2. Now, here is where the snowball effect comes in.
Imagine that you will not only earn 5% interest on
the original $600, but your interest also earns
interest! Calculate the value of the account during
the 2nd year if the 5% applies to both the $600 and
the $30 in interest that you earned the first year.
Hint: To find the value of the account after 2 years,
use $630 as the principal and increase the amount
by 5%. Then repeat this process to earn another 5%
on top of the new value over one year to find the
value after 3 years, then repeat one more time to
see the total after 4 years. It should be bigger than
before!

The matrix operation add -4(row 1) to row 3 is\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

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

\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\4&-1&6&-8\end{array}\right]\)

From the question, we understand that

We are to add -4(row 1) to row 3

This means that

row 3 = row 3 - 4 * row 1

When these values are evaluated, we have

4: 4 - 4 * 1 = 0

-1: -1 - 4 * 2 = -9

6: 6 - 4 * 1 = 2

-8: -8 - 4 * -5 = 12

This means that we relace 4, -1, 6, and -8 in row 3 with 0, -9, 2 and 12

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

\(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

Hence, the result of the matrix expression is \(\left[\begin{array}{ccc | c}1&2&1 & -5\\0&4&-2 & 3\\0&-9&2&12\end{array}\right]\)

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➨ Let (x+2) = a ➩ \(xa+1a\)

Then we factor a-term out of the expression ➩ Common Factor ➩ \(a(x+1)\)

Then convert from a back to x+2

Thus, our answer would be ➩ \((x+2)(x+1)\)

Answer:

a) The point estimate of the proportion is the sample proportion p=0.23.

b) The 95% confidence interval for the population proportion is (0.17, 0.29).

Step-by-step explanation:

The question is incomplete:

"According to statistics reported on CNBC, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the CNBC report, showed 46 of 200 vehicles were not covered by insurance."

a) The point estimate of the proportion is the sample proportion and is calculated as:

\(\hat p=\dfrac{X}{n}=\dfrac{46}{200}=0.23\)

b) We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.23.

The standard error of the proportion is:

\(\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.23*0.77}{200}}\\\\\\ \sigma_p=\sqrt{0.000886}=0.03\)

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

\(MOE=z\cdot \sigma_p=1.96 \cdot 0.03=0.06\)

Then, the lower and upper bounds of the confidence interval are:

\(LL=p-z \cdot \sigma_p = 0.23-0.06=0.17\\\\UL=p+z \cdot \sigma_p = 0.23+0.06=0.29\)

The 95% confidence interval for the population proportion is (0.17, 0.29).

Answer:-3

Step-by-step explanation:

Given

F(x)=-3 x +5

in the interval x=-1 to x=1

Average rate of change is given by

over x=a to x=b

F(1)=-3+5=2

F(-1)=3+5=8

The property you are referring to is called the associative property of multiplication. According to this property, when multiplying three numbers, the grouping of the numbers does not affect the result. In other words, you can change the grouping of the factors without changing the product.

In the equation you provided: 3x(5x7) = (3x5)7

The associative property allows us to group the factors in different ways without changing the result. So, whether we multiply 5 and 7 first, or multiply 3 and 5 first, the final product will be the same.

Answer:

2. Half a lap, 0.5 or 1/2

3. 20/0.5 or 20/(1/2)

Step-by-step explanation:

Since it takes 40 seconds to skate 1 lap,

20 secs would be 20/40 laps, which is 1/2

Ratio is time/number of laps. So, 20/(1/2)

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Explanation:

We can rewrite y = -3 as y = 0x-3 or y = 0x+(-3)

Compare that to y = mx+b and we can see that m = 0 is the slope and b = -3 is the y intercept. The slope of 0 indicates a horizontal line.

We can think of it is as slope = rise/run = 0/1 = 0. A rise of 0 tells the reader "the graph does not go up or down at all". Every point on the line y = -3 has y coordinate of -3. Two such points are (0,-3) and (1,-3).

a. The center of the circle is (-2, -1).

b. The radius of the circle is √136.

c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:

Midpoint = ((-7 + 3)/2, (-4 + 2)/2)

= (-4/2, -2/2)

= (-2, -1)

Therefore, the center of the circle is at the coordinates (-2, -1).

b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.

Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)

Using the distance formula:

Distance = √[(3 - (-7))^2 + (2 - (-4))^2]

= √\([(3 + 7)^2 + (2 + 4)^2]\)

= √\([10^2 + 6^2\)]

= √[100 + 36]

= √136

Therefore, the radius of the circle is √136.

c. The equation for a circle with center (h, k) and radius r is given by:

\((x - h)^2 + (y - k)^2 = r^2\)

In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:

\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)

\((x + 2)^2 + (y + 1)^2 = 136\)

Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.

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Answer:

(2*2+3)squared-[(4+3)*5]

Step-by-step explanation:

(2*2+3)squared-[(4+3)*5]

= (4+3)squared-[7*5]

= 7 squared-35

= 49-35

= 14

Step-by-step explanation:

Well the reason why this is 2.5 is show here.

arrange them like they're tens

 50

- 25

--------

25

Then replace the decimals back

25 turns into 2.5

it's just normal subtraction mate.

Answer:

6x^2-17x+12

Step-by-step explanation:

took the test

Answer:

130

Step-by-step explanation:

160 - 30

I'm very good with angles :)

Hope this helps!

-kiniwih426

Answer:

Answer Option B and C

Reason

Others are proportional.

A Non proportional relationship is a graph that does not pass through the origin.

Option A and D has point (0,0) which shows the origin and thus makes it Proportional.

Answer B and C

Answer:

{4*[6+(18-7)] } ÷1/3

{4*[6+18+7] }÷1/3

{24+72+28}÷1/3

{124}÷1/3

124*3/1

372/1=372

The answer is A

Hope this helps!

The graph is given below. Then the intersection point will be (-9, 11).

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

An unknown number y is 20 more than an unknown number x.

The number y is also x less than 2.

The equations to find x and y are shown below:

y = x + 20 ...1

y = −x + 2 ...2

Add both equations, then we have

2y = 22

 y = 11

Then put the value of y in equation 1, then we get

11 = x + 20

x = 11 - 20

x = -9

Then the intersection point will be (-9, 11)

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Answer:

4 is next in NUMBER OF DAYS

9 is the first in NUMBER OF TADPOLES

41 is the 2nd answer ON NUMBER OF TADPOLES

Step-by-step explanation:

hope this helps a lot!!

If λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

The equation Av = λv, where v is a non-zero vector, is satisfied by an eigenvector v and an eigenvalue given a square matrix A. In other words, the eigenvector v is multiplied by the matrix A to produce a scalar multiple of v. Due to their role in illuminating the behaviour of linear transformations and differential equation systems, eigenvectors play a crucial role in many branches of mathematics and science. When the eigenvector v is multiplied by A, the eigenvalue indicates how much it is scaled.

The eigenvalue and eigenvector states that, let v be a non-zero eigenvector of A corresponding to the eigenvalue λ.

Then, we have:

Av = λv

Taking transpose on both sides we have:

\(v^T A^T = \lambda v^T\)

The above equations thus relates transpose of vector and transpose of A to λ.

Now, consider a matrix:

\(\left[\begin{array}{cc}1&2\\3&4\\\end{array}\right]\)

Now, the eigen values of this matrix are λ1 = -0.37 and λ2 = 5.37.

The eigenvectors are:

\(v1 = [-0.8246, 0.5658]^T\\v2 = [-0.4159, -0.9094]^T\)

Now, for transpose of A:

\(A^T=\left[\begin{array}{cc}1&3\\2&4\\\end{array}\right]\)

The eigen vectors are:

\(u1 = [-0.7071, -0.7071]^T\\u2 = [0.8944, -0.4472]^T\)

Hence, we see that, if λ is an eigenvalue of A, then λ is an eigenvalue of \(A^T\). Show with an example that the eigenvectors of A and \(A^T\) are not the same.

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Answer:

The answer would be C the triangles are not similar

Step-by-step explanation:

Find the percentage of the people who like Chocolate = chocolate/ total x 100

Percentage = 125/300 = 0.41666 x 100 = 41.6667 = 41.67 ( round as needed)

A full circle is 360 degrees.

The central angle = percentage of chocolate x 360:

0.416666 x 360 = 150

The central angle for chocolate is 150 degrees

Answer:

6 months

Step-by-step explanation:

We can set up an equation based on his monthly savings to find out how long it will take for Hatif to reach $630 in his account.

Let's assume it takes Hatif "n" months to reach $630 in his account. Each month, he saves $80.

The equation representing the situation is:

$150 + $80n = $630

Now, let's solve for "n":

$80n = $630 - $150

$80n = $480

n = $480 / $80

n = 6

Therefore, it will take Hatif 6 months to reach $630 in his account.

Answer:

17.6 miles

Step-by-step explanation:

speed = distance/time

distance = speed * time

We multiply the speed of each one by the time, 1 hour, to find the distance each one walked in 1 hour.

Kiran: 3 mph * 1 h = 3 miles

Clare: 3.4 mph * 1 h = 3.4 miles

The total distance they walked is 3 miles + 3.4 miles = 6.4 miles.

After 1 hour, they are 6.4 miles closer than they were at the beginning of the walk.

24 miles - 6.4 miles = 17.6 miles

Answer: 17.6 miles

The daily rental cost of the jet ski, given the discount and the number of days, can be found to be $ 69.

The daily rental cost is denoted as r which means that the cost can be denoted by the expression

5 days × x or 5 r

There was a discount of $ 100 so the daily rental cost would be :

245 = 5 r - 100

The daily rental cost is :

245 = 5 r - 100

5 r = 245 + 100

5 r = 345

r = 345 / 5

= $ 69

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The measure of the angle B of the triangle is 78.15 degrees

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

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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Answer:

Answer:

0.444    (44.4%)

Step-by-step explanation:

All possible ending: 1,2,3,4,5,6,7,8,9        ... 9

ending with 2,4 6,8 to make even number: 4

                                                  ___   ___  ___  ___  ___

even number :                              8   *   7   *   6  *   5  *   4

All 5 digit without repeating:        8   *   7   *   6  *   5  *   9

possibility = (8*7*6*5*4) / (8*7*6*5*9)

                = 4/9

                = 0.444    (44.4%)

_______________________________________________

(4 * ₈P₄) / (9 * ₈P₄) = 4/9

The weighted average of a data set where 20 has a weight of 2, 30 has a weight of 3, and 50 has a weight of 5 is 38.

To find the weighted average of a data set, you need to multiply each data point by its corresponding weight, sum up these products, and then divide by the sum of the weights. In this case, the data set is  {20, 30, 50} with corresponding weights of {2, 3, 5}, respectively.

The calculation for the weighted average would be:

weighted average = (20 x 2 + 30 x 3 + 50 x 5) / (2 + 3 + 5)

= (40 + 90 + 250) / 10

= 38

Therefore, the weighted average of this data set is 38.

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Answer:

Given:

1 mile = 1.6 km

So, to find how many miles are in 100 km, we need to divide 100km by 1.6km because one single mile contains 1.6km.

100km/1.6km = 62.5 miles

Answer:

32

Step-by-step explanation:

Mean = Average = The data values added together/ the number of data values.

The mean of 5 numbers is 22.6=

\(\frac{12+16+n+23+30}{5} = 22.6\)

Multiply both sides by 5.  22.6 becomes 113

12+16+23+30+n=113

n+81 = 113

n= 32

The value of n is 32.

The arithmetic mean of m values \(x_1,x_2,..., x_m\) is

\(\frac{x_1+x_2+...+x_m}{m}\)

The given

mean = \(\frac{12+16+n+23+30}{5}=22.6\)

⇒12+16+n+23+30=22.6×5=113

⇒n=113-81=32

Hence, n=32

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