Please help me with this problem..

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:

  2.2 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]

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: 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:

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]

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:  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:

1/4

decimal- 0.25

percent- 25%

Step-by-step explanation:

Answer:

25%

Step-by-step explanation:

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:

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

~

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:

[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]

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:

Discrepancy = 665,15 L

Step-by-step explanation:

Data: 1 Apple Barrel: 7056 cubic inches

         1 Cranberry Barrel: 5826 cubic inches

The merchant sells 33 cranberry barrels, so we need to find out the total volume of that. So we multiply our cranberry volume (data) 33 times:

33 x 5826 cubic inches = 192258 cubic inches

Now, the customer thinks that he is receiveing apple barrels. To calculate this volume, we need to multiply the apple volume (data) 33 times:

33 x 7056 cubic inches = 232848 cubic inches

(You can see that 33 apple barrels have more volume that 33 cranberry barrels, so the customer will receive less volume than he is expecting)

The problem is asking the discrepancy in the shipment in liters (L). First we calculate the discrepancy (difference) in cubic inches.

Discrepancy (cubic inches) = 232848 cubic inches - 192258 cubic inches = 40590 cubic inches

Finally we need to transform the units. As a general rule, we know that:

1 litre (L) = 61,0237 cubic inches. Using a simple rule of three we can solve it:

Discrepancy (L) = [tex]\frac{40590 cubic inches}{61,0237 cubic inches\\}[/tex] x 1 L

Discrepancy (L) = 665,15 L

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:

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:

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:

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:

Function [tex]sin(60^o)\,\,s=h[/tex]

Height of an equilateral angle of side length 88m: [tex]76.21\,m=h[/tex]

Step-by-step explanation:

An equilateral triangle has 3 equal sides and 3 equal angles. The height of the triangle could be expressed as:

[tex]sin(\theta)=\frac{O}{H}[/tex]

[tex]sin(60^o)=\frac{h}{s}[/tex]

Moving s to the other side we find the function for the height:

[tex]sin(60^o)\,\,s=h[/tex]

As we know that s=88m we have

[tex]sin(60^o)\,\,88m=h[/tex][tex]\frac{\sqrt{3}}{2}88m=h[/tex]

[tex]44\sqrt3 \,m=h[/tex]

[tex]76.21\,m=h[/tex]

Explanation of the height of an equilateral triangle as a function of its side length and calculation for a triangle with a side length of 88m.

Justify that the triangles are similar: Equilateral triangles have all sides equal and all angles equal, therefore they are similar.

Write an equation that relates the sides of the triangles using words to describe the quantities: The height h of an equilateral triangle is equal to √3/2 times the side length s.

Rewrite your equation using your symbols: h = √3/2 * s

Algebraically isolate the unknown quantity: Given s = 88 m, plug it into the formula h = √3/2 * s to find the height h.

Plug-in numbers and calculate answer: h = √3/2 * 88 m ≈ 76.12 m

Check answer: The calculated height of approximately 76.12 m seems reasonable for an equilateral triangle with a side length of 88 m.

So Julia... 6 miles in 30 minutes. Let's find out how much she travelled in 1 hour. Multiply it by 2, since 30 x 2 = 60 mins = 1 hour, you get 12 miles per hour for Julia.

For Alex... 2 miles in 12 minutes. Multiply it by 5, as 12 x 5 = 60 mins = 1 hour, you get 10 miles per hour for Alex.

Julia travelled faster. She travelled 12 miles per hour while Alex travelled 10 miles per hour.

Julia travelled at a greater speed at 12 miles per hour.

Unitary method is a mathematical way of first deriving the value of a single unit and then deriving the required unit by multiplying with it.

According to the given question Julia rode a bicycle 6 miles in 30 minutes.

∴  In 60 minutes Julia rode (6×60)/30 miles which is

= 12 miles per hour.

Alex rode his skateboard 2 miles in 12 minutes.

So, In 60 minutes he rode (60×2)/12 miles which is

= 10 miles per hour.

Therefore the average speed of Julia is more by 2 miles per hour.

learn more about unitary method here :

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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: 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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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

Answer:  20

Step-by-step explanation:

Given : Angel can choose from 4 different types of chocolate and 5 different flavors of gum.

By the fundamental counting principle , the total number of outcomes is the product of the number of outcomes for each event.

i.e. The number of different types of grab bags can she put together if she puts one chocolate and one flavor of gum in each bag will be :_

[tex]4\times5=20[/tex]

Hence, The number of different types of grab bags can she put together if she puts one chocolate and one flavor of gum in each bag =20

Answer:

number 3 is correct

number 4 is also correct