we can conclude that option (A) , (B) and (C) are true.
We know that in a triangle,
• Sum of any to sides is greater than the third side.
• Difference between any two sides is smaller than the third side.
So, in ∆EFG, we have,
• EF + FG > EG
• FG + EG> EF
• EF + EG > FG
and,
• EF - FG <EG or FG - EF <EG
• FG - EG < EF or EG - FG < EF
• EF - EG <FG or EG - EF < FG
From options now we get,
A) EF + FG > EG is true
B)EG + FG > EF is true
C) EG - FG < EF is true
D) EF - FG > EG is false
E) EG + EF < FG is false
Therefore, we can conclude that option () , () and () are true.
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We can conclude that option (A) , (B) and (C) are true.
We know that in a triangle,
• Sum of any to sides is greater than the third side.
• Difference between any two sides is smaller than the third side.
So, in ∆EFG, we have,
• EF + FG > EG
• FG + EG> EF
• EF + EG > FG
and,
• EF - FG <EG or FG - EF <EG
• FG - EG < EF or EG - FG < EF
• EF - EG <FG or EG - EF < FG
From options now we get,
A) EF + FG > EG is true
B)EG + FG > EF is true
C) EG - FG < EF is true
D) EF - FG > EG is false
E) EG + EF < FG is false
Therefore, we can conclude option (A) , (B) and (C) are true.
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12
75°
b
a
35°
Find all the unknow measures using the law of sines
Please help for math thank you!!!!!!!!
Answer:hie
hie
Step-by-step explanation:hie
PLEASE HELP ASAP !! The flight of Jae and Miguel's rocket t seconds after launch is modeled by
h(t) = -5t² + 40t + 1, where h(t) is their rocket's height in meters.
What was their rocket's height in meters 0.5 seconds after launch???How many sec after launch did their rocket hit the ground???What was their rockets maximum height in meters??
The height in meters is 19.75 meters
The rocket hit the ground after 8.06 sec
The maximum height in seconds is 81 meters
What was their rocket's height in meters 0.5 seconds after launchwe would have to use 0.5 as the value for t in the formula
h(t) = -5t² + 40t + 1
h(0.5) = -5(0.5)² + 40(0.5) + 1
= -1.25 + 20 +1
= 19.75
How many sec after launch did their rocket hit the ground?To find when the rocket hit the ground, we need to find when the height of the rocket is equal to 0. So we will set h(t) = 0 and solve for t:
-5t² + 40t + 1 = 0
by using Quadratic equation formula we get t = (-b ± √(b²-4ac))/2a
we solve this using the calculator
so t1 = (40 + 40.6)/10 = 80.6/10 = 8.06 sec
Since the time of the rocket hit the ground should be positive, so the rocket hit the ground after 8.06 seconds after launch.
What was their rockets maximum height in meters?To find the rocket's maximum height, we need to find the vertex of the parabola. The vertex of the parabola can be found by using the formula x = -b/2a,
where x is time and a, b, c are from equation.
so, x = -b/2a
= -40/2*-5
= -40/ -10
= 4 sec
and by using the above formula of x, we get the
h(4) = -5(4)² + 40(4) + 1
= -80 + 160 + 1
= 81 meters
Therefore, the rocket's maximum height is 81 meters.
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Nicole gets paid $2,900 per month. She pays $638 a month for rent. What percent of her monthly pay goes to rent?
21.931% of Nicole's monthly pay goes to rent.
percent = (638/2900) x 100
percent = 0.21931 x 100
percent = 21.931%
Which set of ordered pairs is made up of points on the graph of the function below?
A.
(10,-1), (8,0), (1,6), (2,4)
B.
(10,-1), (8,0), (6,1), (4,2)
C.
(-1,10), (0,8), (1,6), (2,4)
D.
(-1,10), (8,0), (1,6), (4,2)
y=-2x+8
These points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.
What is the linear system?
A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The linear function is given below.
y = 2x – 6
The points (-1,-8), (0,-6), (1,-4), and (2,-2) lies on the equation.
As when the put the given points in the equation , than it satisfies the given condition.
Hence, these points (-1,-8), (0,-6), (1,-4), and (2,-2) are the set of ordered pairs made up of points on the graph of the function y = 2x – 6.
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POSSIBLE POINTS: 5 Your business borrowed 8 bitcoins on May 1, when 1 bitcoin was worth $1,418.86. On June 1, 1 bitcoin was worth $2,441.29. Not counting the 1 month of interest, what amount of profit would your business make buy selling the bitcoins June 1? $3,860.15 $11,350.88 $19,530.32 $8,179.44 $1,022.43 Shy
Answer:
$10,224.30
Step-by-step explanation:
which of these has a slope of -3
Answer:
Option 3. Look at my screenshot so you can see the circled one
Step-by-step explanation:
The reasoning behind this is slope is rise over run (rise/run)
Graph 3 goes down 3 so -3 and runs 1 over so (-3/1)
This is simplified as -3.
I hope this helps you out :D
Sorry you can’t see the photo clearly, I know it’s a reduction but what is the scale factor?
Answer:
1/2
Step-by-step explanation:
Triangle XYZ has endpoints (0,0) (0,8) and (4,6)
Triangle X'Y'Z' has endpoints (0,0) (0,4) and (2,3)
As you can see, all the coordinates from Triangle XYZ are halved to get the coordinates of Triangle X'Y'Z', so the scale factor is 1/2.
Anything would be awesome
Answer:
I believe it's BC
Step-by-step explanation:
I can't really give an explanation but I've done this before and struggled but learned it, hope I'm right
You get a personal loan of $5,000 with 12% simple interest to be paid over 30 months. What is your monthly payment?
Work Shown:
A = P*(1+r*t)
A = 5000*(1+0.12*30/12)
A = 6500
The amount $6500 is what you pay back
Divided over 30 months gives 6500/30 = 216.67 dollars per month.
Side note: The value t is in years, so 30 months = 30/12 years.
What’s 23,760ft in miles
Answer:
So, there are 5,280 feet in a mile, so you will want to find out how many times 5, 280 will go into 23,760. To do this, you will divide.
23,760/5,280 = 4.5
There are 4.5 or 4 1/2 miles in 23,760 feet!
Step-by-step explanation:
Hope it helps! =D
find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1
The center of mass is (2,1) since m1 has a mass of 10 and is located at (4,2). The center of mass is the average of the locations of the masses, weighted by the masses.
We can calculate the center of mass of these two spheres by using the formula c = (m1*L1 + m2*L2) / (m1 + m2). m1 is the mass of the first sphere, and L1 is the location of the first sphere. In this case, m1 is 10, and L1 is (4,2). We assume that m2 is 0 and L2 is (0,0). Plugging these values into the formula, we get c = (10*(4,2) + 0*(0,0)) / (10 + 0), which is (2,1). This is because the center of mass is the average of the locations of the masses, weighted by the masses. In this case, the only mass is 10, and it is located at (4,2). Therefore, the center of mass is simply (4,2) since it is the only mass that contributes to the calculation.
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The complete question: find the center of mass (relative to (0,0)) for the spheres with the following masses and locations: m1 = 10, L1 = ( 4,2)
Which equation matches the hanger diagram 2x=5
The equation that matches the hanger diagram is 2x=5
How to determine the equation of the diagramFrom the question, we have the following parameters that can be used in our computation:
The hanger diagram added as an attachment
From the diagram, we hav
Left = x + x
Right = 1 + 1 + 1 + 1 + 1
This gives
Left = 2x
Right = 5
So, we have
2x = 5
hence, the equation is 2x = 5
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(2+v)^2
how do I rewrite with out parentheses
Answer:
v^2+4v+4
Step-by-step explanation:
To do this we have to know that (2+v)^2 is the same as (2+v) (2+v)
Next, use the distributive property and add like variables to get the final answer of v2+4v+4
I hope this was able to help you out :D
Distribute to create an equivalent expression with the fewest symbols possible.
\dfrac12(2a - 6b+ 8) =
2
1
(2a−6b+8
The equivalent expression for 1/2(2a - 6b+ 8) will be a - 3b + 4
How to calculate the equivalent expression?Expressions that are equivalent do the same thing even though they have different appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
When two expressions can be reduced to a single third expression or when one of the expressions can be written in the same way as the other, they are said to be equivalent. When values are substituted for the variable and both expressions yield the same result, you can also tell if two expressions are equivalent.
This will be:
1/2(2a - 6b+ 8)
= a - 3b + 4
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Complete question
Distribute to create an equivalent expression with the fewest symbols possible 1/2(2a - 6b+ 8) =
PLEASE HELP ME!!! Complete the two-column proof.
The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The equation is given below.
x/6 + 2 = 15
Subtract 2 on both sides. Then we have
x / 6 + 2 - 2 = 15 - 2
x / 6 = 13
Multiply the equation by 6, then we have
x/6 × 6 = 6 × 13
x = 78
The solution of the equation x/6 + 2 = 15 will be 78 by using the property of subtraction and multiplication of equality.
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We found the correlation coefficient for the comparison between height and weight in babies to be -0.12. That means
correlation is strong
the taller the baby, the heavier the baby
the taller the baby, the lighter the baby
Height and weight of babies are independent
The Correlation Coefficient -0.12 shows that The taller the baby, the lighter the baby.
What is Correlation Coefficient?A statistical measure called correlation shows how much two or more variables fluctuate in connection to one another.
A correlation coefficient is a statistical indicator of how well changes in one variable's value predict changes in another. When two variables are positively linked, the value either rises or falls together.
Given:
Correlation Coefficient = -0.12
As, The range of a correlation coefficient ranges from -1 to 1.
When the number is closer to -1 or closer to 1, there is a substantial association, and when the number is closer to 0, there is no link.
The correlation coefficient in this instance is -0.12, indicating a marginally negative correlation. The negative sign indicates that when one component changes, the other decreases, making a baby that is taller and lighter.
Hence, The taller the baby, the lighter the baby.
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Which of the following situations satisfies all the conditions of a binomial setting? (These conditions are: we know the number of repetitions, the outcome of each trial can be considered either a success or a failure, we know the probability of success or failure of any trial, and the probability doesn't change from trial to trial.)
A binomial setting is one in which there are a fixed number of trials, the outcome in each trial is either a success or a failure, the probability of success or failure is known, and the probability doesn't change from trial to trial.
A binomial setting is one in which we know the number of repetitions (n=20), the outcome of each trial can be considered either a success or a failure (p=0.4, q=1-p=0.6), and the probability of success or failure of any trial does not change from trial to trial (p=0.4, q=1-p=0.6).
For example, if we toss a coin 20 times, and we know the probability of success (head) is 0.4 and the probability of failure (tail) is 0.6, then this is a binomial setting. We can calculate the probability of getting exactly 10 heads in 20 tosses using the binomial formula: P(X=10) = (20C10) * (0.4^10) * (0.6^10) = 0.1775.
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Data set: 8, 7, 10, 10, 17, 13, 7, 10
How much does the data set above vary?
Standard Deviation, σ: 3.152
Count, N: 8Sum, Σx: 82Mean, μ: 10.25Variance, σ2: 9.9375What a standard deviation means?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
Given, Data set: 8, 7, 10, 10, 17, 13, 7, 10
variance:
σ² = Σ(xi - μ)²/N
σ²= ((8 - 10.25)² + … + (10 - 10.25)²)/8
σ²= 79.5/8
σ² =9.9375
σ = √9.9375
σ = 3.1523
The sampling mean most likely follows a normal distribution. In this case, the standard error of the mean can be calculated using the following equation:
σ = σ/√N
σ = 1.114
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The period (T) of a pendulum is related to the length (L) of the pendulum and acceleration due to gravity (g) by the formula T=2π√L/g. If gravity is 32 ft/s2 and the period is 1 second, find the approximate length of the pendulum. Round to the nearest inch. Note: 12 in. = 1 ft.
The approximate length of the pendulum is 2 feet.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that period (T) of a pendulum is related to the length (L) of the pendulum and
acceleration due to gravity (g) by the formula T=2π√L/g.
g=32 ft/s2
t=1 sec
We need to find L
1=2×3.14√L/32
32=6.28√L
32/6.28=√L
5.09=√L
Square on both sides
L=25.9 inches
L=2 feet because 12 inches = 1ft.
Hence, the approximate length of the pendulum is 2 feet.
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fill in the blank with a whole number with how many significant figures are in the following: a) 0.04550 b) 5.0003 c) 1.000 x 105 d) 0.00002 e) 1.01 x 10-2 f) 7
a) 0.04550 has four significant figures.
b) 5.0003 has four significant figures.
c) 1.000 x [tex]10^5[/tex] has four significant figures.
d) 0.00002 has one significant figure.
e) 1.01 x [tex]10^{-2}[/tex] has three significant figures.
f) 7 has one significant figure.
Significant figures are the digits in a number that are known with certainty, including one uncertain digit. In general, any non-zero digit is considered a significant figure, and zeros between non-zero digits are also significant figures.
Leading zeros before the first non-zero digit and trailing zeros after the last non-zero digit are not considered significant figures.
For example, in the given number 5.006, there is four significant number,
since all zeros between integers are always significant.
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A bicycle shop keeps the same ratio of wheels to bikes in stock. The ratio of wheels to bikes is always 4:1. How many wheels does the shop have if there are 18 bikes in stock?
Is it
4.5
42
72
76
Answer:
c (72)
Step-by-step explanation:
since there are four wheels to every bike, you just have to multiply the number of bikes to the amount of wheels per bike. given this, 18 * 4=72.
6. To play a board game, there must be at least 4 people on each team. You
divide your friends into 3 groups. Write and solve an inequality to represent
the number of friends playing the game.
The inequality that best represent the expression is x ≥ 12
What is inequality?A relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.
The sign for greater than is >
The sign for less than <
The sign for greater than or equal to is ≥
The sign for less than or equal to is ≤
There must be at least 4 people in the group. This means that a group member must greater or equal to 4. There are 3 groups.
Represent the value of the number of friends by x
then, x/3 ≥ 4
therefore x ≥ 12
this means that the number of friends must be greater or equal to 12
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solve it to find the value of x. also find the actual length of each square
[tex]perimeter square[/tex]
The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.
What is the perimeter of the square?The sum of all the sides of the square or the product of the four and the edge length of the square is known as the perimeter of the square. For a square with a side length of a unit, we get:
Perimeter of the square = 4a unit
The perimeter of the square is 40 cm. And the sides length of the square is (x + 2) cm. Then the perimeter of the square is given as,
4(x + 2) = 40
Simplify the equation, then we have
4(x + 2) = 40
(x + 2) = 10
x = 10 - 2
x = 8
The equation will be 4(x + 2) = 40. Then the value of the variable 'x' will be 8.
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The complete question is given below.
Solve it to find the value of x. Also, find the actual length of each square perimeter of the square is 40 cm and side length is (x + 2).
Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)
A solution of the first order IVP consisting of this differential equation is y = [tex]\frac{1}{x^2-5}[/tex] and the domain of y considered as a function over the reals is (-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).
We have to find the domain of y considered as a function over the reals.
The differential equation is y' + 2x[tex]y^2[/tex] = 0
The solution of the given differential equation is y = 1/([tex]x^2[/tex] + c)......(1)
The given initial value; y(-3) = 1/4
Replace the initial value in the first-order DE solution provided. To obtain the equation for y, locate the constant c and then re-substitute 'c'.
Now put x = -3 and y(-3) = 1/4 in equation 1
[tex]\frac{1}{4}=\frac{1}{(-3)^2+c}[/tex]
[tex]\frac{1}{4}=\frac{1}{9+c}[/tex]
9+c = 4
Subtract 9 on both side, we get
c = -5
Now substitute the value of c again in equation 1
y = [tex]\frac{1}{x^2-5}[/tex]
To find the domain of y we can write it as
y = [tex]\frac{1}{(x)^2-(\sqrt{5})^2}[/tex]
Now the simplified form is
y = [tex]\frac{1}{(x-\sqrt{5})(x+\sqrt{5})}[/tex]
Now the domain of y over R is
(-∞, -√5) ∪ (-√5, +√5) ∪ (√5, ∞).
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The complete question is:
y = 1/([tex]x^2[/tex] + c) is a one parameter family of solutions of the first order DE y' + 2x[tex]y^2[/tex] = 0. Find a solution of the first order IVP consisting of this differential equation and the given initial condition.
y(-3) = 1/4
Find the domain of y considered as a function over the reals. (Enter your answer using interval notation.)
In 2012, the population of a city was 5.89 million. The exponential growth rate was 3.42% per year.
a) Find the exponential growth function.
b) Estimate the population of the city in 2018.
c) When will the population of the city be 8 million?
d) Find the doubling time.
The general form of exponential formula is y = a * b^x, the population of the city in 2018 6.058454 million.(c) the population of the city be 8 million19.38548963 years.
How to find the population?In this problem, a = 5.21 million and b = 1 + 2.86%/100 = 1.0286.
a is a constant.b is the basex is the exponent.In 2012, the population was 5.89 million.
In 2018, the population will be 5.89 * 1.0286 ^ (2018 - 2012) = 5.89 * 1.0286 ^ 6 = 6.058454 million.
To find when the population will be 9 million, your equation becomes:
9 = 5.21 * 1.0286 ^ x divide both sides of this formula by 5.21 to get:
9/5.21 = 1.0286 ^ x take the log of both sides of the equation to get:
log(9/5.21) = log(1.0286^x) since log(1.0286^x) = x * log(1.0286), the equation becomes:
log(9/5.21) = x * log(1.0286)
Divide both sides of this equation by log(1.0286) to get:
log(9/5.21) / log(1.0286) = x
Solve for x to get:
x = 19.38548963.
Confirm by replace x in the original equation to get:
9 = 5.21 * 1.0286 ^ 19.38548963 becomes 9 = 9.
This confirms the value of x is good.
The population will grow to 9 million in 19.38548963 years.
To find when the population will double, the equation becomes:
2 = 1 * 1.0286 ^ x
Simplify to get:
2 = 1.0286 ^ x
Take the log of both sides of this equation to get:
log(2) = log(1.0286 ^ x)
Since log(1.0286 ^ x) = x * log(1.0286), this equation becomes:
log(2) = x * log(1.0286)
solve for x to get:
x = log(2) / log(1.0286) = 24.5808602.
to confirm this is true, replace x in the original equation to get:
2 = 1.0286 ^ 24.5808602 which becomes 2 = 2.
This confirms the value of x is true.
The population will double in 24.5808602 years.
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A farmer is building a cylinder-shaped grain bin. The bin will be 10 feet tall and have a diameter of 12 feet. What is the surface area of the grain
bin in square feet? Use x = 3. 14. Round to the nearest hundredth if necessary.
Answer: 602.88 square feet
Equation for surface area of cylinder:
A = 2πrh+2πr^2
r = 6, because radius is half of the diameter
h = 10
A = 2(3.14)(6)(10) + 2(3.14)(6)^2
A = 376.8 + 226.08
A = 602.88 square feet
7th Grade Exit Ticket Lesson 5.5 "Dividing Fractions"
Answer: -1 7/20
Step-by-step explanation:
hope this helps
In how many months the amount of Rs1000 at the rate of 10%will be RS1200
Answer: To determine how many months it will take for an initial investment of Rs1000 to grow to Rs1200 at a 10% interest rate, we can use the formula:
Time = (ln(final value / initial value)) / (ln(1 + interest rate))
where ln is the natural logarithm function.
Plugging in the given values:
Time = (ln(1200/1000)) / (ln(1 + 0.10))
Time = (ln(1.2)) / (ln(1.10))
Time = 0.18232 / 0.09531
Time = 1.913 months
It will take approximately 1.913 months for an investment of Rs1000 to grow to Rs1200 at a 10% interest rate.
Step-by-step explanation:
fill in the blank. in a certain company, the average salary for college graduates is $62,047 and the average salary for high school graduates is $40,626. the average salary for college graduates is ___% higher than that of high school graduates. (round your answer to the nearest whole percentage point, e.g., enter 14 if the answer is 14%.)
The average salary for college graduates is 53% higher than that of high school graduates.
How to calculate the percentage increase?Mathematically, percentage increase can be calculated by using this mathematical expression:
Percentage increase = [Final value - Initial value]/Initial value × 100
Substituting the given parameters into the percentage increase formula, we have the following;
Percentage increase = [62,047 - 40,626]/40,626 × 100
Percentage increase = 21,421/40,626 × 100
Percentage increase = 0.527 × 100
Percentage increase = 52.7 ≈ 53%.
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A figure is made up of an equilateral triangle and a square of side 7cm. The perimeter of the figure is in stepes