Hello this is my first time on brainly and I saw you could get some help with assignments so this is what I need help with.and Thank you:

Answer:

To find the coordinates of the vertex of the graph of the function -3x^2+12, we can use the formula x = -b/2a to find the x-coordinate of the vertex, and then substitute it back into the function to find the y-coordinate.

In this case, the function is in the form f(x) = -3x^2+12, so we can see that a = -3 and b = 0.

Using the formula x = -b/2a, we get:

x = -0/(2*(-3)) = 0

So the x-coordinate of the vertex is 0.

To find the y-coordinate of the vertex, we can substitute x = 0 into the function:

f(0) = -3(0)^2+12 = 12

So the y-coordinate of the vertex is 12.

Therefore, the coordinates of the vertex of the graph of the function -3x^2+12 are (0, 12).

Step-by-step explanation:

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The circle graph's five transportation parts should be labelled as follows: walk 40%, bicycle 8%, car service 15%, bus 10%, and underground 27%. answer is option (a).

The percentage of visitors for each mode of transportation should be displayed in the appropriate circle graph for the given data. By dividing the total number of visitors by the sum of visitors and multiplying the result by 100, we can get the percentage.

Count of all visits = 80 + 16 + 30 + 20 + 54

                             = 200

percentage of each category of visitor:

Walk: 80/200 × 100% = 40%

Bicycle: 16/200 × 100% = 8%

Car service: 30/200 × 100% = 15%

Bus: 20/200 × 100% = 10%

Subway: 54/200 × 100% = 27%

The information in the table is appropriately represented by the circle graph below:

Consequently, the appropriate circle graph should include five portions with the labels "walk 40%," "bike 8%," "car service 15%," "bus 10%," and "subway 27%."

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Circle graph attached below,

Answer:

a. The London population data cannot be accurately modeled by a linear function because the population growth is not constant over time. A quadratic function may be able to fit the data, but it is unlikely to accurately model the population growth in the long term. An exponential function is a more suitable choice because it can model exponential population growth, which is common in real-world scenarios.

b. Using a logistic growth equation, we can determine if the London population data can be accurately modeled by a logistic equation. We can use a regression analysis to find the values of a, b, and c that best fit the data, and then compare the predicted values to the actual population data to determine the accuracy of the model.

c. The logistic growth equation P(t) = 1 / (a + be^(-b(t-c))) produces an S-shaped curve, which represents the growth of a population that is initially slow, then accelerates, and finally levels off as it approaches a carrying capacity. The value of a represents the initial population size, b represents the growth rate, and c represents the time at which the population growth rate is highest. As a increases, the curve shifts upwards, indicating a larger initial population size. As b increases, the curve becomes steeper, indicating faster population growth. As c increases, the curve shifts to the right, indicating a later time at which the population growth rate is highest.

We are given an equation that models the distance an object has fallen after t seconds.

[tex]\Rightarrow d=13x^2[/tex]

And are asked to find the objects average speed over the interval,[tex]a\leq x\leq a+h[/tex].  

Take the derivative of the "d" function, which is a function of position, to get a function for velocity.        

[tex]\Longrightarrow d=13x^2 \Longrightarrow d'=26x \Longrightarrow \boxed{v=26x}[/tex]

[tex]average \ speed = \boxed{ \bar v=\frac{d'(a)+d'(a+h)}{2}}[/tex]

[tex]\Longrightarrow \bar v = \frac{26a+26(a+h)}{2} \Longrightarrow \bar v = \frac{26a+26a+26h}{2} \Longrightarrow \bar v = \frac{52a+26h}{2} \Longrightarrow \bar v = \frac{52a}{2}+\frac{26h}{2}[/tex]

[tex]\Longrightarrow \boxed{ \bar v=26a+13h} \therefore Sol.[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Alternative way (without derivatives):

[tex]average \ speed = \bar v=\frac{d(a+h)-d(a)}{a+h-a} = \boxed{\frac{d(a+h)-d(a)}{h} }[/tex]

[tex]\Longrightarrow v = \frac{d(a+h)-d(a)}{h} \Longrightarrow \frac{13(a+h)^2-13a^2}{h}\Longrightarrow \frac{13(a^2+h^2+2ah)-13a^2}{h}[/tex]

[tex]\Longrightarrow \frac{13a^2+13h^2+26ah-13a^2}{h} \Longrightarrow \frac{13h^2+26ah}{h} \Longrightarrow \frac{13h^2}{h}+\frac{26ah}{h}[/tex]

[tex]\Longrightarrow \boxed{\bar v = 13h+26a} \therefore Sol.[/tex]

To solve this problem, we can use the formula for the potential energy stored in the spring:
U = 1/2 k x^2
where U is the potential energy stored in the spring, k is the spring constant, and x is the displacement of the spring from its natural length.
From the given information, we can set up two equations:
6J = 1/2 k (0.02)^2
10J = 1/2 k (0.02)^2 + 1/2 k (0.02)^2
Simplifying the equations, we get:
6J = 0.0002 k
10J = 0.0004 k
Dividing the second equation by the first, we get:
10J/6J = 0.0004 k/0.0002 k
Simplifying, we get:
5/3 = 2
This is not possible, so there must be an error in the problem. Therefore, we cannot determine the natural length of the spring with the given information.

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Answer:

Please mark me the brainliest

Step-by-step explanation:

Yes, 3√5 + 2√5 can be simplified to a rational number.

To simplify, we can combine the terms that have the same radical expression (in this case, √5). This gives:

3√5 + 2√5 = (3 + 2)√5 = 5√5

So 3√5 + 2√5 is equal to 5√5. While 5√5 is not a rational number, it can be simplified further by rationalizing the denominator. We can do this by multiplying both the numerator and denominator by √5:

5√5 = 5√5 x √5/√5 = 5√25/√5 = 5(5)/√5 = 25/√5

Now we have a rational number, 25/√5, which can be further simplified by multiplying the numerator and denominator by √5:

25/√5 = 25/√5 x √5/√5 = 25√5/5 = 5√5

Therefore, 3√5 + 2√5 simplifies to 5√5, which can be further simplified to 5√5 or 5 times the square root of 5. Although the final result is not a rational number, the expression itself can be simplified to a rational number.

Answer: the expression itself can be simplified to a rational number.

Step-by-step explanation:

Based on the information given, the histogram is attached

A histogram is a graphical representation of data points organized into user-specified ranges. Similar in appearance to a bar graph, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

From the information, the range of the dataset will be:

= 68 - 32

= 36

The number of classes will be:

= 36 / 10

= 3.6

= 4 approximately.

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Answer: 9430000

Step-by-step explanation: Take the first set of parentheses and simplify:

10^4 = 10000

because there are 4 zeros, move the decimal point to the right 4 times to 2.3

=23000

Then, take the second set of parentheses:

10^2 = 100

move the decimal in 4.1 to the right two times because there are 2 zeros:

=410

Then, you are left with 23000*410

multiply:

9430000

The conditional relative frequency of having more than one dog given there is a flea infestation is equal to 0.464.

The conditional relative frequency of having more than one dog with the condition there is a flea infestation.

Use the formula,

P(more than one dog | flea infestation)

= P(more than one dog and flea infestation) / P(flea infestation)

Looking at the two-way relative frequency table.

The probability of having more than one dog and a flea infestation is 0.032.

And the probability of a flea infestation regardless of the number of dogs is 0.069.

The conditional relative frequency is,

P(more than one dog | flea infestation)

= 0.032 / 0.069

= 0.464 (rounded to the nearest thousandths place)

Therefore, the conditional relative frequency representing there is more than one dog along with there is a flea infestation is 0.464.

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The above question is incomplete , the complete question is:

attached question.

The values of x and y in the right triangle are 24.3 and 12.14 respectively.

We have to find the values of x and y in the right triangle

We know that the sine is a ratio of opposite side and hypotenuse

Sin 60 = 21/x

√3/2 = 21/x

√3x = 42

x=42/√3 = 42/1.73

x=24.3

Now let us find value of y

the cosine is a ratio of adjacent side and hypotenuse

cos 60 = y/x

1/2 = y/(42/√3)

42/√3 = 2y

21/√3 = y

12.14 = y

Hence, the values of x and y in the right triangle are 24.3 and 12.14 respectively.

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Answer:

The correct answer is C. x = 50.

Step-by-step explanation:

To solve for x, we need to isolate it on one side of the equation. To do this, we first need to add 7 to both sides to cancel out the -7 on the left side. We then need to divide both sides by 3/5. This gives us x = 50.

Is there anything else I can help you with?

The solution to the equation -6 - 10log₇(x - 1) = 4 is x = 8/7.

Given the equation in the question;

-6 - 10log₇(x - 1) = 4

To solve for x in the equation -6 - 10log₇(x - 1) = 4,

we can follow these steps:

Add 6 to both sides of the equation to isolate the logarithmic term

-6 + 6 - 10log₇(x - 1) = 4 + 6

-10log₇(x - 1) = 10

Divide both sides of the equation by -10

-10log₇(x - 1) / -10 = 10 / -10

log₇(x - 1) = -1

Rewrite the equation in exponential form

7⁻¹ = x - 1

Simplify and solve for x

7⁻¹ + 1 = x

x = 1 + 7⁻¹

x = 1 + 1/7

x = 8/7

Therefore, the solution is x = 8/7.

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Answer:

-6-10log(7)(x-1)=4

I'm sorry, but the question you provided is unclear and incomplete. It mentions Jordan and Taylor and going to the movie theater, but it does not provide enough information about the distances they will travel or the context of the problem. Please provide a clear and complete question so I can assist you in a better way.

The limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

To find the limit of (x + x²)/(2 − 3x²) as x approaches infinity, we can use l'Hospital's Rule.

First, we need to check if the limit is in the indeterminate form 0/0 or ∞/∞. As x approaches infinity, both the numerator (x + x²) and the denominator (2 - 3x²) approach infinity.

Therefore, the limit is in the indeterminate form ∞/∞, and we can apply l'Hospital's Rule.

l'Hospital's Rule states that if the limit is in the indeterminate form 0/0 or ∞/∞, we can take the derivative of the numerator and denominator separately, and then find the limit of the ratio of their derivatives.

Numerator's derivative: d/dx(x + x²) = 1 + 2x Denominator's derivative: d/dx(2 - 3x²) = -6x

Now, we'll find the limit of the ratio of their derivatives as x approaches infinity: lim (1 + 2x)/(-6x) as x→∞

We can use l'Hospital's Rule again, as this limit is also in the indeterminate form ∞/∞. Numerator's second derivative: d/dx(1 + 2x) = 2

Denominator's second derivative: d/dx(-6x) = -6

Now, we'll find the limit of the ratio of their second derivatives as x approaches infinity: lim (2)/(-6) as x→∞ Since the limit involves constants only, it does not depend on x, and we can directly compute the limit: 2 / (-6) = -1/3

Therefore, the limit of (x + x²)/(2 − 3x²) as x approaches infinity is -1/3.

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A system of inequalities can be used to determine the number of packages of hamburgers, x, and the number of packages of hot dogs, y, that Natalia should buy are;

x + y ≤ 5

4x + 2y ≥ 18

In order to write a system of inequalities to describe this situation, we would assign variables to the number of packages of hamburgers and the number of packages of hot dogs respectively, and then translate the word problem into a linear equation as follows:

Since Natalia needs to buy no more than 18 pounds of meat for a cookout, and hamburgers are sold in 4-lb. packages, and hot dogs are sold in 2-lb. packages and she plans to buy at least 5 packages of meat, a linear inequality that models the situation is given by;

x + y ≤ 5

4x + 2y ≥ 18

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Answer:

The answer is c. 1/12

The angle of rotation about O that maps IJ to RF is 120 degrees.

A hexagon is a polygon with six sides and six angles. It is a two-dimensional geometric shape that can be formed by connecting six straight line segments, where each segment intersects two others to form the six corners or vertices of the shape.

To find the angle of rotation about O that maps IJ to RF, we can follow these steps:

Note that IJ and RF are opposite sides of the regular hexagon, and since the hexagon is regular, they have the same length.

Since the hexagon is regular, we know that the angle between adjacent sides is 120 degrees.

Therefore, the angle between IJ and one of the dashed line segments must be 60 degrees (since it is the supplement of the 120 degree angle).

Let x be the angle of rotation about O that maps IJ to RF.

After the rotation, the angle between IJ and the dashed line segments will be x + 30 degrees (since the dashed line segments form 30 degree angles).

Similarly, the angle between RF and the dashed line segments will also be x + 30 degrees after the rotation.

Since IJ and RF are opposite sides of the regular hexagon, they form a 60 degree angle.

Therefore, we have the equation:

[tex]2(x + 30) + 60 = 360[/tex]

The left-hand side of the equation represents the sum of the angles around O after the rotation. The factor of 2 comes from the fact that each of the dashed line segments contributes to the angle twice.

Simplifying the equation, we get:

[tex]2x + 120 = 360[/tex]

[tex]2x = 240[/tex]

[tex]x = 120[/tex]

Therefore, the angle of rotation about O that maps IJ to RF is 120 degrees.

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The statement the area of bottom of round pan is greater than area of bottom of rectangular pan by about 8.5 square inches is correctly describes how the area of the bottom of the round pan compares to the area of the bottom of the rectangular pan.

What is a area of a surface?

In mathematics, the area of a surface refers to the measurement of the size of a two-dimensional region enclosed by a closed boundary or surface. It is typically expressed in square units such as square inches, square meters, or square feet. The concept of area is used in various fields such as geometry, physics, engineering, and many others to calculate the amount of material needed to cover a surface, to determine the capacity of a container, or to estimate the amount of paint required to paint a wall. The formula for calculating the area of a surface varies depending on the shape and complexity of the surface, but typically involves finding the product of two or more dimensions of the surface or using integration techniques in calculus to calculate the area under a curve.

To find the relation we have to find the areas of the pans.

Area of round pan nr 3.14 x 52 78.5 square = 78.5 inches.

Area of the rectangular pan = length x breadth = 10 x 7 = 70 square inches.

Difference between the area of the circular pan from rectangular pan = 78.5 - 70 = 8.5 square inches.

Hence option 1 is the correct answer.

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Answer:

30 bc he did 20 m and healf way after

If a relay lasts 5.92 miles and there are 4 runners on the team, we can divide the total distance by the number of runners to find the distance each person runs.

5.92 miles / 4 runners = 1.48 miles per runner

Therefore, each person on the relay team would run a distance of 1.48 miles, assuming that each runner runs in the same direction in the race.

It's important to note that in a relay race, each runner usually runs a specific distance that is predetermined by the race organizers. This distance may be different from the total distance of the race, and it may also be different for each runner on the team. However, if all runners on the team are running equal distances, as in this case, then we can simply divide the total distance by the number of runners to find the distance each person runs.

If the original price of the football is $22.00, and the store is offering a 20% discount, then the new price of the football before tax would be:

New price before tax = Original price - Discount

= $22.00 - (20% x $22.00)

= $17.60

Now, we need to calculate the price of the football after adding the sales tax of 5%. To do this, we can calculate the amount of sales tax first, and then add it to the new price before tax:

Sales tax = 5% x $17.60

= $0.88

Price after tax = New price before tax + Sales tax

= $17.60 + $0.88

= $18.48

Therefore, the cost of the discounted football after tax is $18.48.

Answer:

(2)(1/2)(5)(12) + 9(5) + 9(12) + 9(13)

= 60 + 45 + 108 + 117

= 330 square inches

In summary, the critical value for a hypothesis test with an alpha value of 0.01 will be larger than that for an alpha value of 0.05, because the more stringent alpha level requires stronger evidence to reject the null hypothesis.

The critical value for a hypothesis test is determined by the level of significance, which is typically denoted by alpha (α). An alpha level of 0.05 means that the hypothesis test has a 5% probability of rejecting the null hypothesis when it is actually true. An alpha level of 0.01 means that the hypothesis test has a 1% probability of rejecting the null hypothesis when it is actually true.

The critical value is the threshold value beyond which the test statistic is considered to be significant. As the alpha level decreases, the critical value increases. This is because a smaller alpha level implies a greater level of confidence in the test results, and therefore a more stringent threshold for declaring statistical significance.

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1. (x - 3)(x + y + z) = x² + xy + xz - 3x - 3y - 3z. This product is not a sum or difference of two cubes. 2. (3x - 4y)(2x - 3y - 4) = 6x² - 17xy + 12y² + 4y. This product is not a sum or difference of two cubes.

An equation in mathematics is a claim made regarding the equality of two expressions. It comprises of two expressions that express the same value or amount and are joined by an equal sign. The objective is to solve for the unknown value by modifying the equation in accordance with predetermined rules and principles when one side of the equation is typically unknown. From straightforward arithmetic operations to intricate differential equation systems, equations are used to model and solve a wide range of issues in many branches of mathematics, science, and engineering.

1. (x - 3)(x + y + z) = x² + xy + xz - 3x - 3y - 3z. This product is not a sum or difference of two cubes.

2. (3x - 4y)(2x - 3y - 4) = 6x² - 17xy + 12y² + 4y. This product is not a sum or difference of two cubes.

3. (6x + 3)(x - y + 4) = 6x² - 15xy + 18x + 3y - 12. This product is not a sum or difference of two cubes.

4. (x² - 2)(x² + 3x - 1) = x⁴ + 3x³ - x² - 6x - 2. This product is a difference of two cubes: x^6 - 2^3.

5. (x - 3)(3x + 1) (4x (2)) = 12x⁴ - 32x³ - 9x² + 27x. This product is not a sum or difference of two cubes.

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Step-by-step explanation:

Step 1: 11 lies between two perfect squares 9 and 16.

Step 2: Since 32=9 and 42=16 , so the square root of 11 will lie between 3 and 4.

Hopefully this answers your question! :)

56 - 22 can be rewritten using the Distributive Property and the GCF of the numbers as 2 * 17.

GCF stands for Greatest Common Factor. In mathematics, the GCF is the largest positive integer that divides two or more integers without leaving a remainder. It is also known as the greatest common divisor (GCD), highest common factor (HCF), or greatest common measure (GCM). To rewrite 56 - 22 using the Distributive Property and the GCF of the numbers, we first need to find the greatest common factor (GCF) of 56 and 22. The GCF of 56 and 22 is 2.
Using the Distributive Property, we can write:
56 - 22 = 2 * 28 - 2 * 11
Now, we can factor out the GCF of 2: 56 - 22 = 2 * (28 - 11)
Simplifying the expression inside the parentheses, we get:
56 - 22 = 2 * 17
Therefore, 56 - 22 can be rewritten using the Distributive Property and the GCF of the numbers as 2 * 17 = 34.

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The percentage of 120 which gives the value 72 is 60%.

The given number is 120.

We have to find what percent of 120 gives the value as 72.

Let x be the percent for which the value gives 72.

The using the definition of percentage,

120 × x% = 72

120 × x/100 = 72

1.2x = 72

x = 60%

Hence 60% of 120 gives 72.

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False. In a hypothesis test for a mean, if the p-value is 0.13 and the level of significance (α) is 0.05, we fail to reject the null hypothesis.

When conducting a hypothesis test, the p-value is compared to the level of significance (a) to determine whether or not to reject the null hypothesis. The null hypothesis is typically the hypothesis that there is no significant difference between two groups or variables.

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The total surface area of tumbler designed like cube with cylindrical hole is 700.48cm² and cost of glass to make tumbler is $3 (round off).

Shape of the tumbler is cube.

Side length of the edges = 10cm

Radius of the cylindrical hole = 4cm

Depth of the cylindrical hole = 8cm

Total surface area of the tumbler = surface area of the cube and the surface area of the cylinder - (surface area of the cylindrical hole ).

The surface area of a cube with edge length 10 cm is,

6 × (10 cm)² = 600 cm²

The surface area of a cylinder with radius 4 cm and height 8 cm is,

2π(4 cm)² + 2π(4 cm)(8 cm) = 96π cm²

Surface area of the cylindrical hole is the lateral area of a smaller cylinder with radius 4 cm and height 8 cm,

2π(4 cm)(8 cm) = 64π cm²

So the total surface area of the tumbler is,

= 600 cm² + 96π cm² - 64π cm²

= 600 cm² + 32π cm²

≈ 700.48 cm²

Total volume of the tumbler = volume of the cube - volume of the cylindrical hole.

The volume of a cube with edge length 10 cm is,

(10 cm)³ = 1000 cm³

The volume of the cylindrical hole is,

π(4 cm)²(8 cm) = 128π cm³

So the total volume of the tumbler is,

= 1000 cm³ - 128πcm³

≈ 598.08 cm³

The cost of the glass needed to make the tumbler

= cost of one cubic centimeter of glass × total volume of the tumbler.

Since one cubic centimeter of glass costs half a cent.

The cost of the glass needed to make the tumbler is,

= 0.5 cents/cm³ × 598.08 cm³

≈ 299.04cents

≈ $3

Therefore, total surface area of tumbler is 700.48cm² approximately and  cost of glass needed to make tumbler is approximately $3.

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