The table below shows the results of a survey about vacation destinations and the length of those vacations.

Which of the following includes the correct relative frequency and conclusion based on the table?
A
The relative frequency for traveling in state for longer than a week is 17%. This could be low because people want to spend more time if they have traveled farther.
B
The relative frequency for traveling out of state for longer than a week is 48%. This could be high because people want to spend more time if they have traveled farther.
C
The relative frequency for traveling in state for longer than a week is 30%. This could be low because people want to spend more time if they have traveled farther.
D
The relative frequency for traveling out of state for longer than a week is 83%. This could be high because people want to spend more time if they have traveled farther.

Answer:

-46438023156

Step-by-step explanation:

\(\\ \sf\longmapsto -6p+7=3(2p-3)-4(-10+4p)\)

\(\\ \sf\longmapsto 7-6p=6p-9+40-16p\)

\(\\ \sf\longmapsto 7-6p=-10p+31\)

\(\\ \sf\longmapsto 7-31=-10p+6p\)

\(\\ \sf\longmapsto -24=-4p\)

\(\\ \sf\longmapsto 4p=24\)

\(\\ \sf\longmapsto p=6\)

Answer:

Step-by-step explanation:

(-2 , 6)

Slope = m = -1

y =mx + b

y = -x +b

Plugin x = -2 and y = 6

6 = -(-2) + b

6 = 2 + b

6-2 = b

b = 4

y = -x + 4

x + y = 4

The correct option is option D. That is, R'(4,1). The RST coordinates of the given point is: (4,1).

The midpoint is the spot that is in the center of a line that connects two locations. The two reference points that make up a line's endpoints are where it finds its middle. At the halfway point, the line that links these two locations is evenly divided in half. Additionally, if a line is drawn to split the line that links these two points, the midway point is achieved. The midpoint formula may be used to determine the midpoint between two locations when we know their coordinates. The midpoint formula may be used to determine the coordinates of the other endpoint if we know the midpoint's coordinates as well as those of the other endpoint. RST coordinate is (4,1).

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Answer:

Hi there!

Your answer is:

6x^3 -10x^2 +3x -16

Step-by-step explanation:

2x^3 +5x -16 +4x^3 -10x^2 -2x

Combine like terms

6x^3 -10x^2 +3x -16

Hope this helps!

The addition of the polynomial is 6x³ - 10x² + 3x - 16.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

Given:

(2x³+5x−16)+(4x³−10x²−2x)

Now, Adding the above polynomial

=  (2x³+5x−16)+(4x³−10x²−2x)

= 2x³ + 4x³ −10x² + 5x - 2x - 16

= 6x³ - 10x² + 3x - 16

Hence, the polynomial addition gives  6x³ - 10x² + 3x - 16.

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The longest poster that can fit in the box must have dimensions of 10 inches (height) by 20 inches (length) by 12 inches (width).

To find the longest poster that can fit in the box, we need to determine the longest dimension of the box itself. Since the box is 10 inches high, the longest poster that can fit in the box must have a height of no more than 10 inches.

Now, we need to consider the other two dimensions of the box. The box is 20 inches long and 12 inches wide, so the longest poster that can fit in the box must have a length of no more than 20 inches and a width of no more than 12 inches.

As for why we can only fit one maximum-length poster in the box but we can fit multiple 22-inch posters in the same box, it's because the length and width of the box are larger than the length and width of the 22-inch poster.

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Answer:

x=-21

Step-by-step explanation:

x+5x-7(2+x)=7 so 6x-14-7x=7

-x=21 so x=-21

Answer:

\((x + 2)(x + 3)\)

\(x(x + 3) + 2(x + 3)\)

\( {x}^{2} + 3x + 2x + 6\)

\( {x}^{2} + 5x + 6\)

We have proved that square matrix A is invertible if and only if A^T A is invertible.

Given that we have to prove that a square matrix A is invertible if and only if A^T A is invertible.

Proof :We are given that A is a square matrix. Suppose A is invertible. Let A^(-1) be the inverse of A.

We want to prove that A^T A is invertible. That is, we want to show that there exists a matrix B such that (A^T A)B = B(A^T A) = I. In other words, we want to show that A^T A is invertible, and that its inverse is B.

To prove this, let B = A^(-1)(A^T)^(-1). Then,(A^T A)B = A^T AA^(-1)(A^T)^(-1) = I(Because A^(-1)A = I and (A^T)^(-1)A^T = I)

Similarly ,B(A^T A) = A^(-1)(A^T)^(-1)A^T A = IA^(-1)(Because (A^T)^(-1)A^T = I)

Hence A^T A is invertible and its inverse is B.

Thus we have shown that if A is invertible then A^T A is also invertible.

Now suppose A^T A is invertible. We want to show that A is invertible. To prove this, we will show that the equation Ax = 0 has only the trivial solution x = 0.

Suppose that Ax = 0, where x is a column vector. Then we have,A^T Ax = A^T 0 = 0

This equation implies that x is in the null space of A^T A. But since A^T A is invertible, the null space of A^T A is {0}. Therefore, x = 0, and we have shown that the only solution to Ax = 0 is x = 0. Hence A is invertible.

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Answer:

x=0 y=5

trust me I think its right

The probability of catching a defect is approximately 99.9768%.

To calculate the probability of catching a defect, we need to consider the complement of the event, which is the probability of not catching a defect in any of the four inspections.

The probability of not catching a defect in inspection 1 is 1 - 0.9 = 0.1 (since the complement of catching a defect is not catching a defect). Similarly, the probabilities of not catching a defect in inspections 2, 3, and 4 are 1 - 0.8 = 0.2, 1 - 0.12 = 0.88, and 1 - 0.95 = 0.05, respectively.

Since the inspections are independent events, we can multiply these probabilities together to find the probability of not catching a defect in all four inspections: 0.1 × 0.2 × 0.88 × 0.05 = 0.0088.

Therefore, the probability of catching a defect is 1 - 0.0088 = 0.9912, or approximately 99.9768%.

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The equation of the line in point-slope form, with slope equal to 5/6 and passing through the point located at (22 , 12), is (y - 12) = 5/6(x - 22).

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values to set up the equation.

(y - y1) = m(x - x1)

where m = 5/6 and (x1 , y1) = (22 , 12)

(y - 12) = 5/6(x - 22)

In slope-intercept form, the equation of the line is:

(y - 12) = 5/6(x - 22)

y - 12 = 5/6 x - 110/6

y = 5/6 x - 19/3

In standard form, the equation of the line is:

y = 5/6 x - 19/3

5/6 x - y = 19/3

Multiplying both sides by 6,

5x - 6y = 38

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Answer:

y=-1/2x+2

Step-by-step explanation:

You must first flip and change your slope in the original equation (so, 2x would turn to -1/2). Then use the equation y-y1-=m(x-x1) and plug in the new slope and the coordinates (so, (y-3=-1/2(x-(-2)) which now turns to (y-3=-1/2(x+2)) because a negative times a negative is a positive so now your equation will be (y-3=-1/2x-1) then add 3 so (y=-1/2x+2).

Hope this helped!

There are 20 ways to select president, 19 ways to select vice-president, 18 ways to select treasurer.

In this case, the task is to select a president, a vice-president, and a treasurer from the math club, and no member can hold more than one office. There are 20 choices for the president, since there are 20 members in the club and each member is eligible to be president. There are then 19 choices for the vice-president, since the president cannot also be the vice-president. Finally, there are 18 choices for the treasurer, since the president and vice-president cannot also be the treasurer.

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the area inside the curve R is approximately 42.4115 square units.

To find the area inside the curve R, we can use a double integral. The formula for finding the area of a region using a double integral is:

A = ∬R dA

where A is the area of the region R, and dA is an infinitesimal element of area in the region R.

In polar coordinates, dA can be expressed as:

dA = r dr dθ

where r is the radius and θ is the angle.

Substituting this into the formula for the area, we get:

A = ∫₀^2π ∫₀^(5+sinθ) r dr dθ

We can evaluate this integral by integrating first with respect to r and then with respect to θ:

A = ∫₀^2π [1/2 r²] from 0 to (5+sinθ) dθ

A = ∫₀^2π 1/2 (5+sinθ)² dθ

Expanding the square and simplifying, we get:

A = ∫₀^2π 1/2 (25 + 10sinθ + sin²θ) dθ

A = 1/2 ∫₀^2π (25 + 10sinθ + sin²θ) dθ

Using the trigonometric identity sin²θ = (1-cos2θ)/2, we can simplify this to:

A = 1/2 ∫₀^2π (25 + 10sinθ + 1/2 - 1/2cos2θ) dθ

A = 1/2 ∫₀^2π (27/2 + 5sinθ - 1/2cos2θ) dθ

Integrating each term separately, we get:

A = 1/2 [27/2θ - 5cosθ + 1/4sin2θ] from 0 to 2π

A = 1/2 [(27/2)(2π) - 5cos2π + 1/4sin2(2π) - (27/2)(0) - 5cos0 + 1/4sin0]

A = 1/2 (27π)

A = 13.5π

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Answer:

x<5

Step-by-step explanation:

(3x<15)

Divide both sides by 3. Since 3 is positive, the inequality direction remains the same.

x<15/3

Divide 15 by 3 to get 5.

x<5

To calculate the cost of shortage (Cs), we need to find the area under the normal distribution curve to the left of the optimal service level. The cost of shortage is the difference between the selling price and the Monday price, multiplied by the probability of shortage.

To calculate the cost of excess (Ce), we find the area under the normal distribution curve to the right of the optimal service level. The cost of excess is the difference between the cost of making the cake and the selling price, multiplied by the probability of excess. The optimal service level is determined by minimizing the total cost, which is the sum of the cost of shortage and the cost of excess. We can find the corresponding z value for the optimal service level using the standard normal distribution table. Once we have the optimal service level (z value), we can find the corresponding demand value. Since demand is normally distributed, we can calculate the optimal number of birthday cakes to make for the weekend by subtracting the expected demand from the optimal service level demand. However, without specific information on the desired service level or target level of shortage/excess, it is not possible to provide numerical answers to the questions. The optimal service level, corresponding z value, and the optimal number of cakes will depend on the specific parameters and objectives of the supermarket bakery.

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Mia’s distance from the river is decreasing in the interval  0 < t < 2.5 and

Mia drives 100 miles to the beach.

The complete question is added at the end of this solution as an attachment

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

The graph

On the graph, we can see that the values of the graph decrease from t = 0 to t = 2.5

When represented as an interval, we have

0 < t < 2.5

Hence, the decreasing interval is 0 < t < 2.5

From the graph, we can see that the distance travelled in each half is 50 miles

So, the total distance is

total =50 + 50

Evaluate

total = 100

Hence, the total distance travelled is 100 miles

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Complete question

Mia crosses a river when she drives from her house to the beach. The graph of the function d(t) = 40|t − 1.25| shows Mia’s distance from the river d, in miles, after t hours.

The domain of the function is 0 ≤ x ≤ 2.5. The graph shows her entire trip

Complete each sentence to make a true statement.

Mia’s distance from the river is decreasing in the interval  Choose... 0 < t < 1.25 or 1.25 < t < 2.5  .

Mia drives  Choose... 40 or 80 or 60 or 100  miles to the beach.

Complete Question

A certain 50 cm spring will stretch (in  cm) one fifth  the weight (in kg) attached to  it. How long will the spring be if a 35  kg weight is attached to it

Answer:

The value is \(L_w = 57 \ cm\)  

Step-by-step explanation:

The length of the spring is \(L = 50 \ cm = 0.5 \ m\)

 The  mass attached to it is  \(w = 35 \ kg\)

Generally given from that the spring will stretch one fifth of the weight  (in kg)attached to it , it then means that the  new length of the spring whenever a weight is attached to it is mathematically represented as

          \(L_w = L + \frac{W}{5}\)

=>      \(L_w = 50 + \frac{35}{5}\)  

=>      \(L_w = 57 \ cm\)  

Viksim, this is the solution:

• Alex's base salary = $ 2,200

• Alex's commision = 10% of total vacuum cleaners or 0.1

• Total sales one month = $ 4,300

In consequence,

• Total salary = Base salary + Commission

• Total salary = 2,200 + (0.1 * 4,300)

• Total salary = 2,200 + 430

• Total salary = 2,630

Alex earned $ 2,630 of total salary

Answer:

Dude dont spend 100 points! This place is scamming people

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

each jump will increase 3.5

order: 2   3   4    5    6     7

num:   5 8.5 12 15.8 19 22.5

Answer:

  (-1, 0) and (4, 5)

Step-by-step explanation:

You want the solution to the simultaneous equations ...

The function f(x) is equal to itself, so we can write ...

  x² -2x -3 = x +1

  x² -3x -4 = 0 . . . . . . . . subtract (x+1)

  (x -4)(x +1) = 0 . . . . . . . factor

  x = 4  or  x = -1 . . . . . . . values that make the factors zero

  f(x) = x+1 = 5 or 0

The solutions are (x, f(x)) = (-1, 0) and (4, 5).

__

Additional comment

There are numerous ways to solve the equations. We like a graphing calculator for its speed and simplicity. The quadratic can be solved using the quadratic formula, completing the square, factoring, graphing, using a solver app or your calculator.

The constants in the binomial factors are factors of -4 that total -3.

  -4 = (-4)(1) = (-2)(2) . . . . . . sums of these factors are -3, 0

The factor pair of interest is -4 and 1, giving us the binomial factors ...

  (x-4)(x+1) = x² -3x -4.

The "zero product rule" tells you this product is zero only when one of the factors is zero. (x-4) = 0 means x=4, for example.

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Answer:

=0

Step-by-step explanation:

Answer:

All real numbers (infinite amount of x solutions)

Step-by-step explanation:

Distribute the 2: 2x+8-1=2x+7

Combine like terms: 2x+7=2x+7

Since both sides are equal, you could not get x alone, so there is an infinite number of solutions for x (you could put any number for x and they would equal).

The amount of interest for the year was 3,770 cents, and the regular price of the electric drill that Pamela bought before the discount was 21,927 cents

Interest = P x R x T.

Where:

P = Principal amount (the beginning balance).

R = Interest rate

T = Number of time periods

In this case, we are given that;

Principal amount (P) = $580

Interest rate (R) = 6,5 %

Time = 1 year

Hence, The amount of the interest = 6,5% of $580

                                                     = 0.065 × $580

                                                     = $37.7

1 dollar = 100 cents

Hence, $37.7 = 37.7 × 100 cents equal to 3,770 cents

P = (1 – d) x

Where,

P = Price after discount

D = discount rate

X = regular price

In this case, we are given that:

P = $32.89

D = 85% = 0,85

Hence, the regular price:

P = (1 – D) x

32.89 = (1 – 0.85) X

32.89 = 0.15X

X = 32.89/0.15

X= 219.27

1 dollar = 100 cents

Hence, $219.27 = 219.27 × 100 cents equal to 21,927 cents

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Answer: 17

Step-by-step explanation:)

Answer:

7.7 %

Step-by-step explanation:

352-325

=27

27/352 x 100/1

7.670

=7.7%

Answer: 7.7%

Step-by-step explanation:

1. 352 - 325 = 27. This is how many students left.

2. x/100 = 27/352 is the equation.

3. Solve for x: 2700/352 = x = 7.6704

This rounded to the nearest tenth is 7.7%

The given equation's solution is x = 5i or x = i.

An equation has been provided.

x⁴+6x²+5 = 0

We to settle it utilizing replacement.

If u = x2, then u2 = x4 In the above equation, we find that u2+6u+5 = 0. Now, use the factorization method.

Divide the middle term of the previous equation as follows: u2+5u+u+5 = 0; u(u+5)+1(u+5) = 0; u(u+5)(u+1) = 0 Using the zero-product property, we can determine that u+5 or u+1 equals 0; u = -5 or u = -1; x2 equals -5 or x2 equals -1; taking the square root of both sides of.

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Answer:

3 and 5

Step-by-step explanation:

If you do the vertical line test those ones do not pass. The vertical line test is the test you do to see if it is a function. You draw a vertical line and if that line crosses the graphed line only once it is a function.