A new bank account is opened on week 1 with a $200 deposit. After that first week, weekly deposits of $55 are made in the account. If y represents the total deposited into the account and x represents the number of weeks, which function rule describes this situation?

Final answer:

Peter bought regular and premium gasoline at $4.18 and $4.43 per gallon respectively, after solving a system of equations based on the total gallons and cost.

Explanation:

We are given a problem where Peter mixes two grades of gasoline—regular and premium—with premium costing $0.25 more than regular. To solve this, we can set up a system of equations representing the cost of each type of gasoline and the total cost.

Let the cost per gallon of regular gasoline be r, and thus premium will be r + $0.25 as it is $0.25 more expensive. Peter buys 11 gallons of regular and 7 gallons of premium, spending a total of $76.99. So, we have two equations:

Simplifying the first equation:

11r + 7r + $1.75 = $76.99

18r + $1.75 = $76.99

18r = $76.99 - $1.75

18r = $75.24

r = $75.24 / 18

r = $4.18

So the regular gasoline price per gallon is $4.18 and the premium gasoline price per gallon is $4.18 + $0.25 = $4.43.

Answer:

After 3 seconds the object hit the ground.

Step-by-step explanation:

An object is dropped off a building that us 144 feet tall. After how many seconds does the object hit the ground.

Given that displacement, s = 16t²

To reach ground displacement should be 144 feet.

That is

            s = 16t² = 144

                      t² = 9

                       t = 3 seconds.

After 3 seconds the object hit the ground.

10^6 = 10 *10*10*10*10*10 = 1,000,000

10^2 = 10*10 = 100

1000000/100 = 10,000 times larger

In a case whereby a star is 3.4 light years from earth. if 1 light years is 5.87×10^12 mi, the number of miles from earth the star is can be expressed as [tex]3.4 * 5.87 * 10^12 miles[/tex]

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that  star=3.4 light years from earth

1 light years= [tex]5.87*10x^{12} miles[/tex]

The number of miles from earth is

[tex]3.4 * 5.87 *10^{12} miles\\\\=3.4 * 5.87 * 10^12 miles[/tex]

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P = 6,600  

A = 6,000  

t = 4  

k = ?  

6600 = 6000e^(4k)  

6600/6000 = e^(4k)  

1.1 = e^(4k)  

Take the natural log of both sides.  

ln 1.1 = 4k ln e (remember that ln e = 1)  

ln 1.1 = 4k  

(ln 1.1) / 4 = k  

k = 0.0238  

Bacteria after 10 hours.  

P = 6000e^(0.0238*10)  

= 6000e^0.238  

= 7612  

Therefore, the bacteria will grow to 7612 after 10 hours.

surface area = 5ab +5bh

a = 4

b=7

h=18

5*4*7 = 140

5*7*18 = 630

630+140 = 770 square meters

Supposing that the null hypothesis is true, the precise possibility of obtaining a t-test value at least as extreme or as ear to the one that was actually observed was 0.1%. This value can be found in the “Independent Samples t-test” table in the SPSS output, where the exact p value is reported as 0.001. If the null hypothesis is assumed to be true, then statistically noteworthy result should be highly improbable. The rejection of the null hypothesis implies that the correct hypothesis lies in the logical complement of the null hypothesis.

To add, used for non-batched and logical batched statistical analysis, SPSS Statistics was a software package for that specific purpose.

Average growth rate = 4.2 cm/week.

So, common difference d = 4.2

The height of the tree a0 = 200 centimeters.

The height of the tree after end of the first  week a₁ = 200 + 4.2 = 200 + 4.2(1)

The height of the tree after end of the second  week  a₂ = 200 + 4.2 + 4.2 = 200 + 4.2(2).

The height of the tree after end of the third  week a3 = 200 + 4.2 + 4.2 + 4.2 = 200 + 4.2(3).

The height of the tree after the end of the nth week an =  200 + 4.2(n).

The equation is a_n = 200 + 4.2(n).

Answer:

f(x)=x+6

Step-by-step explanation:

its the exact opposite of the answer, so if it was x-6 then the inverse would be x+6

Segments with lengths of 36,48 and 60 can form a triangle. By employing the Pythagorean Theorem, we find that this is a right triangle as the lengths adhere to the theorem.

The question asks if segments with lengths of 36, 48, and 60 can form a triangle, and if so, the type of the triangle. Yes, these segments can form a triangle. To classify the triangle as obtuse, right or acute, we use the Pythagorean Theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as c^2 = a^2 + b^2. Substituting our values: 60^2 equals to 36^2+48^2 (3600 = 1296+2304). Since both sides of the equation are equal, we get the conclusion that this is a right triangle.

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Given that cos theta is 4/5 within the 270 to 360-degree range, sin(theta) is -3/5, tan(theta) is -3/4, sec(theta) is 5/4, csc(theta) is -5/3, and cot(theta) is -4/3.

The question indicates that we are dealing with trigonometry and specifically asks for the remaining trigonometric functions given that cos theta = 4/5 and theta is in the range of 270o to 360o.

This implies that theta is in the fourth quadrant where cosine is positive, and the other trigonometric functions can have different signs.

Since we have the cosine of theta, we can use the Pythagorean identity to find the sine of theta. The identity states that in2(theta) + cos2(theta) = 1.

Plugging in the given cosine value, we have:

sin2(theta) + (4/5)2 = 1
sin2(theta) = 1 - 16/25
sin2(theta) = 9/25
sin(theta) = ±√(9/25) = ±3/5

However, since theta is in the fourth quadrant, the sine is negative, and therefore we find:

sin(theta) = -3/5

For the tangent of theta, we use the definition tan(theta) = sin(theta)/cos(theta), which yields:

tan(theta) = (-3/5) / (4/5) = -3/4

The values of the other three trigonometric functions (secant, cosecant, and cotangent) are the reciprocals of the three we just calculated:

sec(theta) = 1/cos(theta) = 5/4
csc(theta) = 1/sin(theta) = -5/3
cot(theta) = 1/tan(theta) = -4/3

arc length = (central angle/360) x 2 x PI x r

= (35/360) x 2 x 3.14 x 25

=15.2638

round answer as needed, you don't say how to round it.

In the base 6 number system, we would only use numerals from 0 to 5. The idea of base 6 is just like the normal base 10 system, however instead of using the numerals from 0 to 9, we use numerals from 0 to 5. And instead of having a ones digit, a tens digit, a hundreds digit and so on, we use a ones digit, a sixes digit, a thirty-sixes digit, and so on. Therefore in base 6, the number 321 means 1  one plus 2 sixes plus 3 thirty-sixes, or 121. So to count until 15 for example, we  would need:

Base 6                                                                   Base 10

1                                                                                  1   

2                                                                                  2

3                                                                                  3

4                                                                                  4

5                                                                                  5

10  (1 six plus 0 ones)                                                 6

11  (1 six plus 1 one)                                                   7

12  (1 six plus 2 ones)                                                 8

13                                                                                9

14                                                                              10

15                                                                              11

20  (2 sixes plus 0 ones)                                           12

21  (2 sixes plus 1 one)                                             13

22                                                                              14

23                                                                              15

Final answer:

The counting numbers in base 6 are represented using the digits 0 to 5, where each digit position represents a power of six. The sequence starts at 0, followed by 1, 2, 3, 4, 5, and then continues with 10 (which is 6 in decimal), 11 (7 in decimal), etc.

Explanation:

The counting numbers in base 6, also known as base-6 or hexadecimal numbers, consist of the digits 0, 1, 2, 3, 4, and 5. Just like in the decimal system (base 10) where the digits go from 0 to 9, in base 6 we only use the digits 0 to 5 for each place value, and each place is six times greater than the place to its right. After reaching 5, the next number in the sequence would be represented as 10 (base 6), which is equal to 6 in base 10. The sequence continues with 11 (base 6 equals 7 in base 10), 12 (base 6 equals 8 in base 10), and so on.

The concept of base systems is an important aspect of number theory in mathematics. In everyday life, we use the base 10 numbering system, mainly because humans have ten fingers. However, in computing and other scientific fields, different base systems like base 2 (binary) or base 16 (hexadecimal) are often used.

The area of a parallelogram with a base of 20inches and an altitude of 8 inches is 160 inches square.

What is a parallelogram in math?

A parallelogram is a quadrilateral with opposite sides parallel (and therefore opposite angles identical). A quadrilateral with equal sides is called a rhombus, and a parallelogram whose angles are all right angles is referred to as a rectangle.

Conclusion: The opposite sides are equal in length and the opposite angles are identical in degree. To find the area, multiply the base by the height. The formula is: A = B * H where B is the base, H is the height, and * means multiply.

A = base * altitude

A = 20 * 8

A = 160 inches square.

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