Answer:
6
Step-by-step explanation:
You want to know the number of uphill integers divisible by 15, where an uphill integer is one that has its digits strictly increasing.
Divisible by 15An integer will be divisible by 15 if and only if it is divisible by 3 and 5. An integer is divisible by 5 if it ends in 5 or 0. An uphill integer cannot end in 0, so must end in 5.
An integer is divisible by 3 if the sum of its digits is divisible by 3
Uphill integersAn uphill integer will have differences between successive digits that are positive integers. In order for the final digit to be 5, the sum of these differences must be 5. Hence we can find uphill integers by considering the "integer partitions" of 5: the sets of positive integers whose total is 5. Those sets would be ...
{5}, {4, 1}, {3, 1, 1}, {2, 2, 1}, {2, 1, 1, 1}, {1, 1, 1, 1, 1}
Uphill integers will also have digit differences that are some permutation of each of these sets. For example, the digit differences may be {4, 1} or {1, 4}, corresponding to the numbers 45 or 15.
The uphill integers that end in 5 are ...
5, 45, 15, 35, 25, 345, 145, 125, 245, 235, 135, 2345, 1345, 1245, 1235, 12345
Divisible by 3We already know each of these is divisible by 5. The ones that have a digit total that is a multiple of 3 are ...
15, 45, 135, 345, 1245, 12345
There are 6 uphill integers divisible by 15.
6.) In the recent presidential election, Ohio had 20 electoral votes. This is 14 votes less
than Texas had. How many electoral votes did Texas have?
Answer:
Texas had 34 electoral votes
Step-by-step explanation:
Ohio had 20 electoral votes in the recent presidential election.
Those 20 votes are 14 votes less than Texas had.
This means Texas had 14 votes more than Ohio, that is:
Votes of Texas = 20 + 14 = 34
Texas had 34 electoral votes
what is 4.4.4 as an exponent
Answer:
4*4*4=4^3
Step-by-step explanation:
4 is multiplied by itself 3 times so it's to the third power which equals \(4^{3}\)
1 The legs of a triangle are 6 cm and 8 cm. The hypotenuse is 14 cm. Is it a right triangle?
Answer:
this is not a right triangle
Step-by-step explanation:
^ = squared
The formula forthe Pythagorean theorem is a^+ b^ = c^
If this is a right triangle this must be true
6^ + 8^ = 14^
36 + 64 = 196
100 is not equal to 196
So this is not a right triangle
a company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a standard deviation of 0.6 degrees, based on samples of 100. a sample of 100 refrigerators have an average temperature of 37.37 degrees. are the refrigerators within the 90% confidence interval?
Average temperature of sample of 100 refrigerator is 37.37 degrees. yes the refrigerators within the 90% confidence interval.
Yes, the temperature is within the confidence. A company making refrigerators strives for the internal temperature to have a mean of 37.5 degrees with a population standard deviation of 0.6 degrees, based on samples of 100.
The average temperature of the air that is indicated by a thermometer that is properly exposed during a given time period, usually a day, a month, or a year.
The confident choice is the criteria that you choose or the range that you choose that your answer might fall in this area according to your estimation as the chances of getting fail become lesser and lesser as your confidence about for choice increases.
There is a 5% chance if being wrong among the 95% confident choice . And also there is a 10% chance of being wrong with a 90% confident choice .But 99% confident choice will be wider as there will be minimum chance of being wrong.
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PLEASE HELP ASAP!! I’ll give u a virtual hug if u solve it
Answer:
? = 56 m
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
\(\frac{?}{8}\) = \(\frac{21}{3}\) = 7 ( multiply both sides by 8 to clear the fraction )
? = 7 × 8 = 56 m
Answer:
Step-by-step explanation:
The earth has been devastated by a horrible plague, causing the aging process to speed up. The population has decreased by 50%, and it’s just a matter of time before all humans cease to exist. You are given immunity from a deadly disease that causes humans to age rapidly. It is up to you alone to find the cure. Use your powers of deduction to uncover the mysterious origins of this disease and find an antidote—before it’s too late!
What is the specific victory condition of this game?
a) Uncovering the origins of the disease
b) Finding an antidote for the disease before time runs out
c) All humans cease to exist
d) There is no victory condition in this game
e) Gaining immunity from the disease
2) You are a film producer who is trying to build your own production studio. In order to get money from investors, you must answer trivia questions related to popular films. This strategy requires players to apply ______ knowledge in order to advance in the game.
a) imperfect
b) extrinsic
c) perfect
d) transitive
e) intrinsic
f) intransitive
3) In Joseph Campbell's monomyth, what occurs during the "approach to the inmost cave"?
a) The hero embarks on the journey and enters the special world
b) The hero goes through a time of even more tests and trials
c) The hero demonstrates that he/she has been changed by the journey
d) The audience is introduced to the hero's world
e) It usually feels like the story is ending here
4) Your player meets with an elder who tells you that if you can locate the magical chalice, then you can use it's powers to boost the strength of all wooden weapons that you are carrying at the time in which you find it.
This is an example of what type of knowledge?
a) Intrinsic
b) Explicit
c) Perfect
d) Implicit
e) Extrinsic
f) Imperfect
Intrinsic knowledge, also known as intrinsic value or intrinsic understanding, refers to knowledge that is valued for its inherent qualities or qualities that exist within itself. It is knowledge that is pursued or appreciated for its own sake, independent of any external factors or practical applications.
1. The specific victory condition of this game is to find an antidote for the disease before time runs out. You are given immunity from a deadly disease that causes humans to age rapidly. It is up to you alone to find the cure. The earth has been devastated by a horrible plague, causing the aging process to speed up. The population has decreased by 50%, and it’s just a matter of time before all humans cease to exist.
2. The strategy used by the film producer to get money from investors is to answer trivia questions related to popular films. This strategy requires players to apply explicit knowledge in order to advance in the game. 3. In Joseph Campbell's monomyth, the hero goes through a time of even more tests and trials during the "approach to the inmost cave". It is the stage in which the hero leaves the known world and enters into the unknown world, to accomplish the ultimate goal.
4. The given example is an example of intrinsic knowledge. Intrinsic knowledge is the type of knowledge that comes from personal experience and learning. It is knowledge that has been gained by doing something over and over again. Intrinsic knowledge is often associated with philosophical and metaphysical discussions about the nature of knowledge and its value. It is concerned with understanding the essence, truth, or meaning of certain concepts, ideas, or phenomena.
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What is the answer to 3y+6=12
Answer:
y=4
Step-by-step explanation:
Please help with part a b and c, C says “compre the functions algebraically by rewriting them using a common denominator”
Given:
\(\begin{gathered} f(x)=\frac{x+2}{x+3} \\ g(x)=\frac{x+5}{x} \end{gathered}\)Required:
To find the values of the given functions at the given values of x.
Explanation:
At x = 0.5, Put x=0.5 in f(x) and g(x).
\(\begin{gathered} f(0.5)=\frac{0.5+2}{0.5+3} \\ f(0.5)=\frac{2.5}{3.5} \\ f(0.5)=0.714 \\ g(0.5)=\frac{0.5+5}{0.5} \\ g(0.5)=11 \end{gathered}\)Now put x=1 in f(x) and g(x)
\(\begin{gathered} f(1)=\frac{1+2}{1+3} \\ f(1)=\frac{3}{4} \\ f(1)=0.75 \\ g(1)=\frac{1+5}{1} \\ g(1)=6 \end{gathered}\)Now put x=2 in f(x) and g(x).
\(\begin{gathered} f(2)=\frac{2+2}{2+3} \\ f(2)=\frac{4}{5} \\ f(2)=0.8 \\ g(2)=\frac{1+5}{2} \\ f(2)=\frac{6}{2} \\ f(2)=3 \end{gathered}\)Similarly, we will put the other values of x in f(x) and g(x), and then make the table by putting the values.
List the eigenvalues of A. The transformation x-Ax is the composition of a rotation and a scaling. Give the angle op of the rotation, where -x
The transformation x-Ax can be decomposed into a rotation and scaling if and only if A is symmetric.
If A is symmetric, then its eigenvalues will be real and its eigenvectors will be orthogonal. The scaling factor is determined by the magnitude of the eigenvalues, and the rotation angle is determined by the angle between the eigenvectors. However, without knowing the matrix A, I cannot determine the values for these.
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question 3 options: in a race, there are 20 runners. trophies for the race are awarded to the runners finishing in first and second place. in how many ways can first and second place be determined?
There are 380 ways to determine the first and second place in the race.
In a race, there are 20 runners. Trophies for the race are awarded to the runners finishing in first and second place. In how many ways can first and second place be determined?When the trophies for the race are awarded to the runners finishing in first and second place, then it means that there are only two trophies to be awarded. Now, the number of ways in which the two trophies can be awarded can be calculated by permutation, which is a way of counting the arrangements or selections of objects in which order is important.
To determine the number of ways first and second place can be determined in a race with 20 runners, we can use the concept of permutations.
The first-place finisher can be any one of the 20 runners. After the first-place finisher is determined, there are 19 remaining runners who can finish in second place. Therefore, the number of ways to determine the first and second place is given by:
Number of ways = 20 * 19 = 380
So, there are 380 ways to determine the first and second place in the race.
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Suppose Evan is trying to build a frame out of popsicle sticks x inches long. The frame will have length (2x – 3) and width of (x – 2). If the popsicle sticks are 3 inches long, what is the area of the frame in inches and expressed as a polynomial? A. 3 square inches; 2x2 – 7x + 6 B. 3 square inches; 2x4 – 4x + 6 C. 21 square inches; 2x2 – x + 6 D. 15 square inches; 2x2 – 3x + 6
Answer:
The correct option is A) 3 square inches; \(2x^2-7x+6\).
Step-by-step explanation:
It is given that the length of the frame is (2x-3) and the width is (x-2)
The area of the rectangle is: \(A=l\times w\)
Where, A is the area l is the length and w is the width of the rectangle.
Put \(l=(2x-3)\) and \(w=(x-2)\) in the area of the rectangle.
\(A=(2x-3)(x-2)\\A=2x^2-4x-3x+6\\A=2x^2-7x+6\)
The area of the frame expressed as a polynomial is \(2x^2-7x+6\).
Now substitute x=3 in \(A=2x^2-7x+6\).
\(A=2(3)^2-7(3)+6\\A=18-21+6\\A=3\)
The area of the frame is 3 square inches.
Hence, the correct option is A) 3 square inches; \(2x^2-7x+6\).
Solve for x. Please help.
Answer:
x = 2
Step-by-step explanation:
74×2= 148
75x-2= 148
Add 2 on both sides
75x= 150
Divide 75 on both sides
x = 2
Find the general solution for the following linear systems. Describe the long term behaviour. (You need to find eigenvalues of the corresponding 3-by-3 matrices.
x' = -2x
y' = -z
z' = y
The eigenvalues are complex numbers: λ₁ = -1, λ₂ = i√2, λ₃ = -i√2. Since the eigenvalues have non-zero imaginary parts, the system has complex eigenvalues.
To find the general solution for the given linear system:
x' = -2x
y' = -z
z' = y
We can rewrite it in matrix form as:
X' = AX
where X = [x, y, z] and A is the coefficient matrix:
\(\left[\begin{array}{ccc}0&0&-2\\0&-1&0\\0&1&0\end{array}\right]\)
To find the eigenvalues λ, we solve the characteristic equation det(A - λI) = 0, where I is the identity matrix.
The characteristic equation becomes:
det(A - λI) = det([0 0 -2]
[0 -1 0]
[0 1 0] - λ[1 0 0]) = 0
Simplifying the determinant, we get:
λ³ + 2 = 0
Solving this equation, we find that the eigenvalues are complex numbers: λ₁ = -1, λ₂ = i√2, λ₃ = -i√2.
The long-term behavior of the system depends on the eigenvalues. Since the eigenvalues have non-zero imaginary parts, the system has complex eigenvalues. This indicates that the solutions will oscillate or spiral around the equilibrium point rather than converging or diverging.
The real part of the eigenvalues (-1) suggests that the oscillations will decay over time, leading to stable behavior. Overall, the long-term behavior of the system is stable oscillations around the equilibrium point.
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Lines a and b are parallel and lines e and f are parallel.What is the value of x?A)8B)82C)98D)172
Because lines a and b are parallel and lines e and f are parallel, the value of "x" is 82 degrees.
What is parallel lines?Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space. Parallel curves are those that do not touch or intersect and maintain a constant minimum distance. Parallel lines are lines that are always the same distance apart in a plane. Parallel lines never cross. Perpendicular lines are those that connect at a straight angle (90 degrees). Parallel lines are lines in a plane that never intersect, no matter how far they are extended. The distance between the parallel lines is continuous since they never intersect.
Here,
Remember that vertical angles are generated by crossing lines that form two non-adjacent angles. These angles are congruent because they have the same vertex.
Take a look at the attached figure. Because lines "a" and "b" are parallel, the angles 82° and x° are vertical angles. As a result, they are congruent.
The value of "x" is 82 degree as lines a and b are parallel and lines e and f are parallel.
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What is the distance between points A and B?
Answer:
6 units
Step-by-step explanation:
fastt
13. Calculate the compound interest of an annuity due of BD400 paid each 4 months for 6.2 years if the nominal rate is 3% thirdly? (3 Points)
Therefore, the compound interest of the annuity due of BD 400 paid each 4 months for 6.2 years at a nominal rate of 3% per annum is BD 40,652.17.
Compound interest of an annuity due can be calculated using the formula:A = R * [(1 + i)ⁿ - 1] / i * (1 + i)
whereA = future value of the annuity dueR = regular paymenti = interest raten = number of payments First, we need to calculate the effective rate of interest per period since the nominal rate is given per annum. The effective rate of interest per period is calculated as
:(1 + i/n)^n - 1 = 3/1003/100 = (1 + i/4)^4 - 1
(1 + i/4)^4 = 1.0075i/4 = (1.0075)^(1/4) - 1i = 0.0303So,
the effective rate of interest per 4 months is 3.03%.Next, we can substitute the given values in the formula:
A = BD 400 * [(1 + 0.0303)^(6.2 * 3) - 1] / 0.0303 * (1 + 0.0303)A = BD 400 * [4.227 - 1] / 0.0303 * 1.0303A = BD 400 * 101.63A = BD 40,652.17
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48:08 bok sk onces Problem 3-12 (Static) The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle. Sales also exhibit seasonal variations. Ft 40-6.5t+2t
The seasonal problem may be predicted using the difference between actual sales and the trend portion of the sales as given by the equation: \(Ft 40-6.5t+2t².\)
Solving the given equation: \(Ft = 40 - 6.5t + 2t²\)Hence, the trend portion of quarterly sales of condominiums over a long cycle is given by the equation\(Ft = 40 - 6.5t + 2t²\) where t is time in quarters (Q1 1981 is t=1, Q2 1981 is t=2, Q3 1981 is t=3, etc.)
Given that sales exhibit seasonal variations, the seasonal problem may be predicted using the difference between actual sales and the trend portion of the sales as given by the equation Ft = 40 - 6.5t + 2t².
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Can someone please help. I have trouble with this.
The left and right ends of the normal probability distribution extend indefinitely, never quite touching the horizontal axis. True False
It is false as the left and right ends of the normal probability distribution extend indefinitely, approaching but never touching the horizontal axis.
The statement is false because the left and right ends of the normal probability distribution do not extend indefinitely. In reality, the normal distribution is defined over the entire real number line, meaning it extends infinitely in both the positive and negative directions. However, as the values move further away from the mean (the center of the distribution), the probability density decreases. This means that although the distribution approaches but never touches the horizontal axis at its tails, the probability of observing values extremely far away from the mean becomes extremely low. Thus, while the distribution theoretically extends infinitely, the practical probability of observing values far from the mean decreases rapidly.
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6407÷61 as a fraction
Answer:
105.032786885
Step-by-step explanation:
convert that to a fraction and there is ur answer
Hope this helps!
Please mark branliest!
Answer:
105.032786885
6407÷61 as a fraction
6407/61 is 105.032786885
105.032786885=10 and 56557377/200000000
the predicted salary for a player whose position is first base and has played for 10 years in the majors leagues is (round to the nearest dollar):
A player who has played first base for ten years in the majors to have a predicted salary of $700,000 per year
The predicted salary for a player whose position is first base and has played for 10 years in the majors leagues can be found by using the regression equation. Since the regression equation is not given, the solution to this problem cannot be determined with certainty.
However, the general formula for the regression line is:y = a + bx, where y is the predicted variable, x is the independent variable, a is the y-intercept, and b is the slope of the line.
However, if we suppose that the regression equation is:y = 200000 + 50000x, where y is the player's salary and x is the number of years they have played in the majors, then we can substitute x = 10 to get:
y = 200000 + 50000(10) = $700000
Therefore, if we use this equation to make predictions, we would expect a player who has played first base for ten years in the majors to have a predicted salary of $700,000 per year (rounded to the nearest dollar).
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can someone help me with this math hw
Answer:
Step-by-step explanation:
F(x) = x² - 2x + 1
= (x - 1)²
By comparing this equation with the vertex form of the quadratic equation,
y = (x - h)² + k
Here, (h, k) is the vertex
Vertex of the parabola → (1, 0)
x-intercepts → (x - 1)² = 0
x = 1
y-intercepts → y = (0 - 1)²
y = 1
Now we can draw the graph of the given function,
From this graph,
As x → 0,
\(\lim_{x \to 0^{-}} (x-1)^2=1\)
\(\lim_{x \to 0^{+}} (x-1)^2=1\)
f(0) = (0 - 1)²
= 1
Since, \(\lim_{x \to 0^{-}} (x-1)^2=\lim_{x \to 0^{+}} (x-1)^2=1\)
Therefore, given function is continuous at x = 0.
Jeff's preferences can be represented by the following utility function U = In x + In y.
a. What is Jeff's demand function for good x? If Px = 1, Py=2 and W = 200, how much x does he consume?
b. If Px increases to 2, calculate the compensating variation.
c. Calculate the total effect, the substitution effect and the income effect of the price change.
After considering the given data we conclude that the answer for the sub questions are
a) Jeff consumes 33.33 units of good x.
b) the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c) The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
a. To find Jeff's demand function for good x, we can use the following equation:
\(\frac{\partial U}{\partial x}=\frac{1}{x}=\frac{p_x}{p_y}=\frac{1}{2}\)
Solving for x, we get:
\(x=\frac{1}{2}y\)
Substituting the given values, we get:
\(x=\frac{1}{2}(200/3)=33.33\)
Therefore, Jeff consumes 33.33 units of good x.
b. If Px increases to 2, the new demand function for good x is:
\(x'=\frac{1}{2}y'\)where y' is the amount of good y consumed at the new prices and income. To find the compensating variation, we need to find the amount of income Jeff would need at the original prices to achieve the same level of utility as he does at the new prices. We can use the following equation:
\(W'=W+CV\) where W is the original income, W' is the new income, and CV is the compensating variation.
Substituting the given values, we get:
\(8.51=\ln(33.33)+\ln(66.67)8.51=ln(33.33)+ln(66.67)\)
\(y'=\frac{W'}{2}\)
\(x'=\frac{1}{2}y'\) Solving for y', we get:
y'=100
Solving for x', we get:
x'=50
Therefore, the compensating variation is:
\(CV=W'-W=2(50)-200=-100CV\)
c. To calculate the total effect, substitution effect, and income effect of the price change, we can use the following equations:
\(TE=\frac{\Delta U}{U_0}\)
\(SE=\frac{\Delta x_s}{x_0}\)
\(IE=\frac{\Delta x_i}{x_0}\)where \(\Delta U\)is the change in utility, \(U_0\) is the initial utility,\(\Delta x_s\) is the change in consumption due to the substitution effect, \(x_0\) is the initial consumption, and \(\Delta x_i\) is the change in consumption due to the income effect.
The change in consumption due to the price change can be calculated as:
as:
\(\Delta x=x'-x_0=\frac{1}{2}y'-\frac{1}{2}y_0\)
where \(y_0=2x_0\) and \(y'=2x'\)
Substituting the given values, we get:
\(\Delta x=x'-x_0=50-33.33=16.67\)
The substitution effect can be calculated as:
\(SE=\frac{\Delta x_s}{x_0}=\frac{x_s'-x_0}{x_0}=\frac{1}{2}\frac{y_0-y_s'}{x_0}=\frac{1}{2}\frac{p_x}{p_y}\frac{y_0}{x_0}\)
Substituting the given values, we get:
\(SE=\frac{1}{2}\frac{1}{2}\frac{2x_0}{4x_0}=\frac{1}{4}\)
The income effect can be calculated as:
\(IE=\frac{\Delta x_i}{x_0}=\frac{\Delta W}{W_0}=\frac{CV}{W_0}\)
Substituting the given values, we get:
\(IE=\frac{-100}{200}=-0.5\)
The total effect can be calculated as:
\(TE=SE+IE=\frac{1}{4}-0.5=-0.25\)
Therefore, the total effect of the price change is negative, indicating that Jeff will consume less of good x as a result of the price increase. The substitution effect is positive, indicating that Jeff will consume more of good x due to the relative price change. The income effect is negative, indicating that Jeff will consume less of good x due to the decrease in purchasing power caused by the price increase.
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Sharlene purchased a new truck, whose value over time depreciates. Sharlene's truck depreciates according to the function y = 45,529(0.78)x, where x represents the number of months since the truck was purchased. What is the range of the exponential function y based on its equation and the context of the problem?
Based on the context of the problem, the range of the exponential function y = \(45,529(0.78)^x\) is y > 0.
The exponential function for depreciation given in the problem is:
y = 45,529(0.78)^x
This function gives us the value of Sharlene's truck in dollars after x months of ownership, assuming that the depreciation follows a constant rate and is modeled by an exponential function.
To find the range of the function, we need to consider the minimum value that y can take. Since depreciation leads to a decrease in value over time, y should always be greater than zero. In other words, the range of the function is:
y > 0
In practical terms, this means that Sharlene's truck will always have some positive value, even if its market value has decreased due to depreciation. In other words, a truck is never worth zero or less than zero (unless it has additional debts associated with it), and Sharlene's truck will always have some resale or scrap value even if it has depreciated significantly.
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Help pls will give brainliest
Answer:
hello,
answer C
Step-by-step explanation:
area of the rectangle=2b*b=2b²
area of the half cercle= \(\\\dfrac{\pi*(\frac{c}{2})^2}{2} =\dfrac{\pi*c^2}{8} \\\)
Area in blue= 2b²-πc²/8
Help me guys, please and thank u
Answer:
¡¡ Only
Step-by-step explanation:
-8-2x < - 4
-2x < - 4+8
-2x < 4
x > - 2
Triangle X Y Z is shown. Angle X Y Z is 75 degrees and angle Y Z X is 50 degrees. The length of X Y is 2 and the length of X Z is y. Use the law of sines to find the value of y. Round to the nearest tenth. Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction 1.4 units 1.6 units 2.5 units 2.6 units
To find the value of y using the law of sines, we need to use the following formula:
\(sin(Y) / y = sin(X) / 2\)
Given that angle Y is 50 degrees, angle X is 75 degrees, and the length of XY is 2 units, we can substitute these values into the formula:
\(sin(50) / y = sin(75) / 2\)
Now we can solve for y:
\(y = (2 * sin(50)) / sin(75) ≈ 1.4\)units
Therefore, the value of y is approximately 1.4 units (rounded to the nearest tenth).
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Answer:
1.4 units
Step-by-step explanation:
The answer above is correct.
SIMPLIFY THIS ASAP PLS
Answer: 4x / (x + 2)(x + 3)
The answer is 4x / (x + 2)(x + 3)
Step-by-step explanation:
Combine the fractions by finding a common denominator:
Final Solution:
4x / (x + 2)(x + 3)
Hope this helps =)
2. This is the number of people who
attended a football game.
Sixteen thousand, four hundred
thirty-four
Which shows this number written in
standard form?
A 1,634
B16,404
с 16,434
D 160,434
2. What is the area of a triangle whose vertices are
a. What is the formula for the area of the triangle?
b. Find the length of the base. Round to the nearest tenth if needed.
c. Find the length of the height. Round to the nearest tenth if needed.
d. Find the area of the triangle.
a) The formula for the area of the triangle is given as follows:
Area = 0.5 x base x height.
b. The length of the base is given as follows: 6.3 units.
c. The length of the height is given as follows: 5 units.
d. The area of the triangle is given as follows: 15.75 units squared.
How to obtain the area of a triangle?The area of a triangle is calculated as half the multiplication of the triangle's base by the triangle's height, as follows:
Area = 0.5 x base x height.
The vertices for the right triangle in this problem are given as follows:
(-4, -1), (2,1), (2,6).
Hence the base of the triangle is of:
\(B = \sqrt{(2 - (-4))^2 + (1 - (-1))^2} = 6.3\)
The height is given as follows:
6 - 1 = 5.
Which means that the area of the triangle is of:
Area = 0.5 x 5 x 6.3 = 15.75.
More can be learned about the area of a triangle at https://brainly.com/question/21735282
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