h = -4.9t^2 + 9.8t + 28

Approximately, how long does it take the watermelon to hit the ground? Round to the nearest tenth of a second.

9514 1404 393

**Answer:**

3.6 s

**Step-by-step explanation:**

This is nicely solved by a graphing calculator. **It takes about 3.6 seconds to hit the ground**.

__

We notice that the vertical velocity is a multiple of the leading coefficient, so we can solve this by completing the square.

0 = -4.9(t^2 -2t) +28 . . . . . for h = 0

28 +4.9 = 4.9(t^2 -2t +1) . . . . . rearrange, add 4.9 to both sides

32.9/4.9 = (t -1)^2

1 +(1/7)√329 = t ≈ 3.5912. . . . . square root and add 1

**It takes about 3.6 seconds for the watermelon to hit the street**.

What is the slope of (0,0) and (4,12)

[tex] \Large{\boxed{\sf Slope = 3}} [/tex]

[tex] \\ [/tex]

The **s****l****o****p****e**** **of a line passing through two points, also known as its **g****r****a****d****i****e****n****t****,**** **is calculated using the **s****l****o****p****e**** ****f****o****r****m****u****l****a****.**

[tex] \\ [/tex]

[tex] \Large{\left[ \begin{array}{c c c} \underline{\tt Slope \ formula \text{:}} \\~ \\ \tt m = \dfrac{rise}{run} = \dfrac{\Delta y}{\Delta x} = \dfrac{y_2 - y_1}{x_2 - x_1}\end{array} \right] } [/tex]

Where m is the **s****l****o****p****e**** **of the line.

[tex] \\ [/tex]

First, let's **identify our values****:**

[tex] \sf (\underbrace{\sf 0}_{x_1} \ , \ \overbrace{\sf 0}^{y_1} ) \ \ and \ \ (\underbrace{\sf 4}_{x_2} \ , \ \overbrace{\sf 12}^{y_2} ) [/tex]

[tex] \\ [/tex]

Now, **s****u****b****s****t****i****t****u****te **these values into the formula:

[tex] \sf \rightarrow m = \dfrac{12 - 0}{4 - 0} \\ \\ \sf \rightarrow m = \dfrac{12}{4} \\ \\ \\ \rightarrow \boxed{\boxed{\sf m = 3}} [/tex]

[tex] \\ [/tex]

[tex] \hrulefill [/tex]

[tex] \\ [/tex]

▪️Learn more about the **s****l****o****p****e**** ****f****o****r****m****u****l****a**** **here:

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**Answer:**

slope = 3

**How to Solve:**

The question is asking us to find the **slope**, given **two points**.

These points are (0,0) and (4,12).

We will use the slope **formula**:

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

**Where:**

Plug in the data:

[tex]\boldsymbol{m=\dfrac{12-0}{4-0}}[/tex]

[tex]\boldsymbol{m=\dfrac{12}{4}}[/tex]

Simplify the fraction to its lowest terms:

[tex]\boldsymbol{m=3}[/tex]

**Therefore, the slope is 3.**

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours how far did Simon drive in all

**Answer:**

415 miles

**Step-by-step explanation:**

Start with the speed equation:

*speed = distance/time*

Now solve the speed equation for distance:

*distance = speed × time*

Apply the speed equation solved for distance to the two parts of the trip.

4 hours at 55 mph:

distance = 55 mph × 4 hours = 220 miles

3 hours at 65 mph:

distance = 65 mph × 3 hours = 195 miles

Add the two distances to find the total distance:

total distance = 220 miles + 195 miles = 415 miles

Answer: 415 miles

**Answer:**

415 miles

**Step-by-step explanation:**

Simon drove 55 miles per hour for 4 hours then 65 miles per hour for 3 hours.

How far did he drive?

**d=rt**

For the first part of the trip:

d = 55 * 4 = 220 miles

For the second part of the trip:

d = 65*3 =195 miles

**Add the miles together**

220+195 = 415 miles

if all possible samples of size n are drawn from an infinite population with a mean of 36 and a standard deviation of 22, then the standard error of the sample mean equals 2 for samples of size:

Thus , it is False. As there is **confidence level** is not given, then cant calculate the sample size.

The standard deviation in **statistics **is a measure of how widely spread a set of values can be or how much they can vary. A low standard deviation denotes that values are typically close to the mean of the collection, whereas a high standard deviation indicates that values are dispersed across a greater** range**.

Here,

The standard error of the sample mean is equal to 2 for samples of size n if all conceivable samples of that size are taken from a population with an infinite mean and standard deviation.

In the above statement confidence level is not given.

Thus , it is False. As there is confidence level is not given, then cant calculate the sample size.

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Clare would like to buy a video game that costs at least $130. She has saved $48 so far and plans on saving $5 of her allowance each week. Write an inequality to find out the number of weeks it will take until she has enough money to buy the game.

48 + 5x >= 130

X = weeks

X = weeks

**Answer:**

5x+48=130

**Step-by-step explanation:**

5 is the money she gets each week. X is the number of weeks. X can be found easily but for the sake of this question, It's unknown. so 5x and then add the 48 she's already saved you get 5x+48=130 or 5x+48 is greater than or equal to 130.

A pilot flies in a straight path for 130 minutes. She then makes a course correction, heading 10° to the right of her original course, and flies 145minutes in the new direction. If she maintains a constant speed of 600 miles per hour, how far is she from her starting position? Round your answer to the nearest mile. Enter deg after any degree value.

By using properties of **triangle**, it can be calculated that-

The pilot is 2740 miles from her starting position.

**What is a triangle?**

A** triangle** is a** three sided two dimensional figure**. A **triangle** has** three sides** and **three interior angles.**

Here,

The diagram has been attached

**Time** = 130 minutes = 2 hrs 10 minutes = [tex]2 + \frac{10}{60}[/tex] hours = [tex]\frac{13}{6}[/tex] hours

**Speed** = 600 miles per hour

**Distance** = [tex]\frac{13}{6} \times 600[/tex] = 1300 miles

Now,

**Time** = 145 minutes = 2 hrs 25 minutes = [tex]2 + \frac{25}{60}[/tex] hours = [tex]\frac{29}{12}[/tex] hours

**Distance **= [tex]\frac{29}{12}\times 600[/tex] = 1450 miles

**Angle** = [tex]10^{\circ}[/tex]

[tex]c^2 = 1300^2 + 1450^2 - 2\times 1300\times 1450\times cos(180-10)\\c^2 = 1690000 + 2102500 - (-3712725.2)\\c^2= 7505225.2\\c= \sqrt{7505225.2}\\c = 2740[/tex]

The pilot is 2740 miles from her starting position.

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Myra is taking her first hot-air balloon ride! The balloon was at an altitude of 288 meters until an air current caused it to rise another 36 meters.

What is the altitude of the balloon now?

The **altitude **of the **balloon **now is 324 meters

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

**Initial **altitude = 288 meters

**Rise **= 36 meters

The altitude of the balloon now is calculated as

Current altitude = **Initial **altitude + Rise in altitude

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

**Current **altitude = 288 + 36

Evaluate the sum

Current altitude = 324

Hence, the current **altitude** is 324 meters

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This graph best represents the motion of an object that

a

is increasing its' acceleration.

b

first increases acceleration then remains constant.

c

shows no motion.

d

was at rest and is accelerating uniformly.

The **motion **of the object on the **graph**, can best be **represented **as an object that d. was at rest and is accelerating uniformly.

The **object **on the **graph **is **accelerating **such that the acceleration is stable and uniform. This is why the speed - time line is a straight and diagonal line to show that the speed is proportional to time.

We know that the object started from **rest **because at the point where time was 0, the object was not accelerating and so was not moving. As time moves on, the object increases speed, thereby accelerating.

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A cactus casts a shadow 33 feet long. At the same time of day,Liam,who is 6 feet tall,casts a shadow 9 feet long,as shown. how tall is the cactus

**If x = 2, y = 6, and z = 4, which expression is equivalent to 4? à 54+0-3+2=4. D Xtra 4 ... A tree is 12 feet tall and casts a shadow 9 feet long. A building nearby.**

It is given that Cos(A) = 1/4 and Sin(B) = 1/2

Where A is in the 3rd quadrant and B is in the 2nd quadrant

a) Find value of Sin(A)

b) Find Value of Cos(A)

c) Find value of cos(A + B) and cos (A - B)

d) Find Value of Sin(A + B) and sin (A - B)

e) What is the quadrant of A + B and A - B

f) Find the value of Sin(2A + 2B)

The answers for the following **trigonometric functions** are:

a) Sin(A)=√15/4

b) Cos(A)=1/4

c) Cos(A+B)=(√3-√15)/8

Cos (A- B)=(√3+15)/8

d) Sin(A+ B) =(3√5+1)/8

Sin (A- B)==(3√5-1)/8

e) The quadrant of A+B and A-B is 4th quadrant

f) Sin(2A + 2B)= (√15-6√5+4√3)/8

What are trigonometric functions?The trigonometric functions in mathematics are real functions that link the angle of a right-angled triangle to the ratios of two side lengths. They are also known as** circular functions**, angle functions, or goniometric functions. They are widely employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many more. Because they are some of the most basic periodic functions, Fourier analysis is frequently employed to examine periodic events.

The sine, cosine, and **tangent** are the trigonometric functions that are most frequently utilized in contemporary mathematics.

Given,

Cos(A) = 1/4 and Sin(B) = 1/2

4=√1+x²

1+x²=16

x²=15

x=√15

4=1+x²

x²=3

x=√3

a) Sin(A)=√15/4

Sin(B)=1/2

b) Cos(A)=1/4

Cos(B)=√3/2

c) Cos(A+B)=CosACosB-SinASinB

=(1/4)(1/2)-(√15/4)(1/2)

=(√3-√15)/8

Cos(A-B)=CosACosB+SinASinB

=(1/4)(√3/2)+(√15/4)(1/2)

=(√3+15)/8

d) Sin(A+B)+SinACosB+CosASinB

=(√15/4)(√3/2)+(1/4)(1/2)

=(3√5+1)/8

Sin(A-B)=SinACosB-SinBCosA

=(√15/4)(√3/2)-(1/4)(1/2)

=(3√5-1)/8

e) The quadrant of A+B and A -B is 4th quadrant.

f) Sin(2A+2B)=Sin2ACos2B+Cos2ASin2B

=(√15/8)(1-√3)+((4-√15)/4)(√3/2)

=(√15-3√5+4√3-3√5)/8

=(√15-6√5+4√3)/8

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1/4 + 29/16 - 9735/12

**Answer:**

**Step-by-step explanation:**

To solve this problem, we need to add and subtract the fractions given. To do this, we need to find a common denominator for all of the fractions.

The least common multiple of 4, 16, and 12 is 48, so we can rewrite each fraction with a denominator of 48:

1/4 = 3/12

29/16 = 87/48

9735/12 = 4047/48

Then, we can add and subtract the fractions as follows:

3/12 + 87/48 - 4047/48 = (3 - 4047)/48 = -4044/48 = -84/16

Therefore, the final answer is -84/16, or -5 and 1/16 in simplified form.

6 people equally share 1/2 a pan of mac and cheese write a division expression to represent the situation

**Answer:**

6/1.5

**Step-by-step explanation:**

You said equally, so you need to make sure that each person gets an even share. To do this, you can do people/things. Hence why the answer is 6/1.5!

Help please fast!! picture attached below 27 point

What is the mean number of points scored by these players?

A. 7

B. 8

C. 9

D. 10

Option (b) is correct as **mean** of top five scorers on **soccer team** is 8 from given bar graph.

In** statistics**, in addition to the **mode **and median, the **mean** is one of the measures of **central tendency**. Simply put, the mean is the **average** of the values in the given set. It indicates that values in a particular data set are distributed equally. The three most frequently employed measures of central tendency are the mean, **median**, and mode. The total values provided in a datasheet must be added, and the sum must be divided by the total number of values in order to determine the mean. When all of the values are organized in **ascending** order, the Median is the median value of the given data. While the number in the list that is repeated a maximum of times is the mode.

Mean = (Sum of values)/(Total observations)

Using above formula, we get

Calculating mean for given bar graph,

[tex]=\frac{4+6+10+9+11}{5}\\=\frac{40}{5}\\=8[/tex]

So, mean score of five players comes out to be 8.

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y=x² - 4x³

Find the value of y when x = -1.

**Answer:**

y = 5

**Step-by-step explanation:**

standard position intersects the unit circle at (√30/7,-√19/7). What is cot(θ)?

The** cotangent **of the **angle **is -√570/30

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

(√30/7,-√19/7)

This means that

(x, y) = (√30/7,-√19/7)

The **cot(θ)** is calculated as

cot(θ) = y/x

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

cot(θ) = (-√19/7)/(√30/7)

Evaluate

cot(θ) = -√19/√30

Rationalize

cot(θ) = -√570/30

Hence, the **value **of cot(θ) is -√570/30

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Simplify all questions

√(3-√15)²-√(3+√15)²

3√c² if c≥0

√(x²+1)²=5

-5√y² if y>0

0.5√16a² if a<0

The given equations can be** simplified **as :

**a. -2.√15**

**b. c ≥ 0**

**c. x = ±2√6**

**d. y < 0 **

**e. a > 0**

**How to solve inequalities ?**

When solving an inequality:

you can**a. **

Given : √(3-√15)²-√(3+√15)²

√(3-√15)²-√(3+√15)² = (3-√15)-(3+√15)

√(3-√15)²-√(3+√15)² = 0 -2√15

√(3-√15)²-√(3+√15)² = **-2.√15**

**b . **

Given : 3√c² if c≥0

3√c² if c≥0

** c ≥ 0**

**c. **

Given: √(x²+1)²=5

√(x²+1)²=5

on Squaring both sides , we get

(x²+1) = 25

x² = 24

** x = ±2√6**

d.

Given : -5√y² if y>0

-5√y² if y>0

**y < 0 ** [since , -5 < 0]

e.

Given : 0.5√16a² if a<0

0.5√16a² if a<0

**a > 0**

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Graph y +1 = 1/3 (x-3)

The **graph** of the **linear equation**, y + 1 = 1/3(x - 3), is given in the attachment below.

A **linear equation **is an equation of the form "y = mx + b," where x and y are variables, and m is the slope and b is the y-intercept.

To graph a **linear equation**, of y + 1 = 1/3(x - 3), you can use the following steps:

Rewrite the equation in slope-intercept form to determine its slope (m) and the y-intercept (b).

y + 1 = 1/3(x - 3)

y + 1 = 1/3x - 1

y = 1/3x - 1 - 1

y = 1/3x - 2

The slope (m) of the line would be 1/3, which is the rise over the run of the line.

The y-intercept (b) of the line would be -2, which means the line will intercept the y-axis at -2.

The **graph** of y + 1 = 1/3(x - 3) is shown in the image below.

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Patel is solving 8x2 + 16x + 3 = 0. Which steps could he use to solve the quadratic equation? Select three options. (PLEASE HELP!!!)

Refer to the photo taken. You didn’t proved the options to choose from, but here’s how to solve the equation.

Use the scale to help you solve the equation and find the value of x. Enter the

value of x below.

x + 3 = 9

X=_____

**Answer:**

x=6

**Step-by-step explanation:**

9-3=6 or 6+3=9

Patty needs 3/4 cup of bananas to make a loaf of banana bread.

Patty has 1 1/3 cups of bananas.

Does Patty have enough bananas to make 2 loaves of banana bread?

**Answer:**

She Does NOT

**Step-by-step explanation:**

**3/4 is .75 1 1/3 is 1.33 3/4*2= 1.5 which is more than 1.33**

Use the Fundamental Theorem of Calculus to find an expression for the derivative of the given function defined on the given interval, if it exists.

F(x) = â«^x t+1/t-1 dt, [1,5]

The** derivative** of the function is not defined overall on the interval [1, 5]

[tex]F(x)=\int_{a}^{x}\frac{t +1}{t - 1} dt\\\\F^{'}(x) = \frac{x+1}{x-1}[/tex]

The derivative of the function is not defined overall on the interval [1, 5] as x = 1 makes the derivation infinite.To learn more about** calculus**, refer:

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Solve the following

6 2/5 - 4 4/5

[tex]6\frac{2}{5} - 4\frac{4}{5}[/tex]** **can be solved using subtraction of **simple fraction** and the final result is **8/5** .

**what are simple fraction ?**

A fraction in which both the **numerator** and the **denominator** consist of **whole numbers**.

**Simplest form of a fraction:**

A **fraction** is said to be in its simplest form if 1 is the only common factor of its numerator and denominator. For example, 8/9 ,because 1 is the only common factor of 8 and 9 in this fraction.

**Simplifying proper and improper fraction**

We simplify fractions because it is always to work or calculate when the fractions are in the simplest form.

To solve : [tex]6\frac{2}{5} - 4\frac{4}{5}[/tex]

We know that , in simple fraction [tex]6\frac{2}{5} - 4\frac{4}{5}[/tex] can be written as ,

[tex]6\frac{2}{5} - 4\frac{4}{5} = \frac{32}{5} - \frac{24}{5} = \frac{8}{5}[/tex]

Hence , **8/5** is the **final answer** .

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Find the slope of the line y=5x+12.

Write your answer as an integer or as a simplified proper or improper fraction.

**Answer:**

5

**Step-by-step explanation:**

The slope or gradient of the line

using this formula as our guide line

**y**** ****=**** ****m****x**** ****+****b**

**w****h****e****r****e**** ****m**** ****=**** ****s****l****o****p****e**

**x**** ****=**** ****x****–**** ****i****n****t****e****r****c****e****p****t**

**b**** ****=**** ****y****–**** ****i****n****t****e****r****c****e****p****t**

**s****o**

**y**** ****=**** ****5****x**** ****+**** ****1****2**

**th**e** ****slope**** ****w****i****l****l**** ****b****e**** ****5**

**i**** ****h****o****p****e**** ****i**** ****h****e****l****p****e****d**** ****p****l****s**** ****rate**** ****as**** ****brainliest**

Find the GCF of each expression.

The GCF of 12y - 3 is_____.

The GFC of 4y + 10 is_____.

The GCF of 28 − 8 is _____.

The GCF of 30 + 18 is _____.

The **GCF** of each **expression** that was given above are: 3, 2 , 4 , and 6 which can be written as:

The GCF which isthe “**greatest common factor**”. can be defined as the **largest number** that is a factor of two or more numbers.

Intance of this is that the GCF of 24 and 36 is 12, and this is due to the fact that the largest factor that is shared by 24 and 36 is 12.

Option 1:

The GCF of 12y-3=3 because the common factor which is the highest factor of 12 and 3 is 3

Option2

The GCF of 4y+10=2 because the common factor which is the highest factor of 4 and 10 is 2 and so on.

Option 3:

The GCF of 28 − 8= 4 because the **common factor** which is the highest factor of 28 and 8 is 4

Option 4:

The GCF of 30y+18=6 because the **common factor** which is the highest factor of 30 and 18 is 6

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Jocelyn and her children went into a movie theater and she bought $75.50 worth of candies and pretzels. Each candy costs $4.75 and each pretzel costs $3.50. She bought a total of 18 candies and pretzels altogether. Determine the number of candies and the number of pretzels that Jocelyn bought.

Jocelyn buys 41** candies** and 25 pretzels by solving system equation using **elimination method**.

**What is a linear equation?**

The equations with one, zero, or an infinite number of solutions are known as **linear equations** with two variables. Each of the two variables in these equations has the largest exponent order of 1. A** two-variable **linear equation has the conventional form axe + by + c = 0, where x and y are the two variables. The answers can also be expressed as ordered pairs, such as (x, y).

Given that the cost of 1 candy is $4.75 and 1 pretzel is $3.50.

Jocelyn buys 18 candies and pretzels **altogether** with cost $75.50.

Assume that she buys x candies and y pretzels

Therefore,

x + y = 18 ......(i)

The cost of x candies and y pretzels is 4.75x + 3.50y.

4.75x + 3.50y = 75.50 .....(ii)

Solving **equation** (i) and (ii) by using **elimination method**.

Multiply equation (i) by 4.75

4.75x + 4.75y = 85.5 ....(iii)

Subtract equation (ii) from (iii)

4.75x + 4.75y = 85.5

4.75x + 3.50y = 75.50

(-) (-) (-)

________________

1.25 y = 10

y = 8

Putting y = 8 in equation (i)

x + 8 = 18

x = 10

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CAN SOMEONE HELP WITH THIS QUESTION?✨

**Answer:**

351.5625

1,440,000

**Step-by-step explanation:**

[tex]\boxed{\begin{minipage}{7 cm}\underline{General form of an Exponential Function}\\\\$y=Ae^{kt}$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $k$ is a constant.\\ \phantom{ww}$\bullet$ $t$ is time.\\\end{minipage}}[/tex]

Given:

Doubling period = 15 minutesAt t = 120 minutes, y = 90,000(Let t = time in minutes).

If the **doubling period **is **15 minutes**, then at t = 135 minutes, y = 180,000:

[tex]\implies 90000=Ae^{120k}[/tex]

[tex]\implies 180000=Ae^{135k}[/tex]

**Divide **the second equation by the first to **eliminate A**, and **solve for k**:

[tex]\implies \dfrac{180000}{90000}=\dfrac{Ae^{135k}}{Ae^{120k}}[/tex]

[tex]\implies 2=\dfrac{e^{135k}}{e^{120k}}[/tex]

[tex]\implies 2=e^{135k} \cdot e^{-120k}[/tex]

[tex]\implies 2=e^{15k}[/tex]

[tex]\implies \ln 2 = \ln e^{15k}[/tex]

[tex]\implies \ln 2 =15k \ln e[/tex]

[tex]\implies \ln 2 =15k[/tex]

[tex]\implies k=\dfrac{1}{15}\ln 2[/tex]

Substitute t = 120, y = 90000 and the found **value of k** into the **formula **and **solve for A**:

[tex]\implies 90000=Ae^{\left(120 \cdot \frac{1}{15}\ln 2\right)}[/tex]

[tex]\implies 90000=Ae^{\left(8\ln 2\right)}[/tex]

[tex]\implies 90000=Ae^{\ln256}[/tex]

[tex]\implies 90000=256A[/tex]

[tex]\implies A=\dfrac{90000}{256}[/tex]

[tex]\implies A=351.5625[/tex]

Therefore, the function that models the scenario is:

[tex]\large\boxed{y=351.5625e^{\left(\frac{1}{15}t \ln 2\right)}}[/tex]

So the **initial population **at time t = 0 was:

To find the **size **of the **bacteria population** after **3 hours**, substitute t = 180 into the found formula:

[tex]\implies y=351.5625e^{\left(\frac{1}{15}(180) \ln 2\right)}[/tex]

[tex]\implies y=351.5625e^{\left(12 \ln 2\right)}[/tex]

[tex]\implies y=351.5625e^{\left(\ln 4096\right)}[/tex]

[tex]\implies y=351.5625 \cdot 4096[/tex]

[tex]\implies y=1440000[/tex]

Therefore, the **size **of the **bacterial population** after **3 hours** was:

The **initial **population at the time t = 0 is 351.5625. And the size of the **bacterial **population after 3 hours is 1,440,000.

An **exponential **function's curve is created by a pattern of data called exponential **growth**, which exhibits higher increases over time.

If n₀ is the initial size of a population experiencing **exponential **growth, then the **population **n(t) at time t is modeled by the function:

n(t) = n₀(e[tex])^{rt}[/tex]

Where r is the **relative **rate of growth expressed as a fraction of the **population**.

Given:

**Doubling **period = 15 minutes

At t = 120 minutes, n(t) = 90,000

If the doubling **period **is 15 minutes, then at t = 120+15 = 135 minutes,

90000 = n₀(e[tex])^{120r}[/tex]

18000 = n₀(e[tex])^{135r}[/tex]]

To **find **the r:

Take ratio of both of the **equations**,

90000 / 18000 = n₀(e[tex])^{120r}[/tex] / n₀(e[tex])^{135r}[/tex]

2 = (e[tex])^{135r}[/tex] . (e[tex])^{-120r}[/tex]

r = 1/15 ln2

**Substitute **the value of r, t and y.

90000 = n₀(e[tex])^{120r}[/tex]

90000 = 256n₀

n₀ = 351.5652

Now, the **function**

n(t) = n₀(e[tex])^{rt}[/tex]

n(t) = (351.5652)(e[tex])^{(1/15)(180)(ln2)}[/tex]

n(t) = 1440000

Therefore, the **initial **population at the time t = 0 is 351.5625. And the size of the **bacterial **population after 3 hours is 1,440,000.

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What is the common ratio of the geometric sequence below?

625, 125, 25, 5, 1,

The **common ratio** is 1/5. By dividing each word by the term before it, we may find the geometric progression's common difference.

The common ratio in **geometric progression** is the ratio of any term in the sequence to divided by the first term.

The Formula to calculate the common ratio in geometric progression, a, ar, ar2, ar3, ar4, ar5… is,

Common ratio = ar/ a = ar2/ ar = ……. = an/ an-1

As stated in the definition, we can compute the **common difference **of a geometric progression by dividing any term by its preceding term.

Given, the geometric sequence is 625, 125, 25, 5, 1,....

We have to find the common ratio of the given geometric sequence.

In geometric sequence, a, b, c, d, … the common ratio r is given by

r = b/a = c/b = d/c.

So, r = 125/625 = 25/125 = 5/25 = 1/5;

r = 1/5

Therefore, the common ratio is r = 1/5.

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**Answer:**

B. 25/125

**Step-by-step explanation:**

Camilla wants to attach a string of lights to the edges of her patio

for a party She does not want the string to go across the edge with

the steps. White a linear expression that represents the length of

string in feet she will need. Then find the length if x = 3. 7.EE1

4x-2

3r

The** length** of string in feet she will need for her patio is equal to : **L{s} = 2(x + y)**.

Given is Camilla who wants to attach a string of lights to the edges of her patio for a party. She does not want the string to go across the edge with the steps.

Assume the shape of the patio is a** rectangle **with the dimensions of [x] and [y] units long. The length of string in feet she will need will be equivalent to the** perimeter** of the rectangle. So, the** length** of string in feet she will need is equal to **L{s} = 2(x + y)**.

Therefore, the** length** of string in feet she will need for her patio is equal to : **L{s} = 2(x + y)**.

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One person from those who responded will be selected at random. Which of the following is closest to the probability that the person selected will be someone who responded no, given that the person selected is age 55 or older?

a. 0.350

b. 0.427

c. 0.462

d. 0.757

e. 0.818

Given that they are age 55 or older, it is discovered that there is a (E) 0.8181 = 81.81% **probability **that the person said no.

Simply put, probability refers to the likelihood that something will occur.

If we don't know how an event will turn out, one can discuss the probability or likelihood of several events.

Statistics is the study of occurrences that match a **probability distribution.**

So, as 36 out of 44 adults aged 55 or older chose not to answer the question, the probability is given by:

p = 36/44 = 0.8181

Therefore, given that they are age 55 or older, it is discovered that there is a (E) 0.8181 = 81.81% probability that the person said no.

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The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula C(t)=0.05(1−e^−0.2t). What is the concentration after 12 minutes? Round to three decimal places.

Thus after 12 minutes **concentration** of drug is 0.045.

The **concentration** C(t) of a certain drug in the **bloodstream** after t minutes is given by the formula [tex]c(t) = 0.05(1-e^{-0.2t} )[/tex]

Drug concentration is amongst the most important determinants of clinical response to a drug.

Drug concentration will be seen to increase in biological samples drawn from the systemic circulation when the amount of drug absorbed exceeds the amount of drug that is distributed into the extravascular tissues and the drug that is metabolized and/or excreted during this period.

Thus after 12 **minutes** concentration of the drug is = C(5).

Now

C(5) = [tex]0.05(1-e^{-0.2t} )[/tex]

= [tex]0.05(1-e^{-2.4} )[/tex]

= 0.05(1-0.0907)

= 0.05×0.9093

= 0.045

The drug concentration is 0.045.

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for School: Practice & Problem Solving

Amelia needs to buy some cat food. At the nearest store, 3 bags of cat food cost $6.75. How much would Amelia spend on 2 bags of cat food?

**Answer:**

$4.50

**Step-by-step explanation:**

Use a proportion:

$6.75 is to 3 bags as x is to 2 bags.

6.75/3 = x/2

3x = 2 × 6.75

x = 4.50

Answer: $4.50

**Answer:**

$4.50

**Step-by-step explanation:**

Given **3 bags** of cat food **cost $6.75**, you want the **cost of 2 bags**.

Unless there is a volume discount (or surcharge), the price is proportional to the quantity. That means 2 bags will cost 2/3 the amount that 3 bags cost.

cost of 2 bags = 2/3 · $6.75 = $4.50

**Amelia would spend $4.50 on 2 bags of cat food**.

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