Answer:
[tex](a)\ \cos(180 - x)[/tex] --- Never true
[tex](b)\ \cos(90 -x)[/tex] --- Always true
[tex](c)\ \cos(x)[/tex] ---- Sometimes true
[tex](d)\ \cos(2x)[/tex] ---- Sometimes true
Step-by-step explanation:
Given
[tex]\sin(x )[/tex]
Required
Determine if the following expression is always, sometimes of never true
[tex](a)\ \cos(180 - x)[/tex]
Expand using cosine rule
[tex]\cos(180 - x) = \cos(180)\cos(x) + \sin(180)\sin(x)[/tex]
[tex]\cos(180) = -1\ \ \sin(180) =0[/tex]
So, we have:
[tex]\cos(180 - x) = -1*\cos(x) + 0*\sin(x)[/tex]
[tex]\cos(180 - x) = -\cos(x) + 0[/tex]
[tex]\cos(180 - x) = -\cos(x)[/tex]
[tex]-\cos(x) \ne \sin(x)[/tex]
Hence: (a) is never true
[tex](b)\ \cos(90 -x)[/tex]
Expand using cosine rule
[tex]\cos(90 -x) = \cos(90)\cos(x) + \sin(90)\sin(x)[/tex]
[tex]\cos(90) = 0\ \ \sin(90) =1[/tex]
So, we have:
[tex]\cos(90 -x) = 0*\cos(x) + 1*\sin(x)[/tex]
[tex]\cos(90 -x) = 0+ \sin(x)[/tex]
[tex]\cos(90 -x) = \sin(x)[/tex]
Hence: (b) is always true
[tex](c)\ \cos(x)[/tex]
If
[tex]\sin(x) = \cos(x)[/tex]
Then:
[tex]x + x = 90[/tex]
[tex]2x = 90[/tex]
Divide both sides by 2
[tex]x = 45[/tex]
(c) is only true for [tex]x = 45[/tex]
Hence: (c) is sometimes true
[tex](d)\ \cos(2x)[/tex]
If
[tex]\sin(x) = \cos(2x)[/tex]
Then:
[tex]x + 2x = 90[/tex]
[tex]3x = 90[/tex]
Divide both sides by 2
[tex]x = 30[/tex]
(d) is only true for [tex]x = 30[/tex]
Hence: (d) is sometimes true
A teacher is interested in performing a hypothesis test to compare the mean math score of the girls and the mean math score of the boys. She randomly selects 10 girls from the class and then randomly selects 10 boys. She arranges the girls' names alphabetically and uses this list to assign each girl a number between 1 and 10. She does the same thing for the boys. She pairs each girl with the boy having the same number. She then performs a paired Do you think that in this situation a paired is the most appropriate procedure?
Answer:
No
Step-by-step explanation:
A matched pair design is used when we have two different observation about a certain experiment for each subject such that there is a natural pairing between the two population.
In the scenario described above, we have 20 subjects of which 10 are boys and 10 are girls.
Matching boys and girls having similar numbers does not depict natural pairing and thus using a matched paired test would be inappropriate. The test to use for such experiment is the two population t test.
Blake recorded the number of minutes he ran on the treadmill each day for 2 weeks. His data is in
the table below.
Week 1 Week 2
25 minutes 30 minutes
38 minutes 43 minutes
40 minutes 17 minutes
32 minutes 20 minutes
15 minutes 27 minutes
22 minutes 13 minutes
35 minutes 35 minutes
What is the difference in the median between the two weeks that he ran in his treadmill?
3.14 minutes
3 minutes
2 minutes
5 minutes
Answer:
5 minutes
Step-by-step explanation:
Find all working solutions for x.
✓(x-5) - 5 = 3
Answer:
Step-by-step explanation:
✓(x-5) - 5 = 3
✓(x-5) - 8 = 0
(✓(x-5))² - 8² = 0
x-5 - 64 = 0
x - 69 = 0
x = 69
one clothing truck visits avas place every 3 days and another clothing truck visits noahs place every 5 days if both clothing trucks visited today when is the next time both trucks visit on the same day
Answer:
15 days
Step-by-step explanation:
Given
[tex]Truck\ 1: 3\ days[/tex]
[tex]Truck\ 2: 5\ days[/tex]
Required
Next time they both visit
First, list out days of visitation of each truck
[tex]Truck\ 1: 3, 6, 9, 12, 15, 18, 21\ days.....[/tex]
[tex]Truck\ 2: 5, 10, 15, 20, 25, \ days.....[/tex]
Write out the common days;
[tex]Day = 15[/tex]
The next time they both visit is the after 15 days
Which is a chord of circle P?
Answer:
QR
Step-by-step explanation:
A chord is a line that joins two points on the outside of the circle
QR and KL are chords
Explain why sin(A)=sin(D)
I NEED HELP ASAP
becouse The size does not differ whether it is big or small, the degree remains the same
which one makes a right triangle?
=======================================
Explanation:
As mentioned earlier (in a previous post) the triangle with sides 2,5,7 is not a right triangle. So we can rule out choice A.
For choice B, we have a = 6, b = 8, c = 10, and that leads to...
a^2+b^2 = c^2
6^2+8^2 = 10^2
36+64 = 100
100 = 100
The true equation at the end means the beginning equation is true as well for those a,b,c values. Therefore, we have a right triangle and the answer is choice B
Choices C and D are similar to choice A. They make a^2+b^2 = c^2 to be false.
What is the formula for the volume of a pyramid?
Answer:
1/3 area of base * height
Please help me find x and y
Answer:
x = 33
y = 5
Step-by-step explanation:
Line BD splits AC in half so y is also 5Since the triangles are congruent (is known because of the congruence lines) and you know two angles you can find x57+90=147 and 180-147= 33 which is xWhat is the LCD for the given equation? 1/v^2=1/3v-2/v^2
jkajkajkamkjsjsnjjkakkamabzbnananajao
Answer:
Sin T = 0.28
Step-by-step explanation:
Here in this question
Hypotenuse = 25
Base = 24
The third vertex of the triangle is Sqrt (25*25 - 24*24) = 7
SinT = Perpendicular/Hypotenuse
SinT = 7/25
Sin T = 0.28
can someone help me
55 x 7 = 385
dadadsdsadssdgregeg
Marie had 12 pizzas. She wanted to give each person of a 1/4
pizza. How many people would receive a piece of pizza?
Answer:
48 people.
Step-by-step explanation:
Each person gets 1/4 of a pizza meaning that one pizza can serve 4 people. If one pizza can serve 4 people, 12 pizzas can serve 48 people, because 4x12=48.
urgent..
not explanation just answer plzz
Answer:
D 1
Step-by-step explanation:
1. How far is KFC from RCBC Savings Bank? 2. How far is BaliwagLetchon Manok from RCBC Savings Bank? 3. How far is Baliwag Lechon from his residence? 4. How far is KFC from his residence? 5. What is the measure of angle ERK ?
Answer:
Following are the solution to the given question.
Step-by-step explanation:
Please find the graph file and its solution in the attachment.
[tex]4x-15=3x+28\\\\4x-3x=28+15\\\\x=43\\\\[/tex]
Similarly:
[tex]3y+5=2y+50\\\\3y-2y=-5+50\\\\y=45\\\\[/tex]
For point 1:[tex]\to KR=4x-15= 4\times 43-15=172-15=157[/tex]
For point 2: [tex]\to BR=2y+50= 2\times 43+50=86+50=136[/tex]
For point 3:[tex]\to BE=KR=157[/tex]
For point 4:[tex]\to Kf=BR=130[/tex]
For point 5:[tex]\to ERK=KFB=180^{\circ} -\angle B-\angle ERB = 180^{\circ}-92^{\circ}-18^{\circ}=70^{\circ}[/tex]
Given that ΔKER and ΔBRE are congruent triangles, therefore:
1. How far KFC is from RCBC = KR = 157 m
2. How far BaliwagLetchon Manok is from RCBC Savings Bank = BR = 140 m
3. How far Baliwag Lechon is from his residence = BE = KR = 157 m
4. How far KFC is from his residence = KE = BR = 140 m
5. The measure of ∠ERK = 70°
What are Congruent Triangles?Congruent triangles have corresponding parts hat are congruent to each other.
Thus, given that ΔKER ≅ ΔBRE, find the values of x and y as shown below:
KR = BE
4x - 15 = 3x + 28
4x - 3x = 15 + 28
x = 43
KE = BR
3y + 5 = 2y + 50
3y - 2y = -5 + 50
y = 45
Thus:
1. How far KFC is from RCBC = KR
KR = 4x - 15
Plug in the value of x
KR = 4(43) - 15
KR = 157 m
2. How far BaliwagLetchon Manok is from RCBC Savings Bank = BR
BR = 2y + 50
Plug in the value of y
BR = 2(45) + 50
BR = 140 m
3. How far Baliwag Lechon is from his residence = BE = KR = 157 m
4. How far KFC is from his residence = KE = BR = 140 m
5. The measure of ∠ERK = 180 - (92 + 18) = 70°
Learn more about congruent triangles on:
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which is equivalent to this equation
Answer:
The correct option is (b).
Step-by-step explanation:
We need to find the value of the given expression i.e.
3⁷ × 3⁻⁴
We know that, one of the property of exponent is:
[tex]x^{-a}=\dfrac{1}{a}[/tex]
So,
[tex]3^7\times 3^{-4}=3^7\times \dfrac{1}{3^4}\\\\=3^3\\\\=27[/tex]
Hence, the correct option is (b).
Lena wants to replace a glass window in her restaurant. The window is in the shape of a square. Its side lengths are 7 feet. Suppose glass costs $7 for each square foot. How much will the glass cost to replace the window?
Step-by-step explanation:
It helps to draw a picture but also write what you are given
The square measures 7ft on all sides
youre paying by the square foot
to get square feet, use L x W
so 7ft x 7ft = 49 ft^2
so if we are charged $7 for 1 ft^2, then you add $7, 49 times
So youd write and solve
7 + 7 + 7 + 7 +... + 7 = $7 x 49ft^2
A curve has the equation y=x^3+8x^2+5
1. Given f(x) = x2 – X and g(x) = 3x + 2, find f(g(2))
Answer:
56
Step-by-step explanation:
g(2) = 3(2) + 2
= 6 + 2
= 8
f(8) = 8^2 - 8
= 64 - 8
= 56
A measuring cylinder of radius 3cm contains water to a height of 49cm.if this water is poured into a similar cylinder of radius 7cm, what will be the height of the water column
Answer:
9 cm.
Step-by-step explanation:
Volume of a cylinder == pi r^2 h.
The volume of the water is constant so:
pi * 3^2 * 49 = pi * 7^2 h
9 *49 = 49 h
h = 9 cm.
What is the length of NP?
Answer:
c. √174
Step-by-step explanation:
NP²= 10²+7²+5²=100+49+25= 174
NP = √174
The length of NP would be; √174
What is Pythagoras' Theorem?If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:
|AC|^2 = |AB|^2 + |BC|^2
where |AB| = length of line segment AB. (AB and BC are the rest of the two sides of that triangle ABC, AC being the hypotenuse).
We are given the measure of sides;
NP²= 10²+7²+5²
NP²=100+49+25
NP²= 174
NP = √174
Learn more about Pythagoras' theorem here:
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PLEASEEEE HELPPPP MEEEEE
to
Angle JKL is a straight angle.
The measure of angle MKL is 25°.
The measure of angle JKM is xº.
What is the value of x?
M
25°
K
n
Answer:
180-25=155 degrees
Step-by-step explanation:
Suppose that, as course instructor, you decide instead that you want to calculate a 95% confidence interval for the population proportion of all Cal Poly students who have ever marched in a Memorial Day Parade, and that you would like the margin of error of your 95% confidence interval to be .05, and that you would like to use a (most) conservative sample size for this task. What sample size should you use
Answer: 385
Step-by-step explanation:
If prior population proportion p is unknown, then the formula to compute sample size will be:
[tex]n= 0.25(\frac{z^*}{E})^2[/tex]
where, E= Margin of error, z* = Critical zvalue
Given: E= 0.05
Critical value for 95% confidence = 1.96
Required sample size: [tex]n=0.25(\frac{1.96}{0.05})^2[/tex]
[tex]\\=384.16\approx385[/tex]
Hence, the required sample size = 385
PLS HELP 40 POINTS
If the dimensions of the following cylinder are quadrupled, what will be the volume of the new similar cylinder?
340,426.24 in. 3
20,724 in. 3
63,829.92 in. 3
110,528 in. 3
Volume of the new similar cylinder is equals to 340,426.24 in.³.
What is volume?
" Volume is defined as the total space occupied by any three dimensional objects enclosed in it."
Formula used
Volume of the cylinder = πr²h
r = radius of the cylinder
h = height of the cylinder
value of π = 3.14
According to the question,
radius of the cylinder = 11 in.
height of the cylinder = 14 in.
Dimensions of new cylinder are quadrupled means 4times.
New radius = 44 in.
New height = 56 in.
Substitute the value in the formula we get,
Volume of the new cylinder = (3.14) ×(44)² × (56)
= 340,426.24 in.³
Hence, volume of the new similar cylinder is equals to 340,426.24 in.³.
Learn more about volume here
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Find the first term and the common ratio of the following geometric
sequence: 8, 16, 32, ...
Answer:
The first term is 8
The common ratio is 2, because the ratio of 8:16 is 1:2 and the ratio of 16:32 is 1:2
Step-by-step explanation:
Answer:
The common ratio of the following geometric sequence is x2 everytime.
The measure of (angle) 6 is 120. The measure of (angle) 5 is 100. What is the measure of (angle) 4
Answer:
80
Step-by-step explanation:
4x20=80
The question is in the picture (Alegbra 1)
Answer:
[tex] \frac{s}{s + 3} [/tex]
Answer:
S/S+3
Step-by-step explanation:
Hope this helps...
Perform the operation. Enter your answer in scientific notation. 7 × 102 − 5.6 × 102 =
algebra 2 question need help thanks.