Is the relation represented on the graph a function? Complete the explanation.

The value of the radical √48 is 4√3.

Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.

Here, we are given the radical √48

To find the value of the radical, we will factorize 48

i.e., 48 = 2×2×2×2×3

           = 16×3

Now, the square root of 48, that is, √48

                                                       = \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)

We know 16 is a perfect square of 4, that is, the square root of 16= 4

⇒√16=4

Using this, we have √48= 4√3

The correct answer is 4√3.

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Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

Answer:

it's 3gc brought video gloves

Answer:

24 feet.

Step-by-step explanation:

The side  of the square = √36 = 6 feet.

The square has 4 equal sides so the perimeter = 4*6 = 24 feet.

The product of the ages 2 years from today is 924

Let the ages of the three cousins be x, y and z. If the product of their ages is 1716, hence;

xyz = 1716

If the product of their ages last year is 1320, then;

(x-1)(y-1)(z-1) = 1320

Two years ago, the product of their ages will be;

(x-2)(y-2)(z-2) = 1320- (1716-1320)

(x-2)(y-2)(z-2) = 1320-396

(x-2)(y-2)(z-2) =924

Hence the product of the ages 2 years from today is 924

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If T denote the number of coupons one needs to select to obtain at least one of each type., P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}

The problem of finding the probability P(T > n), where T is the number of coupons needed to obtain at least one of each type, can be solved using the principle of inclusion-exclusion.

Let S be the event that the i-th type of coupon has not yet been obtained after selecting n coupons. Then, using the complement rule, we have:

P(T > n) = P(S₁ ∩ S₂ ∩ ... ∩ Sₙ)

By the principle of inclusion-exclusion, we can write:

P(T > n) = ∑(-1)^x * Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ}

where the outer sum is taken over all even values of k from 0 to N, and the inner sum is taken over all sets of k distinct indices.

This formula can be computed efficiently using dynamic programming, by precomputing all values of Σ_{1≤i₁<i₂<...<iₓ≤N} P{i₁} * P{i₂} * ... * P{iₓ} for all x from 1 to N, and then using them to compute the final probability using the inclusion-exclusion formula.

In practice, this formula can be used to compute the expected number of trials needed to obtain all N types of coupons, which is simply the sum of the probabilities P(T > n) over all n.

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The equation of line in the point slope form is y = 2x + 8

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Let temperature be denoted as x

Let the time be denoted as y

Let the initial temperature be = 0°F

Let the final temperature be = 1°F

Let the initial time be = 8 : 00 AM

Let the final time be = 10 :00 AM

And , the first point be P = P ( 0 , 8 )

The second point be Q = Q ( 1 , 10 )

Now , the slope of the equation is given as

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 10 - 8 ) / ( 1 - 0 )

Slope m = 2

Now , the equation of line is given as y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 8 = 2 ( x - 0 )

y - 8 = 2x

Adding 8 on both sides of the equation , we get

y = 2x + 8

Therefore , the value of A is y = 2x + 8

Hence , the equation is y = 2x + 8

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The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

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Answer: Total old car is $2955.89, new car $1080.94 *for 3yrs

Step-by-step explanation:

Old= [(100/19)($2.36)(52)+$770]*3 = $2955.89

New=[(100/34)($2.36)(52)+20(12)]*3= $1080.94

I keep the old car # 1

Answer:

x = 33

Step-by-step explanation:

Creating an equation

The angles shown are corresponding angles

Corresponding angles are angles that occupy the same position and are on the same side of the transversal. For a better sense of this, kindly review the attached image.

Corresponding angles are congruent ( equal to each other )

This means that 124 = 4x - 8

Solving for x

124 = 4x - 8

==> add 8 to both sides

132 = 4x

==> divide both sides by 4

33 = x

Answer:

The 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

Step-by-step explanation:

The (1 - α)% confidence interval for the population mean, when the population standard deviation is not provided is:

\(CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}\)

The sample selected is of size, n = 50.

The critical value of t for 95% confidence level and (n - 1) = 49 degrees of freedom is:

\(t_{\alpha/2, (n-1)}=t_{0.05/2, 49}=2.000\)

*Use a t-table.

Compute the sample mean and sample standard deviation as follows:

\(\bar x=\frac{1}{n}\sum {x}=\frac{1}{50}\times [6+4+6+...+9+6]=6.34\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{50-1}\times 229.22}=2.163\)

Compute the 95% confidence interval estimate of the population mean rating for Miami as follows:

\(CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\ \frac{s}{\sqrt{n}}\)

     \(=6.34\pm 2.00\times\frac{2.163}{\sqrt{50}}\\\\=6.34\pm 0.612\\\\=(5.728, 6.952)\\\\\approx(5.7, 7.0)\)

Thus, the 95% confidence interval estimate of the population mean rating for Miami is (5.7, 7.0).

The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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Answer:

15 shirts

Step-by-step explanation:

Store A charges 12.50 for a custom shirt with 0.40 per each custom character. Store B charges 14.75 for the same shirt but charges 0.25 per each custom character would make the cost from both stores the same

A: 12.5 + 0.40x

B: 14.75 + 0.25x

12.5 + 0.40x = 14.75 + 0.25x

subtract 12.5 from both sides:

12.5 + 0.40x - 12.5 = 14.75 + 0.25x - 12.5

0.40x = 2.25 + 0.25x

subtract 0.25x from both sides:

0.40x - 0.25x = 2.25 + 0.25x - 0.25x

0.15x = 2.25

divide both sides by 0.15:

0.15x/0.15 = 2.25/0.15

x = 15

Answer:

Step-by-step explanation:

$4.50 + $4.50(0.15) = $5.18

$2.25 + $2.25(0.15) = $2.59

$3.00 + $3.00(0.15) = $3.45

The correct matches for the given values of x and y can be found by substituting the values in the equations which are 12-x = 3, x+3y= 27, 4y-10=14, xy=54

What is an equation?

Equation is an expression which have equality symbol in between

It means an expression in variable is equal to the constant.

We are given that x= 9 and y=6

We are asked to match the possible value

i) 12 -x

To solve this we substitute x= 9 in the equation

12-9

=3

ii) x+3y

To solve this we substitute x = 9 and y=6

9+3(6)

=9+18

=27

iii) 4y-10

To solve this we substitute  y=6

=4(6)-10

=24-10

=14

iv) xy

To solve this we substitute x = 9 and y=6

= 9(6

=54

Hence the correct matches are 12-x = 3, x+3y= 27, 4y-10=14, xy=54

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Answer:

f(-7) = -19

Step-by-step explanation:

Let us solve the problem

∵ f(x) = 2x - 5

∵ g(x) = -3x - 1

∵ h(x) = 2x² + x - 7

→ We need to find f(-7), that means substitute x in f(x) by -7

∵ x in f(x) = -7

∵ f(x) = 2x - 5

∴ f(-7) = 2(-7) - 5

→ Calculate 2 × (-7)

∴ f(-7) = -14 - 5

→ Add them

∴ f(-7) = -19

Answer:

0.5027 square meters

Step-by-step explanation:

cm2

Answer:

c

Step-by-step explanation:

To find the x-intercept, we set y to 0 and solve for x:

0 = x + 8

x = -8

Therefore, the x-intercept is -8.

To find the y-intercept, we set x to 0 and solve for y:

y = 0 + 8

y = 8

Therefore, the y-intercept is 8.

Hopes this helps

The ratio of the amount of money Alice has to the amount Bob has is approximately 3.36 : 1.

According to the problem, two equations can be set up:

If Alice receives n dollars from Bob, then she will have 7 times as much money as Bob. This gives us the equation:

A + n = 7(B - n)

If Alice gives n dollars to Bob, then she will have 2 times as much money as Bob. This gives us the second equation:

A - n = 2(B + n)

We can rearrange these equations to make them easier to solve:

8n = 7B - A

3n = A - 2B

Setting these equal to each other, since they are both equal to 24n, gives:

21B - 3A = 8A - 16B

37B = 11A

A / B = 37 / 11

= 3. 36

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Answer:

y=-2/1x+0

y=1x-3

hope this helsp

The balance after 2 years with daily compounding interest is $551.38.

To calculate the balance after 2 years with each day compounding interest, we will use the formulation:

\(A = P(1 + r/n)^{(nt)\)

Where:

In this example, we have:

Substituting those values into the method, we get:

Consequently, the balance after 2 years with daily compounding bis $551.38.

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Answer:

OK so he gets 3000 a year

so 3000t is what we need. thats 3000 times the number of years.

His starting salary is 41250, so we would add that on.  

K = 3000t + 41250.

Step-by-step explanation:

Answer:

3 units

Step-by-step explanation:

The probability of rolling a die and getting a 2, then a 5, is 1/36.

To determine the probability of rolling a die and getting a 2, then a 5, we need to multiply the probabilities of each event happening.

First, let's consider the probability of rolling a die and getting a 2. Since there are six equally likely outcomes when rolling a fair six-sided die (numbers 1 to 6), the probability of rolling a 2 is 1/6.

Now, let's consider the probability of rolling a die and getting a 5. Again, there are six equally likely outcomes, so the probability of rolling a 5 is also 1/6.

To find the probability of both events happening, we multiply the probabilities:

Probability of rolling a 2 and then a 5 = (1/6) * (1/6) = 1/36.

Therefore, the probability of rolling a die and getting a 2, then a 5, is 1/36.

It's important to note that each roll of the die is an independent event, meaning that the outcome of one roll does not affect the outcome of the next roll. Therefore, the probability of rolling a 2 and then a 5 remains constant at 1/36 regardless of previous rolls or the order in which they occur.

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21) In the given figure : there are 7 equal sides.

A regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians.

Internal angle : 5π/7 = 128.571°

The sum of all angles on straight line is 180 degree

So, n + 128.57 = 180

n = 180 - 128.57

n = 51.43

Answer : n = 51.43

Answer:

2.571428571 is the answer

Answer:

Multiplying and dividing fractions are essentially the same process which you multiply the numbers straight across and no need for common denominators. Except in division of fractions, the second fraction is flipped so that the denominator is on the top and the numerator is on the bottom (reciprocal).

Step-by-step explanation:

Example:

\(\frac{3}{4} * \frac{1}{5} = \frac{3}{20}\)

\(\frac{3}{4}\) ÷ \(\frac{1}{5} = \frac{3}{4} * \frac{5}{1} = \frac{15}{4}\)