what is the length of this line? khan academy - Distance between two points

The amount that Goldman's straight-time pay for each week will be $90.75. Then the correct option is A.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Stuart Goldman works at Ruler's Golf Spot. He works 11 hours every week and acquires $8.25 each hour.

Goldman's straight-time pay for each week will be given as,

⇒ $8.25 x 11

⇒ $90.75

The amount that Goldman's straight-time pay for each week will be $90.75. Then the correct option is A.

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If Stuart Goldman works at King's Golf Spot. He works 11 hours a week and earns $8.25 per hour.  Goldman's straight-time pay for each week is: A. $90.75.

To determine Stuart Goldman's straight-time pay for each week we can multiply his hours worked by his hourly wage:

Straight-time pay = Hours worked × Hourly wage

Let plug in the formula

Straight-time pay = 11 hours × $8.25/hour

Straight-time pay = $90.75

Therefore the correct option is A.

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Answer:

Step-by-step explanation:

dad hates me sorry bye

Checking for approximate normality in the population is essential for constructing a valid confidence interval, particularly when dealing with small sample sizes. This ensures the accuracy and reliability of the interval in estimating the true population parameter.

It's important to check whether the population is approximately normal before constructing a confidence interval because the accuracy and validity of the interval depend on the underlying distribution of the population. Here's a step-by-step explanation:

1. A confidence interval is a range of values within which the true population parameter (e.g., mean or proportion) is likely to fall, with a certain level of confidence (e.g., 95% or 99%).

2. The process of constructing a confidence interval relies on the Central Limit Theorem, which states that, for large sample sizes, the sampling distribution of the sample mean will be approximately normal, regardless of the population distribution.

3. However, for small sample sizes, the distribution of the population needs to be approximately normal in order to obtain an accurate confidence interval. This is because the normality assumption is crucial for the proper interpretation of the interval.

4. If the population is not approximately normal, the confidence interval may not provide a reliable estimate of the true population parameter, leading to incorrect conclusions and potentially invalid results.

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a) The probability that the length of a randomly selected axle is less than 595 mm is approximately 0.3528.

b) The probability that the mean length of 20 axles is less than 595 mm is extremely low.

An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center.

(a) Using the normal distribution with mean μ = 597 mm and standard deviation σ = 5.3 mm, we can calculate the z-score for a length of 595 mm:

z = (x - μ) / σ

= (595 - 597) / 5.3

= -0.3774

Using a standard normal distribution table or calculator, we can find the probability that a z-score is less than -0.3774 is 0.3528.

Therefore, the probability that the length of a randomly selected axle is less than 595 mm is approximately 0.3528.

(b) The mean of a sample of 20 axles will also follow a normal distribution, with mean μ = 597 mm and standard deviation σ = 5.3 / sqrt(20) = 1.1847 mm (using the formula for the standard deviation of the sample mean).

To find the probability that the mean length of 20 axles is less than 595 mm, we can calculate the z-score for this value:

z = (x - μ) / (σ / √(n))

= (595 - 597) / (5.3 / √(20))

= -4.1054

Using a standard normal distribution table or calculator, we can find that the probability that a z-score is less than -4.1054 is essentially 0.

Therefore, the probability that the mean length of 20 axles is less than 595 mm is extremely low.

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Answer:

b

Step-by-step explanation:

because im amazing and right and its prob not right but you know i guess you can i dont knwo

Answer:8x+91

Step-by-step explanation:8x + 91

The required answer is "The 90% confidence interval of two sample means is [-15.4798, 3.48001]."The answer should be rounded to four decimal places.

Given that:

n1=8

n2=10

s1=14

s2=11

¯x1=37

¯x2=38

The formula to find the 90% confidence interval of two sample means is given below:Lower limit = ¯x1 - ¯x2 - t(α/2) × SE; Upper limit = ¯x1 - ¯x2 + t(α/2) × SEWhere,t(α/2) = the t-value of α/2 with the degree of freedom (df) = n1 + n2 - 2SE = √{ [s1² / n1] + [s2² / n2]}The degree of freedom = n1 + n2 - 2Here, the degree of freedom = 8 + 10 - 2 = 16The t-value for 90% confidence interval is 1.753So, SE = √{ [14² / 8] + [11² / 10]} = 5.68099Now, Lower limit = 37 - 38 - 1.753 × 5.68099 = -15.4798Upper limit = 37 - 38 + 1.753 × 5.68099 = 3.48001.

The 90% confidence interval of two sample means is [-15.4798, 3.48001].Therefore, the required answer is "The 90% confidence interval of two sample means is [-15.4798, 3.48001]."The answer should be rounded to four decimal places.

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Answer:

There is 57 snails after 14 weeks

Step-by-step explanation:

tripling every week means 3x

NOTE: x is defined as the number of weeks

started with 15 snails means at day 0 (x = 0 also known as y intercept)

y = mx + b       m is the slope, b is the y intercept

our equation: y = 3x + 15

y = 3(14) + 15

y = 42 + 15

y = 57

Using the given graph we can answer the questions:

a. The parabola opens upward.

b. The coordinates of the vertex, which is the point at the bottom of the parabola, are (2,1).

c. The equation of the axis of symmetry is x=2.

d. The y intercept is 5.

The graph has no x intercepts.

Percentage decrease is 17.29 .

Given :

In 2006, 65.2 million people subscribed to cable television.

In 2013, that number had decreased to 54.2 million.

To Find :

The percent decrease in the number of cable TV subscribers from 2006 to 2013.

So,

Decrease in the number of cable TV subscribers from 2006 to 2013 is :

Percentage decrease = Decrease in subscribers / initial subscribers * 100

% decrease = 63.6 - 52.6 / 63.6 * 100

% decrease = 17.29

Hence the percentage decrement in the tv subscribers are 17.29 .

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Answer:Calculate the Land Transfer Tax on a house for 248000

   Calculation example

1.multiply $55,000 by 0.5% (55,000 × 0.005) = $275.

2.multiply the amount exceeding $55,000 up to $250,000 by 1.0% (195,000 × 0.01) = $1,950.

3.multiply the amount exceeding $250,000 up to $400,000 by 1.5% (150,000 × 0.015) = $2,250.

Step-by-step explanation:

Hello there. To solve this question, we have to remember some properties about ordered pairs and equations.

Given the equation:

We want to determine the ordered pair that is solution to this equation.

First, remember what is an ordered pair:

An ordered pair is a 2 element tuple (list) that has its elements disposed as

In this case, all solutions x to this equation will be given as the following ordered pairs:

And these points lies on the line y = 2x - 4, all across the xy-plane.

Okay. Now, we have to check which of the options are correct.

For this, you take the first coordinate of the ordered pair and plug in the equation:

a) (4, 5)

Plugging x = 4, we get

This is not the correct option.

b) (-3, -7)

Plugging x = -3, we get

Not correct as well.

In the end, we find that the only correct option is:

e) (0, -4).

Since plugging x = 0 yields:

As we wanted.

Therefore the final answer is contained in the last option, (0, -4).

Step-by-step explanation:

To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:

m = (9 - 2) / (8 - (-2))

= 7 / 10

= 0.7

The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:

tan(θ) = 0.7

Taking the inverse tangent of both sides, we find:

θ = arctan(0.7)

Using a calculator, we can evaluate this to be approximately:

θ ≈ 35.87 degrees

Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.

The area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

To solve this problem, we can use the formula for the volume of a hexagonal prism:

V = (3√3/2) * a^2 * h

where V is the volume, a is the length of one side of the hexagonal base, and h is the height of the prism.

We are given that the height of the prism is 4 units and the volume is 98 units^3. Plugging these values into the formula, we can solve for the length of one side of the base:

98 = (3√3/2) * a^2 * 4
a^2 = 98 / (12√3)
a ≈ 2.95

Now that we know the length of one side of the base, we can find the area of the hexagon by using the formula:

A = (3√3/2) * a^2

where A is the area of one of the bases. Plugging in the value we found for a, we get:

A = (3√3/2) * (2.95)^2
A ≈ 7.39

Therefore, the area of one of the bases of the hexagonal prism is approximately 7.39 units^2.

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The levels of central tendency are measures that describe the typical or central value of a dataset. The three main levels of central tendency are mode, median, and mean.

The mode is the value that occurs most frequently in a dataset and is used with nominal data, which is data that is divided into categories that cannot be ranked or ordered.

The median is the middle value in a dataset and is used with ordinal data, which is data that can be ranked or ordered but the differences between values cannot be measured.

The mean is the average value of a dataset and is used with interval and ratio data, which are both types of data that can be ranked, ordered, and have measurable differences between values. The difference between interval and ratio data is that ratio data has a true zero point, such as weight or height, while interval data does not have a true zero point, such as temperature on the Celsius or Fahrenheit scale.

In summary, the mode is used with nominal data, the median is used with ordinal data, and the mean is used with interval and ratio data.

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a) Pump A and Pump B break even at 7,751 working hours per year. b) The breakeven chart illustrates the point of equal costs for Pump A and Pump B at 7,751 working hours.


a) To determine the breakeven point, we need to calculate the equivalent annual cost for each pump. Pump A has an initial cost of $1800 and an overhaul cost of $500 every 2000 hours, while Pump B has an initial cost of $3800 and an overhaul cost of $800 every 5000 hours. Considering an interest rate of 10%, the equivalent annual costs are calculated, and it is found that the two alternatives break even at 7,751 working hours per year.
b) The breakeven chart plots the working hours on the x-axis and the total cost on the y-axis for Pump A and Pump B. The chart shows the point at which the costs intersect, indicating the breakeven point at 7,751 working hours.
c) Given the operating conditions of 10 hours/day and 250 working days per year, Pump A is more economical over a 4-year period. By comparing the total costs for each pump, taking into account the initial cost, overhaul cost, and operating cost, Pump A proves to be the more cost-effective option within the specified comparison period.

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1. The total cost for orders of 5 sandwiches and 7 sandwiches are $25 and $33

2. The total cost for orders of x sandwiches is 5 + 4x

3. The graph is attached

Given that

Delivery fee = $5

Charge per sandwich = $4.00

This means that

Total cost = Delivery fee + Charge per sandwich * sandwiches

So, we have

Total cost = 5 + 4 * sandwiches

For 5 sandwiches, we have

Total cost = 5 + 4 * 5 = 25

For 7 sandwiches, we have

Total cost = 5 + 4 * 7 = 33

In (1), we have

Total cost = 5 + 4 * sandwiches

For x sandwiches, we have

Total cost = 5 + 4x

This means that we plot the graph of  5 + 4x

See attachment

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Answer:

EVERYONE REPORT ME PLEASE

Answer:

Given h(x) = -x + 2, find h(4).

Step-by-step explanation:

Answer:

Graph A

Step-by-step explanation:

Because the inequality is

\( \leqslant or \geqslant \)

it means the line will be solid, not dashed. Also, because the y variable is on the less than side of the equation, it means the shaded are will be under the line.

Answer:

10%

Step-by-step explanation:

26.40-24.00/24*100%

=2.4/24*100%

=10%

Answer:

3(x+4)=3x+11

3x + 12 = 3x + 11

3x + 1 = 3x

No solution

-2(x+3)=-2x-6

-2x - 6 = -2x - 6

x = x

Infinite solutions

4(x-1) = 1/2(x-8)

4x - 4 = 1/2x - 4

8x - 8 = x - 8

7x = 0

x = 0

One solution

3x-7=4+6 +4x

3x - 7 = 10 + 4x

x = -17

One solution

Answer:

8, 12, 16, 20

Step-by-step explanation:

those are the domains

The curl of the vector field

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

The divergence of the vector field

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

To find the curl of the vector field F(x, y, z) = 9ex sin(y), 2ey sin(z), 8ez sin(x), we need to compute the determinant of the curl matrix.

(a) Curl of F:

The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k

In this case, we have:

P(x, y, z) = 9ex sin(y)

Q(x, y, z) = 2ey sin(z)

R(x, y, z) = 8ez sin(x)

Taking the partial derivatives, we get:

∂P/∂y = 9ex cos(y)

∂Q/∂z = 2ey cos(z)

∂R/∂x = 8ez cos(x)

∂R/∂y = 0 (no y-dependence in R)

∂Q/∂x = 0 (no x-dependence in Q)

∂P/∂z = 0 (no z-dependence in P)

Substituting these values into the curl formula, we have:

curl(F) = (0 - 2ey cos(z))i + (8ez cos(x) - 0)j + (0 - 9ex cos(y))k

= -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

Therefore, the curl of the vector field F is given by:

curl(F) = -2ey cos(z)i + 8ez cos(x)j - 9ex cos(y)k

(b) Divergence of F:

The divergence of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by the following formula:

div(F) = ∂P/∂x + ∂Q/∂y + ∂R/∂z

In this case, we have:

∂P/∂x = 9e^x sin(y)

∂Q/∂y = 2e^y sin(z)

∂R/∂z = 8e^z

Substituting these values into the divergence formula, we have:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

Therefore, the divergence of the vector field F is given by:

div(F) = 9e^x sin(y) + 2e^y sin(z) + 8e^z

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The right response is that the two linear equation never intersect , because the graph of these two linear equation will be two parallel lines.

How many types of solution are there for two linear equations ?

There are 2 types of solution :
Consistent :

A consistent system is said to be an independent system if it has a single solution.

A consistent system is said to be a dependent system if the equations have the same slope and the same y-intercepts. In other words, the lines coincide, so the equations represent the same line. Each point on the line represents a pair of coordinates that fits the system. So there are an infinite number of solutions.

Non-consistent :

Another type of system of linear equations is the inconsistent system, in which the equations represent two parallel lines. The lines have the same slope and different y-intercepts. There are no common points for both lines; therefore, there is no solution to the system and if we draw the graph of these equations then the graphs of both equation becomes parallel to each other.

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The two linear equations never intersect.

When a system of two linear equations in two variables has no solution, it means that there is no set of values for the variables that satisfies both equations simultaneously. Geometrically, this corresponds to the two lines represented by the equations being parallel. Since parallel lines never intersect, the statement "The two linear equations never intersect" accurately describes the situation.

If the two linear equations were graphed on a coordinate plane, they would appear as two distinct lines that run parallel to each other without ever crossing or intersecting. This indicates that there is no common point of intersection between the lines, and therefore no solution exists for the system of equations.

It is important to note that this scenario is different from the case where the two linear equations represent the same line. In that case, the equations would be equivalent, and every point on the line would satisfy both equations. However, when there is no solution, it means that the lines do not share any common points and never intersect.

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Answer:

\(\frac{3x+4y^2}{3x+y^3}\)

Step-by-step explanation:

Given

\(\frac{6x^3+8x^2y^2}{6x^3+2x^2y^3}\) ← factor numerator/ denominator

= \(\frac{2x^2(3x+4y^2)}{2x^2(3x+y^3)}\) ← cancel 2x² on numerator/ denominator

= \(\frac{3x+4y^2}{3x+y^3}\)

Noah is right. A 180 degree rotation, with center P, will create the same image as reflecting over line `m`.

The lines 'l' and 'm' are perpendicular. We can imagine it as a quadrant with  line 'l' and 'm' two perpendicular axes. So the angle between them is 90 degree at P, where P is the intersection point of 'l' and 'm'.

So to rotate the line 'l' 180 degree, first we rotate it 90 degree which will give the line 'm' itself and another 90 degree from there takes the line 'l' to its opposite side through line 'm'. This is exactly the reflection of line 'l' over line 'm'. The 180 degree rotation is the reflection only for two perpendicular lines.

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Answer:

y = -6x + 2

Step-by-step explanation:

(1, -4)     m = -6

(x₁, y₁)

y - y₁ = m (x - x₁)

y - (-4)= -6 (x - 1)

y + 4 = -6x + 6

  -4             -4

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

y = -6x + 2

I hope this helps!

Answer:

a) 14 cm

b) 12 minutes

Step-by-step explanation:

Rectangular tank with square base:

Initial water in the container = 2.6 liter

To convert 2.6 l to cubic cm, multiply 2.6 by 1000.

                                               = 2.6 *1000

                                               = 2600 cubic cm

Now, let us find the capacity of the cubic container with edge 15 cm.

              \(\boxed{ \text {\bf Volume of cube = $edge^3$}}\)

                                              \(\sf = 15 * 15 * 15\\\\ = 3375 \ cm^3\)

In 3375 cubic cm of water, only 95 cubic cm is left. To find the water that is transferred into the rectangular tank subtract.

    Water transferred into the rectangular tank = 3375 - 95

                                                                              = 3280 cubic cm

To find the full capacity of the tank, add the initial capacity water in the tank with 3280 cubic cm.

Full capacity of the tank = 3280 + 2600

                                         = 5880 cubic cm

     \(\boxed{\text{\bf Volume of rectangular tank with square base = area of the base * h = edge^2 * h}}\) Volume of rectangular tank with square base = area of base * height

   \(\boxed{\text{\bf Volume of rectangular tank with square base = $edge^2*h$}}\)

                                   \(\sf edge^2 * h = 5880 \ cm^3\\\\ edge^2 * 30 = 5880\\\\~~~~~~ edge^2 = \dfrac{3880}{30}\\\\\\~~~~~~ edge^2 = 196\\\\~~~~~~ edge ~~ = \sqrt{196}\\\\~~~~~~ edge ~~ = 14 \ cm\)

 \(\boxed{\text{\bf length of the base = 14 \ cm}}\)

b) Time taken to drain 0.49 liters of water = 1 minute

    Time taken to drain 5.88 liters of water = 5.88 ÷0.49

                                                                      = 12 minutes

Answer:

I hope it will help you :)

Answer:

6! = 720

3! - 2! = 12

6!/3!= 120

Step-by-step explanation:

just finished the assignment.

Answer:

1. x < 3

2. x ≥ 3

3. -3 > x

4. x ≤ -3

5. 3 < x

6. -3 ≤ x

Step-by-step explanation:

To find out whether the circle will be opened or closed, look at the sign. If the sign is "<" or ">", then the circle will be open. If the sign is either "≤" or "≥", then the sign will be closed.

To decide if the arrow goes right or left, again, look at the sign. If the arrow is going left, then that means x is less than whatever value the circle is at. If the arrow is going right, then x is greater than whatever value the circle is on.

Using this information, you can figure out which inequality matches each number line.

hope this helps!