Answer:
We can start solving this problem by first identifying what the elements of the sets really are.
R is composed of real numbers. This means that all numbers, whether rational or not, are included in this set.
Z is composed of integers. Integers include all negative and positive numbers as well as zero (it is essentially a set of whole numbers as well as their negated values).
W on the other hand has 0,1,2, and onward as its elements. These numbers are known as whole numbers.
W ⊂ Z: TRUE. As mentioned earlier, Z includes all whole numbers thus W is a subset of it.
R ⊂ W: FALSE. Not all real numbers are whole numbers. Whole numbers must be rational and expressed without fractions. Some real numbers do not meet this criteria.
0 ∈ Z: TRUE. Zero is indeed an integer thus it is an element of Z.
∅ ⊂ R: TRUE. A null set is a subset of R, and in fact every set in general. There are no elements in a null set thus making it automatically a subset of any non-empty set by definition (since NONE of its elements are not an element of R).
{0,1,2,...} ⊆ W: TRUE. The set on the left is exactly what is defined on the problem statement for W. (The bar below the subset symbol just means that the subset is not strict, therefore the set on the left can be equal to the set on the right. Without it, the statement would be false since a strict subset requires that the two sets should not be equal).
-2 ∈ W: FALSE. W is just composed of whole numbers and not of its negated counterparts.
Step-by-step explanation:
Certain elements and sets are examined for their relationships with the sets of real numbers, integers, and whole numbers; identifying which elements belong to which sets and if one set is a subset of another.
When comparing different sets of numbers, we analyze whether one set is a subset of another and whether certain elements belong to specific sets. The given question involves the sets R (real numbers), Z (integers), and W = {0, 1, 2, ...}, also known as the set of whole numbers or non-negative integers.
→ W ⊂ Z: This is true because all elements of W are non-negative integers, which are a subset of Z, the set of all integers including negative, zero and positive whole numbers.
→ R ⊂ W: This is false because the set of real numbers includes irrational numbers as well as negative numbers, which are not included in W.
→ 0 ∈ Z: This is true because zero is an integer and, therefore, is an element of Z.
→ ∅ ⊂ R: This is true because the empty set is a subset of all sets, including the set of real numbers.
→ {0, 1, 2, ...} ⊆ W: This is true because this set is exactly W itself, and a set is always a subset of itself.
→ -2 ∈ W: This is false because W contains only non-negative integers, and -2 is a negative number.
Any help? Simplify cos^2x-cos^4x/tanx
[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{cos^2(\theta )-cos^4(\theta )}{tan(\theta )}\implies \cfrac{cos^2(\theta )[1-cos^2(\theta )]}{\frac{sin(\theta )}{cos(\theta )}}\implies \cfrac{cos^2(\theta )[sin^2(\theta )]}{\frac{sin(\theta )}{cos(\theta )}} \\\\\\ \cfrac{cos^2(\theta )[sin^2(\theta )]}{1} \cdot \cfrac{cos(\theta )}{sin(\theta )}\implies cos^3(\theta )sin(\theta )[/tex]
A triangle with one angle larger than 90° is called a(n) triangle.
Answer:
Step-by-step explanation:
Obtuse
Best regards
Answer:
Obtuse triangle.
Step-by-step explanation:
An obtuse angle is an angle that is greater than 90 degrees and fans out. When used in a triangle, it makes all the other angles thin, or acute, and makes a very spread out kind of triangle. This is called an obtuse triangle.
Hope this helps!
An office manager needs to decide between two tables for the conference room. One is rectangular, 5 feet wide by 10 feet long. The other is a circle with an 8-foot diameter.
Which table can seat more people? Explain your answer be sure to support your answer using facts about the tables.
Answer:
Circle table
Step-by-step explanation:
More people will fit around the circle table then the rectangle table. You can find the distance around using the circumference.
C = πr² = π(4)²=16π = 50.24 feet
The perimeter of a rectangle table is P = 2l+2w = 2(10) + 2(5) = 30 feet.
With more than 20 feet more, the circle table will fit more.
need help filling in the blanks. (selling price and profit.)
Answer:
$7.73
$131,450
$9,500
$9.44
$12.44
$4,590
$107,600
$-1,620
Step-by-step explanation:
Let's take it one at a time. To find the fixed costs per unit, we use the formula.
[tex]FixedCostPerUnit=\dfrac{FixedCosts}{ForecastUnitSales}[/tex]
So our variables are.
Fixed Costs = $85,000
Forecast = 11,000 units
Now we compute.
[tex]FixedCostPerUnit=\dfrac{85,000}{11,000}[/tex]
[tex]FixedCostPerUnit=$7.73[/tex]
Now for the Gross Sales, we simply take the selling price per unit and multiply it to the forecast unit sales.
GrossSales = Selling Price x Forecast Unit Sales
GrossSales = $11.95 x 11,000
GrossSales = $131,450
To compute for the possible net profit, we use the formula:
[tex]NetProfit=(SellingPrice-TotalCostPerUnit)*ForecastUnitSales[/tex]
SellingPrice = $12.45
TotalCostPerUnit = $11.50
ForecastUnitSales = 10,000
NetProfit = (12.45 - 11.50) x 10,000
NetProfit = 0.95 x 10,000
NetProfit = $9,500
[tex]FixedCostPerUnit=\dfrac{FixedCosts}{ForecastUnitSales}[/tex]
FixedCosts = $85,000
ForecastUnitSales = 9,000
[tex]FixedCostPerUnit=\dfrac{85,000}{9,000}[/tex]
FixedCostPerUnit = $9.44
Now that we have our Fixed Cost Per Unit we simply add our Variable Cost to get the Total Cost Per Unit.
TotalCostPerUnit = FixedCostPerUnit + VariableCost
TotalCostPerUnit = $9.44 + $3.00
TotalCostPerUnit = $12.44
Now for the Net Profit.
[tex]NetProfit=(SellingPrice-TotalCostPerUnit)*ForecastUnitSales[/tex]
SellingPrice = $12.95
TotalCostPerUnit = $12.44
ForecastUnitSales = 9,000
NetProfit = (12.95 - 12.44) x 9,000
NetProfit = 0.51 x 9,000
NetProfit = $4,590
Now we're looking for Gross Sales again, so we use:
GrossSales = Selling Price x Forecast Unit Sales
GrossSales = $13.45 x 8,000
GrossSales = $107,600
[tex]NetProfit=(SellingPrice-TotalCostPerUnit)*ForecastUnitSales[/tex]
SellingPrice = $13.45
TotalCostPerUnit = $13.63
ForecastUnitSales = 8,000
NetProfit = (13.45 - 13.63) x 8,000
NetProfit = -0.18 x 9,000
NetProfit = $-1,620
So we can see that we have a profit loss at 8,000 units and a selling price of $13.45
A farmer sells 8.9 kilograms of apples and pears at the farmer's market. 3 /4 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer:
[tex]2.225\ kg[/tex] of pears
Step-by-step explanation:
Let
x----> kilograms of apples
y----> kilograms of pears
we know that
[tex]x+y=8.9[/tex] ----> equation A
[tex]x=(3/4)8.9=6.675\ kg[/tex]
Substitute the value of x in the equation A
[tex]6.675+y=8.9[/tex]
[tex]y=8.9-6.675[/tex]
[tex]y=2.225\ kg[/tex]
Answer: 2.225 kg
Step-by-step explanation:
You know that:
- The total weight the farmer sold was 8.9 kilograms.
- 3/4 of this weight is apples, and the rest is pears.
Therefore, to calculate the amount of kilograms of pears she sold at the farmer's market (which you can call x), you need to apply the following proccedure.
Thefore, you obtain the following result:
[tex]x=8.9kg-(8.9kg*\frac{3}{4})\\x=2.225kg[/tex]
The michigan state lottery runs a game in which you pay $1 to buy a ticket containing a three–digit number of your choice. if your number is drawn at the end of the day, you win $500.
Answer:Please, edit and put the full question on here
Step-by-step explanation:
otherwise i connot annswer your question
The measurement of one angle of a right triangle is 42°. What is the measurement of the third angle?
Answer:
48°
Step-by-step explanation:
The sum of the three angles of a right triangle is 180°.
If one angle is 90° and another is 42°, then
90° + 42° + x = 180°
132° + x = 180°
x = 180° - 132° = 48°
The third angle is 48°.
Justin Bieber is thrown horizontally at 10.0m/s from the top of a cliff 122.5 m high.
How long does it take to reach the ground?
What is the horizontal displacement?
What is Justin's final velocity?
Answer:
Step-by-step explanation:
How long it takes to reach the ground is a y-dimension thing, and horizontal displacement is an x-dimension thing. So let's set up a table with the info we have in each dimension:
x y
V₀ 10.0 m/s 10.0 m/s
Δx ? -122.5 m
a 0 m/s/s -9.8 m/s/s
v 10.0 m/s ?
t ? ?
That seems like an awful lot of question marks, doesn't it?
The first question asks us for the time, t, it takes for the pathetic and greatly disliked Justin Bieber to hit the ground. We will use the equation:
Δx = V₀t + 1/2at²
Filling in our values using the y-dimension stuff only:
[tex]-122.5 = 10.0t+\frac{1}{2}(-9.8)t^2[/tex] which simplifies to
[tex]-122.5=10.0t-4.9t^2[/tex]
Hmmm...this is beginning to resemble a parabolic equation you probably already studied in Algebra 2!
We can solve for t by getting everything on one side and setting the equation equal to 0. We set it equal to 0 since the height on the ground is 0:
[tex]-4.9t^2+10.0t+122.5=0[/tex]
When you factor that for the 2 values of t, you get
t = -4.1 and 6.1
Of course, since time can't EVER be negative, we use a t value of 6.1. That's how long it takes to hit the ground. That t value can now be filled into the t values in our table above. We need that t value for the next part that asks us the horizontal displacement, Δx. This is x-dimension stuff now. Using the same equation:
Δx =[tex]10.0(6.1)+\frac{1}{2}(0)(6.1)^2[/tex]
Of course since the acceleration in the x-dimension is always 0, the whole portion of the equation after the equals sign is eliminated, leaving us with
Δx = 10.0(6.1)
Δx = 61 m
Poor Justin, upon his demise, hits the ground. Therefore, his final velocity is 0, since his body met the ground and stopped dead.
once again text is for min word req the problem is in the image again
Set the two equations to equal each other and solve:
3x-2 = x+2
Subtract x from each side:
2x -2 = 2
Add 2 to each side:
2x = 4
Divide both sides by 2:
x = 4/2 = 2
Now replace x with 2 in one of the equations and solve for y:
y = 3x -2 = 3(2) - 2 = 6-2 = 4
X = 2, Y = 4
(2,4)
A rock is thrown upwards with in total velocity of 75 ft/s from a height of 225 feet. The height h of the rock above the ground t seconds after being released is given by h(t)=-16tt^2+75+225. Determine the time in seconds required for the rock to reach its maximum height. Round your answer to three decimal places.
Answer:
it would take 33 5.5 s to reach it's maximum height
Step-by-step explanation:
Previous balance = $102.35 Finance charge = $1.24 New purchases = $15.73 Payments/credits = $12.00 New balance = $______
Answer:
$97.38
Step-by-step explanation:
Subtract the finance charge and new purchases from the previous balance.
102.35 - 1.24 - 15.73 = 85.38
Add the payment/credit
85.38 + 12 = 97.38
Answer:
$107.32
Step-by-step explanation:
GivenNew balance = previous balance + finance charge + purchases - payments
Previous balance = $102.35
Finance charge = $1.24
Purchases = $15.73
Payments = $12.00
FindNew balance
SolutionFill in the given information and do the arithmetic.
... New balance = previous balance + finance charge + purchases - payments
... New balance = $102.35 + $1.24 + $15.73 - $12.00
... New balance = $107.32
Amazon receives 5% of the cost of all sales made on their website. How much does Amazon make on a shoes sale of $80?
If Amazon gets 5% of each sale they make, find 5% of the $80 sale. You have to convert 5% to a decimal, which is 0.05. → 80 * 0.05 is $4 which means that if they sell something for $80, Amazon will recieve $4.
Answer:
4$
Step-by-step explanation:
In your own words, without providing the formulas, describe the difference between simple interest and compound interest. Which type of interest earns money more quickly?
Simple interest is when interest is paid once on money. Compound interest is paid periodically. Compound interest earns money more quickly because you are actually earning interest on interest. For example, if interest is compounded monthly you will received interest on your principal in January, and then in February you will receive interest on the principal and on the interest that was earned in January.
A piece of wire 24 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle. (a) How much wire should be used for the square in order to maximize the total area? Incorrect: Your answer is incorrect. m (b) How much wire should be used for the square in order to minimize the total area?
The solution to this problem involves using calculus to model the total area as a function of the lengths of the wire used for the square and the circle. However, without further context or information, a concrete answer cannot be provided.
Explanation:In this given case, you have a wire of length 24m that needs to be bent into two shapes - a square and a circle - and we need to know how much wire should be used for the square to maximize or minimize total area. The problem involves concept of both geometry and calculus.
To find the solution we must determine the lengths for the square and the circle that will maximize or minimize the total area. But the concept of area maximization and minimization comes from calculus, especially derivative application. Specifically, to find the maximum or minimum area, we would model the total area as a function of lengths and use first derivative to find where the area is maximized and minimized. Unfortunately, without more context or information, we cannot provide an accurate answer to this question.
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To maximize the total area, use 192 / (2π + 8) units of wire for the square and 24 - 192 / (2π + 8) units of wire for the circle. To minimize the total area, follow the same wire lengths.
Explanation:To maximize the total area, we need to find the lengths of the wire that will create squares and circles with the largest possible areas. Let's start with part (a).
Part (a)
Let the length of the wire used for the square be x. Then the length of the wire used for the circle would be 24 - x. The perimeter of the square is 4x, so the side length of the square is x/4. The circumference of the circle is 2πr, where r is the radius. Since the wire used for the circle is 24 - x, we have 2πr = 24 - x. Solving for r, we get r = (24 - x) / (2π).
The area of the square is (x/4)^2 = x^2/16. The area of the circle is πr^2 = π((24 - x) / (2π))^2 = (24 - x)^2 / (4π). The total area is the sum of the areas of the square and the circle, so we need to maximize (x^2/16) + (24 - x)^2 / (4π).
Let's find the derivative of this expression with respect to x, set it equal to 0, and solve for x:
(1/8)x - (24 - x) / (2π) = 0
Simplifying, we get (1/8)x = (24 - x) / (2π)
Multiplying both sides by 8 and 2π, we have 2πx = 8(24 - x)
Expanding, we get 2πx = 192 - 8x
Bringing like terms to one side, we have 2πx + 8x = 192
Combining like terms, we get (2π + 8)x = 192
Dividing both sides by (2π + 8), we have x = 192 / (2π + 8)
Now that we have the value of x, we can calculate the lengths of the wire used for the square and the circle. The length of the wire used for the square is x, which is equal to 192 / (2π + 8). The length of the wire used for the circle is 24 - x, which is equal to 24 - 192 / (2π + 8).
So, the solution for part (a) is to use 192 / (2π + 8) units of wire for the square and 24 - 192 / (2π + 8) units of wire for the circle in order to maximize the total area.
Part (b)
To minimize the total area, we follow a similar approach. The area of the square is x^2/16 and the area of the circle is (24 - x)^2 / (4π). We want to minimize (x^2/16) + (24 - x)^2 / (4π).
Again, let's find the derivative of this expression with respect to x, set it equal to 0, and solve for x:
(1/8)x - (24 - x) / (2π) = 0
Expanding and rearranging, we get (2π + 8)x = 192
Dividing both sides by (2π + 8), we have x = 192 / (2π + 8)
As in part (a), the length of the wire used for the square is x, which is equal to 192 / (2π + 8), and the length of the wire used for the circle is 24 - x, which is equal to 24 - 192 / (2π + 8).
Therefore, the solution for part (b) is to use 192 / (2π + 8) units of wire for the square and 24 - 192 / (2π + 8) units of wire for the circle in order to minimize the total area.
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The rectangle below has an area of 81- x^2 square meters and a width of 9 - x meters
The length of a rectangle with an area of 81 - x² square meters and a width of 9 - x meters is (81 - x²) / (9 - x) .
To find the expression that represents the length of the rectangle, we need to use the formula for the area of a rectangle, which is:
Area = Length × Width
Given that the area of the rectangle is 81 - x² square meters and the width is 9 - x meters, we can set up the equation as:
81 - x² = Length × (9 - x)
To isolate the Length, we divide both sides of the equation by the Width (9 - x):
Length = (81 - x²) / (9 - x)
Therefore, the expression that represents the length of the rectangle is:
Length = (81 - x²) / (9 - x)
Complete Question:
The rectangle below has an area of 81- x² square meters and a width of 9 - x meters. What expression represents the length of the rectangle?
Find y of this shape.
as shown in figure LN = KN
triangle KLN is right angle triangle so using Pythagoras theorem
KL^2 = LN^2 + KN^2
KL^2 = LN^2 + LN^2 = 2LN^2
KL = √(2LN^2)
y = LN√2
now lets find value of LN
now LMN is also right angle triangle so using trigonometry
MN/LN = sin 30
putting value of MN=5 and sin 30 which is 1/2
5/LN = 1/2
LN = 5×2= 10
putting it back in our first equation
y = LN√2
y = 10√2
A ladder leans against a building, making a 70° angle of elevation with the ground. The top of the ladder reaches a point on the building that is 39 feet above the ground.
To the nearest tenth of a foot, what is the distance between the base of the building and the base of the ladder?
Question 4 options:
13.3 ft
14.2 ft
36.6 ft
41.5 ft
Question 5
A bird fountain is located 6 m from the base of Joey's apartment building. From his window, Joey can see it at a 51° angle of depression.
To the nearest tenth of a meter, how far up the building is Joey's window?
Question 5 options:
4.9 m
7.4 m
7.7 m
9.5 m
➷ It would help if you drew it out as a triangle
You will notice that you need to use tan
tan70 = 39/x
x = 39/tan70
x = 14.194
The correct option would be 14.2 ft
You will need to use tan
tan51 = 6/x
x = 6/tan51
x = 4.8587
The correct option would be 4.9m
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Classify each function. (a) y = x − 3 x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3 (b) y = x + x2 x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function (c) y = 5x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function (d) y = x5 trigonometric function power function exponential function root function logarithmic function (e) y = 7t6 + t4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6 (f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function
Answer:
a) rational
b) rational
c)exponential
d) power function
e) polynomial function of degree 6
f) trig function
Step-by-step explanation:
Functions can be classified by the operations they contain. Remember the following functions:
Power function has as its main operation of an exponent on the variable.Root function has as its main operation a radical.Log function has as its main operation a log.Trig function has as its main operation sine, cosine, tangent, etc.Rational exponent has as its main function division by a variable.Exponential function has as its main operation a variable as an exponent.Polynomial function is similar to a power function. It has as its main function an exponent of 2 or greater on the variable.Below is listed each function. The bolded choice is the correct type of function:
(a) y = x − 3 / x + 3 root function logarithmic function power function trigonometric function rational function exponential function polynomial function of degree 3
(b) y = x + x2 / x − 2 power function rational function algebraic function logarithmic function polynomial function of degree 2 root function exponential function trigonometric function
(c) y = 5^x logarithmic function root function trigonometric function exponential function polynomial function of degree 5 power function
(d) y = x^5 trigonometric function power function exponential function root function logarithmic function
(e) y = 7t^6 + t^4 − π logarithmic function rational function exponential function trigonometric function power function algebraic function root function polynomial function of degree 6
(f) y = cos(θ) + sin(θ) logarithmic function exponential function root function algebraic function rational function power function polynomial function of degree 6 trigonometric function
The functions (a) y = x − 3 / x + 3 is a rational function, (b) y = x + x2 / x − 2 is a rational function, (c) y = 5ˣ is an exponential function, (d) y = x⁵ is a power function, (e) y = 7t⁶ + t⁴ − π is a polynomial function, (f) y = cos(θ) + sin(θ) is a trigonometric function.
What is function?Each element of X receives exactly one element of Y when a function from one set to the other is used. The sets X and Y are collectively referred to as the function's domain and co-domain, respectively.
(a) y = x − 3 / x + 3 is a rational function, as the terms are rational.
(b) y = x + x2 / x − 2 is a rational function, as the terms are rational.
(c) y = 5ˣ is an exponential function as the x is in the power.
(d) y = x⁵ is a power function, as 5 is the power.
(e) y = 7t⁶ + t⁴ − π is a polynomial function of degree 6 as the highest degree is 6.
(f) y = cos(θ) + sin(θ) is a trigonometric function, as the cos and sin are trigonometric functions.
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If the dimensions of a rectangle are cut in half, then the new area is blank the original area.
1/4
half
four times
twice
[tex]The \: new \: area \: would \: be \: \frac{1}{4} \: of \: the \: original[/tex]
Answer:
1/4
Step-by-step explanation:
Are there less than 1 million, exactly 1 million, or greater than 1 million milligrams in 1 kilograms?
Answer: There is exactly 1 million in 1 kilogram
Step-by-step explanation:
Answer:
ello mate
Step-by-step explanation:
Solve. X2 ? 5x = 14 A) x = 0, x = 5 B) x = 0, x = ?5 C) x = 2, x = ?7 D) x = 7, x = ?2
could someone please just help me out. i’m struggling pleasee
Answer:
NO = 4.5
MO = 3.5
LN = sqrt(44)
Step-by-step explanation:
Since the value of the base of the triangles is 8, and the value of NO is 4.5, the value of MO is MN - NO, which is 8 - 4.5, which comes out to 3.5.
Then, we apply the quadratic formula to triangle MLO to find that the middle line value is sqrt(23.75). Then we use the quadratic formula on traingle OLN to find the LN is sqrt(44).
Julia won the race by one hundredth of a second Write the amount of time she won by as a fraction
Answer:
1/100
Step-by-step explanation:
Eleni bought 3 packs of crayons. She then found 3 crayons in her desk Eleni now has 24 crayons. How many crayons were in each pack? Explain how you solved the problem.
Answer:
7 crayons in each pack
Step-by-step explanation:
1. subtract the 3 found crayons from the total (24)
24-3 = 21
2. divide 21 by 3 packs
21/3 = 7
Final answer:
Eleni ended up with 24 crayons after buying 3 packs and finding 3 more in her desk. To find the number of crayons per pack, we subtract the 3 found crayons from the total, giving us 21 crayons that came from the packs. Dividing 21 by the 3 packs she bought, we get 7 crayons per pack.
Explanation:
The subject of this question is mathematics, specifically an arithmetic problem that involves addition and division. Eleni bought 3 packs of crayons and found 3 more crayons in her desk, which resulted in her having a total of 24 crayons. To solve for the number of crayons in each pack, we start by subtracting the 3 crayons she found from the total, leaving us with 21 crayons that came from the packs. We then divide this number by the number of packs to find out how many crayons were in each pack.
Here's a step-by-step solution:
Start with the total number of crayons Eleni has after finding the extra ones in her desk: 24 crayons.
Subtract the 3 crayons found in her desk: 24 crayons - 3 crayons = 21 crayons.
Divide the resulting number of crayons by the number of packs she bought: 21 crayons \/ 3 packs = 7 crayons per pack.
Therefore, there were 7 crayons in each pack.
What is the area of a triangle (picture provided)
Answer:
C
Step-by-step explanation:
Use the Heron's formula for the area of the triangle:
[tex]A=\sqrt{p(p-a)(p-b)(p-c)},[/tex]
where a, b, c are lengths of triangle's sides and [tex]p=\dfrac{a+b+c}{2}.[/tex]
Since [tex]a=2,\ b=7,\ c=8,[/tex] then
[tex]p=\dfrac{2+7+8}{2}=8.5.[/tex]
Hence,
[tex]A=\sqrt{8.5(8.5-2)(8.5-7)(8.5-8)}=\sqrt{8.5\cdot 6.5\cdot 1.5\cdot 0.5}=\\ \\=\sqrt{41.4375}\approx 6.4\ un^2.[/tex]
Answer:
Area Δ = 6.4 units² ⇒ the answer is (c)
Step-by-step explanation:
* Use the formula of the area:
∵ Area of the triangle = 1/2 (a)(b) sin(C)
∵ We have the length of the 3 sides
∴ Use cos Rule to find the angle C
∵ cos(C) = (a² + b² - c²)/2ab
∵ a = 2 , b = 7 , c = 8
∴ cos(C) = (2² + 7² - 8²)/2(2)(7) = 4 + 49 - 64/28 = -11/28
∴ m∠C = 113.1°
∴ Area Δ = (1/2)(2)(7)sin(113.1) = 6.4 units²
Eduardo has a red 6-sided number cube and a blue 6-sided number cube. The faces of the cubes are numbered 1 through 6. Eduardo rolls both cubes at the same time. The random variable X is the number on the red cube minus the number on the blue cube. What is P(−2≤X≤1)? Enter your answer, in simplest fraction form, in the box.
Answer: 5/9
Step-by-step explanation: Just took the test
Answer:
P(−2≤X≤1) = 5/9.
Step-by-step explanation:
Given:
P(-2≤X≤1) and he random variable X is the number on the red cube minus the number on the blue cube
x = -2. -1. 0 and 1
Let's take first number as in the red cube and the second number is in blue cube.
We get x = -2 for the following outcomes
(1, 3), (2, 4), (3, 5), and (4, 6). which is 4 favorable outcomes.
We get x = -1, for the following outcomes:
(1, 2), (2, 3), (3, 4), (4, 5), and (5, 6). which is 5 favorable outcomes
We get x = 0, when (1, 1) (2, 2)(3, 3)(4, 4) (5, 5),(6, 6) which is 6
We get x = 1, when (2, 1), (3, 2) (4, 3) (5, 4) (6, 5), which is 5.
The number of favorable outcomes= 4 + 5 + 6 + 5 = 20
The number of possible outcomes = 36 (when we toss the two dices, the possible number of outcomes is 36)
The required probability P(−2≤X≤1) = The total number of favorable outcomes / the total number of possible outcomes
= 20/36
P(−2≤X≤1) = 5/9.
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If prices increase at a monthly rate of 3.7%, by what percentage do they increase in a year?
An apple orchard harvested 3,584 apples and separated them evenly into 112 bags. How many apples are in each bag?
Answer: 32
Step-by-step explanation:
3,584 / 112 = 32
Determine if the function is an even function, an odd function or neither. Y=-6x^6-5x^2- 2
Answer:
Even
Step-by-step explanation:
The function Y=-6x^6-5x^2- 2 is a polynomial. A polynomial function is a function where a whole number exponent greater than 1 is on the variable. All polynomial functions have a degree known as the highest exponent. This degree also determines if the functions is even, odd or neither.
The highest exponent on the polynomial is 6 which is an even number. This polynomial is even.
Answer:even
Step-by-step explanation:
got it right on edg. quiz
Jamal will slice a right circular cylinder into two congruent pieces. Which two dimensional plane sections could result from the slice Jamal makes?
Answer:
An ellipse and a rectangle.
Step-by-step explanation:
If Jamal cuts the right circular cylinder anywhere but its extremities, the resulting shapes on both pieces will be an ellipse.
If he cuts precisely in a perpendicular way in relation to the ends, he will then form two new right circular cylinders, then the ellipses obtained would be circles.
If Jamal cuts the right circular cylinder lengthwise, going from one end to the other, even if it's not perpendicular to the base, he will obtain a rectangular shape.
A two-dimensional plane section that could result from slicing a right circular cylinder into two congruent pieces is a circle.
When a right circular cylinder is sliced at the center of the vertical height, the surface of either section is a circle.
However, when a right circular cylinder is sliced at the center of the circular surface, the surface of either section is a rectangle.
Hence, the resulting shapes are circles and rectangles
Read more about two-dimensional planes at:
https://brainly.com/question/13067715