Answers
Answer:
4th option
Step-by-step explanation:
using the addition formula for cosine
cos(a - b) = cosacosb + sinasinb
note that 15° = (45 - 30)° , then
cos15°
= cos(45 - 30)°
= cos45°cos30° + sin45°sin30°
= ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{\sqrt{3} }{2}[/tex] ) + ( [tex]\frac{\sqrt{2} }{2}[/tex] × [tex]\frac{1}{2}[/tex] )
= [tex]\frac{\sqrt{6} }{4}[/tex] + [tex]\frac{\sqrt{2} }{4}[/tex]
= [tex]\frac{\sqrt{6}+\sqrt{2} }{4}[/tex]
= [tex]\frac{\sqrt{2}+\sqrt{6} }{4}[/tex]
Answer:
[tex]\cos 15^{\circ}= \dfrac{\sqrt{2}+\sqrt{6}}{4}[/tex]
Step-by-step explanation:
Trig Identity:
[tex]\cos (A-B)=\cos A \cos B + \sin A \sin B[/tex]
[tex]\begin{aligned}\implies \cos 15^{\circ}=\cos (45^{\circ}-30^{\circ}) & =\cos 45^{\circ} \cos 30^{\circ} + \sin 45^{\circ} \sin 30^{\circ}\\\\& = \dfrac{\sqrt{2}}{2} \cdot \dfrac{\sqrt{3}}{2} + \dfrac{\sqrt{2}}{2} \cdot \dfrac{1}{2}\\\\& = \dfrac{\sqrt{2}\sqrt{3}}{2 \cdot 2}+\dfrac{\sqrt{2} \cdot 1}{2 \cdot 2}\\\\& = \dfrac{\sqrt{2\cdot 3}}{4}+\dfrac{\sqrt{2}}{4}\\\\& = \dfrac{\sqrt{6}+\sqrt{2}}{4}\\\\& = \dfrac{\sqrt{2}+\sqrt{6}}{4}\end{aligned}[/tex]
Related Questions
Here is a set of data
Answers
Answer:
a) 1.8
b) 11.8
c) 23.6
a)(2.4 + 1.6 + 3.2 + 0.3 + 1.5) / 5 = 1.8
b)(12.4 + 11.6 + 13.2 + 10.3 + 11.5) = 11.8
c)(24.8 + 23.2 + 26.4 + 20.6 + 23) / 5 = 23.6
or,
11.8 × 2 = 23.6
Answer+Step-by-step explanation:
a)
original mean = (2.4+1.6+3.2+0.3+1.5)÷5
= 9÷5
= 1.8
b)
New mean = ((2.4+10)+(1.6+10)+(3.2+10)+(0.3+10)+(1.5+10))÷5
= (12.4) + (11.6) + (13.2) + (10.3) + (11.5)) ÷ 5
= 59÷5
= 11.8
Note:
11.8-10 = 1.8
then
New mean = original mean + 10
c)
Newest mean = ((2×12.4)+(2×11.6)+(2×13.2)+(2×10.3)+(2×11.5))÷5
= ((24.8)+(23.2)+(26.4)+(20.6)+(23))÷5
= 118÷5
=23.6
Note :
Newest mean = 2×(New mean)
= 2×(original mean + 10)
please tell me how u got the answer no bots pleaseeeee
Answers
Answer:
x = - 21
Step-by-step explanation:
[tex]\frac{-12+x}{11}[/tex] = - 3 ( multiply both sides by 11 to clear the fraction )
- 12 + x = 11 × - 3 = - 33 ( add 12 to both sides )
x = - 21
-12+x = -33
x=-21
Answer is -21
First step is to times both sides by 11 which would take away the fraction on the left and multiply -3 by 11 which makes it -33. Then you are left with -12+x=-33 so you add -12 on both sides so you are left with x=-21
If a teacher gives a quiz that is normally distributed and has a mean score 50 and a standard deviation of 5:
a) what z score is associated with a 60th percentile
b) what score is associated with the 60th percentile
Answers
Using the normal distribution, it is found that:
a) The z-score associated with a 60th percentile score is of Z = 0.253.
b) The score associated with the 60th percentile is of 51.265.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 50, \sigma = 5[/tex]
The 60th percentile is X when Z has a p-value of 0.6, so X when Z = 0.253, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.253 = \frac{X - 50}{5}[/tex]
X - 50 = 5(0.253)
X = 51.265.
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PLS HELP NEED ANSWER ASAP
Answers
Answer:
a. 38
b. 12
Step-by-step explanation:
i used calculator. net
The height of the kite is 38.042(approx.) and the shadow of kite from Dmitri is 12.36 m (approx.)
What is angle of elevation?The term angle of elevation denotes the angle from the horizontal upward to an object. An observer’s line of sight would be above the horizontal.
According to the question
Kite string = hypotenuse = 40m
angle of elevation = 72 °
a) Height of kite = perpendicular
sin( 72 °) = [tex]\frac{Perpendicular}{hypotenuse}[/tex]
0.951 = [tex]\frac{Perpendicular}{40}[/tex]
38.042 ≈ Perpendicular or Height of kite ≈ 38.042
b) Sun is directly above the kite , kite's shadow from Dmitri is = base
Tan (72°) = [tex]\frac{perpendicular }{base}[/tex]
3.077 = [tex]\frac{38.042 }{base}[/tex]
Base ≈ 12.36 m
Hence, height of the kite is 38.042(approx.) and the shadow of kite from Dmitri is 12.36 m
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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Sho
Answers
Answer:
Top Left (<A) = 86 degrees // Top Right (<B) = 112 degrees // Bottom Left (<C) = 68 degrees // Bottom Right (<D) = 94 degrees
Step-by-step explanation:
So with inscribed quadrilaterals opposing corners are supplementery. This means they will add to 180 degrees. So first what we can do is set (x + 2) and (x - 6) equal to 180 ----> 2x - 4 = 180 ----> 2x = 184 ----> x = 92
So if x = 92 then <A = 86 degrees //// <B = 112 degrees //// <C must equal 68 degrees because <B and <C are supplementery //// <D = 94 degrees
I need help ASAP with this pyramid scale factor question!
Answers
Answer:
C
Step-by-step explanation:
because 14 is 7 x 2 the scale factor from the small pyramid to the big pyramid would be 1/2
Answer:
(b) 1/8
Step-by-step explanation:
You want the ratio of the volume of the small pyramid to that of the larger one, given their base lengths are 7 and 14 units.
Scale factorThe pyramids are presumed to be similar, so the ratio of the sides given is also the ratio of the unmarked sides and the heights. The volume ratio is the cube of this ratio of side lengths:
smaller/larger sides = 7/14 = 1/2
smaller/larger volumes = (1/2)³ = 1/8
The ratio of the volume of the small pyramid to the larger is 1/8.
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Pls help max Point + brainliest
Determine which set has the greatest Radius. Several cylinders are separated into 4 sets. The cylinders with the same radius are in the same set. The graph of the equations represents the volume of each set of cylinders as they are being filled with water.
o Set 1
o Set 2
o Set 3
o Set 4
Answers
So it's volume vs water filled graph
Higher the volume higher the radiusFor this y should be highest
Observe all 4
In set 1
The line is more stepped towards y axis means y is higherSo set 1 has highest volume
Hence it has greatest radius
A basketball is shot into the air. Its height is represented by the polynomial equation
h(t) = -162 + 35t + 5, where h is the height of the basketball at t seconds. What is
the height of the basketball at 1 second?
A) 56 feet
B) 24 feet
C) 14 feet
D) 8 feet
Answers
Answer:
B) 24 feet
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Functions
Function NotationStep-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle h(t) = -16t^2 + 35t + 5[/tex]
Step 2: Find Height
Since we are trying to find the height of the basketball at 1 second, it implies that t = 1. Therefore, we can simply substitute t = 1 into our function:
[tex]\displaystyle\begin{aligned}h(1) & = -16(1)^2 + 35(1) + 5 \\& = -16(1) + 35(1) + 5 \\& = -16 + 35 + 5 \\& = \boxed{24} \\\end{aligned}[/tex]
∴ the height of the basketball at 1 second is equal to 24 feet.
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Topic: Algebra I
A rectangle portrait is 6 feet wide and 4 feet high. What is its perimeter?
Answers
Answer:
20 feet
Step-by-step explanation:
Perimeter :
2(height + width)2(4 + 6)2(10)20 feetFind the number of sample outcomes that are common to the two events.
Answers
Answer:
The event space is the number of outcomes in the event you are interested in. The event space for rolling a number less than three is 1 or 2. So the size of the event space is 2. For equally likely outcomes, the probability of an event E can be written P(E).
The number of sample outcomes that are common to the two events would depend on the specific events and the information provided about their sample spaces.
To find the number of sample outcomes that are common to two events, we need to determine the intersection of the two events. The intersection represents the outcomes that satisfy both events simultaneously.
If we know the number of sample outcomes for each individual event, we can find the number of outcomes that are common to both events by finding the smaller of the two numbers.
For example, let's say event A has 50 possible outcomes and event B has 30 possible outcomes. The number of sample outcomes that are common to both events would be the smaller of the two, which is 30 in this case.
Therefore, the number of sample outcomes that are common to the two events would depend on the specific events and the information provided about their sample spaces.
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If y varies jointly with x and z, and y = 200 when x = 8 and z = 10, what is x when y = 165 and z = 11? what is the value of k? 250 160 5.2 2.5
Answers
The value of x is 6 and the value of k is 2.5. The correct option is the last option - 2.5
VariationFrom the question, we are to determine the value of k, that is, the constant of proportionality
From the given information,
y varies jointly with x and z
Mathematically, this can be written as
y ∝ xz
Then, introducing the constant of proportionality, k, we get
y = kxz
Also, from the given information
y = 200 when x = 8 and z = 10
Putting these values into the equation, we get
200 = k × 8 × 10
200 = 80k
∴ k = 200/80
k = 2.5
Now, for the value of x when y = 165 and z = 11
Using the equation
y = kxz
Then, put the parameters into the equation
165 = 2.5 × x × 11
165 = 27.5x
∴ x = 165 / 27.5
x = 6
Hence, the value of x is 6 and the value of k is 2.5. The correct option is the last option - 2.5
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Answer: 2.5
Step-by-step explanation: I did the quiz
12.3 - 2.2 x 8.4 ÷ 2 =
Please help quick!!
Answers
A rectangular hotel room is 11 feet wide and 25 feet long. What is its perimeter?
Answers
Answer:
The answer is 72
Step-by-step explanation:
The formula for perimeter is (L+W)x2
So in your case (11+25)x2
Or add all 4 sides of the rectangle up and you have your answer <3
What are the x-coordinates for the maximum points in the function f(x) = 4 cos(2x − π) from x = 0 to x = 2π? (1 point) a x = 3 pi over 2 , x = π b x =
Answers
x-coordinates for the maximum points in any function f(x) by f'(x) =0 would be x = π/2 and x= 3π/2.
How to obtain the maximum value of a function?To find the maximum of a continuous and twice differentiable function f(x), we can firstly differentiate it with respect to x and equating it to 0 will give us critical points.
we want to find x-coordinates for the maximum points in any function f(x) by f'(x) =0
Given f(x)= 4cos(2x -π)
[tex]f'(x) = 0\\- 4sin(2x -\pi ) =0\\\\sin (2x -\pi ) =0 \\2x -\pi = k\pi ... k in Z[/tex]
In general [tex]x=(k+1)\pi /2[/tex]
from x = 0 to x = 2π :
when k =0 then x = π/2
when k =1 then x= π
when k =2 then x= 3π/2
when k =3 then x=2π
Thus, X-coordinates of maximum points are x = π/2 and x= 3π/2
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HELP ME PLEASE!!!!!!
Answers
Answer:
x = 5
Step-by-step explanation:
216 ^x = 6^(x+10) notice that 216 = 6^3
(6^3 )^x = 6^(x+10)
6^3x = 6^(x+10) now just equate the exponents
3x = x + 10
2x = 10 x = 5
What is the domain of the function?
Domain: x
Answers
can someone figure this out for me?
Answers
Answer:
it spells ucla, or U C LA
get it you see Los Angeles
or the school name in Los Angeles
Step-by-step explanation:
you shade in 12.5in^2
77cm
1.35m^2
48m
17cm^2
11400 in ^2
20.8cm
25m
20in
275 cm ^2
120 ft
43.4 cm^2
6.6m
105m^2
544 in
30m^2
28.8cm
600ft^2
Geometry
A cylinder has a diameter of 14
centimeters and a volume of 11211
cubic centimeters. What is the height,
in centimeters, of the cylinder?
Answers
Answer:
72.828
Step-by-step explanation:
h=V
π(d
2)2=11211
π·(14
2)2≈72.828
Darren’s teacher stated that 20% of his grade would come from his homework. What fractional part of his grade will NOT come from homework?
Answers
Answer:
80% = 80/100 = 8/10
I hope this helps! If it does, please mark me Brainliest! Thanks in advance!
please help me thank you if you do
Answers
2 2/3 of a fraction
________________
2 full and 2/3
- Jackson
find the area of sector =?
Answers
Step-by-step explanation:
270°/360° ×π×13²cm
=398.20cm²
the area of the sector with a radius of 13 units and a central angle of 270 degrees is approximately 398.25 square units.
To find the area of a sector, we use the formula:
Area of sector = (θ/360) * π * r²
Where:
θ is the central angle of the sector in degrees,
r is the radius of the sector.
In this case, the radius (r) is 13 units, and the central angle (θ) is 270 degrees.
Area of sector = (270/360) * π * 13²
Area of sector = (3/4) * π * 169
Area of sector = (3/4) * 169π
Area of sector ≈ 398.25 square units
So, the area of the sector with a radius of 13 units and a central angle of 270 degrees is approximately 398.25 square units.
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simplify (4x^2-7x+14)(3x+5x^2-6)
Please show work
Answers
Answer:
-23x^3+20x^4+25x^2+84x-84
Step-by-step explanation:
1 Expand by distributing sum groups.
4x^2(3x+5x^2-6)-7x(3x+5x^2-6)+14(3x+5x^2-6)
2 Expand by distributing terms.
12x^3+20x^4-24x^2-7x(3x+5x^2-6)+14(3x+5x^2-6)
3 Expand by distributing terms.
12x^3+20x^4-24x^2-(21x^2+35x^3-42x)+14(3x+5x^2-6)
4 Expand by distributing terms.
12x^3+20x^4-24x^2-(21x^2+35x^3-42x)+42x+70x^2-84
5 Remove parentheses.
12x^3+20x^4-24x^2-21x^2-35x^3+42x+42x+70x^2-84
6 Collect like terms.
(12x^3-35x^3)+20x^4+(-24x^2-21x^2+70x^2)+(42x+42x)-84
7 Simplify.
-23x^3+20x^4+25x^2+84x-84
The spinner game at the school carnival has a long line, but Edgar thinks that the fun prizes are worth the wait. The spinner is divided into 4 unequal sections. As he moves up in line, Edgar notices the spinner results of the people ahead of him: 3 glow sticks, 5 bouncy balls, 8 whistles, and 2 foam gliders
Answers
The probability of the spinner landing on whistle during Edgar's turn is 4/9
How to determine the probability?The experimental results are given as:
3 glow sticks, 5 bouncy balls, 8 whistles, and 2 foam gliders
The total number of sample is:
Sample = 3 + 5 + 8 + 2
Sample = 18
The probability that Edgar's spin land on whistle is:
P(Whistle) = Whistle/Sample
This gives
P(Whistle) = 8/18
Evaluate
P(Whistle) = 4/9
Hence, the probability of the spinner landing on whistle during Edgar's turn is 4/9
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Which picture shows 5/6?
Answers
Answer:
Bottom right option
Step-by-step explanation:
5 boxes out of 6 are shaded.
Answer:
d) Bottom right picture
Step-by-step explanation:
There are 6 boxes in that rectangle and 5 boxes are shaded. Hence, this diagram shows the required fraction of 5/6.
Math question explain throughly
Answers
The value of the discriminant is 24. Then the factor of the polynomial is not a whole number.
What is a factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
The expression is given below.
x² + 8x + 10
If the value of the discriminant is a perfect square then the factor of the polynomial will be in whole number.
D = b² - 4ac
D = 8² - 4 x 1 x 10
D = 64 - 40
D = 24
The value of the discriminant is not a perfect square.
The solution of the polynomial can be determined by the formula method.
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Rewrite the following polynomial in standard form. - 10 - 9x2 +x
Answers
Answer:
-9x² + x - 10
Step-by-step explanation:
To write in a standart form, variables go in an alphabetical order, from highest to lowest exponent. The last thing to write is a number by itself (ex. 10)
A restaurant chef wants to install a new floor in his kitchen. The kitchen measures 8 yards wide and 12 yards long, and the flooring costs $7.01 per square yard. How much will the chef's new floor cost?
Answers
Use that to find the total cost by multiplying the cost with the area.
Answer is $672.96
Hope this helps!!
Enter the volume of the right rectangular prism in cubic centimeters.
Answers
Answer:
37.95
Step-by-step explanation:
3.3x2.5x4.6=37.95
I need a answer quick!
Answers
Answer: The answer for 16 is -6 and 3
The answer for 18 is -9 and -4
x^2 + 3x - 18 = 0
(x + 6) (x - 3) = 0
x^2 + 13x + 36
(x + 9) (x + 4) = 0
I need to figure out on how to do this, please help me
Answers
Answer:
Q = 108°
R = 72°
Step-by-step explanation:
Quadrilateral means this is a four-sided shape. Parallelogram means that both sets of opposite side are parallel, so all the angles are either equal or add up to 180° (supplementary)
The order of the letters matters bc PQRS means that you go along an edge from P to Q, but you have to go thru the middle of the shape to get from P to R. So P and Q add up to 180°.
P + Q = 180°
72° + Q = 180°
Q = 108°
Opposite from each other, across the middle of the shape, P and R are equal.
P = R = 72°
