we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell.
What is mean ?
Mean can be defined as the ratio of sum of the given observations and total number of observations.
a) Since the life spans of the hot water heaters are normally distributed with a mean of 13 years and a standard deviation of 1.5 years, we can use the empirical rule to estimate the range of years we would expect the hot water heater to last. The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% of the data falls within two standard deviations of the mean, and approximately 99.7% of the data falls within three standard deviations of the mean.
Using this information, we can estimate that the range of years we would expect the hot water heater to last is approximately 10.5 to 15.5 years. This is because one standard deviation below the mean is 13 - 1.5 = 11.5 years, and one standard deviation above the mean is 13 + 1.5 = 14.5 years. Therefore, we can reasonably expect the hot water heater to last between 10.5 and 15.5 years with about 95% confidence.
b) To set the warranty on the product so that we have to replace at most 5% of the hot water heaters that we sell, we need to find the number of years that corresponds to the 5th percentile of the distribution. This is the value below which 5% of the data falls.
We can use a standard normal distribution table or a calculator to find the z-score corresponding to the 5th percentile, which is -1.645. We can then use the formula z = (x - mu) / sigma to find the number of years, x, that corresponds to this z-score.
-1.645 = (x - 13) / 1.5
Solving for x, we get x = 10.83 years.
Therefore, we should claim a warranty of 11 years (rounded to the nearest whole number) to ensure that we replace at most 5% of the hot water heaters that we sell
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Solve for lengths of the missing sides in each pair of similar triangles. Round to nearest tenth if if necessary jk kl
For the given similar triangles, the length of the missing side in the second triangle is 20.
To solve for the length of the missing side in the pair of similar triangles, we can use the SSS similarity theorem. The theorem states that 'if all three pairs of corresponding sides of two triangles are proportional, then the two triangles are similar'. Since the triangles are similar, the ratio of their corresponding sides will be equal.
The given measurements of the first triangle are 12, 18, and 24, and the measurements of the second triangle are 10, 15, and x. To solve for x, you can use the ratio of corresponding sides of similar triangles. The ratio for the sides of the first triangle are 12:18:24 and for the second triangle are 10:15:x. The ratio of the corresponding sides is 10:12, 15:18, and x:24.
We can set up a proportion using the given dimensions and solve for x.
The proportion will look like this:
12/10 = 18/15 = 24/x
Cross-multiplying and simplifying, we get:
12x = 240
x = 20
Therefore, the length of the missing side in the second triangle is 20.
Note: The question is incomplete. The complete question probably is: Solve for length of the missing side in the pair of similar triangles. The dimensions of one triangle are 12, 18, and 24, and the dimensions of the second triangle is 10, 15, and x. (These are corresponding measurements).
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Can someone help me answer this question??? LOL :)
For the exponential function:
g(x) = 14*(2)^x
We can see that:
a = 14, and b = 2.
How to identify the parts of the exponential function?A general exponential function is written as:
y = a*(b)^x
Where a is the inital value of the exponential function and b is the base.
Here we have the exponential function:
g(x) = 14*(2)^x
Comparing that to the general one, we can see that the initial value is 14 and the base is 2.
Then:
a = 14
b = 2
The correct option is the second one.
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Solve each system by graphing
x-y=3
7x-y=-3
How many milliliter in 1 microliter?
From the given information provided, by converting the units there are 0.001 milliliters in 1 microliter.
This means that if you have 1 microliter of liquid, it is equal to 0.001 milliliters of liquid.
The conversion factor between milliliters (mL) and microliters (μL) is:
1 mL = 1000 μL
Therefore, to convert microliters to milliliters, you divide the number of microliters by 1000.
For example, if you have 500 μL of liquid, you can convert it to milliliters by dividing 500 by 1000:
500 μL / 1000 = 0.5 mL
So, 500 microliters of liquid is equal to 0.5 milliliters of liquid.
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Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)
Translation: 2 units left and 1 unit down. Q(0,-1), D(-2,2), V (2,4), J(3,-3)
New coordinates are respectively, (-2, -2), (-4, 1), (0, 3), (1, -4)
What is the point?A point is a location of an object by taking reference of origin, In general case we consider it at (0,0), At the origin value of both the coordinate position is considered as Zero, In simple words point indicates how much it is above or below from the coordinate axes.
Vertical distance from the x axis is known as y coordinate and horizontal distance from the y axis is known as x coordinate.
Given the points Q(0,-1), D(-2,2), V (2,4), and J(3,-3),
we can see that each point has been translated 2 units to the left and 1 unit down.
This is because each x-coordinate has decreased by 2 and each y-coordinate has decreased by 1.
So, the translation of 2 units left and 1 unit down has moved each point along the plane in the negative x-direction and the negative y-direction.
the points are respectively (-2, -2), (-4, 1), (0, 3), (1, -4)
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What is the equation of the line that passes through the point (5,0) and has a slope of 6/5?
The solution is, the equation of the line that passes through the point (5,0) and has a slope of 6/5 is , y=6/5*x - 6
What is a straight line?A straight line is an endless one-dimensional figure that has no width. It is a combination of endless points joined both sides of a point and has no curve.
here, we have,
the line that passes through the point (5,0) and has a slope of 6/5
now, w know, the point slope form of straight line is,
y-y1=m(x-x1)
so, putting the values , we get,
y-0=6/5(x-(5))
y-0=6/5(x-5)
y=6/5*x- 30/5
y=6/5*x- 6
Hence, The solution is, the equation of the line that passes through the point (5,0) and has a slope of 6/5 is , y=6/5*x - 6
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Examine this system of equations. Which numbers can be multiplied by each equation so that when the two equations are added together, the x term is eliminated?
One-fifth x + three-fourths y = 9
Two-thirds x minus five-sixths y = 8
–10 times the first equation and 3 times the second equation
10 times the first equation and 3 times the second equation
–3 times the first equation and 5 times the second equation
3 times the first equation and 5 times the second equation
The numbers that can be multiplied by each equation so that when the two equations are added together, the x term is eliminated is: A. –10 times the first equation and 3 times the second equation.
How to solve these system of linear equations?In order to determine the solutions to a system of two linear equations, we would have to evaluate and eliminate each of the variables one after the other, especially by selecting a pair of linear equations at each step and then applying the elimination method.
Given the following system of linear equations:
1/5(x) + 3y/4 = 9 .........equation 1.
2x/3 - 5y/6 = 8 .........equation 2.
In this scenario, the number that should be used to multiply first equation can be calculated by using the following ratio:
Ratio = -(x-coefficient of second equation)/(x-coefficient of first equation)
Ratio = -(2/3)/(1/5)
Ratio = -10/3
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Mrs. Gregory, the golf course superintendent at a country club, plans to reseed the putting green of the first hole. The circular putting green has a diameter of 38 ft.
People on golf course, aerial view.
What is the area of the putting green?
Use π=3.14.
Question 1 options:
------------------------
ANSWERS:
1133.54 ft²
119.32 ft²
1133 ft²
1314.14 ft²
Answer:
Step-by-step explanation: 1133.5.
You pick a card at random.
1 2 3 4
What is P(factor of 10)?
Write your answer as a fraction or whole number.
The probability of picking a factor of 10 is 1/4 or 0.25 as a decimal.
What is probability?Probability can be defined as the ratio of favorable outcomes to the total number of events.
Here,
To calculate the probability of picking a factor of 10, we need to count the number of cards that are factors of 10 and divide that by the total number of cards.
The factors of 10 are 1, 2, 5, and 10. Out of the given cards, only 2 is a factor of 10.
Therefore, the probability of picking a factor of 10 is 1/4 or 0.25 as a decimal.
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What does 500x235 equal?
Answer:
[tex]117500[/tex]
Step-by-step explanation:
[tex]500 \times 235=100\times (5\times 235)=1175 \times 100=117500[/tex]
Answer: 117,500
Step-by-step explanation: 500 x 235 = 117,500
Consider the equation pT=kVN, where k is a constant. Select all of the correct
answers that describe the variation between variables.
p varies [inversely or directly]with V
N varies [inversely or directly]with V
p varies [ inversely or directly]With T
T varies [ inversely or directly] with N
The correct answer is P and T directly varies with V and N, and P and N inversely varies with T and V respectively.
What is direct variation?It is the mathematical relationship between two variables which can be expressed by an equation in which one variable is equal to a constant times the other.
Given that, the equation pT = kVN, where k is a constant.
pT = kVN
If we remove constant, then,
pT ∝ VN
or
p 1/∝ T
V 1/∝ N
Hence, the correct answer is P and T directly varies with V and N, and P and N inversely varies with T and V respectively.
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how much 3 million yen to usd ?
Answer:
about 23,000 usd
Step-by-step explanation:
If you want a quick way to translate yen to usd, take the yen amount and take away two zeros. So 3 mil yen would be 30,000. This method is a bit off but is quick and easy.
1 us dollar is about 130 yen
what is the solution to the system
line 1: y= -2x-4
line 2: y=2/5x + 16/5
The solution of system of equation y= -2x-4 and y=2/5x + 16/5 is (-3, 2).
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The system of equations are y= -2x-4
and y=2/5x + 16/5
By substitution method let us find the solution.
2/5x + 16/5=-2x-4
2/5x+2x=-4-16/5
12x/5=-20-16/5
12x=-36
Divide both sides by 12
x=-3
Now plug in x value in any of the equation
y=-2(-3)-4
y=6-4
y=2
Hence, the solution of system of equation y= -2x-4 and y=2/5x + 16/5 is (-3, 2).
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Question in the picture.
The domain and range of the function for the given graph is -
Domain : (-∞, + ∞)Range: [3, ∞)Define the term domain and range of the function?The range of values which we're permitted to enter into our function is known also as domain of a function.
The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.The collection of all potential inputs for a function is its domain.The collection of potential output values for a function is known as its range. For instance, the range seems to be the non-negative real numbers for the function f(x)=x2 here on domain among all real numbers (xR), which may be represented as f(x)≥0 (or [0,∞) using interval notation).Thus, the domain and range of the function for the given graph is -
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At what points does the helix r(t) = sin(t), cos(t), t intersect the sphere x2 + y2 + z2 = 26? (round your answers to three decimal places. If an answer does not exist, enter dne. ).
At (0.958, 0.287, 5) and (0.958, -0.287, -5) points, the helix r(t) = sin(t), cos(t), t intersect the sphere x^2 + y^2 + z^2 = 26.
The sphere x^2 + y^2 + z^2 = 26 is a sphere with center at the origin and radius sqrt(26).
The helix r(t) = sin(t), cos(t), t is parameterized by sine and cosine functions, which oscillate between -1 and 1.
To find the points at which the helix intersects the sphere, we need to find the values of t such that the distance between r(t) and the origin is equal to sqrt(26).
The distance between a point (x, y, z) and the origin is given by the formula:
d = sqrt(x^2 + y^2 + z^2)
So, substituting the values from r(t), we have:
d = sqrt(sin^2(t) + cos^2(t) + t^2)
Setting d equal to sqrt(26), we have:
sqrt(sin^2(t) + cos^2(t) + t^2) = sqrt(26)
Squaring both sides, we have:
sin^2(t) + cos^2(t) + t^2 = 26
Recall that sin^2(t) + cos^2(t) = 1, so we have:
1 + t^2 = 26
Subtracting 1 from both sides, we have:
t^2 = 25
Taking the square root of both sides, we have:
t = ±5
So, the two points of intersection are (sin(5), cos(5), 5) and (sin(-5), cos(-5), -5).
Rounding the results to three decimal places, we have:
(sin(5), cos(5), 5) = (0.958, 0.287, 5)
(sin(-5), cos(-5), -5) = (0.958, -0.287, -5)
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please help me on this
"Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all" is the true statement.
How to determine which statement is true?This a problem on addition and subtraction of fractions
Since Hope's dad gives her 7/8 of a chocolate bar one day and then gives her 6/12 of a chocolate bar the next day. Hope received approximately 1 chocolate bar. Total chocolate received will be:
Total chocolate received = 7/8 + 6/12 = 1 3/8
This statement is not true
Since Dee has 10/12 of a cake and gives 4/8 to her neighbor. Dee has approximately 1 cakes left. The cakes left will be:
cakes left = 10/12 - 4/8 = 1/3
This statement is not true
Since Joe ran 8/15 of a mile on Thursday. He ran 4/5 of a mile on Friday. Joe ran approximately 1/2 mile in all. The total mile ran will be:
total mile ran = 8/15 + 1/2 = 2 1/10
This statement is not true
Monica swam 9/16 of a mile on Tuesday. She swam 1 5/8 of a mile on Wednesday. She swam approximately 2 miles in all.
mile swam = 9/16 + 1 5/8 = 2 3/16
This statement is true
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The result of a number, when decreased by 66 2/3%, is 432. Find the number
Answer:
1298/3 is the answer
Step-by-step explanation:
Answer:
1296
Step-by-step explanation:
Let the unknown number be x.
If 432 is the result of x being decreased by 66²/₃%, then 432 is 33¹/₃% of x since 100% - 66²/₃% = 33¹/₃%.
Therefore:
[tex]\implies 33\frac{1}{3}\%\;\textsf{of}\;x=432[/tex]
[tex]\implies \dfrac{33\frac{1}{3}}{100} \cdot x=432[/tex]
[tex]\implies \dfrac{33\frac{1}{3}x}{100} =432[/tex]
Multiply both sides of the equation by 100:
[tex]\implies 33\frac{1}{3}x =43200[/tex]
Rewrite 33¹/₃ as an improper fraction:
[tex]\implies \dfrac{100}{3}x =43200[/tex]
Multiply both sides by 3:
[tex]\implies 100x=129600[/tex]
Divide both sides by 100:
[tex]\implies x=1296[/tex]
Therefore, the number that when decreased by 66²/₃% is 432, is 1296.
if y varies inversly as x², and y=11/4
when x=4, find y when x=2
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with }x^2}{y = \cfrac{k}{x^2}}\hspace{5em}\textit{we also know that} \begin{cases} x=4\\ y=\frac{11}{4} \end{cases} \\\\\\ \cfrac{11}{4}=\cfrac{k}{4^2}\implies \cfrac{11}{4}=\cfrac{k}{16}\implies \cfrac{(11)(16)}{4}=k\implies 44=k~\hfill \boxed{y=\cfrac{44}{x^2}} \\\\\\ \textit{when x=2, what's "y"?}\qquad y=\cfrac{44}{2^2}\implies y=\cfrac{44}{4}\implies y=11[/tex]
Answer:
y = 11 when x = 2
Step-by-step explanation:
This is indirect proportionality where:
y ∝ [tex]\frac{1}{x^{2}}[/tex]
This means:
[tex]y_{1} x_{1}^{2} = y_{2}x_{2}^{2}[/tex]
Substitute the following values in the above equation to solve for [tex]y_{2}[/tex]
[tex]y_{1} = \frac{11}{4}[/tex]
[tex]y_{2} = ?[/tex]
[tex]x_{1} = 4[/tex]
[tex]x_{2} = 2[/tex]
= [tex](\frac{11}{4})(4^{2}) = y_{2}(2^{2})[/tex]
= [tex](\frac{11}{4})(16) = y_{2}(4)[/tex]
= [tex]44 = 4y_{2}[/tex]
= [tex]y_{2} =\frac{44}{4}[/tex]
∴ y = 11
How many inches are there in 150 meters?
1 m≈39.37 in.
Responses
3.8 in.
3.8 in.
1554.1 in.
1554.1 in.
4355.5 in.
4355.5 in.
5905.5 in.
5905.5 in.
Is it possible to form a triangle with side lengths 3.5, 3.5, and 9? If so, will it be scalene, isosceles, or equilateral? A. Yes; scalene O B. Yes; isosceles O C. Yes; equilateral O D. No
No , it is not possible to form a triangle with side lengths 3.5, 3.5, and 9 , because of the rule that sum of any two sides must be greater than other side. So, Option D is correct.
A triangle is a two-dimensional shape formed by three line segments connecting three points. In order to form a triangle, a necessary and sufficient condition is that the sum of the lengths of any two sides must be greater than the length of the third side. This is known as the triangle inequality theorem.
If the sum of the lengths of any two sides is less than or equal to the length of the third side, then the three line segments will not be able to form a closed shape, and therefore cannot form a triangle.
In the case of the triangle with side lengths 3.5, 3.5, and 9, the sum of the lengths of the first two sides is 7, which is less than the length of the third side, 9. Hence, these three side lengths do not satisfy the triangle inequality theorem, and therefore cannot form a triangle.
In general, to determine the type of triangle that can be formed with three given side lengths, it is necessary to compare the lengths of the sides and check if any two sides are equal in length (isosceles), or if all three sides are equal in length (equilateral). If none of the sides are equal, then the triangle is called scalene.
In this case, since it is not possible to form a triangle with the given side lengths, it is not possible to determine the type of triangle that would be formed.
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20,−10,5,___ what comes next
The next term is -25.
What is the number pattern?A number pattern is a pattern in a series of numbers that represents the common relationship between the numbers. In Maths, number patterns are the patterns in which a list number that follows a certain sequence. usaually, the patterns establish the relationship between two numbers. It is known as the sequences of series in numbers.
Given;
The pattern20,−10,5,___
Here, first term is 20, second is -10
Difference=20+10
=30
Now,
=5-30
=-25
Therefore, the answer of the given pattern will be -25.
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find the length of the missing side leave your answer in simplest radical form
The length of the missing side in the given triangle is equal to option c. 5.
Figure is attached.
In the attached figure of a right angle triangle,
Let the triangle be named as ABC.
AC is the hypotenuse of a triangle.
AB is the altitude of a triangle.
BC is the base of a triangle.
Form the attached figure
Length of altitude AB = 3
Length of base BC = 4
Using Pythagoras theorem we have,
Hypotenuse² = Altitude² + Base²
⇒ AC² = AB² + BC²
Substitute the value we get,
⇒ AC² = 4² + 3²
⇒AC = √ 16 + 9
⇒ AC = √25
⇒ AC = 5
Therefore, the length of the missing side in the given triangle is equal to option c . 5.
The above question is incomplete, the complete question is:
Find the length of the missing side. Leave your answer in simplest radical form.
The triangle is not drawn to scale.
A.) 25
B.) 144
C.) 5
D.) Square root of 5
Figure is attached .
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Help. This is 2 parts
Answer:can u take a picture that is a bit more closer
Step-by-step explanation:
please submit a closer picture
if a residual is negative, then that data point lies _________________ the regression line.
A residual is the difference between an observed value and the predicted value from a regression line.
A negative residual indicates that the observed value lies below the regression line. This can be expressed mathematically using the formula [tex]y = mx + b[/tex], where y is the observed value, m is the slope, x is the independent value, and b is the y-intercept of the line.
For example, if the observed value is y = 3, the predicted value is y = 5, and the slope and intercept of the line are m = 2 and b = 1, respectively, then the residual can be calculated as [tex]y = 3 - (2*1 + 1) = -1.[/tex] Since the residual is negative, this indicates that the observed value lies below the regression line.
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Write an exponential function for a graph that passes through the points (3, 2.8) and (4, 5.6) . Write the function in the form y=a(b)x.
The formula of the given exponential function whose graph passes through the points (3, 2.8) and (4, 5.6) is :
y = 0.35* (2)ˣ
What is an exponential function?
When the input variable x appears as an exponent in the formula
f(x) = aˣ, an exponential function is indicated. The exponential curve is influenced by both the exponential function and the value of x. It is mostly used to determine exponential growth or decay.
When there is exponential growth, the quantity grows initially extremely slowly and subsequently quickly. Over time, the rate of change quickens. As time goes on, the rate of increase accelerates. In exponential decay, the quantity initially falls very quickly and then gradually. Over time, the rate of change slows. As time goes on, change happens at a slower rate.
The general formula of an exponential function is:
y = abˣ
It is said that points (3, 2.8) and (4, 5.6) are present on the graph of the given exponential function.
W can substitute these value values in the above formula.
2.8 = ab³
5.6 = ab⁴
Dividing the above equations,
2.8 /5.6 = b³/b⁴
1/2 = 1/b
b = 2
Now substituting this value in one of the equations to find the value of a.
2.8 = a. (2)³
a = 2.8/8 = 0.35
Therefore the formula of the given exponential function is :
y = 0.35* (2)ˣ
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What is the difference between positive and negative z-score table?
Z-scores can be either positive or negative, with a positive number signifying a score above the mean and a negative value signifying a score below the mean according to the z-score table.
The statistical measurement known as the Z-score describes the relationship between a value and the mean of a group of values. Z-score is quantified by the standard deviations from the mean. The mean score and the data point's score are equal when the Z-score is 0. The Z-score for a value that deviates by one standard deviation is 1.0. Z-scores are binary, with a positive value denoting a score above the mean and a negative value denoting a score below the mean.
Equation of the z-score: z = ( x - μ ) / σ
Get the value corresponding to one decimal place of the z-score by first looking at the left side column of the z-table.
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Find the measure of the indicated angle in each triangle?
The measure of ∠U= 80°, ∠B=44°, ∠Q= 93° respectively which indicates the angle of each triangle.
First take the Triangle TUV:
⇒∠T+∠U+∠V=180°
⇒37°+∠U+63°=180°
⇒∠U+100°=180°
⇒∠U=80°
Now, take triangle ABC:
⇒∠A+∠B+∠C=180°
⇒46°+∠B+90°=180°
⇒∠B+136°=180°
⇒∠B=44°
Finally take triangle PQR:
⇒∠P+∠Q+∠R=180°
⇒51°+∠Q+36°=180°
⇒∠Q+87°=180°
⇒∠Q=93°
Therefore, measure of the indicated angle in each triangle are 80°, 44 and 93° respectively.
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Fine the value of each variable show proofs
The value of x is 11.3
The value of y is 11.3
How to determine the valuesUsing the different trigonometric identities such as sine, cosine, tangent, secant, cosecant, cotangent.
To determine the value of x, we use the sine identity
sin θ = opposite/hypotenuse
sin 45 = x/16
Find the value
0.7071= x/16
cross multiply
x = 11.31
To determine the value of y, we get;
tan 45 = 11.3/y
Determine the value and cross mutiply
1 = 11.3/y
Then,
y = 11.3
Hence. the values are equivalent
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PLS HELP i rlly don't understan this
Answer:
SInce 2 is 2 less than 4, the value of x+2 is 4 less than 31. So x+2=29
Step-by-step explanation:
Answer:
Step-by-step explanation:
Since 2 is 2 less than 4, the value of x + 2 is 2 less than 31.
So, x + 2 = 29.
Use the triangles to answer the question. Triangle A B C with A B = square root of 13, B C = 2, A C = 3, and angle C is labeled as a right angle. Also shown is triangle D E F with E F = 4, D F = 6, and angle F is labeled as a right angle. © 2016 StrongMind. Created using GeoGebra. If △ABC∼△DEF, what is the scale factor for the dilation that maps △ABC to △DEF? Enter your answer as a number.
The scale factor for the dilation that maps △ABC to △DEF is 0.75.
What is triangle?A triangle is a geometric shape that consists of three line segments that connect to form three angles. These angles always add up to 180 degrees. A triangle has three sides and three vertices (corners). Triangles can have different shapes and sizes, and they are often classified based on the length of their sides or the size of their angles. Some common types of triangles include equilateral triangles (where all sides are equal in length and all angles are equal to 60 degrees), isosceles triangles (where two sides are equal in length), and right triangles (where one angle is a right angle, or 90 degrees). Triangles have many properties and are an important part of geometry and mathematics.
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To determine the scale factor for the dilation that maps △ABC to △DEF, we need to find the ratio of the corresponding side lengths of the two triangles.
Since △ABC ∼ △DEF, we know that the corresponding angles of the two triangles are congruent. Therefore, angle B in △ABC corresponds to angle E in △DEF, and angle A in △ABC corresponds to angle D in △DEF.
Using the Pythagorean theorem, we can find the length of the missing side of △DEF:
DF² = DE² + EF²
6² =DE² + 4²
DE=√20
DE=2√5 units
3/4=2/2√5=√13/6=0.75
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