Answer:
[tex]XY=2YZ\\XY=2\times4\\XY=8[/tex]
The value of XY is given by the trigonometric relation and the measure of side of the triangle is XY = 8
What are trigonometric relations?Trigonometry is the study of the relationships between the angles and the lengths of the sides of triangles
The six trigonometric functions are sin , cos , tan , cosec , sec and cot
Let the angle be θ , such that
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
tan θ = sin θ / cos θ
cosec θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Given data ,
Let the triangle be represented as XYZ
Let the measure of the side XY of the triangle be A
The measure of side YZ = 4
Now , from the trigonometric relations , we get
sin θ = opposite / hypotenuse
when θ = 30°
Substitute the value of θ in the equation , we get
sin θ = YZ / XY
On simplifying the equation , we get
sin 30° = 4 / XY
Multiply by XY on both sides of the equation , we get
XY ( sin 30° ) = 4
The value of sin 30° = 1/2
So , XY / 2 = 4
Multiply by 2 on both sides of the equation , we get
XY = 8
Hence , the measure of side XY of triangle is XY =8
To learn more about trigonometric relations click :
https://brainly.com/question/14746686
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Marci has taken out a loan of $5,000 for a term of 24 months (2 years) at an interest rate of 8.5%. Use the amortization table provided to complete the statement.
Monthly Payment per $1,000 of Principal
Rate 1 Year 2 Years 3 Years 4 Years 5 Years
6.5% $86.30 $44.55 $30.65 $23.71 $19.57
7.0% $86.53 $44.77 $30.88 $23.95 $19.80
7.5% $86.76 $45.00 $31.11 $24.18 $20.04
8.0% $86.99 $45.23 $31.34 $24.41 $20.28
8.5% $87.22 $45.46 $24.65 $24.65 $20.52
9.0% $87.45 $45.68 $31.80 $24.89 $20.76
Marci’s monthly payment will be $------, and her total finance charge over the course of the loan will be $------- .
Answer:
Correct answers are Marci's monthly payment: $227.30, and total finance charge: $455.20.
Step-by-step explanation:
24 months (2 years)
$45.46 x 5 = $227.30
$227.30 x 24 = $5,455.20
$5,455.20 - $5,000 = $455.20
The circumference of a circle 69.1 yard. what is the diameter?
Answer:
D = 22 yards
Step-by-step explanation:
D = C ÷ π
D = 69.1 ÷ 3.14
D = 22.006
D = 22 yards
I need the answer to number 9. Please! And if you have answers to the other questions;sharing them would be greatly appreciated. :D
Answer:
the correct answer for 9 is A) N 3-
Step-by-step explanation:
First CORRECT answer WILL get Brainliest. I’m on a limited time so if you don’t know, don’t answer. No guesses, not what you think, accurate and correct answers. I apologize if I am coming off as rude, but I honestly don’t have the time to delete questions. Thank you in advance!
Answer:
Square feet of Carpeting : 136 ft^2
Step-by-step explanation:
Let us divide this figure into two shapes, each being rectangles;
Considering the first, smaller shape, with a given dimension of 7 feet we can see that the second dimensions is 13 - 9, ⇒ 4 feet
The Area of this part would thus be ⇒ 7 * 4 = 28 ft^2
Now this second figure is provided with dimensions 12 by 9 feet, so that the area would, by definition ⇒ length * width = 12 * 9 ⇒ 108 ft^2. The total area of this figure is, by Partition Postulate : 108 + 28 ⇒ 136 square feet
If Sara plans to carpet the room, clearly the carpeting's area should be equivalent to that of the area of the room. This would mean;
Square feet of Carpeting : 136 ft^2
What is the midpoint of a line segment with endpoints (-2, 6) and (4, 3) in the
standard (x, y) coordinate plane?
Answer:
(1, 9/2) or (1, 4.5)
Step-by-step explanation:
To find the midpoint, take the x1 and x2 values and divide it by 2, same for the y values.
(4-2)/2 and (6 + 3)/2
1 and 4.5
(1, 4.5)
Solving for x and y
Answer:
105/13 = x ; 64/13 = y
Step-by-step explanation:
12x + 2 = y + 94 --> 24x + 4 = 2y + 188
11x + 12 = 2y + 91 -->
13x - 8 = 97 -->
13x = 105 -->
105/13 = x -->
64/13 = y
help me please and thank you
Answer:
m<10 = 92°
m<5 = 106° (I think because of correspondence)
m<8 =92°
m<14 = 74°
m<3 = 106°
<1 and <4 are corresponding angles
<2 and <3 are same side interior angles
<3 and <4 are vertical angles
<4 a d <6 are Alt. Interior Angles
Calculate area of triangle
Answer:
99cm²
Step-by-step explanation:
Area of a Triangle: [tex]A=\frac{1}{2} bh[/tex]
B- base
H- height
We are given a base of 18 cm and a height of 11cm.
[tex]A=\frac{1}{2} 18*11\\\\A=\frac{1}{2} 198\\\\\boxed{A=99}[/tex]
The area of the triangle should be 99cm².
Richard has just been given a 8-question multiple-choice quiz in his history class. Each question has five answers, of which only one is correct. Since Richard has not attended class recently, he doesn't know any of the answers. Assuming that Richard guesses on all eight questions, find the indicated probabilities. (Round your answers to three decimal places.)
(a) What is the probability that he will answer all questions correctly?
(b) What is the probability that he will answer all questions incorrectly?
(c) What is the probability that he will answer at least one of the questions correctly? Compute this probability two ways. First, use the rule for mutually exclusive events and the probabilities shown in the binomial probability distribution table.
Then use the fact that P(r ≥ 1) = 1 − P(r = 0).
(d) What is the probability that Richard will answer at least half the questions correctly?
Answer:
1. P(all are correct) =0.00000256
2. P ( all are incorrect) = 0.1677
3. P( at least one correct ) = 0.8310
c. P(r ≥ 1) = 0.8322
d. P ( half the questions are incorrect) = 0.046
Step-by-step explanation:
Let A be the event that he will choose the correct answer and there is only one correct answer out of 5 choices so the probability of A = P(A)= 1/5
As there are 8 number of questions so n= 8
Applying the binomial theorem
P(all are correct) = ⁸C₈ (1/5)⁸ (4/5)°= 1* 1/5*5*5*5*5*5*5*5 (1)
a. P(all are correct) = 1/625 *625= 1/390625= 0.00000256
b. P ( all are incorrect) = ⁸C₀ (1/5)° (4/5)⁸= 1* 4*4*4*4*4*4*4*4/5*5*5*5*5*5*5*5 (1)= 256*256/625 *625= 65336/390625 = 0.1677
c. P( at least one correct ) = P (one Correct) + P( 2 Correct) + P (3 correct) + P( 4 correct) + P ( 5 correct) + P ( 6 correct) + P ( 7 correct) + P ( 8 correct)
P( at least one correct ) = 0.00008192+ 0.00114688+ 0.00917504 + 0.0458752 + 0.14680064 + 0.29360 + 0.335544 +0.00000256
P( at least one correct ) = 0.8310
P (one Correct) = ⁸C₇ (1/5)⁷ (4/5)= 8* 1/5*5*5*5*5*5*5 * 4/5 = 0.00008192
P( 2 Correct) = ⁸C₆ (1/5)⁶ (4/5)²= 28 * 1/5*5*5*5*5*5* 16/25= 0.00114688
P (3 correct)=⁸C5₅ (1/5)⁵ (4/5) ³= 56* 1/5*5*5*5*5* 64/125 = 0.00917504
P( 4 correct) = ⁸C₄(1/5)⁴ (4/5)⁴= 70* 1/5*5*5*5 * 256/625 = 0.0458752
P ( 5 correct) = ⁸C₃ (1/5)³ (4/5)⁵= 56 * 1/5*5*5 *1024/ 3125 = 0.14680064
P ( 6 correct)= ⁸C₂ (1/5)² (4/5) ⁶= 28* 1/5*5 * 4096 /15625= 0.29360
P ( 7 correct) = ⁸C₁ (1/5) (4/5)⁷= 8* 1/5 * 16384/78125 = 0.335544
P(r ≥ 1) = 1 − P(r = 0).
=1- 0.1 677 = 0.8322
d. P ( half the questions are incorrect) =⁸C₄ (1/5)⁴ (4/5)⁴
= 70 * 1*1*1*1/ 5*5*5*5* 4*4*4*4/5*5*5*5 = 70 * 1/ 625* 256/625 = 0.0458= 0.046
Find the coordinates of the reflection without using the coordinate plane.
Q (-3,5) over the y-axis.
Answer:
(3,5)
Step-by-step explanation:
in order to reflect over an axis, you put a negative in front of the opposite axis's coordinate.
in this case, you reflect over the y axis so you put a negative in front of the x coordinate. (--3,5) two negatives make a positive so you get (3,5)
If your'e going to ask a question here, you might as well just use a coordinate plane
If my answer helps, please give me brainliest, it helps a lot
Answer:
(3,5)
Step-by-step explanation:
What design principle is stressed for experiments or observational studies?
Choose the correct answer below.
A. Using dependent samples with paired data is generally better than using two independent samples.
B. When using paired data, keep the sample very small in order to keep the data manageable.
C. The methods for dependent samples can be used for any matched pairs.
D. Using two independent samples is the best choice for accurate results.
Answer:
A). Using dependent samples with paired data is generally better than using two independent samples.
Explanation:
Observational studies is the research/study design in which the investigator observes the samples collected from the population in their natural pattern to make valid inferences without any kind of manipulation or interference. While the experimental studies involves a controlled or manipulated variable in order to check its impact over the independent variable and the relation between the two.
As per the question, the design principle that is emphasized for both the studies would be 'employing dependent samples along with the paired data is usually effective than employing two independent samples' as the former concerns one set of elements that makes them 'self-evident'(as the subjects of one sample can be employed to determine the subjects of other). Thus, option A is the correct answer.
What is 9/7-6/10 equals
Answer:
48/70 or24/35
Step-by-step explanation:
9/7-6/10 u find the LCD or lowest common denominator. 90/70-42/70=48/70=24/35
Answer:
24/35
Step-by-step explanation:
9/7 - 6/10
Simplify 6/10 by dividing the top and bottom by 2
9/7 - 3/5
The common denominator is 7*5 = 35
9/7 * 5/5 - 3/5 *7/7
45/35 - 21/35
24/35
After four years in college, Josie owes $21000 in student loans. The interest rate on the federal loans is 3% and the rate on the private bank loans is 4.4%. The total interest she owes for one year was $714.00.What is the amount of each loan?
Answer:
$104.27 is the amount at 3% and $20895.73 is the amount at 4.4%
Step-by-step explanation:
We are given that Josie owes $21000 in student loans.
Let x be principal at 3% rate of interest
Time = 1 year
Formula:[tex]A=P(1+r)^t[/tex]
[tex]A=x(1+0.03)^1[/tex]
A=1.03x
Interest = Amount - Principal
Interest = 1.03x-x=0.03x
So, (21000-x) is the principal at 4.4% rate of interest
Formula:[tex]A=P(1+r)^t[/tex]
[tex]A=(21000-x)(1+\frac{4.4}{100})^1[/tex]
A=21924-1.044x
Interest = 21924-1.044x-21000-x=924-2.044x
The total interest she owes for one year was $714.00
So, 0.03x+924-2.044x=714
x=104.27
So, $104.27 is the amount at 3%
The principal at 4.4% rate of interest =21000-x=21000-104.27=20895.73
Hence $104.27 is the amount at 3% and $20895.73 is the amount at 4.4%
PLZZ HELP!
Given the function f(x)=2(x-1)^2+3
a)What is the vertex?
b)What is the axis of symmetry?
Answer:
a) (1,3)
b) x=1
Step-by-step explanation:
The general form of a parabola in vertex form is f(x)=a(x-h)^2+k, where h is the x coordinate of the vertex, and k is the y coordinate, while a indicates how "squished" the graph is, or how quickly it grows in relation to the parent graph. In this case, h is shown to be 1, and k is 3, meaning that the vertex is at (1,3). The axis of symmetry , for a vertical parabola, just runs vertically through the vertex, meaning that in this case it is at x=1. Hope this helps!
Answer:
(1,3) and y-axis
Step-by-step explanation:
The vertex is the value of x at maximum or minimum point
At maximum point
dy/ dx = 0;
dy/dx = 4(x-1)= 0
=>x= 1 and is the vertex
Y when x = 1; we substitute x=1 in the original equation.
f(x) =y =2(x-1)^2+3
y = 2(1-1)^2 +3
y = 0 + 3= 3
The vertex is (1,3)
2.
A symmetrical equation is given by
b^2 = 4ac
Looking at the equation above x has an order of 2 meaning a possibility of cutting the x axis on two values of x
Hence the axis of symmetry is the y-axis
Assuming this was the expression; the axis of rotation would have been the x-axis.
f(y)=2(y-1)^2+3
Whats the geometric sequence for 5,20,80,320
Select each expression that is equivalent to 5(n + 4).
Answer:
5n+20
Step-by-step explanation:
5(n+4)
Distribute
5*n+5*4
5n+20
If you have time in the day please help me
Answer:
i think its B
Step-by-step explanation:
i think itd most accurate t b
The string of a kite is 100 meters long and it makes an angle of 60° with the ground. What is the height of the kite?
Answer:
86.5 m
Step-by-step explanation:
Length of the string forms the hypotenuse AC of right angle triangle ABC.
C is the kite. A is the hand of the person (or, one end of the string). CB is the perpendicular (height of the kite ) from C on the ground. BC is the horizontal.
Sin 60° = CB/AC = √3/2
height = 1.73/2 * AC = 0.865 * 100 m = 86.5 m
If the radius of a circle is 44 cm, then what is the diameter?
no guessing!!
Step-by-step explanation:
diameter = 2 * radius
= 2 * 44
= 88 cm (ANS)
Answer:
The diameter will be 88cm (Not a guess :P)
Step-by-step explanation:
So since we know that the radius is half the diameter we simply multiply 44*2 to get 88 as our diameter
Not hard, right? :P
Hope this helped! :)
Brainiest is most appreciated if possible
Sorry for any mistake that I made in advance
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
In the attached file
What is the area of the shaded region between the two z-scores indicated in the standard normal curve shown below. z=-1.23 z=0.83
Answer:
Correct option A: 0.6874
Step-by-step explanation:
Hello!
To calculate the area within the interval [-1.23; 0.83], you have to subtract to the probability accumulated till the lower value to the probability accumulated to the higher value, symbolically:
P(Z≤0.83)-P(Z≤-1.23)
You have to use the Z table to look for the corresponding values of probability. The negative value is in the left entry and the positive value is in the right entry. The first column shows the integer and first decimal value, the second decimal value is in the first row, you cross both values and find the value of probability.
P(Z≤0.83)-P(Z≤-1.23)= 0.7967 - 0.1093= 0.6874
I hope it helps!
cuantos metros de encaje se necesita para el borde del un mantel circular que tiene 50 cm de radio
Answer:
157 cm
Step-by-step explanation:
El valor que se necesita para el borde del mantel es equivalente al perímetro del mantel.
Para un circulo de 50 cm de radio, el perímetro es:
[tex]P=\pi r=3.14\cdot 50=157[/tex]
Se necesitan 157 cm de encaje.
The value needed for the edge of the tablecloth is equivalent to the perimeter of the tablecloth.
For a circle with a radius of 50 cm, the perimeter is:
[tex]P=\pi r=3.14\cdot 50=157[/tex]
157 cm of lace are required.
The mean age of 5 people in a room is 40 years.
A person enters the room.
The mean age is now 37.
What is the age of the person who entered the room?
Answer:
22years
Step-by-step explanation:
The sum of ages of people in the room is 40 * 5= 200
[ Remember mean = total ahead of people/ number of people]
Let the age of the 6th person be X
200+x. / 6 = 37
200 + x = 37 * 6 = 222
x = 222- 200 = 22
What is the best estimate for the width of a sidewalk?
>) 10 meters
>) 1 meter
10 centimeters
1 centimeter
Answer:
10 meters because it can't be 1 or 10 cenemiters because that's way too short and 1 meter i ls only 12 inches so thats also too short so it has to be 10 meters
What is the TOTAL surface area?
Answer:
SA=571.77
Step-by-step explanation:
SA==2πrh+2πr2=2·π·7·6+2·π·72≈571.76986
pls mark brainliest
When faced with needing additional money during college which is option is NOT true?
The options to the questions are:
A. Taking on a job can cut into study time
B. Paying with credit cards can end up conting more money
C. Paying with additional loans can lead to connections and opportunities
D. Taking on a job can make connections that lead to opportunities
Answer:
C. Paying with additional loans can lead to connections and opportunities
Step-by-step explanation:
When faced with needing additional money during college, an individual may chose to take on job so to get extra money to finance his or her needs. However, such venture often leads to redcution in study time, as working on jobs will also needs it own time of execution.
Also, paying for financial needs during college days with credit card can lead to counting more money on the card. This implies that one can accumulate credit card rewards which can be in form of cashback, or points from certain purchases when using credit card.
More so, taking a job during college days, will definitely brings connections with different people, and thereby leads to opportunities.
However, paying with additional loans will never lead to connections and opportunities, but rather more debt, that the debtor will have to pay, which may take months or years. And it can only be a burden on the debtor.
Hence, when faced with needing additional money during college the option that is NOT true is Paying with additional loans can lead to connections and opportunities
You deposit $2,000 at the end of each year into an account earning 2% interest compound annually. How much will you have in the account in 15 years?
Answer:
Simple interest = $600
Step-by-step explanation:
In this word problem, we will need to find the simple interest.
Formula:
I = prt or I = p x r x t
Simple interest: final answer
I = (2,000)(.02)(15) multiply.
I = 600
Simple interest: $600
ASAP! GIVING BRAINLIEST! Please read the question THEN answer correctly! No guessing. Show your work or give an explaination.
Answer:
B
Step-by-step explanation:
A function has at most one y value for every x value. This means that for every vertical line, there can be at most one intersection.
This example clearly doesn't satisfy this requirement.
Test the given claim about the means of two populations. Assume that two dependent samples have been randomly selected from normally distributed populations. A test of abstract reasoning is given to a random sample of students before and after they completed a formal logic course. The results are given below. At the 0.05 significance level, test the claim that the mean score is not affected by the course. Assume all requirements are met. Use the critical value method of testing hypotheses.
Before 74 83 75 88 84 63 93 84 91 77
After 73 77 70 77 74 67 95 83 84 75
A. State the null hypothesis (H_0) and the alternate (H_1).
B. What is the test statistic and the critical value(s.
C. Find the confidence interval values.
D. Interpret the information and state what can you say about the claim?
Answer:
Step-by-step explanation:
The hypotheses are:
Null Hypothesis
[tex]H_0 : \muafter = 0[/tex]
Alternative Hypothesis
[tex]Ha: \mu\neq 0[/tex]
Since the t-statistic score is greater than the critical t-score, so the decision is to reject the null hypothesis.
See image for detailed solution
Answer:
Step-by-step explanation:
Corresponding test scores of students before and after they completed a formal logic course.
The data for the test are the differences between the test scores.
μd = the score before minus score after
Score before score after diff
74 73 1
83 77 6
75 70 5
88 77 11
84 74 10
63 67 - 4
93 95 - 2
84 83 1
91 84 7
77 75 2
Sample mean, xd
= (1 + 6 + 5 + 11 + 10 - 4 - 2 + 1 + 7 + 2)/10 = 3.7
xd = 3.7
Standard deviation = √(summation(x - mean)²/n
n = 10
Summation(x - mean)² = (1 - 3.7)^2 + (6 - 3.7)^2 + (5 - 3.7)^2+ (11 - 3.7)^2 + (10 - 3.7)^2 + (- 4 - 3.7)^2 + (-2 - 3.7)^2 + (1 - 3.7)^2 + (7 - 3.7)^2 + (2 - 3.7)^2 = 220.1
Standard deviation = √(220.1/10
sd = 4.69
For the null hypothesis
H0: μd ≥ 0
For the alternative hypothesis
H1: μd < 0
The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 10 - 1 = 9
The formula for determining the test statistic is
t = (xd - μd)/(sd/√n)
t = (3.7 - 0)/(4.69/√10)
t = 2.49
The test is a left tailed test. From the t distribution table, the t score corresponding to the significance level is 2.262
In order to reject the null hypothesis, the test statistic must be smaller than - 2.262 or greater than 2.262
Since - 2.49 < - 2.262 and 2.49 > 2.262, we would reject the null hypothesis.
Therefore, at 5% significance level, we can conclude that for the test scores before and after, the mean difference is lesser than zero
What is the first step to simplify the expression 5(8x-4)+12
Answer:
8 • (5x - 1)
Step-by-step explanation:
Step 1 : See below
Step 2 : See below
Pulling out like terms/ factors
8x - 4 = 4 • (2x - 1)
Equation at the end of step 2 :
20 • (2x - 1) + 12
Step 3 : See below
Step 4 : See below
Pull out like factors:
40x - 8 = 8 • (5x - 1)
Answer: 8 • (5x - 1)
Hope this helps.