Answer:
x = 0, 2π/3, 4π/3
Step-by-step explanation:
2 cos(2x) − 2 cos x = 0
Use double angle formula.
2 (2 cos²x − 1) − 2 cos x = 0
Simplify.
4 cos²x − 2 − 2 cos x = 0
2 cos²x − 1 − cos x = 0
2 cos²x − cos x − 1 = 0
Factor.
(cos x − 1) (2 cos x + 1) = 0
Solve.
cos x = 1 or -½
x = 0, 2π/3, 4π/3
To solve this problem, we have to use trigonometric function in which we can use some trigonometric equations on this. The solutions to this equation is
[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
Trigonometric FunctionsWe would apply a simple mathematical rule here;
[tex]a(b+c)=ab+ac[/tex]
Let's substitute our functions and solve
[tex]2cos(2x)+2cosx=0\\2(2cos^2x-1)+2cosx=0\\4cos^2x-2+2cosx=0\\2cos^2x+cosx-1=0\\2cos^2x=2cosx-cosx-1=0\\2cos^2x+cosx-1=0\\[/tex]
We can solve the quadratic equation and get a solution to this problem.
[tex](cosx+1)(2cosx-1)=0[/tex]
Using factorization method,
[tex]cosx+1 = 0\\cosx = -1\\x = cos^-^1(-1)\\x = \pi[/tex]
The second solution is
[tex]2cosx-1=0\\2cosx=1\\cosx=\frac{1}{2} \\x = cos^-^1(\frac{1}{2} \\x = \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
From the above calculations, the solutions to this equation is
[tex]\pi , \frac{\pi}{3}, \frac{5\pi}{3}[/tex]
Learn more on trigonometric functions here;
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An item that regularly sells for $425 is marked down to $318.75. What is the
discount rate?
Answer: 25%
Step-by-step explanation:
[tex]\frac{425}{318.75}=\frac{100}{x}[/tex]
[tex]x=\frac{(318.75*100)}{425}\\x=75[/tex]
100-75=25
HELP FAST PLZ I HAVE LITTLE TIME I DONT WANT TO FAIL.
Given:
Given that the diameter of the circle is [tex]\frac{7}{2} \ cm[/tex]
We need to determine the radius, circumference in terms of π and circumference using π = 3.14.
Radius:
The radius of the circle can be determined using the formula,
[tex]r=\frac{d}{2}[/tex]
Substituting [tex]d=\frac{7}{2}[/tex], we get;
[tex]r=\frac{(\frac{7}{2})}{2}}[/tex]
Simplifying, we get;
[tex]r=\frac{7}{4} \ cm[/tex]
Thus, the radius of the circle is [tex]\frac{7}{4} \ cm[/tex]
Circumference in terms of π:
The circumference of the circle can be determined using the formula,
[tex]C=2 \pi r[/tex]
Substituting [tex]r=\frac{7}{4} \ cm[/tex], we get;
[tex]C=2 \pi (\frac{7}{4})[/tex]
[tex]C=\frac{7}{2} \pi \ cm[/tex]
Thus, the circumference in terms of π is [tex]\frac{7}{2} \pi \ cm[/tex]
Circumference using π = 3.14:
Substituting π = 3.14 in the circumference of the circle [tex]C=\frac{7}{2} \pi \ cm[/tex], we get;
[tex]C=\frac{7}{2}(3.14)[/tex]
[tex]C=10.99 \ cm[/tex]
Thus, the circumference of the circle is 10.99 cm
A hypothesis test was used to see if less than 5% of all Americans would still drive to work if gas prices went above $10.00 a gallon. The P-value for this test was 0.03. We can conclude that only 3% of all Americans would still drive to work if gas prices went above $5.00.True / False.
Answer:
The correct option is;
False
Step-by-step explanation:
Here, we note that the proportion of the test statistic which is used in the test is 5% and the P-value for the test is 0.03
The hypothesis test is meant to check if people will still drive to work when the gas prices are above $10.00 and the suggestion was that we can conclude that when the fuel price is above $5.00 everyone would still drive to work without a P-value for the test, hence we can not come to the stated conclusion.
You buy a ticket to the Warriors game for $409.20. You get the ticket and it says the
cost was originally sold for $62. What was the markup?
Jared made 4 bird houses in 3 days. How many days will work to make 20 bird houses?
Answer:
15 days
Step-by-step explanation:
We can use a ratio to solve
4 bird houses 20 bird houses
--------------------- = -------------------------
3 days x days
Using cross products
4x = 3*20
4x = 60
Divide each side by 4
4x/4 = 60/4
x = 15
15 days
Answer:
15 days
Step-by-step explanation:
i hope this help you
i have to find the answer if 33% of 21
Answer:
6.93 is you're answer.
Step-by-step explanation:
6.93/21 = 33%
What’s 20 times 1000
to answer this it's simple
the answer is 20,000
A researcher wishes to estimate, with 95% confidence, the proportion who own a laptop. A previous study shows that 70% of those interviewed had a laptop computer. How large a sample should the researcher select so that the estimate will be within 3% of the true proportion?
Answer:
The sample needs to be at least n = 897 in size.
Step-by-step explanation:
Given
Confidence Level = 95%
Let p = those who had laptop
p = 70% = 0.7
Margin of Error = 3% = 0.03
Let n = required sample.
To estimate the proportion of laptop owners with 95% confidence, first the z-value is calculated. [tex]z_{(a/2)}[/tex]
Given that confidence level = 95%
α = 1 − 95 %
α = 1 − 0.95
α = 0.05
So;
[tex]z_{(a/2)}[/tex] = [tex]z_{(0.05/2)}[/tex]
[tex]z_{(a/2)}[/tex] = [tex]z_{(0.025)}[/tex]
From the z table
[tex]z_{(0.025)} = 1.96[/tex]
Using formula for margin of error
[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]
where p + q =1
q = 1 - p
q = 1 - 0.7
q = 0.3
So,
[tex]M.E = z_{(0.025)} * \sqrt{\frac{pq}{n} }[/tex]
[tex]0.03 = 1.96 * \sqrt{\frac{0.7 * 0.3}{n} }[/tex] --- Make n the subject of formula
First, square both sides
[tex]0.03^{2} = 1.96^{2} * {\frac{0.7 * 0.3}{n} }[/tex] ------ Multiply both sides by [tex]{\frac{n}{0.03^{2}}}[/tex]
[tex]0.03^{2} * {\frac{n}{0.03^{2}}} = 1.96^{2} * {\frac{0.7 * 0.3}{n} } * {\frac{n}{0.03^{2}}}[/tex]
[tex]n = 1.96^{2} * {\frac{0.7 * 0.3}{0.03^{2}} }[/tex]
[tex]n = {\frac{0.806736}{0.0009} }[/tex]
[tex]n = 896.473[/tex]
Hence, the sample needs to be at least n = 897 in size.
A pizza chain records how long it takes customers to receive their delivery orders. Suppose the distribution of these delivery times is strongly skewed to the right with a mean of 30 minutes and a standard deviation of 10 minutes. Management plans on calculating the mean delivery time from a random sample of 25 orders. We can assume independence between orders in the sample.
What is the probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean?
Answer:
The probability that the mean delivery time from the sample of 25 orders xˉ is farther than 2 minutes from the population mean cannot be calculated.
Step-by-step explanation:
As given in the question statement, the distribution of delivery times is strongly skewed to the right. The population distribution is skewed to right. Too much skewed distribution can cause the statistical model to work ineffectively and affects its performance. The probability can also not be calculated because the sample size is too small. Small sample size affects the results and makes them less reliable because it results in a higher variability and likelihood of skewing the results.
Answer:
We cannot calculate this probability because the sampling distribution is not normal.
Step-by-step explanation:
Since the parent population is not normally distributed, the small sample size will result in a sampling distribution that isn't normal.
i need help with rhombus,rectangles and squares
Answer:
a= 11, b= 12
Opposite angles of parallelogram are equal.
m<D = m<B
9b-2=106°
9b= 108°
b= 12°
Sum of the adjacent angles of a parallelogram = 180°
m<B+m<C = 180°
106°+7a-3=180°
7a = 180°-106°+3
7a=77°
a= 11°
x^2+3x−4=0 Solve for x. Write the smaller solution first, and the larger solution second.
smaller x=
larger x=
Answer:
smaller x: -4
larger x: 1
Step-by-step explanation:
We need to factor this. In order to do so, we need to find factor pairs of the coefficient of x^2 (which is 1 in this case) and of the constant (-4 in this case) such that they add up to 3.
Here, the factors of 1 are obviously just 1 and 1. The factors of -4 are (1, -4), (-1, 4), and (2, -2). Notice that 1 * 4 + 1 * (-1) = 3, so we know that our factor pair from 1 is (1, 1) and our factor pair from -4 is (-1, 4).
Then, we factor this quadratic into: (x - 1)(x + 4) = 0. Now, solve for x by setting each of these two factors equal to 0:
x - 1 = 0 ⇒ x = 1
AND
x + 4 = 0 ⇒ x = -4
So, the solutions are x = -4 and x = 1.
Hope this helps!
Answer:
smaller x= -4
larger x= 1
Step-by-step explanation:
x² + 3x - 4 = 0
x² + 4x - x - 4 = 0
x(x + 4) - (x + 4) = 0
(x - 1)(x + 4) = 0
x = -4, 1
To gain access to his account, a customer using an automatic teller machine (ATM) must enter a four-digit code. If repetition of the same four digits is not allowed (for example 5555), how many possible combinations are there?
Final answer:
The number of possible four-digit PIN combinations for an ATM, where no repetition of the same four digits is allowed, is 5040. This is calculated by multiplying the number of choices for each digit position, which are 10, 9, 8, and 7 respectively.
Explanation:
Calculating ATM PIN Code Combinations
To determine the number of possible four-digit PIN combinations for an ATM that does not allow the repetition of the same four digits (such as 5555), we have to consider how many choices we have for each digit. Since there are 10 possible digits (0-9) for each placement and repetition of the same four digits is not allowed, the first digit can be any of the 10 digits, the next digit can also be any of the 10 digits (except for the first digit), and so on.
The number of combinations can be calculated using factorial notation. For the first digit, there are 10 possibilities. For the second digit, there are 9 remaining possibilities (since the digit cannot be the same as the first), for the third digit, there are 8 possibilities, and for the fourth digit, there are 7 possibilities.
The calculation then becomes 10 x 9 x 8 x 7, which equals 5040 possible combinations. This shows that there are numerous ways to create a unique four-digit code without repeating the same digit four times.
The distribution of the scores on a standardized math exam in a school district is skewed to the right. Which of the following statements is true about this distribution? Please hurry it is a timed test
Answer:
If the distribution is skewed right, then the mode is greater than the mean.
Step-by-step explanation:
There's a graph below that I hope will help!
The true statement is that the mode of the scores is greater than the mean score
How to determine the true statement?From the question, we understand that:
The distribution is skewed to the right
For a right skewed distribution, the mean value is lesser than the mode value
i.e. mean < mode or mode > mean
Hence, the true statement is that the mode of the scores is greater than the mean score
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Which concept is used to prove that the opposite sides of a parallelogram are congruent?
congruent rectangles
similar rectangles
congruent triangles
similar triangles
1 Intro
Done
Answer:
congruent triangles
Step-by-step explanation:
You can eliminate useless answers based on their wording. "Similar" anything cannot be used to prove congruence. "Rectangles" will not help you prove congruence of parallelogram sides. The only reasonable choice is ...
congruent triangles
_____
Typically, a diagonal is drawn through the figure, and the two triangles created are shown to be congruent, often by ASA. Then, by CPCTC, sides of the parallelogram are shown to be congruent.
Answer: congruent
Step-by-step explanation:
For what values of x is x2-36=5x true?
Answer:Its B. -4 and 9
Step-by-step explanation:
Answer:
x = - 4, x = 9
Step-by-step explanation:
Given
x² - 36 = 5x ( subtract 5x from both sides )
x² - 5x - 36 = 0 ← in standard form
Consider the factors of the constant term (- 36) which sum to give the coefficient of the x- term (- 5)
The factors are - 9 and + 4, since
- 9 × 4 = - 36 and - 9 + 4 = - 5, thus
(x - 9)(x + 4) = 0
Equate each factor to zero and solve for x
x + 4 = 0 ⇒ x = - 4
x - 9 = 0 ⇒ x = 9
define these terms
social reform
predestination
revival
Answer:social reform:is a kind of social movement that aims to make gradual change, or change in certain aspects of society, rather than rapid or fundamental changes.
predestination:The act of predestining or the condition of being predestined. revival:is an act or instance of reviving or the state of being revived.
Answer:
Social Reform: A kind of social movement that aims to make gradual change, or change in certain aspects of society, rather than rapid or fundamental changes.
Predestination: The act of predestining or the condition of being predestined.
Revival: An act or instance of reviving or the state of being revived.
You have a bag of 12 marbles. Six are blue, two are green, three are yellow, and one is red. If you reach into the bag and pull out one marble, what is the probability that it will be yellow?
Answer:
1/4 or 25%
Step-by-step explanation:
Given that:
blue marbles : 6 green marbles : 2yellow marbles: 3red marble: 1Total marbles: 12If you reach into the bag and pull out one marble, so the probability that it will be yellow is:
P (Yellow) = Number of yellow marbles in the bag / Number of marbles in the bag
= 3/12
= 1/4 or 25%
Hope it will find you well.
A class of 25 students shares a class set of 100 markers. On a day with 5 students absent, which statement is true?
A
For every 5 students, there is 1 marker.
B
For every 4 students, there is 1 marker.
C
For each student, there are 4 markers.
D
For each student, there are 5 markers.
Answer:
D
Step-by-step explanation:
Answer:
D. For each student, there are 5 markers.
Step-by-step explanation:
A class of 25 students shares a set of 100 markers.
5 students are absent.
Therefore,
No. of students present = 25 - 5 = 20
No. of markers = 100
No. of markers each student gets = 100/20 = 10/2 = 5
Hence, each student gets 5 markers.
i really need helppppp
Could it be a im doing the same thing
Answer: A which is x=-3
Step-by-step explanation:
You put 2x to the left hand side which makes it a negative. Then you move the 5 to the other side since 2x has a variable and 5 doesn't. You need to put one side of the equation with a variable and one not. Then 5 becomes -5 because you move it over. So it will be 6x-2x= - 7- 5.Then subtract 6x and 2x which is 4x. -7 subtract -5 equals -12. Divide -12 and 4 which makes it -x=3.
Solve the system of equations. -10y+9x=-9
10y+5x=-5
by the use of elimination method
make all coefficients of subject to be eliminated similar..by multiplying the coefficients with one another
for eqn(i)
5(-10y+9x=-9)
-50y+45x=-45
for eqn(ii)
9(10y+5x=-5)
90y+45x=-45
-50y+45x=-45
90y+45x=-45
...subtract each set from the other...
we get
-140y+0=0
y=0
from eqn(i)
10y+5x=-5
0+5x=-5
x= -1
SAT Scores 1510 1480 2100 1800 1300 1250 1400 1430 1390 1520 The SAT scores for a group of 10 students are shown. What is the mean absolute deviation of the group (round to the nearest tenth)
The mean absolute deviation of the group of SAT scores is approximately 169.8.
To find the mean absolute deviation (MAD) of the group of SAT scores, we follow these steps:
1. Calculate the mean (average) of the scores.
2. Find the absolute deviation of each score from the mean.
3. Calculate the mean of these absolute deviations.
Let's proceed with the calculations:
1. Calculate the mean:
[tex]\[ \text{Mean} = \frac{1510 + 1480 + 2100 + 1800 + 1300 + 1250 + 1400 + 1430 + 1390 + 1520}{10} \][/tex]
[tex]\[ \text{Mean} = \frac{14,580}{10} \][/tex]
[tex]\[ \text{Mean} = 1458 \][/tex]
2. Find the absolute deviation of each score from the mean:
[tex]\[ \text{Absolute deviations: } |1510 - 1458| = 52, |1480 - 1458| = 22, |2100 - 1458| = 642, |1800 - 1458| = 342, \][/tex]
[tex]\[ |1300 - 1458| = 158, |1250 - 1458| = 208, |1400 - 1458| = 58, |1430 - 1458| = 28, |1390 - 1458| = 68, |1520 - 1458| = 62 \][/tex]
3. Calculate the mean of these absolute deviations:
[tex]\[ \text{MAD} = \frac{52 + 22 + 642 + 342 + 158 + 208 + 58 + 28 + 68 + 62}{10} \][/tex]
[tex]\[ \text{MAD} = \frac{1698}{10} \][/tex]
[tex]\[ \text{MAD} = 169.8 \][/tex]
Therefore, the mean absolute deviation of the group of SAT scores is 169.8 (rounded to the nearest tenth).
The mean absolute deviation of the group of SAT scores is 162 (rounded to the nearest tenth).
To find the mean absolute deviation (MAD) of a set of data, you first need to calculate the mean (average) of the data, then find the absolute difference between each data point and the mean, and finally, calculate the average of these absolute differences.
Calculate the mean of the given SAT scores: (1510 + 1480 + 2100 + 1800 + 1300 + 1250 + 1400 + 1430 + 1390 + 1520) / 10 = 14660/10
= 1466
Calculate the absolute deviation of each score from the mean: |1510 - 1466|, |1480 - 1466|, and so on.
This gives - 44+14+634+334+166+216+66+36+76+54
= 1620
Calculating MAD -
= 1620/10
= 162
The mean absolute deviation of the group of SAT scores is 162 (rounded to the nearest tenth).
Which triangle shows the incenter at point A?
The Images are placed in order A- D
Answer:
B
Step-by-step explanation:
the incenter is found by constructing angle bisectors and then intersecting the three angle bisectors.
20 = r + 11
Solve the equation.
Answer: r = 9
Step-by-step explanation:
Simplifying
20 = r + 11
Reorder the terms:
20 = 11 + r
Solving
20 = 11 + r
Solving for variable 'r'.
Move all terms containing r to the left, all other terms to the right.
Add '-1r' to each side of the equation.
20 + -1r = 11 + r + -1r
Combine like terms: r + -1r = 0
20 + -1r = 11 + 0
20 + -1r = 11
Add '-20' to each side of the equation.
20 + -20 + -1r = 11 + -20
Combine like terms: 20 + -20 = 0
0 + -1r = 11 + -20
-1r = 11 + -20
Combine like terms: 11 + -20 = -9
-1r = -9
Divide each side by '-1'.
r = 9
Simplifying
r = 9
Answer:
r=9
Step-by-step explanation:
Step 1: Flip the equation
r + 11 = 20
Step 2: Subtract 11 from both sides
r + 11 - 11 = 20 - 11
A ball is thrown into a lake, creating a circular ripple that travels outward at a speed of 5 cm per second. Express the area, A. of the circle in terms of the number of seconds, t, that have passed since the ball hits the lake. A = 25t A = 2576 A = Ar? A = 5t? None of the above
Answer:
The area of the circular ripple after t second is
A =25π t²
where A is in cm².
Step-by-step explanation:
Given that,
Circular ripple that travels outward at a speed of 5 cm per second.
It means that, the radius of the circular ripple increases at a seed 5 cm/ s.
Therefore the radius of the circular ripple after t seconds is
r(t)= 5t
where r(t) is in cm.
We know ,
The area of a circular object is = π r²
The area of the circular ripple after t second is
A= π(5t)²
=25πt²
where A is in cm².
The area, A. of the circle in terms of the number of seconds, t, that have passed since the ball hits the lake is A(t)= 25t²π
The formula for calculating the area of the circular ripple as a function of time is expressed as:
A(t) = πr(t)²
Given that the ripple travels outward at a speed of 5 cm per second, hence;
r(t) = 5tcm/s
Substitute the radius into the formula to have:
A(t) = π(5t)²
A(t)= 25t²π
Hence the area, A. of the circle in terms of the number of seconds, t, that have passed since the ball hits the lake is A(t)= 25t²π
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Find the domain of the following function:
y = x^3 − 8
________
x^2 + 5x + 6
Select the appropriate response:
A) domain: x cannot equal −3, −2
B) domain: x equals −3, −2
C) None of the above
Help please! 40 points!
Answer:
The answer is C.
Step-by-step explanation:
You can do it by solving both equations :
y = x³ - 8
Let y=0,
x³ - 8 = 0
x³ = 8
x = ³√8
= 2
x² + 5x + 6 = 0
(x+3)(x+2) = 0
x = -3
x = -2
So the domain for 1st equation is 2 and 2nd equation is -2 & -3.
In 1st equation, the answer cannot be option A & B and in 2nd equation, the answer is B.
Answer:
A) domain: x cannot equal −3, −2
Step-by-step explanation:
y = x^3 − 8
________
x^2 + 5x + 6
The function is undefined when the denominator goes to zero
x² + 5x + 6 = 0
x² + 3x + 2x + 6 = 0
x(x + 3) + 2(x + 3) = 0
(x + 2)(x + 3) = 0
x = -3, -2
Domain can take any value except -2 and -3
Help please
This question is stressing me out
Answer:
Maximum: C= 6(5) + 2y or C= 30 + 2y
Step-by-step explanation:
X can be greater than or equal to 0, but can also be less than or equal to 5.
Y is greater than or equal to 0.
4 times x then subtracted by y is greater than or equal to 1.
Since X can't go higher than 5, the maximum is 5.
Y can be anything since it can be greater than or egual to 0 and either way it would be greater than one.
I hope I could help!
The High Roller wheel in Las Vegas has a diameter of 520 feet and its base is 30 feet off the ground. You board a gondola on the wheel and rotate 240 degrees counterclockwise before the wheel temporarily stops. How high above the ground are you when the wheel stops?
Answer:
420 feet
Step-by-step explanation:
GIVEN: The High Roller wheel in Las Vegas has a diameter of [tex]520[/tex] feet and its base is [tex]30[/tex] feet off the ground. You board a gondola on the wheel and rotate [tex]240[/tex] degrees counterclockwise before the wheel temporarily stops.
TO FIND: How high above the ground are you when the wheel stops?
SOLUTION:
Consider the figure attached.
As wheel rotate counter clockwise [tex]240^{\circ}[/tex], its current position is [tex]120^{\circ}[/tex] clock wise.
Total height [tex]=260+30+h\rightarrow290+h[/tex]
Calculating value of [tex]h[/tex]
[tex]\sin 30^{\circ}=\frac{h}{260}\impliesh=260\sin30^{\circ}[/tex]
[tex]\implies h=260\times\frac{1}{2}=130feet[/tex]
Total height [tex]=290+130[/tex] feet
[tex]=420\text{ feet}[/tex]
Hence total height is 420 feet
Which is a quadratic function?
f(x) = 2x + x + 3
f(x) = 0x2 – 4x + 7
f(x) = 5x2 – 4x + 5
Answer:
C. f(x)=5x^2-4x+5 is the correct answer on edge 2021
drop down 8x – 2 – 5x + 7 =
Answer:
3x + 5
Step-by-step explanation:
Add like terms together:
8x - 2 - 5x + 7
3x - 2 + 7
3x + 5
The expression 15p+12r shows the total cost of buying p printed shirts and r plain shirts find the total cost if you buy two printed shirts and three plain shirts
In Mathematics, we use algebraic expressions to solve problems. In this case, substituting the numbers of printed and plain shirts into the given expression determines the total cost, which is 66.
Explanation:The subject of this question is in the discipline of Mathematics, specifically within algebraic expressions. The expression representing the total cost of buying shirts is 15p+12r, where p is the number of printed shirts and r is the number of plain shirts.
To find the total cost for buying two printed shirts and three plain shirts, we substitute p with 2 and r with 3 in the given expression.
So, the total cost becomes: 15*2 + 12*3 = 30 + 36 = 66. Therefore, the total cost of buying two printed shirts and three plain shirts is 66.
Learn more about Algebraic Expressions here:https://brainly.com/question/953809
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Final answer:
The total cost of buying two printed shirts and three plain shirts can be calculated by substituting into the expression 15p + 12r. The result is a total cost of $66.
Explanation:
The student is asking how to calculate the total cost of buying printed and plain shirts. The expression to find the total cost is given as 15p + 12r, where p is the number of printed shirts and r is the number of plain shirts. To find the total cost for two printed shirts and three plain shirts, we substitute p with 2 and r with 3 into the expression, which gives us:
Total Cost = 15(2) + 12(3)
Total Cost = 30 + 36
Total Cost = 66
Therefore, if you buy two printed shirts and three plain shirts, the total cost would be $66.