20 in

Surface area = 2πrh + 2πr²

Plug in the values:

Surface area = (2π × 9 × 20) + (2π × 9²)

Surface area = 522π in²

Therefore, the surface of the cylinder is 522π in².

Option B) 522π in² is the correct answer.

Answer:

Option B. B = 70.05° B' = 109.95°

Step-by-step explanation:

By the sine rule in a given triangle

sin 45°/16.5 = sinB/22

1/(1.414×16.5) = sinB/22

sinB = 22/(1.414×16.5) = 0.94

[tex]B = sin^{-1}(0.94)[/tex]

B = 70.05°

Now we know B' = 180 - Supplementary angle of B'

and B = B' ( opposite angles of equal sides are equal)

B' = 180 - B = 180 - 70.05 = 109.95°

Therefore option B is the answer.

C=14 +1.5(x-4)

 c= total cost

x = number of cards

cost for 9 cards:

x=9

c=14+1.5(9-4)

14+1.5(5) = 21.50

 total cost = $21.50