A freight train travels 1445 miles in 25 hours. What is the train's average rate of speed?

Answer:

Half-life of uranium-238 [tex]18 \times 10^{3} \text { times greater }[/tex] that of uranium-234

Explanation:

Half time of uranium-238 = [tex]4.5\times 10^9[/tex]  years

Half time of Uranium-234 = [tex]2.5\times 10^5[/tex] years

To find how much times greater the half life of uranium-238 is from uranium-234

= [tex]\frac{\text { Half life of Uranium-238 }}{\text { Half time of Uranium - 234 }}[/tex]

=[tex]\frac{4.5 \times 10^{9}}{2.5 \times 10^{5}}[/tex]

=[tex]18 \times 10^{3} \text { times greater }[/tex]

Hence Uranium-238 is  [tex]18 \times 10^{3} \text { times greater }[/tex] than Uranium-234

Final answer:

The half-life of uranium-238 is 18,000 times greater than the half-life of uranium-234, determined by dividing the half-lives.

Explanation:

The half-life of uranium-238 is 4.5x10⁹ years, and the half-life of uranium-234 is 2.5x10⁵ years. To determine how many times greater the half-life of uranium-238 is than that of uranium-234, we divide the half-life of uranium-238 by the half-life of uranium-234:

(4.5x10⁹ years) / (2.5x10⁵ years) = 4.5/2.5 x [tex]10^{9-5[/tex] = 1.8 x 10⁴

Therefore, the half-life of uranium-238 is 18,000 times greater than the half-life of uranium-234.

For this case we have a factorized quadratic equation. We equal each factor to zero and thus find the roots:

[tex]x + 5 = 0[/tex]

Subtracting 5 from both sides we have:

[tex]x = -5[/tex]

Thus, the first solution of the equation is:

[tex]x_ {1} = - 5[/tex]

On the other hand we have:

[tex]x-3 = 0[/tex]

Adding 3 to both sides:

[tex]x = 3[/tex]

Thus, the second solution of the equation is:

[tex]x_ {2} = 3[/tex]

Answer:

The solutions of the equation are:

[tex]x_ {1} = - 5\\x_ {2} = 3[/tex]

Answer:

(95/31, -118/31)

Step-by-step explanation:

-7x-8y=9

4x+9y=-22

----------------

4(-7x-8y)=4(9)

7(4x+9y)=7(-22)

-----------------------

-28x-32y=36

28x+63y=-154

-----------------------

31y=-118

y=-118/31

-7x-8(-118/31)=9

-7x+944/31=9

-7x=9-944/31

-7x=279/31-944/31

-7x=-665/31

7x=665/31

x=(665/31)/7

x=(665/31)(1/7)

x=665/217=95/31

x=95/31, y=-118/31

Answer:

(2, 6)

Step-by-step explanation:

Because 8(2)-2(6)=16-12=4.

The ordered pair of the equation 8x - 2y = 4 is (2,6).

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the equation is 8x - 2y = 4. The ordered pair will be calculated as,

8x - 2y = 4

( 8 x 2 ) - ( 2 x 6) = 4

16 - 12 = 4

4 = 4

Therefore, the ordered pair of the equation 8x - 2y = 4 is (2,6).

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Answer:

M∠DEC equals 123º.

Step-by-step explanation:

The sum of a triangle's three angles always equal 180º. The exterior angle, x, equals the two non-adjacent interior angles.

180 - {(x - 45)+(x - 12)} = m∠DEC

m∠DEC + x = 180

(x - 45) + (x - 12) = x

Solving for x:

(x - 45) + (x - 12) = x

x - 45 + x - 12 = x                             Remove parenthesis

2x - 57 = x                                       Combine like terms

2x = x + 57                                      Add 57 to both sides

x = 57                                             Subtract x from both sides

Finding m∠D:

x - 45 = ?

57 - 45 = 12º                                          

Finding m∠C:

x - 12 = ?

57 - 12 = 45º                                          

** (Checking x: 12 + 45 = 57) **

Finding m∠DEC:

AC is a straight line, and because straight lines are equivalent to 180º, we subtract 57 from 180:

180 - 57 = 123º

Hope this helps,

❤A.W.E.S.W.A.N.❤

Answer:

227/6

Step-by-step explanation:

454/12=227/6

Answer:

abs(-1/4), abs(-0.5), abs(6/10), abs(6.25).

Step-by-step explanation:

abs(-1/4)=1/4=0.25

abs(6/10)=6/10=3/5=0.6

abs(6.25)=6.25

abs(-0.5)=0.5

-----------------------------------

abs(-1/4)=0.25 is the smallest, then comes abs(-0.5)=0.5, next comes abs(6/10), finally, comes abs(6.25).

Answer:

The measure of the three angles are 120°, 20° and 40°

Step-by-step explanation:

Let

x ----> the measure of the first angle

y ---> the measure of the second angle (smallest angle)

z ---> the measure of the third angle

Remember that

The sum of the angles in a triangle must be equal to 180 degrees

so

[tex]x+y+z=180[/tex] ----> equation A

[tex]x=y+100[/tex] -----> equation B

[tex]z=2y[/tex] ------> equation C

solve the system by substitution

substitute equation B and equation C in equation A

[tex](y+100)+y+(2y)=180[/tex]

solve for y

[tex]4y+100=180[/tex]

[tex]4y=180-100[/tex]

[tex]4y=80[/tex]

[tex]y=20\°[/tex]

Find the value of x

[tex]x=y+100[/tex]  ---- [tex]x=20+100=120\°[/tex]

Find the value of z

[tex]z=2y[/tex] ----> [tex]z=2(20)=40\°[/tex]

therefore

The measure of the three angles are 120°, 20° and 40°

Answer:

Step-by-step explanation:

120,20 and 40

Answer:

A) 6/13 B) 7/40 C) 45/36 D) 37/43

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

7 is higher than 4 so you round up one

A Whole number is any non-negative integer without a fractional or decimal portion. The whole number that is nearest to 15.74 is 16.

Any positive integer without a fractional or decimal portion is referred to as a whole number. This indicates that all whole numbers, such as 0-1, 2, 3, 4, 5, 6, and 7, are whole numbers.

If the number 15.74 is rounded to the nearest whole number, then the number that will be close to the number will be 16.

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Answer:

x = 7/3

Step-by-step explanation:

To find the of x, isolate it from the other numbers (moving everything to the other side)

What you do to one side, you must do to the other:

3x + 8 = 15

3x + 8 - 8 = 15 - 8  (subtract 8 on both sides to rid of the "+ 8")

3x = 7

3x/3 = 7/3   (divide by 3 on both sides to rid of the 3 attached to "x")

x = 7/3

Answer:

x=2.3

Step-by-step explanation:

15-8=7

Divide 3 on each side (3x=7)7 divided by 3 is 2.3

so X=2.3

Answer:

4 inches long

Step-by-step explanation:

2+1=3

6÷3=2

2×2=4

The length of a chameleon's tongue is 4 inches

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

We have been given that the ratio of the length of a chameleon's tongue to the length of its body is 2:1

Let the length of a chameleon's tongue is 2x and the length of its body is x

⇒ 2x + 1x = 3x

We have been given that a chameleon is 6 inches long

⇒ 3x = 6

⇒ x = 6/3

⇒ x = 2

Therefore, the length of a chameleon's tongue = 2(2) = 4 inches

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Answer:

slope is 1/2 or 0.5

Step-by-step explanation:

ΔX = 7 – -5 = 12

ΔY = 9 – 3 = 6

A Staghorn Coral can grow as much as 3.35 feet in 5 years under ideal conditions, assuming it grows at a fixed rate of 0.67 foot per year.

The question asks us to find out how much a Staghorn Coral, a type of branching coral, can grow in 5 years. Each year, the coral can potentially increase its size by 0.67 foot. To figure this out, we would use multiplication, a basic arithmetic operation.

First, we need to multiply the annual growth rate (0.67 foot) by the number of years (5). So, 0.67 * 5 equals 3.35 feet. This signifies that the Staghorn Coral can grow as much as 3.35 feet over the course of five years under optimal conditions.

Therefore, a Staghorn Coral can potentially add 3.35 feet to its branches during a 5 year span if it grows at the rate of 0.67 foot per year.

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Answer:

The height of the rock is 15 mm.

Step-by-step explanation:

Given : Cristian put a large rock on the bottom of the terrarium he made for his pet turtle.

To find : How high is the rock?

Solution :

The rock is a right rectangular prism 10 cm wide by 12 cm long.

Let the height be 'h'.

The volume of the right rectangular prism is [tex]V=L\times B\times H[/tex]

i.e. [tex]V=10\times 12\times h[/tex]

[tex]V=120h[/tex]

The rock displaces 1800 cm³ of water.

i.e. The volume of the right rectangular prism is equal to the rock displaces of water.

So, [tex]120h=1800[/tex]

[tex]h=\frac{1800}{120}[/tex]

[tex]h=15[/tex]

Therefore, the height of the rock is 15 mm.

The exact answer is going to be equal to 15mm

Hope this helped

Answers:

What is the ratio?         120:2

What is the unit rate?   60:1

What is the rate?          60 jumping jacks per minute

===================================================

Further Explanation:

To find the ratio of jumping jacks to minutes, you just write the two values 120 and 2 separated by a colon. That's how we get 120:2 as our first answer.

--------

Once we have 120:2, we divide both parts by 2 to get 60:1

120/2 = 60

2/2 = 1

The reason why we do this is so that the "2 minutes" turns into "1 minute". A unit ratio has the time value in unit increments so we can see how many jumping jacks Samuel can do. Writing "60:1" means "60 jumping jacks in 1 minute"

-------

Saying "60 jumping jacks in 1 minute" is the same as saying "60 jumping jacks per minute", which is similar to a car's speed of something like 60 miles per hour. The unit "X per Y" is the template for speed, where X is the number of items you get done and Y is the unit of time. In this case, X = 60 jumping jacks and Y = 1 minute.

Answer:

They are actually equal.

Step-by-step explanation:

8.09 is equal to 8.090

They both have the same tenth(0) and the same hundredth(9).

A simple way to put this is to just add a zero to 8.09.

8.090

8.090

Answer:

false

Step-by-step explanation:

the only zero that matters is the one before the 9. so, if it was 8.009, ts smaller by one thousandth. if i had 8.09000000000, all the underlined zeros would mean nothing because they arent anything. they are the absence of a value.

Answer:

The length of the original rectangle is 73.4 mm.

The breadth of the original rectangle is 86.6 mm.

Step-by-step explanation:

Given : The perimeter of a rectangle is 320 mm. If its length increases by 10 mm and its breadth decreases by 10 mm then it its area will be 32 less.

To find : Calculate the length and breadth of the original rectangle ?

Solution :

The area of the rectangle is [tex]A=L\times B[/tex]

Let the length of the rectangle be 'x'

The breadth of the rectangle be 'y'

The area is [tex]A=xy[/tex]

Now, length increases by 10 mm i.e. L=x+10

breadth decreases by 10 mm i.e. B=y-10

The new area is [tex]A_n=(x+10)(y-10)[/tex]

According to question,

[tex]A-A_n=32[/tex]

[tex]xy-(x+10)(y-10)=32[/tex] ......(1)

The perimeter of a rectangle is 320 mm.

i.e. [tex]P=2(L+B)[/tex]

[tex]320=2(x+y)[/tex]

[tex]x+y=160[/tex]

[tex]x=160-y[/tex] .....(2)

Substitute the value of y from eqn (2) in (1),

[tex]y(160-y)-(160-y+10)(y-10)=32[/tex]

[tex]160y-y^2-(170-y)(y-10)=32[/tex]

[tex]160y-y^2-(180y-1700-y^2)=32[/tex]

[tex]160y-y^2-180y+1700+y^2=32[/tex]

[tex]1700-20y=32[/tex]

[tex]20y=1732[/tex]

[tex]y=\frac{1732}{20}[/tex]

[tex]y=86.6[/tex]

Substitute in (2),

[tex]x=160-86.6[/tex]

[tex]x=73.4[/tex]

The length of the original rectangle is 73.4 mm.

The breadth of the original rectangle is 86.6 mm.

Answer:

The  number of adults visiting the zoo =  51

The number of children visiting the zoo =  134

Step-by-step explanation:

Let us assume the number of adults  going to the zoo = m

Total number of people visiting the zoo = 185

SO, the number of children visiting the zoo = 185 - m

Now, the cost of 1 adult ticket = $15

So, the total cost of m adult tickets = m x ( cost of 1 adult ticket)

= m  x ( $15)  = 1 5 m

And, the cost of 1 children ticket = $6

So, the total cost of ( 185 - m) adult tickets

= ( 185 - m) x ( cost of 1 children ticket)   = (185 - m )  x ( $6)  = 6( 185 - m)

Also, the combined cost of all tickets  = $ 1569

⇒ The cost of ( Adult's tickets  + Children's Tickets)  = $1569

or,  15 m + 6( 185 - m)  = $1569

or, 15 m + 1110 - 6 m = 1569

or, 9 m =  459

⇒ m = 459/9 =  51 , or m = 51

Hence the  number of adults visiting the zoo = m = 51

The number of children visiting the zoo = 185 -m =  134

Final answer:

To evaluate -6(4 2/3), convert 4 2/3 to an improper fraction, then multiply it by -6 and simplify the result.

Explanation:

To evaluate the expression -6(4 2/3), we need to simplify the expression inside the parentheses first. 4 2/3 can be converted to an improper fraction as follows: (4 * 3 + 2) / 3 = 14 / 3. Then, we multiply -6 by 14/3 to get: -6 * 14/3 = -84/3. The final step is to simplify -84/3, which is -28.

Answer:

7+7+7+6+4+2=33

Each friend will have to pay $11

Step-by-step explanation:

The possible values of tutoring hours are 12 hours, 13 hours, 14 hours, 15 hours.

Given that, Nicole is working two summer jobs, making $10 per hour babysitting and making $20 per hour tutoring.  

In a given week, she can work at most 17 total hours and must earn a minimum of $250.  

Nicole worked 2 hours babysitting, then we have to determine all possible values for the number of whole hours tutoring that she must work to meet her requirements.  

Now, as she worked for 2 hours of babysitting, she will get 2 x $10 = $ 20  

Now, after this, she can work at most (17 - 2) = 15 hours for tutoring and she has to earn minimum of 250 – 20 = $230

Now, let the number of hours she tutored be "n"

Then, from above cases n ≤ 15  

And n x $20 ≥ 230

n ≥ 11.5  

Here we have to cases,  n ≥ 11.5 and n ≤ 15

So, the possible list of n values will be 12, 13, 14, 15

Hence, the possible values of tutoring hours are 12 hours, 13 hours, 14 hours, 15 hours.

The possible values for the number of whole hours tutoring that Nicole must work are: {12, 13, 14, 15} .

Given:

- Nicole can work at most 17 total hours: [tex]\( b + t \leq 17 \)[/tex].

- Nicole must earn a minimum of $250: [tex]\( 10b + 20t \geq 250 \)[/tex].

Nicole worked 2 hours babysitting, so ( b = 2 ).

Substituting ( b = 2 ) into the inequality [tex]\( b + t \leq 17 \)[/tex], we get:

[tex]\[ 2 + t \leq 17 \]\[ t \leq 17 - 2 \]\[ t \leq 15 \][/tex]

Now, let's find the minimum number of hours tutoring that Nicole must work to meet her requirements:

[tex]\[ 10(2) + 20t \geq 250 \]\[ 20 + 20t \geq 250 \]\[ 20t \geq 250 - 20 \]\[ 20t \geq 230 \]\[ t \geq \frac{230}{20} \]\[ t \geq 11.5 \][/tex]

Since Nicole must work a whole number of hours tutoring, the minimum number of hours tutoring she must work is 12 hours.

Answer: Graph A

Graph A: function f of x equals 5 multiplied by 2 to the power of negative x => f (x) = 5 (2)^-x

Graph B: function f of x equals 5 multiplied by 2 to the power of x => f (x) = 5 (2)^x

Graph C: function f of x equals 10 to the power of x => f (x) = 10^x

Graph D: function f of x equals 10 to the power of negative x => f (x) = 10^-x

 Therefore based on the mathematical interpretations above, only Graph A is similar to the given function. Hence the correct answer is:

Graph A

Answer:

The answer is A

Answer:

[tex]A_{21} = 6[/tex]

Step-by-step explanation:

We are given that  

[tex]A = \left [\begin{array}{cccc}10&4&11&12\\6&3&2&8\end{array}\right][/tex] and we have to find the value of [tex]A_{21}[/tex]

Now, the general term [tex]A_{mn}[/tex] denotes the term in the matrix whose position is mth row and nth column.  

So, [tex]A_{21}[/tex] denotes the term in matrix A whose position is 2nd row and 1st column.

Hence, the term is 6.

So, [tex]A_{21} = 6[/tex] (Answer)

Answer:

m=100-5c

Step-by-step explanation:

she starts with 100 bucks, and you take away 5 every time she buys a charm.

Answer:

x = (-4/3)

y = (-5)

Step-by-step explanation:

there ya go, I think this was the answer you were looking for. :)

Step-by-step explanation:

Step 1: -x^2 is -1 because x is always 1.

Now that you found your first step take -1x+10=6. You're going to subtract 10 from both sides which leaves you with a sum of -4. So -1x= -4 now divide -4/-1x which gives you a positive number.

Answer:

x = -2 or 2

Step-by-step explanation:

-x² + 10 = 6

Move everything to one side.  I suggest moving the left side to the right so that the leading coefficient becomes positive.

0 = x² − 4

Factor the difference of squares:

0 = (x − 2) (x + 2)

Set each factor to 0 and solve.

x − 2 = 0

x = 2

x + 2 = 0

x = -2

Therefore, the solution is x = -2 or 2.

Answer:

The x-intercept is (3,0).

The vertex of the function is (3,0).

Step-by-step explanation:

Given : Function [tex]g(x)=-5(x-3)^2[/tex]

To find : What are the x-intercept and vertex of this quadratic function?

Solution :

Function [tex]g(x)=-5(x-3)^2[/tex]

The x-intercept is when g(x)=0.

i.e.  [tex]-5(x-3)^2=0[/tex]

Divide by -5 both side,

[tex](x-3)^2=0[/tex]

Taking root both side,

[tex]x-3=0[/tex]

Add 3 both side,

[tex]x=3[/tex]

The x-intercept is (3,0).

The general vertex form of the quadratic function is [tex]y=a(x-h)^2+k[/tex]

where, (h,k) is the vertex

Compare the given function [tex]g(x)=-5(x-3)^2[/tex]

a=-5 , h=3 and k=0

The vertex of the function is (3,0).

The x-intercept and the vertex of the quadratic function g(x) = -5(x - 3)² are both (3, 0).

Step-by-Step Solution

Finding the x-intercept:

Therefore, the x-intercept is (3, 0).

Finding the Vertex:

Therefore, the vertex is (3, 0).