Hi, can someone help please? Thanks! Calculate the correlation coefficient of the following data

Answer:

[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]

[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]

Rewrite 100 as 10²:

[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]

[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies (f \cdot g)(x)=10x[/tex]

Answer:

A

Step-by-step explanation:

Comment (and answer)

Both start with the plus x axis as one of the arms. The other arm of 110o goes anti clockwise until it is 30 degrees into the second quadrant.

The answer can be found by using 110 - 360 = negative angle.

So 110 - 360 = - 250 which goes clockwise from the plus x axis. The answer must be A.

Make sure you understand the concept of clockwise and anti clockwise. If you don't know, ask your teacher, write it down, and try not to forget it. The distinction comes up a lot.

Answer:

It will take 55.08 seconds.

Step-by-step explanation:

6 seconds = 210m

1 second = (210÷6)

= 35m

1928m ÷ 35m

=55.08 seconds

Answer = it will take 55.08 seconds to travel 1928m

The solution to the inequality 5x - y > -3 is shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

An inequality shows the non equal comparison of two or more variables and numbers.

The solution to the inequality 5x - y > -3 is shown in the graph.

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The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.

The climate in which these mice live has slowly gotten colder.

The change in the environment most likely affect the mouse population will be

The adjustment of thicker fur will be selected over thinner fur, and the population will develop.

Then the correct option is D.

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Answer:

x = -2

Step-by-step explanation:

2x^3 +16 = 0

We are solving for x

Subtract 16 from each side

2x^3 +16- 16 = 0-16

2x^3 = -16

Divide each side by 2

(2x^3 ) /2 = -16/2

x^3 = -8

Take the cube root of each side

[tex]\sqrt[3]{x^3} = \sqrt[3]{-8}[/tex]

x = -2

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]2x^3+16=0[/tex]

To solve for the unknown variable x, apply arithmetic operations to isolate the variable.

Subtract 16 from both sides:

[tex]\implies 2x^3+16-16=0-16[/tex]

[tex]\implies 2x^3=-16[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}[/tex]

[tex]\implies x^3=-8[/tex]

Take the cube root of both sides:

[tex]\implies \sqrt[3]{x^3}=\sqrt[3]{-8}[/tex]

[tex]\implies x=-2[/tex]

When taking the cube root of a negative number, the result will be negative.  To understand why, examine what happens when we cube a negative number.

When a number is cubed, it is multiplied by itself, then by itself again.

When multiplying a negative number by another negative number, the result is always positive.

When multiplying a positive number by a negative number, the result is always negative.

Therefore:

[tex]\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}[/tex]

So if -8 is cube rooted, the result is -2.

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Answer:  [tex]\textsf{x = 1000}[/tex]

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Given: [tex]\textsf{log(x) = 3}[/tex]

Find: [tex]\textsf{The value of x}[/tex]

Solution:  In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base.  When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.

Get rid of log

Therefore, the final answer would be that x is equal to 1000.

Answer:

36 problems

Step-by-step explanation:

so let's say x = how many problems Marcela was assigned

she completed half of them so the amount of problems left is x/2

She then completed 7 more so now we can subtract 7. We then set this to 11 to solve for x

x/2 - 7 = 11

x/2 = 18

x = 36

Answer:

mAngle1 = 33°

Step-by-step explanation:

The three angles in a triangle add up to 180°.

31° + 116° + x = 180°

147° + x = 180°

Subtract 147° from both sides.

x = 33°

The measure of Angle1 is 33°

Answer:

6 : 1

Step-by-step explanation:

The length is the longer side compared to the width.

Hence, the length is 42 inches and width is 7 inches.

Taking the ratio :

Answer:

1 : 6

Step-by-step explanation:

42 /7 = 6

We will have to simply the ratios in order to get the answer.

When we simplify (3 + √5)(3 + √2), the result obtained is:

9 + 3√2 + 3√5 + √10

a√b × c√d = (a × c)√(b × d)

(3 + √5)(3 + √2)

Expand by clearing the bracket

3(3 + √2) + √5(3 + √2)

9 + 3√2 + 3√5 + √10

Thus,

(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10

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1. In terms of x and y, the height of the tree is [tex]h = y \times tan \ t^\circ[/tex] and[tex]h = x \times tan \ s^\circ[/tex]

2. The height of the tree is 6.71 meters

From the question, we are to determine the height of the tree in terms of x and y

Using SOH CAH TOA, we can write that

[tex]tan \ t^\circ =\frac{h}{y}[/tex]

∴ [tex]h = y \times tan \ t^\circ[/tex]

Also,

[tex]tan \ s^\circ =\frac{h}{x}[/tex]

∴ [tex]h = x \times tan \ s^\circ[/tex]

2. If m∠t = 40° and y = 8 meters,

Then, the height of the tree

h = 8 × tan40°

h = 6.71 meters

Hence, the height of the tree is 6.71 meters

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Answer:

PA = [tex]\sqrt{29}[/tex]

AC =[tex]\sqrt[2]{5}[/tex]

Step-by-step explanation:

distance formula : if [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] are two points on a line segment then distance between both the points is given by distance formula.

[tex]d = \sqrt{[(x_{2} - x_{1} )^2 +(y_{2} - y_{1})^2]}[/tex]

therefore ,

given points are , A(2, 5),  P(0, 0), C(-2, 7).

so PA = [tex]\sqrt{[({2} - {0} )^2 +({5} - {0})^2]} = \sqrt{({2} )^2 +({5} )^2}[/tex]

    PA = [tex]\sqrt{\229}[/tex]

similarly,

AC = [tex]\sqrt{[({-2} - {2} )^2 +({7} - {5})^2]} = \sqrt{({4} )^2 +({2} )^2}[/tex]

AC = [tex]\sqrt{20} = \sqrt[2]{5}[/tex]

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find the length using the Pythagorean theorem.

Length = sqrt(20^2 - 12^2)

Length = 16 feet

area = 12 x 16 = 192 square feet

Answer:

That is the answer for you step 2

Answer:

3 and 4

Step-by-step explanation:

well you can approximate by squaring values

2^2 = 4

3^2 = 9

4^2 = 16

the value should fall somewhere between 3 and 4 since the square root of 9 is 3 and the square root of 16 is 4

Answer:

To solve the answer, you can do it in 2 ways:

1) you could take the square root on both sides and solve for x

OR

2)you could multiply 3x-5 times itself and subtract 19 on both sides and use the grouping or quadratic formula method to find x.

Hope it helps.

Answer: A,B,C

Step-by-step explanation: A,B,C is the answer

Answer:

A

Step-by-step explanation:

both numbers are negative, you can rearrange them in any order provided you keep the sign

Reason:

An expression in the form -a-b is the same as -a + (-b)

Recall we can add two numbers in any order we want. For instance, 2+3 = 3+2 since both sides are equal to 5. This is the commutative property of addition.

Therefore, the -a + (-b) is the same as -b + (-a) which in turn becomes -b - a

In short:  -a - b = -b - a

This rule lets us say that -71n - 29 = -29 - 71n

Step-by-step explanation:

please mark me as brainlest

Answer #1:

The total cost with 6 snacks is $78.

Answer #2:

The total cost with x snacks is represented by the expression 60 + 3x.

Step-by-step explanation for answer #1:

Starting off with what we know:

To answer the question of how much money Genesis would have to pay for her family if she bought 6 snacks for everybody, first consider the total cost of the movie tickets.

Multiply the total number of people by the cost of each movie ticket:

[tex]4* 15=60[/tex]

Genesis will be paying $60 total only to see the movie with her 3 kids. To find the total cost of both seeing the movie and buying 6 snacks, simply multiply the number of snacks by the cost of each snack:

[tex]6 * 3=18[/tex]

Then, add the total cost of the movie tickets by the total cost of the snacks to achieve your first answer:

[tex]60+18=78[/tex]

The total cost with 6 snacks is $78.

Step-by-step explanation for answer #2:

To find the total cost of "x" snacks (x is being used as a variable term to represent a quantity subject to change), we can create an algebraic expression.

Let "t" represent the total cost.

Since we've established that finding the total cost is just a matter of adding the total cost of movie tickets (60) and the total cost of snacks (3 multiplied by the number of snacks), let "x" represent the number of snacks in the equation to find the total cost with x snacks:

[tex]60+3x=t[/tex]

The total cost with x snacks is represented by the expression 60 + 3x.

Based on the given data, the total cost of 6 snacks: $78. total cost with x snacks: $60 + (3x).

Use the concept of multiplication defined as:

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that,

Genesis is going to see a movie with her 3 kids.

Each movie ticket costs $15.

There are snacks available for purchase at $3 each.

Genesis wants to buy 6 snacks for everybody to share.

To calculate the total cost for Genesis and her 3 kids,

Consider the movie tickets and the snacks.

The cost of the movie tickets can be calculated by multiplying the number of people (4 in this case) by the cost of each ticket ($15).

So, Genesis would have to pay 4 x $15 = $60 for the movie tickets.

Now, let's calculate the total cost if Genesis were to buy 6 snacks for everybody to share.

Each snack costs $3, so 6 snacks would cost 6 x $3 = $18.

Therefore, the total cost for Genesis would be,

$60 (movie tickets) + $18 (snacks) = $78.

If we consider x snacks for everybody to share,

The total cost for snacks would be x $3.

So, the final cost would be $60 (movie tickets) + (3x) (snacks).

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Answer:

well done mr wong lol

Step-by-step explanation:

what's the question is it the percent he beat his prediction?

if it is then its 48 divided by 45 times 100

this equals 106.67%

then take this away from his prediction percent originally which is 100%

106.67-100= 6.67%

The smallest digit of the smallest number is at the thousands place.

The system of representing numbers is called Number System.

The given numbers are 6895 , 4875 , 5689

The smallest number among these is 4875

The smallest digit in this number is 4

4 is at thousands place

Therefore , The smallest digit of the smallest number is at the thousands place.

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Answer:

7+45/n or 5

Step-by-step explanation:

45 divided by n or technically 5 is 9 plus 7 is 16 :)

Answer:7+45/n or 5

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

given the graph of y = 0.5x

Then any point on the line satisfies y = 0.5x

consider the points given

x = 1 then y = 0.5 × 1 = 0.5 ⇒ (1, 0.5 ) is on the line

x = 4 then y = 0.5 × 4 = 2 ⇒ (4, 2 ) is on the line

Answer:

P =2(x+ y) [tex]ft[/tex].

A =xy [tex]ft^{2}[/tex]

Step-by-step explanation:

perimeter of rectangle (P)= 2(L+B

Area of rectangle (A)        =    L×B

Given,

width = 'x'

length = y = x+20

therefore using above formula

P = 2(x+20 + x) = 2(2x+20)

A = (x+20)(x)

cost of land per square foot = $12

cost of land per linear foot   = $8

total cost of land                   = $10560

now,

P×8 + A×12   = 10560

2(2x+20)×8 +  (x+20)(x)×12 = 10560

32x + 320 + 12x²+ 240x     = 10560

12x² + 272x                         = 10240

12x² + 272x - 10240           = 0

solving this quadratic equation using Discriminant method

x = [-b ±√(b² - 4ac)]/2

where b is the coefficient of x

a is the coefficient of x²

and c is the constant term

by replacing values in the above formula

x = 19.5  , x = -42.24

as the area cannot be negative therefore -42.24 is neglected

hence x = 19.5ft

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Answer:

7/9

Step-by-step explanation:

Divide the numerator and denominator by 4.

28/36 = 7/9

Answer:

7/9

Step-by-step explanation:

28 and 36 are both divisible by 4.

28÷4 is 7 and

36÷4 is 9

28/36 = 7/9

Answer:

[tex]y=\frac{1}{3}x[/tex]

Step-by-step explanation:

Perpendicular lines

Perpendicular lines have slopes whose product is -1.  In other words, to find a line that is perpendicular to a given line, the new line must have a that is the opposite reciprocal of the original line.

Passing through a point
Additionally, if a line contains a point, then the point must be a solution to the equation (meaning, when you plug in the "x" and "y", the equation must be true).

Finding our perpendicular line

Work on slope first

To find the slope of the original line, rewrite the original line in slope-intercept form: [tex]y=mx+b[/tex]

[tex]y=6-3x\\y=6+(-3x)\\y=(-3x)+6\\y=-3x+6\\y=-\frac{3}{1}x+6[/tex]

In this form, the slope is the number multiplied to the "x", so the original slope is -3/1.

Thus, the slope of the new perpendicular line will be the opposite reciprocal of -3/1 ... which is 1/3.

Writing what we do know about the new perpendicular line, we have [tex]y=\frac{1}{3}x+b[/tex]

Making sure it passes through the point
This new line is also supposed to contain the point (-3,-1), so (-3,-1) must be a solution to the equation, for whatever constant-value the "b" is.  To find out the "b", substitute the known quantities, and solve:

[tex]-1=\frac{1}{3} (-3)+b\\-1=-1+b\\(-1)+1=(-1+b)+1\\0=b[/tex]

Substituting this into our equation:

[tex]y=\frac{1}{3}x+(0)\\y=\frac{1}{3}x[/tex]

Conclusion

So, the equation for a line that is perpendicular to the original line [tex]y=6-3x[/tex], and that also passes through (-3,-1) is [tex]y=\frac{1}{3}x[/tex]

Answer:

The second statement is true.

Step-by-step explanation:

Draw the corresponding parabola and use it to verify  all statements.

Answer:

The function is negative for all real values of x where

x < –3 and where x > 1.

Step-by-step explanation:

The answer above is correct.