1) Given that 1789 children visited a Taco Bell in 24 hours. We can calculate the number of students who went every hour by dividing this number by the number of hours:
[tex]1789 / 24 = 74.54\\\frac{1789}{24} = 74.54[/tex]
We get 75 students each hour, rounded up to the nearest whole number.
If 24 children shared, we can calculate the total number of children who shared by multiplying the number of hours by the number of children shared every hour:
24 x 75 = 1800
As a result, 1800 children shared.
How many men cheated on their wives in 7 weeks?2)If 1638 men cheated on their wives in one week, multiplying by 7 gives us the number of men who cheated on their wives in seven weeks:
1638 x 7 = 11,466
As a result, 11,466 men cheated on their wives in just 7 weeks.
How many men have cheated before?c) If 47% of the men who cheated on their spouses in 7 weeks cheated numerous times before, we can calculate the number of men who cheated previously by multiplying the total number of men who cheated by the proportion of men who cheated previously:
11,466 x 0.47 = 5,390.02
Rounding to the nearest whole number, we get 5,390 men who have cheated in the past.
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do you remember how to find a discontinuity of a rational function? how is it different from an asymptote
the discontinuities of a rational function involves finding the values of x that make the denominator equal to zero, while finding the asymptotes of a rational function involves examining the behavior of the function as x approaches certain values.
Describe the function.
There will be questions on every subject, including created and real places as well as algebraic variable design, on the midterm test. a schematic illustrating the connections between various components that work together to produce the same outcome. A service is made up of many unique parts that work together to produce unique outcomes for each input.
To find the discontinuities of a rational function, we need to determine where the function is undefined. In general, a rational function is a function of the form:
f(x) = p(x) / q(x)
where p(x) and q(x) are polynomials in x, and q(x) is not the zero polynomial. The rational function f(x) is undefined at any value of x that makes the denominator q(x) equal to zero, since division by zero is undefined.
Therefore, to find the discontinuities of a rational function, we need to solve the equation q(x) = 0. The values of x that make q(x) equal to zero are called the "zeros" or "roots" of the denominator q(x). These values of x are the discontinuity points of the function, since the function is undefined at those points.
On the other hand, to find the asymptotes of a rational function, we need to examine the behavior of the function as x approaches certain values. In general, a rational function may have three types of asymptotes: horizontal, vertical, and oblique (also called slant).
Vertical asymptotes occur when the function approaches positive or negative infinity as x approaches a certain value, typically where the denominator q(x) equals zero.
Horizontal asymptotes occur when the function approaches a constant value as x approaches positive or negative infinity.
Oblique asymptotes occur when the degree of the numerator is exactly one greater than the degree of the denominator. In this case, the function approaches a straight line (i.e., a slant asymptote) as x approaches positive or negative infinity.
To summarize, finding the discontinuities of a rational function involves finding the values of x that make the denominator equal to zero, while finding the asymptotes of a rational function involves examining the behavior of the function as x approaches certain values.
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David cut a piece of pizza for his son in the shape of an isosceles triangle. The sides were
2.75
inches each and the base was
7.5
inches. He wanted a new piece, so he cut a piece that had sides of
4.4
inches and a base of
12
inches. What is the scale factor of the dilation in size from the first piece of pizza to the second piece of pizza?
The scale factor of the dilation in size from the first piece of pizza to the second piece of pizza is 1.6.
We must compare the corresponding side lengths of the two triangles in order to determine the scale factor for the size expansion from the first to the second piece of pizza. The scaling factor will equal the ratio of any two matching side lengths because the two triangles are similar.
Let's select the first pizza's sides that correlate to the second pizza's sides. The first pizza has a base that is 7.5 inches in diameter and sides that are 2.75 inches apiece. The base and sides of the second pizza are also 12 inches in diameter. To determine the scale factor, we can utilize the ratio of the corresponding side lengths:
Scale factor = (second pizza's matching side length) / (corresponding side length in first pizza)
Either side length can be used as the equivalent side length. Let's decide that the corresponding side length is 2.75 inches. Next, we have
scale factor=4.4/2.7
If we simplify, we get:
1.6 scale factor
As a result, the scale factor for the size difference between the first and second pizzas is 1.6. In all dimensions, this indicates that the second pizza is 1.6 times bigger than the first.
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Answer each blank please
The answers are:
The spot (-1, 5) is on the parabola and is 4 units away from both the directrix and the focus.The spot (3, 3) is not on the parabola because it is 2.83 units away from the focus and 2 units away from the directrix.Because it is 2.24 units from the focus and 0 units from the directrix, the location (5,5) is on the parabola.What is parabola?The directrix, which is made up of all locations (x, y) in a plane that are evenly spaced from it, and the focus, which is a fixed point but not on the directrix, are collectively referred to as a parabola. The graph of the parabola has the standard shape of a parabola with vertex (0,0) as well as the x-axis as its axis of symmetry.
Apollonius, who found many properties of conic sections, is responsible for the term "parabola." The word has the meaning "application," and as Apollonius had shown, this idea of "application of areas" is related to this curve. Pappus is responsible for the focus-directrix characteristic of the parabola and other conic sections.
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10 in 10 in 15 in what is the surface area of this ?
Answer:
The surface area of the figure is 40 + 5π.
Step-by-step explanation:
(d) water is pumped into the tank. when the height of the water is 5 feet, the height is increasing at the rate of 0.26 feet per minute. using the model from part (c), find the rate at which the volume of water is changing with respect to time when the height of the water is 5 feet. indicate units of measure.
please hurry!!! timed quiz!!!!!!
formula is a(y)= bounds of y f(x) dx
The rate at which the volume of water is changing with respect to time when the height of the water is 5 feet is (5.2/3)π√3 cubic feet per minute.
When the height is 5 feet, it is stated that the height of the water in a tank rises at a pace of 0.26 feet per minute.
When the water reaches five feet high, we can determine the rate of change in water volume with respect to time using the model from part (c).
We may calculate the volume of water in the tank using the formula V = (1/3)r2h, where r is equal to 3 feet and h is the height of the water in feet.
The Pythagorean theorem can be used to get the tank's radius at a height of 5 feet: r = ((102 - 52) = 75 = 53 feet.
Taking the derivative of the volume with respect to time, we get:
dV/dt = (1/3)π(2r)(dh/dt)
Substituting the values we have:
dV/dt = (1/3)π(2(5√3))(0.26)
= (5.2/3)π√3 cubic feet per minute
As a result, when the water level is 5 feet high, the rate of change in water volume with respect to time is (5.2/3)3 cubic feet per minute.
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A manufacturer of pencils randomly selects 25 pencils and measures their length (in inches). Their data is shown. Create a frequency distribution with 6 classes and a class width of 0.4 inches. What is the shape of frequency histogram?
A- The histogram is bimodal
b- The histogram is roughly symmetrical
c- The histogram is skewed right
d- the histogram is uniform
e- the histogram is skewed left
Answer: The histogram is roughly symmetrical
Step-by-step explanation:
I took the test
If you repeat this experiment
600 times, how many repetitions do
you predict will result in picking the
same color marble twice?
If you repeat this experiment 600 times, you predict that 300 repetitions will result in picking the same color marble twice.
To predict the number of repetitions that will result in picking the same color marble twice in 600 experiments, we need to find the probability of this event occurring and then multiply it by the total number of experiments.
Calculate the probability of picking the same color marble twice:
Assuming there are two colors (A and B) and an equal number of each
color, the probability of picking the same color twice is:
P(AA) = P(A) × P(A|A) = (1/2) × (1/2) = 1/4
P(BB) = P(B) × P(B|B) = (1/2) × (1/2) = 1/4
Add the probabilities of picking two marbles of the same color:
P(same color twice) = P(AA) + P(BB) = 1/4 + 1/4 = 1/2
Multiply the probability by the total number of experiments:
Predicted repetitions = Probability × Total experiments
= (1/2) × 600
= 300
So, if you repeat this experiment 600 times, you predict that 300
repetitions will result in picking the same color marble twice.
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If f varies inversely as x, and y= 2 when x= 2, find y when x= 1
The value of y is 4.
What is an inverse function?
The inverse function of a function f in mathematics is a function that reverses the operation of f. If f is bijective, then and only if it is, the inverse of f exists.
Here, we have
Given: If f varies inversely as x, and y= 2 when x= 2, find y when x= 1.
We have to find the value of f.
f ∝ 1/g
f₁ ×g₁ = f₂ ×g₂
Let the required value of f = x and g = y
Inserting in equation (1) and we get
2 ×2 = 1 ×y
4 = y
Hence, the value of y is 4.
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Find the shaded area. Round your answer to the nearest tenth, if necessary.
Area of the Trapezoid =
Area of the Triangle =
Total Shaded Area =
Area of trapezoid = 675 in², Area of triangle = 54 in² and Total Shaded Area = 621 in²
What is trapezoid?A trapezοid, alsο knοwn as a trapezium, is a flat clοsed shape having 4 straight sides, with οne pair οf parallel sides.
The parallel sides οf a trapezium are knοwn as the bases, and its nοn-parallel sides are called legs. A trapezium can alsο have parallel legs. The parallel sides can be hοrizοntal, vertical οr slanting.
The perpendicular distance between the parallel sides is called the altitude.
From the figure given:
Area of trapezoid [tex]\rm = \frac{a + b}{2} \cdot h[/tex]
Area of trapezoid [tex]\rm = \frac{24 + 51}{2} \cdot 18[/tex]
Area of trapezoid = 675 in²
Area of triangle = 1/2 × base × height
Area of triangle = 1/2 × 9 × 12
Area of triangle = 54 in²
Total Shaded Area = 675 - 54
Total Shaded Area = 621 in²
Thus, Area of trapezoid = 675 in², Area of triangle = 54 in² and Total Shaded Area = 621 in²
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a car traveled for 12 minutes. in the first six minutes, the car traveled 2 miles. in the last six minutes, the car traveled 8 miles. which best describes the motion of the car in the last six minutes?
The car traveled at a faster rate in the last six minutes compared to the first six minutes.
In the first six minutes, the car traveled 2 miles, which means it had a speed of (2 miles)/(6 minutes) = 0.33 miles per minute.
In the last six minutes, the car traveled 8 miles, which means it had a speed of (8 miles)/(6 minutes) = 1.33 miles per minute.
Comparing the two speeds, we can see that the car traveled at a faster rate in the last six minutes. This could be because the driver increased the speed or drove on a more favorable road surface. It is also possible that the driver had to slow down in the first six minutes due to traffic or other road conditions.
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7. Writing Write a paragraph proof showing that if
5(2x-3)= 25, then x = 4.
Answer:
We know that when 5(2x-3) = 25 x = 4 because when you plug 4 back into the equation you get 25=25. To solve this equation first you will distribute 5 into 2x -3 you will then get 10x-15 = 25. Then you will add 15 to both sides and get 10x = 40, next divide 10 from both sides and you will get x=4. To check this you can plug 4 back into the equation so it will look like this. 5(2(4)-3) = 25, first you will solve what is in the parenthesis, you will set 5(5)=25. Then multiply 5 by 5 and you will get 25=25. This proves that when 5(2x-3) = 25 x = 4
Step-by-step explanation:
What are the values of a and b?
W
50°
X
(3b)⁰
3a-5
70°
Z
nosvica
Y
a +11
answer
W
50°
X
Xy-step explanation:
Q
19) Choose the correct answer.
The perimeter and area of a wall have the same value. If the base of the wall is 7 meters long,
what is the height of the wall?
O 4.48 meters
O 5.6 meters
O2.8 meters
O 1.4 meters
Let's assume the height of the wall as 'h' meters.
Given, the perimeter of the wall = area of the wall
The perimeter of the wall = 2(length + breadth) = 2(7+h) = 14+2h meters
The area of the wall = length × breadth = 7 × h = 7h square meters
According to the problem, the perimeter and area of the wall have the same value.
So, 7h = 14 + 2h
Subtracting 2h from both sides, we get:
5h = 14
Dividing both sides by 5, we get:
h = 2.8 meters
Therefore, the height of the wall is 2.8 meters.
Hence, the answer is 2.8 meters
Answer:
2.8 meters
I've done the quiz
refer to problem 18. a. is the estimate of age based on 500 plots influenced by sampling error? why? b. how would the sampling error of the estimate of mean age change if the investigators had used a sample of only 100 plots?
a. Yes, the estimate of age based on 500 plots is influenced by sampling error.
Sampling error occurs because the sample is only a portion of the entire population, and the sample may not perfectly represent the whole population.
Therefore, the estimate of the mean age derived from the sample might deviate from the true mean age of the entire population.
b. If the investigators had used a sample of only 100 plots instead of 500, the sampling error of the estimate of mean age would likely increase. As the sample size decreases, the likelihood of the sample representing the whole population accurately decreases as well.
Consequently, the deviation between the sample means age and the true population mean age would likely be larger, leading to a higher sampling error.
Sampling error refers to the difference or discrepancy between a sample's characteristics and the corresponding characteristics of the entire population from which the sample was drawn. It arises due to the fact that a sample is only a subset of the population, and the sample may not perfectly represent the whole population. Sampling error can impact the accuracy of statistical inferences and conclusions drawn from the sample, such as estimates of mean, variance, or correlation.
As the sample size decreases, the likelihood of the sample representing the whole population accurately decreases as well, leading to higher sampling error.
Therefore, minimizing sampling error is crucial in ensuring the validity and reliability of research findings.
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i need help i dont knoow how to do this
27.42 cm2
you multiply the length of a shape by its width.
Please answer quick missing assignment
9 bananas can be bought with $3.25, and we will have $0.10 left over.
Define Selling PriceSelling price is the price at which a product or service is sold to customers. It is the amount of money that a business receives in exchange for its goods or services. The selling price is often determined by considering factors such as production costs, market demand, and competition.
Number of bananas = $3.25 ÷ $0.35/banana
Number of bananas = 9.285 (rounded to 3 decimal places)
Since we cannot buy a fractional part of a banana, we need to round down to the nearest whole number. Therefore, we can buy 9 bananas with $3.25.
Total cost of bananas = 9 bananas × $0.35/banana
Total cost of bananas = $3.15
So, we will not use all our money. We will have $3.25 - $3.15 = $0.10 left over.
Therefore, we can buy 9 bananas with $3.25, and we will have $0.10 left over.
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On the model scale drawing, approximately how much empty space lies between the bed and the dresser? Use complete sentences to explain your reasoning. whoever answers gets brainliest
Distance from Breadth of one side of the wall = L/3 units
Distance from one corner i.e from Breadth = L - L/3 - L/6 = L/2
Distance from floor i.e surface = H/6 units
Distance from Ceiling= H - H/6 = 5H/6 units
Considering the room to be in the shape of a Cuboid as well as the Bed to be in the shape of a Cuboid.
Dimensions of Room:
In mathematics, space is the only light without elements; its magnitude or cardinality (number of elements in the set) is zero.
Let the Length of the cuboid which is in the shape of a room = L
The breadth of the cuboid which is in the shape of a room = B
Height of cuboid which is in the shape of a room = H
Considering, L>B>H
Dimension of Bed
Length = L/6 units
Breadth = B/4 units
Height = H/6 units
Taking one corner at origin i.e (0,0,0)
You can keep your bed at any place inside the room, but you want your bed to be at that place inside the room where the window is located so that proper ventilation and sunlight can enter your room.
Taking the bed to be in the middle of the room near the window and considering its upper face
Distance from one corner i.e from length= B- B/4 = 3B/4 Units
Distance from other corner = 0 Units
Distance from Breadth of one side of the wall = L/3 units
Distance from one corner i.e. from Breadth = L - L/3 - L/6 = L/2
Distance from floor i.e. surface = H/6 units
Distance from Ceiling= H - H/6 = 5H/6 units
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in an octagon, the interior angles are in the ratio 1:2:3:4:5:6:7:8. what is the measure of the smallest angle?
The measure of the smallest angle is 30° in an octagon when the interior angles are in the ratio 1:2:3:4:5:6:7:8.
The sum of the interior angles of an octagon is (8 - 2) x 180° = 1080°.
Let x be the minimum angle measure and write down the other angle equations concerning x using the ratios given.
2x, 3x, 4x, 5x, 6x, 7x, 8x.
by adding all the angles we get,
x + 2x + 3x + 4x + 5x + 6x + 7x + 8x = 36x.
Since the sum of the interior angles of an octagon is 1080°,
Simplifying the equation:
36x = 1080
x = 30
The minimum angular dimension is x = 30°.
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Seven times Hector’s age minus two times Sandra’s age equals 5. Sandra’s age is also three times Hector’s age. How old is Sandra?
the amount of money available can be represented by the following inequality: 5a + 7b ≤ 200
What is inequality?
Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Since the aprons with 2 pockets cost $5 each and the aprons with 4 pockets cost $7 each, the constraint on the number of aprons that can be purchased based on
Hence, the amount of money available can be represented by the following inequality: 5a + 7b ≤ 200
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PERIMETER AND AREA HELP ASP
The following are the expressions for the perimeter and area for the rhombus:
9). perimeter = 4(x + 2) in
area = (x + 10)(x + 9)/2 in²
10). perimeter = 4(x - 3) mm
area = (x - 8)(x + 6)/2 mm²
What is a rhombusA rhombus is a two-dimensional geometric shape with four equal sides and four equal angles, but the angles are not necessarily 90 degrees. It is a type of parallelogram.
Two same triangles make up the rhombus so we evaluate for the area expression of one triangle and multiply the result by 2 to get the areas. And multiply each side by 4 to get the expression for the perimeters
area of a triangle = 1/2 × base × height
9). base = (x + 10) and height = (x + 9)/2
area of one triangle = 1/2 × (x + 10) × (x + 9)/2
area of one triangle = (x + 10)(x + 9)/4
area of rhombus = 2 × (x + 10)(x + 9)/4
area of rhombus = (x + 10)(x + 9)/2 in²
perimeter of rhombus = 4(x + 2) in
10). base = (x - 8) and height = (x + 6)/2
area of one triangle = 1/2 × (x - 8) × (x + 6)/2
area of one triangle = (x - 8)(x + 6)/4
area of rhombus = 2 × (x - 8)(x + 6)/4
area of rhombus = (x - 8)(x + 6)/2 mm²
perimeter of rhombus = 4(x - 3) mm
Therefore, the rhombus have the expression for the perimeter and area as:
9). perimeter = 4(x + 2) in
area = (x + 10)(x + 9)/2 in²
10). perimeter = 4(x - 3) mm
area = (x - 8)(x + 6)/2 mm²
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find the limit. use l'hospital's rule where appropriate. if there is a more elementary method, consider using it. lim x→[infinity] x9e−x8
the limit is:
lim (x→∞) x⁹ * e^(-x⁸) = 0
To find the limit of the given function as x approaches infinity, we can use L'Hospital's Rule since it involves an indeterminate form. The given function is:
lim (x→∞) x⁹ * e^(-x⁸)
First, let's rewrite the function as a fraction:
lim (x→∞) x⁹ / e^(x⁸)
Now, since this is an indeterminate form (infinity over infinity), we can apply L'Hospital's Rule by taking the derivative of both the numerator and the denominator with respect to x:
Numerator derivative: d(x⁹)/dx = 9x⁸
Denominator derivative: d(e^(x⁸))/dx = x⁸ * e^(x⁸)
Now, rewrite the limit with the derivatives:
lim (x→∞) (9x⁸) / (x⁸ * e^(x⁸))
We can simplify this expression:
lim (x→∞) 9 / e^(x⁸)
Now, as x approaches infinity, the denominator becomes infinitely large, making the whole fraction approach 0. Therefore, the limit is:
lim (x→∞) x⁹ * e^(-x⁸) = 0
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Joe went to a restaurant and left a 35% tip if the bill was 115 how much tip did Joe leave
Answer: 40.25
Step-by-step explanation:
Answer:
$40.25
Step-by-step explanation:
35% of $115 = 0.35 × $115 = $40.25
Find the area of the figure below composed of a parallelogram and one semicircle rounded to the nearest tenths place 
We have a parallelogram and a half of circle.
The area of parallelogram are: A=basis*height
The area of circle are: A=πr², where r is the radius (half of diameter). Thus the half circle have Area equals to:
Approaching π to 3,14
parallelogram:
b=26
h=13
A=13*26
A=338
Half circle:
r=12
A=(3,14*12²)/2
A=226,08
Total Area of the figure are:
A=338+226,08
A=564,08
distributive property
6(r-1)+5(r+4)
1. 6r-1+5r+4
2. 6r+6+5r+20
3. 6r-6+5r+20
4. 6r-6+5r-4
Answer:
the answer is 3) 6r-6+5r+20
Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 11 inches, and the hole had side lengths of 5 inches, how much wood was left after the hole was cut out?
Note: Figure is not drawn to scale.
A.
1,206 cubic inches
B.
1,331 cubic inches
C.
1,056 cubic inches
D.
96 cubic inches
The volume of the cube-shaped = 1,331 volume of the hole cut out of the block = 125 cubic inches Subtract 1331 - 125 = 1206, the correct option is A
volume of the hole cut out of the block = 5 inches x 5 inches x 5 inches
volume of the hole cut out of the block = 125 cubic inches.
volume of the cube-shaped block = 11 inches x 11 inches x 11 inches
volume of the cube-shaped block = 1,331
To find the volume of the wood remaining after the hole is cut out, we can subtract the volume of the hole from the volume of the block:
1,331 cubic inches - 125 cubic inches = 1,206 cubic inches
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a complete graph is one in which there is an edge connecting every vertex to every other vertex. for what values of n does complete graph with n vertices have an euler circuit? a hamiltonian circuit
A complete graph is one in which there is an edge connecting every vertex to every other vertex. In order to determine for what values of n a complete graph with n vertices has an Euler circuit and a Hamiltonian circuit, let's discuss the definitions and requirements of each type of circuit.
1. Euler Circuit: An Euler circuit is a path that traverses each edge of a graph exactly once and returns to its starting vertex. For a graph to have an Euler circuit, all vertices must have an even degree (number of edges connected to the vertex).
2. Hamiltonian Circuit: A Hamiltonian circuit is a path that visits every vertex in a graph exactly once and returns to its starting vertex. A complete graph always has a Hamiltonian circuit, regardless of the number of vertices.
Now, let's determine for what values of n a complete graph has an Euler circuit:
In a complete graph with n vertices, each vertex is connected to every other vertex, which means the degree of each vertex is (n-1). For a complete graph to have an Euler circuit, all vertices must have an even degree. This implies that (n-1) must be even, so n must be odd.
So, for a complete graph with n vertices to have an Euler circuit, n must be an odd number.
In summary:
- A complete graph with n vertices always has a Hamiltonian circuit.
- A complete graph with n vertices has an Euler circuit if n is an odd number.
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7. The parabola shown has the form y = ax2 + bx + c.
a. What is the axis of symmetry? x=
b. Look at the width of the parabola to find a.
c. Use the formula x = to find b.
2a
d. What is the equation of the parabola?
Answer: y = ax2 + bx + c
Step-by-step explanation:
Step 1: The equation of any parabola is given by y = ax2 + bx + c, where a, b, and c are constants.
Step 2: We can calculate the axis of symmetry (x-coordinate) by using the formula x = -b/2a.
Step 3: We can calculate the value of a by looking at the width of the parabola.
Step 4: Once we have the values of a and b, we can substitute them into the equation to get the equation of the parabola: y = ax2 + bx + c.
Bridget grew 6,624 flowers with 96 seed packets. How many seed packets does Bridget need to have a total of 6,762 flowers in her garden? Assume the relationship is directly proportional.
Bridget needs 98 seed packets to have a total of 6,762 flowers in her garden. Since she can't buy fractional seed packets, she would need to buy 99 seed packets.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
Since the relationship between the number of flowers and the number of seed packets is directly proportional, we can set up a proportion to solve the problem.
Let x be the number of seed packets Bridget needs to have a total of 6,762 flowers in her garden.
We can set up the proportion:
624 flowers ÷ 96 seed packets = 6,762 flowers ÷ x seed packets
To solve for x, we can cross-multiply and simplify:
624 * x = 96 * 6,762
x = (96 * 6,762) ÷ 6,624
x = 98.38
Therefore, Bridget needs 98 seed packets to have a total of 6,762 flowers in her garden. Since she can't buy fractional seed packets, she would need to buy 99 seed packets.
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abby began her pizza delivery route with 11/12 of a tank of gas in her car. when she made it back to the pizzeria, 3/4 of a tank of gas was left. how much gas did abby use?
The gas used by Abby while travelling in her pizza delivery route is 1/4.
As per the given question here we have to implement the basic principles of subtraction along with application of LCM.
The total amount of gas that Abby had in her car = 11/12
After coming to pizzeria the amount of gas left in her tank = 3/4
Here, we have to perform Subtraction to find out the amount of gas used for travelling. Therefore,
= 11/12 - 3/4
performing the LCM, we get
= 11 - 9/12
= 3/12 => 1/4
The gas used by Abby while travelling in her pizza delivery route is 1/4.
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Evaluate the definite integral. Use a graphing utility to verify your result.[tex]\int\limits^2_0 ({9-t)\sqrt{t} } \, dt[/tex]
The shaded area under the curve is approximately 9.11, which confirms our result.
What is integral?In calculus, an integral is a mathematical object that represents the area between a curve and the x-axis. It is a fundamental concept in calculus, and is used to calculate quantities such as the area under a curve, the volume of a solid, and the work done by a force. The process of finding an integral is called integration, and it involves finding an antiderivative (or indefinite integral) of a function, which is a function whose derivative is equal to the original function. The definite integral is then calculated by evaluating the antiderivative at two limits, which represent the beginning and end points of the area being calculated.
Here,
We can start by expanding the integrand using the distributive property:
(9 - t)√t = 9√t - t√t
Now we can integrate each term separately using the power rule of integration:
∫(9 - t)√t dt = ∫9√t dt - ∫t√t dt
= 18/2 * [tex]t^{(1/2)}[/tex] - 2/3 * [tex]t^{(3/2)}[/tex] + C
where C is the constant of integration.
Evaluating the definite integral from 0 to 2:
∫(9 - t)√t dt from 0 to 2 = [18/2 * [tex]2^{(1/2)}[/tex] - 2/3 * [tex]2^{(3/2)}[/tex]] - [18/2 * [tex]0^{(1/2)}[/tex] - 2/3 * [tex]0^{(3/2)}[/tex]]
= 9√2 - 4/3
≈ 9.11
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