Write an equation for the nth term of the arithmetic sequence 8, 3, -2, -7,... Find the 9th term of the sequence.

The pints of vegetable stock the chef needs is [tex]3\frac{1}{2}[/tex].

The first step is to determine the unit of conversion of cups to pints.

1 cup = 0.5 pints

To convert cup to pints, multiply 7 by 0.7

7 x 0.5 = 7/2 = [tex]3\frac{1}{2}[/tex]

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Answer:

17.32

Step-by-step explanation:

since there is a 5 in the thousandths, we round the 1 in the hundredths up and get 17.32

Answer:

a) 9×2=18

b)16×2=32

c)14×9=126

d)20×10=200

e)10×3=30

Answer:

36 Adult Tickets. 352 Student Tickets

Step-by-step explanation:

Firstly, we have to create 2 expressions to solve a problem like this. If we use the variable s to mean student and a to mean adult, we can create the expressions:

3s + 6a = 1272 to represent how much they made with all ticket sales

s = 10a - 8 to represent how many student tickets there are.

Now, we plug our definition of s into the first expression to get:

3(10a - 8) + 6a = 1272

30a - 24 + 6a = 1272

36a - 24 = 1272

36a = 1296

a = 36

We have determined the number of adult tickets so we can move on to the number of students:

s = 10(36) - 8

s = 360 - 8

s = 352

Question Solved

The distance traveled by the driver during her reaction time based on her speed was 44 feet.

find the speed in feet per second to be:

= (40 x 5,280 feet per hour) / Number of seconds in an hour

= 211,200 / 3,600

= 58.67 feet per second

With a reaction speed of 3/4 seconds, the distance traveled is:

= 58.67 x 3/4

= 44 feet

Full question is:

The driver of a car traveling at a speed of 40 miles per hour had to stop the car quickly. Using the driver's speed in feet per second, how far did her car travel during her reaction time of 3/4 of a second?Round your answer to two decimal places

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Hello!

The weight is 4,338 pounds and 2.169 tons.

Answer: 2 tons and 338 pounds

Step-by-step explanation:

1 ton is 2000 pounds

4338 has 2 tons and 338 pounds

Option A graph represents  S(x).

Function is a statement that relates tow variables.

It is given that

the side length of the larger frame S(x)

S(x) =  [tex]\rm 3 \sqrt{x -1}[/tex]

X is the area of the smaller frame in square inches

A square root function is given by

s(x) = [tex]\rm \sqrt{x}[/tex]

when the graph is shifted towards right and stretched by  3 , due to which the graph is taller as compared to the parent graph and

Therefore Option A graph represents  S(x).

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1) You can find the number of possible methods through a tree diagram or the fundamental counting principles.

2) The total number of combinations is 360

To find the total number of combinations,

A Tree Diagram is a the various possibilities in a pictorial way. The diagram begins with a single point, which represents the initial decision, then branches out to indicate all possible outcomes for each successive option.

The Fundamental Counting Principle tells us that if there are 'n' ways doing a thing and 'm' ways to do another, there are n x m ways to do both. Which means that the total number of outcomes equals the product of the number of ways each job can completd.

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As a result of climatic peculiarities the seasonal changes of oak tree in Florida and oak in Maine are distinguished such that the differences are remarkably satisfactory.

We know that many oaks are native to Florida and some of the Florida oaks include;

Northern red oaks can also be found in northern Florida. Some other oak trees in Florida include;

From the information above, we can conclude that as a result of climatic peculiarities the seasonal changes of oak in Florida and oak in Maine are distinguished such that the differences are remarkably satisfactory.

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Answer:

3:04

Step-by-step explanation:

see image

They will meet after 4 minutes from 3:00 p.m. So, they will meet at 3:04 p.m.

Let's find the time it takes for Tommy and his Dad to meet.

Let t be the time (in seconds) from 3:00 p.m. when they meet.

Tommy's distance covered (T) after t seconds is given by:

T = Tommy's speed * t

   = 1.35 m/s * t

His Dad's distance covered (D) after t seconds is given by:

D = Dad's speed * t

  = 1.65 m/s * t

Since they meet when the sum of their distances is equal to the total distance between home and school, we can write the equation:

T + D = 720 meters

Substitute the expressions for T and D:

1.35t + 1.65t = 720

t = 240 seconds

Since 1 minute is equal to 60 seconds, let's convert the time to minutes:

t = 240 seconds / 60 seconds/minute

t = 4 minutes

They will meet after 4 minutes from 3:00 p.m. So, they will meet at 3:00 p.m. + 4 minutes = 3:04 p.m.

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The values of k (i.e. +3 and -2) in functions b and c change the rational graph by (b) shifts right/left

The functions are given as:

[tex]y = \sqrt x[/tex]

[tex]y = \sqrt {x + 3[/tex]

[tex]y = \sqrt {x - 2[/tex]

See attachment for the graphs of the three functions.

From the attached graph, we can see that [tex]y = \sqrt {x + 3[/tex] and [tex]y = \sqrt {x - 2[/tex] are at the left and right of the function [tex]y = \sqrt x[/tex]

Hence, the values of k in functions b and c change the rational graph by shifting it right/left

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The whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

Let x be the speed of a whale in calm water

and y be the speed of the current

In 7 hours the whale swims against the current and travels 140 miles:

7(x - y) = 140

x - y = 140/7

x - y = 20 ...........(1)

In 3.5 hours the whale swims the same distance with the current:

3.5(x + y) = 140

x + y = 140/3.5

x + y = 40 ...........(2)

Adding (1) and (2), we get the value of x:

x - y = 20  + ...........(1)

x + y = 40 ...........(2)

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

2x = 60

x = 60/2

x = 30

Using this value for "x" in either (1) or (2) we can solve for "y":

x - y = 20 ...........(1)

substitute for "x"

30 - y = 20

10 = y

Therefore, the whale exists swimming at 30 mph in calm water and the current exists flowing at 10 mph.

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Answer:

6 projects

Step-by-step explanation:

Original ribbon length = 24 yards

After 10 yards given to sister, Mia is left with 24-10 = 14 yards of ribbon

Each project requires 2 1/4 yards of ribbon.

2 1/4 is 9/4 yards as an improper fraction (2 * 4 + 1 is the numerator and the denominator is unchanged)

We now have to figure out how many times 9/4 yards goes into 14 yards.

For this,

14 ÷ 9/4.
To do this, flip the numerator and denominator of the fraction and multiply

14 ÷ 9/4 = 14 × 4/9 = 56/9 . We ignore any remainder.

9 goes into 56 6 times with remainder of 2 (ignore remainder)
In other words the greatest number of projects = 6

The dimensions of the crate that will minimize the total cost of material are 10, 10, and 29.

The volume will be:

= Length × Width × Height

= lwh

For the square base, w = l

2880 = w²h

The cost function will be:

C = 12wl + 4wh + 4lh

Put l = w.

C = 12w² + 8wh

C = 12w² + 8w(2880/w²)

C = 12w² + 23040/w

Differentiate with respect to w

C'(w) = 0

24w = 23040/w²

24w³ = 23040

w³ = 960

w = 10 approximately

The length is 16 as well as they are the same. The height will be:

= 2880/w²

= 2880/10²

= 28.8 = 29

Therefore, the dimensions are 10, 10, and 29.

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Answer:

4,9,14,19,24,29,34,39

Answer: 15cm and 5cm

Step-by-step explanation:

A rectangle's area is the product of the length and width

Given length x and width y, 2x+2y = 40 and x*y = 75.

Verifying my answer:

2(15)+2(5) = 40

30+10 = 40

40 = 40

15*5 = 75

75= 75

This is a week late so I hope this helped.

The length and the width of the rectangle​ are 15cm and 5cm respectively

The given parameters are:

Area (A) = 75

Perimeter (P) = 40

The area of a rectangle is LW, while the perimeter is 2(L + W)

So, we have:

LW = 75

2(L + W) = 40

Divide by 2

L + W = 20

Make L the subject

L = 20 - W

Substitute L = 20 - W in LW = 75

(20 - W)W = 75

Expand

20W - W^2 = 75

Rewrite as:

W^2 - 20W + 75 = 0

Expand

W^2 - 15W - 5W + 75 = 0

Factorize

(W - 15)(W -5) = 0

Split

W - 15 = 0 or W - 5 = 0

Solve for W

W = 15 or W = 5

Recall that:

L= 20 - W

So, we have

L = 20 - 15 or L = 20 - 5

This gives

L = 5 or L = 15

Hence, the length and the width of the rectangle​ are 15cm and 5cm respectively

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The slope m = -6 and y-intercept = ( 0, 5 ).

The graph is a dash line, shaded area above the boundary line since y is greater than -6x + 5.

Given that;

y > -6x + 5

We use the slope intercept form y = mx + b to determine the slope (m) and the y-intercept (b).

y > -6x + 5

y = mx + b

We can see that;

m = -6 and b = 5

Hence, slope = -6 and y-intercept = ( 0, 5 ).

The graph is a dash line, shaded area above the boundary line since y is greater than -6x + 5.

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The solution to the system of inequalities given is: [tex]\frac{4}{3} \leq y \leq 4[/tex]

The solution is the set of values that respect all conditions of the system.

The first condition is:

[tex]3y - 13 \geq -9[/tex]

[tex]3y \geq 4[/tex]

[tex]y \geq \frac{4}{3}[/tex]

The second condition is:

[tex]3y - 13 \leq -1[/tex]

[tex]3y \leq 12[/tex]

[tex]y \leq \frac{12}{3}[/tex]

[tex]y \leq 4[/tex]

The intersection of the conditions, which is the solution to the inequality, is:

[tex]\frac{4}{3} \leq y \leq 4[/tex]

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The slope-intercept form is y=mx+b

m=slope=-5

y-int/b = 300

so, y = -5x+300 is the equation of the line

Answer:

C

Step-by-step explanation:

The area of a rectangle is lw or length * width.

We can add the parts to make up the whole of each side.

Thus, for the entire width, we have 4x+3 and for the entire length we have 8 + 5x.

To solve for area in terms of x, we just multiply our width and length, which gives us:  

[tex](4x+3)(8+5x)\\32x+20x^2+24+15x\\20x^2+47x+24[/tex]

The linear inequality depicted by the graph is: [tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

A linear function is modeled by:

y = mx + b

In which:

For this line, when x = 0, y = 0.2, hence the y-intercept is of b = 0.2. When x = 3, y = 2.2, hence the slope is given as follows:

[tex]m = \frac{2.2 - 0.2}{3 - 0} = \frac{2}{3}[/tex]

Hence the equation of the line is:

[tex]y = \frac{2}{3}x + 0.2[/tex]

[tex]y = \frac{2}{3}x + \frac{1}{5}[/tex]

The inequality is the values below(less) than the line, also including it, as it is not dashed, hence:

[tex]y \leq \frac{2}{3}x + \frac{1}{5}[/tex]

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A function assigns the values. For every increase of 1 ounce in frozen yogurt the cost will increase by $49.

A function assigns the value of each element of one set to the other specific element of another set.

Given the frozen yogurt store charges C dollars for w ounces of frozen yogurt, C can be modelled by C = 49w+80/100. Therefore, for every increase of 1 ounce in frozen yogurt the cost will increase by $49.

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Answer:

water pollution or any one of them.

Step-by-step explanation:

Technically, these are all issues in the Netherlands.

However, based on a statista opinion chart of Netherland concerns, the biggest concern at the moment is pollution.

So, picking any of these might work because they are all issues - but I found that the environmental one is most likely to be correct.

Answer:

Water pollution

Explanation:

"Crime (48 percent) and environmental pollution (45 percent) are most often seen as (very) serious problems." - cbs

Since for each trial there are more than two outcomes, the random variable x is not a binomial variable.

Three things are required:

In this problem, for each trial, there are six possible outcomes for the sum, hence the random variable x is not a binomial variable.

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See the graph in the attached image.

Answer:

y = x/3

Step-by-step explanation:

y = 3x

x = 3y

3y = x

y = x/3

⊱_____________________________________________________⊱

Answer:

Step-by-step explanation:

[tex]\large\displaystyle\begin{gathered} \rm{To \ find \ the \ inverse, \ switch \ the \ places \ of \ x \ and \ y} \\ \sf{ y=3x} \\ \sf{x=3y} \\ \rm{Now \ solve \ for y} \\ \sf{x/3=y} \\ \sf{\dfrac{x}{3}=y \end{gathered}[/tex]

done !!

⊰______________________________________________________⊱

The probability that a randomly selected PC costs more than 1200 will be 0.006. The least expensive 10% of personal computers cost less than what amount will be 820.8.

The Gaussian distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.

The z-score is given as

z = (x – μ) / σ

Where μ is the mean, σ is the standard deviation, and x is the sample.

The average price of a personal computer (PC) is $949.

If the computer prices are approximately normally distributed and standard deviation is $100.

Then the probability that a randomly selected PC costs more than 1200 will be

z = (1200 – 949) / 100

z = 2.51

Then  the probability will be

P(x > 1200) = P(z > 1200)

P(x > 1200) = 1 – P(z < 1200)

P(x > 1200) = 1 – 0.99396

P(x > 1200) = 0.0060366

The least expensive 10% of personal computers cost less than what amount will be

z-value for 10% will be -1.282.

– 1.282 = (x – 949) / 100

– 128.2 = x – 949

          x = 820.8

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Answer:

[tex]\frac{\sqrt{15} }{2}[/tex]

Step-by-step explanation:

[tex]\sqrt{f(\frac{3}{2} )[/tex] , substitute [tex]\frac{3}{2}[/tex] to x

[tex]f(\frac{3}{2} )=4(\frac{3}{2} )-(\frac{3}{2} )^2[/tex] = [tex]\frac{15}{4}[/tex] or 3.75

[tex]\sqrt{f(\frac{3}{2} )[/tex]=[tex]\sqrt{3.75}[/tex] = [tex]\frac{\sqrt{15} }{2}[/tex]

The number line first represents the solution to the inequality x/-1 > -6 option first is correct.

It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.

The complete question is:

Which of the following number lines represents the solution set of x/-1 > -6?

For the number lines shown in the attached picture, please refer to the picture.

We have an inequality:

x/-1 > -6

x < 6  

x ∈ (-∞, 6)

Thus, the number line first represents the solution to the inequality x/-1 > -6 option first is correct.

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Explanation:

Dalvin drives 190 miles in 5 hours. His speed is 190/5 = 38 mph.

From here we would say the following

distance = rate*time

distance = (38 mph)*(8 hrs)

distance = 304 miles