The probability that the family has no boys is [tex]\(\frac{1}{16}\)[/tex] or 0.0625.
At each level, the tree branches into two, representing the two possible genders for that child. Since there are four children, there will be [tex]\(2^4 = 16\)[/tex] branches at the end of the tree, each representing a unique sequence of genders for the four children.
The sample space, therefore, consists of 16 possible outcomes, which are:
1. BBBB
2. BBBG
3. BBGB
4. BBGG
5. BGBB
6. BGBG
7. BGGB
8. BGGG
9. GBBB
10. GBBG
11. GBGB
12. GBGG
13. GGBB
14. GGBG
15. GGGB
16. GGGG
Now, we want to find the probability that the family has no boys. From the sample space, there is only one outcome where all four children are girls (GGGG).
Since each outcome is equally likely, and there are 16 possible outcomes, the probability of having no boys is the number of favorable outcomes (in this case, 1) divided by the total number of possible outcomes (16).
Therefore, the probability [tex]\(P\)[/tex] of having no boys is:
[tex]\[ P(\text{no boys}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{16} \][/tex]
Michelle bought 76 pounds of cocoa powder for her bakery. Every day she used the same amount of cocoa powder to make bakery items. After 10 days, Michelle was left with 20.2 pounds of cocoa powder. On average, how many pounds of cocoa powder did Michelle use each day?
5.58 pounds
7.45 pounds
9.62 pounds
12.6 pounds
An invoice dated March 28 with terms 1/10, E.O.M. results in the end of the credit period on:
Answer:
April 10
Step-by-step explanation:
EOM (End Of Month) to receive a discount attached to the invoice when paying before the payment is due.
In this case, 1/10 means that there will be a 1% discount if the invoice is paid within 10 days of receipt.
But since the terms of credit are EOM, the 10 days are counted from the end of March, that brings us to April 10.
Therefore, an invoice dated March 28 with terms 1/10, E.O.M. results at the end of the credit period on April 10.
Hope this helps!
Tran drove his car at a constant speed of 55 mph.
Which is an equation for the distance Tran drove?
A. 55d=t
B. d=55t
C. t/d=55
D. 55/d=t
Plz help I think the answer is D am not sure.
The correct equation for the distance Tran drove at a constant speed of 55 mph is B. d = 55t.
In this equation:
"d" represents the distance in miles that Tran drove.
"t" represents the time in hours.
So, the distance "d" is equal to Tran's constant speed of 55 mph multiplied by the time "t" in hours, which is why the equation is written as d = 55t.
Option D is not the correct equation because it has the variables and constants in the wrong order.
The correct order is distance (d) on the left side of the equation, followed by the constant speed (55) and then the time (t) on the right side of the equation.
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divide 9x^2 square root by square root 18y^2
Need to show work for problem x+9.72=21
A 25-foot streetlight casts a showdown 20feet long.If Melanie is standing at the end of the shadow casted by a 60. -foot tall building,how far is she from the building.
By setting up a proportion based on the similar triangles created by the streetlight and the building, we can find that Melanie is standing 48 feet away from the building.
To solve the problem of determining how far Melanie is standing from the building using the shadows, we can use similar triangles. We are given a 25-foot streetlight that casts a 20-foot shadow and a 60-foot tall building. The goal is to find the length of the shadow cast by the building, which will tell us how far Melanie is from the building.
By setting up a proportion based on the similar triangles, we have:
Height of the streetlight / Length of streetlight's shadow = Height of the building / Length of the building's shadow.25 feet / 20 feet = 60 feet / x feet.To find the value of x, we cross multiply:25x = 60 * 20.x = (60 * 20) / 25.x = 1200 / 25.x = 48 feet.Therefore, Melanie is standing 48 feet away from the building.
The amount of money that is left in a medical savings account is expressed by the equation y = -24x+ 379, where x represents the number of weeks and y represents the amount of money, in dollars, that is left in the account. After how many weeks will the account have $67 left in it?
y = amount left so y = 67
rewrite the equation as:
67 = -24x+379
subtract 379 from both sides
-312 = -24x
divide both sides by -24
x = -312 / -24
x = 13
the answer is 13 weeks
A house painting company charges $376 plus $12 per hour. Another company $280 plus $15 per hour. A. how long is a job for which both companies will charge the same amount? B.What will the cost be?
Both companies will charge the same amount in 32 hours
From the information given, the equation to solve the question will be:
376 + (12 × h) = 280 + 15(h)
376 + 12h = 280 + 15h
Collect like terms
15h - 12h = 376 - 280
3h = 96
Divide both side by 3.
3h/3 = 96/3
h = 32
The amount charged will be:
376 + 12h = 376+12(32)
= 376 + 384
= 760
The amount charged will be $760
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The correct option is d. 8 oz. can of juice is most convenient to meet this requirement.
First, let's convert 240 milliliters to ounces because the answer choices are in ounces.
1 milliliter is approximately equal to 0.0338 ounces.
So, 240 milliliters is approximately \( 240 \times 0.0338 \) ounces, which is about 8.112 ounces.
Now, let's examine the options:
a. 5 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.
b. 4 oz. can of juice: Not enough juice. It's less than the required 8.112 ounces.
c. 12 oz. can of juice: More than enough juice. It's more than the required 8.112 ounces.
d. 8 oz. can of juice: Exactly the amount needed. It matches the required 8.112 ounces, which is the closest to the calculated amount of 8.112 ounces.
Therefore, the 8 oz. can of juice is the most convenient option to meet the requirement of having 240 milliliters of juice every 2 hours.
(8.166×10^8)×(1.515×10^9)
Which number line correctly shows 2 2/5, 2 4/5, and 11/5?
The Andersons can set up 6 tables in 1 hour. How many tables can they set up in 5 hours?
Write a 3-digit number using the digits 5,9, and 2. Then write your number using words.
What is 128/56 simplified⁉️
A vat contains 21.12 L of cleaning solution. Kenyon pours the solution into 0.44-L containers.
How many containers of solution does he create?
Answer:
48
Step-by-step explanation:
Which of the following is a multiple of 4?
A. 620
B. 891
C. 734
D. 626
solve the equation by completing the square 5x(x+6)=-50
To solve the equation 5x(x+6) = -50 by completing the square, we first isolate the quadratic term and then add the square of half the coefficient of x to both sides of the equation. Taking the square root gives us the solution x = -3 + i and x = -3 - i.
Explanation:
To solve the equation by completing the square, we first need to isolate the quadratic term on one side of the equation. So, let's distribute the 5x to get 5x^2 + 30x = -50. Next, we move the constant term to the other side and divide the equation throughout by the leading coefficient to get x^2 + 6x + 10 = 0.
Now, we can complete the square by adding the square of half the coefficient of x (which is 3) to both sides of the equation. This gives us (x + 3)^2 + 10 - 9 = 0, which simplifies to (x + 3)^2 + 1 = 0.
Taking the square root of both sides, we get x + 3 = ±√(-1), which means x = -3 ± i. Hence, the solution to the equation is x = -3 + i and x = -3 - i.
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What is the value of the expression? 3.2(2.3)−4.8 Enter your answer in the box as a decimal.
3.2(2.3) - 4.8
Simplify.
(3.2 × 2.3) - 4.8
Simplify.
(7.36) - 4.8
Simplify.
2.56
Hope this helped. :)
After the drama club sold 100 tickets to a show, it had $300 in profit. After the next show, it had sold a total of 200 tickets and had a total of $700 profit. Which equation models the total profit, y, based on the number of tickets sold, x?
I really need help with this one...
I need Help with my multi step equations!
What is x for 7x plus 4 over 6 equals negative 4
it costs $150 to be a member of a music club. A member of the club pays $5 per music lesson. A nonmember pays $15 per music lesson. How many music lessons must a member and a non member take so the cost for each is the same?
The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
PEMDAS rule means the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.
It costs $150 to be a member of a music club. A member of the club pays $5 per music lesson. A nonmember pays $15 per music lesson.
Let x be the number of music. Then the equation is given as,
15x = 5x + 150
Simplify the equation, then we have
15x - 5x = 150
10x = 150
x = 15
The number of music lessons must a member and a non-member take so the cost for each is the same will be 15.
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sela's piano lesson starts at 4:45 pm the lesson is 30 minutes long when does her lesson ends
Answer:
Sela's piano class will end at 5 : 15 pm
Step-by-step explanation:
Sela's piano lesson starts at 4 : 45 pm.
If we have to calculate the time when her lesson ends we will add the duration of the class in minutes.
After 30 minutes time will be
4 : 45 + 00 : 30 = 4 : 75
Now we know 00 : 75 or 75 minutes means 1 hour 15 minutes
therefore, 4 : 75 will become 5 : 15 pm
Sela's piano class will start at 4 : 45 pm and end at 5 : 15 pm
MAXIMUM POINTS!!!!! PLEASE HELP
A popular cellular phone family plan provides 1,500 minutes. It charges $89.99/month for the first two lines and $9.99/month for every line after that. Unlimited text messages for all phone lines costs $30.00/month, and Internet costs $10.00/month per phone line. If a family with a $200 monthly budget buys this plan and signs up for unlimited text messaging and Internet on each phone line, how many cell phone lines can they afford? Use an inequality to solve this problem. Graph your solution on the number line and explain the meaning of your graph in a sentence.
Drag and drop a phrase to make the statement true.
Triangles ABC and DEF are..
A. Similar triangles.
B. Not similar triangles.
The triangles ABC and DEF are similar
What are similar triangles?If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.
Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides
Given data ,
Let the first triangle be represented as ΔABC
Let the second triangle be represented as ΔDEF
Now , the measure of ∠ABC = 35°
So , the measure of ∠ACB = 55° ( given ∠BAC = 90° )
And , the measure of ∠EFD = 55°
So , the measure of ∠DEF = 35°
And , the corresponding sides of similar triangles are in the same ratio
Hence , they are similar triangles
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A whale dives at a speed of 3 feet per second. What is the change in position of the whale relative to where it started after 12 seconds?
What is 68√ in simplest radical form?
If you work for an hourly wage, your gross pay is a function of the number of hours that you work. Your hourly wage is $8 per hour. Assuming you work 40 hours per week, what is the practical domain and the practical range of the function? a. The practical domain is 0 through 8. The practical range is 0 through 32. b. The practical domain is 0 through 320. The practical range is 0 through 40. c. The practical domain is 0 through 40. The practical range is 0 through 320. d. The practical domain is 0 through 32. The practical range is 0 through 8.
Answer:
The correct option is C.
Step-by-step explanation:
It is given that gross pay is a function of the number of hours that you work.
Let y represents the gross pay and x represents the number of hours. So, the value of x and y can be negative.
Hourly wage = $8 per hour.
The weekly gross pay function is
[tex]y=8x[/tex] .... (1)
Domain is the set of inputs and ranges is the set of outputs.
It is given that you work 40 hours per week. It means the value of x lies between 0 to 40.
Domain = [0,8]
Substitute x=40 in equation (1), to find the gross pay when number of hours is 40.
[tex]y=8(40)=320[/tex]
Range = [0,320]
The practical domain is 0 through 40. The practical range is 0 through 320.
Therefore the correct option is C.
The practical domain for the function representing gross pay is the range of hours worked, 0 to 40 hours. The practical range is the corresponding gross pay, from $0 to $320, based on an $8 per hour wage for up to 40 hours of work. So correct answer is option C.
To determine the practical domain and range of the function that represents your gross pay based on an hourly wage of $8 per hour, we must consider the possible number of hours you can work in a week and the corresponding earnings. Given that you work 40 hours per week, the practical domain (which represents the number of hours worked) would be any value from 0 to 40 hours, since you cannot work negative hours and we're assuming a standard full-time workweek.
The practical range (which represents the gross pay) is calculated by multiplying the number of hours worked by the hourly wage. Therefore, the range would be 0 (if you work 0 hours) to $320 (if you work 40 hours), because 40 hours times $8 per hour equals $320.
So, the correct answer from the given options is Option C.
Practical domain: 0 through 40.
Practical range: 0 through 320.
rotate 270 clockwise around the origin (8,0)(11,-5)(14,-2)