9.63 years are required for $390 to become $660. A charge for borrowing money or other assets is called an interest.
What is Compound Interest?Compound interest simply indicates that the interest paid on a savings account, loan, or investment grows exponentially over time rather than linearly.
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Here, A = Amount,
P = Principal Amount
r = Rate of interest
n = Number of times interest is charged in a year
t = number of years
Given ,Here Principal Amount is $390, the rate of interest is 5.5%(0.055),
the number of times the interest is charged in a year (n=4),
and the final amount is $660,
therefore, number of years will be equal to,
[tex]660 = 390(1 + \frac{0.055}{4} )^{4*t}[/tex]
[tex]\frac{660}{390} = (1.01375)^{4*t}[/tex]
[tex]1.6923 = (1.01375)^{4*t}[/tex]
[tex]log_{1.01375}1.6923 = 4t[/tex]
[tex]4t = 38.5234[/tex]
[tex]t = 9.63[/tex]
Hence, number of years it will take for $390 to become $660 is 9.63 years.
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A restaurant is hosting a party for 901 guests. If each table can seat 6 guests, how many tables should the restaurant plan to use?
Answer:
151 tables
Step-by-step explanation:
If 1 table is used for 6 guests then for 901 guest we need to divide 901 by 6
901÷6= 150.15
Rounding of the answer 151 tables needed
The dollar cost of producing x bagels is C(x) = 300 +0.25x - 0.4(x/1000)^3. Determine the cost of producing 2000 bagels. (Use decimal notation. Give your answer to one decimal place.)
C(2000) = $_______
The cost of producing 2000 bagels is $796.8.
To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8
Therefore, the cost of producing 2000 bagels is $796.8.
In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:
Profit = Revenues - Costs
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N=6 Which value for N would make the statement above true?
Answer:6
Step-by-step explanation:
N=6
⇒6=6
∴LHS=RHS
Using long division to find each quotient.
(2x³ 3x² + 4x + 2) = (x + 2)
Answer:
Step-by-step explanation:
Here's the long division of (2x³ + 3x² + 4x + 2) ÷ (x + 2):
2x^2 - x + 6
x + 2 | 2x^3 + 3x^2 + 4x + 2
- (2x^3 + 4x^2)
--------------
- x^2 + 4x
- (- x^2 - 2x)
-------------
6x + 2
- (6x + 12)
--------
-10
Therefore, the quotient is 2x^2 - x + 6, and the remainder is -10.
The quotient represents the result of the division of the polynomial (2x³ + 3x² + 4x + 2) by the divisor (x + 2). In particular, the quotient 2x^2 - x + 6 represents the quadratic polynomial that, when multiplied by the divisor x + 2, gives the dividend 2x³ + 3x² + 4x + 2.
In other words, we have:
(2x³ + 3x² + 4x + 2) = (x + 2)(2x^2 - x + 6) - 10
The remainder -10 indicates that the division is not exact, and that there is a "leftover" term of -10 when we try to divide the polynomial (2x³ + 3x² + 4x + 2) by (x + 2).
Please help, I need an explanation.
The measure of the angle N to the nearest degree for the given triangle is 23 degrees.
What is degree and radians?Degree and radian both serve as angles' units of measurement in geometry. Two radians (in radians) or 360° can be used to symbolise one whole anticlockwise rotation (in degrees). As a result, degree and radian can be compared as follows:
2π = 360°
The given triangle is an right triangle.
Using the trigonometric functions we can write the relation between the segments as:
Sin (N) = 1.5 / 3.9 = opposite/hypotenuse
N = arcsin (1.5 / 3.9)
N = 22.61 = 23 degrees.
Hence, the measure of the angle N to the nearest degree for the given triangle is 23 degrees.
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Lyla buys 30 balloons. She buys foil balloons for $5.49 each and toy balloons for $2.29 each. She pays
a total of $123.10 for the balloons.
Write a system of linear equations, and find the number of foil balloons f and the number of toy
balloons t she buys.
Answer:
Let f be the number of foil balloons Lyla buys, and let t be the number of toy balloons she buys. Then, we can set up a system of linear equations based on the information given:
f + t = 30 (since Lyla buys a total of 30 balloons)
5.49f + 2.29t = 123.10 (since Lyla pays a total of $123.10 for the balloons)
To solve for f and t, we can use the substitution method. From the first equation, we can solve for t in terms of f:
t = 30 - f
Substituting this expression for t into the second equation, we get:
5.49f + 2.29(30 - f) = 123.10
Simplifying and solving for f, we get:
5.49f + 68.70 - 2.29f = 123.10
3.20f = 54.40
f = 17
So Lyla buys 17 foil balloons. We can substitute this value of f back into the first equation to solve for t:
17 + t = 30
t = 13
Therefore, Lyla buys 17 foil balloons and 13 toy balloons.
What are the 3 sectors of economy?
Answer:
The three sectors of our economy -- private, public and non-profit -- are inextricably intertwined.
The 3 sectors of economy are:
Primary sectorSecondary sectorTertiary sectorThere are three sectors of the economy, each consisting of the following:
Primary sector: This sector is involved in the extraction and production of natural resources, such as agriculture, mining, and forestry.Secondary sector: This sector is involved in the processing and manufacturing of goods, such as factories and production facilities.Tertiary sector: This sector is involved in the provision of services, such as retail, education, healthcare, and hospitality.Each of these sectors plays a crucial role in the overall economy and contributes to the production and distribution of goods and services.
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5. Select all problems that have a sum or difference of -12.45
a. 9.44+ (-21.89)
b. -18.56 + 6.29
C. -3.18 - 9.27
d. -5.75 +(-6.7)
Which is it?????
Answer: A, C, and D all have the sums of -12.45
Step-by-step explanation:
A) -21.89 + 9.44 = -12.45
C) -3.18 - 9.27 = -12.45
D) -5.75 + -6.7 = -12.45
Maximize p = 10x + 20y + 15z subject to
x+2y+z ≤ 20
2y-z ≥ 5
2x-y+z ≥ 10
x 0, y 0, z ≥ 0
p = ___
(x,y,y) = ( _____ )
Maximize using simplex method, show work/calculations and matricies
The maximum value of p is 280 and the optimal solution is (x,y,z) = (14, 5, 2).
To maximize p = 10x + 20y + 15z subject to the given constraints, we will use the simplex method. The simplex method is a mathematical technique used to solve linear optimization problems.
Convert the inequalities to equations by adding slack variables. This will give us the following system of equations:
x + 2y + z + s1 = 20
-2y + z - s2 = -5
2x - y + z + s3 = 10
Write the equations in matrix form. The matrix will have the coefficients of the variables on the left-hand side and the constants on the right-hand side.
| 1 2 1 1 0 0 | 20 |
| 0 -2 1 0 -1 0 | -5 |
| 2 -1 1 0 0 1 | 10 |
Convert the matrix to reduced row echelon form using elementary row operations. This will give us the following matrix:
| 1 0 0 1/5 2/5 0 | 14 |
| 0 1 0 1/10 -1/10 0 | 5 |
| 0 0 1 -1/10 3/10 1 | 2 |
From the reduced row echelon form, we can see that the optimal solution is (x,y,z) = (14, 5, 2) and the maximum value of p is 10(14) + 20(5) + 15(2) = 280.
Therefore, the maximum value of p is 280 and the optimal solution is (x,y,z) = (14, 5, 2).
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The equations y= -(x+7)(x+4) and y=-(x-(3) are equivalent. How can both x intercepts be determined if the equation y=-(x+7)(x+4) is given
Answer:
To find the x-intercepts of the equation y = -(x+7)(x+4), we need to set y = 0 and solve for x. So, we have:
0 = -(x+7)(x+4)
This equation will be true if either (x+7) = 0 or (x+4) = 0. Solving each of these equations, we get:
x+7 = 0 => x = -7
x+4 = 0 => x = -4
Therefore, the x-intercepts of the equation y = -(x+7)(x+4) are x = -7 and x = -4.
Now, we know that the equations y = -(x+7)(x+4) and y = -(x-3) are equivalent. This means that they have the same solutions, or the same x-intercepts. So, we can use the x-intercepts we found for the first equation to determine the x-intercepts of the second equation.
To find the x-intercepts of the equation y = -(x-3), we set y = 0 and solve for x:
0 = -(x-3)
This equation will be true if (x-3) = 0, which gives us:
x-3 = 0 => x = 3
Therefore, the x-intercept of the equation y = -(x-3) is x = 3, which is different from the x-intercepts of the equation y = -(x+7)(x+4). This means that the two equations are not equivalent.
Step-by-step explanation:
Answer:
x-intercepts can be found below
Step-by-step explanation:
The equation:
[tex]y=-(x+7)(x+4)[/tex]
Can also be written as:
[tex]y=-1(x+7)(x+4)[/tex]
In order to find the x-intercepts, we must set each of the factors equal to 0.
[tex]-1=0[/tex]
[tex]x+7=0, x=-7[/tex]
[tex]x+4=0, x=-4[/tex]
The x-intercepts are:
[tex](0,0)[/tex]
[tex](-7,0)[/tex]
[tex](-4,0)[/tex]
The equation:
[tex]y=-(x-3)[/tex]
Can also be written as:
[tex]y=-1(x-3)[/tex]
In order to find the x-intercepts, we must set each of the factors equal to 0.
[tex]-1=0[/tex]
[tex]x-3=0, x=3[/tex]
The x-intercepts are:
[tex](0,0)[/tex]
[tex](3,0)[/tex]
There are 9.10^6 citizens in a country. Each citizen, independently from others, decides whether to take a vaccine against a certain virus or not. If a person gets a shot, which happens with probability 1/5, she will not become ill and will not require treatment. If a person does not get vac- cinated, she will fall ill and the state will have to cover the expenses of treating the virus-inflicted illness. This cost, for a single non-vaccinated individual, is a random variable from a uniform distribution over the interval [0, 2000) dollars and does not depend on the decisions or costs of other individuals. (a) Using the de Moivre-Laplace theorem, approximate the probabi- lity that less than 1801800 citizens will get vaccinated. (5 pts) (b) Using the CLT, approximate the probability that the total aggre- gate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars. Hint: for any citizen of the country, the treatment cost for this individual may be expres- sed as X · Y, where X, Y are independent random variables such that Y ~ U [0, 2000) and P(X = 0) = 1/5 = 1- P(X = 1). (5 pts) 9
The approximate probability that the total aggregate cost of fighting
The approximate probability that less than 1801800 citizens will get vaccinated can be calculated using the de Moivre-Laplace theorem. This theorem states that the probability distribution of the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is whether or not a citizen gets vaccinated, and the sum is the total number of citizens who get vaccinated.
To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of getting vaccinated, which is 9.10^6 * (1/5) = 1820000. The standard deviation is equal to the square root of the number of citizens times the probability of getting vaccinated times the probability of not getting vaccinated, which is sqrt(9.10^6 * (1/5) * (4/5)) = 1200.
Using the de Moivre-Laplace theorem, we can approximate the probability that less than 1801800 citizens will get vaccinated as the probability that a normal random variable with mean 1820000 and standard deviation 1200 is less than 1801800. This can be calculated using the standard normal distribution:
P(Z < (1801800 - 1820000)/1200) = P(Z < -1.52) = 0.064
Therefore, the approximate probability that less than 1801800 citizens will get vaccinated is 0.064.
The approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars can be calculated using the Central Limit Theorem (CLT). The CLT states that the sum of a large number of independent random variables approaches the normal distribution as the number of variables increases. In this case, the random variable is the cost of treating a single non-vaccinated individual, and the sum is the total cost of treating all non-vaccinated individuals.
To calculate the approximate probability, we need to find the mean and standard deviation of the distribution. The mean is equal to the number of citizens times the probability of not getting vaccinated times the expected value of the cost of treating a single non-vaccinated individual, which is 9.10^6 * (4/5) * (2000/2) = 7207200000. The standard deviation is equal to the square root of the number of citizens times the probability of not getting vaccinated times the variance of the cost of treating a single non-vaccinated individual, which is sqrt(9.10^6 * (4/5) * (2000^2/12)) = 1633333.33.
Using the CLT, we can approximate the probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars as the probability that a normal random variable with mean 7207200000 and standard deviation 1633333.33 is greater than 7207200000. This can be calculated using the standard normal distribution:
P(Z > (7207200000 - 7207200000)/1633333.33) = P(Z > 0) = 0.5
Therefore, the approximate probability that the total aggregate cost of fighting the virus-inflicted illness for all citizens of the country will surpass 7207200000 dollars is 0.5.
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Please help me as ASAP!!! BEGGING.. homework is due in 10 mins
Part A: Which converse is used to prove the given set of lines are parallel using the given angle pair?
<13 ≌ <15
j ∥ k
Part B: Which converse is used to prove the given set of lines are parallel using the given angle pair?
m<14+m<15=180
j ∥ k
The converse that can be used to prove that the given lines are parallel given each angle pair is:
1. Corresponding angles theorem
2. Same-side interior angles can be used
What is the Converse of Corresponding Angles Theorem?The converse of the corresponding angles theorem states that if a transversal intersects two lines, and the corresponding angles formed by the transversal and the lines are congruent, then the two lines are parallel.
What is the Converse of Same-Side Interior Angles Theorem?The converse of the same-side interior angles theorem can be stated as if a transversal intersects two lines, and the sum of the interior angles on one side of the transversal is 180 degrees, then the two lines are parallel.
Therefore we can conclude that:
A. The converse of the corresponding angles theorem
B. The converse of the same-side interior angles can be used
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DETAILS KAUFIALG 10 9.1.023. Specify the domain for the function. f(t)=(5)/(t^(2)+4) {t|t!=-4} {t|t>=0} {t|t!=4} {t|t!=-2 and t!=2} {all reals }
The correct domain for the function f(t)=(5)/(t^(2)+4) is {all reals}.
The domain of a function is the set of all possible inputs or values for the independent variable, t in this case. The function f(t)=(5)/(t^(2)+4) has a denominator of t^(2)+4. To find the domain, we need to determine the values of t that would make the denominator equal to zero, as those values would make the function undefined.
t^(2)+4=0
t^(2)=-4
t=±√(-4)
Since the square root of a negative number is not a real number, there are no real values of t that would make the denominator equal to zero. Therefore, the domain of the function is {all reals}.
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Please help me find the answer to this question
The measure of Angle D in a parallelogram is 88 degrees.
Explain about parallelogram ?
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other. The opposite angles are also equal in measure.
Properties of a parallelogram:
Opposite sides are parallel.Opposite sides are equal in length.Opposite angles are equal in measure.Consecutive angles are supplementary, i.e. their sum is 180 degrees.Diagonals bisect each other.According to the question:
Since EFDM is a parallelogram, we know that opposite angles are equal. Therefore,
Angle E = Angle M
Angle D = Angle F
We're given:
Angle E = 16x + 12
Angle D = 18x - 2
So we have:
Angle M = 16x + 12
Angle F = 18x - 2
The sum of the angles in a parallelogram is 360 degrees. Therefore, we have:
Angle E + Angle F + Angle D + Angle M = 360
Substituting the given values, we get:
(16x + 12) + (18x - 2) + (16x + 12) + (18x - 2) = 360
72x + 20 = 360
72x = 340
x = 5
Now we can find the values of Angle E, Angle D, Angle F and Angle M:
Angle E = 16x + 12 = 16(5) + 12 = 92 degrees
Angle D = 18x - 2 = 18(5) - 2 = 88 degrees
Angle F = Angle D = 88 degrees
Angle M = Angle E = 92 degrees
Therefore, the measure of Angle D is 88 degrees.
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Write the following linear equation in function notation. y = 2x + 5
Answer:
y=mx+b
It's already in function notation. Unless you need to graph it or show it.
HELP WORTH 10 POINTS
The picture shows the top view of a piece of glass.
A rectangular piece of glass is shown. The length is measured as 4 feet. The width is measured as 2 and one-half feet.
Which equations can be used to find the area, in square feet, of the piece of glass? Select all that apply.
A.
A
=
2
1
2
×
4
B.
A
=
5
2
+
4
C.
A
=
(
2
1
2
+
2
1
2
)
+
(
4
+
4
)
D.
A
=
5
2
×
4
E.
A
=
(
2
×
2
1
2
)
+
(
2
×
4
)
F.
A
=
2
1
2
+
4
The equation that can be used to determine the area of the glass is A = 2 1/2 x 4.
What is the equation that can be used to determine the area of the glass?A rectangle is a 2-dimensional quadrilateral with four right angles. A rectangle has two diagonals of equal length which bisect each other. The sum of interior angles is 360 degree and opposite sides are parallel
The area of the rectangle is the product of the length and the width.
Area of a rectangle = length x width
A = 4 x 2 1/2
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Assume that each package of a company contains 4 products and the number of defective products in one package has the following distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1. Find the average and the standard deviation of the number of defective products in a package. Answer: E(X) 2.46 Answer: 0(X) = 0.9635 2. Suppose that the numbers of defective products are independent between packages . Find the probability that there are not greater than 859 defective products in 359 package. Answer: 0.0934
The probability that there are not greater than 859 defective products in 359 packages is 0.9999.
We are given that;
Distribution: X 0 3 4 1 2 Р 0.02 0.14 0.34 0.36 0.14 1
0(X) = 0.9635 2
Now,
We need to know the probability of success for each package, which is the probability of having a defective product. Assuming that each product has an equal chance of being defective, we can calculate this probability by dividing the number of defective products by the number of products in a package. In this case, we have:
[tex]p = \frac{0.02 + 0.14 + 0.34 + 0.36 + 0.14}{4} = 0.25[/tex]
This means that each product has a 25% chance of being defective, and each package has a binomial distribution with n=4 and p=0.25.
To find the average and the standard deviation of the number of defective products in a package, we can use these formulas³:
[tex]$$E(X) = np$$$$\sigma(X) = \sqrt{np(1-p)}$$[/tex]
Plugging in the values of $n$ and $p$, we get:
[tex]$$E(X) = 4 \times 0.25 = 1$$$$\sigma(X) = \sqrt{4 \times 0.25 \times (1-0.25)} = \sqrt{0.75} \approx 0.866$$[/tex]
Therefore, the average number of defective products in a package is 1, and the standard deviation is 0.866.
To find the probability that there are not greater than 859 defective products in 359 packages, we need to use the binomial distribution again, but with different values of n and p. In this case, we have:
[tex]$$n = 359 \times 4 = 1436$$$$p = 0.25$$[/tex]
We want to find the probability that [tex]$X \leq 859$[/tex], where [tex]$X$[/tex] is the number of defective products in 1436 trials. We can use this formula:
[tex]$$P(X \leq k) = \sum_{i=0}^{k} \binom{n}{i}p^i(1-p)^{n-i}$$Plugging in the values of $n$, $p$, and $k$, we get:$$P(X \leq 859) = \sum_{i=0}^{859} \binom{1436}{i}0.25^i(1-0.25)^{1436-i}$$[/tex]
Therefore, by probability the answer will be 0.9999.
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Hi due today pls help! Ty!
red counter to blue
There are 15 blue counters in the bag.
What are ratios and proportions?
Two quantities are compared to form a ratio. An equality of two ratios is a proportion.
We know that the initial ratio of red counters to blue counters was 4:5. Therefore, we can write:
4x : 5x
We also know that 10 more red counters were added to the bag. Therefore, the new number of red counters in the bag is:
4x + 10
The ratio of red counters to blue counters then became 6:5. Therefore, we can write:
(4x + 10) : y = 6 : 5
We can simplify this equation by cross-multiplying:
5(4x + 10) = 6y
20x + 50 = 6y
Dividing both sides by 6, we get:
y = (20x + 50)/6
Simplifying, we get:
y = (10x + 25)/3
Since y has to be a whole number, 10x + 25 has to be divisible by 3. The only value of x that satisfies this condition is x = 2.
Therefore, the initial number of red counters was 4x = 8, and the initial number of blue counters was 5x = 10.
After adding 10 more red counters, the new number of red counters was 18, and the new ratio of red counters to blue counters was 6:5.
To find the new number of blue counters, we can use the equation we derived earlier:
y = (10x + 25)/3
Substituting x = 2, we get:
y = (10(2) + 25)/3 = 15
Therefore, there are 15 blue counters in the bag.
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A classmate poses the following question to you:
"Is zero a prime number, composite number, odd number, or even number?"
Write your response to your classmate’s question. Explain the reasoning for your response
Zero is an even number, but neither a prime number nor a composite number.
Prime numbers are numbers that are only divisible by one and itself, while composite numbers are numbers that are divisible by more than one and itself. Since zero is divisible by more than one and itself (zero, one, and two), it is neither prime nor composite.
As for odd and even numbers, odd numbers are any integer that is not divisible by two, while even numbers are any integer that is divisible by two. Since zero is divisible by two, it is an even number.
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Use the remainder theorem to find the remainder when f(x) is divided by x-1. f(x). f(x)=2x^(3)+3x^(2)-12x+7
The remainder when f(x) is divided by x-1 is 0.
What is remainder theorem?Remainder Theorem states that given a polynomial function and a value for x, the remainder when the polynomial is divided by (x-a) is equal to the value of the polynomial when x=a. This theorem can be used to quickly and accurately find the remainder of a division problem, making it a very useful tool.
The remainder theorem states that if a polynomial f(x) is divided by x-a, then the remainder is f(a). In this case, we want to find the remainder when f(x) is divided by x-1. Therefore, we need to find f(1).
f(1) = 2(1)^(3) + 3(1)^(2) - 12(1) + 7
f(1) = 2 + 3 - 12 + 7
f(1) = 0
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Problem 2
Let A= [ 9 2 -22]
[ 0 -2 0 ]
[ 1 0 -4 ]
a) find the characteristic polynomial of A
b) Find the two eigenvalues of A
(c) Find a basis for the eigenspace corresponding to the smallest eigenvalue. (d) Find a basis for the eigenspace corresponding to the largest eigenvalue.
{-2 2 22}
a) The characteristic polynomial of A is given by:
$$p_A(\lambda) = \lambda^3 - 5\lambda^2 + 18\lambda + 36$$
b) The two eigenvalues of A are:
$$\lambda_1=2, \lambda_2=-4, \lambda_3=9$$
c) A basis for the eigenspace corresponding to the smallest eigenvalue $\lambda_2=-4$ is given by the set of vectors:
$$\begin{bmatrix} 0\\1\\0 \end{bmatrix}, \begin{bmatrix} 2\\0\\1 \end{bmatrix}$$
d) A basis for the eigenspace corresponding to the largest eigenvalue $\lambda_3=9$ is given by the set of vectors:
$$\begin{bmatrix} 1\\0\\-4 \end{bmatrix}, \begin{bmatrix} -2\\2\\22 \end{bmatrix}$$
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HELPPPP PLEASEEEEEE ASAP
Answer: I remember this question very well. I believe that the correct answer is 99.7%
68% of data falls between 15 and 25.
95% of data falls between 10 and 30.
99.7% of data falls between 5 and 35.
PLEASE HELP! WILL GIVE BRAINLIEST!!
Susie owns an upholstery shop. She has a customer with an odd request. They want fringe placed on only one edge of each of 3 different square shaped pillows.
The area of the pillows are:
A. 3 saft
B. 8 sq ft
C. 16 sq ft.
How much fringe should she use for each one?
The same customer also has a circular pillow that is 2' in diameter and wants fringe placed all the way around it (this customer REALLY likes fringe!)
Money
Minutes
• A. Describe how Susie could figure out how much fringe to use.
To solve
B.
Write an equation and solve.
Answer: Susie needs to find the length of one side of each square pillow and the circumference of the circular pillow, add them all together, and that is how much fringe she must use.
Equation: √3 + √8 + √16 + 2π
(This might not be what you are looking for but this is how I would answer this question)
Step-by-step explanation:
All decimals to 4 decimal places
Area of a square = side x side
To find the length of each side, square root the area
Pillow 1:
Side = √3
Fringe needed = 1.7321
Pillow 2:
Side = √8
Fringe needed = 2.8284
Pilow 3:
Side = √16
Fringe needed = 4
Circumference of a circle = 2πr
radius = half of the diameter
Pillow 4:
Side = 2π(1)
Side = 2π
Fringe needed = 6.2832
Total: 1.7321 + 2.8284 + 4 + 6.2832 = 14.8437
Answer:
Square pillow A: √3 ft ≈ 1.73 ft (nearest hundredth)
Square pillow B: √8 ft ≈ 2.83 ft (nearest hundredth)
Square pillow C: 4 ft
Circular pillow: 6.28 ft
Step-by-step explanation:
The area of a square is the square of the measure of its side length.
Therefore, if the customer wants fringe placed on only one edge of each of 3 different square shaped pillows, we can calculate how much fringe should be used for each pillow by square rooting the given areas.
[tex]\boxed{\textsf{Fringe needed}=\sqrt{\sf Area}}[/tex]
Pillow AArea = 3 ft²
[tex]\begin{aligned} \implies \textsf{Fringe needed}&=\sqrt{3\; \sf ft^2}\\&=\sqrt{3}\sqrt{\sf ft^2}\\&=\sqrt{3}\; \sf ft\\&\approx1.73 \sf \; ft\;(nearest\;hundredth)\end{aligned}[/tex]
Pillow BArea = 8 ft²
[tex]\begin{aligned} \implies \textsf{Fringe needed}&=\sqrt{8\; \sf ft^2}\\&=\sqrt{8} \sqrt{\sf ft^2}\\&=\sqrt{8} \; \sf ft\\&\approx 2.83\; \sf ft\;(nearest\;hundredth)\end{aligned}[/tex]
Pillow CArea = 16 ft²
[tex]\begin{aligned} \implies \textsf{Fringed needed}&=\sqrt{16\; \sf ft^2}\\&=\sqrt{16}\sqrt{\sf ft^2}\\&=4 \; \sf ft\end{aligned}[/tex]
If the same customer also has a circular pillow that is 2 ft in diameter and they want fringe placed all the way around it, we can calculate the amount of fringe to use by calculating the circumference of the circle.
The formula for a circumference of a circle is C = πd, where d is the diameter of the circle. Given that d = 2 ft and using π ≈ 3.14:
[tex]\begin{aligned}\implies \textsf{Fringe needed for the circular pillow}&=\pi \cdot 2\\&=3.14 \cdot 2\\&=6.28\; \sf ft\end{aligned}[/tex]
Performance task prize patrol
A performance task is any educational activity or assessment that calls for students to perform in order to demonstrate their comprehension, competency, and knowledge.
How would you define activity?Mathematical activity includes the search for patterns as well as experimentation, description, fiddling, invention, picturing, conjecture, and guesswork.
A series of recurrent numbers, symbols, or shapes is referred to in mathematics as a pattern. Every kind of event or thing has a pattern that can be connected to it. A rule that distinguishes between items that are a part of a pattern and those that are not is known as a pattern.
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Complete question:
What is Performance task?
Question
Determine the value of x in the diagram.
The quadrilateral with the specified value for x has a 45° angle.
What is quadrilateral?A polygon with four sides, four angles, and four vertices is called a quadrilateral.
The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.
A quadrilateral is a four-sided polygon with four edges and four corners that is used in geometry.
The Latin words quadri, a variation of four, and latus, meaning "side," are the source of the name.
The exterior angles of the given quadrilateral are x°, 3x°, x°, and 3x°.
We are aware that a quadrilateral's total exterior angles are 360°.
Now, x°+3x°+x°+3x°=360°
8x°=360°
x°=45°
Therefore, the quadrilateral with the specified value for x has a 45° angle.
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what is the answer to this?
I need help ASAP IM IN A HURRY SO PLEASE
Step-by-step explanation:
Refer to pic...........
3. You and two friends go out and want to order appetizers from GREAT
BEGINNINGS a 12 piece Grilled Tuscan Chicken Wings, Mozzarella
Fritta and Pan Sauteed Mussels. You decide to share a CRAFT
YOUR OWN PIZZA, and order a 2 Topping Small Pizza, One of your
friends has a coupon for 20% off your entire order. You give the
coupon to the waiter and your discount is removed before tax. After
the discount the sales tax on your bill is 8% and you tip the waiter
15%. What is the cost of your meal?
The cost of the meal, including the 20% discount, 8% sales tax, and 15% tip, is $43.72.
How to find how much percent 'a' is of 'b'?Suppose a number is 'a'
Suppose another number is 'b'
We want to know how much percent of 'b' is 'a'.
Then, it is calculated as:
[tex]\dfrac{a}{b} \times 100[/tex]
(in percentage)
We are given that;
Items ordered= a 12 piece Grilled Tuscan Chicken Wings, Mozzarella
Fritta and Pan Sauteed Mussels.
Coupon percent off =20%
Sales tax= 8%
Waiter tip= 15%
Now,
Let's start by finding the cost of the appetizers and the pizza before any discounts or taxes are applied:
Grilled Tuscan Chicken Wings: let's assume this is $12
Mozzarella Fritta: let's assume this is $8
Pan Sauteed Mussels: let's assume this is $14
Craft Your Own Pizza: let's assume this is $10 for a small 2-topping pizza
So the total cost of the food before any discounts or taxes is:
$12 + $8 + $14 + $10 = $44
With the 20% coupon, we can apply a discount of:
0.2 x $44 = $8.80
So the new total before taxes is:
$44 - $8.80 = $35.20
Now we can calculate the sales tax on this amount:
0.08 x $35.20 = $2.82
Adding the sales tax to the discounted amount gives:
$35.20 + $2.82 = $38.02
Finally, we can calculate the total cost of the meal after adding the 15% tip:
$38.02 + 0.15 x $38.02 = $43.72
Therefore, by the given percentages the answer will be $43.72.
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The Island of Paradis is divided into the following zones (Districts) which are given as follows Determine the total number of trips between the zones. Zone Production/Generation Attraction 1. Shinganshina 3643 3040 2. Utopia 3484 2524 3. Karanes 3156 2535 4. Trost 3204 4217 5. Krolva 2167 2122 6. Stohess 2542 1638 7. Ehrmich 2275 1245 8. Yarckel 2210 3714 9. Orvud 3597 4542 10. Mitras 3172 3754
Determine the total number of trips between the zone:
a. 1 and 6
b. 3 and 10
c. 5 and 10
d. 4 and 9
The total number of trips between the zone: a. 1 and 6 is 10863 trips. b. 3 and 10 is 12617 trips. c. 5 and 10 is 11215 trips. d. 4 and 9 is 15560 trips.
To determine the total number of trips between the zones, we can simply do addition of the production/generation and attraction values for the two zones in question. Based on the values in the table:
a. For zones 1 and 6, the total number of trips would be 3643 + 3040 + 2542 + 1638 = 10863 trips.
b. For zones 3 and 10, the total number of trips would be 3156 + 2535 + 3172 + 3754 = 12617 trips.
c. For zones 5 and 10, the total number of trips would be 2167 + 2122 + 3172 + 3754 = 11215 trips.
d. For zones 4 and 9, the total number of trips would be 3204 + 4217 + 3597 + 4542 = 15560 trips.
Therefore, the total number of trips between the zones are: a. 10863 trips between zones 1 and 6 b. 12617 trips between zones 3 and 10 c. 11215 trips between zones 5 and 10 d. 15560 trips between zones 4 and 9.
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The lenght of a rectangular floor is twice its breadth if the perimeter of the floor is 216 m find it length and breadth
As per the perimeter, the length of the rectangular floor is 72 meters, and the breadth is 36 meters.
Now we can use the formula for the perimeter of a rectangle to write an equation in terms of x and solve for x.
Perimeter of the rectangle = 2(length + breadth)
Given that the perimeter is 216 m, we can substitute the values of length and breadth in terms of x to get:
216 = 2(2x + x)
Simplifying this equation, we get:
216 = 2(3x)
Dividing both sides by 2, we get:
108 = 3x
Solving for x, we get:
x = 36
Now that we have the value of x, we can use it to find the length and breadth of the rectangular floor.
Length = 2x = 2(36) = 72 m
Breadth = x = 36 m
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