8) A certain rubber ball, when dropped from a height of 2 meters onto a
hard floor, bounces back up to 75% of the height from which it was
dropped.
What is the height of the ball after the 5th bounce?

The true statements are

From the question, we have the following parameters that can be used in our computation:

The sequence:

640, 160, 40, 10, ...

Because the current term is less than the previous term, then it represents a decay function

And also, the domain will be the set of natural numbers

This is so because the input values are 1, 2, 3 and so on

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Complete question

Which statements correctly describe how the graph of the geometric sequence below should appear?

640, 160, 40, 10, ...

Select two options.

The graph will show exponential growth.

The graph will appear linear.

The domain will be the set of natural numbers.

The range will be the set of natural numbers.

The graph will show exponential decay.

Answer:

C & D

Step-by-step explanation:

The value of b is given as follows:

b = 8.4.

The value of b is obtained solving the definite integral in this problem.

The integral of the function 2x - 6 is given as follows:

x² - 6x.

At x = b, the numeric value of the integral is given as follows:

b² - 6b.

At x = -1, the numeric value of the integral is given as follows:

(-1)² - 6(-1) = 1 + 6 = 7.

Applying the Fundamental Theorem of Calculus, the equation to obtain the value of b is given as follows:

b² - 6b - 7 = 13.

b² - 6b - 20 = 0.

Which is a quadratic function with the coefficients given as follows:

a = 1, b = -6 and c = -20.

The discriminant is given as follows:

D = b² - 4ac

D = (-6)² - 4(1)(-20)

D = 116.

Hence the positive solution is given as follows:

b = (-b + sqrt(D))/2a

b = (6 + sqrt(116))/2

b = 8.4.

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Answer:

Step-by-step explanation:

The graph of the geometric sequence 640, 160, 40, 10, ... should have the following characteristics:

Decreasing: The values in the sequence decrease at a constant rate, so the graph should decrease as well.

Straight Line: Since the sequence is a geometric sequence, the graph will be a straight line when plotted on logarithmic axes.

Negative Slope: The slope of the line should be negative, since the values are decreasing.

Non-Linear: When plotted on linear axes, the graph will not be a straight line and will curve downward, since the difference between consecutive terms is decreasing.

Therefore, the graph of the geometric sequence should appear as a straight line with a negative slope when plotted on logarithmic axes, and as a non-linear curve with a downward slope when plotted on linear axes.

On solving the provided question we can say that the sets are as

U = {6, 7, 8, 9, 10, 11, 12}, and z(180) = (180-185)/4  = -1.25

A mathematical representation of a variety of different things is called a set. Any type of mathematical object may be one of the elements or terms that make up a set. Symbols, numbers, lines, other geometric shapes, points in space, variables, and even other quantities. A proposition in mathematics is a structured group of items that can be expressed as a list or a proposition builder. Curly brackets are commonly used to identify sets. For instance, A = 1, 2, 3, 4 is a set. A set is essentially a group of items that are seen together. The items that make up a set are referred to as its members or elements. The components of a set may consist of any item, but for our purposes, they usually consist of mathematical objects like numbers, functions,

the sets are as

U = {6, 7, 8, 9, 10, 11, 12},

A = {6, 7, 8, 9},

B = {6, 7, 10, 11},

C = {8, 10, 12}

1){8,10}

2)z(180) = (180-185)/4  = -1.25

P(x < 180) = P(z < -1.25)

3)28c5

4)-4

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The graph of the quadratic function is given below.

Quadratic functions are polynomial functions consisting of variables and exponents and the degree of the variable is 2.

The general form of a quadratic function is f(x) = ax² + b x + c.

Given is a quadratic function.

y = 3x² + 1

We know that graph of a quadratic function is a parabola.

Since the leading coefficient is +3, positive. So the graph opens upward.

Vertex = (-b/2a, f(-b/2a))

-b/2a = -0/(2 × 3) = 0

f(-b/2a) = (3 × 0) + 1 = 1

(0, 1) is the vertex.

x = 1, then y = 3 + 1 = 4

x = -1, then y = 3 + 1 = 4

x = 2, then y = 12 + 1 = 13

x = -2, then y = 12 + 1 = 13

x = 3, then y = 27 + 1 = 28

x = -3, then y = 27 + 1 = 28

Some of the points are (-3, 28), (-2, 13), (-1, 4). (0, 1), (1, 4), (2, 13) and (3, 28).

Hence the graph through the given points is given below.

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Step-by-step explanation:

The center of the circle is (-2,-3)

The radius is 2 since the distance from the center to the point on the circle is 2

Therefore the standard equation is

[tex](x + 2) {}^{2} + (y + 3) {}^{2} = 4[/tex]

a. This is an example of continuous growth, as the functions for the GDPs of both countries are given as continuous functions of time.

(b) In the function for China's GDP, the parameter 1.35 represents the initial level of GDP in the year 2000, and the parameter 1.076 represents the annual rate of growth of GDP. In the function for the US's GDP, the parameter 10.4 represents the initial level of GDP in the year 2000, and the parameter 1.024 represents the annual rate of growth of GDP.

It should be noted that on order to calculate the projected level of GDP for each country for the years 2011, 2025 and 2047, we can substitute the corresponding values of t into the functions for YChina and YUSA:

For China:

YChina(11) = 1.35 * 1.076^11 ≈ 4.65 trillion dollars

YChina(25) = 1.35 * 1.076^25 ≈ 30.83 trillion dollars

YChina(47) = 1.35 * 1.076^47 ≈ 516.97 trillion dollars

For the US:

YUSA(11) = 10.4 * 1.024^11 ≈ 15.63 trillion dollars

YUSA(25) = 10.4 * 1.024^25 ≈ 30.19 trillion dollars

YUSA(47) = 10.4 * 1.024^47 ≈ 57.17 trillion dollars

So according to these projections, China's GDP has already surpassed the US's GDP as of 2025 and is expected to continue to grow at a much faster rate than the US's GDP in the future.

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The solution of the inequality is -4≤x<7. Therefore, option D is the correct answer.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -12≤2x-4<10.

Here, -12≤2x-4

Add 4 on both the sides of an inequality, we get

-8≤2x

Divide 2 on both the sides of an inequality, we get

-4≤x

Now, 2x-4<10

Add 4 on both the sides of an inequality, we get

2x<14

Divide 2 on both the sides of an inequality, we get

x<7

So, the solution of the inequality is -4≤x<7

Therefore, option D is the correct answer.

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E1, E3, and E2, E3 are independent variables.

[tex]$& \mathrm{P}\left(\mathrm{E}_1\right)=\frac{1}{6} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_2\right)=\frac{1}{6} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_3\right)=\frac{2+4+6+4+2}{36}=\frac{1}{2} \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_2 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_2\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]

Then,

[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_3\right)=\frac{1}{2} \times \frac{1}{6}=\mathrm{P}\left(\mathrm{E}_1\right) \times \mathrm{P}\left(\mathrm{E}_3\right) \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right)=0 \\[/tex]

[tex]$& \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right) \equiv 0 \\[/tex]

Simplify,

[tex]$& \therefore \mathrm{P}\left(\mathrm{E}_1 \cap \mathrm{E}_2 \cap \mathrm{E}_3\right) \equiv \mathrm{P}\left(\mathrm{E}_1\right) \mathrm{P}\left(\mathrm{E}_2\right) \mathrm{P}\left(\mathrm{E}_3\right)[/tex]

E1, E3 are independent

E2, E3 are independent

The complete question is:

Let two fair six-faced dice A and B are thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

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Answer:

x    y

0    -2

4    -1

graph: should look like the picture attached

explanation:

Answer:

Step-by-step explanation:

TEP 1: Find an interest by using the formula , I=P.i.t  where I is interest, P is total principal, i is rate of interest per year, and t is total time in years.

In this examplee P = $2700, i = 6.25% and t = 3 years, so

I=506.25

STEP 2: Find an amount by using the formula . A= P+I

Since P = $2700 and I = $506.25 we have,

A=I+P

A=3206.25

Answer:

The expected number of blue marbles in a sample of 8 marbles would be 4 times the number of green marbles, so 4 * 8 = 32. Thus, the expected number of blue marbles in a sample of 8 marbles is 32.

Step-by-step explanation:

The discount on each orange is 81.3%

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

A sales discount is a reduced price offered by a business on a product or service.

The total price for the oranges is;

0.75 × 7 = $5.25

She paid $ 4.30 for the oranges, this means that the discount = 5.25-4.30 = $0.95

Therefore the percentage discount on all the oranges = 0.95/5.25 × 100

= 18.1%

by discount each orange = 4.30/7 =$ 0.61

Therefore the discount on each orange = 0.61/0.75 ×100 = 81.3 %

Therefore the discount on each orange is 81.3%

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The measure of the angles are 60 degrees each

From the question, we have the following parameters that can be used in our computation:

AOB = 138 degrees

Also, we have:

The line OX bisects the angle AOB

Using the above as a guide, we have the following:

AOX = AOB/2 = 138/2 = 69

Also, we have

XOB = AOB/2 = 138/2 = 69

Hence, the angles are 69 degrees each

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The equation that describes the graphed function is given as follows:

A. y = f(-x + 3).

A translation happens when either a figure or a function are moved horizontally or vertically.

The four translation rules for functions are given as follows:

The parent function for this problem is given as follows:

[tex]y = \sqrt{x}[/tex]

The function was reflected over the y-axis, hence it is given as follows:

[tex]y = \sqrt{-x}[/tex]

Then it was moved 3 units right, hence the definition is given as follows:

[tex]y = \sqrt{-(x - 3)}[/tex]

[tex]y = \sqrt{-x + 3}[/tex]

Hence:

y = f(-x + 3), as x was replaced by -x + 3.

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Answer:

Step-by-step explanation:

C. There is a moderate correlation between the scores and grades.

Based on the scatter plot and the calculated correlation coefficient, we can conclude that there is a moderate positive correlation between the pretest scores and the course grades. This means that as the pretest scores increase, the course grades tend to increase as well. However, the correlation is not extremely strong, so other factors may be affecting the course grades besides the pretest scores.

The correlation between two variables describes the relationship between them. The strength of the correlation can be classified into four categories: no correlation, weak correlation, moderate correlation, and strong correlation.

In this case, since the values of X and Y appear to have a moderate association, it might be concluded that there is a moderate correlation between the scores on the pretest and the course grade.

However, correlation does not imply causality, meaning that even if there is a correlation between two variables, it does not mean that one variable causes the other. Further analysis, such as regression analysis, is needed to determine the strength and direction of the relationship and to determine if there is a causal relationship.

Angles are measured in degrees, with a full circle being 360°, and can be thought of as the amount of rotation that two straight lines or planes undergo.

The class definition of angle changed from a collection of ambiguous expressions, such as “the measurement of all the sides,” “the place where lines meet,” and “the corner of a shape or anything,” to

The equation below can be set up to calculate this.

Tan(angle) = 80 ft / (200 ft – 4 ft)

Solving for the angle, we get:

angle = tan-1(80 ft / 196 ft (ca. 60 m))

angle = tan-1(0.408163265)

Angle = 36.87 degrees (to the nearest hundredth of a degree).

Therefore, The law of tangents indicates that the angle between the subject's eyes and the top of the structure is roughly 36.87 degrees.

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Answer: x = 10

Step-by-step explanation:

4x+89=129

(2 parallel straight lines have congruent angles)

then solve for x.

Step 1: Subtract 89 from both sides of the equation.

4x = 40

(We want to isolate the variable x on one side of the equation. To do this, we need to get rid of the number 89 that is currently on the right side of the equation. To do this, we subtract 89 from both sides of the equation.)

Step 2: Divide both sides of the equation by 4.

x = 10

(To isolate the variable x further, we need to get rid of the coefficient 4 that is currently in front of x. To do this, we divide both sides of the equation by 4.)

Answer: 44.20-10.68=33.52

He need 33.52$

Step-by-step explanation:

How these current asset may fit into your business, like mine, is explained as follows:

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On solving the provided question, we can say that The percentage (P) = 34%

A percentage in mathematics is a figure or ratiο that is stated as a fractiοn of 100. The abbreviations "pct.," "pct," and "pc" are alsο οccasionally used. It is frequently denoted using the percent symbοl "%," though. The amount of percentages has nο dimensions. With a denominatοr of 100, percentages are basically fractiοns.

To shοw that a number is a percentage, place a percent symbοl (%) next to it. Fοr instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To cοmpute percentages, divide the amount by the tοtal and multiply the result by 100. The percentage is calculated using the fοrmula (value/total) x 100%.

the total frequency:

Total = 29+53+50+22+1

Total = 155

The proportion (p)

p = f/total

The percentage (P)

P = p × 100

P =0.34 × 100 = 34%

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The slope of the line passing through the points (8, -4) and (8, -7) is undefined.

The slope of the line passing through the points (-3, -9) and (-3, 9) is undefined.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given data points into the slope formula, we have the following;

Slope, m = (-7 - (-4))/(8 - 8)

Slope, m = (-7 + 4)/0

Slope, m = -3/0

Slope, m = undefined.

Since the change in the x-axis equals to zero, the slope of the two lines are undefined:

Slope, m = (9 - (-9))/(-3 - (-3))

Slope, m = 18/0

Slope, m = undefined.

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a) The probability that on a random minute, at least 3 people show up is 0.080.

b) The probability that he will have to wait at least 3 minutes for the next person to show up is 1 - (5/2e) .

c) The probability that he will have to wait at least 3 more minutes for the next person to show up is 2/e.

A probability distribution called the Poisson distribution is used to indicate how frequently an event is likely to happen over a given timeframe.

Given:

a)  Let X be the number of people who show up during a random minute.

Then X follows a Poisson distribution with parameter λ = 1.

The probability of at least 3 people showing up in a random minute is:

P(X ≥ 3) = 1 - P(X < 3)

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

We can use the Poisson probability mass function to find P(X = k) for k = 0, 1, 2:

P(X = k) = ([tex]e^{-\lambda[/tex]) x ([tex]\lambda^k[/tex]) / k!

Plugging in λ = 1, we get:

P(X = 0) = [tex]e^{-1[/tex] / 0! = 1/e

P(X = 1) = [tex]e^{-1[/tex] x 1 / 1! = 1/e

P(X = 2) = [tex]e^{-1[/tex] x 1 / 2! = 1/2e

So, the probability of at least 3 people showing up in a random minute is:

= 1 - (P(X = 0) + P(X = 1) + P(X = 2))

= 1 - (1/e + 1/e + 1/2e)

= 1 - (2/e + 1/2e)

= 1 - (5/2e)

= 0.080

b) The probability of having to wait at least 3 minutes for the next person to show up

= 1 - P(X <= 2)

= 1 - (5/2e)

c) Now,

P(X ≤ 1)

= P(X = 0) + P(X = 1)

= (1/e) + (1/e)

= 2/e

So, the probability of having to wait at least 3 more minutes for the next person to show up

= 1 - (2/e)

= 1 - P(X <= 1).

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The output of the equation for input of 2 is 1.

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.

The given equation is:

y = 3x - 5

Here, x is the input value and y is the output value.

Substituting input that is x = 2.

y = 3(2) - 5

y = 6 - 5

y = 1

Hence, the output of the equation for input of 2 is 1.

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The values of p for which the equation (p+1)x² + 4px +9=0 has equal roots:

p =  (36 ± 59.8)/32

An equation is a mathematical term, which indicates that the value of two algebraic expressions are equal. There are various parts of an equation which are, coefficients, variables, constants, terms, operators, expressions, and equal to sign.

For example, 3x+2y=0.

Types of equation

1. Linear Equation

2. Quadratic Equation

3. Cubic Equation

Given that,

The quadratic equation,

(p+1)x² + 4px +9=0

So, for equal roots, we have:

(4p)² - 4 x (p + 1) x 9 = 0

Solving for p, we get:

16p² - 36 p -36 = 0

This is a quadratic equation, and we can find the roots using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Where a = 16, b = -36, and c = -36.

Plugging in the values into the formula, we get:

p = (36 ± 59.8)/32

Thus, the values of p for which the equation (p + 1)x² + 4px + 9 = 0 have equal roots are  (36 ± 59.8)/32.

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Answer:

See below

Step-by-step explanation:

You should just use a graphing calculator or an online graphing site to do this

If you were to do this manually on  a graph sheet, here is how you proceed

Given line is

y = -x - 4

We need to find 2 points to plot a straight line

Choose x = 0 ==> y = - 0 - 4 = -4

So (0, - 4) is one point

Choose another value for x. x = -4 is a good point
At x = - 4, y = -(-4) - 4 = 0

So (-4, 0) is another point.

Plot these two points on the graph and draw a straight line through those points

The attached graph shows this all

Answer:

you see

Step-by-step explanation:

The fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

If the probability that the red team wins is 0.55, then the probability that they lose is 1-0.55 = 0.45.

Similarly, if the probability that the blue team wins is 0.60, then the probability that they lose is 1-0.60 = 0.40.

If we assume that the outcomes of each game are independent of each other and that there are no ties, then the expected number of games that the red team will win in a season of 160 games is:

Expected number of wins for the red team = (probability of winning) x (number of games)

= 0.55 x 160

= 88

Similarly, the expected number of wins for the blue team is:

Expected number of wins for the blue team = (probability of winning) x (number of games)

= 0.60 x 160

= 96

Therefore, the fan should expect the red team to win 8 fewer games than the blue team in a season of 160 games (96 - 88 = 8).

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The percentage of R90 that will give 90c is 4%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.

1 cent = R0.04

R1 = 1/0.04

R 90 = 90/0.04 = 2,250c

x/100 × 2250 = 90

2250x = 9000

x = 9000/2250

x= 4%

therefore 4 percent of R 90 is 90c

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