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Two runners are saving money to attend a marathon.
The first runner has $110 in savings, received a $45 gift
from a friend, and will save $25 each month. The
second runner has $50 in savings and will save $60
each month.
After how many months will both runners have the
same amount of money?
02
O 3

The speed of the rabbit in miles per hour is 50.33 mi/h.

We know that the speed of the jackrabbit is:

1.35 km/min.

Now we need to use the relations:

1 hour = 60 minutes.

So, in one hour, the rabit runs 60 times the distance that it runs in one minute, then:

1.35 km/min = 60*(1.35 km/h) = 81km/h

Now we need to change kilometers for miles.

1km = 0.6214 mi

Then we can rewrite:

81km/h = 81*0.6214mi/h = 50.33 mi/h

The speed of the rabbit in miles per hour is 50.33 mi/h.

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Answer:

[tex]P = A - I[/tex]

Step-by-step explanation:

Answer:

3x²

Step-by-step explanation:

0.482 to 1sf is 0.5

61.2x² to one sf is 60x²

√98.01 to 1sf is √100

√100 = 10

0.5 x 60x² = 30x²

30x² / 10 = 3x²

If a polyhedron has a volume of 35 cm cube and is dilated by a factor of 5/2 then the volume of dilated polyhedron will be 50.6 cm cube.

Given Volume of polyhedron=35 cm cube . Factor from which is dilated 5/2.

If the polyhedron is dilated by factor 5/2 then the volume of the polyhedron will change by the cube of that  factor because when it is dilated by factor its material also increases.

Volume =35[tex]cm^{3}[/tex]

After dilation

Volume=35+[tex](5/2)^{3}[/tex]

=35+15.625

=50.625

After Rounding nearest to thousand we will get 50.6 [tex]cm^{3}[/tex].

Hence after dilation the volume which is 35 cm cube will change from 35 to 50.6[tex]cm^{3}[/tex].

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Answer:

Step-by-step explanation:

The answer would be "me" as the indirect object

The ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

The median weekly earnings on the graphs are

Represent as a ratio

Ratio = $750 : $1250

Divide by 250

Ratio = 3 : 5

Hence, the ratio of the median weekly earnings is 3 : 5

In (a), we have:

Ratio = 3 : 5

The horizontal scale is given as:

Ratio = 1 unit : 1 grid mark

The rectangles in graph A have a width of 1 unit.

So, we have:

Ratio = 3 * 1: 5 * 1

Ratio = 3 : 5

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph A is 3 : 5

Recall that:

Ratio = 3 : 5

Ratio = 1 unit : 1 grid mark

From the graph, we have the following widths:

Red = 3 units

Blue = 5 units

So, we have:

Ratio = 3 * 3 : 5 * 5

Simplify

Ratio = 9 : 25

Hence, the ratio of the area of the red rectangle to the blue rectangle in graph B is 9 : 25

Recall that:

Ratio = 3 : 5

Ratio = 1 unit : 1 grid mark

From the graph, we have the following widths:

Red = 3 units

Blue = 5 units

Since the base are squares, we have:

Ratio = 3 * 3  * 3 : 5 * 5 * 5

Simplify

Ratio = 27 : 125

Hence, the ratio of the volume of the red cube to the blue cube in graph C is 27 : 125

The most misleading graph is graph B.

This is so because the blue rectangle and the red rectangle do not have the same width when plotted on the same scale

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Answer:

1/90

Step-by-step explanation:

Comment

To begin with, there are 10 tiles.. You draw one and don't replace it. Then you draw another tile from the 9 that remain.  The job is to figure out the probability of that happening.

You have a 1/10 chance of drawing the M.

But now there are only 9 tiles left and you have a 1 in 9 chance of drawing a T

Solution

P(M,T) = 1/10 * 1/9 = 1 / 90

You have a 1 in 90 chance of getting the two tiles in the order you have specified.

The slope for both the line is m= 1/3 and  they are parallel lines , Option B and C are correct two options

The first equation is

 y = (1/3)x-4 and not y = -x-4

(if the equation is not corrected then it will not have two true statements)

A system of equation is a set of equation which have a common solution

The given system of equation is

y = (1/3)x-4

3y -x = -7

3y = x-7

As it can seen from the standard equation of a line that

y =mx+c

so slope for both the line is m= 1/3

Therefore they are parallel lines

Thus , Option B and C are correct two options

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D.

[tex]m(x) = 0 \\ - 3x = 0 \\ x = 0[/tex]

E.

[tex]m(x) = \frac{ - 3}{25} [/tex]

[tex] \frac{ - 3x}{x {}^{2} + 2x - 24} = \frac{ - 3}{25} [/tex]

[tex] - 3(x {}^{2} + 2x - 24) = - 3(x)(25) \\ divide \: both \: sides \: by - 3[/tex]

[tex]x {}^{2} + 2x - 24 = 25x[/tex]

[tex]x {}^{2} - 23x - 24 = 0[/tex]

[tex](x - 24)(x + 1) = 0 [/tex]

[tex]x = 24 \\ x = - 1[/tex]

Answer:

D

x=0

Step-by-step explanation:

E)

[tex]\frac{-3x}{x^2+2x-24} =\frac{-3}{25} \\x^2+2x-24=25x\\x^2+2x-25x-24=0\\x^2-23 x-24=0\\x^2-24x+x-24=0\\x(x-24)+1(x-24)=0\\(x-24)(x+1)=0\\x=24,-1[/tex]

Answer:

Step-by-step explanation:

Comment

I find the wording a bit confusing. Does the question mean that the laws of algebra determine what single vale of x will make the right side = the left side in both equations?

I think that's the way I will interpret it.

The easiest way to solve both of them is to divide by 4 on both sides of the top equation and divide by 2 on the bottom equation.

Solution

Top equation

4(x - 2) = 1000                                 Divide by 4

4(x-2 )/ 4 = 1000/4          

(x - 2)  = 250                                    Remove the brackets

x - 2 = 250                                       Add 2 to both sides

x - 2 + 2 = 250 + 2                           Combine

x = 252

Bottom equation

2(x - 2) = 50                                      Divide by 2

2(x - 2)/2 = 50/2

(x - 2) = 25                                        Remove the brackets

x - 2 = 25                                          Add 2 to both sides

x - 2 + 2 = 25 + 2                              Combine

x = 27

Conclusion

If the equations are structured the same way but have different numbers then the answers will be unique.

Answer:

hjjj gogo fgjvsgjgccvvggggggffffffddsddddfffgv

Answer:

3

Step-by-step explanation:

Cardinalities are the number of elements in a set.

(A∩B∩C) is the very middle part of the circle, and there are 3 elements there.

The cash flow in year 1 is $15.

A growing perpetuity increases continuously and indefinitely.

Cash flow = present value x (rate of return - growth rate)

214 x (10% - 3%)

214 x 0.07 = $15

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Answer:

Let us assume that √2 is a rational number.

So it can be expressed in the form p/q where p, q are co-prime integers and q≠0

√2 = p/q

Here p and q are coprime numbers and q ≠ 0

Step-by-step explanation:

√2 = p/q

On squaring both the sides we get,

=>2 = (p/q)2

=> 2q2 = p2……………………………..(1)

p2/2 = q2

So 2 divides p and p is a multiple of 2.

⇒ p = 2m

⇒ p² = 4m² ………………………………..(2)

From equations (1) and (2), we get,

2q² = 4m²

⇒ q² = 2m²

⇒ q² is a multiple of 2

⇒ q is a multiple of 2

Hence, p, q have a common factor 2. This contradicts our assumption that they are co-primes. Therefore, p/q is not a rational number

√2 is an irrational number.

Answer:

First Graph:  -2x - 1 = 3(^-x)

Last Graph: 2^(-x) + 2 = 5^-x + 3

Step-by-step explanation:

For a system of equations to have a solution set, the graphs that depict them must intersect at one point.

Both graphs #1 and #5 do not intersect, hence graphs #1 and #5 are the only graphs that do not have solutions while the other graphs do.

Answer:

[tex] \frac{289}{111} [/tex]

Step-by-step explanation:

[tex]2 + \frac{603}{1000 - 1} = 2 \frac{603}{999} = 2 \frac{67}{111} = \frac{289}{111} [/tex]

Answer:

Step-by-step explanation:

4c + 11 = -25

4c = -25 - 11

4c = -36

c = -36 : 4

c = -9

or

4c + 11 + 25 = 0

4c + 36 = 0

c = (-36)/4

c = -9

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

check

4 *(-9) + 11 = -25

-36 + 11 = -25

-25 = -25

the answer is good

Answer:

c= -9

Step-by-step explanation:

1. 4c + 11 = -25

2. Put all like terms together and change the sign. In this case, the +11 will go to the right with the -25 and it will become -11.

Therefore:

4c= -25 -11

4c= -36

3. Make c the subject. Since 4 is being multiplied by c, when it goes to the right, it will divide.

Therefore:

c= -36/4

c= -9

Answer:

Vicks monthly interest payment is $91

Step-by-step explanation:

Total: $1800

Down payment: $500    (already paid)

Current balance need to be paid:

$1800 -  $500 = $1300

7% of  $1300 is, 1300 x 0.07 = $91

Therefore, we can write it as f(x) ≥ 0 over the interval [-1,1].

The given coordinates of the given table are (-3,15), (-2,-5), (-1,0), (0,5), and (1,0).

We need to write a valid prediction about the continuous function f(x).

In mathematics, a continuous function is a function such that a continuous variation of the argument induces a continuous variation of the value of the function.

Now, it is clear from the values of f(x) with respect to x, that the function reaches zero at x = -1, then goes up to 5 at x = 0 and then again reaches zero at x = 1.

So, the value of f(x) remains positive within the interval of [-1,1].

Therefore, we can write it as f(x) ≥ 0 over the interval [-1,1].

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The average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

The slope:

[tex]\rm m =\dfrac{16717-12078}{2017-2009}[/tex]

m = 4639/8

m = 579.875

Thus, the average rate of change (slope) is 579.875 if, in 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants.

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Answer:

b) angles 1 and 4 are congruent.

Hope it helps!

Answer:

-6/11 goes with -1/2

-7/9 goes with -3/4

-3/13 goes with -1/4

Step-by-step explanation:

6/11 is close to 6/12 which is the same as 1/2, so -6/11 goes with -1/2

7/9 is close to 6.75/9 which is 3/4, so -7/9 is close to -3/4

3/13 is close to 3/12 which is the same as 1/4, so -3/13 goes with -1/4

Answer:

This is my answer↓:

Step-by-step explanation:

He school play sold $550 in tickets one night.

The number of $8 adult tickets was 10 less than twice the number of

$5 child tickets.

How many of each ticket were sold

Let say child ticket sold = x

Adult tickets was 10 less than twice the number of    child tickets.

=> Adult ticket sold = 2x - 10

Child ticket sold = x

$5 child tickets price

=> Revenue = 5x  $

Adult ticket sold = 2x - 10

$8 Adult tickets price

=> Revenue = 8(2x - 10) =16x - 80 $

5x + 16x - 80 = 550

=> 21x = 630

=> x = 30

Child ticket sold = 30

Adult ticket sold = 50

Total ticket sold = 80

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The short leg of a 90-45-45 triangle is 3 and the long leg is 7. The hypotenuse would be [tex]c = \sqrt{58}[/tex].

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

The short leg of a 90-45-45 triangle is 3 and the long leg is 7.

Since this is a right triangle, we can use the Pythagoras theorem

a^2+b^2 = c^2  

where a and b are the legs and c is the hypotenuse

[tex]3^2 + 7^2 = c^2\\\\9 + 49 = c^2\\\\58 = c^2\\\\c = \sqrt{58}[/tex]

Hence, The hypotenuse would be [tex]c = \sqrt{58}[/tex].

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Answer:

-4.5

Step-by-step explanation:

You arrange the numbers from lowest to highest value:

-17, -12, -11, -10, -7, -2, 7, 10, 16, 20

Then you find the one in the middle:

-7, -2

Because there are two in the middle, you add them and divide them by two:

(-7 + -2)/2 = -4.5

Your answer is -4.5.

Step-by-step explanation:

firstly arrange it increasingly

-2,-7,-10,-11,-17, 7,10,16,20

n=9 it is odd so we use (n+1/2 )th formula

9+1/2

10/2=5th

os it is -17