4.3 you can't expand a number, only an equation
The expanded form of a number shows the value of each digit. Meaning you must separate each digit by its placement.
4 is in the ones, therefore it just remains as 4
.3 is in the tenths, and therefore turns into 0.3
Now combine the two terms. The expression would be the answer:
4 + 0.3
32%
of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.
To solve this problem, one would need to use the binomial probability formula, substituting different values of 'x' into the formula depending on the requirement of the question. To calculate probabilities for specific numbers of people saying cashews are their favorite, substitute those numbers into the formula and solve, adding appropriate probabilities together for situations with ranges of people.
Explanation:The subject of this question is probability. We can use the binomial probability formula, which is P(X=x) = C(n, x) * (p^x) * ((1-p)^(n-x)), where 'p' is the probability of success, 'n' is the number of trials, and 'x' is the number of successful outcomes.
(a) For exactly 3 people loving cashews, substitute x=3, p=0.32 (32%), and n=12 into the formula to calculate the probability.
(b) For at least 4 people loving cashews, calculate the probability for x=4, x=5,....x=12 and add these probabilities together as this is an 'or' condition.
(c) For 2 or fewer people loving cashews, calculate the probability for x=0, x=1, x=2 and add them, because it says 'at most two' which includes 0 to 2 people.
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Work out (3.6 x 10^-5) ÷ (1.8 x 10^2) give your answer in standard form
Answer:
2e-7 or 2x10^-7
Step-by-step explanation: correct me if i'm wrong
When a third of a number is subtracted from a half of the same number, 60 is the result. Find the number
the answer is 360 because if you take a third you will have 120 then if you take half of that then you get 60
Using a system of equations, it is found that the number is of -360.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem:
The number is n.A third of the number is n/3.Half the number is n/2.Hence:
[tex]\frac{n}{3} - \frac{n}{2} = 60[/tex]
[tex]\frac{2n - 3n}{6} = 60[/tex]
[tex]-n = 360[/tex]
[tex]n = -360[/tex]
The number is of -360.
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1348 rounding to the nearest thousand
1000 would be the answer
The rounding number to the nearest thousand will be 1,000.
What is Rounding number?
To making a number simpler but keeping its value close to what it was, is called Rounding.
Given that;
The number is;
1348
Now, To round a number to the nearest thousand, look at the hundreds digit. If the hundreds digit is 5 or more, then round up.
If the hundredth digit is 4 or less, then round down.
So, Here the hundreds digit is 3, which is less than 5.
Then, we round down.
Thus, The rounding number = 1,000
So, The rounding number to the nearest thousand will be 1,000.
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Carol is given a 10% pay decrease. Her new wage is £306 per week. What would be her weekly wage if, instead, she had received a 10% pay increase?
the answer would be 374.00
the original value before any increase or decrease is 340.00
so...
340.00 X 1.10 = 374.00
Answer:
New Wage after 10% increase =£374
Step-by-step explanation:
Let us assume Carol's initial weekly wage be £ x
Now there is 10% decrease in weekly wage
10 % of weekly wage = 10 % of x
= [tex]\frac{10x}{100} = 0.1x[/tex]
New wage after 10% decrease = initial weekly wage - 10% of x
= [tex]x- 0.1x = 0.9x[/tex]
It is given that new weekly wage is £ 306
so we equate £306 and 0.9x , so we have
[tex]0.9x=306[/tex]
[tex]x=\frac{306}{0.9}[/tex] ( divide both sides by 0.9)
[tex]x= 340[/tex]
So we got
Initial weekly wages = £ 340
Now Let us find weekly wage when there is 10% increase,
10% of initial weekly wage = [tex]10% of 340[/tex]
=[tex]\frac{10}{100}[/tex]×[tex]340[/tex]
= [tex] 34[/tex]
New Wage after 10% increase = [tex]340+34[/tex]
=£ 374
Factorise completely (2x+1)^2 -(x-1)^2
To factorize the expression completely, we use the difference of squares formula and simplify the expression to get 6x.
Explanation:The given expression is (2x+1)^2 -(x-1)^2. To factorize it completely, we can use the difference of squares formula, which states that (a^2 - b^2) = (a + b)(a - b). Applying this formula, we have:
(2x+1)^2 -(x-1)^2 = [(2x+1) + (x-1)][(2x+1) - (x-1)]
Simplifying further, we get:
(2x+1+x-1)(2x+1-x+1) = (3x)(2) = 6x.
In which section of the number line is √5?
We know that [tex]\sqrt(4)[/tex] and [tex]\sqrt(9)[/tex] are 2 and 3 respectively. Therefore, [tex]/sqrt(5)[/tex] is between 2 and 3, approximately 2.2.
50 apples cost $25 how much would it cost for 75 apples
It would cost $37.50.
The temperature in degrees Kelvin is 273 degrees more than the temperature in degrees Celsius. Use the formula C=59(F−32) to write a formula for the temperature in degrees Fahrenheit F in terms of the temperature in degrees Kelvin K.
Answer:
F = (9/5) (K - 273) + 32
Step-by-step explanation:
The problems asks to use the formula C=59(F−32), but check that this is not correct, it should be:
[tex]C = \frac{5}{9} (F - 32)[/tex]
We also know that temperature in degrees Kelvin K is 273 more than in degrees Celsius C, so we can write this as:
K = C + 273
The question asks to write a formula for the temperature in degrees Fahrenheit F in terms of the temperature in degrees Kelvin K.
So first lets isolate F in the first formula
[tex]C = \frac{5}{9} (F - 32)[/tex]
[tex]C = \frac{5}{9} (F - 32)\\C * \frac{9}{5} = \frac{5}{9}* \frac{9}{5}(F - 32)\\C * \frac{9}{5} = F - 32\\C * \frac{9}{5} +32 = F - 32 +32\\F = \frac{9}{5} C +32[/tex]
Now to make the formula in terms of K, lets first write C in terms of K:
K = C + 273
C = K -273
And now we can replace C in the F formula to write it in terms of K:
F = (9/5) (K - 273) + 32
The radius of a sphere is increasing at a rate of 2 mm/s. How fast is the volume increasing when the diameter is 100 mm?
Answer:
Volume increasing rate = [tex]62831.85 mm^3/s[/tex]
Explanation:
We rate of change of radius of sphere, [tex]\frac{dr}{dt} =2mm/s[/tex]
Diameter of sphere = 100 mm
Radius of sphere = 50 mm
Volume of sphere, V = [tex]\frac{4}{3} \pi r^3[/tex]
Rate of change of volume = [tex]\frac{dV}{dt}[/tex]
[tex]\frac{dV}{dt}=\frac{d}{dt} (\frac{4}{3} \pi r^3)=\frac{4}{3} \pi\frac{d}{dt}(r^3)=\frac{4}{3} \pi*3r^2*\frac{dr}{dt}[/tex]
Substituting known values
[tex]\frac{dV}{dt}= \frac{4}{3}* \pi*3*50^2*2=62831.85 mm^3/s[/tex]
Volume increasing rate = [tex]62831.85 mm^3/s[/tex]
The average score that Kat gets on her exams is proportional to the amount of time she studies for the exam. Kat scored a 75 after studying for 15 hours. How many hours should she study for the next exam if she needs a 90 to pass the class?
Kat's study score rate is 5 points per hour. To achieve a score of 90, given her current study rate, she should spend 18 hours studying for the exam.
Explanation:Since the average score Kat gets on her exams is proportional to the amount of time she studies, her score is a measure of her rate of study. This 'rate' can be computed as the score divided by the time she studies. She got a 75 after studying for 15 hours, so her rate is 75/15 = 5 - this means she scores 5 points per hour of studying.
To figure out how many hours she needs to study to score a 90 in the next exam, divide the score she needs (90) by her rate (5). So, 90/5 = 18. Thus, Kat needs to study for 18 hours to achieve a score of 90 on her next exam.
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please help I hope someone can:Brian and Chris went together to Target to find party favors for a birthday party they are throwing together.
Brian found 4 items that cost the same amount. Chris bought 3 items that each cost $2.50 more than Brian’s items each cost. Brian and Chris both paid the same amount of money. What was the individual cost of each person's items?
(a) Write an equation. Let x represent the cost of one of Brian's items.
(b) Solve the equation. Show your work.
(c) Check your solution. Show your work.
(d) State the solution in complete sentences.
Answer:
one Brian's item cost: x
one Chris' item cost: x+2.5
Set up equation:
Brians amount = Chris amount
4*x = 3*(x+2.5)
solve for x:
4x = 3x + 7.5
x = 7.5
Brian's items cost $7.5 each.
Check:
Brian paid 4*7.5 = $30
Chris paid 3*10 = $30
The individual cost of Brian's items was $7.50, and the indiv. cost of Chris' items was $10.
3-12t+8t simplify each Expression
the members of the drama club used .5 of the school gymnasium floor space to build a stage for a play. the drama club used .4 of this part of the gymnasium floor to build a backstage area. write an equation.
Hello,
If this is the case, i would division.
4 devided by 5 is 1 reminder 1.
Plz mark brainliest
*i think i got it right!*
The drama club used 0.5 of the gymnasium floor for the stage, and 0.4 of that for the backstage area. Therefore, the equation representing the portion of the gymnasium used for the backstage area is 0.2F = backstage area, where F represents the total gymnasium floor space.
Explanation:The drama club used 0.5 of the total gymnasium floor space to build a stage. But they further used 0.4 of that space for a backstage area. If the total floor space is represented by the variable F, the portion used for the stage would be 0.5F. The space used for the backstage area would be 0.4 of that, so it would be 0.4 * 0.5F = 0.2F. So the equation representing the situation is 0.2F = backstage area.
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Compute the permutations and combinations. 4 P 4
1
4
24
[tex]nPk=\dfrac{n!}{(n-k)!}\\\\4P$=\dfrac{4!}{(4-4)!}=\dfrac{4!}{0!}=\dfrac{24}{1}=24[/tex]
Final answer:
The number of permutations for 4 P 4 is calculated as 4! (four-factorial), which is 4 x 3 x 2 x 1, resulting in 24 different permutations.
Explanation:
The question asks for the number of permutations for 4 P 4, which is the number of ways to arrange 4 unique items. When dealing with permutations, if we want to select r items from a set of n items, the formula for permutations is given by nPr = n! / (n-r)!. In this case, both n and r are equal to 4, so we would calculate 4P4 as 4! / (4-4)! which simplifies to 4! / 0!. Because 0! is defined to be equal to 1, the calculation becomes 4! Therefore, 4 P 4 equals 24.
Peter sets out on a run 4 miles west of his school he ran 14 miles east how far past is school is he after his run
he is 10 miles east of his school because:
N
W-|-E So if you consider the middle of the lines the school and draw a line four S miles west then you go backwards (east) fourteen miles. you get 10.
Equation: 0+4=4 |4-14|=10
Peter is 10 miles east of his school after his run.
Explanation:To determine how far past his school Peter is after his run, we need to calculate the total displacement from his starting point. Since he ran 4 miles west and then 14 miles east, the total displacement is the difference between the two distances, which is 10 miles east. Therefore, Peter is 10 miles east of his school after his run.
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4(px+1)=64 the value of x in terms of p is
[tex]4(px+1)=64\qquad|\text{divide both sides by 4}\\\\px+1=16\qquad|\text{subtract 1 from both sides}\\\\px=15\qquad|\text{divide both sides by}\ p\neq0\\\\\boxed{x=\dfrac{15}{p}}[/tex]
3 hours 20 minutes + 1 hour 48 minutes =___ days
zero days, 3 hours + 20 min + 1 hour + 48 min = 308 min which is about 5 hours.
3 hours 20 minutes + 1 hour 48 minutes = 0.2139 days
Let’s calculate the total time in hours and minutes:
Add the hours: [tex]3 \text{ hours} + 1 \text{ hour} = 4 \text{ hours}[/tex]Add the minutes: [tex]20 \text{ minutes} + 48 \text{ minutes} = 68 \text{ minutes}[/tex]Now, let’s convert the total time to days:
1 day = 24 hours1 hour = 60 minutesFirst, convert the minutes to hours:
[tex]68 \text{ minutes} = \frac{68}{60} \text{ hours} = 1.1333 \text{ hours}[/tex]
Next, add the converted hours to the original 4 hours:
[tex]4 \text{ hours} + 1.1333 \text{ hours} = 5.1333 \text{ hours}[/tex]
Now, divide the total hours by 24 to find the equivalent days:
[tex]5.1333 \text{ hours} \div 24 = 0.2139 \text{ days}[/tex]
Therefore, 3 hours 20 minutes + 1 hour 48 minutes equals approximately 0.2139 days
2(x+14) + 2(x) Distributive Property
2(x+14) + 2(x) after using the distributive property will be 2x+28+2x. What I did to find this is multiply the number outside of the opening parentheses by everything inside of the pair of parentheses.
The quotient of 14 and 7
It's 21. You just divide one by the other.
The quotient is 2.
A quotient is the result of division. In division, the dividend Divided by the Divisor = the Quotient, in your question 14 is the Dividend and 7 is the Divisor,
Hope this Helps :D
(12 ÷ 3 + 6) -4 Math help
Answer:
Well, we have to remember that we must use PEMDAS, or the order of operations, to solve the expression.
Therefore, we must first either divide or multiply anything that is inside of the parentheses. (In this case divide)
[tex]12/3=4[/tex]
[tex](4+6)-4[/tex]
Now solve what remains in the parentheses.
[tex]4+6=10[/tex]
[tex]10-4[/tex]
Finally, subtract 4 from 10 and get your answer:
6
Hello!
Answer:⇒⇒⇒=6
Step-by-step explanation:
This question it should be used pemdas.
Hint:
P-parenthesis (12÷3+6)=4+6=10
E-exponents 8²=8*8=64
M-multiply 21*2=42
D-divide 20÷5=4
A-add 5+5=10
S-subtract 30-10=20
First calculate with parenthesis.
[tex](12\div3+6)[/tex]
Then multiply and divide from (left to right).
[tex]12\div3=4[/tex]
Add and subtract from (left to right).
[tex]4+6=10[/tex]
[tex]10-4=6[/tex]
Hope this helps!
Thank you for posting your question at here on brainly.
Have a great day!
-Charlie
If y varies inversely as x and y=3 when x=4, then y=12 when x=15
True or false ?
y=12 is false answer.
2^x . 3^x =200 solve the x
[tex]2^x\cdot 3^x=200\\\\(2\cdot3)^x =200\\\\6^x=200\\\\x=\log_6200\\\\x=\dfrac{\ln 200}{\ln 6}\\\\x\approx2.96[/tex]
What percent of 29 is 3?
Hello!
The answer should be 0.34%
Explanation: First you had to start by representing by the percent with a variable by the x%. Then you can also used x% to create an algebraic expression. It gave us 29%*x=3. Next solve for x by dividing by 29 from both sides. It gave us 29x÷29=3÷29, or x≈0.1034. Then convert 0.1034 into a percent by multiplying by the decimal by 100%. And it gave us x≈0.1034*100%, and the answer is x≈10.34% is the right answer. Hope this helps! And thank you for posting your question at here on Brainly. Have a great day! -Charlie
The percentage of 29 that is equal to 3 is 10.34% calculated by making percentage the subject of the equation.
Understanding How to Solve PercentageTo find the percentage of one number in relation to another, you can use the following formula:
(Percentage / 100) * Number = Part
In this case, we want to find what percent 3 is of 29.
Let's substitute the values into the formula:
(Percentage / 100) * 29 = 3
To isolate the percentage, we divide both sides of the equation by 29:
(Percentage / 100) = 3 / 29
To find the percentage, we multiply both sides by 100:
Percentage = (3 / 29) * 100
Calculating this expression:
Percentage = 10.34
Therefore, 3 is approximately 10.34% of 29.
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Which set of points lies on given graph?
A.(4,11),(-2,7),(1,-1)
B. (4,11),(2,-7), (1,1)
C. (-4,11),(-2,7),(1,-1)
D. (-4,11),(-2,7),(1,1)
Set of points lies on given graph
(-4,11) , (-2,7), and (1, 1)
Answer
D. (-4,11),(-2,7),(1,1)
Janet is 3 yrs older than her sister julie. Janet brother is eight yrs younger than their sister julie. The sum of all their ages is 55 yrs
Janet: x + 3
Julie: x
brother: x - 8
Janet + Julie + brother = sum
x + 3 + x + x - 8 = 55
3x - 5 = 55
+5 +5
3x = 60
[tex]\frac{3x}{3} = \frac{60}{3}[/tex]
x = 20
Janet: x + 3 ⇒ (20) + 3 = 23
brother: x - 8 ⇒ (20) - 8 = 12
Answer: Janet=23, Julie=20, brother=12
Which scatterplot has a correlation coefficient closest to r = 1?
Answer:
The scatter diagram that contains the correlation coefficient closest to r = 1 is the first one shown in the attached images.
Step-by-step explanation:
The correlation coefficient "r" measures how much two variables x and y are related. When the variables are highly related, the value of r is closer to one and the points contained in the scatter diagrams are assimilated more and more to a line. When the value of r is positive the relation is crescent and therefore the slope of the line drawn by the points in the diagram has a positive slope
Therefore, to answer this question, one must search among the attached images for the dispersion diagram in which the points resemble a straight line with a positive slope.
The scatter diagram that meets the requirements mentioned is the first one that appears in the attached images
The scatterplot with a correlation coefficient closest to r = 1 is the one shown in the image below.
Scatterplot Showing CorrelationA scatterplot shows a relationship between two variables.This relationship is denoted by a correlation coefficient that is between -1 and 1.If a line slopes upwards to the right, it shows a positive correlation and vice versa.The closer the data points on a scatter plot, the closer the correlation coefficient is to either 1 or -1.Therefore, a scatterplot with a correlation coefficient that is closest to r = 1 will have a slope whose data points lie almost on a straight line and slopes upwards to the right.
Therefore the scatterplot with a correlation coefficient closest to r = 1 is the one shown in the image below.
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Jon ate too many holiday cookies and gained 2.2 kilograms in December. Then he went on a diet and lost 1.5 kilograms in January. Then lost another 3.7 kilograms in February. Jon wants to know the total change in his weight was over these three months. Which of the following equations matches the situation above
Answer:
Jon lost a total of 3 kilograms in these 3 months.
Step-by-step explanation:
Weight that Jon gained in December = 2.2 kilograms
Weight that Jon lost in January = 1.5 kilograms
Weight that Jon lost in February = 3.7 kilograms
Overall Change in his weight = Total Weight he gained - Total weight he Lost
Total weight he gained is 2.2 kilograms as he only gained weight in December. Total weight he lost will be sum of weights he lost in January and February.
So, total weight Jon lost = 1.5 + 3.7 = 5.2 kilograms
Thus,
Total change in Jon's Weight = 2.2 - 5.2 = -3.0 kilograms
This shows that Jon lost a total of 3 kilograms in these 3 months.
Conclusion:
The statement that best describe the total change in his weight is: Jon lost a total of 3 kilograms in these 3 months
Answer:
2.2+(-1.5)+(-3.7)=?
Step-by-step explanation:
QUICK HELP!! Will give brainliest!! Thank you
3 is the y-intercept
and -6 is the x-intercept
usually they don't have y behind the y-intercept so usually its the one that doesn't have x, they usually only put x.
The correct answer to this equation is X-inter=(-3.15,0) and Y-inter=(0,6.3) and heres why:
To solve this problem we must isolate the y-variable and then graph. Here are the steps to do that
[tex]-6x+3y=18.9[/tex] Now add 6x to both sides to get:
[tex]3y=18.9+6x[/tex] Next we divide both sides by the 3 next to the "y" to get:[tex]y=\frac{18.9+6x}{3}\\[/tex]
Then you can simply graph this new equation to find your points. There is also another way to do it without graphing but it will take a lot more explaining and this way is faster.
If you find out that my answer is wrong, please tell me and I promise I will come back and rework my math. Thanks :)
solution for C and how to solve 5c-6=4-3c
Answer,
C = 5/4Explanation,
Add 6 to both sides,
5c - 6 + 6 = 4 - 3c + 6
Simplify,
5c = -3c + 10
Add 3c to both sides,
5c + 3c = 3c + 10 + 3c
Simplify,
8c = 10
Divide both sides by 8,
8c/8 = 10/8
Simplify,
C = 5/4
Hope this helps :-)