Recall the double angle identity for cosine:
cos(x) = cos(2×x/2) = 1 - 2 sin²(x/2)
Then the equation can be rewritten as
sin(x/2) + (1 - 2 sin²(x/2)) - 1 = 0
sin(x/2) - 2 sin²(x/2) = 0
sin(x/2) (1 - 2 sin(x/2)) = 0
sin(x/2) = 0 or 1 - 2 sin(x/2) = 0
sin(x/2) = 0 or sin(x/2) = 1/2
[x/2 = arcsin(0) + 360n ° or x/2 = 180° - arcsin(0) + 360n °]
… … or [x/2 = arcsin(1/2) + 360n ° or x/2 = 180° - arcsin(1/2) + 360n °]
x/2 = 360n ° or x/2 = 180° + 360n °
… … or x/2 = 30° + 360n ° or x/2 = 150° + 360n °
x = 720n ° or x = 360° + 720n °
… … or x = 60° + 720n ° or x = 300° + 720n °
(where n is any integer)
We get only three solutions in 0° ≤ x < 360° :
720×0° = 0°
60° + 720×0° = 60°
300° + 720×0° = 300°
Answer:
B: (0, 60, 300)
Step-by-step explanation:
right on edge
A right pyramid with a square base has
volume of 252 cubic centimeters. The
length of one of the sides of its base is 6
centimeters. Rounded to the nearest
centimeter, what is the vertical height of
the pyramid?
Hey there!
A right pyramid with a square base just means that it isn't slanted all funny. If you create a triangle with a point on one of the edges of the base, the center of the base, and the top of the pyramid, it would be a right triangle.
To find the volume of a right pyramid, you just take the base area, multiply it by the height, and then divide by three.
However, we are looking for the height. We have been given, so we will just go backwards.
252×3=756 (multiply instead of divide)
6×6=36 (base is a square, so you just square 6. This is our base area)
756/36=21
So, the vertical height of the pyramid is 21 cubic centimeters.
Have a wonderful day! :D
Helpp me plzzz im being timed
Help!!! Make brainliest
Answer:
b=(2a-1)/(3a-1)
Step-by-step explanation:
a=(b-1)/(3b-2)
3ab-2a=b-1
3ab-b=2a-1
b(3a-1)=2a-1
b=(2a-1)/(3a-1)
How many solutions exist for the given equation?
121 x+ 1 =3(4x+1)-2
zero
one
two
infinitely many
Answer: infinitely many
Which function describes this graph
Answer:
C.
Step-by-step explanation:
A P E X
URGENT PLEASE HELP DUE TMMR MORNING Half of the difference between a number and 3 is 5. What is the number?
Answer:
Not sure but I think it's 3.75
Interpret the coefficient of determination. Choose the correct answer below. A. The coefficient of determination measures the percent of variation not explained by the multiple regression model. B. The coefficient of determination measures the percent of variation explained by the multiple regression model. C. The coefficient of determination measures the expected error of the predicted sales given a specific total square footage and number of shopping centers. D. The coefficient of determination measures the average predicted sales for the multiple regression model.
Answer:
B.The coefficient of determination measures the percent of variation explained by the multiple regression model.
Step-by-step explanation:
The answer to this question is option b because the coefficient of variation R² gives a measure of the variability that is ending y values or the dependent variables which can be explained in a multiple linear regression.
In simpler words, it is the percentage of proportion of variation in the dependent variable that can be predicted using the explanatory variables.
If average of the numbers 3,9,5,7 and Q is 5 times the value of Q, find the value of Q
Answer:
q=6
Step-by-step explanation:
3+9+5+7+Q=5Q
5Q-Q=24
Q=6
180 °
35 °
X °
X = ? °
Answer:
x=145°
Step-by-step explanation:
180 = 35 + x
x = 180-35
x= 145°
find the greatest number that divides 56 and 84 exactly
Answer:
28
Step-by-step explanation:
Find the gcf
Which is the answer choice to this question?
Answer:
D
Step-by-step explanation:
Graph it
there were 578 tickets sold for a basket all game. the activity cardholder's tickets cost $1.25 and the non-cardholders' tickets cost $2.00. the total amount of money collected was $880.00. how many of each kind of ticket were sold?
9514 1404 393
Answer:
non-cardholder: 210cardholder: 368Step-by-step explanation:
Let n represent the number of non-cardholder tickets sold. Then total revenue is ...
2.00n +1.25(578 -n) = 880.00
0.75n + 722.50 = 880.00
0.75n = 157.50 . . . . . . . . . . . subtract 722.50
n = 210 . . . . . . . . . . . . . . . divide by 0.75. Number of non-cardholder tickets
578 -n = 368 . . . . . number of cardholder tickets
368 cardholder and 210 non-cardholder tickets were sold.
PLSS HELPPPP WILL GIVE BRAINLESSS A 22-foot ladder is resting against the side of a building. The bottom of the ladder is 3 feet from the building. Find the measure of the angle the ladder makes with the ground. Round your answer to the nearest tenth of a degree.
Answer:
The answer is 82.2
Step-by-step explanation
hope this helps
The sum of two numbers is is 49 and the difference between these two numbers is 9 what are these two numbers please show the workout
Step-by-step explanation:
x=29
y=20
that's the answer
O is the center if the regular polygon beloe. Find its perimeter. Round to the nearest tenth if necessary HURRY
Answer:
24.8 units
Step-by-step explanation:
Given
[tex]n = 10[/tex] --- sides
The attached decagon
Required
The perimeter
The decagon is made up of 10 isosceles triangles.
The angle at the vertex of each is:
[tex]Angle = \frac{360}{10}[/tex]
[tex]Angle = 36[/tex]
Next, we create a right-angled triangle from the shape (see attachment)
[tex]\theta[/tex] is calculated as:
[tex]\theta = \frac{Angle}{2}[/tex]
[tex]\theta = \frac{36}{2}[/tex]
[tex]\theta = 18[/tex]
Next, calculate x using:
[tex]\sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
So, we have:
[tex]\sin(18) = \frac{x}{4}[/tex]
Make x the subject
[tex]x = 4 * \sin(18)[/tex]
[tex]x = 1.24[/tex]
So, the length (L) of one side of the decagon is:
[tex]L = 2x[/tex]
[tex]L = 2 * 1.24[/tex]
[tex]L = 2.48[/tex]
The perimeter (P) of the shape is:
[tex]P = 10 *L[/tex]
[tex]P = 10 * 2.48[/tex]
[tex]P = 24.8[/tex]
The perimeter of the given polygon rounded to the nearest tenth is; 24.7
What is the perimeter of the Polygon?
The given polygon as we can see has 10 sides.
Now, when we draw a line from the center to the next vertex to the left of the one currently having a line, we will see that the angle can be calculated as; 360/10 = 36° because sum of exterior angles of a polygon sums up to 360°.
Thus, the other two angles will be; (180 - 36)/2 = 72° each
Using sine rule, we can find the length of a side of the polygon as;
x/sin 36 = 4/sin 72
x = (4 * sin 36)/sin 72
x = 2.472
Thus, perimeter = 2.472 * 10 = 24.72 ≈ 24.7
Read more about perimeter at; https://brainly.com/question/397857
There are 165 children taking swimming lessons at the pool. If 10 children will be assigned to each instructor, how many instructors are needed?
Answer:
17 instructors
Step-by-step explanation:
If each instructor will get 10 children, we have to divided the total number of children taking swimming lessons by the number of children assigned to each instructor (10):
165/10 = 16.5
Unfortunately, we can't have 16 and a half instructors. Since 5 children are remaining, we can round up 16.5 to 17 and get 17 instructors. This implies that 16 instructors will teach 10 children (160 in total) and 1 instructor will teach 5 children (5 in total). 160+5 = 165 total children.
IF D and G are the number of degrees and grades of the same angle, prove that G/10=D/9.
Answer:
see explanation
Step-by-step explanation:
The relationship between D and G is
90D = 100G
that is there are 100 grades in 90°
Given any angle in degrees (D)
Divide by 90 to find how many right angles
Then multiply by 100 to convert to grades , so
G = [tex]\frac{D}{90}[/tex] × 100 = [tex]\frac{10}{9}[/tex] D ( multiply both sides by 9 to clear the fraction )
9G = 10D ( divide both sides by 10 )
[tex]\frac{9G}{10}[/tex] = D ( divide both sides by 9 )
[tex]\frac{G}{10}[/tex] = [tex]\frac{D}{9}[/tex]
Suppose 1 in 5 (1/5) JWU students own their own car. If four students are randomly selected, what is the probability that all four own their car?
Answer:
1/625 = 0.0016
Step-by-step explanation:
update, oh sorry, this is about 4 picks and not 5.
so, it is 1/5⁴ = 1/625 = 0.0016
1 in 5 own their own car.
that is 20% or a chance of 1/5 = 0.2 of picking a student owning a car.
let's assume that the total number of students is large enough that each pick does not change the individual probabilities.
each event (picking a student and checking the ownership of a car) is independent and non-overlapping.
so, the probability that all 5 own a car is the chance of picking the 5th student owning a car AND all 4 previous student picks owning a car.
the probability that all 4 previous picks own a car is the chance of picking the fourth student owning a car AND all 3 previous student picks owning a car.
the probability that all 3 previous picks own a car is the chance of picking the third student owning a car AND all 2 previous student picks owning a car.
the probability that all 2 previous picks own a car is the chance of picking the second student owning a car AND the previous student pick owning a car.
the probability that the first student pick owns a car is 1/5 or 0.2
so, we have a clean
1/5×1/5×1/5×1/5×1/5 = 1/5⁵ probability = 1/3125 = 0.00032
Please help I don’t know the answer
The last option is none of the above
Answer:
The two lines are:
y=x+2 and y=-2x+6
Dotted lines represent < or >, whereas the opposite is true for solid lines.
So the correct answer is the first option.
Hope this helps!
please help me with both questions
Answer:
(b) 829 seconds
(c) 13.8 minutes
Step-by-step explanation:
(b) 2.48×10⁸/2.99×10⁵ = 829 seconds
(c) 829/60 = 13.8 minutes
HELP PLEASE!!!
Oak wilt is a fungal disease that infects oak trees. Scientists have discovered that a single tree in a small forest is infected with oak wilt. They determined that they can use this exponential model to predict the number of trees that will be infected after t years.
f(t)=e^0.4t
Question:
Rewrite the exponential model as a logarithmic model that calculates the # of years, g(x) for the number of infected trees to reach a value of x.
The logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
-------------
We are given an exponential function, for the amount of infected trees f(x) after x years.To find the amount years needed for the number of infected trees to reach x, we find the inverse function, applying the natural logarithm.-------------
The original function is:
[tex]y = f(x) = e^{0.4x}[/tex]
To find the inverse function, first, we exchange y and x, so:
[tex]e^{0.4y} = x[/tex]
Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So
[tex]\ln{e^{0.4y}} = \ln{x}[/tex]
[tex]0.4y = \ln{x}[/tex]
[tex]y = \frac{\ln{x}}{0.4}[/tex]
Thus, the logarithmic model is:
[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]
A similar question is given at https://brainly.com/question/24290183
Determine if the described set is a subspace. Assume a, b, and c are real numbers. The subset of R3 consisting of vectors of the form [a b c] , where at most one of a , b and c is non 0.
The set is a subspace.
The set is not a subspace.
If so, give a proof. If not, explain why not.
Answer:
Not a subspace
Step-by-step explanation:
(4,0,0) and (0,4,0) are vectors in R3 with zero or one entries being nonzero, but their sum, (4,4,0) has two nonzero entries.
Round 5,821 to the nearest thousands place:
Answer:
6000 hope this helps
if the question is 5,422 then the round figure is 5000
but the question is 5,821 its above 5500 will be 6000
Question
Find the volume of a cone with a height of 9 centimeters and a radius of 5 centimeters.
Use 3.14 to approximate pi, round your answer to the nearest hundredth if necessary, and do not include units.
Answer:
235.5
Step-by-step explanation:
Substitute the values into the equation [tex]V=\pi r^2 \frac{h}{3}[/tex], which is the formula for finding the volume of a cone.
[tex]V=(3.14)(5^2)\frac{(9)}{3}[/tex]
Simplify.
[tex]V=(3.14)(25)(3)[/tex]
Simplify again.
[tex]V=(78.5)(3)[/tex]
Simplify for the last time.
[tex]V=235.5[/tex]
Note, using 3.14 will give you 235.5, but if you use the [tex]\pi[/tex] button on a scientific calculator, your answer will be 235.62. Given the constraints of the problem, your best bet will be 235.5.
From quadrilateral ABCD is a quadrilateral with area of 48 square units, find the length of AC.
A. 48/5
B. 24
C. 24/5
D. 48
Step-by-step explanation:
I do hope that you understand through the steps in the attachment, if not kindly reach out!
Police estimate that 25% of drivers drive without their seat belts. If they stop 6 drivers at random, find theprobability that more than 4 are wearing their seat belts.
Answer:
%17.80
Step-by-step explanation:
17.8% is the probability that more than 4 are wearing their seat belts.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that Police estimate that 25% of drivers drive without their seat belts.
If they stop 6 drivers at random we need to find the probability that more than 4 are wearing their seat belts.
For each driver stopped, there are only two possible outcomes. Either they are wearing their seatbelts, or they are not.
he drivers are chosen at random, which mean that the probability of a driver wearing their seatbelts is independent from other drivers.
Police estimate that 25% of drivers drive without their seat belts.
This means that 75% wear their seatbelts, so P=0.75
If they stop 6 drivers at random, find the probability that all of them are wearing their seat belts.
[tex]P(X=x)=C_{n,x} p^{x} (1-p)^{n-x}[/tex]
[tex]P(X=6)=C_{6,6} 0.75^{6} (1-0.75)^{0} =0.1780[/tex]
Hence, 17.8% is the probability that more than 4 are wearing their seat belts.
To learn more on probability click:
https://brainly.com/question/11234923
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which table shows a proportional relationship between x and y?
Answer:
Table C
Step-by-step explanation:
For x and y to be proportional , then the values of
[tex]\frac{y}{x}[/tex] = constant k
Table B
[tex]\frac{y}{x}[/tex] = [tex]\frac{6}{3}[/tex] = 2
[tex]\frac{y}{x}[/tex] = [tex]\frac{24}{6}[/tex] = 4
[tex]\frac{y}{x}[/tex] = [tex]\frac{36}{9}[/tex] = 4
The values are not constant
Table C
[tex]\frac{y}{x}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{y}{x}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
[tex]\frac{y}{x}[/tex] = [tex]\frac{6}{9}[/tex] = [tex]\frac{2}{3}[/tex]
These values are constant
Then Table C shows a proportional relationship between x and y
F(x)=-2x^2+4x+5
Find the critical numbers
Answer:
To find critical points, take the first derivative and set it equal to zero:
f(x) = -2x^2 + 4x + 5
f'(x) = -4x + 4
-4x+4 = 0
-4x = -4
x = 1
Critical point at x = 1
Alternatively, if you mean zeros, or where the x intersects, you can use the quadratic equation.
In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute. On
On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.
Test at 5% significance level on the typist’s claim.
Using the hypothesis test for one sample mean, There is NO SIGNIFICANT EVIDENCE to support the typist's claim
[tex]H_{0} = 45\\H_{1} < 45\\\\[/tex]
The test statistic :
T = (x - μ) ÷ (s/√(n))
T = (43 - 45) ÷ (15/√70)
T = - 2 ÷ 1.7928429
T = -1.12
At α = 0.05
Pvalue :
Degree of freedom, df = 70 - 1 = 69
Pvalue = 0.1333
Decision region :
Reject [tex]H_{0}[/tex] if Pvalue < α
0.1333 > 0.05
Since Pvalue > α We fail to reject the Null
Learn more on hypothesis testing: https://brainly.com/question/20262540
if a gallon of milk costs $2.49 how much will 3 1/2 gallons cost
