Answer:
3,200 Square centimeters
Step-by-step explanation:
In order to solve for the perimeter of a square with side lengths of 60, we can use this expression:
60 × 4 = 240(We multiply by 4 because a square has four equal side lengths, and the perimeter is all of the side lengths added up)
Therefore, the perimeter of the square is 240cm.
Now that we know this, we can now take that perimeter, and subtract 160 from it.
(We subtract 160 from it because the length of the rectangle is 80cm, and because a rectangle has two sides that represent the length, we multiply the 80 by 2.)
240 - 160 = 80Now, we can divide the 80 by 2 to get the length of the other 2 sides.
80 ÷ 2 = 40Therefore, the rectangles dimensions are 80cm by 40cm.
What is the area?The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.
To solve for the area of a rectangle, we use the expression:
length × width = heightInserting the numbers into the equation:
80 × 40 = 3200Therefore, the area of the rectangle is 3,200 square centimeters.
vLindsay can mow the lawn in 10 hours, but if her brother Grant helps it would take 2 hours. How long would it take Grant to mow the lawn alone?
If Lindsay he mows the lawn in 10 hours and with his brother Grant he does it in 2 hours, Grant would mow the lawn alone in 2.5 hours.
To find out how long it would take Grant to mow the lawn alone, we can use the formula for combined work:
1/t₁ + 1/t₂ = 1/ttotal
Where t₁ is the time it takes Lindsay to mow the lawn alone, t₂ is the time it takes Grant to mow the lawn alone, and ttotal is the time it takes both of them to mow the lawn together.
Plugging in the given values:
1/10 + 1/t₂ = 1/2
Multiplying both sides by 20t₂ to clear the fractions:
2t₂ + 20 = 10t₂
Rearranging and simplifying:
8t₂ = 20
t₂ = 20/8
t₂ = 2.5
So it would take Grant 2.5 hours to mow the lawn alone.
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Please help!
Simplify arctan1/3 + arctan2/3
(round to the nearest degree).
a. 38°
b. 72°
c. 52°
The simplified expression is 45°, which is closest to option a. 38°.
What is lines and angles?Lines are one-dimensional geometrical objects that extend infinitely in both directions. Angles are formed when two lines intersect, and they measure the amount of rotation between the lines.
We can use the formula:
arctan(x) + arctan(y) = arctan[(x + y) / (1 - xy)]
to simplify the expression.
Setting x = 1/3 and y = 2/3, we have:
arctan(1/3) + arctan(2/3) = arctan[(1/3) + (2/3) / (1 - (1/3)(2/3))]
= arctan(1)
= 45°
Therefore, the simplified expression is 45°, which is closest to option
a. 38°.
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Segment in a circle: XY=
A biassed coin is tossed a total of n+ m times and shows Heads with probability p on each toss. Let S, be the number of heads in the first n coin tosses, and Tm be the number of heads in the last m coin tosses. You may assume that m (d) What is the distribution of Sn +Tm? Prove this.
The distribution of Sn + Tm is a binomial distribution with parameters (n+m, p).
This can be proved using the fact that the sum of independent binomial random variables follows a binomial distribution with the sum of the number of trials and the same probability of success.
Let X ~ Binomial(n, p) and Y ~ Binomial(m, p) be independent random variables representing the number of heads in the first n coin tosses and the last m coin tosses, respectively.
Then, the sum of X and Y, Z = X + Y, follows a binomial distribution with parameters (n+m, p).
The probability mass function of Z can be written as:
P(Z = k) = P(X + Y = k) = ∑ P(X = i) * P(Y = k-i) for i = 0 to k
Since X and Y are independent, we can write:
P(Z = k) = ∑ P(X = i) * P(Y = k-i) = ∑ (n choose i) * p^i * (1-p)^(n-i) * (m choose k-i) * p^(k-i) * (1-p)^(m-k+i)
Simplifying the above equation, we get:
P(Z = k) = (n+m choose k) * p^k * (1-p)^(n+m-k)
Therefore, Z ~ Binomial(n+m, p).
As a result, the distribution of Sn + Tm has the parameters (n+m, p) of a binomial distribution.
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Multiply each term by the LCD. (A[x(x-4)(x-3)])/(x)+(B[x(x-4)(x-3)])/((x-4))+(C[x(x-4)(x-3)])/((x-3))
The final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.
To multiply each term by the LCD, we need to first find the LCD of the given expression. The LCD of the expression is the product of the denominators, which is x(x-4)(x-3).
Now, we can multiply each term by the LCD to get rid of the denominators:
A[x(x-4)(x-3)]/(x) * x(x-4)(x-3) = A(x-4)(x-3)
B[x(x-4)(x-3)]/((x-4)) * x(x-4)(x-3) = B(x)(x-3)
C[x(x-4)(x-3)]/((x-3)) * x(x-4)(x-3) = C(x)(x-4)
Now, we can combine the terms to get the final expression:
A(x-4)(x-3) + B(x)(x-3) + C(x)(x-4) = (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC
So, the final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.
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Use the word bank and fill in the blanks. (Use each word only once) Word Bank: natural number, whole number, integer, rational, irrational
A meteorologist analyzes data about a rainstorm in an area starting at 10 p.m. and uses the linear model u = 0.75t + 1.5 of rain accumulation, , in inches, hours after midnight when t > 0 Which best describes the value 1.5 to represent the total amount
A slope and the change in the total amount of rain, in Inches per hour
B slope and the initial amount of rain, in inchesat midnight
C y-intercept and the change in the total amount of rainin inches per hour
D y-Intercept and the initial amount of rain, in inches at midnight
The option that best describes the value 1.5 in the linear equation; u = 0.75·t + 1.5 is option D
D. y-intercept and the initial amount of rain, in inches at midnight
What is a linear equation?A linear equation is an equation of the form; y = m·x + c, where, m is the slope, and c is the y-intercept of the graph of the equation.
The time at which the analysis of the rainstorm by the meteorologist starts = 10 p. m.
The linear model for the accumulation of rain is; u = 0.75·t + 1.5
The number of hours, t after midnight where; t > 0
The model for the accumulation of rain, indicates that the coefficient of t, which is 0.75 is the rate at which the rain accumulates in inches per hour, therefore, the rain accumulates at a rate of 0.75 inches per hour
The constant term in the linear equation, u = 0.75·t + 1.5, which is the constant, 1.5, is the y-intercept of the graph of the equation.
The y-intercept is the value of the equation, when the input value, the time, t = 0, which is the time at midnight
The 1.5 therefore, indicates that the y-intercept, and the level of the accumulated rain at midnight, when the time, t = 0, which is the initial amount of rain at midnight is 1.5 inches.
The correct option is therefore;
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Given cot A = 21/20 and that angle A is in Quadrant I, find the exact value of A in simplest radical form using a rational denominator.
Answer fast for 100pt
Answer:
We know that cot A = adjacent side / opposite side = 21/20.
Let x be the length of the adjacent side and y be the length of the opposite side.
Using the Pythagorean theorem, we have:
x^2 + y^2 = (20k)^2, where k is some positive constant.
Since angle A is in Quadrant I, x is positive and y is positive. Thus, we can take the square root of both sides to get:
x + y = 20k.
Now, we can use the fact that cot A = adjacent side / opposite side = 21/20 to get:
x/y = 21/20.
Multiplying both sides by y, we get:
x = (21/20)y.
Substituting this into x + y = 20k, we get:
(21/20)y + y = 20k
Simplifying, we get:
(41/20)y = 20k
y = (20k)/(41/20) = (400k)/41
Now, we can use the Pythagorean theorem to find x:
x^2 + y^2 = (20k)^2
(21/20)y^2 + y^2 = (20k)^2
(441/400)y^2 = (20k)^2
y^2 = (400/441)(20k)^2
y = (20k/441)sqrt(441 x 20)
y = (20k/21)sqrt(20)
Therefore, angle A in simplest radical form using a rational denominator is given by:
tan A = y/x = [(20k/21)sqrt(20)] / [(21/20)y] = sqrt(20)/21
A = arctan(sqrt(20)/21)
a bird flies 961 km in 24 hours what was the birds velocity
The velocity of the bird is approximately 40.04 km/hour.
What is velocity ?
Velocity is a measure of the rate at which an object changes its position in a particular direction. It is a vector quantity, which means that it has both a magnitude (speed) and a direction.
To find the velocity of the bird, we can use the formula:
velocity = distance/time
Given that the bird flies 961 km in 24 hours, we can substitute these values into the formula:\
velocity = 961 km / 24 hours
Simplifying this expression, we get:
velocity = 40.04 km/hour (rounded to two decimal places)
Therefore, the velocity of the bird is approximately 40.04 km/hour.
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Raphael is flying a small plane that has a weight limit of 1,200 pounds. The plane is already carrying a combined weight of 800 pounds. Each bag weighs 75 pounds. Write an inequality to find the number of bags b that can be taken on board.
Answer: yes
Step-by-step explanation:
yes because it is less than or equal to seeing that the dominoes reach the whole room
find the measure kyc pls its urgent
The measure of angle KYC, considering the concept of vertical angles, is given as follows:
m < KYC = 69º.
What are vertical angles?Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.
The vertical angles for this problem are given as follows:
<KYC and 69º.
As they are opposite by the vertex at the crossing of the two diagonal segments for this problem.
Hence the measure of angle KYC is given as follows:
m < KYC = 69º.
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Ben reads 6 books in ten days what fraction of a book did Ben read each day
Of 35 cars, one-fifth are blue and the rest red. How many are red?
Answer:
28 are red
Step-by-step explanation:
(1/5) are blue. The rest are red, which would be 4/5 of the total. (1/5)+(4/5) = 1 or 100%
(1/5)*(35) = 7 are blue
(4/5)*(35 = 28 are red
--------------------
Total = 35 cars
Identify the number as prime, composite or neither. If the number is composite, write it as the product of prime factors. 240
The number 240 is a composite number and can be written as the product of prime factors 2 x 2 x 2 x 2 x 3 x 5.
The number 240 is a composite number. This is because it can be divided by numbers other than 1 and itself.
To write 240 as the product of prime factors, we can use the factor tree method:
240
/ \
2 120
/ \
2 60
/ \
2 30
/ \
2 15
/ \
3 5
So, the prime factors of 240 are 2, 2, 2, 2, 3, and 5.
We can write this as:
240 = 2 x 2 x 2 x 2 x 3 x 5
Therefore, the number 240 is a composite number and can be written as the product of prime factors 2 x 2 x 2 x 2 x 3 x 5.
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Solve.
Solve all they are part of one question that's y
1) What is the sale price on a painting that has a regular price of $1,900 and is on sale for 35% off the regular price?
2) A mechanic's tool set is on sale for $204 after a markdown of 40% off the regular price. Find the regular price.
3)A battery with a discount price of $85 is on sale for 24% off the regular price. Find the regular price. Round to the nearest cent.
1) The sale price on the painting is $1,235.
2) The regular price of the mechanic's tool set is $340.
3) The regular price of the battery is $111.84.
1) To find the sale price on a painting that has a regular price of $1,900 and is on sale for 35% off the regular price, we can use the formula: sale price = regular price - (regular price * discount rate).
In this case, the sale price would be $1,900 - ($1,900 * 0.35) = $1,900 - $665 = $1,235.
So the sale price of the painting is $1,235.
2) To find the regular price of a mechanic's tool set that is on sale for $204 after a markdown of 40% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $204 / (1 - 0.40) = $204 / 0.60 = $340.
So the regular price of the mechanic's tool set is $340.
3) To find the regular price of a battery that has a discount price of $85 and is on sale for 24% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $85 / (1 - 0.24) = $85 / 0.76 = $111.84.
So the regular price of the battery is $111.84.
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Example: According to the Census Bureau of the people 21 to 64 years old, 12 3% are not high school graduates, 27.8% have graduated high school, 30.6% have some college, 16.9% have a bachelor's degree, and 8.8% have an advanced degree. What words in this paragraph look like different answers to one question? Perhaps the question is something about your education?
According to the Census Bureau, of the people 21 to 64 years old, 12.3% are not high school graduates, 27.8% have graduated high school, 30.6% have some college, 16.9% have a bachelor's degree, and 8.8% have an advanced degree. The words that look like different answers to one question are "not high school graduates," "graduated high school," "some college," "bachelor's degree," and "advanced degree."
These words all describe different levels of education and could be potential answers to a question about a person's education level. The paragraph describes the educational attainment of people between the ages of 21 and 64. The different percentages represent the proportion of individuals in each education category.
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In the diagram, BC = 9. Find AB and AC by dragging the correct distance to its corresponding side?
Answer is: AC= 9[tex]\sqrt{3}[/tex] Units, AB = 18 units.
What is triangle?Triangles have three interior angles that add up to 180 degrees, and they can be classified based on the lengths of their sides and the measures of their angles.
In ΔABC, angle C is right angle,
so the triangle is right angle triangle;
tan30° = BC/AC
[tex]\frac{1}{\sqrt{3} }[/tex] = 9/AC
AC= 9[tex]\sqrt{3}[/tex] Units
and
Sin 30° = BC/AB
1/2 = 9/AB
AB = 18 units
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PLEASE HELP!!!!!!!!!!!!!!
The perimeter of the base is 32 cm.
The area of the base is 48 cm².
The total surface area of the triangular prism is 1184 cm².
How to find the surface area of triangular prism?The diagram above is a triangular prism. Therefore, let's find the perimeter of the base, area of the base and surface area of the triangular prism.
Hence,
perimeter of the base = 10 + 10 + 12
perimeter of the base = 20 + 12
perimeter of the base = 32 cm
Area of the base = 1 / 2 bh
where
b = baseh = heightTherefore,
Area of the base = 1 / 2 × 12 × 8
Area of the base = 48 cm²
Hence,
total surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)
total surface area of the triangular prism = 12(8) + 34(10 + 10 + 12)
total surface area of the triangular prism = 96 + 34(32)
total surface area of the triangular prism =96 + 1088
total surface area of the triangular prism = 1184 cm²
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Find m<ADB
a) 59°
b) 44°
c) 13°
d) 33°
Answer:
A) 59°
Step-by-step explanation:
m<ADC is a right angle, therefore it is 90°
so that means you can now subtract the angle that you already know [31°] from it to get the angle that is left over, m<ADB
90°-31°= 59° (subtracting m<ADC [90°] from m<BDC [31°] leaves your remaining angle m<ADB [59°]
[tex][(-2xyx^{2} )x^{3}]x^{2}[/tex]
Exponent laws The abbreviated formula is -2x7y.
What exponent law is made simpler?This leads to another exponent rule called the Power Rule for Exponents. A power of a power can be made simpler by multiplying the exponents while leaving the base fixed. In this instance, (23)5 equals 215. For any positive number x and integers a and b, (xa)b=xa b holds true.
What are the eleventh grade exponent laws?Exponent laws comprise: Rule of the product of powers: Add the powers together when multiplying like bases. Take off the powers when separating like bases according to the quotient of powers rule. Rule of the power of powers: Add all the powers together when raising a power by another exponent.
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Complete question:
Find the Exponent law of the given formula [tex][(-2xyx^2)x^3]x^2[/tex] .
During Cristiano tenure for the first two seasons (2014_15&2015_16) he made 251 passes each. Estimate to find about how many passes he made in the third Year
Cristiano is said to have racked up around 300 assists in his third year in power.
This estimate is based on the fact that Cristiano has been a prolific passer in his whole career and has frequently improved every season. Assuming he's maintained similar level of assists in his third season and Cristiano has improved season after season, his tally assists in his third year is likely higher than his average of 251 per season.
That's why it is safe to assume that Cristiano completed around 300 passes in his third year, a significant improvement over the previous 2 years. It increase in assists is likely due to Cristiano's increased confidence and comfort in the team, as well as learning more about the club and their plan. All of this together would allow Cristiano to make more passes and become a more efficient player overall.
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A company sells a regular version of software for $17.45 and a deluxe version for $21.95. The company gives a bonus to any salesperson who sells at least
100 units and has at least $2000 in total sales. Complete parts a through c below.
a. Write a system of inequalities that describes the requirements a salesperson must meet to receive the bonus. Let R represent the number of regular
units sold and D represent the number of deluxe units. Choose the correct system of inequalities below.
OA.
O C.
O A.
AD
R+Dz 100
17.45R+21.95D z 2000
120-
R+Dz 100
17:45R+21.95D = 2000
b. Solve the system by graphing. Let the horizontal axis be the regular version and the vertical axis be the deluxe version. Choose the correct graph
below.
B.
AD
B.
120-
O D.
O C.
AD
R+D≤ 100
17.45R+21.95D ≤ 2000
120-
R+D≤ 100
17.45R+21.95D z 2000
Q
D.
AD
120-
The graph of the system of inequalities is a circle with center (0,0) and radius of 100 units for the regular version and 2000/21.95 units for the deluxe version.
What is inequality?Inequality in math is a mathematical statement that states two expressions are not equal. It can be written using symbols such as <, >, or ≠. Inequality statements are used to compare values or expressions and to describe ranges of values that satisfy certain conditions.
The salesperson must sell at least 100 units of either the regular or deluxe version and their total sales must be at least $2000 in order to receive the bonus.
The company offers a bonus to salespeople who can meet certain sales goals. This encourages salespeople to be more motivated to sell the product and to increase their overall sales. It also helps the company increase their profits by providing incentives for salespeople to increase their sales. By offering the bonus, the company is able to attract more salespeople who are willing to work hard and reach their sales goals in order to receive the bonus. This allows the company to increase their market share and their profits.
The bonus also helps to retain existing salespeople who might otherwise be tempted to leave the company. By offering the bonus, the company is able to reward loyal salespeople who have consistently performed well and have contributed to the company's success. This helps the company to maintain a stable and productive sales team, which is beneficial for the company's long-term success.
Overall, offering a bonus to salespeople who meet certain sales goals is a beneficial strategy for the company. It encourages salespeople to be more motivated and increase their sales, while also helping the company to attract and retain quality salespeople. This helps the company to grow and increase their profits in the long run.
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Work out the area of this circle.
Take it to be 3. 142 and give your answer to 2 decimal places.
R: 9 m
The area of the circle is 63.62 square meters
To work out the area of a circle, we need to use the formula A = πr^2, where A is the area of the circle, π is a mathematical constant approximately equal to 3.142, and r is the radius of the circle.
In this problem, we are given the diameter of the circle, which is the distance across the circle passing through its center. The radius is half of the diameter, so we can find it by dividing the diameter by 2.
In this case, the diameter is 9 meters, so the radius is 9/2 = 4.5 meters. We then substitute this value into the formula:
A = πr^2
A = 3.142 x (4.5)^2
A = 3.142 x 20.25
A = 63.6175
A ≈ 63.62 square meters
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The given question is incomplete, the complete question is:
Work out the area of the circle where diameter is 9 meter
Take π it to be 3.142 and give your answer to 2 decimal places.
Indicate whether the given system of linear equatio he solution. -1.2x+0.3y=-8.4 -1.4x+0.2y=10.6
The solution to the system of linear equations -1.2x+0.3y=-8.4 -1.4x+0.2y=10.6, is x = -27 and y = -136.
The given system of linear equations is:
-1.2x+0.3y=-8.4
-1.4x+0.2y=10.6
To determine whether the system has a solution, we can use the method of elimination. First, we need to multiply each equation by a constant to make the coefficients of one of the variables the same in both equations. In this case, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same:
-2.4x+0.6y=-16.8
-4.2x+0.6y=31.8
Next, we can subtract the second equation from the first equation to eliminate the y variable:
1.8x=-48.6
Finally, we can solve for x:
x=-27
Now we can plug this value of x back into one of the original equations to solve for y:
-1.2(-27)+0.3y=-8.4
32.4+0.3y=-8.4
0.3y=-40.8
y=-136
So the solution to the system of linear equations is x=-27 and y=-136. Therefore, the given system of linear equations does have a solution.
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56 = k - 42
What does k equal
What is 2 times the square root of 48 - the square root of 3
Answer: 12.124355653
Step-by-step explanation: I did the math on a calculator
please help me get the answer to this question
The answer of this question is -4,298,008. We solve this question by taking the LCM of denominators.
What do you mean by term LCM?The smallest multiple that two or more numbers share is known as the least common multiple. Least Common Multiple short form is LCM.
We can find LCM of these number by taking least common multiple.
LCM of 3, 3, 17, 13 is 663 .
(a) [tex]-\frac{22}{3} *663 = -22*221[/tex]
[tex]= -4862[/tex]
(b) [tex]\frac{4}{3} * 663 = 4 * 221[/tex]
[tex]= 884[/tex]
(c) [tex]\frac{6}{17} *663 = 6 * 17[/tex]
[tex]= 102[/tex]
(d) [tex]\frac{2}{13}*663 = 2*51[/tex]
[tex]=102[/tex]
So, the answer is -4,298,008 .
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The lengths of the sides of a triangle are 6, 9, and 12. Classify the triangle as acute, right, or obtuse. Explain how you know
Answer: :)
Step-by-step explanation:
To classify the triangle as acute, right, or obtuse, we need to determine the measure of the largest angle in the triangle. We can use the Law of Cosines to find the angles of the triangle:
c^2 = a^2 + b^2 - 2ab cos(C)
where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.
For this triangle, we have:
c = 12
a = 6
b = 9
Using these values in the Law of Cosines, we get:
12^2 = 6^2 + 9^2 - 2(6)(9)cos(C)
144 = 117 - 108cos(C)
27 = 108cos(C)
cos(C) = 0.25
To find angle C, we can take the inverse cosine (cos^-1) of both sides:
C = cos^-1(0.25)
C ≈ 75.5°
Now we can classify the triangle based on its largest angle:
- If C is less than 90 degrees, then the triangle is acute.
- If C is exactly 90 degrees, then the triangle is right.
- If C is greater than 90 degrees, then the triangle is obtuse.
In this case, since C ≈ 75.5°, which is less than 90 degrees, we know that this triangle is an acute triangle.
Multiply. 8x2 y4 (−3x6 y2 + 4y)
answers:
5x8 y6 + 12x2 y5
−24x8 y6 + 32x2 y5
−24x12 y8 + 32y4
8x9 y7 + 8x3 y6
Answer:
-24x^8y^6+32x^2y^5
Step-by-step explanation:
Megan And Mindy saw a plan for 2/6 of a playground they each drew a picture of the whole playground which one is NOT correct tell how you know
By answering the above question, we may state that Without having both expressions the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.
what is expression ?In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.
If Megan and Mindy both depicted the entire playground, then their pictures ought to match. Their designs ought to depict the remaining 4/6 of the playground if the plan they viewed only showed 2/6 of it.
You may assess a drawing's accuracy by contrasting it with the first design that Megan and Mindy viewed. They are correct if their designs depict the remaining 4/6 of the playground and the original plan matches. Their drawings are incorrect if they do not reflect the original design or do not depict the remaining 4/6 of the playground.
Without having both the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.
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