Qualitative data a. can not be numeric b. indicate either how much or how many c. must be nonnumeric d. are labels used to identify attributes of elements

The function for the garden's perimeter in terms of the width "w" would be P(w) = 4w + 24

What is the perimeter?

The perimeter is a mathematical term that refers to the total distance around the outside of a two-dimensional shape. It is the length of the boundary or the sum of the lengths of all the sides of a closed figure.

Let's call the width of the rectangular garden "w".

According to the problem, the length of the garden is 12 feet longer than its width. So, the length would be w + 12.

The perimeter is the sum of all four sides of the rectangular garden. So,

Perimeter = w + w + (w + 12) + (w + 12)

Simplifying this expression, we get:

Perimeter = 4w + 24

Therefore, the function for the garden's perimeter in terms of the width "w" would be P(w) = 4w + 24.

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Answer:

16p-1

Step-by-step explanation:

-3+17p+2-p

-1+16p

Answer:

16p - 1

Step-by-step explanation:

= -3 + 17p + 2 - p

= 17p - p - 3 + 2

= 16p - 1

Answer: (52,72) (52 adults and 72 children)

Step-by-step explanation:

1) Create 2 formulas that show the information show above, 2.5x+2y=274 showing how the x is how many adults paid for a ticket and y is how many children paid for a ticket. The second formula being x+y=124 meaning the combination of children and adults equal 124 people.

2) Take those formulas and input them into a graph as shown in the picture (Graph 1)

3) Find the common point shown on the graph (should be the middle grey dot if on Desmos as shown (Graph 2)

4) The common point is (52, 72)

And if you plug these numbers in by replacing the x's and y's i shown in step 1 they bring an output of 274 and 124

Hope this helps :)

Explanation:

In 1977, the cpi value is

In 2017 the cpi value is

To figure out the cost of the value in 2017, we will interpolate below

Hence,

The final answer is

1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

\(T_n = -97n\)

Step-by-step explanation:

The actual sequence is: -97, -194, -291, -388

Required

Determine the nth term

nth term of an arithmetic progression is:

\(T_n = T_1 + (n - 1)d\)

Where

\(T_1 = First\ Term = -97\)

\(d = Common\ Difference = -194 - (-97) =-97\)

So:

\(T_n = T_1 + (n - 1)d\) becomes

\(T_n = -97 + (n - 1) * -97\)

\(T_n = -97 -97n + 97\)

Collect Like Terms

\(T_n = -97n + 97-97\)

\(T_n = -97n\)

Hence, a term of the sequence is:

\(T_n = -97n\)

The height of the candle change over time as a linear function

The height of the candle decreases by 2 inches every hour, which means the height of the candle is a linear function of time.

We can write the equation for the height of the candle as:

h(t) = 12 - 2t

where h is the height of the candle in inches and t is the time in hours.

If the candle burned for 2 hours, we can plug in t=2 into the equation to find the height:

h(2) = 12 - 2(2) = 8

So the height of the candle after 2 hours of burning is 8 inches.

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The domain of the relation in the graph is:

{-2, -1, 0, 2, 5}

A relation maps elements from one set (the domain) into elements from another set (the range).

Such that the domain is represented in the horizontal axis.

In the graph, we can see the points:

{(-2, -3), (-1, -1), (0, 3), (2, 1), (5, 2)}

The domain is the set of the first values of these points, then the domain is:

{-2, -1, 0, 2, 5}

The correct option is the first one.

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Answer:

a). k ≥ -1

b). k < 5

c). k ≤ 2

d). k > -3

Step-by-step explanation:

a). k ≥ - 3 + 2

k ≥ -1

b). 3k < 16 - 1

3k < 15

k < 5

c). -4k ≥ -5 - 3

4k ≤ 8

k ≤ 2

d). 3k > -10 + 1

3k > -9

k > -3

Answer:

solution is on the picture attached

Hope this helps

Answer:

Step-by-step explanation:

Triangle A)

use Pythagoras  to find hypotenuse

c =\(\sqrt{a^{2} +b^{2} }\)

c = √(\(8^{2}\)+\(5^{2}\))

c= √(64+25)

c=√89

c=9.43398 mm

it's a right triangle so just find one angle using SOH CAH TOA to remember how the trig function fit on the triangle

Tan(Ф) = Opp / Adj

Ф = arcTan( 5/8)

Ф = 32.0053°

Ф = 32°  approx

∠A=Ф

∠B= 180-90-32

∠B=58°

Triangle B)

∠L = 180-90-72

∠L = 18°

use CAH

Cos(Ф) = Adj / Hyp

Cos(18) =Adj / 10

10 * Cos(18)  = Adj

9.51056 cm = Adj

KL = Adj

now use SOH  

Sin(Ф) = Opp / Hyp

Sin(18) =Opp / 10

10* Sin(18) = Opp

3.09016 cm = Opp

KJ = Opp

Triangle C)

∠Q = 180-90-42

∠Q = 48°

CAH

Cos(∅) = Adj / Hyp

Cos(48) = 13 / Hyp

Hyp = 13 / Cos(48)

Hyp = 19.4281 km

QS = Hyp

SOH

Sin(∅) = Opp / Hyp

Sin(48) = Opp / 19.4281

19.4281 * Sin(48) = Opp

14.4379 Km = Opp

Opp = RS

Using  SOH CAH TOA is super helpful to place the trig function onto a triangle  :)

Recall that:

Therefore the given equation has no solutions.

Answer: Option B.

Answer:

16a^21

Step-by-step explanation:

Answer:

16 a^21

Step-by-step explanation:

= (2a^3)^4 (a^3)^3

= (2^4 a^3*4) (a^3*3)

= (16a^12) (a^9)

= 16 a^21

Answer: 150:30

Step-by-step explanation: First, put 150. Next, put a : sign. Lastly, put the number 30. Hopefully this helped! :D

Thus, the series converges for -4 < x < 2.In interval notation, the convergence sets are:

1)(-2, 2)

2)(-∞, ∞)

3)(-∞, ∞)

4)(-4, 2)

1) The power series ∑(n=0)∞ xn/(n+1)^(2n) converges for all x in (-1,1) by the ratio test.

2) The power series ∑(n=1)∞ (x-1)^n/n converges for x in the interval (0,2), with the endpoints excluded. To see this, we can use the ratio test and find that |(x-1)/(n+1)| → |x-1| as n → ∞. Thus, the series converges absolutely when |x-1| < 1, and diverges when |x-1| > 1. At x = 0, the series is the harmonic series which diverges, and at x = 2, the series becomes the alternating harmonic series which converges but not absolutely.

3) The power series ∑(n=1)∞ (x-n)^n/n! converges for all x in (-∞,∞). We can use the ratio test and find that |(x-n)/(n+1)| → 0 as n → ∞, and thus the series converges absolutely for all x.

4) The power series ∑(n=1)∞ (x+1)^n/3^n converges for x in the interval (-4,2) by the ratio test. When x = -4, the series becomes ∑(-1)^n/3^n which converges by the alternating series test. When x = 2, the series becomes ∑3^n which diverges.

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The series converges if |x+1|/3 < 1, i.e. if -4 < x < 2. The series converges at x=2 and diverges at x=-4, so the convergence set is (-4,2].

For the first power series, we use the ratio test:

lim |(x_{n+1}/(n+2)^{2(n+2)})/(x_n/(n+1)^{2n+2})| = lim |x_{n+1}|(n+1)^{2n+3}/|x_n|(n+2)^{2n+2}

= lim |x_{n+1}/x_n| ((n+1)/(n+2))^{2n+3} (n+1)/(n+2)

= lim |x_{n+1}/x_n| lim ((n+1)/(n+2))^{2n+3} lim (n+1)/(n+2)

= |x| lim (1/4)^n lim 1/2 = 0

Therefore, the series converges for all x.

For the second power series, we also use the ratio test:

lim |((x-1)^(n+1)/(n+1))/((x-1)^n/n)| = lim |x-1| (n+1)/n = |x-1|

Therefore, the series converges if |x-1| < 1 and diverges if |x-1| > 1. The series converges at x=0 and x=2, so the convergence set is [0,2].

For the third power series, we use the ratio test again:

lim |((x-(n+1))/(n+1)) ((x-n)/n!)| = lim |x-(n+1)|/|n+1| lim |x-n|/n! = 0

Therefore, the series converges for all x.

For the fourth power series, we use the root test:

lim sup |(x+1)/3|^n = |x+1|/3

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If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

For this question we need to subtract and multiply the numbers. We know that 2 = 25% of 8 so:

\(\boxed{8-2=6}\\\boxed{6/2=3}\)

We are going to take that 25% and multiply it with 3 to get are final answer.

\(\boxed{25*3=75}\\\boxed{So,2=75}\)

Therefore, If the original quantity is 8 and the new quantity is 2, then the correct answer is 75%.

It will take the golf ball some amount of time to hit the pavement.

Using the function h = -16t^2 + 75, where t is the time in seconds since the ball was dropped. To graph this function, we can plot points on a coordinate grid. For example, when t = 0, the ball is at its initial height of 75 feet, so we plot the point (0, 75). When t = 1, we can use the function to find that the ball is at a height of h = -16(1)^2 + 75 = 59 feet. So we plot the point (1, 59). Continuing in this way, we can plot more points and connect them to form a smooth curve.

To find out how many seconds it takes for the golf ball to hit the pavement, we need to find the time t when the height h is equal to 0 (since the ball will have hit the pavement by then). So we set h = 0 in the function and solve for t:

0 = -16t^2 + 75
16t^2 = 75
t^2 = 75/16
t = sqrt(75/16) ≈ 1.85

Therefore, it will take about 1.85 seconds for the golf ball to hit the pavement.

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Answer:

Don't have the ability to graph here but graph as follows:

X=1, Y=4

X=2, Y=8

X=3, Y=12

etc....etc....etc

The points will be proportional so your line will be straight.

Step-by-step explanation:

The depth of water after 10 minutes is 20 inches which is the option A.

Given that:-

Depth of water in a tank after t minutes is modeled by the function f(t) = 5+1.5t, measured in inches.

Let us check for Option A.

Putting t = 10 min in the given equation, we get,

f(10) = 5 + 1.5*10 = 5 + 15 = 20 inches.

Hence, option A is the right answer.

We can also check the other options to confirm our answer.

Putting t = 20 minutes,

f(20) = 5 + 1.5*20 = 5 + 30 = 35 inches

As 10 inches is written in B, hence, it is not the right answer.

We already know that t = 10 gives 20 inches.

Hence, C is not the answer.

Putting t = 65 minutes,

f(20) = 5 + 1.5*65 = 5 + 97.5 = 102.5 inches

As 10 inches is written in D, hence, it is not the right answer.

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dimensions of the poster with margin are L  =  12 in and h  = 24 in

The shape/polygon of a rectangle is two dimensional, having four sides, four vertices, and four right angles. The rectangle's two opposing sides are equal and parallel to one another. The space a rectangle occupies is known as its area. The area of a rectangle can also be defined as the region inside its border.

We utilise the unit squares to calculate a rectangle's area. Rectangle ABCD should be divided into unit squares. The total number of unit squares that make up a rectangle ABCD is its area.

Rectangle area equals length times width.

Let call length of printed area of the poster be " x "  and  height of printed area of the poster be " y ".

Area of the poster = length and height

200 = x*y  

y = 200/x

We also know that dimensions of the poster with margin is:

L  =  x + 2   in  and     H  =  y + 4 in

Therefore area of the poster is:

A(p)  = ( x + 2 ) * ( y + 4 )

And area as function of x is:

A(x)  =   ( x + 2 ) * ( 200/x + 4 )

A(x)  =  200 + 4*x + 400 /x  + 8

Taking derivatives on both sides of the equation we have:

A´(x)  =  4 - 400/x²

By taking A´(x)  = 0

4 - 400/x² = 0 ⇒ 4*x² - 400 = 0

x² = 400 / 4

x² = 100

x = 10 in

and y = 200/x ⇒ y = 20

The second derivative A´´(x) = 400/x4 which is > 0

there is a minimum for the function at the point x = 10

As x and y are dimensions of the printing area of the poster, dimensions of the poster with margin are

L  = x  +  2   =   10  + 2  =  12 in   and

h = y  +  4   =   20  + 4  =  24  in

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The amount of money in Kara's account at the end of the month is  342.50.

The amount of money in Kara's account would be reduced by the amount of money that the bank fee charged by the bank.

In order to determine the amount of money in the account at the end of the month, subtract the amount of bank fee from the amount of money in the account.

Subtraction is the mathematical operation that is used to determine the difference between two or more numbers. The sign used to represent subtraction is -. Other mathematical operations are addition, division and multiplication.

Money in the account at the end of the month = amount in the account - bank fee

350 = 7.50 = 342.50

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Answer:

5x-22<9<x

Step-by-step explanation:

5 times x = 5x

subtract 22 = 5x-22

less then = 5x-22<

9 more then x = 5x-22<9<x

If there is an axis deviation, it can result in a reversal of the QRS complex polarity in certain leads. Leads that normally have positive QRS complexes may have negative QRS complexes, and vice versa.

For example, if there is a left axis deviation, leads I and aVL, which normally have positive QRS complexes, may have negative QRS complexes.

Axis deviation refers to the direction in which the electrical activity is traveling through the heart. If the electrical activity is deviated from its normal pathway, it can cause a change in the orientation of the QRS complex, which is a graphical representation of the electrical activity generated by the ventricles during the cardiac cycle.

The change in polarity occurs because the direction of the electrical activity is now opposite to what it would be in a normal heart. This change in polarity can be used to help diagnose the location and type of axis deviation. Understanding the significance of the polarity changes can help healthcare providers determine appropriate treatment plans for patients.

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Answer:

I would say it's 8 because if the y=8 so if 8 is there you times it by 2 to get 16 so now you get 2 from x the exponent is 4 so 4x2 is 8 so 16-8=8 if that's wrong it's probable -8 because I haven't done exponents in a long time

Approximately 62.5% of the 44 players or 27.75 players, weigh less than or equal to 229 pounds.

Given the information from the box plot, we can estimate the percentage of players weighing less than or equal to 229 pounds. First, we need to find the number of players by dividing the summary of weights by the weight of one player: 44 players. Next, we can estimate the number of players weighing less than or equal to 229 pounds by finding the percentage of the data that is below 229 pounds and multiplying it by the total number of players. Based on the quartiles given in the box plot, we know that 50% of the data is below 214 pounds and 75% of the data is below 253 pounds. We can estimate that approximately 62.5% of the data is below 229 pounds by taking the average of these two values: (50% + 75%) / 2 = 62.5%. So, approximately 62.5% of the 44 players, or 27.75 players, weigh less than or equal to 229 pounds

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Complete Question

a high school has 44 players on the football team. the summary of the players' weights is given in the box plot. approximately, what is the percentage of players weighing less than or equal to 229 pounds?

The box Plot, the minimum weight is 154 pounds. The first quartile Q1 is 159 which 25% of the data. The second Quartile Q2 is 214 which 50% of the data. The third Quartile Q3 is 253 which is 75% and the maximum weight is 268.