Ms. Willow's birth year = x
This year = 2020
80th birth year = x + 80
30th birth year = x + 30
Present age = 2020 - x
(x + 2020) - (x + 80 + x + 30) + (2020 - x) = 42
Simplify the right side.
-2x + 3930 = 42
Subtract 3930 from both sides.
-2x = -3888
Divide both sides by -2
x = 1944
1944 is Ms. Willow's birthday year.
As stated previously, her present age is 2020 - x, which equals 78
Ms. Willow is 78 years old
Here we want to interpret a word problem and transform it into an equation that we can solve.
We will find that her current age is 76.
First, let's define variables:
Her birth year = x
This year = 2021 (naturally this depends on the year we are on)
80th birth year = x + 80
30th birth year = x + 30
Then the actual age is the difference between the current year and the year when she was born:
Age = 2021 - x
What she says is:
"If you add the year of my birth to this year, subtract the year of my 80th birthday and the year of my 30th birthday, and then add my present age, the result is 42."
(x + 2021) - (x + 80 + x + 30) + (2021 - x) = 42
Now we can solve this for x:
x + 2021 - x - 80 - x - 30 + 2021 - x = 42
(x - x - x - x) + 2021 - 80 - 30 + 2021 = 42
-2*x + 3932 = 42
3932 - 42 = 2*x
3890 = 2*x
3890/2 = x = 1945
The current age is:
age = 2021 - x = 2021 - 1945 = 76
Her current age is 76.
If you want to learn more, you can read:
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Ten times a number is 36 more than four times that number. Find the number.
Answer:
6
Step-by-step explanation:
10x=36+4x
6x=36
x=6
How many 3/4
cups of juice can be poured from 6 cups of juice?
Answer:8
Step-by-step explanation: 4x6=28
28 divided by 4 = 8
Iveta takes out a mortgage of $100,000 to purchase a property. The interest rate is calculated as a simple interest rate of 5% per year. How much interest would Iveta have to pay after six years?
Washington Middle School has the annual musical production this weekend. Of the 900 tickets sold, 45 percent are for the Friday night performance. How many tickets were sold for the Friday night performance?
Answer:
405 tickets
Step-by-step explanation:
Answer:
45% of 900=900(0.45)=405. The third answer Is correct.
Step-by-step explanation: i took a quiz with this
in which quadrant is the point (4,- 2) located
Answer:
4
Step-by-step explanation:
To save money you set aside $50. For each following month you set aside 10% more than the previous month.How much money will you save in a year? Explain each step.
what is - 5/6 divided by 9/10?
- 27/25
- 4/3
- 25/27
- 3/4
Answer
-25/27
Step-by-step explanation:
a seed company has a test plot in which it is testing the germination of a hybrid seed, They plant 50 rows of 40 seeds per row. After a two week period, the researchers count how many seed per row have sprouted. They noted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germination data is given below in the table. The random variable x represents the number of seed in a row th
Answer:
Mean =[tex]\sum x P(x) = 36.86[/tex]
Standard deviation =[tex]\sum x^2P(X)=1360.9[/tex]
Step-by-step explanation:
x P(x) [tex]x \times P(x)[/tex] [tex]x^2 \times P(x)[/tex]
33 0.02 0.66 21.78
34 0.06 2.04 69.36
35 0.1 3.5 122.5
36 0.2 7.2 259.2
37 0.24 8.88 328.56
38 0.26 9.88 375.44
39 0.1 3.9 152.1
40 0.02 0.8 32
1 36.86 1360.9
We are supposed to find mean and standard deviation
Mean =[tex]\sum x P(x) = 36.86[/tex]
Standard deviation =[tex]\sum x^2P(X)=1360.9[/tex]
4+ (-3) - 2*(-6)
What is the answer to
Answer:
13
Step-by-step explanation:
4+(-3)-2*(-6)
4-3-2*-6
1-(-12)
1+12
13
Answer: 13
Step-by-step explanation:
I Had The Same Problem So Try And Its Gonna Be Right.
Simplify the following:
a
2
b
•
b
2
a
2
c
=
a
2
b • b
2
a
2
c =
Answer:
It is A
Step-by-step explanation:
Carol and Linda are both selling cookies.
Carol sells her cookies for $1.25 per box, and she
already made $64.00. Linda sells her cookies for
$220 per box, and she already made $45.00. If both
of them sell the same number of boxes of cookies,
which one of the following inequalities can help you
find the least possible value of b, the number of
boxes of cookies Linda must sell so she will make
more money than Carol?
Answer:
This inequality is impossible. Assuming this is realistic, Linda cannot sell part of a box of cookies and therefore cannot make less than $220.
Step-by-step explanation:
What is the simplified form of square root of 45?
Answer:
I'm pretty sure the answer is C
Grady is excavating the foundation of a house. If the hole will be
40 feet long, 24 feet wide, and 4 feet deep, how many cubic feet
of dirt must be removed from the site?
Answer:
3,840 cubic feet
Step-by-step explanation:
V=LWH
V= 40X24X4
V=3,840 cubic feet
20 points
plz answer soon!
A square on a coordinate plane is translated 9 units down and 1 unit to the right. Which function rule describes
the translation?
O T 1,-9 (x,y)
O T -1,-9 (x,y)
O T -9, 1 (x, y)
O T -9, -1 (x, y)
Answer: it should be the first one!! :)
Step-by-step explanation:
Answer:its the first one
Step-by-step explanation:did the test
PLS HELP :(
Solve the inequality and graph the solution on the line provided.
Answer:
[tex]x\leq -1[/tex]
Step-by-step explanation:
1. [tex]7x\leq 7-14[/tex]
2.[tex]7x\leq -7[/tex]
3. divide both sides by 7
4. [tex]x\leq -1[/tex]
Closed circle on -1 and the line goes to the left
Please pass this on... ( #helpsavelives )
Whoever is reading this:
I love u.
U matter.
The world needs u
hang in there ik it may be bad but u deserve the world <3
ur beautiful no matter ur shape, size, color, gender.. anything
don't give up I need u to live.
I wish I could take everyone's problems so yall wouldn't have to have em but I can't so just know ily and if anyone needs to talk u can talk to me
Please, pass this on. Everyone deserves to know this.❤❤
just copy and paste its not hard pls this could save someone's life
Answer:
Ive seen lots of these and just saw this one too but this actually really does help so thankyou for passing it on ily too<3
Step-by-step explanation:
According to a study done by a university student, the probability a randomly selected individual will not cover his or her mouth when sneezing is . Suppose you sit on a bench in a mall and observe people's habits as they sneeze. (a) What is the probability that among randomly observed individuals exactly do not cover their mouth when sneezing? (b) What is the probability that among randomly observed individuals fewer than do not cover their mouth when sneezing? (c) Would you be surprised if, after observing individuals, fewer than half covered their mouth when sneezing? Why? (a) The probability that exactly individuals do not cover their mouth is nothing. (Round to four decimal places as needed.) (b) The probability that fewer than individuals do not cover their mouth is nothing. (Round to four decimal places as needed.) (c) Fewer than half of individuals covering their mouth ▼ would would not be surprising because the probability of observing fewer than half covering their mouth when sneezing is nothing, which ▼ is is not an unusual event. (Round to four decimal places as needed.)
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
[tex]P(X = 8) = 0.0037[/tex]
b
[tex]P(X < 5) = 0.805[/tex]
c
[tex]P(X > 6) = 0.0206[/tex]
I would be surprised because the value is very small , less the 0.05
Step-by-step explanation:
From the question we are told that
The probability a randomly selected individual will not cover his or her mouth when sneezing is [tex]p = 0.267[/tex]
Generally data collected from this study follows binomial distribution because the number of trials is finite , there are only two outcomes, (covering , and not covering mouth when sneezing ) , the trial are independent
Hence for a randomly selected variable X we have that
[tex]X \ \ \~ \ \ { B ( p , n )}[/tex]
The probability distribution function for binomial distribution is
[tex]P(X = x ) = ^nC_x * p^x * (1 -p) ^{n-x}[/tex]
Considering question a
Generally the the probability that among 12 randomly observed individuals exactly 8 do not cover their mouth when sneezing is mathematically represented as
[tex]P(X = 8) = ^{12} C_8 * (0.267)^8 * (1- 0.267)^{12-8}[/tex]
Here C denotes combination
So
[tex]P(X = 8) = 495 * 0.000025828 * 0.28867947[/tex]
[tex]P(X = 8) = 0.0037[/tex]
Considering question b
Generally the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
[tex]P(X < 5 ) =[P(X = 0 ) + \cdots + P(X = 4)][/tex]
=> [tex]P(X < 5 ) =[ ^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0} + \cdots + ^{12} C_4 * (0.267)^4 * (1- 0.267)^{12-4} ][/tex]
=> [tex]P(X < 5 ) = 0.02406 + 0.10516 + 0.21067 + 0.25580 + 0.20964[/tex]
=> [tex]P(X < 5) = 0.805[/tex]
Considering question c
Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as
[tex]P(X > 6) = 1 - p(X \le 6)[/tex]
=> [tex]P(X > 6) = 1 - [P(X = 0) + \cdots + P(X =6)][/tex]
=> [tex] P(X > 6)=1 - [^{12} C_0 * (0.267)^0 * (1- 0.267)^{12-0}+ \cdots + ^{12} C_4 * (0.267)^6 * (1- 0.267)^{12-6} ][/tex]
=> [tex] P(X > 6)= 1 - [0.02406 + \cdots + 0.0519 ][/tex]
=> [tex]P(X > 6) = 0.0206[/tex]
I would be surprised because the value is very small , less the 0.05
(a )randomly observed individuals exactly do not cover their mouth when sneezing
[tex]P[x=8]=0.0037[/tex]
(b) randomly observed individuals fewer than do not cover their mouth when sneezing
[tex]P[x < 5]=0.805[/tex]
(c) fewer than half covered their mouth when sneezing
[tex]P(x > 6)=0.0206[/tex]
What will be the probability?It is given in the question that
The probability a randomly selected individual will not cover his or her mouth when sneezing is
[tex]P=0.267[/tex]
Generally, data collected from this study follows binomial distribution because the number of trials is finite, there are only two outcomes, (covering, and not covering mouth when sneezing ), the trial is independent
The probability distribution function for binomial distribution is
[tex]P(x=8)=n C_X\times p^x\times (1-p)^{n-x}[/tex]
Generally, the probability that among 12 randomly observed individuals exactly 8 does not cover their mouth when sneezing is mathematically represented as
[tex]P(x=8)=12c_8\times (0.267)^8\times (1-0.267)^{12-8}[/tex]
[tex]p(x=8)=495\times 0.000025828\times 0.2886794[/tex]
[tex]p(x=8)=0.0037[/tex]
Generally, the probability that among 12 randomly observed individuals fewer than 5 do not cover their mouth when sneezing is mathematically represented as
[tex]p(x < 5)=[p(x=0)+......+p9x=4)][/tex]
[tex]p(x < 5)=[12c_0\times(0.267)^0\times(1-0.267)^{12-0}+........+12c_4\times(0.267)^4\times (1-0.267)^{12-4}[/tex]
[tex]p(x < 5)=0.02406+0.10516+0.21067+0.25580+0.20964[/tex]
[tex]p(x < 5)=0.805[/tex]
Generally the probability that fewer than half(6) covered their mouth when sneezing(i.e the probability the greater than half do not cover their mouth when sneezing) is mathematically represented as
[tex]p(x > 6)=1-p(x\leq 6)[/tex]
[tex]p(x > 6)=1-[p(x=6)+......+p(x=6)][/tex]
[tex]p(x > 6)=1-[12c_0(0.267)^0\times(1-0.267)^{12-0}+....+12c_4\times(0.267)^6\times(1-0.267)[/tex]
[tex]p(x > 6)=1-[0.02406+.....+0.0519][/tex]
[tex]p(x > 6)=0.0206[/tex]
Thus
(a )randomly observed individuals exactly do not cover their mouth when sneezing
[tex]P[x=8]=0.0037[/tex]
(b) randomly observed individuals fewer than do not cover their mouth when sneezing
[tex]P[x < 5]=0.805[/tex]
(c) fewer than half covered their mouth when sneezing
[tex]P(x > 6)=0.0206[/tex]
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Paul is training for a bike race and is attempting to improve his average speed. With his old trainer, Paul averaged a pace of 20 MPH. With his new trainer, he rode at an average speed of 27 MPH. By what percent did his average speed increase?
Answer:
5.4%
Hope This Helps!
WHAT 10 x 10 ÷ 5 x 1000 ?
PLS SOMEONE HELP ME!!!!!!!!!!!
Answer:
20000
Step-by-step explanation:
10 * 10 = 100
100 / 5 = 20
20 * 1000 = 2000
PLEASE HELP!
Casey has 48 red peppers and 16 yellow peppers.
If Casey wants to put the peppers into baskets so that each basket has the same number of red peppers and the same number of yellow peppera, what is the greatest number of baskets he can make? How many of each type of pepper will be in each basket?
Answer:
Casey should use 16 baskets and put 4 red peppers 1 yellow pepper into each one of them.
Step-by-step explanation:
Greatest Common Divisor (GCD)
The GCD of x and y is the maximum possible number that evenly divides both of them.
For example, GCM(36,48) is 12 because 36/12 is a whole number and 48/12 is also a whole number and 12 is the greatest of all possible candidates. Note that 6 is also a common divisor (36/6 and 48/6 are whole numbers), but it's not the maximum.
Casey has 48 red peppers and 16 yellow peppers. Since he wants to put them into baskets in such a way that each basket has the same number of red peppers and the same number of yellow peppers, we must find the greatest divisor for both numbers to maximize the number of baskets.
The GCM(48,16) is 16. Number of red peppers per basket=48/16=4. Number of yellow peppers per basket=16/16=1, thus:
Casey should use 16 baskets and put 4 red peppers 1 yellow pepper into each one of them.
Sean is comparing dog food prices.At pet foods store,the total weight of a bag of dog food varies directly with the number of bags.Each bag costs $46.04.another store Healthy Pets sells dog food in 50 lb bags. Each bag costs $88.45. How much would Sean save by buying a 150 lb of dog food from Pet Foods instead of Healthy pets?
Answer:
Step-by-step explained :
How could you describe the maximum the LCM between two numbers could be?
Answer:
the product of the two numbers
Step-by-step explanation:
The LCM of two numbers is their product, divided by their GCF. If their GCF is 1, then the LCM will be their product. That is the most it can be.
__
We assume you're concerned with whole numbers. For rational numbers, the GCF may be a fraction, so the LCM may be larger than the product of the numbers.
LCM(5, 6) = 5·6/GCF(5, 6) = 5·6/1 = 30
LCM(1/2, 3/4) = (1/2)(3/4)/GCF(1/2, 3/4) = (3/8)/(1/4) = 3/2
(16/81
[tex](16 \div 81)1 \div 4[/tex]
Simplify this expression 1/2k^2+g-3+1/2k^2-3+2g
Step-by-step explanation:
the answer is 4 there are these steps you need to do this but I am not going to sit hee for an hour and tell you how to solve this answer so that is the answer
Answer:
THE CORRECT ANSWER IS A.
Step-by-step explanation:
An object’s speed and direction is its ________.
Write an equation in slope-intercept form for the line that passes through (0, 1) and is perpendicular to the line whose equation is y = 2x? Ay= -2x + 1 B y = 2x + 1 C y = x + 1 Dy=-%2x + 1
Answer:
y= -1/2 x + 1
Step-by-step explanation:
The line passes through point (0, 1) and is perpendicular to line with equation :
y=2x
Perpendicular lines are those that give -1 when the product of their slopes is calculated.
This means m₁ *m₂= -1
In this case, m₁=2, finding m₂ as;
m₁ * m₂ = -1
2 * m₂ = -1
m₂ = -1/2
Using point (0, 1),m₂ = -1/2, and imaginary line (x, y) then the equation of the line in slope-intercept form y= mx + b will be;
-1/2 = y-1/x-0
-1/2 x = y-1
1-1/2x = y
The equation will be ;
y= -1/2 x + 1
Six of 8 stores have power drinks on sale saturday. In simplest form, what fraction of the stores has power drinks on sale saturday?
What is the value of g? 18g+7=g
Answer:
The model below represents an equation. Which value of x makes the value true?
x=
Step-by-step explanation:The model below represents an equation. Which value of x makes the value true?
x=
The city has granted you a low property tax rate on your new hotel, and you will be paying $302,850 in taxes in the first year. After the first year, the tax you pay will then increase by 2% per year for the next 3 years. What will you pay in taxes at the end of the third year?
Answer:
the answer is $332135 for this question
Put these numbers in order from least to greatest.
Answer:
[tex]\sqrt{1}[/tex], 1.23, 5/4, [tex]\sqrt{3}[/tex], 1.9, 11/3
Step-by-step explanation:
5/4 = 1.25
11/3 = 3.67
[tex]\sqrt{3} =1.73[/tex]
[tex]\sqrt{1} =1[/tex]
1.23
1.9
Numbers from least to greatest:
[tex]\sqrt{1}[/tex], 1.23, 5/4, [tex]\sqrt{3}[/tex], 1.9, 11/3