Mindy is saving money she started with $0 after six weeks she had $90 saved mindy is not sure exactly how much money she saved each week she assumes that she saved money at a constant rate from when she started saving money through week 6 what is the proportional relationship

Answers

Answer 1

The amount saved per week is $15 assuming a constant saving rate per week.

Initial amount = $0Final amount = $90

Number of week, n = 6

Assume she has saved at a constant rate ;

The amount saved per week will be :

(Final amount - initial amount) / number of weeks

($90 - $0) ÷ 6$90 ÷ 6 = $15

The amount saved per week is $15

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Answer 2

Final answer:

Mindy saved $90 over 6 weeks, suggesting a constant rate of saving $15 per week. The proportional relationship between her total savings (y) and the number of weeks (x) is y = 15x.

Explanation:

Mindy started with $0 and after six weeks had $90. To find the proportional relationship between the money saved and the number of weeks, we assume that she saves the same amount every week. Since we know the total savings and the total time, we can divide the total savings by the number of weeks to find the constant rate.

Mindy's weekly saving rate would be:

Calculate the total amount saved: $90.

Divide the total amount by the number of weeks: $90 ÷ 6 weeks.

The result is $15 per week.

Therefore, the constant rate of saving is $15 per week. The proportional relationship can be represented as y = 15x, where y represents the total amount saved and x represents the number of weeks.


Related Questions

The function shown below was created to track the different intervals of speed that an automobile travels over a period of 28 seconds. Use the graph of the function to complete Parts 1-3. After traveling for 16 seconds, the automobile begins to slow its speed at a steady rate. Use the coordinates on the graph to determine the rate at which the car is slowing down, in miles per hour per second. During which interval of time does the automobile experience the greatest change in its speed? What is the change in the automobile’s speed during this interval? For a time period of approximately 10 seconds, the automobile experiences no change in its speed. During which interval of time does the automobile’s speed remain constant? At what speed is the automobile traveling during this interval?

Answers

Answer:

1. The car is slowing down at a rate of 2.5mph/s

2. The greatest acceleration is 10 mph/s.

3. In the interval 4s to 16s the speed remains constant and has magnitude 25 mph.

Step-by-step explanation:

1. The deceleration of the car is from 16 seconds to 24 seconds is the slope [tex]m[/tex] of the graph from 16 to 24:

[tex]m=\dfrac{\Delta speed }{\Delta time } = \dfrac{5-25}{24-16} =-2.5mph/s[/tex]

the negative sign indicates that it is deceleration.

2. The automobile experiences the greatest change in speed when the slope is greatest because that is when acceleration/deceleration is greatest.

From the graph we see that the greatest slope of the graph is between 28 and 24 seconds. The acceleration the interval is the slope [tex]m[/tex]:

[tex]m= \dfrac{45-5}{28-24}= 10mph/s[/tex]

3. The automobile experiences no acceleration in the interval 4 s to 16 s—that's the graph is flat.

The speed of the automobile in that interval, as we see from the graph, is 25 mph.

For the following exercises, write the interval in set-builder notation

10. (-infinity, 6)
11. (4, infinity)
12. [-3,5)
13. [-4,1]U[9, infinity)
14. (-infinity, infinity)

Answers

Final answer:

Set-builder notation is a method to define intervals through a property shared by all members. The notation for the given intervals includes conditions that represent the endpoints or infinity, expressing the range of the variable in each set.

Explanation:

Writing intervals in set-builder notation involves describing a set through a property that its members share. Here is the set-builder notation for each interval provided:

10. (-infinity, 6) in set-builder notation is: [tex]\{x | x < 6\}[/tex]11. (4, infinity) in set-builder notation is:[tex]\{x | x > 4\}[/tex]12. [-3,5) in set-builder notation is: [tex]\{x | -3 \leq x < 5\}[/tex]13. [-4,1]U[9, infinity) in set-builder notation is: [tex]\{x | -4 \leq x \leq 1\} \cup \{x | x \geq 9\}[/tex]14. (-infinity, infinity) in set-builder notation is simply the set of all real numbers, which can be written as: [tex]\{x | x \text{ is a real number}\}[/tex]

To express these sets, we use 'x' as our variable and conditions such as x < 6 that define the range of values 'x' can take. The 'U' symbol represents the union of two sets, indicating that the set includes all elements from both intervals.

Katelynn earned $1240 in two weeks at the recreation
center during a trap shooting tournament. She earned
$480 the first week and the rest the second week.
Write an algebraic equation to model the situation.

Answers

Answer:

The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  

Step-by-step explanation:

Given as :

The total money earn by Katelynn in tow weeks = $ 1240

The money earn by Katelynn in first week = $ 480

Let The money earn by Katelynn in second week = $x

Now,

From equation

The total money earn by Katelynn in tow weeks = The money earn by Katelynn in first week  + The money earn by Katelynn in second week

Or,  $ 1240 =  $ 480 + $ x

Or, $ x =  $ 1240 - $ 480

So, x = $ 760

So, The money earn in second week is $ 760

∴ The algebraic equation to model the situation is $ x = $ 1240 - $ 480

Hence ,  The money earn in second week is $ 760 and

The algebraic equation to model the situation is $ x = $ 1240 - $ 480  Answer

When Angela turned 10, her parents deposited $5,000 in a college fund for her. When Angela enrolled in college at 18, her account had $6,800 to help pay her expenses. If the account paid simple interest, what was the annual interest rate?

Answers

Answer:

The annual interest rate was 4.5% in Angela's college fund.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment when Angela was 10= US$ 5,000

Duration of the investment = 8 years

Balance of the account when Angela turned 18 = US$ 6,800

2. Let's find the annual interest rate of this investment after 8 years or 20 quarters, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment when Angela turned 10 = US$ 5,000

FV = Balance of the account when Angela turned 18 = US$ 6,800

number of periods (n) = 8

Replacing with the real values, we have:

6,800 = 5,000 * (1 + r) ⁸

6,800/5,000 = (1 + r) ⁸ (Dividing by 5,000 at both sides)

34/25 = 1⁸ + r⁸

34/25 - 1 = r⁸ (1⁸ = 1)

34/25 - 25/25 =r⁸ (1 = 25/25)

9/25 =  r⁸

0.36 = r⁸ (9/25 = 0.36)

⁸√0.36 = ⁸√r⁸

0.045 = r

r = 4.5%

The annual interest rate was 4.5% in Angela's college fund.

Answer:

The answer is 4.5

Step-by-step explanation:.

To determine the interest rate, substitute the numbers for the values in the I equals Prt formula. I equals one thousand eight hundred, P equals five thousand and t equals eight because the money was in the bank for eight years.

Multiply five thousand by eight.

Divide both sides by forty thousand and evaluate.

Finally, convert the decimal zero point zero four five to four point five percent.

Which of the following is not a composition of isometries:
A. Reflection over x=2 then rotation 90 degrees clockwise about the origin
B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin
C. Translation (x,y)->(x-2,y+1) then reflection over the y-axis
D. Reflection over the x-axis then reflection over the y-axis

Answers

Answer:

B

Step-by-step explanation:

When you dilate a shape you change the size, changing the composition of isometries.

Final answer:

Option B is not a composition of isometries.

Explanation:

The composition of isometries refers to combining multiple isometries (transformations that preserve distance) to create a new transformation. To determine which of the options is not a composition of isometries, we need to verify if each option preserves distance. If any option does not preserve distance, it is not a composition of isometries. Let's analyze each option:

A. Reflection over x=2 then rotation 90 degrees clockwise about the origin: Both reflection and rotation are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

B. Dilation with scale factor 1/2 then rotation 270 degrees clockwise about the origin: Dilation, when the scale factor is not 1, does not preserve distance. Therefore, this option is not a composition of isometries.

C. Translation (x,y)-> (x-2, y+1) then reflection over the y-axis: Both translation and reflection are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

D. Reflection over the x-axis then reflection over the y-axis: Both reflections are isometries, as they preserve distance. Therefore, this option is a composition of isometries.

In summary, option B is the only one that is not a composition of isometries.

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HELP ME YOU MUST EXPLAIN THE ANSWER ​

Answers

Answer: 4) 7c ^2d - 7c + 4d - 10

Explanation:

First write equastion as seen:

5c^2d - 4c + 3d - 3 + 2c^d - 3c+ d - 7

Next add the c^2d’s together:

7c^2d - 4c + 3d - 3 + 3c + d - 7

Add the c’s together:

7c^2d - 7c + 3d - 3 + d - 7

Add the d’s:

7c^2d - 7c + 4d - 3 - 7

Lastly add the normal numbers:

7c^2d - 7c + 4d - 10

Thus, that is your answer!

Hope this helps! :)

((just a formatting note - n^2 is the same as n squared))

To answer the question you have to group all like terms together
(eg n^2 + n^2 is 2n^2)

5c^2d - 4c + 3d - 3 + 2c^2d - 3c + d - 7
First group the similar terms together
5c^2d + 2c^2d - 4c - 3c + 3d + d - 3 - 7
Then add or subtract the terms from each other depending on the symbol separating them
5c^2d + 2c^d = 7c^2d
-4c - 3c = - 7c
3d + d = 4d
-3 - 7 = -10

Then collect the now simplified terms together to make an expression
7c^2d - 7c + 4d - 10
The correct answer is the second box down.

Which functions are decreasing?

Select ALL answers that are correct.

Answers

Answer:

1st and 2nd graph are decreasing functions

Step-by-step explanation:

Increasing function means, as we go from left to right, the function goes "ABOVE" and thus, increases.

Decreasing function means, as we go from left to right, the function goes "DOWN" and thus, decreases.

We will look at all the 4 graphs given. We look from "LEFT-TO-RIGHT".

The first one goes "DOWN", so its decreasing.

The second one also goes "DOWN, so this is decreasing as well.

The third one goes "UP", so it is increasing.

The fourth function stays the same, so it is neither increasing nor decreasing. It is constant.

Thus,

1st and 2nd graph are decreasing functions, only

True or False: The given number is a solution to the corresponding equation

a=−3

4a+3=−9

Answers

Answer:

TRUE.

a = -3 is a Solution to the equation 4a + 3 = -9  

Step-by-step explanation:

Given:

a = -3

4a + 3 = -9

Proof for Solution:

Let there be two part of the equation, left-hand side and right hand side.

If a  = -3 is a solution ,

left-hand side = right hand side

left-hand side = 4a +3

                       = 4×-3 + 3...............{ For a = -3}

                       = -12 + 3

                       = -9

                       = right hand side

∴ left-hand side = right hand side

a = -3 is a Solution to the equation 4a + 3 = -9  

If h(x) = 5 + x and k(x)= 1/x, which expression is equivalent to (kxh)(X)?

Answers

Answer:

It can be solve this in two ways,

1) as if the h(x) = 5x and 2) as if h(x) = 5 + x

1) If h(x) = 5x and k(x) = 1/x

Then (k o h) (x) = k ( h(x) ) = k(5x) = 1/(5x)

2) If h(x) = 5 + x and k (x) = 1/x

Then (k x h)(x) =k ( h(x) ) = k (5+x) =  1 / [5 + x]

1/(5+x) is the correct answer

Step-by-step explanation:

(2x^3-4x^2-3x-9) by x-3

Answers

Answer:

2x² + 2x + 3

Step-by-step explanation:

x = 3 is a zero of both the numerator and the denominator, so the denominator will factor completely into the numerator with no remainder.  Using grouping to factor:

(2x³ − 4x² − 3x − 9) / (x − 3)

(2x³ − 4x² − 6x + 3x − 9) / (x − 3)

(2x (x² − 2x − 3) + 3x − 9) / (x − 3)

(2x (x − 3) (x + 1) + 3 (x − 3)) / (x − 3)

2x (x + 1) + 3

2x² + 2x + 3

To use long division instead, see image.

Which graph represents 7 x − 2 y ≤ 5 7x−2y≤5

Answers

Answer:

7x-2y≤5

7x-2y≤5

Step-by-step explanation: Graph is down below!!

Hope this helps you out!☺

Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.

We need to find the graph which represents the inequality 7x−2y≤5.

What is inequality?

In mathematics, a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Now,

Write in y=mx+b form.

y≥7/2x-5/2

Use the slope-intercept form to find the slope and y-intercept.

Slope: 7/2

y-intercept:(0, -5/2)

Graph a solid line then shade the area above the boundary line since y is greater than 7/2 x-5/2 as given below.

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2. What elevation is Point E on Map 1? *


10 feet

30 feet

50 feet

70 feet


3. What elevation is Point F on Map 1? *


10 feet

30 feet

50 feet

70 feet

Answers

Answer:

c then b

Step-by-step explanation:

2 - The elevation at Point E is 50 feet, marked by a contour line, 3 - Point F is at 70 feet elevation, illustrating the informative nature of topographic maps.

On Map 1, Point E is situated at an elevation of 50 feet, as it lies directly on the contour line representing this specific elevation. Contour lines on a topographic map connect points of equal elevation, allowing us to visualize the three-dimensional terrain on a two-dimensional surface.

In this context, every point on the contour line labeled "50 feet" shares the same elevation—50 feet above a reference point, typically sea level. Moving to Point F on Map 1, it is positioned on the contour line corresponding to an elevation of 70 feet.

This indicates that Point F is situated 70 feet above the same reference point. Topographic maps are invaluable tools for understanding the landscape's elevation variations, aiding hikers, geologists, and cartographers in navigating and representing the Earth's surface features accurately.

The contour lines on such maps provide a detailed depiction of the elevation changes, and by closely following them, one can trace the undulations of the terrain.

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What is the area of the rectangle
A) 50 units
B) 54 units
C) 60 units
D) 65 units

Answers

Answer:

I'd say C.60but because of the half units its possibly B. but definitely not A or D.

Step-by-step explanation:

Because the short sides are approximately 6 units long and the long sides are 10 units long. You multiply it to find the area and you get 60.

hope this helps

The area of the graph rectangle is 60 sq. units.

The correct option is D) 60 sq. units.

What is the area of the rectangle on the graph?

The area of a rectangle is expressed as:

Area = length × width

First, we use the distance formula to find the length and width of the rectangle.

[tex]Distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

From the graph, the length is between the points (-1,1) and (8,-2):

Hence;

[tex]Length = \sqrt{(8-(-1))^2 + (-2 - 1)^2}\\\\Length = \sqrt{(8+1)^2 + (-2 - 1)^2}\\\\Length = \sqrt{(9)^2 + (-3)^2}\\\\Length = \sqrt{81 + 9}\\\\Length = \sqrt{90}\\\\Length = 3\sqrt{10}[/tex]

Next, we find the width which is between the points (-1,1) and (-3,-5):

[tex]Width = \sqrt{(-3 - (-1))^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-3 + 1)^2 + (-5 - 1)^2}\\\\Width = \sqrt{(-2)^2 + (-6)^2}\\\\Width = \sqrt{4 + 36}\\\\Width = \sqrt{40}\\\\Width = 2\sqrt{10}[/tex]

Now, plug the values for the length and width into the above formula and solve for the area:

Area = length × width

Area = 3√10 × 2√10

Area = 3 × 2 × 10

Area = 60 sq. units

Therefore, the area measures 60 sq. units.

Option D) 60 sq. units is the correct answer.

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The table shows the age and finish time of ten runners in a half marathon.

Identify the outlier in this data set. Drag into the table the ordered pair of the outlier and a reason why that point is an outlier.

Answers

Answer:

Left box: Outlier in this data set is (57,132)

Right box: because the finish time looks faster than expected for the age.

Step-by-step explanation:

As per the given table shows the [tex]age[/tex] and [tex]finish \ time[/tex] of [tex]10[/tex] runners.

It is clear that people of age around [tex]35[/tex] are finishing at around [tex]142 \ minutes[/tex]

and person with older age takes longer to finish.

One person of age [tex]57[/tex] finishes in [tex]175 \ minutes[/tex] , that looks as expected.

Another person of same age [tex](57)[/tex] finishes it too fast which is unexpected.

Therefore [tex](57,132)[/tex] is an outlier, because it looks a faster finish as per expected.

Answer:

The left box = (57 , 132)

The right box= The finished time is expected for the age.

Step-by-step explanation:  

Which of the following is a step in simplifying the expression (see first image)

(the second image is the options for multiple choice)


Please be serious and don't joke around! <3 I really need help.

Answers

Answer:

D) (x^-3*y^-12)/(x^15*y^-15)

Step-by-step explanation:

If you simplify that further, then you'll get x^(-18)*y^3.

Given that (3, 3, -2) is a solution to the given
system, which of the following statements are
possibly true of the system?
Check all of the boxes that apply.
The three planes represented by the
equations in the system are parallel.
The system is consistent.
The system is inconsistent.
The system is independent.

Answers

The system is consistent

Answer: B & D

Step-by-step explanation:

The system is consistent.

The system is independent.

One of the solutions to the equation 5x^2+bx+12=0 is − 4/5 . Find the other solution.

Answers

Answer:

-3 is the other solution.

Step-by-step explanation:

As, [tex]\frac{-4}{5}[/tex] is One of the solutions of the equations , So, it should satisfy the equation.

Putting [tex]\frac{-4}{5}[/tex]  in equation 5[tex]x^{2}[/tex] + bx + 12 = 0 ,

We get,

               5×[tex]\frac{-4}{5}[/tex]×[tex]\frac{-4}{5}[/tex]   +    b×[tex]\frac{-4}{5}[/tex]   +  12 = 0.

 5×[tex]\frac{16}{25}[/tex]  +  [tex]\frac{-4b}{5}[/tex]   +  12 = 0.

 After solving ,    16 - 4b  + 60  = 0.

                             4b = 76

                                b = 19.

So, the equation is  5[tex]x^{2}[/tex]  +  19x  + 12 = 0.

      After factorizing , 5[tex]x^{2}[/tex]  + 15x + 4x + 12 = 0.

                                    5x(x+3) + 4(x+3) = 0

                                     (5x+4)(x+3) = 0

Clearly the roots of the equation are  -3 and [tex]\frac{-4}{5}[/tex] .

So, the other solution is -3.

Help with question 1 please.

Answers

Answer:

x is more than or equal to 35

20 points!!!
What is the equation in point slope form of the line that passes through the point (−1, −3) and has a slope of 4?



y+3=4(x+1)

y+1=4(x+3)

y−3=4(x−1)

y−1=4(x−3)

Answers

Answer: y+3 = 4( x + 1)

Step-by-step explanation:

The equation in point slope form is given as :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] ) , where m is the slope

slope = 4

point given : (-1,-3)

Using the formula :

y - [tex]y_{1}[/tex] = m ( x - [tex]x_{1}[/tex] )

and substituting the value , we have

y - (-3) = 4 (x -{-1} )

y+3 = 4( x + 1)

A line segment has endpoints of (-3, 2) and (5, -2). Find the distance between the endpoints.

Round your answer to the nearest tenth (one number past the decimal). If the second number past the decimal is 5 or greater, round up.

Answers

Answer:

[tex]d=8.9\ units[/tex]

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

we have

(-3, 2) and (5, -2)

substitute the values in the formula

[tex]d=\sqrt{(-2-2)^{2}+(5+3)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(8)^{2}}[/tex]

[tex]d=\sqrt{80}\ units[/tex]

[tex]d=8.94\ units[/tex]

Round to the nearest tenth

[tex]d=8.9\ units[/tex]

The sum of three consecutive integers is 105. What are the three integers?

Answers

Answer:

34, 35, 36

Step-by-step explanation:

34 + 35 + 36 = 105

Answer:

34

35

36

Step-by-step explanation:

Here we will use algebra to find three consecutive integers whose sum is 105.

We assign X to the first integer. Since they are consecutive, it means that the 2nd number will be X+1 and the third number will be X+2 and they should all add up to 105. Therefore, you can write the equation as follows:

X + X + 1 + X + 2 = 105

To solve for X, you first add the integers together and the X variables together. Then you subtract 3 from each side, followed by dividing by 3 on each side. Here is the work to show our math:

X + X + 1 + X + 2 = 105

3X + 3 = 105

3X + 3 - 3 = 105 - 3

3X = 102

3X/3 = 102/3

X = 34

Which means that the first number is 34, the second number is 34+1 and third number is 34+2. Therefore, three consecutive integers that add up to 105 are:

34

35

36

Svetlana’s hair is 3 cm long. Her hair grows 1.5 cm per month. Svetlana wanted her hair to be less then 18 cm long. Write an inequality to determine the number of months Svetlana can allow her hair to grow. Then, solve the inequality.

Answers

Svetlana can allow her hair to grow for 10 months.

Step-by-step explanation:

Current length of hair = 3cm

Growth per month = 1.5cm

Let, m be the number of months.

As she wants her hair no longer than 18cm, therefore, according to given statement;

1.5m + current length of her hair ≤ 18

[tex]1.5m+3\leq 18\\1.5m\leq 18-3\\1.5m\leq 15[/tex]

Dividing both sides by 1.5

[tex]\frac{1.5m}{1.5}\leq \frac{15}{1.5}\\m\leq 10[/tex]

Svetlana can allow her hair to grow for 10 months.

Keywords: linear inequality, division

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Richard paints a picture on a rectangular canvas that is 3 feet by 2.64 feet. What is the area in Richards painting?​

Answers

Answer:

7.92 Feet

Step-by-step explanation:

Since area is Length × Height in comparison to perimeter being Length + Length + Height + Height, the equation is simply:

3 × 2.64 = 7.92 Feet

Final answer:

The area of Richard's painting is calculated by multiplying the length of 3 feet by the width of 2.64 feet, which equals 7.92 square feet.

Explanation:

To calculate the area of Richard's rectangular painting, we use the formula for the area of a rectangle, which is the product of its length and width. In this case, the length of the canvas is 3 feet and the width is 2.64 feet. So, the calculation to find the area will be as follows:

Area = Length × Width

Area = 3 feet × 2.64 feet

Area = 7.92 square feet

Therefore, the area of Richard's painting is 7.92 square feet.

Help with hw due tomorrow plz help!!!!!!!!

Answers

Item + tax = total price

Answer: see the explanation

Step-by-step explanation:

Add the price of the item and the tax on the item, or just multiply the price of the item by the tax rate plus 1 (to include the price of the item)

Let's say the cost of an item is

100 dollars and the tax rate is 5% or 0.05. To get the amount of tax that has to be paid on

the $100 item, multiply 100 by 0.05 to get 5 .

Add the amount of the tax ( $5 ) to the price of the item ( $100) to get a total cost of $100.

Or you could multiply 100 by 1+0.05 or 1.05 to get the same answer. The reason why the

1 can be added in is because the total cost includes the price of the item, not just the sales tax on it.

What is the solution set of 4x^2-36= 0?

(-3)
(3)
(-3,3)

Answers

Answer:

(-3, 3).

Step-by-step explanation:

4x^2-36= 0

4x^2 = 36    Taking square roots of both sides:

2x = +/- 6

x = +/- 3.

Answer:

(-3, 3)

Step-by-step explanation:

The equation is:

[tex]4x^2-36=0[/tex]

to clear for x, first we move the -36 to the right as a +36 (or you can also say that we add 36 to both sides):

[tex]4x^2=36[/tex]

dividing by 4:

[tex]x^2=36/4\\x^2=9[/tex]

taking the square root:

[tex]x=[/tex] ± [tex]\sqrt{9}[/tex]

we add the ±  because a square root has two solutions, a positive one, and a negative one.

Then we get:

[tex]x=[/tex] ± 3

The solutions are -3 and +3

which is represented in the option (-3, 3)

the first four terms of a geometric sequence is a1 = 3
a2=12
a3=48
a4=192
What formula can be used to find an
HURRY PLEASE

Answers

Answer:

not 100% sure of this but I think its a4=192

A sphere has a diameter of 10 in. What is the volume of the sphere?
v= 125 in.
©
0
v= 500 in
v = 590 x in.
0
v - 4000 x in.
0

Answers

Answer:

The volume of sphere is 500 in³

Step-by-step explanation:

Given:

Diameter of sphere is 10 in.

Now, to find the volume we need radius.

Radius(r) = half of the diameter

[tex]r=\frac{10}{2}[/tex]

[tex]r=5[/tex]

And, now putting the formula to get the volume of sphere:

[tex]volume(v)=\frac{4}{3}\pi r^{3}[/tex]

Putting the value of π = 3.

[tex]v=\frac{4}{3} \times 3.14\times 5^{3}[/tex]

[tex]v=1.33\times 3.14\times 125[/tex]

[tex]v=522.025[/tex]

So, the volume is 522.025 in³.

By estimating the value the volume is 500 in³.

Therefore, the volume of sphere is 500 in³.

Answer:

B

Step-by-step explanation:

for those that didnt understand like me

mrs. white buys a used car for $3,000 she makes monthly payments of $300 until the car is paid for. mr. brown buys a used car for $2,400 his makes a monthly payment of $300 until the car is payed for. find and compare the rate of change and the inital value

Answers

Answer:

Initial value for Mrs. White is $600 more than Mrs. Brown.

The rate of change is same for both.

Step-by-step explanation:

Cost of car purchased by Mrs. White = $3,000

Rate at which she pays for the car = $300 per month

Cost of car purchased by Mrs. Brown = $2,400

Rate at which she pays for the car = $300 per month

So,

Initial value for Mrs. White was =$3,000

Initial values for Mrs. Brown was =$2,400

difference in initial values  [tex]=3000-2400[/tex]  =$600

∴ Initial value for Mrs. White is $600 more than Mrs. Brown.

Rate of change of payment due for  Mrs. White = $300 per month

Rate of change for payment due for Mrs. Brown = $300 per month

∴ The rate of change is same for both.

Since Mrs White had a higher initial value than Mrs Brown and both having same rates of change, therefore Mrs. White will take a longer time to pay the due.

Elijah and Jonathan play on the same soccer team. They have played 3 of their 15,
games. They each create a model to represent x, the number of games their team has left
to play. Their models are shown below. Explain whether each model is correct.

Who is correct

Answers

Answer:

Only Elijah's model is correct

Step-by-step explanation:

The data given in the question tells us they have 12 games left on their soccer team. Each one of them tried to simulate the fact by creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance. On the other side, he placed 15 cubes of value 1. He was obviously modeling the fact that 15 cubes (games due to play in our case) should be equal to 3 cubes (games already played) plus the x numbers left to play

This model if perfect, since the only way to equilibrate the balance is setting x to 12, the games left to play

Jonathan used a table with 3 x's in a row and a 15 in the second row, trying to model the same situation. To our interpretation, this table doesn't show the number of games left to play. If we equate 3x = 15, we get x=5 which has nothing to do with the situation explained in the question, so this model is not correct.

Elijah's model is correct .

Elijah and Jonathan play on the same soccer team. They have played 3 of their 15 games.  

x is the number of games that are left to be played.

Elijah and Jonathan have 12 games left on their soccer team.

Elijah  and Jonathan  both try to simulate the situation which are shown in figure.

Creating some model which look like a balance between quantities.

Elijah placed 3 cubes of value 1 and a cube of value x on one side of a balance.

On the other side Elijah placed 15 cubes.

The value of each cube = 1

so  15 [tex]\times 1 = 15[/tex] which are equal to total number of games.  

Since 3 games are already played so on the left hand side

3 boxes of magnitude 1 each are placed.

[tex]x[/tex] is the number of  games that are left.

Jonathan uses a table  with  three x values  in a row and a 15 is the total number of games to be played are represented in the second row trying to model the same situation.

This table doesn't show the number of games left to play.

Which are 12 in number

According to Jonathan's model

[tex]3x = 15 \\x =5[/tex]

This does not model the number of games left which are 12 in number and hence

Jonathan's model  does not explains the situation

For more information please refer to the link below

https://brainly.com/question/24197246

A net force F acts on a mass m and produces an acceleration a. What mass would accelerate at a rate 8a if the force is decreased to F/2?​

Answers

Answer:

The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]

Step-by-step explanation:

Given as :

The net force = F Newton

The mass of the object = m kg

The acceleration = a  m/s²

Now, As The force is define as the product of mass and velocity

So, F = m × a

Now, Again , if the acceleration = 8 a

and The force decrease to [tex]\frac{F}{2}[/tex] = 0.5 F

So, Let The mass = M

∵ F = m × a

∴ mass = [tex]\frac{\textrm Force}{\textrm acceleration}[/tex]

Or. M = [tex]\frac{\textrm 0.5 F}{\textrm 8 a}[/tex]

or, M =0.0625 × [tex]\frac{F}{a}[/tex]

∴ M = 0.0625 × m = [tex]\frac{m}{16}[/tex]

so, The mass =  [tex]\frac{m}{16}[/tex]

Hence The mass of the object if body accelerate at the rate 8 a is [tex]\frac{m}{16}[/tex]  Answer

Final answer:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a). If the force is decreased to F/2, the mass that would accelerate at a rate 8a can be found by rearranging the equation and solving for mass.

Explanation:

According to Newton’s second law of motion, the force (F) acting on an object is equal to its mass (m) multiplied by its acceleration (a), expressed as F = ma.

If the force is decreased to F/2, the new force is now (F/2). To find the mass (m) that would accelerate at a rate 8a, we need to rearrange the equation as follows:

(F/2) = m * (8a)

To solve for the mass (m), we divide both sides of the equation by (8a), which gives us:

m = (F/2)/(8a)

Therefore, the mass that would accelerate at a rate 8a when the force is decreased to F/2 is (F/2)/(8a).

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