Give the starting value a, the growth factor b, and the growth rate r if q = abt = a(1 r)t. write r as a percent. q = 79 (1.002) superscript t a. a. a = 79 b = 1.002 r = 0.2% b. a = 79.158 b = 1.002 r = 0.002% c. a = 79 b = 0.002 r = 1.002% d. a = 79.158 b = 0.002 r = 0.2%

The expression [tex]m^{7} * n^{4}[/tex] divided by [tex]m^{4} * n^{3}[/tex] simplifies to [tex]m^{3} * n[/tex], meaning m raised to the power of 3 times n. This is found by subtracting the exponents in the denominator from the exponents in the numerator.

To simplify the expression [tex]\frac{m^{7} * n^{4}}{m^{4} * n^{3}}[/tex] , we need to divide the exponents of m and n. To do this, we subtract the exponents of m and n in the denominator from the exponents of m and n in the numerator.

Starting with m, we have:

[tex]\frac{m^{7}}{m^{4}}[/tex] = [tex]m^{(7-4)}[/tex] = [tex]m^{3}[/tex]

This means that we divided the exponent of m in the numerator (7) by the exponent of m in the denominator (4), and the result is m raised to the power of 3.

Next, we do the same thing with n:

[tex]\frac{n^{4} }{n^{3} }[/tex] = [tex]n^{(4-3)}[/tex] = [tex]n^{1}[/tex] = n

This means that we divided the exponent of n in the numerator (4) by the exponent of n in the denominator (3), and the result is n raised to the power of 1, which is just n.

Finally, we can combine the results:

[tex]m^{3}*n[/tex] = [tex]m^{3}*n[/tex]

So, the simplified form of the expression [tex]\frac {m^{7 }* n^{4}} { m^{4} * n^{3}}[/tex] is [tex]m^{3}*n[/tex].

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Answer:

m^3n

Step-by-step explanation:

m3n

The probability of picking three black cards in a row, without replacement, from a standard deck of 52 playing cards is 2/17, or approximately 0.1176 (rounded to four decimal places).

The probability of picking a black card on the first draw = 26/52 = 1/2

        (since there are 26 black cards in the deck)

The probability of picking a black card on the second draw, given that a one was picked on the first draw and the card is not replaced = 25/51,    

        (since there are now only 25 black cards left out)

The probability of picking a black card on the third draw, given that the ones picked on the first two draws are not replaced = 24/50 = 12/25,

        (since there are now only 24 black cards left out)

To pick three black cards in a row, we need to multiply the probabilities of each individual draw = (1/2) * (25/51) * (12/25) = 6/51

Simplifying this fraction, we get = 6/51 = 2/17

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The approximate cost of 5-hour trip if the price of fuel is R78 per liter by finding the average speed is R3000.68.

To find the the total distance travelled by the car in 5 hours at an average speed of 100 km/h is:

Distance = Speed x Time

Distance = 100 km/h x 5 h

Distance = 500 km

The total amount of fuel consumed during the trip is:

Fuel consumed = Distance / Fuel efficiency

Fuel consumed = 500 km / 13 km/l

Fuel consumed = 38.46 liters (rounded to two decimal places)

The cost of the fuel consumed during the trip is:

Cost of fuel = Fuel consumed x Price per liter

Cost of fuel = 38.46 liters x R78/liter

Cost of fuel = R3000.68 (rounded to two decimal places)

Therefore, the approximate cost of the 5-hour trip is R3000.68, assuming that the only cost incurred is for the fuel consumed during the trip.

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The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function over the x-axis, shifting it left by 3 units, and down by 2 units.

To reflect a quadratic function over the x-axis, we need to multiply the function by -1. Let's assume that our original quadratic function is f(x).

After reflecting the function over the x-axis, we get the new function g(x) = -f(x).

To perform a horizontal shift left 3 units, we need to replace x with (x + 3) in the function g(x). This gives us the new function h(x) = g(x + 3) = -f(x + 3).

Finally, to shift the function down 2 units, we need to subtract 2 from the entire function h(x).

Note that the order of the transformations is important. We first reflect the function over the x-axis, then shift it horizontally, and finally shift it vertically.

Hence,

The transformed function is y = -f(x + 3) - 2, obtained by reflecting the quadratic function

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The length of each of the three remaining sides, in order from least to greatest, is x = 8, y = 18 and z = 3.

What is Perimeter?

Perimeter is the total length of the boundary of a two-dimensional shape or figure. It is the distance around the outside of a closed shape, such as a rectangle, triangle, circle, or any other polygon. To find the perimeter of a shape, you add up the lengths of all its sides. Perimeter is usually measured in units of length, such as centimeters, meters, feet, or inches. Perimeter is an important concept in geometry, and it is used to calculate the amount of material needed to surround a shape or to measure the distance around a path or track.

Let's denote the lengths of the three remaining sides of the kite as x, y, and z, where x is the shortest side.

The perimeter of the kite is the sum of the lengths of all four sides:

P = x + y + z + 18

We also know that the total length of plastic used to frame the perimeter is 94 inches:

94 = 2x + 2y + 2z + 36

Simplifying the equations by dividing both sides of the second equation by 2, we get:

47 = x + y + z + 18

47 = x + y + z + 18

Substituting the first equation into the second equation, we get:

x + y + z + 18 = 2x + 2y + 2z + 36

Simplifying this equation, we get:

x = 8

Substituting x = 8 into the first equation, we get:

y + z + 26 = 47

Simplifying this equation, we get:

y + z = 21

We want to find the values of y and z. Since we don't have enough information to solve for each of them individually, we'll use a bit of logic to determine their relative values.

The only combination that satisfies these conditions is:

y = 18

z = 3

Therefore, the length of each of the three remaining sides, in order from least to greatest, is:

x = 8

y = 18

z = 3

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At a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.

The rectangle's area in square meters The area's width and length should be measured in feet. To calculate area, multiply your length by your width. Use our length converter to convert your measures if they aren't already in feet.

Area is length times breadth, or 12 feet by 16 feet, or 192 square feet. The cost of the carpet is $10 per square foot. By dividing the square footage of the room by the price per square foot, we can get the overall cost to carpet it.

Total cost is equal to Area. Cost per square foot is $1920 or 192 square feet (around 18 m2) times $10 per square foot.

Therefore, at a price of $10 per square foot, it will cost $1920 to carpet the 12 by 16-foot space.

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Answer: I agree with Moriah. If two equations represent the same proportional relationship, then they should have the same constant of proportionality. In this case, the constant of proportionality in p = 1.5 and 2/3p = q is different, so the two equations cannot represent the same proportional relationship.

It's possible that the two equations represent two different proportional relationships, but without more information it's impossible to determine if that is the case.

Step-by-step explanation:

Las actividades de apertura son descripciones de diferentes relaciones geométricas. Aquí está la explicación de cada una:

a) Dos ángulos rectos tienen una medida de 90 grados.

b) Dos ángulos agudos tienen una medida menor a 90 grados.

c) Dos ángulos suplementarios suman a 90 grados.

d) Dos ángulos complementarios suman a 90 grados.

e) Dos rectas paralelas no se cruzan.

f) Dos rectas perpendiculares se cruzan en un ángulo recto de 90 grados.

g) Una recta transversal corta a dos o más rectas, creando ángulos en los puntos de intersección.

Dos ángulos rectos son dos ángulos que tienen una medida de 90 grados. En geometría, un ángulo recto es un ángulo que tiene una medida de 90 grados y se representa con una línea diagonal que forma cuatro cuartos iguales.

Los ángulos rectos son importantes en la construcción y el diseño, ya que permiten la creación de formas simples y precisas. Por ejemplo, dos ángulos rectos pueden ser utilizados para formar un cuadrado o un rectángulo, mientras que un ángulo recto y un ángulo agudo pueden ser utilizados para formar un triángulo rectángulo.

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The equation of the total bill with x number of refills is y = 5 + x and the refills if the bill is $9 is 4.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

Let us consider the number of times we refill = x.

For every refill the cost will be = 1(x) = x.

Then, a basket of fries for $5, and each refill basket of fries is only $1 is:

y = 5 + x

The equation of the total bill with x number of refills is y = 5 + x.

The graph of the equation is obtained by substituting different values of x.

For x = 1:

y = 5 + 1 = 6

Similarly, x = 2:

y = 5 + 2 = 7

If the bill is $9 then,

y = 5 + x

9 = 5 + x

9 - 5 = x

x = 4

Hence, the equation of the total bill with x number of refills is y = 5 + x and the refills if the bill is $9 is 4.

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Answer:160

Step-by-step explanation:

A man brought some glasses at 12 each and 5 broke so he sold remaining at 16 each and made profit of rupees 160. Find number of glasses he bought

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Answer: Dear Editor,

I am writing to bring to your attention the serious issue of rising air and noise pollution in our area. The daily air quality index that appears in the newspaper highlights the extent of the problem, and I believe it is important for the public to be aware of its effects.

Air pollution has been linked to a number of health problems, including respiratory issues, heart disease, and even cancer. The presence of harmful pollutants in the air we breathe is cause for concern and demands immediate attention. Similarly, noise pollution can lead to hearing loss, sleep disturbance, and increased stress levels.

It is imperative that we take action to curb the effects of air and noise pollution. There are several measures that can be taken, both by individuals and by the government. On an individual level, we can reduce our carbon footprint by using public transportation, carpooling, or biking instead of driving alone. We can also plant trees and install air purifiers in our homes.

The government, on the other hand, can take steps to regulate industrial emissions, enforce stricter penalties for violators, and promote the use of clean energy sources. Additionally, they can create green spaces and establish noise-free zones in residential areas.

In conclusion, the rise in air and noise pollution is a pressing issue that affects the health and well-being of everyone in our community. I urge the public to take this matter seriously and support efforts to reduce its impact. Together, we can work towards a cleaner and healthier future.

Sincerely,

[Your Name]

Step-by-step explanation:

Area of a circular swimming pool is 154m², So radius of the circular swimming pool is approximately 7.88 meters

The area of a circle is given by the formula:

A = πr²

where A is the area, r is the radius, and π is a mathematical constant approximately equal to 3.14.

We are given the area of the circular swimming pool as 154m². So we can set up the equation:

154 = πr²

Solving for r, we get:

r = √(154/π) ≈ 7.88 m

Hence,

The radius of the circular swimming pool is approximately 7.88 meters.

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Answer:

(i) The volume of each hemispherical bowl can be calculated as follows:

Volume of a hemispherical bowl = (2/3) x pi x (d/2)^3, where d is the internal diameter of the bowl.

Substituting d = 21 cm, we get:

Volume of a hemispherical bowl = (2/3) x pi x (21/2)^3 = 4851.97 cubic centimeters

The total volume of compost required to fill all 16 bowls is therefore:

Total volume of compost = 16 x 4851.97 = 77631.52 cubic centimeters

If 1 cm³ of compost weighs 2.31 gm, then the total weight of required compost is:

Total weight of compost = 77631.52 x 2.31 = 179231.83 grams or 179.23 kilograms

Therefore, Mrs. Thapa would need 179.23 kilograms of compost to fill all 16 hemispherical bowls.

(ii) The outer curved surface area of each hemispherical bowl can be calculated as follows:

Outer curved surface area of a hemispherical bowl = 2 x pi x (d/2)^2, where d is the internal diameter of the bowl.

Substituting d = 21 cm, we get:

Outer curved surface area of a hemispherical bowl = 2 x pi x (21/2)^2 = 693.84 square centimeters

The total outer curved surface area of all 16 bowls is therefore:

Total outer curved surface area = 16 x 693.84 = 11101.44 square centimeters

If Mrs. Thapa covers the outer curved surface of each bowl with polythene sheet, then the total amount of polythene required would be equal to the total outer curved surface area of all 16 bowls.

Therefore, the total amount of polythene required would be 11101.44 square centimeters.

Step-by-step explanation:

Answer:

Step-by-step explanation:

You are currently converting speed units from foot per minute to miles per hour 1 ft/min = 0.011363636 mph foot per minute ft

so 0.011363636 times 2000 equals 27.727272

so your answer is [B]

If an AP has first term 7 and common difference 4. If the sum of all it's terms is 900, then there are 3 terms.

Let's use the formula for the sum of an arithmetic progression to solve this problem:

S = n/2[2a + (n-1)d]

where S is the sum of the first n terms, a is the first term, d is the common difference, and n is the number of terms.

We know that a = 7 and d = 4, and we're given that S = 900. Substituting these values into the formula, we get:

900 = n/2[2(7) + (n-1)(4)]

Simplifying the expression inside the brackets:

900 = n/2[14 + 4n - 4]

900 = n/2[10 + 4n]

Multiplying both sides by 2 to eliminate the fraction:

1800 = n[10 + 4n]

Simplifying the right-hand side:

1800 = 4n^2 + 10n

Rearranging to get a quadratic equation in standard form:

4n^2 + 10n - 1800 = 0

We can solve for n using the quadratic formula:

n = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 4, b = 10, and c = -1800, so:

n = (-10 ± √(10^2 - 4(4)(-1800))) / 2(4)

n = (-10 ± √(100 + 28800)) / 8

n = (-10 ± √(28900)) / 8

n = (-10 ± 170) / 8

n = 20/8 or n = -180/8

n = 2.5 or n = -22.5

Since the number of terms must be a positive integer, we can discard the negative solution and conclude that there are 2.5 terms. However, this doesn't make sense because the number of terms in an arithmetic progression must be a whole number. Therefore, we need to round up to the nearest whole number, which gives us:

n = 3

Therefore, there are 3 terms in the arithmetic progression with first term 7 and common difference 4, and the sum of these terms is 900.

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Answer:

6x^2 + 17x + 12

Step-by-step explanation:

(3x + 4)(2x + 3) - Distribute

6x^2 + 9x + 8x + 12

6x^2 + 17x + 12

If Jim missed 6 out of 16 free throws, then he made 10/16 free throws. At the same time Gracia made 4/15 free rows. The common denominator of those fractions (if we simplify 10/16 to 5/8) is 120, so:

Garcia made 4/15 = 32/120 free throws

Jim made 5/8 = 75/120 free throws

We can clearly see that Jim was more than two times better than Garcia

Answer:

75%

Step-by-step explanation:

If you have a calculator, you can divide 39/52. If not,

39/52 = x/100

52x = 3900

x = 75

75/100 = 75%

There are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

To find the number of acres in a lot, you can use the following formula:

Number of acres = (length in feet) x (width in feet) / 43,560

First, convert the length and width from miles to feet. There are 5,280 feet in a mile, so:

Length in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet
Width in feet = 1/2 mile x 5,280 feet/mile = 2,640 feet

Next, plug these values into the formula:

Number of acres = (2,640 feet) x (2,640 feet) / 43,560 = 174,240,000 / 43,560 = 160 acres

Therefore, there are approximately 160 acres in a lot that is 1/2 mile by 1/2 mile.

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Answer:

22/7 or 3 1/14

Step-by-step explanation:
the most common denominator is 28 for both so the denominator is 28
then added them and simplified them in mixed and normal form because I forgot which was which. Hopefully this is correct, if not I am sorry.

The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

The length of the ladder is 10 feet. And the inclination angle is 65°. Then the distance from the bottom of ladder to the wall is given as,

cos 65° = x / 10

x = 4.23 feet

If the ladder reaches a window 9.6 feet above the ground, then the angle is given as,

sin θ = 9.6 / 10

sin θ = sin 73.74°

     θ = 73.74°

The distance from the base of the ladder to the wall is 4.23 feet. And the inclination angle will be 73.74°.

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To accurately represent men's and women's shoe sizes separately, it is recommended to calculate and compare the average or median shoe size for each group separately.

The problem with the central measure, mean or median, in this case is that the data is not gender-specific and there is a possibility that male and female shoe size distributions are different. Therefore, calculating the average or median shoe size for all students may not accurately reflect the typical male and female shoe sizes, respectively.

For example, if the males in the sample have, on average, a larger shoe size than the females, then the average shoe size of all students might be biased towards the larger size, even if most of the students are female. On the other hand, if you have several boys with very large shoe sizes, the median shoe size of all students may be biased toward the larger size, even if most of the students are women with small shoe sizes.

To accurately represent men's and women's shoe sizes separately, it is recommended to calculate and compare the average or median shoe size for each group separately. Alternatively, a fashion report representing the most common shoe sizes in the data might be a better measure of the centroid.

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The only option that represents an object with volume is; Option D: Water Bottle

An object that will have volume is a 3-D object which means that it has length, width and height. Thus, 2D objects cannot have a volume.

Let us access the given options;

A) Baseball diamond: This refers to the baseball field because of the shape of the infield. Thus, it has only length and width and is a 2D shape which doesn't have a volume.

B) Floor Rug: A floor rug, is a plane shape which means it s a 2D shape which doesn't have a volume.

C) A piece of paper: This is a plane shape which means it s a 2D shape which doesn't have a volume.

D) Water Bottle: This is a 3D shape that has length, width and height and as such it has volume.

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According to the information, the area of the parallelogram plotted from the points would be: 36 cm²

To find the area of the parallelogram we must divide the parallelogram into a quadrilateral section and another triangular section and find the area of these segments.

According to the above, we can infer that the area of the quadrilateral zone would be

On the other hand, the area of the triangular section would be:

Additionally, we must multiply the area of the triangular segment by two because there are two triangular sections in the parallelogram. Finally we have to add the area of the quadrilateral and triangle segments to get the total area.

Note: This question is incomplete. Here is the complete information:

TASK

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Susan bought 6 boxes of chocolate cookies, and 2/5(6) = 2.4 or 2 boxes of butter cookies.

Let's call the number of boxes of chocolate cookies that Susan bought "C". Then, she bought 2/5 as many boxes of butter cookies, which is 2/5C.

Let's call the cost of each box of chocolate cookies "x". Then, the cost of each box of butter cookies is x-2, since each box of butter cookies costs $2 less.

We know that the total cost of the chocolate cookies was $84 more than the total cost of the butter cookies. This can be expressed as:

Cx = 2C/5(x-2) + 84

Simplifying this equation, we get:

3/5Cx = 84 + 2/5C(2)

Multiplying both sides by 5/3, we get:

Cx = 140 + 4C/3

We also know that the total cost of all the cookies was $156, which can be expressed as:

Cx(x) + (2/5C)(x-2) = 156

Substituting Cx from the previous equation, we get:

(140 + 4/3C)(C) + (2/5C)(C-2) = 156

Simplifying and solving for C, we get:

C = 6

So Susan bought 6 boxes of chocolate cookies, and 2/5(6) = 2.4 or 2 boxes of butter cookies.

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Answer:

  1.8 m³

Step-by-step explanation:

You want the volume of the rectangular prism with dimensions L=4 m, W = 0.3m, H = 1.5 m.

The volume formula is given in the problem statement:

  V = LWH

Substituting the given values of L, W, H, we find the volume to be ...

  V = (4 m)(0.3 m)(1.5 m)

  V = 1.8 m³

The volume of the rectangular prism is 1.8 cubic meters.