Joy is training for a triathlon. she runs a distance of 2x miles, cycles a distance of (x2 7) miles, and swims a distance of (x − 2) miles. which simplified expression is equivalent to the total distance, in miles, joy covers? x2 3x 5 x2 3x 9 3x2 5 3x2 9

The average density of the rod is  0.704 kg/m.

For given question,

We have been given the linear density in a rod 5 m long is 10 / x + 4 kg/m, where x is measured in meters from one end of the rod.

We need to find the

The length of rod is, L = 5 m.

The linear density of rod is, ρ = 10/( x + 4) kg/m

To find the average density we need to integrate the linear density from x₁ = 0 to x₂ = 5,  

The expression for the average density is given as,

⇒ ρ'

[tex]=\int\limits^5_0 {\rho} \, dx\\\\=\int\limits^5_0 {\frac{m}{L} } \, dx\\\\=\int\limits^5_0 {\frac{10}{5(x+4)} }\, dx\\\\=\int\limits^5_0 {\frac{2}{x+4} }\, dx[/tex]                        ......................(1)

Using u = x + 4  

du = dx

u₁ = x₁ + 4

u₁ = 0 + 4

u₁ = 4

and

u₂ = x₂ + 4

u₂ = 5 + 4

u₂ = 9

By entering the values above into (1), we have:

⇒ ρ'

[tex]=2\int\limits^9_4 {\frac{1}{u} } \, du\\\\ = 2[(log~u)]_4^{9}\\\\=2[(log~9-log~4)]\\\\=2\times[0.352][/tex]

= 0.704

Thus, we can conclude that the average density of the rod is  0.704 kg/m.

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Answer:17.64

Step-by-step explanation:44762/54/47= 17.6367 or 17.64

The analysis of the kidney exists named urology.  The kidney exists as a bean-shaped organ. The Kidney exists metanephric in nature and is located retroperitoneal in position.

The organ current in the body which regulates the fluid concentration of the body exists named the kidney.

The nephron exists as the structural and operational unit of the kidney.

The sequence of the appearance of the kidney exists as pursues:-

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Answer:

1. Given

2. Definition of Congruent Angles

3. Triangle Interior Angle Sum Theorem

4. Transitive Property of Equality

5. Substitution Property of Equality

6. Definition of Congruent Angles

Horizontal asymptote of c(x) is 450.

A horizontal asymptote is a line that guides the graph of a function for x-values but is not itself a part of the graph. "far," either "far" to the right or "far" to the left. Eventually, whether the graph is large enough or little, it may intersect.

Since we have given that

Cost to produce one refrigerator = $450

Fixed monthly cost = $200,000

Thus, the following formula represents the average cost to produce x refrigerators:

C(x) = (200000 + 450x)/x

Horizontal asymptote of c(x) would be

= 450x/x

= 450

Hence, Horizontal asymptote of c(x) is 450

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The shape that we have here is sued to show the infinite geometric progression.

This is the sequence of numbers that has all the other values in the sequence gotten by the multiplication of a certain factor

In this question or the shape we can see that the triangle is made up of smaller other triangles embedded in it.

The area of the traingle that is in the red color is seen to have been made up of 1/3 of the total triangles that we have in the shape. This can be seen to be similar as the triangles that are represented by the green and the blue color.

Putting a  lot of triangles inside one big triangle gives up a pictorial diagram on how to add infinite amount of things up.

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The probability distribution of X when X~B(1,1/25) is (Option A)

See the explanation below.

Given X~B(n,p)

P(x=1) = C¹ₙ * P¹ * (1-P)ⁿ⁻¹ (n≥1)

Thus, X~B [1, 1/25]

1/25 = 0.04

hence, p(x=0)

= C⁰₁ * 0.04⁰ (1 - 0.04)¹

= 0.96

P (x=1)

=  C¹₁ 0.04¹ (1-0.04)⁰

= 0.04

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Answer:   100 square cm

Step-by-step explanation:   the triangle is 33 cm and the big rectangle is 9x7 square cm. There is a small square that is 2x2 =4 cm so the total is 33 +63 + 4 which is 100 cm.

Answer: 104

Step-by-step explanation:

area of trangle =33 because 6*11/2=33

area of rectangle 9*7=63

area of rectangle  2*2=4

33+63+4=100^2

The analogous equation for the square will be; (x-10)²=87.

Algebraic equations with equivalent solutions or roots are called equivalent equations.

Based on information provided, an equivalent equation is created by adding or deleting the same quantity or expression from both sides of a given equation;

Using the original equation as a starting point as;

-20x+ x² + 13 = 0

Now x² - 20x = -13.

We need to take the "x" term's coefficient, or b, to complete the square.

Then Divide by 2 and write the equation in the quadratic formula (ax² + bx + c = 0).Then,

B = -20

b/2 = -10

(b/2)² = 100

x² - 20x +100 = -13 + 100

On the left side,

LHS: (x + b/2)² = (x-10)2

RHS: -13 + 100 = 87

(x-10)² = 87

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Answer:

numbers

Step-by-step explanation:

numbers

Answer:

it's C. 2.26s

but you wrote 2.16s nearly

The soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds,  option D.

To determine how long the soccer ball was in the air, we can use the vertical motion of the ball. When a projectile is launched at an angle, its vertical motion can be analyzed separately from its horizontal motion.

In this case, the initial velocity of the soccer ball can be divided into vertical and horizontal components. The initial velocity in the vertical direction can be calculated using the sine of the launch angle:

Vertical component (Vy) = initial speed (v) * sin(angle)

Vy = 16 m/s * sin(45°)

Vy = 11.31 m/s

Now, we can use the vertical motion equation to find the time the ball spends in the air:

Vertical displacement (y) = Vy * time - (1/2) * gravity * time^2

Since the ball reaches the same vertical position when it lands as when it was launched, the vertical displacement is 0. Therefore, we can set the equation equal to zero:

0 = (11.31 m/s) * time - (1/2) * 9.8 m/s^2 * time^2

Simplifying the equation:

4.9 * time^2 = 11.31 * time

Dividing both sides by time:

4.9 * time = 11.31

time = 11.31 / 4.9

time ≈ 2.31 seconds

Therefore, the soccer ball was in the air for approximately 2.31 seconds. Rounding to two decimal places, the answer is approximately 2.30 seconds, which corresponds to option D.

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Answer:

y ≤ 2.5x + 5

Step-by-step explanation:

first step is to obtain the equation of the line in slope- intercept form

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 2, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-2)}[/tex] = [tex]\frac{5}{0+2}[/tex] = [tex]\frac{5}{2}[/tex] = 2.5

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = 2.5x + 5 ← equation of line

since the line is solid then inequality will be ≤

the solution to the inequality is the blue region below the line , then

y ≤ 2.5x + 5 ← inequality represented by graph

Answer:

1/2^6 = 1/64

Step-by-step explanation:

Half life = 10 years

Time = 60 years

No of half life = T/t

= 60 / 10 = 6

Remaining fraction = 1/2^(no of half life)

= 1/2^6

= 1/64

From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°

The lines ZY and ZW are tangents to the attached circle which is centered at x.

From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.

From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.

Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;

∠WZY = 360° - (90° + 90° + 109°)

∠WZY = 360° - 289°

∠WZY = 71°

Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°

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Answer:  B. 71°

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!! :)

I got it right!

Substitute [tex]y=\ln(2x+1)[/tex] and [tex]dy=\frac2{2x+1}\,dx[/tex], so that

[tex]\displaystyle \int \frac2{(2x+1) \ln(2x+1)} \, dx = \int \frac{dy}y = \ln|y| + C = \boxed{\ln|\ln(2x+1)| + C}[/tex]

Answer:

Step-by-step explanation:

TheThe number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.

A. Let assume the two are linear relationship

Let y represent juice made

Let x represent the concentrate remaining

Hence:

Slope=600-200/200-280

Slope=400/-80

Slope=-5

y=-5x+b

Where:

x=200

y=-5(200)+b=600

y=-1000+b=600

b=1600

Thus,

y=-5x+1600

y=0.  -5x+1600=0

        -5x=-1600

divide both side by 5x

x=-1600/-5

x=320 ounces

B. x=0

y=1600 ounces

Therefore the number of ounces of concentrate that were in the original container before any juice was made is 320 ounces and the number of juice that can be made using the whole container of concentrate is 1600 ounces.

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The time it will take the thermometer to hit the ground is 22 seconds

From the question, we are to determine the how long it would take the thermometer to hit the ground

From the given information,

The equation for the height as a function of time is

h(t) = -16t² + initial height

From the given information,

The thermometer falls from a weather balloon at a height of 7744 ft

∴ Initial height = 7744 ft

When the thermometer hits the ground, h(t) = 0

Thus, we get

0 = -16t² + 7744

16t² = 7744

t² = 7744/16

t² = 484

t = √484

t = 22 seconds

Hence, the time it will take the thermometer to hit the ground is 22 seconds

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The following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.

If the measuring has a level of precision of 0.01 ml, this means that the measured quantities are only sensible to the smallest hundreths. Any change less than 0.01 ml and any decimal less than a hundreths are "invisible" for measuring processes.

Hence, the following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.

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Answer:

B,D,E

Step-by-step explanation:

The error made by zacharias in solving the quadratic equation 0 = -2x² + 5x - 3 using quadratic formula is; the 2 in the numerator should be –2.

There are four methods of solving quadratic equation. Namely;

0 = -2x² + 5x - 3

x = -b ± √b² - 4ac / 2a

where,

x = -b ± √b² - 4ac / 2a

x = -5 ± √5² - 4(-2)(-3) / 2(-2)

= -5 ± √25 - (24) / -2

= -5 ± √1 / -2

= -5/2 ± 1/2

= -5/2 - 1/2 or x = -5/2 + 1/2

= -5-1 / 2 or -5+1/ 2

x = -6/2 or -4/2

x = -3 or -2

Therefore, the solution to the quadratic equation is x = -3 or -2

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Step-by-step explanation:

Arranging fractions in descending order means arranging the fractions starting from the highest to the lowest.

Finding the LCM of 3, 16, 12, 24,

[tex] \frac{2}{3} \: \frac{5}{16} \frac{7}{12} \frac{11}{24} \\ \\ \frac{32 + 15 + 28 + 22}{48} \\ \\ Arranging \: the \: fractions \: in \: descending \: order \\ \frac{2}{3} \frac{7}{12} \frac{11} {24} \frac{5}{16} [/tex]

The volume of the cylinder is [tex]3.14 inch^3[/tex]

Given that

radius = 1 inch

height = inch

we know that volume =[tex]V = \pi \times r^2 \times h[/tex]

now put the value in the above equation we get

[tex]V = 3.14 \times 1 ^2\times 1\\V = 3014inch ^3[/tex]

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The probability that the person is over 40 and prefers cola exists at 1.3725.

The probability of an event exists in the ratio of the size of the event space to the size of the sample space.

The size of the sample space exists the entire number of possible outcomes.

The event space exists the number of outcomes in the event you exists interested in.

So, P = size of the event space/size of the sample space

To estimate the probability that the person exists over 40 years.

Size of the sample size = 255

Size of the event space = 85

P = 85/255

P = 1/3

To estimate the probability that they drink cola.

Size of the sample size = 255

Size of the event space = 95

P = 95/255

P = 19/51

To estimate the probability that the person exists over 40 years of age or that they drink cola

So, P = (1/3) + (19/51)

[tex]$P = (51*3+3*19)/153[/tex]

P = 1.3725

Therefore, the probability that the person is over 40 and prefers cola exists at 1.3725.

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Answer:

8√3

I hope this helps you

The solution for the given equation is -5/8. By using simple algebraic operations, the equation is solved.

A linear equation is represented by ax + b = 0. The solution for this equation is

ax + b = 0

⇒ ax = -b

⇒ x = -b/a

The given equation is

7/8 + x = 1/4

On simplifying,

x = 1/4 - 7/8

⇒ x = -5/8

Therefore, the solution of the given equation is -5/8.

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Answer:

12 ft²

D

Step-by-step explanation:

Area of parallelogram = Base × Height

Here, base = 3ft

height = 4ft

So, Area = 3×4 ft² = 12 ft²

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Area of parallelogram is:}[/tex]

[tex]\rm{\bold{b}ase\times\bold{h}eight = \bold{a}rea}[/tex]

[tex]\huge\text{Your equation should look like: }[/tex]

[tex]\rm{3\times4 = \boxed{\bf area}}[/tex]

[tex]\huge\text{Simplify the equation above \& you will have}\\\\\huge\text{the answer to the area of the parallelogram.}[/tex]

[tex]\mathsf{3[base] \times 4[height] = ?[area]}[/tex]

[tex]\huge\text{Simplify it:}[/tex]

[tex]\rm{12\ ft^2}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{\frak{12\ ft^2}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

3

Step-by-step explanation:

- 4x³y² + 6

the x is raised to the power of 3 , that is exponent of x is 3

Answer:

[tex]x =\frac{5}{3} \pm \frac{\sqrt{10}}{3} \\\\x=2.72076\\x=0.612574\\[/tex]

Step-by-step explanation:

The quadratic equation is:

[tex]3x^2 - 10x + 5 = 0[/tex]

The roots (solutions) of a quadratic equation of the form
[tex]a^2 + bx + c = 0\\[/tex]

are

[tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]

in this case we have a = 3, b = -10, and c = 5

So, substituting for a, b and c we get

[tex]x = \frac{ -(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{ 2(3) }[/tex]

[tex]x = \frac{ 10 \pm \sqrt{100 - 60}}{ 6 }\\[/tex]

[tex]x = \frac{ 10 \pm \sqrt{40}}{ 6 }[/tex]

Simplifying we get

[tex]x = \frac{ 10 \pm 2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 10 }{ 6 } \pm \frac{2\sqrt{10}\, }{ 6 }\\\\x = \frac{ 5}{ 3 } \pm \frac{ \sqrt{10}\, }{ 3 }\\\\\frac{ 5}{ 3 } + \frac{ \sqrt{10}\, }{ 3 } = 2.72076\\\\\\[/tex]  (First root/solution)

[tex]\frac{ 5}{ 3 } - \frac{ \sqrt{10}\, }{ 3 } = 0.612574[/tex]  (Second root/solution)

The solution to 0.5^(x + 2) > 9 is x  > -5.170

The inequality expression is given as:

0.5^(x + 2) > 9

Take the logarithm of both sides of the inequality expression

log(0.5^(x + 2)) > log(9)

Rewrite the inequality expression as

(x + 2)log(0.5) > log(9)

Divide both sides by log(0.5)

x + 2 > -3.170

Subtract 2 from both sides

x  > -5.170

Hence, the solution to 0.5^(x + 2) > 9 is x  > -5.170

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