James and Padma are on opposite sides of a 100-ft-wide canyon. James sees a bear at an angle of depression of 45 degrees. Padma sees the same bear at an angle of depression of 65 degrees.


​​What is the approximate distance, in feet, between Padma and the bear?


A


21. 2ft


B


75. 2ft


C


96. 4ft


D


171. 6ft

Answer:

2x - 8 = 12  has the same solution as 12/x-4 = 2

Step-by-step explanation:

They both equal 10

The solution to the linear equation can be found to be :

To solve this system of linear equations, first, we'll eliminate the fractions by finding the least common multiple (LCM) of the denominators and then multiplying each equation by the LCM.

x + 2y = 24

x + 8y = 48

Subtract equation (1) from equation (2) to eliminate x:

(8y - 2y) = (48 - 24)

6y = 24

Now, we can solve for y:

y = 24 / 6

y = 4

Now that we have y, we can substitute it into equation (1) to solve for x:

x + 2(4) = 24

x + 8 = 24

x = 24 - 8

x = 16

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If X is a normally distributed random variable and X ~ N(μ, σ), then the z-score is:                              z = x−μ/ σ

The z-score indicates the number of standard deviations that the value x is above (right) or below (left) the mean μ. Values ​​of x greater than the mean have positive z values, and values ​​of x less than the mean have negative z values. The z-score of x is zero if x is equal to the mean.

The standard normal distribution is the normal distribution of standardized values ​​called z-scores. Z-scores are measured in units of standard deviation. For example, if the normal distribution has a mean of 5 and a standard deviation of 2, then the value 11 is 3 standard deviations above (or to the right of) the mean. Here's the calculation:

                      x = μ + (z)(σ)  

                         = 5 + (3)(2)

                         = 11

The standard normal distribution has zero mean and one standard deviation. The transformation

                                    z= x − μ/σ

gives the distribution Z ~ N(0, 1). The value x comes from a normal distribution with mean μ and standard deviation σ.

The next two videos explain what it means to have a "normal" distributed data set.

If X is a random variable and follows a normal distribution with mean µ and standard deviation σ, the rule of thumb states within 1 standard deviation of the mean.

About 95% of the x-values ​​lie between –2σ and +2σ of the mean µ (within two standard deviations of the mean).

About 99.7% of the x-values ​​lie between –3σ and +3σ of the mean μ (within 3 standard deviations of the mean) .

Almost all x-values ​​are within 3 standard deviations of the mean.

1) +1σ and -1σ have z-scores of +1 and -1 respectively.

2) +2σ and -2σ have Z-scores of +2 and -2 respectively.

3) +3σ and -3σ have Z-scores of +3 and -3 respectively.

The rule of thumb is also known as the 68-95-99.7 rule.

The exact value used to calculate the median; further decreasing the minimum value or increasing the maximum value will not change the median value. Therefore, the median does not use all the information in the data and is therefore shown to be less efficient than the mean or average, which uses all the values ​​in the data. To calculate the average, add the observations and divide by that number.

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Answer:

yes

Step-by-step explanation:

Answer:

C. 126

Step-by-step explanation:

We can use ratios to solve for corresponding side lengths.

\(\frac{140-x}{81} =\frac{x}{9}\)

Cross multiply.

\(9(140-x)=81x\)

\(140-x=9x\)

\(140=10x\)

\(14=x\)

Plug x as 14.

\(140-14=126\)

Answer:

Step-by-step explanation:

Hello,

The table is as below

\(\begin{array}{c|c|c|c} &2&1&-2\\4&\boxed{4}&\boxed{4}&\boxed{-8}\\-8&\boxed{-8}&\boxed{-8}&\boxed{16}\\\ 0&\boxed{0}&\boxed{0}&\boxed{0} \end{array}\)

It gives

\(4x^4+(4-8)x^3-(8+8)x^2+16x=4x^4-4x^3-16x^2+16x\)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

none

Step-by-step explanation:

If (x + h) is a factor of f(x) then f(- h) = 0

Given

f(x) = \(x^{4}\) + x³ - x² + x - 1

If (x + 1) is a factor then f(- 1) = 0

f(- 1) = \((-1)^{4}\) + (- 1)³ - (- 1)² + (- 1) - 1 = 1 - 1 - 1 - 1 - 1 = - 3 ≠ 0

Thus (x + 1) is not a factor

If (x - 1) is a factor then f(1) = 0

f(1) = \(1^{4}\) + 1³ - 1² + 1 - 1 = 1 + 1 - 1 + 1 - 1 = 1 ≠ 0

Thus (x - 1) is not a factor

Dyscalculia is a learning disorder that affects a person’s ability to do the math.

A learning problem called dyscalculia diminishes a person's capacity for math. Similar to how dyslexia impairs reading-related brain regions, dyscalculia interferes with the knowledge and skills connected to math and numbers. Although dyscalculia often first manifests in childhood, it can even affect adults who are unaware of it.

The signs of this condition typically emerge in childhood, particularly as kids start to master the fundamentals of math. However, many adults who suffer from dyscalculia are unaware of it. When forced to do the math, people with dyscalculia frequently experience mental health problems like anxiety, depression, and other distressing emotions.

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Answer:

0.336?

Step-by-step explanation:

The length of side b is 56m, angle A is 45°, and angle C is 67°.

In the given triangle with side lengths a = 74m, b ≈ 56m, and c = 36m, the length of side b is approximately 56m.

To solve the triangle, we can use the Law of Cosines and the fact that the sum of angles in a triangle is 180 degrees. Given angle B = 67°51', we have:

Using the Law of Cosines, we have:

b² = a² + c² - 2ac * cos(B)

Substituting the known values:

b² = 74² + 36² - 2 * 74 * 36 * cos(67°51')

Calculating the value of b:

b ≈ √(74² + 36² - 2 * 74 * 36 * cos(67°51'))

b ≈ 55.92m (rounded to the nearest whole number, b ≈ 56m)

Using the Law of Cosines again, we have:

cos(A) = (b² + c² - a²) / (2 * b * c)

Substituting the known values:

cos(A) = (56² + 36² - 74²) / (2 * 56 * 36)

Calculating the value of A:

A = cos⁻¹((56² + 36² - 74²) / (2 * 56 * 36))

A ≈ 45° (rounded to the nearest whole number)

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180° - A - B

Substituting the known values:

C ≈ 180° - 45° - 67°51'

Calculating the value of C:

C ≈ 67°9' (rounded to the nearest whole number, C ≈ 67°)

Therefore, in the given triangle, the length of side b is approximately 56m, angle A is approximately 45°, and angle C is approximately 67°.

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The function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

Given that,

f(x) = 1 + |2x - 5|

And,

f(x) = {f₁       x < a

         {f₂      x ≥ a

Now,

We have,

f(x) = 1 + |2x - 5|

And,

By definition of absolute value,

|x| = {x        x ≥ 0

       {-x       x < 0

And,

Given the absolute value,

|2x - 5|

Solve for x,

i.e.

2x - 5 = 0

We get,

x = 5/2 = 2.5

i.e.

a = 5/2

i.e.

For all values greater than x = 5/2, 2x - 5 is positive,

And,

For all values less than x = 5/2, 2x - 5 is negative.

So,

|x| = {x        x ≥ 5/2

       {-x       x < 5/2

i.e.

|2x - 5| = {2x - 5        x ≥ 5/2

              {-(2x - 5)       x < 5/2

Now,

f(1) = 1 + |2(1) - 5|

We get,

f₁ = 4

And,

f(2) = 1 + |2(2) - 5|

We get,

f₂ = 2

Hence we can say that the function f(x)=1+|2x-5| in piecewise form without using absolute values will be f₁ = 4, f₂ = 2 and  a = 5/2.

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Answer: 235 people got a real one

Step-by-step explanation:

Answer:

-2 is the answer

Step-by-step explanation:

y=mx+b

b= y intercept

because it is a negative it replaces the addition sign so that it is not a positive 2.

A conditional statement has the same truth value as Contrapositive

Here we have,

to complete the statement:

From the question, we are to determine which type of conditional statement has the same truth value as the original statement

As a general rule, if the truth value of an original statement is True, the truth value of the contrapositive would also be true

Similarly;

If the truth value of an original statement is false, the truth value of the contrapositive would also be false

Hence, a conditional statement has the same truth value as contrapositive

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complete question:

A conditional statement has the same truth value as:

Contrapositive

Converse

, ,

Inverse

Considering the expression of a line, the equation of the line that passes through the points (-9,-7) and (-11,-6) is the equation of the line is y= -1/2x -23/2.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of a line can be calculated as:

m= (y₂ - y₁)÷ (x₂ -x₁)

Substituting the value of the slope m and the value of one of the points in y=mx +b, the value of the "b" can be obtained.

Being (x₁, y₁)= (-9, -7) and (x₂, y₂)= (-11, -6), the slope m can be calculated as:

m= (-6 - (-7))÷ (-11 -(-9))

m= (-6 +7)÷ (-11 +9)

m= (1)÷ (-2)

m= -1/2

Considering point 1 and the slope m, you obtain:

-7= (-1/2)×(-9) + b

-7= 9/2 +b

-7 -9/2= b

-23/2= b

Finally, the equation of the line is y= -1/2x -23/2.

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Answer:

6.5

Step-by-step explanation:

To find the distinct equivalence classes of the relation "r," we need to determine the sets of elements in set "a" that are related to each other based on the given condition. In this case, the condition is that for any "m" and "n" in set "a," "m r n" if and only if "5|(m^2 - n^2)."

To list the distinct equivalence classes using set-roster notation, we need to identify sets of elements that are related to each other under the relation "r." Let's proceed with finding these sets:

Start by picking an arbitrary element "x" from set "a."
Identify all elements "y" in set "a" such that "x r y." In other words, find elements that satisfy the condition "5|(x^2 - y^2)."
Repeat steps 1 and 2 until all elements in set "a" have been considered.
Group all elements found in step 2 for each iteration into distinct sets.

For instance, let's assume set "a" contains the elements {1, 2, 3, 4, 5}. We will go through the steps mentioned above:

Pick 1 from set "a."
Identify elements related to 1: 1 r 4 (since 5|(1^2 - 4^2)), and 1 r 3 (since 5|(1^2 - 3^2)).
Repeat steps 1 and 2 for the remaining elements: 2 r 5 (since 5|(2^2 - 5^2)).
Group the elements found in step 2 into sets: {1, 4, 3}, and {2, 5}.

Therefore, the distinct equivalence classes of "r" are {1, 4, 3} and {2, 5}. The distinct equivalence classes of the relation "r" on set "a" are {1, 4, 3} and {2, 5}. To find the distinct equivalence classes, we need to determine sets of elements in set "a" that are related to each other under the relation "r." The relation "r" is defined as "5|(m^2 - n^2)." This means that for any elements "m" and "n" in set "a," "m r n" if and only if "5" divides the difference between the squares of "m" and "n." Using the set-roster notation, we can list the distinct equivalence classes as {1, 4, 3} and {2, 5}. These sets represent elements that are related to each other based on the given condition. To find these sets, we follow the steps outlined above. Starting with an arbitrary element from set "a," we identify all elements related to it. We repeat this process for all elements in set "a" and group the related elements into distinct sets.

The distinct equivalence classes of the relation "r" on set "a" are {1, 4, 3} and {2, 5}. These sets represent elements that are related to each other based on the given condition "5|(m^2 - n^2)."

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The measure of angle1 and angle3 is equal that is 39° , and the measure of angle2 is 51° .

We know that , Kites have two sets of equivalent adjacent sides and one set up of congruent opposite angles.

So, the sides "AB" and "AD" are equivalent adjacent sides.

From the figure , m∠1 = 39° ,So , m∠2 = 39° ,

We see that , AC and BD are diagonals.

We also know that diagonals of kite always meet at right angles.

Let the diagonals "AC" and "BD" intersect at point O.

So , In Triangle AOB ,

⇒ m∠O + m∠1 + m∠2 = 180° ,

⇒ 90° + 39° + m∠2 = 180° ,

⇒ m∠2 = 180° - (90° + 39°) ,

⇒ m∠2 = 180° - 129° ,

⇒ m∠2 = 51°

Therefore , the required measure of angles are m∠1 = 39°, m∠2 = 51°, m∠3 = 39°.

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The given question is incomplete , the complete question is

Find m∠1 , m∠2 and m∠3 in the kite. The diagram is not drawn to scale.

The dimensions of the region bounded by the curve, y² = x, the lines,  x = 1 and x = 4, and the x-axis exists the dimensions ABCD

Thus area of ABCD = \(\int_1^4 \mathrm{ydx} \\\)

\(& =\int_1^4 \sqrt{\mathrm{x}} \mathrm{dx} \\\)

\($& =\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\frac{3}{2}}\right]_1^4 \\\)

\($& =\frac{2}{3}\left[(4)^{\frac{3}{2}}-(1)^{\frac{3}{2}}\right]\)

simplifying,

\($& =\frac{2}{3}[8-1] \\\)

Then we get,

\($& =\frac{14}{3} \text { units }\)

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The volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

The given vectors are:

A = [-4, 3, 2] cm, B = [2,1,3] cm and C= [1, 1, 4] cm

In order to calculate the volume of parallelepiped, we will use vector triple product equation:

Volume = A . (BXC)|, where BXC represents the cross product of vectors B and C.

Step-by-step solution:

We have, A = [-4, 3, 2] cm

B = [2,1,3] cm

C = [1, 1, 4] cm

Now, let's find BXC, using the cross product of vectors B and C.

BXC = | i    j     k|                    2      1     3                            1      1     4        | i    j     k |  = -i + 5j - 3k

Where, i, j, and k are the unit vectors along the x, y, and z-axes, respectively.

The volume of the parallelepiped is given by:

Volume = A . (BXC)|

Therefore, we have: Volume = A . (BXC)

\(Volume = [-4, 3, 2] . (-1, 5, -3)\\Volume = (-4 \times -1) + (3 \times 5) + (2 \times -3)\\Volume = 4 + 15 - 6\\Volume = 13\)

Therefore, the volume of the parallelepiped with sides given by vectors A, B and C is 13 cubic cm, which is the final answer.

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By verifying the Pythagorean Theorem for the vectors u and v,

∥u∥²= 2

∥v∥²= 2

∥u+v∥²= 8

u and v are not orthogonal.

We have verified that the conditions of the Pythagorean Theorem hold do not for these vectors.

To verify the Pythagorean Theorem for the vectors u and v, we need to calculate the norm of each vector and the norm of their sum.

The norm of u is √(1² + (-1)²) = √(2).

The norm of v is √(1² + 1²) = √(2).

The norm of u+v is √((1+1)² + (-1+1)²) = √(4) = 2.

Then, we can check if the Pythagorean Theorem holds by verifying if ||u+v||² = ||u||² + ||v||²:

||u||² + ||v||² = 2 + 2 = 4.

||u+v||² = 4.

Therefore, ||u+v||² = ||u||² + ||v||², and we can conclude that the Pythagorean Theorem holds for these vectors. Additionally, since the dot product of u and v is zero (1 × (-1) + 1 × (-1) = -2 + (-1) = -3), we can confirm that u and v are orthogonal.

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The question is -

Verify the Pythagorean Theorem for the vectors u and v.

U=(1,−1), v=(1,1)

Are u and v orthogonal?

Yes

No

Calculate the following values.

∥u∥²=

∥v∥²=

∥u+v∥²=

We draw the following conclusion.

We have verified that the conditions of the Pythagorean Theorem hold _____ (do/do not) for these vectors.

Answer:

No solutions

Step-by-step explanation:

Let's solve your equation step-by-step.

5m−2(m+3)+6/2  

=3m−4/2  

Step 1: Simplify both sides of the equation.

5m−2(m+3)+6/2  

=3m−4/2  

5m+(−2)(m)+(−2)(3)+6/2  

=3m+−2(Distribute)

5m+−2m+−6+3=3m+−2

(5m+−2m)+(−6+3)=3m−2(Combine Like Terms)

3m+−3=3m−2

3m−3=3m−2

Step 2: Subtract 3m from both sides.

3m−3−3m=3m−2−3m

−3=−2

Step 3: Add 3 to both sides.

−3+3=−2+3

0=1

Answer:

There are no solutions

Answer:

No solutions

Step-by-step explanation:

\(5m-2(m+3)+\frac{6}{2} =3m-\frac{4}{2}\)

\(5m-2m-6+\frac{6}{2} =3m-\frac{4}{2}\)

\(5m-2m-6+3 =3m-2\)

\(5m-2m-3 =3m-2\)

\(3m-3 =3m-2\)

\(3m-3+3 =3m-2+3\)

\(3m=3m+1\)

\(3m-3m =3m- 3m+1\)

0 = 1

No solutions

Answer:

B. 38°​

Explanation:

From the given figure, angles x and 142 degrees are on a straight line.

The sum of angles on a straight line is 180 degrees, therefore:

Next, we solve the equation for x:

The correct choice is B.

Answer: i don't care

Step-by-step explanation: I am doing it for the points

sry for not knowing the answer

Answer:

Below

Step-by-step explanation:

f(b) = population in 2015 =   39.1

f(a) = population in 2010 =    36.5

b-a   is   2015 - 2010 = 5 yrs

plug in the values    (39.1 - 36.5) / 5 = .52 million ppl / year

As similarity theorem, the value of x that will make the triangles similar by SSS similarity theorem is 77.

Similarity theorem:

In math, similarity theorem refers the line segment splits two sides of a triangle into proportional segments if and only if the segment is parallel to the triangle's third side.

Given,

Here we need to find the t value of will make the triangles similar by the similarity theorem.

For example, we are told that the 2 triangles are similar by SSS theorem.

Here we know that, SSS means Side - Side -Side and it is a congruence theorem which states that the 3 corresponding sides of two triangles have same ratio, then we can say that the two triangles are congruent by SSS theorem

Therefore, in the triangles ,applying the SSS postulate gives;

=> x/35 = 44/20

Then by applying the multiplication property of equality, let us multiply both sides by 35 to get;

=> x = (44 * 35)/20

When we simplify this one then we get,

=> x = 77

Therefore, the value of x is 77.

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Answer:

3(2x+y)

Step-by-step explanation:

3 is the gcf. So it would be 3(2x+y)

the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587

The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.

To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.

We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.

We the look up the probability for a value of 1 in the z-table, which is 0.1587.

This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.

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Answer:

Step-by-step explanation:

There is no solution as you have two variables and only one equation. The best you can do is solve for one variable as a function of the other.

\(7x^2+11y^2=40\\ \\ 11y^2=40-7x^2\\ \\ y^2=\frac{40-7x^2}{11}\\ \\ y=\sqrt{\frac{40-7x^2}{11}}\)

Answer:20

Step-by-step explanation:hope this helps you

Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store.

Michael is trying to determine where to open two new store locations. He has population data to determine the amount of revenue he will receive for each location.

He is charged a $1000 fee for opening a new store at a certain location. However, he is unsure whether the population of the city would be large enough to warrant opening a new store at that location.

The first step that Michael needs to take is to analyze the population data that he has.

Based on the population data, he needs to make an informed decision about whether or not to open a new store at that location. This would require him to take into consideration the average income of the population as well as the demographics of the city.

Another important factor that Michael needs to take into consideration is the competition in the area. If there are already several stores in the area, then opening a new store might not be a good idea.

This is because the competition would be too high and he would not be able to generate enough revenue to make up for the cost of opening a new store.

However, if there are no stores in the area, then Michael might consider opening a new store. This would require him to invest a significant amount of money, but he could also generate a significant amount of revenue in return.

Additionally, he needs to take into consideration the cost of opening a new store and whether or not he can generate enough revenue to make up for that cost.

Overall, Michael needs to carefully analyze all the data that he has before making an informed decision about where to open new store locations.

In conclusion, Michael needs to analyze the population data, demographics of the city, and the competition in the area to determine whether or not to open a new store. If the population is large enough and there is no competition in the area, then he should consider opening a new store. However, if there is already a significant amount of competition in the area, then he should avoid opening a new store.

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