[tex]sin3( \alpha ) = 3 \sin( \alpha ) - 4 { \sin^{3} ( \alpha ) }[/tex]
[tex]2( 3 \sin( \ \frac{\pi}{18} ) - 4 { \sin^{3} ( \ \frac{\pi}{18} ) })[/tex]
[tex]2(sin3( \ \frac{\pi}{18} ))[/tex]
[tex]2( \sin( \frac{\pi}{6} ) )[/tex]
[tex]2 \times \frac{1}{2 } = 1[/tex]
Identify the symmetrical interval that includes 95% of the sample means for a population with a mean equal to 44 and a standard deviation equal to 9 using a sample size of 36
The lower bound of this interval is 51.08, and the upper bound is 58.92.
Given:
Mean = 44
Standard deviation = 9
n = 36
The formula for the confidence interval of the sample mean:
Confidence Interval = [tex]X \pm z * (\sigma / \sqrt n)[/tex]
For a 95% confidence level, the z-score is approximately 1.96.
Plugging in the values into the formula, we have:
Confidence Interval = 44 ± 1.96 * (9/ √36)
= 44 ± 1.96 * (9/ 6)
= 44 ± 1.96 * 1.5
= 44 ± 2.94
Therefore, the symmetrical interval that includes 95% of the sample means is (46.94, 41.06).
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By selling an exhaust fan for Rs. 1470, a man gains profit of 1/6 of its cost price. Find its cost price.
Answer:
₹245 is the cost
Step-by-step explanation:
Given:
Cost of the fan = ₹1470
1/6th = 1470/1 × 1/6
(do not cross multiply and simplify)
= ₹245
Answer:
Rs 1260
Step-by-step explanation:
let x be the cost price , then
x + [tex]\frac{1}{6}[/tex] x = 1470 , that is
[tex]\frac{7}{6}[/tex] x = 1470 ( multiply both sides by 6 to clear the fraction )
7x = 8820 ( divide both sides by 7 )
x = 1260
The cost price was Rs 1260
A store is having a sale in which all bookbags are discounted by `30\%`. Mai has a coupon for `\$5` off the regular price of one bookbag. The store first applies this coupon, and then takes `30\%` off the reduced price. If Mai pays `\$23.10` for the bookbag, what was the original price, `x`, before the sale and without the coupon?
Answer:
$35.56
Step-by-step explanation:
I think.....
;-;
The original price would be $38 before the sale and without the coupon.
Given that Mai offers a $5 off the regular price of one book bag coupon. The store first uses the discount, then deducts 30% off the lowered price.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
Let the original price would be x before the sale and without the coupon.
As per the given condition,
Since Mai pays $23.10 for the bookbag
⇒ (x -5) - 30% (x -5) = 23.10
⇒ (x -5) - 0.30(x -5) = 23.10
Apply the distributive property of multiplication,
⇒ x - 5 - 0.30x + 1.5 = 23.10
Rearrange the likewise terms and apply the arithmetic operation,
⇒ x - 0.30x = 23.10 + 5 - 1.5
⇒ 0.70x = 26.60
⇒ x = 29.60/0.70
⇒ x = 38
Therefore, the original price would be $38 before the sale and without the coupon.
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Explain Exponential growth and decay?
Answer:
Exponential growth is a mathematical development based on an exponential function that grows indefinitely. Exponential decay occurs in mathematical functions where the rate of change decreases and must thus reach a limit, which is the horizontal asymptote of an exponential function.
11 Triangle HJK is similar to triangle LMN.
H
11.25 cm
7.5 cm
4.5 cm
K
6 cm
9 cm
Which proportion can be used to calculate the length of LM in centimeters?
A
7.5
11.25
LM
4.5
LM
B
6
7.5
С
11.25
LM
4.5
7.5
D
9
LM
6
4.5
The length of side LM in the triangle LMN is 6.75 cm.
Similar figuresTwo figures are said to be similar if they are of the same shape and the ratio of their corresponding sides are in the same proportion.
From the diagram:
LM / HJ = JK / MN
LM / 4.5 = 9 / 6
LM = 6.75 cm
The length of side LM in the triangle LMN is 6.75 cm.
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Answer:
9/6 = LM/4.5
Epxlanation:
I go to K-12 and I did the test
Determine the center and radius of the following circle equation
We will see that this circle is centered at the point (-5, -49) and has a radius of 1.
How to work with the general circle equation?
For a circle of radius R centered at the point (a, b), the equation is:
(x - a)^2 + (y - b)^2 = R^2
In this case, we have:
x^2 + y^2 + 10x + 14y + 73 = 0
We can rewrite this as:
(x^2 + 10x) + (y^2 + 14y) + 73 = 0
(x^2 + 2*5*x + 25) + (y^2 + 2*7*y + 49) - 25 - 49 + 73 = 0
(x + 5)^2 + (y + 49)^2 -74 + 73 = 0
(x + 5)^2 + (y + 49)^2 = 1
So we have a circle centered at the point (-5, -49) with a radius equal to 1.
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circumference and area
To find the area of a circle: [tex]\pi r^2[/tex]
To find the circumference of a circle: [tex]\pi *d[/tex] or [tex]2\pi r[/tex]
The image attached below has more equations for circles.
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
-[tex]Kallmekris[/tex]
Zalia meets her friend at the science museum to see a special exhibition. The admission to the museum is $12. 50 per person plus tax. Zalia pays for herself and her friend. They have lunch at the museum’s cafe. Zalia has a sandwich for $5. 95, an apple for $1. 25 and a drink for $1. 69. She is charged tax and also tips her server 15%. If tax is 7. 25%, how much did Zalia pay all total for her day at the science museum? a. $41. 43 b. $37. 68 c. $36. 35 d. $24. 27 Please select the best answer from the choices provided A B C D.
Zalia paid all total for her day at the science museum is $41.43 including all taxes and tips and other expenses.
It is given that
Admission to the museum = $12.50 per person
Number of persons= 2
Sandwich charge = $5.95
Apple charge = $1.25
Drink charge = $1.69
Tax rate = 7.25%
Tip = 15%
What is the percentage?The percentage is value per hundred
Total amount without tax and tip(a)= 12.50*2+5.95+1.25+1.69 = $33.89
Tax(b) = 7.25% of $33.89 = 7.25*33.89/1000= $2.457025
Tip(c) = 15% of $33.89 = 15*33.89/100 = $5.0835
Net amount = a+b+c = $41.43
Therefore, Zalia paid all total for her day at the science museum is $41.43
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In parallelogram LMNP is shown at the right, m angle MLN=32 degrees, m angle NLP=x^2, m angle MNP=12x degrees, and angle MNP is an acute angle. Find m angle NLP. The picture of the shape is down below.
Answer: 16 degrees
Step-by-step explanation:
URGENT
Which best describes the slope of the line that passes through (-9,5) and (4,3)?
Let's find slope:-
(-9,5)(4,3)Slope:-
[tex]\\ \rm\Rrightarrow m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\\ \rm\Rrightarrow m=\dfrac{3-5}{4+9}[/tex]
[tex]\\ \rm\Rrightarrow m=\dfrac{-2}{13}[/tex]
Riley, a child psychologist, claims that for all samples of size 40 from the population of infant boys and all samples of size 40 of newborn girls, the mean of the sampling distribution of the difference in sample means (boys minus girls) is 0.2 month. Is Riley correct
Using subtraction of normal variables, it is found that Riley is not correct, as the mean is of 8 - 8 = 0.
What is the distribution of the subtraction of normal variables?The mean is the subtraction of the means, while the standard deviation is the square root of the sum of the variances.
Researching this problem on the internet, it is found that, for both samples, the mean is of 8, hence:
8 - 8 = 0.
Thus, Riley is not correct.
More can be learned about the subtraction of normal variables at https://brainly.com/question/14397951
Esperanza is helping her aunt bag apples to sell at the market. They have 98 apples and they want to put 14 apples in each bag. How many full bags of apples will they have when they are done? a Make and explain a reasonable estimate for this problem. About how many bags will they fill? How do you know?
Answer:
They will have 7 full bags of apples.
Step-by-step explanation:
if you divide the 98 apples into groups of 14 you will have 7 groups (bags) of apples.
Can somebody help with this question i attached a screen shot of the question and what it's asking for.
Please answer with steps
|3+5x|
----------- =4
9
Answer:
x=4.5, 36/9
step by step explanation: First we find what 4 wholes is (36) and than we see what we are multiplying x by (8) to solve for x we divide 8 by 36 you should get 4.5 now we plug the number into the eqation to see if we were correct.
Sophia works at the library for 3 weeks longer than 2/3 of the quarter. A
quarter is 15 weeks long at Sophia's college. How many weeks in the quarter does Sophia work at the library?
Answer:
13
Step-by-step explanation:
we are looking for 2/3 of 15
15/3=5
5+5=10
10=2/3 of a quarter
2/3+3
10+3=13
Of the 15 students on the playground, one-fifth want to play kickball. How many students want to play kickball?
Answer:
3 students want to play kickball.
Step-by-step explanation:
15 divided by 1/5 is 3 because 3x5=15
Each 1/2 inch on a scale model represents an actual length of 1/6 of a yard.
What length on the model represents 1 yard?
1 1/2 inch
2/3 inches
2 inches
3 inches
Answer:
3 inches
Step-by-step explanation:
Hello!
We can set up a proportion: [tex]\frac{\frac{1}{2}}{\frac16}} = \frac{x}{1}[/tex]
(Check the last answer for information on setting up proportions)
Solve:
Cross multiply the terms:1 yard in real life is 3 inches on the model.
1 yard represent:
1/2/(1/6)1/2(6)3inToday, the price of a new cell phone is $129. In 2000, the price of a similar cell phone was $240. What is the percent of change in the price of a cell phone from 2000 to today? Since it wen from $240 in the year 2000 to $129 today, this would indicate a percent decrease. Round to the nearest percent.
Answer:
86.05
Step-by-step explanation:
Its hard to explain but trust me and look at my ranking and see all the people Ive helped :)
Algerbra one slope intercept form
Answer:
y=x+5
Step-by-step explanation:
y-y1=m(x-x1) POINT-SLOPE FORM
Plug in your point and slope
y-3=1(x+2) (The signs flip because of the negative)
y-3=x+2 (SIMPLIFY)
y=x+5 (Move the three. It is now slope int form)
You can check by plugging in -2 for x, and get 3 for y. (it works)
Simple maths question... i just don't understand how to do it
Answer:
Cut the prism into 2 parts like the picture below
Name the upper part A, and the lower part B
Calculate the volume of part A:
12 - 8 = 4 cm
4 * 5 * 6 = 120 [tex]cm^{3}[/tex]
Calculate the volume of part B:
15 * 8 * 6 = 720 [tex]cm^{3}[/tex]
Volume of the whole prism:
Volume of part A + volume of part B
120 + 720 = 840 [tex]cm^{3}[/tex]
Answer:840 cm squared
Step-by-step explanation:
What is the value of x? Round to the nearest tenth.
Answer:
4.8
Step-by-step explanation:
[tex]Cos \ 64 =\dfrac{adjacent \ side}{hypotenuse}\\\\0.4384 =\dfrac{x}{11}\\\\\\0.4384*11=x[/tex]
x = 4.82
x = 4.8
A taxi service charges you $ 1.50 plus
$0.60 per mile for a trip to the airport.
Angie paid $13.50 for her ride to the
airport. How far did she travel?
Answer:
20 Miles
Step-by-step explanation:
13.50 - 1.50 = 12
12 / 0.60 = 20
20 Miles
Write an equation in point-slope form of the line that passes through the point (2, 1) and has a slope of
m = 2.
-
y
--(2-0)
[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{1})\qquad \qquad \stackrel{slope}{m}\implies 2 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{2}(x-\stackrel{x_1}{2})[/tex]
find the range of the function y= 9x-2, where x>-2
Answer:The given function is .Minimum or maximum value:At the extremum (maximum or minimum) value, the function will have zero slope. So, differentiate the given function once and equate it to zero to get the extremum point.dy/dx=0Now, check whether the point x=0 is corresponding to the maximum value or minimum value by differentiating the function twice,As for all value of x, so x=0 is the point corresponding to minima.Put x=0 in the given function to get the minimum value.Domain and range:The function defined for all the values of the independent variable, x.So, the domain is .The range of the function is the possible value of y.The minimum value, for x=0, is y=7.The maximum value, as .Hence the range of the function is .The value of x for which the function is increasing and decreasing:If the slope of the function is negative than the function is decreasing, soThen, from equation (i), the value of x for which dy/dx<0,18x<0Hence, the function is decreasing for .While if the slope of the function is positive than the function is increasing, soThen, from equation (i), the value of x for which dy/dx<0,18x>0Hence, the function is increasing for
Step-by-step explanation:hope this helps
Last month the cost of using the air pump at a garage was 20p.
This month the cost of using the air pump is 50p.
Tom says,
"50 = 20 = 2. 5 so the cost of using the air pump has increased by 250%"
(a) Is Tom correct?
Explain your answer.
Answer:
Tom is incorrect
The cost of using the air pump has increased by 150%
Step-by-step explanation:
Tom is incorrect
percent change = [ (difference between initial and final value) ÷ initial value] × 100
⇒ [ (50 - 20) ÷ 20) × 100 = 150%
Therefore, the cost of using the air pump has increased by 150%
Factor completely 9x3 36x2 − x − 4. (3x 4)(3x − 4)(x 1) (3x 1)(3x − 1)(x 4) (9x2 − 1)(x 4) (3x 1)(3x − 1)(x − 4).
The factor of the provided polynomial after the factorization process are similar to option B, which is
[tex](x+4)(3x+1)(3x-1)[/tex]
How to find the factor of polynomial?The factor of a polynomial is the terms in linear or equation form, which are when multiplied together, give the original polynomial equation as result.
Find these factors by taking out the common factors.
The given polynomial equation in the problem is,
[tex]9x^3 +36x^2 - x - 4[/tex]
The above equation has the unknown variable x and the highest power of this unknown variable is 3.
Take out the highest common factor 9x², which can divide each term of the first two terms of equation (9x³, 36x²). Thus,
[tex]9x^2(x +4) - x - 4[/tex]
Take out the highest common factor -1 from the second two terms as,
[tex]9x^2(x +4) -1( x + 4)[/tex]
Now take out the common group (x+4) as,
[tex](x +4) ( 9x^2 -1)[/tex]
The second group can be rewritten using the difference of square formula as,
[tex](x +4) ( (3x)^2 -1^2)\\(x+4)(3x+1)(3x-1)[/tex]
Thus, the factor of the provided polynomial after the factorization process are similar to option B, which is
[tex](x+4)(3x+1)(3x-1)[/tex]
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I need help with eight and nine you are to multiply the binominaals using the horizontal format
Answer:
8. [tex]15m^2-31m+10\\[/tex]
9. [tex]x^2y^2z^2+2xyz-3[/tex]
Step-by-step explanation:
[tex](a+b)(c+d)=ac+ad+bc+bd\\(3m-5)(5m-2)=3m*5m+3m(-2)-5*5m(-2)\\=3m*5m+3m(-2)-5*5m(-2)\\=15m^2-31m+10[/tex]
^#8^
[tex](xyz+3)(xyz-1)=xyzxyz+xyz(-1)+3xyz+3(-1)\\=xyzxyz+xyz(-1)+3xyz+3(-1)\\=x^2y^2z^2+2xyz-3[/tex]
^#9^
Please help me I will give
BRAINLY
FIVE STARS
and a THANKS
Answer:
Graph 7 [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
We need to make [tex]\frac{15}{2}[/tex] a mixed number instead of an improper fraction.To do this, divide 15 by 2. This would get us 7 [tex]\frac{1}{2}[/tex].I believe you are able to graph 7 [tex]\frac{1}{2}[/tex] on the small line right below the 8.If I am incorrect in my reasoning, please let me know so that I can plan better for my future answers. Have an amazing day.
Math help please show work
Step-by-step explanation:
8). 5 ft² into squared Inches:
=> since 1 ft² = 144 in²
=> 5x144
=> 720 in²
9). 16 000 cm² to m²:
=> since 1 m²= 10 000 cm²
=> 16 000 ÷ 10 000
=> 1.6 m²
10). 90 km/h to m/h
=> since 1000 m= 1 km
=> 90x1000
=> 90 000 m/h
11). 30 m/s to m/min
=> since 60 s= 1 min
=> 30÷60
=> 0.5 m/min
12). 15 rpm into rps
=> since 1 min= 60 s
=> 15x60
=> 900 rps
Math help. please show work. Thank you.
Answer:
13. 204.49 cm²
14. 15 cm²
15. 36 cm²
Step-by-step explanation:
Area of a square is:
A = a² where a is the side length
A = 14.3² cm
A = 204.49 cm²
Area of a triangle is:
[tex]A = \frac{hb}{2}[/tex] or [tex]A = \frac{1}{2}hb[/tex] where h is the vertical height and b is the base length
A = (5×6)÷2
A = 30÷2
A = 15
Area of a rectangle is:
A = L×W where l is the length and w is the width
A = 8×4.5
A = 36
