The velocity of the bowling ball is approximately 20.104 meters per second.
What is velocity?The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity.
The formula given is used to calculate the velocity of a moving object in meters per second, given the object's mass in kilograms and its kinetic energy in joules. The formula is:
V = √(2E/m)
where V is the velocity, E is the kinetic energy, and m is the mass of the object.
To use this formula to find the velocity of the bowling ball, we need to substitute the given values into the formula. The mass of the bowling ball is 5.5 kilograms, and the kinetic energy is 2223 joules. Substituting these values, we get:
V = √(2 × 2223 J / 5.5 kg)
Now, we can simplify the equation:
V = √(404.1818)
Using a calculator, we can find the square root of 404.1818:
V = 20.104 m/s (rounded to three decimal places)
Therefore, the velocity of the bowling ball is approximately 20.104 meters per second.
This formula is useful for calculating the velocity of a moving object when the mass and kinetic energy of the object are known. It can be used in a variety of situations, such as in physics experiments, engineering design, or in understanding the motion of objects in sports.
To learn more about velocity click:
https://brainly.com/question/80295?source=archive
#SPJ1
Graph: 3y = 6
-
-6 -4 -2
6
4
2
-2
त्र
-6
y
2 4
st
Click or tap the graph to plot a point.
6
X
४
Draw
y
Given the diagonals of square ABCD intersect at M. If the measure of
The value of x is 17.5 when the given diagonals of square ABCD points intersect at M and the measure 0f <MAD = 6x-15.
The diagonals are perpendicular bisectors of each other in a square and they intersect at the center of the square. By using diagonals we can divide the square into four congruent right triangles and assume that diagonals are all right angles (90 degrees).
let us consider the angle MAD as one of these angles. we can find the value of x by using the equation
6x - 15 = 90
6x = 105
x = 105/6
= 17.5.
Therefore, the value of the x is 17.5.
To learn more about the diagonals:
https://brainly.com/question/28164360
#SPJ4
The complete question is,
Given the diagonals of square ABCD points intersect at M: If the measure 0f <MAD = 6x-15, find the value of x Show the work that justifies your answer: M B Your answer
Find the slope of the line through points 6,3 and 12,7
The slope of the line through points (6,3) and (12,7) is 2/3.
To find the slope of a line, we use the formula:
Slope = (y2 - y1) / (x2 - x1)
In this case, we have two points: (6, 3) and (12, 7). We can label them as follows:
x1 = 6
y1 = 3
x2 = 12
y2 = 7
Now we can plug these values into the formula:
Slope = (y2 - y1) / (x2 - x1)
Slope = (7 - 3) / (12 - 6)
Slope = 4 / 6
Slope = 2/3
Therefore, the slope of the line through the points (6, 3) and (12, 7) is 2/3.
The slope of a line tells us how steep it is. A positive slope means the line goes up as you move from left to right, while a negative slope means the line goes down. In this case, since the slope is positive (2/3), we know that the line goes up as we move from left to right.
The slope also tells us how much the y-value changes for every one unit of x-value. In this case, for every one unit we move to the right, the y-value goes up by 2/3.
To learn more about slope of the line refer here
https://brainly.com/question/14511992#
#SPJ11
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?
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.
To learn more about liter: https://brainly.com/question/24686351
#SPJ11
All-star trinkets estimates its monthly profits using a quadratic function. the table shows the total profit as a function of the number of trinkets produced. which function can be used to model the monthly profit for x trinkets produced? f(x) = –4(x – 50)(x – 250) f(x) = (x – 50)(x – 250) f(x) = 28(x 50)(x 250) f(x) = (x 50)(x 250)
The function used to model the monthly profit for x trinkets produced are f(x) = -4(x - 50)(x - 250). The maximum profit occurs when 150 trinkets are produced.
The quadratic function that can be used to model the monthly profit for x trinkets produced is:
f(x) = -4(x - 50)(x - 250)
This is because the function is in the form of a quadratic equation, which is y = ax² + bx + c. In this case, a = -4, b = 1200, and c = 0. When we expand and simplify the equation, we get:
f(x) = -4x² + 1200x
This equation represents a parabola with a maximum value at x = 150. Therefore, the maximum profit occurs when 150 trinkets are produced.
The other answer choices are not correct because they are not quadratic functions. For example, f(x) = (x - 50)(x - 250) is a product of linear factors, and f(x) = 28(x - 50)(x + 250) and f(x) = (x + 50)(x + 250) have a coefficient of x² that is not equal to -4.
Know more about profit here:
https://brainly.com/question/15699405
#SPJ11
25 acres of a forest is covered by coniferous trees. The remaining are shrubs and bushes which constitutes 42% of the total area of the forest. What is the total area of under the forest?
Therefore, the total area of the forest is approximately 43.10 acres.
What is area?Area is the measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters (m²) or square feet (ft²). The area of a shape can be calculated by multiplying the length and the width of the shape. Different shapes have different formulas for calculating their area, such as the formula for the area of a rectangle, which is length x width, or the formula for the area of a circle, which is πr², where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14159.
Here,
Let's call the total area of the forest "T".
We know that 25 acres of the forest is covered by coniferous trees. Therefore, the remaining area of the forest is:
T - 25
We also know that the shrubs and bushes constitute 42% of the total area of the forest. This means that:
0.42 x T = area covered by shrubs and bushes
Putting it all together, we can set up the following equation:
T = 25 + (0.42 x T)
Simplifying, we can solve for T:
0.58 x T = 25
T = 25 / 0.58
T = 43.10 acres (rounded to two decimal places)
To know more about area,
https://brainly.com/question/13194650
#SPJ1
Kyla has a concrete patio in the shape of a semi-circle. What is the area of the patio? Use 3. 14 for π. It’s s i circle and is 6. 75 ft and in squared
The area of the semi-circle patio is approximately 17.91 square feet.
To find the area of the semi-circle patio, we need to use the formula for the area of a circle, which is A = πr^2, where π is 3.14 and r is the radius of the circle.
However, since we only have a semi-circle, we need to divide the result by 2 to get the area of the half-circle.
In this case, the radius of the semi-circle is half of the diameter, which is given as 6.75 feet. So, the radius is 6.75/2 = 3.375 feet.
Now, we can plug this value into the formula:
A = (π)(3.375)^2 / 2
A = (3.14)(11.390625) / 2
A = 35.81765625 / 2
A = 17.908828125 square feet
Therefore, the area of the semi-circle patio is approximately 17.91 square feet.
To learn more about radius, refer below:
https://brainly.com/question/13449316
#SPJ11
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.
Learn more about expression -
https://brainly.com/question/723406
#SPJ4
ANALYZE In Europe, fuel economy is measured in liters per 100 kilometers. On a 2500 km road trip a car used 150 liters of fuel. The car used an average of how many liters per 100 km?
To find out the car's average fuel consumption in liters per 100 kilometers, we need to use the following formula:
Fuel consumption (liters per 100 km) = (Total fuel used / Total distance traveled) x 100
Using the information given, we know that the car traveled 2500 km and used 150 liters of fuel. Plugging these values into the formula, we get:
Fuel consumption (liters per 100 km) = (150 / 2500) x 100 = 6
Therefore, the car used an average of 6 liters of fuel per 100 kilometers on its 2500 km road trip.
It is important to note that fuel economy is an important factor in Europe, where fuel prices are generally higher than in other parts of the world.
By measuring fuel consumption in liters per 100 kilometers, European consumers can easily compare the fuel efficiency of different vehicles and make more informed purchasing decisions.
Additionally, analyzing fuel consumption data can help drivers identify ways to improve their fuel efficiency, such as reducing their speed, maintaining proper tire pressure, and avoiding excessive idling.
This not only saves money on fuel costs, but also reduces carbon emissions and contributes to a more sustainable transportation system.
To know more about average fuel consumption refer here
https://brainly.com/question/24625535#
#SPJ11
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.
for such more question on distances
https://brainly.com/question/7243416
#SPJ11
algebra 2 PLEASE if you know
The system of inequalities that has a solution set that is a line is [x + y ≥ 3; x + y ≤ 3]; option A
What is a system of inequalities?A system of inequalities is a set of two or more inequalities that are solved simultaneously to find the values of variables that satisfy all the inequalities in the system.
Considering the given system of inequalities:
The system of inequalities that has a solution set that is a line is:
[x + y = 3;]
This is because the solution set of this equation is a line with slope -1 passing through the point (3, 0) and (0, 3).
Therefore, the system of inequalities [x + y ≥ 3; x + y ≤ 3] has a solution set that is a line.
Learn more about inequalities at: https://brainly.com/question/24372553
#SPJ1
1) harriett has a cylindrical pool with a diameter of 11 feet and a height of 2 feet.
the inside of the pool is lined with a plastic material. how many square feet of plastic material does the pool have? use 3.14 for pi. round your answer to the nearest tenth.
please help me because i really need with this question <3
The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.+
To calculate the surface area of the pool that is lined with plastic material, we need to find the area of the curved part and the area of the top and bottom circles.
First, let's find the radius of the pool, which is half of the diameter:
radius = 11 feet / 2 = 5.5 feet
The curved part of the pool is a cylinder with a height of 2 feet and a circumference of [tex]2 * π *radius:[/tex]
curved area = height * circumference
[tex]curved area = 2 feet * 2 * 3.14 * 5.5 feet[/tex]
[tex]curved area = 68.2 square feet[/tex]
The top and bottom of the pool are two circles with a radius of 5.5 feet:
circle area = π * radius²
[tex]circle area = 3.14 * 5.5 square feet[/tex]
[tex]circle area = 95.0 square feet[/tex]
To find the total surface area of the pool that is lined with plastic material, we add the area of the curved part and the area of the top and bottom circles:
Total area = curved area + 2 * circle area
Total area = 68.2 square feet + 2 * 95.0 square feet
Total area = 258.2 square feet
The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.
To know more about surface area refer here
https://brainly.com/question/8389124#
#SPJ11
Kevin needs 2/3 of a yard to make a pillow. He has 3 1/3 yards of fabric. How many pillows can he make? A). 2 2/9 B. ) 3 2/3 C. ) 5 D. ) 6
The number of pillows requiring [tex]\frac{2}{3}[/tex] yards that can be made from [tex]3\frac{1}{3}[/tex] yards is 5. Thus the right answer to the given question is C.
Material required for making one pillow = [tex]\frac{2}{3}[/tex] yards
Total material = [tex]3\frac{1}{3}[/tex] yards
To find the number of pillows made we have to divide the material required for one pillow by the total material available to Kevin for making pillows
Number of pillows = [tex]3\frac{1}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]
= [tex]\frac{10}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]
To divide two fractions, we take the reciprocal of the second number and multiply it by the first number.
= [tex]\frac{10}{3}[/tex] * [tex]\frac{3}{2}[/tex]
= 5
Thus, the number of pillows made is 5.
Learn more about Division:
https://brainly.com/question/28722090
#SPJ4
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.
Learn more about teaspoons in: https://brainly.com/question/25928464
#SPJ1
I’m having trouble with this
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
Learn more about length of triangle here: https://brainly.com/question/24597672
#SPJ1
Make 20 questions subtraction and addition of fractions only like this
e. G saina ,anika and mercy got some money saina got 1/6 and mercy got 3/4 and anka got the rest
a. Caculate the fraction of saina and mercy
b. What is anika s share in fractions
c. How much was the money
you can use money,fruits or any thing
due 24/04/22
20 questions subtraction and addition of fractions only like this:
A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?
John had 3/4 of a pizza and gave 1/3 of it to his friend. What fraction of the pizza does John have left?If 2/5 of a cake is chocolate and 1/5 is vanilla, what fraction of the cake is another flavor?If Tom can run 5/6 of a mile in 4 minutes, how many minutes will it take him to run 1 mile?If 3/8 of a bag of apples is rotten, what fraction of the bag is not rotten?A store had 5/6 of its shelves stocked with books. If 1/4 of the books were science books, what fraction of the shelves were stocked with science books?If Maria has 3/8 of a tank of gas and she uses 1/4 of it to drive to work, what fraction of the tank is left when she arrives at work?A recipe calls for 1/3 cup of sugar and 1/4 cup of butter. What is the total amount of sugar and butter needed in fraction?If 2/3 of a box of crayons is blue and 1/4 of the box is red, what fraction of the box is another color?If a recipe calls for 3/4 cup of milk and you have only 1/2 cup, what fraction of milk do you need to buy to have enough?If a school has 7/8 of its students enrolled in math and 3/4 of those enrolled in math are also enrolled in science, what fraction of the school is enrolled in both math and science?A store had 1/2 of its apples on sale for 1/4 off. What fraction of the original price did a customer pay for a discounted apple?If a train travels 1/2 of a mile in 2 minutes, how long will it take to travel 1 mile?A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?If a recipe calls for 3/4 cup of oil and you have only 1/3 cup, what fraction of oil do you need to buy to have enough?If 3/8 of a class is girls and 2/5 of the girls have brown hair, what fraction of the class is girls with brown hair?If a recipe calls for 1/2 cup of brown sugar and 1/4 cup of white sugar, what is the total amount of sugar needed in fraction?If a store sells 3/4 of a bag of apples and has 2/3 of a bag left, what fraction of the original bag is left?If a car travels 3/4 of a mile in 2 minutes, how long will it take to travel 1 mile?If a recipe calls for 1/3 cup of butter and you have only 1/6 cup, what fraction of butter do you need to buy to have enough?If a recipe calls for 1/4 cup of honey and 1/3 cup of sugar, what is the total amount of honey and sugar needed in fraction?To know more about fractions, refer to the link below:
https://brainly.com/question/29092269#
#SPJ11
(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.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ1
The Rialto Theater sells balcony seats for $10 and main floor seats for
$25. One afternoon performance made $6250. The number of balcony
seats sold was 20 more than 3 times the number of main floor seats. Write
the system of equations to determine the number of main floor and
balcony seats.
The system of equations is:
Revenue from balcony seats = $10 × B
Revenue from main floor seats = $25 × M
Total revenue = $6250
B = 3M + 20
Let's define the following variables:
B = number of balcony seats sold
M = number of main floor seats sold
We know that the price of a balcony seat is $10 and the price of a main floor seat is $25.
From the given information, we can create the following equations:
The total revenue from balcony seats sold (B) is given by: Revenue from balcony seats = $10 × B
The total revenue from main floor seats sold (M) is given by: Revenue from main floor seats = $25 × M
The total revenue from the afternoon performance is $6250: Total revenue = Revenue from balcony seats + Revenue from main floor seats
The number of balcony seats sold (B) is 20 more than 3 times the number of main floor seats (M): B = 3M + 20
To know more about system of equations, refer here:
https://brainly.com/question/20067450
#SPJ11
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.
To know more about capítulos refer here
https://brainly.com/question/26166308#
#SPJ11
In a group of 20 people, 13 people like tea, 12 people like coffee and 3 people like neither tea nor coffee. How many people like tea but not coffee?
Answer:
8 people
Step-by-step explanation:
Tea- 13 people
Coffee- 12 people
Neither- 3 people
20 - 3 = 17
12 + 13 = 25
25 - 17 = 8
the operation manager at a tire manufacturing company believes that the mean mileage of a tire is 37,014 miles, with a standard deviation of 4617 miles. what is the probability that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires if the manager is correct? round your answer to four decimal places.
Probability or p-vale that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires is equals to zero if the manager is correct.
We have data of an operation manager at a tire manufacturing company.
Mean mileage of a tire, [tex] \mu[/tex]
= 37,014 miles
standard deviation, [tex] \sigma[/tex]
= 4617 miles.
Sample size, n = 56
We have to determine the probability that the sample mean would differ from the population mean by less than 221 miles. Using Z-score formula in normal distribution, [tex]\small z= \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}},[/tex]
Plugging all known values in above formula, [tex]z = \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}[/tex]
= 59.634
[tex]P( \bar x < 221) = P ( \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}} < \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}) \\ [/tex]
=> P ( z < 59.63) = P( \bar x < 221)
Using the Z-distribution table, probability value is equals to 0. Hence, required probability is zero.
For more information about P-value, refer:
https://brainly.com/question/4621112
#SPJ4
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.
To know more about average speed, refer here:
https://brainly.com/question/10449029
#SPJ11
Peter had to solve a puzzle.which mathematical symbol can be placed between 5 and 9, to get a numbergreater than 5, but less than 9?
To get a number greater than 5,but less than 0, Peter can use the mathematical symbol of a decimal point (.) to solve this puzzle.
If Peter places decimal point between 5 and 9, he can get a number like 5.1, 5.2, 5.3... up to 8.9, which meets the conditions of being greater than 5 but less than 9.
A decimal point (.) is a mathematical symbol. When this decimal point is placed in between two numbers, suppose x and y, then x.y means x.y is greater than x and less than y.
So to solve the puzzle, Peter can use decimal point.
To learn more about puzzle: https://brainly.com/question/30209521
#SPJ11
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.
To learn more about scale click on,
https://brainly.com/question/23864395
#SPJ4
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
Read more about Trigonometric Ratios at: https://brainly.com/question/13276558
#SPJ4
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.
#SPJ1
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).
Learn more about Reflection here
https://brainly.com/question/31873964
#SPJ4
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.
To know more about cuboid, visit:
https://brainly.com/question/29568631#
#SPJ11