Answer : The sixth term in the binomial expression is, [tex]^{10}C_5a^{5}b^{5}[/tex]
Step-by-step explanation :
The general formula to calculate the term of binomial expression is:
[tex]T_(r+1)=^nC_ra^{(n-r)}b^r[/tex]
where,
(r+1) = number of term
As we are given the binomial expression :
[tex](5y+3)^{10}[/tex]
For sixth term :
a = 5y
b = 3
n = 10
As, r + 1 = 6
So, r = 6 - 1
r = 5
Now put all the given values in the above formula, we get:
[tex]T_(r+1)=^nC_ra^{(n-r)}b^r[/tex]
[tex]T_(5)=^{10}C_5a^{10-5}b^5[/tex]
[tex]T_(5)=^{10}C_5a^{5}b^{5}[/tex]
Thus, the sixth term in the binomial expression is, [tex]^{10}C_5a^{5}b^{5}[/tex]
Can someone help me on both of the questions?!
Step-by-step explanation:
The expression for the pressure in terms of force is as follows;
[tex]P= \frac{F}{A}[/tex]
Here, F is the force, P is the pressure and A is the area.
It is given in the problem that an object exerts 140 N of force on a surface that has an area of 2.0 meter square.
Put F= 140 N and A= 2 meter square in the above expression.
[tex]P= \frac{140}{2}[/tex]
[tex]P= 70 N/m^2[/tex]
Therefore, the pressure exerts on the object is 70 N/m^2.
The motion of air particles inside an inflated balloons:
In the inflated balloons, the molecules of air are far apart. These molecules are in random motion. They collide each other inside the surface of the balloons. The pressure will be exerted by the air molecules on the surface of the balloons. The pressure caused by atmospheric molecules collides with the outside the surface is equal to the pressure caused by atmospheric molecules collides with inside the surface of the inflated balloons. Therefore, the volume of the balloons remains constant.
A party is thrown where 25 tables are used. Each table either sits 4people or 6 people. A total of 116 people can be sat at the tables.
1- if f represent the number of four person tables and s represents the number of six person tables, write a system of equations that models this equation.
2- how many six person tables are there?
Which sentence best describes the function shown?
A) The function is odd.
B) The function is even.
C) The function is symmetric about the x-axis.
D) The function is symmetric about the origin.
Answer:
B) The function is even.
Step-by-step explanation:
The function shown in the graph is ƒ(x) = |x|. This function is symmetric about the y-axis and is therefore, even.
In simple words: If you fold the picture in half then the lines should be on top of each other and become one. If this happens, then this is an even function.
What is the differencence betwenn the volume
The area of the triangle shown is represented by A= square root of s(s-10)(s-7)(s-5), where s is equal to half the perimeter. What is the height of the triangle? Round your answer to the nearest tenth.
There are 52 blades of grass in 2 in2 of lawn. There are 580 blades of grass in 8 in2 of the same lawn. Which equation models the y blades of grass found in x in2 of lawn?
The equation that models the relationship between the number of blades of grass (y) and the area of lawn (x) is y=88x−124. This equation represents the rate of 88 blades per square inch with an initial count of 52 blades.
To find the equation that models the relationship between the number of blades of grass (y) and the area of lawn (x), we can use the given information to form a linear equation.
Step 1: Determine the rate of change. Subtract the initial number of blades from the final number and divide by the change in area: (580 - 52) / (8 - 2) = 528 / 6 = 88 blades per square inch.
Step 2: Write the equation in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Step 3: Plug in the slope (m = 88) and one point (x = 2, y = 52) to find the y-intercept:
52 = 88(2) + b
52 = 176 + b
b = -124
Step 4: Write the equation:
y = 88x - 124
Does 60, 63, 87 form a right triangle
You are playing a game and it is your turn to spin the spinner shown. There are four possible results: blue, green, yellow, or purple. What is the probability that you land on purple?
You have a 25% chance on landing on any of the colors
You Look at all of the possible ways you can land on which is purple, Blue, Green, and Yellow there are four colors in the spinner if you divide the number of colors (4) and divide it by 100 you will get 25 and that is your answer
At a certain time of day, a 30-foot building casts a 10 foot shadow. How tall is a person who casts a 2 foot shadow?
A. 4 feet
B. 5 feet
C. 6 feet
D. 7 feet
A cube-shaped item needs to be painted. The item’s edge length is 2 centimeters. What is the total surface area that will be painted? 16 cm² 24 cm² 32 cm² 48 cm²
Answer: A) 24
Hope This Helps ^_^
A survey asked 10 boys and 10 girls how many hours they spent playing video games the previous week. The number of hours are given in the line plots.And please explain how you got the answer
The date set with the greater range is neither as the range is the same.
The median is not the same for both sets of data.
What is a median?
It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
Number of boys = 10
The number of hours from the 10 boys.
= 8, 10, 10, 10, 12, 13, 14, 15, 15, 20
Range = Highest value - Lowest value
= 20 - 8
= 12
Median = (12 + 13)/2 = 25/2 = 12.5
Number of girls = 10
The number of hours from the 10 girls.
= 3, 4, 4, 4, 6, 7, 8, 10, 10, 15
Range = Highest value - Lowest value
= 15 - 3
= 12
Median = (7 + 8)/2 = 15/2 = 7.5
Thus,
The range of both boys and girls is the same.
The median of boy's number of hours is 12.5.
The median of girl's number of hours is 7.5.
Learn more about median here:
https://brainly.com/question/28060453
#SPJ2
Fiona earns $15 for each lawn she mows. Which inequality can be used to find out how many lawns she must mow to earn at least $135?
Final answer:
Fiona needs to mow at least 9 lawns to earn at least $135, represented by the inequality 15L ≥ 135, where L is the number of lawns mowed.
Explanation:
To determine how many lawns Fiona must mow to earn at least $135, we can set up an inequality. Fiona earns $15 for each lawn she mows, therefore if we let L represent the number of lawns mowed, then Fiona's earnings can be represented by 15L. She needs to earn at least $135, so we can write the inequality as 15L ≥ 135. To find L, we divide both sides of the inequality by 15, which gives us L ≥ 9. Therefore, Fiona must mow at least 9 lawns to earn at least $135.
A kite has vertices at (2,4) (5,5) (5,1) and (0,-1) what is the approximate perimeter of the kite?
A savings account was opened with an initial deposit and never touched again. An account that does not meet the minimum balance requirement is charged a service fee.
Assuming the account was open with an initial deposit below the minimum amount, the current account balance, B, is equal to the product of the initial deposit, I, and the quantity of the difference of 1 and the monthly service fee, f, raised to the power of n, the number of months since the account was open.
If an initial deposit of $2,713.00 is made to the account with a monthly service fee of 5%, what will be the value of B after 13 months? Round to the nearest cent.
To find the current balance B after 13 months with an initial deposit of $2,713.00 and a 5% monthly service fee, you multiply the initial deposit by 0.95 to the power of 13, resulting in a balance of approximately $1,392.64.
Explanation:The student's question involves using a given mathematical formula to find the current balance of a savings account affected by a monthly service fee. The formula provided states that the current balance B is equal to the initial deposit I times the quantity (1 - monthly service fee f) raised to the power of the number of months n. To calculate the current balance after 13 months, given an initial deposit of $2,713.00 and a monthly service fee of 5%, you'd perform the following calculation:
Convert the percentage fee to a decimal: 5% = 0.05.Subtract the service fee from 1: 1 - 0.05 = 0.95.Raise the difference to the power of the number of months: 0.9513.Multiply the result by the initial deposit: $2,713.00 × 0.9513.Using a calculator, this gives:
B = $2,713.00 × (0.9513) ≈ $2,713.00 × 0.5133421 ≈ $1,392.64
Rounded to the nearest cent, the value of B after 13 months is $1,392.64.
2/3 - 1/6 finding the common denominator show me how to do it
Rectangle ABCD is similar to rectangle QRST. The width of ABCD is 5 inches and the length is 8 inches. If the length of QRST is 12 inches, what is the width of QRST?
Answer:
7.5
Step-by-step explanation:
1.3-2.1g when g is 1.9. Can you please help? I keep getting 2.69 but the paper shows the answer to be 5.29
An object accelerates 5.0 m/s2 when a force of 20.0 newtons is applied to it. What is the mass of the object?
how many kilograms is in 2,500 dekagrams
round each amount to the nearest hundred to find an estimate of: 3891÷289
Can You show me how to do this?
Write an exponential growth function to model each situation. Please answer questions 1 2 3 and 4
Sandy spun a spinner with 5 equal parts labeled 1-5. What is the probability she will Not spin a 4
The probability that she will not spin a 4 will be 0.80 or 4/5.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Sandy spun a spinner with 5 equal parts labeled 1-5. Then the total number of events will be given as,
Total events = 5 {1, 2, 3, 4, 5}
Then the favorable events are given as,
Favorable events = 4 {1, 2, 3, 5}
Then the probability is given as,
P = 4 / 5
P = 0.80
The probability that she will not spin a 4 will be 0.80 or 4/5.
More about the probability link is given below.
https://brainly.com/question/795909
#SPJ5
Final answer:
The probability that Sandy will not spin a 4 on a spinner with 5 equal parts is 4/5 or 80%. There are 4 favorable outcomes and 5 possible outcomes in total.
Explanation:
The question asks for the probability that Sandy will not spin a 4 on a spinner that's divided into 5 equal parts, each labeled with the numbers 1-5. Since there are 5 outcomes and only one of them is the one we want to avoid, that leaves us with 4 favorable outcomes (spinning a 1, 2, 3, or 5). The probability of not spinning a 4 is therefore the number of favorable outcomes (not spinning a 4) divided by the total number of possible outcomes (spinning any number from 1 to 5).
To calculate this, we divide the favorable outcomes by the total number of outcomes. This gives us a probability of 4/5, or 80%. The calculation is as follows:
Number of favorable outcomes: 4 (spinning a 1, 2, 3, or 5)Total number of outcomes: 5 (spinning any number from 1 to 5)Therefore, P(not spinning a 4) = 4 favorable outcomes / 5 total outcomes = 4/5 or 0.8, which means there is an 80% chance that Sandy will not spin a 4.
4) A sales associate in a department store earns a commission on each suit and each pair of shoes sold. One week, she earned $47 in commission for selling 3 suits and a pair of shoes. The next week, she earned $107 in commission for selling 7 suits and 2 pairs of shoes.
a) Write a system of equations to represent the situation. Explain what your x and y will represent.
b) Solve the system of equations.
c) How much commission does she earn for selling each suit and each pair of shoes?
The sales associate earns a commission of $13 for each suit sold and $8 for each pair of shoes sold, found by solving the system of equations representing her commission earnings for two different weeks.
To represent the sales associate's commission earnings, we will use two variables: let x be the commission for each suit sold, and y be the commission for each pair of shoes sold.
(a) System of Equations:
The first week's commission can be represented by the equation 3x + y = 47. The second week's commission can be written as 7x + 2y = 107.
(b) Solving the System:
Multiply the first equation by 2 to get 6x + 2y = 94.Subtract the first modified equation from the second week's equation: (7x + 2y) - (6x + 2y) = 107 - 94.This simplifies to x = 13, meaning the commission for each suit is $13.Substitute x = 13 into the first equation: 3(13) + y = 47.Solve for y: 39 + y = 47, so y = 8.(c) The commission for each pair of shoes is $8.
Is my answer correct?
Will give brainliest!!
Each option below lists three expressions. Which option lists expressions that are not equivalent?
A) 81^3/4 ; 27 ; ^4square root of81^3
B) 8 ; ^4square root of16^3 ; 16^.75
C) (625^.25)^3 ; (625^3)^1/4 ; 125
D) 256 ; 1,296^3/4 ; ^4square root of1,296^3
Answer:
D) 256; 1,296 ^ 3/4; ^ 4square root of1,296 ^ 3
Let's rewrite the expression step by step:
1296 ^ 3/4
(1296) ^ (3/4)
(1296 ^ 3) ^ (1/4)
(2176782336) ^ (1/4)
216
This result is different from 256.
Answer:
D) 256; 1,296 ^ 3/4; ^ 4square root of1,296 ^ 3
Step-by-step explanation:
Which ordered pair is a solution to the system of equations?
Which word has line symmetry, DAD, ODE, or HOME
Horace buys 2/4 pounds of blueberries for a pie he needs 48 ounces for the pie how many more pounds of blueberries does he need to buy
Horace need to buys 2.5 pounds of blueberries
Horace buys 2/4 pounds of blueberries48 ounce of blueberries needed for a pieTo determine how many pounds of blueberries that Horace need to buy, we have to convert ounces because this mathematical question is related to unit conversion.Further Explanation1 pounds = 16 ounces, therefore,
3 pounds = 48 ounces (we multiply 16 and 3 = 48)
To find how many pounds he need to by = 3 ounces – [tex]\frac{2}{4}[/tex]
= 3 – [tex]\frac{2}{4}[/tex]
= [tex]\frac{3}{1}[/tex] – [tex]\frac{2}{4}[/tex] (4 is the smallest number can divide both denominator) therefore, we have
= (4 x 3) – (1 x 2) / 4
= 12 - 2 / 4
= [tex]\frac{10}{4}[/tex]
= 2.5
Thus, Horace buys 2.5 pounds of blueberries.
LEARN MORE:
The canadian side of niagara falls has a flow rate of 600000 gallons per second how many gallons of water flow over the falls in one minute brainly.com/question/3524504Charlotte is traveling 15 meters per second. Which expression could be used to convert this speed to kilometers per hour brainly.com/question/11053063KEYWORDS:
Horace2/4 poundsblueberriespie48 ouncesZacarias and Paz together have $756.80. If Zacarias has $489.50, how much does Paz have? Write and solve an addition equation to find how much money belongs to Paz