ACTIVITY 1 Directions: Interpret these circle graphs

A. The pie graph below shows what a normal human body is made of.


Questions:

1. As shown in the graph,what composes the human body?

2. Which makes up the greatest part of the human body? the least?
​

We have the following equation:

since we need P, we must move k and V to the left hand side as

By substituting the given values, we get

that is, P is equal to 2.

Simplify the integrand:

\(\dfrac{4x^4 + 3x^2 + 5x}{x^2} = 4x^2 + 3 + \dfrac5x\)

Now integrate one term at a time.

\(\displaystyle \int 4x^2 \, dx = \frac43 x^3 + C\)

\(\displaystyle \int 3 \, dx = 3x + C\)

\(\displaystyle \int \frac5x \, dx = 5 \ln|x| + C\)

Putting everything together,

\(\displaystyle \int \frac{4x^4 + 3x^2 + 5x}{x^2} \, dx = \int \left(4x^2 + 3 + \frac5x\right) \, dx = \boxed{\frac43 x^3 + 3x + 5 \ln|x| + C}\)

The correct answers are option A and option D.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction

From the given graph it is clear that the spaceship is located at (-4,3). The alien is at (-2, -3).

If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,

then the equation of line is

y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)

y - 3 = (-3 -3 ) / (-2 + 4) x (x + 4)

y - 3 = -3x -12

y = -3x -9

The equation of the line is;

y = -3x -9    {equation 1}

Slope intercept form of a line is

y = mx + b          {equation 2}        ,

where m is the slope and b is the y-intercept.

On comparing the equation (1) and (2) we get

It means,

Slope = -3

y-intercept = -9

Points from -6 to 6 are labeled on y-axis. The y-intercept is -9, so it is not visible on the graph.

Option A is correct.

Substitute y=0 in equation (1) to find the x-intercept.

Divide both sides by 3.

x-intercept is -3. It means the line crosses the x-axis at -3.

Option D is correct

Therefore, the correct options are A and D.

To learn more about the slope;

brainly.com/question/3605446

#SPJ6

Part A: The total area of the brick paver border is \(960\) square feet.

Part B: The total cost of the brick pavers needed for this project is $\(7,680\).

Part A: To find the total area of the brick paver border, we need to subtract the area of the pool from the area of the larger rectangle. The area of the pool is \(32\) feet multiplied by 12 feet, which is equal to \(384\)square feet.

The area of the larger rectangle is \(48\) feet multiplied by \(28\) feet, which is equal to \(1,344\) square feet. Therefore, the area of the brick paver border is \(1,344\) square feet minus \(384\) square feet, which equals \(960\) square feet.

Part B: If brick pavers cost $\(8\)per square foot, we can calculate the total cost by multiplying the cost per square foot by the total area of the brick paver border. The total area of the brick paver border is \(960\) square feet, and the cost per square foot is $\(8\).

Therefore, the total cost of the brick pavers needed for this project is $\(8\)multiplied by \(960\) square feet, which equals $\(7,680\).

Note: The calculations provided assume that the border consists of a single layer of brick pavers.

For more such questions on area:

https://brainly.com/question/2607596

#SPJ8

Answer:

$42.00

Step-by-step explanation:

We can represent the given information as a ratio:

% of original price : price

                          5% : $2.00

Then, we can multiply both sides of this ratio by 20 (or 100% / 5%) to get 100% of the original price, which IS the original price.

5%      :  $2.00

↓ × 20   ↓ × 20

100%  :  $40.00

Now that we know the original price, we can add $2.00 to get the new price.

$40.00 + $2.00 = $42.00

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{1}~,~\stackrel{y_1}{-1})\qquad N(\stackrel{x_2}{5}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PN=\sqrt{(~~5 - 1~~)^2 + (~~-8 - (-1)~~)^2} \implies PN=\sqrt{(5 -1)^2 + (-8 +1)^2} \\\\\\ PN=\sqrt{( 4 )^2 + ( -7 )^2} \implies PN=\sqrt{ 16 + 49 } \implies PN=\sqrt{ 65 }\implies PN\approx 8.06\)

Answer:

Step-by-step explanation:

Triangle area formula: 1/2bh

Then use the Pythagorean theorem to find out what AB is.

AB= sqrt 76

8.72

8.72*18*1/2

78.5 approx

Answer:

The answer is 10,650. Just use the calculator next time you get one of these questions. :D

Answer:

Sure.. the answer is 10650.

Step-by-step explanation:

here's how.

first, Simplify 4 × 2 to 8.

\(6 + 4 - 8 + 22 ^{3} \)

then, turn 22³ into exponent from and solve.

\(6 + 4 - 8 + 10648\)

now, Simplify 6 + 4 to 10.

\(10 - 8 + 10648\)

and now, Simplify 10 - 8 to 2

\(2 + 10648\)

lastly, add 2 + 10648 to 10650.

\(10650\)

hence, the answer is 10650.

Answer:

perimeter = 56 in

area = 192 sq. in.

Step-by-step explanation:

area of a triangle = 0.5 * b * h

b = 12

h = 8

At = (0.5 * 12 * 8)  = 48

Area of a square

As = 12 * 12 = 144

total area = At + As

total area = 48 + 144

total area = 192 sq. in.

perimeter = add all sides

12 + 12 + 12 + 10 + 10 = 56 in

hope it helps

Answer:

Angle sum Theorem says that the sum of the measures of the interior angles of a triangle is 180 degrees. ... This creates alternate interior angles that are congruent. Sum of two interior angles equals the opposite exterior angle...33 + 87 = yy = 120°

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use distributive property: a*(b - c) = (a*b) -(a*c).

Here, a = 2 ; b = 9p  & c = 1/2

\(2*(9p - \dfrac{1}{2})=2*9p-2*\dfrac{1}{2}\\\\\\ = 18p - 1\)

As a result, the angle's measure is 135° and its supplement is 45°.

Two angles are referred to as supplementary angles when the sum of their measures is 180 degrees.

For instance, 70 degrees and 110 degrees complement one another.

Two angles are said to be supplementary if their sums total 180 degrees.

A linear pair's two angles, are always supplementary.

Let x be the angle's measurement. If so, (180x) is the size of its supplementary angle.

Now, calculate:

180 - x = 1/3x

3(180 - x) = x

4x = 540

x = 135

Supplementary angle = 180 - 135 = 45°

Therefore, as a result, the angle's measure is 135° and its supplement is 45°.

Know more about the supplement angle here:

https://brainly.com/question/12919120

#SPJ4

Answer with step-by-step explanation:

First of all, ORDER OF OPERATIONS!! 2x/x is 2/1, which is 2. Then, subtract 1, which is 1.

2x ÷ x - 1 = 1

Same thing: x/x = 1. Subtract 1 from 1, which is 0.

x ÷ x - 1 = 0

1 + 0 = 1

Hope this helped!

Answer:

\(\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

Step-by-step explanation:

Replace f(x) with y in the given function:

\(y=(x+2)^x\)

Take natural logs of both sides of the equation:

\(\ln y=\ln (x+2)^x\)

\(\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a\)

\(\ln y=x\ln (x+2)\)

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

\(\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

\(\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)\)

Now use the product rule to differentiate the terms in x (the right side of the equation).

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1\)

\(\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}\)

Therefore:

\(\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}\)

Multiply both sides of the equation by y:

\(\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Substitute back in the expression for y:

\(\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)\)

Therefore, the differentiated function is:

\(f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right]\)

\(f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right]\)

The required average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is 32 meters/second.

Given that,

A particle travels along the x-axis such that its position at time t is given by,

Function; \(\rm x(t)=2t^2+t\)

We have to find,

What is the average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10?

According to the question,

The position of the particle is given by,

\(\rm x(t)=2t^2+t\)

The average speed of this particle is determined by differentiating the function with respect to x,

\(\rm \dfrac{dx}{dt} = \dfrac{d(2t^2+t)}{dx}\\\\\dfrac{dx}{dt} = 4t + 1 \\\\v(t) = 4t+1\)

Then,

The average speed of the particle over interval 2 is,

\(\rm v(t) = 4t+1 \\\\v(2) = 4(2)+1\\\\v(2) = 8+1 \\\\v(2) = 9 \ meter \ per \ second\)

And the average speed of the particle over interval 10 is,

\(\rm v(t) = 4t+1 \\\\v(10) = 4(10)+1\\\\v(10) = 40+1 \\\\v(10) = 41 \ meter \ per \ second\)

Therefore,

The average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is,

\(\rm v(t) = v(10)-v(2)\\\\v(t) = 41-9\\\\v(t)= 32 \ meter \ per \ second\)

Hence, The required average speed of this particle over interval 2 is less than or equal to t which is less than or equal to 10 is 32 meters/second.

For more details refer to the link given below.

https://brainly.com/question/2292357

Answer:

Very basically, the answer is 3

Step-by-step explanation:

Know this cause Edge 2023

The equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

1. Start with the given equation: 2-3cos(x) = 5+3cos(x).

2. Subtract 3cos(x) from both sides to isolate the constant term: 2-3cos(x) - 3cos(x) = 5.

3. Combine like terms: 2-6cos(x) = 5.

4. Subtract 2 from both sides: -6cos(x) = 3.

5. Divide both sides by -6: cos(x) = -1/2.

6. To find the solutions for cos(x) = -1/2 in the range of 0° to 180°, we need to determine the angles where cos(x) equals -1/2.

7. These angles are 120° and 240°, as cos(120°) = cos(240°) = -1/2.

8. However, the given equation states that 2-3cos(x) equals 5+3cos(x), which is not satisfied by cos(x) = -1/2.

9. Therefore, the equation 2-3cos(x) = 5+3cos(x) has no solution in the range of 0° to 180°.

For more such questions on equation, click on:

https://brainly.com/question/17145398

#SPJ8

There is a probability of 94/315 that the problem will be solved.

We are given that P has a chance of solving the problem of 2/7, Q has a chance of solving the problem of 4/7, and R has a chance of solving the problem of 4/9. To find the probability that the problem is solved, we need to consider all possible scenarios in which the problem can be solved.

The probability of this scenario is 2/7. If P solves the problem, then it does not matter whether Q or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 2/7.

The probability of this scenario is 4/7. If Q solves the problem, then it does not matter whether P or R solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/7.

The probability of this scenario is 4/9. If R solves the problem, then it does not matter whether P or Q solve it, the problem is already solved. Therefore, the probability of the problem being solved in this scenario is 4/9.

The probability of this scenario is (1-2/7) * (1-4/7) * (1-4/9) = 3/35. This is because the probability of P not solving the problem is 1-2/7, the probability of Q not solving the problem is 1-4/7, and the probability of R not solving the problem is 1-4/9. To find the probability of none of them solving the problem, we multiply these probabilities together.

To find the probability of the problem being solved, we need to add the probabilities of all the scenarios in which the problem is solved. Therefore, the probability of the problem being solved is:

2/7 + 4/7 + 4/9 = 94/315

To know more about probability here

https://brainly.com/question/11234923

#SPJ1

Answer:

a triangle that may not have the same dimensions as the bases

Step-by-step explanation:

The cross section of the figure that is perpendicular to the triangular bases and passes through a vertex of the triangular bases would be a triangle that may not have the same dimensions as the bases.

To figure this out, simply divide 4 by 42

4/42 = 0.0952

0.0952 x 100 = 9.52%

9.52% of the regular price were savings :D

Answer:

6p+5

Step-by-step explanation:

3(2p+5)−10

Use the distributive property to multiply 3 by 2p+5.

6p+15−10

Subtract 10 from 15 to get 5.

6p+5

Answer:

Step-by-step explanation:

Typically yes you need to know

Mean

Median

Mode

and Range

Mean = average, add all numbers then divide by how many

Median = midpoint, middle number.  Be sure to list numbers from small to large if there are 2 middle numbers (this happens when there are an even amount), take the average of the 2 middle numbers

Mode = numbers that occurs the most in the list of numbers

Range = This is the largest number minus the smallest number.  

-36 would be the answer

hope that helped :)

Answer:

-36

Step-by-step explanation:

-12-58-(-34) or -12-58+34

-70+34 or 34-70

subtract 70 from 34

-36

Hope this helps. Have a nice day you amazing bean child.

Answer:

C) 515 hours.

D) 500 hours

c) sample 3

Step-by-step explanation:

1. Sample 2 mean = x2`= ∑x2/n2= 2060/4= 515 hours

Sample Service Life (hours)

1                2              3

495      525            470

500         515           480

505        505            460

500         515             470        

∑2000     2060         1880

x1`= ∑x1/n1= 2000/4= 500 hours

x2`= ∑x2/n2= 2060/4= 515 hours

x3`= ∑x3/n3= 1880/4=  470 hours

2. The mean of the sampling distribution of sample means for whenever service life is in control is 500 hours . It is the given mean in the question and the limits are determined by using  μ ± σ , μ±2 σ  or μ ± 3 σ.

In this question the limits are determined by using  μ ± σ .

3. Upper control limit = UCL = 520 hours

Lower Control Limit= LCL = 480 Hours

Sample 1 mean = x1`= ∑x1/n1= 2000/4= 500 hours

Sample 2 mean = x2`= ∑x2/n2= 2060/4= 515 hours

Sample 3 mean = x3`= ∑x3/n3= 1880/4=  470 hours

This means that the sample mean must lie within the range 480-520 hours but sample 3 has a mean of 470 which is out of the given limit.

We see that the sample 3 mean is lower than the LCL. The other  two means are within the given UCL and LCL.

This can be shown by the diagram.

Answer:

11 y 23

Step-by-step explanation:

Nombrando los números como \(x\) y \(y\),

Planteamos las siguientes ecuaciones:

\(xy=253\) (el producto de los numeros es 253)

\(x=2y+1\) (uno de los enteros debe ser uno más que el doble del otro).

Sustituimos la segunda ecuación en la primera:

\((2y+1)(y)=253\)

resolvemos para encontrar y:

\(2y^2+y=253\\2y^2+y-253=0\)

usando la formula general para resolver la ecuación cuadrática:

\(y=\frac{-b+-\sqrt{b^2-4ac} }{2a}\)

donde

\(a=2,b=1,c=-253\)

Sustituyendo los valores:

\(y=\frac{-1+-\sqrt{1-4(2)(-253)} }{2(2)} \\\\y=\frac{-1+-\sqrt{2025} }{4}\\ \\y=\frac{-1+-45}{4} \\\)

usando el signo mas obtenemos que y es:

\(y=\frac{-1+45}{4} \\y=\frac{44}{4}\\ y=11\)

(no usamos el signo menos, debido a que obtendriamos fracciones y buscamos numeros enteros)

con este valor de y, podemos encontrar x usando:

\(x=2y+1\)

sustituimos \(y=11\)

\(x=2(11)+1\\x=22+1\\x=23\)

y comprobamos que el producto sea 253:

\(xy=253\)

\((23)(11)=253\)

Answer:

C.

Step-by-step explanation:

The numbers in the front will be the first number and the ones behind it will be the second number.

So the numbers are 79,82,82,83,86,90,91,93,94 and 97

Then you want to add the lowest number and the greatest number which is 79 and 97

equals to 176

Answer:

Explanation:

√8², 3² and √17² satisfy a²+b²=c²

√8²+3² = √17²

8+9=17

Answer:

Step-by-step explanation:

The perimeter is the distance around the edge of the shape.

    \(P=2+4+2+1+4+5=18cm\)