Answer:
See below for proof of identity.
Step-by-step explanation:
Since both terms of [tex]\sin^3\theta+\cos^3\theta[/tex] are perfect cubes, we can use the formula [tex]a^3+b^3=(a+b)(a^2-ab+b^2)[/tex] where [tex]a=\sin\theta[/tex] and [tex]b=\cos\theta[/tex]:
[tex]\displaystyle \frac{\sin^3\theta+\cos^3\theta}{\sin\theta+\cos\theta}\\\\\frac{(\sin\theta+\cos\theta)(\sin^2\theta-\sin\theta\cos\theta+\cos^2\theta)}{\sin\theta+\cos\theta}\\ \\\frac{(\sin\theta+\cos\theta)(1-\sin\theta\cos\theta)}{\sin\theta+\cos\theta}\\\\1-\sin\theta\cos\theta[/tex]
Thus, the identity is proven.
What is the domain of the function shown in the graph?
Answer:
the answer is b you have it right
Step-by-step explanation:
your welcome
jorge makes fruit snacks for his friends. He uses 1 1/2 apples to make 3 fruit snacks.
How many apples does jorge need to make 1 fruit snack
Answer:
Jorge needs 1/2 apple to make the snack.
The roof of braeden's house is shaped like a parallelogram. The base of the roof is 12m and the area is 114 cm square. Choose a number and unit to make this statement true.
A soup can has a diameter of 8 cm and a height of 12 cm. What is the volume of the soup can? Use 3. 14 for Pi. A cylinder has a height of 12 centimeters and diameter of 8 centimeters. 192. 00 cubic centimeters 301. 44 cubic centimeters 602. 88 cubic centimeters 2,411. 52 cubic centimeters.
Answer:
The volume of the soup can is 602. 88 cubic centimeters
Step-by-step explanation:
Volume of a cylinder = π {r} ^{2} h
Where π = 3.14
r = diameter ÷ 2
r= 8 ÷ 2
r= 4 cm
h= 12 cm
Volume of the soup can= 3.14 × 4 × 4 × 12
= 602. 88 cubic centimeters
The description for a certain brand of house paint claims a coverage of 410 ft2/gal. How many liters of paint are required to apply a single coat of paint to the (4) walls of a 7.7 m by 14.8 m room with a height of 2.4 m
Answer:
10.7 liters of paint requiredStep-by-step explanation:
Dimensions of the room
7.7 m by 14.8 m with the height of 2.4 mFind the surface area of the 4 walls
A = Ph = 2(l + w)h = 2(7.7 + 14.8)*2.4 = 108 m²Convert the area to ft²
108 m² = 108*10.7639 ft² = 1162.5012 ft²Find the amount of paint required
1162.5012/410 = 2.84 gal (rounded)Covert the volume to liters
2.84 gal = 2.84*3.76 l = 10.7 l (rounded)I need help I don’t know the answer
Answer:
Option 2
Step-by-step explanation:
Height of lemon tree = 8
Height of date tree = 8 x 3
On comparing, we understand that the date tree is 3 times as tall as the lemon tree.
Answer:
the answer is B or the second one
Step-by-step explanation:
8 x 3 = 24
the data tree is 3 times as tall as the lemon tree
please can someone do this for me? thanks alot x
Answer:
Learning Objective: Use the mean and range to compare the spread and averages.
a) Sarah Mean = 70.9, Katie Mean = 78.9
b) Sarah Range = 15, Katie Range = 25
c) Sentences
- The mean shows, on average, Sarah was 8 seconds quicker than Katie.
- The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.
Step-by-step explanation:
Given:
Sarah's Data Set:
79, 70, 68, 75, 69, 64, 69, 75, 64, 76Katie's Data Set:
79, 79, 76, 81, 89, 76, 64, 85, 82, 78To Find:
The mean and range of both data sets separately.Work:
The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is [tex]\mu = \frac{{\sum}x}{N}[/tex].
The formula for the mean of a sample is [tex]\bar{x} = \frac{{\sum}x}{n}[/tex].
Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values given above, the solution is: [tex]\frac{709}{10} = 70.9[/tex]
Therefore, the mean of Sarah's data set is 70.9.
For Katie's Data Set, [tex]\frac{789}{10} = 78.9[/tex].
Therefore, the mean of Katie's data set is 78.9.
To fill in the summary, we have to use the data we just calculated.
That summary can be found in the answer section.
Answer:
Sarah's mean = 70.9
Katie's mean = 78.9
Sarah's range = 15
Katie's range = 25
The mean shows that on average Sarah was 8 seconds faster than Katie. The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.
Step-by-step explanation:
Identifying the mean time for Katie and Sarah
The mean ( average ) is equal to the sum of the numbers in the data set ( the sum of the swimming times ) divided by the number of values in the data set ( which is given as 10 )
Mean for Sarah : Sum of her swimming times : 79 + 70 + 68 + 75 + 69 + 64 + 69 + 75 + 64 + 76 = 709
Number of values = 10
So mean = 709 / 10 = 70.9 seconds.
Mean for Katie : Sum of her swimming times : 79 + 79 + 76 + 81 + 89 + 76 + 64 + 85 + 82 + 78 = 789
number of values = 10
so mean = 789 / 10 = 78.9
Using this information we can identify what the first to blanks are. The mean shows that on average Sarah was ___ seconds ____ than Katie.
The mean time for Sarah was 70.9 seconds and the mean time for Katie was 78.9 seconds. So on average Sarah was faster and by 8 seconds ( which can be found by subtracting Sarah's mean from Katie's )
Identifying the range
The range is equal to the largest value ( longest swim time ) subtracted by the smallest value ( or quickest swim time )
Range for Sarah : Sarah's highest swim time is 79 seconds and her lowest is 64 seconds.
So her range = 79 - 64 = 15 seconds
Range for Katie : Katie's highest swim time is 89 seconds and her lowest time is 64 seconds
So her range = 89 - 64 = 25
Using this information we can fill out the remaining blanks.
The range shows that ____ was more consistent with her times. ___ had a larger spread of times which shows she was ____ consistent.
The higher the range the less consistent you are vise versa. Katie had a larger range hence, Sarah was more consistent and Katie was less consistent.
The coordinates of the endpoints of the diameter of a circle are (-1, 5) and (3, -1). The center of the circle has coordinates
Answer: (1,2)
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so using the midpoint formula, we get the answer to be [tex]\left(\frac{-1+3}{2}, \frac{5-1}{2} \right)=\boxed{(1,2)}[/tex]
Suppose a normal distribution has a mean of 26 and a standard deviation of 4. What is the probability that a data value is between 28 and 35? Round your answer to the nearest tenth of a percent.
A. 29.6%
B. 23.6%
C. 27.6%
D. 25.6%
Using the normal distribution, it is found that the probability that a data value is between 28 and 35 is given by:
A. 29.6%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Researching the problem on the internet, the mean and the standard deviation are given by:
[tex]\mu = 26, \sigma = 4[/tex].
As a proportion, the probability that a data value is between 28 and 35 is the p-value of Z when X = 35 subtracted by the p-value of Z when X = 28, hence:
X = 35:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{35 - 26}{4}[/tex]
Z = 2.25
Z = 2.25 has a p-value of 0.988.
X = 28:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{28 - 26}{4}[/tex]
Z = 0.5
Z = 0.5 has a p-value of 0.692.
0.988 - 0.692 = 0.296 = 29.6%, which means that option A is correct.
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Nine balls, each marked with a number from 1 to 9, are placed in a bag and one ball is taken at random. What is the probability that the number on the ball is multiple of 2?
A.1/9
B.2/9
C.4/9
D.1
Total balls=sample space=9
Multiples of 2
{2,4,6,8}Total multiples=4
Probability
4/9Option C
Hello, the answer should be [tex]\frac{4}{9}[/tex], C option.
First, let's define the numbers that are a multiple of 2 from the balls we have.
2468Then, we will calculate our probability. To do this correctly, we must divide the amount of expected states into the amount of all the states.
Expected numbers: 2-4-6-8
All numbers: 1-2-3-4-5-6-7-8-9
[tex]P=\frac{{2,4,6,8}}{1,2,3,4,5,6,7,8,9} =\frac{4}{9}[/tex]
Good luck! If you have any questions, then feel free to ask in comments!
Evaluate the following expression. You should do this problem without a calculator. log 5 125
Answer:
3
Step-by-step explanation:
log(5) 125 =x
5^x = 125
5^x = 5^3
x=3
AABC and AXYZ are similar. Find the missing side length.
Y
21
AA
3
6
4
Z
C X
28
(The triangles are not drawn to scale.)
Answer:
42
Step-by-step explanation:
it is stated that the triangle are similar so their side lengths must be proportional, we can use this to find the missing side length
AB/XY = BC/YZ write this with the side lengths
3/21 = 6/? cross multiply expressions
3? = 126 divide both sides by 3
? = 42
A baseball team is hosting a dance as a fundraiser. the cost of 1 individual ticket is $7. the cost of 1 group ticket is $16. the baseball team sold 36 more individual tickets than group tickets. the fundraiser raised $574 as a result of all ticket sales. if x is the number of the individual tickets that were sold and y is the number of group tickets that were sold, how many individual tickets were sold (what is the value of x)?
To form equations from word problems, we can do the following:
Identify variablesFind key informationIdentify word equations and translate into numerical equationsSolveSolving the QuestionWe're given:
Let x be the number of individual tickets that were soldLet y be the number of group tickets soldCost of 1x = 7 dollarsCost of 1y = 16 dollarsBaseball team: 36 more x than yQuestion: How many individual tickets were sold? (What is the value of x?)
Here are all the equations we have created:
x = 36 + y7x + 16y = 574We can solve for the value of x using systems of equations.
First, isolate y in the first equation:
[tex]x = 36 + y\\y=x-36[/tex]
Now, plug this into the second equation:
[tex]7x + 16y = 574\\7x + 16(x-36)= 574\\7x+ 16x-586= 574\\23x=1150\\\\x=\dfrac{1150}{23}\\\\x=50[/tex]
Therefore, x is equal to 50.
Answer50 individual tickets were sold.
NEED TO PASS HELP WILL GIVE BRAINLY!!!
Answer:
[tex]\bigodot[/tex] None of the other answers are correct.
Step-by-step explanation:
[tex]2b^2-3b+85=-5[/tex] (Given)[tex]\implies 2b^2-3b+85+5=0[/tex][tex]\implies 2b^2-3b+90=0[/tex]Comparing it with the general form of quadratic equation [tex]ax^2+bx+c=0,[/tex] we find:a = 2, b = -3, c = 90Next, we find the value of the discriminant [tex] b^2-4ac[/tex][tex] b^2-4ac= (-3)^2-4(2)(90)=9-720=-711<0[/tex][tex] \because b^2-4ac<0[/tex], which means the roots of the given quadratic equation are non-real or imaginary.Thus, last option is the correct answer.V-125 - 5 X 32
[tex]3 \sqrt{ - 125} - 5 \times {3}^{2} [/tex]
Simplify the following and show all your workings
Answer:
Because of the order of operations, we start the equation backwards because exponents are what we prioritize here.
[tex]3^2 = 9\\\\9 * 5 = 45\\\\\sqrt{-125} = -11.1803399\\\\45 - -11.1803399 = 56.1803399\\\\56.1803399 * 3 = \boxed{168.54}[/tex] Result rounded to 2 DP
4 of 8
Given that y = 6 cm and 0 = 32", work out I rounded to 1 DP.
x =
Answer:
[tex]x=3.18[/tex] [tex]cm[/tex]
Explanation:
[tex]x=3.18[/tex] [tex]cm[/tex]
Substitute [tex]y=6 cm[/tex] into [tex]\frac{}{AC} =y:\frac{}{AC} =6cm[/tex]
Substitute [tex]0=32[/tex] into ∠[tex]CAB=0:[/tex] ∠[tex]CAB=32^o[/tex]
sinA=leg opposite ∠A/hypotenuse : [tex]sin(CAB)=\frac{\frac{}{BC} }{\frac{}{AC} }[/tex]
Substitute [tex]\frac{}{BC} =x,\frac{}{AC}=6cm,[/tex] ∠[tex]CAB=32^o[/tex]
into sin(∠[tex]CAB[/tex]) [tex]=\frac{\frac{}{BC} }{\frac{}{AC} }:sin(32^o)=\frac{x}{6}[/tex]
Calculate [tex]sin(32^o)=\frac{x}{6} :x=3.18cm[/tex]
Draw polygon abcdef in this coordinate plane, given its vertices a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)
The polygon abcdef in the coordinate plane shown with area of 18 square units.
What is a regular polygon?A polygon is a geometric figure with a finite number of sides in two dimensions. On the sides or edges of a polygon, straight-line segments are joined end to end to form a closed shape. The vertices, also known as corners, are the points where two line segments meet and form an angle.
We have vertices for the polygon:
a=(-2,-3), b=(0,-3), c=(0,1), d=(3,1), e=(3,3), f=(-2,3)
After marking the coordinates on the coordinate plane and connecting the lines, we will get a polygon.
We can find the area of the shape:
Area of the shape = 18 square units
Thus, the polygon abcdef in the coordinate plane shown with area of 18 square units.
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Write a cosine function that has a midline of 3, an amplitude of 4 and a period
of pi.
Answer:
[tex]f(x)=4\cos(2x)+3[/tex]
Step-by-step explanation:
Using the general equation [tex]f(x)=a\cos(bx+c)+d[/tex], we already know that [tex]a=4[/tex] and [tex]d=3[/tex], but we need to find [tex]b[/tex] from the period:
[tex]\frac{2\pi}{|b|}=\pi\\ 2\pi=b\pi\\2=b[/tex]
Hence, the cosine function is [tex]f(x)=4\cos(2x)+3[/tex]
Amber is solving the inequality |x+6| - 12 < 13 by graphing. Which equations should Amber graph?
Answer:
y₁ = |x+6| ; y₂ = 25
Step-by-step explanation:
|x+6| - 12 < 13
⇔ |x+6| < 25
Equation for the given inequality is equals to [tex]y_{1} =| x+ 6| , y_{2} =25[/tex]
What is inequality?" Inequality is defined as the algebraic expression which represents the relation between two variables using sign of inequality."
According to the question,
Given inequality,
|x+6| - 12 < 13
Add both the side of the inequality 12 we get ,
|x+6| - 12+12< 13 + 12
⇒ |x+6| < 25
As represent in the graph equation for the given inequality are,
[tex]y_{1} =| x+ 6| , y_{2} =25[/tex]
Hence, equation for the given inequality is equals to [tex]y_{1} =| x+ 6| , y_{2} =25[/tex].
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Expand to write an equivalent expression
-1/4 (-8x + 12y)
The equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y
Expansion of expressionExpansion of expression can be carried out using the distributive rule a shown:
A(B + C) = AB + AC
Note that A is distributed over B and C
Given the expression
-1/4 (-8x + 12y)
-1/4(-8x) - 1/4(12y)
2x - 3y
Hence the equivalent expression on expanding -1/4 (-8x + 12y) is 2x - 3y
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NEED HELP ASAP 100 POINTS AND BRAINLIEST FOR THE CORRECT ANSWER!!!
Determine the solution to the system of equations graphed below and explain your reasoning in complete sentences.
g(x)=3x+2
f(x)=|x-4|+2
As it's already graphed their inetresection point is solution for both functions
Red one is g(x) as it's linearOther one is f(x) as it's modulusThe solution is (1,5)
Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations would be where the lines of the two intersect. The point of intersection (based on the graph) is :
(1, 5)which expression has a value of 2/3?
(8+24) (12 × 4)
824 12 x 4
8+ (2412) × 4
8+24 (12 x 4)
Answer:
(8 + 24) ÷ (12 x 4) = 2/3
Step-by-step explanation:
To Find: an expression that has a value of 2/3
Solution :
A. [8 + (24 ÷ 12)] x 4
= [8 + (2)] x 4
= 10 x 4
= 40
B. (8 + 24) ÷ (12 x 4)
= 32 ÷ 48
= 2 ÷ 3
= 2/3
C. 8 + (24 ÷ 12) x 4
= 8 + 2 x 4
= 8 + 8
= 16
D. 8 + 24 ÷ 12 x 4
8 + 2 x 4
= 8 + 8
= 16
The correct option is :
(8 + 24) ÷ (12 x 4) = 2/3
Please answer ASAP! I will give you brain L. #8
Answer:
AC = [tex]3\sqrt{3}[/tex]
BC = [tex]6\sqrt{3}[/tex]
Step-by-step explanation:
AC is [tex]x\sqrt{3}[/tex] and x = 3 so [tex]3\sqrt{3}[/tex] and it [tex]=3\sqrt{3}[/tex]
BC is [tex]2x[/tex] and x = 3 so [tex]2(3\sqrt{3}) = 6\sqrt{3}[/tex]
Hopefully this was what you wanted, and is correct!
According to the fundamental theorem of algebra, which polynomial function has exactly 6 roots? f (x) = 5 x superscript 4 baseline 10 x squared 2 f (x) = 5 x superscript 5 baseline 3 x superscript 4 baseline 12 x cubed 7 x squared minus 2 x 15 f (x) = 6 x superscript 5 baseline x cubed minus 4 x squared x minus 5 f (x) = 7 x superscript 6 baseline 3 x cubed 12
The polynomial with 6 roots is the one of degree 6, so the correct option is:
[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]
Which polynomial function has 6 roots?
You need to remember that if p(x) is a polynomial of degree N, then it has N roots (such that some of these N roots may be equal or not).
Then we just need to find the polynomial of degree 6. (Remember that the degree represents the maximum exponent of the polynomial).
In this case, the only one of degree 6 is:
[tex]f(x) = 7x^6 + 3x^2 + 12[/tex]
Which is the last option.
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Answer:
The answer is D
Step-by-step explanation:
I took the test
29. Having a large enclosed space has advantages, but it can be more expensive to heat and cool. Assume an air conditioner uses about 4 BTUs/cubic foot each hour (a BTU is a measure of energy). How many BTUs will the air conditioner need to produce each hour to cool the structures? Hint: Multiply the enclosed space by the number of BTUs needed per cubic foot. (3 points)
1: Cylinder
2: Pyramid
3: Dome
The BTU required by the air conditioner/hour to cool the following structures is given as:
Cylinder: 4*π r² h (Where h is height, and r is the radius);Pyramid: 4 (lwh/3) (Where l is the length, w - the width, and h, the height;Dome: 4 * (4/3 πr³)What is the explanation for the above?It is to be noted that the BTU required to cool per cubic foot of space is 4BTUs.
Since we are not given the dimensions of the structures, the required constant is thus, multiplied by the volume of the structures whose equations have been given above.
Note that:
Volume translates to enclosed space; and
BTU means British Thermal Unit.
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Vince is cutting fabric strips for a project. He needs fabric strips that are 1212 inches wide. He cut his first fabric strip too wide. His percent error was 5%. How wide did Vince cut the fabric strip?
Answer:
13.125 inches wide
Step-by-step explanation:
5% more than 12.5 which is 12 1/2 as a decimal, equals 13.125 inches.
Multiply your needed fabric width (12.5 or 12 1/2) by (1 + %/percent you're increasing it by) to equal the width you cut instead:
[tex]12.5(1+5) = 12.5(1.05) = 13.125[/tex]
An extension cord 6 yards long costs $8.46. What is the price per foot? There are 3 feet in 1 yard.
Submit
The extension cord is an illustration of unit rates, and the price per foot is $0.47 per foot
How to determine the price per foot?The given parameters are:
Length = 6 yards
Cost = $8.46
Convert the length from yard to feet.
So, we have:
Length = 6 feet * 3
This gives
Length= 18 feet
The price per foot is then calculated using:
Rate = Cost/Length
This gives
Rate = 8.46/18
Evaluate
Rate = 0.47
Hence, the price per foot is $0.47 per foot
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#79 will give brainliest please help!
Step-by-step explanation:
this means the factors of the various terms of x and the constant.
a = 4
b = 1
c = 9
and yes, if there would be negative factors, the signs wold be part of a, b and c too.
overall, this is then used to solve the quadratic equation.
the general solution is
x = (-b ± sqrt(b² - 4ac))/(2a)
Describe the transformations necessary to transform the graph of f(x) into that of g(x).
Using translation concepts, it is found that the necessary transformations are given as follows:
Reflection over the y-axis. Horizontal stretch by a factor of 2.Shift left 3 units.Reflection over the x-axis.Shift down 1 unit.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
The original function f(x) is given by:
[tex]f(x) = \sqrt{x}[/tex]
The transformations are as follows:
For the values of x, the function was multiplied by -1/2 and then 3 was added. Thus it was reflected over the y-axis, horizontally stretched by a factor of 2 and shifted left 3 units.Outside the domain, in the values of y, the function was multiplied by -1 and then subtracted by 1, hence it was reflected over the x-axis and shifted down one unit.More can be learned about translation concepts at https://brainly.com/question/4521517
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Evaluate
-
b
2a
when a = 4 and b = -3.
Answer:
=24
Step-by-step explanation:
Correct Q:
-b•2a
Ans:
Put the values.=+3*2•4
=24