What is the coefficients of x4 in the expansion of (1+x)4(1+2x)3.
By the binomial theorem,
(1 + x)⁴ = 1 + 4x + 6x² + 4x³ + x⁴
(1 + 2x)³ = 1 + 6x + 12x² + 8x³
In the expansion of (1 + x)⁴ (1 + 2x)³, we get an x⁴ when multiplying
• x⁴ and 1 to get x⁴;
• 4x³ and 6x to get 24x⁴;
• 6x² and 12x² to get 72x⁴; and
• 4x and 8x³ to get 32x⁴.
Add these up:
x⁴ + 24x⁴ + 72x⁴ + 32x⁴ = 129x⁴
In a family of 11, what is the probability that there will be more boys than girls
Answer:
P(all female)= 1/2 x 1/2 x 1/2 = 1/8
P(all male ) = 1/2 x 1/2 x 1/2 = 1/8
P(all one gender) = P(all female) + P(all male) = 1/8 + 1/8 = 1/4
What is the probability that a three-child family is two girls and one boy?
Each possible birth order has P=1/8. That is, P(G,G,B)=P(G,B,G)=P(B,G,G)=1/8.
So, P(2G,1B)= 3/8 and P(1G,2B)= 3/8.
This allows us to write the overall gender probability distribution for families of three children as follows:
1/8 will be three girls
3/8 will be two girls and one boy
3/8 will be one girl and two boys
1/8 will be three boys
Adding it all up, we have 1/8 + 3/8 + 3/8 + 1/8 = 1 (100%)
Step-by-step explanation:
Anna sells candy apples at her yard sale. She wants to earn more than $40. She sells the apples for $2 and has earned $26. How many apples does she need to sell to reach her goal?
Answer:
7 apples
Step-by-step explanation:
40 - 26 = 14
14 / 2 = 7
33 is 90% of what number? Round to the tenths place.
Answer:
36.7
Step-by-step explanation:
Since 33 is 90% of a number, you can divide 33 by 9 to get 3 2/3. This 3 2/3 is 10% of the number, so multiply 3 2/3 by 10 to get 36 2/3. 36 2/3 rounded to the nearest tenth is 36.7, so there's your answer. Hope it helps!
2.) Find the measure of exterior angle X
Answer:
x = 90
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles, then
x = ∠ A + ∠ B = 30 + 60 = 90
There is a shirt that originally costs $10.00. Now it is 45% off. How much is the shirt after the discount?
Answer:
$5.50
Step-by-step explanation:
1.) The first step is finding what 45% of $10 is. We can do this by turning 45% into a decimal number (45%=0.45). We then multiply 0.45 by the $10.
2.) 0.45×$10=$4.50 ; We just found that 45% of $10 is $4.50
3.) Because the shirt is 45% less than the original price (45% off), we need to subtract the 45% (which is equal to $4.50) from the original price, $10
4.) $10-$4.50=$5.50, the new price
The Hydro water department has a monthly service charge of $12.90 and a volume charge of $1.67 for every 100 cubic feet of water. The total monthly cost is equal to the service charge plus the charge for the volume used during the month. If we let x represent the number of cubic feet of water (in hundreds) and y represent the total monthly cost, then we have: total monthly cost = volume charge + service charge y = 1.67x + 12.90 If the Johnson family used 200 ft3 more water this month than last month, then they can expect
Answer:
y = $346.90
Step-by-step explanation:
Given:
y = 1.67x + 12.90
Where,
y = total monthly cost,
x = month. If we let x represent the number of cubic feet of water (in hundreds)
If the Johnson family used 200 ft3 more water this month than last month, then they can expect
x = 200 ft³
y = 1.67x + 12.90
y = 1.67(200) + 12.90
= 334 + 12.90
= 346.90
y = $346.90
The interior angles of a triangle have measures 100°, (4y+25)°, and (3y+20)°.
What is the value of y?
Enter your answer in the box.
y =
Answer:
The value of y = 5⁰...........
Answer:
y=5
Step-by-step explanation:
The directions on a sewing pattern say to cut an extra 15% of fabric to account for error.
Chloe needs 0.75 yard of fabric to make a skirt, and she cuts 0.1125 yard.
Did Chloe cut the correct amount of fabric? Why or why not?
Chloe cut enough fabric because she cut the amount of fabric for the skirt.
Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric.
Chloe did not cut enough fabric because she only cut the amount of fabric for the skirt.
Chloe did not cut enough fabric because she only cut the amount of extra fabric.
Answer:
D
Step-by-step explanation:
She only cut the 15% extra and no the other 75%
Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric. The correct option is B.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that The directions on a sewing pattern say to cut an extra 15% of fabric to account for errors. Chloe needs 0.75 yards of fabric to make a skirt, and she cuts 0.1125 yards.
Calculate the percentage of the fabric from the given data,
Percentage = 0.1125 / 0.75
Percentage = 0.15 x 100
Percentage = 15%
Chloe cut enough fabric because she cut enough fabric for the skirt and the amount of extra fabric.
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there are 325 7th graders in 12 classes . determine the unit rate
Mr. Alvarez is buying every boy on his son's football team a new football. The footballs are sold in packages of 4. There are a total of 15 boys on the football team.
Part A:
In order for every boy to receive a football, how many packages of footballs does Mr. Alvarez need to buy?
Part B:
Using your findings in Part A, if every package costs $20.97, how much will Mr. Alvarez spend on footballs? PLEASEE HELP
Answer:
A)4 packs of footballs
B)$83.88
Step-by-step explanation:
If every boy needs a football then he is unable to buy just 3 cause then he would only have 12 footballs
3*4=12
So he would need 4 packs of footballs
B) because he needs 4 packs he multiplies 4 by 20.97 a pack.
4*20.97=83.88
A group of 8 children and 10 adults ate going to a movie. Child tickets cost $2 and adults tickets cost $4. How much will the movie tickets cost in all ?
Answer:
56$
Step-by-step explanation:
8*2=16
10*4=40
16+40=56
Which graph shows data whose r-value is most likely closest to 0?
A graph shows both axes unnumbered. Points show a downward trend.
A graph shows both axes unnumbered. Points show an upward trend.
A graph shows both axes unnumbered. Points show a downward trend.
A graph shows both axes unnumbered. Points are scattered all over the graph.
Answer:
D. A graph shows both axes unnumbered. Points are scattered all over the graph.
Step-by-step explanation:
The r-value is also known as the correlation coefficient. This number shows how correlated points on a graph are. It ranges from -1 to 1, with numbers being closest to 0 being the least correlated. So a graph in which the points are scattered all over would have an r-value closest to 0 because the points are not correlated. If a graph shows either an upwards or downwards trend that means there is some correlation, therefore having an r-value of around -1 or 1.
Answer:
d
Step-by-step explanation:
edge
I need the answers bad
Answer:
53
Step-by-step explanation:
90 - 37 = 53
Calculate the area of the rectangle.
Answer:
12
Step-by-step explanation:
You count all of the blue squares
Given the answer to a
problem asking you to simplify the expression,
write the possible problem. Explain how you
created the problem.
I really need help I don’t understand this. I will be given 20 points to whoever helps me. Thank you
Can exponents be integers
Answer:
NO
Step-by-step explanation:
Exponents are expressed as numbers or variables in superscript above a base number. When the exponent is equal to or greater than 2, it directs how many times the base number is to be multiplied. The numbers 1 and 0 are special exponents, and negative integers as exponents stand for reciprocal values.
Answer:
It matters of what the whole number in front is.
Step-by-step explanation:
For example: 6 to the power of 2 = 36
if the first number is a decimal: 1.6 to the power of 2.56
Its NOT an exponent if the starting number is a decimal usually.
- There are 75 cars at a dealership. 35 are blue or red. Suppose 16 are red and 3 are
both.
How many cars are just blue ?
How many cars are neither blue or red?
Answer:
19 are blue
37
Step-by-step explanation:
35 - 16 = 19
35 + 3 = 38 & 75 - 38 = 37
Solve for x in the equation below.
(x - 2) = - 1/4 (x – 8)
Select the correct answer.
A x = 0
B. x = - 5 1/3
C x = - 3 1/5
D. x = 3 1/5
Maria has a job picking apples. She can pick 52 apples per hour. How many apples can she pick in 45 minutes.
Answer:
39
Step-by-step explanation:
Althea traveled 280 miles at a speed of 70 miles/hour. How much time did she take to cover this distance?
An employee earns a 12 percent commission rate in the cameras he sells if he earns 384$ in commission what were his total sales
Answer:
I do questions like these a little different than most people so...
384/12= 32 (32 is 1% of his sales)
32*100= 3200
His total sales were $3200.
A treat bag has 2 green gum balls to read gumball and one blue gumball, if you were to reach into the treat bag right as a fraction, with the probability would be that you would randomly choose.
Answer:
2/5 ; 2/5 ; 1/5
Step-by-step explanation:
Given that :
Numbe red gumballs = 2
Number of green gumballs = 2
Number of Blue gumballs = 1
The probability of making a random choice :
Probability = required outcome / Total possible outcomes
Probability of choosing (red) :
P(red) = number of red balls / total number of balls
P(red) = 2 / 5
P(green) = number of green balls / total number of balls
P(green) = 2 / 5
P(blue) = Number of blue balls / total number of balls
P(blue) = 1 / 5
The price of mangoes in a grocery store is 3 for $5. How much will 5
mangoes cost? Round the answer to the nearest hundredth.
Answer:
8 and one thirds
Step-by-step explanation:
5 times 5 is equal to 25 and 25 divided by 3 is 8.3333
Answer:
$8.33
Step-by-step explanation:
So, to figure out how much one mango costs, I did $5 divided by 3, which gave me 1.66.
I then multiplied that by 5 to see how much 5 mangos cost, and I got $8.33
Enter an equation to describe the linear relationship.
The temperature, y, of a pot of water is 45 °F. The temperature increases by 25 °F per minute,x , when being heated.
The equation is y=
What is the value of x?
155
105
A. 55°
B. 160°
C. 50°
O D. 20°
expand and simplify completely (log). PLEASEE HELP ASAP!!! I WILL GIVE BRAINLIEST!! thank you so much!!!!
Answer:
c. [tex]2 log3(y)+1+log3(x)[/tex]
Step-by-step explanation:
When expanding and simplifying, we can see that the answer is [tex]1+log3(x) + 2log3(y)[/tex], which matches Answer Choice C.Answer:
( C ) 1+log3x+2log3y
Step-by-step explanation:
Need help ASAP plzzz
Answer: D
Step-by-step explanation: i did the math
The distance, d, that a car has traveled, as a function of time, t, is given in the table below. What is the average
rate of change of the distance over the interval 2 < t < 9
Answer: 56 miles/hour
Step-by-step explanation: 498-106=392
9-2=7
392/7= 56 , units- miles/hour
The average rate of change of the distance over the interval 2 < t < 9 is 56 units- miles/hour.
What is the distance?Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.
It is given that:
The distance, d, that a car has traveled, as a function of time, t, is given in the table below.
Difference = 498 - 106
= 392
= 9 - 2
= 7
From the formula:
Rate of change = change in distance/change in time
= 392/7
= 56 units- miles/hour
Thus, the average rate of change of the distance over the interval 2 < t < 9 is 56 units- miles/hour.
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A system of two linear equations has infinite solutions. What does this tell you about the graph of the system?
А) The system graphs as parallel lines.
B) The system graphs as one line
C) The system graphs as perpendicular ones.
D) The system graphs as intersecting lines
Answer:
B) The system graphs as one line.
Step-by-step explanation:
The solutions of systems are basically the points where the two lines of the linear equations meet, or intersect.
So, picture it like this: if a system of linear equations has INFINITE (never-ending) solutions, then it must mean that the two lines intersect at EVERY single one of their points. And if they intersect at every one of their points, then that must mean that they are the same line, even if the equations are written differently.
Hope this helps!