The population of a city is currently 45,000 and is declining at a rate of 2% each year. Give a formula for determining the total population after a period of t years.
A) A = (45,000) e-0.02t
B) A= 45,000 + e-0.02t
C) A = (45,000) e0.02t
D) A = 45,000 + e
0.02t​

-sint is the acceleration at time t.

Acceleration is the rate of change of the velocity of an object with respect to time.

Given, the height (cm) of an object oscillating up and down at the end of a spring is s(t) = 100 + cos t.

We need to find the  acceleration at time t.

s(t) = 100 + cos t.

To find the acceleration we have to differentiate the above equation.

d/dt=d/dt(100+cost)

=d/dt(100)+d/dt(cost)

=0+(-sint)

s'(t) = -sint.

Hence, the acceleration at time t is -sint.

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The time it takes Carly to walk 7 miles is 91 minutes

From the question, we have the following parameters that can be used in our computation:

Time = 39 minutes

Distance = 3 miles

The speed can be calculated as

Speed = Distance/Time

Substitute the known values in the above equation, so, we have the following representation

Speed = 3 miles/39 minutes

So, we have

Speed = 1/13 miles per minute

From the question, we have

Distance = 7 miles

Recall that

Speed = Distance/Time

Make time the subject

Time = Distance/Speed

So, we have

Time = 7/(1/13)

Evaluate

Time = 91 minutes

Hence, the time is 91 minutes

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Answer: The answer is 8/5

Answer:

Each person gets 8/5 part of cookie

Answer:

Mixture B

Step-by-step explanation:

A) the concentrate per cup is 2/3

B) the concentrate per cup is 6/8 = 3/4

The concentration of B is higher, so it will taste juicier.

Answer:

  (-6, -2)

Step-by-step explanation:

For points A(-10, 2) and B(-3, -5), you want the point P that makes AP/PB = 4/3.

Using (x, y) for the coordinates of P, we have ...

  AP/PB = 4/3

  ((x, y) -(-10, 2))/((-3, -5) -(x, y)) = 4/3

This simplifies to ...

  (x+10, y-2)/(-3-x, -5-y) = 4/3

Cross multiplying gives ...

  3(x +10, y -2) = 4(-3 -x, -5 -y)

  (3x+30, 3y-6) = (-12-4x, -20-4y)

Treating these equations separately, we have ...

  3x +30 = -12 -4x   ⇒   7x = -42   ⇒   x = -6

  3y -6 = -20 -4y   ⇒   7y = -14   ⇒   y = -2

The point that partitions the segment is (-6, -2).

__

Additional comment

The point that partitions AB in the ratio m/n is ...

  P = (mB +nA)/(m+n)

  P = (4(-3, -5) +3(-10, 2))/(4+3) = (-12-30, -20+6)/7 = (-42, -14)/7 = (-6, -2)

Above, we started from the basic requirement, rather than using the formula that results from that requirement.

A: 16.09 %  of the survey respondents liked neither hamburgers nor burritos

B) 0.65  is the marginal relative frequency.

C) The lowest joint relative frequency of those who like Hamburgers but not burritos.

The ratio of a row total's or column total's frequency to the overall frequency of the data is known as marginal relative frequency. It is frequently used to examine broad trends in a single type of data.

Given:

                          Like Hamburgers    Does Not Like Hamburgers    Total

Likes burritos                  39                           38                                   77

Does not like burritos     95                           33                                 128

Total                                 134                           71                                 205

A) There are 33 such respondents.  

So, percentage is

= 33/205 x 100

= 16.095

B) It will be the ratio of the sum of the customers that like hamburgers to the total number of respondents

So, the ratio is

= 134/205

= 0.65 :1

Part C:  For this, we need to find the ratio of all the four data with the total.

Those who like Hamburgers and burritos

= 39/134

Those who like Hamburgers but not burritos

= 95/134

Those who like burritos but not Hamburgers

=38/71

Those who do not like burritos or Hamburgers = 33/71

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The demand function is given by the expression -

D{x} = mn(a²x + 2b + b²)

Given is the revenue function as follows -

f(x) = mn (ax + b)²

The revenue function is simply [x] multiplied by the demand function.

R{x} = x (D{x})

The revenue function is -

f(x) = mn (ax + b)²

So, the demand function can be written as -

mn(ax + b)² = x (D{x})

D{x} = {mn(ax + b)²}/x

D{x} = {mn(a²x² + b² + 2abx)}/x

D{x} = {a²x²mn + mnb² + 2bmnx}/x

D{x} = a²xmn + 2bmn + mnb²

D{x} = mn(a²x + 2b + b²)

Therefore, the demand function is given by the expression -

D{x} = mn(a²x + 2b + b²).

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The value of x after solving −0.28x − 8.4 = 8.26  is   x = −59.5 .

What is linear equation in one variable ?

The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution. For example, 2x+3=8 is a linear equation having a single variable in it.

To solve linear equation in one variable:

Step 1: Simplify each side, if needed.

Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.

Step 3: Use Mult./Div. Properties to remove any values that are in front of the variable.

Given :

-0.28x - 8.4 = 8.26

Adding 8.4 both the sides , we get

-0.28x + (-8.4 + 8.4) = 8.26 + 8.4

-0.28x = 16.66

x = - (16.66/0.28)

x = -59.5

Hence , the value of x after solving −0.28x − 8.4 = 8.26  is   x = −59.5 .

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Answer:

y - intercept = 6

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6 + 2x , that is

y = 2x + 6 ← is in slope- intercept form

with y- intercept c = 6

Answer:

-2/4

Step-by-step explanation:

To find out how much the wool costs, we need to multiply the price of a yard of nylon by 3, since the wool is 3 times more expensive. So a yard of wool costs $3 * 3 = $<<3*3=9>>9.

To find out how many yards of wool Caleb bought, we need to divide the total number of yards by the number of fabrics, since he bought the same amount of each fabric. So Caleb bought 68 / 2 = <<68/2=34>>34 yards of wool.

To find out how much Caleb spent on wool, we need to multiply the number of yards of wool by the price of a yard of wool. So Caleb spent 34 * $9 = $<<34*9=306>>306 on wool.

To find out how much Caleb spent on nylon, we need to multiply the number of yards of nylon by the price of a yard of nylon. So Caleb spent 68 * $3 = $<<68*3=204>>204 on nylon.

To find out how much Caleb spent in total, we need to add the amount he spent on wool and the amount he spent on nylon. So Caleb spent $306 + $204 = $<<306+204=510>>510 in total. Answer: \boxed{510}.

Answer:

x is the first mile marker

then, x+%2B+1 the second mile marker

given:

x%2Bx+%2B+1=655

2x+=655-1

2x+=654

x+=654%2F2

x+=327->the first mile marker

and

x+%2B+1=328 the second mile marker

No solution: 1/2y + 3.2 = 20, 15/2 + 2z -1/4 = 4z + 29/4 - 2z, 1.1 + 3/2x + 2 = 3.1 + 3/4x, and 4.5r = 3.2 + 4.5r. One solution: 2x + 4 = 3x + 1/2

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

If the value of the variable is zero, then the no solution.

If the value of the variable is one, then the one solution.

If the value of the variable is infinity, then the infinite many solutions.

No solution: 1/2y + 3.2 = 20, 15/2 + 2z -1/4 = 4z + 29/4 - 2z, 1.1 + 3/2x + 2 = 3.1 + 3/4x, and 4.5r = 3.2 + 4.5r.

One solution: 2x + 4 = 3x + 1/2

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Answer:

y=5x+0

Step-by-step explanation:

wouldn't the equation be something like y=5x+0?  If x=5 then x would be the slope. So then if the slope is 5 you'd start off your equation y=5x but there might not be a y-int for this equation because the equation only has an x and there is no y.

(Not sure if you understand it, but if it were to me I'd do something like this because there is only one number in the equation, hope this helps in some way....)

Step-by-step explanation:

You start with x+1=7x-5

Basically you want all the x's on one side and all the constants on the other

(x+1)+5=(7x-5)+5, to get rid of the 5 on the right side

(x+6)-x=7x-x, to get rid of the x on the left side

We are now left with 6x=6

No we simplify, 6x/6=6/6

Now we have x=1, which is the answer

I hope this made sense.

x= 1.

[tex](x+1)=(7x-5)\\ \\x+1=7x-5[/tex]

[tex]x+1-1=7x-5-1\\ \\x=7x-6[/tex]

[tex]x-7x=7x-6-7x\\ \\-6x=-6[/tex]

[tex]\frac{-6x}{-6} =\frac{-6}{-6} \\ \\x=1[/tex]

[tex](1)+1=7(1)-5\\ \\2=7-5\\ \\2=2[/tex]

That's correct!

x= 1.

The required probability for the given case is obtained as 1/6.

Probability is the measurement of the chance for a random event.

It is the ratio of the favorable outcome to the total possible outcome.

It always lies in the interval [0, 1].

The sample space for the given case can be written as follow,

The total number of sample space elements are,

Possible outcomes for coin × Possible outcomes for cube

= 2 × 6 = 12

Now, the number of favorable outcomes for the given event is as below,

Number of head × Number of numbers less than 3

= 1 × 2 = 2

Now, the probability is given as,

P(Head on coin and less than 3 on cube) = 2/12 = 1/6

Hence, the probability of getting heads on the coin and a number less than 3 on the number cube is given as 1/6.

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Answer:

Step-by-step explanation:

Use the figure to complete each sentence. The base of this rectangle is cm. The height of this rectangle is cm. The area of this rectangle is cm2.

Answer:

24 cm²

Step-by-step explanation:

Solution Given:

The base of this rectangle is 4 cm. The height of this rectangle is 6 cm

height =6 cm

base = 4cm

Since

Area of Rectangle= base*height

=6*4

=24 cm²

Therefore, the area of this rectangle is 24 cm².

The equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x  - 6*y +21 =0

Given that, the points (3,0) and (7,6)

(x1, y1) = (3,0) and (x2, y2) = (7,6)

We know that the formula for the equation of circle whose points of diameter are given is equal to :

(x - x1) * (x - x2) + (y - y1) * (y - y2)

So now,

(x - 3) * (x - 7) + (y - 0) * (y - 6) = x² + y² - 10*x  - 6*y +21 =0

so the equation of a circle that has a diameter that passes through the points (3,0) and (7,6) is x² + y² - 10*x  - 6*y +21 =0

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If a train traveled 300 miles. The time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.

Distance = Rate × Time

Time =Distance/Rate

1. 50 mph

Time = 300/50

Time = 6 hours

2. 70 mph

Time = 300/70

Time = 4.29 hours

3. x mph

Time = 300/x

Time = 300/x hours

4. (x+10)mph

300/(x+10) hours

5. (x-5)mph

300/(x-5) hours

Therefore the  time is, 6 hours, 4.29 hours, 300/x hours, 300/(x+10) hours,300/(x+5) hours.

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There are X automobiles, with a mean of 12.5 cars. The standard deviation for X is also SD = 12.0.

First, a data set's mean and standard deviation convey distinct information. The average (center) of a data collection is provided by mean (it is a measure of central tendency). You may learn about the range (dispersion) of data around the mean by looking at the standard deviation. We may investigate a data set's characteristics and characterize it using both the mean and standard deviation. To provide confidence intervals for data that has a normal distribution, they are frequently combined. If two or more data sets need to be compared:

The mean reveals whether data set is, on average, greater or lower (or better or worse). We can determine whether data set has a wider dispersion using the standard deviation (higher standard deviation means data is more spread out from the mean). Second, there are variations in how each metric is calculated. In particular, we utilize squaring to get the standard deviation but not the mean. We completely avoid using squaring when determining the mean of a data collection. Simply multiplying the total number of data points in the set by the sum of all the values in the data set yields the answer.

The mean is calculated as follows:

Mean = (all data values added together) / (number of data values)

However, when calculating standard deviation, we do employ squaring. We take the square of the deviation between each data point and the mean in particular.

The standard deviation equation is as follows:

Finally, when we add the identical value to each data point in the data set, the mean and standard deviation "respond" differently. If we multiply every value in a data collection by the constant "K":

No of the size of the data collection, the mean rises by precisely K.

No matter how many observations are in the data collection, the standard deviation does not vary. The identical value is then added.

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This person has walked a total of 21 miles and the total displacement vector for this walk is 13.153 in northeast direction by the concept of distance and displacement.

Unaffected by direction, distance describes an object's entire movement. Displacement, in contrast, refers to a shift in an object's position. Because of this, the primary distinction between distance and displacement is that one is a scalar and the other is a vector.

According to question let us determine the total distance 2 miles+3 miles+6 miles+7 miles+3 miles =21 miles

So, this person has walked a total of 21 miles

Now let us find displacement vector as follows:

Divide into parts: Each leg on the Southeast and Southwest diagonals is the hypotenuse, therefore multiply by (2) /2.

x-axis is given as 2+3*(√ (2) /2) +0 -7(√ (2) /2) +3 =1.464

Similarly, y-axis is given as 0- 3(√ (2) /2)- 6- 7(√ (2) /2) +0=-13.071

The coordinates of the given ques are as follows: <1.464, -13.071>

By Pythagoras theorem, the hypotenuse of the given coordinates is 13.153 in northeast which is our required displacement.

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The Factors of 3x^4-5x^3+6x^2-15x completely over the set of integers will give 5(1-3x).

In mathematics, factorization or factoring consists of writing a number or another mathematical object as a product of several factors, usually smaller

The expression can be broken down after the other as

[2x4 = 8] + [5x3=15] + [6x2=12]

= [8-15+12-15x]

=5-15x

then we can factorize as

5(1-3x)

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Answer:

Step-by-step explanation:

j = 3s

(j-10 + s-10) =44

3s-20 + s =44

4s = 64

s = 16

j=3*16

j=48

currently Joseph is 48,  the son is 16,  so

16 years ago,  when the son was born,  Joseph was 32

Answer:

Joseph was 34 years old when his son was born.

The interquartile range (IQR) is a measure of dispersion, which is a measure of how spread out a data set is. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3).

Q1 = ( n +1 ) / 4th observation

    = ( 9 + 1) / 4

    = 2.5 th obseravation

That is the average of 2nd and 3rd observations.

Q1 = 2

Q3 = 3 ( n + 1) / 4 th observation

     = 3 ( 9 + 1) / 4

     = 7.5 th observation

That is the average of the 7th and 8th observation

Q3 = 5.5

Interquartile range = Q3 - Q1 = 5.5 - 2 = 3.5

In this data set, the first quartile is the average of the second and third observations (2), and the third quartile is the average of the seventh and eighth observations (5.5). Subtracting the first quartile from the third quartile gives us an IQR of 3.5. This means that the values in the data set are spread out over a range of 3.5 dollars.

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Answer:

Look at the image I attached to this answer for the answers.

This is a crossword puzzle on geometry terms and concepts, including lines, angles, and planes.

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The expression that gives the perimeter of the A'B'C is 2 (a + b + c).

Option B is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

The side length of triangle A'B'C' is twice the length of the corresponding side length of triangle ABC.  

The perimeter of a triangle.

= Sum of all the three sides

Now,

The perimeter of the triangle ABC.

= a + b + c

Thus,

The perimeter of the triangle A'B'C'.

= 2 (a + b + c)

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Answer:−cnotu+53.65

Step-by-step explanation: I don't really know how I got it. But it was quite easy.

Answer:

the answer is 10

Step-by-step explanation:

The value of the numerical expression 24 / (4 × 2 - 2) will be 4.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expression is given below.

⇒ 24 / (4 × 2 - 2)

Simplify the expression, then we have

⇒ 24 / (4 × 2 - 2)

⇒ 24 / (8 - 2)

⇒ 24 / 6

⇒ 4

The value of the numerical expression 24 / (4 × 2 - 2) will be 4.

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