Answers
Answer:
Use the law of cosines to find c:
c = [tex]\sqrt{a^2 + b^2 - 2ab*cos C}[/tex]c = [tex]\sqrt{2^2+6^2-2*2*6*cos 95}[/tex] = [tex]\sqrt{42.09}[/tex] = 6.49Use the low of sines to find one of the missing angles:
sin A / 2 = sin 95° / 6.49A = arcsin (2 sin 95° / 6.49)A = 17.9°Find the missing angle:
B = 180° - (A + C)B = 180° - (95° + 17.9°) = 67.1°Answer:
c ≈ 6.49
A ≈ 17.9°
B ≈ 67.1°
Step-by-step explanation:
To find the length of side c, use the Cosine rule.
Cosine rule
[tex]\sf c^2=a^2+b^2-2ab \cos C[/tex]
(where a, b and c are the sides and C is the angle opposite side c)
From inspection of the given triangle:
a = 2b = 6C = 95°Substitute the given values into the formula and solve for c:
[tex]\implies \sf c^2=2^2+6^2-2(2)(6) \cos 95^{\circ}[/tex]
[tex]\implies \sf c^2=4+36-24 \cos 95^{\circ}[/tex]
[tex]\implies \sf c=\sqrt{40-24 \cos 95^{\circ}}[/tex]
[tex]\implies \sf c=6.49\:\:(2\:d.p.)[/tex]
To find angles A and B, use the Sine Rule.
Sine Rule
[tex]\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}[/tex]
(where A, B and C are the angles and a, b and c are the sides opposite the angles)
From inspection of the given triangle:
a = 2b = 6[tex]\sf c=\sqrt{40-24 \cos 95^{\circ}}[/tex]C = 95°Substitute the given values into the formula:
[tex]\implies \sf \dfrac{\sin A}{2}=\dfrac{\sin B}{6}=\dfrac{\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}[/tex]
Solving for A:
[tex]\implies \sf \dfrac{\sin A}{2}=\dfrac{\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}[/tex]
[tex]\implies \sf A=\sin^{-1}\left(\dfrac{2\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}\right)[/tex]
[tex]\implies \sf A=17.9^{\circ}\:\:(1\:d.p.)[/tex]
Solving for B:
[tex]\implies \sf \dfrac{\sin B}{6}=\dfrac{\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}[/tex]
[tex]\implies \sf B=\sin^{-1}\left(\dfrac{6\sin 95^{\circ}}{\sqrt{40-24 \cos 95^{\circ}}}\right)[/tex]
[tex]\implies \sf B=67.1^{\circ}\:\:(1\:d.p.)[/tex]
Learn more about Sine Rule here:
https://brainly.com/question/28033514
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Related Questions
find BC. any help will be appreciated:)
Answers
Answer:
4
Step-by-step explanation:
Here,BC=1/2FH
BC=8/2
BC=4
This is the required answer
hope it helps u and keep smiling :)
Please help asap i give you all my points!
Answers
Answer:
it dropped 9% from last year
An airline operates a call center to handle customer questions and complaints. The airline monitors a sample of calls to help ensure that the service being provided is of high quality. Ten random samples of calls each were monitored under normal conditions. The center can be thought of as being in control when these samples were taken. The number of calls in each sample of not resulting in a satisfactory resolution for the customer is as follows:
4 5 3 2 3 3 4 6 4 7
Required:
a. What is an estimate of the proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control?
b. Construct the upper and lower limits for a p chart for the manufacturing process, assuming each sample has 100 calls.
Answers
Answer:
A) p = 0.041
B) UCL = 0.1004
LCL = 0
Step-by-step explanation:
We are told that Ten random samples of calls each were monitored .
Thus; n_x = 10
We are told that each sample has 100 calls. Thus; n = 100
A) We are given the number of calls in each sample not resulting in a satisfactory resolution for the customers as;
4 5 3 2 3 3 4 6 4 7
Thus, sum of this is;
Σx = 4 + 5 + 3 + 2 + 3 + 3 + 4 + 6 + 4 + 7
Σx = 41
proportion of calls not resulting in a satisfactory outcome for the customer when the center is in control is given by;
p = Σx/(n_x•n)
p = 41/(10 × 100)
p = 41/1000
p = 0.041
B) let's first find the standard deviation.
It's given by the formula;
σ = √(p(1 - p)/n)
σ = √(0.041(1 - 0.041)/100)
σ = 0.0198
Formula for Upper control limit(UCL) and Lower control limit(LCL) are given as;
UCL = p + 3σ
LCL = p - 3σ
Thus;
UCL = 0.041 + 3(0.0198)
UCL = 0.1004
LCL = 0.041 - 3(0.0198)
LCL = -0.0184
Rule is that when LCL is negative, we adopt LCL = 0.
Thus;
UCL = 0.1004
LCL = 0
What is the area of the figure?
Answers
Answer:
b. 366 square inches
Step-by-step explanation:
The area of a triangle is 1/2×Base×Height. There are 2 pairs of identical triangles so you multiply each equation by 2.
2×(1/2×10×12) = 120 in²
2×(1/2×18×12) = 216 in²
120 in² + 216 in² = 336 in²
Answer:
336 square units
Step-by-step explanation:
Generally, to find the area of the given quadrilateral (which is presumably a kite), one uses the following formula,
[tex]\frac{(base)*(hieght)}{2}[/tex]
In this picture, one can see that the diagonals (dotted lines that connect opposite corners) are given, but their measurements are split up as per the segments they are divided into. In order to find the lengths of each diagonal, add up the two parts. To find the area of the figure, substitute the results into the given formula to find the area,
[tex]12+12=24\\\\10 + 18 = 28[/tex]
Substitute,
[tex]\frac{24*28}{2}\\\\=\frac{672}{2}\\\\=336[/tex]
The result of a game is Win, Lose or Draw.
After 80 games
relative frequency of the result Win is 0.4
relative frequency of the result Lose is 0.25
How many of the games had the result Draw?
Answers
Answer:
Step-by-step explanation:
Find the value of x.
Answers
Assuming the dark gray area is a straight line, the whole thing should add up to 180*. If we have our 180*, minus 79*, you'll have 101*. BUT, we also have to divide that by two to get our x answer, so the value of x would be 50.5*.
WHICH EXPRESSION CAN GO IN THE BLANK TO MAKE THE EQUATION TRUE.
-4.5+4.4+ ? =0
A -6.7 +6.8
B -6.7 +(-6.6)
C 7.2 + (-7.2)
D 7.2 + (-7.3) ILL GIVE YOU WILL GET 95 POINTS IF YOU HELP ME SOLVE THIS!! ASAP!!
Answers
Answer:its a
Step-by-step explanation:-4.5+4.4 is -0.1 so if you add that to -6.7 you get
-6.8 + 6.8 =0
Answer pls and thank you
Answers
Answer:
54 degrees
Step-by-step explanation:
So, lets go over what we know.
Angle PRS is 90 degrees(we can tell by the small square shape inside of the angle)
We also know that Angle PR is 36 degrees.
We need to find x, angle RS.
To do this, lets subtract Angle PR from Angle PRS, or 36 from 90:
90-36
=
54
Since Angle PRS - Angle PR = Anlge RS, this means:
90-36=54
So 54 is our answer!
Hope this helps!
Triangle DEF with vértices D(2,1), E(3,5), F(6,2) is reflected acreage the x-axis to make triangle D’E’F
Which rule represents the transformation?
A. (x,y)—>( x,-y)
B. (x,y)—>(-x,y)
C. (x,y)—>(y,-x)
D. (x,y)—>(-y,x)
(Pls help I don’t understand)
Answers
And the answer is literally on top of that question
What is the surface area of the solid?
Answers
Answer:
im pretty sure its C
Step-by-step explanation:
answer:
c)780
step-by-step explanation:
a=2(wl+hl+hw)
=2·(10·4+25·4+25·10)
=780
a=780
good luck :)
i hope this helps
brainliest would be highly appreciated
have a nice day!
Help With box and whisker plot! Will give brainless!
Answers
Find the value of each trigonometric ratio
Answers
Answer:
3) D) 4 / 5
4) A) 4 / 5
5) B) 7 / 25
Step-by-step explanation:
Each of these trigonometric ratios can be remembered by the moniker
SOH - CAH -TOA
Sine = opposite over hypotension
Cosine = adjacent over hypotenuse
Tangent = adjacent over opposite
3) D) 4 / 5
4) A) 4 / 5
5) B) 7 / 25
Step-by-step explanation:
Each of these trigonometric ratios can be remembered by the moniker
SOH - CAH -TOA
(Sin)Sine = opposite/ hypotenuse
(Cos)Cosine = adjacent/hypotenuse
(Tan)Tangent = adjacent/opposite
solution of f'(x) = 9x2+2x (-2,2)
Answers
Answer:
f(x) = 3x³ + x² + 22
Step-by-step explanation:
Given
f'(x) = 9x²+2x
To get f(x), we will be integrating the function
f(x) = 9x³/3 + 2x²/2 + C
f(x) = 3x³ + x² + C
at (-2,2)
2 = 3(-2)³ +(-2)² + C
2 = -24 + 4 + C
2 = -20 + C
C = 2+20
C = 22
Get the required function
f(x) = 3x³ + x² + C
f(x) = 3x³ + x² + 22
Four students are selected for a relay team. In how many ways can
they line up for the race?
Answers
Answer:
24 possible ways
Step-by-step explanation:
When a member is chosen to occupy a leg of the 4-member relay, the same member can not be chosen again, because one member cannot occupy more than one leg.
As one person is chosen to run one leg, the options decrease by one. And like the first leg, one person cannot run more than one leg.
This cycle will repeat until the last person occupies the remaining empty leg.
[tex]4! \\= 4*3*2*1\\=12 * 2 * 1\\=24*1\\=24[/tex]
whoknowsthecorrectanswernofakeones
Answers
Answer:
The correct answer is 30 in.
Step-by-step explanation:
In order to find the diagonal length of the face of the suitcase, you need to use the Pythagorean Theorem, a formula used to calculate the sides of a right triangle. Since the length and width of the suitcase are 24 in. and 18. respectively, that means the diagonal length will be equal to [tex]\sqrt{24^2+18^2}[/tex] = [tex]\sqrt{576+324}[/tex] = [tex]\sqrt{900}[/tex] = 30 inches.
YALL HELP ASAP tell me if this is correct
NO LINKS
Answers
Answer:
its correct
Step-by-step explanation:
great job can i have brainliest
Answer:
it is correct
Step-by-step explanation:
Mrs. Joyce calculated the class mode on her latest test. 18 students took it and the mode was 83. Three days later the four absent kids made it up and scored 77, 83, 68, and 80. What is the new mode
Answers
Answer:
83 is still the mode
Step-by-step explanation:
The maximum possible value for the new mode is 83.
What is mode?The data value that is repeated the most in the data set is called the mode of the given data set.
Given is that Mrs. Joyce calculated the class mode on her latest test. 18 students took it and the mode was 83. Three days later the four absent kids made it up and scored 77, 83, 68, and 80.
Initially, the mode of the class of 18 students is 83. This means that most of the students scored the 83 marks in the test. After four students took the test, the maximum probability that the mode will remain 83 is the highest. Also, one of the four numbers scored 83 itself.
Therefore, the maximum possible value for the new mode is 83.
To solve more questions on functions, visit the link below-
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what is the solution set represented by this number line graph?
Answers
Answer:
x ≥ 2
Step-by-step explanation:
Shaded circle means ≥ or ≤ . Since the arrow is pointing right, it's showing 2 is greater than or equal to x, meaning ≥ .
Determine whether each pair of triangles is similar. Justify your answer.
Answers
Answer:
Your answer is C
Step-by-step explanation:
The definition of similarity is when one shape can become another after a resize, flip, slide or turn.
If you multiply AD, which is 6, by 1.5 you get 9. Which is the length AC.
If you multiply AE, which is 10, by 1.5 you get 15. Which is the length of AB.
Both triangles share angle A, so that leaves you with SAS Similarity.
Carlos started an exercise program in
January. He kept a record of how many
sit-ups he did each day.
Which correlation value best describes
the data?
Your answer:
O r=-0.9
O r=-0.5
O r= 0
O r=0.5
r = 0.9
Answers
pls help!
how many faces does it have?
Answers
Answer:
6
Step-by-step explanation:
I just learned this!! :)
Answer:
it has 6 faces
Step-by-step explanation:
20 points ! what is the area of the surface of the desk in square feet?
Answers
9514 1404 393
Answer:
B. 8.625 ft²
Step-by-step explanation:
The total area is the sum of the areas of the two rectangular sections and the area of the triangular section. The area formulas are ...
A = LW . . . rectangle
A = 1/2bh . . . triangle
Here, the dimensions are such that we can simplify the problem a bit
total area = (1.5)(2.5) +1/2(1.5)(1.5) + (1.5)(2.5)
= (1.5)(2.5 + 1.5/2 + 2.5)
= (1.5)(5.75) = 8.625 . . . . . ft²
The total surface area of the desk is 8.625 square feet.
(Hypothetical.) Suppose five measurements of the volume of a liquid yield the following data (in milliliters).
52 48 49 52 5.3
Assume that the different measurements are due only to measurement error, and that measurement error is Normally distributed. The goal is to set up an approximate 95% confidence interval for the correct measurement. In each part, answer correct to three decimal places. First find the average and SD of the data. Calculator welcome and recommended. Average of the data: SD of the data (remember, it's a small sample): Estimate the correct measurement. Attach a give-or-take value to the estimate (that is, estimate the standard error). There are 5 measurements. If measurements follow a Normal distribution (e.g., if they vary only due to chance measurement error), then the standardized average of 5 measurements follows a Student t-distribution with So, for 95% confidence, we include our estimate. degrees of freedom. standard error(s) on each side of An approximate 95% confidence interval for the correct measurement is ______.
Answers
Answer:
(48.106 ; 53.494)
Step-by-step explanation:
Given the data:
X : 52 48 49 52 53
Sample mean = ΣX / n
n = 5
Sample mean, xbar = 254 / 5 = 50.8
Standard deviation, s = 2.17 (using calculator)
The standard error (SE) : s/√n =2.17/√5 = 0.970
The degree of freedom, df = n-1
df = 5 - 1 = 4
Tscore(0.05, 4) = 2.776
Confidence interval :
Xbar ± Tscore*standard error
50.8 ± (2.776 * 0.970)
50.8 ± 2.694
Lower boundary = 50.8 - 2.694 = 48.106
Upper boundary = 50.8 + 2.694 = 53.494
(48.106 ; 53.494)
What is the order of steps to calculate the volume of a prism?
Label the answer with the
Substitute the values
Simplify by multiplying.
Write the formula
Calculate the area of the
correct units
in for known variables.
V = Bh
prism base, B.
Answers
Answer:
answer in picture
Step-by-step explanation:
what are all the possibilities that make the inequality 2x + 3 > 11 that are TRUE
Answers
Answer: x > 4 OR (4, infinity)
Step-by-step explanation:
2x + 3 > 11 subtract 3
2x > 8 divide by 2
x > 4 your answer
(14 ÷ 2) x 5 + 6
{ 3 x (4 + 1) } ÷ 5
EXPLAIN GIVING BRAINLIEST
Answers
Answer:
25
Step-by-step explanation:
(14÷2)×5+6(3×(4+1))÷5
using BODMAS
7×5+6(3×5)÷5
=7×5+6×15÷5
=35+90÷5
=125÷5
=25
Answer:
1. (14 ÷ 2) x 5 + 6 = 41
2. {3 x (4 + 1)} ÷ 5 = 3
Step-by-step explanation:
PEMDAS. VERY IMPORTANT. THIS ACRONYM WILL HELP YOU WHEN SOLVING MULTI-STEP PROBLEMS. IF YOU DO NOT KNOW IT, SEARCH IT UP. I'LL BE USING PART OF THIS ACRONYM TO SOLVE THIS PROBLEM.
First you solve things in paratheses:
1. (14 ÷ 2) x 5 + 6 -> (7) x 5 + 6
2. {3 x (4 + 1)} ÷ 5 -> {3 x 5} ÷ 5 -> 15 ÷ 5
Then, you multiply or divide next:
1. (7) x 5 + 6 -> 35 + 6
2. 15 ÷ 5 = 3
We already have the answer to number 2, but not number one, so we will keep going. Finally, you subtract or add:
1. 35 + 6 = 41
Now you have your answers. Hope this helps!
Plss help mee tyyyy
Answers
Answer:
57 i think
Step-by-step explanation:
At Ken's school, tickets for a concert sold at the rate of 40 per half-hour. How many tickets were sold in 7 hours?
Answers
Answer:
560 Tickets
Step-by-step explanation:
40 tickets in 30 minutes will become 80 tickets in 60 minutes (an hour)
Multiply 80 by 7 to get 560
A cube is labeled 1 - 6 what is the probability that it will land on a number less that 3
Answers
Answer:
1/3
Step-by-step explanation:
There are 6 sides on a number cube, and 2 numbers on the cube that are less than 3... 1 and 2. So, 2/6 or 1/3 is the probability that the cube would land on a number less than 3.
What is 25% of 50= please help
Answers
Answer:
answer 12.5
Step-by-step explanation:
25% of 50 is 12.5 because 50 ÷ 4 = 12.5 Hope that helps!