1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
What is a ratio?
A ratio is a quantitative comparison between two or more quantities, indicating how many times one quantity contains another. It is expressed as the quotient of the two quantities or in the form of a fraction. Ratios can be represented in various ways, including as decimals, percentages, or fractions.
Complete the table to show the amounts of yellow and red paint needed for different numbers of batches of the same shade of orange paint.
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
To get the same shade of orange paint, we need to mix yellow and red paint in a certain ratio. This ratio will determine the hue, saturation, and brightness of the final color. In this case, we can see that the ratio of yellow to red paint is 5:3 in the first row of the table, and 6:3.6 (which simplifies to 5:3) in the second row. This means that we need the same amount of yellow and red paint for each batch of orange paint, in a 5:3 ratio.
A car is traveling at a constant speed, as shown by the double number line.
The distance traveled by the car is directly proportional to the amount of time it travels. This means that the ratio of distance to time is constant. From the given double number line, we can see that the car travels 21 miles in 3 hours. Therefore, the ratio of distance to time is 21:3 or 7:1. To find how far the car travels in 14 hours, we can set up a proportion:
distance/time = 7/1
distance/14 = 7/1
distance = 7 x 14
distance = 98 miles
Therefore, the car travels 98 miles in 14 hours.
The olive trees in an orchard produce 3000 pounds of olives per year. It takes 20 pounds of olives to produce 3 liters of olive oil.
To find how many liters of olive oil the orchard can produce in a year, we need to divide the total weight of olives by the amount of olives needed to produce one liter of oil, and then multiply by the conversion factor:
Liters of oil = (Pounds of olives / Pounds per liter) x Conversion factor
Liters of oil = (3000 / 20) x 3
Liters of oil = 150 x 3
Liters of oil = 450
Therefore, the orchard can produce 450 liters of olive oil in a year.
Hence,
1)The completed table is
Yellow paint (quarts) | Red paint (quarts)
5 | 3
6 | 3.6
2) The car travels 98 miles in 14 hours.
3) The orchard can produce 450 liters of olive oil in a year.
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Let X be a random variable whose characteristic function ∅ satisfies ∫▒〖|∅(t)|dt< [infinity].〗 . Show that (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 is the Lebesgue density of X.
(2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗
The characteristic function of a random variable X is defined as ∅(t) = E[e^(√(-1)tx)]. To show that (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 is the Lebesgue density of X, we need to demonstrate that it is a probability density function.
We first calculate the integral to obtain (2π)^(-1) ∫▒〖e^(-√(-1) xt)∅(t)dt〗 = (2π)^(-1) ∫▒〖E[e^(-√(-1) xt +√(-1) tx)]dt〗.
Since the expectation is a constant, we can pull it out of the integral to get (2π)^(-1)E[∫▒〖e^(-√(-1) xt +√(-1) tx)]dt〗.
Now, if we substitute t = y-x and rewrite the integral, we obtain (2π)^(-1)E[∫▒〖e^(-√(-1) x(y-x))e^(√(-1) xy)]dy〗.
This simplifies to (2π)^(-1)E[∫▒〖e^(-√(-1) xy)]dy〗.
Because the integrand is 1, the integral is simply y. Then, the expectation becomes E[y] which is the mean of the random variable X. Thus, the Lebesgue density of X is (2π)^(-1)E[y], which is the probability density function of X.
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After a number of months, a bank balance was -$46. 83. Each month, the bank charges a $5. 95 fee for having a negative balance. Write an inequality to determine at most how many months the fee was charged. Let x be how many months the fee was charged
If x is the number of months the fee was charged, then the inequality to determine at most months the fee was charged is x ≥ (y + 46.83)/5.95 .
Let x be the number of months the fee was charged.
Let y be the initial balance before the fee was charged.
So, we can write the inequality as : y - 5.95x ≤ -46.83
where y is = positive number representing the initial balance.
Since the initial balance is "y" , we can determine the value of x that satisfies this inequality.
The inequality is represented as : x ≥ (y + 46.83)/5.95 .
Therefore, the inequality to determine number of months is x ≥ (y + 46.83)/5.95.
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(a) Show that the F statistic for testing that all effects equal
0 has expression in terms of the R2 value as
(b) Show that the F statistic for comparing nested models has
expression in terms of the
(a) The F statistic for testing that all effects equal 0 is given by:
F = [(R2 / k) / ((1 - R2) / (n - k - 1))]
where R2 is the coefficient of determination, k is the number of predictor variables, and n is the total number of observations.
To derive this expression, we start with the definition of the F statistic:
F = [(SSR / k) / (SSE / (n - k - 1))]
where SSR is the sum of squares for regression and SSE is the sum of squares for error.
We know that R2 = SSR / SST, where SST is the total sum of squares. Therefore, we can rewrite SSR as:
SSR = R2 * SST
Substituting this back into the F statistic, we get:
F = [(R2 * SST / k) / (SSE / (n - k - 1))]
We also know that SST = SSR + SSE, so we can substitute this back into the F statistic:
F = [(R2 * (SSR + SSE) / k) / (SSE / (n - k - 1))]
Simplifying the expression, we get:
F = [(R2 / k) / ((1 - R2) / (n - k - 1))]
This is the expression for the F statistic in terms of the R2 value.
(b) The F statistic for comparing nested models is given by:
F = [(R2_2 - R2_1) / (k_2 - k_1)] / [(1 - R2_2) / (n - k_2 - 1)]
where R2_1 and R2_2 are the R2 values for the smaller and larger models, respectively, and k_1 and k_2 are the number of predictor variables in the smaller and larger models, respectively.
To derive this expression, we start with the definition of the F statistic:
F = [(SSR_2 - SSR_1) / (k_2 - k_1)] / [(SSE_2 / (n - k_2 - 1))]
where SSR_1 and SSR_2 are the sum of squares for regression for the smaller and larger models, respectively, and SSE_2 is the sum of squares for error for the larger model.
We know that R2 = SSR / SST, so we can rewrite SSR_1 and SSR_2 as:
SSR_1 = R2_1 * SST
SSR_2 = R2_2 * SST
Substituting these back into the F statistic, we get:
F = [((R2_2 * SST) - (R2_1 * SST)) / (k_2 - k_1)] / [(SSE_2 / (n - k_2 - 1))]
Simplifying the expression, we get:
F = [(R2_2 - R2_1) / (k_2 - k_1)] / [(1 - R2_2) / (n - k_2 - 1)]
This is the expression for the F statistic for comparing nested models in terms of the R2 values.
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Consider the code over F4 with generator matrix 11 10 01 10 00
11 Construct a standard array for the code, and use it to decode
the words 00 11 01 and 11 11 10.
To decode the words 0011, 0101, 0110 and 1111, we can find the corresponding codeword in the standard array. The codewords for 0011, 0101, 0110 and 1111 are 0011, 0101, 0110 and 1111, respectively.
To construct a standard array for this code, we can start by finding the generator polynomial of the code. This can be done by multiplying the generator matrix with its transpose and finding the resultant matrix. This results in the generator polynomial: 110101001.
To construct the standard array, we first construct a parity check matrix, which is the transpose of the generator matrix: 0101 1001 1100 1000.
From the parity check matrix, we can then construct the standard array. The standard array consists of all the possible codewords given the generator polynomial and the parity check matrix. It can be constructed by multiplying the generator matrix with all possible vectors of length 3.
The standard array of the code is:
0011 0101 0110 1001 1010 1100 1101 1111
To decode the words 0011, 0101, 0110 and 1111, we can find the corresponding codeword in the standard array. The codewords for 0011, 0101, 0110 and 1111 are 0011, 0101, 0110 and 1111, respectively.
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help me do this pls it is to hard
The fraction amount of pizza eaten is given by A = ( 5/6 ) of the pizza
The amount of pizza left over B = ( 1/6 ) of the pizza
What is a Fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
Given data ,
Let the fraction of pizza eaten be represented as A
Now , the value of A is
Let the amount of pizza eaten by Tyler be p = ( 1/2 ) of the pizza
Let the amount of pizza eaten by Dean be q = ( 1/3 ) of the pizza
Now , the fraction of pizza eaten A = p + q
On simplifying , we get
The fraction of pizza eaten A = ( 1/2 ) + ( 13 )
The fraction of pizza eaten A = ( 3 + 2 ) / 6
The fraction of pizza eaten A = ( 5/6 ) of the pizza
And , the amount of pizza left B = 1 - A
On simplifying , we get
The amount of pizza left = 1/6 of the total pizza
Hence , the fractions are solved
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Four more than the quotient of a number and 8 is equal to 2
If f (x = x-2) any y (x) = -2 x +7 what value makes f (x) =y (x) ?
The x number for which the following functions are equivalent is determined to be 3 by the preceding statement.
What is a simple definition of a function?The term "function" refers to the correlation between a set of inputs and outputs. Simply defined, a function is an input-output relationship where each input is coupled to exactly one output.
The given functions are f(x) = x - 2 and f(x) = -2x + 7.
Assign the functions the following equivalences to determine the value of x:
variable x - 2 = -2x + 7
variable x + 2x = 7 + 2
Therefore, x = 3
Hence, the specified value for x is 3.
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Part One: Line DE is tangent to circle A at point E. If line CD = 8cm and line DE = 12cm, what is the length of line BC. (You may assume A, B, C, and D are colinear)
Part 2: What is the area and circumstance of Circle A
The length of line BC is 10cm ,The area of the circle is 78.5 cm² and The circumstance of Circle is 31.4 cm.
Part-1
To Find the length of BC, We have the lenghts of CD=8cm and DE=12cm
To find out length. We have to make a perpendicular line construction joins AE.
Triangle AED forms a right angled triangle.
As we all know pythagoras theorem.
Pythagoras formula c²=a²+b²
To findout radius of circle
Let AE=AC=r
AD=CD+AC
AD=8+r
AD²=AE²+DE²
Submit all values in the above equation.
(8+r)²=r²+12²
(a+b)²=a²+b²+2ab use the formula
64+r²+16r=r²+144
Cancel r² each other.
64+16r=144
16r=144-64
16r=80
r=5
Radius of the circle r=5cm
Therefore , the value of BC=2AC
BC=2r
BC=2*5
BC=10cm
The length of line BC is 10cm
Part-2
To find out area of the circle
We have the formula for area of circle.
Area=πr²
Area=(22/7)*5*5
Area=78.5 cm²
The area of the circle is 78.5 cm².
To find out the circumstance of Circle
We have the formula for circumstance of circle. 2πr
circumstance=2*(22/7)*5
circumstance=31.4 cm
The circumstance of Circle is 31.4 cm.
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guys i need this asap PLEASE
if
a real estate office sells 1.6 houses on an average weekday and
sales of houses on weekdays are poison distributed. What is the
probability of selling exactly 4 hours in one day ?
The probability of selling exactly 4 houses in one day is 0.0548, or about 5.48%.
To find the probability of selling exactly 4 houses in one day, use the Poisson distribution formula:
P(X = x) = (λ^x)(e^-λ) / x!
Where:
λ = the average number of events (in this case, the average number of houses sold)
x = the number of events we want to find the probability of (in this case, 4 houses)
e = the base of the natural logarithm (approximately 2.71828)
So, plugging in the values: P(X = 4) = (1.6^4)(e^-1.6) / 4! = (6.5536)(0.2019) / 24 = 0.0548
Therefore, since the data is Poisson distributed, selling exactly 4 houses in one day has a probability of 0.0548, or about 5.48%.
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BM bisects ABC. If MBC = 32°, what is the ABC?
The measure of angle ABC is 64°.
What is an angle bisector?The angle bisector in geometry is the ray, line, or segment which divides a given angle into two equal parts.
Given that, BM bisects ∠ABC and ∠MBC=32°.
Here, ∠ABC=∠MBC+∠MBA
Since, BM bisects ∠ABC, ∠MBC=∠MBA
∠ABC=∠MBC+∠MBC
∠ABC=2∠MBC
∠ABC=2×32°
∠ABC=64°
Therefore, the measure of angle ABC is 64°.
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Pencil Problen Find all real numbers that mus the domain of each rational e? (x+5)/(x^(2)-25)
In interval notation, the domain can be written as: (-∞, -5) ∪ (-5, 5) ∪ (5, ∞). In set notation, the domain can be written as: {x ∈ ℝ | x ≠ -5 and x ≠ 5}
To find the domain of the given rational expression, we need to determine the values of x that make the denominator equal to zero. This is because division by zero is undefined and therefore, these values of x cannot be included in the domain.
The denominator of the given expression is x^(2)-25. We can set this equal to zero and solve for x:
x^(2)-25=0
(x+5)(x-5)=0
x=-5 or x=5
These values of x make the denominator equal to zero, so they cannot be included in the domain. Therefore, the domain of the given rational expression is all real numbers except -5 and 5.
In interval notation, the domain can be written as: (-∞, -5) ∪ (-5, 5) ∪ (5, ∞)
In set notation, the domain can be written as: {x ∈ ℝ | x ≠ -5 and x ≠ 5}
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Write and solve the inequality.
Eight more than the quotient of a number b and 45 is greater than 6.
Fill in the boxes.
b
45
+8
b
45
6
-2
b
(Type integers or fractions.)
The answer choice which represents the solution to the inequality given as required is; b > -90.
What is the solution for b in the inequality?Quotient refers to a number resulting from the division of one number by another.
As evident in the task content; the given inequality is;
Eight more than the quotient of a number b and 45 is greater than 6.
The symbols of inequalities are;
Greater than >
Less than <
Equal to =
Greater than or equal to ≥
Less than or equal to ≤
Therefore, the algebraic expression is;
b/45 + 8 > 6
Therefore; b/45 > -2
b > -90.
Ultimately, the required inequality is; b/45 + 8 > 6 and it's solution is; b > -90.
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I need help with this question can you also go step by step because tomorrow I have a quiz?
Answer:
3/5
Step-by-step explanation:
In your problem you have a right triangle.
For this problem, you need to know what sine is. Sin is [tex]\\\frac{opposite}{hypotenuse}[/tex]
In this problem we know that the hypotenuse is 20, but we do not know the opposite. The opposite refers to the side that is opposite to the angle. In this case, the angle we are using is c. Also, in this case, the name of the opposite side is ED. To figure out that side, we need to use the pythagorean theorem.
[tex]a^{2} +b^{2} =c^{2}[/tex]
A is 16, c is 20
Therfore we can plug those values into our formula
[tex]16^{2} +b^{2}=20^{2}[/tex]
Simplify:
[tex]256 + b^{2} =400[/tex]
Simplify even more:
[tex]b^{2} = 144[/tex]
Square root both sides:
[tex]b = 12[/tex]
Now we Know all 3 sides of our triangle: 20, 16, and 12.
Sin refers to OPPOSITE/HYPOTENUSE
Our opposite is 12, and our hypotenuse is 20.
Plugging those values into our formula gives us:
12/20
Simplify:
3/5.
THERFORE, THE ANSWER IS 3/5
**Also, this whole process seems long, but in reality it is very short and you'll master it in no time!
Happy Paws charges $18.00 plus $2.50 per hour to keep a dog during the day. Woof Watchers charges $12.00 plus $3.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
The total cost of the services from Happy Paws and Woof Watchers will be equal if the dog is kept for 12 hours.
How Do You Solve Linear Equations?Finding the answer to a linear equation with one, two, three, or more variables is known as solving a linear equation. A linear equation's solution is, to put it simply, the value or values of the variables that make up the equation. Any coefficient can be deleted using the elimination procedure after being initially equated. Elimination is followed by equations being solved to get the other equation.
Let us suppose the number of hours = h.
Given that, Happy Paws charges $18.00 plus $2.50 per hour.
H = 18 + 2.50h
Woof Watchers charges $12.00 plus $3.75 per hour.
W = 12 + 3.75h
The cost is equal for:
18.00 + ($2.50 x h) = $12.00 + ($3.75 x h)
18 - 12 = 3.75h - 2.50h
h = 12
Hence, the total cost of the services from Happy Paws and Woof Watchers will be equal if the dog is kept for 12 hours.
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Find a function f whose graph is a parabola with the given vertex and that passes through the given point. vertex (−1, 3); point (−2, −2)
Answer:
Equation of parabola in vertex form:
y = -5( x + 1)² + 3
Equation of parabola in standard form:
y = -5x² -10x - 2
Step-by-step explanation:
The vertex form equation for a parabola is
y = a(x - h)² + k
where (h, k) is the vertex and a is a constant
Given (h, k) = (- 1, 3)
h = -1 , k = 3
y = a( x - (-1) )² + 3
y = a(x + 1)² + 3
To find a, we know the parabola passes through point(- 2, - 2). Plug in x = -2, y = -2 and solve for a
- 2 = a( -2 + 1)² + 3
-2 = a(-1)² + 3
-2 = a · 1 + 3
-2 = a + 3
Subtract 3 from both sides:
-2 - 3 = a + 3 -3
-5 = a
or
a = -5
Equation of parabola in vertex form:
y = -5( x + 1)² + 3
The standard form of this parabola is y = ax² + bx + c
Expand (x + 1)² = x² + 2 · 1 · x + 1² = x² + 2x + 1
Therefore
y = -5( x + 1)² + 3 becomes
y = -5( x² + 2x + 1) + 3
y = -5x² -10x - 5 + 3
y = -5x² -10x - 2
Write the gradient and y-intercept of each line
a. Y=10x+20
b. Y=10-20x
c. Y=-2. 5+0. 5x
The required gradient and y-intercept for the given lines is given by ,
1. gradient = 10 and y-intercept = 20
2. gradient = -20 and y-intercept = 10
3. gradient = 0.5 and y-intercept = 2.5
Equation of a line in slope-intercept form = y = mx + c.
where 'm' is the slope of the line
And 'c' is the y-intercept.
For the line Y = 10x + 20
Compare with standard form we get,
Slope of the line is 10 .
And the y-intercept is 20.
This implies,
gradient is 10 and the y-intercept is (0, 20).
For the line Y=10-20x
Compare with standard form we get,
Slope of the line is -20
And the y-intercept is 10.
This implies,
the gradient = -20
And the y-intercept = (0, 10).
For the line Y=-2. 5+0. 5x
Compare with standard form we get,
Slope of the line is 0.5
And the y-intercept is -2.5
This implies,
the gradient = 0.5
And the y-intercept = (0, -2.5)
Therefore, the gradient and the y-intercept for each line is equal to,
Y=10x+20 , gradient = 10 and y-intercept = 20
Y=10 -20x , gradient = -20 and y-intercept = 10
Y=-2. 5+0. 5x , gradient = 0.5 and y-intercept = 2.5
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Determine whether the lines L1(t) = ⟨3 − t, 8 − 3t, 1 − t⟩ and
L2(s) = ⟨−1 − 2s, 3 + s, s⟩ intersect. If they do, state where they
intersect.
The answer of lines intersect at the point is (1, 2, -1)
To determine whether the lines L1(t) = ⟨3 − t, 8 − 3t, 1 − t⟩ and L2(s) = ⟨−1 − 2s, 3 + s, s⟩ intersect, we need to find a value of t and s that make the x, y, and z components of both lines equal.
First, let's set the x components of both lines equal to each other:
3 − t = −1 − 2s
Next, let's set the y components of both lines equal to each other:
8 − 3t = 3 + s
Finally, let's set the z components of both lines equal to each other:
1 − t = s
Now we can solve for t and s. From the first equation, we get:
t = 4 + 2s
Substituting this value of t into the second equation, we get:
8 − 3(4 + 2s) = 3 + s
Simplifying this equation gives us:
-4 − 6s = 3 + s
Solving for s gives us:
s = -1
Substituting this value of s back into the first equation gives us:
t = 4 + 2(-1) = 2
So the lines intersect at t = 2 and s = -1. To find the point of intersection, we can substitute these values back into either line equation. Substituting into L1(t) gives us:
L1(2) = ⟨3 − 2, 8 − 3(2), 1 − 2⟩ = ⟨1, 2, -1⟩
Therefore, the lines intersect at the point (1, 2, -1).
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Which inequality represents the graph? Iready Level F Write and Solve Inequalities
A "pool toy" is thrown into a swimming pool, but floats on the surface of the water. It displaces 200mL of water in the pool. Use this information to select a correct conclusion.
(a) The toy weighs 200 grams. (b) The toy absorbed 200 mL of water. (c) The toy has a surface area of 200 cm². (d) The toy has a volume of 200 cm³.
The toy has a volume of 200 cm³. The correct answer is Option d.
This is because when an object is submerged in water, it displaces an amount of water equal to its volume. In this case, the pool toy displaces 200 mL of water, which means it has a volume of 200 cm³ (since 1 mL is equal to 1 cm³). The correct answer is Option d.
It is not correct to say that the toy weighs 200 grams (option a), as the weight of the toy is not related to the amount of water it displaces. Similarly, it is not correct to say that the toy absorbed 200 mL of water (option b), as the toy is simply displacing the water, not absorbing it.
Finally, it is correct to say that the toy has a surface area of 200 cm² (option c), as the amount of water displaced is related to the toy's volume, not its surface area.
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Someone help me please, I am struggling with this
Answer:
79° , 65° , 144°
Step-by-step explanation:
65° , x° and 36° lie on a straight line and sum to 180° , that is
65° + x° + 36° = 180°
101° + x° = 180 ( subtract 101° from both sides )
x= 79°
y + 10 and 65° are alternate angles and are congruent , then
y + 10 = 65°
z and 36° are same- side interior angles and sum to 180° , that is
z + 36° = 180° ( subtract 36° from both sides )
z = 144°
Suppose a city with population 500,000 has been growing at a rate of 2% per year. If this rate continues, find the population of this city in 25 years
[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &500000\\ r=rate\to 2\%\to \frac{2}{100}\dotfill &0.02\\ t=\textit{elapsed time}\dotfill &25\\ \end{cases} \\\\\\ A = 500000(1 + 0.02)^{25} \implies A=500000(1.02)^{25}\implies A \approx 820303[/tex]
Find the inverse of the following matrix,
if it exists.
[ -1 0 1]
A = [ 2 2 0]
[ 1 0 1]
Inverse of the given matrix is
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
the matrix in question is
−1 0 1
2 2 0
1 0 1
now, we are given that inverse of the matrix exists.
A⁻¹ = adjoint of A/|A|
The determinant of the matrix A is:
det(A) = (-1) [(2)(1) - (0)(0)] - 0 [(2)(1)-(0)(1)] + 1 [(2)(0) - (2)(1)] = -4
The adjoint of the matrix A is:
2 2 −2
0 −2 −2
−2 −2 −2
Therefore, the inverse of the matrix A is:
A⁻¹ = 1/(-4) [2 2 −2]
[0 −2 −2]
[−2 −2 −2]
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
So, the inverse of the matrix A is:
A⁻¹ = [0.5 0.5 -0.5]
[ 0 -0.5 -0.5]
[-0.5 -0.5 -0.5]
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12 cm
12 cm
Work out the area of the
yellow part of the pattern
This is a pattern that is
being used to make a
patch quilt. Each pattern is
a square, measuring 12cm
by 12cm square. These are
the measurements of each
trapezium
3 cm
3 cm
9 cm
The area of the yellow part of the pattern is found as: 72 cm²
Explain about the square shape?It has four vertices and four sides. Its sides all equal in length. Since all interior angles being equal as well as right angles, they are all 90° in length. 360° is the total of all interior angles.In geometry, a square is a flat shape with 4 separate sides plus four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle .The dimension of the square: 12 x 12
Area of yellow part = Area of triangle with base height equals side of square.
Then,
Area of yellow part = 1/2 * B * H
Area of yellow part = 1/2 *12 *12
Area of yellow part = 72 cm²
Thus, the area of the yellow part of the pattern is found as: 72 cm².
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The correct question is-
Work out the area of the yellow part of the pattern. This is a pattern that is being used to make a patch quilt. The pattern is a square, measuring 12cm
by 12cm square.
Audrey’s university English teacher Mr. Dalton has told her she will have 28 assignments this semester. Audrey has discovered that she needs to spend 2.5 hours on each assignment.
How many hours will Audrey spend on her English assignments?
AND
How many days will it take Audrey to complete her assignments?
I need explanation please!
70 hours will Audrey spend on her English assignments.
2.9 days will it take Audrey to complete her assignments.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Mr. Dalton has told her she will have 28 assignments this semester.
She needs to spend 2.5 hours on each assignment.
So, she will spend on Assignments
= 28 x 2.5
= 70 hours
Now, In one day = 24 hours
So, to complete the assignments it will take
= 70/ 24
= 2.9 days
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write the equation for the sequence below
Answer: x = p/2
Step-by-step explanation:
x = next one
p = previous
in order to solve the next one, you would do :
x (the one you are trying to solve) = p (the previous one : 1/8) divided by 2
x = p/2
A university law school accepts 4 out of every 11 applicants. If the school accepted 360 students, find how many applications they received.
Answer:
990 applicants
Step-by-step explanation:
We know
A university law school accepts 4 out of every 11 applicants.
If the school accepted 360 students, find how many applications they received.
To get from 4 to 360, we time 90
We take 11 times 90 = 990 applicants
So, they received 990 applicants.
Find out how long it takes a $2500 investment to earn $400 interest if it is invested at 8% compounded quarterly. Round to the nearest tenth of a year
It will take approximately 2.9 years (or 2 years and 11 months) for the $2500 investment to earn $400 interest at a rate of 8% compounded quarterly.
A = [tex]P(1 + r/n)^{nt}[/tex]
Where:
A = the total amount that includes principal and interest, P = the principal that is the initial amount invested, r = the annual interest rate, n = the number of times is the interest is compounded per year, and t = the time
$2900 = [tex]$2500(1 + 0.08/4)^{4t}[/tex]
Simplifying this equation, we get:
1.16 = (1 + 0.02
By calculating the natural logarithm of both sides, we arrive at:
ln(1.16) = 4t ln(1.02)
t ≈ 2.9 years
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help me please, I been trying to get help for hours now.
We can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.What is exponential function?The exponential function is of the form -
f(x) = eˣ
Given is to write the exponential growth and exponential decay equation.
{ 1 } -
The general exponential growth equation is -
[tex]$f(x)=a(1+r)^{x}[/tex]
{ 2 } -
The general exponential decay equation is -
[tex]$\frac {dN}{dt}= -\lambda N[/tex]
Option {A} and option {E} represent the exponential decay. Option {B}, {E} and {D} represent exponential growth.
Therefore, we can conclude that -
General exponential growth equation is : [tex]$f(x)=a(1+r)^{x}[/tex]General exponential decay equation is : [tex]$\frac {dN}{dt}= -\lambda N[/tex]Option {A} and option {E} represent the exponential decay.Option {B}, {E} and {D} represent exponential growth.To solve more questions on functions, visit the link-
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darr Question Details 9. Divide using synthetic division. (x^(3)-2x^(2)+10)-:(x-2)
The answer is: x^(2) + 20/(x-2)
Synthetic division is a method of dividing a polynomial by a linear factor. It is a shorthand version of long division that is quicker and easier to do.
Here are the steps to solve this problem using synthetic division:
1. Write the coefficients of the dividend in a row: 1 -2 0 10
2. Write the constant term of the divisor to the left of the row: 2 | 1 -2 0 10
3. Bring down the first coefficient: 2 | 1 -2 0 10
|_______
1
4. Multiply the first coefficient by the divisor and write the result under the second coefficient: 2 | 1 -2 0 10
|___2___
1 0
5. Add the second coefficient and the result: 2 | 1 -2 0 10
|___2___
1 0
6. Repeat the process with the remaining coefficients: 2 | 1 -2 0 10
|___2__0_20
1 0 0 20
7. The final row of numbers represents the coefficients of the quotient and the remainder: (x^(2) + 0x + 0) + 20/(x-2)
So, the answer is: x^(2) + 20/(x-2)
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