Answer:
c=1
Step-by-step explanation:
add 2 to both sides
c-2+2=-1+2
then simplify
What is the sum of the series?
5
Σ3i
i=1
Σ
6
1
(
3
i
−
1
)
-1 is repeated 6 times
Σ
6
1
(
3
i
)
−
6
=
3
(
1
+
2
+
3
+
4
+
5
+
6
)
−
6
=
3
(
21
)
−
6
=
63
−
6
=
57
Step-by-step explanation:
Write the Roman Numeral CXXXIV in standard???
Answer:
Step-by-step explanation: C is 100 X is 10 IV is 4 since the smaller number is in the front so you subtract instead of add
C=100 3X=30 IV=4
100+30+4=134
CXXXIV=134
3
a) The average rainfall of the last week was 35 mm. If the records of daily
rainfall from Sunday to Friday were 45 mm, 22 mm, 28 mm, 36 mm, 30 mm
and 24 mm, find the rainfall on Saturday.
Answer:
The rainfall on Saturday was of 60 mm.
Step-by-step explanation:
Average rainfall:
The average rainfall is given by the total rainfall divided by the number of days(7). So
If the records of daily rainfall from Sunday to Friday were 45 mm, 22 mm, 28 mm, 36 mm, 30 mm and 24 mm
On Saturday it was of x mm. So
\(35 = \frac{45 + 22 + 28 + 36 + 30 + 24 + x}{7}\)
\(185 + x = 245\)
\(x = 245 - 185\)
\(x = 60\)
The rainfall on Saturday was of 60 mm.
What expression in terms of x can be used to represent the area of parallelogram PQRS?
There is a parallelogram PQRS in which the diagonal PR and the diagonal QS bisect each other into two equal parts at right angle . Each part of both the diagonals has a length 5x.
Answer:
\(Area = \frac{25x^2}{2}\)
Step-by-step explanation:
Given
Shape: Parallelogram
\(PR = 5x\)
\(QS = 5x\)
\(\theta = 90\)
Required
Find the area of the parallelogram
Because we were given the measure of the diagonals, the area is:
\(Area = \frac{1}{2} * PR * QS * \sin \theta\)
This gives:
\(Area = \frac{1}{2} * 5x * 5x * \sin \ 90\)
\(Area = \frac{1}{2} * 5x * 5x * 1\)
\(Area = \frac{1}{2} * 25x^2\)
\(Area = \frac{25x^2}{2}\)
The area of Sharon's garden is 40
sq ft. List all the possible lengths
and widths of Sharon's garden.
Answer:
1 and 40
2 and 20
4 and 10
5 and 8
Step-by-step explanation:
need to know the factors of 40
factors of are 1, 2, 4, 5, 8, 10, 20 and 40
possible lengths and widths would be
1 and 40
2 and 20
4 and 10
5 and 8
Please see the attached
(a). The Tanakas paid a total of $523,906.40 for the townhome.
(b). The Tanakas paid $206,906.40 in interest on their mortgage over the 15-year period.
What is simple intresst?Simple interest is the type of interest that is calculated on the principal amount only.
It is a fixed percentage of the principal amount that is charged or earned over a certain period of time, without any compounding of interest.
(a) The total amount they ended up paying for the townhome is the sum of the down payment and the total amount of the mortgage payments.
Down payment = $41,000
Total amount of mortgage payments = monthly payment x number of payments = $2675.04 x 12 months/year x 15 years = $482,906.40
Total amount paid = down payment + total amount of mortgage payments = $41,000 + $482,906.40 = $523,906.40
(b) The amount of interest paid on the mortgage can be calculated by subtracting the principal (the amount borrowed) from the total amount paid.
Principal = Total cost of townhome - Down payment = $358,000 - $41,000 = $317,000
Total interest paid = Total amount paid - Principal = $523,906.40 - $317,000 = $206,906.40
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LOOK AT CAPTURE AND ASNWER 100 POINTS
Answer:
132 degrees
Step-by-step explanation:
Looking at angle A and angle B, they are alternate interior angles. That means they are congruent to one another. Knowing that, we can set up an equation A=B
We can now fill A and B with their given equations
5x-18=3x+42
Now we solve
2x=60
x=30
Now that we know x is 30, we can replace it in the equation for A
5x-18
5(30)-18
150-18
132 degrees
Answer:
132
Step-by-step explanation:
ANGLE A = ANGLE B
(INTERIOR ALTERNATE ANGLES)
5x - 18 = 3x + 42
2x = 60
x = 30
angle a = 150 - 18
= 132
drag tiles to the boxes to form correct pairs. match the cube roots and square roots with their values.
For Mean = 73.19, Mode = 79.56 and Variance = 16, the Karl Pearson's Coefficient of Skewness will be -0.0256 -1.64 0.0256 0
Answer:
To calculate Karl Pearson's coefficient of skewness, we need to use the formula:
Skewness = 3 * (Mean - Mode) / Standard Deviation
Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.
Standard Deviation = √Variance = √16 = 4
Now we can substitute the values into the formula:
Skewness = 3 * (73.19 - 79.56) / 4
Skewness = -6.37 / 4
Skewness = -1.5925
Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.
Mrs. Brown wants to assign eight homework
problems to her Algebra 1 class tonight. If
there are eleven problems she could choose
from, how many different homework sets
could she assign?
A
88
B
165
C
495
D
990
Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.
We have,
The number of different homework sets Mrs. Brown could assign can be calculated using the combination formula.
In this case, she wants to choose 8 problems out of 11 available problems. The formula for combinations is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items to choose from and r is the number of items to be chosen.
Using this formula:
C(11, 8) = 11! / (8! x (11 - 8)!)
C(11, 8) = 11! / (8! x 3!)
Simplifying the factorial expressions:
C(11, 8) = (11 x 10 x 9 x 8!) / (8! x 3 x 2 x 1)
The factorial terms cancel out:
C(11, 8) = (11 x 10 x 9) / (3 x 2 x 1)
C(11, 8) = 165
Therefore,
Mrs. Brown can assign 165 different homework sets to her Algebra 1 class.
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How do you find the asymptotic complexity of a function?
To find the asymptotic complexity of a function, you need to analyze the behavior of the function as the size of the input grows. You need to determine the number of operations that are performed by the algorithm, and express this as a function of the size of the input.
What is the asymptotic complexity?
Asymptotic complexity is a measure of the growth rate of the running time of an algorithm as the size of the input grows towards infinity. It is expressed using big O notation, which provides an upper bound on the growth rate of the running time.
Here are the steps to find the asymptotic complexity of a function:
Identify the dominant operation: Identify the operation in the algorithm that takes the most time, and consider only this operation for analyzing the asymptotic complexity.Express the dominant operation as a function of the size of the input: Express the number of times the dominant operation is performed as a function of the size of the input. This function will represent the running time of the algorithm.Simplify the function: Simplify the function by ignoring lower order terms and constant factors. The goal is to express the running time in terms of a basic mathematical function that grows at the same rate as the original function.Express the simplified function using big O notation: The big O notation provides an upper bound on the growth rate of the running time. The simplified function can be expressed using the big O notation, which expresses the running time in terms of the size of the input, 'n', and a basic mathematical function.To learn more about asymptotic complexity, Visit
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ap exam a small class of five statistics students received the following scores on their ap exam: 5, 4, 4, 3, 1. a) calculate the mean and standard deviation of these five scores.
The mean of the score is 3.4 and the standard deviation is 3.2.
Scores of students = 5, 4, 4, 3 and 1
When determining the mean of a group of numbers, add up all the numbers and divide by the total number in the group.
Calculating the mean -
= Sum of total values / Total values
= 5 + 4 + 4 + 3 + 1 / 5
= 17/5
= 3.4
By averaging the squared deviations of each integer from the mean, you may get the variance before calculating the standard deviation.
Calculating the Standard deviation -
σ = √ ∑ (xi - u)²/n
σ² = (1² + (3.4 - 1)² + (3.4 - 4)² + (3.4 - 4)²+ (3.4 - 5)²) / 5
= 3.2
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\(\int\limits^5_1 {x^2+2x-tanx} \, dx\)
The definite integral for this problem has the result given as follows:
\(\int_1^5 x^2 + 2x - \tan{x} dx = 212 - \ln{|\sec{5}|} + \ln{|\sec{1}|}\)
How to solve the definite integral?The definite integral for this problem is defined as follows:
\(\int_1^5 x^2 + 2x - \tan{x} dx\)
We have an integral of the sum, hence we can integrate each term, and then add them.
For the first two terms, applying the power rule, the integrals are given as follows:
Integral of x² = x³/3.Integral of 2x = 2x²/2 = x².The integral of the tangent is given as follows:
ln|sec(x)|
Then the integral is given as follows:
I = x³/3 + x² - ln|sec(x)|, from x = 1 to x = 5.
Applying the Fundamental Theorem of Calculus, the result of the integral is obtained as follows:
I = 5³/3 + 5² - ln|sec(5)| - (1³/3 + 1² - ln|sec(1)|)
I = 625/3 - 1/3 + 5 - 1 - ln|sec(5)| + ln|sec(1)|
I = 208 + 5 - 1 - ln|sec(5)| + ln|sec(1)|
I = 212 - ln|sec(5)| + ln|sec(1)|.
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There are 30 treasures hidden in a castle in a video game. Latoya found 80% of them. How many of the treasures did Latoya find?
Answer:
It is 24
Step-by-step explanation:
trust me
Answer: She found 24 of the treasures, hope this answers your question:)
Solve the system.
y=x2+2x-2
y=x+10
Answer:
(3,13) , (-4,6)
Step-by-step explanation:
(08.03|08.04 HC)
For the regions A and B shown in the graph:
Part A: Discuss the limits of integration. (3 points)
Part B: Set up an integral expression that represents the total area. (4 points)
Part C: Calculate the total area. (3 points)
The total area from the graph is 2.737.
What is area?Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.
First of all, lets calculate the points of intersection (P, Q, R)
x²+3=(x+2) +5
x²-2=√(x+2)
x⁴+4-4x²=x+2
x⁴-4x²-x+2=0
(x-2)(x³+2x²-1)=0
(x-2)(x+1)(x²+x-1)=0
x=2, -1, -1±√(1+4)/2
Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2
So the limit of integration will be
P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))
Q(-1, (-1)²+3)=Q(-1, 4)
Area A:
\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)
= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)
= 2.07
Area B:
\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)
= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)
= 0.667
Total area = 2.07+0.667
= 2.737
Therefore, the total area from the graph is 2.737.
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Kendrick caught 22 rainbow trout and 18 tiger trout while fishing last month. What percent of the trout were tiger trout?
Answer:81%
Step-by-step explanation:
Answer:
60% tiger trout
Step-by-step explanation:
First, do 22+18= 40
Then, when doing % its always out of 100. So, 100 - 40= 60%
Which means, there were 60% Tiger trout.
evidence of climate change indicates each of the following earth vital signs have been on the rise except:
Climate change is causing an increase in air temperature, sea surface temperature, sea level, ocean acidity, and snow cover, but not humidity.
Humidity
Climate change is the long-term change in average weather patterns, and is caused by increased atmospheric concentrations of greenhouse gases. Earth's vital signs that have been on the rise due to climate change include air temperature, sea surface temperature, sea level, ocean acidity, and snow cover. Humidity is not one of these vital signs, and actually is expected to decrease in some areas due to climate change.
Climate change is causing an increase in air temperature, sea surface temperature, sea level, ocean acidity, and snow cover, but not humidity.
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6x+2y=20 2x-3y=3 solve by substitution
The solution of the system of linear equation by substitution method is (3,1).
What is the method of substitution?The method of substitution is the method for solving the linear equation where the value of one variable of one equation is placed in the place of that variable in another equation.
Given here the linear equations are
Equation 1: 6x+2y=20
Equation 2: 2x-3y=3
in equation 1 the value of y will be
6x+2y=20
⇒2y=20-6x
⇒y=(20-6x)/2
⇒y=10-3x
substituting the value of y in the equation 2, we will get
2x-3y=3
⇒2x-3(10-3x)=3
⇒2x-30+9x=3
⇒11x-30=3
⇒11x=30+3
⇒11x=33
⇒x=33/11
⇒x=3
putting the value of x in value of y in equation 1
y=10-3x
⇒y=10-3(3)
⇒y=10-9
⇒y=1
The solution of the system of linear equation by substitution method is (3,1).
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2. The table shows the amount
spent on tomatoes at three different stands
at a farmer's market. Which stand sold their
tomatoes at the least
expensive price per
pound, and what is that price? Round to the
nearest cent, if necessary. (Lesson 1)
Stand
Weight (lb)
Cost ($)
A
3
4
2.00
B
mit - ab
3.45
с
14.85
Answer:
I think the answer might be b.
Step-by-step explanation:
the volume of a cylinder is 196x in. 3 and the hight of the cylinder is 1 in. what is the radius of the cylinder
The radius of the cylinder is 7. 9 in
How to determine the radiusFirst, we need to know the formula for volume of a cylinder
The formula for calculating the volume of a cylinder is expressed as;
V = πr²h
Such that the parameters of the formula are expressed as;
V is the volume of the cylinderr is the radius of the cylinder h is the height of the cylinderFrom the information given, we have that;
Substitute the values
196 = 3.14 × 1 × r²
Divide both sides by the values
r² = 62. 42
Find the square root of both sides
r = 7. 9 in
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A couple has a combined income of $15,720 per year.
If they spend 20% of their income on rent,
how much rent do they pay per year?
O $12,576
O $3,144
O $262
O $314.40
On solving the provided question, we can say that by percentage
20% of 1570 => 20/100 X 1570=314; rent = 1570 - 314 = $1256
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
A couple has a combined income of = $15,720 per year.
they spend 20%
by percentage
20% of 1570
20/100 X 1570
=314
rent = 1570 - 314 = $1256
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2(x+a)=4b solve for A
Step-by-step explanation:
2(x+a)=4b
2x-2a=4b
a=2x-4b/2
Answer:
\({ \tt{2(x + a) = 4b}} \\ \\ { \tt{2x + 2a = 4b}} \\ \\ { \tt{x + a = 2b}} \\ \\ { \tt{a = 2b - x}}\)
what is the domain of the relation {(0,1),(2,4),(3,7),(5,4)}
Answer:
(0 2,3,5)
Step-by-step explanation:
Domain is the x factor of every relation
If x =y, then x-a=y-a represents the blank property of equality. A-addition B-symmetric C-subtraction D.transitive
Answer:
Subtraction property
Step-by-step explanation:
Answer:
Subtraction
Step-by-step explanation:I took the test
If angle C is a right angle and angle A equals 50º, then prove that the measure of angle B equals 40º. Which of the following would be the first step to assume in order to prove the statement above by contradiction using an indirect proof?
The measure of angle B equals 40º.
Angle C is not a right angle.
The measure of angle A equals 50º.
Angle C is a right angle.
The measure of angle B does not equal 40º.
The first step would be to assume that "the measure of angle B does not equal 40º".
Which would be the first step to prove the contradiction using an indirect proof?The first step to assume in order to prove the statement above by contradiction using an indirect proof would be to assume the opposite of what you are trying to prove.
In this case, the opposite of the statement "the measure of angle B equals 40º" is "the measure of angle B does not equal 40º".
So, the first step would be to assume that "the measure of angle B does not equal 40º".
This assumption will be used to reach a contradiction, which will ultimately prove that the original statement is true.
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find the surface area of the figure below
In ΔSTU, u = 220 cm, ∠T=145° and ∠U=18°. Find the length of s, to the nearest 10th of a centimeter
Answer:
208.1
Step-by-step explanation:
Delta math
The U.S. Bureau of Labor Statistics is a government agency that collects information about jobs in the U.S. In 2014, the Bureau reported that police officers had a median yearly salary of $52,936.
Calculate the average hourly wage for police officers. Round to the nearest cent. Assume that police officers generally work 40 hours a week. There are 52 weeks in the year.
Answer = $ per hour
Answer:25.45
Step-by-step explanation:
52936/1 year x 1 year/52 weeks x 1 week/40hours
The local orchestra has been invited to play at a festival. There are 111 members of the orchestra and 6 are licensed to drive large multi-passenger vehicles. Busses hold 25 people but are much more expensive to rent. Passenger vans hold 12 people. Create a system of equations to find the smallest number of busses the orchestra can rent.
Let x= the number of busses and y= the number of vans
Create an equation representing the number of vehicles needed.
Preview Change entry mode
Create an equation representing the total number of seats in vehicles for the orchestra members.
Create an equation representing the total number of seats in vehicles for the orchestra members.x*25 + y*12 = 111 Create an equation representing the total number of licensed drivers.x + y = 6
The local orchestra has been invited to play at a festival, and they need to figure out how to transport the 111 members. We can create a system of equations to find the smallest number of busses the orchestra can rent. We need to create an equation representing the number of vehicles needed and one representing the total number of seats in vehicles for the orchestra members. We also need an equation representing the total number of licensed drivers. The equation for the number of vehicles needed is x + y = 6, where x is the number of busses and y is the number of vans. The equation for the total number of seats in vehicles is x*25 + y*12 = 111. Solving these equations will give us the smallest number of busses the orchestra can rent.
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