Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y =
64(0.97)x

Answer:

Step-by-step explanation:

remember that the surface area is

S=2lw+2lh+2hw

S=2(15*20)+2(15*8)+2(8*20)=600+240+320=1160 cm^2

The surface area of the cuboid is 1160 square cm whose dimensions are

l= 20cm, w= 8 cm and h = 15 cm.

Given:

Length = 20 cm

width = 8 cm

Height = 15 cm

So, the formula for Surface area of Cuboid is

= 2(lw+ wh + lh)

Substituting the values l= 20cm, w= 8 cm and h = 15 cm into the formula as

= 2(lw+ wh + lh)

= 2 (20 x 15 + 8 x 15 + 8 x 20)

= 2 (300 + 120 + 160)

= 2 (580)

= 1160 square cm

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The statement holds true for the base case and it holds true for any k=n assuming it holds true for k=n, we can conclude that the statement holds true for all positive integer values of k. Hence, if we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in k binomial trees of the smaller orders.

The statement to be proven is: "If we remove the root of a \($\mathrm{k}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{k}$\) binomial trees of the smaller orders."

We will prove this statement by mathematical induction.

Base case k=1 :

Inductive step:

Suppose the statement holds true for some \($\mathbf{k}=\mathbf{n}$\), i.e., if we remove the root of an \($\mathbf{n}^{\text {th }}$\) order binomial tree, it results in \($\mathrm{n}$\) binomial trees of the smaller orders. We need to show that it also holds true for \($\mathbf{k}=\mathbf{n}+1$\)

using definition of mathematical induction.

Consider a \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, which can be formed by joining two \($\mathrm{n}^{\text {th }}$\) order binomial trees. If we remove the root of this \($(\mathrm{n}+1)^{\text {th }}$\) order binomial tree, we are left with two nth order binomial trees. By the induction hypothesis, each of these \($\mathbf{n}^{\text {th }}$\) order binomial trees will result in n binomial trees of the smaller orders. Hence, the result of removing the root of the \($(n+1)^{\text {th }}$\) order binomial tree will be n + n = 2n binomial trees of the smaller orders, which implies that the statement holds true for \($\mathrm{k}=\mathrm{n}+1$\) as well.

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The number of flyers Fernando handed out in 2 hours is 116

If Fernando handed out 29 flyers in 30 minutes, then we can find how many flyers he would hand out in one hour by multiplying by 2:

29 flyers/30 minutes = X flyers/60 minutes

X = (29 flyers/30 minutes) × (60 minutes/1 hour) = 58 flyers/hour

So Fernando hands out 58 flyers per hour. We can use this information to find how many flyers he hands out in 2 hours:

f = 58 flyers/hour × 2 hours = 116 flyers

Therefore, the equation to determine f, the number of flyers Fernando handed out in 2 hours, is:

f = 58 × 2 = 116

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The graph of the equation -2x = y + 3 is drawn below.

Given that:

Equation: -2x = y + 3

The linear equation is given as,

x/a + y/b = 1

Where 'a' is the x-intercept of the line and ‘b’ is the y-intercept of the line.

Convert the equation into intercept form, then we have

-2x = y + 3

2x + y = -3

x / (-1.5) + y / (-2) = 1

The graph of the equation is drawn below.

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The club needs 8 more students to meet the minimum requirement of 25 students.

In order for the club to be formed at the school:

To determine how many more students the club needs to reach the minimum required, we need to subtract the current number of students from the minimum number of students required.

The equation to determine how many more students the club needs is:

25 - 17 = 8

So the club needs 8 more students to reach the minimum

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The event was attended by 467 sixth graders.

Let's start by setting up a proportion to represent the ratio of 6th graders to the total number of students at the dance:

6th graders / total students = 4/3

We can solve for the number of 6th graders by cross-multiplying:

6th graders = (4/3) * total students

Now we can substitute the given total number of students, 350, to find the number of 6th graders:

6th graders = (4/3) * 350

          = 466.67

Since we can't have a fraction of a student, we'll round the number of 6th graders to the nearest whole number:

6th graders ≈ 467

Therefore, approximately 467 6th graders attended the dance.

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Answer:  A

Step-by-step explanation:

Notes: Dividing by a fraction means to multiply by its reciprocal.

           The denominator cannot equal zero.

\(\dfrac{5a^3bc}{8ab^3}\div\dfrac{-ab^2}{6a^5b}\cdot \dfrac{2a^2b^3}{3b}\qquad \rightarrow a\neq 0,b\neq 0\\\\\\=\dfrac{5a^3bc}{8ab^3}\cdot\dfrac{6a^5b}{-ab^2}\cdot \dfrac{2a^2b^3}{3b}\\\\\\=\dfrac{5\cdot 6\cdot 2\quad a^3\cdot a^5\cdot a^2\quad b\cdot b\cdot b^3\quad c}{8\cdot -1 \cdot 3\quad a\cdot a\qquad b^3\cdot b^2\cdot b \quad}\\\\\\=\dfrac{-60a^{10}b^5c}{-24a^2b^6}\\\\\\=\dfrac{-5a^8c}{2b}\)

The solutions of the equation sin² 2θ - 8sin 2θ - 1 = 0 are (15.4°, 47.5°, 72.5°, and 104.6°).

To solve this equation, let x = sin 2θ, then the equation becomes a quadratic equation in x: x² - 8x - 1 = 0.

Using the quadratic formula, we get x = (8 ± √(64 + 4))/2 = 4 ± √17. Therefore, sin 2θ = 4 ± √17.

To find the solutions for θ, we need to take the inverse sine of both sides:

sin 2θ = 4 + √17, so 2θ = sin⁻¹(4 + √17) ≈ 72.5° or 180° - 72.5° ≈ 107.5°. Therefore, θ = 36.25° or 53.75°.

sin 2θ = 4 - √17, so 2θ = sin⁻¹(4 - √17) ≈ 15.4° or 180° - 15.4° ≈ 164.6°. Therefore, θ = 7.7° or 82.3°.

Note that we used the fact that sin (180° - θ) = sin θ to find the second set of solutions.

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Answer: The first and last table.

As the x increases by 2, the y goes down by 1, so both tables have the same rate of change which means they are the same function.

Tables 1 and 5 are equal.

Given are 5 tables in x and y with two values each.

We are to find out which two represent the same function.

As for every function, two points are given.

Let us compare the slopes of each function.

Slope=change in y coordinate/change in x coordinate

Table           Slope

I                 -0.5

2               -0.5

3               -0.5

4                 1

5                -0.5

Table 4 is eliminated now.

Though slopes are the same for 1 and 2,f(4) =8 and 5 different . Hence I and II cannot be the same.  Similarly for 2 different values are there in table 3,4,5.  Hence 3,4,5 cannot be pairwise equal.

We find that table I and table 5 have the same slope. Also when pairwise taken, (4,8) and (2,9) slope = -0.5

So table I = table 5

Hope this helps... Stay safe and have a great day/night!!! :D

Answer:

9.6

Step-by-step explanation:

We are rounding to the nearest tenth, so we look at the hundredth place. Since 7 is bigger than 5, we round the digit in the tenths place up. We get 9.6 as our answer.

I hope this helped and please mark me as brainliest!

9.57 rounded up to the nearest tenth is 9.6

Answer:

Rectangle and Square.

Step-by-step explanation:

Let's evaluate the characteristics of each quadrilateral:

Parallelogram

Both pairs of opposite sides are congruent - OK

Both pairs of opposite sides are parallel - OK

All four angles are right angles - NO

Trapezoid

Both pairs of opposite sides are congruent - NO

Both pairs of opposite sides are parallel - NO

All four angles are right angles - NO

Rhombus

Both pairs of opposite sides are congruent - OK

Both pairs of opposite sides are parallel - OK

All four angles are right angles - NO

Rectangle

Both pairs of opposite sides are congruent - OK

Both pairs of opposite sides are parallel - OK

All four angles are right angles - OK

Square

Both pairs of opposite sides are congruent - OK

Both pairs of opposite sides are parallel - OK

All four angles are right angles - OK

So, only rectangle and square have all of the distinguishing characteristics listed.

Answer:

buy a total of 800 yds

Step-by-step explanation:

I believe that the best option for the designer would be to buy a total of 800 yds of the fabric. This is assuming that the designer needs 400 yd for a specific item. Therefore, buying 800yds would allow her to make two entire items while also meeting the minimum that the Manufacterer requires for the purchase. This would cost more but would also efficiently put to use all of the fabric that is bought for the items. Therefore, making it the best option.

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Answer:

The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²vvvThe diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²The diagram shows measures of some of the line segments in APQR. 4.5 /62.58° Q Length of QS P Area of APQR S ㅏ Use the given information to find the measures of the unknown angles and segment shown below. Round your answers to the nearest whole number. Length of PS units 6.4 -5.0- units R units²v

Step-by-step explanation:

its E and A

Answer:

The solutions to the inequality are B, E, and F: 25, 36, and 9.

Step-by-step explanation:

The solutions to the inequality √x < 10 are the values of x that make the inequality true when plugged in. To find these values, we can square both sides of the inequality:

√x < 10

x < 10^2 = 100

So, the values of x that make the inequality true are those that are less than 100. The options that satisfy this condition are:

A. 100 (not a solution)

B. 25 (solution)

C. -100 (not a solution)

D. 105 (not a solution)

E. 36 (solution)

F. 9 (solution)

Answer:

3.60

Step-by-step explanation:

Kahn Academy

The number of Students enrolled in US universities & Colleges in 2017 will be 20, 460,000

Mathematical formulas can be used to solve issues or situations in the real world thanks to the area of mathematics known as algebra. To create a valid mathematical expression, you need variables like x, y, and z as well as mathematical operations like addition, subtraction, multiplication, and division. Calculus, trigonometry, and coordinate geometry are just a handful of mathematics subjects that use algebra. A simple algebraic equation is 2x + 4 = 8. Operations on variables and constants, such as addition, subtraction, multiplication, and division, result in algebraic expressions.

Students' enrollment in US universities

in 1980 = 12, 400, 000

In 2017 the percent increase = 65%

So,

65% of 12, 400,000

= 12,400,000 X 65%

= 8,060,000

The number of Students enrolled in US universities & Colleges in 2017 will be

= 12, 400,000 + 8,060,000

=20, 460,000

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Answer: ”Building your credit score” is what many people try to do and is an important part of your financial health. You want good credit scores because they can unlock many savings and benefits, including access to loans and credit cards with the most favorable terms.

Step-by-step explanation: Establishing a good credit score is one of the most important things you'll ever do. Good credit is essential throughout your life, whether you want to buy a house or car, get insurance or maybe even pay less of a deposit for utilities. It will take about six months of credit activity to establish enough history for a FICO credit score, which is used in 90% of lending decisions. FICO credit scores range from 300-850, and a score of over 700 is considered a good credit score. Scores over 800 are considered excellent. Therefore, 850 would be the best credit score.

''Building your credit score'' is what many people try to do and is an important part of your financial health. You want good credit scores because they can unlock many savings and benefits, including access to loans and credit cards with the most favorable terms.

Here, we have,

Establishing a good credit score is one of the most important things you'll ever do.

Good credit is essential throughout your life, whether you want to buy a house or car, get insurance or maybe even pay less of a deposit for utilities.

It will take about six months of credit activity to establish enough history for a FICO credit score, which is used in 90% of lending decisions.

FICO credit scores range from 300-850, and a score of over 700 is considered a good credit score.

Scores over 800 are considered excellent.

Therefore, 850 would be the best credit score.

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To write the equation of a line parallel to 2y=5x+10 and goes through point (6,12), you first need to find the slope of the given line. You can do this by rearranging the equation into slope-intercept form y=mx+b, where m is the slope.

Rearranging 2y=5x+10 gives y=(5/2)x+5. So the slope of the given line is 5/2. Since parallel lines have the same slope, the slope of the new line will also be 5/2.

Next, you can use point-slope form to find the equation of the new line. The point-slope form is y-y1=m(x-x1), where (x1,y1) is a point on the line and m is the slope. Plugging in the point (6,12) and the slope 5/2 gives y-12=(5/2)(x-6).

Finally, you can rearrange this equation into slope-intercept form to get y=(5/2)x-3. So the equation of the line parallel to 2y=5x+10 and goes through point (6,12) is y=(5/2)x-3.

Answer:

thee ordered pair was both (1,2) and (2,4)

The binary combination of the decimal 23 in a 6-bit one's complement system is 010000.

In a one's complement system, negative numbers are represented by taking the one's complement (flipping all the bits) of the corresponding positive number and adding a sign bit at the leftmost position. For example, in a 6-bit one's complement system, the positive number 23 would be represented as 010111 (since 23 in binary is 10111), and the negative number -23 would be represented as 101000 (which is the one's complement of 010111 with a sign bit of 1 at the leftmost position).

However, since we are asked to find the binary combination of the decimal 23 (which is a positive number), we can simply convert 23 to binary and pad it with zeros to get a 6-bit representation. The binary representation of 23 is 10111, so we can add two zeros at the left to get 010111. Therefore, the binary combination of the decimal 23 in a 6-bit one's complement system is 010000.

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Sector perimeter equals 2 radius plus arc length. The formula for calculating arc length is: arc length = l = (/360) 2 r. As a result, the sector's perimeter is equal to 2 Radius plus ((/360) 2r).

The perimeter of a form is its entire outer circumference. Using what we know about determining the length of an arc, we can get the perimeter of a sector. The intersection of two radii and an arc creates a sector. We must sum these values in order to determine the perimeter. Arc length plus two is the perimeter.

Sector area is easily calculated by multiplying the central angle by the radius squared and dividing by two: Sector Area is equal to r2 / 2.

When the sector angle = 360° , curved length of the arc = 2πR

Hence when the central angle = 80 degree, the curved length = (80/360x(2πR)

= 1.3963 R = 1.3963 * 6 = 8.3776 cm.

Hence the perimeter = R + R + 8.3776 = 20.3776 cm

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Answer:36

Step-by-step explanation:

because

The puppy's weight at 6.5 months, to at least 4 significant figures, is 8.229 kg.

How many six month old puppy weighs?

The Euler method of integration, we can approximate the puppy's weight at 6.5 months by first finding its weight at 6 months and then iteratively applying the given equation.

Starting at t = 6 months, we know the puppy's weight is x = 7.0 kg.

At each time step of delta t = 0.1 months, we can use the equation dx/dt = 10 - x to find the change in weight:

dx/dt = 10 - x
dx = (10 - x) dt

Using Euler's method, we can approximate the change in weight over a small time step as:

delta x = dx/dt * delta t
delta x = (10 - x) * 0.1

We can then update the puppy's weight by adding the change in weight to its current weight:

x_new = x + delta x

Repeating this process iteratively, we can find the puppy's weight at 6.5 months:

t = 6 months:
x = 7.0 kg

t = 6.1 months:
delta x = (10 - 7.0) * 0.1 = 0.3
x_new = 7.0 + 0.3 = 7.3 kg

t = 6.2 months:
delta x = (10 - 7.3) * 0.1 = 0.27
x_new = 7.3 + 0.27 = 7.57 kg

t = 6.3 months:
delta x = (10 - 7.57) * 0.1 = 0.243
x_new = 7.57 + 0.243 = 7.813 kg

t = 6.4 months:
delta x = (10 - 7.813) * 0.1 = 0.2197
x_new = 7.813 + 0.2197 = 8.0327 kg

t = 6.5 months:
delta x = (10 - 8.0327) * 0.1 = 0.19673
x_new = 8.0327 + 0.19673 = 8.2294 kg

Therefore, the puppy's weight at 6.5 months, to at least 4 significant figures, is 8.229 kg.

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Answer:

one solution.            

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

g(x) =( x² - 2 )

Step-by-step explanation:

We have the orignal function, and that is x².

to shift 2 units to the right, we add two the value of the x² in parebtheses, and it shifts 2 units to the right in the graph.

Answer:

Step-by-step explanation:

As we move from the x-intercept (-2, 0) to the y-intercept (0, 4), x increases by 2 (this is the run) and y by 4 (this is the rise).  Thus, the slope of this line is

m = rise/run = 4/2 = 2.

Given the y-intercept (0, 4) and the slope (2), the slope-intercept form of the equation of this line is y = 2x + 4.

From this we get the point-slope form:

y = 2x + 4 becomes y - 4 = 2(x - 0), or just y - 4 = 2x.

The Area of the gable is 0.9 m²

Prudence's statement is not valid.

1. Convert 500 cm to meters:

Since 1 meter is equal to 100 centimeters,

So, 500 cm ÷ 100 = 5 meters

2. The formula for the area of a rectangle is Area = Length x Width.

Given the dimensions:

Length = 1.2 m

Width = 1.4 m

Area of one window = 1.2 m x 1.4 m = 1.68 m²

3. Calculate the area of the vent:

The formula for the area of a circle is Area = π x r².

Radius = (2.6 m) / 2 = 1.3 m

Area of the vent = 3.142 x (1.3 m)² ≈ 5.309 m²

4. Length = 1.1 m

Width = 1.6 m

Area of the rectangular part of the wall = 1.1 m x 1.6 m

= 1.76 m²

5. Calculate the area of the gable:

Given the dimensions:

Base = 0.6 m

Height = 1.8 m

Area of the gable = 0.5 m x 1.8 m = 0.9 m²

Prudence states that the area of the wall that must be painted is 14.42 m².

So, Area of the rectangular part of the wall + Area of the gable

= 1.76 m² + 0.9 m² = 2.66 m²

Therefore, Prudence's statement is not valid.

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Answer:

(c) is correct.

Step-by-step explanation:

(c) 9 + 2(4) = 9 + 8 = 17