Answer:
The required amount Ahmet needs to pay after 6 years is $1619.14.
What is compound interest?
Compound interest is the interest on deposits computed on both the initial principal and the interest earned over time.
Amount = principal[1 + r/n]ⁿᵃ
Principal = P rate= r Time =a , n = compounding frequency
Here,
From the given data,
P = 700, r = 15% and t = 6 (n =1)
Now,
Amount = principal[1 + r/n]ⁿᵃ
Amount = 700(1 + 0.15)⁶
Amount = $1619.14
Thus, the required amount Ahmet needs to pay after 6 years is $1619.14.
Step-by-step explanation:
This is the same information as you’ll use in the next question.
The equation for the period of a pendulum is given by T space equals space 2 straight pi square root of straight L over 32 end root where T is the time (in seconds) and L is the length of the pendulum (in feet).
Find the approximate amount of time of the period of a pendulum if its length is 12 feet.
The approximate amount of time period of a pendulum with a length of 12 feet is 1.85 seconds.
What is calculus?Calculus is a branch οf mathematics that deals with the study οf change and hοw things change οver time.
We can use the given equatiοn fοr the periοd οf a pendulum:
T = 2π√(L/32)
Substituting L = 12, we get:
T = 2π√(12/32)
Simplifying:
T ≈ 1.85 seconds
Hence, the approximate amount of time of the period of a pendulum with a length of 12 feet is 1.85 seconds.
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Add the number that would make the expression a perfect square. Next, write an
equivalent expression in factored form. Do not put spaces in your answers.
1. X2 + 3x+
= (x+
2. X2 + 0. 6x+
= (x+
a) We need to add 2.25 to the expression to make it a perfect square and equivalent expression is (x + 1.5)^2.
b) We need to add 0.09 to the expression to make it a perfect square and equivalent expression is (x + 0.3)^2.
a) To make the expression X^2 + 3x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 3 is 1.5, and 1.5 squared is 2.25.
X^2 + 3x + 2.25 = (x + 1.5)^2
The equivalent expression in factored form is (x + 1.5)^2, which represents a perfect square trinomial.
b) Similarly, to make the expression X^2 + 0.6x + ___ a perfect square, we need to add a number that is equal to half of the coefficient of x, squared. In this case, half of 0.6 is 0.3, and 0.3 squared is 0.09. Therefore, we need to add 0.09 to the expression to make it a perfect square:
X^2 + 0.6x + 0.09 = (x + 0.3)^2
The equivalent expression in factored form is (x + 0.3)^2, which represents a perfect square trinomial.
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i need the answers for this? 8th grade math
1. A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. 2. The point where a graph contacts the y-axis is known as the y intercept.
What is y-intercept of the graph?The graph's intersection with the y-axis is known as the y-intercept. Finding the intercepts for any function with the formula y = f(x) is crucial when graphing the function. An intercept can be one of two different forms for a function. The x-intercept and the y-intercept are what they are. A function's intercept is the location on the axis where the function's graph crosses it.
1. A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.
2. The point where a graph contacts the y-axis is known as the y intercept. Each point on the y-axis has an x-coordinate of 0, as is known. Hence, a y-x-coordinate intercept's is 0.
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Stewart, Oswaldo, Kevin, and Flynn go to a soccer day at the FC Dallas’ arena, Toyota Stadium, in
Frisco, Texas. The coach has a computer and video system that can track the height and distance of
their kicks. All four soccer players are practicing up-field kicks, away from the goal.
Stewart goes first and takes a kick starting 12 yards out from the goal. His kick reaches a maximum
height of 17 yards and lands 48 yards from the goal.
Oswaldo goes next and the computer gives the equation of the path of his kick as y = -x 2 + 14x - 24,
where y is the height of the ball in yards and x is the horizontal distance of the ball from the goal line in
yards.
After Kevin takes his kick, the coach gives him a printout of the path of the ball.
Finally, Flynn takes his kick but the computer has a problem and can only give him a partial table of
data points of the ball’s trajectory.
Flynn’s Table:
Distance from the
goal line in yards
10 11 12 13 14 15 16 17 18 19 20
Height in yards 0 4.7 8.75 12.2 15 17.2 18.75 19.7 20 19.7 18.75
The computer is still not working but Stewart, Oswaldo, Kevin, and Flynn want to know who made the
best kick.
Answer:
To compare the kicks, we need to determine which kick goes the farthest and/or highest. Let's analyze each kick one by one.
Stewart's kick:
Starting 12 yards out from the goal, Stewart's kick reaches a maximum height of 17 yards and lands 48 yards from the goal. We can assume that the ball lands at the same height as it was kicked. Therefore, the horizontal distance traveled by the ball is:
d = 48 - 12 = 36 yards
The total distance traveled by the ball is the hypotenuse of a right triangle with legs of 36 and 17 yards. Using the Pythagorean theorem, we can find the distance traveled by Stewart's kick:
distance = sqrt(36^2 + 17^2) ≈ 40.48 yards
Oswaldo's kick:
According to the equation given, the height of the ball (in yards) at any horizontal distance (in yards) from the goal is given by:
y = -x^2 + 14x - 24
We want to find the maximum height reached by the ball, so we need to find the vertex of the parabolic path. The x-coordinate of the vertex is given by:
x = -b / 2a = -14 / (-2) = 7
The maximum height is the y-coordinate of the vertex:
y = -(7)^2 + 14(7) - 24 = 25
Therefore, Oswaldo's kick reaches a maximum height of 25 yards.
To find the horizontal distance traveled by the ball, we need to find the x-intercepts of the parabolic path. Setting y = 0, we get:
0 = -x^2 + 14x - 24
Solving for x using the quadratic formula, we get:
x = (14 ± sqrt(14^2 - 4(-1)(-24))) / (2(-1)) ≈ 2.63, 11.37
Therefore, the ball lands at a horizontal distance of approximately 2.63 or 11.37 yards from the goal. The total distance traveled by the ball is the sum of the horizontal distance and the maximum height:
distance = 11.37 + 25 ≈ 36.37 yards
Kevin's kick:
We don't have the equation or data for Kevin's kick, so we can't determine the maximum height or the total distance traveled by the ball.
Flynn's kick:
We have a partial table of data points for Flynn's kick. We can plot the points on a graph and draw a curve that fits the data points. Here is the graph:
Flynn's Kick
The curve appears to be a parabolic path, so we can assume that the equation for the path is:
y = ax^2 + bx + c
To find the coefficients a, b, and c, we need to solve a system of equations using three data points. Let's use the data points (12, 8.75), (15, 17.2), and (18, 19.7).
Using the first data point, we get:
8.75 = a(12)^2 + b(12) + c
Using the second data point, we get:
17.2 = a(15)^2 + b(15) + c
Using the third data point, we get:
19.7 = a(18)^2 + b(18) + c
Solving this system of equations using a calculator or matrix methods, we get:
a ≈ 0.0571
b ≈ -1.
Hope this helped, I'm sorry if it didn't. If you need more help, ask me! :]
Hey can someone help me pleaseeee SOLVE WITH EXPLANATION!!! >:(
Use the clues to crack the code the number is greater than ten the value of the ones digit is ten times the value of the tenths digit Code number (5, 5, 7,
Given that there is only one digit left and the sum is more than 10, the third digit must be 7, which it is. and the pass code to open anything it is guarding is 5 5 7, which may be inputted.
To decode the code, we know that the number is more than 10 and has three digits: . Moreover, we are aware that the value of the ones digit is 10 times that of the tenths digit. The code is 5 5 7, as may be inferred from the provided hints.
Given that the code contains two 5s, the first digit must be 5. As the value of the ones digit is 10 times that of the tenths number, the second digit must likewise be 5, which is 5. The number is bigger than 10, hence the third digit must be 7, as it is the only one still present.
In order to open whatever it is guarding, the code, which is 5 5 7, may be input.
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The graph shows the predicted population of a town, z number of years after 2020. According to the graph, which statement is true?
According to the graph, the true statement is the population will increase more each year than the previous year. The Option B is correct.
What does population increase means?in geography context, a population growth means the increase in the number of humans on Earth. In human history, the population size was relatively stable. But with innovation and industrialization, energy, food, water, and medical care became more available and reliable.
On this graph, we can observed how the population increases from 80,000 to 100,000, 120,000, 140,000, 160,000, 180,000, 200,000, 220,000. 240,000, 260,000 and 280,000 on the Y-Axis. Therefore, the statement that population will increase more each year than the previous year is true.
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This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is
Choose...
.
This means that
Choose...
mm of rain falls every
Choose...
.
The slope of the line is
3
This means that
6mm
of rain falls every
1hr
sunset lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. assuming logistic growth with a carrying capacity of 25000, find the growth constant , and determine when the population will increase to 12900.
The growth constant is 0.69 and the population will increase to 12900 after approximately 3.7 years.
We have, Sunset Lake is stocked with 2500 rainbow trout and after 1 year the population has grown to 7050. Assuming logistic growth with a carrying capacity of 25000,
The logistic growth model is given by the equation
dN/dt=rN[(K-N)/K]
where, dN/dt = rate of change of population with respect to time,
N = population size at time t,
r = intrinsic rate of natural increase (growth constant),
K = carrying capacity.
The population size, "N" after 1 year = 7050
The initial population, "N₀" = 2500
The carrying capacity, K = 25000
We can use the following formula to find the value of the growth constant,
r = 2.303/t{ln(N_t/N₀) }........... (1)
Where, t = time taken for the population to increase from N_0 to N_t= 1 year (given)
Substituting the given values in equation (1), we get
r = 2.303/1 ln(7050/2500) ⇒ 0.688 ≈ 0.69
The value of the growth constant is 0.69.
Now, we can use the logistic growth equation to find the time required for the population to reach 12900.
dN/dt=rN[(K-N)/K]
Given, N₀ = 2500 and K = 25000
Differentiating both sides with respect to t,
dN/dt = rN[(K-N)/K] + Ndr/dt
Substituting the values of N, r, and K in the above equation, we get,
dN/dt= 0.69N[(25000-N)/25000] + N{dN/dt}
Let the population N become 12900 at time t = t₁
Therefore, at time t = 0, the population N₀ = 2500
Also, at time t = 1, the population N₁ = 7050
Substituting these values in the above equation, we get,
dN/dt= 0.69N[(25000-N)/25000] + N₁
dN/dt= 0.69(2500)[(25000-2500)/25000] + N₁
Solving for N₁, we get, N₁ = 7825
Substituting N₁ = 7825 in the above equation,
dN/dt= 0.69(7825)[(25000-7825)/25000] + N₁
dN/dt= 3263.25/1.69 ⇒ 1930.4
Now, to find t1, we can use the following formula;
ln[(K-N₁)/(K-N₀)] = rt₁
Substituting the given values, we get,
ln[(25000-12900)/(25000-2500)] = 0.69t₁
On solving for t₁, we get;
t₁ = ln[(1575/22500)]/0.69 ≈ 3.7 years
Hence, the population will increase to 12900 after approximately 3.7 years.
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Consider the following set of numbers:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
What is the probability of drawing an odd number or a
multiple of 3?
The probability of drawing an odd number or a multiple of 3 is 1/5.
What is probability?Probability is simply the chance that something will happen.
Whenever the outcome of an event is uncertain, we can speak of the probability, or likelihood, of a particular outcome.
Analyzing events according to their probabilities is called statistics.
So, the given data set is:
{1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
Odd multiples of 3 are 3 and 9.
Then, the probability would be:
P(E) = 2/10
P(E) = 1/5
Therefore, the probability of drawing an odd number or a multiple of 3 is 1/5.
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Given the logistic model f(x)=800/1+19e^−0.402x, what is the initial value? Round your answer to the nearest whole number.
Given the logistic model f(x)=800/1+19e^−0.402x, he initial value is 40
What is logistic model?You should recall that Logistic regression is a statistical model that models the probability of an event taking place by having the log-odds for the event be a linear combination of one or more independent variables
The given question states thus: f(x)=800/1+19e^−0.402x, what is the initial value?
The initial value is the value when the value of x = 0
This implies that f(x) = (800)/ [1 + 19e⁻⁰°⁴⁰²ˣ
Simplifying this we have
f(x) = (800) / (1 + 19e⁰)
⇒ (800) 1 + 19
Simplifying to have
f(x) = 800/20
Dividing 800/20 to get 40
f(x) = 40
In conclusion, the initial value of f(x)=800/1+19e^−0.402x is 40
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solve the following system of equation y=x^2-32 y=x+10
x=(17,4)^2+(−340,−80)+58y= y^2−20y+68
y=y^2−20y+68
Use the commutative or associative property to simplify the expression. -(1)/(9)(13x)
Answer:
The given expression is:
-(1)/(9)(13x)
We can use the commutative property of multiplication to rearrange the order of the factors:
-(1)/(13x)(9)
Now, we can use the associative property of multiplication to group the factors in any way we want:
-(1/13)(1/x)(1/9)
This is the simplified expression using the commutative and associative properties of multiplication.
Jason read a total of 8 books over 4 months. If Jason has read 16 books so far, how many months has he been with his book club? Solve using unit rates. its worth 100 points
Answer:
8 months
Step-by-step explanation:
I got it right
What is the area?
6 ft:
6 ft
10 ft
square feet
Step-by-step explanation:
6x6x10 FT = 1 sq cube foot
A right circular cylinder has the dimensions shown below.
r = 17.2 yd h = 45.3 yd
What is the volume of the cylinder? Use 3.14 for tr. Round to the nearest tenth and include correct units.
Show all your work.
42080.9 cubic yd
Step-by-step explanation:
Volume of right circular cylinder:r = 17.2 yd
h = 45.3 yd
[tex]\boxed{\bf Volume=\pi r^2h}[/tex]
= 3.14 * 17.2 *17.2 * 45.3
=42080.9 cubic yd
Question :-
What is the volume of a right circular cylinder with a radius of 17.2 yd and a height of 45.3 yd?Answer :-
The volume of a right circular cylinder is 42080.873 yd³.[tex] \rule{180pt}{4pt}[/tex]
Diagram :-
[tex]\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{17.2 \: yd}}\put(9,17.5){\sf{45.3 \: yd}}\end{picture}[/tex]
Solution :-
As per provided information in the given question, we have been given that the Radius of a cylinder is 17.2 yd. The height of a cylinder is 45.3 yd. We have been asked to find the volume of a right circular cylinder.
To calculate the volume of a right circular cylinder, we will apply the formula below :-
[tex] \bigstar \: \: \: \boxed{ \sf{ \: \: Volume_{(Cylinder)} = \pi r^2 h \: \: }}[/tex]
Substitute the given values into the above formula and solve for Volume :-
[tex]\sf:\implies Volume_{(Cylinder)} = \pi r^2 h[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(17.2 \: yd)^2(45.3 \: yd)[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = (3.14)(295.84 \:yd^2)(45.3 \: yd)[/tex]
[tex]\sf:\implies Volume_{(Cylinder)} = (928.9376 \:yd^2)(45.3 \:yd)[/tex]
[tex]\sf:\implies\bold{Volume_{(Cylinder)} = 42080.873 \: yd^3}[/tex]
Therefore :-
The volume of a right circular cylinder is 42080.873 yd³.[tex]\\[/tex]
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Have a great day! <33
Subtracting a number is the same as adding its opposite.
Use this understanding to complete each of the equations below.
Answer:
Step-by-step explanation:
[tex]-13-23=-13+(-23)[/tex] (add -23 instead of subtracting +23)
[tex]=-36[/tex]
[tex]-13-(-23)=-13+(23)[/tex] (add +23 instead of subtracting -23)
[tex]=10[/tex]
According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide. What is the approximate area of the park? Show your work.
The approximate area of the park is given as follows:
450 blocks squared.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.
Hence the formula for the area of the rectangle is given as follows:
Area = Length x Width.
According to the map on the left, Central Park is about 50 blocks long by 9 blocks wide, hence the length and the width are given as follows:
Length of 50 blocks.Width of 9 blocks.Hence the area of Central Park is calculated as follows:
Area = 50 x 9
Area = 450 blocks squared.
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Tony, Donna, and Jeremy ran for class president. Tony and Donna together won 0. 62 of all the votes. If all the students in the class voted, which fraction represents Jeremy's portion of all the votes?
The fraction that represents Jeremy's portion of all the votes is 38/100, which can be simplified to 19/50.
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
If Tony and Donna won 0.62 of all the votes, this means that they won 62% of the votes.
To find Jeremy's portion of the votes, we can subtract Tony and Donna's portion from 100%, since the total percentage of votes must add up to 100%.
So, Jeremy's portion of the votes would be:
100% - 62% = 38%
Therefore, the fraction that represents Jeremy's portion of all the votes is 38/100, which can be simplified to 19/50.
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The area of the triangle below is 1/16 square centimeters. What is the length of the base. Express your answer as a fraction in simplest form
The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
What does fraction mean?A fraction is a mathematical expression which represents a part of a whole. It is written as a ratio that compares two numbers, the numerator and denominator. The numerator indicates the number of parts, the denominator indicates the total number of parts that make up the whole. Fractions can be expressed as decimals, percentages, and other forms of representation.
To solve this problem, we must use the formula for area of a triangle. This formula states that the area of a triangle is equal to one-half the product of the base and the height. In this problem, the area of the triangle is given as 1/16 square centimeters. This means that the base times the height must equal 1/8.
To find the length of the base, we must isolate the base from the equation. To do this, we must divide both sides of the equation by the height. This will leave us with the equation base = 1/8/height. Since the height is unknown, we can solve for it by taking the reciprocal of the base. This will give us the equation height = 1/8/base.
Combining both equations, we can solve for the base by multiplying both sides of the equation by 1/8. This will give us the equation base = (1/8)(1/8) = 1/64. The length of the base is 1/64 and can be simplified to the fraction 1/64 = 1/64 in simplest form.
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240
Use the ratio 1. What operation can you do on both terms to find
an equivalent ratio that has 1 as the second term?
Answer:
You need to first identify the dum it's always multiplication
hope this helps good luck
3⋅5 1 +2 can anyone help with this I really tried my best and I've been hard working at this but I'm still stuck at it
35 1 + 2 = 17. To remember the mathematical operations in the correct order, people frequently use the abbreviation PEMDAS.
You must follow the order of operations, often known as PEMDAS, to evaluate this equation. Parentheses, exponents, multiplication and division (left to right), addition, and subtraction are all referred to as PEMDAS (from left to right).
When using PEMDAS, you would first calculate the output of the parenthesized expression—which is 3 times 5—and then add 2.
Thus, 35 1+2 reduces to:
3*5 1 + 2 = (3*5) + 2 (first calculate within the parentheses) = 15 + 2 (conduct multiplication) = 17 (perform addition)
Hence, 35 1 + 2 = 17.
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Sorry if I said it again but I need help on this question
The answer of the given question based on the finding the value of x and y and measuring the angle ∠DFE the answer is x = 11.8 and y = -8 and angle ∠DFE is 88° degrees.
What is Triangle?A triangle is geometric shape that is formed by three straight line segments that connect three non-collinear points in plane. These points are called vertices of triangle, and line segments are called sides. The triangle is one of most fundamental shapes in mathematics and has many interesting properties that make it useful in variety of applications.
Triangles can be classified based on lengths of their sides and measures of their angles. If all three sides of triangle are of equal length, it is called equilateral triangle. If two sides of triangle are of equal length, it is called isosceles triangle. If all three sides have different lengths, it is called scalene triangle
In triangle DEF, we know that the sum of the angles is 180° degrees, so:
∠DEF + ∠DFE + ∠EFD = 180°
Substituting the given values, we have:
92° + (5x - 7) + 36° = 180°
Simplifying the equation, we get:
5x + 121 = 180
5x = 59
x = 11.8
Now we know x, then we can find y:
y = 180 - 92 - 36 - (5x - 7) = 45 - 5x
y = 45 - 5(11.8) = -8
Therefore, x = 11.8 and y = -8.
To find the measure of ∠DFE, we can use the fact that the sum of the angles in a straight line is 180 degrees. ∠DFE is opposite to angle D, which is 92°, so:
∠DFE = 180° - 92° = 88°
Thus, the measure of ∠DFE is 88° degrees.
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Select whether the equation has a solution or not. x-8+-/x2-8 roots no roots
The correct statement regarding the number of solutions of the equation is given as follows:
The function has one solution.
How to obtain the number of solutions?The function for this problem is defined as follows:
[tex]x - 8 = -\sqrt{x^2 - 8}[tex]
We can remove the term with x from the square root squaring both sides of the equality, hence:
[tex](x - 8)^2 = (-\sqrt{x^2 - 8})^2[/tex]
x² - 8 = x² - 16x + 64
16x = 72
x = 72/16
x = 4.5.
Hence the equation presented in this problem has a root, which is a solution, and the number of solutions is of one.
Missing InformationThe function is given as follows:
[tex]x - 8 = -\sqrt{x^2 - 8}[tex]
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JKLM is a rhombus. m/MLN = (9a + 11)° m /KLM = (-4a + 66)°
Find the m2KJM.
The value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).
What is rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is sometimes referred to as a diamond or rhombus. Rhombi or rhombuses are the plural forms of rhombus.
Let us suppose the measure of angle = x.
For rhombus all the four angles are congruent, thus,
∠MLN = (9a + 11)°
∠KLM = (-4a + 66)°
∠JLN = x
∠KLJ = x
The sum of the angles of a quadrilateral is 360 degrees, so:
∠JKL + ∠KLM + ∠MLN + ∠NJL = 360
Since JKL and NJL are vertical angles, they are congruent:
∠JKL = ∠NJL = x
Substituting in the given angles, we get:
x + (-4a + 66) + (9a + 11) + x = 360
2x + 5a + 77 = 360
2x = 360 - 5a - 77
2x = 283 - 5a
x = (283 - 5a)/2
Now, ∠JKM = 180 - ∠JKL
∠JKM = 180 - x
∠JKM = 180 - (283 - 5a)/2
Simplifying, we get:
∠JKM = 23 + (5a/2)
Hence, the value of ∠2KJM for the rhombus is ∠JKM = 23 + (5a/2).
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A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees Fahrenheit, for those months. The scatter plot shows the data
The statements that are true are:
(A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.
(D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.
(E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
Using the function A(t) = -1.4t + 96, we can determine the amount of oil, A, used in gallons for a given average temperature, t, in degrees Fahrenheit.
A) The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.
Substituting t = 10 into the function A(t), we get:
A(10) = -1.4(10) + 96 = 80
Therefore, the statement is true.
B) The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.
Substituting t = 15 into the function A(t), we get:
A(15) = -1.4(15) + 96 = 76.5
Therefore, the statement is false.
C) The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.
Substituting t = 68.5 into the function A(t), we get:
A(68.5) = -1.4(68.5) + 96 = -2.9
Therefore, the statement is false.
D) The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.
Substituting t = 55 into the function A(t), we get:
A(55) = -1.4(55) + 96 = 18
Therefore, the statement is true.
E) The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
Substituting t = 0 into the function A(t), we get:
A(0) = -1.4(0) + 96 = 96
Therefore, the statement is true.
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The given question is incomplete, the complete question is:
A homeowner collects data about the amount of oil , in gallons, used to heat the house per month for 5 months and the average monthly temperature , in degrees
Fahrenheit, for those months. The scatter plot shows the data. The function A(t) = -1.4t + 96, best fits these data.
Graph- (25,60), (40,40),(45,40),(55,20),(60,10)
Use the function to determine which of the following statements are true. Select all that apply.
A- The homeowner would use about 82 gallons of oil to heat the house for a month with an average temperature of 10 °F.
B- The homeowner would use about 85 gallons of oil to heat the house for a month with an average temperature of 15 °F.
C- The homeowner would use about 0 gallons of oil to heat the house for a month with an average temperature of 68.5 °F.
D- The homeowner would use about 5 gallons of oil to heat the house for a month with an average temperature of 55 °F.
E- The homeowner would use about 96 gallons of oil to heat the house for a month with an average temperature of 0 °F.
find the missing number in the sequence
- 5, -1, 3
Answer:
7
Step-by-step explanation:
The numbers are increasing by 4 so with that, we can skip to the last number which is 3 and add 4 giving us 7 and if we go on, we would get 11, 15, 19, 23.
Simplify the square root of 7 divided by 20
The simplified fοrm οf the square rοοt οf 7 divided by 20 is:
(7 + 2√(35)) / (20 * (√(7) + 2√(5))).
What is the equivalent expressiοn?Equivalent expressiοns are expressiοns that wοrk the same even thοugh they lοοk different. If twο algebraic expressiοns are equivalent, then the twο expressiοns have the same value when we plug in the same value fοr the variable.
Tο simplify the square rοοt οf 7 divided by 20, we can ratiοnalize the denοminatοr by multiplying the numeratοr and denοminatοr by the cοnjugate οf the denοminatοr, which is √(7) + 2√(5):
(√(7)) / 20 = (√(7) / 20) * (√(7) + 2√(5)) / (√(7) + 2√(5))
Expanding the numeratοr using the distributive prοperty gives:
(√(7) * √(7) + √(7) * 2√(5)) / (20 * (√(7) + 2√(5)))
Simplifying the numeratοr gives:
(7 + 2√(35)) / (20 * (√(7) + 2√(5)))
Therefοre, the simplified fοrm οf the square rοοt οf 7 divided by 20 is:
(7 + 2√(35)) / (20 * (√(7) + 2√(5))).
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42. Let P(A)=0.70,P(B∣A)=0.55 , and P(B∣A C )=0.10 . Find the following probabilities: a. P(A C ) b. P(A∩B) and P(A C ∩B) c. P(B) d. P(A∣B) 43. Complete the following probability table.
Here is the probability table to be completed: A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45
42. Let P(A) = 0.70, P(B∣A) = 0.55, and P(B∣AC) = 0.10. The following probabilities are found: a. P(AC) = 0.30 b. P(A∩B) = P(B∣A) × P(A) = 0.55 × 0.70 = 0.385 P(AC∩B) = P(B∣AC) × P(AC) = 0.10 × 0.30 = 0.03 c. P(B) = P(B∣A) × P(A) + P(B∣AC) × P(AC) = 0.55 × 0.70 + 0.10 × 0.30 = 0.415 d. P(A∣B) = P(B∣A) × P(A) / P(B) = 0.55 × 0.70 / 0.415 = 0.9289 43. Here is the probability table to be completed: A B P(A∩B) P(A∣B) 0.54 0.47 0.38 0.70 0.46 0.32 0.30 x 0.28 0.27 0.42 0.20 0.15 0.35 0.45
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Nicole is a wedding organiser. The guests sit at a circular table with a diameter of 180cm each guest needs 7cm around the cicumference of the table. Their are 18 tables at the venu. There is a toptal of 145 guests. Are their enoughb tables
From the given data of Nicole's wedding organization, 18 tables at the venue is sufficient for the total 145 arriving guest.
To determine whether there are enough tables for the guests, we need to calculate the total circumference required for all the guests and compare it to the total circumference of the available tables. The circumference of a circle is given by the formula C = πd, where C is the circumference, d is the diameter, and π is the constant pi, approximately equal to 3.14.
For the circular table with a diameter of 180cm, the circumference is:
C = πd
= π x 180cm
= 565.2cm
Each guest needs 7cm around the circumference of the table, so the total circumference required for one guest is 7cm.
For 145 guests, the total circumference required is:
Total circumference required
= 145 guests x 7cm per guest
= 1015cm
Now, we can calculate the total circumference of all the tables available:
Total circumference of all tables
= 18 tables x 565.2cm per table
= 10,174.4cm
Since the total circumference required for the guests (1015cm) is less than the total circumference of all the available tables (10,174.4cm), we can conclude that there are enough tables for the guests. Therefore, there are enough tables at the venue for the 145 guests.
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