Answers
Answer:
[tex]\tan \dfrac{\theta}2 = \dfrac{1}2[/tex]
Step by step Explanation:
[tex]\sin \theta = \dfrac{\text{Perpendicular} }{\text{Hypotenuse}} = \dfrac{12}{15}\\\\\\\cos \theta = \dfrac{\text{Base}}{\text{Hypotenuse}}= \dfrac{9}{15}\\\\\text{Now,}\\\\\tan \dfrac{\theta}2 = \dfrac{\sin \tfrac{\theta}2}{\cos \tfrac{\theta}2}\\\\\\~~~~~~~~=\dfrac{2\cos \tfrac{\theta}2 \sin \tfrac{\theta}2 }{2\cos^2 \tfrac{\theta}2}~~~~~~;\left[\text{Multiply by}~ 2\cos\tfrac{\theta}2 \right][/tex]
[tex]=\dfrac{\sin \theta}{1+ \cos \theta}~~~~~~~~~~~~;[2 \sin x \cos x = \sin 2x ~ \text{and}~ 2\cos^2 x =1+\cos 2x]\\\\\\=\dfrac{\tfrac{12}{15}}{1+ \tfrac{9}{15}}\\\\\\=\dfrac{\tfrac{12}{15}}{\tfrac{24}{15}}\\\\\\=\dfrac{12}{15}\times \dfrac{15}{24}\\\\\\=\dfrac{12}{24}\\\\\\=\dfrac{1}2[/tex]
Related Questions
Area of a Square
Side Length (cm)
1
2
Area (cm²)
1
4
3
9
4
16
5
25
Describe how the area of a square is related to the length of the side.
a.
As the length of the side increases, the area decreases.
b.
As the length of the side increases, the area increases and then decreases.
As the length of the side increases, the area increases.
CA
d.
As the length of the side increases, the area decreases and then increases.
Answers
The description of the area of a square is (c) as the length of the side increases, the area increases.
How to describe the area of a square?The table of values is given as:
Side Length (cm) Area (cm²)
1 1
2 4
3 9
4 16
5 25
In the above table, we can see that:
As length increases, the area also increases
Hence, the description of the area is (c) as the length of the side increases, the area increases.
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The area of the base of a cylinder is 36 square inches and its height is 10 inches. A cone has the same area
for its base and the same height. What is the volume of the cone?
The volume of the cone is
in³.
I need help:((
Answers
Reason
Cone volume is 1/3 BH
(or 1/3 volume of a cylinder)
1/3 x 36 x 10
Answer = 120
Are these numbers rational or irrational? -7 √10 (square root of 10) √16 (square root of 16) 52% 1.235 > > > > 1. Rational 2. Irrational please answer quickly
Answers
Answer:
hope you can understand
if for 5 pounds of beans it cost 4 dollars than how much money is needed for 50 pounds of beans
Answers
Answer:
40 dollars
Step-by-step explanation:
We can use a ratio to solve the problem
5 pounds 50 pounds
---------------- = -----------------
4 dollars x dollars
Using cross products
5 * x = 4 * 50
5x = 200
Divide by 5
5x/5 = 200/5
x = 40
40 dollars
Step-by-step explanation:
[tex]\sf 5 \: pounds \longrightarrow 4 \: dollars[/tex]
[tex]\sf 1\: pounds \longrightarrow \dfrac{4}{5} \: dollars[/tex]
[tex]\sf 50\: pounds \longrightarrow \dfrac{4}{5}×50 \: dollars[/tex]
[tex]\sf \longmapsto 40 \: dollars[/tex]
Which steps are needed to solve this equation?
.
b + 6 = 21
Answers
Answer:
15
Step-by-step explanation:
Isolate the b by subtracting 6 from both sides
Question: b + 6 = 21
Subtract 6 from both sides
b + 6 - 6 = 21 - 6
b = 15
Answer:b=15
Step-by-step explanation:
Just subtract 6 from 21 to get b.
what is linear relationship
Answers
Step-by-step explanation:
a linear relationship is simply a straight line relationship.
any equation that can be pot in the form of y = mx + b is a linear relationship.
linear = straight
hope this helps
If the simple interest on $4000 for 2 years is $400, then what is the interest rate?
Answers
Step-by-step explanation:
the answer is 5 percentage because the formula is 100 * 400 over 4000 * 2
multiply: (a+b),(a+b) and (a+b)
Answers
Answer:
Here,
[tex](a + b) [(a + b)(a + b)][/tex]
[tex](a + b)( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex]a( {a}^{2} + 2ab + {b}^{2} ) + b( {a}^{2} + 2ab + {b}^{2} )[/tex]
[tex] {a}^{3} + {2a}^{2} b + {ab}^{2} + {a}^{2} b + {2ab}^{2} + {b}^{3} [/tex]
[tex] {a}^{3} + 3 {a}^{2} b + {3ab}^{2} + {b}^{3} [/tex]
Thus,[tex](a+b)^3=a^3+3a^2b+3ab^2+b^3[/tex]
Thus, in case of multiplication of a binomial or a trinomial by a binomial or a trinomial each term of the binomial or the trinomial should multiply each term of the given binomial or the trinomial and if needed, simplification should be performed.
A group surveyed a mix of people below and above 40 years old about whether or not they visit a dentist once a year. This table gives the survey results.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 8 22
Above 40 17 13
Which table shows the relative frequency of people above 40 years old who do not visit a dentist once a year? Round your answers to the nearest hundredth.
A.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.32 0.68
Above 40 0.63 0.37
B.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.35 0.65
Above 40 0.68 0.32
C.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.37 0.63
Above 40 0.53 0.47
D.
Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
Answers
The frequency table that shows the relative frequency of people older than 40 and don't visit the dentist is:
D. Visit Dentist Yearly Don’t Visit Dentist Yearly
Below 40 0.27 0.73
Above 40 0.57 0.43
What is the relative frequency required?The relative frequency of those older than 40 and don't go annually to a dentist can be found as:
= Number of over 40 who don't go to dentist / Total of those over 40 surveyed
Solving gives:
= 13 / (17 + 13)
= 13 / 30
= 0.43
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Answer:
Its D, I got it right on a test :)
Step-by-step explanation:
Kenzie makes quilts from blue and purple pieces of fabric. The diagram shows the ratio of blue pieces to
purple pieces.
Blue pieces
Purple pieces
The table shows the number of purple pieces and the number of total pieces that Kenzie will make on two
of her quilts.
Based on the ratio, complete the missing values in the table.
Quilt Purple pieces Total pieces
A
56
B
20
Answers
The purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.
What is the ratio?
It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The question is incomplete.
The complete question is in the picture, please refer to the picture.
Total number of pieces = 3+5 = 8
So, the purple pieces = 5(5/8) = 35
Total pieces = 20/(5/8) = 4×8 = 32
Thus, the purple pieces are 35 and total pieces is 32 if the Kenzie makes quilts from blue and purple pieces of fabric.
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The athlete jogged a distance of 4850 yards in 20 minutes. What is the time needed to cover 9215 yards at the same rate?
Equation:
Answer
Answers
Answer:
38 minutes
Step-by-step explanation:
Yards covered in a minute = 4850/20 = 242.5
Time needed to cover 9215 yards = 9215/242.5 = 38 min
please help me Fast!!!!! slove the question in picture
Answers
Step-by-step explanation:
A)
Class Width=8
Median= 28.1
Modal Class= 20.5-28.5
B)
Mean=31.34
Marc Gasol scored 18 points on Monday, 29 points on Wednesday, and 8 points on Saturday. What
was his average number of points per game for those three nights?
Answers
Answer: 18.33 ppg
Step-by-step explanation:
He played three games
18+29+8=55
55/3=18.33
Can someone solve this eq (integration)
I did it but the answer I got is different to what my textbook says
Answers
Answer:
I hope you can help
Which graph represents 2x + 3y < 6?
Answers
A
I believe that I am correct
The diameter of a circle is 94 cm.
By first calculating the radius, work
out the area of the circle.
2
Give your answer in cm² to 1 d.p.
Answers
[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]
Substitute the values according to the formula.
[tex]r=\frac{94}{2}[/tex]
[tex]\large\boxed{r=47 \: cm}[/tex]
Now, let's find the area.
[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]
So, we'll have to multiply π, 47 and 47.
Substitute the values according to the formula.
[tex]a= \pi{47}^{2}[/tex]
[tex]a= 6939.778172 \: {cm}^{2}[/tex]
[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]
Hence, the area of the given circle is 6939.8 square centimeters.
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to find the radius & area of the circle.
To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:
[tex]\star~\bf{94\div2}[/tex]
[tex]\star~\bf{Radius=47}\star[/tex]
Now that we have the radius, let's compute the area! :)
///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\
Calculating the Area
We can work out the area of a circle by using this formula:
[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]
Where
[tex]\dag[/tex] A=Area of a circle
[tex]\dag[/tex] [tex]\pi =3.14...[/tex]
[tex]\dag[/tex] r=radius
Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.
Now it's time to substitute the values:
[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]
Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)
Here's what it stands for:
P=Parentheses
E=Exponents
M=Multiplication
D=Division
A=Addition
S=Subtraction
2 is an exponent.
So what do you think we should do first?
[tex]\square[/tex] Square 47.
[tex]\square[/tex] Multiply 3.14 times 47 and then square.
That's right, we should square 47 first. :)
[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]
Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:
[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]
Remember, the area of any shape is measured in units squared.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]
Hope this helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]
(8.2 x 10^4) + (9.7 x 10^5)
Answers
Answer:
1.052 × 10⁶
Step-by-step explanation:
82,000 + 970,000 = 1,052,000
Answer:
[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)=1,052,000[/tex]
Step-by-step explanation:
[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)\\=8.2\cdot \:10^4+9.7\cdot \:10^5\\\\\rightarrow 10^4 = 10000\\= 8.2 \cdot 10000\\= 82000\\\rightarrow 10^5 = 100000\\= 9.7 \cdot 100000\\= 970000[/tex]
[tex]970000 + 82000 = 1052000[/tex]
Greg deposited $4000 into an account with a 9.8% annual interest rate, compounded semiannually. Assuming that no withdrawals are made, how long will it
take for the investment to grow to $4616?
Do not round any intermediate computations, and round your answer to the nearest hundredth.
Answers
The number of years it would take $4000 to grow to $4616 is 2.92 years.
How many years would it take the investment to have a value of $4616?When an amount earns compound interest compounded semi annually, it means that both the amount invested and the interest accrued increases in value twice yearly.
Number of years = (In FV / PV) / r
r = 9.8/2 = 4.90%FV = future value = 4616PV = present value = 4000(In 4616 / 4000) / 0.049 = 2.92 years
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A study of a local high school tried to determine the mean amount of money that each
student had saved. The study surveyed a random sample of 69 students in the high
school and found a mean savings of 5000 dollars with a standard deviation of 1400
dollars. At the 95% confidence level, find the margin of error for the mean, rounding
to the nearest whole number. (Do not write ).
Answers
Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The margin of error is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.
The standard deviation and sample size are given, respectively, by:
s = 1400, n = 69.
Hence, the margin of error in dollars is given by:
[tex]M = t\frac{s}{\sqrt{n}}[/tex]
[tex]M = 1.9955\frac{1400}{\sqrt{69}}[/tex]
M = 336.
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Lydia is making tickets for her class
concert. Each ticket measures 4cm by
3cm. What is the maximum number of
the tickets that can be cut off a sheet of
bristol board measuring 48cm by 36cm
Answers
A football stadium holds 17,700 seats. The lower level has 300 seats less than 4 times the number of seats in the upper level. The middle level has 500 more seats than twice the number of seats in the upper level. Let x represent the seats in the upper level. Which equation can be used to find the number of seats in the upper level?
7 x + 200 = 17,700
6 x + 200 = 17,700
7 x minus 200 = 17,700
6 x minus 200 = 17,700
Answers
Answer:
6x + 200 = 17,000
Step-by-step explanation:
Lower level = 4x - 300
Mid level = 2x + 500
Combine the two equations to find the number of seats in the upper level
(2x + 500) × (4x - 300) = 17,000
Combine like terms
4x × 2x + 500 - 300 = 17,000
6x + 200 = 17,000
Question 14 of 14
Rachel buys
1
gallon of milk. Her sister Abby uses
1
1
2
quarts of the milk in a recipe. Then her mother uses
3
cups of the milk in a different recipe.
Select all of the true statements below.
A.
Rachel's mother uses more milk than her sister Abby uses.
B.
There are
56
fluid ounces of milk left.
C.
There are
9
cups of milk left.
D.
There is more than
1
4
gallon of milk left.
E.
There is more than
1
2
gallon of milk left.
Answers
The true statements are:
There are 56 fluid ounces of milk left.
There is more than 1 / 4 gallon of milk left.
What are the true statements?
The first step is to convert gallons to cups.
1 cup = 16 gallons
Then, convert quarts to cups
1 quart = 4 cups
1 1/2 x 4
3/2 x 4 = 6 cups
Total cups left = 16 - 6 - 3 = 7 cups
1 cup = 8 ounces
Total milk left in ounces: 8 x 7 = 56 ounces
1 cup = 1/16 gallons
Total milk left in gallons: 1 / 16 x 7 = 7/16 gallons
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The current salaries in Sasha's department are $42,000, $32,000, $33,000, $38,000, and $50,000. Sasha wants to adjust the lowest salary up to $40,000. If Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary, Find the total cost for the increment?
Answers
The total cost for the increment if Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary is $13000.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The lowest salary is $32000, hence to increase to $40000, we need an additional $8000.
Also, giving every employee a $1,000 raise accounts for $5000 since there are 5 staff.
The total cost of increment = 8000 + 5000 = 13000
The total cost for the increment if Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary is $13000.
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Maya invested $2,100 in an account paying an interest rate of 7\tfrac{3}{8}7 8 3 % compounded continuously. Jack invested $2,100 in an account paying an interest rate of 7\tfrac{5}{8}7 8 5 % compounded monthly. After 12 years, how much more money would Jack have in his account than Maya, to the nearest dollar?
Answers
This are interest added on a sum of money invested. Jack will have $168.95 more than Maya in his account
Compound interestThis are interest added on a sum of money invested. The formula for calculating compound amount is given as;
A = P(1 +r/n)^nt
Given the following parameter
P =$2100
rate r = 7 5/8% = 0.07625
time t = 12 years
n =12 (monthly)
Substitute
A = 1200(1+0.07625/12)^12(12)
A = 1200 (2.4895)
A = $2987.46
For Maya
A = 1200(1+0.07375)^12
A = 2818.50
Take the difference
Difference =$2987.46 - $ 2818.5
Difference = $168.95
Hence Jack will have $168.95 more than Maya in his account
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Find the minimum distance between the point (-3,2) and the line y = -x + 1
(Enter an exact answer with a square root.)
Answers
The minimum distance between the point(-3,2) and the line y = -x + 1 is [tex]\sqrt{2}[/tex] units.
What is a line segment?The line that joins two points on a cartesian plane is a line segment.
Analysis:
The formula for calculating distance between a line and a point is
d = [tex]\frac{Ax1 + By1 + c}{\sqrt{A^{2} + B^{2} } }[/tex]
where A = coefficient of x term of the line, B = coefficient of y in the line and C is the constant term of the line.
x1 and y1 are coordinates of the point.
for the line y = -x + 1 which is = y + x -1 = 0, A = 1, B = 1, C = -1, x1 = -3, y = 2
d = [tex]\frac{1(-3) + 1(2) + (-1)}{\sqrt{(-3)^{2} + 2^{2} } }[/tex]= [tex]\sqrt{2}[/tex] units
In conclusion, the distance between the point and the line is [tex]\sqrt{2}[/tex] units
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a fridge costs €336 after a price increase of 40%. what was the original price
Answers
the original cost is "x", which is the 100% of the original price, and we also know that €336 is its price increased by 40%, namely 100% + 40% = 140%, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 336& 140 \end{array} \implies \cfrac{x}{336}~~=~~\cfrac{100}{140} \\\\\\ \cfrac{x}{336}=\cfrac{5}{7}\implies 7x=1680\implies x=\cfrac{1680}{7}\implies x=240[/tex]
The definition of a circle uses the undefined term _______.
O arc
O line
O plane
O ray
Answers
Answer:
The correct answer is:
Plane.
Step-by-step explanation: There are three terms generally considered to be undefined in geometry: point, line and plane.
A circle is the set of all points in a plane the same distance from a given point called the center. The only of our options that is used in this definition is
The correct answer is;
⇒ Plane.
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Since, We know that;
There are three terms generally considered to be undefined in geometry: point, line and plane.
Hence, A circle is the set of all points in a plane the same distance from a given point called the center.
And, The only of our options that is used in this definition is plane.
Thus, The correct answer is;
⇒ Plane.
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Fabian took a taxi from his house to the airport. The taxi company charged a pick-up fee of $4.80 plus $4 per mile. The total fare was $44.80, not including the tip. How many miles was the taxi ride?
Answers
Answer:
10 miles
Step-by-step explanation:
total amount=$44.80
pick up fee=$4.80+$4 per mile
to get the miles of the taxi ride it will be=total amount-pick up fee÷$4
$44.80-$4.80÷$4
$40÷$4
=10 miles
THANK YOU
in the figure, angle D measures 31° and angle A measures 27
The measurement of angle B Is ?The measurement of angle F is?
Answers
The acute angles of a right triangle are complementary, so:
[tex]m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}[/tex]
Factor higher degree polynomials
(x^2 - 4) (x^2 + 6x + 9)
Answers
[tex]~~~(x^2 -4)(x^2 +6x +9)\\\\=(x^2 -2^2)(x^2 +2 \cdot 3x +3^2)\\\\=(x+2)(x-2)(x+3)^2[/tex]