Answer:
sin (x) ≥ 0, between 0° and 180° or 0 and π,
sin(x) ≥ 1/2, between 30° and 150° or π/6 and 5π/6
Step-by-step explanation:
This is how I would do it. Subtract sin(x) from both sides
2[tex]sin^{2} (x)[/tex] - sin(x) ≥ 0 , then factor out sin(x)
sin(x) [2 sin(x) - 1] ≥0, then set each factor ≥ 0
sin(x) ≥ 0 and 2 sin(x) - 1 ≥ 0
sin (x) ≥ 0, between 0° and 180° or 0 and π
2 sin(x) ≥ 1
sin(x) ≥ 1/2, between 30° and 150° or π/6 and 5π/6
7^8 ÷ 7^y = 7^6 Find the value of y
Answer:
[tex]\boxed{\df \ \ \ y = 2 \ \ \ }[/tex]
Step-by-step explanation:
We need to solve the following
[tex]\dfrac{7^8}{7^y}=7^6[/tex]
that we can write
[tex]\dfrac{7^8}{7^y}=7^8*7^{-y}=7^{8-y}=7^6\\<=> 8-y = 6\\<=> y=8-6=2[/tex]
so the answer is 2
Answer:
[tex]y=2[/tex]
Step-by-step explanation:
[tex]7^8 \div 7^y = 7^6[/tex]
Apply the law of exponents.
[tex]7^{8-y}= 7^6[/tex]
Cancel the same bases.
[tex]8-y=6[/tex]
Subtract 8 on both sides.
[tex]-y=6-8[/tex]
[tex]-y=-2[/tex]
Cancel negative signs.
[tex]y=2[/tex]
A boy was watching the show standing on the ground. A jet fighter when 1000m high passes vertically above an other jet fighter at an instant, when the angle of elevation of the two jets from the boy are 60 degrees and 45 degree respectively. At what distance (vertical) the pilots were flying the jets at that instant
Answer:
The pilot above at 1000m above ground and pilot below 742.23 metres above ground
Step-by-step explanation:
Imagine everything as triangles. Mark where the boy stands and the 2 jets are in the air
Anyone know this ? Please help
Answer:
3018
Step-by-step explanation:
an = a1 + (n-1)d
a1 is the first term in the sequence = 24
n is the term number which is 500
d is the common difference
Take the second term and subtract the first term to find the common difference
d = 30-24 = 6
a500 = 24 + (500-1) *6
=24+ 499*6
=24 + 2994
=3018
Answer:
3018 is the correct answer.
Shelly biked 21 miles in 4 hours. What is shelly's average speak in miles per hour? What is shelly's average speed in miles per hour?
Answer:
5 1/4 mph
Step-by-step explanation:
21 divided by 4= 5 1/4
Answer:
Average Speed = 5.25 mph
Step-by-step explanation:
Given:
Distance = 21 miles
Time = 4 hours
Required:
Average Speed
Formula:
Average Speed = Total Distance Covered / Total Time Taken
Solution:
Average Speed = 21/4
Average Speed = 5.25 mph
What is the y-intercept of the graph below?
Answer:
C
Step-by-step explanation:
The y-intercept is where the line passes through the y-axis
On this graph, we can see this is at the point (0, 2)
Answer:
(0,2)
Step-by-step explanation:
The y intercept is where the graph crosses the y axis ( where x =0)
The graph crosses at y=2
(0,2)
How can a triangular prism have a greater volume than a rectangular prism?
Answer:
Step-by-step explanation:
Assume that the two prisms have bases of equal area.
Then the volume of the rectangular prism is V = (base area)(height).
The volume of the triangular prism is V = (1/3)(base area)(height)
We could compare the two volumes by creating the ratio inequality
(1/3) (base area)(t-height)
------------------------------------------
(base area)(r-height)
The triangular prism will have the greater volume for (1/3)((t-height) > r-height.
Calculate 85% of 2 500m
Answer:
Step-by-step explanation:
85% of 2500 m
= 85/100 × 2500 = 2125 m
hope this helps
plz mark it as brainliest!!!!!!
Answer:
2125
Step-by-step explanation:
85% times 2500
Find the fifth term in the sequence that is defined as follows:
Answer : The fifth term in the sequence is -2.
Step-by-step explanation :
As we are given that the expression to calculate the [tex]n^{th}[/tex] term.
The expression is as follows:
[tex]a_n=2(-1)^n[/tex]
where,
n is the number of term
Given:
n = 5
Now putting the value of n in the above expression, we get:
[tex]a_n=2(-1)^n[/tex]
[tex]a_5=2(-1)^5[/tex]
[tex]a_5=2\times (-1)[/tex]
[tex]a_5=-2[/tex]
Therefore, the fifth term in the sequence is -2.
Let p, q be the solutions of the quadratic equation x^2 − 2mx − 5n = 0 and let m, n be the solutions of x^2 − 2px − 5q = 0. If p,q,m and n are real and non-equal, then the value of p + q + m + n is ....
(A) 15
(B) 30
(C) 75
(D) 150
(E) 225
Answer:
The correct option is;
(B) 30
Step-by-step explanation:
The equations are;
x² - 2·m·x - 5·n = 0.............(1)
Solution = p, q
x² - 2·p·x - 5·q = 0..............(2)
Solution = m, n
For equation (1), we have;
x² - 2·m·x - 5·n = 0 = (x - p)·(x - q)
x² - 2·m·x - 5·n = x² -x·p - x·q + q·p = x² -x·(p + q) + q·p
2·m = p + q..............(3)
5·n = -q·p..............(4)
Given the similarity between equation (1) and (2), we have;
2·p = m + n..............(5)
5·q = -m·n..............(6)
Therefore;
m = (p + q)/2
n = -q·p/5
Substituting the value of m and n in equation (5) and (6), we have;
2·p = (p + q)/2 - q·p/5.............(7)
5·q = (p + q)/2·q·p/5.............(8)
Making q the subject of equation (7) gives;
[tex]q = \dfrac{-7.5 \cdot p}{p -2.5}[/tex]
Substituting the value of q above in equation (8) gives;
[tex]-\dfrac{75\cdot p}{2\cdot p-5}=-\dfrac{3\cdot p^{4}-30\cdot p^{3}}{4\cdot p^{2}-20\cdot p+25}[/tex]
By cross multiplying and collecting like terms we have;
6·p⁵ -75·p⁴-150·p³+1500·p²-1875·p = 0
Which gives
(p+0)(p-1.91)(p-2.5)(p+5)(p-13.1)
p = 1.91 or 2.5 or -5 or 13.1
q = 24.27 or undef or -5 or -9.27
m = 13.09 or undef or -5 or 1.95
n = -9.27 or undef or -5 or -24.29
Therefore, p + q + m + n = 1.91 + 24.27 + 13.09 + (-9.27) = 30
The correct option is (B) 30
what is the value of y?
please help !!
In how many ways can the letters in a word spoon be arranged?
14. Suppose that 1 out of every 10,000 doctors in a certain region is infected with the SARS virus; in the same region, 20 out of every 100 people in a particular at-risk population also are infected with the virus. A test for the virus gives a positive result in 99% of those who are infected and in 1% of those who are not infected. A randomly selected doctor and a randomly selected person in the at-risk population in this region both test positive for the disease. Who is more likely to actually have the disease?
Answer:
The person in the at-risk population is much more likely to actually have the disease
Step-by-step explanation:
The probability of a randomly selected doctor having the disease is 1 in 1,000 (P(I)=0.0001).
The probability that a doctor is infected with SARS, given that they tested positive is:
[tex]P(I|+)=\frac{P(I)*0.99}{P(I)*0.99+(1-P(I))*0.01}\\P(I|+)=\frac{0.0001*0.99}{0.0001*0.99+(1-0.0001)*0.01}\\P(I|+)=9.9*10^{-3}[/tex]
The probability of a randomly selected person from the at-risk population having the disease is 20 in 100 (P(I)=0.20).
The probability that a person in the at-risk population is infected with SARS, given that they tested positive is:
[tex]P(I|+)=\frac{P(I)*0.99}{P(I)*0.99+(1-P(I))*0.01}\\P(I|+)=\frac{0.2*0.99}{0.2*0.99+(1-0.2)*0.01}\\P(I|+)=0.962[/tex]
Therefore, the person in the at-risk population is much more likely to actually have the disease
Which expression is equivalent to 9 p minus 3 p + 2? 8p
Answer:
6p - 2
Step-by-step explanation:
9p - (3p + 2) = 9p - 3p - 2 = 6p - 2
The expression that is equivalent to 9 p minus 3 p + 2 is 6p - 2
What is the expressionFrom the question, one have 9p - 3p + 2.
So, one has to combine the like terms, which means adding or subtracting the coefficients of the same variable. For the terms with 'p', one have 9p - 3p.
Combining the coefficients, one get 9 - 3 = 6.
So, 9p - 3p is simplifies to 6p.
So, one have 6p + 2.
The expression is said to be now simplified to 6p + 2.
Learn more about expression from
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Let x be a constant. The 5th term of an arithmetic sequence is a5=16x+11. The 9th term of the sequence is a9=28x+19. Find the first term of the sequence. Write your answer in simplest form
19
Step-by-step explanation:
The first term of the arithmetic sequence is 4x+3.
What is arithmetic sequence?An ordered group of numbers with a shared difference between each successive term is known as an arithmetic sequence.
The formula to find the nth term of an arithmetic sequence is,
aₙ= a+(n-1)d
Where a is the 1st term and d is the common difference.
Let the first term of sequence is a and the common difference is d.
Given that,
The 5th term of the arithmetic sequence = 16x+11,
⇒ a+4d= 16x+11 (1)
And the 9th term of the arithmetic sequence = 28x+19,
⇒ a+8d= 28x+19 (2)
To find the first term of the sequence, multiply equation (1) with 2 and subtract equation (2) from it.
(2a+8d)-(a+8d) = (32x+22) - (28x+19)
a = 4x+3
The first term of the arithmetic sequence is 4x+3.
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Which of the following are like radicals? Check all of the boxes that apply.
Answer:
3x√x²y, –12x√x²y, x√yx², 2√x²y.
Step-by-step explanation:
Data obtained from the question include:
3x√x²y, –12x√x²y, –2x√xy², x√yx²,
–x√x²y², 2√x²y
Like radical in this case talks about those havin the same entity in the square root.
With a careful consideration of the data obtained from the question, the like radicals are:
3x√x²y, –12x√x²y, x√yx², 2√x²y.
Like radicals are those whose entities in the square root are the same. So, from the given options like radicals are [tex]3x\sqrt{x^2y}[/tex], [tex]-12\sqrt{x^2y}[/tex], [tex]-12\sqrt{x^2y}[/tex] and [tex]2\sqrt{x^2y}[/tex].
Like radicals are those whose entities in the square root are the same. So, from the given options like radicals are:
A) [tex]3x\sqrt{x^2y}[/tex]
This is like radical with the entity [tex]x^2y[/tex] inside the square root.
B) [tex]-12\sqrt{x^2y}[/tex]
This is like radical with the entity [tex]x^2y[/tex] inside the square root.
C) [tex]-2x\sqrt{xy^2}[/tex]
This is not the like radical with the entity [tex]xy^2[/tex] inside the square root.
D) [tex]-12\sqrt{x^2y}[/tex]
This is like radical with the entity [tex]x^2y[/tex] inside the square root.
E) [tex]-x\sqrt{x^2y^2}[/tex]
This is not the like radical with the entity [tex]x^2y^2[/tex] inside the square root.
F) [tex]2\sqrt{x^2y}[/tex]
This is like radical with the entity [tex]x^2y[/tex] inside the square root.
So, the correct options are A), B), D), and F).
For more information, refer to the link given below:
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Solve the system of equations. 6x-5y=-32, -7x+8y=46
Answer:
x = -2
y = 4
Step-by-step explanation:
6x-5y=-32
-7x+8y=46
Solve for x in the first equation.
6x = -32 + 5y
x = (-32 + 5y) /6
x = 5/6y - 16/3
Put x as 5/6y - 16/3 in the second equation and solve for y.
-7(5/6y - 16/3) +8y = 46
-35/6y+112/3 +8y = 46
13/6y + 112/3 = 46
13/6y = 46 - 112/3
13/6y = 26/3
y = 26/3 × 6/13
y = 4
Put y as 4 in the first equation and solve for x.
6x-5(4)=-32
6x-20 = -32
6x = -32+20
6x = -12
x = -12/6
x = -2
The cost in dollars C(x), where x is the number of miles driven, of renting a car for a day is C(x)=1.95x+32. What is the independent variable and its units? ______ (dollars, miles, miles per dollar, or dollars per mile) - select the correct units What is the dependent variable and its units? ______ (miles or dollars) - select the correct units
Answer:
the independent variable is 32 (price of the car in dollars) as it stands alone without a variable and 1.95 is the dependent (cost per mile)
Answer 1 of the 2 questions in this picture in the next 5 min I’ll give you a lot of points please and thank you!
Answer:
B=264 b5/34 a576 5739 7985
Find the area of the circle.
Use 3.14 for pi
Answer:
A =153.86 cm^2
Step-by-step explanation:
The diameter is 14 so the radius is d/2 = 14/2 = 7
A = pi r^2
A = (3.14) (7)^2
A =153.86 cm^2
Answer:
Step-by-step explanation:
First you take the diameter and cut it in half to find the radius. 14/2 = 7
Next you times the radius to the power of 2. 7^2= 49
Then you times your answer by 3.14. 49*3.14 = 153.86
153.86cm² is your answer
Some red, white, and blue candies were placed in a bowl. Some contain nuts,
and some do not. Suppose one of the candies were chosen randomly from all
the candies in the bowl. According to the table below, if the candy is blue,
what is the probability that it does not contain any nuts?
Answer:
20%
Step-by-step explanation:
Answer:
40%
Step-by-step explanation:
Are the mean, median and mode of a list of numbers equal or no? Please explain!
Answer:
nope!
Step-by-step explanation:
mean= average, total of numbers/ amount of numbers
median- if all the numbers were in a line what would be in the middle
mode-most reoccuring number- remember it cos it rhymes with most :)
hope this helps :)
can u pls give brainliest? :)
Answer:
No
Step-by-step explanation:
when you have a list of numbers:
The mean is all of the numbers added up and then divided by the number of numbers.
The median is "the middle number" So line them up in numerical order and find the middle number.
The Mode is the biggest number subtracted from the smallest number.
Sue has 20 biscuits There are: 12 plain biscuits 5 chocolate biscuits 3 currant biscuits Sue takes two random biscuits Work out the probability that the two biscuits were not the same type
Answer:
58.43%
Step-by-step explanation:
The first thing we must do is calculate the probability of when both are equal, that is, take out two cookies of the same type, since we can calculate that they are not equal by means of their complement:
The probability that they are equal is:
P (plain, plain) = (12/20) (11/19)
= 132/380
P (chocolate, chocolate) = (5/20) (4/19)
= 20/380
P (currant, currant) = (3/20) (2/19)
= 6/380
The final probability would be the sum of these:
P (equal) = 132/380 + 20/380 + 6/380
P (equal) = 158/380
P (equal) = 0.4157
The probability that they are different is the opposite of the probability that they are equal, that is, the complement. Therefore, the probability that they are different is:
P (different) = 1 - 0.4157
P (different) = 0.5843
In other words, the probability would be 58.43%
What is the factorization of 729x15 + 1000?
Answer:
A
Step-by-step explanation:
can someone help me with this and explain me how to do it please :) ^
Answer:
x= 4
[tex]perpendicular (p) = \sqrt{x} + 1[/tex]
[tex]base(b) = 2 \sqrt{x} [/tex]
[tex]hypotenuse(h) = 2 \sqrt{x} + 1[/tex]
According to the Pythagoras Theoram,
p²+b²= h²
[tex] {( \sqrt{x } + 1) }^{2} + {(2 \sqrt{x} )}^{2} = {(2 \sqrt{x} + 1)}^{2} [/tex]
=>x+2√x+1+4x = 4x +4√x +1=> x = 4x - 4x +4√x- 2√x+ 1- 1=>x= 2√x=> x/√x = 2=> √x = 2Therefore, x= (√x)² = (2)² = 4Answer:
4
Step-by-step explanation:
2√x, √x + 1, 2√x + 1 sides of triangle
√x= y
2y, y+1, 2y+1
(2y)²+(y+1)²= (2y+1)²
4y²+y²+2y+1= 4y²+4y+1
y²-2y=0
y=0 (discarded as side can't be zero) or y= 2
so √x=2 ⇒ x= 4
Mrs. Hudson has made another assignment that Karen and Dakota are excited to try. To conduct your own experiment, you will need dice and a place to record your results. In this assignment, you will first calculate the theoretical probability for rolling a sum of 7. Then, you will roll the dice and add the numbers shown, recording your results as you go. Calculate the experimental probability for rolling a 7 after the 1st, 10th, and 100th rolls. Compare these results with the theoretical probability of rolling a sum of 7. How does this comparison change as the number of trials increase? 1. List out the sample space for the experiment and then calculate the theoretical probability. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________
I belive,
The experimental probability could be more, the same or less than the theoretical probability of rolling a 1 (which is 1/6).
The larger your sample (i. e., as you go beyond 60 tosses), the closer the two different probabilities are likely to be. (Think: Law of Large Numbers).
Answer:
Step-by-step explanation:
Jsiehsjsndj im here to get you a brainliest
What is the value of x? 10 PTS
Answer:
X=4
Step-by-step explanation:
Answer:
x = 4
Step-by-step explanation:
We can find the length of the hypotenuse of the 45 45 90 triangle using the other triangle (which is 30 60 90)
Since the hypotenuse is 8[tex]\sqrt{2}[/tex], the short leg (hypotenuse of other triangle) will be 4[tex]\sqrt{2}[/tex]
This means the value of x must be 4
A bakery's production is modeled by function f(x), where f(x) is the number of donuts made in a day and x is the number of bags of flour needed. Choose the ordered pair that represents a possible domain and range of the function.
(−1, 15)
(5, 92.75)
(10, 100)
(−5, 110.5)
A sequence is defined by the explicit formula an=3n+4 Which recursive formula represents the same sequence of numbers?
Answer:
Option (3)
Step-by-step explanation:
Explicit formula of the sequence is,
[tex]a_n=3^n+4[/tex]
From this explicit formula,
First term of the sequence will be,
[tex]a_1=(3^1)+4[/tex]
[tex]a_1=7[/tex]
Second term of the sequence,
[tex]a_2=(3^2)+4[/tex]
[tex]a_2[/tex] = 13
3rd term of the sequence,
[tex]a_{3}=(3^3)+4[/tex]
= 31
Sequence formed,
7, 13, 31 ..........
From the given options,
Recursive formula,
[tex]a_n=3a_{n-1}-8[/tex]
[tex]a_2=3(a_1)-8[/tex]
[tex]a_2=3(7)-8[/tex]
[tex]a_2=21-8[/tex] = 13
[tex]a_3=3a_2-8[/tex]
[tex]a_3=3a_2-8[/tex]
[tex]a_3=3(13)-8[/tex]
= 39 - 8
= 31
Sequence formed from this recursive formula will be,
7, 13, 31........
Therefore, Option (3) will be the answer.
Answer:
C
Step-by-step explanation:
i took the test
I NEED EVERY BODIES HELP ASAP!!!!!!!!!! the question is 15.6/-3
Answer:
-5.2
Step-by-step explanation:
15.6/-3= - 15.6/3= -5.2
I will mark you brainliest!!!! Which ordered pair is the best approximation of the solution?
Answer:
D
Step-by-step explanation:
We can substitute y = 2x + 1 in the second equation
2x + 1 = -7x + 8
Add 7x to both sides
9x + 1 = 8
Subtact 1 from both sides
9x = 7
x = 7/9
Substituing x in the first equation
y = 14/9 + 1
x rounds to 0.8
y rounds to 2.5