The average speed, in miles per hour, of car X for the 2-hour trip is 56 mph.
The average speed, in miles per hour, of car x for the 2-hour trip is 56 mph.Let’s first identify what the given is.The problem states that car X and car Y started from the same point and traveled on a straight course in opposite directions for 2 hours, at which time they were 208 miles apart. The problem also states that car X traveled, on average, 8 miles per hour faster than car Y.So we have two cars, X and Y, that traveled in opposite directions.
In this problem, we are asked to find the average speed of car X for the 2-hour trip.Let’s use the formula that relates distance, speed, and time. For any given problem, this formula will help us determine which variable we need to solve for.distance = speed × timeSo, in this problem, we know the time and distance, but we need to find the speed.
We can use the information given in the problem to set up an equation for the two cars.Using the formula, we can set up the following equation for car X:dX = speedX × 2Using the same formula, we can set up the following equation for car Y:dY = speedY × 2Since car X traveled, on average, 8 miles per hour faster than car Y, we can write this as speedX = speedY + 8.
Now we know that the sum of the distances that car X and car Y traveled is equal to the total distance that separates them. Using this information, we can set up the following equation:dX + dY = 208To solve for the speed of car X, we need to isolate speedX in the equation that relates speedX and speedY. We can do this by substituting the equation for dX and dY in the equation that relates speedX and speedY.
This gives us the following equation:(speedY + 8) × 2 + speedY × 2 = 208Simplifying this equation, we get:4 speedY + 16 = 2084 speedY = 192speedY = 48 mphNow that we know the speed of car Y, we can use the equation for speedX and speedY to find the speed of car X. This gives us:speedX = speedY + 8 = 48 + 8 = 56 mph.
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f(x) = x + 6 g(x) = 5x Work out the value of gf(3)
Answer:
45
Step-by-step explanation:
[tex]g(f(x))=5(x+6)[/tex]
[tex]g(f(3))=5(3+6)\\[/tex]
[tex]g(f(3))=5(9)\\[/tex]
[tex]g(f(3))=45[/tex]
Answer:
f(x) =x + 6g(x) =5x =
Calculate the formula weights:
mass of mole of
F(x) = x + 6g (x) = 5x = 19g
Jackie purchases a monthly pass to see movies at the theater in order to buy each movie ticket at a discounted rate. The graph shows the costs for different numbers of movie tickets. Find the slope and y-intercept and their meaning.
Fill the blanks.
(A) The slope is $____________ and means that________________
(B) The y-intercept is $________ and means that________________
(A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
What is slope?
Slope is a measure of the steepness of a line. It describes the rate at which the line rises or falls as it moves horizontally, and it is defined as the change in y-coordinates divided by the change in x-coordinates between any two points on the line. Mathematically, slope can be represented as:
Slope = (change in y-coordinates) / (change in x-coordinates)
To find the equation of the line passing through these points, we can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept.
To find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the first two points (1,30) and (3,40) to find the slope:
m = (40 - 30) / (3 - 1) = 10 / 2 = 5
Now we can use any of the given points and the slope to find the y-intercept. Let's use the point (1,30):
y = mx + b
30 = 5(1) + b
30 = 5 + b
b = 30 - 5
b = 25
So the equation of the line passing through the points (1,30), (3,40), (5,50), and (7,60) is:
y = 5x + 25
Therefore, (A) The slope is $5 and means that for each additional movie ticket purchased, the cost increases by $5.
(B) The y-intercept is $25 and means that even if no movie ticket is purchased, there is still a fixed cost of $25.
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bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb
a company plans to manufacture a rectangular box with a square base, an open top, and a volume of 246 in.3. the cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch. determine the dimensions of the box that will minimize the cost of manufacturing it. what is the minimum cost?
The dimensions of the box that will minimize the cost of manufacturing it: base = 9.04 in and y = 3.01 in
And the minimum cost is 32.65 cents
Let us assume that x represents the base side of the box, and y represents the height of the box.
The volume of the box would be:
V = x²y
246 = x²y ........(1)
The cost of the material for the base is 0.2 cents per square inch, and the cost of the material for the sides is 0.3 cents per square inch.
Since this box has 4 sides and 1 base, the total cost would be,
C = (0.2 × x² × 1) + (0.3 × 4 × xy)
C = 0.2x² + 1.2x(246x⁻²) (from (1) y = 246x⁻²)
C = 0.2x² + 295.2 x⁻¹
Consider derivative with respect to x,
dC/dx = 0.4x - 295.2 x⁻²
Consider dC/dx = 0
So, 0.4x - 295.2 x⁻² = 0
0.4x³ = 295.2
x³ = 738
So, x = 9.04
So, the value of y would be:
y = 246 x⁻²
y = 246 × (9.04)⁻²
y = 3.01
So, the minimum cost would be:
C = (0.2 × 0.04² × 1) + (0.3 × 4 × 9.04 × 3.01)
C = 32.65
Therefore, the minimum cost is: 32.65 cents
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Find the exact side length of a square with an area of 9/49 square meters.
Answer:
3/7 meters
Step-by-step explanation:
[tex] \sqrt{ \frac{9}{49} } = \frac{ \sqrt{9} }{ \sqrt{49} } = \frac{3}{7} [/tex]
HELP PLEASE MATH IS HARD
The box plot displays the number of flowers planted in a town last summer. A box plot uses a number line from 6 to 21 with tick marks every one-half unit. The box extends from 10 to 15 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 20. The graph is titled Flowers Planted In Town, and the line is labeled Number of Flowers. Which of the following is the best measure of center for the data shown, and what is that value? The mean is the best measure of center and equals 11. The mean is the best measure of center and equals 12. The median is the best measure of center and equals 11. The median is the best measure of center and equals 12.
After answering the presented question, we can conclude that thus, the equation correct answer is: The median, which equals 11, is the best measure of center.
What box plot represent?The box plot depicts the distribution of the quantity of flowers planted in a town last summer based on the information provided. The box spans the number line from 10 to 15, with a line at 11 inside the box and lines outside the box ending at 7 and 20.
The median is depicted by the line in the box, which is positioned at 11 in the box plot. As a result, the median is the best measure of center for the data provided, and its value is 11.
Thus, the correct answer is: The median, which equals 11, is the best measure of center.
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2,188,180 rounded to nearest tenth
Answer:
2,188,180
Step-by-step explanation:
since 0 can't give anything to 8 the number would stay the same
You made $25,000 last year and spend 20% of your money on food. How much money did you spend on food?
Answer:
$5,000 was spent on food.Step-by-step explanation:
To find:-
Money spent on food .Answer:-
We are here given that, out of the total money made 20% was spent on food .
To calculate the money spent on food we need to find out 20% of $25,00 .
So that,
==> 20% of $25,000
==> 20/100 * $25,000
==> 0.2 * $25,000
==> $5,000
Hence the total money spent on food was $5,000 .
What fraction of 1/2 square centimeter 1/2 centimeter square?
1/4 square centimeter is therefore equal to 1/2 square centimeter.
In math, what is a fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears inside the numerator and denominator of a complex fraction. The numerator of a proper fraction has a smaller denominator.
While "1/2-centimeter square" refers to a square having the side length of half a centimeter, the marking "1/2 square centimeter" typically refers to an area equal half a square centimeter. Even though these aren't the same object, we can still calculate the ratio of one to the other.
The area of such a square of side length 1/2 centimeter is:
(1/2 cm) x (1/2 cm) = 1/4 square centimeter
We may divide 1/4 by 1/2 to determine the percentage of 1/2 square centimeter that corresponds to 1/4 square centimeter:
(1/4 square cm) ÷ (1/2 square cm) = (1/4) x (2/1) = 1/2
Hence, 1/4 square centimeter is equal to 1/2 square centimeter in size.
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If the triangle above is reflected over the y-axis, what is the correct coordinate for A'?
A'(0,5)
A'(2,5)
A'(5,2)
A'(-5, -2)
The coordinate A when the triangle is reflected over the y-axis is (2, 5)
Reflecting the triangle over the y-axisFrom the triangle, we have
A = (-2, 5)
Reflecting a point over the x-axis is a type of transformation that involves flipping the point across the x-axis.
The reflection involves keeping the y-coordinate of the point the same, but changing the sign of the x-coordinate.
In this case, the original point is (-2, 5). To reflect this point over the y-axis, we keep the y-coordinate (5) the same, but change the sign of the x-coordinate to positive,
Resulting in the reflected point (2, 5).
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find the area of the image below
Edin has £300 in his savings account. His bank offers him a fixed 5% simple interest rate per annum, for a period of 3 years. How much interest will he have earned after 3 years?
Answer:
$45
Step-by-step explanation:
Interest earned in a year
5/100x300= $15
Interest earned in 3 years
=$15x3
=$45
Solve the system of inequalities 2x +y >3 and x- 2y 5- 1
The system of inequalities "2x – y > 1 and x – 2y < –1." are graphically shown below in the image section.
Inequalities in mathematics describe the connection between two non-equal values. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, a number of inequality comparisons are made to determine whether one value is greater than or less than another. The various inequality symbols, their meanings, and methods for solving them will all be covered in this article using examples of both one- and two-variable linear inequalities. We'll also discuss the algebraic inequalities that are commonly used.
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—------ CORRECT QUESTION FORMAT IS GIVEN BELOW - - - - - -
(Q). Solve the following system of inequalities graphically: 2x – y > 1 and x – 2y < –1.
The number of air conditioner units that 10 sales representatives sold last year are:
{6, 8, 10, 11, 12, 16, 17, 21, 32, 36}
How is the mean effected if the representative who sold the lowest number of units left the department, causing his sales to cancel out?
Responses:
The mean would increase.
The mean would remain the same.
The mean would decrease.
The correct option is (a), i.e. The mean would increase.
What is mean?
Mean is a measure of central tendency that is commonly used in statistics and mathematics. The mean of a set of numbers is calculated by adding up all the numbers in the set and dividing the sum by the total number of values in the set.
The mean of the number of air conditioner units sold by the 10 sales representatives last year can be calculated by adding up all the sales and then dividing by the total number of representatives, which is 10:
Mean = (6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36) / 10
= 169 / 10
= 16.9
So the mean number of air conditioner units sold per representative is 15.9.
If the representative who sold the lowest number of units left the department and his sales are cancelled out, the new sum of sales will be:
6 + 8 + 10 + 11 + 12 + 16 + 17 + 21 + 32 + 36 - 6 = 163
This is because we subtract the sales of the representative who left (which is 6 units in this case). The new mean can then be calculated by dividing this sum by the new total number of representatives, which is 9:
New mean = 163 / 9
= 18.11
So the new mean number of air conditioner units sold per representative is 18.11, which is higher than the original mean of 16.9. This is because removing the lowest value (which is smaller than the mean) increases the overall average.
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The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α
= 0.01 is:
A) 2.33
B) 2.96
C) 2.05
D) 2.575
The critical value for a two-tail hypothesis test when the population standard deviation is known, the sample size is 30 or more, and α = 0.01 is 2.575. The right option is (D).
What is a hypothesis test?In statistics, a hypothesis test is an examination of a particular hypothesis regarding a population parameter with the help of data from a sample. Hypothesis testing is a statistical method used to make decisions about a population based on a sample's data.
The following are the four stages of hypothesis testing:
1. Formulation of Hypothesis
2. Selection of a Significance Level
3. Calculation of Test Statistics
4. Acceptance or Rejection of the Null Hypothesis
The critical value for a two-tail hypothesis test is 2.575 when the sample size is greater than or equal to 30, the population standard deviation is known, and the significance level is α=0.01.
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if f(x)=1-2x then what is 2f(x)
functions
The given function is f(x) = 1 - 2x.
To find 2f(x), we simply multiply the function f(x) by 2:
2f(x) = 2(1 - 2x)
Distributing the 2 across the expression, we get:
2f(x) = 2 - 4x
Therefore, 2f(x) = 2 - 4x.
find the equation of the straight line passinh throigh (3,5) and making x-intercept 3 times the y-intercept.
After answering the presented question, we can conclude that As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is: 5x - 9y = -42
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
To find a straight line's equation, we must first establish its slope and y-intercept.
[tex](y - 5) = m(x - 3) (x - 3)\\b - 5 = -3m\\[/tex]
When we solve for b, we get:
[tex]b = -3m + 5\\5 - 5 = m(3 - 3) (3 - 3)\\0 - 5 = m(3b - 3) (3b - 3)\\-5 = 3bm - 3m\\[/tex]
When we simplify, we get:
[tex]m = 5/(9b) (9b)\\[/tex]
Substituting this expression for m in the equation for the y-intercept b results in:
[tex]b = -15/(9b) + 5\\9b^2 = -15b + 45b\\9b^2 - 30b = 0\\3b(3b - 10) = 0\\b = 10/3\\(y - 5) = m(x - 3) (x - 3)\\(y - 5) = 5x/(9*10) - 1/3\\9y - 45 = 5x - 3\\5x - 9y = -42\\[/tex]
As a result, the equation of the straight line passing through (3,5) and having an x-intercept three times the y-intercept is:
5x - 9y = -42
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I NEed HELP ON THIS ASAP!
Answer:
length times with equals to base times height
Step-by-step explanation:
length times with times height equals to 3400
What is the answer in the photo
The sale price of the reusable water bottle is $18.
Describe Algebra?Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating these symbols. It is a broad area that includes various subfields such as elementary algebra, abstract algebra, and linear algebra, among others.
In elementary algebra, the focus is on the basic rules and operations involving variables, numbers, and equations. These concepts are used to solve problems in a wide range of fields, such as science, engineering, and finance. Abstract algebra, on the other hand, deals with the study of algebraic structures such as groups, rings, and fields. Linear algebra is the study of vector spaces and linear transformations, and is used extensively in fields such as computer science, physics, and engineering.
The discount on the reusable water bottles is 10%, which means that the customer pays only 90% of the regular price. To find the sale price, we can multiply the regular price by 90% or 0.9.
Sale price = Regular price x (1 - Discount rate)
Sale price = $20 x (1 - 0.1)
Sale price = $20 x 0.9
Sale price = $18
Therefore, the sale price of the reusable water bottle is $18.
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in a sample of 500 customers, 140 say that service is poor. you select two customers without replacement to get more information on their satisfaction. what is the probability that both say service is poor?
The probability that both customers say that the service is poor is 0.0588 or 5.88%.
To determine the probability that both customers say the service is poor, use the binomial distribution and the following formula:P(X = k) = (nCk) * p^k * (1 - p)^(n - k)Where:P(X = k) represents the probability that k successes occurn is the sample sizep is the probability of successk is the number of successes requested(1 - p) represents the probability of failure.Substitute the given values and calculate:P(X = 2) = (2C2) * (140/500)^2 * (1 - 140/500)^(2 - 2) = 0.0588 or 5.88%
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Maria needs to wraps the box shown below with no overlap of the wrapping paper. How much wrapping paper does she need?
As each side of the cube has a surface area of 24in².the total amount of wrapping paper needed is 64in².
What is surface area?Surface area is the total area of a three-dimensional object's surface, including the area of its faces and any curved surfaces.
To calculate the amount of wrapping paper needed for the cube, we can use the formula for the surface area of a cube:
SA = 6 x (side)²
In this case, the side of the cube is 2in,
so the SA = 6 x (2in)² = 24in²
To get the amount of wrapping paper needed, we would need to multiply this by 4, as each side of the cube has a surface area of 24in².
Therefore, the total amount of wrapping paper needed is
24in² x 4 = 96in²
To convert this to a square, we would need to divide it by 4, as each side of the square is equal in length.
Therefore, the total amount of wrapping paper needed is
96in² / 4
= 24in x 4
= 64in².
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Bob's dog, Buster, is a finicky eater. Bob is trying to determine which of two brands of
canned cat food Buster prefers, Busted Nuggets or Busted Tenders. For two months, he
flips a coin each day to decide which of the two foods to feed Buster, and weighs how
much Buster eats (in grams). Here are the data:
Dog Food
n X
S
Busted Nuggets 31 152.6 4.45
Busted Tenders 31 163.7 5.75
Construct and interpret a 98% confidence interval for the difference in mean amount of
food Buster eats when he is offered Busted Nuggets and when he is offered Busted
Tenders.
We can be 98% cοnfident that the true difference in mean amοunt οf fοοd Buster eats when οffered Busted Nuggets and Busted Tenders is between -14.566 and -7.634 grams
Hοw tο cοnstruct cοnfidence interval?Calculate the sample mean difference and the standard errοr οf the difference in οrder tο build the cοnfidence interval fοr the difference in the mean amοunt οf fοοd that Buster cοnsumes when served Busted Nuggets and Busted Tenders.
The sample mean difference is:
X1 - X2 = 152.6 - 163.7 = -11.1 grams.
The standard errοr οf the difference can be calculated as fοllοws:
SE = √(S1²/n1 + S2²/n2)
where S1 and S2 are the sample standard deviatiοns οf the twο grοups and n1 and n2 are the sample sizes.
Substituting the values, we get:
SE = √(4.45²/31 + 5.75²/31) = 1.463
ME = t x (SE) = 2.365 x 1.463 = 3.466
Finally, the cοnfidence interval fοr the difference in mean amοunt οf fοοd Buster eats is:
-11.1 - 3.466 < µ1 - µ2 < -11.1 + 3.466
-14.566 < µ1 - µ2 < -7.634
Hence, we have a 98% cοnfidence level that Buster actually cοnsumes between -14.566 and -7.634 grammes less fοοd οn average when given the chοice between Busted Nuggets and Busted Tenders. This periοd can be understοοd as Buster favοring Busted Tenders because οf the negative.
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2.8 is what percent of 2.24
in how many ways can we list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions?
There are 144 ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions.
We have to list the digits {1, 1, 2, 2, 3, 4, 5} so that two identical digits are not in consecutive positions. We can use the knowledge of permutations and combinations to solve this problem. We can start by selecting the positions for the distinct digits, i.e., (3, 4, 5). There are 3 distinct digits, so there are 3! = 6 ways to arrange them.
Once we have placed the distinct digits, we can place the two 1's and two 2's in the remaining positions such that no two identical digits are in consecutive positions. To do this, we can use the following approach:
We can start by placing one of the 1's. There are 4 positions available for the first 1.
We can then place one of the 2's. There are 3 positions available for the first 2.
We can then place the second 1. There are 2 positions available for the second 1.
We can then place the second 2. There are 1 positions available for the second 2.
Therefore, the total number of ways to list the digits {1, 1, 2, 2, 3, 4, 5} such that two identical digits are not in consecutive positions is:
6 (arrangements of distinct digits) x 4 x 3 x 2 x 1 = 144.
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Question
Julio buys a salad and a container of yogurt. These bills and coins represent the cost of each item.
How much did Julio spend in all?
The total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.
To determine how much Julio spent while buying a salad and a container of yogurt, we have to multiply the value of each notes into their quantity then add all of them.
Number of 25 cents coins = 4
⇒ 4×0.25 = 1.00
Number of 5 dollar note = 1
⇒ 1×5 = 5.00
Number of 10 cents coins = 3
⇒ 3×0.10=0.30
Number of 1 cents = 3
⇒ 3×0.01=0.03
Number of 5 cents = 1
⇒ 1×0.05=0.05
Julio spent = 1.00 + 5.00 + 0.30 + 0.03 + 0.05
= $6.38
Therefore, the total amount Julio spent on a salad and a container of yogurt in the form of note and coin is equal to $6.38.
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The complete question is :
Julio buys a salad and a container of yogurt. These bills and coins shown in attached image represent the cost of each item. How much did Julio spend in all?
[Questions in image]
Answer:
tesla electric company:
hours :cost
0:$50
1:$ 75
2: $100
3: $125
4: $150
Ac-Ad electric
hours: cost
0: $0
1: $50
2: $100
3: $150
4: $200
The temperature at 8 P.M. was - 6.8 degrees Celsius. • Between 8 P.M. and 10 P.M., the temperature change was -3.9 degrees Celsius. • The temperature change was -4.4 degrees Celsius between 10 P.m. and midnight. What was the temperature at midnight?
Using mathematical operations we can conclude that the temperature at the midnight was -15.1°C.
What are mathematical operations?A rule that specifies the right procedure to follow while evaluating a mathematical equation is known as the order of operations.
The rules that specify the order in which we should solve an expression involving many operations are known as the order of operations.
PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction (from left to right).
So, we can solve for the temperature as follows:
8 pm = -6.8
8 - 10 pm = -6.8 -3.9 = -10.7
10 - 12 midnight = -10.7 -4.4 = -15.1°C
Therefore, using mathematical operations we can conclude that the temperature at the midnight was -15.1°C.
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alana is making a ball out of rubber bands. when the ball has 54 rubber bands, it has a diameter of 3 cm. how many rubber bands should alana add to the ball to increase its diameter by 1 cm? assume that all of alana's rubber bands have the same volume.
The number of rubber bands that Alana has to add to the ball to increase its diameter by 1 cm is 74.
Given that:
Alana is making a ball out of rubber bands.
The volume of the ball with 54 rubber bands is found as below:
Diameter of the ball = 3 cm
The radius of the ball is half of the diameter.
So, radius, r = 1.5 cm
So, the volume of the ball formed by 54 rubberbands is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Substitute r = 1.5.
[tex]V=\frac{4}{3} \pi (1.5)^3[/tex]
[tex]V=4.5\pi[/tex]
Now, the volume of the ball formed by 1 rubber band or the volume of the rubber band is:
[tex]V(r)=\frac{4.5\pi }{54}[/tex]
[tex]V(r)=\frac{\pi }{12}[/tex]
When the diameter increased by 1 cm, the new diameter is 4 cm and thus the radius is 2 cm.
So, the increase in volume is:
[tex]\frac{4}{3} \pi (2)^3-\frac{4}{3} \pi (\frac{3}{2} )^3=\frac{37\pi }{6}[/tex]
Now, divide this by the volume of one rubber band to get the number of rubber bands to be added.
[tex]\frac{\frac{37\pi }{6}}{\frac{\pi }{12} } =74[/tex]
Hence, the number of bands added is 74.
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119. What is the linear equation for the pricing formula for Logan's Paint? One gallon cost $11 (1,11) and 5 gallons cost $35 (5, 35).
The linear equation is y = 6x + 5
Define the term equation?A statement that shows the equality of two mathematical expressions is known as an equation. The goal is typically to ascertain the values of the variables that keep the equation true, and it may have one or more variables. In that both sides must be equal for an equation to hold true, it might be likened to a balance scale.
To find the equation for the pricing formula, we can use the slope-intercept form of a linear equation:
y = mx + b
where y is the cost, x is the number of gallons, m is the slope (i.e., the rate of change of the cost per gallon), and b is the y-intercept (i.e., the cost when x = 0).
Using the given information, we can calculate the slope:
m = (35 - 11) / (5 - 1) = 24 / 4 = 6
The y-intercept can be found by plugging in one of the points:
11 = 6(1) + b
b = 5
Therefore, the linear equation for the pricing formula for Logan's Paint is:
y = 6x + 5
where y is the cost in dollars and x is the number of gallons.
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Does anyone know how to answer this?
The probability that Esteban wins the game is 29/49.
What does probability mean?Probability is a concept that refers to the likelihood of a particular event occurring. It is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Let's consider an example: Esteban is playing a matching card game where he wins if the cards are identical. To calculate the probability of winning, we can use the following formula:
Probability of winning = Number of favorable outcomes / Total number of possible outcomes
If we assume that the deck of cards contains seven crosses and seven stars, the probability of getting a cross on both cards is:
2/7 x 2/7 = 4/49
The probability of getting a star on both cards is:
5/7 x 5/7 = 25/49
To calculate the overall probability of winning the game, we add the probabilities of getting a cross on both cards and getting a star on both cards:
4/49 + 25/49 = 29/49
Therefore, the probability that Esteban will win the game is 29/49.
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What is the probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards?
a) 0.17583334
b) 0.00000026
c) 0.00000214
d) 0.00000029
e) 0.00000016
The probability that 3 hearts are chosen if 7 cards are chosen from a well-shuffled deck of 52 playing cards is option (c) 0.00000214.
The probability of selecting exactly 3 hearts if 7 cards are chosen from a well-shuffled deck of 52 playing cards can be calculated using the hypergeometric distribution.
The total number of ways to choose 7 cards from 52 is given by the combination C(52,7), which is the total number of possible outcomes.
The number of ways to choose 3 hearts and 4 non-hearts is given by the product of the number of ways to choose 3 hearts from 13 and the number of ways to choose 4 non-hearts from 39. That is:
C(13,3) [tex]\times[/tex] C(39,4)
Therefore, the probability of selecting exactly 3 hearts is:
P(3 hearts) = [C(13,3) [tex]\times[/tex] C(39,4)] / C(52,7)
Calculating this probability gives:
P(3 hearts) ≈ 0.00000214
Therefore, the correct answer is option (c).
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