Mark runs to catch a ball. Explain how the structure of muscle tissue helps him perform this function

The required explanation for log of base 10 is described.

The ability of logarithms to solve exponential problems is a large part of their strength. Examples of this include sound (measured in decibels), earthquakes (measured on the Richter scale), starlight brightness, and chemistry (pH balance, a measure of acidity and alkalinity).

The distinction between log and ln is that log is expressed in terms of base 10, while ln is expressed in terms of base e. As an illustration, log of base 2 is denoted by log2 and log of base e by loge = ln (natural log).

The logarithm can be rewritten using the general rule. The common logarithm, which has a base of 10 always, is what you're dealing with when the log has no base.

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Answer:

54

Step-by-step explanation:

5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

5. We have Angle, Angle and Side to constitute the AAS theorem and prove the triangles are congruent.

6. We have Side, Side and angle not between them so we don't have enough information to prove the congruency of the triangles.

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Answer:

58.58

Step-by-step explanation:

\( \frac{1}{2} \times 10 \times 3 \\ 5 \times 3 = 15.....(1)\)

\( \frac{1}{2} \times 10 \times 10 \\ 5 \times 10 = 50...(2)\)

Add one and two :- 15+ 50 = 65

The probability of success is a measure of the likelihood that a specific event or outcome will occur successfully, typically expressed as a value between 0 and 1.

In a clinical trial with two treatment groups, group A and group B, the probability of success in group A is 0.5, while the probability of success in group B is 0.6. Each group consists of five patients.

To calculate the probability of a specific outcome, such as all patients in group A being successful, we can use the binomial distribution formula.

The binomial distribution formula is:
\(P(X = k) = \binom{n}{k} p^k (1 - p)^{n - k}\)

Where:
- P(X=k) represents the probability of getting exactly k successes
- nCk represents the number of ways to choose k successes from n trials
- p represents the probability of success in a single trial
- n represents the total number of trials

In this case, we want to find the probability of all five patients in group A being successful. Therefore, we need to calculate P(X=5) for group A.

Using the binomial distribution formula, we can calculate this as follows:
\($P(X&=5) \\\\&= \binom{5}{5} (0.5^5) (1-0.5)^{5-5} \\\\&= \boxed{\dfrac{1}{32}}\)

Simplifying the equation, we get:
\($P(X&=5) \\&= 1 (0.5^5) (1-0.5)^0 \\&= \boxed{\dfrac{1}{32}}\)

Simplifying further, we have:
\($P(X&=5) \\&= (0.5^5) (1) \\&= \boxed{\dfrac{1}{32}}\)

Calculating this, we get:
P(X=5) = 0.03125

Therefore, the probability of all five patients in group A being successful is 0.03125, or 3.125%.

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Answer:

(0, -7)

Step-by-step explanation:

In y = mx + b, b is the y intercept.

In the given equation, y = -5x - 7, b is -7.

So, this means the y value of the y intercept -7.

The y intercept of the line is (0, -7)

The radius of the wheel 0.35m

The number of revolutions is 100

The distance is 220 meter

Distance in one revolution= 220/100

= 2.2 meter

The radius of the wheel can be calculated as follows

radius= 2.2/2(3.142)

= 2.2/6.29

= 0.35

Hence the radius of the wheel is 0.35 meter

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The mass of salt in the tank at time t.

dS/dt = 10 - S/400

S(0) = 100 grams

The solution is S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

A tank holds water V(0) = 4000 liters in which salt S(0) = 100 grams.

So dS/dt = S(in) - S(out)

S(in) = 1 × 10 = 10 gram/liters

S(out) = S/V × 10 = 10S/V gram/liters

V = V(0) + q(in) - q(out)

V = 4000 + 10t - 10t

V = 4000 liters

dS/dt = 10 - 10S/V

dS/dt = 10 - 10S/4000

dS/dt = 10 - S/400

Now given; S(0) = 100.

Here, p(t) = 1/400, q(t) = 10

\(\int p(t)dt = \int\frac{1}{400}dt\)\(\int p(t)dt = \frac{1}{400}t\)

\(\mu=e^{\int p(t)dt}\)

\(\mu=e^{\frac{t}{400}}\)

So, S(t) = \(\frac{\int\mu q(t)dt+C}{\mu}\)

S(t) = \(\frac{\int e^{\frac{t}{400}} \cdot10dt+C}{e^{\frac{t}{400}}}\)

S(t) = \(e^{\frac{-t}{400}} \left({\int e^{\frac{t}{400}} \cdot10dt+C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({10\times\frac{e^{\frac{t}{400}}}{1/400} +C}\right)\)

S(t) = \(e^{\frac{-t}{400}} \left({4000\times{e^{\frac{t}{400}} +C}\right)\)

Now solving the bracket

S(t) = 4000 + \(e^{\frac{-t}{400}}\)C.....(1)

At S(0) = 100

100 = 4000 + \(e^{\frac{-0}{400}}\) C

100 = 4000 + \(e^{0}\) C

100 = 4000 + C

Subtract 4000 on both side, we get

C = -3900

Now S(t) = 4000 - 3900\(e^{\frac{-t}{400}}\)

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The complete question is:

A tank holds 4000 liters of water in which 100 grams of salt have been dissolved. Saltwater with a concentration of 1 grams/liter is pumped in at 10 liters/minute and the well mixed saltwater solution is pumped out at the same rate. Write initial the value problem for:

The mass of salt in the tank at time t.

dS/dt =

S(0) =

The solution is S(t) =

The sequence of natural numbers that leaves a remainder of 3 when divided by 10 is:

3, 13, 23, 33, 43, 53, 63, 73, 83, 93, 103, 113, ...

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

The approximate distance between Padma and the bear is 21.2 ft, which corresponds to option A.

The approximate distance between Padma and the bear, we can use trigonometry. Since James and Padma are on opposite sides of the 100-ft-wide canyon,

we can form two right triangles with the bear's position as one of the vertices.

Step 1: Determine the horizontal distance from James to the bear.

Since the angle of depression from James to the bear is 45 degrees, the horizontal distance (x) and vertical distance (y) are equal due to the properties of a 45-45-90 right triangle. Therefore, x = y. Since the canyon is 100 ft wide, x + y = 100 ft. We can solve for x:

x + x = 100

2x = 100

x = 50 ft

Step 2: Determine the vertical distance from James to the bear.
Since x = y in the 45-45-90 right triangle, the vertical distance from James to the bear is also 50 ft.

Step 3: Determine the horizontal distance from Padma to the bear.
We can now use Padma's angle of depression, 65 degrees, to find the horizontal distance (p) from Padma to the bear. Using the tangent function:

tan(65) = vertical distance / horizontal distance

tan(65) = 50 ft / p

Solving for p:

p = 50 ft / tan(65) ≈ 21.2 ft

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Answer:

1.x,y is the answer to first question

2.y=2x+5

Answer:

Yes commutative property of multiplication

Step-by-step explanation:

Answer:

c)  1 foot per 2 hours

Step-by-step explanation:

1/6 of a foot (which is 12 inches) is 2 inches

1/3 of an hour (which is 60 minutes) is 20 minutes

2 inches in 20 minutes is the same as 12 inches (which is 1 foot) in 120 minutes (which is 2 hours)

Answer:

the answer is 40

Step-by-step explanation:

U multiply then subtract.

By calculating the cost per yard, Marianne can compare the options and determine which one offers the best value for her quilting project. In this case, option 3 has the lowest cost per yard, making it the most cost-effective choice.

To determine how much each piece of fabric costs per yard, Marianne can divide the cost of each option by the number of yards in that option.

Let's calculate the cost per yard for each option:

Option 1:

Cost = $12

Yards = 6

Cost per yard = $12 / 6 = $2 per yard

Option 2:

Cost = $14

Yards = 8

Cost per yard = $14 / 8 = $1.75 per yard

Option 3:

Cost = $16

Yards = 10

Cost per yard = $16 / 10 = $1.60 per yard

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a. the equation of the tangent line to the curve at (3,3) is 9x + 13y = 78.

b. This is false, so (4,2) does not lie on the curve.

c. the equation of the tangent line to the curve at (1,y) is 2x - y - 1 = 0.

For the first problem, we have:

\(3x^2 + 3xy + 4y^2 = 90\)

To verify that (3,3) lies on the curve, we substitute x = 3 and y = 3 into the equation and check if it is satisfied:

\(3(3)^2 + 3(3)(3) + 4(3)^2 = 27 + 27 + 36 = 90\)

Therefore, (3,3) lies on the curve.

To determine the equation of the line tangent to the curve at (3,3), we need to find the derivative of the curve with respect to x, then evaluate it at x = 3 to find the slope of the tangent line, and use the point-slope form to write the equation of the tangent line.

Taking the derivative with respect to x, we get:

6x + 3y + 3x(dy/dx) + 8y(dy/dx) = 0

Simplifying and solving for dy/dx, we get:

dy/dx = -(6x + 3y)/(3x + 8y)

Evaluating at (3,3), we get:

\(dy/dx = -(6(3) + 3(3))/(3(3) + 8(3)) = -27/39 = -9/13\)

Using the point-slope form with the point (3,3) and slope -9/13, we get:

y - 3 = (-9/13)(x - 3)

Simplifying, we get:

9x + 13y = 78

Therefore, the equation of the tangent line to the curve at (3,3) is 9x + 13y = 78.

For the second problem, we have:

\(16(x^2 + y^2)^2 = 400xy^2\)

To verify that (4,2) lies on the curve, we substitute x = 4 and y = 2 into the equation and check if it is satisfied:

\(16(4^2 + 2^2)^2 = 400(4)(2^2)\)

\(16(16 + 4)^2 = 400(4)(4)\)

20,736 = 3,200

This is false, so (4,2) does not lie on the curve.

For the third problem, we have:

\(x + y^2 - y = 1\)

To find the equations of all lines tangent to the curve at x = 1, we need to find the derivative of the curve with respect to x, then evaluate it at x = 1 to find the slope of the tangent line, and use the point-slope form to write the equation of the tangent line.

Taking the derivative with respect to x, we get:

1 + 2y(dy/dx) - dy/dx = 0

Solving for dy/dx, we get:

dy/dx = (2y - 1)/(2x - 1)

Evaluating at x = 1, we get:

dy/dx = (2y - 1)/1 = 2y - 1

Using the point-slope form with the point (1,y) and slope 2y - 1, we get:

y - y1 = (2y - 1)(x - 1)

Simplifying, we get:

2x - y - 1 = 0

Therefore, the equation of the tangent line to the curve at (1,y) is 2x - y - 1 = 0.

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The FV is $107 for the simple interest.

The formula to calculate simple interest is given as:

I = P × R × T

Where,I is the simple interest, P is the principal or initial amount, R is the rate of interest per annum, T is the time duration.

Formula to find FV:

FV = P + I = P + (P × R × T)

where,P is the principal amount, R is the rate of interest, T is the time duration, FV is the future value.

Given that P = $100, R = 7%, and T = 1 year, we can find the FV of the investment:

FV = 100 + (100 × 7% × 1) = 100 + 7 = $107

Therefore, the FV of $100 invested at 7% for one year (simple interest) is $107.

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Answer:

It's counting by 2's so count by 2's 88 more times. Not sure if that is completely right. Also there is probably an equation that you can use to find the answer, but i don't remember it.

Step-by-step explanation:

Answer:

200

add by 2's 88 times

The modulus is 1, argument is π/4 and the principal value is π/4 mod 2π

From the question, we have the following parameters that can be used in our computation:

\(z = \sqrt{ \frac{1 + i}{1 - i}\)

Rationalize the expression

So, we have

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

This means that

z = √i

The modulus of a complex number is calculated as

|z| = √(a^2 + b^2)

where z = a + bi. In this case, a = 0 and b = 1

So, we have

|z| = √(0^2 + 1^2)

|z| = 1

The argument of a complex number is calculated as

\(\arg(z) = \tan^{-1} \left( \frac{b}{a} \right)\)

So, we have

\(\arg(z) = \tan^{-1} \left( \frac{1}{0} \right)\)

This gives

arg(z) = π/4

The principal value of the argument of z is

arg(z) mod 2π

So, we have

π/4 mod 2π

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The implicit solution to the given differential equation Dx/dt = 4x² + (9t/√(6²+x²)) / (4tx) using the method for solving homogeneous equations is F(t,x) = C, where C is an arbitrary constant.

To solve the given differential equation, we can separate the variables and integrate both sides. Rearranging the equation, we have:

(4tx) Dx = (4x² + (9t/√(6²+x²))) dt. Next, we integrate both sides. Integrating the left side with respect to x and the right side with respect to t, we get:

∫(4tx) Dx = ∫(4x² + (9t/√(6²+x²))) dt. Integrating both sides will result in a function F(t,x) on the left side and the integral on the right side. Since we are looking for an implicit solution in the form F(t,x) = C, we can write the equation as:

F(t,x) = C. cccThis represents the general solution to the given differential equation, where C is an arbitrary constant. The specific form of the function F(t,x) will depend on the integration process and the initial conditions, if provided.

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For the Given function f(x) = 3x + 1, h(x) = sqrt(x + 4)  f o h(x) = 3(sqrt(x + 4)) + 1

To find the composition of functions f o h, we substitute h(x) into f(x) and simplify.

Given:

f(x) = 3x + 1

h(x) = sqrt(x + 4)

To find f o h, we substitute h(x) into f(x):

f o h(x) = f(h(x)) = 3(h(x)) + 1

Now we substitute h(x) = sqrt(x + 4):

f o h(x) = 3(sqrt(x + 4)) + 1

This is the composition of the functions f o h.

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Answer: 1/2

Step-by-step explanation:

The given summation expression ∑i=29​(i−8) has the index of summation (i), the upper bound (29), and the lower bound (unspecified).

The index of summation, denoted by the letter in the summation notation, represents the variable that takes on different values as the sum is computed.

In this case, the index of summation is "i". The upper bound specifies the last value of the index for which the summation is performed. In this case, the upper bound is 29.

However, the lower bound is not specified in the given expression. The lower bound represents the starting value of the index for which the summation begins. Without a specified lower bound, we cannot determine the full range of values over which the summation is computed.

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Answer:

21sqrt(6)

Step-by-step explanation:

Hope it helps......

If the sum of the height and the perimeter of the square base is 14 in, the maximum possible volume is 54 in³.

Let x represent the square box's rectangular base's side length.

Suppose h is the height.

Volume V should be used.

Considering that the square base's height plus perimeter equals 14 inches.

h + 4x = 18

Subtract 4x on both side, we get

h = 18 - 4x..........(1)

The volume is given as:

V = Area × Height

V = x² × h

Substitute the value of h

V = x² × (18 - 4x)

V = 18x² - 4x³..........(2)

Differentiate the equation 2 with respect to x

dV/dx = 36x - 12x²..........(3)

For the critical numbers,

dV/dx = 0

So, 36x - 12x² = 0

x(36 - 12x) = 0

x(-12x + 36) = 0

Equating equal to 0

x = 0                      -12x + 36 = 0

x = 0                      -12x = -36

x = 0                       x = 3

Differentiate the equation 3 with respect to x

d²V/dx² = 36 - 24x

At x = 3 the value of d²V/dx² is

d²V/dx²  = 36 - 24 × 3

d²V/dx² = 36 - 72

d²V/dx² = -36 < 0

x = 3 corresponds to the maximum of the volume V according to the second derivative test.

Now from the equation 1;

\(V_{\text{max}}\) = 18(3)² - 4(3)³

\(V_{\text{max}}\) = 18(9) - 4(27)

\(V_{\text{max}}\) = 162 - 108

\(V_{\text{max}}\) = 54 in³

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The length of segment RS is given as follows:

RS = 24.

The angle addition postulate states that if two or more angles share a common vertex and a common angle, forming a combination, the measure of the larger angle will be given by the sum of the measures of each of the angles.

The segment RT is the combination of segments RS and ST, hence:

RT = RS + ST.

Hence the length of segment RS is given as follows:

41 = RS + 17

RS = 24.

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For this circle M, the missing reason in step 8 is substitution property.

The theorem of intersecting chord states that when two (2) chords intersect inside a circle, the measure of the angle formed by these chords is equal to one-half (½) of the sum of the two (2) arcs it intercepts.

The substitution property states that assuming x, y, and z are three (3) quantities, and if x is equal to y (x = y) based on a rule and y is equal to z (y = z) by the same rule, then, x and z (x = y) are equal to each other by the same rule.

From step 6, we have:

m∠KML = 2(m∠MJL) ⇒ substitution property.

By the same substitution property, we have:

Step 8: m∠KL = 2(m∠MJL)

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When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

According to me , independent is the word which is associated with multiplication when computing probabilities . Because when the events are independent then we multiply the probabilities .

According to the multiplication rule of probability, the probability of occurrence of both the events A and B is equal to the product of the probability of B occurring and the conditional probability that event A occurring given that event B occurs.

The probability of the union of two events is equal to the sum of individual probabilities. The union of two set contains all the elements of previous sets. The union is denoted by ∪. The equation for the students earnings will be expressed as P(A∪B). The occurrence of event A changes the probability of B then the events are dependent. If the probability of two events happening together is zero then the events are mutually exclusive.

Therefore,

When we calculate probabilities involving one event AND another event occurring, we multiply their probabilities.

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Answer:

no property

Step-by-step explanation:

Name the property used: no property