When an object is dropped vertically from a platform, its height after t

t

seconds can be estimated with the formula shown.


h=h0−16t2

h=h0-16t2

h is the height of the object in feet.
h0 is the initial height of the object in feet.
t is the time in seconds after the drop.


Which equation and solution tells how long it takes the object to reach a height of 96 feet if its initial height is 208

The total cost for a meal of $110 plus a service charge of 18% is $129.8.

Given that, the meal costs $110 plus a service charge of 18%.

The total cost of the meal will be the addition of cost of meal and the service charge.

Total cost = cost of meal + service charge

Total cost = $110 + ( 18% × $110 )

Note that 18% is the same as 18/100

Total cost = $110 + ( 18/100 × $110 )

Total cost = $110 + ( 0.18 × $110 )

Total cost = $110 + ( $19.8 )

Add $110 and $19.8

Total cost = $129.8

Therefore, the total cost of the meal is $129.8.

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Answer:

2a^2b^3−a^2b^4

Answer:

Distance = [tex]\sqrt{(1-5)^{2} + (5-2)^{2} }[/tex] units

               = [tex]\sqrt{(-4)^{2} + (3)^{2} }[/tex] units

               =[tex]\sqrt{25}[/tex] units

               = 5 units

Ramon expression for price on sale d - 0.2d is equal to the calculated expression for the price on sale, hence correct

Raquel expression for the price 0.08d is not equal to calculated expression for price after discount 0.8d , hence incorrect.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given,

Expression by Ramon to show the price of winter clothing with discount

= d - 0.2d

Expression of Price by Raquel = 0.08d

Let the price of the clothing is d,

Discount = 20% = 20% × d = 20d/100 = 0.2d

Price on sale = d - 0.2d

Solving the expression,

Price = d(1 - 0.2)

Price after discount = 0.8d

Hence, by the calculation

Ramon expression for the price on sale d - 0.2d is correct

while Raquel expression is incorrect because the expression for the price is 0.8d.

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The value of the domain and the range of the composite function (gof)(x)  as per f(x) = e^x and g(x) = x + 6 is equal to x∈ R⁺  ( real numbers ) and

x > 6 , x∈ R⁺  respectively.

Function f(x) is equal to e^x

Function g(x) = x + 6

Composite function  (gof)(x) is equal to:

(gof)(x)

= g ( f(x))

= g ( e^x )

= e^x + 6

Domain represents all input values and range represents all output values.

Domain of the composite function (gof)(x) is equal to x∈ R⁺  (real numbers)

Range of the composite function (gof)(x)  is equal to  x > 6 , x∈ R⁺

Therefore, the domain and range of the composite function (gof)(x)  is equal to x∈ R⁺  ( real numbers ) and  x > 6 , x∈ R⁺  respectively.

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Median of the probability distribution is 1.

Correct option is B.

The median of a set of data is the middlemost number or center value in the set. The median is also the number that is halfway into the set.

The median for a random variable X is m such that P(X≤m)≥1/2 and P(X≥m)≥1/2.

Given,

The probability distribution for the number of events in which a student competes is provided.

X is number of events,

P(X) is probability

Here,

For median value, P(x) ≥ 1/2

P(x) = 4/8 = 1/2

Value of X for P(x) = 1/2 is 1.

Median = 1

Hence, 1 is the median of probability distribution.

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Answer:



Step-by-step explanation:

X+

(2x+3)-(x+2)

First you subtract 3 by 2. You wil get 1.

They you subtract 2x by x. You will get 1

So, your answer is x+1

The term that best describes the analysis conducted by the researcher is "descriptive statistics".

What is Descriptive statistics?

A descriptive statistic is a summary statistic that quantitatively describes or summarizes features from a set of data, whereas descriptive statistics is the process of employing and analyzing those statistics.

The term that best describes the analysis conducted by the researcher is "descriptive statistics".

Descriptive statistics is the branch of statistics that deals with the summarization, presentation, and interpretation of data. In this case, the researcher recorded the height of all 217 adult members of a tribe and calculated the average height, which is a measure of central tendency. The purpose of this analysis was to describe the distribution of height among the tribe members, rather than to make inferences about the population or test hypotheses about the population parameters.

In summary, the researcher used descriptive statistics to describe the distribution of height among the tribe members by summarizing the data using measures such as the average height.

Therefore, The term that best describes the analysis conducted by the researcher is "descriptive statistics".

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No, it is not possible to have a connected graph with six vertices of degrees 1, 1, 2, 2, 2, and 3.

As we know that the sum of the degrees of the vertices in a connected graph must be equal to twice the number of edges.

So, in this case, the sum of the degrees must be equal to 2 * K, where K is the number of edges in the graph.

Since the degrees of the vertices are 1, 1, 2, 2, 2, and 3,

the sum of the degrees is 1 + 1 + 2 + 2 + 2 + 3 = 11.

The number of edges must be K = 11 / 2 = 5.5,

which is not possible as the number of edges must be a positive integer.

Therefore, it is not possible to have a connected graph with six vertices of degrees 1, 1, 2, 2, 2, and 3.

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The similarity statement for the triangle is ΔPQR ~ ΔSTM

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words similar triangles have the same angles and the sides of the triangles are ratio of each other.

Hence, let find the statement of proportionality of the triangles as follows:

Therefore,

∠P ≅ ∠S

∠Q ≅ ∠T

∠R ≅ ∠M

And finally,

ΔPQR ~ ΔSTM

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Jorge has a ticket has a probability of 0.3 of winning a prize. after seven days, probability that jorge has won at least one prize is 0.9176

Let the probability of Jorge winning be 0.3 so ,

Probability of not winning be (1-0.3)⁷

(0.7)⁷

= 0.0823

Therefore, Jorge not winning is 0.0823.

If he wins at least one prize is,

1 - P(win nothing)

1 - 0.0823

= 0.9176

Therefore, the probability that the Jorge wins at least one prize is 0.9176.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

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Answer:

Option A (You chose it right)

Step-by-step explanation:

Base of triangle = [tex](\frac{\sqrt{2}}{2} + \frac{\sqrt{2}}{2})[/tex] units

Since the two fractions have the same denominator, the resulting simplified fraction will have the same denominator and everything written in the numerator level will be copied down as it is:

                           = [tex]\frac{\sqrt{2} + \sqrt{2}}{2}[/tex]

                           =[tex]\frac{2\sqrt{2}}{2}[/tex]

                           = [tex]\sqrt{2}[/tex] units

Area:

Area of a triangle = [tex]\frac{1}{2}[/tex] × base of triangle × perpendicular height

                             = [tex]\frac{1}{2}[/tex] × ([tex]\sqrt{2}[/tex] units) × ([tex]\frac{\sqrt{3}}{2}[/tex] units)

                             = ([tex]\frac{\sqrt{2}}{2}[/tex] ×[tex]\frac{\sqrt{3}}{2}[/tex]) square units

     ∴ Area            [tex]= \frac{\sqrt{6}}{4}[/tex] square units

Perimeter:

It is the sum of all the outer sides (or outer boundaries) of the triangle:

Perimeter = Base of triangle + first slanted height + second slanted height

                = [tex](\sqrt{2} + \sqrt{2} + \sqrt{2})[/tex] units

                [tex]= 3\sqrt{2}[/tex] units

∴ Option A

Answer:

10.4

Step-by-step explanation:

m² =10²+3² = 109

so m =√109 = 10.4

The equation of the parallel lines is y = x + 2.

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline. No matter how far we extend a parallel line, it will never meet another parallel line.

The slope of two parallel lines are equal.

The equation of the given line is:

y = x + 6

here, the slope of the line is 1.

So, the slope of the new line is 1.

The new line has the coordinates (-4, 1).

Using the point-slope form we have:

y - y1 = m (x - x1)

y - 1 = 1 (x + 1)

y - 1 = x + 1

y = x + 2

Hence, the equation of the parallel lines is y = x + 2.

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Answer: -13

Step-by-step explanation:

Answer:

Step-by-step explanation:

It would be 4+g

Since we are trying to find how many lbs in total we would add the total we already know which is 4 and then add the g pounds of green apples

To calculate the total amount of apples Alan has bought, we simply apply the concept of Algebraic Expressions and add the pounds of red apples (which is 4) to the pounds of green apples (which is represented by g). This can be represented in a mathematical expression as 4 + g.

Alan bought 4 pounds of red apples and g pounds of green apples. To find out how many pounds of apples he bought in total, we need to add the quantities together. So, the expression that shows that is 4 + g. This means that Alan bought 4 pounds of red apples and g pounds of green apples, adding those two quantities together gives the total pounds of apples he bought.

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The expression for x² in standard form is x² = (yˣ×10)²= y²×10².

Expression  is a mathematics combination of symbol such as number and operators which produce the mathematical result and expression can involve a single trauma multiple term and usually consist of a combination of constant variables operators function.

This means that if x is given in the form of x = y×10, then x² can be expressed as y² × 10². This form is advantageous because it allows for easier manipulation of the numbers. For example, if x = 5 ×10², then x²can be expressed as (5×10²)²= 5²× 10²×²= 25 × 10⁴. This expression is much easier to understand than the expanded form of x² = 5²× 10² × 10² = 25 ×10².

In addition, this expression for x²allows for efficient calculation of larger powers of x. For example, if x = 5 ×10², then x²can be expressed as (5×10² = 5³ × 10²×³= 125 × 10⁶. This is much faster to calculate than the expanded form of x³= 5³ ×10² ×10²× 10² = 125 ×10⁶.

Therefore, the expression for x² in standard form is an effective way to manipulate and calculate larger powers of x.

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Answer:

Below

Step-by-step explanation:

Rate of change is   slope  = rise / run =  (0 - -3) / (-3 - -2) = 3/-1 = -3

The 3 couples can be seated in 20 ways.

The answer I provided uses the concept of permutations. In permutation, we calculate the number of arrangements or ways in which a set of elements can be arranged.

In this case, the question is asking for the number of ways in which 6 individuals (3 married couples) can be seated in a row. To find the number of arrangements, we can use the formula for permutations of multiples:

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

Where n is the number of items to arrange and k is the number of identical items. In this case, n = 6 (number of individuals) and k = 3 (number of married couples).

However, we need to also account for the fact that within each married couple, the two individuals can be seated in either order. Hence, we need to divide the result by 2! for each couple, giving us the formula:

P(6, 3) / (2! * 2! * 2!) = 6! / (3! * 3!) = 20

So there are 20 different ways in which the 3 married couples can be seated in a row.

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The line perpendicular to the line with an equation y = 6x have a slope of -1/6

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

The slope intercept form of a linear equation is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are perpendicular if the product of their slopes is -1.

Line M goes through the points (0, 0) and (1, 6). Hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\y-0=\frac{6-0}{1-0} (x-0)\\\\y=6x[/tex]

The slope of the line y = 6x is 6.

The line perpendicular to y = 6x have a slope of -1/6

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The solution of the expression (9t³n³)(−2t n²) will be -18t⁴n⁵.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is (9t³n³)(−2t n²). The given expression will be solved as:-

E =  (9t³n³)(−2t n²)

E = 9 x -2 x t³ x t x n³ x n²

E = -18 x t³⁺¹ x n³⁺²

E = -18t⁴n⁵

Therefore, the solution of the expression is E = -18t⁴n⁵.

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Answer:

I could but can you please put down the problem.

Step-by-step explanation:

Answer:

The length of the hypotenuse is 6.4 yards.

Step-by-step explanation:

We can use the Pythagorean Theorem to evaluate the hypotenuse.

The formula for the Pythagorean Theorem is

[tex]a^2+b^2=c^2[/tex]

Where [tex]a[/tex] and [tex]b[/tex] are the legs of the triangle; and [tex]c[/tex] is the hypotenuse.

We are given the values of both legs.

[tex]a=4\\b=5[/tex]

Inserting these values into the equation gives us

[tex]4^2+5^2=c^2[/tex]

Lets solve for [tex]c[/tex].

Evaluate [tex]4^2[/tex].

[tex]16+5^2=c^2[/tex]

Evaluate [tex]5^2[/tex].

[tex]16+25=c^2[/tex]

Add [tex]16[/tex] and [tex]25[/tex].

[tex]41=c^2[/tex]

Take the square root of both sides to eliminate the exponent.

[tex]\sqrt{41} =c[/tex]

[tex]\sqrt{41}=6.40312[/tex]

Rounding to the nearest tenth leaves us with

[tex]c=6.4[/tex]

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Implications of an empty row in the roof portion of the house of quality Customer requirements are potentially not being met by the product.

The house of quality serves as a form of conceptual road map for interfunctional communication and planning. In order to discuss design goals, people with various issues and responsibilities can refer to evidence patterns on the grid of the home.

Quality function deployment is a set of planning and communication procedures that concentrates and organises capabilities inside an organisation in order to first create, then manufacture, and finally sell products that consumers want to buy and will continue to buy. The idea that items should be high-quality is the cornerstone of the house of quality.

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The percent error would be : {c - 78}/{c} x 100

Given is that the team ends up selling 78 cookies at next year's opening game.

Let the estimated value be {c} cookies. Now, we know -

%error = {a - x}/{x} x 100

%error = {c - 78}/{c} x 100

Therefore, the percent error would be : {c - 78}/{c} x 100.

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Therefore, the new triangle XYZ with vertices X'(-8,3), Y'(-1,2) and Z'(-2,-7) is obtained after the transformation.

Triangles are called polygons if they have four quadrants or more. Its form is a simple geometric figure. When put together, the characters ABC create a right-angled triangle. When the boundaries are incompatible, Euclidean geometry generates a new rectangle with square corners. Triangles are regarded as polygons because they have three edges and three corners. Where a triangle's three edges intersect determines where its corners are. A triangle's interior sides add up to 180 degrees.

Here,

After the transformation, the new vertices of the triangle will be:

X(1-9, 8-5) = (-8,3)

Y(8-9, 7-5) = (-1,2)

Z(7-9, -2-5) = (-2,-7)

Therefore, the new triangle XYZ with vertices X'(-8,3), Y'(-1,2) and Z'(-2,-7) is obtained after the transformation.

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The image here given an example of perpendicular line.

Correct option is: yes, the lines are intersect at right angle.

Two lines are perpendicular if they cross at a point where they provide a pair of linear angles that are congruent. If a transversal in a plane is parallel to one of two parallel lines, it is also parallel to the other line. Lines that cross at a straight angle (90°) are said to be perpendicular. Perpendicular lines are those that cross at a right angle when two non-vertical lines in the same plane. Vertical and horizontal lines, or the axes of the coordinate plane, are perpendicular to one another. Two parallel lines' slopes have negative reciprocal slopes.

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