A grocer makes a display of cans in which the top row has one can and each lower row has two more cans than the row above it. If the display contains $100$ cans, how many rows does it contain

Answers

Answer 1

A grocer makes a display of cans in which there are 10 rows.

The top row has one can and each lower row has two more cans than the row above it.

We can write it as sequence:

1, 3, 5, 7, . . .

We can observe that it's an arithmetic sequence: 1, 3, 5, 7, . . . , 2n-1

We know that the formula for the sum of n-terms of arithmetic sequence:

S(n) = (n/2)(1 + 2n-1)

Here, Sn = 100

So, (n/2)[1 + 2n-1] = 100

n(1 + 2n + 1)

n(2n) = 200

2n^2 = 200

n^2 = 100

n = 10

Hence, the number of rows = 10

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Related Questions

What is the smallest positive integer that is both a multiple of $7$ and a multiple of $4$?

Answers

The smallest positive integer that is both multiple of 4 and 7 is 2

What are multiples?

In mathematics, multiples are the results of multiplying an integer by a given number.

The given numbers for this problem are 4 and 7. The positive multiples of 4 and 7 will be listed and the first number that appeared in the both multiples s the smallest positive integer that is both a multiple of 7 and a multiple of 4.

The multiples of 4

4 8 12 16 20 24 28 32 36 .......

The multiples of 7:

7 14 21 28 35 42 49 56 63 70 77 84 91 98 .....

The smallest common multiple is 28

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Customary System Units Metric System Units 1 gallon 3.79 liters 1 quart 0.95 liters 1 pint 0.473 liters 1 cup 0.237 liters Approximately how many centiliters are in 3 quarts

Answers

3 quarts is equal to approximately 285 centilitres.

To Calculate this we have:

3 quarts is equal to 3 x 0.95 liters = 2.85 liters.

1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.

Therefore, 3 quarts is equal to approximately 285 centilitres.

In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.

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simplify (2√2+3√5) square 2​

Answers

Answer:

The answer is 22.4

help i have 5 mins left

Answers

Answer: c = P - a - 5

Step-by-step explanation:

P= a + 5 + c

P - a - 5= c

Mark each of the following graphs as (a) a function, but not one-to-one, (b) one-to-one function, or (c) not a function. In each case, explain how you know. (1 point each)

Answers

The graph is forming a function but it is not an one-one function.

If the vertical line test is satisfied, then the graph represents a function and a vertical line will cross it at most once.

If a horizontal line crosses the graph in no more than one spot, the function is one-to-one and passes the horizontal line test.

The graph in this case is made up of several horizontal, non-overlapping lines. It is a function and passes the vertical line test, however a horizontal line can cross the graph at any number of locations (is not one-to-one).

However, the graph is not a one-to-one function.

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What is the midpoint of f/x )=( x 2 )( x 4?

Answers

The midpoint of the x-intercepts of f(x) = (x - 2)(x - 4) is (3, 0).

The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.

A compass and straightedge setup can be used to locate the midpoint of the line segment they determine given two points of interest. By initially building a lens out of circular arcs with equal radii centered at the two endpoints and joining the cusps of the lens, one can determine the midpoint of a line segment immersed in a plane. The midpoint of the segment is then the place where the line joining the cusps intersects the segment.

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55 pecans put them in 2 buckets where one has 15 more than the other

Answers

The number of pecans in each bucket will be 20 and 35.

How to illustrate the expression?

From the information, there are 55 pecans are put in 2 buckets where one has 15 more than the other. An expression show the relationship between the variables.

In this case, 55 pecans put them in 2 buckets where one has 15 more than the other.

This will be:

x + x + 15 = 55

2x + 15 = 55.

Collect the like terms

2x = 55 - 15

2x = 40

Divide

x = 20

The other number will be:

x + 15.

= 20 + 15

= 35

The numbers are 20 and 35.

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55 pecans are put in 2 buckets where one has 15 more than the other. What is the amount in each bucket.

The points (p, 6) and (4, 7) fall on a line with a slope of 1/9. What is the value of p?
Please find the missing coordinate using slope.

Answers

Step-by-step explanation:

(7 - 6)/(4 - p)= 1/9

4 - p = 9

-p= 5

p = -5

Find the value of x.

Answers

Answer:

x = 32

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

All the indicated angles in the diagram are exterior angles of the polygon.

sum the 5 exterior angles and equate to 360

2x + 71 + 85 + 44 + 3x = 360

5x + 200 = 360 ( subtract 200 from both sides )

5x = 160 ( divide both sides by 5 )

x = 32

A grocery tore ha 13%-off ale on all bread. You decide to purchae 6 loave of bread. Let b be the original price of a loaf of bread. Expand the expreion 6(b-0. 13b). Once the expreion i expanded, who do the term repreent

Answers

6b - 0.78b it will result after expanding the expression.

What is an expression?

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. Any one of the following mathematical operations can be used i.e. addition, subtraction, multiplication, or division.

There are three different expression types:

There is just one arithmetic value that an arithmetic expression may produce.A character expression evaluates to just one character value.One logical value is produced by the evaluation of a logical or relational statement.

Let, b represent the original price of a loaf of bread.

Given that,

A grocery store has 13%-off sale on all bread.

This means that the amount by which the price of bread was reduced would be

13/100 × b = 0.13 × b = 0.13b

The new price for the loaf of bread would be: b - 0.13b

you decide to purchase 6 loaves of bread. The expression would be:

6(b - 0.13b)

Expanding the expression, it becomes: 6b - 0.78b

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Would it be possible for 3x2 to equal 1?

Answers

Answer:

no

Step-by-step explanation:

3x2=6 ;-;

Is it possible for [tex]3\times2[/tex] to equal 1?

[tex]3\times2=6[/tex]

[tex]6\neq 1[/tex]

Therefore, [tex]3\times2[/tex] DOES NOT equal to 1.

A baby manatee weighs 58 kilograms. At birth the manatee weighed 30 kilograms. What is the percent increase in the manatee's weight rounded to the nearest whole number?

Answers

Answer:

93.3% i hope this is right

Step-by-step explanation:

percentage increase= final-original/originalx100

58-30/30x100=93.3333%

In the triangle below, with right angle R, suppose that m is Angle Q=(5x-13) and m is Angle S=(4x-5) Find the degree measure of each angle in the triangle.

Answers

Answer:

Degree measure of each angle is 90⁰, 47⁰ and 43⁰

Step-by-step explanation:

since the triangle is right angled, we assume that Q and S are the other angles of this triangle R

Thus using the concept that angles inside a triangle add up to 180⁰ and we already have one angle as 90⁰( since the triangle is right angled). we therefore know that Q + S = 90⁰

5x - 13 + 4x - 5 = 90⁰

9x = 108

x = 12

We now replace x in Q and S to get the angles

Q = 5(12) -13

= 47⁰

S = 4(12) - 5

= 43⁰

( r - 8 ) - ( r + 15 )

Find the Sum or Difference! :)

Answers

Answer:

-23

Step-by-step explanation:

Open up the parenthesis

R - 8 - R - 15

R - R - 8 - 15

-23

Answer:-23    ITS SUPER EASY:0

Step-by-step explanation:

Open up the parenthesis

R - 8 - R - 15

R - R - 8 - 15

-23

Can u please help me...............

Answers

Please find attached the graph showing the translation transformation of the triangle ΔABC with vertices A(2, 1), B(-1, 2), and C(-2, -1) using the rule (x, y) → (x - 1, y - 3), to produce triangle ΔA'B'C' with vertices A'(1, -2), B'(-2, -1), and C'(-3, -4), created with MS Excel

What is a translation transformation?

A translation transformation is one in which the location of the points on the original figure slides by the same amount and in the same direction to form the image.

The vertices of the triangle ΔABC are; A(2, 1), B(-1, 2), and C(-2, -1)

The specified transformation is; (x, y) → (x - 1, y - 3)

Applying the specified transformation, we get;

A(2, 1) ⇒ (x, y) → (x - 1, y - 3) ⇒ A'(2 - 1, 1 - 3) = A'(1, -2)

B(-1, 2) ⇒ (x, y) → (x - 1, y - 3) ⇒ B'(-1 - 1, 2 - 3) = B'(-2, -1)

C(-2, -1) ⇒ (x, y) → (x - 1, y - 3) ⇒ C'(-2 - 1, -1 - 3) = C'(-3, -4)

The vertices of the image ΔA'B'C' of the triangle ΔABC following the transformation, (x, y) → (x - 1, y - 3) are therefore;

A'(1, -2), B'(-2, -1), C'(-3, -4)

Please find attached the graph of the triangle ΔABC and its image ΔA'B'C' after the translation (x, y) → (x - 1, y - 3), created with MS Excel

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PLEASE HELPPP

what is the simplified expression for (picture below)

Answers

Answer:

[B] 6²

Step-by-step explanation:

Given:

[tex]\frac{6^4\cdot \:6^3}{6^5}[/tex]

Solve:

Add the exponents - [tex]6^4 \times 6^3=6^7[/tex]

Now we have - [tex]\frac{6^7}{6^5}[/tex]

Exponent Rule: [tex]\frac{x^a}{x^b}=x^{a-b}[/tex]

Which means - [tex]\frac{6^7}{6^5}=6^{7-5}[/tex]

Subtract the exponent - [tex]6^2[/tex]

Hence, the answer is [B] 6²

RevyBreeze

what's the equation of a line in slope-intercept form of a line that has a slope of -6 and contains (3,-4)
HELP ME PLEASE!!!!!!

Answers

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ - 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{- 6}(x-\stackrel{x_1}{3}) \implies y +4= -6 (x -3) \\\\\\ y+4=-6x+18\implies {\Large \begin{array}{llll} y=-6x+14 \end{array}}[/tex]

Graph the following system of equations.
y = 3x + 15
3x + 3y = 9
What is the solution to the system?
There is no solution.
There is one unique solution (-3, 6).
There is one unique solution (0, 15).
There are infinitely many solutions.

Answers

Answer:

There is one unique solution (-3, 6)

Step-by-step explanation:

Desmos graphing calculator helps a lot with this stuff

Answer: b) there is only one unique solution (-3, 6)

Step-by-step explanation:

$710 is invested in an account earning 3.7% interest (APR), compounded monthly. Write a function showing the value of the account after tt years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.

Answers

The function for the amount after {t} years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]

What is compound interest?

Compound interest is the addition of interest to the principal sum of a loan or deposit. Mathematically -

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

where -

[A] = final amount

[P] = initial principal balance

[r] = interest rate

[n] = number of times interest applied per time period

[t] = number of time periods elapse

Given is that $710 is invested in an account earning 3.7% interest (APR), compounded monthly.

We can write -

A = 710(1 + 0.37/12)¹²⁽¹⁾

A = 710(1 + 0.037/12)¹²

A = 710(1 + 0.031)¹²

A = 710(1.031)¹²

A = 710 x 1.45

A = 1029.5

Let the annual growth rate be R. Then, we can write the function for annual growth rate after {t} years as -

1029.5 = [tex]$ 710(1 + R/1)^{t}[/tex]

1029.5 = [tex]$710(1+R)^{t}[/tex]

1.45 = [tex]$(1 + R)^{t}[/tex]

1.45 = 1 + tR + .....                        {Binomial expansion}

Neglecting the binomial series from the third term as the value of the terms become negligible -

1.45 = 1 + tR

R = 0.45/t

Function for the amount after t years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]= A

Therefore, the function for the amount after {t} years can be written as -

[tex]$710(1 + 0.45/12nt)^{nt}[/tex]

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How do you find the difference between two different numbers?

Answers

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them.

Subtract the smaller of the two numbers from the larger of the two numbers to discover the difference between them. The difference between the two numbers is the sum's product.

Subtracting two integers from each other is a type of subtraction.

The process for determining the difference between two decimals and two whole numbers is the same.

We only add a new step.

Finding the difference between 8.967 and 7.2, for instance, could appear more difficult.

To give them all the same amount of decimal places, we must first convert each decimal.

7.2 becomes 7.200 as a result.

The computation may now be done as before:

8.967 - 7.200 = 1.767

Therefore, there is a 1.767 discrepancy between these figures.

In order to find the difference between two fractions, simplify and find the lowest common denominator of each fraction.

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What is the equation of the function
shown in the graph, given that the
equation of the parent function is
f(x) = (-/-)² ?
(}})

Answers

The equation of the function shown in the graph is f(x) = (-2x)^2.

What is function?

In mathematics a function is a relation between two states that assigned to each element of the first set exactly one element of the second set in order words it is the rule that is describe how unstead of values is related to another set a values function are used to model real voice scenario and to solve mathematical problems example of function include linear equation polynomials and trigonometric function.

This is based on the equation of the parent function, which is f(x) = (-/-)^2. The graph shows that the function has been shifted two units to the left, which is why the coefficient of x is -2 instead of -1.

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How do you plot a graph step by step?

Answers

Plotting a graph step by step is mentioned below.

Define Graph.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

What is Bar graph?

Using rectangular bars with heights or lengths proportionate to the values they represent, a bar chart or bar graph displays categorical data. Both a vertical and a horizontal bar plot are possible. A column chart is another name for a vertical bar graph.

There are a few steps to follow when plotting a graph:

Identify the variables in the problem and choose which one to plot on the x-axis and which one to plot on the y-axis.Determine the range of values for each variable. This will help you decide how big to make the scales on the x and y-axis.Choose a scale for each axis. The scale should be such that all the points in the problem can be plotted on the graph. A typical scale is to have equal intervals between each tick mark on the axis.Plot the points on the graph by locating their x-coordinate and y-coordinate on the x-axis and y-axis, respectively, and connecting them with a dot.Draw the x- and y-axes and label them with the appropriate units and ranges. Be sure to include a label on the graph itself so that it's clear what the graph represents.Plot any lines or curves that are also a part of the problem. This could be a line of best fit, a linear regression line, a polynomial function or any other lines or curves that the problem calls for.Once you finished with the line/curve, it is a good practice to give the graph a title and to label the axis with the units used.Lastly, review the graph and ensure that it is accurate and clearly presents the information from the problem.

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I want to know how to get the GCF and LCM of 8,24,48

Answers

Answer:

GCF = 8

LCM = 48

Step-by-step explanation:

5)48 I need help I suck at math

Answers

On solving the question resultant answer from the given data we have  algebraic  expression 5/48 could be  0.10

what is an algebraic expression ?

Algebraic expression can be defined as the combination of  constants , variables and operators. Algebraic expressions are the concept of expressing numbers using letters or alphabets without specifying their real values. The basics of algebra taught us a way to specific an unknown value the usage of letters which includes x, y, z, and many others. those letters are called here as variables. An algebraic expression may be a combination of each variables and constants. Any value this is positioned before and increased through a variable is a coefficient.

So, the given expression , 5/48

5/48 = 0.10

The resultant answer from the given expression 5/48 could be 0.10

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The correct question is -

Solve the equation.

p= −6p=48

Please help I suck at math

A newsletter publisher believes that more than 47% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to substantiate the publisher's claim?

Answers

There is no sufficient evidence at the 0.05 level to substantiate the publisher's claim

How to determine the substantial claim?The parameters for the claim is more than 47% of their readers own a personal computer0.05 level of significance

Note that the significance level, also known as alpha or α, is a measure of the strength of the evidence that must be present in your sample before you will reject the null hypothesis and conclude that the effect is statistically significant

In conclusion, the advertiser failed to reject the null hypotenuse so this would mean there is not sufficient evidence at the 0.02 level of significance to say that the percentage of people who own a Rolls Royce is higher than 47%

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without computing, decide whether the vaule of each expresstion is much smaller than 1, close to 1, or much greater than 1

Answers

Answer: uhm...

Step-by-step explanation:

2...?

How do you find the ordered pair?

Answers

On a Cartesian (or "coordinate") plane in which  each point is represented by an ordered pair (x , y) belongs to  x coordinate  , y coordinate .

An ordered pair is a set of numbers in which it gives the location of a point on a coordinate plane.

The ordered pair is always expressed exactly the same way (x , y).

The first number  in an ordered pair represents the x coordinate on the plane while the second number in an ordered pair  represents the y coordinate.

The x-coordinate shoes that  how far away the point is horizontally from the x-axis.

The y-coordinate shows that  how far away the point is vertically from the x-axis.

Quadrant I: the upper-right quadrant of the plane in which all points in this quadrant have  the  positive x coordinates and positive y coordinates as { (+,+)}  ,  {(+,+)}

Quadrant II: the upper-left quadrant of the plane in which all points in this quadrant have negative x coordinates and positive y coordinates

{ (+,-)}{ (+,-)}

Quadrant III: the lower-left quadrant of the plane in which  all points in this quadrant have negative x coordinates and negative y coordinates

{ (-,-)}{(-,-)}

Quadrant IV: the lower-right quadrant of the plane in which  all points in this quadrant have positive x coordinates and negative y coordinates

{(+,-)}{ (+,-)}

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How do you write coordinates for translation?

Answers

Coordinates (x ,y ) of the given geometrical figure after translation is written as ( x + h , y + k ) where h ∈ R  and k ∈ R.

As given in the question,

Let us consider the coordinates of any geometrical figure is represented by ( x, y ) in the coordinate plane.

Translation is the representation of transformation the change in the location of the given geometrical figure without change in the shape and size.

It can be translated in four ways :

Translation to the right is written as ( x + h , y )

Translation to the left is ( x - h, y)

Translation in the up is ( x, y + k )

Translation in the down is ( x , y - k ).

Therefore, the original coordinate ( x ,y )  after translation written as

( x + h , y + k ) where h ∈ R  and k ∈ R.

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A hot air balloon is cruising at an altitude of 120 m above ground when it begins its descent the balloon descends at a rate of 4.5 m per minute explain how you would set up the equation to model when the balloon will reach an altitude of 75 m above ground then solve the equation and check your solution

Answers

The equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

What is an equation?

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation.

The balloon will reach an altitude of 75 meters above the ground.

Now, 120-75 =45 meters

Let t be the time to descends 45 meters

So, 120 - 4.5t= 75

= -4.5 t = 75-120

= -4.5t = -45

= t = -45/(-4.5)

= t = 10 minutes

Hence, the equation to model the given situation is 120 - 4.5t= 75 and the solution to the equation is 10 minutes.

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Which expression simplifies to
m-2
—— ?
m-1

Answers

C (m ^ 2 - m - 2)/(m ^ 2 - 1)
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