find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1

Answer:  We can start by using algebra to represent the information given in the problem. Let x be the number of gallons consumed by the first car and y be the number of gallons consumed by the second car.

We know that:

x + y = 45 (the total number of gallons consumed by both cars)

15x + 30y = 975 (the total number of miles driven by both cars, given the fuel efficiency of each car)

We have two equations and two unknowns, so we can use these equations to solve for the value of x and y.

From the first equation, we can solve for x:

x = 45 - y

We can substitute this expression of x into the second equation:

15(45 - y) + 30y = 975

Simplifying the left side of the equation:

675 - 15y + 30y = 975

Subtracting 675 from both sides:

15y = 300

And finally divide both sides by 15:

y = 20

So the second car consumed 20 gallons of gas that week.

We can substitute this value of y back into the equation x = 45 - y to find the value of x

x = 45 - 20 = 25

So the first car consumed 25 gallons of gas that week.

Step-by-step explanation:

Answer:

[tex]\textsf{45.} \quad \log_5\left(\dfrac{x^3y}{w^2}\right)[/tex]

[tex]\textsf{46.} \quad \log 12[/tex]

[tex]\textsf{47.} \quad \ln(x-4)+2\ln(2x+5)[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Quotient law:\;\;\;$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\end{minipage}}[/tex]

[tex]\begin{aligned}3\log_5x + \log_5y - 2\log_5w&=\log_5x^3 + \log_5y - \log_5w^2\\&=\log_5\left(x^3 \cdot y\right)- \log_5w^2\\&=\log_5\left(\dfrac{x^3y}{w^2}\right)\end{aligned}[/tex]

[tex]\begin{aligned}\log21 - 2 \log7 + \log28 &=\log21 - \log7^2 + \log28\\&=\log21 - \log49 + \log28\\&=\log\left(\dfrac{21}{49}\right) + \log28\\&=\log\left(\dfrac{3}{7} \cdot 28\right)\\&=\log\left(\dfrac{84}{7}\right)\\&=\log12\end{aligned}[/tex]

[tex]\begin{aligned}\ln \left[(x - 4)(2x+5)^2\right]&=\ln(x-4)+\ln(2x+5)^2\\&=\ln(x-4)+2\ln(2x+5)\\\end{aligned}[/tex]

The correct answer is Unit Price, Units in Stock, Units on Order, and Reorder Level.

The unit price is the cost of a single item or unit of a product or service. It is usually expressed as a monetary value, such as dollars per item. It can be calculated by dividing the total cost of a product or service by the number of units.

Units in stock refer to the number of items or units of a product or service that are currently available for purchase. It is used to track inventory levels and to manage the replenishment of products or services.

Units on order refer to the number of items or units of a product or service that have been ordered by a company but have not yet been received. It is used to track expected inventory levels and to manage the replenishment of products or services.

The reorder level, also known as the reorder point, is the point at which a company needs to replenish its inventory of a particular product or service. It is determined by calculating the lead time (the time it takes to receive new inventory after placing an order) and the average daily usage of the product or service.

Therefore, The correct answer is Unit Price, Units in Stock, Units on Order, and Reorder Level.

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The polygon's 39 unit squared surface area.

A polygon with "n" sides has a total of 180 degrees in its inner angles (n-2) n-sided polygons have [n(n-3)]/2 diagonals as their number of sides. For a regular polygon with n sides, the interior angle measure is [(n-2)180°]/n. A regular polygon with n sides has exterior angles that are 360°/n in length.

Using the equation Area = (number of sides x length of one side x apothem)/2, one may determine the area of a regular polygon.

To create the polygonal shape shown in the attachment, sketch it.

It is therefore possible to separate the polygon into a rectangle and a triangle.

The polygon's 39 unit squared surface area.

The complete question is,

What size polygon does this one have? Put your response in the provided box. points M, V, E, D, and R are located within a 5-sided polygon of unit 2 on a coordinate plane. Points M is at (negative 5, 2), V is at (negative 2, 3), E is at (3, 3), D is at (3, negative 3), and R is at (negative 5, 2). (negative 2, negative 3).

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No, Its is not reasonable that 1/5 plus 5/8 is about 3/4.

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

⇒ 1/5 plus 5/8 is about 3/4

Now, We can add as;

⇒ 1/5 + 5/8

⇒ (8 + 25) / 40

⇒ 33/40

≠ 3/4

Thus, Its is not reasonable that 1/5 plus 5/8 is about 3/4.

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Answer:

3.53%

Step-by-step explanation:

annual 3.5%

So half a year =1.75% and compound twice a year.

equivalent annual rate is (1+1.75%)^2 -1 =.0353 =3.53%

A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.

In order to to graph the solution to the given system of inequalities on a coordinate plane, we would translate the word problem into an algebraic equation and then use an online graphing calculator to plot the given system of inequalities;

Based on the graph (see attachment), we can reasonably infer and logically deduce that the solution to the given system of inequalities is the shaded region as shown in the image attached below.

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Answer:4

Step-by-step explanation:

13-9=4

if you are subtracting 9 add more than the number. for example, 17-9=8

8 is one more than the number 7 in 17.

The formula for the standard matrix for the linear transformation is as follows: beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & & cosfracpi2 & 0 & & -1 endbmatrix

The following linear transformation rotates the points by[tex]$fracpi$[/tex]radians in the direction of rotation before reflecting the points through the line. We begin by examining the rotational component of the transformation to determine the standard matrix. A matrix beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0 & 0 & 1 endbmatrixan be used to describe the rotation by radians. We can use the matrix beginbmatrix 1 & 0 & 0 0 & -1 & 0 0 & 0 & 1 endbmatrixfor the reflection component. We obtain the final standard matrix for the linear transformation by multiplying these two matrices. $$beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0.

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The complete question is

let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for the standard matrix of the transformation can be found by first computing the matrix of the rotation and then the matrix of the reflection.

Given matrix equation as a vector equation:

[tex]\begin{bmatrix}c_1 & c_2 & c_3 & c_4 & c_5\\d_1 & d_2 & d_3 & d_5 & d_5\end{bmatrix}~\begin{bmatrix}v_1\\ v_2\\v_3\\ v_4\\v_5\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]

We know tha a matrix equation is nothing but the equation of the form Av = b,

where A is m × n matrix, ( It is called the coefficient matrix),

v is n × 1 column vector,

and b is m × 1 column vector.

A matrix equation is also called a matrix–vector equation.

Consider given matrix equation.

[tex]\begin{bmatrix}-3 & 5 & -4 & 9 & 7\\5 & 8 & 1 & -2 & -4\end{bmatrix}~\begin{bmatrix}-3\\ 2\\4\\ -1\\2\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]

We need to write the this matrix equation as a vector equation, using symbols v₁, v₂, v₃, . . . for vectors and c₁, c₂ and c₃, . . . for scalars.

We can observe that the first matrix is 2 × 5 matrix and the solution matrix is also 2 × 1

So, it can be rewritten as c₁, c₂, c₃, c₄ and c₅ for the first row and for the second row of matrix d₁, d₂, d₃, d₄ and d₅

Then we multiply those rows with vector v₁, v₂, v₃, v₄ and v₅ we'll get the resultant matrix.

So, we get a vector equation as:

[tex]\begin{bmatrix}c_1 & c_2 & c_3 & c_4 & c_5\\d_1 & d_2 & d_3 & d_5 & d_5\end{bmatrix}~\begin{bmatrix}v_1\\ v_2\\v_3\\ v_4\\v_5\end{bmatrix}=\begin{bmatrix}8\\-1\end{bmatrix}[/tex]

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Find the complete question below.

Answer: Bird A's top speed is 1428 MPH.

Step-by-step explanation: 238x6 = 1428

answer4534bottles

Step-by-step explanation:

All together the number of yards of material Erin will need to sew jacket and skirt is 4 1/4 yards

From the question the following can be gotten

She needs 2 3/4 yards of material for the jacket and 1 1/2 yards of material for the skirt.

The total number of yards she will require is calculated using the addition operation

The total number of yards

Addition of fractions

= 2 3/4 + 1 1/2

= 17 / 4

= 4 1/4

The total number of yard required is 4 1/4

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The equation for the graph will be

[tex]y=1 cos(3x)[/tex]

The function y = cos(2x + π/4) is a cosine function where the independent variable x is multiplied by 2 and then has π/4 added to it before the cosine is applied. The amplitude of this function is 1 and the period is π.

In this question

[tex]we assume, \\y=acos(bx)\\\\when x=0y=1\\\\y=acos(bx)\\\\1=acos0\\\\a=1\\so y=cos(bx)\\\\when x=\pi/3 y=-1\\y=cos(b.\pi/3)\\-1=cos1b.pi/3=cos(pi)\\b=3[/tex]

[tex]y=acosbx[/tex]

[tex]so, y=1.cos(3x)[/tex]

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The expression that represents how much more Company X​ charges, in​ cents, for n minutes is 15 + n

An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be used to represent a specific value or a range of values e.g. 2x+3.

For Company X:

Since it costs 30c to connect and then 4c for each minute, we can write the expression as:

30 + 4n

For Company Y:

Since it costs 15c to connect and then 3c for each minute, we can write the expression as:

15 + 3n

An expression that represents how much more Company X​ charges, in​ cents, for n minutes is:

(30 + 4n) - (15 + 3n) = 30 - 15 + 4n -3n = 15 + n

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Answer: One way to calculate the percent increase in Robin's monthly bill is to use the following formula:

% increase = (new amount - original amount) / original amount x 100

In this case, the original amount is $120 and the new amount is $150. So, the calculation would be:

% increase = (150 - 120) / 120 x 100 = 30 / 120 x 100 = 0.25 x 100 = 25

Therefore, the percent increase in Robin's monthly bill is 25%.

Another way to calculate the percent increase is to use the formula:

(New amount - original amount) / original amount

In this case: (150-120)/120 = 0.25, and multiply by 100 to get 25%

So, both formula gives the same answer 25%

Step-by-step explanation:

With constant of proportionality= 0.45 the New Hamsphire would have 51 golf courses.

What is a constant of proportionality?

The constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.

Direct Variation: The equation for direct proportionality is y = kx,  which shows as x increases, y also increases at the same rate. Example: The cost per item(y) is directly proportional to the number of items(x) purchased, expressed as y ∝ x

Inverse Variation: The equation for the indirect proportionality is y = k/x, which shows that as y increases, x decreases and vice-versa. Example: The speed of a moving vehicle (y) inversely varies as the time taken (x) to cover a certain distance, expressed as y ∝ 1/x

In both cases, k is constant. The value of this constant is called the coefficient of proportionality. The constant of proportionality is also known as the unit rate.

Now,

As given Georgia has 401 golf courses with a population of 10, 736, 059 while New Hampshire has 113 golf courses with a population of 1, 371, 246.

So Georgia have 1 golf course for 26773 people and New hamsphore have 1 golf course for 12135 people.

that means they have constant of proportionality= 0.45 with respect to population/golf course ratio .

population/golf course ratio for georgia=26773

population/golf course ratio for new hamsphire=12135

and For new hamsphire to have same ratio for population/golf ratio as georgia it will need 113*0.45=51 golf courses

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The distance between the two points in simplest radical form (3, 2) and (-5, -7)​ is [tex]\sqrt{40}[/tex]

We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.

We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.

The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).

The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).

Distance = [tex]\sqrt{(x2 - x1)(y2 - y1)}[/tex]

Distance between the two positions (3, 2) and (--5, --7) equals

Distance =root of ( -5 - 3,-7 - 2)

               root of (-8 * -5) = [tex]\sqrt{40}[/tex].

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Yes, she does have the enough soil as she needs 4 pounds of soil.She have [tex]7 \frac{5}{12}[/tex] pound of soil.

What is Fraction?

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

What is BODMAS?

The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems. B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as Bodmas.

Given that;

               She has

                 ⇒ [tex]2\frac{1}{3} + 1\frac{3}{4}[/tex]

                 ⇒ 17/3 + 7/4

                 ⇒ [tex]\frac{17*4 + 7 *3}{12}[/tex]

                  ⇒ 68 + 21 /12

                  ⇒ 89/12

                  ⇒    [tex]7 \frac{5}{12}[/tex]

So, She has [tex]7 \frac{5}{12}[/tex] pound of soil and she need 4 pounds only.

Hence, Denise have enough soil to fill the flower plot.

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The gauge pressure, or the difference between the inner pressure and the external pressure p0, is what the pressure gauge on a gas cylinder measures. Give the gauge pressure the letter pg.

The gas in the cylinder weighs mi at pgi gauge pressure when it is full. We can apply the ideal gas formula, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature, assuming the cylinder's temperature stays constant.

We can assume that the product nRT is constant because the temperature is constant. Consequently, we can write:

(pgf + p0) = (pgi + p0)(Vi) (Vf)

where Vi is the cylinder's initial volume and Vf is the cylinder's final volume when the pressure is pgf.

We also know that the gas's mass, m, is determined by multiplying the number of moles, n, by the molar mass, M, or m = nM.

The ideal gas law can be used to express the number of moles in terms of volume and pressure:

m/M = P(V/RT) = n

Thus, mf = pgf(Vf/RT).

M equals (pgf + p0)(Vf/RT).

(Vi/RT) Mi (pgi + p0)

where mf is the mass of gas still present in the cylinder at pgf pressure.

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The tatment which describe best a bar graph is data are presented with bars that are proportional in height to the measured value.

Let us know more about a bar graph .

The pictorial representation of grouped data, in the form of vertical or horizontal rectangular bars, where the lengths of the bars are equivalent to the measure of data, are known as bar graphs or bar charts.

The bars drawn are of uniform width, and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable, and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.

The three major attributes of bar graphs are:

1) The bar graph helps to compare the different sets of data among different groups easily.

2) It shows the relationship using two axes, in which the categories are on one axis and the discrete values are on the other axis.

3) The graph shows the major changes in data over time.The bar graphs can be vertical or horizontal. The primary feature of any bar graph is its length or height. If the length of the bar graph is more, then the values are greater than any given data.

Bar graph normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labelled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.

The types of bar charts are as follows:

Vertical bar chart

Horizontal bar chart

Even though the graph can be plotted using horizontally or vertically, the most usual type of bar graph used is the vertical bar graph. The orientation of the x-axis and y-axis are changed depending on the type of vertical and horizontal bar chart. Apart from the vertical and horizontal bar graph, the two different types of bar charts are:

Grouped Bar Graph

Stacked Bar Graph

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The statment which describe best a bar graph is data are presented with bars that are proportional in height to the measured value.

Let us know more about a bar graph .

The pictorial representation of grouped data, in the form of vertical or horizontal rectangular bars, where the lengths of the bars are equivalent to the measure of data, are known as bar graphs or bar charts.

The bars drawn are of uniform width, and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable, and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.

The three major attributes of bar graphs are:

1) The bar graph helps to compare the different sets of data among different groups easily.

2) It shows the relationship using two axes, in which the categories are on one axis and the discrete values are on the other axis.

3) The graph shows the major changes in data over time.The bar graphs can be vertical or horizontal. The primary feature of any bar graph is its length or height. If the length of the bar graph is more, then the values are greater than any given data.

Bar graph normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labelled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.

The types of bar charts are as follows:

Vertical bar chart

Horizontal bar chart

Even though the graph can be plotted using horizontally or vertically, the most usual type of bar graph used is the vertical bar graph. The orientation of the x-axis and y-axis are changed depending on the type of vertical and horizontal bar chart. Apart from the vertical and horizontal bar graph, the two different types of bar charts are:

Grouped Bar Graph

Stacked Bar Graph

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Answer:

To calculate the percent decrease in the number of rejected items, we can use the following formula:

Percent decrease = ((initial value - final value) / initial value) x 100

In this case, the initial value is 372 (the number of items rejected in the first period) and the final value is 323 (the number of items rejected in the second period).

So, the percent decrease is:

((372 - 323) / 372) x 100 = 13.1%

Therefore, there is a 13.1% decrease in the number of rejected items from the first period to the second period.

The probability of flipping a coin and getting heads is 7/16

from the question, we have the following parameters that can be used in our computation:

Number of flips = 16

Number of heads = 7

The probability is then calculated as

P = Head/Flips

substitute the known values in the above equation, so, we have the following representation

P = 7/16

Hence, the probability is 7/16

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Answer: The session was 1 hour long.

75% of an hour is 45 minutes.

Answer:

m=12b

Step-by-step explanation:

m (money raised) is equal to 12b, or 12 tickets per b (b = people)

The measure of ∠2 is [tex]54^{0}[/tex], ∠3 is [tex]23^{0}[/tex], ∠6 is [tex]121^{0}[/tex].

7.- The sum of the internal angles in a triangle equals 180°.

2x + 22 + 4x + 11 + [180- (9x - 15)] = 180

6x + 180 - 9x + 15 = 180 - 33

-2x = 147 - 180 - 15

-2x = -48

x = -48/-3

x = 16

∠X = 2(16) + 22

∠X = 54°                  

8. 8x - 31 + 6x - 8 + [180 - (10x + 17)] = 180

14x - 39 + 180 - 10x - 17 = 180

4x = 56

x = 56 / 4

x = 14

∠ ECD = 180 - 10(14) - 17

∠ECD = 180 - 140 - 17

∠ECD = 23°                          

9.- In ΔABC

m ∠C = m ∠A - 9

m ∠B = 4m∠A - 15

The sum of the internal angles in a triangle equals 180°.

∠A + ∠B + ∠C = 180°

∠A + 4∠A - 15 + ∠A - 9 = 180

6∠A = 180 + 24

6∠A = 204

∠A = 204 / 6 = 34

Then, ∠B = 4∠A - 15

∠B = 4(34) - 15

∠B = 121                  

10.- ∠XYZ = 2∠X - 9

m ∠W = 38°

38 + ∠X + [180 - (2∠X - 9)] = 180

38 + ∠X + 180 - 2∠X + 9 = 180

-1∠X = -47⇒∠X = -47/-1

∠X = 47

Then, ∠XYZ = 2(47) - 9

∠XYZ = 85°                

Therefore, the measure of ∠2 is [tex]54^{0}[/tex], ∠3 is [tex]23^{0}[/tex], ∠6 is [tex]121^{0}[/tex] and ∠XYZ is [tex]85^{0}[/tex].  

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Answer:

x=60

Step-by-step explanation:

The function h(t) = (2t - 3t²)/(1 + t³) is continuous at x = 1, as the limit exists and is equals to the numeric value of the function.

A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal to the numeric value of the function, that is:

[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]

The function is defined as follows:

h(t) = (2t - 3t²)/(1 + t³)

At t = 1, the first step is trying to obtain the limit as the numeric value, hence:

h(1) = (2 - 3)/(1 + 1) = -1/2.

As the limit does not result in an undetermined result, the limit exists, is equals to the numeric value of the function, the function is continuous at x = 1.

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The change in height divided by the change in time yields the firework's average speed from t=1 to t=3 seconds.

Average change speed is equal to (h(3) – h(1)) (3 - 1)

h(3) = 16*32 + 105*3 + 10 = 536

h(1) = 16*12 + 105*1 + 10 = 126

Average speed = (536 - 126)/(3 - 1) = 410/2 = 205 ft/sec

h(t) = 16r2 + 105t + 10 models the height of a firework t seconds after it is released. We must determine the change in height divided by the change in time in order to get its average speed between t=1 and t=3 seconds.

By entering t = 3 into h(t), we can determine the height at 3 seconds, which gives us h(3) = 16*32 + 105*3 + 10 = 536. We can figure out the height.

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