Solve the system of equations.

6x – y = 6
6x2 – y = 6

(0, 6) and (0, –6)
(1, 0) and (0, –6)
(2, 6) and (1, –11)

Answer:

D

Step-by-step explanation:

Convert all of the fractions' denominators so that they are 8. This is because 4,2, and 8's least common multiple is 8.

Remember that when multiplying the denominator, we must also multiply the numerator. So:

[tex]\frac{1}{2} * \frac{4}{4} = \frac{4}{8} \\[/tex]

[tex]\frac{1}{4} *\frac{2}{2} =\frac{2}{8}[/tex]

Since we are asked to add all of them, we can do that easily since all of the fractions now share a common denominator.

[tex]\frac{2}{8} +\frac{4}{8} + \frac{1}{8} = \frac{7}{8}[/tex]

Therefore, the answer is D.

If there are 40 bottles in the machine when is it to be serviced, 40 number will go in the second column.

Numbers are used to performing arithmetic calculations. Examples of numbers are natural numbers, whole numbers, rational and irrational numbers, etc. 0 is also a number that represents a null value.

A number has many other variations such as even and odd numbers, prime and composite numbers.

To determine the number that will go in the second column, we need to understand the context of the problem.

Assuming the second column refers to the number of bottles in the machine when it should be serviced, the answer

would be 40.

The machine should be serviced when there are 40 bottles in it.

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Question

A vending machine in an office building sells bottled beverages. The machine keeps track of all changes in the number of bottles from sales and from machine refills and maintenance. This record shows the changes for every 5-minute period over one hour.  The machine must be emptied to be serviced. If there are 40 bottles in the machine when it is to be serviced, what number will go in the second column in the table?

time number of bottles

8:00–8:04 -1

8:05–8:09 +12

8:10–8:14 -4

8:15–8:19 -1

8:20–8:24 -5

8:25–8:29 -12

8:30–8:34 -2

8:35–8:39 0

8:40–8:44 0

8:45–8:49 -6

8:50–8:54 +24

8:55–8:59 0

service

Answer:

x = 10

Step-by-step explanation:

using the cosine ratio in the right triangle and the exact value

cos60° = [tex]\frac{1}{2}[/tex] , then

cos60° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{5}{x}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

x = 5 × 2 = 10

Answer: The length, breadth, and height of the given object are 3x+y cm, 2x+2y cm, and 3y cm, respectively. To find the volume of this object, we need to multiply these three dimensions:

Volume = Length x Breadth x Height

= (3x+y) x (2x+2y) x (3y)

= 18x^2y + 27xy^2 + 6xy^2 + 6y^3

= 18x^2y + 33xy^2 + 6y^3

Therefore, the volume of the object is 18x^2y + 33xy^2 + 6y^3 cubic cm.

Step-by-step explanation:

Answer:

3 more kids

Step-by-step explanation:

Answer:

3 kids can join in on the fun.

Step-by-step explanation:

Total number of kids who can jump on the trampoline = 6

Kids jumping currently = 3

Therefore, The number of kids who can join the fun will be the difference of the total number of kids who can jump on the trampoline and kids jumping currently.

= 6 - 3

= 3

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The surface area of the triangular prism 5ft 11ft 15 ft is 515 sq ft.

To find the surface area of a triangular prism, we need to calculate the area of each face and then add them together.

The triangular base has dimensions of 5ft and 15ft, so its area is:

Area of triangular base = (1/2) x 5ft x 15ft = 37.5 square feet

There are two identical triangular faces, so the total area of the triangular faces is:

Total area of triangular faces = 2 x 37.5 = 75 square feet

The rectangular faces have dimensions of 5ft x 11ft and 11ft x 15ft, so their areas are:

Area of first rectangular face = 5ft x 11ft = 55 square feet

Area of second rectangular face = 11ft x 15ft = 165 square feet

There are two identical rectangular faces, so the total area of the rectangular faces is:

Total area of rectangular faces = 2 x (55 + 165) = 440 square feet

Hence, the triangular prism's total surface area is:

Total surface area = Total area of triangular faces + Total area of rectangular faces

Total surface area = 75 + 440 = 515 square feet

The triangular prism offered has a surface area of 515 square feet.

The complete question is:-

Find the surface area of the triangular prism below 5ft 11ft 15 ft

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Thus, using the slope intercept form of for the equation of line: equation 11 = 6 + k  can be written as: 11 = 2*3 + k.

Every equation that describes the slope and at least one point on a line is said to be the equation of that line.

We can bypass point-slope form and directly enter the numbers into the slope-intercept equation if the observed point of such an equation is the y-intercept. If not, we must enter the numbers into point-slope, solve for y, and then transform the data into slope-intercept form.

Given data:

Passing point (2,11)

Equation of line:

11 = 6 + k  

11 = 2*3 + k ...eq 1

The standard equation of line in slope intercept form is:

y = mx + c

In which, m is the slope and c is the y-intercept.

The given passing points must satisfy the line. So, putting the values in standard form.

11 = 2m + c  ...eq 2

Comparing the eq 1 and 2

slope m = 3 and c = k.

Thus, using the slope intercept form of for the equation of line: equation 11 = 6 + k  can be written as: 11 = 2*3 + k.

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The value of the probability P(sum of 6) is five thirty sixths

When rolling a 6-sided die, there are 6 possible outcomes: {1, 2, 3, 4, 5, 6}.

The sum of two rolls can be any number between 2 (when both rolls are 1) and 12 (when both rolls are 6).

To find the probability of getting a sum of 6, we need to count how many ways we can get a sum of 6, and then divide that by the total number of possible outcomes.

We can get a sum of 6 in the following ways:

P(1,5) + P(2,4) + P(3,3) + P(4,2) + P(5,1)

Therefore, the probability of getting a sum of 6 is:

P(sum of 6) = P(1,5) + P(2,4) + P(3,3) + P(4,2) + P(5,1)

This gives

P(sum of 6) = 1/6 + 1/6 + 1/6 + 1/6 + 1/6

P(sum of 6) = 5/36

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Therefore , the solution of the given problem of expressions comes out to be hire 15 chairs in order for the rental costs to be equal.

Instead of producing approximations at random, it is better to use moving numeral variables, which may be rising, declining, or blocking. They could only help one another by sharing materials, information, or solutions to issues. The justifications, parts, and mathematical comments for equation techniques like additional disapproval, production.

Here,

Assume that Erin needs to hire x chairs in order for the rental costs to be equal.

The following equation provides the price for purchasing from A-1 Rental:

=> C(A-1) = 1.74x + 61.31

The following equation provides the price for purchasing from Tonka Tents:

=> C(Tonka) = 1.99x plus 57.56

We must solve the following equation to determine how many chairs Erin must hire in order for the rental costs to be equal:

=> C(A-1) = C(Tonka)

=> 1.74x + 61.31 = 1.99x + 57.56

1.74x and 57.56 are subtracted from both sides to yield:

=> 0.25x = 3.75

By multiplying both parts by 0.25, we obtain:

=> x = 15

Erin must therefore hire 15 chairs in order for the rental costs to be equal.

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About 0.331 grams of the substance is left after 180 days have passed.

The decay of iodine-131 can be modelled by the equation:

[tex]y(t) = y0 * e^(-kt)[/tex]

where y0 is the initial mass, t is time in days, and k is the decay constant.

We are given that y(7) = 6 grams, so we can plug in these values and solve for k:

[tex]6 = y0 * e^(-7k)\\y0 = 6 / e^(-7k)[/tex]

We are also given that 180 days have passed, so we can use the equation to find y(180):

[tex]y(180) = y0 * e^(-k*180)[/tex]

Substituting y0 from the previous equation:

[tex]y(180) = 6 / e^(-7k) * e^(-k*180)[/tex]

Simplifying:

[tex]y(180) = 6 * e^(-k*173)[/tex]

We need to find k in order to evaluate this expression. To do so, we can use the fact that the half-life of iodine-131 is about 8 days. This means that:

[tex]1/2 = e^{(-k*8)}[/tex]

Taking the natural logarithm of both sides:

[tex]ln(1/2) = -8k\\k = -ln(1/2) / 8\\k \approx 0.08664[/tex]

Substituting this value of k into the expression for y(180):

[tex]y(180) = 6 * e^(-0.08664*173)\\y(180) \approx 0.331 grams[/tex]

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THE GRAPH SHOWING (X=2,5) (Y=10,9) (Z=6,1) Thus, taking YZ as the base, the area of the triangle XYZ is 2√(98)square units.

The total area filled by a triangle's three sides in a two-dimensional plane is what is known as the triangle's area. The basic formula for calculating a triangle's area is A = 1/2× b× h, which equals half the product of the triangle's base and height.

We can use the following formula to determine a triangle's area given its coordinates:

Area is equal to half of |x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|.

where the triangle's vertices' coordinates are (x₁,y₁), (x₂,y₂), and (x₃,y₃).

As YZ serves as our base in this instance, we must first determine its length. When we apply the distance formula, we obtain:

√((1-9)2 + (6-1)2) Equals √YZ (98)

Finding the perpendicular distance from X to YZ will allow us to determine the height of the triangle now that we know YZ. This distance is equivalent to 2-6 = -4, which is the x-coordinate of X less the x-coordinate of Z.

As a result, the triangle's area is:

Area is equal to 1/2 × YZ × height

= 1/2×√(98)× |-4|

= 2 √ (98)

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Answer:

4x^2 + x + 3 + 4/x-1

Step-by-step explanation:

The value of angle x in the intersecting chords is determined as  146⁰.

The value of angle x is determined by applying intercepting chord theorem for tangent angle at circumference of a circle.

The intercepting chord theorem, also known as the tangent chord theorem, states that when a tangent line intersects a chord of a circle at a point on the chord, then the measure of the angle formed by the tangent line and the chord is equal to half the measure of the intercepted arc (the arc that lies between the endpoints of the chord).

So if the tangent angle = 73⁰, the arc angle X = 2(73) = 146⁰

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Answer:

The length of diagonal EG and FH in rectangle EFGH can be expressed as 8x - 1 and 3x + 9, respectively.

Step-by-step explanation:

In a rectangle, the diagonals are equal in length. Therefore, we can set 8x - 1 equal to 3x + 9 and solve for x:

8x - 1 = 3x + 9

5x = 10

x = 2

Now that we know x = 2, we can find the length of both diagonals:

EG = 8x - 1 = 8(2) - 1 = 15

FH = 3x + 9 = 3(2) + 9 = 15

Therefore, the length of both diagonals in rectangle EFGH is 15.

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From the histogram, we can see that there are 4 outcomes in which three heads appear. Therefore, the probability that three heads will appear on any toss is 4/16 = 0.25.

Consider the toss of four coins. There are 24 possible outcomes of a single toss. Develop a histogram of the number of heads (one side of the coin) that can appear on any toss. Does it look like a normal distribution? Should this be expected? What is the probability that three heads will appear on any toss?Solution:When four coins are tossed, there are 16 possible outcomes.

Each outcome has an equal probability of 1/16 of occurring. A histogram of the number of heads that can appear on any toss is shown below:Based on the histogram, the probability of getting 0 heads or 4 heads is 0.375, while the probability of getting 1 head or 3 heads is 0.25, and the probability of getting 2 heads is 0.125.

The histogram does not look like a normal distribution. This is because a normal distribution has a bell-shaped curve, which is not the case with this histogram. This is because there are a finite number of possible outcomes, and the probabilities of these outcomes are not normally distributed.

Thus, the histogram is not expected to look like a normal distribution .The probability that three heads will appear on any toss is the sum of the probabilities of the outcomes in which three heads appear.

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This result doesn't make sense in the context of the problem, so it's likely that there was a mistake in the problem setup or in the information given.

What is Algebraic expression ?

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

Let's assume that they both sold a total of $x.

Since Rita sold each box of cookies for $10, she must have sold x/10 boxes.

Likewise, since John sold each box for $8, he must have sold x/8 boxes.

We know that they both sold the same dollar amount, so we can set their two sales expressions equal to each other and solve for x:

x/10 = x/8

Multiplying both sides by the least common multiple of 10 and 8, which is 40:

4x = 5x

Subtracting 4x from both sides:

x = 0

Therefore, This result doesn't make sense in the context of the problem, so it's likely that there was a mistake in the problem setup or in the information given.

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Answer:

55/99

Step-by-step explanation:

To express 0.55 repeating as a fraction, we can use the following steps:

Let x = 0.55 repeating

Multiplying both sides by 100 to eliminate the repeating decimal gives:

100x = 55.55 repeating

Subtracting the left-hand side (100x) from the right-hand side (55.55 repeating) gives:

99x = 55

Dividing both sides by 99 yields:

x = 55/99

Therefore, 0.55 repeating can be expressed as the fraction 55/99.

Answer: 125

Step-by-step explanation: First you need to find the surface area of triangles which the equation to find it is 1/2(base x height).

1/2(10x5) = 25

Then because there are 4 sides alike you multiply it by 4 which would be 100

In order to find the surface of a square which is relatively easy you would do 5x5 which is 25.

The last step is to add both numbers together which would leave us to your answer 125  I really hope this helped!!

Answer:

the mode is 2 In order 0,1,2,3,9,12,14

Step-by-step explanation:

The reason is the mode equals the middle and 2 is there twice and the 2 is in the middle

The two lengths that separate the top 10% and the bottom 10% are  3.25 cm and 3.04 cm.

This is used to measure how different an individual data point is from the mean of the data set and is a helpful tool when comparing data points to each other.

To find the two lengths, we start by finding the z-scores that correspond to the top 10% and the bottom 10%. The z-score for the top 10% is 1.28 and the z-score for the bottom 10% is -1.28. We then use these z-scores to find the two lengths.

To find the two lengths, we use the following formula:

length = mean + (z-score * standard deviation)

For the top 10%:

length = 3.15 + (1.28 * 0.08)

length = 3.25 cm

For the bottom 10%:

length = 3.15 + (-1.28 * 0.08)

length = 3.04 cm

Therefore, the two lengths that separate the top 10% and the bottom 10% are 3.25 cm and 3.04 cm.

These lengths could serve as limits used to identify which nails should be rejected.

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The average number of calls per day is approximately 5.298 calls.

To solve this problem, we'll first use the information given about the probability of receiving no calls (0.5%) and the Poisson distribution formula to find the average number of calls per day (λ).

Step 1: Convert the percentage of no calls into a decimal.
0.5% = 0.005

Step 2: Use the Poisson distribution formula for the probability of receiving no calls (k = 0).
P(X = 0) = (e^(-λ) * λ^0) / 0! = 0.005

Step 3: Simplify the equation.
(e^(-λ) * 1) / 1 = 0.005

Step 4: Solve for λ.
e^(-λ) = 0.005
-λ = ln(0.005)
λ = -ln(0.005)

Step 5: Calculate the average number of calls per day.
λ ≈ 5.298

So, the average number of calls per day is approximately 5.298 calls.

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The questions can be answered directly with statistical reasoning are:  how many observations do I need?, how do we control for other factors? option C and F.

Statistical reasoning entails considering and comprehending uncertainty as well as creating mental models to represent important features of occurrences that occur in the actual world. Students should be able to create questions about data and decide what data they need to answer these questions as they reason with this uncertainty. They then compile, arrange, analyse, and present this material in order to summarise and draw conclusions that will aid in resolving their queries.

The capacity to apply models that quantify significant features of data that might contain uncertainty, noise, and mistake allows students to reason about and debate what data means when they are competent in statistical and probabilistic reasoning.

The context of the data or events can affect both statistical and probabilistic reasoning. Furthermore, the calibre of students' statistical reasoning may be impacted by their past information, views, and any misperceptions they may have regarding chance or uncertain circumstances.

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The magnitude of w is approximately 25.298 and its direction is approximately 64.654 degrees counterclockwise from the positive x-axis.

In the context of vectors, the term "magnitude" refers to the size or length of a vector. It is a scalar value that represents the distance between the initial point and the terminal point of the vector in a geometric space.

The size W = ❬–9, –19❭ is obtained from the formula:

||w|| = square((-9)² (-19)²) = square(81+361) = square(442) ≈ 25.298

Therefore ||w|| is approximately 25.298.

The direction of W measured counterclockwise from the positive x-axis is given by the following formula:

θ = arctan (-19/-9) ≈ 64.654°

Therefore, the direction of w is approximately 64.654°.

Therefore the answer is: ||w|| = 25.298; 6 = 64.654°.

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The required probability and average for the given arrival rate and service rate are,

Average time a car in the given system is 2.13 minutes.

Average number of cars in the given system is 0.852 cars.

Average number of cars waiting is 0.052 cars.

Average time a car spends waiting is 0.13 minutes.

Probability of no cars is 0.2.

Percentage of time the serving pharmacist is 80%.

Probability of exactly 2 cars is 0.64.

Arrival rate per minute λ = 4/10 = 0.4

And service rate per minute µ = 1/2

                                                  = 0.5 .

Average time a car is in the system is given by,

W = Wq + 1/µ

where Wq is the average time a car spends waiting in the queue.

1/µ is the average service time.

Using Little's Law, we have,

L = λW

where L is the average number of cars in the system.

Using the given values,

Wq

= (0.4^2)/(2×(1-0.4))

= 0.13 minutes

W

= Wq + 1/µ

= 0.13 + 2

= 2.13 minutes

Average time a car is in the system is 2.13 minutes.

Average number of cars in the system is,

L = λW

  = λWq + λ/µ

L = λWq + λ/µ

   = 0.4×0.13 + 0.4/0.5

   = 0.052 + 0.8

   = 0.852 cars

Average number of cars in the system is 0.852 cars.

Average number of cars waiting in the queue is,

Lq = λWq

    = 0.4×0.13

    = 0.052 cars

Average number of cars waiting in the queue is 0.052 cars.

Average time a car spends waiting in the queue is,

Wq = Lq/λ

     = 0.052/0.4

     = 0.13 minutes

Average time a car spends waiting in the queue is 0.13 minutes.

Probability that there are no cars at the window is,

P(0) = (1 - λ/µ)

      = (1 - 0.4/0.5)

      = 0.2

Probability that there are no cars at the window is 0.2.

Percentage of time the serving pharmacist is busy is ,

ρ = λ/µ

  = 0.4/0.5

  = 0.8

Percentage of time the serving pharmacist is busy is 80%.

Probability that there are exactly 2 cars in the system is,

P(2) = ((λ/µ)^2/(1-ρ)) × P(0)

where P(0) is the probability that there are no cars at the window.

P(2)

= ((0.4/0.5)^2/(1-0.8))×0.2

= 0.64

Probability that there are exactly 2 cars in the system is 0.64.

Therefore, the probability for the given situations are,

Average time is 2.13 minutes.

Average number of cars is 0.852 cars.

Average number of cars waiting in the queue is 0.052 cars.

Average time a car spends waiting in the queue is 0.13 minutes.

Probability of no cars at the window is 0.2.

Percentage of time the serving pharmacist is busy is 80%.

Probability that there are exactly 2 cars is 0.64.

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Answer:

So Adam has eaten 1/6 of the pizza.  :)  ;)

Step-by-step explanation:

Assuming the pizza is cut into 8 equal pieces (which would each be 45 degrees of the total 360 degrees of the pizza), we can calculate how much of the pizza Adam has eaten with the given information.

First, we add up the angles of the two pieces Adam has eaten:

35 degrees + 25 degrees = 60 degrees

This means that Adam has eaten 60 degrees out of the total 360 degrees of the pizza. To convert this to a fraction, we divide 60 by 360:

60 / 360 = 1/6

So Adam has eaten 1/6 of the pizza.

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Simplifying the fraction by dividing both the numerator and denominator by 7: 7/42 = (1 × 7)/(6 × 7) = 1/6Hence, Adam has eaten 1/6 or 7/42 of the pizza.

Let's begin with the solution by calculating the fraction of the pizza that has been consumed:

Pizza's central angle = 360°

The central angle of Adam’s first piece = 35°

The central angle of Adam’s second piece = 25°

The total central angle of Adam's pizza pieces = 35° + 25° = 60°

The fraction of pizza was eaten by Adam = (Total central angle of Adam's pizza pieces)/(Central angle of one whole pizza)Fraction of pizza eaten by Adam = 60/360 = 1/6So,

Adam has eaten 1/6 of the pizza. Now, we can represent 1/6 as a fraction in which the numerator and denominator have the same value.

We do this by multiplying the numerator and denominator of the fraction by 7/7.

Thus, we get:1/6 = (1 × 7)/(6 × 7) = 7/42Therefore,

Adam has eaten 7/42 of the pizza.

Simplifying the fraction by dividing both the numerator and denominator by 7:7/42 = (1 × 7)/(6 × 7) = 1/6Hence, Adam has eaten 1/6 or 7/42 of the pizza.

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The equation of the least-squares regression line based on these data is, y= 106.92 +2.044x where y =predicted height of child and x = child’s foot length.

To determine the equation of the least-squares regression line, we need to fit a linear model to the data using the method of least squares. The equation of the line can be written as:

height = intercept + slope * foot length

where the intercept and slope are the parameters we need to estimate from the data. The intercept represents the predicted height when foot length is 0, and the slope represents the change in height for each unit increase in foot length.

Substituting the values form the graph,

y= 106.92 +2.044x where y =predicted height of child and x = child’s foot length.

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--The complete question is, Can we predict the heights of school-aged children from foot length? below is computer output from a regression analysis of this relationship for 15 randomly-selected canadian children from 8 to 15 years old, along with a residual plot. the explanatory variable is each child's foot length (in centimeters), and the response variable is the child's height (in centimeters).

What is the equation of the least-squares regression line based on these data?  Define any parameters used.--

Step-by-step explanation:

Let's start by representing the change in depth of the snowdrift as negative, since it decreased by 8 inches over the first four days.

Change from Monday to Thursday = -8 inches

Now we need to find the change in depth from Thursday to Friday. We're told that the depth changed by half as much as it did from Monday to Thursday. So we can start by finding half of -8 inches:

Half of -8 inches = (-8)/2 = -4 inches

Therefore, the change in depth from Thursday to Friday is -4 inches.

To summarize:

Change from Monday to Thursday = -8 inches

Change from Thursday to Friday = -4 inches

Answer:

20736

Step-by-step explanation:

12*12*12*12=20736