Samantha started with $25 in her account. she saves $7 per week. Australia has no money in his account, but adds $15 per week. for how many weeks will Australia have more money in his account than Samantha

Answers

Answer 1

In this problem we can made a function to calculate the total amount for Samantha (S) and total amound of Australia (A) fon any time:

[tex]\begin{gathered} S=25+7t \\ A=0+15t \end{gathered}[/tex]

when t is the number of weeks. if we made equal the ecuation we will have the time when they would have the same amound:

[tex]\begin{gathered} S=A \\ 25+7t=15t \end{gathered}[/tex]

and we solve for t

[tex]\begin{gathered} 25=15t-7t \\ 25=8t \\ \frac{25}{8}=t \\ 3.125=t \end{gathered}[/tex]

This means that in the next full number Australia will have more money than Samantha, so in 4 weeks this is going to happen.


Related Questions

can you please find the slope and the y intersept of the graph of the linear equation y= 4x-5

Answers

the slope of the linear equation is 4 and the y intercept is -5

Explantion:

we apply the equation of line to find the slope and intercept

Equation of line is in the form: y = mx + c

where m = slope and c = y - intercept

comparing the given equation with the equation of line:

linear equation y= 4x-5 ​

y = y

4x - 5 = mx + c

This means m = 4

4x = mx

m = 4

-5 = c

Hence, the slope of the linear equation is 4 and the y intercept is -5

This question is from a MATH extra credit assignment, so unless I accidentally clicked on a subject other than maths... This question is also not from a test. Please help me if you can. Thank you if you do :)

Answers

Answer

$6,314

Step-by-step explanation

Compound interest formula

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]

where

• A: final amount, in dollars

,

• P: principal, in dollars

,

• r: interest rate, as a decimal

,

• n: number of times interest is applied per year

,

• t: time in years

In this case, the investment is compounded annually, that is, once per year (n = 1). Substituting P = $4,625, r = 0.0352 (=3.52/100), n = 1, and t = 9 years, we get:

[tex]\begin{gathered} A=4,625(1+\frac{0.0352}{1})^{1\cdot9} \\ A=4,625(1.0352)^9 \\ A=\text{ \$}6,314 \end{gathered}[/tex]

A baseball stadium has 50,100 seats. Each ticket for a seat costs $30. Tara created a function to model this situation and drew the graph of the function, where y represents profit from ticket sales, in dollars, given the number of tickets sold, x.

Is the graph function correct? why or why not?

Answers

The graph as shown in the image is the correct graph of the function.

What is the correct graph of the function?

A function shows a mathematical relationship. We would need to look at the graph very closely so as to know weather or not the graph as it has been shown is the correct graph that is befitting of the function must be a straight line graph.

Clearly, the slope of the graph would be positive and beginning from the origin because the number of tickets that is sold is increasing just and the amount of the tickets is increasing. Thus the graph follows the general equation of a straight line; y = mx + c

All these goes to show that what we have befits the function.

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7. Which expression is equivalent to the distance between -2 and -15 on a number line? Select all that apply. OT-15 - (-2)] O 1-15-2 O 1-15+ (-2) 1-2 + (-15) 1-2-(15)

Answers

[tex]\begin{gathered} \mleft|-2-(-15)\mright|=\mleft|-2+15\mright| \\ or \\ \mleft|-15-(-2)\mright|=\mleft|-15+2\mright| \end{gathered}[/tex]

factor completely5r^3-10r^2+3r-6

Answers

You have the following polynomial:

5r³ - 10r² + 3r - 6

In order to factorize the given polynomial, use synthetic division:

5 -10 3 -6 | 2

10 0 6

5 0 3 0

The remainder is zero in the previous division, then, r - 2 is a factor of the given polynomial, the other factor is formed with the coefficients of the division, just as follow:

5r³ - 10r² + 3r - 6 = (r - 2)(5r² + 3)

Hence, the factor are (r - 2)(5r² + 3)

Answer:(r-2) x (5r^2+3)

Step-by-step explanation:

Can you tell me if im right or wrong

Answers

I will begin typing in the answer tab. It will take me approximately _

Find the reference angle of [tex] \frac{ - 13\pi}{6} [/tex]

Answers

Reference angle

The reference angle of a given angle A is the acute angle that A forms with the x-axis

We need to calculate the reference angle of

[tex]\frac{ - 13\pi}{6}[/tex]

This angle is greater than any angle of a single turn on the trigonometric circle.

Let's convert the improper fraction to a mixed fraction:

[tex]-\frac{13\pi}{6}=-2\pi-\frac{\pi}{6}[/tex]

-2π corresponds to a complete turn around the circle, so we can discard that part and take only the -π/6

Since it's a negative angle, it runs clockwise and is located at the IV quadrant. The reference angle is π/6 because it's the angle it forms with the x-axis.

We'll include an image of the angle below

Yasmin went to the store and bought 3 and 1/2 pounds of ground beef for 11:20 how much do the ground beef cost per pound

Answers

Yasmin bought 3 1/2 pounds of ground beef, we can express the amount that she bought as a fraction like this:

[tex]3\frac{1}{2}=\frac{3\times2+1}{2}=\frac{6+1}{2}=\frac{7}{2}[/tex]

Since she bought it for $11.2, if we divide the cost by the amount that she purchased, we get the cost per pound, like this:

[tex]\frac{11.2}{\frac{7}{2}}[/tex]

To divide by a fraction, we just have to invert its numerator and denominator:

[tex]\frac{11.2}{\frac{7}{2}}=11.2\times\frac{2}{7}=\frac{22.4}{7}=3.2[/tex]

Then, the cost per pound equals $3.2

What is the probability of drawing a jack from a standard deck of cards, replacing it,shuffling, then drawing an ace?

Answers

- We have 52 cards in a deck of cards.

- We have 4 cards of the same number (4 jack, 4 aces...).

Probability of drawing a jack = 4/52

Probability of drawing a jack followed by an ace =(4/52)*(4/52)=0.00592

A company orders business cards for their employees. The company pays $9.00 per 100 cards ordered. The company orders2,000 business cards for Karen and 2,500 business cards for Lamar. How much more do the business cards for Lamar cost than thebusiness cards for Karen?$9$45$450d $500

Answers

Take into account what the company pays per 100 cards ordered, which is $9.00.

To determine the cost of the cards for Karen and Lamar

2. A bag contains 50 marbles, 28 red ones and 22 blue ones. A marble is picked at random from the bag. What is the probability of picking: a red marble first? a blue marble?

Answers

Answer:

28/50

Step-by-step explanation:

If there is 50 marbles and you have 22 blue and 28 red and they want you to find what the chance of picking a red marble out of the bag your chances would be 28/50 hope this helps!

From question: Montell is practicing his violin. He is able to play six songs for every nine minutes he practices.*Picture has the table and other questions*

Answers

Answer:

The complete table:

6 18 2 42

9 27 3 63

Explanation:

We know that for every 9 minutes Montell practices he is able to play 6 songs. This means that the ratio between the number of minutes practices to the number of songs played is

[tex]\frac{\min}{\text{song}}=\frac{9}{6}[/tex]

Therefore, if we want to solve for minutes plated, we just multiply both sides by 'song' to get

[tex]song\times\frac{\min}{\text{song}}=\frac{9}{6}\times\text{song}[/tex]

which gives

[tex]min=\frac{9}{6}\times\text{song}[/tex]

This means the number of minutes practised is 9/6 of the number of songs played.

Now 9/ 6 can be simplfied by dividing both the numerator and the denominator by 3 to get

[tex]\frac{9\div3}{6\div3}=\frac{3}{2}[/tex]

therefore, we have

[tex]min=\frac{3}{2}\times\text{song}[/tex]

Now we are ready to fill the table.

If Montell plays 18 songs then we have

[tex]\min =\frac{3}{2}\times18[/tex][tex]\min =27[/tex]

the minutes practised is 27 for 18 songs.

If Montell practices for 3 minutes then we have

[tex]3=\frac{3}{2}\times\text{song}[/tex]

then the value of song must be song = 2, since

[tex]\begin{gathered} 3=\frac{3}{2}\times2 \\ 3=3 \end{gathered}[/tex]

Hence, for 3 minutes of practice, Montell sings 2 songs.

Now for 42 songs, the number of minutes played would be

[tex]\min =\frac{3}{2}\times42[/tex]

which simplifies to give

[tex]\min =63[/tex]

Hence, for 42 songs played, the practice time is 63 minutes.

To summerise, the complete table would be

songs 6 18 2 42

minutes 9 27 3 63

Refer to the rectangle ABCD, shown below, where m(<4)=10degrees. Need help.

Answers

From the statement of the problem, we know that:

[tex]m(\angle4)=18^{\circ}\text{.}[/tex]

From the diagram, we see that:

1) ∠1 and ∠4 are complementary angles, so they sum up 90°:

[tex]\begin{gathered} m\mleft(\angle1\mright)+m\mleft(\angle4\mright)=90\degree \\ m\mleft(\angle1\mright)=90\degree-m\mleft(\angle4\mright), \\ m(\angle1)=90\degree-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]

2) ∠4, ∠3 and a right angle are inner angles of a triangle, so they must sump up 180°:

[tex]\begin{gathered} m(\angle4)+m(\angle3)+90^{\circ}=180^{\circ}\text{.} \\ m(\angle3)=180^{\circ}-90^{\circ}-m(\angle4), \\ m(\angle3)=180^{\circ}-90^{\circ}-18^{\circ}=72^{\circ}\text{.} \end{gathered}[/tex]

3) ∠3 and ∠2 are complementary angles, so they sum up 90°:

[tex]\begin{gathered} m(\angle3)+m(\angle2)=90^{\circ}, \\ m(\angle2)=90^{\circ}-m(\angle3), \\ m(\angle2)=90^{\circ}-72^{\circ}=18^{\circ}\text{.} \end{gathered}[/tex]

Answer

c. m(∠1) = 72°, m(∠2) = 18°, m(∠3) = 72°.



4. A pool measuring 24 feet by 16 feet is
surrounded by a uniform path of width x feet.
The total enclosed area is 768 ft².
Find x, the width of the path.

Answers

The width of the path, x, is 48 feet

How to determine the parameters

The formula for determining the area of a rectangle is expressed as;

Area = lw

Where;

l is the length of the given rectanglew is the width of the given rectangle

From the image shown and the information given, we can see that;

The width is given as = x

The area of the rectangle =  768 ft²

The length of the rectangle = 16

Now, substitute the values, we have;

768 = 16x

Make 'x' the subject of formula by dividing both sides by its coefficient, we have;

768/16 = 16x/16

Find the quotient

x = 48 feet

But, we have;

Width = x = 48 feet

Hence, the value is 48 feet

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3. f(x) = |-3x - 1|3. For this function, findeach of the following:a. f(-1)b. f(0)c. f(3)

Answers

Given the absolute function;

[tex]f(x)=|-3x-1|[/tex]

(a)

[tex]\begin{gathered} f(-1)=|-3x-1| \\ f(-1)=|-3(-1)-1| \\ f(-1)=|3-1| \\ f(-1)=|2| \\ f(-1)=2 \end{gathered}[/tex]

(b)

[tex]\begin{gathered} f(0)=|-3(0)-1| \\ f(0)=|0-1| \\ f(0)=|-1| \end{gathered}[/tex]

Here, we recall the absolute rule that;

[tex]|-a|=a[/tex]

Thus, we have;

[tex]f(0)=|-1|=1[/tex]

(c)

[tex]\begin{gathered} f(3)=|-3(3)-1| \\ f(3)=|-9-1| \\ f(3)=|-10| \\ f(3)=10 \end{gathered}[/tex]

Using the order of operations, which operation should you perform last to evaluate the expression below?(7*4)+(10 ÷ 2)*(14.7 - 9)A.multiplicationB.divisionC.additionD.subtractionHELP! A.P.S

Answers

Explanation

Given (7*4)+(10 ÷ 2)*(14.7 - 9), we can see that only two operations occur outside of the parenthesis which is multiplication and addition.

In the order of evaluation of expressions, the parenthesis comes first before multiplication and then addition. Therefore,

Answer: Option C (Addition)

write an equation and solvefour times the complement of an angle is 40° lessthan twice the angles supplement. Find the angle,its complement, and its supplement

Answers

Let the angle be 'x' degrees.

The complement (C) of the corresponding angle will be,

[tex]C=90-x[/tex]

And the supplement (S) of the corresponding angle will be,

[tex]S=180-x[/tex]

According to the condition given in the problem,

[tex]4C=2S-40^{}[/tex]

Substitute the values,

[tex]\begin{gathered} 4(90-x)=2(180-x)-40 \\ 360-4x=360-2x-40 \\ -4x=-2x-40 \\ 4x-2x=40 \end{gathered}[/tex]

Simplify the expression further,

[tex]\begin{gathered} 2x=40 \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]

Substitute this value of 'x' to obtain the complement and supplement angles as follows,

[tex]\begin{gathered} C=90-20=70 \\ S=180-20=160 \end{gathered}[/tex]

Thus, the angle measures 20 degrees, its complement measures 70 degrees, while its supplement measures 160 degrees.

A card is drawn from a deck of 52 cards. What is the probability that it is a numbered card (2-10) or a heart?

Answers

we know that

Total cards=52

Total numbered card (2-10)=36

Total heart=13

numbered card and heart=9

therefore

The probability is equal to

P=(36+13-9)/52

P=40/52

P=20/26=10/13

The answer is 10/13

A straight line l1 with equation 5x - 7 = 0 cuts the x axis at point A. Straight line l2 is perpendicular to straight line l1 and passes through point A. What is the coordinates of point A and the equation of the straight line l2?

Answers

The coordinates of point A are (7/5, 0), and the perpendicular line that also passes through that point is:

y = 0.

How to get the perpendicular line?

Here we want to get a line perpendicular to:

5x - 7 = 0

Solving this for x, we get:

5x = 7

x = 7/5.

This is a vertical line, so the perpendicular line will be a horizontal line, which is of the form:

y = a.

We know that the line:

x = 7/5.

Cuts the x-axis at point A.

Remember that the x-axis as coordinates (x, 0).

So the coordinates of point A are (7/5, 0).

Now, the perpendicular line:

y = a

Needs to pass through the point (7/5, 0), so the value of a must be zero, then the line is:

y = 0.

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=Given f(x) = -0.4x – 10, what is f(-12)? If it does not exist,enter DNE.

Answers

We have the function:

[tex]f\mleft(x\mright)=-0.4x-10[/tex]

And we need to find its value when x = -12. So, replacing x with -12, we obtain:

[tex]f(-12)=-0.4(-12)-10=4.8-10=-5.2[/tex]

Notice that the product of two negative numbers is a positive number.

Therefore, the answer is -5.2.

for #5 solve for x. then find the missing piece(s) of parallelogram.

Answers

Answer:

Given that,

From the parallelogram, the opposite sides of the parallelogram are -2+4x and 3x+3

Explanation:

From the properties of parallelogram, we have that

Opposite sides of a parallelogram are equal

We get,

[tex]-2+4x=3x+3[/tex]

Solving we get,

[tex]4x-3x=3+2[/tex][tex]x=5[/tex]

Answer is :x=5

The number of chaperones on a field trip must include 1 teacher for every 4 students, plus 2 parents total. The function describing the number of chaperones for a trip of x students is f(x) = 1/4x + 2.

a. How will the graph change if the number of parents is reduced to 0?

b. How will the graph change if the number of teachers is raised to 1 for every 3 students?

Answers

Number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,

a. If the parents is reduced to 0 then the graph passes through origin (0,0).

b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .

As given in the question,

Given conditions:

Field trip must include 1 teacher for every 4 students and add 2 parents in total.

Number of chaperones for a trip defined by function f(x) = (1/4)x+2

a. If the parents is reduced to 0 then the changes seen in the graph are as follow:

f(x) =  (1/4)x+2 passes through the point (0,2)

when parents changes to 0 then graph passes through (0,0).

b.  If the number of teachers is raised to 1 for every 3 students then the changes seen in the graph are as follow:

For f(x) = (1/4)x+2 the graph cut axis at (-8,0)

When for every 1 teacher there are 3 students then graph cut x-axis at (-6,0).

Therefore, number of chaperones for a trip defined by function f(x) = (1/4)x+2 then,

a. If the parents is reduced to 0 then the graph passes through origin (0,0).

b. If the number of teachers is raised to 1 for every 3 students then line cut x-axis at (-6,0) .

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Question 9 (1 point) Jennifer is a car saleswoman. She is paid a salary of $2200 per month plus $300 for each car that she sells. Write a linear function that describes the relationship between the number of cars sold x and the monthly salary y. Then, graph the function to show the relationship.

Answers

[tex]\begin{gathered} y=2200+300x \\ \end{gathered}[/tex]

In the triangle below, suppose that mZW=(x+4)º, mZX=(5x-4)°, and mLY= (4x)".Find the degree measure of each angle in the triangle.

Answers

[tex]\begin{gathered} W+X+Y=180 \\ x+4+5x-4+4x=180 \\ 10x=180 \\ x=18 \end{gathered}[/tex][tex]\begin{gathered} \text{The angle W is,} \\ W=x+4 \\ W=18+4=22 \\ \text{The angle X is,} \\ X=5x-4 \\ X=5\times18-4=86 \\ \text{The angle Y is,} \\ Y=4x \\ Y=4\times18=72 \end{gathered}[/tex]

Teachers' Salaries The average annual salary for all U.S. teachers is $47,750. Assume that the distribution is normal and the standard deviation is $5680Find the probabilities.P (X>45,500)

Answers

[tex]\begin{gathered} \mu=47,750 \\ \sigma=5,680 \\ X>45,500 \\ Z=\frac{X-\mu}{\sigma} \\ Z=\frac{45,500-47,750}{5,680} \\ Z=\frac{-2,250}{5,680} \\ Z=-0.3961 \\ P(X>45,500)\text{ using chart for z} \\ P(X>45,500)\text{ =}0.654=65.4\text{ \%} \\ \text{The }probability\text{ }is\text{ }0.654\text{ or }65.4\text{ \%} \end{gathered}[/tex]

You go to the pet store with $25. You decide to buy 2 fish for $3.69 each and fish foos for $4.19. Rounded tanks are $11.48 square-shaped tanks are $14.89. Estimate your total cost to find which tank you can can buy. About how much money will you have left?

Answers

Answer: you will only have enough money for the rounded tank, after buying everything you will have 9 cents left

Step-by-step explanation: two $3.69 fish, $4.19 fish food. 2x3.69=7.38+4.19=11.57

25-11.57=13.43

13.43+11.48=24.91

25-24.91=0.09

You need to estimate the prices of the fish and food. I going to round to the whole amount. 3.69= 4.00; 4.19=4.00. 2 fish at 4.00 equals 8.00; plus the 4.00 for food equals 12.00. 25.-12=13.00. You will only have enough to buy the round tank at 11.48.
Even if you add the fish and food together minus the 25. You can still only get the round tank.

Solve for x in the equation below:3(x - 5) = 5x - (3 - x)

Answers

Step 1: We have the following equation:

3(x - 5) = 5x - (3 - x)

Step 2: Solve the parentheses

3x - 15 = 5x - 3 + x

Step 3: Like terms

3x - 5x -x = - 3 + 15

-3x = 12

Step 4: Dividing by -3 at both sides

-3x/-3 = 12/-3

x = -4

Step 5: Let's prove the answer is correct

3 (-4 - 5) = 5 * -4 - (3 - -4)

3 (-9) = -20 -3 - 4

-27 = - 27

The solution is correct

Find the slope of the line?Ordered pairs (-4, 1) and (1, -2)

Answers

The slope of the line is:

[tex]m=-\frac{3}{5}[/tex]

To find the slope of a line with two points, P and Q, the formula is:

[tex]\begin{gathered} P=(x_p,y_p);Q=(x_q,y_q) \\ m=\frac{y_p-y_q}{x_p-x_q} \end{gathered}[/tex]

Then if P = (-4, 1) and Q = (1, -2)

We can replace inthe formula:

[tex]m=\frac{1-(-2)}{-4-1}=-\frac{3}{5}[/tex]

Find the volume of cylinder with r=25.5 ft and height=45ft use 3.14 for pi. Round the answer to the nearest hundredth

Answers

The Volume of a Cylinder

Given a cylinder of base radius r and height h, its volume is calculated as follows:

[tex]V=\pi r^2h[/tex]

We have a cylinder with dimensions r = 25.5 ft and h = 45 ft. Substituting the values in the formula:

[tex]V=\pi\cdot25.5^2\cdot45[/tex]

Using π = 3.14:

[tex]\begin{gathered} V=3.14\cdot650.25ft^2\cdot45ft \\ V=91,880.325ft^3 \end{gathered}[/tex]

Rounding to the nearest hundredth:

V = 91,880.33 cubic ft

Maxim has been offered positions by two car companies. The first company pays a salary of $12000 plus a commission of $800 for each car sold. The second pays a salary of $15600 plus a commission of $600 for each car sold. How many cars would need to be sold to make the total pay the same?

Answers

Answer:

To make the total pay the same, 18 cars would need to be sold

Explanation:

Let the number of cars sold be x

The first company pays a salary of $12000 plus a commission of $800 for each car sold

Total pay for the first company = 12000 + 800x

The second pays a salary of $15600 plus a commission of $600 for each car sold

Total pay for the second company = 15600 + 600x

If the total pay is the same:

12000 + 800x = 15600 + 600x

800x - 600x = 15600 - 12000

200x = 3600

x = 3600/200

x = 18

To make the total pay the same, 18 cars would need to be sold

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