The number of students are as follows:
novel and textbook is 7textbook and comics is 3comic and novel is 4What is the number of students who read comics and novels only?To find the number of students who read comics and novels only:
there are a total number of students 5021 students read novel24 students read comics18 students read textbook 3 read novel only9 read comic only2 read textbook only5 read all 3 booksLet novel and textbook = x
Let textbook and comics = y
Let comic and novel = z
y + x = 11 --- (1)
y + z = 10 --- (2)
x + z = 13 --- (3)
Make y subject of the formula in (2)
y = 10 - z
substitute for y in (1)
10 - z + x = 11 --- (4)
solve (3) and (4) simultaneously by addition
10 - z + x + x + z = 11 + 13
2x = 24 - 10
x = 7
y = 11 - 7
y = 3
z = 13 - 7
z = 4
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5/3X + 1/3X= 2 2/3+ 8/3X
The solution of the given equation 5X/3 + X/3 = 2 (2/3) + 8X/3 is, X = - 4.
The equation is a mathematical statement involving mathematical variable, numerical values, mathematical operation with a equal sign.
The given equation is,
(5/3)*X + (1/3)*X = 2 (2/3) + (8/3)*X
Solving the equation we get,
5X/3 + X/3 = (2*3 + 2)/3 + 8X/3
5X/3 + X/3 - 8X/3 = (6 + 2)/3
(5X + X - 8X)/3 = 8/3
- 2X/3 = 8/3
- 2X = 8
X = 8/(-2)
X = - 4
Hence the solution is, X = - 4.
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Find the polar coordinates of a point with Cartesian coordinates (x,y)=(√3,1).
(1,π/6)
(1,2π/3)
(2,7π/6)
(2,2π/3)
(2,π/6)
(1,7π/6)
Answer: The Correct answer is E (2,pie/6)
Step-by-step explanation:
To find the polar coordinates of a point given its Cartesian coordinates (x, y), we can use the following formulas:
r = √(x^2 + y^2)
θ = atan2(y, x)
where r is the radial distance from the origin to the point, and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin and the point.
Given the Cartesian coordinates (x, y) = (√3, 1), we can plug these values into the formulas to find the polar coordinates:
r = √(√3^2 + 1^2) = √(3 + 1) = 2
θ = atan2(1, √3)
Using a calculator, we can find that θ is approximately 0.5236 radians.
So, the polar coordinates of the point (√3, 1) are (r, θ) = (2, 0.5236 radians).
10% of ivy tech students are dual credit students. If there are 13,129 dual credit students, how many Ivy Tech students are there?
Answer:131290
Step-by-step explanation:13129*100/10=131290
find an equivalent equation in rectangular coordinates
r sin theta = 10
The equivalent equation of r sinθ = 10 in rectangular coordinates is y² + y⁴/x² - 100 = 0.
What are the rectangular coordinates?
The rectangular coordinates is calculated from the polar equation as follows;
r sinθ = 10
the conversion from polar to rectangular coordinates;
r² = x² + y²
r = √(x² + y²) ----- (1)
y/x = tanθ ------ (2)
r sinθ = 10
√(x² + y²)(y/x) = 10
(x² + y²)(y²/x²) = 100
y² + y⁴/x² = 100
y² + y⁴/x² - 100 = 0
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2 3/4=pints as a mixed numbers
2 3/4 cups is equivalent to 1 3/8 pints as a mixed number.
There are 2 cups in a pint. To convert 2 3/4 cups into pints, we can follow these steps:
Convert the whole number part of the mixed number to pints by dividing by 2.
Convert the fractional part of the mixed number to cups, then divide by 2 to get the corresponding pints.
Add the two results together to get the total in pints as a mixed number.
So, let's apply these steps to 2 3/4 cups:
The whole number part is 2, so 2 cups = 1 pint.
The fractional part is 3/4 cups, which is equivalent to 3/4 ÷ 2 = 3/8 pints.
Adding the two results, we get:
1 pint (from the whole number part) + 3/8 pint (from the fractional part) = 1 3/8 pints.
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Last week a certain brand of bottled water cost $1.25 for a 16-ounce bottle. This week the water is on sale for $1.00 for a 16-ounce bottle. What is the percent decrease in the price of this bottled water?
The percent decrease in the price of this bottled water is 20%
What is percentage?Percentage can simply defined as the ratio of a number or a variable and 100.
Percentage is represented with the symbol, %.
From the information given, we have that;
Original amount for 16-ounce bottle = $1.25
New amount for 16-ounce bottle = $1. 00
The formula for calculating the percent decrease is represented as;
Percent decrease = original value - new value/original value × 100/1
Substitute the values, we have;
Percent decrease = 1.25 - 1.00/1.25 × 100
Subtract the values
Percent decrease = 20%
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Calculate the volume of this cylinder in terms of Pi and to the nearest hundredth
The volume of the given cylinder in terms of pi as required to be determined in the task content is; 5000 pi.
What is the volume of the given cylinder?It follows from the task content that the volume of the cylinder which is as represented is to be determined.
Since the volume of a cylinder is;
V = 2πr²h
where r = 10 and h = 25.
V = 2π × 10² × 25.
V = 5000π.
Ultimately, the volume of the given cylinder as required to be determined is; V = 5000 pi.
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The diameter of a bicycle wheel is 60 centimeters. How far does the wheel travel when it makes 35 revolutions? Give your answer in. meters( Math in focus singapore math course 1 B)
Answer:
The circumference of a circle is given by the formula "C = pi x d" where "d" is the diameter and "pi" is the mathematical constant with an approximate value of 3.14.
In this problem, the diameter of the bicycle wheel is 60 centimeters, so its circumference is:
C = pi x d = 3.14 x 60 = 188.4 centimeters
When the wheel makes one revolution, it travels one circumference distance. Therefore, when the wheel makes 35 revolutions, it will travel:
distance = 35 x circumference = 35 x 188.4 = 6584 centimeters
We can convert centimeters to meters by dividing the distance by 100:
distance = 6584 ÷ 100 = 65.84 meters
Therefore, the wheel travels 65.84 meters when it makes 35 revolutions.
Find the partial sum for the sequence.
{0, −1, −3, −6, −10, ...}; S14
S14=
Answer:
-91
Step-by-step explanation:
To find the partial sum for the sequence
[tex]\large \boxed{\mathrm{ \ 0, \ -1, \ -3, \ -6, \ -10,}}[/tex]
We first notice that the first term is
[tex]\large \boxed{\mathrm{0}}[/tex],
And each subsequent term is the sum of the previous term and the next integer in the sequence starting with [tex]-1.[/tex] Therefore, we can use the formula for the sum of an arithmetic series to find the partial sum S14:
S14 = 14/2 * (2(0) + (14-1)(-1+0)/2) = 14/2 * (13/2 * -1) = -91
Therefore, the partial sum for the sequence up to the [tex]14th[/tex] term is [tex]-91.[/tex]
Answer:
[tex]91[/tex]
Step-by-step explanation:
The partial sum of a sequence is the sum of a certain number of terms in the sequence. For the given sequence
{0, −1, −3, −6, −10, ...},
The nth term can be represented as Tn = n(n-1)/2. This means that the partial sum of the first 14 terms of the sequence, denoted by S14, can be calculated by adding up the first 14 terms using the formula: S14 = 0 + (-1) + (-3) + (-6) + (-10) + ... + T14.
Simplifying this expression using the formula for Tn, We get S14 = 91. Therefore, the partial sum for the given sequence up to the 14th term is equal to 91.
A contractor needed a small workshop. He found a preengineered steel building advertised for $12,099. If the building is a 36-ft by 36-ft square, what is the cost of the
building per square foot?
The cost of the building per square foot is $(Round to the nearest cent as needed.)
Answer:
$9.34 per square foot
Step-by-step explanation:
You want the cost per square foot of a 36 foot square building that costs $12,099.
Cost per square footThe cost per square foot is found by dividing the cost by the number of square feet. That area is found as the square of the side length:
A = s²
A = (36 ft)² = 1296 ft²
Then the cost is ...
cost per square foot = ($12099)/(1296 ft²) ≈ $9.34/ft²
The cost of the building is about $9.34 per square foot.
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Let f = x^4 − 5.
(a) Determine the Galois group of f over R.
b)Let F be the splitting field of f over Q. Show that the Galois group
AutQ(F) is a non-abelian group of order eight which is generated by automorphisms φ and σ, where φ has order four and σ order two. Prove or give a counterexample: Each intermediate field of F/Q is a Galois extension of Q.
The Galois group of f over R is isomorphic to the symmetric group S4. The given statement "Each intermediate field of F/Q is a Galois extension of Q." is true because f is separable.
The roots of f are given by
x = ±(√(5) + √(2)), ±(√(5) - √(2))
Let φ be the automorphism defined by
φ(√(5) + √(2)) = √(5) + i√(2)
φ(√(5) - √(2)) = √(5) - i√(2)
φ(-√(5) + √(2)) = -√(5) - i√(2)
φ(-√(5) - √(2)) = -√(5) + i√(2)
where i is the imaginary unit. Then φ has order four since φ⁴ is the identity automorphism. Let σ be the automorphism defined by
σ(√(5) + √(2)) = -√(5) + √(2)
σ(√(5) - √(2)) = √(5) - √(2)
σ(-√(5) + √(2)) = -√(5) - √(2)
σ(-√(5) - √(2)) = √(5) + √(2)
Then σ has order two since σ² is the identity automorphism. It can be shown that the Galois group of f over Q is generated by φ and σ. Since φ has order four and σ has order two, the Galois group is a non-abelian group of order eight.
To prove or disprove that each intermediate field of F/Q is a Galois extension of Q, we need to show that each intermediate field is a splitting field of a separable polynomial over Q. Since F is the splitting field of f over Q, any intermediate field of F/Q is also a splitting field of f over Q. Since f is separable (its roots are distinct), every intermediate field of F/Q is a Galois extension of Q, and hence a splitting field of a separable polynomial over Q. Therefore, the statement is true.
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Consider the curve given by the equation x2 − y2 = 2x + y + xy − 4. Find the equation
of the tangent line to the curve at the point (1, 1).
The equation of the tangent line at (1,1) is given as follows:
y - 1 = -0.25(x - 1).
How to obtain the equation of the tangent line?The curve for this problem is given as follows:
x² - y² = 2x + y + xy - 4.
Applying implicit differentiation, we obtain the slope of the tangent line, as follows:
2x - 2y(dy/dx) = 2 + (dy/dx) + x(dy/dx) + y
(dy/dx)(1 + x + 2y) = 2x - 2 - y
m = (2x - 2 - y)/(1 + x + 2y).
At x = 1 and y = 1, the slope is given as follows:
m = (2 - 2 - 1)/(1 + 1 + 2)
m = -0.25.
Hence the point-slope equation is given as follows:
y - 1 = -0.25(x - 1).
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An employee is considering two job offers.
First offer: $57,000 yearly salary with an 8% matching 401k
Second offer: $63,000 yearly salary with a 4% matching 401k
The employee plans to stay at either job for at least 4 years, assumes there are no salary increases, and will make 401k contributions at the same rate the company matches. After 4 years, the total value of the first offer, including gross income and total 401k contributions, is $264,480.
Which job has the better overall pay structure, and by how much?
(MULTIPLE CHOICE ONLY)
The second job offer is better by $6,780.
The first job offer is better by $6,780.
The second job offer is better by $7,680.
The first job offer is better by $7,680.
The second job offer is better by $21,840.
We have :
An employee is considering two job offers.
First offer: $57,000 yearly salary with an 8% matching 401k
Second offer: $63,000 yearly salary with a 4% matching 401k
Let's calculate the total value of the second offer after 4 years:
Yearly salary is : $63,000
Total gross income after 4 years: $63,000 x 4 = $252,000
The company matches 5% of the employee's salary.
So, the employee contributes 5% of $63,000 = $3,150 per year
After 4 years,
Company matches: $3,150 x 4 = $12,600
Employee contributions: $3,150 x 4 = $12,600
Total 401k contributions: $12,600 + $12,600 = $25,200
The total value of the second offer after 4 years is:
Total value: $252,000 + $25,200 = $277,200
Now, let's compare this to the total value of the first offer, which is : $255,360.
Therefore, the second job offer is better by:
$277,200 - $255,360 = $21,840
Hence, The second job offer is better by $21,840.
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A
16.2
16.2-foot slide has an angle of elevation of
49.4
°
49.4° from the ground to the slide. What is the horizontal distance traveled by someone sliding from the top of the slide to the bottom of the slide? Round your answer to one decimal place. Enter
deg
deg after any degree value.
Answer:
Set your calculator to degree mode.
Please sketch the figure to confirm my answer.
cos(49.4°) = d/16.2
d = 16.2cos(49.4°) = 10.5 feet
Candace is flipping a coin a certain number of times. The theoretical probability of her flipping tails on all flips is 1/32 . How many times is she flipping the coin?
Answer:
Cadence is flipping her coin 32 times
Step-by-step explanation:
So the fraction is 1/32 which means 32 is the number of times the coin was flipped.
y = 2x X 0 2 3 4 6 4 8 5 10 Click to select points on the graph. 10 9 8 0 7 5
Answer:
The points selected on the graph are:
(0, 0), (2, 4), (3, 6), (4, 8), (6, 12), (4, 8), (8, 16), (5, 10)
Here is a table showing the coordinates of the selected points:
x y
0 0
2 4
3 6
4 8
6 12
4 8
8 16
5 10
London invested $3,400 in an account paying an interest rate of 6 7/8% compounded
quarterly. Victoria invested $3,400 in an account paying an interest rate of 6 3/8%
compounded monthly. After 5 years, how much more money would London have in
her account than Victoria, to the nearest dollar?
Answer:
Step-by-step explanation:
Answer: 108
Step-by-step explanation:
Christo wants to buy a small wine farm worth R8 500 000. He plans to sell his current home for R3 400 000 which he will use as a deposit for the purchase of the farm. He secures a loan with a bank with a repayment period of 10 years and an interest rate of 9, 5% compounded monthly. Calculate his monthly repayments.
Christo's monthly repayments for a loan of R5,100,000 for 10 years at 9,5% interest compounded monthly is R65,992.75.
How is the monthly repayments determined?The monthly repayments can be determined using an online finance calculator as follows:
The monthly repayments show the periodic payments to settle the loan.
Wine Farm Price = R8,500,000
Down Payment = R3,400,000
Loan Term = 10 years
Interest Rate = 9.5%
Start Date = Apr. 2023
Monthly Pay: R65,992.75
Loan Amount = R5,100,000.00
Total of 120 Mortgage Payments = R7,919,130.52
Total Interest = R2,819,130.52
Mortgage Payoff Date = Apr. 2033
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12 total, 8 girls, 4 boys, probability boys will be selected
0.333 is the probability of choosing a boy.
The probability of boys being selected can be calculated as the ratio of the number of boys to the total number of children:
Probability of selecting a boy = Number of boys / Total number of children
Probability of selecting a boy = 4 / 12 = 1/3
Therefore, the probability of selecting a boy is 1/3 or approximately 0.333.
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IN CASE YOU ARE LOOKING FOR THE ANSWER
A climber is standing at the top of Mount Kilimanjaro, approximately 3.7 mi above sea level. Earth has a radius of 3959 mi.
What is the climber's distance to the horizon?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
Answer: The answer is 171.2 Miles
Step-by-step explanation: You can easily find a "Horizon finder" online. It helps for harder equations like this.
Also I just realized that you put 171.20. When a question asks for a nearest tenth, only put the first digit of the decimal.
Bridget Riley was just one of many artists associated with the 1960's 'Op Art' Movement. True or false
Answer:
True
Explanation:
Bridget Riley was one of the most prominent artists associated with the 1960s 'Op Art' movement, which was an art movement that explored optical illusions and effects to create abstract art that played with the viewer's perception. However, there were many other artists associated with this movement, including Victor Vasarely, Richard Anuszkiewicz, and Yaacov Agam, among others.
The number 58,391 was rounded to 58,000. What place value was the number rounded to? Hundred Thousand Ten thousand Hundred thousand
Answer:
Thousand
Step-by-step explanation:
Solve:
58,391
Knowing that:
Digit Less than 5 goes downDigit greater than 5 goes upWhen rounding to:
Hundred Thousand - 100,000Ten Thousand - 60,000Hundred - 58,400Thousand - 58,000Because the digit to the right in the hundreds place is 3 which is less than 5- Thus, it goes down to 58,000.
RevyBreeze
Answer:
I think it's Thousand
Luke is 5 years younger than 3 times Sydney’s age, s. In this situation, what does 3s represent?
Luke’s age
Sydney’s age
three times Luke’s age
three times Sydney’s age
Based on the given context, 3s represent (d) three times Sydney’s age
Explaining what 3s represent?From the question, we have the following parameters that can be used in our computation:
Sydney's age = s
Luke is 5 years younger than 3 times Sydney’s age
The interpretation of the second statement above is
Luke's age = Sydney's age - 5
Mathematically, this can be expressed as
l = s - 5
Where
Luke's age = l and
Sydney's age = s
Also from the question we have:
3s = 3 times Sydney's age
Hence, 3s represent (d) three times Sydney’s age
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Which linear equation is represented in the graph?
A. y = x – 1
B.y = 2x – 1
C. y = x + 1
D. y = 3x – 1
graph the piecewise function. f(x)= {3x-5 if x is less than or equal to -1. -2x+3 if -1 is less than x is less than 4. 2 if x is greater than of equal to 4.
Answer:
Here's how to graph the piecewise function:
First, we graph the function for the first interval, which is f(x) = 3x - 5 when x ≤ -1. This is a straight line with a slope of 3 and a y-intercept of -5. Since this interval includes -1, we draw a closed circle at x = -1 to indicate that it is included in the interval. The line is decreasing as x increases.
Next, we graph the function for the second interval, which is f(x) = -2x + 3 when -1 < x < 4. This is also a straight line, but with a slope of -2 and a y-intercept of 3. Since this interval does not include -1, we draw an open circle at x = -1 to indicate that it is not included in the interval. We also draw an open circle at x = 4 to indicate that it is not included in the interval. The line is increasing as x increases.
Finally, we graph the function for the third interval, which is f(x) = 2 when x ≥ 4. This is a horizontal line at y = 2. Since this interval includes 4, we draw a closed circle at x = 4 to indicate that it is included in the interval.
When we put all three intervals together, we get a graph that looks like this:
```
| /
2 | /
| /
| /
| /
| /
| /
| /
| /
|/
_______|_____________
-1 4
```
The graph consists of a downward-sloping line from (-∞, -1], an upward-sloping line from (-1, 4), and a horizontal line from [4, ∞).
5. How far does the tip of a minute hand on a clock travel in 45 minutes if the
distance from the center to the tip is 10 in? Leave your answer in terms of .
work:
distance traveled =
15
in.
Answer:
The tip of the minute hand on a clock travels 15π inches in 45 minutes if the distance from the center to the tip is 10 inches.
For the demand function d(x) and supply function s(x), complete the following.
d(x) = 600 − 0.8x, s(x) = 0.4x
(a) Find the market demand (the positive value of x at which the demand function intersects the supply function).
x =
Answer: The market demand is x = 750.
Step-by-step explanation:
Answer: The market demand is x = 750.
Explanation:
To find the market demand, we need to set the demand function equal to the supply function and solve for x:
d(x) = s(x)
600 − 0.8x = 0.4x
Combining like terms, we get:
600 = 1.2x
Dividing both sides by 1.2, we get:
x = 500
However, we need to find the positive value of x. Since x represents the quantity demanded, it cannot be negative.
Substituting x = 500 into both the demand and supply functions, we find that:
d(500) = 600 - 0.8(500) = 200
s(500) = 0.4(500) = 200
Since d(500) = s(500), x = 500 is not the market demand.
Substituting x = 750 into both the demand and supply functions, we find that:
d(750) = 600 - 0.8(750) = 0
s(750) = 0.4(750) = 300
Since d(750) = s(750), x = 750 is the market demand.
Therefore, the market demand is x = 750.
The sides of a triangle are 30, 64, and 90. Use the Pythagorean Theorem to determine if the triangle is right, acute, or obtuse.
Answer:
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's check if the triangle with sides of 30, 64, and 90 is a right triangle:
30^2 + 64^2 = 900 + 4096 = 4996
90^2 = 8100
Since 4996 is less than 8100, the triangle is not a right triangle.
In an acute triangle, all angles are less than 90 degrees. In an obtuse triangle, one angle is greater than 90 degrees.
To determine if the triangle is acute or obtuse, we need to find the largest side. The largest side is 90. Let's find the sum of the squares of the other two sides:
30^2 + 64^2 = 900 + 4096 = 4996
Since 4996 is less than 90^2, the triangle is acute.
Therefore, the triangle with sides of 30, 64, and 90 is an acute triangle.
the triangle is obtuse
Step-by-step explanation:
[tex] {90}^{2} = 8100[/tex]
[tex] {30}^{2} + {64}^{2} = 4996[/tex]
[tex] {30}^{2} + {60}^{2} < {90}^{2} [/tex]
triangle is obtuse because the square of the largest is greater than the sum of the square of the other 2 sides
what is the volume of the cube shown?
The volume of the cube shown can be found to be 132. 65 inch ³ .
How to find the volume of a cube ?To ascertain the volume of a cube , knowledge of one edge's length is mandatory . This side would correspond to all other sides; therefore , multiplying it by three inversely gauges its complete space as a cubic structure.
The formula for the volume of a cube is:
= Side x Side x Side
The side is 5. 1 inch so the volume is:
= 5. 1 x 5 .1 x 5. 1
= 132. 65 inch ³
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Tom made some beads and packed all the bead in 14 small boxes and 3 large boxes. She filled each small box with the same number of beads and each large box with the same number of beads. There were 4 more beads in each large box than in each small box. 7/9 of the beads made were packed in the small boxes. How many beads were there in each small box?
Answer:
Each small box has 24/17 beads.
Step-by-step explanation:
Let's call the number of beads in each small box "s" and the number of beads in each large box "l".
We know that there are 14 small boxes, so the total number of beads in the small boxes is 14s. We also know that there are 3 large boxes, so the total number of beads in the large boxes is 3l.
From the problem, we know that there are 4 more beads in each large box than in each small box, so we can write:
l = s + 4
We also know that 7/9 of the total number of beads were packed in the small boxes, so we can write:
14s + 3l = 7/9(total number of beads)
We can simplify this expression by substituting l = s + 4:
14s + 3(s + 4) = 7/9(total number of beads)
Expanding and simplifying:
17s + 12 = 7/9(total number of beads)
Now, we need one more equation to solve for s. We know that the total number of beads is equal to the sum of the beads in the small and large boxes:
total number of beads = 14s + 3(s + 4)
Simplifying:
total number of beads = 17s + 12
Now we have two equations that we can use to solve for s:
17s + 12 = 7/9(total number of beads)
total number of beads = 17s + 12
We don't know the total number of beads, but we do know that it is a multiple of both 14 and 3 (since there are 14 small boxes and 3 large boxes). The smallest multiple of both 14 and 3 is 42, so let's assume that the total number of beads is 42x, where x is some number.
Substituting 42x for "total number of beads" in the two equations:
17s + 12 = 7/9(42x)
42x = 17s + 12
Simplifying:
153s + 108 = 98x
42x = 17s + 12
Now we have two equations and two unknowns (s and x). We can solve for s in terms of x by isolating s in the second equation:
17s = 42x - 12
s = (42x - 12)/17
We can substitute this expression for s into the first equation:
17((42x - 12)/17) + 12 = 7/9(42x)
Simplifying:
42x - 12 + 12 = 14x
28x = 24
x = 24/28 = 0.857
Now we know that the total number of beads is:
42x = 42(0.857) = 36
And we know that each small box has:
s = (42x - 12)/17 = (36 - 12)/17 = 24/17
So each small box has 24/17 beads.
