can someone please help me with this.​

The first function is a linear function while the second function is neither a linear nor exponential

A linear function is of the form f(x) = mx + c,

where m is the slope (or rate of change) and y-intercept

m = y2-y1 / x2-x1

An exponential function is of the form f(x) = abˣ

where a and b are constants

In a linear function, the slope must be constant. Also, in exponential function a and b must be constants

Given:

(x) 2 3 4

F(x) 5.5 7 8.5

For x = 2 and 3:

slope = 7-5.5 / 3-2 = 1.5

For x = 3 and 4:

slope = 8.5-7 / 4-3 = 1.5

The slope is the same, thus, it is a linear function

Note: f(x) = y

(x) 0 2 4

F(x) 2 5 9

This is not linear, check for exponential

y = abˣ

when x = 0, y =2

2 = ab⁰

a = 2

when x =2, y = 5

5 = 2b²

b² = 5/2

b = √(5/2)

when x =4, y = 9

9 = 2b⁴

b⁴ = 9/2

b = \(\sqrt[4]{(9/2)}\)

Since the b are not the same. Thus, this is an exponential function also

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Answer:

4 and 5

Step-by-step explanation:

\( \because \: \sqrt{23} = 4.79583152 \\ \therefore \: 4 < \sqrt{23 } < 5 \\ so \: \sqrt{23} \: lie \: between \: the \: integers \: 4 \: and \: 5\)

The amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.

It deals with the size of geometry, region, and density of the different forms both 2D and 3D.

Henry has a box in the shape of a square pyramid.

He wants to wrap the box with paper.

If the base has side lengths of 5 in. and the lateral height is 8 in.

Then the amount of the wrapping paper that he needs to cover the pyramid will be

\(\rm Area = 4 \times \dfrac{1}{2} \times 5 \times 8 + 5 \times 5\\\\\\Area = 80 + 25\\\\\\Area = 105 \ in^2\)

Thus, the amount of wrapping paper that he needs to cover the pyramid will be 105 square inches.

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Answer:

A) 30

Step-by-step explanation:

3*10=30

A 30

Answer:

grab two of our datas in a row

goal: get to y=mx+h

m = (-6-(-12))/(0-(-2))=6/2=3

now we have: y=3x+h

z=0 → y = -6 → h = -6

answer: y = 3x-6

The equation best describes the relationship between the corresponding values of x and y shown in the table is:

Option C. y = 3x - 6

To determine the equation that best describes the relationship between x and y in the table, we can apply the slope-intercept formula, which has the form: y = mx + b, where "m" is the slope and "b" is the y-intercept.

From the table, let's calculate the slope using two points (x, y):

Using (-2, -12) and (0, -6):

Slope (m) = (y2 - y1) / (x2 - x1) = (-6 - (-12)) / (0 - (-2)) = 6 / 2 = 3

Now, let's use the slope (m) and any point (x, y) from the table to find the y-intercept (b).

Using (0, -6):

y = mx + b

-6 = 3 * 0 + b

b = -6

So, the equation that best describes the relationship is:

y = 3x - 6

Thus, the correct option is C. y = 3x - 6.

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The chance that the hospital will run out of sleeping pills on any given day is 0.5000 (or 0.5000 with four decimal places).

To calculate the chance that the hospital will run out of sleeping pills on any given day, we can use the normal distribution and Z-score.

First, let's calculate the Z-score using the formula:

Z = (X - μ) / σ

Where:

X = consumption rate per day (1,155 pills)

μ = average consumption rate per day (1,155 pills)

σ = standard deviation (81 pills)

Z = (1,155 - 1,155) / 81

Z = 0

Now, we need to find the probability associated with this Z-score. However, since the demand for sleeping pills can be considered continuous and not discrete, we need to calculate the area under the curve from negative infinity up to the Z-score. This represents the probability of not running out of sleeping pills.

We discover that the region to the left of a Z-score of 0 is 0.5000 using a basic normal distribution table or statistical software.

To find the probability of running out of sleeping pills, we subtract this probability from 1:

Probability of running out of sleeping pills = 1 - 0.5000

Probability of running out of sleeping pills = 0.5000

Therefore, on any given day, the hospital has a 0.5000 (or 0.5000 with four decimal places) chance of running out of sleeping tablets.

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The next three terms in the following arithmetic sequence -4, 5, 14, 19 … include the following:

Term 5 = 32.

Term 6 = 41

Term 7 = 50

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

Next, we would determine the common difference as follows.

Common difference, d = a₂ - a₁

Common difference, d = 5 - (-4)

Common difference, d = 9

Next, we would determine the next three terms as follows:

a₅ = a₁ + (n - 1)d

a₅ = -4 + (5 - 1)9

a₅ = 32

a₆ = a₁ + (n - 1)d

a₆ = -4 + (6 - 1)9

a₆ = 41

a₇ = a₁ + (n - 1)d

a₇ = -4 + (7 - 1)9

a₇ = 50

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Therefore , the solution of the given problem of volume comes out to be a)   \(\int\limits^{2\pi }_0 \int\limits^a_0\) \(e^{-r^{2}\)(r) drdθ  , b) V = π ( 1- \(e^{-a^{2} }\) ) and   \(\lim_{a \to \infty} V\) = π .

the amount of space something occupies in three dimensions. Consider how much water might be present. known also as capacity .

The volume = area * height in this instance is equal to 200 units (10 x 4 x 5). 3 Volume units consist of:• Metric units: liters, cubic centimeters (cm3), and cubic meters (m3)

• US Standard: ounces, pints, gallons, cubic inches, and cubic feet

Here,

Given : z=e−x^2−y^2

and  x^2+y^2≤a2 where a>0.

Thus ,

volume  = \(\int\limits\int\limits\) \(e^{-x^{2} -y^{2} }\) dxdy

=>  \(\int\limits^{2\pi }_0 \int\limits^a_0\) \(e^{-r^{2}\)(r) drdθ

and

b)  volume    =  \(\int\limits^{2\pi }_0 \int\limits^a_0\) \(e^{-r^{2}\)(r) drdθ

let \(r^{2}\) = t

2rdr =dt

rdr = 1/2 dt

then,

V = 2π * 1/2 * \(\left \{ {{a^{2} } \atop {0}} \right.\) - \(e^{-t}\)

=> V = π * - \(e^{-a^{2} }\) + \(e^{0}\)

=> V = π ( 1- \(e^{-a^{2} }\) )

c) \(\lim_{a \to \infty} V\) = >    \(\lim_{a \to \infty}\)(π ( 1- \(e^{-a^{2} }\) ))

=>  π ( 1- \(e^{-\infty }\) )

=> π ( 1- 1/ \(e^{\infty }\) )

= > π ( 1- 0 )

=>   \(\lim_{a \to \infty} V\) = π

Therefore , the solution of the given problem of volume comes out to be a)   \(\int\limits^{2\pi }_0 \int\limits^a_0\) \(e^{-r^{2}\)(r) drdθ  , b) V = π ( 1- \(e^{-a^{2} }\) ) and   \(\lim_{a \to \infty} V\) = π .

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Answer:

8551.56

Step-by-step explanation:

\(A=5300(1+(0.08)/12)^{(12)(6)} \approx 8551.56\)

The volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L, calculated using the ideal gas law equation.

To compute this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

First, we need to convert the initial temperature of 25 °C to Kelvin:

T1 = 25 + 273.15 = 298.15 K

Next, we can rearrange the ideal gas law equation to solve for V2:

V2 = (P1 * V1 * T2) / (P2 * T1)

We have:

P1 = 1.08 atm (initial pressure)

V1 = 50.0 L (initial volume)

P2 = 0.855 atm (final pressure)

T2 = 10.0 °C (final temperature)

Converting the final temperature to Kelvin:

T2 = 10 + 273.15 = 283.15 K

Substituting the values into the equation:

V2 = (1.08 * 50.0 * 283.15) / (0.855 * 298.15)

V2 ≈ 42.81 L

Therefore, the volume of the helium-filled balloon at 0.855 atm and 10.0 °C will be approximately 42.81 L.

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Answer:

22 m/s

Step-by-step explanation:

Take the distance and divide by the time

1210 m/55s

22 m/s

Answer:

Step-by-step explanation:

\(speed = \frac{distantce}{time} \\ = \frac{1210m}{55s} \\ = 22m {s}^{ - 1} \)

Answer:

Mutually Exclusive

Dependent

Step-by-step explanation:

Given that both events cannot occur at the same time, that is "both dice cannot be odd (event A) if at least one of the dice is even (event B).

Hence, this is MUTUALLY EXCLUSIVE.

Also, given the fact that the occurrence of one event (event A) affects the probability of the other (event B).

Hence, this is DEPENDENT.

On solving the provided question, we can say that permutation will = 1/2(26) = 13 ways

The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order.

here,

by permutation,

1 through 26

permutation will = 1/2(26) = 13 ways

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Step-by-step explanation:

(3x-63) = (2x+2)

since the parentheses are doing anything we can drop them

3x-63 = 2x+2

subtract 2x from both sides

x-63 = 2

add 63 on both sides

x = 65

Answer/Step-by-step explanation:

✔️The point (8, 6) represents seasonal plant growth of 6 mm with 8 cm of rainfall during the growing season.

✔️To determine how much rain fell if the plants grew 12 mm one season, find the value of x (rainfall) when y (plant growth) = 12.

From the graph, when y = 12, x = 16.

This means that when the plant grew 12 mm, 16 cm of rainfall was recorded.

Therefore:

If the plants grew 12 mm one season, 16 cm rainfall fell.

Nonverbal instruments have been developed primarily in an attempt to d. assess issues that individuals cannot verbalize.

The answer is d. Nonverbal instruments have been developed primarily to assess issues that individuals cannot verbalize. These instruments are often used in psychology and educational assessments to measure skills and abilities in areas such as mathematics, language, and pre-reading skills, while controlling for the influences of language and culture. Nonverbal instruments can be particularly useful for individuals who struggle with verbal communication or have language barriers.

The exchange of information between people without the use of spoken or written language is referred to as nonverbal communication. Facial expressions, eye contact, gestures, posture, body movements, tone of voice, and even the use of time and space are all included in this broad category of behaviors.

A lot of information about a person's emotional state, intentions, attitudes, and personality traits can be communicated nonverbally. A person's posture and body language, for instance, might show whether they are feeling confident or uneasy, and their tone of voice and facial expressions can show whether they are happy, angry, or sad.

A crucial component of human contact is nonverbal communication since it can improve our ability to understand others, establish rapport, and communicate.

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The height of the tree is 6.4m

the difference is that in one case the shadow of the tree is 60 - 20 = 40 m, and in the other case it is 60 + 20 = 80 m long.

anyway, for a certain angle of the sunlight we know the shadow of the pole is 60 m long, which creates with the 4.8 m height a right-angled triangle, with the line of sight from the top of the pole to the ground end of the shadow being the Hypotenuse or radius for or trigonometric triangle in a circle.

the shadow length (60 m) is sine of the sunshine angle multiplied by the radius.

the height (4.8 m) is cosine of that sunshine angle multiplied also by that radius.

Pythagoras gets us the radius for the pole triangle :

radius² = 60² + 4.8² = 3600 + 23.04 = 3623.04

radius = sqrt(3623.04) = 60.19169378... m

sin(angle) × radius = 60

sin(angle) = 60/radius = 0.996815279...

angle = 85.42607874...°

the sunshine creates with the tree also a right-angled triangle with the same sunshine angle (the sun is so far away, that the tiny, tiny difference is irrelevant, we can simply assume the angles are equal).

but the shadow is of different length (sin(angle)×radius), which means also the radius for the tree triangle has to be different. and that defines the height of the tree (cos(angle)×radius).

but now we know the angle, and we can reverse calculate the side lengths.

but the question is (as mentioned at the beginning) : is the tree shadow 40 m or 80 m long.

we have therefore 2 solutions for the height of the tree.

1. the shadow is 40 m long.

sin(angle) × radius = 40

radius = 40/sin(angle) = 40.12779585... m

tree height = cos(angle)×radius = 3.2 m

2. the shadow is 80 m long.

sin(angle) × radius = 80

radius = 80/sin(angle) = 80.25559171... m

tree height = cos(angle)×radius = 6.4 m

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We can ensure trigonometric functions compute values appropriately by validating the results against known values. In order to ensure that the argument is in a short interval surrounding a place where an approximation is highly accurate, one performs a range reduction prior to computing things like a cos or sin.

By comparing the results to established values, we can make sure trigonometric functions compute values correctly. As an example, if we wanted to validate the cosine of 45 degrees, we could compare the result to the known value of 0.707. If the computed value is within a small margin of error of the known value, then we can assume the trigonometric function is computing values appropriately.

In order to calculate functions like cos or sin, one must first perform a range reduction to make sure the input is inside a narrow range surrounding a point where an approximation is highly accurate. It is typically close to zero.

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Answer:

5 r o 2 t

Step-by-step explanation:

(√3+√7)²

We know ,[(a+b)²=a²+2ab+b²]

=>(√3+√7)²=(√3)²+2(√3)(√7)+(√7)²

=>(√3+√7)²=3+2√21+7

=>(√3+√7)²=10+2√21

Answer:

85,910

You get this because whenever there are three digits after a number you add a comma as seen in the number there are three digits after 85 so you add a comma.

Hope it helps bai!

Answer:

85,910

I think this is the right answer so..

I HOPE THIS HELPS YOU

Answer:

900 grams.

Step-by-step explanation:

1 kg = 1000 grams.

0.9 kg = 1000 * 0.9

= 900 grams.

Answer:

900 grams is the answer

The constant of proportionality is equals to four quarters per dollar. The one dollar amount is equals to four quarters.

The constant of proportionality is the ratio of the called proportional relationship that relates two given values to each other. Other names for constant of proportionality are constant ratio, constant rate, unit rate etc . Formula :

We have, a proportional relationship between the amount of money in dollars, x, and the number of quarters, y. Now, we have to calculate constant of proportionality for provide data.

x ( dollars) 4 7 11 13

y(quarters ) 16 28 44 52

a) constant of proportionality, k = y/x = 16/4 = 4

b) constant of proportionality,k = 28/7 = 4

c) constant of proportionality, k = 44/11 = 4

d) constant of proportionality,k = 52/13 = 4

So, the constant of proportionality,k = 4 quarters per dollar , that is one dollar = four quarters.

Hence, one dollar is equals to 4 quarters.

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According to estimates, there were 7,060,268,214 people on Earth as of August 16, 2012. Rounding to the nearest hundred million, 7,060,268,214 equals 7,100,000,000.

Find the digit that is 100,000,000 places away first. The next step is to check if the number that comes after the hundred million place is 5 or higher. Next, multiply the result by 100 million to the nearest billion. 200,000,000 is the reply. 4,000,000 or 5,000,000 may be the million closest to you.

Take a glance at the number in the right-hand column, the hundred thousands, to determine the nearest million. 5 appears in the column for "hundred thousands." It is standard practise to round up numbers that are five or more. This means that you should look at the digit in the ten thousand spot to round numbers out to the nearest hundred thousand. 1,000,000 is added as a rounding error.

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You should deposit approximately $340.84 monthly to reach $293,000 in 28 years at a 4.4% annual interest rate compounded monthly.

To calculate the monthly deposit required for an investment plan paying 4.4% interest compounded monthly to reach $293,000 in 28 years, we use the future value of an annuity formula:

FV = P * (((1 + r)^n - 1) / r)

Here, FV is the future value, P is the monthly deposit, r is the monthly interest rate, and n is the number of payments. First, convert the annual interest rate (4.4%) to a monthly rate by dividing by 12, which gives 0.0367 (4.4%/12) or 0.00367 as a decimal. The number of payments (n) is 28 years * 12 months/year = 336.

We want to find P, so rearrange the formula:

P = FV / (((1 + r)^n - 1) / r)

Substitute the values:

P = $293,000 / (((1 + 0.00367)^336 - 1) / 0.00367)

P ≈ $340.84

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By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

In this question we must derive two complex numbers such that the following conditions are fulfilled:

a² + b² = 5²     (1)

c² + d² = 13²     (2)

13 · (a + i b) - 5 · (c + i d) = 27 - i 99     (3)

If we assume that a, b, c, d are integers, then we can suppose that (a, b) = (4, -3) and (c, d) = (5, 12) and we check if these values satisfy (3):

13 · (4 - i 3) - 5 · (5 + i 12)

52 - i 39 - 25 - i 60

27 - i 99

By applying knowledge on complex analysis, the complex numbers that satisfy the three conditions defined in the statement are z₁ = 4 - i 3 and z₂ = 5 + i 12.

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Given:

Point is T(-3,8).

To find:

The coordinates of T' after \(R(y-axis)\circ R(x-axis)\).

Solution:

We know that, \(R(y-axis)\circ R(x-axis)\) means the figure reflected across the x-axis then reflected across y-axis.

If a figure reflected across x-axis, then

\((x,y)\to (x,-y)\)

\(T(-3,8)\to T_1(-3,-8)\)

If a figure reflected across y-axis, then

\((x,y)\to (-x,y)\)

\(T_1(-3,-8)\to T'(-(-3),-8)\)

\(T_1(-3,-8)\to T'(3,-8)\)

Therefore, the required point is T'(3,-8).

Answer:

Step-by-step explanation:

The best measure of variability for this data is the range, and its value is 10.