Pyrotechnicians can use polynomials to plan complex fireworks displays. A firework is launched from a platform 6 feet above the ground at a speed of 200 feet per second. The firework has a 5-second fuse. The height of the firework in feet is given by the polynomial -16t² + 200t + 6, where t is the time in seconds. How high will the firework be when it explodes?

The  sign of r is positive and  there is a positive and weak correlation.

What is Statistics ?

In statistics, association is any statistical relationship, whether causal or not, between two random variables or bivariate data.  One is independent and other is dependent variable.  

In the broadest sense correlation is any statistical association, though in common usage it most often refers to how close two variables are to having a linear relationship with each other.

Examples are exercise and sickness are negatively correlated.

Study hours and marks are positively correlated

When correlation is nearer -1 or +1 there is a strong correlation.  When correlation is nearer to 0 than to 1 or -1 we say that there is a negative correlation.

Hence, The  sign of r is positive and  there is a positive and weak correlation.

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The perimeter of the floor of the office building  which was given as 127.5 feet is equal to 42.5 yards.

Perimeter of the floor in an office building is equal to 127.5 feet.

Convert perimeter of the floor of the given office building in feet into yards:

Number of feet in one yard = 3 feet

3 feet = 1 yard

⇒ 1 feet = ( 1 / 3 ) yard

⇒ 127.5 feet = ( 127.5 ) ×   ( 1 / 3 ) yards

⇒127.5 feet = ( 127.5 / 3 ) yards

⇒127.5 feet = ( 42.5 ) yards

Therefore, the perimeter of the floor of the given office building is equal to 42.5 yards.

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Answer:

Without exponents: a * a * a * a * a

Fill in the blank: [tex]a^5[/tex]

Step-by-step explanation:

We have to use exponent rules:

[tex]x^y * x^y = x^{y+y} \\= x^{2y}[/tex]

So for this problem, we can apply that rule here:

[tex]a^3 * a^2 = a^{3+2}[/tex]

= [tex]a^5[/tex]

^ This will be the answer to the second question.

Now, to find the equation without exponents, we can use the information we have from above. We need to use this rule: [tex]x^2 = x * x[/tex]

Since our equation is [tex]a^5[/tex], we can rewrite it as a * a * a * a * a.

Answer:

C

Step-by-step explanation:

At the height of 2500 m, the temperature will be T = 16 ℃.

Given is that air temperature of a mountain drops by 2 ℃ for every 500 m of elevation. If the air temperature is 26 ℃ at the base of the mountain, at what elevation will the air temperature be 16 ℃.

2 ℃ for every 500 m of elevation.

Then, for 1 m of elevation, it will change by (2/500) or (1/250) ℃

We can write the function as -

T{x} = 26 - {x/250}

Now, for T = 16 ℃, we can write -

26 - {x/250} = 16

26 - 16 = x/250

10 = x/250

x = 2500 m

Therefore, at the height of 2500 m, the temperature will be T = 16 ℃.

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The value of x would be √2.

What is the 45-45-90 triangle?

A 45-45-90 triangle is a special type of right triangle where the angles measure 45 degrees, 45 degrees, and 90 degrees. The sides of the triangle are in a specific ratio to each other. The hypotenuse, or the longest side of the triangle, is the same length as the other two sides (the legs). This side length is also equal to the square root of 2 times the length of either leg. The legs of the triangle are congruent to each other. This triangle is also known as an "isosceles right triangle".

In the given figure, we can apply a 45-45-90 triangle,

side opposite to 45 = 1/√2 * Hypotenuse

x = 1/√2 * 2

x = √2

Hence, the value of x would be √2.

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Answer:

x = 20

Step-by-step explanation:

Because these are alternate interior angles, 2x+20 and 3x are equivalent to each other. Therefore, we can set up this equation:

2x+20 = 3x

Now, we can solve this equation and find x:

20 = 3x-2x

x = 20

These provided angle measures (3x and 2x + 20) are a pair of alternate interior angles because they satisfy the following required conditions:

Since the two angles ARE alternate interior angles, they are EQUAL! Therefore, we can equate the two angles and solve for the variable (x).

{2x + 20 is equal to 3x} ⇒ 2x + 20 = 3x

The key step in solving the linear equation is to ISOLATE the variable completely by removing the coefficient until you have 1 as the coefficient.  

There are 4 possible ways to isolate the variable:

Once your variable is completely isolated, simplify (if possible) on the other side of the equation. If the opposite side of the variable is simplified, you can conclude your solution for the linear equation.

Now, let us solve the equation using the above step by step processes.

Isolating the variable from the constant(s) on the R.H.S:  

Simplify both sides of the equation:

Therefore, the solution to the linear equation (x) is 20.

__________________________________________________________

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The expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

A base must be raised to a certain exponent or power, or logarithm, in order to produce a specific number.

If bx = n, then x is the logarithm of n to the base b, which is expressed mathematically as x = logb n.

For instance, 23 = 8; hence, 3 is the base-2 logarithm of 8 or 3 = log2 8.

Common logarithms, with a base of 10, binary logarithms, with a base of 2, and natural logarithms, with a base of e 2.71828, are the four most popular varieties of logarithms.

So, we must keep in mind the following characteristics of the logarithms in order to solve the issue:

[tex]\begin{aligned}& \log (x . y)=\log (x)+\log (y) \\& \log \left(x^y\right)=y \cdot \log (x)\end{aligned}[/tex]

Then, the expression we have:

[tex]P=\log \left(6 x^4\right)[/tex]

The factor of 6=2*3:

[tex]P=\log \left(2 \cdot 3 x^4\right)[/tex]

Apply the product's feature:

[tex]P=\log (2)+\log (3)+\log \left(x^4\right)[/tex]

Apply the exponent's property now:

P=log(2)+log(3)+4.log(x)

Therefore, the expanded form of the given logarithm using the properties of logs is P=log(2)+log(3)+4.log(x).

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Correct question:

Expand the logarithm fully using the properties of logs. Express the final answer in

terms of log .

log 6x^4

The quotient for the given division of fractions [tex]5\dfrac{2}{3} \div 4[/tex]  is 17/12.

We are given the equation - [tex]5\dfrac{2}{3} \div 4[/tex]

First we will convert the mixed fraction 5\dfrac{2}{3} in to improper fraction as follows -

[tex]5\dfrac{2}{3}[/tex]   [tex]= \frac{3*5+2}{3}[/tex]

[tex]5\dfrac{2}{3}[/tex]   [tex]= \frac{17}{3}[/tex]

Now we will divide the fraction as follows -

[tex]5\dfrac{2}{3} \div 4[/tex]

= 17/3 ÷ 4

taking the reciprocal of 4 and changing the divide sign into multiplication we get,

= 17/3 x 1/4

= 17*1 / 3*4

= 17/12

Hence, the quotient for the given division of fractions is 17/12.

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An arithmetic progression (AP) is a sequence of numbers such that the difference between any two consecutive terms is always the same.

This common difference is called the common ratio of the arithmetic progression. The general form of an arithmetic progression is a, a + d, a + 2d, ..., where a is the first term and d is a common difference.

The nth term of an arithmetic progression can be found by using the formula: a_n = a + (n-1)d, where a is the first term, d is a common difference, and n is the position of the term in the progression.

If a, b, and c are in arithmetic progression, then the common difference is (b-a) = (c-b).

If d, e, and f are also in arithmetic progression, then the common difference is (e-d) = (f-e).

If a, d are the same and b, e are the same, then c = f.

so the common difference between both progressions is the same, and c = f

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let , and be arithmetic progressions. if and , then what is ? let , and be arithmetic progressions. if and , then what is the common difference

Step-by-step explanation:

you did not provide an expression. only fragments, I suspect.

I can give you the basic rules.

always remember the order of operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

a fraction is a division.

e.g. 2/3 = 2 divided by 3

e.g. (a/b)⁵ = a⁵/b⁵

(a×b)⁵ = a⁵×b⁵

e.g. a^-b = 1/(a^b)

e.g. a^(c/b) =

[tex] \sqrt[b]{ {a}^{c} } [/tex]

I think that is all about exponents and fractions.

The relative frequency of Selena's friends who speak more than one language is 3/16 or 0.1875

To create a relative frequency distribution, we first need to find the total number of responses by summing up the number of languages spoken by Selena's friends. In this case, the total number of responses is 2 + 1 + 1 + 1 + 2 + 3 + 1 + 2 + 1 + 1 = 16.

Next, we need to find the relative frequency for each category, which is the number of responses in that category divided by the total number of responses. To find the relative frequency of her friends who speak more than one language, we need to add up the number of responses in categories 2, 3, and above.

In this case, the number of responses in category 2 is 2, the number of responses in category 3 is 1, and there are no responses above 3.

So the relative frequency would be (2+1)/16 = 3/16 or 0.1875

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1 hour and 12 minutes is the time that will it take her to develop 8 rolls of film.

According to the question,

Tara develops 2 rolls of film in about 18 minutes.

Tara develops 1 roll of film in about  = (18 ÷2) minutes

                                                                = 9 minutes (using division)

Tara develops 8 rolls of film in about = ( 8 × 9) minutes

                                                                   = 72 minutes

we know that, 1 hour = 60minutes

Tara can develop 8 rolls of film in about = (72 ÷ 60)

                                                                   = 1 hour 12 minutes

So, Tara can develop 8 rolls of film in about 1 hour and 12 minutes.

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Answer: The inequality one fifth times the difference of m and five is less than or equal to one tenth times the difference of m and twenty can be rewritten as:

(1/5)(m-5) <= (1/10)(m-20)

To find the integers in the set S that will make this inequality false, we need to find the values of m that do not satisfy it. We can start by simplifying the inequality:

(1/5)(m-5) <= (1/10)(m-20)

(1/5)m - (1/5)5 <= (1/10)m - (1/10)20

(1/5)m <= (1/10)m - (1/10)20 + (1/5)5

(1/5)m <= (1/10)m - 2 + (1/5)5

(4/5)m <= (1/5)5 - 2

m <= -5

So, the integers in the set S that do not satisfy the inequality are 20 and 40. These integers will make the inequality false.

Step-by-step explanation:

Answer: I believe the solutions your looking for would be x = 0 or x = −8

Step-by-step explanation:

x (x + 8) = 0

Step 1: Simplify both sides of the equation.

x² + 8x = 0

Step 2: Factor left side of equation.

x (x + 8) = 0

Here are factors equal to 0:

x = 0 or x + 8 = 0

x = 0 or x = −8

I hope this helps!

Answer:

Step-by-step explanation:

x inside the () is equal to -8

then that will be ( -8 + 8=0)

the x multiply by 0 is 0

You welcome

It's important to note that even if the sample is random, there's still a chance that the sample may not be representative of the population, this is known as sampling error.

The fundamental act of thinking about anything logically and sensibly is best described as reasoning.

It depends on how the teacher choose the class members. Because every student had an equal chance of being chosen, the sample, if the students were chosen at random, is likely to be indicative of the class' performance on the quiz. However, the sample would not be indicative of the class's performance on the quiz if the teacher arbitrarily chose the students, for instance, by selecting only the best or the worst performers.

In general, if a sample is large enough and random, it is thought to be representative of the population. The likelihood that the sample is representative of the population rises with greater sample sizes. Since only 8 students were chosen in this instance, it's possible that the results don't accurately reflect how the entire class did on the quiz.

The term "sampling error" refers to the possibility that a sample, even one drawn at random, may not be representative of the population as a whole.

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The required simplified value of the m is given as -37. as of the given information.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
According to the question, we have variable m, and 35 less than m is -72

m - 35 = -72

Add 35 on both sides
m = -72 + 35
m = -37

Thus, the required simplified value of the m is given as -37.

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Answer:

x = 7 , y = 4

Step-by-step explanation:

the triangle on the right has 3 congruent angles and is therefore equilateral with 3 congruent sides, so

3x - 5 = 5y - 4 → (1)

the triangle on the left has 2 congruent angles and is therefore isosceles with the 2 legs being congruent, so

3x - 5 = y + 12 → (2)

we have 2 equations with 3x - 5 on the left side so equate the right sides

5y - 4 = y + 12 ( subtract y from both sides )

4y - 4 = 12 ( add 4 to both sides )

4y = 16 ( divide both sides by 4 )

y = 4

Then

5y - 4 = 5(4) - 4 = 20 - 4 = 16 , so

3x - 5 = 16 ( add 5 to both sides )

3x = 21 ( divide both sides by 3 )

x = 7

Answer:

Jude: y = 5x

Ian: y = 45 - 10x

Step-by-step explanation:

Jude:

y = 5x

Ian:

y = 45 - 10x

The expression that is equivalent is options D. (-g - 3h)(-6) and E. -2(-3g + 9h)

Factorization is a process in which a given term is reduced to its lowest form by comparing common divisible number, or alphabet.
Considering the given expressions, that one that will be equivalent to 6g - 18h can be determined by;

i. 6g - 18h

factor out 6 to have;

6g - 18h = (g - 3h)6

             = (-g - 3h)(-6)

ii. 6g - 18h

The common divisor is 2, so that;

6g - 18h = 2(3g - 9h)

minus sign can be factor out

2(3g - 9h) = -2(-3g + 9h)

So that on expansion, the initial expression in the question can be gotten.

Therefore, the expression that are equivalent are (-g - 3h)(-6) and -2(-3g + 9h)

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The equation of the inverse of y = x + 3 is y = x - 3.

The theory used in this question is the concept of inverse relationships. In mathematics, an inverse relationship is a relationship where two variables are related in such a way that when one variable increases, the other decreases.

In this case, the relationship between x and y is represented by the equation y = x + 3.

To find the inverse of this equation, we need to switch the coordinates in each ordered pair, which is done by subtracting 3 from the output (y) for each ordered pair.

This gives us the equation y = x - 3, which is the inverse of y = x + 3.

y=x+3

Input (x) Output (y)

3   6

-1   2

5   8

Inverse of y=x+3

Input (x) Output (y)

6   3

2   -1

8   5

The equation of the inverse of y = x + 3 is y = x - 3.

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∠XBC is 55 degrees because it is corresponding to ∠AXY..

The angle ∠BXC is 70 degrees

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, same interior angles, vertically opposite angles etc.

Therefore, XY and BD are parallel lines.

XB = XC

ΔXBC is an isosceles triangle.

Therefore, ∠XBC is 55 degrees because it is a corresponding angle to ∠AXY.

Let's find ∠BXC.

Therefore, the base angles of an isosceles triangle are congruent.

Hence,

∠XBC = ∠BCX = 55 degrees

Therefore,

55 + 55 + ∠BXC = 180

110 + ∠BXC = 180

∠BXC = 180 - 110

∠BXC = 70 degrees

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The amount that Brian and Jamie have to plan on spending should be: $4859.

The security deposit is equal to 1 month's rent, which is $1350.

The first and last month's rent is also $1350, so that's a total of $2700 for the first and last month's rent and the security deposit.

The broker's fee is 12% of the yearly rent, which is $1350 x 12 = $16,200.

12% of $16,200 is $1944.

So in total, they will have to pay $150 application deposit + $15 credit report + $2700 + $1944 = $4859.

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The radius of circle for the given length of rod is found as 1.65 ft

Perimeter of circle = 2 π r

In which,

When the length of the rod is bent to form the circle.

Length of rod = Perimeter of circle

10.38 = 2 π r

r = 10.38 /  2 π

r = 1.65

Thus, the radius of the circle for the given length of rod is found as 1.65 ft.

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Party planner 2 charges $15 more per person than party planner 1.

What is linear equation ?

Linear equation can be defined as the equation in which the highest degree is one.

Given ,

Melanie is comparing the price of two party planners. Party Planner 1 and Party Planner 2. Party Planner 1 uses the equation, y = 10x + 70,

where x is the number of people attending the party and y is the total cost.

y=15x+75 means that they charge $15 for every person but $75 right away. For planner 2, they charge $20 a person because comparing coordinates 1 and 2,

every 5 people charge $100. So to find the amount per person for planner 2, divide 100 by 5 and you'll get 20, and

since 20 is 5 more than 15. A is true.

Therefore, Party planner 2 charges $15 more per person than party planner 1.

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If Fran swims at 2.2 mph in still water and  Lazy River flows at a speed of 0.6 mph , the the time required by Fran to go 2.4 mi upstream is 1.5  hours and 2.4 mi downstream is 0.857  hours .

the speed of Fran in still water (rate) = 2.2 mph ;

the sped of the river (current) is = 0.6 mph  ;

The time  taken by Fran to swim 2.4 miles upstream and 2.4 miles downstream can be calculated by formula :

⇒ time = distance/(rate + current)  ;

the distance to be covered is = 2.4 miles ;

For the time taken by Fran to swim upstream , the speed of current is subtracted from the Speed of Fran ;

So , time = 2.4/(2.2-0.6) = 2.4/1.6 = 1.5 hours

For the time taken by Fran to swim downstream, the speed of current is added to the Speed of Fran ;

So , time = 2.4/(2.2 mph + 0.6) = 2.4/2.8 = 0.857 hours

Therefore , by Fran it will take 1.5 hours to travel 2.4 miles upstream and 0.857 hours to travel downstream .

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y = 4x is the only function that represents the proportionality.

the property of having suitable proportions in terms of size, number, degree, harshness, etc.: If a defensive action against an unfair attack results in destruction that contravenes the proportionality criterion, it may even go far beyond a justifiable defense.

Given there are Few functions, we need to find which of the given function is proportional:

Since, We know that only the linear functions that pass through the origin are proportional.

So only function that provides the value of y at x = 0 is 0 will shoe properties of proportionality

Therefore, only function that is proportional is y = 4x.

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The coordinates after a dilation of scale factor k = 4 are (-16, 48)

If we have a general point (x, y), and we apply a dilation of scale factor k and the center of dilation is the origin, then the coordinates of the image after the dilation are (k*x, k*y)

Here we start with the point (-4, 12), and we apply a dilation of scale factor 4 and the center is the origin, then the coordinates  of the image are::

(-4*4, 12*4) = (-16, 48)

The coordinates after the dilation are (-16, 48).

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