two cars start moving from the same point. one travels south at 60 miles per hour. the other car travels west at 25 miles per hour. at what rate is the distance between the cars increasing 2 hours later?

The time elapsed, to the nearest minute, until only 2 grams of the element remains is 15 minutes.

We have an element. The element has a mass of 400 grams. The element decays by 29.8% per minute. We need to find the time duration after which there will be only 2 grams of the element remaining. Let the initial mass of the element, the final mass of the element, the rate of decay, and the time elapsed be represented by the variables m, M, r, and t. We can write the equation as given below.

M = m(1 - r)^t

2 = 400(1 - 0.298)^t

0.005 = (0.702)^t

log(0.005) = t*log(0.702)

t = log(0.005)/log(0.702)

t = 14.97

The time taken, to the nearest minute, is 15 minutes.

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Answer:

B

Step-by-step explanation:

[tex]\frac{1}{5}[/tex] b - 5( [tex]\frac{2}{5}[/tex] a - [tex]\frac{1}{10}[/tex] b ) + 4a ← distribute parenthesis by - 5

[tex]\frac{1}{5}[/tex] b - 2a + [tex]\frac{1}{2}[/tex] b + 4a ← collect like terms

= 2a + [tex]\frac{1}{5}[/tex] b + [tex]\frac{1}{2}[/tex] b ( express fractions with a common denominator of 10 )

= 2a + [tex]\frac{2}{10}[/tex] b + [tex]\frac{5}{10}[/tex] b

= 2a + [tex]\frac{7}{10}[/tex] b

The correct statement regarding the message in the graph title is of:

a. No, the three candidates were only separated by a margin of about 2%.

The bar graph shows the number of votes obtained by each candidate, which are listed as follows:

These amounts of votes where quite close, however the bar graph has a bad scale, giving the idea that Roberts got about the double number of votes as Johnson and four times as Gomez.

This bad scale is also used to insert the word wide into the text of the article. However, due to the low absolute difference  in the number of votes between these candidates, this work is not correct, and hence, option a is correct.

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Answer:

-0.98

Step-by-step explanation:

Answer:-0.98

Step-by-step explanation:

The coordinates of the midpoint of segment FG are (3,-1) which was found using midpoint formula.

When it comes to practical application, the midpoint formula is rather straightforward.

Step 1: Determine the line segment or the two ends.

Step 2: Determine their coordinates.

Step 3: Add the x coordinates of both ends and divide by 2.

Step 4: Adding the y coordinates of both endpoints, divide by 2, and complete the step.

Step 5: As you specify the coordinates of any point, write the values that were acquired in Steps 3 and 4.

Given: Endpoints of a line segment are F(2, -1) and G(-8, -1).

We need to find the coordinates of its midpoint.

Using midpoint formula,

(a,b) = (x₁ + x₂)/2,(y₁ + y₂)/2

       = (2-8)/2,(-1-1)/2

       = 3,-1

So, coordinates are (3,-1)

Therefore, the coordinates of the midpoint of segment FG are (3,-1) which was found using midpoint formula.

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Answer:

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

Answer:

Step-by-step explanation:

Forming the equation,

→ 2x + 3 = -3x + 3

Now the value of x will be,

→ 2x + 3 = -3x + 3

→ 2x + 3x = 3 - 3

→ 5x = 0

→ x = 0/5

→ [ x = 0 ]

Then the value of y will be,

→ y = -3x + 3

→ y = -3(0) + 3

→ y = 0 + 3

→ [ y = 3 ]

Hence, the value of y is 3.

Answer: 224/155

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Convert proper Fractions to improper fractions!

-6 2/5/ -4 3/7=

=-32/5/-31/7

2. Multiply by switching Denominator and Numerator of the Fraction!

-32/5/-31/7=

-32/5*-7/31=

224/155=

1 69/155

3. Answer:1 69/155

Answer:

4x

Step-by-step explanation:

bcoz

y = 6 - 2x

6-2x = 4x

y=4x

Note that because the graph is slightly deformed to the left, it is impossible to work out the exact bearing. Below, however, are steps on how to get the bearing of a map.

Calculate the angle clockwise from north to determine a bearing. Begin with the first site by drawing a vertical line symbolizing north. Draw a line from the starting point to the ending point. Calculate the clockwise angle formed by the north line and this line.

When measuring a bearing, three principles must be followed:

Note that a bearing is an angle in degrees calculated clockwise from north in mathematics. Bearings are often specified in three figures. 30° clockwise from north, for example, is generally represented as 030°.

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150 cm

look at the beginning of the axis. it goes 140 to 160. then 160 to 170. it isnt in order. the missing mumber is 150

Answer:

y>14/3

Step-by-step explanation:

Let's solve your inequality step-by-step.

8<3(y−2)

Step 1: Simplify both sides of the inequality.

8<3y−6

Step 2: Flip the equation.

3y−6>8

Step 3: Add 6 to both sides.

3y−6+6>8+6

3y>14

Step 4: Divide both sides by 3.

3y/3 > 14/3

Answer: y>14/3

Hope it helps!

The multiple of 2 and 4 is 48.

A number that is the result of a given number and another natural number is called a multiple of that number. To find the multiple of a number, multiply the number by any whole number.

The given options are A. 50,  B. 58,  C. 54, and D.48.

The multiples of 50 can be written as,

[tex]50=2\times5\times5[/tex]

The multiples of 58 can be written as,

[tex]58=2\times29[/tex]

The multiples of 54 can be written as,

[tex]54=2\times3\times3\times3[/tex]

Therefore, the first three options are not multiples of both 2 and 4.

The multiples of 48 can be written as,

[tex]\begin{aligned}48&=2\times2\times2\times2\times3\\&=4\times2\times2\times3\end{aligned}[/tex]

Therefore, 48 is a multiple of 2 and 4.

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The complete question is -

Which of the following is a multiple of 2 and 4?

A. 50 B. 58 C. 54 D.48

An equation to describe the relationship between g, the number of gems, and c, the number of chests is; g = 300c

In adventure A, when number of gems is 600, we see that number of chests is 2. Thus;

Rate of gems per chests = 600/2 = 300 g/c

In adventure B, when number of gems is 1500, we see that number of chests is 5. Thus;

Rate of gems per chests = 1500/5 = 300 g/c

In adventure C, when number of gems is 4800, we see that number of chests is 16. Thus;

Rate of gems per chests = 4800/16 = 300 g/c

Thus;

There is a constant rate and we can say that the equation that shows the relationship between the two variables is;

g = 300c

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Complete question is;

Lulu the Lucky puts chests of gems into her treasure vault. Each chest holds the same number of gems. The table below shows the number of gems Lulu received from three different adventures and the number of chests she needed to hold the gems.

                      Number of gems(g)     Number of chests(c)

Adventure A    600                            2

Adventure B    1500                           5

Adventure C    4800                          16

Write an equation to describe the relationship between g, the number of gems, and c, the number of chests.

Answer:

Step-by-step explanation:

314 inches  *  (1 foot / 12 inches) * ( 1 meter / 3.28084 foot) * ( 1 kilometer / 1000 meter)

0.0079755997 Km

The lengths of the major and minor axis are 4√6 and 4√3.

A point on a curve is described by an ellipse if its location is such that the sum of the distances between its two focal points is a constant.

(x−h)²/ b² +(y- k)² /a² = 1

Given:

(x−3)²/ 27+(y+4)² /45=1

The above equation can be compared to the standard equation of an ellipse

(x−h)²/ b² +(y- k)² /a² = 1

where, (h, k) = coordinates of the center of the ellipse

a =  length of the semi major axis

b = length of the semi minor axis

By comparison, we have;

(h, k) = (3, -4)

a = √(24) = 2 x√6

b = √(12) = 2 x√3

and, length of the major axis = 2a

length of the minor axis = 2b

Thus, The length of the major axis is

2x a = 2 × 2 x √6 = 4√6

and, length of the minor axis is

2•b = 2 × 2√3 = 4√3

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Answer: 6sqrt(5) and 6sqrt(3)

Step-by-step explanation:

I took the test and these were the correct answers.

The fraction that shows the number of hours Saide's dog sleeps every 4 hours in a day is 1/6.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

It should be noted that there are 24 hours in day. Since the dog sleeps for 4 hours in a day, the fraction will be:

= Number of hours slept / Total hours

= 4 / 24.

= 1/6

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Answer:f^-1(x)= square root x-1 over 4 and square root -square root over 4

Step-by-step explanation:

interchange the variables and solve for y

Answer:

Opposite sides of a parallelogram are:

1. Congruent

2. Parallel

Step-by-step explanation:

Opposite parallel and congruent sides are the features of a parallelogram and are the criteria for a quadrilateral to be a parallelogram.

The coordinates of the points dividing the line in 5:3 is (3/2, 3)

The section formula gives the coordinates of a point which divides the line joining two points in a ratio, internally or externally.

Given a line LM, passing through points  (-1,-2) and (3,6) a point is dividing it in a ratio of 5:3

According to section formula,

(x, y) = (5*3 - 3*1)/8, (5*6 - 3*2)/8

(x, y) = (3/2, 3)

Hence, The coordinates of the points dividing the line in 5:3 is (3/2, 3)

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Answer:

Step-by-step explanation:

1=88

2=42

3=42+25+x=180

3=180-67

The vertices of the transformed image D'E'F'G' is D'(0, 4) E' (4, 3) G'(-2, -4) F'(2, -5)

Rectangle DEFG with vertices D(-4, 3), E(0, 2),and G(-6, -5), F(-2,-6),

is transformed into an image as per  (x,y) → (x + 4, y + 1 )

D(-4, 3)

x = -4, y = 3

The image D' will be (x + 4, y + 1) = (-4 + 4, 3 + 1 ) = (0, 4)

E(0, 2)

x = 0, y = 2

The image E' will be (x + 4, y + 1) = (0 + 4, 2 + 1 ) = (4, 3)

G(-6, -5)

x = -6, y = -5

The image G' will be (x + 4, y + 1) = (-6 + 4, -5 + 1 ) = (-2, -4)

F(-2, -6)

x = -2, y = -6

The image F' will be (x + 4, y + 1) = (-2 + 4, -6 + 1 ) = (2, -5)

Therefore, the vertices of the transformed image D'E'F'G' is D'(0, 4) E' (4, 3) G'(-2, -4) F'(2, -5)

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Convergent Series:

A Convergent Series is a series whose partial sums tend to a specific member is called a limit.

  ∑ 1/2n = 1/2+ 1/4 + 1/8 + 1/16 +........

Given an infinite series ∑₁ ∞ an determine the series is convergence. Recall that we can actually do better with geometric series not only we can determine convergence but also divergence. We can also calculate geometric series.

Suppose we are given a series ∑ aₙ which is not quite a geometric series but becomes a geometric series for sufficiently large n. That is we can find an integer N such that aₙ = aₓⁿ for all n > N. we don't have a general formula for aₙ when n ≤ N. The values of aₙ for small n don't effect Sₙ is convergence or not.

As a moment of fact, we never used the fact that aₙ eventually become geometric. More general ∑aₙ is convergent series, we can add a finite number of terms to the be gaining of this series or remove a finite number of terms from the be gaining of the series without affecting the convergence  of the series. For Example: if ∑aₙ convergence then so does

                        10 + 10¹⁰ + 10 ¹⁰⁰ + 10¹⁰⁰⁰ + ∑aₙ

Similarly, if ∑aₙ convergence then,

                a₁₀₀₀ +a₁₀₀₁ +a₁₀₀₂ + ..... = ∑₁₀₀₀ ∞ aₙ

However, the fact that we are only adding finitely many terms to the series is essential. That is, when it comes to determining convergence of a series ∑aₙ , we can see that only the asymptotic  behavior of ∑aₙ matter, that is, only the behavior of the sequence aₙ as n--- ∞ affects convergence.

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Answer:

Have Dracula pay you $5

Step-by-step explanation:

This whole thing happened because Dracula was broke. If $5 is given to Dracula, he can give you back $5 so you can return 5$ to Frankenstein. Then Frankenstein can give $2 back to Dracula.

You walked 16 blocks in a time of 28 minutes. At this rate you walk 1 block in 1 minute 75 seconds.

In Science, distance can be defined as the amount of ground that is covered (travelled) by a physical object over a particular period of time and speed, irrespective of its direction, starting point or ending point.

Mathematically, the distance traveled by a physical object (body) can be calculated by using this formula:

Distance = speed (rate) × time

Note: Let the variable x represent the halfway distance.

Since it takes the same amount of time to walk each block and halfway there, half of the berries are gone. Therefore, we have the following:

At point x, the number of strawberries that is left is equal to 12 strawberries while the distance after walking 3 more blocks, you still have 5 blocks to go would be given by:

1/2 × x = (3 + 5) = 8

1/2 × x = 8

Distance, x = 8 × 2

Distance, x = 16 blocks.

Now, we can determine the rate at which this person walks a block:

Rate (speed) = 28/16

Rate (speed) = 1.75 minutes.

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Answer:

Answer:

1 2/3

Step-by-step explanation:

How much does 6 go into 10? Only 1 time so the whole number will be 1.

Next, subtract 6 from 10 and you get 4.

1 4/6 reduces to 1 2/3

Answer: 1 2/3 (pls give me brainiest not to be greedy but pls)

Step-by-step explanation:

Answer:

answer -a dilation followed by a translation

-a dilation followed by a reflection

-a reflection followed by a dilation

-a rotation followed by a dilation

Applying the inscribed angle theorem, we have:

9. B. m∠ABC = 70°

10. F. m∠Z = 54°

11. According to the two-tangent theorem, x is: D. 8 m

An inscribed angle in a circle has a measure that is half of the measure of the intercepted arc, based on the inscribed angle theorem.

The two-tangent theorem states that if two tangents are drawn from a circle to meet at a point outside the circle, the two tangents are equal to each other.

9. Measure of arc AC = 360 - 120 - 100

Measure of arc AC = 140°

m∠ABC = 1/2(measure of arc AC) [inscribed angle theorem]

m∠ABC = 1/2(140)

m∠ABC = 70° [option B]

10. Arc XYZ = 2(m∠X) [inscribed angle theorem]

Arc XYZ = 2(126) = 252°

Arc WXY = 360 - arc XYZ

Arc WXY = 360 - 252

Arc WXY = 108°

m∠Z = 1/2(arc WXY) [inscribed angle theorem]

m∠Z = 1/2(108)

m∠Z = 54° [option F]

11. x = 10 - 2 [two-tangent theorem]

x = 8 m [option D]

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The price of 72 rolls of toilet rolls in each shop is:

The shop with the best value for money is Lidal.

Lidal sells 8 toilet rolls for $2.80 and so if it was to sell 72 rolls, it would sell at a price of:

= Price per 8 rolls x Number of rolls / Number of rolls in packages

= 2.80 x 72 / 8

= 2. 80 x 9

= $25.20

Oldi sells 9 toilet rolls for $3.24 so the cost of 72 rolls would be:

= 3. 24 x 72 / 9

= 3. 24 x 8

= $25. 92

The shop with the best value for money is the cheaper one which is Lidal.

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Answer:

FALSE

Step-by-step explanation:

3.6ft is 43.2

3ft 6in is 42 in