4) Two cars leave the same parking lot, with one heading north and the other heading east.
After several minutes, the northbound car has traveled 8 kilometers, and the eastbound car
has traveled 2 kilometers. Measured in a straight line, how far apart are the two cars? If
necessary, round to the nearest tenth.
Video

Answer: The given line has a slope of -1, since its equation is y = -x + 5. The line that is perpendicular to this line will have a slope that is the negative reciprocal of -1, which is 1. So, we know that the equation of the line we're looking for will have a slope of 1.

To find the equation of this line, we need to use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope of the line, and (x1, y1) is a point on the line.

We know that the point (-2, 5) is on the line we're looking for, and we know that the slope of the line is 1. So we can substitute these values into the point-slope form:

y - 5 = 1(x - (-2))

Simplifying, we get:

y - 5 = x + 2

Adding 5 to both sides, we get:

y = x + 7

Therefore, the equation of the line that passes through the point (-2, 5) and is perpendicular to the line y = -x + 5 is y = x + 7.

Step-by-step explanation:

The first three terms of the sequence Tₙ = n^2 - 2n - 6 are -7, -8, and 0, and the sequence is a quadratic sequence with a parabolic graph that opens upward.

To find the first three terms of the sequence Tₙ = n^2 - 2n - 6, we simply need to substitute the first three positive integers for n, which gives us:

T₁ = 1^2 - 2(1) - 6 = -7

T₂ = 2^2 - 2(2) - 6 = -8

T₃ = 3^2 - 2(3) - 6 = 0

Therefore, the first three terms of the sequence are -7, -8, and 0.

The sequence Tₙ is a quadratic sequence, which means that it has a second-order difference. In other words, the differences between the terms of the sequence form a linear sequence.

Specifically, the first differences are 2, 4, 6, 8, and so on, which form an arithmetic sequence with a common difference of 2. The second differences are all equal to 2, which confirms that the sequence is quadratic.

The graph of the sequence Tₙ is a parabola that opens upward, with a vertex at (1, -7). This means that the sequence starts with a negative term, then decreases until it reaches a minimum at n = 1, and then increases indefinitely.

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In the right-angled triangle ABC the value of line segment BD is obtained as x = 21.91.

What is a right-angled triangle?

Any two sides of a triangle's three sides must always add up to more than the third side since a triangle is a regular polygon with three sides. This distinguishing characteristic of a triangle. A right-angle triangle is one that has angles between its two sides that equal 90 degrees.

A right-angled triangle ABC with drawn with angle B = 90°.

A line BD is drawn which is perpendicular to AC.

The angle BDC is also 90 degrees.

The measure for line segment AD = 12 and CD = 40.

The measure for line segment BD is x.

The side BD is common for triangle ABC and BDC.

So, by the formula of indirect measurement we have -

DC / BD = BD / AD

Substitute the values in the equation -

40 / x = x / 12

x² = 480

x = 21.908

x = 21.91

Therefore, the value of x is obtained as 21.91.

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Answer:

Sin Q

7/25

Cos Q

24/25

Tan Q

7/24

Sin R

24/25

Cos R

7/25

Tan24/7

Step-by-step explanation:

The formula that describes a way to produce each term from the previous term in the given geometric sequence is: aₙ = ¹/₂(2)ⁿ⁻¹

In mathematics, a geometric sequence, is defined as a sequence that consists of non-zero numbers whereby each of the terms after the first is found by multiplying the previous one by a fixed, non-zero number that is referred to as the common ratio.

The formula that is usually utilized in finding the nth term of a geometric sequence is expressed as:

aₙ = arⁿ⁻¹

where:

a is first term

r is common ratio

Thus:

a = 1/2

r = 2/1 = 2

Thus:

aₙ = ¹/₂(2)ⁿ⁻¹

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Answer: 3000m

Step-by-step explanation:

Half of 6 km is 3 km

To convert to meters multiply 3 times 1000

That will give you 3000m=3km

The OLS assumption that is violated when predicted errors have a kurtosis of 5 is normality. The correct option is (d). Kurtosis is a statistical measure of the peak of a probability distribution curve. It measures how the tails of the distribution compare to a normal distribution.

Oridinary Least Squares (OLS) is a regression technique that assumes that the response variable has a linear relationship with the explanatory variable(s) and that the response variable has normal distribution error terms. However, in some cases, such as when the predicted errors have a kurtosis of 5, this assumption of normality is violated. If the distribution has more of its observations in the tails than a normal distribution, it is said to be leptokurtic. If it has fewer of its observations in the tails than a normal distribution, it is said to be platykurtic.

Kurtosis of 5 means that the distribution is leptokurtic and has fatter tails than the normal distribution.Assuming normality of the errors means that the residuals or errors are normally distributed. If the errors are not normally distributed, then the residuals will not be normally distributed either. This will affect the accuracy of the confidence intervals and hypothesis tests. The coefficient estimates may be biased and the confidence intervals may be too wide or too narrow. Therefore, normality of the errors is an important assumption of OLS regression and in this case it has been violated.

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Answer:

6.2 × 10-2

Step-by-step explanation:

The distance between the two points (-6, 8) and (6, 3) is equal to 13 units.

Mathematically, the distance between two (2) points that are on a coordinate plane can be calculated by using this formula:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represents the data points (coordinates) on a cartesian coordinate.

Substituting the given points into the distance formula, we have the following;

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(6 - (-6))² + (3 - 8)²]

Distance = √[(12)² + (-5)²]

Distance = √(144 + 25)

Distance = √169 units.

Distance = 13 units.

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Answer:

1 game, for $5.75

Step-by-step explanation:

To find this answer, all you need to do is create an equation for both Rock and Bowl and the Super Bowling and then set them equal to each other to find out and solve which value of x games makes them equal.

The first equation is 2.75x +3

The second one is 2.25x + 3.5

2.75x + 3 = 2.25x + 3.5

2.75x = 2.25x + .5

From here, you can either solve for x or realize that x being equal to 1 makes both values equal.

So, the answer is 1 game now to plug it into one of our equations, we get

2.75(1) + 3 which we know is equal to the other equation too which is $5.75 dollars

Answer:

8 apples

Step-by-step explanation:

Step-by-step explanation:

n = Nancy's apples.

j = Jay's apples.

a = Ava's apples.

n = 22

n = j × 2

j = n / 2 = 22/2 = 11

j = a + 3

a = j - 3 = 11 - 3 = 8

Ava has 8 apples.

Therefore , the solution of the given problem of probability comes out to be there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

The primary goal of the form of patterns defined as hyper parameters is to calculate the likelihood that a remark is accurate or a specific event will occur. Any number between 0 but instead 1, where 1 usually denotes assurance and range 0 typically connotes possibility, can be used to represent chance. A probability diagram shows the chance that a specific event will occur.

Here,

We must count the number of outcomes in which there are 3 or 4 thunderstorms in order to calculate the chance that a thunderstorm will occur on at least 3 of the following 4 days using the simulation.

We can see from the programme that there are 6 scenarios where there are at least 3 thunderstorms:

=>  1-2-3-4

=>  1-2-4-3

=>  1-3-2-4

=>  1-3-4-2

=>  1-4-2-3

=>  1-4-3-2

Since there are a total of 16 potential outcomes (since a thunderstorm can occur every day or not), the likelihood of at least 3 thunderstorms is:

=> 6/16 = 0.375

This means that there is a 37.5% chance of thunderstorms occurring on at least three of the next four days.

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The angle R is  53.1° by the use of the cosine which is one of the trigonometric ratios that we have.

In trigonometry, the three most important trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions relate the angles of a triangle to the ratios of its sides. For example, the sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse (the longest side of the right-angled triangle).

Cos R = 3/5

R = Cos-1(3/5)

R = 53.1°

Hence, we can see that the required angle R is obtained as  53.1°

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According to the conditions, in right angled triangle, the value of x is 6.

What is angle ?

In mathematics, an angle is a geometric figure formed by two rays (or line segments) that share a common endpoint, known as the vertex of the angle.

In a right-angled triangle, the sum of the two acute angles is always 90 degrees. Therefore, we can use this fact to find the value of x.

We are given that one of the acute angles is 60 degrees, and the other angle is 7x - 12 degrees. So we can write:

60 + (7x - 12) = 90

Simplifying this equation, we get:

7x + 48 = 90

Subtracting 48 from both sides, we get:

7x = 42

Dividing both sides by 7, we get:

x = 6

Therefore, in right angled triangle, the value of x is 6.

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The value of p is 2 and 4.

What is a quadratic equation?

Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation. Any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Here, we have

Given: p² - 6p + 8

we have to solve the quadratic formula or complete the square.

= p² - 6p + 8

= p² -4p - 2p + 8

= p(p-4) -2(p-4)

= (p-4)(p-2)

(p-4)(p-2) = 0

p-4 = 0,

p-2 = 0

p = 4, 2

Hence, the value of p is 2 and 4,

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Answer:

-11.

Step-by-step explanation:

We know that the velocity function v(t) is the derivative of the position function x(t).

So, we can integrate v(t) to find x(t) up to a constant of integration:

∫v(t) dt = ∫(4 - 6t^2) dt = 4t - 2t^3 + C

where C is the constant of integration.

We can find the value of C by using the initial condition that the particle is at position x=7 at t=1:

x(1) = 4(1) - 2(1)^3 + C = 7

C = 5

So, the position function is:

x(t) = 4t - 2t^3 + 5

To find the position of the particle at time t=2, we can substitute t=2 into the position function:

x(2) = 4(2) - 2(2)^3 + 5 = -11

Therefore, the position of the particle at time t=2 is -11.

Answer:%40.50

Step-by-step explanation: i tired

Due to Alex's salary falling inside the 22% tax bracket, his short-term capital gains would be subject to the same rate of taxation as his income.

A profit realized from the sale of a capital asset, such as a piece of personal or investment property, that has been possessed for one year or less is referred to as a short-term gain.

These profits are classified as ordinary income subject to tax at your personal income tax rate. Gain earned by selling assets that are held for a year or less are called short-term capital gains.

Alex is a single taxpayer who has taxable income of $80,000.

His investment income is made up of $2,000 in short-term capital gains and $500 in qualifying dividends.

As a result of his tax rate income falling between 38,601 and 425,800, which is below 15%, his qualifying dividends would be subject to a 15% tax.

Hence, we must deduct 15% of 500 and 22% of 2000 before combining them.

15% x 500

= 15 x 5

=  75

22% x 2000

= 22 x 20

= 440.

The total is = 75 + 440 = 515.

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a) Sample space = {36}

b) Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6

c) Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.

We need to find, What is the size of the sample space? Probability of the sum of the dice is a 7 ?Probability of the sum of the dice is at least a 7? Solution a)Sample space is defined as the set of all possible outcomes. Suppose that you roll two 6 sided dice. So, The possible outcomes of each die is {1,2,3,4,5,6}.The total outcomes for rolling two dice are {1,1}, {1,2}, {1,3}, {1,4}, {1,5}, {1,6}, {2,1}, {2,2}, {2,3}, {2,4}, {2,5}, {2,6}, {3,1}, {3,2}, {3,3}, {3,4}, {3,5}, {3,6}, {4,1}, {4,2}, {4,3}, {4,4}, {4,5}, {4,6}, {5,1}, {5,2}, {5,3}, {5,4}, {5,5}, {5,6}, {6,1}, {6,2}, {6,3}, {6,4}, {6,5}, and {6,6}.Therefore, Sample space = {36}.b)Let E be the event that the sum of the dice is a 7.The events where the sum of the dice is a 7 are {1,6}, {2,5}, {3,4}, {4,3}, {5,2}, and {6,1}.The number of events where the sum of the dice is a 7 is 6.Therefore, Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6.c)Let F be the event that the sum of the dice is at least a 7.Therefore, F = {(1,6), (2,5), (3,4), (4,3), (5,2), (6,1), (2,6), (3,5), (4,4), (5,3), (6,2), (3,6), (4,5), (5,4), (6,3), (4,6), (5,5), (6,4), (5,6), and (6,5)}The number of events where the sum of the dice is at least a 7 is 21.Therefore, Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.a) Sample space = {36}.b) Probability of the sum of the dice is a 7 = P(E) = 6/36 = 1/6.c) Probability of the sum of the dice is at least a 7 = P(F) = 21/36 = 7/12.

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If $40.90 divided by 66, the rounded answer to the nearest set of 40 is given as $0.

To round the answer of $40.90 divided by 66 to the nearest set of 40, we need to perform the division and then round the quotient to the nearest multiple of 40.

First, let's perform the division:

$40.90 / 66 = 0.6206...

The quotient is a decimal, but we need to round it to the nearest multiple of 40. To do this, we need to find out how close the quotient is to each of the multiples of 40 and then round to the nearest one.

The nearest multiples of 40 are 0, 40, 80, 120, etc.

To determine how close the quotient is to each of these multiples, we can subtract the quotient from each multiple and take the absolute value of the result:

|0 - 0.6206| = 0.6206

|40 - 0.6206| = 39.3794

|80 - 0.6206| = 79.3794

The smallest absolute difference is between the quotient and 0, so we round down to 0.

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The length QR of the right angle triangle is 26 cm.

A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.

Therefore, the side of a right angle triangle can be found using Pythagoras's theorem as follows:

Hence,

c² = a² + b²

where

Therefore,

24² + 10² = QR²

576 + 100 = QR²

QR² = 676

QR = √676

QR = 26 cm

Therefore,

length of QR = 26 cm

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Answer:

13/20 written as a decimal is 0.65 and as a percent is 65%

1) Make the denominator 100 (20 x 5)

2) Multiply by five from the numerator too (13 x 5 = 65)

Answer: i believe its 5

Step-by-step explanation:

a. The inequality required is 2x-y≤3 b. We can graph the inequality of x+2y<4. c.  it is not common solution point.

An inequality is a mathematical statement that compares two quantities and indicates whether one is greater than, less than, or equal to the other. Inequalities use special symbols, such as "<" (less than), ">" (greater than), "≤" (less than or equal to), and "≥" (greater than or equal to), to represent the relationship between the two quantities.

For example, the inequality 2x + 3 < 7 means that the quantity 2x + 3 is less than 7. To solve this inequality, we can subtract 3 from both sides to get 2x < 4, and then divide both sides by 2 to get x < 2.

Inequalities can also involve variables, such as x or y, and they can be used to represent real-world situations, such as the amount of money in a bank account, the temperature of a room, or the speed of a car.

Inequalities are important in mathematics and other fields because they allow us to compare quantities and make decisions based on those comparisons. They are used in a variety of applications, including economics, physics, engineering, and statistics.

a. Here the inequality, represented by graph

Take two points lying in the line

(x1,y1)=(0,-3) and (x2,y2)= (2,1)

So,

equation of line is

y+3= [tex]\frac{1-(-3)}{2} (x-0)=[/tex] 2x-y-3=0

Thus, the inequality required is 2x-y≤3.

b. We can graph the inequality of x+2y<4

c. Here, we are not agree with Oscar
Reason:- Since (2,1) point lies on inequality 2x-y≤3 but it did not lie on inequality x+2y<4

So it is not common solution point.

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Step-by-step explanation:

*change density to kg per cubic meter

*change volume to cubic meter

*rearrange the formula to solve for mass

If a square base has a volume of 4 cubic feet, the dimensions that minimize the surface area are: x = 2√2 and h = 4/x^2 = 1/2.

Let x be the side length of the square base and h be the height of the box. Since the volume is 4 cubic feet, we have:

V = x^2h = 4

Solving for h, we get:

h = 4/x^2

The surface area of the box, A, is given by:

A = x^2 + 4xh

Substituting h in terms of x, we get:

A = x^2 + 4x(4/x^2) = x^2 + 16/x

To minimize A, we take the derivative with respect to x and set it equal to zero:

dA/dx = 2x - 16/x^2 = 0

Solving for x, we get:

x = 2√2

To ensure that this is a minimum, we take the second derivative:

d^2A/dx^2 = 2 + 32/x^3

At x = 2√2, this is positive, indicating a minimum.

The box has a square base with side length 2√2 feet and height 1/2 feet.

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(A) The interquartile range for numbers of employees at Mall A is 65 and at Mall B is 7.5. (B) Mall B would we expect to have greater variability in regard to numbers of employees.

Part A: To determine the interquartile range (IQR) for numbers of employees at each mall, we first need to find the median for each mall. The median is the middle value of a set of data when arranged in order.

For Mall A:

Arrange the numbers in ascending order: 18, 20, 21, 22, 25, 26, 27, 28, 28, 29

The median is the average of the two middle numbers, which are 25 and 26.

Median = (25 + 26) / 2

             = 25.5

Next, we need to find the first quartile (Q1) and the third quartile (Q3). The first quartile is the median of the lower half of the data, and the third quartile is the median of the upper half of the data.

For Mall A:

Lower half: 18, 20, 21, 22, 25

Upper half: 26, 27, 28, 28, 29

Q₁ = median of the lower half

    = (21 + 22) / 2

    = 21.5

Q₃ = median of the upper half

     = (28 + 28) / 2

     = 28

The interquartile range for Mall A is:

IQR = Q3 - Q1

      = 28 - 21.5

      = 6.5

For Mall B:

Arrange the numbers in ascending order: 19, 21, 23, 24, 25, 26, 27, 29, 30, 33

The median is the average of the two middle numbers, which are 25 and 26.

Median = (25 + 26) / 2

             = 25.5

Lower half: 19, 21, 23, 24, 25

Upper half: 26, 27, 29, 30, 33

Q₁ = median of the lower half

    = (21 + 23) / 2

    = 22

Q3 = median of the upper half

     = (29 + 30) / 2

     = 29.5

The interquartile range for Mall B is:

IQR = Q3 - Q1

      = 29.5 - 22

      = 7.5

Part B: To determine which mall would have greater variability in regard to numbers of employees, we can compare the interquartile ranges for each mall. The interquartile range measures the spread of the middle 50% of the data. The larger the interquartile range, the greater the variability.

In this case, Mall B has a larger interquartile range than Mall A (7.5 vs. 6.5). This suggests that there is greater variability in the number of employees at Mall B.

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The distance between Thomas St and Denny Way on Broad St is 0.1 miles.

0.45 miles on Aurora Ave is equivalent to the distance between Mercer St and Denny Way on Broad St.

0.2 miles on Aurora Ave is equivalent to the distance between Thomas St and Denny Way on Aurora Ave.

We say X  be the distance between Thomas St and Denny Way on Broad St,

and have the following proportion:

0.45 miles / (Mercer St to Denny Way on Broad St) = 0.2 miles / (Thomas St to Denny Way on Broad St)

Solving for x, we get:

x = 0.45 miles x  (Thomas St to Denny Way on Broad St) / (Mercer St to Denny Way on Broad St) = 0.45 * 0.2 / 0.7 = 0.1286 miles

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Complete question:

Use the following information and the map of downtown Seattle to answer questions one and two. Harrison St, Thomas St, and Denny Way are parallel. On Broad St, the distance between Mercer St and Denny Way is 0.7 miles. The distance between those same streets on Aurora Ave is 0.45 miles.

a) On Aurora Ave the distance between Thomas St to Denny Way is 0.2 miles. What is the distance

between these two streets on Broad St? Round your answer to the nearest tenth of a mile.

In response to the given question, we can state that we know that sum of all angles in a triangle is 180. m∠C = 4*11.67+43 = 89.68 = =90

A triangle is a polygon because it contains four or more parts. It features a simple rectangular shape. A triangle ABC is a rectangle with the edges A, B, and C. When the sides are not collinear, Euclidean geometry produces a single plane and cube. If a triangle contains three components and three angles, it is a polygon. The corners are the points where the three edges of a triangle meet. The sides of a triangle sum up to 180 degrees.

we know that sum of all angles in a triangle is 180.

2x - 12 + 4x + 43 + 9x - 26 = 180

15x  + 5 = 180

15x = 175

x = 11.67

m∠C = 4*11.67+43 = 89.68 = =90

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Answer:

m∠C = 119°

Step-by-step explanation:

According to the Exterior Angle Theorem, the exterior angle of a triangle is equal to the sum of the two non-adjacent interior angles of the triangle.

From inspection of the given triangle, the exterior angle is (9x - 26)° and the two non-adjacent interior angles are ∠B and ∠C.

Equate the sum of the two non-adjacent angles to the exterior angle and solve for x:

⇒ (2x - 12)° + (4x + 43)° = (9x - 26)°

⇒ 2x - 12 + 4x + 43 = 9x - 26

⇒ 6x + 31 = 9x - 26

⇒ 57 = 3x

⇒ x = 19

To calculate the measure of angle C, substitute the found value of x into the expression for the angle:

⇒ m∠C = (4x + 43)°

⇒ m∠C = (4(19) + 43)°

⇒ m∠C = (76 + 43)°

⇒ m∠C = 119°