a. Is the relation shown below a function? Explain.
Relation: (4,16) (5,25) (3,9) (6,36) (2,4) (1,1)
b. What are the domain and range of the relation?

If b1,b2 are nonzero, the value of {b1}/{b2} will be 3/2.

If a is inversely proportional to b. Let a1,a2 be two nonzero values of a such that {a1}/{a2}={2}/{3}. Let the corresponding b values be b1,b2. If b1,b2 are nonzero

a = k *1/b

2/3 =k * 1/b1 /k * 1/b2 [k = constant cancels out]

2/3 =1/b1 * b2

2/3 = b2/b1

b1 =3 and

b2 =2. Therefore:

b1/b2 =3/2.

Another way of looking at it, is this:

When a1 =2, b1=1/2

When a2 =3, b2=1/3

So, when a1/a2 = 2/3, then:

b1/b2 =(1/2) / (1/3) =(1/2) x (3/1)

         =3/2

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The scientific notation of Pill's mass 5 × 10⁻³ g.

And, In milligrams, The pill's mass is 5.0 milligram.

Scientific notation is a way of writing a very large or very small numbers. For example; 230,000,000 can be written in scientific notation as 2.3 x 10⁸.

Given that;

A pain-relieving pill has a mass of 0.005 g.

Now, We can write the mass in scientific notation as;

⇒ 0.005 g

⇒ 5 × 10⁻³ grams

And, We can write the pill's mass in milligram as;

Since, 1 g = 1000 milligram

Hence, We get;

⇒ 0.005 g = 0.005 × 1,000 milligrams

                = 5.0 milligrams.

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The equation of the slant asymptote of the function is y=2x³+5x²+1.

A slant asymptote, also known as an oblique asymptote, occurs when the degree of the numerator polynomial is greater than the degree of the denominator polynomial. The slant asymptote gives the linear function which is neither parallel to x-axis nor parallel to the y-axis.

The given function is f(x)=2x³+5x²+(x-5)/x² +1

Find the oblique asymptote using long polynomial division.

Vertical Asymptotes: x=0

No Horizontal Asymptotes

Oblique Asymptotes: y=2x³+5x²+1

Therefore, the equation of the slant asymptote of the function is y=2x³+5x²+1.

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The side lengths given as 4 8 9 shows that it is an obtuse Triangle.

It should be noted that to determine whether the triangle is acute, right, or obtuse, add the squares of the two smaller sides, and compare the sum to the square of the largest side. Since this sum is greater, the triangle is acute

In a situation if the sum of the squares of the two shorter sides of a triangle is smaller than the square of the longest side, the triangle is obtuse

This will be:

4² + 8² < 9²

16 + 64 < 81

80 < 81

It is obtuse.

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The total number of beads will be 1128 beads.

A word problem in mathematics simply refers to a question that is written as a sentence or in some cases more than one sentence which requires an individual to use his or her mathematics knowledge to solve the real.life scenario given.

In this case, Jennifer has 256 beads stella has 3 times more beads tiah had 104 beads.

The total number of beads will be:

= 256 + (256 × 3) + 104

= 256 + 768 + 104

= 1128

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Complete question

Jennifer has 256 beads stella has 3 times more beads tiah had 104 beads. What is the total number of beads?

The hours that it would take Nisha to make the gungharoos is 301.5 hours

The equation of the line in the scatter plot is given as

y= 4.75x - 2.5

Where x is the number of ghungaroos that Nisha would make

We have to put in the value of x as 64 because the question tells us that She made a total of 64 gungharoos

Hence we would have:

y = 4.75 * 64 - 2.5

y = 304 - 2.5

y =301.5

The hours that it would take Nisha to make the gungharoos is 301.5 hours

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Therefore , the solution of the given problem of relative frequency comes out to be 20% of student population is between the ages of 35 and 38.

To find it, multiply the ratio of the total number of pupils (2 + 2 + 8 + 2 + 10 + (6 = 30) by 100%, which equals the number of individuals with a lower limit of 35 (of whom there are 6).

Here,

Simply put, the relative frequency in this case is

20%: RF = (6/30)*100%

Consequently, 20% of student population is between the ages of 35 and 38.

Therefore , the solution of the given problem of relative frequency comes out to be 20% of student population is between the ages of 35 and 38.

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Answer:

90

Step-by-step explanation:

a times by b is equal to 3600 and b divided by a is equal to 4/9 which means that a must be a mulitiple of 4 and b must be a multiple of 9. An easy multiple of 4 and a easy mulitple of 9 that times together eqaul 3600 is 90 and 40. So therefore a= 90

Answer:

  $20

Step-by-step explanation:

You want to know the pre-tax price if the price with 5% tax added is $21.

The added tax is 5% of the original amount (x), so the amount with tax added is ...

  $21 = x + 0.05x = 1.05x

  $21/1.05 = x = $20 . . . . . divide by the coefficient of x

The cost before tax was added was $20.

Step-by-step explanation:

Percentage left after the tax percentage is

100%-5%=95%

95% is equal to 95/100 = 0.95

therefore, the cost after tax divided by the percentage that is left after the tax percentage

costs after tax is 21 dollars which is

21/0.95 = 22.1dollars

The line that cuts through (1, 2) and is perpendicular to (y = 1/3x + 4) has the equation (y = -3x + 5).

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

On the y-axis, this value c is referred to as the intercept.

Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.

y = 1/3x + 4 is the line that crosses (1,2) and is perpendicular to it.

To ascertain the equation of the line, utilize the procedures below:

Step 1: Two lines that are perpendicular to one another have the following slopes:

mm' = 1

Where the slopes of the lines are m and m'.

Step 2 - The line that is perpendicular to the line (y = 1/3x + 4) has the following slope:

1/3 * m' = -1

m' = -3

Step 3: The equation for a line passing through the points (1, 2) and having a slope of -3 is as follows:

(y - 2) = -(x - 1)

Implicate the equation above:

y = -3x + 5

Therefore, the line that cuts through (1, 2) and is perpendicular to (y = 1/3x + 4) has the equation (y = -3x + 5).

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Answer: A

Step-by-step explanation: To solve any problem where we are given a function f(x) and asked to find f(n), we replace the number n will all Xs in the function.

For this problem g(x) = 39 * (1/3)^x and we are asked to find g(3). We plug in 3 for x in g(x) and get 39*(1/3)^3. Now we just simplify.

39*1/27, 39/27, 13/9

The value of g(3) for the function below g(x)=39•(1/3) is A. 13/9.

Function is a type of relation, or rule, that maps one input to specific single output.

We are given a function f(x) and asked to find f(n), we replace the number n will all Xs in the function.

For this problem [tex]g(x) = 39 (1/3)^x[/tex]

We need to find g(3).

We plug in 3 for x in g(x) and get [tex]39(1/3)^3[/tex].

Now we just simplify;

39 1/27, 39/27, 13/9

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Answer:v=-4

Step-by-step explanation:We move all terms to the left:

-5v+6-(26)=0

We add all the numbers together, and all the variables

-5v-20=0

We move all terms containing v to the left, all other terms to the right

-5v=20

v=20/-5

Answer:

To calculate the marginal tax rate on the investment, you'll need to figure out the additional tax on the new income. In this example, $500 will be taxed at 15% and $500 at 25%. This produces tax of $200, which on income of $1,000 makes the marginal tax from making that investment equal to $200 / $1,000 or 20%.

Answer: Attached

Step-by-step explanation:

The correct option is A X[tex]\neq[/tex]-2,1,5

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The value of the combined function f(g(x)) will be -16x^2+88x-120.

What is a function?

A function is defined as a relation between a set of inputs having one output each. In simple words, a function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and co-domain or range. A function is generally denoted by f(x) where x is the input. The general representation of a function is y = f(x).

There are several types of functions in math. Some important types are:

Injective function or One to one function: When there is mapping for a range for each domain between two sets.

Surjective functions or Onto function: When there is more than one element mapped from domain to range.

Polynomial function: The function which consists of polynomials.

Inverse Functions: The function which can invert another function.

Now,

Given functions are f(x)=1-x^2 and

g(x)=11-4x

Therefore,

the combined function will be f(g(x))=1-(11-4x)^2

=1-121-16x^2+88x

Hence,

           The value of the combined function f(g(x)) will be -16x^2+88x-120.

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Right question would be :-

Consider functions f and g. f ⁡ ( x ) = 1 − x 2 g ⁡ ( x ) = 11 − 4 ⁢ x Evaluate f(g(x))?

The solution to the equation 120 + 18 1/4x = 180 –13/4x is x = 120/43

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

120 + 18 1/4x = 180 –134x

Express the equation properly

This gives

120 + 18 1/4x = 180 –13/4x

Collect the like terms in the above equation

So, we have the following representation

18 1/4x + 13/4x = 180 - 120

Evaluate the like terms in the above equation

So, we have the following representation

21 1/2 x = 60

Express as decimal

21.5x = 60

Divide both sides by 21.5

x = 60/21.5

Simplify the fraction

x = 120/43

Hence. the solution is x = 120/43

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A graph which shows relationship between the number of days and total amount of sunglasses is shown in the image attached below.

In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

here, we have,

From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 62

In conclusion, we can reasonably infer and logically deduce that the scatter plot indicates an inverse relationship between the number of days and total amount of sunglasses.

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Answer:

See attached photo.

"Choice D" The dot plot with the outlier at 4 feet and data points condensed on the right from 5.5-7 feet is the correct dot plot.

Step-by-step explanation:

A dot plot is a statistical chart consisting of data points plotted on a simple scale, typically using filled-in circles.

A skew represents the direction in which the data points follow.

An outlier is a data point that "stands out" from other data points.

Please let me know if this helped!!!

The surface area of the figure is found by multiplying the area of each face together.

Net Area Surface Area

24 cm²   22 cm³

Net Area: 24 cm²

Surface Area: 22 cm³ + 11 cm = 33 cm³.

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Answer:

a)  See below.

b)  Arithmetic sequence

[tex]\textsf{c)} \quad a_n=10n-7[/tex]

Step-by-step explanation:

From inspection of the given table, t(n) increases by 10 each time n increases by 1.

Therefore:

[tex]\implies a_7=53+10=63[/tex]

[tex]\implies a_8=63+10=73[/tex]

Completed table:

[tex]\begin{array}{|c|c|}\cline{1-2} \vphantom{\dfrac12} n&t(n) \\\cline{1-2} \vphantom{\dfrac12} 4& 33\\\cline{1-2} \vphantom{\dfrac12} 5& 43\\\cline{1-2} \vphantom{\dfrac12} 6&53 \\\cline{1-2} \vphantom{\dfrac12} 7&63\\\cline{1-2} \vphantom{\dfrac12} 8& 73\\\cline{1-2} \end{array}[/tex]

As the given sequence has a constant difference of 10, it is an arithmetic sequence.

[tex]\boxed{\begin{minipage}{8 cm}\underline{General form of an arithmetic sequence}\\\\$a_n=a+(n-1)d$\\\\where:\\\phantom{ww}$\bullet$ $a_n$ is the nth term. \\ \phantom{ww}$\bullet$ $a$ is the first term.\\\phantom{ww}$\bullet$ $d$ is the common difference between terms.\\\phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

The common difference is 10. Therefore:

To find the first term, a, substitute the value of d and one of the terms into the formula:

[tex]\begin{aligned}\implies a_4=a+(4-1)(10)&=33\\a+3(10)&=33\\a+30&=33\\&a=3\end{aligned}[/tex]

Therefore, to write an equation for the given arithmetic sequence, substitute the found values of a and d into the formula:

[tex]\implies a_n=3+(n-1)(10)[/tex]

[tex]\implies a_n=3+10n-10[/tex]

[tex]\implies a_n=10n-7[/tex]

The scale drawing is thus 10 cm long and 6 cm wide, which corresponds to the actual dimensions of her bed.

A rectangle is a type of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.4 sides, 4 corners, and 4 right angles make up the 2D shape of a rectangle. A rectangle's diagonal sides are equal in length, with one pair being longer than the other. A rectangle would be referred to as a square if all of its sides were the same size.

given

1 m equals 100 cm, to start.

Then

3 meters are equal to 300 centimeters, while 5 meters are equal to 500 centimeters.

If Elena wishes to sketch out her bedroom in scale (1 to 50), then

The scale drawing is thus 10 cm long and 6 cm wide.

The actual measurements of her bed are the scale drawing is thus 10 cm long and 6 cm wide.

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Answer:

12345

Step-by-step explanation:

j

Answer:

112500

Step-by-step explanation:

a) The approximate slope of the line is; 2

b) The equation of the line is; y = 2x - 1

The tangent of the angle formed by a straight line will give us the slope of the line.

a) Now, we are told that the slope angle is 63.5°. Thus;

Slope of given line = tan 63.5°

Slope = 2

b) The formula for equation of a line in point slope form is;

y - y₁ = m(x - x₁)

where m is slope

The line passes through the point (2, 3). Thus;

Equation of line is;

y - 3 = 2(x - 2)

y - 3 = 2x - 4

y = 2x - 1

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Answer:

The 2021 summer camp registration was $285, so the percent decrease would be $15/$285, or 5.26%.

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Jason can claim a total of 3 allowances.

The number of allowances that Jason can claim on his taxes depends on the number of dependents that he has and the deductions that he is eligible for.

As a married person with one child and taking care of his dad, Jason can claim the highest number of allowances which is three. He can claim one allowance for himself, one for his child and one for his dad. Therefore, Jason can claim a total of 3 allowances.

It's important to note that the number of allowances is based on personal financial situation and this should be confirmed through IRS guidelines or tax professional.

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If the town will permit a parking lot at angle J if the measure of angle Ji is greater than 38°, then yes, a parking lot can be erected at angle K.

In Euclidean geometry, an angle is a shape that is made up of two rays, known as the hood's sides, that meeting at a middle point known as the wall's apex. Two rays may combine to form an angle in the planes where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two photons or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, sometimes known as two sides of the angle, converge.

given

Find the measure of angle K

we know that

m <K = m < green ------> by vertical angles

so

-----> by complementary angles

solve for m<K

m<K > 38

therefore

If the town will permit a parking lot at angle J if the measure of angle Ji is greater than 38°, then yes, a parking lot can be erected at angle K.

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In fraction 5 / 6 the number of the groups of 1²/₃ is only 1.

The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction.

A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given that there are two fractions 5/6 and 1²/₃. The group will be calculated as,

Fraction =  1²/₃ = 5 / 3

Fraction = 5 / 6 = ( 5 / 3 ) x ( 1 /2 )

Here in the above fraction of 5 / 6 there is only one 5 / 3 or 1²/₃.

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Answer: We need to add 1 7/8 to 5 5/8 to make 7 as an improper fraction. ✅

PLEASEEEE GIVE BRANLIEST

Step-by-step explanation: To add 5 5/8 to a number to make 7 as an improper fraction, we need to convert 5 5/8 to an improper fraction.

To convert a mixed number to an improper fraction, we take the whole number, multiply it by the denominator of the fraction, and add the numerator. So, 5 5/8 becomes (5 x 8) + 5 / 8 = 40 + 5 / 8 = 45/8.

Now, we can add 45/8 and the number that we need to add to make 7 as an improper fraction.

45/8 + x = 7

To find x, we can subtract 45/8 from both sides of the equation:

x = 7 - 45/8

x = 1 7/8

So, we need to add 1 7/8 to 5 5/8 to make 7 as an improper fraction. ✅