The turbocharged model is moving 41.25 ft/sec faster than the model with the standard engine at the end of the 11-second test run.
We need to find how much faster the turbo-charged model is moving than the model with the standard engine at the end of an 11-second test run at full throttle.
To find the final velocity of each model at the end of 11 seconds, we need to integrate their respective acceleration functions with respect to time from 0 to 11 seconds:
For the standard engine model:
v(t) = ∫(5 + 0.8t) dt = 5t + [tex]0.4t^2[/tex]
v(11) = 5(11) +[tex]0.4(11)^2[/tex] = 72.4 ft/sec
For the turbo-charged model:
v(t) = ∫(5 + 1.2t + 0.03[tex]t^2[/tex]) dt = 5t +[tex]0.6t^2 + 0.01t^3[/tex]
v(11) = 5(11) + [tex]0.6(11)^2 + 0.01(11)^3[/tex]= 113.65 ft/sec
The difference in final velocity between the two models is:
[tex]v_{turbo} - v_{standard[/tex] = 113.65 - 72.4 = 41.25 ft/sec
Therefore, the turbo-charged model is moving 41.25 ft/sec faster than the model with the standard engine at the end of the 11-second test run.
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Meg has 3/10 liter of juice left in her bottle, Ines has 3 times as much juice in her bottle as Meg has How much juice, in liters, does Ines have?
Ines has 9/10 liter of juice, if Meg has 3/10 liter of juice left in her bottle and Ines has 3 times as much juice in her bottle as Meg has .
It is need to find how much juice does Ines have.To calculate it, it is need to know how much liter of juice does Meg have. Meg have 3/10 liter of juice left in her bottle, and Ines has 3 times as much juice her bottle as Meg has.
That is Ines has 3 times means multiplying how much juice meg have by 3.
That is Juice left in bottle of Ines = juice left in bottle of Meg * 3 = 3/10 liter x 3 = 9/10 liter. Therefore, Ines has 9/10 liter of juice in her bottle.
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please help with this photo problem
and describe the resulting transformation
The option that represents the resulting transformation is: Option C
How to find the reflection over a line?A reflection over line is defined as a transformation in which each point of the original figure which is also called the pre-image possesses an image that is the essentially the same distance from the reflection line as the original point, but then is on the opposite side of the line. In a reflection, the image is the same size and shape as the pre-image.
Now, looking at the letter Q, when we reflect it once, it should be the mirror image but when reflect it the second time about same line, it becomes exactly the original copy.
Thus, we can conclude that Option C represents the resulting transformation.
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please help me on this question
Based on the data, we can infer that Kallie needs 6 teaspoons of water conditioner for the 12 fish tanks.
How to calculate how many teaspoons of water conditioner Kallie needs?To calculate how many teaspoons of water conditioner we must take into account the information on the capacity of each tank:
Each tank is equivalent to 20 quarts, that is, 5 gallons.There are 12 tanks in total.For every 10 gallons, you need 1 teaspoon of water conditioner.In accordance with the above, we do the following logical procedure.
We multiply the capacity of each tank by the number of tanks.
5 * 12 = 60So we need 60 gallons of water to fill the tanks, and we divide by 10 to find how many teaspoons we need to fill all 12 tanks.
60 / 10 = 6Based on the above, we need 6 teaspoons to condition the water in the 12 tanks.
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the girl lifts a painting to a height of 0.5 m in 0.75 seconds. how much
power does she use? *
Power is the rate at which work is done or energy is transferred. In this case, the girl used a force of 98 N to lift the painting to a height of 0.5 m in 0.75 seconds, resulting in 49 J of work done. The power used was calculated to be approximately 65.33 watts.
To calculate the power used by the girl while lifting the painting, we need to use the formula: Power (P) = Work (W) / time (t).
Firstly, we need to calculate the work done by the girl in lifting the painting. Work is defined as the product of force and distance. As there is no information about the force applied, we will assume that the girl lifted the painting with a constant force. Therefore, the work done can be calculated as:
Work (W) = force x distance
Here, the distance is 0.5 m, and we can use the formula for weight to calculate the force required to lift the painting. As we know that the mass of the painting is not given, we can assume it to be 10 kg (a medium-sized painting).
Weight (Wt) = mass x acceleration due to gravity
Wt = 10 kg x 9.8 m/s² = 98 N
Therefore, the work done by the girl is:
W = 98 N x 0.5 m = 49 J
Now, we can use the formula for power to calculate the power used by the girl.
P = W / t
P = 49 J / 0.75 s
P = 65.33 W (approx.)
Therefore, the girl used approximately 65.33 watts of power while lifting the painting.
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The girl used 65.3 watts of power to lift the painting.
How to find power?To calculate power, we need to know the work done and the time taken.
We can use the formula:
power = work/time
The work done is equal to the force applied multiplied by the distance moved. Since we don't know the force, we can use the formula for work in terms of mass, gravity, and height:
work = mgh
where m is the mass, g is the acceleration due to gravity, and h is the height lifted.
Assuming the painting has a mass of 10 kg and the acceleration due to gravity is 9.8 m/s², the work done is:
work = (10 kg) x (9.8 m/s²) x (0.5 m) = 49 J
The time taken is 0.75 seconds.
So the power used is:
power = work/time = 49 J / 0.75 s = 65.3 watts
Therefore, the girl used 65.3 watts of power to lift the painting.
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In ΔXYZ, ∠Y=90° and ∠X=60°. ∠ZWY=69° and XW=240. Find the length of ZY to the nearest 10th.
The value of length ZY in nearest 10th place is 1,240.8 units.
What is the value of length ZY?The value of length ZY is calculated as follows;
Considering triangle XYZ;
tan 60 = ZY/XY
let length WY in triangle WYZ = ntan 60 = (ZY)/(240 + n)
ZY = 1.732(240 + n) ------ (1)
Considering triangle WYZ;
tan 69 = ZY/WY
tan 69 = ZY/n
n = ZY/tan69
n = 0.384(ZY) ---------- (2)
The length ZY is calculated as;
Substitute the value of n into equation (1)
ZY = 1.732(240 + 0.384ZY)
ZY = 415.68 + 0.665ZY
0.335ZY = 415.68
ZY = 415.68 / 0.335
ZY = 1,240.8 units
From equation (2);
n = WY = 0.384 (1,240.8)
WY = 476.5 units
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Consider the line segment defined by the points A(0, 1) and B(4,6). How does a
reflection across the x-axis affect AB?
Select all that apply.
A. The x-values of the reflection are the opposite values of the x-values of the
original segment.
B. The y-values of the endpoints become their opposites.
C• The length of the reflection of AB is greater than the length of AB.
DThe length of the reflection of AB is less than the length of AB.
E. The length of the reflection of AB is the same as the length of AB.
Considering "line-segment" defined by points A(0, 1) and B(4,6), then effects of reflection across the "x-axis" are :
(b) The "y-coordinate" of "end-points" become opposites in sign.
(e) The length of reflection of AB is same as length of line-segment AB.
When reflecting a line segment across the x-axis, the x-coordinates of all points remain the same, but the y-coordinates become their opposites.
So, for the line segment AB, the x-coordinate of point A remains 0, and the x-coordinate of point B remains 4. However, the y-coordinate of point A becomes -1, and the y-coordinate of point B becomes -6. This results in a new line segment A'(0, -1) and B'(4, -6).
Since the reflection is across a horizontal line, the length of the reflection is the same as the length of the original segment.
Therefore, the correct options are (b) and (e).
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in right triangle abc, mzb + m2c. let sinb = r and cos b = s. what is sinc-cosc?
The value of the trigonometric expression sin c - cos c is: s - r
How to solve Trigonometric Ratios?The three most common trigonometric ratios are:
sin x = opposite/hypotenuse
cos x = adjacent/hypotenuse
tan x = opposite/adjacent
We are given that:
sinb = r and cos b = s
Thus, from the diagram attached, we can see that:
sin B = rh/h = r
cos B = sh/h = s
Thus, using trigonometric ratios, we can equally say that:
cos C = rh/h = r
sin C = sh/h = s
Thus:
sin c - cos c = s - r
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A cuboid has a square base of side (2 + √3)m. the area of one side is (2√3 - 3)m². find the height of the cuboid in the form (a+ b√3)m, where a and b are integers.
The height of the cuboid, after calculations, in the form (a+ b√3)m, is (6√3 - 9)/47 meters.
Let the height of the cuboid be h meters. The area of the square base is given by:
(2 + √3)² = 4 + 4√3 + 3 = 7 + 4√3 m²
The total surface area of the cuboid is the sum of the areas of the six rectangular faces. Since the base is a square, the area of each of the four vertical rectangular faces is also (2 + √3) × h = (2h + h√3) m². Therefore, we have:
Total surface area = 4(7 + 4√3) + 2(2h + h√3)(2 + √3) = 8h + 26 + (22 + 16√3)h
Since we know that one of the sides has area (2√3 - 3) m², we can set up another equation:
(2h + h√3)(2 + √3) = 2√3 - 3
Expanding the left side and simplifying, we get:
(2h + h√3)(2 + √3) = 2√3 - 3
4h + 7h√3 = 2√3 - 3
h(4 + 7√3) = 2√3 - 3
h = (2√3 - 3)/(4 + 7√3)
We can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator:
h = [(2√3 - 3)/(4 + 7√3)] × [(4 - 7√3)/(4 - 7√3)]
h = (8√3 - 12 - 14√3 + 21)/(16 - 63)
h = (9 - 6√3)/(-47)
h = (6√3 - 9)/(47)
Therefore, the height of the cuboid is (6√3 - 9)/47 meters.
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I need help ASAP (will give brainliest)
Answer:
92°
Step-by-step explanation:
All angles should add up to 360°
Opposite angles are equal so that means two angles are 88°
88+88=176
360 - 176 = 184
184 / 2 = 95
Measure of angle A is 92°
HELP ME PLEASE AND YOU GET BRAINLIEST PLEASE HELP ME FAST
Answer:
48
Step-by-step explanation:
can be divided into two 4x6 rectangles. Therefore, the area is 4x6 + 4x6 = 48
A political candidate feels that she performed particularly well in the most recent debate against her opponent. Her campaign manager polled a random sample of 400 likely voters before the debate and a random sample of 500 likel voters after the debate. The 95% confidence interval for the true difference (post-debate minus pre-debate) in proportions of likely voters who would vote for this candidate was (-0. 014, 0. 064). What was the difference (pre- debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate?
The difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
The range of the 95% confidence interval for the actual difference between the proportions of probable voters who would support this candidate before and after the debate was (-0.014, 0.064). To find the difference (pre-debate minus post-debate) in the sample proportions of likely voters who said they will vote for this candidate, we need to find the midpoint of the confidence interval, which is the point estimate of the true difference.
In the given question, the interval is (-0.014, 0.064), then the expression for the likely difference is
(0.064 + (-0.014))/2 = 0.050/2
= 0.025
Hence, the difference in the sample proportions of likely voters who said they will vote for this candidate is 0.025.
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(a)
The masses of two animals at a zoo are described, where band care integers.
•The mass of an African elephant is 6, 125,000 grams, or about 6 x 10 grams.
• The mass of a silverback gorilla is 185, 000 grams, or about 2 x 10 grams.
What are the values of b and c?
bu
CH
(b) Part B
Using these estimated values, the mass of the African elephant is about 3 x 10 times the mass of the silverback gorilla, where m is an integer.
What is the value of m?
m
The value of m by the given data is m=2
We are given that;
Number of elephants= 125000gram
The mass of african elephant= 3 x 10
Now,
To find the values of b and c, we need to write the given masses in scientific notation, which means that the coefficient must be between 1 and 10. For example, 6 x 10 grams is not in scientific notation, because 6 is not between 1 and 10. To fix this, we need to move the decimal point one place to the left and increase the exponent by one. We get:
6x106 grams=6.0x106 grams=6.0x106−1×101 grams=6.0x105×101 grams=6.0x105+1 grams=6.0x107 grams
Similarly, for the silverback gorilla, we get:
2x105 grams=2.0x105 grams=2.0x105−1×101 grams=2.0x104×101 grams=2.0x104+1 grams=2.0x105 grams
Therefore, the values of b and c are b=7,c=5
To find the value of m, we need to divide the mass of the African elephant by the mass of the silverback gorilla and write the result in scientific notation. We get:
Mass of silverback gorillaMass of African elephant=2.0x105 grams6.0x107 grams=2.06.0×105107=3.0×107−5=3.0×102
Therefore, by unitary method the answer will be m=2.
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1) Last year a computer cost $1,600 to purchase. A year later the same computer cost $1,850 to purchase. By what percent did the cost of the computer increase? (please show your work)
2)A flock of 50 geese landed at a pond. Later that day there were 75 in the pond. By what percent did the number of geese increase?
a
80%
b
50%
c
2%
d
10%
Answer:
1) 15.625% increase. 1850-1600=250. 250/1600=0.15625. 0.15625x100= 15.625.
2) 50%
Step-by-step explanation:
1) 1850-1600=250. 250/1600=0.15625. 0.15625x100= 15.625.
2) 75-50=25. 25/50=0.5. 0.5x100=50
There are 100 dears within a circular area with a radius of 10. Find the density of deer for 400 square miles.
The density of deer for 400 square miles is around 1:4 based on stated number of deers.
The density of deer will be given by the formula -
Population density of deer = number of deer/ area
Population density is the amount or number of individuals of a population on land per unit area.
Keep the value in formula to find the population density
Population density = 100/400
Cancelling zero as common in both numerator and denominator
Population density = 1:4
Thus, there is 1 deer for every 4 square mile.
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I’m having trouble with this
A right rectangular prism has a length of 1 foot, a width of 1 3/8 feet, and a height of 5/8 foot. unit cubes with side lengths of 1/8 foot are added to completely fill the prism with no space remaining. how many cubes can fit inside the prism? explain how to find the number by using the volume formula. explain how to find the number by using the side lengths of the prism and the cubes.
The number of cubes of dimensions of [tex]\frac{1}{8}[/tex] foot that can fit into a rectangular prism of a length of 1 foot, a width of 1 [tex]\frac{3}{8}[/tex] foot, and a height of [tex]\frac{5}{8}[/tex] foot is 55.
Volume of cuboid = l * b * h
where l is the length
b is the breadth
h is the height
l = 1 foot
b = 1 [tex]\frac{3}{8}[/tex] foot = [tex]\frac{11}{8}[/tex] foot
h = [tex]\frac{5}{8}[/tex] foot
Volume of cuboid = 1 * [tex]\frac{11}{8}[/tex] * [tex]\frac{5}{8}[/tex]
= [tex]\frac{55}{64}[/tex] cubic foot
Volume of cube = [tex]s^3[/tex]
where s is the side
s = [tex]\frac{1}{8}[/tex] foot
Volume = [tex]\frac{1}{8}^3[/tex]
= [tex]\frac{1}{64}[/tex] cubic foot
Number of cubes = [tex]\frac{\frac{55}{64} }{\frac{1}{64} }[/tex]
= 55
The number of cubes that fit into the prism is 55.
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Draw a triangle with one side length of 5 units and another side length
of 7 units. What additional piece of information will guarantee that only
one triangle can be drawn?
It should be noted that to craft a triangle with an edge measuring 5 units of length, another side 7 units in magnitude, we can get underway by sketching an uninterrupted line of 7-units duration.
How to explain the informationSubsequently, draw an additional segment arriving at a peak of 5-units from the starting point of the former line. From the end-point of the line calculated as 7 units, draw a joined line towards the conclusion of the 5 unit-length section. This enables two distinctive triangles:
Also, to guarantee that just a single triangle can be drawn, it is imperative to recognize the angle resting between the two assigned sides. In case we are endowed with the inclination between both varying lengths of five and seven units, then only an original composition of triangle can be constructed.
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From a Word Problem
An online camera store charges $3 for every
8x10 picture that you order. The
shipping cost is $8. Write an equation to
model this situation. How much will it cost to
get 5 pictures printed?
Problem
Yoshi is a basketball player who likes to practice by attempting the same three-point shot until he makes the shot. His past performance indicates that he has a
30
%
30%30, percent chance of making one of these shots. Let
X
XX represent the number of attempts it takes Yoshi to make the shot, and assume the results of each attempt are independent.
Is
X
XX a binomial variable? Why or why not?
Choose 1 answer:
Choose 1 answer:
(Choice A)
A
Each trial isn't being classified as a success or failure, so
X
XX is not a binomial variable.
(Choice B)
B
There is no fixed number of trials, so
X
XX is not a binomial variable.
(Choice C)
C
The trials are not independent, so
X
XX is not a binomial variable.
(Choice D)
D
This situation satisfies each of the conditions for a binomial variable, so
X
XX has a binomial distribution
There is no fixed number of trials, so X is not a binomial variable. (Choice B) B is the right response.
Discrete random variables are within the category of binomial random variables. A binomial random variable keeps track of how frequently an event occurs over a predetermined number of trials. ALL of the following prerequisites have to be satisfied for a variable to qualify as a binomial random variable:
A predetermined sample size (number of trials) is used.
The relevant occurrence either takes place or doesn't in every trial.
On each trial, the likelihood of occurrence (or not) is the same.
Trials run separately from one another.
While Yoshi has a 30% chance of success for each shot and the trials are independent, the number of attempts is not fixed, as he continues until he makes the shot.
Thus, the correct answer is (Choice B) B. There is no fixed number of trials, so X is not a binomial variable.
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I will give brainlyist to who ever answers it.
A family with travel 475 miles on the Road trip which inequality can be used to find all possible values of T the time it would take to reach their destination if they travel in an average speed of at least in miles per hour
The inequality that can be used to find all possible values of T, the time it would take to reach their destination if they travel at an average speed of at least "r" miles per hour, can be expressed as:
T ≤ 475 / r
This inequality states that the time taken (T) should be less than or equal to the distance traveled (475 miles) divided by the average speed (r miles per hour). By dividing the total distance by the average speed, we obtain the maximum time it would take to reach the destination. Any time less than or equal to this value would satisfy the condition of traveling at an average speed of at least "r" miles per hour.
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Anita has saved $43. 75 of the $112. 50 that she needs for a new snowboard.
She saves $13. 75 from her paper route each week. The equation
13. 75w + 43. 75 = 112. 50 can be used to represent the number of weeks
it will take her to reach her goal. In how many more weeks will Anita have
saved enough money for the snowboard?
Anita will take 5 more weeks to save enough money for the snowboard. when she saved $43. 75 of the $112. 50 that she needs for a new snowboard.
Given data :
Total money needs for a new snowboard = $112. 50
Anita saved money = $43. 75
Money saved each week = $13. 75
From the given data we can write the equation to find the number of weeks as,
13. 75w + 43. 75 = 112. 50
By solving the equation 13.75w + 43.75 = 112.50 we can find out how many more weeks it will take Anita to save enough money for the snowboard by using the elimination method.
Subtracting 43.75 from both sides of the equation, we get:
13.75w + 43.75 - 43.75 = 112.50 - 43.75
13.75w = 68.75
w = 68.75 / 13.75
w = 5
Therefore, Anita will take 5 more weeks to save enough money for the snowboard.
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A floor plan of a house was drawn using a scale of 1 inch:5 feet. if the kitchen is drawn 2 1/2 inches by 3 inches, what are the dimensions of the actual kitchen?
If the kitchen is drawn 2 1/2 inches by 3 inches, the actual dimensions of the kitchen are 12.5 feet by 15 feet.
The given scale of 1 inch:5 feet means that for every 1 inch on the floor plan, the actual length in real life is 5 feet. To find the actual dimensions of the kitchen, we need to convert the length and width of the kitchen on the floor plan into real-life measurements.
The length of the kitchen on the floor plan is 2 1/2 inches, which in real life would be:
2.5 inches x 5 feet/1 inch = 12.5 feet
Similarly, the width of the kitchen on the floor plan is 3 inches, which in real life would be:
3 inches x 5 feet/1 inch = 15 feet
To verify this result, we can also use the scale to convert the actual dimensions of the kitchen back into the measurements on the floor plan. The length of the kitchen in real life is 12.5 feet, which on the floor plan would be:
12.5 feet x 1 inch/5 feet = 2.5 inches
Similarly, the width of the kitchen in real life is 15 feet, which on the floor plan would be:
15 feet x 1 inch/5 feet = 3 inches
As expected, these measurements match the dimensions of the kitchen as drawn on the floor plan.
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Question 3
CLASS PRESIDENT In a poll for senior class president, 68 of the 145 male students said they planned to vote for Santiago. Out of 139
female students, 89 planned to vote for his opponent, Measha.
Construct a conditional relative frequency table based on voter preference. Show your calculations on a separate sheet of paper. Round to
the nearest whole percent if necessary
The given data is tabulated for conditional relative frequency table as follows.
Total male = 145, Total female = 139
Total male votes for Santiago = 68, Total female votes for Measha = 89
Total female votes for Santiago = 50, Total male votes for Measha = 77
Now total votes for Santiago = 68+50=118
Total votes for Measha = 166
Total votes casted = 284
The above data is formulated in tables attached below.
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1.
(03. 01 MC)
Part A: Find the LCM of 8 and 9. Show your work. (3 points)
Part B: Find the GCF of 35 and 63. Show your work. (3 points)
Part C: Using the GCF you found in Part B, rewrite 35 + 63 as two factors. One factor is the GCF and the other is the sum of two numbers that do not have a common factor. Show your work. (4 points)
The LCM of 8 and 9 is 72. The GCF of 35 and 63 is 7.35 + 63 can also be written as 7 X 14.
Part A
Here we have been given 2 numbers 8 and 9. We need to find the LCM. LCM is the Lowest Common Multiple. It is the smallest number which can be divided by all the mentioned number. To take the LCM of 8 and 9 we first will factorize them
8 = 2 X 2 X 2
9 = 3 X 3
Here we see that 8 and 9 do not have any common factor. Hence we need to simply multiply them together to get
8 X 9 = 72
Part B.
We need to find GCF of 35 and 63. GCF or the Greatest common factor is the highest number that can divide all the given numbers. Here too we will first factorize 35 and 63.
35 = 5 X 7
63 = 3 X 3 X 7
Here we see that between the numbers, 7 is the only common factor
Hence, 7 is the GCF.
63 can also be written as 63 = 7 X 9
Hence we can write 35 + 3
= (7 X 5) + (7 X 9)
Taking 7 common we get
7(5 + 9)
= 7 X 14
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La rueda de una bicicleta mide 62.2 cm de diámetro, ¿cuál es el perímetro de la rueda?
Answer:
"Querido hijo, estás despedido" es una novela juvenil escrita por Jordi Sierra i Fabra que se divide en 17 capítulos. A continuación, se presenta un breve resumen de cada uno de ellos:
Capítulo 1: El protagonista, Leo, es un adolescente que vive en un hogar en el que sus padres son muy estrictos y le exigen que saque buenas notas en la escuela.
Capítulo 2: Leo tiene una discusión con su padre, quien le dice que si no mejora sus notas, lo echará de casa.
Capítulo 3: Leo tiene un accidente de bicicleta y es atendido por la enfermera del colegio, la señorita Rovira.
Capítulo 4: Leo recibe la noticia de que su padre ha muerto en un accidente de tráfico.
Capítulo 5: En el funeral de su padre, Leo se siente alejado de su familia y amigos.
Capítulo 6: Leo recibe una carta de su padre en la que le explica que ha dejado un testamento y que su hermana mayor, Berta, será la administradora de la herencia.
Capítulo 7: Berta le comunica a Leo que su padre le ha dejado una empresa de limpieza y que él será el encargado de dirigirla.
Capítulo 8: Leo descubre que la empresa está en quiebra y que tendrá que tomar medidas drásticas para salvarla.
Capítulo 9: Leo empieza a tomar el control de la empresa y a hacer cambios en su funcionamiento.
Capítulo 10: Leo contrata a un joven llamado Iván, quien se convierte en su mano derecha en la empresa.
Capítulo 11: Leo se encuentra con la señorita Rovira, quien lo ayuda a tomar una importante decisión en la empresa.
Capítulo 12: Leo tiene una reunión con los trabajadores de la empresa y les comunica los cambios que va a hacer.
Capítulo 13: Leo se siente muy presionado por las exigencias de la empresa y se desahoga con su amigo Santi.
Capítulo 14: Leo tiene un encontronazo con su hermana Berta, quien intenta influir en la gestión de la empresa.
Capítulo 15: Leo descubre que Iván le ha estado robando dinero a la empresa y tiene que tomar medidas para solucionar el problema.
Capítulo 16: Leo consigue salvar la empresa y hace balance de lo que ha aprendido en el proceso.
Capítulo 17: La historia termina con Leo en paz consigo mismo y con su familia, habiendo aprendido importantes lecciones sobre la vida y el trabajo.
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Use this data set, which shows how many miles Tisha ran each week for 10 weeks
4,9,8,6,14,8,16,12
Find the statistical measures that you need tomake a box plot of Tisha's running distances.
(what’s a statistical measure)
Statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.
A statistical measure is a numerical value that provides information about a specific aspect of a dataset's distribution, such as its central tendency, spread, or variability. Box plots require several statistical measures to be constructed, including:
Minimum: The smallest value in the dataset. In this case, the minimum value is 4.
Maximum: The largest value in the dataset. In this case, the maximum value is 16.
Median: The middle value of the dataset when it is arranged in numerical order. In this case, the median is the average of the two middle values, which are 8 and 9. The median is therefore (8 + 9) / 2 = 8.5.
First Quartile (Q1): The value below which 25% of the data falls. In this case, the first quartile is the median of the first half of the data, which is 6.
Third Quartile (Q3): The value below which 75% of the data falls. In this case, the third quartile is the median of the second half of the data, which is 14.
With these statistical measures, you can construct a box plot that shows the range, median, and quartiles of Tisha's running distances over the 10 weeks.
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In Triangle JKL, ∠J is congruent to ∠L.
The measure of ∠L in Triangle JKL is 56.1 degrees.
What is the measures in triangles?In geometry, the measures in triangles refer to the angles and sides within a triangle. Triangles are three-sided polygons, and the measures of their angles and sides are important properties that determine their shape and characteristics.
In a triangle, the sum of the measures of all three angles is always 180 degrees. Therefore, to find the measure of ∠L in Triangle JKL, we can use the information given:
∠J is congruent to ∠L, which means they have the same measure.
∠K is given as 67.8 degrees.
Since ∠J is congruent to ∠L, we can denote their measure as "x".
So, the sum of the measures of ∠J, ∠K, and ∠L is 180 degrees:
∠J + ∠K + ∠L = 180
Substituting the given values:
x + 67.8 + x = 180
Simplifying the equation:
2x + 67.8 = 180
Subtracting 67.8 from both sides:
2x = 180 - 67.8
2x = 112.2
Dividing both sides by 2:
x = 112.2 / 2
x = 56.1
Hence, the measure of ∠L in Triangle JKL is 56.1 degrees.
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can someone help me please.
Reema and Quinton both babysit for extra money. Reema charges $10 per hour and
Quinton charges based on the equation m= 5h + 25. Where h is the number of hours
worked and m is the total amount of money charged. Who would make more money if
they both worked 4 hours?
o Quinton would make $10 more than Reema
O Quinton would make $5 more than Reema
o Reema would make $10 more than Quinton
O Reema would make $5 more than Quinton
On babysitting for four hours, the differently earned money will be Quinton would make $5 more than Reema.
Reema's charge for babysitting for four hours = 10 × 4
Reema's charge = $40
For Quinton, keep the value of hours in expression -
Quinton's charge = 5 (4) + 25
Quinton's charge = 20 + 25
Quinton's charge = $45
As Quinton's charge is greater than Reema, she makes more money.
Amount of more money made by Quinton = 45 - 40
Subtract to find the difference
Amount of more money made by Quinton = $5
Hence, correct answer is Quinton would make $5 more than Reema.
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A triangle shaped table top with an area of 324 square inches has a base of 8x+4 inches and a height of 4x+2 inches. Given the area of a triangle is half of its base times height, what is a reasonable value of x in this situation?
If the area of a triangle is half of its base times height then the reasonable value of x is = 4.
A triangle-shaped table top with an area of 324 square inches has a base of 8x+4 inches and a height of 4x+2 inches. Given that the area of a triangle is half of its base times height, we can use the formula:
Area = (1/2) * base * height
Plug in the given values:
324 = (1/2) * (8x + 4) * (4x + 2)
Now, we need to solve for x. Follow these steps:
1. Multiply both sides of the equation by 2 to get rid of the fraction:
2 * 324 = (8x + 4) * (4x + 2)
2. Simplify the equation:
648 = (8x + 4) * (4x + 2)
3. Expand the equation by multiplying the terms in the parentheses:
648 = 32x^2 + 16x + 16x + 8
4. Combine like terms:
648 = 32x^2 + 32x + 8
5. Move all terms to one side of the equation to set it equal to zero:
32x^2 + 32x - 640 = 0
Now, we need to find a reasonable value of x. You can solve this quadratic equation using factoring, the quadratic formula, or a graphing calculator. Using a graphing calculator, we find that x is approximately 4.
Therefore, a reasonable value of x in this situation is 4.
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