Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.
Alonso has $21.00 to spend on eggs and avocados. He buys eggs that cost $2.50, which leaves him with $18.50. Since the store only sells avocados in bags of 3, he will need to find the cost per bag in order to calculate how many bags he can buy.
First, divide the cost of 3 avocados by 3 to find the cost per avocado. $5.00 ÷ 3 = $1.67 per avocado.
Next, divide the money Alonso has left by the cost per avocado to find how many avocados he can buy.
$18.50 ÷ $1.67 per avocado = 11.08 avocados.
Since avocados only come in bags of 3, Alonso needs to round down to the nearest whole bag. He can buy 11 avocados, which is 3.67 bags.
Thus, he will buy 3 bags of avocados.Let's test our answer to make sure that Alonso has spent all his money:
$2.50 for eggs3 bags of avocados for $5.00 per bag, which is 9 bags of avocados altogether. 9 bags × $5.00 per bag = $45.00 spent on avocados.
Total spent:
$2.50 + $45.00 = $47.50
Total money had:
$21.00
Remaining money:
$0.00
Since Alonso spent all of his money, this confirms that he can buy 3 bags of avocados.
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I need help please!!
Answer:
25,
-7
Step-by-step explanation:
r ° q= r(q(x))= (-x+2) ^2
So, using perfect square trinomial,
[tex](-x+2)^{2} =x^{2} -4x+4[/tex]
Thus q(-3)=25
q(r(x))= (-x^2)+2=-7
pls help i have finals tomorrow and i want to know how to answer this question
The values in the expression is as follows:
a = 2
b = 0
c = -1
How to solve an expression?The expression can be solve using the exponential law. Therefore,
g = 2³ × 3 × 7²
h = 2 × 3 × 7³
Therefore, let's solve the following:
g/h = 2ᵃ × 3ᵇ × 7ⁿ
Therefore,
g = 2³ × 3 × 7² = 2 × 2 × 2 × 3 × 7 × 7
h = 2 × 3 × 7 × 7 × 7
Hence,
g / h = 2 × 2 × 2 × 3 × 7 × 7 / 2 × 3 × 7 × 7 × 7
Hence,
g / h = 2 × 2 / 7
g . h = 2² × 3° × 7⁻¹
Hence,
a = 2
b = 0
c = -1
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Yuri’s sister Karina is 12 years old. In the equation below, y represents Yuri’s age in years.
12 = 3 y minus 2
Which statement accurately relates their ages?
Yuri is 3 years younger than twice Karina’s age.
Yuri is 2 years younger than triple Karina’s age
Karina is 3 years younger than twice Yuri’s age.
Karina is 2 years younger than triple Yuri’s age.
Yuri is 2 years younger than triple Karina’s age
Answer:
yo
Step-by-step explanation:
i think its d
A piece of wood is in the shape of a rectangular prism with a length of 10 inches, a width of 4 inches, and a height of 5 inches. You cut the wood in half to form two pieces of wood, each with a length of 5 inches. What is the percent increase in the total surface area? Round your answer to the nearest hundredth, if necessary. %
Answer: 18.18%
Step-by-step explanation:
First, let's calculate the surface area of the original piece of wood. The surface area (SA) of a rectangular prism is given by the formula:
[tex]$$SA = 2lw + 2lh + 2wh$$[/tex]
where [tex]\(l\)[/tex] is the length, [tex]\(l\)[/tex] is the width, and [tex]\(h\)[/tex] is the height. For the original piece of wood, [tex]\(l = 10\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex].
After the piece of wood is cut in half, the length becomes 5 inches, but the width and height remain the same. So, for each of the two new pieces of wood, [tex]\(l = 5\) inches[/tex], [tex]\(w = 4\) inches[/tex], and [tex]\(h = 5\) inches[/tex]. The total surface area of the two new pieces of wood is twice the surface area of one of the new pieces.
The percent increase in the total surface area is given by the formula:
[tex]$$\text{Percent Increase} = \frac{\text{New Total SA} - \text{Original SA}}{\text{Original SA}} \times 100\%$$[/tex]
Let's calculate these values.
The percent increase in the total surface area when the piece of wood is cut in half is approximately 18.18%.
Find the area of the triangle below be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
it is my first time taking my baby to the cinemas in Junes 2023, and the cinemas have sales because there are tons of kids' movies to be seen. For adults the ticket costs 70$ and for children it costs 30$, which tickets sell like 1000$ a day leading to 31000 a month. Calculate the number of tickets that were sold for adults and children in a day. A+C=1000 70+30=31000.
A+C=1000
70+30=31000
if we wanted to extend this discussion beypnd what has been shared so far, what additional question could we ask?
Step-by-step explanation:
If we wanted to extend the discussion beyond what has been shared so far, an additional question we could ask is:
"What is the ratio of adult tickets to children's tickets sold in a day?"
This question would provide insight into the distribution of ticket sales between adults and children and help us understand the demand for different movie genres or screenings among the audience.
Cecilia se compra un libro con la cuarta parte de su dinero y un cómic con la mitad del dinero que le quedaba. Al salir de la librería se da cuenta que le sobraron $8. ¿Cuál es la ecuación para conocer la cantidad de dinero que tenía en un inicio?
The equation to determine the initial amount of money Cecilia had is x = 0.
Let's denote the initial amount of money Cecilia had as "x" dollars.
According to the given information, Cecilia spent one-fourth (1/4) of her money on a book, which is (1/4)x dollars. After buying the book, she had (x - (1/4)x) dollars left.
Next, Cecilia spent half (1/2) of the remaining money on a comic, which is ((1/2)x - 8) dollars. After buying the comic, she had ((x - (1/4)x) - ((1/2)x - 8)) dollars remaining.
Since she had $8 left, we can set up the equation:
((x - (1/4)x) - ((1/2)x - 8)) = 8
To simplify the equation, we can first combine like terms:
(x - (1/4)x - (1/2)x + 8) = 8
Now, let's solve the equation step by step:
(x - (1/4)x - (1/2)x + 8) = 8
Multiplying the fractions by their common denominator, which is 4, we get:
(4x - x - 2x + 32) = 32
Simplifying further:
(x + 32) = 32
Subtracting 32 from both sides:
x = 0
Therefore, the equation to determine the initial amount of money Cecilia had is x = 0.
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NEED HELP ASAP
Y
B
^^
CX
A
Previous Activity
N
Which would prove that AABC~ AXYZ? Select two
options.
OBA-BC-A
=
YX
YZ XZ
OBA = BC₁
YX
YZ
O
AC
XZ
=
=
BA
XX.
YX
AC
BC
BA = AE = 8C
YX
YZ
XZ
OBC=BA ₁ <=
XY
ZX
Next Activity
The two options that would prove that ΔABC ~ ΔXYZ include the following:
A. BA/YX = BC/YZ = AC/XZ
C. AC/XZ = BA/YX, ∠A≅∠X
What are the properties of similar triangles?In Mathematics and Geometry, two triangles are said to be similar when the ratio of their corresponding side lengths are equal and their corresponding angles are congruent.
Based on the side, side, side (SSS) similarity theorem, we can logically deduce the following congruent angles and similar triangles:
BA/YX = BC/YZ = AC/XZ (ΔABC ≅ ΔXYZ)
Based on the side, angle, side (SAS) similarity theorem, we can logically deduce the following congruent angles and similar sides:
AC/XZ = BA/YX, ∠A≅∠X
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Find the focus of the parabola defined by the equation 100 points.
Answer : Focus is (0,3)
To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).
In the given equation, we have:
(y - 3)² = -8(x - 2)
Comparing it with the standard form, we can determine the values of h, k, and a:
h = 2
k = 3
4a = -8
Solving for a, we get:
4a = -8
a = -8/4
a = -2
Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.
The focus of the parabola can be found using the formula:
F = (h + a, k)
Substituting the values, we get:
F = (2 + (-2), 3)
F = (0, 3)
Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).
Answer:
Focus = (0, 3)
Step-by-step explanation:
The focus is a fixed point located inside the curve of the parabola.
To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".
The standard equation for a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.
Given equation:
[tex](y-3)^2=-8(x-2)[/tex]
Compare the given equation to the standard equation to determine the values of h, k and p:
h = 2k = 34p = -8 ⇒ p = -2The formula for the focus is (h+p, k).
Substituting the values of h, p and k into the formula, we get:
[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]
Therefore, the focus of the parabola is (0, 3).
Solve the inequality.
x
_ -3 >2
4
The solution to the inequality[tex](x/4) - 3 > 2 is x > 20.[/tex]
To solve the inequality [tex](x/4) - 3 > 2,[/tex]we'll follow these steps:
Step 1: Eliminate the fraction by multiplying both sides of the inequality by the denominator, which is 4 in this case. This step allows us to get rid of the fraction and simplify the inequality.
[tex](x/4) - 3 > 2[/tex]
Multiply both sides by 4:
[tex]4 * [(x/4) - 3] > 4 * 2[/tex]
This simplifies to:
x - 12 > 8
Step 2: Isolate the variable on one side of the inequality by adding 12 to both sides:
x - 12 + 12 > 8 + 12
This simplifies to:
x > 20
So, the solution to the inequality is x > 20. This means that any value of x greater than 20 will satisfy the inequality.
To represent this solution graphically, we can plot the number line and shade the region to the right of 20, indicating that any value greater than 20 is a valid solution.
---------------------------------
-∞ 20 +∞
--------------------------
●=================
---------------------------------
In the number line above, the shaded region represents the solution x > 20. Any value to the right of 20, including 20 itself, will satisfy the original inequality.
In summary, the solution to the inequality [tex](x/4) - 3 > 2 is x > 20.[/tex]
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A cargo truck traveled 261 miles in 4 hours. About what speed was the truck averaging on this trip?
a.
65 mph
c.
55 mph
b.
1044 mph
Answer:
To find the average speed of the truck, we can divide the total distance travelled by the total time taken.
Average speed = Total distance / Total time
In this case, the truck travelled 261 miles in 4 hours.
Average speed = 261 miles / 4 hours
Average speed = 65.25 mph (rounded to two decimal places)
Therefore, the truck was averaging approximately 65 mph on this trip.
The correct option is (a) 65 mph.
10. A triangular prism is shown.
a. Find the area of the base.
b. Find the volume of the prism.
d
5 cm
10 cm
3 cm
8 cm
5 cm
Answer:
Step-by-step explanation:
A parabola can be drawn given a focus of... 100 pts
Answer:
[tex](y+1)^2=8(x+3)[/tex]
Step-by-step explanation:
The focus of a parabola is a fixed point located inside the curve. It is equidistant from the vertex and the directrix.
The directrix is a line that is located outside the curve. As the directrix on the given graph is a vertical line, the parabola is horizontal (sideways). The directrix is located to the left of the focus, which means the parabola opens to the right.
The axis of symmetry is perpendicular to the directrix and passes through the focus. So the axis of symmetry in this case is y = -1.
The vertex is the turning point of the parabola. It is located on the axis of symmetry, and is halfway between the focus and the directrix. Therefore, the y-coordinate of the vertex is y = -1. Given the focus is (-1, -1) and the directrix is x = -5, the vertex is (-3, -1).
The standard equation of a sideways parabola is:
[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]
where:
Vertex = (h, k)Focus = (h+p, k)Directrix: x = (h - p)Axis of symmetry: y = kAs the vertex is (-3, -1), then h = -3 and k = -1.
Use the formula for the focus to find the value of p:
[tex]\begin{aligned}(h+p, k)&=(-1,-1)\\(-3+p, -1)&=(-1, -1)\\\implies -3+p&=-1\\p&=2\end{aligned}[/tex]
To write an equation for the parabola based on the given focus and directrix, substitute the values of h, k and p into the standard equation :
[tex](y-(-1))^2=4(2)(x-(-3))[/tex]
[tex](y+1)^2=8(x+3)[/tex]
Therefore, the equation of the parabola is:
[tex]\boxed{(y+1)^2=8(x+3)}[/tex]
The equation of the parabola with focus (-1, -1) and directrix x = -5 is (x + 1)² = 16(y + 1).
What is the equation of the parabola?The equation of a parabola with a focus at (-1, -1) and a directrix of x = -5 can be written in standard form as:
(x - h)² = 4p(y - k)
Where (h, k) represents the vertex of the parabola and p is the distance between the vertex and the focus (or directrix).
In this case, the x-coordinate of the focus (-1, -1) is h = -1, and the y-coordinate is k = -1. The directrix is a vertical line x = -5, which means the parabola opens to the right.
Step 1: Determine the value of p
The distance between the vertex and the directrix is given by the absolute difference of their x-coordinates. In this case, p = |-5 - (-1)| = |-5 + 1| = 4.
Step 2: Write the equation
Substituting the values into the standard form equation, we have:
(x - h)² = 4p(y - k)
(x - (-1))² = 4(4)(y - (-1))
(x + 1)² = 16(y + 1)
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Identify an equation in point-slope form for the line parallel to y = 3/4x - 4 that passes through (-1, 7).
Answer:
A) [tex]y-7=\frac{3}{4}(x+1)[/tex]
Step-by-step explanation:
[tex]y-y_1=m(x-x_1)\\y-7=\frac{3}{4}(x-(-1))\\y-7=\frac{3}{4}(x+1)[/tex]
Parallel lines must have the same slope, and then plugging in [tex](x_1,y_1)=(-1,7)[/tex], we easily get our equation.
Answer:
the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to use the same slope. The given line has a slope of 3/4.
Using the point-slope form of a line, which is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the coordinates of a point on the line, and m represents the slope of the line, we can substitute the values (-1, 7) for (x₁, y₁) and 3/4 for m:
y - 7 = (3/4)(x - (-1))
Simplifying further:
y - 7 = (3/4)(x + 1)
Multiplying through by 4 to eliminate the fraction:
4(y - 7) = 3(x + 1)
Expanding:
4y - 28 = 3x + 3
Rearranging the equation to put it in standard form:
3x - 4y = -31
So, the equation in point-slope form for the line parallel to y = (3/4)x - 4 that passes through (-1, 7) is 3x - 4y = -31.
John Doe produces two kinds of men’s shirts: polo and t-shirts. Polo shirts require 2 hours in the pattern and cutting section and 1 hour in the sewing section. T-shirts require 1 hours in the pattern and cutting section and 2 hours in the sewing section. The pattern and cutting section has 84 hours available weekly. The sewing section has 106 hours available weekly. Past sales indicate that at most 36 polo shirts can be sold. The profit on each polo shirt is $30 and on each t-shirt is $22. How many of each kind should the company produce in order to maximize its profit?
a) Define your variables (2):
b) Constraints (5):
c) Objective function (1):
d) Graph (label the axes) and Work
The evaluation of the constraints with regards to the production of the polo and t-shirts, and to maximize the profit, using linear programming indicates that we get;
a. x = The number of polo shirts produced, y = The number of t-shirts produced
b. The inequalities representing the constraints are;
2·x + y ≤ 84
x + 2·y ≤ 106
x ≤ 36
x ≥ 0, y ≥ 0
c. P = 30·x + 22·y
d. Please find attached the graph of the feasible region
To maximize profit, the company should produce;
21 polo shirts and 43 t-shirts
What is linear programming?Linear programming is a method used for optimizing (maximizing or minimizing a value) operations with some specified constraints.
a. The details indicates that the question is related to linear programming. Let x represent the number of polo shirt produced, and let y represent the number of t-shirts produced.
x = The number of polo shirt produced
y = The number of t-shirts produced
b) The constraints are;
Pattern and cutting section; 2·x + y ≤ 84
Sewing section; x + 2·y ≤ 106
Sales constraints; x ≤ 36
The values of x and y are non negative, numbers, therefore;
x ≥ 0, y ≥ 0
c) The objective of the company is to maximize profit, P, therefore, the objective function is; P = 30·x + 22·y
d) The graph can be plotted from the constraint inequalities, by making y the subject in the inequalities that includes both x and y as follows;
2·x + y ≤ 84, therefore; y ≤ 84 - 2·x
x + 2·y ≤ 106, therefore; y ≤ 53 - x/2
x ≤ 36
Please find attached the graph of the inequalities, showing the feasible region which is the polygon with boundaries which are the lines representing the constraints.
The objective function evaluated at the vertices of the feasible region indicates that we get;
[tex]\begin{tabular}{ | l | l | c | }\cline{1-3}(x, y)& 30\cdot x + 22\cdot y & P(\$) \\ \cline{1-3}(0, 53 & 30\times 0 + 22\times 53 & 1166 \\\cline{1-3}(21, 42.5 & 30\times 21 + 22\times 42.5 & 1565 \\\cline{1-3}(32, 12) & 30\times 36 + 22\times 12 & 1344 \\\cline{1-3}(36, 0) & 30\times 36 + 22\times 0 & 1080 \\\cline{1-3}(0, 0) & 30\times 0 + 22\times 0& 0 \\\cline{1-3}\end{tabular}[/tex]
The feasible region and the objective function indicates that the values of x and y that maximizes the profit is; (x, y) = (21, 42.5)
Therefore, to maximize profit, the number of polo and t-shirts the company should produce are 21, and 42.5 ≈ 43 respectively.
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find the surface area of the composite figure 12cm x 2cm x 10cm x 3cm x 6cm x 8cm SA=
Answer:
If you are in Acellus trust me the answer is 394
Step-by-step explanation:
SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )
SA = 48 + 40 + 48 + 48 + 18 + 192
SA = 394 square cm.
what percent of 41.12 is 10.28 ?
Ki Tae uses 54 meters of fencing to make a 6-sided outdoor dog pen. Two of the sides of the dog pen are each 15 meters long. The remaining 4 sides each have the same length.
Ki Tae used 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides are each 15 meters long, while the remaining four sides are each 6 meters long.
Let's solve the problem step by step. We know that Ki Tae used a total of 54 meters of fencing to construct a 6-sided outdoor dog pen. Two of the sides have a length of 15 meters each.
Let's denote the length of the remaining four sides as "x."
Since the dog pen has six sides, we can set up an equation based on the total length of the fencing:
15 + 15 + x + x + x + x = 54
Simplifying the equation, we have:
30 + 4x = 54
Subtracting 30 from both sides, we get:
4x = 24
Dividing both sides by 4, we find:
x = 6
Therefore, each of the remaining four sides has a length of 6 meters.
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Verify that the given point is on the curve. Find the lines that are a. tangent and b. normal to the curve at the given point.
The point (2, 7π / 2) does not belong to the implicit curve 8 · x · y + π · sin y = 55π and tangent and normal lines cannot be determined.
Does a point given belong to an implicit curve?
In this question we find the definition of an implicit curve, in which we must determine if point (2, 7π / 2) belongs to the curve. First, we check that point:
8 · x · y + π · sin y = 55π
8 · 2 · (7π / 2) + π · sin (7π / 2) = 55π
56π + 0.191π = 55π
56.191π = 55π
56.191 = 55 (CRASH!)
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Because f(x) ___ its inverse is a function.
○ is one to one
X is a function
○ Passes the vertical line test
The inverse of the function f(x) = 2·x - 4, is the option;
g(x) = (1/2)·x + 2
The completed statement is; Because f(x) is one to one, its inverse is a function
What is the inverse of a function?The inverse of a function is one that takes the output of a specified function to produce the input of the function.
The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;
f(x) = 2·x - 4
f(x) + 4 = 2·x
2·x = f(x) + 4
x = (f(x) + 4)/2 = f(x)/2 + 2
x = f(x)/2 + 2
Substituting f(x) = x and x = g(x) in the above equation, we get;
g(x) = x/2 + 2
The inverse of the function is therefore, g(x) = (1/2)·x + 2The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function
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Answer:
A
Step-by-step explanation:
is one to one
Tenía unas matas en el vivero.
Sembré 23 el lunes, 28 el
martes, 29 el miércoles. Si el
jueves tenía 90, ¿con cuántas
matas empecé?
If 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially.
To determine how many plants to start with initially, we need to perform a series of calculations based on the information provided.
On Monday 23 plants were planted, on Tuesday 28 plants were planted and on Wednesday 29 plants were planted. If on Thursday there were a total of 90 plants, we can add all the plants planted until Thursday and then subtract them from the total to obtain the initial amount.
Adding the plants planted:
23 + 28 + 29 = 80
Then, we subtract this amount from Thursday's total:
90 - 80 = 10
Therefore, we started with 10 plants initially.
In summary, if 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially. This is obtained by adding the plants planted until Thursday and then subtracting that amount from the total for Thursday.
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Please help I am so lost thank you so much
The speed of the plane is equal to 120 mph.
What is speed?In Mathematics and Geometry, speed is the distance covered by a physical object per unit of time. This ultimately implies that, speed can be measured by using miles per hour (mph).
Mathematically, the speed of any a physical object can be calculated by using this formula;
Speed = distance/time
Time = distance/speed
Let the variable s represent the speed of the plane in miles per hour. Therefore, an equation that models the situation can be written as follows;
240/s = 80/s - 80
80s = 240s - 19200
19200 = 160s
s = 19200/160
s = 120 mph.
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Brianna wants to purchase a vehicle. She has $15,670 saved for a down payment. Chevrolet has a 33% off sale on their Silverado. The Silverado Brianna wants costs $57,999. If she takes advantage of the sale and applies her down payment, how much will Brianna owe on her new vehicle?
Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.
To solve this problemWe need to follow these steps:
Calculate the discount on the Silverado:
Discount = 33% of $57,999
Discount = 0.33 * $57,999
Discount = $19,079.67
Subtract the discount from the original price of the Silverado:
Price after discount = $57,999 - $19,079.67
Price after discount = $38,919.33
Subtract Brianna's down payment from the price after discount:
Amount owed = Price after discount - Down payment
Amount owed = $38,919.33 - $15,670
Amount owed = $23,249.33
So, Brianna will owe $23,249.33 on her new vehicle after applying the down payment and taking advantage of the 33% off sale.
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PLEASE HELP
Suppose that the functions fand g are defined for all real numbers x as follows.
f(x) = 5x
g(x)=4x-4
Write the expressions for (g.f)(x) and (g-f)(x) and evaluate (g+f)(2).
(g•f)(x) =
(g-f)(x) =
(g+r) (2)=
Let f(x) = 4x² - 2x +11
The slope of the tangent line to the graph of f(x) at the point (3, 41)
Slope =
M=
B=
Answer:
f(x) = 4x² - 2x + 11
f'(x) = 8x - 2
m = f'(3) = 8(3) - 2 = 24 - 2 = 22
41 = 22(3) + b
41 = 66 + b
b = -25
y = 22x - 25
A small grocery store selling jugs of milk, loafs of bread and pieces of cheese sold a total of 224 of those three items today. It sold
three times as many loafs of bread as jugs of milk, and it sold 4 times as many pieces of cheese as loafs of bread.
a) Write an equation that represents the information.
b) Solve the equation in (a) to find the number of jugs of milk, loafs of bread, and pieces of cheese the store sold today
Answer: the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.
Step-by-step explanation:
a) Let's represent the number of jugs of milk as 'm', the number of loaves of bread as 'b', and the number of pieces of cheese as 'c'. According to the given information:
The total number of items sold today is 224. Therefore, we can write the equation:
m + b + c = 224
The store sold three times as many loaves of bread as jugs of milk. We can write this as:
b = 3m
The store sold four times as many pieces of cheese as loaves of bread. We can write this as:
c = 4b
b) Now, let's solve the equation:
Substituting the value of 'b' from equation (2) into equation (3):
c = 4(3m)
c = 12m
Substituting the values of 'b' and 'c' from equations (2) and (3) into equation (1):
m + 3m + 12m = 224
16m = 224
m = 224 / 16
m = 14
Using the value of 'm' in equation (2):
b = 3m
b = 3(14)
b = 42
Using the value of 'b' in equation (3):
c = 4b
c = 4(42)
c = 168
Answer:
Step-by-step explanation:
a) Let's denote the number of jugs of milk as 'x', the number of loaves of bread as 'y', and the number of pieces of cheese as 'z'.
Based on the given information, we can form two equations:
1) The total number of items sold today is 224:
x + y + z = 224
2) The store sold three times as many loaves of bread as jugs of milk:
y = 3x
3) The store sold four times as many pieces of cheese as loaves of bread:
z = 4y
b) To solve the equations and find the number of jugs of milk, loaves of bread, and pieces of cheese the store sold today, we will substitute equation (2) and equation (3) into equation (1):
x + y + z = 224
x + 3x + 4y = 224
4x + 4y = 224
Now, substitute y = 3x into the equation:
4x + 4(3x) = 224
4x + 12x = 224
16x = 224
Divide both sides by 16:
x = 224 / 16
x = 14
Now substitute the value of x back into equation (2) to find y:
y = 3x
y = 3(14)
y = 42
Finally, substitute the value of y into equation (3) to find z:
z = 4y
z = 4(42)
z = 168
Therefore, the store sold 14 jugs of milk, 42 loaves of bread, and 168 pieces of cheese today.
Find the value of x.
40 POINTS: PLEASE HELP!! urgent! using half-angle identities questions
Answer:
try gauth. math! Take a photo of each question and upload the photo to see if it works
D
Drag the expressions to the correct locations on the image. Not all expressions will be used.
Consider this quotient.
(2³ - 8z + 6) ÷ (2² - 2x + 1)
Use long division to rewrite the quotient in an equivalent form as q(z) +
2³ - 8z + 6
2² - 2x + 1
where g(z) is the quotient, r(2) is the remainder, and b(z) is the divisor.
-5z + 4
Reset
H
Next
-11x + 12
x + 2
The solution to the polynomial division in quotient and remainder form is: (x + 2) + (-5x + 4)/(x² - 2x + 1)
How to carry out Long Division of Polynomials?The polynomials we want to divide are:
x³ - 8x + 6 by x² - 2x + 1 and as such we can write it as:
x + 2
x² - 2x + 1|x³ - 8x + 6
- x³ - 2x² + x
2x² - 9x + 6
- 2x² - 4x + 2
-5x + 4
Thus, the solution expressed in quotient and remainder form is:
(x + 2) + (-5x + 4)/(x² - 2x + 1)
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PLEASE HELP ME
How are conditional probability and independent events related?
Select the correct phrase or notation from each drop-down menu to complete the explanation.
The notation P(A|B) reads the probability of Event
choose... (A occurring given that Event B has occurred) or (B occurring given that Event A had occurred)
. If two events are independent, then the probability of one event occurring
Choose... (affects the probability of the other event occurring) or (Does not affect the probability of the other event occurring)
. Events A and B are independent if
Choose... P(A|B)= P(A), P(B|A)= P(B), P(A|B)= P(B|A)
.
Conditional probability, denoted as P(A|B), represents the probability of event A occurring given that event B has occurred. If events A and B are independent, P(A|B) = P(A) and P(B|A) = P(B).
The notation P(A|B) reads the probability of Event (A occurring given that Event B has occurred). If two events are independent, then the probability of one event occurring (does not affect the probability of the other event occurring). Events A and B are independent if (P(A|B) = P(A), P(B|A) = P(B), P(A|B) = P(B|A)).
To understand the relationship between conditional probability and independent events, let's consider two events A and B. The conditional probability P(A|B) represents the probability of event A occurring given that event B has already occurred. It measures the likelihood of event A happening under the condition that event B has already taken place.
On the other hand, if two events A and B are independent, it means that the occurrence or non-occurrence of one event has no effect on the probability of the other event happening. In other words, the probability of event A happening is not influenced by the occurrence or non-occurrence of event B, and vice versa.
Mathematically, if events A and B are independent, it implies that P(A|B) = P(A) and P(B|A) = P(B). This means that the probability of event A occurring is the same whether or not event B has occurred, and the probability of event B occurring is the same whether or not event A has occurred.
Therefore, the concepts of conditional probability and independent events are related in the sense that if two events are independent, the conditional probabilities P(A|B) and P(B|A) become equal to the unconditional probabilities P(A) and P(B) respectively.
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