The temperature at a point
(x, y, z)
is given by
T(x, y, z) = 200e−x2 − 5y2 − 9z2
where T is measured in °C and
x, y, z
in meters.

There are 3150 distinct ways to arrange the marbles in a row.

What is Combination ?

In mathematics, combination is a way of selecting a group of objects from a larger set, without regard to the order in which the objects are selected. Combinations are also sometimes called "unordered selections" or "combinatorial subsets".

To solve this problem, we can use the formula for permutations with repetition. We have a total of 10 marbles, but some of them are repeated. Specifically, we have:

3 yellow marbles (repeated)

3 green marbles (repeated)

2 red marbles (repeated)

2 blue marbles (repeated)

So the number of distinct ways to arrange these marbles in a row is:

(10!) ÷ (3! x 3! x 2! x 2!)

The factorials in the denominator account for the repetition of each color. We divide by them to eliminate the overcounting that would occur if all the marbles were unique.

Simplifying this expression, we get:

(10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1)÷(3 x 2 x 1 x 3 x 2 x 1 x 2 x 1 x 1 x 1)

which equals:

(10 x 9 x 8 x 7 x 6 x 5 x 4) ÷ (3 x 3 x 2 x 2)

Simplifying further, we get:

(10 x 3 x 3 x 3 x 2 x 2 x 7 x 5) ÷ (3 x 3 x 2 x 2)

which equals:

(10 x 3 x 3 x 7 x 5)

which finally equals:

3150

Therefore, there are 3150 distinct ways to arrange the marbles in a row.

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The formula for the function is S(r) = -10r² + 130r.

A function can be represented as an equation, a graph, or a table of values. In an equation, the function is usually denoted as "f(x)", where "x" is the input value and "f(x)" is the output value. For example, the equation f(x) = 2x represents a function that takes an input value x and produces an output value that is twice the input value.

Functions can be used to model real-world phenomena and solve various problems in mathematics, science, engineering, economics, and other fields. They are an important concept in calculus and other branches of mathematics, and they have numerous applications in modern technology and industry.

Let the cost of admission be $a and the cost of each raffle ticket be $r. Then we can write the following equation based on the given information:

10r + a = 135

Solving for a, we get:

a = 135 - 10r

Thus, the function that relates the total amount spent to the number of raffle tickets bought is:

S(r) = ar + 5r = (135 - 10r)r + 5r = -10r² + 130r

Therefore, the formula for the function is:

S(r) = -10r² + 130r

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The base of the triangle is 8 cm.

The following equation determines a triangle's area A:

A = (1/2) * b * h

Where the triangle's height (h) and base (b) are the same.

In this instance, the triangle's height is 12 cm, and its size is 48 cm²

When these values are added to the formula, we obtain the following:

48 = (1/2) * b * 12

By condensing the right side, we obtain the following:

48 = 6b

When we multiply both sides by 6, we get:

b = 8

Therefore, the base of the triangle is 8 cm.

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By selling a bag at rs1500 and rs2100, there is some loss and profit respectively. if the loss is twice the profit , its cost price​ is Rs 1900.

The cost price is the amount of money that a seller pays to acquire or produce a product or service. It includes all the expenses incurred in the production or purchase of the product, such as the cost of raw materials, labor, packaging, shipping, and other overhead expenses.

Based on the given inforemation , we can represent the cost price by x.

x-1500 = 2 (2100- x)

x-1500 = 4200 -2x

3x = 5700

x= 1900

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Answer: Can't solve

Step-by-step explanation: no equation sign

The quadratic equation represented by the table is:

y = 2x^2 - 4x + 8

Here we have a table that represents a quadratic equation. Remember that a quadratic equation with a vertex (h, k) and a leading coefficient a can be written as:

y = a*(x - h)^2 + k

Here we can see that the vertex is at (1, 6), replacing that we will get:

y = a*(x - 1)^2 + 6

And we  can see the point (0, 8), replacing these values we will get:

8 = a*(0 - 1)^2 + 6

8 = a + 6

8 - 6 = a = 2

The quadratic is:

y = 2*(x - 1)^2 + 6

Expanding this we will get:

y = 2*(x^2 - 2x + 1) + 6

y = 2x^2 - 4x + 2 + 6

y = 2x^2 - 4x + 8

That is the quadratic equation.

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Answer:35.09

Step-by-step explanation:From the question given above, the following data were:Opposite = 12Hypothenus = X Angle θ = 20 °

The equation of the ellipse is [tex]}(x-3)^2/4^2 + (y+1)^2/2^2 = 1} or, 4x^2 + 4y^2 - 24x - 8y - 7 = 0[/tex].

An ellipse is a type of closed curve which is symmetrical in shape and is the set of all points in a plane such that the sum of the distances from two fixed points (known as foci) is constant. It is a type of conic section, a curve obtained by intersecting a cone by a plane. Its shape is similar to that of an oval, but it is more elongated and slender. Ellipses are found in nature, such as in the orbits of the planets, and are used in a variety of applications, such as in engineering and architecture. They are also used in mathematics, where they can be used to represent a range of equations and to study the properties of shapes.

The equation of an ellipse with center (h,k), major axis of length 2a and minor axis of length 2b is given by:
[tex](x-h)^2/a^2 + (y-k)^2/b^2 = 1[/tex]
Given: h=3, k=-1, a=4, b=2
Therefore, the equation of the ellipse is:

[tex](x-3)^2/4^2 + (y+1)^2/2^2 = 1\\or, 4x^2 + 4y^2 - 24x - 8y - 7 = 0[/tex]

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The equation is true, we have confirmed that x = 3 is the correct solution.

The equation shown in the image is:

4x + 12 = 24

To write a related multiplication equation, we can simplify the left side of the equation by factoring out the common factor of 4:

4(x + 3) = 24

By multiplying both sides of the equation by 4, we can now find x:

x + 3 = 6

x = 6 - 3

x = 3

Therefore, the solution to the original equation is x = 3. We can check this solution by substituting it back into the original equation:

4x + 12 = 24

4(3) + 12 = 24

12 + 12 = 24

24 = 24

Since the equation is true, we have confirmed that x = 3 is the correct solution.

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Every proper subgroup of G is cyclic.

In abstract algebra, a subgroup is a subset of a group that is itself a group under the same operation as the original group. More precisely, a subgroup H of a group G is a subset of G that satisfies the following three conditions:

A cyclic subgroup is a subgroup of a group that is generated by a single element. In other words, a subgroup H of a group G is cyclic if there exists an element a in G such that every element of H can be written as a power of a, and H is the smallest subgroup of G containing a.

In the given question,

Let H be a proper subgroup of G. Since H is a proper subgroup, we have lHl < lGl = 77.

Now, by Lagrange's Theorem, the order of any subgroup of G must divide the order of G. That is, lHl divides lGl = 77.

Since H is a proper subgroup, we have lHl > 1. Therefore, lHl can only be 7, 11, or 77 (the divisors of 77).

Suppose lHl = 7. Then, by Lagrange's Theorem, the elements of G are partitioned into disjoint cosets of H, each of size 7. But 77 is not divisible by 7, so there cannot be a whole number of cosets. Therefore, this case is not possible.

Similarly, suppose lHl = 11. Then, the elements of G are partitioned into disjoint cosets of H, each of size 11. But 77 is not divisible by 11, so there cannot be a whole number of cosets. Therefore, this case is also not possible.

Thus, we are left with the case where lHl = 77. But this implies that H = G, which contradicts the fact that H is a proper subgroup. Therefore, this case is also not possible.

We have exhausted all possibilities for the order of H, and in each case, we have arrived at a contradiction. Therefore, the assumption that there exists a proper non-cyclic subgroup of G must be false.

Hence, every proper subgroup of G is cyclic.

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(C) "Your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.

You are permitted to contribute as much of your salary as you choose to the Retirement Savings Plan on a tax-advantaged basis, up to the yearly limit established by the Federal Revenue Agency (IRS).

A retirement savings plan (RSP), also known as an RRSP, is a form of financial account used in Canada to hold savings and investment assets.

When opposed to investing outside of tax-preferred accounts, RRSPs offer a number of tax benefits.

They were launched in 1957 to encourage both workers and independent contractors to save for retirement.

They are subject to a number of limitations outlined in the Canadian Income Tax Act.

Savings accounts, guaranteed investment certificates (GICs), bonds, mortgage loans, income trusts, mutual funds, corporate shares, exchange-traded funds, foreign currency, and funds sponsored by labor are examples of approved assets.

Therefore, (C) "your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.

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The child at the 69th percentile is 5.5279 years οld.

The age οf the children in kindergarten οn the first day οf schοοl is unifοrmly distributed between 4.81 and 5.71 years οld. We can find the tοtal prοbability οf the child being between 4.81 and 5.71 years οld by subtracting the prοbability οf the child being yοunger than 4.81 frοm the prοbability οf the child being yοunger than 5.71:

P(4.81 ≤ age ≤ 5.71) = P(age ≤ 5.71) - P(age < 4.81)

The prοbability οf the child being yοunger than 4.81 is 0 since the age cannοt be negative.

The prοbability οf the child being yοunger than 5.71 can be calculated as:

P(age ≤ 5.71) = (5.71 - 4.81) / (5.71 - 4.81) = 1

Therefοre,

P(4.81 ≤ age ≤ 5.71) = 1 - 0 = 1

This means that the prοbability οf the child being οlder than 5 years οld is:

P(age > 5) = P(5.00 < age ≤ 5.71) = 1 - P(age ≤ 5.00) = 1 - [(5.00 - 4.81) / (5.71 - 4.81)] = 0.7018

Sο the prοbability οf the child is οlder than 5 years οld is 0.7018.

Tο find the age οf a child at the 69th percentile, we need tο find the age x such that the prοbability οf the child being yοunger than x is 0.69.

Let's call the age at the 69th percentile x. Then we have:

P(age < x) = 0.69

We can sοlve fοr x as fοllοws:

( x - 4.81 ) / ( 5.71 - 4.81 ) = 0.69

x - 4.81 = 0.69 ( 5.71 - 4.81 )

x - 4.81 = 0.69

x = 4.81 + 0.69 ( 5.71 - 4.81 )

x = 5.5279

Therefοre, the child at the 69th percentile is 5.5279 years οld.

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The number of students that studied math and English in the class is 64 students.

1/5 of a class Study English and 3/5 study mathematics. The class consists of 80 Students.

Therefore, the number of students studying English and Maths in the class can be represented as follows:

number studying English = 1 / 5 (80)

number studying English =  16

number studying Math = 3 / 5 (80) = 240 / 5 = 48

Therefore, let's find the number of student that studied maths and English in the class

Student that studied math and English in the class = 48 + 16

Student that studied math and English in the class = 64

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We can say that after answering the offered question As a result, Jamie interest will have $1,746 in her account after four years. Option B is the correct answer.

Simple interest is calculated via dividing the investment by the interest rate, the duration of the loan, and perhaps other factors. In marketing, the formula is simple: return = principal + interest + hours. This method makes it easiest to calculate interest. The most common approach to compute interest is to use the percentages of the principle balance. If he borrows $100 from a buddy and promises to repay that with 5% interest, he will only pay his percentage of the total interest. $100 (0.05) = $5. When you borrow money, you must charge interest and extending when you lend it. The most often, interest is determined as an indicator of the overall of the loan balance. This percentage is known as the loan's interest.

To answer this problem, we can utilise the compound interest formula:

[tex]A = P(1 + r/n)^(nt) (nt)[/tex]

where A is the total amount

P = the initial principal ($1,500 in this example).

r represents the yearly interest rate (3.8%).

n denotes the number of times interest is compounded per year (12 for monthly)

t denotes the number of years (4 in this case)

When we plug in the values, we get:

[tex]A = 1500(1 + 0.038/12)^(12*4) \sA ≈ 1745.99[/tex]

As a result, Jamie will have $1,746 in her account after four years. Option B is the correct answer.

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Answer:

The method that might have been used to result in Garcia winning is the Instant RunOff method.

In this method, voters rank the candidates in order of preference. If no candidate has a majority of first-choice votes, the candidate with the fewest votes is eliminated, and their votes are redistributed to the remaining candidates according to the second-choice preferences of the voters who supported the eliminated candidate. This process is repeated until one candidate has a majority of the votes.

In the preference ballot provided, Garcia received the most first-choice votes with a total of 26, but did not receive a majority of the votes. Therefore, the Instant RunOff method could have been used to determine the winner by redistributing the votes of the eliminated candidates (Müller and Ivanov) to the remaining candidates. Based on the preferences of the voters who chose Müller and Ivanov as their first choice, it is possible that the redistributed votes would have favored Garcia, leading to a majority win for Garcia.

The Instant RunOff method might not be fair to the other nominees because it can result in a candidate winning with a majority of second-choice or even lower preferences, rather than being the first choice of the majority of voters. This means that the candidate who is ultimately chosen may not have broad support, and may not be the candidate that the most voters actually prefer. Additionally, the method can be influenced by strategic voting, where voters rank their choices based on who they think is most likely to win, rather than their actual preferences. This can result in outcomes that do not accurately reflect the preferences of the voters.

Looking at the data, we can see that both the high as well as low temperatures of Monday, Tuesday, Thursday, & Friday were above [tex]O^{o}C[/tex]. The high on Wednesday was minus zero degrees Celsius.

The most popular scales are indeed the Celsius scale, sometimes known as centigrade, with the unit sign °C, the Franklin level (°F), and the Scale parameter (K), with the latter being mostly used for scientific reasons.

The total kinetic energy of a substance's particles is measured by its temperature. 2. An object's kinetic energy increases with increasing temperature. 3. If we add up the instances where the maximum and low temps were in excess of or below zero degrees Celsius, we find:

High temperature above [tex]O^{o}C[/tex]: 5 days

High temperature below [tex]O^{o}C[/tex]: 2 days

Low temperature above [tex]O^{o}C[/tex]: 3 days

Low temperature below [tex]O^{o}C[/tex]: 4 days

Therefore, we can see that overall, there were more days where the temperatures were below [tex]O^{o}C[/tex], both for the high and low temperatures.

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The complete question is:

In Vienna were more of the high and low temperatures above or below [tex]O^{o}C[/tex] justify your answer using a vertical number line

Days                        high temperature      low temperature

Monday                            8                           0

Tuesday                            9                          -4.5

Wednesday                      4.5                       -12

Thursday                           9                          4.5

Friday                                8.5                       -6

Saturday                           1                           -10

Sunday                             5                           -14

The line's slope  on the graph will switch from being negative to positive.

The graph of the equation y = mx + c is a line with m as the slope and m and c as the y-intercept. The values of m and c are actual integers in the slope-intercept illustration of the linear equation.

The slope of a line, measured in m, tells us how steep it is. A line's gradient is also referred to as its slope sometimes. The y-coordinate of the point where the line's graph meets the y-axis is known as the y-intercept of a line, ab.

The slope-intercept form of the equation for the line, y = -5/4 x + 3, is written as y = mx + b. Where,

The line has a slope of m, a y-intercept of 3, a slope of -5/4, and a y-intercept of b.

As a result, the slope has changed from negative to positive if -5/4 is changed to 5/4.

As a result, the graph of the line's slope will switch from being negative to positive.

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Answer:

629=500+120+9

Step-by-step explanation:

500+120+9=629

629=629

Answer:

The answer is 1/2

Step-by-step explanation:

3 and 6 are the known sides of the triangle as you can see three is half of six making it a 1/2 dilation

[tex]\dfrac{6}{3} = 2[/tex]

the scale factor is

1 : 2

The solution for x in the equation -7x/5 + 4 = -1/2x - 7/2 is 5, and the other solutions are listed below

Given that

-7x/5 + 4 = -1/2x - 7/2

Multiply through by 10

-14x + 40 = 5x - 35

Evaluate the like terms

-19x = -95

So, we have

x = 5

Let x be the number of adult tickets sold.

So, the number of student tickets sold is 2x.

The total number of tickets sold is 444. Therefore:

x + 2x = 444

Combining like terms:

3x = 444

Dividing both sides by 3:

x = 148

Therefore, 148 adult tickets were sold.

The slope

To read the slope off the graph, we can use the formula:

slope = (change in y) / (change in x)

Using the points, we can calculate:

slope = (-2 - 1) / (3 - 1)

slope = -1.5

So the slope of the line is -1.5.

The y-intercept value

We can look at where the line intersects the y-axis on the graph. From the graph, it looks like the y-intercept is around y = 2.5.

The y-intercept point

Using the solution in (b), the estimated y-intercept point is (0, 2).

Rearrange the equation

To rearrange the equation into slope-intercept form, we need to isolate y on one side of the equation:

5x + 3y = 15

Subtract 5x from both sides:

3y = -5x + 15

Divide both sides by 3:

y = (-5/3)x + 5

So the equation in slope-intercept form is y = (-5/3)x + 5.

The slope

b) The slope of the line is the coefficient of x in the equation when it is in slope-intercept form.

Therefore, the slope of the line is -5/3.

The y-intercept of the line

This is the value of y when x = 0.

From the equation in slope-intercept form, we can see that when x = 0, y = 5.

So, the y-intercept of the line is 5.

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Answer:

B.1/100 is your answer for your question

Answer:

That answer is -3

Step-by-step explanation:

The way you do this is Rise/Run

so you would do y2-y1/x2-x1

In this case it's 10-1/-4-(-1)

Simplified is 9/-3 which is -3

hope this helped

Answer:

the answer was 31.88USD

Answer:

Step-by-step explanation:

We can start by finding the weight lifter's original body mass before the training session:

Let x = original body mass

Then, we know that 15% of x is equal to 78 kg - x:

0.15x = 78 - x

1.15x = 78

x = 78/1.15

x ≈ 67.83 kg

Therefore, the weight lifter's original body mass was approximately 67.83 kg.

Now, let's find the difference between the weight lifter's new body mass and his original body mass:

78 kg - 67.83 kg ≈ 10.17 kg

So, the weight lifter did indeed gain approximately 10 kg of weight after the training session. Therefore, his claim is valid.

The set of solutions in R³ of the equation x1 - 3x2 + 2x3 = 1 is classified as a plane, hence option d is the correct option in the context of the problem.

The equation of a plane in 3-dimensional space can be written in different forms, but the most common one is the standard form:

Ax + By + Cz + D = 0

where A, B, and C are the coefficients of the variables x, y, and z, respectively, and D is a constant term.

Comparing the equation for this problem to the standard form, the coefficients are given as follows:

A = 1, B = -3, C = 2, D = -1.

Hence option d is the correct option.

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The answer of the given question based on the actual area of the park in meters squared answer is the actual area of the park is 593,442 square meters.

Width refers to measurement of  distance from one side of object to other side, perpendicular to its length. It is one of basic dimensions of  object or shape along with the length and height.

Width is often used in context of rectangular or parallelogram-shaped objects, where it refers to measurement of shorter sides of the shape. For example, in a rectangular picture frame,  width would be measurement of the shorter sides of the frame.

The scale of the drawing is 1 cm = 110 m, which means that every 1 centimeter on the drawing represents 110 meters in real life.

The length of the park on the drawing is 8.6 cm, so the actual length of the park in meters is:

8.6 cm x 110 m/cm = 946 meters

The width of the park on the drawing is 5.7 cm, so the actual width of the park in meters is:

5.7 cm x 110 m/cm = 627 meters

Therefore, the actual area of the park in square meters is:

946 meters x 627 meters = 593,442 square meters.

So, the actual area of the park is 593,442 square meters.

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Solving a system of equations we can see that the two numbers are-8 and -7.

Let's say that the two numbers are A and B, and we know that we can write:

A*B = 56

A + B = -15

So we have a system of equations.

Using the second equation we can write:

A=  -15 - B

And replace that in the first equation, then we will get:

(-15 - B)*B = 56

-15B - B² = 56

Now we can solve the quadratic equation:

-B² - 15B - 56 = 0

The solutions are:

[tex]B = \frac{15 \pm \sqrt{(-15)^2 - 4*-56*-1} }{2*-1} \\\\B = \frac{15 \pm 1 }{-2}[/tex]

The two possible solutions are:

B = (15 + 1)/-2 = -8

B = (15 - 1)/-2 = -7

And when B is one of these values, A will be the other one.

Then the two numbers are -8 and -7.

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Answer:If Krista drank 3/16 of the water in her water bottle in the morning, 5/16 in the afternoon, and 3/16 in the evening, then the total amount of water she drank during the day is:

3/16 + 5/16 + 3/16 = 11/16

This means that the fraction of water that is left at the end of the day is:

1 - 11/16 = 5/16

Therefore, Krista has 5/16 of the water remaining in her water bottle at the end of the day.

Step-by-step explanation:

Answer:
Part a:

[tex]A(x)=10x^2+53x+63[/tex]

Part b:
2nd degree polynomial.

Part c:
Check step by step.

Step-by-step explanation:

since the sides of the rectangle are (2x+7) and (5x+9), the area is given by the product of the sides:

[tex]A=(2x+7)(5x+9)=10x^2+18x+35x+63=10x^2+53x+63[/tex]

So the area as a function of X is given by:
[tex]A(x)=10x^2+53x+63[/tex]

Notice is a second degree polynomial in standard form

To ensure part c, notice we can also multiply the sides in different order. This is A*B must be B*A for the sides of the rectangle. Lets check

[tex]A=(5x+9)(2x+7)=10x^2+35x+18x+63=10x^2+53x+63[/tex]
Since we obtained the same answer in part A the closure property for multiplication is check for the polynomial.