terri, aaron, and jamal all walked along straight paths. terri walked 3.95 km north in 48 min. aaron walked 2.65 km west in 31 min. jamal walked 6.50 km south in 81 min.

Answer:

See Below.

Step-by-step explanation:

The sum of an A.P. is given by:

\(\displaystyle S_n=\frac{n}{2}(a+x_n)\)

Where n is the number of terms, a is the initial term, and xₙ is the last term.

Therefore:

\(\displaystyle S_{30}=\frac{30}{2}\Big(a+x_{30}\Big)=15(a+x_{30})\)

And likewise:

\(\displaystyle S_{20}=\frac{20}{2}\Big(a+x_{20}\Big)=10(a+x_{20})\\\\ S_{10}=\frac{10}{2}\Big(a+x_{10}\Big)=5(a+x_{10})\)

Substitute:

\(15(a + x_{30}) = 3(10 (a + x_{20}) - 5(a + x_{10} ))\)

Distribute:

\(15a+15x_{30}=30a+30x_{20}-15a-15x_{10}\)

Simplify:

\(15x_{30}=30x_{20}-15x_{10}\)

Simplify:

\(x_{30}=2x_{20}-x_{10}\)

The nth term for an A.P. is:

\(x_n=a+d(n-1)\)

Where a is the initial term and d is the common difference.

So, it follows that:

\(x_{30}=a+d(30-1)=29d+a\\ x_{20}=a+d(20-1)=19d+a\\ x_{10}=a+d(10-1)=9d+a\)

Therefore:

\(29d+a=2(19d+a)-9d-a\)

Which follows that:

\(29d+a=38d+2a-9d-a\\ \\ 29d=29d \\\\ d\stackrel{\checkmark}{=}d\)

QED.

After 20 years, the investment compounded periodically will be worth $ 3, 238. 47 more than the investment compounded annually.

First, find the value of the investment when it is compounded periodically, 12 times a year.

The formula is:

= Amount invested x ( 1 + rate ) ^ number of periods

= 9, 000 x ( 1 + 9 % / 12 ) ^ ¹² ˣ ²⁰

= $ 53, 678. 16

If compounded annually, the value would be :

= 9, 000 x ( 1 + 9 % ) ²⁰

= $ 50, 439. 69

The difference is :

= 53, 678. 16 - 50, 439. 69

= $ 3, 238. 47

Find out more on investments at https://brainly.com/question/15201573

#SPJ1

Answer:

The number y decreased by 12.

Step-by-step explanation:

Answer

the answer is b y decreased by 12

Step-by-step explanation:

that is what y-12 is

Please find attached the image of the graph that models the function.

A graph is a pictorial representation of data. A graph is made up of the x-axis and the y-axis.  On this graph, the number of years is on the y-axis and the profit is on the x-axis.

To learn more about graphs, please check: https://brainly.com/question/21527145

#SPJ1

Answer: other dude is correct

Step-by-step explanation:

Answer:

210-300=-90

Step-by-step explanation:hope this helps plz mrk me brainliest

Answer:

dont post stuff like this on brainly, it is for homework only

Step-by-step explanation:

Answer:

\( {3}^{3} \\ {g}^{5 } \\ a \\ {y}^{ - 2} \\ 1\)

Answer:

12

Step-by-step explanation:

Mode is the number that shows up the most in a data set.

The numbers: 8, 6, 12, 5, 15, 12, 3, 10, 9

Number 12 shows up the most in the list, so the mode is 12.

Yes, you can relate a given quantity to the indicated amount using more than one symbol.

In mathematics, symbols are used to represent mathematical objects and operations, making it easier to understand and communicate mathematical ideas.

Each symbol has a specific meaning and can be used in different ways to represent the same quantity.

For example, the number 7 can be represented by the numeral 7, the Roman numeral VII, or even the symbol 7 in scientific notation. All of these symbols represent the same quantity, but they each have a different context and use.

The numeral 7 is commonly used in everyday life, the Roman numeral VII is used in ancient times and in some specific contexts, and the scientific notation 7 x 10⁰ is used in scientific and mathematical calculations.

Similarly, in algebra, a variable such as x can represent a quantity and can be used in different ways to represent the same value.

For example, the equation x + 3 = 6 can be solved for x to find that x = 3. This same value can also be represented by the expression 3x, which shows that x is equal to 3.

To know more about symbol here.

https://brainly.com/question/11260830

#SPJ4

A binary tree is a structure in which each node is capable of having two successor nodes, called "left child" and "right child."

In a binary tree, each node can have at most two successor nodes, known as the left child and the right child. These successor nodes branch out from the parent node, forming two distinct paths or branches. The left child represents the left branch, and the right child represents the right branch. This hierarchical structure allows for efficient organization and traversal of data, as each node can connect to two other nodes, creating a branching pattern throughout the tree. The concept of left and right children enables various operations and algorithms to be performed on the binary tree, such as insertion, deletion, searching, and sorting.

To know more about binary tree,

https://brainly.com/question/33461694

#SPJ11

Colin purchases a package of pasta with 8 2/3 cups of spaghetti inside. He makes dinner with 2 1/2 cups. Pasta is down to 6 1/6 cups for Colin.

To find out how much pasta is left, we need to subtract the amount used from the total amount of pasta:

8 2/3 cups - 2 1/2 cups

First, we need to convert the mixed numbers to improper fractions, which will make it easier to subtract them:

8 2/3 = (8 x 3 + 2) / 3 = 26/3

2 1/2 = (2 x 2 + 1) / 2 = 5/2

Now we can subtract:

26/3 - 5/2

We must identify a common denominator in order to subtract fractions with various numerators. Since 3 and 2 have a least common denominator of 6, we can convert both fractions to have a denominator of 6:

26/3 = (26/3) x (2/2) = 52/6

5/2 = (5/2) x (3/3) = 15/6

Now we can subtract:

52/6 - 15/6 = 37/6

Therefore, Colin has 6 1/6 cups of pasta left.

When the numerator (the top number) exceeds the denominator (the bottom number), the fraction is said to be improper. This means that the fraction represents a value greater than one, and is often expressed as a mixed number (a whole number and a proper fraction).

Improper fractions are commonly used in math and can represent values in a variety of contexts, such as in measurements or in calculations. They can be added, subtracted, multiplied, and divided just like any other fraction. It is important to know how to convert improper fractions to mixed numbers and vice versa, as well as how to perform operations with them, in order to effectively solve mathematical problems.

To learn more about Improper fractions visit here:

brainly.com/question/21449807

#SPJ4

Answer:

2 x 2 x 2 x 3 x 3 = 72

The coordinate matrix of a set of matrices with respect to a given basis. The final coordinate matrix is a matrix that represents the given matrix in the given basis and can be used for various calculations.

Given a vector space V with a basis B = {b1, b2, ..., bn} and an element v ∈ V. The coordinate matrix of v with respect to the basis B is the n × 1 matrix [v]B = (a1, a2, ..., an) where v = a1b1 + a2b2 + ... + anbn. This is also referred to as the coordinate vector of v with respect to B.Exercise 11:Let A = {[1 0], [0 1]} be a matrix and B = {[3 1], [2 4]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = {[1 0], [0 1]}B = {[3 1], [2 4]}Hence,X = A⁻¹B = {[1 0], [0 1]}{[3 1], [2 4]}= {[3 1], [2 4]}Coordinate matrix of A with respect to B is Xᵀ = {[3 2], [1 4]}Exercise 12:Let A = {[2 -1], [3 1]} be a matrix and B = {[1 1], [2 1]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = 1/(ad - bc) [d -b, -c a] = [1 1, -2 2]B = {[1 1], [2 1]}Hence,X = A⁻¹B = [1 1; -2 2][1 1; 2 1]= [3 2; -4 1]Coordinate matrix of A with respect to B is Xᵀ = {[3 -4], [2 1]}Exercise 13:Let A = {[1 1 1], [0 1 1], [0 0 1]} be a matrix and B = {[1 0 0], [1 1 0], [1 1 1]} be a basis of R3. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = {[1 -1 0], [0 1 -1], [0 0 1]}B = {[1 0 0], [1 1 0], [1 1 1]}Hence,X = A⁻¹B = {[1 0 0], [0 1 0], [0 0 1]}Coordinate matrix of A with respect to B is Xᵀ = {[1 0 0], [0 1 0], [0 0 1]}Exercise 14:Let A = {[1 2], [3 4]} be a matrix and B = {[1 -1], [1 1]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = -1/2 [4 -2, -3 1] = [-2 3/2, 1/2 -1/2]B = {[1 -1], [1 1]}Hence,X = A⁻¹B = [-2 3/2; 1/2 -1/2][1 -1; 1 1]= [3/2 1/2; 5/2 3/2]Coordinate matrix of A with respect to B is Xᵀ = {[3/2 5/2], [1/2 3/2]}Exercise 15:Let A = {[1 2 3], [4 5 6], [7 8 9]} be a matrix and B = {[1 0 0], [0 1 0], [0 0 1]} be a basis of R3. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B.

Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = [(-2/3) 0 (1/3); (-2/3) (1/3) (4/3); (1/3) (-2/3) (1/3)]B = {[1 0 0], [0 1 0], [0 0 1]}Hence,X = A⁻¹B = [(-2/3) 0 (1/3); (-2/3) (1/3) (4/3); (1/3) (-2/3) (1/3)][1 0 0; 0 1 0; 0 0 1]= [(-2/3) 0 (1/3); (-2/3) (1/3) (4/3); (1/3) (-2/3) (1/3)]Coordinate matrix of A with respect to B is Xᵀ = {[(-2/3) -2/3 1/3], [0 1/3 -2/3], [(1/3) (4/3) (1/3)]}Exercise 16:Let A = {[1 -1], [2 -2]} be a matrix and B = {[1 1], [1 0]} be a basis of R2. We are to find the coordinate matrix of A with respect to B. We are looking for the solution to the equation AX = B. Rearranging, we have X = A⁻¹B. We can then get the coordinate matrix of A with respect to B by taking the transpose of X. Solving, we haveA⁻¹ = 1/2 [2 1, -2 -1] = [1 -1/2, -1 1/2]B = {[1 1], [1 0]}Hence,X = A⁻¹B = [1 -1/2; -1 1/2][1 1; 1 0]= [0.5 1; -0.5 1]Coordinate matrix of A with respect to B is Xᵀ = {[0.5 -0.5], [1 1]}.

so each main answer consists of finding the inverse of the given matrix, multiplying it by the given basis matrix, and transposing the result to obtain the coordinate matrix.

To know more about coordinate matrix visit:

brainly.com/question/31052618

#SPJ11

Answer:

B

Step-by-step explanation:

because  when simplified we get b

Answer:

Step-by-step explanation:

\( {x}^{2} - 4x - 12 \\ {x}^{2} + 2x - 6x - 12 \\ x(x + 2) - 6(x + 2) \\ (x - 6)(x + 2) \\ \)

Answer:

270 inches

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Answer:

100900000099899887765544422

Step-by-step explanation:

Let,

According to the question,

→ Money received by Jan = $200

→ 4x = $200

→ x = $200 ÷ 4

→ x = 50 ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀… ( 1 )

Now,

→ Money received by Jane = 9x

→ Money received by Jane = 9($50)

→ Money received by Jane = $450 [Ans]

And,

→ Money received by Jello = 6x

→ Money received by Jello = 6($50)

→ Money received by Jello = $300 [Ans]

Answer:

start by plotting number 5 on the y-axis, and from that point move up 3 and to the left 4

Step-by-step explanation:

The number of miles that a signal sent from Station 1 to the satellite and then to Station 2 will have to travel is; 48135 miles

Let us first find the distance from Station 1 to the satellite:

Using trigonometric ratio, we have;

tan 8.7 = length of longest leg/length of shortest leg

Thus;

tan 8.7 =  3963/length of longest leg

Length of longest leg = 3963/tan8.7°

Length of longest leg = 3963/0.15302150298

Length of longest leg = 25,898 miles

Distance from Station 2 to satellite:

Using trigonometric ratio again, we have;

sin 8.7 = length of longest leg/ length of hypotenuse

sin  8.7 =  3963/length of hypotenuse

Length of hypotenuse =3963/ sin 8.7

Length of hypotenuse =3963/0.1526082024

Length of hypotenuse = 26, 200 miles

Thus, the difference is;

26200 - 3,963 = 22237 miles

Total distance will calculated as;

25898 miles  + 22237 miles = 48135 miles

Read more about Distance of separation at; https://brainly.com/question/20629991

#SPJ1

The complete question is:

A satellite orbiting the earth uses radar to communicate with two control stations on the earth's surface. The satellite's orbit maintains a 10-degree angle of separation between the two stations, as shown in the picture below. Knowing that the earth's radius is 3,963 miles.

How many miles will a signal sent from Station 1 to the satellite and then to Station 2 have to travel?

252 is the answer

total amount=the whole amount

total amount =amount of pants+amount of shirts

total amount=138+114

total amount=252

Answer=252

Answer:

hope this answer helps you dear...take care and may u have a great day ahead!

Answer:

Step-by-step explanation:

Photo Proof

The missing value should be in the table is 750 and 1250.

1                     250

2                    500

3                     750

4                    1000

5                    1250

Since we can see that there is the gap of 250 in each words

like

= 250 + 250

= 500

So

= 500 + 250

= 750

And, so on

learn more about quantities here: https://brainly.com/question/13690145

Answer:

53.3 rotations

Step-by-step explanation:

135/180=x/40

solve by cross multiply

There is evidence of a negative correlation between systolic blood pressure and heart rate because the sample correlation is -0.057. This value indicates that there is a small negative correlation between systolic blood pressure and heart rate.

There is evidence of a negative correlation between systolic blood pressure and heart rate. In a sample of 200 patients, a sample correlation of -0.057 was found. Correlation is a statistical measure used to assess the degree to which two variables are related to one another. A correlation coefficient ranging from -1 to 1 is used to represent this relationship. A negative correlation exists when two variables move in opposite directions.

It means that as one variable increases, the other variable decreases or vice versa.In the given case, there is evidence of a negative correlation between systolic blood pressure and heart rate because the sample correlation is -0.057. This value indicates that there is a small negative correlation between systolic blood pressure and heart rate. Systolic blood pressure is the amount of pressure exerted by blood against the walls of the arteries when the heart pumps. It is the top number in a blood pressure reading.

When your heart beats and pushes blood out, the systolic pressure is created.Heart rate is the number of times your heart beats per minute. It is also known as the pulse rate. It represents the number of times your heart contracts and relaxes with each heartbeat.

Learn more about Sample correlation

brainly.com/question/14018989

#SPJ11

The same person also took a midterm in their marketing course and the class mean for this exam was 77 with a standard deviation of 4.7. The z-score for the score on this exam is 1.9. Calculate the actual score this person received for the marketing exam (to 2 decimal places).

Here is how we can calculate the actual score this person received for the marketing exam. First, we know that the Z score is given by the formula:

Z = (X - μ)/ σ

where X = actual score, μ = Mean, σ = Standard Deviation

Given that the Z score is 1.9, i.e., Z = 1.9

Hence,X = μ + Zσ

On substituting the given values, we get: X = 77 + 1.9 * 4.7X = 86.13 (approx.)

Therefore, the actual score that this person received for the marketing exam is 86.13 (to 2 decimal places).Note that the score is rounded to 2 decimal places as required by the question.

Know more about standard deviation here:

https://brainly.com/question/29115611

#SPJ11

To find the number of degrees of freedom, you would need additional information about the sample size and any restrictions or conditions. Without that information, it is not possible to determine the number of degrees of freedom.

To find the critical values and confidence interval estimate, you need to know the desired confidence level. Let's assume you want a 95% confidence level.

To find the critical values, you can use a t-distribution table or a statistical calculator. The critical values correspond to the tails of the distribution and are based on the confidence level and the degrees of freedom.

To find the confidence interval estimate, you need the sample mean, sample standard deviation, and the critical value(s). The formula for the confidence interval is:

CI = sample mean ± (critical value * (sample standard deviation / √n))

Finally, the conclusion would be a statement summarizing the confidence interval estimate. For example, "We are 95% confident that the true mean nicotine in menthol cigarettes falls within the calculated confidence interval."

Note: Since the question provided incomplete information, the answer cannot be completed with precise numbers or values.

To know more about  degrees   visit

https://brainly.com/question/364572

#SPJ11