In triangle $XYZ,$ $\angle Y = 45^\circ$ and $\angle Z = 60^\circ.$ If $XZ = 4,$ then what is $XY$?
[asy]
unitsize(3 cm);
pair X, Y, Z;
X = (0,1);
Y = (-1,0);
Z = (1/sqrt(3),0);
draw(X--Y--Z--cycle);
label("$45^\circ$", Y + (0.3,0.1), fontsize(10));
label("$60^\circ$", Z + (-0.2,0.1), fontsize(10));
label("$X$", X, N);
label("$Y$", Y, SW);
label("$Z$", Z, SE);
label("$4$", (X + Z)/2, NE);
[/asy]
Answers
Answer:
[tex]XY = 4.9[/tex]
Step-by-step explanation:
[tex]\angle Y = 45^\circ[/tex]
[tex]\angle Z = 60^\circ[/tex]
[tex]XZ = 4[/tex]
Required
Determine the length of XY?
This question is supported with the attachment.
To solve for the length of XY, we make use of the sine law which states:
[tex]\frac{sin\ A}{a} = \frac{sin\ B}{b} = \frac{sin\ C}{c}[/tex]
In this case:
[tex]\frac{sin\ \angle Y}{XZ} = \frac{sin\ \angle Z}{XY} = \frac{sin\ X}{YZ}[/tex]
Substitute in, the following values:
[tex]\angle Y = 45^\circ[/tex]
[tex]\angle Z = 60^\circ[/tex]
[tex]XZ = 4[/tex]
The expression becomes:
[tex]\frac{sin\ 45}{4} = \frac{sin\ 60}{XY}[/tex]
Cross multiply
[tex]XY * \sin\ 45 = 4 * \sin\ 60[/tex]
Make XY the subject
[tex]\frac{XY * \sin\ 45}{\sin\ 45} = \frac{4 * \sin\ 60}{\sin\ 45}[/tex]
[tex]XY = \frac{4 * \sin\ 60}{\sin\ 45}[/tex]
[tex]XY = \frac{4 * 0.8660}{0.7071}[/tex]
[tex]XY = \frac{3.4640}{0.7071}[/tex]
[tex]XY = 4.89888276057[/tex]
[tex]XY = 4.9[/tex] --- approximated
![In Triangle $XYZ,$ $\angle Y = 45^\circ$ And $\angle Z = 60^\circ.$ If $XZ = 4,$ Then What Is $XY$?[asy]unitsize(3](https://brainimage.s3.us-east-005.backblazeb2.com/answers/attachments/G5zteLlnPSvJGseq8GHCIFfp4wGkiDix.png)
Answer:
XY = 4.9
Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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A square pyramid is shown. What is the surface area?
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation
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Answer:
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Step-by-step explanation:
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Belleville High School offers classes on three different foreign languages. Let A be the event that a student is in eleventh grade, and let B be the event that a student is enrolled in French class. A 5-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, total. The second column is labeled Spanish with entries 107, 56, 89, 252. The third column is labeled French with entries 122, 68, 82, 272. The fourth column is labeled German with entries 6, 14, 8, 28. The fifth column is labeled Total with entries 235, 138, 179, 552. Which statement is true about whether A and B are independent events? A and B are independent events because P(A∣B) = P(A). A and B are independent events because P(A∣B) = P(B). A and B are not independent events because P(A∣B) ≠ P(A). A and B are not independent events because P(A∣B) ≠ P(B).
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
Example of a story problem to match the equation 36÷5=7 R1
Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
you want to obtain a sample to estimate a population proportion. at this point in time, you have no reasonable preliminary estimation for the population proportion. you would like to be 95% confident that you estimate is within 2% of the true population proportion. how large of a sample size is required
Answers
Answer:
The value is [tex]n =2401 [/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is E = 2%= 0.02
From the question we are told the confidence level is 95% , hence the level of significance is
[tex]\alpha = (100 - 95 ) \%[/tex]
=> [tex]\alpha = 0.05[/tex]
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[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
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Generally the sample size is mathematically represented as
[tex]n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) [/tex]
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Shaun estimated that the attendance at a college game was 1,200 people. The actual attendance was 1,158. What is the percent error of Shaun's estimate? (Round your answer to the nearest tenth) HELP!!! PLEASE THIS IS MY LAST POINT I CAN DO PLEASE PLEASEPLEAPLEAPLEAPLSEPAEEASE HELP
Answers
Answer:
3.5%
Step-by-step explanation:
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42/1200 =0.035
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Answers
Answer:
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Step-by-step explanation:
1. If x=3-√3,
prove that x²
+36
x²
= x²
Answers
Answer:
we get [tex]x^2=12-6\sqrt{3}[/tex]
Step-by-step explanation:
We are given: [tex]x=3-\sqrt{3}[/tex]
We need to find [tex]x^2[/tex]
Note: Since question is not clear, I am assuming that we need to find [tex]x^2[/tex]
Solving:
[tex]x=3-\sqrt{3} \\Taking \ square \ on \ both \ sides\\x^2=(3-\sqrt{3})^2\\[/tex]
We know that [tex](a-b)^2= a^2-2ab+b^2[/tex]
Using formula and simplifying
[tex]x^2=(3)^2-2(3)(\sqrt{3})+(\sqrt{3})^2\\x^2=9-6\sqrt{3} +3\\x^2=12-6\sqrt{3} \\[/tex]
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Answers
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Step-by-step explanation:
In the previous reasons you have proven that all of the sides of each triangle are equal to the corresponding side. You can use SSS to prove that the two triangles are congruent.
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Answers
Answer:
[2,6]
Step-by-step explanation:
3x+5y=36
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What is an equation parallel to y=3x-5
Answers
Answer:
ANY line that has a slope of 3, and any y intercept other than -5.
Step-by-step explanation:
Parallel lines have the same slopes, but different y intercepts.
So, it would be ANY line that has a slope of 3, and any y intercept other than -5.
here are a few examples:
y=3x-17
y=3x+4
y=3x+3293248032843209.3432492384032984032984023840398249082
y=3x+5
y=3x-1
y=3x
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Answers
Answer:
I believe the answer to question (a) is 3085 ft and for (b) i think it's 238 ft
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Step-by-step explanation:
Suppose 30% of the U.S. population has green eyes. If a random sample of size 1200 U.S. citizens is drawn, then the probability that less than 348 U.S. citizens have green eyes is _______.
Answers
Answer:
P(X is less than 348) = 0.2148
Step-by-step explanation:
Given that:
Sample proportion (p) = 0.3
Sample size = 1200
Let X be the random variable that obeys a binomial distribution. Then;
[tex]X \sim Bin(n = 1200,p =0.3)[/tex]
The Binomial can be approximated to normal with:
[tex]\mu = np = 1200 \times 0.3 \\ \\ \mu= 360[/tex]
[tex]\sigma = \sqrt{np(1-p) } \\ \\ \sigma = \sqrt{1200 \times (0.3)(1-0.3) } \\ \\ \sigma = 15.875[/tex]
To find:
P(X< 348)
So far we are approximating a discrete Binomial distribution using the continuous normal distribution. 348 lies between 347.5 and 348.5
Normal distribution:
x = 347.5, [tex]\mu[/tex] = 360, [tex]\sigma[/tex] = 15.875
Using the z test statistics;
[tex]z = \dfrac{x - \mu}{\sigma}[/tex]
[tex]z = \dfrac{347.5 - 360}{15.875}[/tex]
[tex]z = \dfrac{-12.50}{15.875}[/tex]
z = -0.7874
z ≅ - 0.79
The p-value for P(X<347.5) = P(Z < -0.79)
From the z tables;
P(X<347.5) = 0.2148
Thus;
P(X is less than 348) = 0.2148
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56 : 7 = ?
?×? = 64
What number will make all of Drew's equations true? Enter your answer in the box.
? =
Answers
Answer:
8
Step-by-step explanation:
4*8=32
7*8=56
8*8=64
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Answer: Katie, Josie, Ramona, Teri
Step-by-step explanation:
Answer:
1.Katie,ramona,josie,Katie.2.katie,josie,romona,teri 3.teri,Ramona,josie,katie 4.Ramona,teri,katie,josie
Step-by-step explanation:
What is the simplified value of the exponential expression 27 1/3?
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Answers
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Answers
Answer:
False, becasue 8*1/2 is 4 and 4 doesn't equal 16
Step-by-step explanation:
which point on the line represents 3/5
Answers
Step-by-step explanation:
The correct answer is: Point B.
The easiest way to solve this is to make the fraction, 3/5, to a decimal.
3/5 = 0.6
Since point B is the closest estimate to 0.6 on the number line, we can confirm that Point B represents 3/5.
Answer:
Step-by-step explanation:
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Write an equation of a line that has a slope of "negative one-half" in each form: a) point-slope form
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Describe how linear data given in a table can help you write an equation of a line in slope-intercept
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Answers
Answer: Find the Equation of a Line Given That You Know a Point on the Line And Its Slope. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.
Step-by-step explanation:
The lines P an Q intersect at point O. What is the value of x?
Answers
Answer:
17
Step-by-step explanation:
you add the b and x coordinate divide it by 2 to get the value of p and q which you then divide by the value of ur mom to get x
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Be sure to show your work and solve for f:
8 = f (13-2)
Answers
Answer:
8 = f (13-2)
8=13f-2f
8=11f
8 / 11 = 11f / 11
8/11=f
f=8/11
Step-by-step explanation:
Answer:
Simplifying
8 = F + -1(13 + -2)
Combine like terms: 13 + -2 = 11
8 = F + -1(11)
Multiply -1 * 11
8 = F + -11
Reorder the terms:
8 = -11 + F
Solving
8 = -11 + F
Solving for variable 'F'.
Move all terms containing F to the left, all other terms to the right.
Add '-1F' to each side of the equation.
8 + -1F = -11 + F + -1F
Combine like terms: F + -1F = 0
8 + -1F = -11 + 0
8 + -1F = -11
Add '-8' to each side of the equation.
8 + -8 + -1F = -11 + -8
Combine like terms: 8 + -8 = 0
0 + -1F = -11 + -8
-1F = -11 + -8
Combine like terms: -11 + -8 = -19
-1F = -19
Divide each side by '-1'.
F = 19
Simplifying
F = 19
The list shows the number of miles six people drove in a month .
445, 380, 365, 375, 370, 315
What is the mean absolute deviation of these numbers ?
Answers
Mean Absolute Deviation (MAD) = 25
A rectangular roof has a length of 13g and a width of 4g+7. write an expression for the area of the roof.
Answers
Answer:
13g*4g+7
Step-by-step explanation:
Solve each equation. Check your solution.
4t - 2 = 14
Answers
Answer:
t=4
Step-by-step explanation:
4t-2=14
You then add 2 to both sides and get
4t=16
Then you must divide 16 by 4 and get
t=4
The solution of the linear equation 4t - 2 = 14 will be 4.
What is the solution to the equation?In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.
The equation is given below.
4t - 2 = 14
The degree of the equation is one, so the equation will be a linear equation. Then solve the equation for 't', then we have
4t - 2 = 14
4t = 16
t = 16 / 4
t = 4
The solution of the linear equation 4t - 2 = 14 will be 4.
More about the solution of the equation link is given below.
https://brainly.com/question/22613204
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