A company owns two dealerships. The first dealership sells a total of 138 vehicles (cars and trucks). The second dealership sells half as many cars and five times as many trucks as the first dealership, and sells a total of 213 vehicles (cars and trucks).

How many cars do the two dealerships sell in total?

Answer:

x ≤ - 5

Step-by-step explanation:

Given

x - 5 ≤ - 10 ( add 5 to both sides )

x ≤ - 5

Answer:

11,550.

Step-by-step explanation:

Since we are trying to find the number of people in the stadium, we just need to find 75% of 15,400.(The reason is because each seat is for each person)

To calculate this, you have to:

0.75 x 15,400(The percentage is converting a whole number into decimal)

11,550. (And after you solve it, here is the answer)

Hope you have a nice day!!

Answer:

11,550 people are in the stadium when 75% of the seats are occupied.

Step-by-step explanation:

To solve this, we first need to set up our equation to solve the percent.

Our equation is: \(\frac{75}{100} = \frac{x}{15400}\)

To solve, we do cross multiplication.

75*15,400=100x

Now, multiply

1,155,000=100x

Now, divide both sides by 100 to get x by itself.

1,155,000/100=100/100x

11,550= x

As such, 11,550 people are in the stadium when 75% of the seats are occupied.

Answer:

x = 1

Step-by-step explanation:

Both equations can be set equal to each other since they are both equal to y:

\(x-10=-4x-5\\5x-10=-5\\5x=5\\x=1\)

equate both equations !

x - 10 = -4x - 5

5x - 10 = -5

5x = 5

x = 1

therefore x = 1

From the fundamental identities, we know that

By substituting this result into the given expression, we have

Now, by distributing sine of phi into the parentheses, we have

or equivalently,

Now, from the Pythagorean identity:

we can note that

Then, by substituting this result into our last result from above, we obtain

Therefore, the answer is:

Answer:

70

Step-by-step explanation:

Hello there! Let's work this through:

Firstly, we might want to simply 2 1/2 into 5/2, for simplification.

So, we now have 4 * 7 * 5/2

Simplifying we have \(\frac{4*7*5}{2}\)

We see that we can easily simplify 4/2 into 2 * 7 * 5

Further simplifying we get 10*7

Last bit and we get our answer of 70

From here we get 2

Chebyshev's theorem can be used to estimate the minimum proportion of observations that fall within a certain number of standard deviations from the mean. In this case, at least 75% of the daily contributions will fall between 90 and 110, and at least 89% of the daily contributions will fall between 85 and 115.

Given the mean of 100 daily contributions and a standard deviation of 5, we can use Chebyshev's theorem to estimate the proportion of daily contributions that fall within a certain range.

a) To find the percentage of daily contributions between 90 and 110, we need to find the number of standard deviations from the mean that correspond to this range. To do so, we subtract the mean from the upper and lower bounds and divide by the standard deviation (110-100)/5 = 2 and (90-100)/5 = -2. We take the absolute value of -2 to get 2. The minimum proportion of daily contributions that fall within this range is given by the formula 1 - 1/k^2, where k is the number of standard deviations from the mean. Therefore, at least 1 - 1/2^2 = 75% of daily contributions will fall between 90 and 110.

b) To find the percentage of daily contributions between 85 and 115, we repeat the same process and find that this range corresponds to 3 standard deviations from the mean. Therefore, at least 1 - 1/3^2 = 89% of daily contributions will fall between 85 and 115.

If the Empirical Rule were used, the percentages would be larger since the Empirical Rule only applies to normally distributed data and provides exact answers for the proportions. Chebyshev's Theorem, on the other hand, provides approximations and can be used for all probability distributions.

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Answer:

14 units

Step-by-step explanation:

To find the perimeter of a rectangle, use the formula p=2l+2w

First, graph the points.  You can count the units of the length and width of the rectangle. For the length, you'll get 5 units, and for the width, you'll get 2 units.

Use the formula and substitute what we know.

p=2(5)+2(2)

p=10+4

p=14

The perimeter is 14 units.

Option c is correct.

The gradual shifting or movement of a time series to relatively higher or lower values over a longer period of time is called a trend. Therefore, option c. "a trend" is the correct answer.

Periodicity refers to the tendency of a time series to exhibit patterns that repeat at regular intervals, such as daily, weekly, or seasonal cycles.

Regression refers to the statistical method used to analyze the relationship between two or more variables.

A cycle refers to a repeating pattern of fluctuations in a time series that are not necessarily regular or periodic.

Hence, option c is correct.

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a) the expression of P(t) describing the population of crocodiles at any time t is: P(t) = 10 * e\(^{(0.1823t)}\)

b) it would take approximately 4.522 time units (months or years, depending on the unit of t) for the population of crocodiles to reach 30.

a) To determine the expression of P(t) describing the population of crocodiles at any time t, we can use the formula for exponential growth, which states that P(t) = P0 * e\(^{(rt)}\) where P0 is the initial population, r is the growth rate, and t is the time.

Given that the initial population P0 is 10 crocodiles and the population after 6 months is 12 crocodiles, we can use this information to find the value of r.

Using the formula P(t) = P0 * e\(^{(rt)}\) and plugging in the values, we have:

12 = 10 * e\(^{(r * (6/12))}\)

Simplifying further:

12/10 = e\(^{(r/2)}\)

1.2 = e\(^{(r/2)}\)

To find the value of r, we can take the natural logarithm of both sides:

ln(1.2) = r/2

r/2 ≈ 0.1823

Therefore, the expression of P(t) describing the population of crocodiles at any time t is:

P(t) = 10 * e\(^{(0.1823t)}\)

b) To find the population of crocodile species A after 2 years, we substitute t = 2 into the expression we derived in part a:

P(2) = 10 * e\(^{(0.1823 * 2)}\)

P(2) ≈ 10 * e\(^{(0.3646)}\)

P(2) ≈ 10 * 1.4406

P(2) ≈ 14.406

Therefore, the population of crocodile species A after 2 years is approximately 14.406 crocodiles.

c) To determine how long it would take for the population of crocodiles to reach 30, we can set the population P(t) equal to 30 and solve for t in the expression we derived in part a:

30 = 10 * e\(^{(0.1823t)}\)

3 = e\(^{(0.1823t)}\)

Taking the natural logarithm of both sides:

ln(3) = 0.1823t

t = ln(3) / 0.1823

t ≈ 4.522

Therefore, it would take approximately 4.522 time units (months or years, depending on the unit of t) for the population of crocodiles to reach 30.

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Answer:

\(2x^5+3x^4\)

Step-by-step explanation:

\(x^3\left(2x^2+3x\right)\)

Apply distributive law: \(a\left(b+c\right)=ab+ac\)

OAmalOHopeO

Answer:

\(2\sqrt{14}\)

Step-by-step explanation:

To find, do 9^2-5^2=\(\sqrt{x\\}\), so 81-25=56 which is 2\(\sqrt{14}\)

Answer:

\(2\sqrt{14}\)

Step-by-step explanation:

The missing side must be \(2\sqrt{14}\) for the Pythagorean Theorem to be true.

Hope it helps, have a fantastic day.

Answer:

So the probability of this happening is exactly 1 - it must be true

Step-by-step explanation:

If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.

By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.

So the probability of this happening is exactly 1 - it must be true

Answer:

Point D

Step-by-step explanation:

:)

The matrix A of T

a. \(A = [ 0 -1 ]\)

b. \(A = [ 0 -1 ]\)

c. \(A = [ 1/sqrt(2) 1/sqrt(2) ]\)

d. \(A = [ -1/sqrt(2) 1/sqrt(2) ]\)

To find the matrix A of the reflection transformation T in the line \(y = -x\), we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A of the transformation \(T(x) = -x\) for each x in R2, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [-1 0]\) and \(T(e2) = [0 -1]\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ -1 0 ]\)

\([ 0 -1 ]\)

To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 1] / sqrt(2)\)  and \(T(e2) = [-1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) -1/sqrt(2) ]\)

\([ 1/sqrt(2) 1/sqrt(2) ]\)

d. To find the matrix A, we can use Theorem 2.6.2 as follows:

Let e1 = [1 0] and e2 = [0 1] be the standard basis vectors of R2. Then, the images of these basis vectors under T are:

\(T(e1) = [1 -1] / sqrt(2)\) and \(T(e2) = [1 1] / sqrt(2)\)

The matrix A of T with respect to the standard basis is:

\(A = [T(e1) T(e2)] = [ 1/sqrt(2) 1/sqrt(2) ]\)

\([ -1/sqrt(2) 1/sqrt(2) ]\)

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Answer:it is B

Step-by-step explanation:

I swear . On my momma. On god. On everything.

Answer:

B.

Step-by-step explanation:

Answer: 30 degrees

Step-by-step explanation:

1 hour = 60 min = 360 degree

1 min = 360/60 degree

1 min = 6 degree

and the gap of hour hand and minute hand at 1pm, is of 5 min

therefore acute angle formed is 5 X 6 = 30 degrees.

:-)

Answer:

30 degrees

Step-by-step explanation:

1 hour = 60 min = 360 degree

1 min = 360/60 degree

1 min = 6 degree

and the gap of hour hand and minute hand at 1pm, is of 5 min

therefore acute angle formed is 5 X 6 = 30 degrees.

Answer:

They are all true

Step-by-step explanation:

1. 3² +4² = 5²

3x3 + 4x4 = 5x5

  9   +  16  =  25

25 = 25

-----------------------

2. 6² + 8² = 10²

36 + 64 = 100

100 = 100

------------------

3. 9² + 12² = 15²

81 + 144 = 225

225 = 225

-------------------

4. 5² +12² =13²

25 + 144 = 169

169 =169

-------------------

Answer:

(a)  {(3,4),(3,5), (6,8), (6,9),(9,12), (9,13)}

(b) The inverse relation is not a function

Step-by-step explanation:

Inverse Function

If a relation is given as a set of points (x,y), the inverse relation will have the same points with its coordinates switched.

The relation is given as the set:

{(4,3),(5,3), (8,6), (9,6),(12,9), (13,9)}

(a) The inverse relation is:

{(3,4),(3,5), (6,8), (6,9),(9,12), (9,13)}

(b)

A relation is a function if each element of the input set is related to one and only one element of the output set.

The inverse relation is not a function because several points don't meet the above condition. For example, (3,4) and (3,5) relate the element 3 with two elements.

QR factorization is a convenient method to solve linear equations.

By normalizing columns of a matrix A, we obtain Q matrix. And by solving R = QᵀA, we obtain R matrix.

                 Q = [−(1/√2) 3/√10;(1/√2) −1/√10]

                 R = [√32 √8; 0 2√10/√8].

Solution:

In the matrix A= [−4 −2; 4 0], we are to find its QR factorization.

QR factorization of A = [−4 −2; 4 0] can be computed by following these steps:

i) Calculate the magnitude of v1 as 4² + 4² = 32

ii) Normalize the first column of A by dividing it by the magnitude of v1 to obtain the first column of Q.

Thus,

         q1 = [−4/√32, 4/√32]

              = [−2/√8, 2/√8]

               = [−(1/√2), (1/√2)]

iii) Calculate v2 = a2 − projv1(a2)

                          = [4 0] - [−(1/2) −(1/2); (1/2) (1/2)][4 0]

                          = [4 0] − [−2 2] = [6 −2]

iv) Compute the magnitude of v2 as v2 = 62 + (−2)²

                                                                  = 40

v) Normalize v2 to obtain the second column of Q as

                       q2 = [6/√40, −2/√40] = [3/√10, −1/√10]

vi) Form the matrix Q from q1 and q2.

Thus,

             Q = [−(1/√2) 3/√10;(1/√2) −1/√10]

vii) Solve for R in R = QᵀA, which gives

                R = [√32 √8; 0 2√10/√8]

Hence the factorization is,

                 A = QR

                      = [−(1/√2) 3/√10;(1/√2) −1/√10][−4 −2; 4 0]

                       = [√32 √8; 0 2√10/√8]

Therefore, the QR factorization of A = [−4 −2; 4 0] is given as,

                 Q = [−(1/√2) 3/√10;(1/√2) −1/√10] and

                 R = [√32 √8; 0 2√10/√8].

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The expression (x^12)(y^13)(x^5)(y^4) simplifies to x^17 y^17. Therefore, the value of N is 17.

To simplify the given expression, we need to combine the like terms and add their exponents. Let's break down the expression step by step:

(x^12)(y^13)(x^5)(y^4)

First, we can combine the x terms by adding their exponents: x^12 * x^5 = x^(12+5) = x^17.

Next, we combine the y terms by adding their exponents: y^13 * y^4 = y^(13+4) = y^17.

Therefore, the simplified form of the expression is x^17 y^17. From this, we can see that the value of N, which represents the exponent of y, is 17. This means that the original expression is equivalent to x^17 y^17.

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9514 1404 393

Answer:

  21,356,801,630

Step-by-step explanation:

The product can be found using any calculator that will display 11 digits or more.

Of course, it can also be found by long multiplication (second attachment). Many students learn this method in 5th grade.

Answer:

21,356,801,630

Step-by-step explanation:

just use a calculator

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

Answer:

28 feet

Step-by-step explanation:

20 + 10 = 30 - 2 = 28 feet

The dolphin is 20 feet below the surface, goes down another 10 feet, so 30 feet below the surface, and raises two feet, so 28 feet below the surface.

output of the given input/output relationships is 36 and 25.

To illustrate a function, an input-output table can be used, as in the example below. The same function rule connects every pair of numbers in the table. To find each output number, multiply each input number (-value) by 3. ( -value).

Input-output analysis table: what is it?

The table of input-output analysis measures the flows of outputs from one industry as inputs into another (in rows) (in columns). In the input-output analysis paradigm, the original demand shift and its direct, indirect, and induced implications can be used to examine the overall economic impact of an event.

output = input +29

input= 7

output = input +29=7+29=36

input= -4

output = input +29= -4+29=25.

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It is stated that y = 10x + 60 is the equation for the line of greatest fit for all of this data set. indicating that the third choice is the right one.

How can I get the formula for the best fit line?

It is stated that a linear function has the following slope-intercept definition:

y = mx + b.

which contains the following coefficients:

The slope, or m, shows how quickly the function's output changes in relation to its input.

The y-intercept, or b, represents the value that the input function assumes to be zero.

Since the function passes through the given point (0,60), the following is the line's b-intercept:

b = 60.

When x rises by two from zero to two, y rises by twenty from sixty to eighty.

Consequently, the slope m is determined as follows:

m = 20/2 = 10.

Therefore, the following is the line of fit:

y = 10x + 60.

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It is stated that y = 10x + 60 is the equation for the line of greatest fit for all of this data set. indicating that the third choice is the right one.

How can I get the formula for the best fit line?

It is stated that a linear function has the following slope-intercept definition:

y = mx + b.

which contains the following coefficients:

The slope, or m, shows how quickly the function's output changes in relation to its input.

The y-intercept, or b, represents the value that the input function assumes to be zero.

Since the function passes through the given point (0,60), the following is the line's b-intercept:

b = 60.

When x rises by two from zero to two, y rises by twenty from sixty to eighty.

Consequently, the slope m is determined as follows:

m = 20/2 = 10.

Therefore, the following is the line of fit:

y = 10x + 60.

False associations between two variables which are actually influenced by a third variable are known as the Spurious Relationship

Within the context of the question, there are two types of relationships between variables.

These relationships are:

When two variables are influenced by another factor or variable, then the relationship is said to be a spurious relationship;

Otherwise, the relationship is non-spurious relationship

Using the above highlight as a guide, the term that completes the given definition is spurious relationship

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The coordinates of your position are (6, 0, -4).

Throwing a dart at a stationary dart board can be classified as a projectile motion.

:

When a dart is thrown at a stationary dartboard, it follows a curved path known as projectile motion. Projectile motion occurs when an object is launched into the air and moves along a curved trajectory under the influence of gravity, with no other external forces acting on it. In this case, the dart is subjected to the force of gravity but doesn't experience any significant air resistance or external forces once it leaves the hand of the thrower.

The motion of the dart can be described using principles of kinematics. The dart moves in two dimensions: horizontally and vertically. The horizontal motion is uniform and unaffected by gravity, while the vertical motion is influenced by the force of gravity acting in the downward direction. The dart follows a parabolic path, with its maximum height reached at the peak of the trajectory.

To determine the distance and accuracy of the dart throw, various factors need to be considered, such as the initial velocity, launch angle, and the height of the dartboard. These factors can be used to calculate the range, time of flight, and maximum height of the dart.

Throwing a dart at a stationary dartboard involves projectile motion, where the dart follows a curved path influenced by gravity. Understanding the principles of projectile motion can help improve accuracy and distance in dart throwing by considering factors like initial velocity and launch angle. By mastering the art of projectile motion, dart players can enhance their skills and aim for higher scores on the dartboard.

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Therefore, the probability that a randomly selected value is between 215.2 and 241 is approximately 0.1366.

To solve this problem, we need to standardize the values using the z-score formula:

z = (x - μ) / σ

where x is the value of interest, μ is the mean, and σ is the standard deviation.

For the value of 215.2:

z1 = (215.2 - 193.6) / 43.1 = 0.4995 (rounded to 4 decimal places)

For the value of 241:

z2 = (241 - 193.6) / 43.1 = 1.0912 (rounded to 4 decimal places)

Now we can use a standard normal table or calculator to find the area under the standard normal curve between these two z-scores:

P(0.4995 < Z < 1.0912) = 0.1366

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Answer:

a

Step-by-step explanation: