Final answer:
Using the Law of Cosines, we find that the cosine of angle Z is approximately 0.6333, and therefore, angle Z in triangle XYZ is approximately 51° when rounded to the nearest degree.
Explanation:
To find the measure of angle Z in triangle XYZ, with sides XY = 15, YZ = 21, and XZ = 27, we can use the Law of Cosines. The Law of Cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. In our case, we can find the cosine of angle Z by the equation:
cos(Z) = (XY² + XZ² - YZ²) / (2 · XY · XZ)
Plugging in the values, we get:
cos(Z) = (15² + 27² - 21²) / (2 · 15 · 27)
Calculating further:
cos(Z) = (225 + 729 - 441) / (810)
cos(Z) = 513 / 810
cos(Z) = 0.6333
The next step is to find the angle whose cosine is 0.6333. We can use a calculator to find the inverse cosine:
Z = cos⁻¹(0.6333)
Hence, the measure of angle Z to the nearest degree is approximately:
Z ≈ 51°
The measure of angle Z is approximately 70 degrees (rounded to the nearest degree).
To find the measure of angle Z in triangle XYZ, you can use the Law of Cosines. The formula is:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos(C) \][/tex]
where:
- c is the side opposite the angle you want to find (in this case, side XZ),
- a and b are the other two sides (XY and YZ),
- C is the angle opposite side c.
In this case, let C be the angle Z, and a = XY = 15, b = YZ = 21, and c = XZ = 27.
[tex]\[ 27^2 = 15^2 + 21^2 - 2(15)(21) \cos(Z) \][/tex]
Now, solve for cos(Z):
[tex]\[ 729 = 225 + 441 - 630 \cos(Z) \][/tex]
[tex]\[ 630 \cos(Z) = 441 - 225 \][/tex]
[tex]\[ 630 \cos(Z) = 216 \][/tex]
[tex]\[ \cos(Z) = \frac{216}{630} \][/tex]
[tex]\[ \cos(Z) \approx 0.343 \][/tex]
Now, find the angle Z:
[tex]\[ Z = \cos^{-1}(0.343) \][/tex]
[tex]\[ Z \approx 70.18 \][/tex]
So, the measure of angle Z is approximately 70 degrees (rounded to the nearest degree).
f=11gh solve the formula for the variable h.
The formula f=11gh can be solved for h by dividing both sides of the equation by 11g. This will give h = f / (11g), where h is isolated on one side of the equation.
Explanation:To solve the formula f=11gh for the variable h, we need to isolate h on one side of the formula. The current formula tells us that the value of f is equal to the result of 11 times g times h.
As our goal is to solve for h, we can do this by dividing both sides of the equation by 11g. In doing so, the 11g on the right side of the equation will cancel out, leaving us with just h on one side.
So the formula solved for h will look like this:
h = f / (11g).
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Consider a normal population distribution with the value of σ known. (a) what is the confidence level for the interval x ± 2.88σ/ n ? (round your answer to one decimal place.) % (b) what is the confidence level for the interval x
The confidence level for the interval x ± 2.88σ/√n is approximately 99.9%. The term 'confidence level' speaks to how frequently the true value of the parameter would be inside the interval for replicated experiments. Without additional information, we cannot compute the confidence level for just 'x'.
Explanation:In statistics, a formula exists to find the confidence interval. For the interval x ± 2.88σ / √n, the confidence level is nearly 99.9%. We find this by referring to the z-table (standard normal table) with a z-score of 2.88. This leaves 0.05% in each tail of the distribution.
On the topic of confidence levels, a 95% confidence interval implies that if you were to take 100 random samples from your population, approximately 95 of those samples would capture the true population parameter.
For the other part of your question, when we talk about the interval x, it doesn't provide enough detail to calculate a confidence level. It needs to be stated in context of the standard deviation and the sample size.
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Triangle ABC has vertices A(0,0), B(3,2), and C(0,4). This triangle may be classified as ?..?
1) equilateral
2) isosceles
3) right
4) scalene
Btw it wasn’t number 2 because that one was inaccurate.
The triange may be classified as (2) isosceles triangle
How to classify the triangle?The vertices are given as:
A(0,0), B(3,2), and C(0,4)
Calculate the side lengths using:
d = √(x2 - x1)^2 +(y2 - y1)^2
So, we have:
AB = √(3 - 0)^2 +(2 - 0)^2
AB = √13
AC = √(0 - 0)^2 +(4 - 0)^2
AC = 4
BC = √(3 - 0)^2 +(2 - 4)^2
BC = √13
Side lengths BC and AB are equal
i.e. AB = BC = √13
Hence, the triange may be classified as (2) isosceles triangle
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What is the exact value of 400,000x200
Answer:
80,000,000
Step-by-step explanation:
We can rewrite this expression as:
(4 x 10⁵) x (2 x 10²)
To solve this, we multiply first 4 x 2 = 8 and then we multiply the powers of ten using law of exponents:
10⁵x10²= 10₇.
Therefore, the answer is: 8 x 10⁷. If we write it in decimal form we would have:
80,000,000
What is the correct solution for the arithmetic expression (2+8)/2*9/3 using the order of operations employed by oracle 12c when solving equations??
The order of operations is the steps used to simplify any mathematical expression. Order of operations refers to which operations should be performed in what order and it is denoted by PEMDAS, This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right). If parentheses are enclosed within other parentheses, work from the inside out.
[tex] (2+8)/2*9/3\\ Performing \; the \; operation\; in\; Parenthesis\; first\\ \\ 10/2 *9/3\\ Dividing \; 10/2\; from\; left\; to\; right\\ \\ 5*9/3\\ Multiply\; from\; left\; to\; right\\ \\ 45/3\\ Divide \; to\; get\; final\; answer\\ \\ 15 [/tex]
Conclusion:
The correct solution for the arithmetic expression (2+8)/2*9/3 using the order of operations is 15
The area of a triangle is 1440cm^2 the base of tge triangle is 5 times the height of the triangle
Dante Michael's charge account statement showed a previous balance of $277.45 a finance charge of $3.22 new purchases of $299.33 and a payment of $316.00. what is the new balance?
How large in square meters is the land area of australia (2941526 mi 2)?
Final answer:
The land area of Australia is roughly 7.62 trillion square meters, calculated by multiplying the area in square miles (2,941,526) by the conversion factor of 2,590,000 square meters per square mile.
Explanation:
The student is asking for the conversion of Australia's land area from square miles to square meters. To convert square miles to square meters, we use the conversion factor that 1 square mile is equal to 2.59 square kilometers or 2,590,000 square meters. Therefore, the land area of Australia in square meters is calculated by multiplying the area in square miles by the conversion factor:
2,941,526 mi2 × 2,590,000 m2/mi2 = 7,619,652,340,000 m2
The land area of Australia is approximately 7.62 trillion square meters.
what does 4x+5x-30=180 equal
Combining like terms gives
9x−30=180. Adding 30 to both sides yields
9x=210. Dividing by 9, we find x=23.3333.
To solve the equation
4x+5x−30=180, we first combine like terms:
4x+5x=9x
So the equation becomes:
9x−30=180
Next, we isolate the variable
x by adding 30 to both sides:
9x=180+30
9x=210
Finally, we divide both sides by 9 to solve for
Hilda has $210 worth of $10 and $12 stock shares.
The number of $10 shares is five more than twice the
number of $12 shares. How many of each type of share
does she have?
Is 5,000cm greater than 5m
Zakai cuts a piece of birthday cake as shown below.
What is the volume of the piece of cake?
write the equation of a line that includes the point (1,5) and has a slope of 3 in slope intercept form
A. y= 3x + 5
B. y= 3x - 5
C. y= 3x + 2
D. y= 3x - 5
What are the zeros of the function f(x)=3x^2-3x-6
Samantha works at a nursery where she pots plants. It takes her 1 1/2 hours to pot 12 plants. How many plants can Samantha pot in 1 hour? (Please give me the equation you used.) Please help fast!
write the integer 9 as m/n in simplest form where m and n are integers
Let u = <-6, 1>, v = <-5, 2>. Find -4u + 2v.
A) <34, -8>
B) <14, 0>
C) <14, 3>
D) <44, -12>
The area of the square represented in item 1 is revised to be 90.0 in.2. note that the original grid spacing no longer applies. what is the side length of the square
Which word best describes the degree of overlap between the two data sets? none moderate low high Two line plots with the same scale and interval, from zero to sixty, with tick marks every five units. The plots are stacked vertically for comparison. Each plot has fifteen data values. Values appear as x marks above the line. Upper plot data values are one x mark above thirty, two x makrs above thirty-five, four x marks above forty, four x marks above forty-five, one x mark above fifty, two x marks above fifty-five, and one x mark above sixty. Lower plot data values are three x marks above five, four x marks above ten, three x marks above fifteen, two x marks above twenty, one x mark above twenty-five, one x mark above thirty, and one x mark above thirty-five.
HURRY PLEASE
Answer:
High
Step-by-step explanation:
From a top-down 2D perspective, a car moves in a diagonal line and travels a distance equivalent to 80 miles. If the angle between the diagonal line and a horizontal reference line is 25 degrees, how far did the car travel horizontally and vertically? If necessary, round your answers to the nearest tenth of a mile. Horizontal distance? Vertical distance?
If the arrival of major road vehicles can be described by the poisson distribution, and the peak hour volume is 1000 veh/hr. the value of the critical gap is 4 seconds. the expected number of available gaps during the peak hour is equal to:
[x÷(y–1)](−4)–[xy+(−3)]÷(−1) if x=−5, y=−2
Answer:
94
Step-by-step explanation:
1 89
2321
33
214
write an expression with a value of 10. it should contain four numbers and two different operations
write a congruence statement for the pair of triangles zyb
Simplify the expression. 103 + 33 ÷ 3 A. 10,011 B. 21 C. 1011 D. 111
A book us in the shape of a right rectangle prism. It measures 8 1/2 inches tall, 7 inches wide and 2 1/3 inches thick. What is the volume of the book
a cell phone company sold 4,000 cell phones in the month of November. In December, the company held its annual sale and sold 22 percent more cell phones than it did in November. In January , the company experienced its slowest month , managing to sell only 50 percent of the number of cell phones sold during the month of December. What is the total number of cell phones sold by the company during the three months combined ?
The height of the pyramid in the diagram is three times the radius of the cone. The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?
The volume of the pyramid is πr³ cubic units. Then the correct option is A.
What is the volume of the pyramid?Suppose the base of the pyramid has length = L units, width = W units, slant height = K units, and the height of the pyramid is of H units.
Then the volume of the pyramid will be
V = (A × H) / 3
V = (L × B × H) / 3
Where, A is the base area of the pyramid.
Let r be the radius of base circle of the cone.
The height of the pyramid in the diagram is three times the radius of the cone.
Then the height of the pyramid will be 3r.
The base area of the pyramid is the same as the base area of the cone.
Base area of pyramid = Base area of cone
Base area of pyramid = πr²
Then the volume of the pyramid will be
Volume of pyramid = (1/3) x πr² x (3r)
Volume of pyramid = πr² x r
Volume of pyramid = πr³ cubic units
The volume of the pyramid is πr³ cubic units.
Then the correct option is A.
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After a concert for 1600 people only 8 people said they would not go see the band again what percent of the people who went to the concert said they would not go see the band again
O.5 is the correct answer
Which is the graph of g(x) = 2x – 1 + 3?
Answer:
The graph given can be further simplified as follows:
[tex]g(x)=2x+2[/tex]
I have drawn and attached the graph with the answer.
Step-by-step explanation:
The graph given can be further simplified as follows:
[tex]g(x)=2x-1+3[/tex]
[tex]g(x)=2x+2[/tex]
Slope of the graph is 2 as x has a coefficient of 2 and intercept is 2.
To graph the above substitute several values to x and calculate the corresponding g(x) values.
[tex]g(1)=2*1+2\\g(1)=4[/tex]
So when x=1, g=4
[tex]g(3)=2*3+2\\g(3)=8[/tex]
So when, x=3, g=8
Calculate several values in the same way and then plot the values is a Cartesian plane, x values in x axis and take g(x) values as y axis.
Then you will get a few dots in a straight line, join those dots with a line and that is the graph.
I have drawn and attached the graph with the answer.
Answer:
The graph is shown below.
Step-by-step explanation:
The given function is
[tex]g(x)=2^{x-1}+3[/tex]
It is an exponential function.
The given exponential function is defined for all real numbers. So, the domain of given function is all real numbers.
Domain = { x | x ∈ R }
Domain = (-∞,∞)
We know that
[tex]2^{x-1}>0[/tex]
Add 3 on both sides.
[tex]2^{x-1}+3>0+3[/tex]
[tex]g(x)>3[/tex]
Range of the function is
Range = (3,∞)
Table of values is
x y
0 3.5
1 4
2 5
Plot these point on a coordinate plane.
The graph of given function is shown below.