To fill up a car with 16 gallons cost $30.24. Which of the following is an equation that determines the
cost c for g gallons of gas?

Answer:

The correct option is;

Two-tailed test

Step-by-step explanation:

From the interpretation of the question statement, the trader wants to conduct a hypothesis test on the trader's claim that the proportion of stocks that offer dividends is different from 0.14

Given that the difference is hypothesized, then the null hypothesis, H₀ and the alternative hypothesis, H₁ should be written as follows;

H₀: Null hypothesis (no difference, or no change)

H₁: μ ≠ μ₀ which is hypothesizing  difference which is known as a two-tailed test

The confidence level is then selected and the test statistic is calculated

Answer:

y = -4

Step-by-step explanation:

x = 3 is a vertical line.

The perpendicular line passes through (0, -4) (x, y)

y = -4

The line is perpendicular, so the line should be also horizontal.

Answer:

y = -4

Step-by-step explanation:

The line x = 3 is a vertical one; any line perpendicular to x = 3 is a horizontal line (which has a zero slope).  

Thus, the desired line is a horizontal one that passes through (0, -4) and is represented by y = -4.

Answer:

No

Step-by-step explanation:

The question is:

Are 3/5 and 6/25 equivalent fractions?

Multiply the first fraction by 5/5:

3/5 * 5/5 = 15/25

3/5 is equivalent to 15/25

15/25 is not equal to 6/25.

Answer: No

Answer:

  21h miles

Step-by-step explanation:

The appropriate relation is ...

  distance = speed · time

__

We are given that ...

  biking time = h

  walking time = 2h

  running time = (1/4)(2h) = h/2

The total distance traveled is ...

  total distance = biking distance + walking distance + running distance

     = (10)(h) +(3)(2h) +(10)(h/2)

     = 10h + 6h + 5h

  total distance = 21h . . . miles

Answer:

21h miles

Step-by-step explanation:

The appropriate relation is ...

 distance = speed · time

__

We are given that ...

 biking time = h

 walking time = 2h

 running time = (1/4)(2h) = h/2

The total distance traveled is ...

 total distance = biking distance + walking distance + running distance

    = (10)(h) +(3)(2h) +(10)(h/2)

    = 10h + 6h + 5h

 total distance = 21h . . . miles:

Answer:

Step-by-step explanation:

In general, the graph of an n-th degree function can make n-1 turns. However, in specific cases, the number of turns is limited by the number of real zero-crossings of the derivative.

__

1. This 5th-degree function can have at most 4 turns. However, the derivative, f'(x) = 5x^4 -3, has only two (2) real zeros. Hence the graph of this function can only have 2 turns.

__

2. This 7th-degree function can have at most 6 turns. However, the derivative, f'(x) = -7x^6 -35x^4-12x^2, has an even-multiplicity root at x=0 only. The derivative never crosses 0. Hence the graph makes no turns.

power of a quotient

edge 2021

The law used to simplify the expression is quotient of powers.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, 3¹⁰ / 3⁴, we need to determine the law used to simply the expression,

3¹⁰ / 3⁴

For this case we have an expression formed by a division of powers of the same base in which we must apply a law to simplify said expression.

By the definition we have the property of the power quotient of the same base set:

xᵃ / xᵇ = x⁽ᵃ⁻ᵇ⁾

So, using the same,

3¹⁰ / 3⁴ = 3⁽¹⁰⁻⁴⁾ = 3⁶

Thus, to simplify the expression we must use the property of the power quotient of the same base.

Hence, the law used to simplify the expression is quotient of powers.

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Answer:

16

Step-by-step explanation:

[tex] {w}^{2} - 8w + { {4}^{2} } \\ = {w}^{2} - 8w + \boxed{ 16} \\= (w-4)^2 [/tex]

Answer:

Step-by-step explanation:

a² + 2ab +b² = (a+ b)²

w² - 8w + _?___

a = w

2ab = -8w

2*w*b = -8w

b = -8w/2w

b = 4

8w = 2 * 4*w

w² - 8w + 4² =w² -8w + 16

Answer:

The independent variable is the depth below the surface of the lake the dependent is the tempeature of the water

Step-by-step explanation:

Tempeture = depth x

Answer:

-9ab3a3b-52

Step-by-step explanation:

-8a3b+3a2b2-52+5a2b3a3b+7-9a2b2

-8a3b-6a-52+5a2b3a3b

-14a3b-52+5a2b3a3b

-9ab3a3b-52

Answer:

Option (A)

Step-by-step explanation:

Parent function of the function graphed is,

G(x) = x²

Graph shows the vertex of the given parabola is at (3, 3).

Vertex form of a parabola is,

F(x) = a(x - h)² + k

where (h, k) is the vertex.

By substituting the coordinates of the vertex in the equation,

F(x) = a(x - 3)² + 3

Since the given parabola is opening upwards, value of 'a' will be positive.

So the equation will be,

F(x) = 2(x - 3)² + 3

Therefore, from the given options, equation given in Option (A) matches the answer.

Answer:

A is the correct answer.

Step-by-step explanation:

Answer:

t

Step-by-step explanation:

The letter that comes next in the given sequence is K.

The given sequence is F H K N Z.

We need to find which letter comes next in the given sequence.

The pattern followed by the given sequence is they are letters of sounding board consonants.

Therefore, the letter that comes next in the given sequence is K.

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Answer:

C

Step-by-step explanation:

It is an iscoceles triangle because there are 180 degrees in a triangle and the right angle plus the 45 degree equals 135 and 180 minus 135 is 45.

Since it is an iscoceles triangle that means that n = 3 and the pythagorean theorom says that a^2 + b^2 = c^2 which means that m = 3^2 plus 3^2 with a root.

3^2 is 9 so you get 18

the root of 18 is infinite, however can be simplified to 3 root to 2 because 3 times 3 equals 9 times 2 equals a root of 18

Hope this helps!

Answer:

(0,3)

Step-by-step explanation:

y = 2x+3

y = -3x+3

Since both equations are equal to y, set them equal to each other

2x+3 = -3x+3

Subtract 3 from each side

2x = -3x

Add 3x to each sdie

2x+3x = -3x+3x

5x =0

Divide by 5

x=0

Now solve for y

y =2x+3

y = 0+3

y=3

(0,3)

Answer:

(0,3)

Step-by-step explanation:

y = 2x+3

y = -3x+3

2x+3 = -3x+3

2x = -3x

2x+3x = -3x+3x

5x =0

x=0

The solve for y

y =2x+3

y = 0+3

y=3

(x,y)=(0,3)

Then (0,3) will be your answer!

Hope this help!

Answer:

Simplifying

41 = 12d + -7

Reorder the terms:

41 = -7 + 12d

Solving

41 = -7 + 12d

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '-12d' to each side of the equation.

41 + -12d = -7 + 12d + -12d

Combine like terms: 12d + -12d = 0

41 + -12d = -7 + 0

41 + -12d = -7

Add '-41' to each side of the equation.

41 + -41 + -12d = -7 + -41

Combine like terms: 41 + -41 = 0

0 + -12d = -7 + -41

-12d = -7 + -41

Combine like terms: -7 + -41 = -48

-12d = -48

Divide each side by '-12'.

d = 4

Simplifying

d = 4

Answer:

money invested at 3% is $4000

Step-by-step explanation:

let the money invested in 3% account be x

then money invested in 5% account = 6000 - x

we know interest = p*r*t/100

p is the principle amount invested

here t = 1 year

interest on 3% money

interest= x*3*1/100 = 3x/100

interest on 5% money

interest= (6000-x)*5*1/100

Total interest earned on both the account

3x/100 + 5(6000-x)/100 = (3x + 30,000 - 5x)/100 =( 30000-2x)/100

given that total interest earned = $220

thus

( 30000-2x)/100 = 220

=> 30000-2x = 220*100= 22,000

=> -2x = 22,000- 30,000

=> x = -8000/-2 = 4000

Thus, money invested at 3% = x = $4000

Answer:)

$4000

Step-by-step explanation:

Answer:

15 miles

Step-by-step explanation:

Currently, he can run 3.5 * 2 = 7 mph. Adding 1/2 mph to that gives us 7.5 mph, so therefore, in 2 hours he can run 7.5 * 2 = 15 miles.

Answer:

15

Step-by-step explanation:

because its correct just did the thing.

Answer:

The number of distinct triangles that can be drawn using the dots = 6

Step-by-step explanation:

The parameters given are;

Two rows of three evenly spaced dots

To form a triangle, two dots will be selected from 1 row while the third dot will be selected from the other row

The number of ways of selecting the dots are therefore;

₃C₂ × ₃C₁ = 3 × 3 = 9 triangles

The same procedure can be done from the top row to give another 9 triangles

Which gives the total number of triangles = 18 triangles

The number of distinct triangles are found as follows;

Given that triangles obtained from the top row are similar to those of the bottom row, we reduce the range from which the distinct triangles can be found to 19 - 9 = 9 triangles

Of the 9 triangles formed by one dot on top and two dots on the bottom, the two adjacent dots of the three dots which are on the left and on the right of the lower row of dots, form the same three triangles with the three dots on the top row

Therefore, since there are 3 sets of two dots forming 9 triangles, each pair of dots can form 3 triangles, and as mentioned, 2 pairs of dots of the 3 pairs form the same triangles making the distinct triangle = 9 - 3 = 6.

Answer:

mean =sum of all data values

total number of data

13+91+44+68+54+16+88+74

8

448

8

=56

therefore the mean is 56

Answer: 51

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

You only need two points to find the slope.

Let's use (1,7) and (2,8).

The formula for slope is (y2-y1)/(x2-x1)

Let's plug the values in:

(8-7)/(2-1) = 1.

So, the slope is 1.

Answer:

377 choices

Step-by-step explanation:

The following values were given in the question:

The restaurant offered

6 choices of appetizer

8 choices of main meal

5 choices of dessert.

We are also told in the question that the customer can choose to eat just one course, or two different courses, or all three courses.

Let us represent each choice by :

A = Appetizer = 6

B = Main meal = 8

C = Dessert = 5

a) The 3 choices together

ABC=6 × 8 × 5=240 choices

b) AB= Appetizer and Main meal

= 6 × 8 = 48 choices

c) AC= Appetizer and Dessert

= 6 × 5 = 30 choices

d) BC = Main meal × Dessert

= 8 × 5 = 40 choices

e) A,B,C = the customer having each of the choices only

Appetizer + Main meal + Dessert

= 6 + 8 + 5

= 19 choices

The number of possible meals is calculated as:

240 choices + 48 choices + 30 choices + 40 choices + 19 choices

= 377 choices

Answer:

last three questions are statistical question

Answer:

The last three questions

Step-by-step explanation:

Answer:

a) half life is 3h 17 minutes

b) function of residue drug after t hours with initial quantity = 500 mg

        f(t) = 500 (0.81^t)

c) drug left in patient's system after 24 hours

   = 0.00 grams (to the hundredth of a gram.

Step-by-step explanation:

Given:

Drug initial active weight, A = 500 mg

Residue active weight, f(t) = A 0.81^t

t = time in hours.

a) half life

Half life is T, such that f(T) = 0.5A =>

0.5A = A(0.81^t)

0.81^t = 0.5

t*log(0.81) = log(0.5)

t = log(0.5) / log(0.81) = -0.6931 / -0.2107 = 3.2894 hours

= 3 h 17.36 minutes

b) Equation of function of residue drug as a function of time t in hours

A=500 mg

f(t) = A(0.81^t)    substitute A = 500 mg

= 500(0.81^t)  mg

c) weight of residue drug after 24 hours to the hundredth of a gram.

t=24 hours

A=500

f(t) = 500(0.81^t)    substitute t=24 hours

= 500(0.81^24)

= 3.181 mg

= 0.003181 g

Answer:

B. The variable s represents the number of students in each class.

C. The coefficient 14 represents the number of classes in the 9th grade.

Step-by-step explanation:

The total number can be found by multiplying the number of the things with the number of people producing it. For example if 5 boys make 5  colored ropes the total number of ropes will be 5*5= 25.

In this question the combinations rule is used for variuos number of classes which are 14. Now we have to find the number of students which are s (s-1). Suppose s= 6 so the number of students would be 6(6-1) = 6(5) = 30

We will multiply the number of classes 14 with the number of students s(s-1) to get the total number of cards produced.

Answer:

The answer is option A.

Step-by-step explanation:

Surface area of a sphere is 4πr²

where r is the radius

radius = diameter / 2

radius = 16/2 = 8cm

Surface area of the sphere is

4π (8)²

= 4(64)π

= 256π

= 804.2cm²

Hope this helps you.

Answer:

We decreased by 37%

Step-by-step explanation:

Let x be the starting temperature

We decrease by 10 percent which means we are left with 100-10 =90 percent

.90 x

Then we decrease by 30 percent, 100 - 30 = 70

( .90x) * .70

.63x

We  have .63 of the original left or 63%

100 -63 = 37

We decreased by 37%

Answer:

37% and it decreased

Step-by-step explanation:

We can find roots by setting f(x) = 0 --> x^4 - x^3 - 13x^2 + x + 12 = 0.

Factoring f(x) to make things easier for us gives us (x - 1)(x + 1)(x - 4)(x + 3), which, equal to 0, gives us the ability to set each set of parentheses = 0.

x - 1 = 0 gives us x = 1.

x + 1 = 0 --> x = -1.

x - 4 = 0 --> x = 4.

x + 3 = 0 --> x = -3.

our roots are x = 1, -1, 4, and -3.

Answer:

2 1/3 hours or 2 hours 20 minutes.

51.4 mph to 1 decimal place.

Step-by-step explanation:

Time = distance  speed

First 50 miles time taken = 50 / 60  = 5/6 hours

Second 50 miles  -  time  =  50/40 = 5/4 hours.

Final 20 miles - time taken =  20 / 80 = 1/4 hours.

Total time taken = 5/6 + 5/4 + 1/4

= 5/6 + 6/4

= 10/12 + 18/12

= 28/12

=  7/3 or 2 1/3 hours or 2 hours 20 minutes.

Average speed = total distance / total time

=  120 / 7/3

= 120 * 3/7

=  51.4 mph to 1 decimal place.

Answer:

parallel = 4/3

perpendicular =-3/4

Step-by-step explanation:

Solve for y

-4x+3y=11

Add 4x to each side

3y = 4x+11

Divide by 3

y = 4/3 x +11/3

This is in the form y = mx+b where m is the slope

m =4/3

The parallel line has the same slope

parallel slope is 4/3

The perpendicular line has a negative reciprocal slope

m = -(1 /4/3) = - 3/4

Answer:

[tex]\frac{4}{3}[/tex] and - [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

- 4x + 3y = 11 ( add 4x to both sides )

3y = 4x + 11 ( divide all terms by 3 )

y = [tex]\frac{4}{3}[/tex] x + [tex]\frac{11}{3}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{4}{3}[/tex]

Parallel lines have equal slopes, thus

slope of parallel line = [tex]\frac{4}{3}[/tex]

Give a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{4}{3} }[/tex] = - [tex]\frac{3}{4}[/tex]

Answer:

[tex]x = 500[/tex]

Step-by-step explanation:

Given

[tex]log20x^3 - 2logx = 4[/tex]

Required

Solve for x

[tex]log20x^3 - 2logx = 4[/tex]

Using law of logarithm which says;

[tex]nlogx = logx^n[/tex]

The expression becomes

[tex]log20x^3 - logx^2 = 4[/tex]

Also, using laws of logarithm which says:

[tex]loga - logb = log\frac{a}{b}[/tex]

The expression becomes

[tex]log(\frac{20x^3}{x^2}) = 4[/tex]

[tex]log(20x) = 4[/tex]

Also, using laws of logarithm which says

[tex]If\ loga = b\\then\ a = 10^b[/tex]

The expression becomes

[tex]20x = 10^4[/tex]

[tex]20x = 10000[/tex]

Divide through by 20

[tex]\frac{20x}{20} = \frac{10000}{20}[/tex]

[tex]x = \frac{10000}{20}[/tex]

[tex]x = 500[/tex]

Answer:

500

Step-by-step explanation: