What are the values of the constants in the vertex form of the quadratic equation that models the bird's path? with answers.

h = 0


k = 20


a = -0.12


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which system of equations could you use to determine where the paths intersect? b.

y = 0.8x and y = -0.12x2 + 20

To find the height of a stack of 8x10^9 books, we need to calculate the total thickness of all the books.

The thickness of one book is 3.1x10^-4 meters. So, the total thickness of 8x10^9 books can be calculated by multiplying the thickness of one book by the number of books:

3.1x10^-4 meters/book * 8x10^9 books = 24.8 meters

Therefore, the height of a stack of 8x10^9 books, each with a thickness of 3.1x10^-4 meters, would be 24.8 meters.

It's equivalent to about 81 ft.

Answer:

40 peaches.

Step-by-step explanation:

We can set up an equation using this information:

(x + 3) * 5 = x * 8

Expanding and simplifying the equation:

5x + 15 = 8x

Subtracting 5x from both sides:

15 = 3x

Dividing both sides by 3:

x = 5

So, if the peaches were shared among 8 people, each person would get 5 peaches. If each person got 3 more peaches if the peaches were shared among 5 people, each person would get 8 peaches.

So the box has 8 peaches per 5 people, 8*5 = 40 peaches

Answer:

There are 8 peaches in the box.

Step-by-step explanation:

It states that if the peaches were shared among 8 people, each person would get x/8 peaches, and if the peaches were shared among 5 people, each person would get x/5 + 3 peaches.

To find the total number of peaches in the box, we can use the equation to find the value of x.

We know that x/8 = x/5 + 3 , we can multiply both sides by 8*5 to get rid of the denominator

8(x/8) = 8(x/5 + 3)

x = 8(x/5 + 3)

5x = 8x + 24

Subtracting x from both sides

3x = 24

Dividing both sides by 4

x = 8

There are 8 peaches in the box.

As per the unitary method, the number of matches produced in Oregon over the same period is 64

The term unitary method is known as the method of finding the value of a single unit from the value of multiple units

Here we have given that the increase in the number of matches produced in California from 1980 to 1990 exceeds.

Therefore, the number of increase is calculated as,

CA = 0.33(1.2) = 396

If the increase is calculated as,

=> 0.33(1.6) = 528

Then the difference is calculated as,

=> 528 - 396 = 132

Similarly the number of matches in Oregon is calculated as.

=>  0.17(1.2) =204 M

=> 0.17(1.6) = 272 M

Therefore, the difference is calculated as

=> 272 -204 = 68

Therefore the total difference between increases is written as,

=> 132-68 = 64

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No the relation doesn't necessarily represent a function.

The term function is known as a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Here we have given that you record the number x of runs scored by the winning team and the number y of runs scored by the losing team for each softball game in a team's season.

As we all know that in any two games here we have given that if the winning teams had the same numbers of runs while the losing teams had different numbers of runs then the given relation is not a function.

Here we have to remember that for a relationship to be a function then it must be fulfilled and it is possible for every input value there must be only one output value

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Answer:

A and D

Step-by-step explanation:

The Empirical Rule states that for a bell-shaped distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean.

Given that the mean value of land and buildings per acre from the sample of farms is $1800 and the standard deviation is $300, we can use this information to determine which farms are unusual (more than two standard deviations from the mean).

A. $615 is unusual, it is more than two standard deviations from the mean, which is $1800. $615 is $1185 less than the mean. Since it is more than $600 less than the mean, it is more than two standard deviations from the mean.

B. $1656 is not unusual, it is less than 2 standard deviations from the mean.

C. $1625 is not unusual, it is less than 2 standard deviations from the mean.

D. $2493 is unusual, it is more than two standard deviations from the mean, which is $1800. $2493 is $693 more than the mean. Since it is more than $600 more than the mean, it is more than two standard deviations from the mean.

E. $1521 is unusual, it is more than two standard deviations from the mean, which is $1800. $1521 is $279 less than the mean. Since it is more than $600 less than the mean, it is more than two standard deviations from the mean.

F. $1664 is not unusual, it is less than 2 standard deviations from the mean.

None of the data values are very unusual (more than three standard deviations from the mean).

So the farms that are unusual (more than two standard deviations from the mean) are A and D.

Answer: Using the empirical rule, if the distribution is bell-shaped, we know that about 68% of the data falls within one standard deviation of the mean, about 95% of the data falls within two standard deviations of the mean, and about 99.7% of the data falls within three standard deviations of the mean.

To determine which of the farms are unusual (more than two standard deviations from the mean), we need to calculate the lower and upper bounds for two standard deviations from the mean:

Lower bound = Mean value - (2 * Standard deviation) = $1800 - (2 * $300) = $1200

Upper bound = Mean value + (2 * Standard deviation) = $1800 + (2 * $300) = $2400

So, any data value outside this range is considered unusual. Therefore, the farms that are unusual are:

$2493 (more than two standard deviation from the mean)

None of the data values are very unusual (more than three standard deviations from the mean)

Step-by-step explanation:

The only statements that is false is A. I only: 1. We use one-sample procedures when our samples are equal in size but aren't independent.

A one-sample procedure is used when we want to compare a sample mean to a known population mean or when we want to estimate a population mean using a sample mean. In a one-sample procedure, the sample is selected independently and is typically assumed to be random. So, independence of the sample is a requirement for one-sample procedure.

While statement II and III are true.

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Answer: Apples $0.18 (18 Cents) Bananas $0.14 (14 cents)

Step-by-step explanation:

Math knowledge would give the cost for each item. We have:

4 apples + 6 bananas = $1.56

and

9 apples + 7 bananas = $2.60

To find a cost, we encode an apple as 'a', and a banana as 'b' in the following two main equations:

4a+6b=1.56

9a+7b=2.6

The following formula represents the situation by using elimination method to find, let's say, the banana value:

4a+6b=1.56 , 9a+7b=2.6

9×4a+9×6b=9×1.56, 4×9a+4×7b=4×2.6

36a+54b=14.04, 36a+28b=10.4

36a−36a+54b−28b=14.04−10.4

54b−28b=14.04−10.4

26b=14.04−10.4

26b=3.64

b=3.64÷26

b=0.14

That is a banana costs $0.14 (14¢).

Now we have found the value of a banana, we substitute this new value in one of the main equations above to reduce variables so that we can find the value of an apple as follows:

4a+6b=1.56

4a+(6×0.14)=1.56

4a+0.84=1.56

4a=1.56-0.84

4a=0.72

a=0.72÷4

a=0.18

Simply enough, an apple costs $0.18 (18¢), and a banana costs $0.14 (14¢).

The area of the shaded portion is given by the difference between the area of the outer circle and the area of the inner circle.

First, let's find the areas of the circles:

Outer Circle: Area = πr^2 = π (2)^2 = 4π square meters

Inner Circle: Area = πr^2 = π (0.75)^2 = 0.5625π square meters

Area of shaded portion = Area of outer circle - Area of inner circle = 4π - 0.5625π = 3.4375π square meters

So the area of the shaded portion is approximately 10.8 square meters.

This test batch can be chosen is 455 ways. (Option A).

The problem is asking for the number of ways to choose 3 batteries out of a box of 15.

This is a combination problem and the number of ways to choose k items out of a set of n items, without regard to the order of selection, is given by the binomial coefficient:

C(n,k) = n!/(k!(n-k)!)

where ! denotes factorial.

So in this case, we have:

C(15,3) = 15!/(3!(15-3)!) = 151413/(321) = 455

So, the answer is 455.

Therefore, This test batch can be chosen is 455 ways. (Option A).

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An explicit formula for aₙ, the nth term of the arithmetic sequence is aₙ = 3 + 5(n - 1)..

Mathematically, the nth term of an arithmetic sequence can be calculated by using this mathematical expression:

aₙ = a₁ + (n - 1)d

Where:

From the information provided, we have the following parameters:

First term, a₁ = 3

Second term, a₂ = 8

Next, we would determine the common difference as follows:

Common difference, d = a₂ - a₁

Common difference, d = 8 - 3

Common difference, d = 5

Substituting the parameters into the mathematical expression, we have;

aₙ = 3 + (n - 1)(5)

aₙ = 3 + 5(n - 1).

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By solving a system of equations and a quadratic equation, we will see that x = 2.

We know that x and y are positive integers, that x < y and:

x*y = 56

We also know that "seven times the reciprocal of the smaller integer plus 14 times the reciprocal of the larger integer equals 4"

Then we can write the equation:

7*(1/x) + 14*(1/y) = 4

So we have a system of equations:

x*y = 56

7*(1/x) + 14*(1/y) = 4

We can rewrite the first equation to get:

x = 56/y

And the second equation as:

14/y = 4 - 7/x

Then the system becomes:

56/y = x

14/y = (4 - 7/x)

Taking the quotient between these, we can remove the variable y:

(56/y)/(14/y) = x/(4 - 7/x)

56/14 = x/(4 - 7/x)

4*(4 - 7/x) = x

4*(4x - 7)/x = x

4*(4x - 7) = x^2

So now we have a quadratic equation:

x^2 - 16x + 28 = 0

Using the quadratic formula, we will get:

[tex]x = \frac{16 \pm \sqrt{(-16)^2 -4*1*28} }{2*1} \\\\x = \frac{16 \pm 12 }{2}[/tex]

So the solutions are:

x = (16 - 12)/2 = 2

x = (16 + 12)/2 = 14

But notice that if x = 14, then:

14 = 56/y

y = 56/14

y = 4

And y is larger than x, then x = 14 can be discarded.

The solution is x = 2.

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0.05, fail to reject null hypothesis..

What is hypothesis in math

A proposition is considered to be a hypothesis if it is plausible given the available information but has not been proven true or wrong.

                  A statement on which hypothesis testing will be based is referred to as a hypothesis in statistics (also known as a statistical hypothesis).

Below are the null and alternative Hypothesis,

Null Hypothesis: μ = 9.2

Alternative Hypothesis: μ ≠ 9.2

Test statistic,

t = (xbar - mu)/(s/sqrt(n))

t = (8.25 - 9.2)/(5.1478/sqrt(8))

t = -0.522

P-value Approach

P-value = 0.6178

As P-value >= 0.05, fail to reject null hypothesis..

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Answer:

   20 miles

Step-by-step explanation:

first, draw a diagram. Then, use the pythagorean theorem to calculate.

[tex]\textit{Product to Sum Identities} \\\\ cos(\alpha)sin(\beta)=\cfrac{1}{2}[sin(\alpha+\beta)\quad -\quad sin(\alpha-\beta)] \\\\[-0.35em] ~\dotfill\\\\ cos(3x)sin(x)\implies \cfrac{1}{2}[sin(3x+x)~~ - ~~sin(3x-x)] \\\\\\ ~\hfill {\Large \begin{array}{llll} \cfrac{1}{2}[sin(4x)-sin(2x)] \end{array}}~\hfill[/tex]

El primer término de la progresión geométrica es 9 y la suma de los primeros veinte términos es 1.569 × 10¹⁰.

En este problema tenemos el caso de una progresión geométrica, es decir, una serie de elementos generados por un expresión de la forma:

y = a · rⁿ⁻¹

Where:

El primer término se determina como sigue: (y = 81, r = 3, n = 3)

a = y / rⁿ⁻¹

a = 81 / 3³⁻¹

a = 9

Por último, determinamos la suma de los veinte primeros elementos mediante la siguiente fórmula:

S = [y(n) · r - a] / (r - 1)

Primero, determinamos y(20):

y(20) = 9 · 3²⁰⁻¹

y(20) = 1.046 × 10¹⁰

Segundo, calculamos la suma:

S = [(1.046 × 10¹⁰) · 3 - 9] / (3 - 1)

S = 1.569 × 10¹⁰

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A poster is being designed that is to contain 2 150. In of printed material with margins of 2 inches at the top and bottom and 3 inches at each side. the dimensions that will minimize the amount of paper used is that should be 12 inches wide by 6 inches tall.

The margins are 2 inches at the top and bottom and 3 inches at each side. The margins are then added to the two 150s, making a total width of 12 inches and a total height of 6 inches. This is the minimum amount of paper that can be used for the poster.   In order to minimize the amount of paper used, it is important to consider the size of the margins.

The margins should be kept as small as possible in order to maximize the amount of space available for the printed material. Generally speaking, a margin of 1 inch is sufficient for most printed materials. If a larger margin is necessary, then the overall dimensions of the poster should be adjusted accordingly.

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The required value of the given function is (f ⋅ g)(4) = 130.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

f(x)=3x+1 and g(x)=x²-6

(f ⋅g)(x) is the composition of the functions f and g, which means f(x) × g(x).

(f ⋅ g)(x) = f(x) × g(x)

So, substituting x = 4:

(f ⋅ g)(4) = f(4) × g(4)

= (3 × 4 + 1)×(4² - 6)

= 13 × 10

= 130

So, (f ⋅ g)(4) = 130.

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The cost of one hundred kilowatt-hours of electricity is $16.4

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, the formula for calculating the cost per one thousand kilowatt-hours of electricity is twice the sum of 36 and 4 times the difference of 7 and 2 dollars per thousand kilowatt-hours.

The cost for 1000 kilowatt-hours of electricity =

2(36+36) + 4(7-2)

= 2(72) + 4(5)

= 144 + 20

= $164

Since, 1000 kilowatt-hours of electricity costs $164

Then, 1 kwh will cost = $164 / 1000

And, 100 KWh will cost = $164 / 1000 × 100

= $16.4

Hence, The cost of one hundred kilowatt-hours of electricity is $16.4

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It will take (miles / (mph eastbound + mph westbound)) hours for the two trains to be miles apart.

(miles / (mph eastbound + mph westbound)) * 60 minutes/hour = minutes

The time it takes for two trains to be a certain distance apart depends on the speed of each train and the distance between them. To calculate this, we can use the equation time = distance/speed. We can also use this equation to calculate the time for two trains traveling in opposite directions. To do this, we add the speed of the eastbound train (mph eastbound) and the speed of the westbound train (mph westbound) and divide the distance between the two trains (miles) by the total. This gives us the amount of time it will take for the two trains to be miles apart. After converting the answer to minutes, we get the amount of time it will take for the two trains to be miles apart.

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Answer:

a) To find out how much money is added to the account each year, we use the simple interest formula: I = Prt, where I is the interest, P is the principal (initial deposit), r is the annual interest rate (expressed as a decimal), and t is the number of years.

In this case, P = 1800, r = 0.03, and t = 1 (because we are finding the interest added for 1 year)

So the formula becomes:

I = 1800 * 0.03 * 1 = 54

Therefore, £54 is added to the account each year.

b) To find out how much money will be in the account after two years, we add the original deposit to the total interest earned over two years.

We know that the interest added each year is £54, and since we are trying to find the balance after 2 years, we will multiply it by 2 to find the total interest earned over 2 years:

Interest = 54 * 2 = £108

Now we add the original deposit and the total interest to find the total amount in the account after 2 years:

Total = 1800 + 108 = £1908

So the amount of money in the account after two years will be £1908.

The account will have £1909.62 after two years.

Simple interest is the amount of interest charged on a specific principal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.

a) The amount of money added to the account each year is determined by multiplying the principal amount (initial amount) by the interest rate. So, the amount added to the account each year is:

Interest = Principal x Rate

Interest = £1800 x 0.03

Interest = £54

Therefore, £54 will be added to the account each year.

b) To find the amount of money in the account after two years, we need to add the interest earned in each year to the principal amount. After one year, the account will have:

Amount after 1 year = £1800 + £54 = £1854

After the second year, the account will have earned another 3% interest on the new balance of £1854. So, the interest earned in the second year is:

Interest = £1854 x 0.03

Interest = £55.62

Therefore, the total amount of money in the account after two years is:

Amount after 2 years = £1854 + £55.62 = £1909.62

So, the account will have £1909.62 after two years.

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Answer: 0.875 for decimal, 87.5 for percent.

Step-by-step explanation- Pretty easy, all you gotta do is divide the top by the bottom. So 7 divided by 8= 0.875!

For percent, divide 7 by 8 and then multiply by 100, it would be 87.5

Answer: The system of equations to determine the number of each item sold would be:

4x + 5y = 340 (where x is the number of cakes and y is the number of pies)

and

x + y = 75 (where x and y is number of cakes and pies)

This system of equations can be solved using methods such as substitution or elimination.

Step-by-step explanation:

So, on solving the provided question, we can say that, here  by differential equations So, 2(400)(25) = 2(500)(dy/dt) => [tex]dy/dt = 20 ft/sec[/tex]

Sequences in which the difference between succeeding terms is constant are known as arithmetic progressions. For instance, an arithmetic progression with a tolerance of 2 is the sequence 5, 7, 9, 11, 13, and so on. An arithmetic progression (A.P.) is a progression where the tolerance between two succeeding numbers is always the same.

Let x be the girl's distance from the kite at time t and y be the length of the string at that same moment.

The right triangle at time t has a hypotenuse of length y, a hypotenuse of length 300, and a hypotenuse of length x.

[tex]dx/dt = 25[/tex]

By the Pythagorean Theorem,

[tex]x2 + 3002 = y2[/tex]

[tex]2x(dx/dt) = 2y(dy/dt)[/tex]

Since [tex]x2 + 3002 = y2 and y = 500, x = 400[/tex]

So, 2(400)(25) = 2(500)(dy/dt)

[tex]dy/dt = 20 ft/sec[/tex]

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According to the information, we can infer that there are 20 games left. To solve this problem we have to use a linear equation.

To calculate how many games do the Rockets have left to play we have to use a linear equation. Additionally, we have to take into account the information that we have:

Also, we know that if the rockets loses all the remaining games, and the rangers win all the remaining games, both will win the same number of games. Finally, to solve this problem we have to make the following equation:

In this equation, X is equal to the number of games won by both teams.

(100 - X)*(7/20) + X = (100 - X)*(3/5)

X = (100 - X)*(3/5) - (100 - X)*(7/20)

X = (100 - X)*(3/5 - 7/20)

X = (100 - X)*(12/20 - 7/20)

X = (100 - X)*(5/20)

(20/5)*X = 100 - X

4*X = 100 - X

4*X + X = 100

5*X = 100

X = 100/5

X = 20

According to the above, the number of games won by both teams is 20.

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Answer: 3ml:4ml:7ml

Step-by-step explanation: To simplify ratios you have to find the highest number that you can divide all the parts in the ratio by (AKA as highest common factor)

In this case the common factor of 18,24 and 42 is 6.

so now divide all the parts by 6:

18/6=3

24/6=4

42/6=7

finally put these numbers back into the correct ratio format and for this question put on the units.

final answer= 3ml:4ml:7ml

Answer:

f(-2) = 7

Step-by-step explanation:

For this, we need to substitute -2 for x, giving us:

[tex]-2^{2} + 3[/tex]

Simplifying:

4 + 3 = 7

So, f(-2) = 7.

Hope this helped!

W is an invariant sub-space under T if and only if all non-zero vectors in W are eigenvectors of T because T=αI,α∈F.

The vector is an entity with both magnitude and direction. The movement of an item between two points is described by a vector. The directed line segment can be used to graphically represent vector math.

Given that,

For each vector v ∈ V, there exists [tex]a_{v}[/tex] such that [tex]T_{v}=a_{v}v[/tex] (because [tex]T_{v}[/tex] ∈ span(v) ). Suppose there are vectors u, v∈V such that [tex]a_{u}\neq a_{v}[/tex]. Then

T(u+v)=Tu+Tv⇒[tex]a_{u+v}(u+v)=a_{u}u+a_{v}v[/tex]

which means (u,v) is linearly dependent (since both coefficients cannot be zero simultaneously, by assumption). Therefore, either [tex]a_{u}= a_{v}[/tex], and T is a scalar transformation, or V has a dimension of at most 1, which also implies Tx=αx, with constant α.

Hence, T=αI,α∈F

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the distance between the tree and the flagpole is approximately 23.29 feet.

To find the distance between the tree and flagpole, we can use the Pythagorean theorem, which states that the square of the distance between the two points (the hypotenuse of the right triangle) is equal to the sum of the squares of the other two sides.

In this case, the distance between the tree and flagpole (the hypotenuse of the triangle) is equal to the square root of (20^2 + 12^2) = square root of (400 + 144) = square root of 544.

So the distance between the tree and the flagpole is approximately 23.29 feet.

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Answer:

I think the answer is A. I hope this is helpful