Answer:
pi/2 and 3pi/2
Step-by-step explanation:
on edge
The required solutions to sin(2x) = 2cos(x) are the following as : [tex]\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].
What are Trigonometric functions?Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.
The equation of trigonometry functions is given in the question:
sin(2x) = 2cos(x)
We have to determine the solution to the given trigonometry equation
As per the question, we have
⇒ sin(2x) = 2cos(x)
Rewrite the above trigonometry equation,
⇒ sin(2x) - 2cos(x) = 0
⇒ 2sin(x)cos(x) - 2cos(x) = 0
Common factor out from the equation,
⇒ 2cos(x)[sin(x) - 1] = 0
Solving each part separately
2cos(x) = 0 and sin(x) - 1 = 0
cos(x) = 0 and sin(x) = 1
[tex]\:x=\frac{\pi }{2}+2\pi n, and \:x=\frac{3\pi }{2}+2\pi n[/tex].
Thus, the required solutions to sin(2x) = 2cos(x) are the following: [tex]\:x=\frac{\pi }{2}+2\pi n,\:x=\frac{3\pi }{2}+2\pi n[/tex].
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Question 2 options: A consumer advocate group selects a random sample of 205 snack foods and finds that 174 of them contain more fat grams than what is indicated in the snack's nutritional information. Create a 90% confidence interval for the population proportion for snack foods that contain more fat grams that what is indicated in the snack's nutritional information.
Answer:
156 snack foods.
Step-by-step explanation:
205 - 174 = 31
To find 90% of 174, multiply 174 by 0.90.
174 x 0.90 = 156
The answer is 156 snack foods.
A recipe uses 150g butter, 500g sugar, and 100g currants to make 18 small cakes?
a. how many of each ingredient will be needed to make 6 dozen cakes
b. how many whole cakes could be made with 1kg of butter
Answer:
a. The following will be needed to make 6 dozen cakes:
Number of grams of butter needed = 600g
Number of grams of sugar needed = 2,000g
Number of grams of currants needed = 400g
b. The number whole that cakes could be made with 1kg of butter is still 18 whole cakes.
Step-by-step explanation:
a. how many of each ingredient will be needed to make 6 dozen cakes
This can be calculated as follows:
One dozen = 12
Number of small cakes in 6 dozen cakes = 6 * 12 = 72 small cakes
Number of 18 small cakes that can be obtained from 72 small cakes = 72 / 18 = 4
Therefore, we multiply each ingredient by 4 to obtain the number oof each ingredient that will be needed to make 6 dozen cakes as follows:
Number of grams of butter needed = 150 * 4 = 600g
Number of grams of sugar needed = 500 * 4 = 2,000g
Number of grams of currants needed = 100 * 4 = 400g
b. how many whole cakes could be made with 1kg of butter
Ordinary in terms of measurement, we have:
1kg = 1,000g
Since it is not indicated in the question that additional grams of other ingredients are made available, only 150g butter will be used out of the 1,000g butter made available together with already available 500g sugar and 100g currants to make just 18 cakes. This implies that no additional whole cakes will be made to add to the current 18 small cakes that is being made. Additional whole cakes would only be made when additional grants of sugar and currants are made available.
Therefore, the number whole that cakes could be made with 1kg of butter is still 18 small cakes.
evaluate 103 × 97 without directly multiplying
Answer:
9991
Step-by-step explanation:
103 × 97
(100 +3) (50+47)
get two number which you can add to get the value in the question
n then expand
100(50+47) +3(50+47)
5000+4700+150+141
9991
Margaret is making strawberry milkshakes for the kids party. The recipe calls for 1/3 of a cup of strawberry syrup to make 8 milkshakes. How many cups of Strawberry syrup are needed to make 48 milkshakes?
A.) 3
B.)2
C.)16
D.) 8
Answer:
B. The answer is 2 cups.
A radius of 8.5m what is the area
Answer:
22/7 * 8.5 * 8.5 = answer
Answer:
Step-by-step explanation:
A = π r² ≈ 3.14 × (8.5)² = 226.865 m²
find the slope and the y-intercept of 7x = 2y-4
Answer:
Slope: [tex]\frac{7}{2}[/tex]
Y-intercept: (0, 2)
Step-by-step explanation:
7x = 2y - 4
-2y = -7x - 4
y = [tex]\frac{-7}{-2}[/tex] x - [tex]\frac{4}{-2}[/tex]
y = [tex]\frac{7}{2}[/tex] x + 2
The slope is always the coefficient of x and the y-intercept is always the constant. It looks like (0, constant) when written in y-int form.
Answer:
slope (m) is 7/2 (aka 3.5) and y-int is (0,2)
Step-by-step explanation:
I don't really have an explanation, basically rearrange the problem so that to y is on the left but it would be 2y so divide the right side by two. I an explain further in depth if needed
Jen paid 26 cents for a mini bag of candy.She bought 4 bags of candy for herself and a friend.How much will she pay for the candy?
Answer: 1.04 I think
Step-by-step explanation:
Answer:
1.04
Step-by-step explanation:
26x4=104 and I put the decimal point in.
On a map , 1 inch represents 10 feet . How many inches would represent 35 feet .
Answer:
3 and a half inches or 3.50 inches
Step-by-step explanation:
if ten feet is 1 inch 30 feet would be 3 inches, 5 feet would make a half a inch since 10 feets divided by 2 is 5. one inch divided by 2 is 0.50 inches (or a half)
there for the answer is 3 and a half inches
Consider the equation 1.5x+4.5y=18. Where does the graph intersect the y-axis? *
Answer:
intersect y axis at (0,4)
Step-by-step explanation:
lemme know if u need work
HURRY!! At the snack bar, hot dogs cost $4 each and bottled water costs $2 each:
Answer: (2,1) (1,3)
Step-by-step explanation: Assume that the number of hot dogs is X and the number of water bottles is y.
Is 4/10 closer to 0, 1, 1/2
Answer:
1/2
Step-by-step explanation:
Divide the denominator in half
10/2 = 5
4 is close to 5 so 4/10 is close to 1/2
Answer:
4/10 is closer to 1/2.
Think of a pie. There are 10 slices total, but only 4 slices remain, because I ate them all! Do you think that 4 out of 10 slices would be closer to a whole pie or half a pie? It would be closer half a pie.
Further explanation:
If you were to round the number 44 to the closest ten, it would be 40. If you were to round 47 to he nearest ten, it would be 50. If you were to round 45 to the nearest ten, it would also be 50. I hope this helps!
Half (1/2) is the answer.
A garden is in the shape of a rectangle 90 m by 60 m.
Flowers are grown in 40% of the garden.
The rest of the garden is grass.
Work out the area of the garden that is grass.
Answer:
3240 sq meters
Step-by-step explanation:
Area of garden = 90*60= 5400 square meters.
Flowers grown on = 40%
So, grass grown on = (100 -40)% = 60%
60% of 5400 = 0.6*5400 = 3,240.
So, the area of the garden that is grass = 3,240 square meters
Sierra, an Event Planner for Hilton, has group medical insurance with an annual premium of $8,245. Her employer pays 74%. If she is paid semi monthly, a) what is her portion of the annual premium? b) her medical insurance deduction per pay period?
9514 1404 393
Answer:
$2,143.70$89.32Step-by-step explanation:
If 74% is paid by Hilton, then Sierra pays 26% of $8245 per year. Her annual share is ...
0.26 × $8245 = $2143.70 . . . Sierra's share
__
Then the deduction in each of her 24 pay periods is ...
$2143.70/24 = $89.32 . . . per pay period
For a given population of high school seniors, the Scholastic Aptitude Test (SAT) in mathematics has a mean score of 500 with a standard deviation of 100. Assume that the SAT scores are normally distributed. What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
b) between 450 and 675?
Answer:
The probability that a randomly selected high school senior's score on mathematics part of SAT will be
(a) more than 675 is 0.0401
(b)between 450 and 675 is 0.6514
Step-by-step explanation:
Mean of Sat =[tex]\mu = 500[/tex]
Standard deviation = [tex]\sigma = 100[/tex]
We will use z score over here
What is the probability that a randomly selected high school senior's score on mathe- matics part of SAT will be
(a) more than 675?
P(X>675)
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]
Z=1.75
P(X>675)=1-P(X<675)=1-0.9599=0.0401
b)between 450 and 675?
P(450<X<675)
At x = 675
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{675-500}{100}[/tex]
Z=1.75
At x = 450
[tex]Z=\frac{x-\mu}{\sigma}\\Z=\frac{450-500}{100}[/tex]
Z=-0.5
P(450<X<675)=0.9599-0.3085=0.6514
Hence the probability that a randomly selected high school senior's score on mathematics part of SAT will be
(a) more than 675 is 0.0401
(b)between 450 and 675 is 0.6514
Samir usually drink 3 cups of coffee in the morning how many liters of coffee does he drink round
Answer:
0.709765 liters
Step-by-step explanation:
Geometry please help!!!!!!!?
Answer:
It is same as the length of YX =8 inches so the length of VW=8 inches
rationalise the denominator and simplify
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Step-by-step explanation:
[tex] \bf \underline{Given-} \\ [/tex]
[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ [/tex]
[tex] \bf \underline{What\: to\: do-} \\ [/tex]
To rationalise the denominator
[tex] \bf \underline{Solution-} \\ [/tex]
[tex]\textsf{We have,}[/tex]
[tex] \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \\ \\ [/tex]
[tex]\textsf{The denominator is 5+2√3. Multiplying the numerator and denominator by 7-4√3,}\\[/tex]
[tex]\textsf{we get,}\\[/tex]
[tex] ⟹\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ [/tex]
[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 + 4 \sqrt{3} )(7 - 4 \sqrt{3}) } \\ \\ [/tex]
[tex]\textsf{⬤ Applying Algebraic Identity
(a+b)(a-b) = a² - b² to the denominator}\\[/tex]
[tex]\textsf{We get,}\\[/tex]
[tex]⟹ \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7 {)}^{2} - (4 \sqrt{3} {)}^{2} } \\ \\ [/tex]
[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 8 \sqrt{3 \times 3} }{49 - 48} \\ \\ [/tex]
[tex]⟹ \frac{35 + 14 \sqrt{3} - 20 \sqrt{3} - 24 }{1} \\ \\ [/tex]
[tex]⟹(35 - 24) - 6 \sqrt{3} \\ \\ [/tex]
[tex]⟹11 - 6 \sqrt{3} \: \: \: \tt \red{ Ans}. \\ \\ [/tex]
[tex] \bf \underline{Hence \:the \:denominator\: is\: rationalised.}\\[/tex]
archilles ordered a pizza with 16 slices every hour he ate half of the remaining slice
Answer:
so there is 8 slice left
Step-by-step explanation:
HELP I GIVE BRAINLIEST
Answer:
The answer is 15/19
Step-by-step explanation:
Both 60 and 76 are divisible by 4:
60/4 = 15 and 76/4 = 19
Final answer; 15/19
Which ordered pair would form a proportional relationship with the point graphed below?
(10.-20)
(-30, 20)
(-10,5)
(35, -20
Mr. Jones got four seats on the school's trip to Grand
Canyon for his students. In how many different ways Mr.
Jones can select a group of four from his class of 36?
Answer:
D. 58,905
Step-by-step explanation:
Number of seats available for Mr. Jones had for the trip = 4
Number of students in his class = 36
Number of ways he can select a group of 4 out of 36 students from his class is calculated as follows:
[tex] C \binom{36}{4} = \frac{36!}{(36 - 4)! * 4!)} [/tex]
[tex] = \frac{36!}{(32! * 4!)} = 58,905 [/tex]
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $20per foot, and the fencing for the east and west sides costs $10 per foot. If I have a budget of $200 for the project, what are the dimensions of the garden with the largest area I can enclose? HINT [See Example 2.]
ft (smaller value) ? ft (larger value)
ft2
Answer:
Length = [tex]5\ \text{ft}[/tex]
Breadth = [tex]5\ \text{ft}[/tex]
Step-by-step explanation:
Let [tex]x[/tex] be the length of the garden
and [tex]y[/tex] be the width of the garden
From the details of the cost in the question we get
[tex]20x+2\times (10y)=200\\\Rightarrow 20x+20y=200\\\Rightarrow x+y=\dfrac{200}{20}\\\Rightarrow x+y=10\\\Rightarrow y=10-x[/tex]
Now area of the garden is
[tex]A=xy\\\Rightarrow A=x(10-x)\\\Rightarrow A=10x-x^2[/tex]
Differentiating with respect to x we get
[tex]\dfrac{dA}{dx}=10-2x[/tex]
Equating with 0
[tex]0=10-2x\\\Rightarrow x=\dfrac{-10}{-2}\\\Rightarrow x=5[/tex]
Double derivative of the area is
[tex]\dfrac{d^2A}{dx^2}=-2<0[/tex]
So, area is maximum at [tex]x=5[/tex]
[tex]y=10-x=10-5\\\Rightarrow y=5[/tex]
So, the length and breadth of the rectangle is [tex]5\ \text{ft}[/tex].
Question 1 (1 point)
(05.01)
The graph of a system of equations will intersect at more than 1 point. (1 point)
a
Always
b
Sometimes
c
Never
Answer: Sometimes
Step-by-step explanation:
A system of equations can intersect at no points; this is when the lines are parallel, which means they have the same slope and different y-intercept.
A system of equations can intersect at one point; this is when the lines have different slopes.
A system of equations can intersect in infinitely many points; this is when the graphs overlay one another, which means they are graphs of the same line. The two equations would equal the same thing.
2. What is the place value of the 5 in 3562?
Answer:
Hundreds Place
Step-by-step explanation:
The 5 is in the hundreds place.
Hope this helps :D
3 is the thousands place
5 is the hundreds place
6 is the tens place
2 is the ones place
You tell me the answer.
Do you guys know this.
Answer:
0.77
Step-by-step explanation:
You solve the inner first, then move to the outer.
Plug in x = 20 for g(x) = [tex]\frac{2x+2}{x-6}[/tex]. It should give you [tex]\frac{42}{14}[/tex], which simplifies to 3.
You then need to solve f(x) with the given value from g(x), which is 3.
Plug in x = 3 for the equation [tex]\sqrt{0.4x^2-x}[/tex], and you should get [tex]\sqrt{0.6}[/tex].
The answer is roughly 0.77.
What number divided by−3 gives 12 as the result?
Answer:
-36
Step-by-step explanation:
x / (-3) = 12
x = 12*(-3)
x = -36
Rewrite −x−6 with a positive exponent. Assume x is not equal to zero.
A square has a perimeter of 72 cm what is the length of each side
Answer:
each side is 12 cm
Step-by-step explanation:
This is a simple equation, since a square is equal an all 4 sides, all you have to do it divide 72 by 4 to get your answer.
May I have brainliest please? :)
Solve the formula 5x + 2y = 19 for y
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]5x + 2y = 19[/tex]
Subtract sides 5x
[tex] - 5x + 5x + 2y = - 5x + 19[/tex]
[tex]2y = - 5x + 19[/tex]
Divide sides by 2
[tex] \frac{2y}{2} = \frac{ - 5x + 19}{2} \\ [/tex]
[tex]y = \frac{ - 5x}{2} + \frac{19}{2} \\ [/tex]
[tex]y = - \frac{5}{2} x + \frac{19}{2} \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
The solution of the equation 5x + 2y = 19 for the value of y is y = (-5 / 2)x + ( 19 / 2).
What is an expression?
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given expression is 5x + 2y = 19. The value of y will be calculated as:-
5x + 2y = 19
2y = 19 - 5x
y = ( 19 / 2 ) - ( 5x / 2 )
Therefore, the solution of the equation 5x + 2y = 19 for the value of y is y = (-5 / 2)x + ( 19 / 2).
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y-4=-x+7 in standard form.
Answer:
Step-by-step explanation:
x + y = 11