A car traveled 63 miles on 3 gallons of gas. What proportion can you set up to determine how many miles, m, the car can travel on 7 gallons of gas?

Final answer:

Stephanie's annual income is $49,348, while Tahlia's is $45,852, making Stephanie's weekly earnings $67.61 higher than Tahlia's. Stephanie earns $949.38 per week, and Tahlia earns $881.77 per week.

Explanation:

To calculate each person's equivalent annual income, we must standardize their earnings to a common time frame. We consider a year to have 26 fortnights and 12 months.

Stephanie's Annual Income

Stephanie is paid every fortnight, so we multiply her fortnightly income by the number of fortnights in a year:

$1898 per fortnight x 26 fortnights per year = $49,348 per year.

Tahlia's Annual Income

Tahlia is paid monthly, so we multiply her monthly income by the number of months in a year:

$3821 per month x 12 months per year = $45,852 per year.

To determine who earns more per week, we divide the annual income by the number of weeks in a year (52). Stephanie earns $949.38 per week ($49,348 / 52), while Tahlia earns $881.77 per week ($45,852 / 52). Stephanie earns more per week by:

$949.38 - $881.77 = $67.61.

Therefore, Stephanie earns $67.61 more than Tahlia per week.

Answer:

the x-coordinate is 1 in the graph

Answer: The area (A) of a circle is a function of its radius (r) and is given by the function A = f(r) = πr2.

Step-by-step explanation: google help

The area is a function of the radius and the radius is a function of the area.

For a circle of radius R, we can write the area as:

A = pi*R^2

So we can write the area in terms of the radius, meaning that yes, the area is a function of the radius of a circle.

If we take the above equation and we isolate R, we get:

R = √(A/pi)

So you can also write the radius in terms of the area, meaning that the radius is also a function of the area.

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Answer:

C. (-5,0) and (3,0)

Step-by-step explanation:

y= x² + 2x-15

y = 0

x² + 2x-15 = 0

(x - 3) (x + 5) = 0

x = 3 or x = -5

The x-intercepts of the graph of the function are (-5,0) and (3,0).

Option C is the correct answer.

A function has an input and an output.

A function can be one-to-one or onto-one.

It simply indicated the relationships between the input and the output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

To find the x-intercepts of the graph of the function,

We need to set y = 0 and solve for x.

So we have:

x² + 2x - 15 = 0

Factoring this quadratic equation.

(x + 5) (x - 3) = 0

Setting each factor equal to zero.

x + 5 = 0 or x - 3 = 0

Solving for x.

x = -5 or x = 3

Therefore,

The x-intercepts of the graph of the function are (-5,0) and (3,0).

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Answer:

3

Step-by-step explanation:

Answer:

$6,632.55

Step-by-step explanation:

What a coincidence I was doing the same question. Ok so you should know about the Compound Interest formula which is A=P (1+r/100) n. (n) is btw in the exponent.

A= ?

P=6250

r=2

n=3

   Anyways we will input everything we are given so it will be:

A=6250(1+2/100)3

   Since A is final amount - it will be our answer which is  $6,632.55

Final answer:

Carol invested $6,250 at a rate of 2% per year compound interest. After 3 years using the compound interest formula A = P(1 + r/n)^(nt), her investment will grow to $6,632.55.

Explanation:

Carol invested $6,250 at a rate of 2% per year compound interest. To calculate the total amount Carol has after 3 years, we can use the formula:

A = P(1 + r/n)^(nt)

Where:

Since the interest is compounded yearly, n will be 1. Assuming the 2% interest rate is already in decimal form (0.02), and the time is 3 years, we substitute these values into the formula:

A = 6250(1 + 0.02/1)^(1*3)

A = 6250(1 + 0.02)^3

A = 6250(1.02)^3

A = 6250 * 1.061208

A = $6632.55

Therefore, after 3 years, Carol's investment will have grown to $6632.55.

The value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]

Explanation:

Given that the functions [tex]f(x)=4 x^{2}+1[/tex] and [tex]g(x)=x^{2}-5[/tex]

We need to determine the value of [tex](f+g)(x)[/tex]

The value of [tex](f+g)(x)[/tex] can be determined by substituting the value of [tex]f(x)[/tex] and [tex]g(x)[/tex] and simplifying the terms.

Thus, let us assign [tex]f(x)=4 x^{2}+1[/tex] in the function [tex](f+g)(x)[/tex], we have,

[tex]4 x^{2}+1+g(x)[/tex]

Now, let us assign [tex]g(x)=x^{2}-5[/tex] in the function [tex](f+g)(x)[/tex], we get,

[tex]4 x^{2}+1+x^{2}-5[/tex]

Grouping the like terms, we have,

[tex]4 x^{2}+x^{2}+1-5[/tex]

Adding the like terms, we get,

[tex]5 x^{2}-4[/tex]

Hence, the value of [tex](f+g)(x)[/tex] is [tex]5 x^{2}-4[/tex]

To simplify the expression 4 + (14 - 2), subtract 2 from 14, then add 4 to get the equivalent expression. The three equivalent expressions are: 20, -12, and 16.

To simplify the expression 4 + (14 - 2), we need to perform the operations inside the parentheses first. This means subtracting 2 from 14, which gives us 12. Then, we add 4 to 12, resulting in 16. Therefore, the expression 4 + (14 - 2) is equivalent to 16.

The three expressions that are equivalent to 4 + (14 - 2) are:

A. 4 - (-14 - 2) = 4 - (-16) = 4 + 16 = 20

B. (4 - 14) - 2 = -10 - 2 = -12

C. 4 - (-14) - (2) = 4 + 14 - 2 = 16

Answer:

4+5x<x

Step-by-step explanation:

four more than is saying addition so youd add the 4 and the 5x together. the less than is referring to the less than sign. and the number is referring to x.(;

The fish is 2.25 ft above the water surface.

Step-by-step explanation:

⇒ y = -16(0.375)² + 12 × 0.375

      = -2.25 + 4.5

      = 2.25 ft

Answer:

39

Step-by-step explanation:

Let the three consecutive odd numbers be:

x+2, x+4, x+6.

The sum of the consecutive numbers is 123 i.e

x+2 + (x+4) + (x+6) = 123

x + 2 + x + 4 + x + 6 = 123

3x + 12 = 123

Collect like terms

3x = 123 — 12

3x = 111

Divide both side by the coefficient of x i.e 3

x = 111/3

x = 37

Now let us find the value of the three odd numbers. This is illustrated:

1st : x + 2 = 37 + 2 = 39

2nd : x + 4 = 37 + 4 = 41

3rd : x + 6 = 37 + 6 = 43

The smallest of the three consecutive odd numbers is 39

Answer:

Step-by-step explanation:

Mode=77&92&85 (mode is most common number)

Mean= 85+92+65+85+65+85+77+92+92+66+77+92+77+77+65+85=1277

1277/16=79.8 = 80 (Mean is add all numbers and divide how many there is.)

Range=92-65=27 (Range is highest number take away lowest number)

Median: 65,65,65,66,77,77,77,77,85,85,85,85,92,92,92,92

so median is 81 (put numbers in order and find the middle number. if order is even add two numbers in middle and divide by two. If order is odd, find ONE number.)

Final answer:

The median of the sample exam scores is 81, the mean (or average) is 75.75, the mode is bimodal with values 85 and 92, and the range is 27.

Explanation:

Measures of Central Tendency and Variability

To determine the median of the provided exam scores, we must first arrange the scores in ascending order and then find the middle value. With 16 scores, the median will be the average of the 8th and 9th values in this ordered list. For the mean, we add all the scores together and then divide by the total number of scores. The mode is the score that occurs most frequently. The range is calculated by subtracting the smallest score from the highest score.

Calculating the Median

Calculating the Mean

Determining the Mode

Finding the Range

Answer:

Option A) The snow is accumulating at 1.5 inches every hour.

Step-by-step explanation:

The general form of the equation of the line is y = mx + c

where m is the slope or rate of change

For the given equation y = 1.5x + 0.125

Where y is The snow is accumulation and x is number of hours

So, comparing the given equation to the general form

∴ m = 1.5 which represents the The snow accumulation per hour

Which mean every one hour the snow accumulation is 1.5 inches.

According to the previous the answer is option A

A) The snow is accumulating at 1.5 inches every hour.

Answer:

The correct answer is A. The snow is accumulating at 1.5 inches every hour.

Step-by-step explanation:

Let's evaluate the given linear equation, this way:

y = 1.5x + 0.125, where:

Therefore, options B, C, and D are not true. The correct answer is A. The snow is accumulating at 1.5 inches every hour.

The correct equation which represents a function is,

⇒ y= 3x² + 2.

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

To find the correct equation which represents a function.

Now, We know that;

The equation that represents a function is option D,

⇒ y= 3x² + 2.

This is because for every value of x, there is a unique value of y.

In other words, each x value has only one corresponding y value.

And, The other options either have multiple outputs for the same input or do not qualify as a function for other reasons.

Thus, The correct equation which represents a function is,

⇒ y= 3x² + 2.

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Answer:

2,000,000- 653,000= 1,347,000

Step-by-step explanation:

first write this in a equation with numbers

2,000,000- 653,000

million = 1,000,000

hundred thousand= 100,000

now solve the equation

2,000,000- 653,000= 1347000

Answer:

there will be 164 marbles in each bag

Step-by-step explanation:

The question is simply asking you to divide the total number of marbles by five; for each bag. 824/5= 164.8 and 164.8 rounded down; (underline means important), is 164 marbles.

Answer:

164

Step-by-step explanation:

The another way to state the transformation would be [tex](x,y)>(-x,-y)[/tex]

Solution:

Rotation about the origin at [tex]180^\circ[/tex]: [tex]R_{180^\circ}A \rightarrow O = R_{180^\circ} (x, y) \rightarrow (-x,-y)[/tex]

The term R0 means that the rotation is about the origin point. Therefore, (R0,180) means that we are rotating the figure to [tex]180^\circ[/tex] about the origin.

So, the transformation of the general point (x,y) would be (-x,-y) when it is rotated about the origin by an angle of [tex]180^\circ[/tex].

Hence according to the representation, the expression would be [tex](x, y) \rightarrow (-x, -y)[/tex].

The transformation R0, 180° is equivalent to reflecting each point (x, y) in a Pentagon across the origin, resulting in the new coordinates (-x, -y).

The transformation rule R0, 180° involves rotating a point (x, y) within a Pentagon by 180 degrees around the origin. In this transformation, each point is mirrored or reflected across the origin. To express this transformation differently, we can say that (x, y) is mapped to its mirror image in both the x-axis and y-axis. In other words, the x-coordinate is reversed (negated), and the y-coordinate is also reversed (negated).

So, the alternative way to state this transformation is: (x, y) > (-x, -y). This means that any point (x, y) in the original Pentagon will become (-x, -y) after the transformation.

For example, if we have a point (2, 3) within the Pentagon, applying the transformation yields (-2, -3). This means the point's x-coordinate is changed from 2 to -2, and the y-coordinate is changed from 3 to -3. This transformation is essentially a 180° rotation or a reflection through the origin.

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Answer:

y= -2

Step-by-step explanation:

Please see attached picture for full solution.

(From the 4th to 5th line, I multiplied both sides by 8)

Answer:

c)

Step-by-step explanation:

c). Distributive Property

32*15 = 32*(10+5) = 32*10 + 32*5

          =320 + 160 = 480

Answer:

1 + 2

Step-by-step explanation:

When we look at the number line, we can see that the inequality is:

x ≤ 19

This means that all values of "x", must be equal to or less than 19.

To find the correct answer choices, we must keep that equation in mind.

1. at most 19 cups   -   this answer choice does work, because it shows that 19 is the limit (which is what our inequality represents)

2. 19 cups or less    -     this answer choice works as well because it shows that 19 is the maximum and all other values of "x" must be below that.

3. more than 19 cups   -  this goes against our inequality, since "x" can't exceed 19. This means that this answer choice must be incorrect.

4. a minimum of 19 cups   -   this answer choice also cannot be correct since it shows that "x" can go over 19 (which we know is false).

5. no fewer than 19 cups   -    this is also wrong because it wants "x" to go over the value of 19, which it can't do.

Answer:

Step-by-step explanation:

A and b

Answer:

Option B, 61

Step-by-step explanation:

Step 1:  Find the range

To find the range, subtract the lowest number from the highest number.

Example:  1, 50

What is the highest number:  50

What is the lowest number:  1

50 - 1 = 49

Problem:  96, 35

What is the highest number:  96

What is the lowest number:  35

96 - 35

61

Answer: Option B, 61

Answer:

Only one value is in the range,

61

Step-by-step explanation:

Calculate range by subtracting the smaller value from the larger value

96 - 35 = 61

Only one of the given options corresponds with the solution of the range, which is 61, or the second option.

Hope this helps :)

f(4) is 49

Explanation:

Given:

f(x) = 12x + 1

f(4) = ?

we have to substitute the value of x = 4 in the given equation.

f(4) = 12 X 4 + 1

f(4) = 49

Whenever there is such type of question then we have to just put the value of x in the equation. In case of f '(4) then we have to differentiate the given equation with respect to x first and then substitute the value of x in the differentiated equation.

Therefore, f(4) is 49

Answer:

one solutions

Step-by-step explanation:

graph both points on a graph if they cross you have one solution, if they never meet you have no solution and if it's one line you have infinite solutions

Final answer:

The two given linear equations y = -3x + 6 and y = 2x - 4 have different slopes, which means they will intersect at exactly one point, indicating that there is one solution to the system.

Explanation:

To find out how many solutions can be found for the system of linear equations represented on the graph, we can observe the slopes and y-intercepts of the given equations. The two equations are:

y = -3x + 6

y = 2x - 4

These are both linear equations in the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation has a slope of -3 and the second has a slope of 2. Because the slopes are not equal, these lines are not parallel and will, therefore, intersect at one point. When two lines intersect at exactly one point, the system of equations has one solution.

Moreover, since they intersect, they do not have the same line, so they do not have infinitely many solutions. Therefore, the correct answer is one solution (B).

Answer:

The integers are

5 and 7

Step-by-step explanation:

Let

x ---> the first consecutive odd integer

x+2 ---> the second consecutive odd integer

we know that

The algebraic expression that represent this situation is

[tex]x(x+2)=x+30[/tex]

solve for x

[tex]x^2+2x=x+30\\x^2+2x-x-30=0\\x^2+x-30=0[/tex]

Solve the quadratic equation

The formula to solve a quadratic equation of the form

[tex]ax^{2} +bx+c=0[/tex]

is equal to

[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]

in this problem we have

[tex]x^{2} +x-30=0[/tex]  

so

[tex]a=1\\b=1\\c=-30[/tex]

substitute in the formula

[tex]x=\frac{-1\pm\sqrt{1^{2}-4(1)(-30)}} {2(1)}[/tex]

[tex]x=\frac{-1\pm\sqrt{121}} {2}[/tex]

[tex]x=\frac{-1\pm11} {2}[/tex]

[tex]x=\frac{-1+11} {2}=5[/tex]

[tex]x=\frac{-1-11} {2}=-6[/tex]  ---> is not a odd integer

For x=5

The numbers are

[tex]x=5\\x+2=7[/tex]

so

5 and 7

Answer: 1.3

Step-by-step explanation:

Step 1: convert to decimal

56% = 56/100 = 0.56

43% = 43/100 = 0.43

Step 2; divide the values

0.56/0.43= 1.3

I hope this helps.

The length of the edge of the cube is 3.23 cm .

Step-by-step explanation:

We have , The relationship between the weight y gram and the edge x cm for a cube of gold is y = 19.3x3 or [tex]y = 19.3x^3[/tex] .  A cube of gold weighs 652 grams i.e. y = 652 . Let's calculate value of x from above data:

[tex]y = 19.3x^3[/tex]

⇒ [tex]y = 19.3x^3[/tex]

⇒ [tex]652= 19.3x^3[/tex]

⇒ [tex]19.3x^3=652[/tex]

⇒ [tex]\frac{19.3}{19.3}x^3=\frac{652}{19.3}[/tex]

⇒ [tex]x^3=\frac{652}{19.3}[/tex]

⇒ [tex]\sqrt[\frac{1}{3} ]{x^3} = \sqrt[\frac{1}{3} ]{\frac{652}{19.3}}[/tex]

⇒ [tex]({x^3})^\frac{1}{3} =({\frac{652}{19.3}})^\frac{1}{3}[/tex]

⇒ [tex]x =(33.78)^\frac{1}{3}[/tex]

⇒ [tex]x =3.23[/tex]

Therefore, the length of the edge of the cube  is 3.23cm.

Answer:

your answer would be 2

Step-by-step explanation:

Convert 1 3/12 into an improper fraction which is 5/4

Then add it with 9/12

5

/4  + 9

/12

(5 × 12) + (9 × 4)

---------------------------

        4 × 12

= 96/48

=    96 ÷ 48

 -------------------

     48 ÷ 48

= 2

2 is your answer hope this helps :)

Answer:

2 feet

Step-by-step explanation:

To find the total amount of snow that fell, we add

1 3/12 + 9/12

add the fractions

3/12+9/12 = 12/12 =1

Add the whole numbers

1  plus the whole number from the fraction

1+1 =2

The required formula with b subject is [tex]b = a^{2} - 6[/tex].

Given that ,

a is the subject of the formula,

[tex]a = \sqrt{ b + 6}[/tex]

We have to make b is the subject for the formula,

[tex]a = \sqrt{ b + 6}[/tex]

Squaring both the sides,

[tex]a^{2} = b + 6[/tex]

[tex]b = a^{2} - 6[/tex]

Hence , The required formula with b subject is [tex]b = a^{2} - 6[/tex]

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To make b the subject of the formula a = √(b+6), you need to isolate b on one side of the equation. The solution is b = a² - 6.

To make b the subject of the formula a = √(b+6), we need to isolate b on one side of the equation. Here are the steps:

Therefore, b = a² - 6.

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