if an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s what is the value of V0y?​

If the temperature dropped at a constant rate, it would have dropped 4°C per hour. This can be calculated by taking the difference in temperature (24°C) and dividing it by the number of hours that passed (4 hours).

The equation of the rational function with the given features is given as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.

Considering the x-intercepts, the numerator of the function is defined as follows:

y = a(x + 4)(x + 1)

y = a(x² + 5x + 4).

Considering the y-intercept at (0,4), the leading coefficient a is given as follows:

a = 4.

The vertical asymptotes determine the zeros of the denominator, which is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the function is defined as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

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For product=6 and sum=7, the numbers or integers  are 1 and 6.

What exactly are integers?

In mathematics, integers are the collection of positive and negative numbers. Integers, like whole numbers, do not include the fractional element. Thus, integers are numbers that can be positive, negative, or zero, but not fractions. On integers, we can do all arithmetic operations such as addition, subtraction, multiplication, and division. Integers include numbers such as 1, 2, 5, 8, -9, -12, and so on. "Z" is the symbol for integers.

now,

As given product=6 and sum=7  

make factors for 6 i.e 1,2,3,6

from these choose the numbers whose sum=7

and they are 1,6.

Hence,

           For product=6 and sum=7, the numbers are 1 and 6.

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The statement that are true are :

a. Z is an element {y,z}

b. {6,7,8 } is a subset of {1,2,3,4......}

c. 3 is an element of {2,3}

d. r is not an element of {s,t,u}

What is set?

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

The objects in a set are called the elements (or members ) of the set; the elements are said to belong to the set (or to be in the set), and the set is said to contain the elements.

The following statements are true about the set

a. Z is an element {y,z}

b. {6,7,8 } is a subset of {1,2,3,4......}

c. 3 is an element of {2,3}

d. r is not an element of {s,t,u}

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Answer:

Step-by-step explanation:

The terms "4/10, 2/30, n/60" indicate that the buyer can take a discount of 4% if they pay within 10 days from the invoice date, or pay the full amount within 30 days from the invoice date. If the payment is made after 30 days, the buyer must pay the full amount plus any late fees that may apply.

Since the invoice was dated October 15 and the payment was sent on October 28, the payment was made within 30 days from the invoice date, so the buyer cannot take the 4% discount.

The total cost of 50 pairs of shoes at $85 per pair is 50 * 85 = $4250.

Therefore, the total amount of the check would be $4250, which is the full amount of the purchase price without the 4% discount.

The two lengths that Bottom 7%: L= 6.04 cm

Top 7%: L= 6.22 cm

What does "z-score" mean?

The Z-score provides information on how far a given value deviates from the standard deviation. The amount of standard deviations a given data point is above or below the mean is represented by the Z-score, also known as the standard score.

                                       The level of variability within a particular data collection is effectively reflected in the standard deviation.

Mean length of the population (μ) = 6.13 cm

Standard deviation (σ) = 0.06 cm

The z-score for any given length 'X' is

        Z = X - μ/σ

     What we want to know is the length at the 7-th percentile and at the 93-rd percentile.

According to a z-score table, the 7-th percentile has a correspondent z-score of -1.476 and the 93-rd percentile has a z-score of 1.476. Therefore, the bottom 7% and top 7% are separated by the following lengths

      Z(Xb) = Xb - μ/σ

  - 1.476 = Xb - 6.13/0.06

      Xb = 6.04

  z(Xt ) = Xt - μ/σ

   1.476 = Xt - 6.13/0.06

     Xt = 6.22

Bottom 7%: L= 6.04 cm.

Top 7%: L= 6.22 cm.

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On solving the provided question, we can say that from the graphs The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technological advancement.

Mathematicians use graphs to logically convey facts or values using visual representations οr charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue tοgether the nodes, οften referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of expοnential growth. a logarithmic graph in the shape οf a triangle

The curve preceding technolοgical advancement is called PPF0. PPF1 is the curve following technοlogical advancement.

Priοr to technological advancement, the opportunity cost of treating HIV/AIDS rises as the wοrld deviates from its PPF. The pοtential cost of treating more HIV/AIDS cases falls as a result of technοlogical advancements since less other commοdities and services must be sacrificed in οrder to treat more HIV/AIDS patients. Alternatively, the world might treat mοre HIV/AIDS patients right now by forgoing the same number of other commοdities and services.

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No one bank is not always better. Factors such as the fees and the charges in one bank may differentiate it from another bank.

No, one bank is not always better than another. The best bank for an individual depends on a variety of factors, including their financial needs and preferences, location, and the fees and charges associated with different banks.

For example, one bank may have lower fees for checking accounts but higher fees for ATM withdrawals or international transactions, while another bank may have higher fees for checking accounts but lower fees for other services.

Other factors that might affect which bank has the better fee structure include the type of account, the minimum balance required to avoid fees, and the level of customer service provided by the bank. Ultimately, the best bank is the one that meets an individual's financial needs at the lowest cost.

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Answer:

2nd choice  y = 1/2x - 5

Step-by-step explanation:

y = 1/2x - 5  is the only function listed that if you graph it, it makes a straight line.   A linear function forms a straight line when it is plotted on a graph.

The first and last choices are number values of x.

The 3rd choice, if you graph it, makes a parabola.

Answer:

Second option:

[tex]y = \dfrac{1}{2}x -5[/tex]

Step-by-step explanation:

A linear function should have y as a function of x (or x as a function of y) and the degree of the function (the highest power has to be 1)

Both x and y must be present to make it a linear function

General slope intercept form is y = mx + b where m = slope, b = y-intercept

With these restrictions the second option is the correct one
[tex]y = \dfrac{1}{2}x -5[/tex]

This line is in slope intercept form y = mx + b where m = slope(in this case 1/2) and y-intercept b(in this cae -5)

Option 1:  x = 3 is a straight vertical line parallel to the y-axis. Such a line has a slope of ∞

Option 3 is a function with degree 2 and is a quadratic function

Option 4 : 3x - 6 = 4==> 3x = 6 + 4 = 10 or x = 10/3, again another vertical line with slope = ∞

Now , to find the area

Total area of figure = Area of first Triangle + Area of second triangle

The area of the triangle = ( 1/2 ) x Length x Base

Total area of figure = ( 1/2 ) x ( 36 x 15 ) + ( 1/2 ) x ( 15 x 8 )

= ( 1/2 ) x 540 + ( 1/2 ) x 120

= 270 + 60

= 330 inches²

Therefore , the value is 330 inches²

Hence , The area of the figure is 330 inches²

Answer:

Step-by-step explanation:

inequality form

d≤ 1

Interval Notation:

(−∞,1]

Answer:

3% increase

Step-by-step explanation:

Answer: x=56

Step-by-step explanation: Question 2 shows a right angle that is equal to 90 degrees. Since you are already given 34, you just need to subtract 90-34.

Question 4 shows an 180 degree angle and so you need to do the same thing; 180-124

The quotient rule is proved below.

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

Given is the expression -

Q(x) = F(x)/G(x)

Quotient rule in calculus is a method used to find the derivative of any function given in the form of a quotient obtained from the result of the division of two differentiable functions. Mathematically, for a function f(x), we can write -

f'(x) = [u(x)/v(x)]' = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Now, let f(x) = u(x) and g(x) = v(x).

Q(x) = u(x)/v(x)

Q(x) = u(x) v⁻¹(x)

Using the product rule -

Q'(x) = u'(x) v⁻¹(x) + u(x) {d/dx v⁻¹(x)}

Q'(x) = u'(x) v⁻¹(x) + u(x) (-1)(v(x)⁻²) v'(x)

Q'(x) = u'(x)/v(x) - u(x)v'(x)/v²(x)

Q'(x) = [v(x) × u'(x) - u(x) × v'(x)]/[v(x)]²

Therefore, the quotient rule is proved above.

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Answer:

  20 cubic yards

Step-by-step explanation:

You want to know the volume in cubic yards of a layer of topsoil that is 6 inches deep over an area 31 feet by 34 feet.

You know that ...

Then the dimensions of the volume being applied are ...

  6 inches = 6/36 yards

  31 feet = 31/3 yards

  34 feet = 34/3 yards

The volume is the product of the dimensions of the space:

  V = LWH

  V = (31/3 yd)(34/3 yd)(6/36 yd) ≈ 19.519 yd³

About 20 cubic yards are needed to fill the garden.

Using Venn diagram, 49 students participated in only music, 29 students participated in only sports, and 156 students were involved in either music or sports.

Let's use a Venn diagram to represent the information given:

We know that there are 200 students in total, and we can use the information given to fill in the numbers in the Venn diagram.

a.

127 students were involved in music, including 78 who were also involved in sports, so 127 - 78 = 49 students participated in only music.

b.

78 students participated in both music and sports, so 78 - 49 = 29 students participated in only sports.

20 students did not participate in either activity.

c.

The total number of students involved in music or sports is the sum of the number of students in each circle: 49 + 29 + 78 = 156.

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Answer:

Chebyshev's inequality states that for any given dataset, at least 1 - 1/k^2 of the data will lie within k standard deviations from the mean.

When k = 3, at least 1 - 1/3^2 = 1 - 1/9 = 8/9 of the data will lie within 3 standard deviations from the mean.

So, for the temperature data, we can determine that at least 8/9 of the data will lie between 28.8 - 3 × 7.4 = 7°F and 28.8 + 3 × 7.4 = 50.6°F.

In other words, we can say that at least 8/9 of the temperatures recorded during the two months were between 7°F and 50.6°F.

Answer: In each question you have two options, T and F. Then in 6 questions you have 2 options for the first, two for the second, two for the third... At the end you get 2·2·2·2·2·2 = 26 options and 26 = 64.

Step-by-step explanation:

Answer:

---------------------------

According to picture we observe:

The segment connecting the midpoints is the midsegment.

As per property of the midsegment, it is parallel to opposite side and is half of its measure.

It tells us that WB is parallel to AE and:

Answer:

96 in²

Step-by-step explanation:

Length of Semiperimeter

[tex]\displaystyle s=\frac{1}{2}(a+b+c)=\frac{1}{2}(12+16+20)=\frac{1}{2}(48)=24[/tex]

Area of Triangle w/Heron's Formula

[tex]A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{24(24-12)(24-16)(24-20)}=\sqrt{24(12)(8)(4)}=\sqrt{9216}=96[/tex]

Hence, the area of the triangle is 96 in².

73 degrees is the equivalent meausure of m<A

From the given line geometry below, the sum of the adjacent angles is 180 degrees as shown:

m∠A + m∠B = 180

Given the following

∠A = 6x - 35

∠B = 3x + 53

Substitute the given parameters

6x - 35 + 3x + 53 = 180

9x + 18 = 180

9x = 180 - 18

9x = 162
x = 162/9

x = 18

Determine the measure of <A

<A = 6x - 35

<A = 6(18) - 35

<A = 108 - 35

<A = 73 degrees

Hence the measure of angle A from the given diagram is 73 degrees

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At x=2, the function in the graph is approaches to infinity. This is satisfied by equation 1 that models the rational function, hence option 1 is the correct answer.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13.

Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

From given graph we can see that

At x=2, the function in the graph is approaches to infinity.

It means function is not defined at x=2

We know that a rational function is undefined when denominator is equal to zero.

For equation 1:

f(x)= 2(x+2)/(x-2)

Equating the denominator:

x-2=0

x=2

It means function is not defined at x=2

The y-intercept is: y= -2

The function is passing through the point (1,-6).

When we substitute x=1

Hence, option 1 is true.

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The doubling time for the investment as required to be determined is; 15.58 years.

It follows from the task content that the model function is;

A(T)=650 (1.0455) ^T

For doubling time;

2 = (1.0455)^T

ln (2) = T ln (1.0455)

T = ln 2 / ln (1.0455)

T = 15.58 years.

Ultimately, the doubling time of the investment as required is; 15.58 years.

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The solution set of the inequality is [3, ∝)

From the question, we have the following parameters that can be used in our computation:

2x + 4 < 10

Subtract 4 from both sides of the inequality

So, we have the following representation

2x + 4 - 4 < 10 - 4

Evaluate the like terms

2x < 6

Divide both sides by 2

x < 3

When represented as an interval notation, we have

[3, ∝)

See attachment for the inequality of the solution set

Hence, the solution is [3, ∝)

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The value of JI in the given triangle is 11.

A triangle is a polygon with three sides, vertices and angles.

Given that, in a triangle DEF, J is the intersection of the three medians.

EI = 33, we are asked to find the value of JI,

Since, all the median is intersecting at J, therefore, J is the centroid.

We know that, the centroid divides each median into two parts, which are always in the ratio 2:1.

Therefore,

Let, EI = 3x,

JI = x,

Therefore, JI = 11

Hence, the value of JI in the given triangle is 11.

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The complete question is :

In Δ DEF, J is the intersection of the three medians. If EI = 33, find JI.

Figure is attached

Answer:

21.7% to win $3, thats ~1/5

Step-by-step explanation:

100/6 = 10.(6) % to roll for each number (let it be just ~10.7)

for rolling a 3 or a 1 u will get $3

10.7 + 10.7 = 21.7% to win $3, thats 1/5