Answer:
A. If the diameter is 6 cm, then the radius is half of that:
radius = 6 cm / 2 = 3 cm
B. The formula for the surface area of a cylinder is:
S.A. = 2πr^2 + 2πrh
C. Plugging in the values for r, h, and π:
S.A. = 2π(3 cm)^2 + 2π(3 cm)(12 cm)
S.A. = 2π(9 cm^2) + 2π(36 cm^2)
S.A. = 18π cm^2 + 72π cm^2
S.A. = 90π cm^2
Therefore, the surface area of the soup can is 90π square centimeters. This can be simplified to approximately 282.74 square centimeters by using the value 3.14 for π.
what is the acceleration of a bus whose speed changes from 126 m/s to 306 m/s over a period of 3seconds
Answer: The acceleration of the bus can be calculated using the formula:
a = (v2 - v1) / t
where:
a = acceleration
v2 = final velocity = 306 m/s
v1 = initial velocity = 126 m/s
t = time = 3 seconds
Substituting the given values into the formula, we get:
a = (306 m/s - 126 m/s) / 3 s
a = 180 m/s / 3 s
a = 60 m/s^2
Therefore, the acceleration of the bus is 60 m/s^2.
Step-by-step explanation:
Determine the voltage dropped across
The answer of the given question based on the Voltage drop the answer is , the voltage dropped across R3 is 277.11 V.
What is Ohm's law?Ohm's law is fundamental principle in electrical engineering and physics that describes relationship between voltage, current, and resistance in electrical circuit. It states that current through conductor between two points is directly proportional to voltage across two points, and inversely proportional to resistance between them.
To determine the voltage dropped across R3, we need to use Ohm's law and Kirchhoff's circuit laws. First, we can calculate the total resistance in the circuit:
Rtotal = R1 + R2 || R3
R2 || R3 = (R2 * R3) / (R2 + R3) (parallel resistance formula)
Rtotal = R1 + (R2 || R3)
Rtotal = 152 + ((18 * 362) / (18 + 362))
Rtotal = 149.89 Ω (rounded to 2 decimal places)
Next, we can use Ohm's law to calculate the current flowing through the circuit:
I = ET / Rtotal
I = 120 / 149.89
I = 0.8004 A (rounded to 4 decimal places)
Finally, we can use Kirchhoff's voltage law to determine the voltage dropped across R3:
ET = IR1 + IR2 || IR3 + IR3
ET = I(R1 + R2 || R3) + IR3
ET - I(R1 + R2 || R3) = IR3
R3 = (ET - I(R1 + R2 || R3)) / I
R3 = (120 - (0.8004 * (152 + ((18 * 362) / (18 + 362))))) / 0.8004
R3 = 277.11 V (rounded to 2 decimal places)
Therefore, the voltage dropped across R3 is 277.11 V.
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the sidesof one of the pentagons are a, , 20,c and 30 respectively if the corresponding sides of hte other pentagon are 46, 50, d, 102 and 24 respectively. what are the mising measures
The missing measures of the pentagon are a = 18.4, c = 61.2, d = 75, and x = 22.08.
What are the missing measures of the pentagon?
Let's label the sides of the first pentagon as a, 20, c, 30, and x, and the sides of the second pentagon as 46, 50, d, 102, and 24.
Since both pentagons have the same shape, we know that the corresponding sides are proportional. This means we can set up the following equations:
a/46 = 20/50 = c/d = 30/102 = x/24
Solving for the missing variables:
a = 46(20)/50 = 18.4
c = 30(102)/50 = 61.2
d = 50(30)/20 = 75
x = 24(46)/50 = 22.08
Therefore, the missing measures are a = 18.4, c = 61.2, d = 75, and x = 22.08.
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I need help with this question.
Answer:
System A: C)infinite answers
System B: B)special answer (x,y)=(3,1)
Step-by-step explanation:
System A:
if we find sum of same variables, we get 5x-5x-y+y=-2+2, it means 0=0 so, this system has infinite answers.
System B:
same thing applied here,
x-x+4y+4y=7+1
8y=8
y=1
so,
x+4*1=x+4=7
x=3
A surveyor wants to know the length of a tunnel built through a mountain. According to her equipment, she is located 212 meters from one entrance of the
tunnel, at an angle of 57° to the perpendicular. Also according to her equipment, she is 119 meters from the other entrance of the tunnel, at an angle of 14° to
the perpendicular, Based on these measurements, fiad the length of the entire tunnel,
Do not round any intermediate computations. Round your answer to the nearest tenth..
Note that the figure below is not drawn to scale.
Answer: Approximately 2 * AC = 737.2 meters. Rounded to the nearest tenth, the answer is 737.2 meters.
Step-by-step explanation: To solve the problem, we can draw a diagram:
A
/|
/ |
/ | x
/ |
/ |
/θ |
/ |
/ |
/ |
/ |
/ |
B-----------C
y
where A and B are the entrances of the tunnel, C is the point in the middle of the tunnel that we want to find, and θ, x, and y are the angles and distances given in the problem. We want to find the length of AC.
Using trigonometry, we can find the distances BC and AB: tan(57°) = x / y => x = y * tan(57°)
tan(14°) = x / (y + 212) => x = (y + 212) * tan(14°)
Setting these two expressions for x equal, we get: y * tan(57°) = (y + 212) * tan(14°)
Solving for y, we get: y = 212 / (tan(57°) / tan(14°) - 1) ≈ 286.5 meters
Now we can use the law of sines to find the length of AC: sin(θ) / AC = sin(14°) / BC = sin(57°) / AB
Solving for AC, we get: AC = AB * sin(θ) / sin(57°) ≈ 368.6 meters
Therefore, the length of the entire tunnel is approximately 2 * AC = 737.2 meters. Rounded to the nearest tenth, the answer is 737.2 meters.
Mr. Bowen rents a lane at a bowling alley for 3.5 hours. The cost to rent the lane is $20 per hour. Which expression represents the change in the amount of money he has after paying for the lane?
Answer:
c= 3.5 x 20
Step-by-step explanation:
rent $20 hr
Time 3.5 hr
Cost $70
Can I get help with this question? I am lost!
Answer:
4x
Step-by-step explanation:
mark me hope it is a good answer
Answer:
The factors of 2x^2 are 2, x, and 2x.
due in 5 minutes 8-1/4n≥20
Answer:
n ≤ -48
Step-by-step explanation:
What is the answer of :20y=-42
Step by step
Answer:
y=-21/10
Step-by-step explanation:
20y=-42
20y/20=-42/20
y=-42/20
y=-21/10
(4-5z)(4+5z)
For multiplying Special cases.
Answer:
16 - 25z²
Step-by-step explanation:
(4 - 5z)(4 + 5z)
each term in the second factor is multiplied by each term in the first factor, that is
4(4 + 5z) - 5z(4 + 5z) ← distribute parenthesis
= 16 + 20z - 20z - 25z² ← collect like terms
= 16 - 25z²
Answer:
16-25z
Step-by-step explanation:
you will use the first term 4 to multiply the first which is (4+5z) then after that you will use the second term which is -5z to multiply the same (4+5z) to give you 16+20z-20z-25z then you will also simplify to give you 16-25z
Question 7 Find the area of the region that is inside the rectangle and outside the circles (blue region ). The circles have a diameter of 3cm
The area of the blue region is 28.93 cm²
How to find the area of the blue region?To find the area of the blue region, we need to subtract the area of the four circle from the area of the rectangle.
Since the diameter of the circle is 3cm. The radius (r) = 3/2 = 1.5 cm.
Length of the rectangle (L) = 4 * diameter of circle (we have 4 circles)
Length of the rectangle = 4 * 3 = 12 cm
Width of the rectangle (W) = diameter of circle = 3 cm
Area of rectangle = L * W
Area of rectangle = 12 * 3 = 36 cm²
Area of circle = πr²
Area of circle = π * 1.5² = 2.25π cm²
Area of the blue region = Area of rectangle - Area of circle
Area of the blue region = 36 - 2.25π
Area of the blue region = 36 - (2.25* 22/7)
Area of the blue region = 28.93 cm²
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Complete Question
Check the attached image
Select the correct answer. Consider functions h and k. The picture shows a one-to-one function diagram. x has values of minus 2, minus 1, 0, 1, and 2, and k of x has values of minus 2, minus 5, minus 6, minus 5, and minus 2. Every x value has a relationship in k of x. What is the value of ? A. B. C. D.
The numeric value of the composite function at x = 1 is given as follows:
(h ∘ k)(1) = 28.
What is the composite function of f(x) and g(x)?The composite function of f(x) and g(x) is given by the rule presented as follows:
(f ∘ g)(x) = f(g(x)).
For the composition of two functions, we have that the output of the inner function, in this example g(x), serves as the input of the outer function, in this case f(x).
Hence the numeric value at x = 1 for the function in this problem is:
h(k(1)).
The numeric value of k at x = 1 is:
k(1) = 3.
Then, as the numeric value of h at x = 3 is of 28, the composite function is:
(h ∘ k)(1) = 28.
Missing InformationThe problem is given by the image presented at the end of the answer.
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Need the answer for A B C
Therefore , the solution of the given problem of percentage comes out to be this amount to the closest dollar, we get $1,042.
What precisely is a percentage?A number or measure that is represented as a proportion of 100 is known as a "a%" in statistics. Additionally, the terms "pct," "pct," and "pc" are not commonly used. However, it is commonly denoted by the symbol "%". There are no dimensions; the percentage total is flat. Since a percentage's numerator is almost always 100, percentages are actually integers. To indicate that a number is a percentage, either the percentage symbol (%).
Here,
a. The formula: can be used to calculate the weekly payment.
=> P = (Ar(1+r)ⁿ) / ((1+r)^n - 1)
A = 9900, r = 0.06/12, and n = 48 in this instance (since there are 4 years or 48 months in total).
Substituting these numbers into the formula, we get:
=> P = (99000.005(1+0.005)⁴⁸) / ((1+0.005)⁴⁸ - 1) ≈ $227.88
Therefore, the monthly payment is roughly $227.88.
=> Overall = P*n = $227.88 * 48 = $10,942.24
We arrive at $10,942 by rounding this sum to the closest dollar.
c. The total interest paid over the course of the loan's four-year term is equivalent to the total amount repaid less the loan balance:
Total interest equals the total sum less A, or $10,942 minus $9,900, or $1,042.
Rounding this amount to the closest dollar, we get $1,042.
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Part 1
The stem-and-leaf plots show the daily produce sales at Farmer's Market A and Farmer's Market B over the last 15 days. Use the stem-and-leaf plots to complete the statements
The mean for Farmer's Market A is $__, and the mean for Farmer's Market B is $__. From the means, you can conclude the average typical daily sales for Farmer's Market __ (A or B) is greater than the average typical daily sales for Farmer's Market __ (A or B)
According to the means, the average typical daily sales for Farmer's equation Market A are higher than the average typical daily sales for Farmer's Market B.
What is equation?A mathematical statement which thus proves the equality of two factors linked by an equal sign '=' is known as an equation. For example, 2x - 5 = 13. Two examples of phrases are 2x-5 and 13. The character '=' is used to connect the two expressions. A mathematical formula with two algebraic expressions on either side of a =) (=) is called an equation. It depicts the relationship of equivalence between left and right equations. In any formula, L.H.S. = R.H.S. (left side = right side).
[tex]$30 + $31 + $32 + $33 + $35 + 36 + $38 + $40 + $41 + $42 + $43 + $45 + $47 + $49 + $50 = $575 for Farmer's Market A[/tex]
Because there are 15 days, we divide the total sales by 15 to find the mean:
Farmer's Market A Mean [tex]= $575/15 = $38.33[/tex]
Farmers' Market B:
[tex]$20 + $22 + $24 + $26 + $28 + $31 + $32 + $34 + $36 + $39 + $40 + $42 + $44 + $46 + $49 = $524[/tex]
Farmer's Market A has a mean of $38.33, while Farmer's Market B has a mean of $34.93. According to the means, the average typical daily sales for Farmer's Market A are higher than the average typical daily sales for Farmer's Market B.
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11. College women who play have had more success than others with using social media to benefit from their name, image, and likeness (NIL).
Cοllege wοmen whο play have had mοre success than οthers with using sοcial media tο benefit frοm their name, image, and likeness. (False)
Why is it false?Female cοllege athletes and their success in using sοcial media tο mοnetize their name, image, and likeness which is false.
This statement means that female cοllege athletes whο participate in spοrts have been mοre successful in leveraging their name, image, and likeness fοr financial gain thrοugh sοcial media platfοrms than their nοn-athlete peers.
In οther wοrds, female athletes whο engage in spοrts don't have an advantage in mοnetizing their sοcial media presence and using it tο prοmοte their persοnal brand, cοmpared tο female cοllege students whο dο nοt participate in spοrts.
Therefore, it is false that college women who play have had more success than others with using social media to benefit from their name, image, and likeness
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Complete question:
True or False:
11. College women who play have had more success than others with using social media to benefit from their name, image, and likeness (___).
Drop down 1:
Select a Value
(2 + 4)(x- 6
(X+ 8)(x- 3)
(x - 8)(x + 3)
(x - 4) (x+ 6)
Drop down2:
Select a Value
(X+ 5)(x - 6)
(x-5)(x+ 6)
(X+ 10)(x - 3)
(X- 15)(x + 2)
Drop down 3:
(X-8)(x-9)
(X+8)(x+9)
(X-12)(x-6)
(X+12)(x+6)
The expressions after factorizing are;
1. (x+4)(x - 6). Option A
2. (x+ 5)(x - 6). Option A
3. (x - 8)(x - 9). Option A
How to determine the expressionsFrom the information given, we have the following quadratic equations;
x² - 2x - 24x² - x -30x² - 17x + 72To factorize the expressions, we need to first, multiply the coefficient of x² by the constant value.
Then, find the pair factors of the product whose sum would give the coefficient of x variable and substitute the values.
For the first expression;
x² - 2x - 24
x² - 6x + 4x - 24
group in pairs
(x² - 6x) + (4x -24)
factorize
x(x - 6) + 4(x - 6): (x+4)(x - 6)
x² - x - 30
x² - 6x + 5x - 30
group in pairs and factorize
x(x - 6) + 5(x - 6): (x+ 5)(x - 6)
x² - 17x + 72
x² - 9x - 8x + 72
Group in pairs and factorize
x(x - 9) - 8(x - 9): (x - 8)(x - 9)
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Set A consists of all odd integers between 0 and 10. Set B consists of all prime numbers less than 16 . How many numbers do Set A and Set B have in common?
Set A and Set B have 2 numbers in common: 3 and 7. The intersection of both sets is the set of numbers that appear in both sets.
Set A consists of all odd integers between 0 and 10, which are 1, 3, 5, 7, and 9. Set B consists of all prime numbers less than 16, which are 2, 3, 5, 7, 11, and 13. There are two numbers that Set A and Set B have in common: 3 and 7.
Sets A and B are both subsets of the set of all integers between 0 and 16. Set A is a subset of the set of all odd integers between 0 and 16, while Set B is a subset of the set of all prime numbers between 0 and 16. While Set A and Set B have 2 numbers in common, they are not the same set. Set A includes the numbers 1, 3, 5, 7, and 9, while Set B includes the numbers 2, 3, 5, 7, 11, and 13.
Each set includes a unique set of numbers, and the intersection of Set A and Set B is the set of numbers that appear in both Set A and Set B. In this case, the intersection of Set A and Set B is the set of 2 numbers that both sets have in common: 3 and 7.
In conclusion, Set A and Set B have 2 numbers in common: 3 and 7. While both sets include a unique set of numbers, the intersection of Set A and Set B is the set of numbers that appear in both sets.
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150 points please help
Answer:
150 isnt a thing but I will gladly take 5 :)
(2x+3)(2x−9)
Step-by-step explanation:
Hope this helps^^
riley afirma que hay infinitas soluciones para la ecuacion.2 (4x+1) + 8 = 4 (2x + 1 ) + 8 - _ por que la constante en cada lado de la ecuacion es 8, por lo que la ecuacion resulta en 8= 8
It should be noted that the value on the blank on the equation will be -2.
How to solve the equationThe equation given is:
2(4x+1) + 8 = 4(2x+1) + 8 - x
Simplifying the left-hand side:
8x + 2 + 8 = 8x + 4 + 8 - x
Simplifying the right-hand side:
8x + 4 + 8 - _ = 8x + 12 - x
Combining like terms on both sides:
8x + 10 = 8x + 12 - x
Subtracting 8x from both sides:
10 = 12 - x
x = 10 - 12
x = -2
The value will be -2 to make the equations equal.
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Elijah invested $94,000 in an account paying an interest rate of
4. 125% compounded quarterly. Kayden invested $94,000 in an account paying an interest rate of 4. 25% compounded daily. After 7 years, how much more money would Kayden have in his account than Elijah, to the nearest dollar?
Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar when compounded daily.
What is Compound interest?The interest that is accrued on both the principle and any prior interest is known as compound interest. This implies that the interest received in succeeding periods rises as the interest is added to the principle. Compound interest is a crucial idea in personal finance that may be utilised in calculations for both savings and loans.
The compound interest is given by the formula:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
For Elijah substituting the values we have:
[tex]A = $94,000(1 + 0.04125/4)^{(4*7)} = $129,852.94[/tex]
For Kayden substituting the values we have:
[tex]A = $94,000(1 + 0.0425/365)^{(365*7)} = $130,963.39[/tex]
The difference between the two amounts is:
$130,963.39 - $129,852.94 = $1,110.45
Therefore, Kayden would have $1,110.45 more in his account than Elijah after 7 years, to the nearest dollar.
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Answer:$1286 when rounded. Got it right
Step-by-step explanation:
Which is Greater? 5^100 or 3^150
It can be concluded that 3¹⁵⁰ is the greater among them.
How to get the solutionThis question can be solved if we use the numerical factorization concepts
Check itFirst, we do the factorization, looking for a number that is common between divisors 3 and 5
[tex]\begin{array}{r|l}\sf 100,150 & \sf 2\\\sf 50,75 & \sf 2\\\sf 25,75 & \sf 3\\\sf 25,25 & \sf 5\\\sf 5,5 & \sf 5\\\sf 1,1&\sf 1\end{array}[/tex]
With this, we can see that the number 25 is common between divisors 3 and 5.
It will be our main exponent, when factoring the exponents 100 and 150.
[tex]\begin{array}{cc}\sf 5^{100}&\sf 3^{150}\\\raisebox{5pt}{$\sf \Big(\big[5^{2}\big]^{2}\Big)^{25}$}&\raisebox{5pt}{$\sf \Big(\big[3^{2}\big]^{3}\Big)^{25}$}\\\raisebox{5pt}{$\sf \big(5^{4}\big)^{25}$}&\raisebox{5pt}{$\sf \big(3^{6}\big)^{25}$}\\\raisebox{5pt}{$\sf 625^{25}$}&\raisebox{5pt}{$\boxed{\bf729^{25}}$}\end{array}[/tex]
Since 729²⁵ > 625²⁵, it follows that 3¹⁵⁰ is the greater of the two
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A toy company is building dollhouse furniture. A rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters. What is the perimeter of the door of a scale drawing that uses a scale factor of 3. 5?
If a rectangle door of a dollhouse has a height of 7 centimeters and a width of 3 centimeters, the perimeter of the door in the scale drawing is 70 centimeters.
To find the perimeter of the door in the scale drawing, we first need to determine the dimensions of the door in the scale drawing. To do this, we need to multiply the actual dimensions of the door by the scale factor of 3.5.
The height of the door in the scale drawing would be 7 cm x 3.5 = 24.5 cm, and the width would be 3 cm x 3.5 = 10.5 cm.
The perimeter of the door in the scale drawing can be calculated by adding up the lengths of all four sides. The two vertical sides have a length of 24.5 cm, and the two horizontal sides have a length of 10.5 cm. Therefore, the perimeter of the door in the scale drawing is:
P = 2(24.5 cm) + 2(10.5 cm) = 49 cm + 21 cm = 70 cm
Note that the scale drawing is a proportional representation of the actual door, where all corresponding dimensions are multiplied by the same factor of 3.5.
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4) At the end of each quarter year, Rod makes a $500 payment into Lanagham Mutual Fund. If his investments earn 7.88% annual interest compounded quarterly, what will be the value of Rod's annuity in 20 years?
5) Bubba contributes $50 per month into the Vanguard National Bond Fund that earns 7.26% annual interest compounded monthly. What is the value of Bubba's investment after 25 years?
6) Ursula is considering opening an account with Crab Key Bank at 5.15% annual interest compounded quarterly. What is the equivalent APY?
7) How can you tell the difference if one bank offers an investment earning 8.75% annual interest compounded quarterly versus one earning 8.7% compounded monthly?
The value of each investment scenario based on the given interest compounded will be:
Rod's annuity after 20 years will be $30,904.95.Buba's investment value after 25 years will be $41,438.55.Ursula equivalent APY will be 5.25%.The different between an investment earning annual investment compounded ed quarterly and one earning compounded monthly is the number of times the interest is compounded each year.Let's discuss each scenario we have.
4) At the end of each quarter year, Rod makes a $500 payment into Lanagham Mutual Fund. If his investments earn 7.88% annual interest compounded quarterly, what will be the value of Rod's annuity in 20 years?The value of Rod's annuity after 20 years will be $30,904.95. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.88%), n is the number of times compounded per year (quarterly, or 4), and t is the number of years (20).
5) Bubba contributes $50 per month into the Vanguard National Bond Fund that earns 7.26% annual interest compounded monthly. What is the value of Bubba's investment after 25 years?The value of Bubba's investment after 25 years will be $41,438.55. This is calculated by using the formula A = P((1+r/n)^(nt)), where P is the payment, r is the annual interest rate (7.26%), n is the number of times compounded per year (monthly, or 12), and t is the number of years (25).
6) Ursula is considering opening an account with Crab Key Bank at 5.15% annual interest compounded quarterly. What is the equivalent APY?The equivalent APY for the account at Crab Key Bank with an annual interest rate of 5.15% compounded quarterly is 5.25%. This is calculated by using the formula APY = (1+r/n)^n - 1, where r is the annual interest rate (5.15%), and n is the number of times compounded per year (quarterly, or 4).
7) How can you tell the difference if one bank offers an investment earning 8.75% annual interest compounded quarterly versus one earning 8.7% compounded monthly?The difference between an investment earning 8.75% annual interest compounded quarterly and one earning 8.7% compounded monthly is the number of times the interest is compounded each year. An investment earning 8.75% compounded quarterly has an interest rate of 8.75% that is compounded four times per year, while an investment earning 8.7% compounded monthly has an interest rate of 8.7% that is compounded twelve times per year.
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Drop down 1:
Select a Value
(4d + 1) (3d - 1)
(4d - 1) (3d + 1)
(6d + 1) (2d - 1)
(6d - 1) (2d + 1)
Drop down 2:
Select a Value
(3x+4)^2
(3x- 4)^2
(3x + 4) (3x - 4)
(9x + 4) (x- 4)
Drop down3:
Select a Value
(6b - 11w)^2
(6b^2 - 11w^2)
(6b+ 11w) (6b - 11w)
(6b^2 + 11w^2) (6b^2- 11w^2)
Drop down 4
Select a Value
(3y-4)^2
(3y +4) (7y - 4)
(3y - 8) (7y + 2)
(3y + 2) (7y - 8)
Answer:
1): (4d + 1) (3d - 1)
2: (3x- 4)^2
3: (6b+ 11w) (6b - 11w)
4. (3y - 8) (7y + 2)
Step-by-step explanation:
See attached worksheet.
A composite figure is represented in the image.
What is the total area of the figure?
75 m2
63 m2
61.5 m2
45 m2
Step-by-step explanation:
area of rectangle= 9×4=36m^2
9-3=6 which is the base of the triangle
6×3=18
18÷2=9m^2
36+9=45m^2
answer: 45m^2
The expression −290+15m represents a submarine that began at a depth of 290 feet below sea level and ascended at a rate of 15 feet per minute. What was the depth of the submarine after 8 minutes?
Select the correct answer below and, if necessary, fill in the answer box to complete your choice.
A) The submarine was (enter answer here) feet below sea level after 8 minutes.
B) The submarine will have reached sea level after 8 minutes.
Answer: A,
Step-by-step explanation:
it will be -170 feet after 8 min
A=(a, e, i, o, u),B=(a, b, c) and C=(a, c, e, g)
B intersaction C= C intersaction B
The given statement "B ∩ C = C ∩ B" is true, since the intersection of two sets is a commutative operation, which means the order in which we list the sets does not matter.
To find the intersection of two sets, we need to identify the elements that are common to both sets. In this case, we can list the elements of each set and identify their common elements:
B = {a, b, c}
C = {a, c, e, g}
B ∩ C = {a, c}
C ∩ B = {a, c}
As we can see, the intersection of B and C is {a, c}, and the intersection of C and B is also {a, c}. The order in which we list the sets does not affect the result of the intersection operation, since the elements of both sets are the same.
Therefore, we can conclude that B ∩ C = C ∩ B is true, and that the intersection of B and C contains the same elements regardless of the order in which we list the sets.
In summary, the intersection of two sets is a commutative operation, which means that the order in which we list the sets does not affect the result. Therefore, B ∩ C = C ∩ B is true, and the intersection of B and C contains the same elements regardless of the order in which we list the sets.
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Complete question is:
If A=(a, e, i, o, u),B=(a, b, c) and C=(a, c, e, g)
Is B ∩ C= C ∩ B true?
Please help me
Conditional probability question
The conditional probabilities are are (a) P(A/B) = 0.69 b) P(A/B) = 31/100
How to determine the conditional probabilities?You should recall that Probability is the chance that a given event will occur; the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes;
The conditional probability P(A|B) is calculated using:
P(A/B)
P(A/B) = P( A and B) / P(B)
P(A/B) = (18/26 * 8/26)/ 8/26
P(A/B) = (0.69 * 0.31)/ 0.31
P(A/B) = 0.69
P(A/B) = 69/100
b) Using the same formula
P(B/A) = P( B and A) / P(A)
P(A/B) = (8/26 * 18/26) / 18/26
P(A/B) = (0.31 * 0.69)/0.69
P(A/B) = 0.31
P(A/B) = 31/100
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A cylindrical candle has a mass of 200 grams. The candle has a diameter of 3 inches
and a height of 4 inches. What is the density of the candle? Round to the nearest
hundredth
Rounding to the nearest hundredth, the density of the candle is 22.46 grams per cubic inch.
The density of the candle can be found by dividing the mass by the volume of the candle.
The volume of a cylindrical candle can be found using the formula V = πr^2h,
where V is the volume, r is the radius, and h is the height.
First, we need to find the radius of the candle.
The diameter is 3 inches, so the radius is 1.5 inches.
Next, we can plug in the values for r and h into the formula for the volume of a cylinder:
V = π(1.5)^2(4) = 9π
Now, we can divide the mass of the candle by the volume to find the density:
Density = 200 grams / 9π
Density= 22.46 grams per cubic inch
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Given: ABCD pyramid All edges congruent AB = 4. 5 Find: V
The volume of the pyramid is found to be approximately 18.046 cubic units.
To find the volume (V) of the pyramid, we need to use the formula for the volume of a pyramid, which is V = (1/3) × Base Area × Height.
In this case, the base is a square, so we can find the area of the base by squaring one of the sides: Base Area = AB² = 4.5² = 20.25.
To find the height of the pyramid, we need to use the Pythagorean theorem to find the slant height, and then use that to find the height. Let h be the height of the pyramid and s be the slant height. We have:
s² = AB² + (1/2) DC² (Pythagorean theorem for triangle ABC)
s² = 4.5² + (1/2) DC²
Since all edges of the pyramid are congruent, we have DC = AB = 4.5. Substituting this into the equation above, we get:
s² = 4.5² + (1/2) × 4.5²
s² = 30.375
s ≈ 5.509
To find the height h, we can use the Pythagorean theorem again for triangle ABD:
h² = AB² - (1/4) s²
h² = 4.5² - (1/4) × 30.375
h² ≈ 7.875
h ≈ 2.807
Now that we have found the base area and the height, we can use the formula for the volume of a pyramid to find V:
V = (1/3) × Base Area × Height
V = (1/3) × 20.25 × 2.807
V ≈ 18.046
Therefore, the volume of the pyramid is approximately 18.046 cubic units.
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