Answer:
2 - [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Using the addition formula for tangent
tan(A - B) = [tex]\frac{tanA-tanB}{1+tanAtanB}[/tex] and the exact values
tan45° = 1 , tan60° = [tex]\sqrt{3}[/tex] , then
tan15° = tan(60 - 45)°
tan(60 - 45)°
= [tex]\frac{tan60-tan45}{1+tan60tan45}[/tex]
= [tex]\frac{\sqrt{3}-1 }{1+\sqrt{3} }[/tex]
Rationalise the denominator by multiplying numerator/ denominator by the conjugate of the denominator.
The conjugate of 1 + [tex]\sqrt{3}[/tex] is 1 - [tex]\sqrt{3}[/tex]
= [tex]\frac{(\sqrt{3}-1)(1-\sqrt{3}) }{(1+\sqrt{3})(1-\sqrt{3}) }[/tex] ← expand numerator/denominator using FOIL
= [tex]\frac{\sqrt{3}-3-1+\sqrt{3} }{1-3}[/tex]
= [tex]\frac{-4+2\sqrt{3} }{-2}[/tex]
= [tex]\frac{-4}{-2}[/tex] + [tex]\frac{2\sqrt{3} }{-2}[/tex]
= 2 - [tex]\sqrt{3}[/tex]
Hello. There is 2 questions in the links below if you could solve them that would be awesome!
Use the given data to find the minimum sample size required to estimate a population proportion or percentage.
Margin of error 0.03: confidence level 95%; and unknown
Answer:
1067
Explanation:
The formula that will be used to calculate the sample size if population proportion isn't given is expressed as;
Sample size n = |Z|² × 0.25/E² where;
Z is the z-score at 95% confidence
E is the margin of error
Given parameters
Z score at 95% confidence interval = 1.96
E = 0.03
Substituting the given values into the formula to get the sample size n we will have;
n = 1.96²×0.25/0.03²
n = 3.8416×0.25/0.0009
n = 0.9604/0.0009
n = 1067.11
n ≈ 1067
Hence, the minimum sample size required to estimate a population proportion is approximately 1067
what is the biggest galaxy in the universe
What percent of 175 is 7?
Answer:
12.25
7 percent of 175 = 12.25
(example attached below)
Write an equation parallel to the line y=3/2x-2 that goes through (5,1) in point slope form.
Answer: y=3/2x-13/2
Step-by-step explanation:
concept to know: two parallel lines have the same slope
y=3/2x+b
in order to find b or the y-intercept, we plug the point in
y=3/2x+b
1=3/2(5)+b
1=15/2+b
b=-13/2
----------------------------
y=3/2x-13/2
Hope this helps!! :)
A sample of single persons in Towson, Texas, receiving Social Security payments revealed these monthly benefits: $426, $299, $290, $687, $480, $439, and $565. (a) What is the median monthly benefit? (b) Is the mean you computed in (a) a statistic or a parameter? Why?
Answer:
a) Median Monthly Benefit = $439
b) The mean computed above is a STATISTIC. This is because, the mean of their monthly benefits ($455.14) was calculated from a SAMPLE (which could have been known or random) of single persons in Towson Texas.
Step-by-step explanation:
In the above question, we are given:
: $426, $299, $290, $687, $480, $439, and $565.
a) Median Monthly benefits
First we arrange the monthly benefits from the lowest to the highest
$290, $299, $426, $439, $480, $565, $687
Median Monthly Benefit is the number found in the middle of the Monthly benefits.
We were given 7 monthly benefit
$290, $299, $426,) $439, ($480, $565, $687
The median monthly benefit = $439
(b) Is the mean you computed in (a) a statistic or a parameter? Why?
The Mean Monthly Benefit = Sum of terms/Number of terms
Number of terms = 7
($290 + $299 + $426 + $439 + $480 + $565 + $687)/ 7
= $3186/7
= $455.14285714286
Approximately ≈$455.14
In the question we are asked if the Mean calculated or computed above is a Statistic or a Parameter.
The mean computed above is a STATISTIC. This is because, the mean of their monthly benefits ($455.14) was calculated from a SAMPLE (which could have been known or random) of single persons in Towson Texas.
A researcher performs an experiment to test a hypothesis that involves the nutrients niacin and retinol. She feeds one group of laboratory rats a daily diet of precisely 41.59 units of niacin and 17,995 units of retinol. She uses two types of commercial pellet foods. Food A contains 0.22 unit of niacin and 100 units of retinol per gram. Food B contains 0.23 unit of niacin and 65 units of retinol per gram. How many grams of each food does she feed this group of rats each day
Answer:
Food A = 165 grams
Food B = 23 grams
Step-by-step explanation:
Daily precise diet fed to the group:
Niacin = 41.59 units
Retinol = 17,995 units
Two food types :
Food A :
Niacin = 0.22 units per gram
Retinol = 100 units per gram
Food B:
Niacin = 0.23 units per gram
Retinol = 65 units per gram
Let:
a = gram of food A fed per day
b = gram of food B fed per day
Hence in 'a' grams of food A:
0.22a of Niacin + 100a of Retinol
In 'b' grams of food B:
0.23b of Niacin + 65b of retinol
Recall :
Total Niacin = 41.59 ; total Retinol = 17995
Then,
0.22a + 0.23b = 41.59 - - - (1)
100a + 65b = 17995 - - - (2)
From (2) ; 100a + 65b = 17995
100a = 17995 - 65b
a = 179.95 - 0.65b - - - (3)
Substitute (3) into (1)
0.22(179.95 - 0.65b) + 0.23b = 41.59
39.589 - 0.143b + 0.23b = 41.59
0.087b = 2.001
b = 2.001 / 0.087
b = 23
Put b = 23 in (3)
a = 179.95 - 0.65(23)
a = 179.95 - 14.95
a = 165
Calculate the total installment price the carrying charges in the number of months needed to save them money at the monthly rate to buy the item below for its cash price the computer with the cash price of 750 offered on the installment plan for 39 per month for 24 months
Answer:
the total installment is $936 the carrying charges are $186 the monthly rate to buy the items are 19.23 or 20 monthsStep-by-step explanation:
$39 for 24 months comes to ...
$39 × 24 = $936
The "carrying charges" are the difference between the cash price and the installment price:
$936 -750 = $186
Saving at the rate of $39 per month, it would take ...
$750/$39 = 19.23 months about 20 months to save up the cash price.
Often, such savings would come from a once-a-month paycheck, so it would take more than 19 such paychecks to save the required amount.
hope it will help :)
suppose a certain brand of smoke detector functions properly 85 percent of the time. i installed 3 of thse in my room, what is probability that at least one of the three smoke detectors functions propoerly
Answer:
The probability that at least one of the three smoke detectors functions properly = 0.996625
Step-by-step explanation:
Given that:
a certain brand of smoke detector functions properly 85 percent of the time
Let X represent the certain brand of smoke detector
X = 85%
X = 0.85
Let the probability that at least one of the three smoke detectors functions properly be P(Y)
P(Y) = 1- (1 - X)³
P(Y) =1 - (1 - 0.85)³
P(Y) = 1 - 0.003375
P(Y) = 0.996625
∴
The probability that at least one of the three smoke detectors functions properly = 0.996625
On three science tests, Olivia has received scores of 89%, 98%, and 96%. What is the lowest score Olivia can get on her fourth and final science test to achieve an average score of 95%?
a
94%
b
97%
c
96%
d
95%
Answer:
97%
Step-by-step explanation:
Average = x1 + x2 + x3 + x4 + x5 ........ + xN
------------------------------------------
N
N = total numbers
=> (89 + 98 + 96 + x) / 4 = 95
=> (283 + x) /4 = 95
=> (283+ x) / 4 * 4 = 95 * 4
=> 283 + x = 380
=> 283 -283 + x = 380 - 283
=> x = 97
I divided the sum of all numbers by 4 we are adding 4 numbers.
So, she needs to get 97% in the last test in order to have an average score of 95%
b-3+4b=34
Solve equation
Answer:
b = 7.4
Step-by-step explanation:
b - 3 + 4b = 34
combine like terms:
5b - 3 = 34
5b = 37
divide by 5:
b = 7.4
Answer:
b=7.4
Step-by-step explanation:
1. Combine like terms
5b-3=34
5b=37
2. Isolate x value by dividing
b=7.4
You need to construct an open-top rectangular box with a square base that must hold a volume of exactly 475 cm3. The material for the base of the box costs 8 cents/cm2 and the material for the sides of the box costs 6 cents/cm2. The dimensions for a box that will minimize the cost of the materials used to construct box are:
Answer:
The dimensions of the box are:
x = 8,93 cm and h = 5,95 cm
C(min) = 850,69 cents
Step-by-step explanation:
The volume of the box is:
V = x²*h where x is the side of the square base and h the height
then h = V/ x² ⇒ h = 475 / x²
The total cost of box C is:
C = C₁ + 4*C₂ Where C₁ and C₂ are the costs of the base and one lateral side respectevily
Then cost C = 8*x² + 4* 6*h*x
The cost C as a function of x is
C(x) = 8*x² + (24* 475 /x² )*x
C(x) = 8*x² + 11400/x
Tacking derivatives on both sides of the equation
C´(x) = 16*x - 11400/x²
C´(x) = 0 ⇒ 16*x - 11400/x² = 0
16*x³ = 11400 ⇒ x³ = 11400/16
x³ = 712,5
x = 8,93 cm
and h = 475 / (8,93)² ⇒ h = 5,95 cm
C(min) = 8*79,77 + 4* ( 8,93)*5,95
C(min) = 638,16 + 212,53
C(min) = 850,69 cents
To check if value x = 8,93 would make C(x) minimum we go to the second derivatives
C´´(x) = 16 + 22800/x³ > 0
Then we have a minimum of C at x = 8,93
How do i write 2.200 (in decimals) into word form. Explain pls
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Hi my lil bunny!
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
Two Thousand Two Hundred
❧⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯☙
●✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎❀✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎✴︎●
Have a great day/night!
❀*May*❀
Answer:
Two and Two Tenths.
Step-by-step explanation:
The whole number if you were to just say it is two, so you have that part, but then for the decimals, the zeros don't really matter you can take them off and you have the same number ( but only if there is nothing after the zeros) so now you are left with 2.2 and the first decimal spot is the tenths so the wording for this would Two and Two Tenths.
Solve the following equation algebraically
Answer:
the right answer is d
Step-by-step explanation:
please give 5 star i need it
17.
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) Compute P(all four are red).
(b) Compute P(exactly two are red and exactly two are green).
(c) Compute P(exactly two are red or exactly two are green).
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
Complete Question
An urn contains eight red, six white, and four green balls. Four balls are drawn at random.
(a) The probability that all four balls are red is
(Type an integer or a decimal. Round to two decimal places as needed.)
(b) The probability that there are exactly two red balls and exactly two green balls is
(Type an integer or a decimal. Round to two decimal places as needed.)
(c) The probability that there are exactly two red balls or exactly two green balls is
Answer:
(a) The probability that all four balls are red is
0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
1.398
Step-by-step explanation:
An urn contains
Red balls = 8
White balls = 6
Green balls = 4
Total number of balls = 18 balls
(a) The probability that all four balls are red is?
The probability that a ball drawn is red = 8/18
The probability of drawing a ball that is not red = 1 - 8/18 = 10/18
The probability that all the 4 balls drawn are red = 8/18 × 7/17 × 6/16 x 5/15
= 1680/73440
= 0.022875817
Approximately = 0.023
(b) The probability that there are exactly two red balls and exactly two green balls is
There are 6 ways by which this can be achieved. Where R = Red balls and G = Green Balls
RRGG
GGRR
RGRG
GRGR
RGGR
GRRG
P(Exactly two red balls and two green balls) = P(Exactly two red balls × Exactly two green balls)
=[ (8/18 × 7/17) ×( 4/16 × 3/15)] × 6 ways
= 672/73440 × 6 ways
= 0.0091503268 × 6 ways
= 0.0549019608
Probability of drawing out exactly two two red balls and two green balls is
= 0.055
(c) The probability that there are exactly two red balls or exactly two green balls is
P(Exactly two red balls or two green balls) = P(Exactly two red balls + Exactly two green balls)
P(Exactly two red balls or two green balls) = P(Exactly two red balls or Exactly two green balls)
=[ (8/18 × 7/17) + ( 4/16 × 3/15)] × 6 ways
=0.1830065359 + 0.05
= 0.2330065359 × 6 ways
= 1.3980392154
≈1.398
Are the points B, F, and W coplanar?
Answer:
yes
Step-by-step explanation:
Because the point lie on the plane they are coplanar
PLEASE HELP MEEE
Simplify the expression to a polynomial in standard form
(x+3)(2x2+3x+7)
Answer:
2x^3 + 9x^2 + 16x + 21.
Step-by-step explanation:
We first multiply the expression in the second parentheses by x , then by +3:
(x + 3)(2x^2 + 3x + 7)
= x(2x^2 + 3x + 7) + 3(2x^2 + 3x + 7)
= 2x^3 + 3x^2 + 7x + 6x^2 + 9x + 21 Now we add like terms:
= 2x^3 + 9x^2 + 16x + 21.
f(x)=x2–5x+7, find f(3)
Answer:
1
Step-by-step explanation:
Hello!
To find f(3) we put 3 in for x
[tex]3^{2} -5(3)+7[/tex]
Follow PEMDAS
9 - 5(3) + 7
9 - 15 + 7
-6 + 7 = 1
The answer is 1
Hope this helps!
Answer:
f(3) = 1
Step-by-step explanation:
f(x) = x^2 – 5x + 7
f(3) = 3^2 - 5(3) + 7
f(3) = 9 - 15 + 7
f(3) = -6 + 7
f(3) = 1
i need help bad and fast
Answer: E) CD
Step-by-step explanation:
A segment with a slope of 0 on this graph represents a time where no distance is made, or a break. The only segment with a slope of 0(where distance does not increase) is segment CD.
Hope it helps <3
Answer:
CD
Step-by-step explanation:
CD is the answer because the graph becomes a flat line when a body is at rest
2. The cost of a pair of jeans was changed from $52 to $47.82. What was the percent change?
8% decrease
9% increase
9% decrease
8% increase
Answer:
I Think its 8% decrease
Answer:
The answer is
8% decreaseStep-by-step explanation:
To find the percentage change we use the formula
[tex]Percentage \: \: change = \frac{change}{original \: quantity} \times 100[/tex]
To find the change subtract the lesser one from the larger one
Original price = $ 52
Current price = $ 47.82
Change = 52 - 47.82 = $ 4.18
Substitute the values into the above formula
Percentage change is
[tex] \frac{4.18}{52} \times 100[/tex]
We have the final answer as
Percentage change = 8%
Since the current price was lesser than the original price there is a percentage decrease in the amount
20 POINTSSSSSSSSSSS AND BRAINLIESTTTTTTTTTTTTTSSSSSSSSSSSSSS
Answer:
C
Step-by-step explanation:
Since the exponent on the 10 is negative, we need to move the decimal point to the left instead of the right. After moving the decimal point on the 2.5 to the left 4 places, we see that the answer is 0.00025.
4x+y=10
( ,-6)
find the x value
please hellllpppp !!
Answer:
x=4
Step-by-step explanation:
4x+y=10
y=-6
4x-6=10
4x=16
x=4
(4,-6)
Show that the curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations.
y = __________ (smaller slope)
y = __________ (larger slope)
The equations of the two tangents are; Larger slope; y = (5/7)x Smaller slope; y = (-5/7)x
What is the slope?Slope tells how vertical a line is.
The more the slope is, the more the line is vertical. When slope is zero, the line is horizontal.
To find the slope, we take the ratio of how much the line's height increases as we go forward or backward on the horizontal axis.
This is because the more the height of the line to thee amount we walk or run on the horizontal axis, the more the slope is. Thats why we took difference of horizontal axis in denominator and difference of vertical axis on numerator.
The curve x = 7 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and we need to find their equations.
We can write
cos(t) = x/7
so
y = 5(±√(1 -(x/7)^2)*x/7
Then
y' = (±5/7)*(√(1 -(x/7)^2) + x/(2√(1 -(x/7)^2)*(-2(x/7))
The limit as x → 0 is ±5/7
The equations of the two tangents are;
Larger slope; y = (5/7)x
Smaller slope; y = (-5/7)x
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c+2c+12=75 find the value of c
Answer:
c+2c+12=75
c = 21
Steps:
c+2c+12=75
Simplify both sides of the equation.
c+2c+12=75
(c+2c)+(12)=75(Combine Like Terms)
3c+12=75
3c+12=75
Subtract 12 from both sides.
3c+12−12=75−12
3c=63
Divide both sides by 3.
In a survey of 200 game lovers,it was found that 130 liked football, 90 liked cricket, and 20 didn't like both games.i) How many people were there who liked both football as well as cricket? ii)How many people like only cricket? A. 30,60 B. 40,50 C. 50,40
Step-by-step explanation:
Hey, there!!
Your required answer is:
i). = 40
ii). = 90
See explanation in picture..
Here, no(F) represents no. of people who just like football. and n (F intersection C) represents who like both games.
Hope it helps...
A refrigerator is priced at 525.50 there is a 7% sales tax rate
Answer:
562.29
Step-by-step explanation:
you would just multiply 525.50 by 7 which is 3678.5 and divide that by 100 which is 36.785 and add that to 525.50 which is 562.285 which can be rounded to 562.29
Only a very small (<5) percentage of measurements can be more than 2 standard deviations from the mean of the normal distribution.
A. True
B. False
Answer:
A. True
Step-by-step explanation:
The empirical rule in statistics states that:
68% of the data will be within 1 standard deviation95% of the data will be within 2 standard deviations99.7% of the data will be within 3 standard deviationsSo yes, we can state that 5% or less of the data will be more than 2 standard deviations away from the mean. Of course, statistics is not 100% certain, so this rule is not 100% right all the time. Some exceptions might result, but generally speaking, the results should follow the empirical rule.
Answer:
The answer is true
Step-by-step explanation:
True
A diagonal of a rectangle is 8cm and forms an angel measuring 30 with one side.Find the area of the rectangle.
Answer:
16 * √3 cm² or approximately 27.71 cm²
Step-by-step explanation:
Given the 8 cm length of the diagonal and the 30° (π/6 radians) angle with one of the sides, we can calculate the width and height of the rectangle using:
8 * cos(π/6) = 8 * ((√3)/2) = 4 * √3
8 * sin(π/6) = 8 * (1/2) = 4
Multiply those two values together to get the area and you get
16 * √3 cm²
The density of an object has the equation d = m/v. If an object has a mass of 20 g and a volume of 3.5 cm^3, what is its density?
Answer:
[tex]\Large \boxed{\mathrm{5.71 \ g/cm^3 }}[/tex]
Step-by-step explanation:
[tex]\sf \displaystyle density = \frac{mass}{volume}[/tex]
[tex]\displaystyle \rho = \frac{m}{V}[/tex]
[tex]\sf Mass \rightarrow 20 \ g \\ Volume \rightarrow 3.5 \ cm^3[/tex]
[tex]\displaystyle \rho = \frac{20}{3.5}[/tex]
[tex]\rho \approx 5.71[/tex]
Density is defined as the mass per unit volume of an object and It is calculated using the equation: density (d) = mass (m) / volume (v).
In this scenario, the mass of the object is given as 20 grams and the volume is given as 3.5 cm^3. To find the density, we can substitute these values into the equation: density =[tex]20 g / 3.5[/tex] cm^3 To simplify the unit of the measurement, we can convert cm^3 to mL (since 1 cm^3 is equal to 1 mL).
Thus, the equation becomes: density = [tex]20 g / 3.5[/tex] mL Calculating the division: density ≈ 5.71 g/mL Therefore, the density of the object is approximately 5.71 g/mL.
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Represent the following sentence as an algebraic expression, where "a number" is the
letter x. You do not need to simplify.
Twice the difference of a number and 8.
Answer:
2(x - 8)
Step-by-step explanation: