Answers
Answer:
The answer is C.
Step-by-step explanation:
You should plug the numbers into the quadratic formula to get the answer.
Answer:
A: -5 ± √ 17 / 2
Step-by-step explanation:
Consider the following equations:
ax^2 + bx + c - This is an equation you use in understanding quadratic functions.
x= (−b± √b^2−4ac) / 2a - This is the quadratic formula used to solve quadratic functions
So: ax^2 + bx + c = x^2 + 5x + 2
SOLVE:
-(5) ± √ 5^2−4(1)(2)) / 2(1)
= -5 ± √ 25− 8 / 2
= -5 ± √ 25− 8 / 2
= -5 ± √ 17 / 2
Related Questions
2(x + 7)=?
I NEED HELP!!!!
Answers
Answer:
2x+14
Step-by-step explanation:
There are two sets of rainfall data for two different time periods in the same location.
Period 1: 2.3, 2.1, 2.2, 2.2, 2.2, 2.1, 2.4, 2.5, 2.2, 2.0, 1.9, 1.9, 2.1, 2.2, 2.3
Period 2: 2.3, 2.1, 3.3, 1.5, 3.6, 1.6, 3.0, 1.1, 4.7, 2.1, 2.4, 1.9, 2.8, 0.5, 2.3
Draw a conclusion based on the data provided.
has to be a sentence
Answers
Comparing the two sets of rainfall data for two different time periods in the same location, it can be concluded that the amount of rainfall in Period 1 was fairly constant whereas the amount of rainfall in Period 2 varied greatly.
What conclusion can be drawn from the rainfall data?The rainfall data for two different time periods in the same location provides information about the pattern of rainfall over the time periods.
The rainfall data over the period did not vary widely apart. The data shows that the amount of rainfall did not change too much.
However, for Period 2, the amount of rainfall had very different values.
Hence, it seems rainfall was more precise in frequency in Period 1 than in Period 2.
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A marketing firm conducts a survey to determine the ages of their survey subjects who like a new health drink.
This is the resulting data from their survey:
49, 63, 78, 22, 41, 39, 75, 61, 63, 65,
58. 37. 45, 52, 81, 75, 78, 72, 68, 59,
72, 85, 63, 61, 75, 39, 41, 48, 59,55
61, 25, 61, 52, 58, 71, 75, 82, 49, 51
The mean age of the subjects who like the new health drink is (type your answer...)
and the median age of the subjects is (type your answer..)
Answers
Answer:
Mean = 59.1, Median = 61
(there might have been a mistake in calculation (a lot of numbers!))
Step-by-step explanation:
The sample size is 40,
Now, the formula for the mean is,
Mean = (sum of the sample values)/(sample size)
so we get,
\(Mean = (49+63+78+22+41+39+75+61+63+65+58+37+45+52+81+75+78+72+68+59+72+85+63+61+75+39+41+48+59+55+61+25+61+52+58+71+75+82+49+51)/40\\Mean = 2364/40\\Mean = 59.1\)
To find the median, we have to sort the list in ascending (or descending)order,
we get the list,
22,25,37,39,39,41,41,45,48,49,
49,51,52, 52,55,58, 58, 59, 59, 61,
61, 61, 61, 63, 63, 63, 65, 68, 71, 72,
72, 75, 75, 75, 75, 78, 78, 81, 82, 85
Now, we have to find the median,
since there are 40 values, we divide by 2 to get, 40/2 = 20
now, to find the median, we takethe average of the values above and below this value,
\(Median = ((n/2+1)th \ value + (n/2)th \ value )/2\\where, \ the\ (n/2)th \ value \ is,\\n/2 = (total \ number \ of \ samples) /2\\n/2=40/2\\(n/2)th = 20\\Hence\ the (n/2)th \ value \ is \ the \ 20th \ value\)
And the (n+1)th value is the 21st value
Now,
The ((n/2)+1)th value is 61 and the nth value is 61, so the median is,
Median = (61+61)/2
Median = 61
PLEASE FOR THE LOVE OF GOD HELPPPP!!!!! THESE ARE DUE TONIGHT!!!
1. Twelve hungry teenagers can devour a very large pizza in 20 minutes. How many teenagers would it take to finish a very large pizza in 15 minutes? (Assume that all teenagers eat pizza at the same rate.)
2. For a statue of Miss Levans, the amount of gold required is directly proportional to the square of the height of the statue. A statue of Miss Levans that is 20 feet tall requires 80 pounds of gold. How many pounds of gold does a statue that is 25 feet tall require?
3. Tina lives 30 miles away from her work, and she normally drives at 45 miles per hour. If she wants to get to work 10 minutes earlier, how fast should she drive to work, in miles per hour?
4. All of the members of our spray-painting team paint at the same speed. If 5 team members can paint a certain wall in 27 minutes, then how many minutes would it take 15 of our team members to paint the same wall?
5. All of the members of our spray-painting team paint at the same speed. If 8 team members can paint a 5000 square foot wall in 30 minutes, then how many minutes would it take the 8 members to paint an 8000 square foot wall?
6. All of the members of our spray-painting team paint at the same speed. If 12 team members can paint a 2400 square foot wall in 45 minutes, then how many minutes would it take for 9 team members to paint a 3600 square foot wall?
7. I drove to my parents' house at 60 miles per hour. If I had driven 50 miles an hour instead, then I would have gotten there 40 minutes later. How many miles did I drive?
8. Fake gold bricks are made by covering concrete cubes with gold paint, so the cost of the paint is directly proportional to their surface area while the cost of the concrete is directly proportional to their volume. A cube with edges of length 1 inch costs $1.30 to make, while a cube with edges of length 2 inches costs $6.80 to make. How much would a cube with edges of length 3 inches cost to make?
9. Anabel's horse runs 24 miles per hour. Jackie's horse runs 28 miles per hour. Both horses stand at the starting line of a straight 2-mile track, and Jackie's horse starts running 30 seconds after Anabel's. How many miles from the starting line does Jackie's horse catch up to Anabel's?
10. Mrs. Danforth packed 5 bags of fun-sized candies for her family's picnic. Each bag contains 16 pieces. She had intended to pass out the same number of candies to each of her 4 children. But Cameron, her second-youngest, argues that she should instead distribute the candies in proportion to the children's ages. All of the children have different ages. If Cameron can convince his mother to give out the candies his way, he will gain two candies while his four-year-old sister will lose twelve. How old is Mrs. Danforth's oldest child?
Answers
Answer:
1) 9 teenagers
2) 100 pounds
3) . . .
4) 81 minutes
5) 48 minutes
6) 67.5 minutes
7) . . .
8) $10.20
9) . . .
10) . . .
Sorry that I wasn't able to get all of the answers.
I'm also not sure if number 4 is correct, but I don't know what else it would be.
But anyway, hope it helps!
Solution:
The shadow of an object is directly proportional to its height. Thus,
\[\frac{\text{Height of object}}{\text{Length of shadow}} = \frac{6}{16} = \frac{3}{8}.\]
Therefore, the height of the flagpole is $\frac{3}{8} \cdot 72 = \boxed{27}$ feet.
Your Response(s):
$ 27
VtProblem 2 – Correct! – Score: 7 / 7 (28044)
Problem: Report Error
Twelve hungry teenagers can devour a very large pizza in $20$ minutes. How many teenagers would it take to finish a very large pizza in $15$ minutes? (Assume that all teenagers eat pizza at the same rate.)
(Based on Problem 7.5 of the textbook.)
Solution:
Each of the twelve teenagers eats $\frac{1}{12}$ of the pizza in $20$ minutes. Thus, the rate of a teenager is
\[\frac{\frac{1}{12} \text{ pizza}}{20 \text { minutes}} = \frac{1}{240} \ \frac{\text{pizza}}{\text{minute}}.\]
This means in $15$ minutes, each teenager can eat
\[(15 \text{ minutes}) \left( \frac{1}{240} \ \frac{\text{pizza}}{\text{minute}} \right) = \frac{1}{16} \text{ pizza}.\]Therefore, it will take $\boxed{16}$ teenagers.
Alternatively, the number of teenagers is inversely proportional to the time it takes them to finish. From the given information, the constant of proportionality is $12 \cdot 20 = 240.$ Therefore, the answer we seek is $\frac{240}{15} = \boxed{16}.$
Your Response(s):
$ 16
VtProblem 3 – Correct! – Score: 1 / 7 (28043)
Problem: Report Error
For a statue of Miss Levans, the amount of gold required is directly proportional to the square of the height of the statue. A statue of Miss Levans that is $20$ feet tall requires $80$ pounds of gold. How many pounds of gold does a statue that is $25$ feet tall require?
We suggest you study Section 7.1 if you find this problem difficult.
Solution:
Let $h$ be the height of the statue, and let $g$ be the amount of gold required. Then
\[g = kh^2\]for some constant $k.$
Since $g = 80$ when $h = 20,$
\[80 = k \cdot 20^2,\]so
\[k = \frac{80}{20^2} = \frac{1}{5}.\]
So when $h = 25,$
\[g = \frac{1}{5} \cdot 25^2 = \boxed{125}.\]
Hint(s):
Let $h$ be the height of the statue, and let $g$ be the amount of gold required. Then $g = kh^2$ for some constant $k.$ Find $k.$
Your Response(s):
% 100
% 625/4
% 10000
$ 125
VtProblem 4 – Correct! – Score: 7 / 7 (28041)
Problem: Report Error
Tina lives $30$ miles away from her work, and she normally drives at $45$ miles per hour. If she wants to get to work $10$ minutes earlier, how fast should she drive to work, in miles per hour?
We suggest you study Section 7.4 if you find this problem difficult.
Solution:
all of the following are possible steps of scientific investigation except for . group of answer choices the development of one or more working hypotheses or models to explain facts development of observations and experiments to test the hypotheses assumption of conclusions without prior experimentation or observation the collection of scientific facts through observation and measurement
Answers
All of the following are possible steps of scientific investigation except for
C. assumption of conclusions without prior experimentation or observation
All of the following are possible steps of scientific investigation except for.
A. the development of one or more working hypotheses or models to explain facts
B. development of observations and experiments to test the hypotheses
C. assumption of conclusions without prior experimentation or observation
D. the collection of scientific facts through observation and measurement
All of the following are possible steps of scientific investigation except for
C. assumption of conclusions without prior experimentation or observation
At the core of biology and other sciences lies a problem-solving approach called the scientific method. The scientific method has five basic steps, plus one feedback step:
Make an observation.
Ask a question.
Form a hypothesis, or testable explanation.
Make a prediction based on the hypothesis.
Test the prediction.
Iterate: use the results to make new hypotheses or predictions.
The scientific method is used in all sciences—including chemistry, physics, geology, and psychology. The scientists in these fields ask different questions and perform different tests. However, they use the same core approach to find answers that are logical and supported by evidence.
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Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ∇f. F(x, y) = (2x − 7y)i + (−7x + 8y − 6)j
Answers
Answer: f = x^2-7yx+4y^2-6y
Step-by-step explanation:
A vector field is conservative if the work done by that vector field around any loop is 0 or the end points only matter when calculating the work done, not the path in between (think of gravity). The curl(F) must equal 0.
curl(F) = ∇ x F =0
= det( \(\left[\begin{array}{ccc}\frac{d}{dx} &\frac{d}{dy} \\(2x-2y)&(-7x+8y-6)\end{array}\right]\) ) (***partial derv)
-7 - (-7) = 0
Yes, it is conservative, which means we can find the potentional energy function by turning the vector field into the gradient of scalar function.
\(f_x=2x-7y\\f_1=x^2-7yx+C(y)\\f_1y=-7x +C'(y)\\\\C'(y)=8y-6\\C(y)=4y^2-6y\\\\f=x^2-7yx+4y^2-6y\\\)
I need help with this question
Answers
Answer:
5/7
Step-by-step explanation:
ratio of boys to girls---> 2:5
ratio sum: 2+5=7
girls ratio =5/7
OR
total of people in 7th grade choir=28
hence, no of girls in 7th grade choir=5/7 × 28
=20
proportion of girls in choir= 20/28 = 5/7
(36)^x+2= 6
Solve and round to the nearest 100th
Please help I am confused and need an explanation
Answers
As the given equation is (36)ˣ⁺² = 6 , then the solution for the given equation is x ≈ -1.54.
The given equation in the question is (36)ˣ⁺² = 6
according to the given equation , the goal is to solve the equation for x.
For solving this equation ,
we'll have to use logarithmic operations which is as follows:
log36(6) = x+2.
We will be further using a calculator to determine the logarithmic value: log36(6) ≈ 0.4607.
Now, By subtracting 2 from both sides, we will get the value of x as:
x ≈ -1.54.
When we round off this value to the nearest 100th, we will get -1.54.
Thus , the solution for the given equation is x ≈ -1.54.
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Which of the following shows the division problem down below
Answers
Question:
Solution:
Synthetic division is a quick method of dividing polynomials; it can be used when the divisor is of the form x-c. In synthetic division, we write only the essential parts of the long division. Notice that the long division of the given problem is written as:
thus, the synthetic division of the given problem would be:
Writing 6 instead of -6 allows us to add instead of subtracting. We can conclude that the correct answer is:
A.
Question 2
5 pts
Which of the following subtraction problems show a difference of 12.93?
Select TWO that apply.
51.639 - 38.709
146.8 - 17.5
136.8 - 122.87
18.63 - 5.7
Answers
Answer:
51.639-38.709
18.63-5.7
Step-by-step explanation:
Hope it helps...
18.63-5.7
Hope it helped
206) A recipe for cupcakes calls for 3-
3
10
200
7
sugar. Julio accidentally put in 4-
10
How many extra cups did he put in?
cups of
cups.
Answers
Julio accidentally put in an extra 1/10 cup of sugar.
To calculate the number of extra cups of sugar that Julio put in, we need to find the difference between what the recipe called for (3/10 cups) and what he actually added (4/10 cups).
The difference can be calculated as follows:
Actual amount - Required amount = Extra amount
= 4/10 - 3/10
= 1/10
Therefore, Julio accidentally put in an extra 1/10 cup of sugar.
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25. Which equation is not proportional? *
Oy=2x-3
Oy=150x
Oy=1/2x
YE 7
Answers
Hi there! Your answer is y = 2x-3
Please see an explanation for a better and clear understanding to your problem.
Any questions about my answer and explanation can be asked through comments! :)
Step-by-step explanation:
For an easy understanding to "proportional equation", It is basically an equation that is in form of y = mx + b where b = 0. Therefore, when b = 0 - Our new equation would be y = mx.
Other choices are in form of y = mx while the first choice isn't in the form of y = mx.
To be a proportional function or equation, the equation must be in the form of y = mx only.
The question asks which equation Is not proportional. Hence, the answer is the first choice.
Hope this helps!
The students in Mrs. Barnett's first-grade class sit down in a circle for show-and-tell. The circle they form has a diameter of 4 meters. What is the circle's radius?
Answers
Answer:
Step-by-step explanation:
If the diameter is 4 meters, then the radius has to be 2 because the radius is half of the diameter.
HELP 10 MIN LEFT!!!!
Answers
Answer:
To one decimal place,
y = 16.3 m
Step-by-step explanation:
Using SOHCAHTOA,
In this case we need to use CAH,
WE know the angle = 25 and the hypotenuse H = 18,
so,
y = adjacent
\(cos(angle) = y/H\\y = (18)(cos(25))\\y = 16.3135\\y = 16.3\)
Answer: 16.3 in.
Step-by-step explanation:
use SOH CAH TOA
cos x = adj/hyp
cos 25 = y/18
18 cos 25 = y
y= 16.3
which could be a possible root of 3x4 10x3 9x2 40x 12 0
Answers
\(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\) is the possible root
What is a root ?
Mathematicians refer to a number as having a root if it can be multiplied by itself to give the original number. The square root of 49, for instance, is 7, as 77=49. 7 is referred to as the square root of 49 in this instance because it takes 49 to multiply 7 by itself twice. Considering that 333=27, the cube root of 27 is 3.
Quadratic equation's roots The roots of a quadratic equation are the values of the variables that fulfill the equation. In other words, if f() = 0, then x = is a root of the quadratic equation f(x). The x-coordinates of the sites where the curve y = f(x) intersects the x-axis are the real roots of an equation f(x) = 0.
3x^4 -10x^3 -9x^2 + 40x - 12
=\(\left(3x-1\right)\frac{3x^4-10x^3-9x^2+40x-12}{3x-1}\)
=\(\left(3x-1\right)\left(x^3-3x^2-4x+12\right)\)
= \(\left(3x-1\right)\left(x-3\right)\left(x+2\right)\left(x-2\right)\)
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Paul plans to buy a movie that has a regular price of $12.99. It is on sale for 15% off, but Paul will have to pay 7% sales tax. Which is the MOST reasonable estimate of the total cost of the movie including tax?
Answers
Answer:
Figure it out yourself
Step-by-step explanation:
If triangles ABC and DEF are similar, what is y? Show your work.
Answers
The value of y is 18
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths. The angles of the two triangle must be equal and it not necessary they have equal sides.
Therefore the corresponding angles of similar triangles are congruent and the ratio of corresponding sides of similar triangles are equal.
Therefore;
14/21 = 12/y
14y = 21 × 12
14y = 252
divide both sides by 14
y = 252/14
y = 18
Therefore the value of y is 18.
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Please show work and thank you
Answers
Answer:
x = 46.13 cm
Step-by-step explanation:
It is a right triangle, the missing side is a cathetum, according to the Pythagorean Theorem:
Assign "x" to the missing side:
\((47)^{2} =(9)^{2} +x^{2}\)
\(x^{2} =(47)^{2} -(9)^{2} =2128\)
\(x=\sqrt{2128} =46.13\)
Hope this helps
Nathaniel mowed 18 lawns in 3 hours. What was his rate of mowing in hours per lawn?
Answers
Answer:
1/6 hours for every 1 lawn:)
Step-by-step explanation:
Nathaniel mow 18 lawns in 3 hours, then the rate of mowing will be 0.16 or 1/6 hours per lawn.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the information given in the question,
Total lawns mowed by Nathaniel = 18
Total time taken by Nathaniel to mow 18 lawns = 3 hours.
Then, the time required to mow each lawn is,
= 18/3
= 1/6 hrs. Or 0.16 hrs.
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The average body temperature of all healthy adults is 98.6 F. A doctor takes a random sample of 100 healthy adults and records the temperature of each. The average temperature of these 100 adults is 98.2 F and the standard deviation is 6.9 F. Identify the values of the statistic and the parameter(s).
Answers
Answer:
Explained below.
Step-by-step explanation:
A parameter is a valuable element of statistical analysis. It denotes the characteristics that are used to define a given population. It is used to define a particular attribute of the population. For instance, population mean, population standard deviation, population proportion and so on.
The parameter of interest is the average body temperature of all healthy adults, μ = 98.6°F.While making a statistical conclusion about the population under study, the parameter value is unknown. This is because it would not be possible to gather data from every single member of the population. So a sample is selected from the population to derive a conclusion about the parameter.
A statistic is the value of the characteristics that are computed using this sample. For instance, sample mean, sample standard deviation, sample proportion and so on.
The statistic is the average body temperature of 100 randoly selected healthy adults, \(\bar x=98.2^{o}F\).4 3/8 + 5 1/2= in fractions
Answers
Answer:
9 7/8
Step-by-step explanation:
1. 4 3/8 can be converted into the improper fraction 35/8, and 5 1/2 can be converted into 11/2.
2. Now that we have 35/8 + 11/2, we have to find a common denominator. Since 2 goes into 8 four times, we can turn 11/2 into 44/8 by multiplying the numerator and denominator (the top and the bottom numbers) by 4.
3. Now we have 35/8 + 44/8. At this point, the all we have to do is add the numerators (the top numbers). 35+44=79, so our answer is 79/8, which we can simplify to 9 7/8.
A summary of the two stocks is shown.
Name of Stock Symbol Closing Price Day 1 Closing Price Day 2 Closing Price Day 3
Metropolis, Ltd MTP 17.95 18.25 18.28
Suburbia, Inc SBR 5.63 4.98 5.25
Suppose you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price. Which day, during the following two days, would be the best to sell both stocks and by how much?
Day 2 is the best by $13.00.
Day 3 is the best by $13.00.
Day 2 is the best by $2.45.
Day 3 is the best by $2.45.
Answers
The day, from the following two days, which would be the best to sell both stocks with the closing price is day 3 by an amount of $2.45.
Given are the closing prices of two stocks in three days.
If you purchase 65 shares of Metropolis stock and 50 shares of Suburbia stock on Day 1 at the closing price,
Amount invested = (65 × 17.95) + (50 × 5.63) = $1448.25
If the stock is sold in day 2,
Amount received = (65 × 18.25) + (50 × 4.98) = $1435.25
Profit = $1435.25 - $1448.25 = -$13
If the stock is sold in day 3,
Amount received = (65 × 18.28) + (50 × 5.25) = $1450.7
Profit = $1450.7 - $1448.25 = $2.45
The profit is more for day 3 than day 2.
Hence it is best to sell on day 3 by $2.45.
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The maxwell family goes out for dinner and the price of the meal is $60 the sales tax on the meal is 7% and they also want to leave a 15% tip what is the total cost of the meal
Answers
Then we add the tax which is $60•0.07= 4.20 that is the tax
Then add the tax to the total $60 + $4.20= $64.20
Next we must add the tip so $60•0.15= 9.
Then $64.20 + $9.00 = $73.20
Total cost of meal $73.20
Any questions? :)
Answer: $ 73.20
Step-by-step explanation:
60+(60*0.07)+(60*0.15)=73.2
The length of a rectangle is four less than twice its width. If the perimeter of the rectangle is 76 units, what is its width?
a
13
b
14
c
20
d
26
e
28
Answers
You are finding a measure of center in the data sets below using either the mean or the median. In which of the data sets should you find the median? Select all that apply.
A) 68, 73, 77, 75, 23, 62 B) 84, 73, 28, 91, 93, 77 C) 24, 22, 21, 19, 23, 25 D) 18, 13, 56, 21, 12, 19 E) 77, 15, 81, 83, 84, 72
Answers
The whole given data sets can have their median calculated after being arranged either in an ascending or descending order. That is option A,B,C,D and E.
What is median of a data set?The median of a data set is defined as the data that is found at the center, otherwise known as the measure of center of a data set, after being arranged in ascending or descending order.
For example the median of option A) is calculated as follows:
Data set= 23,62,68,73,75,77
Median = 68+73/2 = 70.5
Therefore the median is between 68 and 73 which is = 70.5
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you're valuing horn of plenty mining, inc.'s, stock in order to compare its value to its market price. you believe that the company will pay total dividends of $1.45 in 2015 and $1.56 in 2016. you also believe the company's stock price will be $35.80 at the end of 2016. if the appropriate discount rate is 12 percent, what's the value of horn of plenty mining's stock? a. $39.22 b. $38.31 c. $36.87 d. $37.43
Answers
Step 1: Calculate the present value of each dividend payment.
PV(2015) = $1.45 / (1 + 0.12)^1 = $1.29
PV(2016) = $1.56 / (1 + 0.12)^2 = $1.22
Step 2: Calculate the present value of the expected stock price at the end of 2016.
PV(2016 stock price) = $35.80 / (1 + 0.12)^2 = $28.33
Step 3: Add up the present values of the dividend payments and stock price to get the total stock value.
Stock value = PV(2015) + PV(2016) + PV(2016 stock price) = $1.29 + $1.22 + $28.33 = $30.84
Therefore, the value of Horn of Plenty Mining's stock is $30.84, which means that the correct option is e) None of the above.
During the summer vacation Natalie made three hikes. The first took her 2 days 45 minutes, the second 1 day 22 hours 45 minutes and the third 2 days 7 hours 20 minutes.
What was Natalie's total hiking time for the summer vacation?
5 days 6 hours 10 minutes.
5 days 5 hours 50 minutes.
6 days 5 hours 10 minutes.
6 days 6 hours 50 minutes.
Answers
Answer: 6 days 6 hours 50 minuets.
Step-by-step explanation:
Separate each unit of time and add them up:
5 days , 29 hours, 110 minuets.
since there are 24 hours in a day, you will add one to days and subtract 24 from hours.
6 days, 5 hours and 110 minuets.
60 minuets are in an hour, to simplify it, you subtract 60 from 110 mins and carry that 1 to hours.
6 days, 5 hours and 50 mins.
Hope this helps:D
At a supermarket, there are 118 customers. If 45 have purchased shirts, 59 have
purchased pants, and 40 have purchased neither, how many purchased both shirts and
pants?
Answers
Using the Venn Diagram principles, the number of customers at the supermarket who purchased both shirts and pants is 26.
What is a Venn Diagram?A Venn Diagram shows a pictorial or graphical representation of the relationship (similarities and differences) between data sets.
In a Venn Diagram, overlapping circles or other shapes can be used to depict the logical relationships between two or more data sets or items.
The total number of customers at a supermarket = 118
The number of customers who purchased shirts, n(A) = 45
The number of customers who purchased pants, n(B) = 59
The number of customers who purchased neither shirts nor pants = 40
Let the number of customers who purchased both shirts and pants = n(A ∩ B)
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A) = 45 n(B) = 59 n(A ∪ B) = 118 - 40 = 78
Substituting values:
78 = 45 + 59 - n(A ∩ B)
Solving for n(A ∩ B), we get:
n(A ∩ B) = 45 + 59 - 78 n(A ∩ B) = 26
Thus, using the formula of Venn Diagram, we can conclude that at this supermarket with 118 customers, 26 customers purchased both shirts and pants.
Learn more about Venn Diagram at https://brainly.com/question/28060706.
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(Use Pascal's triangle to expand each binomial. (x – 5y)^5
Answers
The n-th row in Pascal's triangle tells you the coefficients of terms in the expansion of (a + b)ⁿ. Starting with n = 0,
1
1 … 1
1 … 2 … 1
1 … 3 … 3 … 1
1 … 4 … 6 … 4 … 1
1 … 5 … 10 … 10 … 5 … 1
In more concrete terms, this translates to
(x - 5y)⁵ = 1 x ⁵ (-5y)⁰ + 5 x ⁴ (-5y)¹ + 10 x ³ (-5y)² + 10 x ² (-5y)³ + 5 x ¹ (-5y)⁴ + 1 x ⁰ (-5y)⁵
Simplify:
(x - 5y)⁵ = x ⁵ - 25x ⁴y + 250x ³y ² - 1250x ²y ³ + 3125xy ⁴ - 3125y ⁵
"alice and Chloe had a total of 308 seashells at first. After Alice sold 56 seashells, Chloe had thrice as many seashells as her. How many sea shells does Alice have at first?" singapore math
Answers
Answer:
119
Step-by-step explanation:
308 - 56 = 252
252/4 = 63
63 + 56 = 119
Hope this helps!
Answer:
let Alice seashells be X and Chloe's be Y
x + Y = 308.........i
3(X - 56) = Y.......... ii
simultaneous equation created
{X + Y = 308}
{3X - 168 = Y}
X + Y = 308
3X - Y = 168........by elimination method
4X + 0 = 476
X = 119
therefore.... Alice had 119 seashells at first
from eqn(i)...
X + Y = 308
119 + Y = 308
Y = 308 - 119
Y = 189
therefore.... Chloe had 189 seashells at first