Maria bicycled every day for 14 days. She traveled 294 miles. How many miles did she travel per day?

The normal stress and shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ 11 are σn = 16−15√3 and τ = 2+15√3/4. The maximum shear stress is 17.5.

The stress tensor σ given in the problem is:

σ = 201504−400−1500−1010

The normal stress is given by

σn = σ11cos²θ+σ22sin²θ−2σ12sinθcosθ

where

θ = 30°

θ = 30° is the angle between the direction perpendicular to the plane and the direction of σ11

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
σn = 20cos²(30)+(-15)sin²(30)-2(-4)sin(30)cos(30)

σn = 20cos²(30)+(-15)sin²(30)+4sin(30)cos(30)

σn = 20(3/4)+(-15)(1/4)+4(1/2)(√3/2)

σn = 12−15√3+4√3

σn = 16−15√3

The normal stress is σn = 16−15√3

The shear stress acting on a plane perpendicular to direction inclined 30° counter clockwise to σ11

σ11 is given by:
τ = σ12(sin²θ−cos²θ)+0.5(σ11−σ22)sin2θ

where

θ = 30°

θ=30° is the angle between the direction perpendicular to the plane and the direction ofσ11.

σ11 = 20

σ22 = −15

σ12 = −4

Here is a detailed calculation:
τ = −4(sin²(30)−cos²(30))+0.5(20−(−15))sin(60)

τ = −4((1/4)−(3/4))+0.5(20+15)(√3/2)

τ = 4(1/2)+0.5(35)(√3/2)

τ = 2+15√3/4

The shear stress is τ = 2+15√3/4

Maximum shear stress
The maximum shear stress is given by

τmax = 0.5(σ1−σ2)

whereσ1σ1 andσ2σ2 are the first and second principal stresses.

The eigenvalues of the stress tensor σ are found by solving the characteristic equation:

det(σ−λI)=0

Here is a detailed calculation:
σ−λI = [20150−λ−400−1500−λ0−400−15−λ10−λ]

σ−λI = 0(20150−λ)[(−λ)(−λ−15)+0(−400)]−(−4)[0(−λ−15)+(−400)(−λ)]+0[0(−400)+(20150−λ)(−λ)]

σ−λI = 0λ³+35λ²−605λ−1875

σ−λI = 0

λ = −25,5,3

The maximum shear stress occurs on the plane of maximum shear stress which is at 45° 45° to the coordinate axes.

The maximum shear stress is found to be

τmax = 0.5(σ1−σ2)

τmax = 0.5(20−(−15))

τmax = 17.5.

Therefore, the maximum shear stress is τmax = 17.5.

Learn more about the normal and shear stress from the given link-

https://brainly.com/question/28485445

#SPJ11

Answer:

A) d(r) = 2r

Value when r = 5 is 10 ft.

diameter is 10 ft when the radius is 5ft

B) A(r) = πr²

Value when r = 5 is 25π ft²

Area is 25π ft² when radius is 5 feet

C) C(r) = 2πr

Value when r = 5 is 10π

Circumference is 10π when radius is 5 feet

Step-by-step explanation:

A) Using function notation, since d = 2r

d(r) = 2r

d(5) = 2(5)

d(5) = 10 feet

This means that the diameter is 10 ft when the radius is 5ft

B) Area = πr²

In function notation, its;

A(r) = πr²

When radius is 5 feet,

Area is; A(5) = π(5²) = 25π

It means Area is 25π ft² when radius is 5 feet

C) Circumference is 2πr

In function notation, it's;

C(r) = 2πr

When r = 5 feet,

Circumference is;

C(5) = 2π(5)

C(5) = 10π

Answer to 1:

\(\frac{x^3}{2y^25}\)

First thing you want to do is combine like terms on the bottom. Since it's multiplication, all you have to do is add the exponents. So for x you'd get x raised to the -9 power and for y you'd get 2y raised to the power of 7

Second thing is the numerator of the fraction. Since this is raising what is inside the paranthesis to a power, you must multiply this power by the powers of x and y, respectively. You should get x raised to the power of -6 and y raised to the power of -18

Here's where it gets complicated. to rationalize the problem, you must add parts from the numerator and denominator or vice versa. You cannot have any negative exponents anywhere in the fraction.  So that means for x you have to add 9 to the x on the top to cancel out the -6 and rationalize the remaining x's. You should end up with x^3.

For y, you work the opposite way. Since the negatives are only on the top, you simply add 18 to the bottom y's and it remains rationalized.

If done correctly this should come out to x^3/2y^25

Answer to 2:

(x^20y^12)/256

First thing you can do on this one is to cancel out the x^0s. Anything to the power of 0 equals one so only the coefficients will remain. Multiply those together and you'll get 4.

Next you will rationalize the ys. Add the bottom 3 to the top to cancel out the denominator and you're left with y^-3. Leave it like this for now.

Now is the difficult part. You must take everything that is inside the parenthesis to the power of -4. That includes the coefficients and the exponents. 4^-4 = 1/256. This means that you now must move the coefficients to the bottom. You should currently have y^-3/(256x^5).

Now take the exponents to the power using the same rules as question 1. -3*-4 = 12 and 5*-4 = -20. You should now have y^12/(256x^-20)

Lastly, we must rationalize the denominator. To do so, move the x^-20 to the numerator and make the exponent positive. After doing this, you have the answer: (x^20y^12)/256

The distribution function of M, FM(-), is given by FM(x) = x, 0 ≤ x ≤ 1.

The probability density function of M is\(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

In order to understand the distribution function of M, we need to consider the probability that M is less than or equal to a given value x. Since each Xi is uniformly distributed over (0,1), the probability that Xi is less than or equal to x is x.

For M to be less than or equal to x, all of the random variables Xi must be less than or equal to x. Since these variables are independent, their joint probability is the product of their individual probabilities. Therefore, the probability that M is less than or equal to x can be expressed as the product of n x's: P(M ≤ x) = x * x * ... * x = \(x^n\).

The distribution function FM(x) is defined as the probability that M is less than or equal to x. Therefore, FM(x) = P(M ≤ x) = \(x^n\).

To find the probability density function (PDF) of M, we differentiate the distribution function FM(x) with respect to x. Taking the derivative of \(x^n\)with respect to x gives us \(n * x^(^n^-^1^)\). Since the range of M is (0,1), the PDF is defined only within this range.

The distribution function of M is FM(x) = x, 0 ≤ x ≤ 1, and the probability density function of M is \(fM(x) = n * x^(^n^-^1^)\), 0 ≤ x ≤ 1.

Learn more about probability

brainly.com/question/32575884

#SPJ11

The probability that a specific vulnerability within an organization will be attacked by a threat is known as potential.

Potential refers to the likelihood that a specific vulnerability in an organization's security will be exploited by a threat actor or attacker. In the field of information security, the concept of potential is used to assess the risk associated with a particular vulnerability.

This risk assessment helps organizations to prioritize their security efforts and allocate resources where they are most needed. Determinism is a philosophical and scientific concept that refers to the idea that events are determined by prior causes, rather than by random chance.

Externality is an economic term that refers to the impact of an economic activity on parties not directly involved in the activity. For example, pollution from a factory may have externalities that affect the health and well-being of people who live near the factory.

To learn more about vulnerability click on,

https://brainly.com/question/29023407

#SPJ4

Answer:

Sample space: 6 Total options: 9

Step-by-step explanation:

The sample space is the amount of variables, this being 6 in total. The options are the total amount of configurations possible with the sample space, this being nine.

I haven't done this in a while so my answer may not be the most reliable, I would use another source if you are still unsure. Good luck!

According to the triangle inequality theorem, the measure for the third side can be GE = 6 units, because: A. 3 + 5 > 6, 5 + 6 > 3, and 6 + 3 > 5.

The triangle inequality theorem states that the set of side measurements that will form a triangle will be the set of side lengths whereby the sum of any two sides will be greater than the third side of the triangle.

For example, if a, b, and c are the side lengths of a triangle, then:

Thus, we have the given lengths:

FE = 3 units

FG = 5 units

Therefore, the third side length would be GE = 6 units based on the triangle inequality theorem because:

3 + 5 > 6

5 + 6 > 3

6 + 3 > 5

Learn more about triangle inequality theorem on:

https://brainly.com/question/309896

#SPJ1

The answer is 0.441 using probabilty.

What is Probability ?

Mathematical explanations of the likelihood that an event will occur or that a statement is true are referred to as probabilities.

x:- Number of crimes solved

X  = B( n = 5 , p = 0.3 )

P[x ] =\((\frac{n}{x})\)* \(p^{x}\) * \((1-p)^{x}\)

Probabilty  that exactly 2 of these 5 crimes will be solved

P[x = 3] = binomial(5,2) * .3² * 0.7³ = 0.441

Hence the probabilty that exactly 2 of these 5 crimes will be solved is 0.441.

Learn more about Probability , by the following link.

brainly.com/question/13604758

#SPJ4

Answer:

0,01

Step-by-step explanation:

0,0001 = 1 / 10000

√0,0001

= √( 1 / 10000 )

= √1 / √10000

= 1 / 100

= 0,01

The quantities needed to make multiple loaves of bread can be solved for by multiplying each recipe used for a loaf of bread by number of loaves of bread

A loaf of bread

2 loaves of bread

multiply each ingredients by 2

3 loaves of bread

multiply each ingredients by 3

4 loaves of bread

multiply each ingredients by 4

Learn more about ratio and proportion:

https://brainly.com/question/1781657

#SPJ1

The percent of area under a normal curve between the mean and −1.18 standard deviations is 38.10% and between z=−1.6 and z = 0.7 is 70.32% and the​ z-score that best satisfies the condition is z=−0.4.

To find the percent of area under a normal curve between the mean and −1.18 standard deviations from the mean, we need to use a standard normal distribution table or calculator.

The area to the left of −1.18 standard deviations is 0.1190, and the area to the left of the mean is 0.5000. To find the area between them, we subtract the smaller area from the larger area:

0.5000 - 0.1190 = 0.3810

Therefore, the percent of area under a normal curve between the mean and −1.18 standard deviations is 38.10%.

To find the percent of the total area under the standard normal curve between z=−1.6 and z = 0.7, we again need to use a standard normal distribution table or calculator.

The area to the left of −1.6 is 0.0548, and the area to the left of 0.7 is 0.7580. To find the area between them, we subtract the smaller area from the larger area:

0.7580 - 0.0548 = 0.7032

Therefore, the percent of the total area between z=−1.6 and z = 0.7 is 70.32%.

To find the​ z-score that best satisfies the condition that 36% of the total area is to the left of z, we need to use a standard normal distribution table or calculator.

We look for the z-score that corresponds to a cumulative probability of 0.36. This is approximately −0.4, which means that 36% of the total area under the standard normal curve is to the left of z=−0.4. Therefore, the​ z-score that best satisfies the condition is z=−0.4.

To Lear learn more about standard deviation and z-score go to:

https://brainly.com/question/17063183#

#SPJ11

The required number of multiplications using a single composite transformation matrix for k transformations of n points is n × k.

In computer graphics, composite transformation matrices are used to transform points and shapes. These matrices are created by combining multiple transformations into a single matrix, allowing for efficient processing of large amounts of data. The number of multiplications required to perform a composite transformation depends on the number of points being transformed and the number of transformations being applied.

If there are n points and k transformations, then the required number of multiplications is n × k.

This is because each point needs to be multiplied by the composite transformation matrix k times.

Therefore, the total number of multiplications is n × k.

To learn more about “transformation matrices” refer to the https://brainly.com/question/20366660

#SPJ11

130 pounds weight is equivalent to 59.09 kg.

To convert pounds (lb) to kilograms (kg), you can use the conversion factor of 1 lb = 0.453592 kg. So to convert 130 lb to kg, you would multiply 130 by 0.453592.

This gives you the equivalent weight of 59.09 kg. It's worth noting that the pound is a unit of weight commonly used in the United States and the United Kingdom, while the kilogram is the standard unit of mass in the International System of Units (SI). It's important to use the correct unit of measurement when working with weights and masses in different contexts.

The conversion factor can be memorized or looked up in a conversion table or calculator. It's important to note that the pound and kilogram are both units of measurement for weight, however, the pound is used mainly in the United States and United Kingdom, while the kilogram is widely used across the world and is the standard unit of weight under International System of Units (SI).

To know more about conversion factor on the link below:

brainly.com/question/30166433#

#SPJ11

We have two right-angled triangles that share a common side, with side lengths 6 and 10. Let's label the sides of the triangles as follows:

Triangle 1:

Side adjacent to the right angle: 6 (let's call it 'a')

Side opposite to the right angle: x (let's call it 'b')

Triangle 2:

Side adjacent to the right angle: x (let's call it 'c')

Side opposite to the right angle: 10 (let's call it 'd')

Using the Pythagorean theorem, we can write the following equations for each triangle:

Triangle 1:\(a^2 + b^2 = 6^2\)

Triangle 2: \(c^2 + d^2 = 10^2\)

Since the triangles share a common side, we know that b = c. Therefore, we can rewrite the equations as:

\(a^2 + b^2 = 6^2\\b^2 + d^2 = 10^2\)

Substituting b = c, we get:

\(a^2 + c^2 = 6^2\\c^2 + d^2 = 10^2\)

Now, let's add these two equations together:

\(a^2 + c^2 + c^2 + d^2 = 6^2 + 10^2\\a^2 + 2c^2 + d^2 = 36 + 100\\a^2 + 2c^2 + d^2 = 136\)

Since a^2 + 2c^2 + d^2 is equal to 136, we can conclude that x (b or c) is between 11 and 12

For more such questions on right angled triangle.

https://brainly.com/question/64787

#SPJ8

The statement "the sampling distribution of the difference between the two sample means will have a mean of one" is not necessarily true, and neither is the statement "will have a variance of one" or "can be approximated by any distribution."

The sampling distribution of the difference between two sample means from independent populations will have a mean equal to the difference between the population means. However, the variance of the sampling distribution will depend on the sample sizes and the variances of the two populations.

If the sample sizes are large enough (usually considered to be greater than or equal to 30) and the population variances are known or assumed to be equal, then the sampling distribution of the difference between two sample means can be approximated by a normal distribution.

Therefore, the statement "the sampling distribution of the difference between the two sample means will have a mean of one" is not necessarily true, and neither is the statement "will have a variance of one" or "can be approximated by any distribution." However, the statement "can be approximated by a normal distribution" is generally true if the sample sizes are large enough and the population variances are known or assumed to be equal.

for such more question on sampling distribution

https://brainly.com/question/15713806

#SPJ11

Answer: 5n²-13n+6=(n-2)(5n-3)=0

Step-by-step explanation:

\(5n^2-13n+6=0\\\\5n^2-10x-3n+6=0\\\\5n(n-2)-3(n-2)=0\\\\(n-2)(5n-3)=0\)

The Equation of the Line is y = 0 which is the equation is of the X-axis

What is Slope of Line?

The slope is defined as the ratio of "rise" divided by "run" between two points on a line, or the ratio of altitude change to horizontal distance between any two locations on the line.

We are given that the slope of the line is 0

and, the intercept point is (4, 0)

Equation of line: y - y1 = m (x - x1)

y - 0 = 0

y = 0

Implies that the equation is of the X-axis

To learn more about Slope of a Line from the given link

https://brainly.com/question/3493733

#SPJ1

A. To represent the value of the car as a function of time, we can use the formula for exponential decay:

Value = Initial Value * (1 - Rate)^(Time)

In this case, the initial value is $18,000 and the rate of depreciation is 1.2% or 0.012. The function can be written as:

Value = $18,000 * (1 - 0.012)^(Time)

Using technology, such as a calculator or spreadsheet software, you can estimate the number of years it will take for the value to reach each given amount by solving for Time in the above equation. Simply substitute the given value for Value and solve for Time.

B. To find the number of years it will take for the value to reach $17,000, solve the equation:

$17,000 = $18,000 * (1 - 0.012)^(Time)

C. To find the number of years it will take for the value to reach $15,000, solve the equation:

$15,000 = $18,000 * (1 - 0.012)^(Time)

D. To find the number of years it will take for the value to reach half of the starting value ($9,000), solve the equation:

$9,000 = $18,000 * (1 - 0.012)^(Time)

E. To find the number of years it will take for the value to reach one-third of the starting value ($6,000), solve the equation:

$6,000 = $18,000 * (1 - 0.012)^(Time)

G. To find the number of years it will take for the value to reach $10,000, solve the equation:

$10,000 = $18,000 * (1 - 0.012)^(Time)

By solving these equations using technology, you can estimate the number of years it will take for the car's value to reach each given amount based on the given rate of depreciation.

Learn more about exponential here

https://brainly.com/question/30127596

#SPJ11

Answer:

S= 5, L= 12

Step-by-step explanation:

To find the value of L and S, we need to first label the 2 equations.

L +S= 17 -----(1)

3L +2S= 46 -----(2)

From (1):

L= 17 -S -----(3) (-S on both sides)

Subst. (3) into (2):

3(17-S) +2S= 46

3(17) -3S +2S= 46 (expand)

51 -S= 46

-S= 46 -51 (-51 on both sides)

-S= -5

S= 5 (divide by -1 throughout)

Subst. S=5 into (3):

L= 17 -5

L= 12

The value of ∠ADC is,

⇒ ∠ADC =  108°.

Since, We know that,

An angle is combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

We have to given that;

In the circle P,

ABCD is inscribed quadrilateral.

And, ∠DAB = 110°,

⇒ ∠ABC = 72°

Hence, To find the value of ∠ADC.

We know that,

Theorem:

A quadrilateral can be inscribed in a circle if and only if the opposite angles are supplementary that is, sum of the opposite angles will be 180°.

Hence, According to the theorem,

⇒ ∠ABC + ∠ADC = 180°

⇒ ∠ADC + 72 = 180

⇒ ∠ADC = 108°

Therefore, We get;

The value of ∠ADC is 108°.

Learn more about the angle visit:;

https://brainly.com/question/25716982

#SPJ1

The size of the typical sampling error in repeated sampling of 20 rods would be 5 millimeters.

The concept of sampling error is related to the idea of sampling from a population to estimate a population parameter. It is the difference between the sample statistic (e.g. mean) and the population parameter.

A sampling error in repeated sampling occurs when the mean of a sample differs from the population mean as a result of randomly selecting a sample. In the case of the given problem, the mean of the entire batch of steel rods is 170 millimeters and the standard deviation is 10 millimeters.

The size of the typical sampling error in this case can be estimated using the formula:

Sampling Error = Standard Error × Standard Deviation/Square Root of Sample Size

Plugging in the given values, the sampling error will be:

Sampling Error = 10 × 10/ √20 = 5 millimeters

Therefore, the size of the typical sampling error in repeated sampling of 20 rods would be 5 millimeters.

Learn more about the random sample here:

https://brainly.com/question/12719656.

#SPJ4

Answer:

10 and 6 I believe

Answer:

A - 7 = -13

Add 7

A = -6

10X - 8 = 9X + 8

Add 8

10X = 9X + 16

Subtract 9X

X = 16

In a right triangle, where a and b are the shorter sides, and c is the longer side a^2+b^2=c^2

Thus, plug in the values.

12^2+16^2=20^2

144+256=400

400=400.

Because the equation is true, 12, 16, and 20 can be a right triangle

Hope it helps <3

Answer:

For the first question/equation, A=-6. You can just add seven on both sides.

A-7+7=-13+7          A=-6

For the second question, X=16. You can minus 9x on both sides, then plus 8 on both sides. 10X-9X-8+8=9X-9X+8+8=X=16

For the last one, yes, it can because of 12^2+16^2=20^2. Which simplified is . 144+256= 400. So, yeah. It can be a right triangle.

Answer:$4029

Step-by-step explanation:

Given

Principal amount \(P=\$8000\)

Interest rate \(R=6\%\)

Time period \(T=7\ yr\)

Amount after T years is given by

\(A=P[1+R\%]^T\)

Put values

\(\Rightarrow A=8000[1+0.06]^7\\\Rightarrow A=\$12,029\)

Interest is the difference of amount and principal, that is

\(\Rightarrow C.I.=12,029-8000=\$4029\)

The midpoint of AR is (1/2 , 1).

Let the points be:

A(0,0) = (x₁,y₁)

B(1,2) = (x₂,y₂)

Midpoint = (x₁₊x₂/2) , (y₁₊y₂/2)

A location in the middle of a line connecting two points is referred to as the midpoint. The midpoint of a line is located between the two reference points, which are its endpoints. The line that connects these two places is split in half equally at the halfway. In addition, the halfway is reached if a line is drawn to divide the line that connects these two places.

= (0₊1/2) , (0₊2/2)

=(1/2 , 2/2)

= (1/2 , 1)

hence the midpoint of the number line is  (1/2 , 1).

Learn more about midpoint form here:

https://brainly.com/question/5566419

#SPJ9