If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.
Since the parabola opens upward, its vertex is the minimum point, and therefore, it will have only one solution.
A parabola is a U-shaped curve in mathematics that can be formed by the graph of a quadratic function. It is a type of conic section, along with circles, ellipses, and hyperbolas.
Mathematically, a parabola can be defined as the set of all points in a plane that are equidistant from a fixed point called the focus and a fixed line called the directrix. The focus lies on the axis of symmetry of the parabola, and the directrix is perpendicular to the axis of symmetry.
If the vertex of a parabola is at (5,0) and it opens UPWARD, it will have one solution.
Your answer: one
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Is the following data an example of a linear function?
Answer:
Yes
Step-by-step explanation:
Yes, because its graph represents a straight line
You and a group of friends are off to have a day of fun! Before you head out on your adventure, you need to choose a mode of transportation to get to your destinations. The four different transportation choices are represented by the functions below. Decide which method of transportation you would like to use for the day. Use your choice to answer the questions that follow.
1. Which mode of transportation did you choose? Why?
The mode of transportation that I will choose is motorized scooter this is because it is relatively cheap when compared to the other forms of transportation.
What is the forms of transportation?A motorized scooter could be a moderately cheap mode of transportation compared to other alternatives such as cars, cruisers, or indeed bikes.
The starting price of obtaining a motorized bike is for the most part lower than that of a car or cruiser, and the continuous costs such as fuel, support, and protections are too ordinarily lower.
From the question, you can see that the price of the scooter at 5 miles is $10 and it is relatively cheap when compared to the rest.
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A cyclist went out for a solo ride but has become lost. He knows from his inexpensive cycletracker GPS the distance he has traveled and in which direction, but he has no idea how to get home short of retracing his path. The different legs of his trip are listed below.
Determine in which direction and how far he needs to ride to get back where he started in the shortest distance possible. (assume there are no obstacles in his way and he can travel in a straight line) (5 marks)
Leg #1-8 km [North]
Leg #2-10 km [East]
Leg #3-12 km [15 S of East]
Leg #4-14 km [South]
The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.
How to solve for the distanceWe can use trigonometry to find the x and y components.
x3 = 12 * cos(15°) ≈ 11.59 km (east)
y3 = -12 * sin(15°) ≈ -3.10 km (south, hence the negative sign)
Leg #4: 14 km [South]
x4 = 0 km (no east/west movement)
y4 = -14 km (south, hence the negative sign)
Now, let's find the total x and y displacements:
x_total = x1 + x2 + x3 + x4 ≈ 0 + 10 + 11.59 + 0 ≈ 21.59 km
y_total = y1 + y2 + y3 + y4 ≈ 8 + 0 - 3.10 - 14 ≈ -9.10 km
Now, we can find the distance and direction he needs to ride to get back to the starting point:
Distance=
[tex]\sqrt{21.59^2 + (-9.10)^2}[/tex])
23.21 km
Direction:
angle =
arctan(9.10 / 21.59)
= 23.13°
The cyclist needs to ride approximately 23.21 km in the direction of 23.13° W of North to get back to the starting point.
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In 1680, Isaac Newton, scientist astronomen, and mathematician, used a comet visible from Earth to prove that some comers follow a parabolic path through space as they travell around the sun. This and other discoveries like it help scientists to predict past and future positions of comets.
Comets could be visible from Earth when they are most likely to fall down into earth
A cement walkway is in the shape of a rectangular prism. The length is 10 feet, the width is three feet and the depth is 1.5 feet. How much cubic feet of cement will they need?
The volume of cement in cubic feet that will be needed is 45 cubic feet.
What is volume?Volume is the space occuppied by an object.
To calculate the volume of cement in cubic feet that will be needed, we use the formula below
Formula:
V = lwh....................... Equation 1Where:
V = Volume of the cement that is neededl = Length of the walkwayw = width of the walkwayh = depth of the walkwayFrom the question,
Given:
l = 10 feetw = 3 feeth = 1.5 feetSubstitute these values into equation 1
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Choose the description that correctly compares the locations of each pair of points on a coordinate plane.
a. (–2, 5) is
choose...
(–2, –1).
b. (1, 212) is
choose...
(4, 212).
c. (3, –6) is
choose...
(3, –3).
d. ( −212, 1) is
choose...
(–3, 1).
e. (312 , 12) is
choose...
( 12, 12).
f. (2, 5) is
choose...
(2, –5).
The point (–2, 5) is located above the point (–2, –1).
The point (1, 212) is located to the left of the point (4, 212).
The point (3, –6) is located below the point (3, –3).
The point (−212, 1) is located to the left of the point (–3, 1).
The point (312, 12) is located to the right of the point (12, 12).
The point (2, 5) is located above the point (2, –5).
Find out the comparisons of the location of each pair of points?a. (–2, 5) is above (–2, –1). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (–2, 5) is located above the point (–2, –1).
b. (1, 212) is to the left of (4, 212). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (1, 212) is located to the left of the point (4, 212).
c. (3, –6) is below (3, –3). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate decreases as you move down on the coordinate plane, the point (3, –6) is located below the point (3, –3).
d. (−212, 1) is to the left of (–3, 1). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate decreases as you move to the left on the coordinate plane, the point (−212, 1) is located to the left of the point (–3, 1).
e. (312, 12) is to the right of (12, 12). The two points have the same y-coordinate, but different x-coordinates. Since the x-coordinate increases as you move to the right on the coordinate plane, the point (312, 12) is located to the right of the point (12, 12).
f. (2, 5) is above (2, –5). The two points have the same x-coordinate, but different y-coordinates. Since the y-coordinate increases as you move up on the coordinate plane, the point (2, 5) is located above the point (2, –5).
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A sheet of dough has six identical circles cut from
it. Write an expression in factored form to represent the
approximate amount of dough that is remaining. Is
there enough dough for another circle
Approximate amount of dough that is remaining. Is (length - 2r)(width - 3r) - 6πr^2.
Without the size of the original sheet of dough or the size of the circles cut from it, it's not possible to give an exact expression. However, assuming that each circle has the same radius of 'r' and the original sheet of dough was a rectangle, we can write an expression in factored form for the remaining area of the dough:
Remaining area of dough = (Area of original rectangle) - 6(Area of circle)
= (length x width) - 6(πr^2)
= (length - 2r)(width - 3r) - 6πr^2
Whether there is enough dough for another circle would depend on the size of the circles and the original sheet of dough.
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The diameter of a circle is 2 kilometers. What is the circle's circumference? d=2 km Use 3. 14 for . Kilometers?
The circumference of the circle is 6.28 kilometers if the diameter of the circle is 2 kilometers and assuming the value of π is 3.14 kilometers.
The diameter of the circle = 2 kilometers
The circumference of a circle is calculated by using the formula,
C = π *d
where,
C = circumference of a circle
d = diameter of the circle
π = Constant value = 3. 14 Km
Substituting the above-given values into the equation, we get:
C = π*d
C = 3.14 x 2 km
C = 6.28 km
Therefore, we can conclude that the circumference of the circle is 6.28 kilometers.
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Suppose a mouse is placed in the maze at the right. if each desicion about direction is made at random, create a simulation to determine the probability that the mouse will find its way out before coming to a dead end or going out in the opening.
The probability of the mouse finding its way out before reaching a dead end or going out in the opening can be estimated by dividing the number of successful outcomes by the total number of trials in the sample.
To create a simulation to determine the probability that the mouse will find its way out before coming to a dead end or going out in the opening, we can follow these steps:
Create a model of the maze in a programming language such as Python.Define the starting position of the mouse as the position on the right side of the maze.Define the exit position of the maze as the position on the left side of the maze.Randomly choose a direction for the mouse to move in (up, down, left or right).Check if the chosen direction leads to a dead end or out of the maze. If it does, return a failure outcome.If the chosen direction leads to a viable path, move the mouse to that position and repeat steps 4-6 until the mouse either reaches the exit or gets stuck in a dead end.Repeat steps 2-6 multiple times to generate a sufficient sample size.Calculate the proportion of successful outcomes (i.e. the mouse finding its way out before reaching a dead end or going out in the opening) from the generated sample.The probability of the mouse finding its way out before reaching a dead end or going out in the opening can be estimated by dividing the number of successful outcomes by the total number of trials in the sample. This simulation approach can help us understand the probability of success in a random maze environment, and also explore the impact of various factors such as maze complexity, size and starting position of the mouse on the outcome.
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Students measured the length of several pencils and recorded their data in a table.
Pencil Lengths (Inches)
3
7
8
,
5
1
4
,
4
,
6
1
8
,
4
1
2
,
5
1
4
,
3
1
2
,
5
3
8
,
4
3
4
,
5
The students will make a line plot of the data. They will use only one fraction in their scale. They must be able to plot all of the data above a label. Which should this fraction be?
Step-by-step explanation:
To determine the appropriate fraction for the line plot, we need to find the greatest common factor (GCF) of all the pencil lengths, and then express each length as an equivalent fraction with the GCF as the denominator.
The GCF of the pencil lengths is 1. Therefore, we can simply express each pencil length as an equivalent fraction with 1 as the denominator:
3/1, 7/1, 8/1, 5/1, 1/1, 4/1, 6/1, 8/1, 4/1, 2/1, 5/1
Now, we can see that the smallest unit increment we can use on the line plot is 1/8. This is because 1/8 is the smallest fraction that can represent all of the pencil lengths above the label (5/8, which is equivalent to 10/16).
Therefore, the students should use 1/8 as the fraction for the line plot.
A laboratory tested 82 chicken eggs and found that the mean amount of cholesterol was 228 milligrams with a = 19. 0 milligrams. Construct a 95% confidence interval for the
true mean cholesterol content,, of all such eggs.
We can say with 95% confidence that the true mean cholesterol content of all such eggs is between 223.99 milligrams and 232.01 milligrams.
To construct a 95% confidence interval for the true mean cholesterol content of all such eggs, we can use the following formula:
CI = X ± Zα/2 * σ/√n
where:
X = sample mean = 228 milligrams
Zα/2 = the critical value from the standard normal distribution corresponding to a 95% confidence level, which is 1.96
σ = population standard deviation = 19.0 milligrams
n = sample size = 82
Substituting the values into the formula, we get:
CI = 228 ± 1.96 * 19.0/√82
= 228 ± 4.01
= (223.99, 232.01)
Therefore, we can say with 95% confidence that the true mean cholesterol content of all such eggs is between 223.99 milligrams and 232.01 milligrams.
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A radioactive isotope is decaying at a rate of 18% every hour. Currently there
are 120 grams of the substance.
Write an equation that will represent the number of grams, y, present after
hours.
=
Can you tell me the answer please
The decay of the radioactive substance can be modeled by the exponential decay function:
y = a(1 - r)^t
where:
- y is the amount of substance present after t hours
- a is the initial amount of substance (in grams), which is 120 grams in this case
- r is the decay rate per hour, which is 18% or 0.18 in decimal form
- t is the time elapsed in hours
Plugging in the values we get:
y = 120(1 - 0.18)^t
Simplifying:
y = 120(0.82)^t
So this is the equation that represents the number of grams, y, present after t hours, given the initial amount of 120 grams and a decay rate of 18% per hour.
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The Greens bought a condo for $110,000 in 2005. If its value increases at 6% compounded annually, what will the value be in 2020?
Answer:
$264,000
Step-by-step explanation:
PV = $110,000
i = 6%
n = 15 years
Compound formula:
FV = PV (1 + i)^n
FV = 110,000 (1 + 0.06)^15
FV = 110,000 · 2.40(rounded) = $264,000
Los lados de un triangulo miden, en cm, tres numeros enteros consecutivos. Encuentra la longitud de los tres lados
There are infinitely many possible solutions for the lengths of the three sides of the triangle.
What is triangle?
A triangle is a three-sided polygon with three angles. It is a fundamental geometric shape and is often used in geometry and trigonometry.
If we call x the length of the smallest side, then the other two sides are x+1 and x+2 (since they are three consecutive integers). According to the triangle inequality, the sum of any pair of sides must be greater than the length of the third side.
Therefore, we have:
x + (x+1) > (x+2) (and also x + (x+2) > (x+1) and (x+1) + (x+2) > x)
Simplifying each inequality, we get:
2x + 1 > x + 2 (and also 2x + 2 > x + 1 and 2x + 3 > x)
Which gives:
x > 1
So the smallest side must be greater than 1 cm.
Now, to find the length of the three sides, we can choose any value greater than 1 for x. For example, if we take x=2, then the three sides are:
2 cm, 3 cm, and 4 cm
If we take x=3, then the three sides are:
3 cm, 4 cm, and 5 cm
And so on. Therefore, there are infinitely many possible solutions for the lengths of the three sides of the triangle.
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Pleas help im stuck on this question and im too afraid to get it wrong
Step-by-step explanation:
g(x) is just f(x) shifted UP three units ...so
g(x) = f(x) +3
(−3m
5
)(−2m
4
)=left parenthesis, minus, 3, m, start superscript, 5, end superscript, right parenthesis, left parenthesis, minus, 2, m, start superscript, 4, end superscript, right parenthesis, equals
The solution to the equation is m = 0.
What is an algebraic expression?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations. It may also include exponents and/or roots. Algebraic expressions are used to represent quantities and relationships between quantities in mathematical situations, often in the context of problem-solving.
To solve the equation:
(-3m^ {5}) (-2m^ {4}) = (-6m^ {9})
We can simplify the left side of the equation by multiplying the terms:
(-3m^ {5}) (-2m^ {4}) = (6m^ {9})
Now we have:
6m^ {9} = (-6m^ {9})
To solve for m, we can divide both sides by 6m^ {9}:
m^ {9} = -m^ {9}
Since the powers of m on both sides are equal, we can simplify to:
2m^ {9} =0
Dividing both sides by 2, we get:
m^ {9} =0
Taking the ninth root of both sides, we get:
m = 0
Therefore, the solution to the equation is m = 0.
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Complete Question:
Simplify the expression: $(-3m^ {5}) (-2m^ {4}) $.
Suppose that you are gambling at a casino. Every day you play at a slot machine, and your goal is to minimize your losses. We model this as the experts problem. Every day you must take the advice of one of n experts (i. E. A slot machine). At the end of each day t, if you take advice from expert i, the advice costs you some c t i in [0, 1]. You want to minimize the regret R, defined as:
To minimize your losses while gambling at a casino and playing slot machines, you need to minimize your regret R in the experts problem. R is defined as the difference between your total cost and the best expert's cost.
To minimize R, follow these steps:
1. Begin by assigning equal weight to each expert (slot machine).
2. After each day t, observe the cost c_ti for each expert i.
3. Update the weights by multiplying them by (1 - c_ti), making sure they remain non-negative.
4. Normalize the weights so they sum up to 1.
5. On day t+1, choose the expert with the highest weight to take advice from.
By following this adaptive strategy, you will minimize your regret R, allowing you to reduce your losses while gambling at the slot machines.
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17. What number is not part of the solution set to the
inequality below?
w - 10 < 16
A. 11
B. 15
C. 26
D. 27
Answer:
Step-by-step explanation:
To find the solution set to the inequality w - 10 < 16, we can solve for w by adding 10 to both sides of the inequality:
w - 10 + 10 < 16 + 10 w < 26
This means that any number less than 26 is part of the solution set to the inequality. So, out of the given options, the number that is not part of the solution set is D. 27 because it is greater than 26.
A grocery store’s earnings in dollars can be modeled by the equation y 5 0. 75x 2 0. 15x, where x represents the number of tomatoes that they sell. If they sell 200 tomatoes in one day, how much money do they earn?
The grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.
We need to find how much the grocery store earns when it sells 200 tomatoes in one day. When The grocery store’s earnings in dollars can be modeled by the equation,
y = 0.75x² + 0.15x
where,
x = number of tomatoes they sell = 200
To find the earnings we need to substitute x in the equation it can be given as,
y = 0.75x² + 0.15x
y = 0.75(200)² + 0.15(200)
y = $30,030
Therefore, the grocery store's earning income is $30,030 if they sell 200 tomatoes in one day.
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Consider the geometric series 1 - x/3 - x^2/9 - x^3/27......
What is the common ratio of the series and for what values of x will the series converge? Determine the function f representing the sum of the series.
The function f representing the sum of the series for x in the interval (-3, 3). Hi! The given geometric series is 1 - x/3 - x^2/9 - x^3/27...
The common ratio of the series is obtained by dividing a term by its preceding term. Let's consider the first two terms:
(-x/3) / 1 = -x/3
Therefore, the common ratio (r) of the series is -x/3.
For a geometric series to converge, the absolute value of the common ratio must be less than 1, i.e., |r| < 1. In this case:
|-x/3| < 1
To find the values of x for which the series converges, we need to solve the inequality:
-1 < x/3 < 1
Multiplying all sides by 3, we get:
-3 < x < 3
So, the series converges for x in the interval (-3, 3).
Now, let's determine the function f representing the sum of the series. For a converging geometric series, the sum S can be calculated using the formula:
S = a / (1 - r)
where a is the first term and r is the common ratio. In this case, a = 1 and r = -x/3. Therefore:
f(x) = 1 / (1 - (-x/3))
f(x) = 1 / (1 + x/3)
This is the function f representing the sum of the series for x in the interval (-3, 3).
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Find the volume of a cylinder with a diameter of 28 meters and a height of 6 and one half meters. Approximate using pi equals 22 over 7.
28,028 cubic meters
4,004 cubic meters
1,274 cubic meters
572 cubic meters
The volume of the cylinder is 4004 cubic metres.
How to find the volume of a cylinder?The diameter of the cylinder is 28 metres and the height of the cylinder is 6.5 metres.
Therefore, the volume of the cylinder can be found as follows:
Hence,
volume of a cylinder = πr²h
where
r = radiush = heightTherefore,
volume of the cylinder = 22 / 7 × 14² × 6.5
volume of the cylinder = 22 / 7 × 196 × 6.5
volume of the cylinder = 28028 / 7
volume of the cylinder = 4004 cubic metres
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Given the center, a vertex, and one focus, find an equation for the hyperbola:
center: (-5, 2); vertex (-10, 2); one focus (-5-√29,2).
The equation of the hyperbola is -(x + 5)²/71 + (y - 2)² = -71
How to calculate the valueWe can also find the distance between the center and the given focus, which is the distance between (-5, 2) and (-5 - √29, 2):
d = |-5 - (-5 - √29)| = √29
Substituting in the known values, we get:
c² = a² + b²
(√29)² = (10)² + b²
29 = 100 + b²
b² = -71
(x - h)²/a² - (y - k)²/b² = 1
where (h, k) is the center of the hyperbola.
Substituting in the known values, we get:
(x + 5)²/100 - (y - 2)²/-71 = 1
Multiplying both sides by -71, we get:
-(x + 5)²/71 + (y - 2)²/1 = -71/1
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What is the graph of g?
Answer:
Vertical Compression by factor of 1/4
Step-by-step explanation:
Two methods:
Method 1. Transformations
Method 2. Algebraic input-output tables
Method 1. Transformations
The Main concept of this question is about Transformations of functions -- specifically, multiplying on the outside by a positive number less than 1.
The transformation that occurs when multiplying a function by a positive number on the outside of the function is a vertical stretch or compression.
Positive numbers larger than 1 will stretch it vertically, whereas positive numbers smaller than 1 will compress it vertically.
Therefore, multiplying by 1/4 on the outside, a positive number less than 1, will vertically compress the function down to one-fourth the size.
This means that for g(x), all points on the original function f will have their heights reduced to 1/4 their original height (or depth) -- making all points on g(x) 1/4 their previous distance from the x-axis on the "f" function.
Method 2. Algebraic input-output tables
Observe on the graph three points on the function f:
(0,0), (1,4) and (3,0) --- points on the function "f"In function notation, this means [tex]f(0)=0[/tex], [tex]f(1)=4[/tex], and [tex]f(3)=0[/tex]Using the equation relating f and g, [tex]g(x)=\frac{1}{4}f(x)[/tex], we can find how those points would look like on the new function g(x).
For [tex]f(0)=0[/tex]
[tex]g(0)=\frac{1}{4}[f(0)]\\g(0)=\frac{1}{4}[0]\\g(0)=0[/tex]
For [tex]f(1)=4[/tex]
[tex]g(1)=\frac{1}{4}[f(1)]\\g(1)=\frac{1}{4}[4]\\g(1)=1[/tex]
For [tex]f(3)=0[/tex]
[tex]g(3)=\frac{1}{4}[f(3)]\\g(3)=\frac{1}{4}[0]\\g(3)=0[/tex]
These known points should correctly identify the graph from the possible choices.
A hot water pipe needs to be insulated to prevent heat loss. The outer pipe has a diameter D = 48.7 cm (correct to 3 significant figures). The inner pipe has a diameter d = 19.25 cm (correct to 2 decimal places). Work out the upper and lower bound of the cross-sectional area of the insulation, A (the shaded area between the inner and outer pipes) in cm2 to the nearest whole number. Give your answer in interval form, using A as the variable.
The upper and lower bound of the cross-sectional area of the insulation, would be A = [ 3129, 3137 ] cm².
How to find the upper and lower bond ?The upper and lower bound of A would be found by the formula :
A = π x ( R ² - r ² )
The upper bound is therefore:
= π x (( 48. 75 / 2) ² - ( 19.2 45 / 2) ²)
= π x ( 1183. 0625 - 184. 857025 )
= π x 998. 205475
= 3, 137 cm²
The lower bound will then be:
= π x ( ( 48. 65 / 2 ) ²- (19. 255 / 2) ²)
= π x ( 1180. 9225 - 184. 963025)
= π x 995. 959475
= 3, 129 cm²
The interval form is therefore A = [ 3129, 3137 ] cm²
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Sariah has just begun training for a half-marathon, which is Latex: 13. 1 13. 1 miles. Since she was on vacation, she started the training program later than the rest of her running club. There are Latex: 6 6 weeks of training runs remaining before the race. In her first week of training, Sariah ran Latex: 3 3 miles. She ran Latex: 4. 5 4. 5 miles the second week and Latex: 6 6 miles the third week. If she continues to increase the length of her runs the same way, will there be enough time left in the training program for her to get up to half-marathon distance?
If she continues to increase the length of her runs the same way, it will not be enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.
Sariah has just begun training for a half-marathon, which is 13.1 miles. There are 6 weeks of training runs remaining before the race. In her first week of training, Sariah ran 3 miles. She ran 4.5 miles the second week and 6 miles the third week.
To determine if there is enough time left in the training program for her to get up to half-marathon distance, let's analyze the pattern of her weekly increases in distance:
Week 2 - Week 1 = 4.5 miles - 3 miles = 1.5 miles increase
Week 3 - Week 2 = 6 miles - 4.5 miles = 1.5 miles increase
Sariah is consistently increasing her weekly mileage by 1.5 miles. With 3 weeks of training already completed, she has 3 more weeks to go. Let's see if she can reach the half-marathon distance of 13.1 miles:
Week 4: 6 miles + 1.5 miles = 7.5 miles
Week 5: 7.5 miles + 1.5 miles = 9 miles
Week 6: 9 miles + 1.5 miles = 10.5 miles
After 6 weeks of training, Sariah will have increased her longest run to 10.5 miles. Unfortunately, this is not enough to reach the half-marathon distance of 13.1 miles within the remaining time of the training program.
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I Need help with a Math Problem (zoom in if you can’t see it) (if you can’t see it the problem is ( x degrees 49 degrees and 39 degrees) find the value of x
Answer:
Step-by-step explanation:
If there are 180 degrees in a triangle total and in this problem we know that one angle is 49 and the other is 39, we can assume that subtracting 39 and 49 from 180 will find x. In this case, x will be 92.
What is the inverse of y = 2^(x - 3)?
show how you got the answer
Answer:
(3-x)^2=y
Step-by-step explanation:
1 Let us consider the series (n + 16)(n+18) Note: Write the exact answer not the decimal approximation (for example write not 0.8). Answer: (0) Let {sn} be the sequence of partial sums. Then 35 2n+32 Osn = 1/2 306 n2+35n+306 32 2n+32 306 72 +32n+306 O Sn = n Osn= ( 35 306 2n+35 12+35n+306 O Sn = 32 306 2n+32 72 +32n+306 (i) If s is the sum of the series then S =
S = lim[n → ∞] sn
= lim[n → ∞] (306n^2 + 35n + 306)
= ∞
So unfortunately, the series (n + 16)(n + 18) diverges to infinity and does not have a finite sum.To find the sum S of the series (n + 16)(n + 18), we need to take the limit of the sequence of partial sums as n approaches infinity. So let's first find the formula for the nth partial sum sn:
sn = (1 + 16)(1 + 18) + (2 + 16)(2 + 18) + ... + (n + 16)(n + 18)
= ∑[(k + 16)(k + 18)] (from k = 1 to n)
Using the formula for the sum of squares, we can expand each term in the sum:
(k + 16)(k + 18) = k^2 + 34k + 288
So now we have:
sn = ∑(k^2 + 34k + 288) (from k = 1 to n)
= ∑k^2 + 34∑k + 288n (from k = 1 to n)
= n(n + 1)(2n + 1)/6 + 34n(n + 1)/2 + 288n
= 306n^2 + 35n + 306
Now we can take the limit of sn as n approaches infinity to find S:
S = lim[n → ∞] sn
= lim[n → ∞] (306n^2 + 35n + 306)
= ∞
So unfortunately, the series (n + 16)(n + 18) diverges to infinity and does not have a finite sum.
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Use the image to determine the direction and angle of rotation.
Graph of triangle ABC in quadrant 1 with point A at 1 comma 3. A second polygon A prime B prime C prime in quadrant 4 with point A prime at 3 comma negative 1.
90° clockwise rotation
180° clockwise rotation
180° counterclockwise rotation
90° counterclockwise rotation
The rotation used in this problem is given as follows:
90º clockwise rotation.
What are the rotation rules?The five more known rotation rules are given as follows:
90° clockwise rotation: (x,y) -> (y,-x)90° counterclockwise rotation: (x,y) -> (-y,x)180° clockwise and counterclockwise rotation: (x, y) -> (-x,-y)270° clockwise rotation: (x,y) -> (-y,x)270° counterclockwise rotation: (x,y) -> (y,-x)A vertex and it's equivalent is given as follows:
A(1,3) and A'(3, -1).
Hence the rule is:
(x,y) -> (y, -x).
Which is the rule for a 90° clockwise rotation = 270º counterclockwise rotation.
Missing InformationThe image is presented at the end of the answer.
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Answer:
90° clockwise rotation
Step-by-step explanation:
I did the exam and got it correct
1/2 (7)(4) + 6(5)=
I can not figure this out! Can you answer with middle school techniques?
The value of the given expression is 44. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
The four basic operations, also referred to as "arithmetic operations," are thought to explain all real numbers. Operations like division, multiplication, addition, and subtraction come before operations like quotient, product, sum, and difference in mathematics.
We are given an expression as [tex]\frac{1}{2}[/tex] (7) (4) + 6 (5).
We know that when there is no sign in between two numbers, it denotes multiplication.
So, we get
⇒ [tex]\frac{1}{2}[/tex] * (7) * (4) + 6 * (5)
⇒ 14 + 30
⇒ 44 (Using addition operation)
Hence, the value of the given expression is 44.
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