HELP ASAP!!!

1. Give the equation of the least-squares regression line. Define any variables you use.

2. Use the model from part (a) to predict the area covered by detergent at 5.5 seconds.

3. Based on the residual plot, do you expect the prediction you made in part (b) to underestimate or
overestimate the area covered by detergent? Justify your answer.

4. Is the least-squares regression line an appropriate model for these data? Justify your answer.

The derivatives for this problem are given as follows:

a) \(f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}\)

b) \(f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}\).

The derivative of the sum is the sum of the derivatives.

In this problem, the function is:

\(f(x) = 4\cos{x} + \ln{(x + 1)}\)

Using a derivative table for the derivatives of the cosine and the ln, the derivative of the function is:

\(f^{\prime}(x) = (4\cos{x})^{\prime} + (\ln{(x + 1)})^{\prime}\)

\(f^{\prime}(x) = -4\sin{x} + \frac{1}{x + 1}\)

What is the product rule?

The derivative of the product is given as follows:

\((f(x) \times g(x))^{\prime} = f^{\prime}(x)g(x) + g^{\prime}(x)f(x)\)

In this problem, we have that:

Hence the derivative is:

\(f^{\prime}(x) = \sec{x}\tan^{2}{x} + \sec^3{x}\).

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Answer:

Step-by-step explanation:

17.52. divided by 3

Hopefully this helps you!

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Answer:

5.84 per bow

Step-by-step explanation:

Take the total cost and divide by the number of bows

17.52 / 3

5.84 per bow

The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440

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

Let R represent the number of Regular gallons, P represent that of Premium and D represent that of Diesel.

A total of 800 gallons was sold, hence:

R + P + D = 800    (1)

Also:

$2910 was sold combined, therefore:

3.5R + 4.25P + 4D = 2910    (2)

440 more gallons of regular was sold, hence:

R = P + D + 440   (3)

The equations are R + P + D = 800, 3.5R + 4.25P + 4D = 2910 and R = P + D + 440

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Answer:

Separately divide each

Step-by-step explanation:

Answer:

A: 12 feet per revolution; B: 3

Step-by-step explanation:

A). You can find the feet Teresa travels per revolution by looking at the graph and identifying the y-value of the x-value of 1, which is 12 feet.

B). The slope can be found by using two methods: \(\frac{y - y_{1} }{x - x_{1} }\) or the counting method where you go up and right (or vice versa) until you reach the point you wish for.

Either way, you are supposed to get a slope of 3.

Hope this helped! :D

Answer:

32+q

Step-by-step explanation:

it doesn't ask for money

Answer:

1 and 4

Step-by-step explanation:

ed 2020

Answer:

Option B. 1 and Option E. 4

Step-by-step explanation:

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Answer:

The probability that a randomly selected member of this class of homeowners will not file a claim of either type is 0.89.

Step-by-step explanation:

Denote the events as follows:

X = liability claim will be filled

Y = property claim will be filled

The information provided is:

P (X) = 0.04

P (Y) = 0.10

P (X ∩ Y') = 0.01

The probability that a randomly selected member of the class of homeowners will not file a claim of either type will be given by:

\(P[(X\cup Y)']=1-P(X\cup Y)=1-[P(X)+P(Y)-P(X\cap Y)]\)

According to the law of total probability:

\(P(B)=P(B\cap A)+P(B\cap A')\)

Use the law of total probability to determine the value of P (X ∩ Y) as follows:

\(P(X)=P(X\cap Y)+P(X\cap Y')\\\\P(X\cap Y)=P(X)-P(X\cap Y')\\\\=0.04-0.01\\\\=0.03\)

The value of P (X ∩ Y) is 0.03.

Compute the value of P (X ∪ Y) as follows:

\(P[(X\cup Y)']=1-P(X\cup Y)\)

                   \(=1-[P(X)+P(Y)-P(X\cap Y)]\\\\=1-[0.04+0.10-0.03]\\\\=1-0.11\\\\=0.89\)

Thus, the probability that a randomly selected member of this class of homeowners will not file a claim of either type is 0.89.

Answer:

\(x=-\dfrac{149}{70}\)

Step-by-step explanation:

Given logarithmic equation:

\(8+\log(7x+15)=7\)

Subtract 8 from both sides of the equation:

\(\implies \log(7x+15)=-1\)

When the log has no base, it is the common logarithm which always has a base of 10. Therefore:

\(\implies \log_{10}(7x+15)=-1\)

\(\textsf{Apply the log law:} \quad \log_ab=c \iff a^c=b\)

\(\implies 10^{-1}=7x+15\)

\(\textsf{Apply the exponent rule:} \quad a^{-n}=\dfrac{1}{a^n}\)

\(\implies \dfrac{1}{10}=7x+15\)

\(\implies 7x+15=\dfrac{1}{10}\)

Multiply both sides of the equation by 10:

\(\implies 70x+150=1\)

Subtract 150 from both sides:

\(\implies 70x=-149\)

Divide both sides by 70:

\(\implies x=-\dfrac{149}{70}\)

Answer:

(4,-2)

Step-by-step explanation:

To solve this, you must move the "Y" axis up

In this case, the "y" axis is -5

You can use an expression to solve this -----> (y= -5+3)

Which equals -2

Hope this helps! Pls mark brainliest if correct :)

Answer:

Step-by-step explanation:

Answer:

For a square or rectangular room you will need the length and width

Then you multiply I.e length x width gives Area

bye :-)

Answer:

45.7°

Step-by-step explanation:

The boy is 630 meters south from his starting point.

We must take into account the southward component of his shift.

We can imagine a right-angled triangle where the hypotenuse represents the boy's total displacement of 1260 meters, the angle between the hypotenuse and the south direction is 120°, and the side next to the angle represents the southward displacement given that the boy walks 1260 meters on a bearing of 120°.

We can use trigonometric functions to calculate the displacement to the south. Since the adjacent side and hypotenuse of a right triangle are connected in this instance, we will use the cosine function.

cos(120°) = adjacent / hypotenuse

cos(120°) = adjacent / 1260

Solving for the adjacent side (southward displacement):

adjacent = cos(120°) * 1260

adjacent = (-0.5) * 1260

adjacent = -630

The negative sign indicates that the southward displacement is in the opposite direction or "south" relative to the starting point.

Therefore, the boy is 630 meters south from his starting point.

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The number of suspects had less than two prior arrests are 3.

Given that, While reviewing the previous day’s arrest report.

Let x be the number of suspects have been arrested once before and y be the number of suspects arrested twice before.

Here, x+y=5 -----(i)

2x+3y=12 -----(ii)

From equation (i), x=5-y in equation (ii), we get

2(5-y)+3y=12

10-2y+3y=12

10+y=12

y=2

Substitute y=2 in equation (i), we get

x+2=5

x=3

Therefore, the number of suspects had less than two prior arrests are 3.

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Answer:

The answer are

B and C

Step-by-step explanation:

r=d/2=12/2=6

r=16/2=8

Circumference=2pir

C=2×6pi

C=12pi

C=2pir

C=2×8pi

C=16pi

Answer:

11 buses

Step-by-step explanation:

Answer:

x= m+3

y= m-3

now,

x+y+1 = 2m

or, m+3+m-3+1 = 2m

or, 2m+1 =2m

or, 3m=2m

or, m= 3/2 is the answer

Answer:

(1, -4)

Step-by-step explanation:

(-5,-4) -> (x,y) so x = -5 and y = -4. Apply the rule (x+6,y) to that point by substituting in your x and y values.

(-5+6,-4) = (1, -4)

3(x-9)/x-3 is the simplified form of the expression.

Quadratic equations are equation that has a leading degree of 2. Given the expression below:

f(x) = 3x²-243/x²+6x-27

Factorize both numerator and denominator as shown:

f(x) = 3(x²-81)/x²+9x-3x-27

f(x) = 3(x+9)(x-9)/x(x+9)-3(x+9)
f(x) = 3(x+9)(x-9)/(x-3)(x+9)

f(x) = 3(x-9)/x-3

Hence the simplified form of the expression is 3(x-9)/x-3

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Since the point negative 4.5 (-4.5) is labeled on this number line representing temperature change, the absolute value of the point labeled in the image means that: B. the temperature equals 4.5 degrees.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

In conclusion, the absolute value of a number is always positive and it can be used for describing the distance of a number from zero (0) on the number line, without taking its direction into consideration.

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Answer:

(1/2)(4)(3)(2) = 12 cubic yards

The correct answer is A.

Answer:

------------------------------

Given is a quadratic equation:

A quadratic equation has no real solutions if its discriminant is negative.

The discriminant of ax² + bx + c is:

Apply to given equation:

Find the value of n when D < 0:

Answer:

A option is correct

Step-by-step explanation:

We know that one foot contain 12inches so 12 inches is equal to one foot

There are 36 inches is equivalent to 3 feet which scales is the correct answer would be option (E).

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The operator that performs the arithmetic operation is called the arithmetic operator.

* Multiplication operation: Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation: Divides left-hand operand by right-hand operand

For example 4/2 = 2

We know that one foot contains 12 inches.

Therefore 12 inches equal one foot

According to option (E),

36 inches is equivalent to 3 feet.

Therefore, the correct answer would be an option (E).

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Step-by-step explanation:

sol;

l=5w

area=l*w

or,45=5w*w

or,45=5w2

or,45\5=w2

0r\(\sqrt{9}\)=w

or,3=w

again,

l=5w

l=5*3

l=15

Therefore, length is 15 inch and width is 3 inch.

Answer:

- 5 - 10i

Explanation:

We given expression is

(-3 - 2i) - (2 + 8i)

To find the difference, we first need to eliminate the parenthesis, so

-3 - 2i - 2 - 8i

Then, we can add the like terms, so

(-3 - 2) + (-2i - 8i)

-5 + (-10i)

-5 - 10i

Therefore, the answer is

- 5 - 10i

Answer:

Let the total number of people in the group=x

So total number of men =3x/8

Hence total number of women=5x/8

No. of men having brown eyes=2/3*3x/8=x/4

Total no. of people having brown eyes=3x/4

No.of women having brown eyes

=3x/4 -x/4=2x/4=x/2

No. of women who don't have brown eyes= 5x/8-x/2 = x/8

So the fraction is x/8x= 1/8

Step-by-step explanation:

Answer: 28 children

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare the numbers, and you can compare them using division.

First, we would need to figure out the total number of students. To do this, we can divide 84 by 3, then add that to the total.

84 ÷ 3 = 28

28 + 84 = 112

This means that there are 112 students in the classroom.

If 3/4 of the children in the school have blue eyes, we know that 1/4 of the children will have brown eyes. We can convert 1/4 into a decimal, or into a percentage, to get the number of children with brown eyes.

1/4 = 0.25 = 25%

To figure out how much 25% of 112 is, we can simply multiply 112 by 0.25.

112 × 0.25 = 28

So, this means that there are 28 children with blue eyes in the school.

The number of turns the wheel makes is 1.93 ≈ 2.

What is Turns?

This is referred to as a cycle. It is a unit of plane angle measurement that is equivalent to 2π radians, 360 degrees, or 400 gradians.

formular for calculating Turns:

Turns =         Lenght

              Circumference

Circumference of a circle, C= πD

Where,

Diameter=D

            π =22/7

Calculating Circumference;

C= 22  * 66

            7

    =207.4

From the question:

D= 66cm

L  =400m

Calculating Turns:

Turns =  Lenght

              Circumference

          =   400m

               207.4

      Turns =1.93

Turns =1.93≈ 2

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