Is the following relation a function?

Answer:

x = root(2)/2

Step-by-step explanation:

x^2 + x^2 = 1
2x^2 = 1
x^2 = 1 / 2
x = +- 1 / root(2)

but x = -1 / root(2) will be rejected because side can't be negative .

x = 1 / root(2)
therefore ,
    x  = root(2) / 2

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)).

Let the functions be f(x) = 4x² + 1 and g(x) = x² - 3

The correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

The function composition exists an operation " ∘ " that brings two functions f and g, and has a function h = g ∘ f such that h(x) = g(f(x)). In this operation, the function g exists used for the outcome of applying the function f to x.

Given:

f(x) = 4x² + 1 and g(x) = x² - 3

a) (f o g)(x) = f[g(x)]

f[g(x)] = 4(x² - 3)² + 1

substitute the value of g(x) in the above equation, and we get

    = 4(x⁴ - 24x + 9) + 1

simplifying the above equation

    = 4x⁴ - 96x + 36 + 1

    = 4x⁴ - 96x + 37

(f o g)(x) = 4x⁴ - 96x + 37

b) (g o f)(x) = g[f(x)]

substitute the value of g(x) in the above equation, and we get

g[f(x)] = (4x² + 1)²- 3

      = 16x⁴ + 8x² + 1 - 3

simplifying the above equation

      = 16x⁴ + 8x² - 2

(g o f)(x) = 16x⁴ + 8x² - 2.

Therefore, the correct answer is (f o g)(x) = 4x⁴ - 96x + 37 and

(g o f)(x) = 16x⁴ + 8x² - 2.

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Step-by-step explanation:

See image below

a. The probability of selecting chips, then crackers is 1/16.

b. The probability of selecting pretzels, then pretzels is 1/8.

A) The probability of selecting a chip on the first draw is 5/16. Since there is no replacement, the probability of selecting a cracker on the second draw is 3/15, as there are now only 15 items left in the basket. Therefore, the probability of selecting chips, then crackers is (5/16) x (3/15) = 1/16.

B) The probability of selecting a pretzel on the first draw is 6/16. Since there is no replacement, the probability of selecting another pretzel on the second draw is 5/15, as there are now only 15 items left in the basket.

Therefore, the probability of selecting pretzels, then pretzels is (6/16) x (5/15) = 1/8.

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A ratio variable should be transformed into a dichotomous variable represented with dummy coding when the research question or analysis requires a simplified comparison between two distinct groups, the relationship between the ratio variable and the outcome variable is non-linear, there is a meaningful cutoff or threshold value, or specific statistical methods necessitate dichotomous variables.

A ratio variable may be transformed into a dichotomous variable represented with dummy coding under the following conditions:

Simplification of Analysis: When the research question or analysis requires a simplified comparison between two distinct groups or categories based on the ratio variable.

Nonlinearity: If the relationship between the ratio variable and the outcome variable is non-linear, it may be beneficial to dichotomize the ratio variable to capture the presence or absence of a certain condition or threshold.

Practical Interpretation: When there is a meaningful and interpretable cutoff or threshold value for the ratio variable that divides the population into two distinct groups.

Statistical Analysis Requirements: Certain statistical methods or models may require dichotomous variables for analysis, and transforming a ratio variable into a dichotomous variable allows for the use of these methods.

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If a multiplies an n x p matrix b then the total number of multiplications involved is m x p. And is given by Dimensional vector.

For explanation, There are two separate cases to consider when multiplying an m-by-n matrix and an n-dimensional vector, or an m-by-n matrix and an n-by-p matrix.

When an m-by-n matrix, A, multiplies an n-dimensional vector, x, the number of separate multiplications involved is m. This is because in order to compute the dot product of A and x, each row of A needs to be multiplied by the vector x, resulting in m separate multiplications.

On the other hand, when A multiplies an n-by-p matrix, B, the number of separate multiplications involved is m x p. This is because in order to multiply A and B, each row of A must be multiplied by each column of B, resulting in m x p separate multiplications.

Therefore, the number of separate multiplications involved when multiplying an m-by-n matrix and an n-dimensional vector is m, and the number of separate multiplications involved when multiplying an m x n matrix and an n x p matrix is m x p.

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Answer:

b. -4 an C  then A

Step-by-step explanation:

hope this helps!

Answer:

It will be 4

Step-by-step explanation:

i know

Answer:

56 feet

Step-by-step explanation:

So the area of a quadrilateral is, length * width

but since the, length = width, in a square then we can say that the area of a square is, length ^ 2, or, width^ 2

so we can say that

length ^ 2 = 196

the sqrt of 196 is 14 so

length = 14

Since there are four sides to a square, we need to multiply the length by 4 to find the total material needed

14 * 4

= 56

Answer:

the length might be 48 I have calculated it so it might be the answer

Step-by-step explanation:

I divided 196 by 2

Jackie pays $130 monthly for her group health insurance.

To find out how much Jackie pays for her group health insurance monthly, we need to calculate 40% of the annual cost. Given that the annual cost is $3,900 and her company pays 40% of that, we can calculate the amount Jackie pays.

First, we find the company's contribution by multiplying the annual cost by 40%: $3,900 × 0.40 = $1,560. This is the amount the company pays towards Jackie's health insurance.

To determine Jackie's monthly payment, we divide her annual payment by 12 (months in a year) since she pays monthly. So, Jackie's monthly payment is $1,560 ÷ 12 = $130.

Therefore, Jackie pays $130 per month for her group health insurance. This calculation takes into account the company's contribution of 40% of the annual cost, resulting in an affordable monthly payment for Jackie.

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The cone shaped pile can hold 235.5 feet sand.

What is volume of cone ?

  One-third the sum of the area of the cone's circular base and its height is the formula for a cone's volume. Cones are described as pyramids with circular cross sections in terms of geometric and mathematical ideas. A cone's volume can be quickly determined by measuring the cone's height and radius.

Here radius of cone = 5 feet

Height of cone h = 8 feet 10 inches = 8+1 = 9 feet

Now volume of cone is

=> V = \(\pi r^2\frac{h}{3}\) cubic unit

=> V= 3.14* 25 * 3 = 235.5 cubic feet.

Hence the cone shaped pile can hold 235.5 feet sand.

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Using a proportional relationship, it is found that she would be able to drive 240 miles on 8 gallons of gasoline.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

Researching the problem on the internet, it is found that she drives 30 miles per gallon, hence the function for the distance driven considering the number of gallons in the tank is given by:

D(n) = 30n.

She has n = 8 gallons, hence the distance is given by:

D(8) = 30 x 8 = 240 miles.

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1) The function is P =650000e^(0.04)5

2) The function is P=800e^(0.02)6

3) The function is P= 2500e^-(0.03)5

Exponential growth is a type of growth pattern in which a quantity or value increases at a constant percentage rate over time, resulting in a rapid and accelerating increase in value

Note that;

P=Poe^rt

30000=20000e^0.05t

30000/20000 = e^0.05t

1.5 = e^0.05t

ln1.5 = 0.05t

t = 8 years

2) The function is a growth function and the percentage is 6%

3) 2000=45000e^-0.2t

2000/45000 = e^-0.2t

0.44 = e^-0.2t

ln0.44 = e^-0.2t

t = 4 years

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Answer:

5 and 3

Step-by-step explanation:

please mark me brainlist

Answer:

if I read it right and it is just asking for the slope then -1.2 should be the answer

Answer:

700

Step-by-step explanation:

Answer:

It’s 64 x 9 equals 576

Step-by-step explanation:

The answer is 9 feet

The value height of shed is 9 feet.

The volume of a rectangular prism is defined as the space occupied within a rectangular prism. A rectangular prism is a polyhedron that has two pairs of congruent and parallel bases.

Here, Vol. of rectangular prism = 576 ft³

          base area = 64 ft²

Volume of rectangular prism = area of base X height

      576 = 64 X h

        h = 576 / 64

       h = 9 ft.

Thus, the value height of shed is 9 feet.

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Answer:

The total volume of the space is 55,000 cm³

Step-by-step explanation:

First, figure out the length for each of the two prisms. The prism on the right has a length of 25 cm, so we can subtract that from 50 cm (the combined length of both prisms) to get 25 cm.

Next, figure out the volume of each area. For a rectangular prism, Volume = length · width · height. The left prism's volume is 30,000 cm³ (do 25 · 60 · 20) while the right prism's volume is 25,000 cm³ (do 25 · 25 · 40).

Lastly, add the volumes together to get the total volume, which is 55,000 cm³

Answer:

2 hours.

Step-by-step explanation:

I would take the car 2 hours to reach 100 miles because

50 * 2 = 100.

Answer:

6

Step-by-step explanation:

Terms are what is separated by addition and subtraction.

Answer:

\(b=\dfrac{2V}{ah}-c\)

Step-by-step explanation:

Given equation:

\(V=\dfrac{1}{2}a(b+c)h\)

Multiply both sides of the equation by 2:

\(\implies 2 \cdot V=2 \cdot \dfrac{1}{2}a(b+c)h\)

\(\implies 2V=a(b+c)h\)

Divide both sides by ah:

\(\implies \dfrac{2V}{ah}=\dfrac{a(b+c)h}{ah}\)

\(\implies \dfrac{2V}{ah}=b+c\)

Subtract c from both sides:

\(\implies \dfrac{2V}{ah}-c=b+c-c\)

\(\implies \dfrac{2V}{ah}-c=b\)

Therefore:

\(\implies b=\dfrac{2V}{ah}-c\)

Answer:

$2450

Step-by-step explanation:

One week = 7 days

$350 = 1 day

$ 2450 = 7 days(1 week)

350 * 7 = 2450

Answer: is not a function

Option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

The given rectangle is ABCD.

The length of segment AB is 9x-16 units

The length of segment AD is 1.5x+42 units

We have to find the inequality which represents the  length of segment AB is greater than  length of segment AD

> is the symbol used to represent greater than

AB>AD

9x-16>1.5x+42

Hence, option B is correct, the inequality which represents the  length of segment AB is greater than  length of segment AD is 9x-16>1.5x+42

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Answer:

x² - 4x + 3 = 0

Step-by-step explanation:

given roots x = a and x = b then the corresponding factors are

(x - a) and (x - b)

the equation is then the product of these factors , that is

(x - a)(x - b) = 0

given

roots x = 3 and x = 1 , then factors are (x - 3) and (x - 1) , then

(x - 3)(x - 1) = 0 ← expand factors using FOIL

x² - 4x + 3 = 0

Answer:

y = - 3x + 5

Step-by-step explanation:

Given

6x + 2y = 10 ( subtract 6x from both sides )

2y = - 6x + 10 ( divide all terms by 2 )

y = - 3x + 5

The correct equation for y in terms of x would be, y = - 3x + 5

Hence, option 2 is true.

Used the concept of an equation that states that,

An equation is a group of numerical variables and functions that have been combined using operations like addition, subtraction, multiplication, and division.

Given that the expression is,

6x + 2y = 10

Now, simplify the equation for y in terms of x as,

6x + 2y = 10

Subtract both sides by 6x,

2y = - 6x + 10

Divide both sides by 2,

y = - 3x + 5

So, The correct equation would be, y = - 3x + 5

Thus, option 2 is true.

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