the unit rate for composing a song will be 3 weeks per song.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, Wayne plays multiple instruments in a rock band. He also composes the songs. He takes 36 weeks to write the songs for an album of 12 songs.
He took 36 weeks to compose 12 songs.
Since,
Unit rate: Divide total weeks by total songs.
Thus,
Unit Rate = 36 / 12 = 3 weeks per song.
Therefore, the unit rate for composing a song will be 3 weeks per song.
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the total cost for baydan and three of her friends to go ice skating can be represented by the expression 4x 36. the four friends pay an amount x to rent the ice skates and an admission fee. how much is the admission fee for one person?
The admission fee for one person is 9.
The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).
Intercept Form of Equation of a Line: x/a + y/b = 1.
Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.
Total cost = 4x +36
It means we have a linear function where 4 is the slope ( the cost per person) and 36( the y-intercept).
The admission fee for four people= 36
So, the admission fee for one person = 36/4 = 9
Thus, the admission fee for one person is 9.
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The admission fee for one person is 9.
The intercept form of the equation of a line has an equation x/a + y/b = 1, where 'a' is the x-intercept, and 'b' is the y-intercept. The x-intercept is the shortest distance of the point on the x-axis from the origin, where the line cuts the x-axis, and the y-intercept is the shortest distance of the point on the y-axis from the origin, where the line cuts the y-axis. Also considering the points, the line cuts the x-axis at the point(a, 0), and it cuts the y-axis at the point(0, b).
Intercept Form of Equation of a Line: x/a + y/b = 1.
Here x, y, are the variables in the equation, a, b, are the x-intercept, and the y-intercept in the equation. This equation has a slope of -b/a.
Total cost = 4x +36
It means we have a linear function where 4 is the slope ( the cost per person) and 36( the y-intercept).
The admission fee for four people= 36
So, the admission fee for one person = 36/4 = 9
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Can anyone help me solve this?
The equation has been verified and the solution has been obtained by using trigonometric identities.
What are trigonometric identities?
Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.
We are given cotθ/1-tanθ + tanθ/1-cotθ = 1 + tanθ + cotθ
Solving the LHS, we get
⇒ [(cosθ/sinθ)/1-(sinθ/cosθ)] + [(sinθ/cosθ)/1-(cosθ/sinθ)]
⇒ [(cosθ/sinθ)/[(cosθ-sinθ)/cosθ]] + [(sinθ/cosθ)/[(sinθ-cosθ)/sinθ)]]
⇒ [cos²θ/(cosθ-sinθ)sinθ] + [sin²θ/(sinθ-cosθ)cosθ]
⇒-[cos²θ/(sinθ-cosθ)sinθ] + [sin²θ/(sinθ-cosθ)cosθ]
⇒[sin²θ/(sinθ-cosθ)cosθ] - [cos²θ/(sinθ-cosθ)sinθ]
⇒(sin³θ - cos³θ)/(sinθ-cosθ)sinθcosθ
⇒(sinθ - cosθ)(sin²θ + sinθcosθ + cos²θ)/(sinθ-cosθ)sinθcosθ
⇒(sin²θ + sinθcosθ + cos²θ)/sinθcosθ
⇒sin²θ/sinθcosθ + sinθcosθ/sinθcosθ + cos²θ/sinθcosθ
⇒tanθ + 1 + cotθ
⇒1 + tanθ + cotθ = RHS
Hence, the expression is verified.
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hector is using a compass and straightedge to construct the bisector of angle ceb.where did he position the fixed point of the compass when he created the two intersecting arcs on the interior of angle bec?
The two intersecting arcs were made by placing the compass' fixed point at points C and E,
Hector would perform the following actions with a compass and straightedge to create the bisector of angle CEB:
Set the compass's point at point C and set the width such that it is only little longer than the line segment CE's length.Create an arc that touches line segment CE twice, at what we'll name A and B.Adjust the width to match the width used in step 1 and move the compass to point E.Create a second arc that touches line segment CE twice, at what we'll name D and F.Points A and D are connected using the straightedge.The two intersecting arcs were made by placing the compass' fixed point at points C and E, respectively.
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What is 50%
percent of 950
Answer:
475
Step-by-step explanation:
475
(50%)%×950= 475.
have a nice day
consider the function g(x) = x^4 + 3x^3 - 19x^2 -27x + k
what is the value of j that makes (x-2) a factor of g(x)? justify your answer.
if (x-2) is a factor of g(x) and -5 is a zero of the function, what are the three other factor of g(x)? justify your answer
The value of k is 90.
The other factor of g(x) is, (x + 5)(x - 3)(x + 3)
What are polynomials?Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.
Given the function,
g(x) = x⁴ + 3x³ - 19x² - 27x + k
and (x - 2) a factor of g(x)
so g(2) = 0
g(x) = x⁴ + 3x³ - 19x² - 27x + k
g(2) = 2⁴ + 3(2)³ - 19(2)² - 27(2) + k
2⁴ + 3(2)³ - 19(2)² - 27(2) + k = 0
16 + 24 - 76 - 54 + k = 0
k = 90
the function is g(x) = x⁴ + 3x³ - 19x² - 27x + 90
B: -5 is a zero of the function,
f(-5) = 0, or x = -5
so factor is (x + 5)
the two factors are (x + 5)(x - 2)
(x + 5)(x - 2) = x² + 5x - 2x -10
(x + 5)(x - 2) = x² + 3x - 10
to find the other two factors we need to divide the function by
x² + 3x - 10
=> (x⁴ + 3x³ - 19x² - 27x + 90) ÷ (x² + 3x - 10)
quotient after division is
x² - 9 = (x - 3)(x + 3)
The factors of the function are (x - 2)(x + 5)(x - 3)(x + 3)
Hence k = 90, and
the three other factors of g(x) are (x + 5)(x - 3)(x + 3)
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n a party, 5 male-female couples attend. the males and females are randomly paired for a dance. what is the probability that exactly two couples are dancing together?
The probability that exactly two couples are dancing together in a party of 5 male-female couples is 1/126, which is a very low probability.
The problem of finding the probability that exactly two couples are dancing together can be solved using the combination formula. The number of ways to choose two couples from the five available couples is given by the binomial coefficient "C(5,2) = 10". The number of ways to arrange the chosen two couples is given by 2! (two factorial), since the order of the couples doesn't matter. The total number of ways to randomly pair the males and females is given by 10!. To find the number of ways in which exactly two couples are dancing together, we need to find the number of arrangements where two couples are dancing together and the remaining three couples are not dancing together.
Therefore, the probability that exactly two couples are dancing together is given by:
(C(5,2) * 2!) / 10! = 1/126
This shows that it is unlikely that exactly two couples will be dancing together in a random pairing of the males and females.
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Last year, 80 students were in after-school activities. This year, 160 students participated in after-school activities.
What is the percent of change from last year to this year?
Answer:200%
Step-by-step explanation: A different way of saying that a number has doubled is by saying it has increased by 200%.
Complete the statement regarding types of economies in a blank system , supply and demand forces affect the production and consumption decisions. There is little to no blank control in such a system
The statement is referring to a market economy, where supply and demand forces affect the production and consumption decisions and there is little to no government control in such a system.
In a market economy, individuals and businesses make the decisions regarding production and consumption, and prices are determined by the interaction of supply and demand. The market is seen as the most efficient allocation mechanism, as prices communicate information about relative scarcities and help to direct resources to their most valuable uses. However, market economies may result in income inequality and market failures, where the market fails to allocate resources efficiently. Government intervention in a market economy is limited to correcting market failures and ensuring a level playing field.
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Three different linear functions are represented in the table. Which is the correct order of the functions from least to greatest steepness with respect to rate of change?.
A linear function is used to depict a relationship between two variables where one variable influences the other.
What is meant by linear functions?Those with a straight-line graph are considered to be linear functions. This is the format of a linear function. y = f(x) = a+bx. The only independent and only dependent variables in a linear function are both independent.
In a relationship between two variables, where one variable affects the other, a linear function is used to represent the relationship. Generally speaking, x and y are the independent and dependent variables, respectively, in a linear function (x influences y).
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
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A parabola has a vertex at (0, -1) and passes
through the point (2, 2). Which of the following is
the equation of
this parabola in the form y = a(x-h)² +k?
A. y=(x-1)²-3
B.y=3/4 (x-1)²-3
C. y=3/4 x²-1
D. y=x²+1
the equation of the parabola will be y=3/4 (x²-1).
What is parabola ?
A parabola is a curve whose equation places a point on it at a same distance from both a fixed point and a fixed line. The parabola's fixed point is referred to as the focus, and its fixed line is referred to as the directrix. The fixed point does not lie on the fixed line, which is another crucial factor to remember. A parabola is a locus of any point that is equally distant from both the focus and directrix of two supplied points. The point where a parabola makes its sharpest turn is known as the vertex. If a parabolic function has the shape of a "," it has a maximum value; otherwise, it has a minimum value.
A parabola has a vertex at (0, -1)
passes through point (2, 2). Which of the following is the equation of
this parabola in the form y = a(x-h)² +k.
The equation will be (2,2)
x=2, y=2
2=a(2²)-1
2=a(4)-1
3=a(4)
a = 3/4
the equation is
y=3/4 (x²-1)
Hence the equation of the parabola will be y=3/4 (x²-1).
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the diagram to the right illustrates a hypothetical demand curve representing the relationship between price (in dollars per unit) and quantity (in 1,000s of units per unit of time).
The demand curve graph demonstrates that when prices rise, fewer goods are demanded overall.
The link between price and quantity desired is graphically depicted by the demand curve. It demonstrates how a change in pricing affects how much of an item or service is wanted. The quantity demanded reduces when a good or service's price rises, and vice versa. The quantity demanded falls as the price rises because the demand curve is typically downward sloping. This is due to the fact that when prices are reduced, consumers are more likely to buy products and services. As the price rises, the amount demanded declines, as shown by the hypothetical demand curve that fits this pattern in the diagram to the right. This is a typical pattern observed in the actual world, which is used to guide business and economic decision-making regarding price and output.
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In testing the equality of population proportions using chi-square, how many categories or populations do you need to be able to perform this analysis? at least 2 at least 4 greater than 3 at least 3
In testing the equality of population proportions using chi-square, at least 3 categories or populations need to be able to perform this analysis
Now, According to the question:
A chi-square test for equality of two proportions is exactly the same thing as a z-test. The chi-squared distribution with one degree of freedom is just that of a normal deviate, squared. You're basically just repeating the chi-squared test on a subset of the contingency table.
The chi-square test is used to compare more than two independent populations. The test is pretty similar to that of two population proportions except for the fact that the contingency table involved in the study includes 2 rows and c number of columns indicating the number of populations.
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Can anyone help on this?
Answer:
AG=38.84
Step-by-step explanation:
Follow the steps in the image
-Hope this helped
Step-by-step explanation:
I just answered this. how often did you post it ?
the "incenter" means that this is the center point of the inscribed circle that is completely inside the triangle and touches every side in exactly one point.
therefore, all right-angled connections from that point to a side are equally long (the radius is the inscribed circle).
therefore,
GB = GF = GD
we know GF = 22
so, GB = 22
and now we use Pythagoras to find AG in the right-angled triangle ABG :
AG² = AB² + GB² = 32² + 22² = 1024 + 484 = 1508
AG = sqrt(1508) = 38.83297568...
if you round to hundredths : 38.83
City A had a population of 175,000 residents in 2018. The population is
increasing at a rate of 10% per year.
City B has a population that can be modeled
B (t) = 350,000 (0. 97)' where t represents the number of years since
2018.
What is the initial population of city A ?
The initial population of city A is 175,000 while its growth rate is 10%. The function that models the population of city B is B(t) = 350,000(0.97)^t, which is a case of exponential decay.
How to find the initial population?Here since nothing else is mentioned we will assume the Initial population of city A to be that of 2018, which is 175,000.
The growth rate of any city will be the percentage increase in its population every year. Here it is mentioned that the population of city A increases by 10% every year. Hence, the growth rate of city A is 10%.
Here we are already given that the function of the population of city B in a year is B(t) = 350,000(0.97)^t.
In model B(t) with every successive increase in time, the value of (0,97)^t will keep on reducing. Due to this, the product of 350,000(0.97)^t will reduce. Hence this is a case of exponential decay.
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Find a domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) uch that thi tatement i true
So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.
The quantifier ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is a statement in first-order logic that says "there exists x and there exists y such that x is not equal to y and for all z, z is equal to x or z is equal to y".
The domain for this quantifier is the set of all values for which the statement inside the quantifier is true.
In this case, the domain for the quantifier is the set of all non-empty sets, since for any non-empty set, we can find at least two distinct elements x and y, such that x is not equal to y and for any element z in the set, either z is equal to x or z is equal to y.
So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.
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So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.
The quantifier ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is a statement in first-order logic that says "there exists x and there exists y such that x is not equal to y and for all z, z is equal to x or z is equal to y".
The domain for this quantifier is the set of all values for which the statement inside the quantifier is true.
In this case, the domain for the quantifier is the set of all non-empty sets, since for any non-empty set, we can find at least two distinct elements x and y, such that x is not equal to y and for any element z in the set, either z is equal to x or z is equal to y.
So, the domain for the quantifier in ∃x∃y(x ≠ y ∧ ∀z((z = x) ∨ (z = y))) is the set of all non-empty sets.
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1. Select the three statements that represent a unit rate.
a. Carrots cost $2 per pound
b. Sylvia buys 5 shirts for $75
C. It takes Juan 3 hours to drive 165 miles
d. A recipe calls for 2 cups of sugar for every gallon of water.
e. A teacher divides her class so there are 11 students per group.
!I will mark Brainliest please help!
The three statements that represent a unit rate are:
a. Carrots cost $2 per pound
d. A recipe calls for 2 cups of sugar for every gallon of water.
e. A teacher divides her class so there are 11 students per group.
Overall Value FormulaThe formula for calculating the overall score is:
overall value = number of units x value per unit.
For example, Budi buys a dozen pencils. The price of one pencil is IDR 2000. What is the total value or purchase price to be paid by Budi?
One dozen equals 12 pieces.
So, the purchase price = 12 x 2000 = 24,000
So, the total purchase price is IDR 24,000.
"The overall value is obtained from the product of the number of units with the value per unit."
Unit Rate FormulaThe formula for calculating the unit rate is:
value per unit = total value : number of units.
For example, Aan bought ten candies for Rp. 2,500. How much does one candy cost?
To calculate it, we must use the value per unit formula.
The price of one candy = 2,500 : 10 = 250.
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What is 3 2/6 + 9 4/10 in lowest terms
The simplest form of the sum of the mixed fraction [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex] is [tex]12\frac{11}{15}[/tex]
What are mixed fractions?A fraction represented with its quotient and remainder is a mixed fraction.
Given is a sum of two mixed fractions, [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex]
Converting into the simplest forms,
[tex]3\frac{2}{6} + 9\frac{4}{10}\\\\= \frac{20}{6} + \frac{94}{10} \\\\= \frac{10}{3} + \frac{47}{5} \\\\= \frac{50+141}{15} \\\\= \frac{191}{15} \\\\= 12\frac{11}{15}[/tex]
Hence, the simplest form of the sum of the mixed fraction [tex]3\frac{2}{6} + 9\frac{4}{10}[/tex] is [tex]12\frac{11}{15}[/tex]
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Can someone help me out thanks
Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it so The value of x is 77.
What is the outside angle ?Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it. The sum of the two internal opposed angles determines the size of an outside angle.
The total of the inner angles is 180 degrees, or 180. (43-34). The outer angles measure 43 , 34, and 120 degrees, respectively, because they are an addition to the inside angles. The outer angles add up to a total of 360 degrees.
Calculate the outside angle's dimensions.
< u = 43 + 34 - 180 = 103.
so
The value of x = 180 - 103 = 77.
Exterior angles are those that run parallel to a polygon's inner angles but are located outside of it so The value of x is 77.
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By reading values from the given graph of f, use five rectangles to L a lower estimate and an upper estimate for the area under the given graph of f from x = 0 to x = 10. In each case sketch the rectangles that you use. Find new estimates using ten rectangles in each case.
By reading values from the given graph of f, use five rectangles to L a lower estimate and an upper the area under the given graph of f from x = 0 to x = 10 are as follows :
Using the five rectangle method , for upper limit choose the area of vertically longer rectangle in each case and vice versa for lower limit.
Upper limit = 5x2+4x2+2x2+1x2+1x2 = 26
Lower limit = 3x2+1x2+0x2+0x2+0x2 = 8
(b) Use the same approach as in the case above, the new estimates using ten rectangles in each case.
Upper limit = 5x1+4x1+4x1+3x1+2x1+2x1+1x1+1x1+1x1+1x1 = 24
Lower limit = 4x1+3x1+2x1+1x1+1x1+0x1+0x1+0x1+0x1+0x1 = 11
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Ellie has $50 in a savings account that earns 5% annually. The interest is not compounded. How much interest will she earn in 6 years?
The amount of interest earned in 6 years will be $15.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific amount of time.
Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to calculate interest, the principal amount in simple interest remains constant.
Given that Ellie has $50 in a savings account that earns 5% annually. The simple interest is calculated as:-
Simple interest = ( P x R x T ) / 100
Simple interest = ( 50 x 5 x 6 ) / 100
Simple interest = $15
Hence, the value of the simple interest after 15 years will be $15.
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plis help
Is (1, 10) a solution to this system of equations?
y = 9x + 1
y = x + 8
yes or no?
The solution to the system of equations is x = 7/8 and y = 71/8
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equations be represented as A and B
Now , substituting the values in the equation , we get
y = 9x + 1 be equation (1)
y = x + 8 be equation (2)
On simplifying the equations , we get
x + 8 = 9x + 1
Subtracting x on both sides of the equation , we get
8x + 1 = 8
Subtracting 1 on both sides of the equation , we get
8x = 7
Divide by 8 on both sides of the equation , we get
x = 7/8
Substitute the value of x in the equation (2) , we get
y = 7/8 + 8
y = 71/8
Hence , the equations are solved and the solution is ( 7/8 , 71/8 )
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6 ft
5. The figure shows a container, in the shape of
a trapezoidal prism, that Pete filled with sand.
12 cm
5cm
7 cm
10 cm
The volume of the trapezoidal prism can be calculated using the formula V = (1/2)(h)(b1 + b2)h, where h is the height, b1 is the length of the top base, and b2 is the length of the bottom base.
In this case, the height is 7 cm, the length of the top base is 10 cm, and the length of the bottom base is 12 cm. Therefore, the volume of the trapezoidal prism is V = (1/2)(7)(10 + 12)7 = 630 cm3.
In addition to calculating the volume of a trapezoidal prism, you can also calculate the surface area of a trapezoidal prism using the formula A = 2h(b1 + b2) + 2(l1 + l2), where h is the height, b1 and b2 are the lengths of the top and bottom bases, and l1 and l2 are the lengths of the lateral faces. The surface area of a trapezoidal prism is the total area of all of the faces of the prism.
Additionally, the lateral surface area of a trapezoidal prism can be calculated by using the formula A = 2h(b1 + b2), where h is the height, b1 and b2 are the lengths of the top and bottom bases. The lateral surface area of a trapezoidal prism is the total area of all of the lateral faces of the prism.
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Review the equation used in writing a partial fraction decomposition. Startfraction negative 15 x + 10 over (5 x minus 2) squared endfraction = startfraction a over 5 x minus 2 endfraction + startfraction b over (5 x minus 2) squared endfraction which system of equations can be used to determine the values of a and b?.
The equation used in writing a partial fraction decomposition is given as:
Negative 15 x + 10 / (5 x - 2) = a / (5 x - 2) + b / (5 x - 2).
To determine the values of a and b, we can use a system of equations. This system of equations consists of two equations, one for a and one for b. The equation for a is: Negative 15 x + 10 = a * (5 x - 2). The equation for b is: 0 = b * (5 x - 2). We can solve these equations simultaneously to get the values of a and b.
For example, if x = 1, then the equation for a becomes: Negative 15 + 10 = a * (5 - 2), which simplifies to -5 = a * 9. Therefore, a = -5/9. The equation for b becomes: 0 = b * (5 - 2), which simplifies to 0 = b * 3. Therefore, b = 0.
In summary, the system of equations used to determine the values of a and b is:
Negative 15 x + 10 = a * (5 x - 2) and 0 = b * (5 x - 2). By solving these equations simultaneously, we can get the values of a and b.
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Answer:
B!!!
Right on Edge
Step-by-step explanation:
right ascension 15 06 53.62 declination 62 20 10.0
Right ascension (RA) and declination (Dec) are coordinates used in astronomy to precisely describe the location of an object in the sky is total of 62.3358° for the Dec.
RA is measured eastward along the celestial equator from the vernal equinox, which is the point in the sky where the Sun crosses the celestial equator from south to north at the beginning of spring. Dec measures the angle of an object above or below the celestial equator.
In this example, the right ascension is 15 06 53.62 and the declination is 62 20 10.0. This is expressed in terms of hours, minutes, seconds for the RA and degrees, minutes, seconds for the Dec. The RA can be converted to a decimal value by taking the 15 hours and multiplying it by 15 (1 hour = 15°) to get 225°. Then add 6 minutes (6/60 of an hour) which is equal to 10°, and add 53.62 seconds (53.62/3600 of an hour) which is equal to 0.1489°. This gives us a total of 225.1489° for the RA. For the Dec, we take the 62° and add 20 minutes (20/60 of a degree) which is equal to 0.333°, and add 10 seconds (10/3600 of a degree) which is equal to 0.0028°. This gives us a total of 62.3358° for the Dec.
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Please help I really do need it
Julian made an apple pie in a pie tin with a diameter of 6 inches. What is the pie tin's radius?
Tyler filled up his bathtub, took a bath, and then drained the tub. The function gives the depth of the water, in inches, minutes after Tyler began to fill the bathtub.
B(0) = 0 Inches of depth are present 0 minutes after filling started, or at time = 0; depth = 0.
B(1) denotes the function one minute into the filling process.
B(9) = 11 shows that 11 inches of water are present in the container 9 minutes after the filling started.
7 minutes after the filling process began, the feature displays the water depth in inches.
A.) B(0)=0
B(0) = 0 indicates that the depth in inches at time = 0 and depth = 0 is 0 minutes after filling started.
B.) B(1) (1) B(1) denotes the function one minute into the filling process.
C.B(9)=11
B(9) = 11 shows that 11 inches of water are present in the container 9 minutes after the filling started.
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How many ounces per pound ?
16 ounces is equivalent to 1 pound. In other words, 16 ounces per pound.
What is one pound?
A weight measurement unit: The weight of one pound is roughly equal to 454 grams. A kilogram is equivalent to about 2.2 pounds. One pound contains 16 ounces.
One pound is equal to 0.4535 kilograms and is referred to as an imperial unit of mass or weight measurement.
16 ounces = 1 pound
1 pound (lb) equals 16 ounces (oz)
Pounds To Ounces Conversion Table
1 pound = 16 ounces
2 pounds = 32 ounces
3 pounds = 48 ounces
5 pounds = 80 ounces
6 pounds = 96 ounces
7 pounds = 112 ounces
8 pounds = 128 ounces
9 pounds = 144 ounces
10 pounds = 160 ounces
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Joe is creating shirts for his ultimate frisbee team. The total cost to produce x shirts can be represented by f ( x ) = 3 x 2 + 2 . Find the average rate of change of the total cost as his shirt production increases from 10 to 20.
the average rate of change of the total cost as the shirt production increases from 10 to 20 is 90.
What is the average rate of change from 10 to 20?Given the function in the question;
f(x) = 3x² + 2
And production increases from 10 to 20.
To find the average rate of change, we use the expression;
[ f(20) - f(10) ] / [ 20 - 10 ]
Now, if f(x) = 3x² + 2
f(20) = 3( 20 )² + 2 = 1202
f(10) = 3( 10 )² + 2 = 302
Plug in the values and simplify
[ f(20) - f(10) ] / [ 20 - 10 ]
[ 1202 - 302 ] / [ 20 - 10 ]
[ 900 ] / [ 10 ]
900/10
90
Therefore, the average rate of change is 90.
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Running bear left the village and traveled 30 miles on a heading of 30° from this point he went 50 miles on a heading of 220° how far did he end up from the village
Running Bear ended up 29.204 miles from the village.
Running Bear left the village and traveled 30 miles in a direction of 30°. Then he went 50 miles in a direction of 220°. To find out how far he ended up from the village, we need to add up the distances he traveled in both directions.
Think of it like putting two arrows end to end on a piece of paper. The first arrow represents the 30 miles he traveled at 30°, and the second arrow represents the 50 miles he traveled at 220°. The total distance from the village to the final point is equal to the length of the combined arrow.
We can represent the two displacements as vectors in a rectangular coordinate system, with the x-axis as the East-West direction and the y-axis as the North-South direction.
The first displacement, 30 miles at 30°, can be written as a vector in the x and y directions using trigonometry:
x1 = 30 cos 30° = 15
y1 = 30 sin 30° = 15
The second displacement, 50 miles at 220°, can be written as a vector in the x and y directions using trigonometry:
x2 = 50 cos 220° = -25
y2 = 50 sin 220° = -43.301
The total displacement from the village to the final point is found by adding the components of the two vectors:
x = x1 + x2 = 15 - 25 = -10
y = y1 + y2 = 15 - 43.301 = -28.301
Finally, we can use the Pythagorean theorem to find the magnitude (distance) of the total displacement:
d = √(-10)^2 + (-28.301)^2 = √851.121 = 29.204 miles
So, Running Bear ended up 29.204 miles from the village.
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