Kayla drives her new car to work every day. It uses 1 3/5 gallons of gas for each round trip. How many round trips to work can Kayla drive on a 16-gallon full tank of gas?

Answer:

Step-by-step explanation:

X = 1(1 - 0.02)ⁿ

X = 1(0.98)²⁰

X = 0.6676

67%

Using an exponential equation, it is found that 66.76% of the current amount will be present in 20 years.

A decaying exponential function has the following format:

[tex]A(t) = A(0)(1 - r)^t[/tex]

In which:

In this problem, breaks down at a rate of 2% a year, hence [tex]r = 0.02[/tex], and:

[tex]A(t) = A(0)(1 - 0.02)^t[/tex]

[tex]A(t) = A(0)(0.98)^t[/tex]

The fraction after 20 years is A(20), hence:

[tex]A(20) = A(0)(0.98)^{20}[/tex]

[tex]A(20) = 0.6676[/tex]

66.76% of the current amount will be present in 20 years.

A similar problem is given at https://brainly.com/question/14773454

Answer:

(a) [tex]\log_72 \approx 0.3562[/tex]

(b) [tex]\log_7(\frac{147}{16} ) = 2[/tex]

Step-by-step explanation:

For the point a:

For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex]

16 can be re-write as [tex]2^4[/tex]. Then you have:

[tex]\log_72^4[/tex]

Using the power property of the logarithm we have:

[tex]\log_ba^c = c\log_ba[/tex]

[tex]\log_72^4 = 4\log_72[/tex]

And this expression is equal to:

[tex]4\log_72 \approx 1.4248\\\log_72\approx \frac{1.4248}{4} \approx 0.3562\\[/tex]

For the point b:

For this problem we use the information of [tex]\log_716 \approx 1.4248[/tex] and [tex]\log_73 \approx 0.5646[/tex]

The first is use the quotient property in the given log.

[tex]\log_c\frac{a}{b} = \log_ca-\log_cb[/tex]

[tex]\log_7\frac{147}{16} = \log_7147 -\log_716[/tex]

We already know the value of [tex]\log_716[/tex] then we have to calculate the value of [tex]\log_7147[/tex].

So we factorize the number 147 in [tex]3 \cdot 7 \cdot 7[/tex] (for factorize the number start with the smaller prime and check if the remainder is 0, it is then is a primer factor of the number).

Now re-write [tex]\log_7147[/tex] as [tex]\log_73 \cdot 7^2[/tex] and by the product property get:

[tex]\log_bmn = \log_b m +\log_b n\\\log_73 \cdot 49 = \log_7 3 +\log_7 49 = 0.5646 + 2 = 2.5646[/tex]

Know replace each value in the subtraction and get the result:

[tex]\log_7147 -\log_716 = 2.5646 - 0.5646 = 2[/tex]

Answer:

The slope is undefined

Step-by-step explanation:

A vertical line has points that have the same x-coordinate.

The equation is x = -3

The slope of a vertical line is undefined.

Answer:

The slope is undefined

let's recal the pythagorean theorem, where c² = a² + b², namely, the largest number squared is equal to the sum of the two smaller ones squared.

well, we can just start by say in A, looking the smaller sides, 3 and √9, if we squared both and add them up, do they give the largest one of √18?

[tex]\boxed{A} \\\\ 3^2+(\sqrt{9})^2 = (\sqrt{18})^2\implies 9+9 =18\qquad \textit{\Large\checkmark} \\\\\\ \boxed{B}\\\\ 3^2+4^2=5^2\implies 9+16=25\implies 25=25\qquad \textit{\Large\checkmark} \\\\\\ \boxed{C}\\\\ 7^2+7^2=(\sqrt{98})^2\implies 49+49=98\implies 98=98\qquad \textit{\Large\checkmark}[/tex]

so they all apply.

Answer:

Step-by-step explanation

just multiply

like 1x2=2

so 60x2=120

2x5=10

120x5=600

and on and on

Answer:

Step-by-step explanation:

Let r be the rate of descent in miles per minute

-3/4 miles / 5/8 minutes

-3/4 • 8/5 = -24 / 20 = -1.2 mi/min

so in one minute

-1.2 mi/min (1 min) = -1.2 miles

Answer: 3

Step-by-step explanation:

[tex](f \circ f)(2) = f(f(2)) = f(3) = \boxed 3[/tex]

Answer:

C

Step-by-step explanation:

For example, if a is equal to 2.

[tex] \sqrt{2} {}^{2} = 2[/tex]

The answer is still the given number a.

The solution of the expression √a² is,

⇒ a

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ √a²

Where, 'a' is nonnegative real number.

Now, We can simplify as;

⇒ √a²

⇒ √ a × a

⇒ a

Thus,  The solution of the expression √a² is,

⇒ a

Learn more about the mathematical expression visit:

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Answer:

271 is the answer of your question

Answer:

Part A would be C because divided 30 by 5 to get the unit rate.

Part B would be B

Answer:

C). −30÷5

B). –$6

Step-by-step explanation:

Answer:

x=115°,y=50°

Step-by-step explanation:

let <B =x

115°+x=180°

x=180°-115°=65°

Since <B=<C

x+65°=180

x=180-65=115°

For y,

y+2(65°)=180°

y+130°=180°

y=180°-130°=50°

Using the law of sines, it is found that the angle that the golfer has between the spectator and the hole is of 25.6º.

Suppose we have a triangle in which:

The lenghts and the sine of the angles are related as follows:

[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]

Hence, in this problem, we have that:

[tex]\frac{\sin{115^\circ}}{200} = \frac{sin{x}}{140}[/tex]

[tex]sin{x} = \frac{140\sin{115^\circ}}{200}[/tex]

[tex]x = \arcsin{0.6344}[/tex]

x = 39.4º.

Considering that the sum of the internal angles of the triangle is of 180º, the angle that the golfer has between the spectator and the hole is given by:

A = 180 - (115 + 39.4) = 25.6º.

More can be learned about the law of sines at https://brainly.com/question/27174058

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Answer:

25.6

Step-by-step explanation:

I got it right

Answer:

10 weeks

Step-by-step explanation:

1 because 20 times 10 is 200 and if he starts with 500 then he can withdraw 20 dollars a week for 10 weeks to have 300 left by the end of the summer, hope this helps :)

Answer:

316 ls the next term greater than 312. in the sequence you are adding 4 to the preceding term

Answer:

1) 9h² - 3h + 2h² when h= -1

11h²- 3h

11(-1)²-3(-1)

11+3

14

2) -6m + 3t +2m² when m= 3 and t=-1

-6( 3) +3(-1)+2(3)²

-18 -3 +18

-3

3) 7g² - 2c³/ 3g - c² when g=2 and c= -1

7(2)² - 2(-1)³ / 3(2) - (-1)²

28 +2 / 6-1

30/5

6

Step-by-step explanation:

Scale Factor (Dilation) The scale factor in the dilation of a mathematical object determines how much larger or smaller the image will be (compared to the original object). When the absolute value of the scale factor is greater than one, an expansion occurs. Hope this helps :)

Answer:

30*1.609=48.27

Hope This Helps!!!

Answer:

Unsure but it might be -8/3

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

divide 3.15 by 0.07 to get 45

Answer:45

Step-by-step explanation:

divide 3.15 by 0.07 answer 45

Answer: y=2x+1 (slope intercept form) & y-1=2(x+2) (point slope form)

Step-by-step explanation:

Parallel means the m value or slope are equal

Given those points and the slope you can begin to write the slope y intercept form

y=2x+B

Solve B or Y intercept x=0 and the Y value we get from the given points.

1=2*0+B

y=2x+1 (slope intercept form)

for point slope plug the points in this equation

y-y1=m(x1-x1)

y-1=2(x+2) (point slope form)

Answer:

A

Step-by-step explanation:

x = √a/√b

x² = √a²/√b²

x² = a/b

Answer:

Hi there

it should be A.

good

Answer:

can you add a pic

Step-by-step explanation:

Answer: a = -2  and  c = 7

Step-by-step explanation:

(this answer uses some basic calculus)

We know that [tex]f'(x) = 2ax + 4[/tex], and since [tex](1,9)[/tex] is a maximum of [tex]f[/tex], then [tex]f'(1) = 0[/tex]. That means [tex]2a + 4 = 0[/tex], so [tex]\boxed{a = -2}[/tex]. Then since [tex]f(1) = 9[/tex], we have [tex]-2(1)^2 + 4(1) + c = 9[/tex], so [tex]\boxed{c = 7}[/tex].

Answer:

a = -2

c = 7

Step-by-step explanation:

Given the quadratic function, f(x) = ax² + 4x + c, for which its vertex is the maximum point occurring at (1, 9), and b = 4.

Since the x-coordinate of the vertex, x = 1, can be calculated using the formula, [tex]x = \frac{-b}{2a}[/tex]:

We can substitute the value of the x-coordinate and b = 4 into the formula, and solve for the value of a:

[tex]x = \frac{-b}{2a}[/tex]

[tex]1 = \frac{-4}{2a}[/tex]

Multiply both sides by 2a:

(2a) 1 =  [tex]\frac{-4}{2a} (2a)[/tex]

2a = -4

Divide both sides by 2 to solve for a:

[tex]\frac{2a}{2} = \frac{-4}{2}[/tex]

a = -2

Therefore, the value of a = -2.

Next, to solve for c, substitute the coordinate values of the vertex, (1, 9) into the given quadratic function:

f(x) = ax² + 4x + c

9 = -2(1)² + 4(1) + c

9 = -2 + 4 + c

9 = 2 + c

Subtract 2 from both sides to isolate c:

9 - 2 = 2 - 2  + c

7 = c

In order to double-check the validity of our values for a and c, substitute a = -2, and c = 7 into the function, along with the coordinates of the vertex, (1, 9):

f(x) = -2x² + 4x + 7

9 = -2(1)² + 4(1) + 7

9 = -2 + 4 + 7

9 = 9 (True statement).

Therefore, the correct answers are: a = -2, and c = 7.

Answer:

7/4

Step-by-step explanation:

Answer:

1/4% of 1 3/4 = 7 or you could say 1/4% of 1.75 = 7

Answer: $8.25

Step-by-step explanation: 33 divided by 4 (find unit rate)

Answer: $8.25

Step-by-step explanation:

Simply divide $33.00 by 4. 33/4 = 8.25

Answer:

-30.28

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

If he uses 2/6 of a liter thats 3 days for 1 liter.

3 x 15 is 45. so 45 days