Write 15*15*15*15 using an exponent

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

Read more about exponential function at

https://brainly.com/question/2396210

#SPJ1

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 sum of the first 8 terms is 13.5

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

9, 3, 1, 1/3, ...

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

First term, a = 9

Common ratio, r = 1/3

The sum of GP (of n terms) is calculated as

Sum = Sn = a(r^n - 1) / (r - 1)

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

Sum = 9 * ((1/3)^8 - 1)/((1/3) - 1)

Evaluate

Sum = 13.5

Hence, the sum is 13.5

Read more about sequence at

https://brainly.com/question/29431864

#SPJ1

Answer:

**DUE TOMORROW, NEED ANSWER ASAP**

NASA has asked you to evaluate a number of proposals for telescopes. These proposals include information about where the telescope would be built and what wavelengths it intends to observe at. Based only on these factors, evaluate whether NASA should consider funding each proposal. Justify your recommendations. (Some telescopes may have more than one "correct" answer depending on how you justify it).

a.) An ultraviolet telescope in space

b.) An optical telescope in a remote location in Michigan's upper peninsula

c.) A radio telescope in the Mojave desert in Arizona

d.) An x-ray telescope in the Andes mountains in Chile

e.) An optical telescope in space

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.

More can be learned about definite integrals at https://brainly.com/question/22008756

#SPJ1

Answer:

58% decrease

Step-by-step explanation:

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.

Learn more about growth on:

https://brainly.com/question/1669287

#SPJ1

In right triangle ABC, the value of x is equal to 0.06.

In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.

Since the angle formed by side A is a right triangle, we have the following complementary angles;

C + B = 90

sin(C) = cos(B)

x + 0.26 = 3x + 0.14

3x - x = 0.26 - 0.14

2x = 0.12

x = 0.12/2

x = 0.06

Read more on right triangle here: https://brainly.com/question/27884177

#SPJ1

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%

To know more about percentage visit:

brainly.com/question/28269290

#SPJ1

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

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.

Learn more about equation here:

https://brainly.com/question/29657988

#SPJ1

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

Read more about angles at

https://brainly.com/question/25716982

#SPJ1

26 is the value of a from the given figure.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We need to find the value of a from the figure.

∠D is 46 degrees.

AD is 28, AT is 37

CosD=Adjacent side/ Hypotenuse

Cos46=a/37

0.695=a/37

a=0.697×37

a=26

Hence, the value of a is 26

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

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:

you see

Step-by-step explanation:

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?

To learn more about independent variable, refer to:

https://brainly.com/question/27894163

#SPJ1

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.

To know more about Equation check:

https://brainly.com/question/1529522

#SPJ1

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:

There are 36 possible outcomes from rolling a die twice (or two dice once) and these result in sums from 2 to 12.

Possible ways to make a sum of 2: 1

Possible ways to make a sum of 3: 2

Possible ways to make a sum of 4: 3

Possible ways to make a sum of 5: 4

Possible ways to make a sum of 6: 5

Possible ways to make a sum of 7: 6

Possible ways to make a sum of 8: 5

Possible ways to make a sum of 9: 4

Possible ways to make a sum of 10: 3

Possible ways to make a sum of 11: 2

Possible ways to make a sum of 12: 1

This means there are 21 ways to make a sum greater than 6.

21/36 ≈ 58.33%

There are 24 ways to make sums that are not divisible by 3 and not divisible by 6.   (Note that if a number isn't divisible by 3, it's also not divisible by 6, so that's a weird thing to include.)

24/36 ≈ 66.67%

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%

learn more about discount from

https://brainly.com/question/1548141

#SPJ1

The height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.

What is called height?

Height, altitude, and elevation mean the vertical distance either between the top and bottom of something or between a base and something above it. height refers to something measured vertically whether high or low.

Each time the ball bounces, it reaches a height of 75% of its previous height.

Since the ball was dropped from a height of 2 meters, its height after the first bounce will be:

2 meters x 0.75 = 1.5 meters

After the second bounce, the height of the ball will be:

1.5 meters x 0.75 = 1.125 meters

After the third bounce, the height of the ball will be:

1.125 meters x 0.75 = 0.84375 meters

After the fourth bounce, the height of the ball will be:

0.84375 meters x 0.75 = 0.6328125 meters

After the fifth bounce, the height of the ball will be:

0.6328125 meters x 0.75 = 0.474609375 meters

Therefore, the height of the ball after the 5th bounce is approximately 0.4746 meters or 47.46 centimeters.

To learn more about the height visit,

https://brainly.com/question/12446886

#SPJ1

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:

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.

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

To know more about set visit:

https://brainly.com/question/28860949

#SPJ1

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).

Learn more about probability here:

brainly.com/question/11234923

#SPJ9

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.

Learn more about Quadratic Functions here :

https://brainly.com/question/9643976

#SPJ1

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

learn more about percentage from

https://brainly.com/question/24304697

#SPJ1

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).

Learn more about Poisson probability here:

https://brainly.com/question/7283210

#SPJ1