A population of bacteria is growing according to the exponential model P = 100e(.70)t, where P is the number of colonies and t is measured in hours. After how many hours will 300 colonies be present? [Round answer to the nearest tenth.]
A) 0.7
B) 1.6
C) 5.7
D) 7.2

Answer:

Step-by-step explanation:

a) When will the height be 307 feet?

h = − 16t^2 + 171t + 17

307 = − 16t^2 + 171t + 17

Solving the quadratic equation by the general formula (find the plot attached). It reaches 307' twice as it is a parabolic shot.

t=2.1141s

t=8,5734s

b) When will the object reach the ground?

h = − 16t^2 + 171t + 17

0 = − 16t^2 + 171t + 17

t=-0.0985s (not real as there exists no negative time)

t=10.786s

The object will be at a height of 307 feet approximately 9.54 seconds after it was thrown. The object will reach the ground approximately 0.21 seconds after it was thrown.

To find when the height will be 307 feet, you can set the equation for the height h to 307 and solve for t:

h = -16t² + 171t + 17

307 = -16t² + 171t + 17

Now, let's rearrange the equation and set it equal to zero:

-16t² + 171t + 17 - 307 = 0

Combine like terms:

-16t² + 171t - 290 = 0

Now, you can solve this quadratic equation for t. You can use the quadratic formula:

t = (-b ± √(b² - 4ac)) / (2a)

In this case, a = -16, b = 171, and c = -290. Plug these values into the quadratic formula:

t = (-171 ± √(171² - 4 * (-16) * (-290))) / (2 * (-16))

Now, calculate the values for t:

t₁ = (-171 + √(171² - 4 * (-16) * (-290))) / (2 * (-16))

t₂ = (-171 - √(171² - 4 * (-16) * (-290))) / (2 * (-16))

Calculate t₁ and t₂ separately:

t₁ ≈ 9.54 seconds

t₂ ≈ -9.69 seconds

Since time cannot be negative in this context, we discard the negative solution. Therefore, the object will be at a height of 307 feet approximately 9.54 seconds after it was thrown.

To find when the object will reach the ground, you can set h equal to 0 and solve for t:

h = -16t² + 171t + 17

0 = -16t² + 171t + 17

Rearrange the equation:

-16t² + 171t + 17 = 0

Now, solve for t using the quadratic formula as we did before:

t = (-171 ± √(171² - 4 * (-16) * 17)) / (2 * (-16))

Calculate t₁ and t₂:

t₁ ≈ 0.21 seconds

t₂ ≈ 10.30 seconds

Again, you discard the negative solution. So, the object will reach the ground approximately 0.21 seconds after it was thrown.

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11(.25)= 2.75

Cryus should order 3 pizzas.

Answer:

x = 1 11/15

Step-by-step explanation:

Using ratios of similar triangles

3            5.2

-------- = ----------

4            (5.2 + x)

Using cross products

3 * (5.2 + x) = 5.2 * 4

Distribute

15.6 + 3x = 20.8

Subtract 15.6 from each side

15.6-15.6 + 3x = 20.8 -15.6

3x =5.2

Divide each side by 3

3x/3 = 5.2/3

x = 5.2/3

x=52/30

x = 26/15

x = 1 11/15

Answer:

40

Step-by-step explanation:

The data is

21,24,25,28,29,35,37,43,44

To find the third quartile we have to arrange the data in increasing order

so the data in increasing order is

21,24,25,28,29,35,37,43,44

total number of values = 9

Median value = (n + 1 )/ 2

                       =(9+1)/2

                       =5th value

so the median is  29

Lower half of the data is the values before the median and upper half of the data is values after the median

so lower half = {21,24,25,28}

Upper half = {35,37,43,44}

so to find the third quartile we will use the upper half of the values

Third quartile means that the median of the values of upper half of the data

As the total No of value in upper half is 4 which is an even no

we will take the middle values of the upper half and take their mean

so

Third Quartile = [tex]\frac{37+43}{2}[/tex]

                        =[tex]\frac{80}{2}[/tex]

                        =40

so the value of third quartile is 40

Final answer:

The third quartile (Q3) of the data set is 40, calculated by finding the average of the two middle numbers of the upper half of the data after excluding the median.

Explanation:

To find the third quartile of a data set, which is also referred to as Q3 or the 75th percentile, one must identify the median of the upper half of the data. For the provided data set (21, 24, 25, 28, 29, 35, 37, 43, 44), with nine values, the median is 29, which is the fifth value. To calculate Q3, we take the upper half of the data set which does not include the median itself. The upper half includes (35, 37, 43, 44), and the median of this half is the third quartile. Since we have an even number of data points in the upper half, we must find the average of the two middle numbers, 37 and 43, which is (37+43)/2 or 40. Therefore, the third quartile of the provided data set is 40.

Answer:

(-10, 0) , (-4, 0)

Step-by-step explanation:

[tex]\text{We know that the parabola is given by the quadratic equation.}\\\text{let the general equation of the parabola is}\\\\y=a(x-h)^2+k, \text{ where (h, k) is the vertex of the parabola.}\\\\\text{here we have given that vertex, }(h,k)=(-7,45), \text{ so above equation gives}\\\\y=a(x-(-7))^2+(45)\\\\y=a(x+7)^2+45\\\\\text{now this parabola has y-intercept at }(0,-200), \text{ so with this point}\\\text{above equation gives}[/tex]

[tex]-200=a(0+7)^2+45\\\\\Rightarrow -200=49a+45\\\\\Rightarrow 49a=-245\\\\\Rightarrow a=-\frac{245}{49}=-5\\\\\text{so the equation of the parabola is}\\\\y=-5(x+7)^2+45[/tex]

[tex]\\\text{Now to find the x-intercepts, we set }y=0, \text{ so we get}\\\\-5(x+7)^2+45=0\\\\\Rightarrow -5(x+7)^2=-45\\\\\Rightarrow (x+7)^2=\frac{-45}{-5}\\\\\Rightarrow (x+7)^2=9\\\\\Rightarrow (x+7)=\pm \sqrt{9}\\\\\Rightarrow x+7=\pm 3\\\\\Rightarrow x=-7\pm 3\\\\\Rightarrow x=-7-3, \text{ and } x=-7+3\\\\\Rightarrow x=-10, \text{ and } x=-4\\\\\text{so x-intercepts of parabola occur at: }(-10,0), \text{ and }(-4,0)[/tex]

Answer:

The arcs are not congruent which makes the statement false.

Step-by-step explanation: Congruent means equal to my understanding.

Answer:

13,000 meters.

Step-by-step explanation:

We have been given that Lisa went on a 52 km hike. She divided the distance traveled evenly over 4 days.

Let us convert our given distance in meters.

1 km = 1,000 meters.

52 km= 52*1,000 meters = 52,000 meters.

Let us divide total distance traveled by total number of days to find the distance traveled per day.

[tex]\text{Lisa walked each day}=\frac{52000\text{ meters}}{\text{ 4 days}}[/tex]

[tex]\text{Lisa walked each day}=13,000\frac{\text{ meters}}{\text{ day}}[/tex]

Therefore, Lisa walked 13,000 meters each day.

Lisa hiked 52 km in 4 days, equaling to 13 km per day. However, this must be converted to meters, so Lisa hiked 13,000 meters each day.

This problem is an exercise in unit conversion and division. Since Lisa divided the total distance of 52 kilometers evenly over 4 days, she hiked 13 kilometers each day (52 km / 4 = 13 km/day). However, the question asks for the answer in meters, not kilometers. Therefore, we must convert kilometers to meters. We know that 1 kilometer is equivalent to 1000 meters, so Lisa hiked 13,000 meters each day (13 km * 1000 = 13,000 m/day).

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Answer:

1 foot = 0.305 meters.

Convert 1 meter to feet:

1 meter = 1/0.305 = 3.28 feet

Find the weight in pounds per meter:

5 pounds x 3.28 feet = 16.4 pounds per meter.

Convert pounds per meter to kilograms per meter:

16.4 pounds x 0.454 kilograms per pound = 7.44 kg/m

Answer:

option A  and E

Step-by-step explanation:

Arithmetic sequence converge,  only  in the case only when r=0

otherwise , arithmetic sequence goes increasing or decreasing at a constant rate.

So we ignore second and fourth option

If |r|<1 then geometric sequence converge

if |r|>1 then geometric sequence diverge

In option A, r= 1/5  that is less than 1  so it converge

In option C, r= -2 , |r| > 1 so geometric sequence diverge

In option E, r= 2/3 that is less than 1  so it  converges

Answer is option A  and E

Answer:

Max for g(x) is 3

Max for f(x) is 2

Step-by-step explanation:

The maximum value of a function is the highest value on the graph of the function. It is the greatest value of the function and is always a y value. We can see on the graph that the blue function peaks at 3. The max is 3.

A normal sine or cosine without any transformations has the max of 1. We can see in the equation for f(x) that there is a vertical stretch of 2. So the max here is 2(1)=2.

Answer:

Hourly labor rate = $14.84

Step-by-step explanation:

Total cost of job = $147.51

Price of parts = $32.50

Labor cost + overhead = Total cost - parts = 147.51 - 32.5

=115.01

Overhead rate = 55%

Labor cost = 115.01/(1+55%) = 115.01/1.55

=74.2

Duration of job = 5 hours

Hourly labor rate = 74.2/5

= $14.84

Answer:

$14.84

Step-by-step explanation:

Total cost of job = $147.51=labor+overhead+parts

Price of parts = $32.50

labor+overhead =147.51-32.5=115.01

Overhead rate = 55%

labor+0.55labor= 115.01

labor=115.01/(1.55)=74.2

Duration of job = 5 hours

hourly labor=74.2/5=$14.84

Answer:

I'm not sure if it is correct but i hope it helps you

Step-by-step explanation:

So you subtract 25 and 15 and you will get 10

then you add 65 and 5 and you will get 70

you add 45 and 20 and you will get 65

Answer: D

Step-by-step explanation:

An on-line electronics store must sell at least $5000 worth of computers and printers per day.

Each printer costs $350 and each computer costs $750.

This equation is: 350p + 750c ≥ 5000

The store can ship a maximum of 20 items per day

This equation is: c + p ≤ 20

Answer:

D.

Step-by-step explanation:

Add the x values and divide by the amount of x's and same with the y's

Final answer:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to multiply the entire equation by 6.

Explanation:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, we need to find a common denominator for both fractions. The common denominator for 2 and 3 is 6. Therefore, we need to multiply the entire equation by 6 to eliminate the fractions.

Multiplying the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3)

Simplifying further, we get: 3x + 2x = 50

Combining like terms, we have: 5x = 50

Finally, dividing both sides of the equation by 5 gives us:  x = 10

Final answer:

To eliminate the fractions in the equation x/2 + x/3 = 25/3, one must multiply each term by 6, which is the least common multiple of the denominators 2 and 3, making option D correct.

Explanation:

The equation x/2 + x/3 = 25/3 should be multiplied by a number that is a common multiple of the denominators 2 and 3 to eliminate the fractions. To find the least common multiple (LCM) of 2 and 3, we can list out the multiples of these numbers (2,4,6,8,... for 2 and 3,6,9,12,... for 3) and identify the smallest multiple they have in common, which is 6. Therefore, multiplying the entire equation by 6 will eliminate the fractions and give us an equation with whole numbers.

Multiplying each term of the equation by 6 gives us: 6(x/2) + 6(x/3) = 6(25/3). Simplifying each term results in: 3x + 2x = 50 which is an equation without fractions.

The correct answer to the question is D. 6.

Answer:

Option a. Greece.

Step-by-step explanation:

According to the table listing average daily expenses for a tourist by country based on high and medium categories,

Brazil has a range from = $12.25 to $18.33

Greece has a range from = $9.48 to $16.55

To find out the difference in range, first we get range of both the countries.

by subtracting lowest from highest

Brazil = $18.33 - $12.25 = 6.08

Greece = $16.55 - $9.48 = 7.07

= 7.07 > 6.08

Therefore, Greece has the larger difference between categories.

Option a. Greece is the correct answer.

Answer:

2.4 hours Electrician works.

Step-by-step explanation:

Let us assume that the number of hours  Electrician works be x.

As given

An Electrician charges $30 for a service call plus $75 per hour of service.

If Electrician  charged $210.

Than the equation becomes

30 + 75x = 210

75x = 210 - 30

75x = 180

[tex]x =\frac{180}{75}[/tex]

x =2.4 hours

Therefore 2.4 hours Electrician works.

Where C = Cost and P = People

C = 2(5p)

In the context of Tia and her five friends:

C = 2(5*6) = 2(30) = 60

C = 60

The cost for Tia and her five friends to be admitted to ice skate and eat is 60$, and the equation to calculate this is C = 2(5p).

w - width

2w - length (l)

30 cm - perimeter

w + w + 2w + 2w = 6w - perimeter

The equation:

6w = 30    divide both sides by 6

w = 5 cm

2w = 2(5) = 10

l = 10 cm

The area of a rectangle: A = lw.

Substitute:

A = (5)(10) = 50

Answer:

The answer would be B

2.5x = 45

(x) would be the number of dolls, multiplied by how much each doll costs ($2.50) and the product would be how much she has to spend. Hope this helps!

Answer:

Step-by-step explanation:

Given triangle WXY and <1 is an exterior angle.

We need to prove <1 is greater than <2.

First statement is:

Triangle WXY and <1 is an exterior angle.

Reason : Given

Note: An exterior angle of a triangle is the sum of two angles side the triangle those don't makes the linear pair with exterior angle.

We can see that <2 and < 3 are the angles of triangle those are not making a linear pair.

Therefore, <1 = <2+< 3.

So, the second statement should be first option <1 = <2+< 3.

Answer:

32 miles.

Step-by-step explanation:  

We have been given that Elton hiked 16 miles each day on a 12 day hiking trip.

So, the number of miles hiked by Elton in 12 days will be: [tex]16\times 12=192[/tex] miles.

Lola hiked 14 miles each day on her 16 day hiking trip.

So, the number of miles hiked by Lola in 16 days will be: [tex]14\times 16=224[/tex] miles.  

Let us subtract number of miles hiked by Elton from Number of miles hiked by Lola.

[tex]\text{Number of miles that Lola hiked more than Elton}=224-192[/tex]

[tex]\text{Number of miles that Lola hiked more than Elton}=32[/tex]

Therefore, Lola hiked 32 miles more than Elton in all.  

To find the width of a rectangle when given the area and length, divide the area by the length:

Width = 59,400 / 330 = 180 feet

Answer:

missing data for the following exponential function is 27

Step-by-step explanation:

To find out missing data , we use the given f(x) equation

Given f(x) = 3^x

WE need to find the missing number f(x) when x=3

To find f(x) we plug in 3 for x  in f(x) = 3^x

[tex]f(x) = 3^3= 3*3*3= 27[/tex]

So missing number is 27

Answer:

B. 27

Step-by-step explanation:

Final answer:

Billie has $2.02 left after buying fabric, craft glue, and craft paper, which in total cost her $14.93 from her initial $16.95.

Explanation:

To find out how much money Billie has left after purchasing her items, we need to calculate the total cost of the items and subtract it from the amount she had initially.

Fabric cost: $8.69

Craft glue cost: $1.95

Craft paper cost: $4.29

We add these amounts together to find the total cost of the items:

$8.69 (fabric) + $1.95 (glue) + $4.29 (paper) = $14.93.

Now, we subtract the total cost of items from the amount she had to start with:

$16.95 - $14.93 = $2.02.

Therefore, Billie has $2.02 left after her purchases.