Answer:
a=1000.10
Step-by-step explanation:
Use the formula d= vt + 16t2, where d is the distance in feet, v is the initial velocity in feet per second, and it is the time in seconds.
An object is released from the top of a building 480 ft high. The initial velocity is 16 ft/s. How many seconds later will the object hit the ground?
Answer:
5 seconds
Step-by-step explanation:
d = vt + 16t² , that is
vt + 16t² = d
substitute d = 480, v = 16 into the equation
16t + 16t² = 480 ( divide through by 16 )
t + t² = 30 ( subtract 30 from both sides )
t² + t - 30 = 0 ← in standard form
(t + 6)(t - 5) = 0 ← in factored form
equate each factor to zero and solve for t
t + 6 = 0 ⇒ t = - 6
t - 5 = 0 ⇒ t = 5
t > 0 , then t = 5
the object will hit the ground 5 seconds later
Answer:
5 seconds.-------------------------
As per given we have:
d = 480 ft,v = 16 ft/s.Substitute these into given equation and solve for t:
480 = 16t + 16t²30 = t + t²t² + t - 30 = 0t² + 6t - 5t - 30 = 0t(t + 6) - 5(t + 6) = 0(t + 6)(t - 5) = 0t + 6 = 0 or t - 5 = 0t = - 6 or t = 5The first value of t is discarded as time can't be negative, so the answer is 5 seconds.
Find the length of WB
Answer:
WB = 16 in---------------------------
According to picture we observe:
W is midpoint of AT and B is the midpoint of TE.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:
WB = AE/2 WB = 32/2WB = 16 inHELPPPP PLS I NEED HELP
According to the given information the lateral surface area of given cylinder is 725.34 in².
What can you say about a cylinder?In mathematics, a cylindrical is indeed a three-dimensional solid that retains two parallel bases spaced apart by a curving surface. These bases frequently have a circular shape (like a circle), and also an axis links their respective centers.
What three qualities does a cylinder have?A cylinder is a three-dimensional form having two parallel, round sides on either end, one side that curves, no vertices or edges.
As we know that the lateral surface area of cylinder (A) = 2πrh
Given
D = [tex]16\frac{1}{2}[/tex]in
h = 14in
r = D/2
= 33/4 in
A = (2 × 3.14 × 33 × 14) / 4
= 2901.36 /4
= 725.34 in²
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Two hundred college students were recently asked if they participated in music or sports. 127 students said they were
involved in music. 78 students said they participated in both activities, while 20 students did not participate in either.
How many students participated in only music?
How many students participated in only sports?
How many students were involved in music or sports?
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.
What is the number of students that participated in only musicLet'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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The temperature in a certain location was recorded each day for two months. The mean temperature was 28.8°F with a standard deviation 7.4°F. What can you determine about these data by using Chebyshev's Inequality with =K3?
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.
LMNO is a parallelogram. If NM = x + 37 and OL = 5x + 9 find the value of x.
The value for the variable x in the parallelogram is equal to 7.
How to evaluate for the variable x in the parallelogramThe parallelogram LMNO have two pairs of parallel sides hence LO = MN and LM = ON.
We shall evaluate for variable x as follows:
5x + 9 = x + 37
5x - x = 37 - 9 {collect like terms}
4x = 28
x = 28/4 {divide through by 4}
x = 7
Therefore, the value for the variable x in the parallelogram is equal to 7.
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The value of the variable x is 7
How to determine the valueIt is important to note that the opposite sides of a parallelogram are congruent or equal in length.
Then, for the parallelogram LMNO
NM is parallel to OL
Now, substitute the values, we get;
NM = OL
x + 37 = 5x + 9
collect like terms
x - 5x = 9 - 37
subtract the like terms
-4x = -28
Make 'x' the subject
x = 7
Hence, the value is 7
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Identify true statements about set membership and subsets
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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More than 50 years after it jumped the species barrier and became one of the most devastating viruses to affect mankind, HIV remains a stubborn adversary. Treatment has improved dramatically over the past 20 years and now, a cure could be in sight.
Source: The Guardian, November 30, 2018
Make a graph of the production possibilities frontier with HIV/AIDS cases treated on the x-axis and other goods and services on the y-axis before and after the advance in technology.
Question content area bottom left
Part 1
The opportunity cost of treating HIV/AIDS cases increases as more HIV/AIDS cases are treated.
Draw a curve that shows the production possibilities for the world economy that produces HIV/AIDS treatments and other goods and services. Label the curve PPF0.
Then draw the PPF that shows the effect of an advance in technology on HIV/AIDS treatments. Label the curve PPF1.
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.
What is graphs?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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Money A savings account increases from $200 to $206. What is the percent increase of the savings account?
Answer:
3% increase
Step-by-step explanation:
Multiply the following radicals and simplify your answer.
2√6⋅−3√12
well asap due today pls
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.
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040. Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.
The average hourly wage for police officers is $30.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
Given:
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S.
In 2018, the Bureau reported that Wisconsin police officers had a mean yearly salary of $62,040.
Assume that police officers generally work 40 hours a week.
There are 52 weeks in the year.
The average hourly wage for police officers is,
= 62040 ÷ (52 x 40)
= 62040 / 2080
= 29.8
≈ $30
Therefore, $30 is the hourly wage.
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Write an equation for a rational function with the given characteristics.
Vertical asymptotes at x = -2 and x = 3,2-intercepts at (-4, 0) and (-1,0), y-intercept at (0,4).
F(x)=
The equation of the rational function with the given features is given as follows:
F(x) = [4(x² + 5x + 4)]/(x² - x - 6).
How to define the rational function?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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Answer the following questions
The system of equations that can be used to find the length of each workout and the duration of each workout are as follows;
(a) 5·x + 3·y = 10
2·x + 6·y = 10
(b) Length of each Plan A workout: 1.25 hours
Length of each Plan B workout: 1.25 hours
What are linear system of equations?A linear system of equation consists of two or more linear equations that share common variables.
(a) The number of Plan A workouts Mary trained on Wednesday = 5
Number of Plan B workouts she trained on Wednesday = 3
The total time (in hours) Mary trained both workouts on Wednesday = 10
Where x represents the length (in hours) of each of the Plan A workout, and B represents the time in hours of each of the Plan B workout, we get;
5·x + 3·y = 10
Similarly, the number of Plan A workouts trained on Thursday = 2
Number of Plan B workout trained on Thursday = 6
The duration of training of all workouts on Thursday = 10 hours
Therefore, we get;
2·x + 6·y = 10
The system of equations that could be used to find the length (in hours) of each type of workout can be presented as follows;
5·x + 3·y = 102·x + 6·y = 10(b) The first equation from the system of equations indicates that we get;
5·x + 3·y = 10
3·y = 10 - 5·x
y = (10 - 5·x)/3Plugging the value of y above into the second equation from the system of equations, we get;
2·x + 6·y = 10
2·x + 6 × ((10 - 5·x)/3) = 10
2·x + 2·(10 - 5·x) = 10
2·x + 20 - 10·x = 10
20 - 8·x = 10
8·x = 20 - 10 = 10
x = 10/8 = 1.25
The length of each Plan A workout, x = 1.25 hoursy = (10 - 5·x)/3,
x = 1.25, therefore;
y = (10 - 5 × 1.25)/3 = 1.25
y = 1.25
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NEED PLS THANK YOU DUE TODAY
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
Graph h(x)=−x2+3.
Use the parabola tool then choose the vertex followed by one point on the parabola.
Answer: I do not have the capability to create a graph. However, I can tell you how to graph the parabola h(x) = -x^2 + 3.
A parabola is defined by its equation in the form y = ax^2 + bx + c, where a, b, and c are constants. In this case, a = -1, b = 0, and c = 3.
The vertex of the parabola is the highest or lowest point on the graph and is given by the coordinates (-b/2a, c - b^2/4a). For this parabola, the vertex is (0, 3), since b = 0 and a = -1.
To find another point on the parabola, you can plug in any x-value and use the equation of the parabola to find the corresponding y-value. For example, if you plug in x = -2, you get:
h(-2) = -(-2)^2 + 3
h(-2) = 4 + 3
h(-2) = 7
So the point (-2, 7) is also on the parabola.
With the vertex and one other point on the parabola, you can now graph the parabola.
Step-by-step explanation:
Solve for x
2,4, and 6 i need help with
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
Xx
Which equation models the rational function shown in
the graph?
2(x+2)
X-2
O f(x) =
O f(x) = x-2
x+2
2(x-2)
x+2
Of(x)=.
O f(x) = x+2
X-2
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.
What is equation?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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Suppose you pay $1.00 to roll a fair die with the understanding that you will get back $
3.00 for rolling a 1 or a 3, nothing otherwise. What is your expected net winnings?
for
lingun?
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
Which of the following equations represents a linear function? Please show the steps of the answer! Thank you
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 = ∞
The triangle below is equilateral. Find the length of side � x in simplest radical form with a rational denominator. x 6
The length of the side is 12 units in simplest radical form with a rational denominator.
What is an equilateral triangle?A triangle is said to be equilateral if all of its sides and angles are equal. An equilateral triangle is also known as an equiangular triangle since each of its angles has a value of 60 degrees.
Given:
The triangle given in the image is an equilateral triangle.
That means the angle measure of the triangle is 60° each.
And all the sides are equal.
To find the value of x:
Sin(60/2)° = opposite/ hypotenuse.
Sin30° = x/6
x = 6/Sin30°
[tex]x = \frac{6}{1/2}[/tex]
x = 6(2)
x = 12
Therefore, the value of x is 12 units.
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The complete question:
The triangle below is equilateral. Find the length of the side in simplest radical form with a rational denominator.
The image is given below.
Is one bank ALWAYS better? What factors might affect which bank has the better fee
structure?
No one bank is not always better. Factors such as the fees and the charges in one bank may differentiate it from another bank.
What may cause a bank to be better than 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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Will is moving from Boston to Philadelphia which is 300 miles away. He is traveling at an
Write System of Equations from Context
Kennedy has $0.81 worth of pennies and nickels. She has 9 more nickels than
pennies. Write a system of equations that could be used to determine the number of
pennies and the number of nickels that Kennedy has. Define the variables that you
use to write the system.
Let __=_________
Let__=___________
System of Equations:
_________________
_________________
gerry's drawer has two black socks and 4 blue socks. if he selects two socks without looking what is the probability that both socks are black
The shape of the distribution of the number of clase friends for the males is best characterized as
The shape of the distribution of the number of clase friends for the males is best characterized as Skewed to the higher values (right or positively skewed).
What are shapes called in math?Construction of closed geometric shapes involves the usage of points, line segments, circles, and curves. These shapes are all around us. Circles, rectangles, triangles, and other shapes are examples of geometric shapes. Triangle-shaped slices make up the shape of a pizza
What are the basic shapes?The basic shapes include the square, circle, triangle, and other simple shapes that cannot be further subdivided into the simpler shapes by general standards.
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If a rock is thrown upward on an exoplanet of a nearby star with initial velocity…..
the displacement is 23.14m and the velocity is 21.28m/s
What is quadratic equation?
it's a second-degree quadratic equation which is an algebraic equation in x. Ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term, is the quadratic equation in its standard form. A non-zero term (a 0) for the coefficient of x2 is a prerequisite for an equation to be a quadratic equation. The x2 term is written first, then the x term, and finally the constant term is written when constructing a quadratic equation in standard form. In most cases, the numerical values of letters a, b, and c are expressed as integral values rather than fractions or decimals.
The given equation y = 25t - 1.86t²
at t = 1
So the displacement y = 25-1.86 = 23.14
to find velocity dy/dt = 25- 2(1.86)t
v = 25 - 3.72 = 21.28m/s
Hence the displacement is 23.14m and velocity is 21.28m/s
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You can work a total of no more than 32 hours each week at your two jobs. Tutoring pays $7 per hour and babysitting pays $8 per hour. You need to earn at least $256 each week to pay your bills.
Let X = the number of hours tutoring. Let Y = the number of hours babysitting
Answer: The correct system of linear inequalities that represents this situation is:
X + Y ≤ 32 (to represent the maximum number of hours you can work)
7X + 8Y ≥ 256 (to represent the minimum amount of money you need to earn)
X ≥ 0, Y ≥ 0 (to represent that you can only work a non-negative number of hours at each job)
Where X represents the number of hours you spend tutoring and Y represents the number of hours you spend babysitting. The first inequality represents the maximum number of hours you can work, and the second inequality represents the minimum amount of money you need to earn. The last two inequalities represent that you can only work a non-negative number of hours at each job.
Step-by-step explanation:
Other than a no solution set, use interval notation to express the solution set and then graph the solution set on a number line.
2x+4<10
The solution set of the inequality is [3, ∝)
How to determine the solution setFrom 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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10. Susan has $800 in her bank account. Every week, she withdraws $100 for spending money.
A) What is the rate of change (or slope) in this situation?
B)
How much will she have left in her account after five weeks?
A) The rate of change in this situation is -$100 per week.
B) She will have $300 left in her account after five weeks.
