Chocolates costing $8 per pound are to be mixed with chocolates costing $3 per pound to make a 20 pound mixture. If the mixture is to sell for $5 per pound, how many pounds of each chocolate should be used? Which of the following equations could be used to solve the problem? 8x + 3x = 5(20) 8x + 3(20) = 5(x + 20) 8x + 3(20 - x) = 5(20)

42

42x2 is 84 and 42x5 is 210

Final answer:

The greatest common factor (GCF) of 84 and 210 is 42, which is found by listing the factors of each number and identifying the largest one they share.

Explanation:

The student is asking for the greatest common factor (GCF) of the number of pages in two books, one with 84 pages and another with 210 pages. To find the GCF, we need to list the factors of each number and then identify the largest factor they have in common.

The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The factors of 210 are 1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210. The common factors of 84 and 210 are 1, 2, 3, 6, 7, 14, 21, and 42. The largest of these is 42, so the GCF is 42.

Answer:

It is a structured, orderly process for conducting a research study.

Step-by-step explanation:

The main steps of the scientific method are:

1) make an observation describing the problem

2) creating and then testing a hypothesis

3) drawing conclusions and refine the hypothesis.

The scientific method is a standard way of making observations and gathering data, forming theories based on the data, finally testing and interpreting results.

So, the answer here is option A. It is a structured, orderly process for conducting a research study.

Answer:

(2,3)

Step-by-step explanation:

We are given that triangle PQR lies in the xy-plane, and coordinates of Q are (2,-3).

Triangle PQR is rotated 180 degrees clockwise about the origin and then reflected across the y-axis to produce triangle P'Q'R',

We have to find the coordinates of Q'.

The coordinates of Q(2,-3).

180 degree clockwise  rotation about the origin  then transformation rule

[tex](x,y)\rightarrow (-x,-y)[/tex]

The coordinates (2,-3) change into (-2,3) after 180 degree clockwise rotation about origin.

Reflect across y- axis the transformation rule

[tex](x,y)\rightarrow (-x,y)[/tex]

Therefore, when reflect across y- axis then the coordinates (-2,3) change into (2,3).

Hence, the coordinates of Q(2,3).

After applying the sequence of transformations, the coordinates of Q′ are Q' (2, 3).

In Mathematics and Geometry, the rotation of a point 180° about the origin in a clockwise or counterclockwise direction would produce a point that has these coordinates (-x, -y).

Additionally, the mapping rule for the rotation of any geometric figure 180° clockwise or counterclockwise about the origin is represented by the following mathematical expression:

(x, y)             →            (-x, -y)

Q (2, -3)       →    Q" (-2, 3)

By applying a reflection over the y-axis to the coordinates of the point (4, -9), we have the following new coordinates for the image;

(x, y)                →      (-x, y)

Q" (-2, 3)         →      Q' (2, 3).

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To find how much wire was used, apply the weight-relationship or mass per unit length specification of the wire. The formula to find the length is ((205 g) / (44.5 g/km)) * 1000m/km. The units cancel out each other, leaving the answer in meters.

To compute the length of the copper wire used, you would need to apply the weight-relationship or mass per unit length specification of the 40-gauge copper wire to the weight reduction of the spool. In precise terms, the unit of weight-relationship is given in grams per kilometer (g/km). Thus, the weight of the wire is directly proportional to its length.

So, to verify the length of wire used in meters, you would calculate:

((205 g) / (44.5 g/km)) * 1000m/km

This expression would give the length of the wire that has been used in meters. The units of the calculation effectively cancel out each other, leaving with the expected unit of meters.

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Final answer:

To find the length of wire used, you divide the weight of the wire removed from the spool (205 g) by the weight per kilometer for the wire (44.5 g/km), and this gives you the length in kilometers.

Explanation:

To calculate the length of 40-gauge copper wire used from the spool, you need to use the given weight per unit length of the wire. First, we have the weight of wire used, which is 205 grams (g). The weight per kilometer (km) of wire is given as 44.5 grams per kilometer (44.5 g/km). To find the length of wire used, you divide the weight of wire used by the weight per kilometer:

Length of wire used (in kilometers) = Total weight removed (÷) Weight per kilometer

Therefore, the expression would be:

(205 g) ÷ (44.5 g/km)

Make sure to include the correct units in your final calculation.

Length = 4.60 m

Answer:

100 dollar rebate

Step-by-step explanation:

ok so since you have to find which deal takes off more money from the initial price you have to start by doing 479.99 times 20% or .2 which gives you 95.998 which is already lower than 100 buuuut just in case you want to check if you subtract 100 and 95.998 from 479.99 then inevitably the 100 dollars ends up being more money off from the initial price

(sorry about my last answer, hope this ones better ^-^)

Answer:

100 dollar rebate

Step-by-step explanation:

Answer:  c. 7,999,999 phone numbers

A can be any digit 2-9, then there are 8 possible numbers.

B can be any digit 0-9, then there are 10 possible numbers.

C can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

X can be any digit 0-9, then there are 10 possible numbers.

Then are possible: 8·10·10·10·10·10·10 = 8·10⁶ = 8,000,000 phone numbers

But the number 867-5309 is not used then 8,000,000 - 1 = 7,999,999 possible phone numbers.

Answer: c. 7,999,999 phone numbers

[tex]\textit{\textbf{Spymore}}[/tex]  

Answer:

x>[tex]\frac{16}{-9}[/tex] and x ≤[tex]\frac{-19}{13}[/tex].

Step-by-step explanation:

Given  : −9x+2>18 AND 13x+15≤−4.

To find : Solve.

Solution : We have given  −9x+2>18 AND 13x+15≤−4.

For  −9x + 2 > 18 .

On subtracting both sides by 2

- 9x > 18-2

- 9x > 16.

On dividing both sides by -9.

x>[tex]\frac{16}{-9}[/tex].

For  13x + 15 ≤ −4.

On subtracting both sides by 15.

13 x ≤  -4 - 15.

13 x ≤ -19.

On dividing both sides by 13.

x ≤ [tex]\frac{-19}{13}[/tex].

Therefore, x>[tex]\frac{16}{-9}[/tex] and x≤[tex]\frac{-19}{13}[/tex].

Answer:

B. x < -16/9

Step-by-step explanation:

I got it right on Kahn Academy

Answer:

Slope: 6

y-intercept: 8

x-intercept: -4/3

Step-by-step explanation:

Isolate the y. Note the equal sign, what you do to one side, you do to the other. First, divide 2 from both sides:

(2y - 6x - 8)/2 = (0)/2

y - 6x - 8 = 0

Isolate the variable, y. Add 6x and 8 to both sides:

y -6x (+6x) - 8 (+8) = 0 (+6x) (+8)

y = 0 + 6x + 8

y = 6x + 8

The slope intercept form is: y = mx + b, in which m = slope, and b = y-intercept.

Slope: 6

y-intercept: 8

To find the x-intercept, plug in 0 for y in the equation:

y = 6x + 8

0 = 6x + 8

Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.

First, subtract 8 from both sides:

0 (-8) = 6x + 8 (-8)

-8 = 6x

Isolate the variable, x. Divide 6 from both sides:

(-8)/6 = (6x)/6

x = -8/6

x = -4/3

x-intercept: -4/3

~

The proof that ∠ABD is congruent to ∠ABE would be detailed below to your understanding

What are Congruent Angles and Bisectors?

Congruent angles are angles that are equal and identical to each other when measured.

A Bisector is a line that divides another line or angle into two equal parts.

Given that;

Line BC divided angle DBE into two equal parts.

It is seen that line BC extends to point A while dividing the external angle DBE into two equal parts.

Therefore, ∠ABD is congruent to ∠ABE.

Answer:

(z - 6)(z + 15)

Step-by-step explanation:

Given

z² + 9z - 90

Consider the factors of the constant term (- 90) which sum to give the coefficient of the z- term (+ 9)

The factors are - 6 and + 15, since

- 6 × 15 = - 90 and - 6 + 15 = + 9, hence

z² + 9z - 90 = (z - 6)(z + 15)

Answer: 33 333,33 per month or 400 000 per year

Step-by-step explanation:

You need 48 000 + 0.035X = 62 000

So ( 62 000 - 48 000 ) / 0.035 = X

Then you can divide X per 12 (months in a year)

And you have your answer per month .

So 33 333,33 total sale per month to have at least as high as the average pay

An equation is formed of two equal expressions. Andre’s total sales need to be $400,000 for his pay to be at least as high as the average pay for this job.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that Andrew will earn $48,000 per year plus 3.5% of his total sales, the average pay for this job is $62,000. Therefore, the amount of sales that Andrew needs to make in order to make his pay equal to the average pay is,

Average pay = Annual pay + 3.5% of sales

$62,000 = $48,000 + (3.5/100)x

$62,000 - $48,000 = 0.035x

$14,000 = 0.035x

$14,000 / 0.035 = x

x = $400,000

Hence, Andre’s total sales need to be $400,000 for his pay to be at least as high as the average pay for this job.

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Answer:

The minimum average speed needed in the second half is 270 km/hr

Step-by-step explanation

We can divide the track in two parts. For the first half of the track the average speed the car achieved was 230 km/hr and we need to make sure that the average speed of the full track is 250 km/hr. Then, we can calculate the average speed of the two parts of the track and force this to be equal to 250 km/hr. In equation, defining [tex]v_2[/tex] as the average speed of the second half:

[tex]\frac{230 + v_2}{2}=250[/tex]

Solving for [tex]x[/tex]

[tex]x=250*2-230\\x=500-230\\x=270[/tex]

Therefore, achieving a speed of 270 km/hr in the second half would be enough to achieve an average speed of 250 on the track.  

Answer:

number 3 is correct

number 4 is also correct

Answer:

  2.2 m/s²

Step-by-step explanation:

Fill in the given values and solve for the unknown variable.

  F = m·a

  7.92 = 3.6·a

  7.92/3.6 = a = 2.2 . . . . . . divide by the coefficient of "a"

The units of this answer are Newtons/kilogram = meters/second/second. We abbreviate those units as m/s².

The acceleration is 2.2 m/s².

Answer:

1) [tex]2.406e^{-4}[/tex]

2) [tex]-5.618e^{-19}[/tex]

3) [tex]-2.14275e^{-16}[/tex]

Step-by-step explanation:

1) First you need to reorder the terms, to do a simple sum:

  (61 x 10⁻⁷) + (2.25 x 10⁻⁵) + (212.0 x 10⁻⁶) =

  [tex]6.1e^{-6} + 22.5e^{-6} + 212e^{-6}=[/tex]

Now you can simply sum each term, because the exponential is the same:

 [tex]240.6e^{-6}=\\ 2.406e^{-4}[/tex]

2) First you need to reorder the terms, to do a simple sum:

  ( ― 54 x 10⁻²⁰ ) + ( ― 2.18 x 10⁻¹⁸ ) =

  [tex]-5.4e^{-19} - 0.218e^{-19}=[/tex]

Now you can simply sum each term, because the exponential is the same:

[tex]-5.618e^{-19}[/tex]

3) First you need to reorder the terms, to do a simple sum:

 ( ― 21.46 x 10⁻¹⁷ ) ― ( ― 3,250 x 10⁻¹⁹ ) =

[tex]-21.46e^{-17} + 0.0325e^{-17}=[/tex]

Now you can simply sum each term, because the exponential is the same:

[tex]-21.4275e^{-17}=\\-2.14275e^{-16}[/tex]

Answer: Infinite solutions. It is the same line

Step-by-step explanation:

Total accidents = 400

Multiple vehicles would be both 2 and 3 or more columns.

Involved alcohol for 2 or more vehicles = 96 +19 = 115

Probability = 115 / 400 = 23/80

Answer:

a) r = 6

b) r = 0

Step-by-step explanation:

See it in the pic.

Answer:

a)r=6  b)r=0

Step-by-step explanation:

Before to get started, Let's to express each number in base r.

We should take in account that it process is similar to express numbers in  decimal base, except that in this case [tex]10^{n}[/tex] is  replaced by [tex]r^{n}[/tex].

a) 14=1x[tex]1*r^{1} +4*r^{0}  =r+4\\[/tex]

  [tex]2=2*r^{0} \\[/tex]

  [tex]5=5*r^{0}[/tex]

Replacing each number in base r  on the equalitie a.

[tex]\frac{r+4}{2} =5[/tex]

Solving this equation

[tex](r+4)=10\\r=6[/tex]

b) [tex]54=5*r^{1} +4*r^{0} =5r+4\\4=4*r^{0} \\1=1*r^{0}[/tex]

Replacing each number in base r  on the equalitie b.

[tex]\frac{5r+4}{4}=1[/tex]

Solving this equation:

[tex]5r+4=4\\r=0[/tex]

Answer:

Answer is f(x)=245(4^1/12)^12x

Step-by-step explanation:

The general formula for the growth of population in years is:

f(x) =P0(1+r)^x

where 1+r is the rate of growth in this case 4 and x is time in years. To take it to months we do not change initial population , this doesn't vary by changing time scale (there are 45 fruit flies in time 0 )

we change the time period x to 12 x because we want our formula to remain equivalent to the original one so if x = 1 year  in months this would be equivalent to twelve months (12x = 12  with x =1 ) taht is the same

However we need to reescale our growth rate to a value that calculates it by month growth.  After 12 time periods of a month our grow rate should be equivalent to the growth rate of a year. So For that reason we elevate to a  1/12 because of  exponent rules

(4^1/12)^12x  =(4^12x/12) because of exponent of an exponent is multiplying exponents

= (4)^x we arrive to the same expression. So

Answer:

(a) If f and t are both even functions, product ft is even.

(b) If f and t are both odd functions, product ft is even.

(c) If f is even and t is odd, product ft is odd.

Step-by-step explanation:

Even function: A function g(x) is called an even function if

[tex]g(-x)=g(x)[/tex]

Odd function: A function g(x) is called an odd function if

[tex]g(-x)=-g(x)[/tex]

(a)

Let f and t are both even functions, then

[tex]f(-x)=f(x)[/tex]

[tex]t(-x)=t(x)[/tex]

The product of both functions is

[tex]ft(x)=f(x)t(x)[/tex]

[tex]ft(-x)=f(-x)t(-x)[/tex]

[tex]ft(-x)=f(x)t(x)[/tex]

[tex]ft(-x)=ft(x)[/tex]

The function ft is even function.

(b)

Let f and t are both odd functions, then

[tex]f(-x)=-f(x)[/tex]

[tex]t(-x)=-t(x)[/tex]

The product of both functions is

[tex]ft(x)=f(x)t(x)[/tex]

[tex]ft(-x)=f(-x)t(-x)[/tex]

[tex]ft(-x)=[-f(x)][-t(x)][/tex]

[tex]ft(-x)=ft(x)[/tex]

The function ft is even function.

(c)

Let f is even and t odd function, then

[tex]f(-x)=f(x)[/tex]

[tex]t(-x)=-t(x)[/tex]

The product of both functions is

[tex]ft(x)=f(x)t(x)[/tex]

[tex]ft(-x)=f(-x)t(-x)[/tex]

[tex]ft(-x)=[f(x)][-t(x)][/tex]

[tex]ft(-x)=-ft(x)[/tex]

The function ft is odd function.

Answer:

$15.06

Step-by-step explanation:

First you add $25.00 and $10.00 Then you multiply $9.97 by two and you would get $19.94 which you would then subtract $19.94 from $35

To find out how much money Brianna has left, we need to first calculate the total cost of the T-shirts, then determine how she paid for them and subtract this from her cash and gift certificate value.

To find out how much money Brianna has left after her purchase, we need to answer a few important questions:

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Answer:

[tex]f(-3)=9[/tex]

Step-by-step explanation:

we have

[tex]f(x)=x^{2}[/tex]

Find f(-3)

we know that

f(-3) is the value of the function f(x) for the value of x equal to -3

so

substitute the value of x=-3 in the function above to get f(-3)

[tex]f(-3)=(-3)^{2}[/tex]

[tex]f(-3)=9[/tex]

Answer: la altura es 13.1 m

Step-by-step explanation:

El movimiento descripto es de tipo rectilineo uniformemente variado, más precisamente tiro vertical.

Para calcular la posición al cabo de 1 seg utilizaremos la ecuacionecuación del movimiento descrita como:

y = v0.t - 1/2 g t^2

Donde y es la altura para cualquier momento

v0 es la velocidad inicial 18 m/s

g la aceleración de la gravedad 9.81 m/s2

y t el tiempo medido en segundos

Entonces para calcular la altura después de un segundo:

y = 18 m/s x 1 seg - 1/2 9.81 m/s2 (1 seg)^2 = 18 m - 4.9 m = 13.1 m

La posición de la pelota, que fue pateada verticalmente hacia arriba desde una altura de 3 metros con una velocidad inicial de 18 m/s, después de 1 segundo, es aproximadamente 11.1 metros por encima del punto de inicio.

La pregunta trata sobre un problema de física relacionado con el movimiento vertical de un objeto. En este caso, una pelota es pateada verticalmente hacia arriba desde una altura de 3 metros con una velocidad inicial de 18 m/s. Para resolverla, podríamos usar la segunda ley del movimiento de Newton para el movimiento vertical, que se puede escribir de la siguiente manera: y = y0 + v0t - 1/2gt^2.

Aquí, y es la posición de la pelota después de un tiempo t, y0 es la posición inicial (3 metros en este caso), v0 es la velocidad inicial (18 m/s), g es la aceleración debido a la gravedad (9.8 m/s^2), y t es el tiempo (1 segundo).

Si sustituimos los valores correspondientes en la ecuación, obtenemos: y = 3m + 18m/s * 1s - 1/2 * 9.8m/s^2 * (1s)^2. Al hacer la respectiva operación, encontramos que la posición de la pelota después de 1 segundo es de aproximadamente 11.1 metros por encima del punto de inicio.

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Final answer:

Solve the equation 3/2x - 4 = 16 by adding 4 to both sides, simplifying to 3/2x = 20, and then multiplying both sides by 2/3 to find the solution, x = 40/3.

Explanation:

To solve the equation 3/2x - 4 = 16, you need to perform a series of algebraic manipulations.

Add 4 to both sides of the equation to isolate the term with the variable on one side: 3/2x = 16 + 4.

Combine like terms: 3/2x = 20.

To find x, multiply both sides by the reciprocal of 3/2, which is 2/3: x = 20 * (2/3).

Simplify the multiplication: x = 40/3 or x = 13.33 repeating.

Therefore, the solution to the equation is x = 40/3.

Answer:

On Saturday, when 12 weeks passed

Step-by-step explanation:

Tom gets his hair cut every 3 weeks.

David gets his hair cut every 4 weeks.

Find the least common multiple of numbers 3 and 4:

[tex]3=3\\ \\4=2\cdot 2\\ \\LCM(3,4)=3\cdot 2\cdot 2=12[/tex]

This means that Tom and David will get their hair cut on the same day at 12th week (if the first week when they started has number 0).

You can think in another way:

Tom gets his hair cut every 3 weeks. He got his hair cut after 3 weeks, after 6 weeks, after 9 weeks, after 12 weeks passed.

David gets his hair cut every 4 weeks. He got his hair cut after 4 weeks, after 8 weeks, after 12 weeks passed.

Answer: x=30

Step-by-step explanation:

The sum of the angles must be 360.

4x+3x+3x+2x = 12x

12x = 360

x =360/12 = 30

Answer:

The answer to your question is:

mABC = 120°               mBCD = 90°        mCDA = 60°          mDAB = 90°

Step-by-step explanation:

To solve this problem, we remember that the sum of the angles in a quadrilateral = 360°.

Then

360° = mABC +  mBCD + mCDA  + mDAB

360 = 3x + 4x + 3x + 2x                   substitution

360 = 12x                                         simplifying

x = 360/12

x = 30                                          

Now, we find the values of each angle

mABC = 4(30) = 120°         mBCD = 3(30) = 90°       mCDA = 2(30) = 60°

mDAB = 3(30) = 90°

Answer:

D. [tex]\frac{x^{2} }{40}[/tex]

Step-by-step explanation:

Compound interest formula is:

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

When compounded annually;

[tex]A=1000(1+\frac{x}{100})^{1}[/tex]

=> [tex]A=1000(1+\frac{x}{100})[/tex]   ....(1)

When compounded semi annually means rate = x/2 and n = 2.

[tex]A=1000(1+\frac{x}{2\times100})^{2}[/tex]

=> [tex]A=1000(1+\frac{x}{200})^{2}[/tex]   .... (2)

Now, subtracting 1 from 2 we get ;

[tex]1000(\frac{x^{2} }{40000} )[/tex]

= [tex]\frac{x^{2} }{40}[/tex]

Hence, option D is correct.

Answer:

  117

Step-by-step explanation:

Put the numbers where the corresponding variables are and do the arithmetic.

  3·4² 5·3·4 +3² = 48 +60 +9 = 117