Suppose you have 10 black, 10 white, 10 blue, and 10 brown
socks. How many socks to pick (blindly, since there is no light in
the room) so that all 3 brothers wear the same color socks
Answers
Suppose you have 10 black, 10 white, 10 blue, and 10 brown socks. The minimum number of socks to pick that all 3 brothers wear the same color socks is 4 of the same color.
You are required to determine how many socks to pick blindly since there is no light in the room so all three brothers wear the same color socks. In this question, we have 4 types of socks. Therefore, we can apply Pigeonhole Principle here. Pigeonhole Principle states that If n+1 items are put into n boxes, then at least one box must contain two or more items.
Assuming that a brother needs to wear 3 socks of the same color. Therefore, for all 3 brothers to wear the same color socks, we must pick 4 socks of the same color. Therefore, the minimum number of socks that needs to be picked = 4.
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Related Questions
All of the select options are the same which are ( -6,-4,-2,0,2,4,6)
Answers
Answer
The coordinates change from their current form into the coordinates of the image as given below.
A (2, 2) = A' (2, -2)
B (2, 4) = B' (4, -2)
C (4, 6) = C' (6, -4)
D (6, 4) = D' (4, -6)
E (6, 2) = E' (2, -6)
Explanation
Rotating a given coordinate A(x, y) 90° about the origin in the clockwise direction gives a new coordinate A'(y, -x)
So, to rotate this coordinate, we will first write out the given coordinates.
A (2, 2)
B (2, 4)
C (4, 6)
D (6, 4)
E (6, 2)
Recalling that the rotation makes A (x, y) change into A' (y, -x), each of these coordinates become
A (2, 2) = A' (2, -2)
B (2, 4) = B' (4, -2)
C (4, 6) = C' (6, -4)
D (6, 4) = D' (4, -6)
E (6, 2) = E' (2, -6)
Hope this Helps!!!
B (2, 4) = B' (4, -2)
C (4, 6) = C' (6, -4)
D (6, 4) = D' (4, -6)
E (6, 2) = E' (2, -6)
There u go
a population of ground squirrels has an annual per capita birth rate of 0.08 and an annual per capita death rate of 0.02. calculate an estimate of the total number of individuals added to (or lost from) a population of 1000 individuals in one year. if individuals are lost, use a negative sign in front of your answer.
Answers
Per year 40 squirrels are added
What is estimation explain?Any of the many statistical methods used to determine the value of a population's attribute based on observations of a sample taken from the population is known as an estimate. For instance, a point estimate is the one figure that is most likely to convey the property's value.
What are the estimation and types?Estimates are created by multiplying the unit cost of the relevant goods by the amounts derived from the dimensions of the designs for various things needed to execute the project. Estimates' objectives: should be aware of the financial requirements for finishing the suggested task.
According to the given question
The birth rate is 0.06 and the death rate is 0.02 per person per year. The number of deaths per year for a population of 1000 is equal to 1000*0.02, or 20. The annual birth rate is equal to 1000 * 0.06, or 60. As a result, the population of squirrels grows by a total of 40 individuals each year
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what is the slope of the line -9x + 7y = 63
Answers
Answer: I think its x = 38
Step-by-step explanation:
Answer:
9/7
Step-by-step explanation:
Is it true that If v1, v2,. . ., vp are in R^n, then Span{v1, v2,. . ., vp} is the same as the column space of the matrix [v1 v2 . . . vp]
Answers
Yes.
It is true that if v1, v2, ..., vp are vectors in Rⁿ, then Span{v1, v2, ..., vp} is the same as the column space of the matrix [v1 v2 ... vp].
True, let A = [v1 v2 ... vp] be the matrix columns are the given vectors.
The column space of A is the set of all linear combinations of the columns of A, which is exactly the same as the span of the vectors v1, v2, ..., vp.
In other words, any vector that can be written as a linear combination of the columns of A is also in Span{v1, v2, ..., vp}, and vice versa.
The tools of linear algebra to study the span of a set of vectors, by considering the column space of the corresponding matrix.
Techniques like row reduction and rank to determine if a set of vectors is linearly independent or spans the whole space Rⁿ.
Yes, the given vectors should be used as the matrix columns in A = [v1 v2... vp].
The span of the vectors v1, v2,..., vp is exactly the same as the column space of A, which is the set of all linear combinations of the columns of A.
This means that any vector that can be expressed as a linear combination of columns from A is also a vector in Spanv1, v2,..., vp and vice versa.
By taking into account the column space of the associated matrix, the techniques of linear algebra may be used to examine the range of a collection of vectors.
To establish if a group of vectors spans the whole space Rn or is linearly independent, use methods like rank and row reduction.
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write 16+32 as a product of two factors one the gcf
Answers
Answer:
4 is one factor as gcf
In 2003, the population of an African country was about 22.5 million people, which is 1 million more than
5 times the population in 1950.
Enter and solve an equation to find the approximate population p (in millions) in 1950.
An equation is
The approximate population in 1950 was
million people.
Answers
Answer:
Population of Africa in 2003 is 22.5 million
population of Africa in 1950 is 1 million - 22.5 million /5
21.5million / 5
21500000/5
4300000
4.3 million people
EXPANDING BRACKETS -
2 (3x + 7)
Answers
Answer:
\( \sf \: 6x + 14 \)
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
The property we use,
→ Distributive property.
The expression is,
→ 2(3x + 7)
Let's simplify the expression,
→ 2(3x + 7)
→ 2(3x) + 2(7)
→ (2 × 3)x + 14
→ 6x + 14
Hence, the answer is 6x + 14.
Somebody help me out please
Answers
Answer:
the correct answer is d.
Step-by-step explanation:
i hope this helps :)
Answer:
D.
Step-by-step explanation:
The line crosses the x-axis at 4 and the y-axis at -2.
Answer: D.
10. A snowstorm dumped 18 inches of snow in a 12-hour period. How many inches were falling per hour?
Answers
Answer:
1.5 inches I think
Step-by-step explanation:
18/12=1.5
4x3 what is 4x3 I really want to know
Answers
Answer:
The answer to 4x3 is 12
same as adding 4 thee times!
4 plus 4 plus 4 equals 12
Answer:
4X3=12
Step-by-step explanation:
It's like adding 4 3 times
What is the forecast for May using a five-month moving average?(Round answer to the nearest whole number.) Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
A. 43 B. 47 C. 52 D. 38 E. 39
Answers
The forecast for May using a five-month moving average is 39 (Option E).
Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.
According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47
We have to add the sales of these five months, which gives:
27 + 40 + 42 + 41 + 47 = 197
To find the moving average for May, we divide this sum by 5:
197 / 5 = 39.4
Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.
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Evaluate: 22 + k for k=25
Answers
solve x in the problem 19+x=7x+11
Answers
Answer:
x = 8/6 or 1 1/3
Step-by-step explanation:
Step 1:
19 + x = 7x + 11 Equation
Step 2:
19 = 6x + 11 Subtract x on both sides
Step 3:
8 = 6x Subtract 11 on both sides
Step 4:
x = 8 ÷ 6 Divide
Answer:
x = 8/6 or 1 1/3
Hope This Helps :)
explanation:
whats the square rout of 1732
Answers
Answer:
41.61730409 you have to use your calculator to get the answer
Mrs. Vincents's science class launched a toy rocket from ground level with an initial upward velocity of 60 feet per
second. The height h of the rocket in feet above the ground after t seconds is modeled by the equation h=60t - 16t^2.
How long was the rocket in the air before it returned to the ground?
Answers
Answer:
3.75 seconds
Step-by-step explanation:
To find the time it hit the ground, we must find the roots of the equation.
Factoring:
Take out the common factor of -4
\(-4(4t-15)=h\)
Find the root with the zero product property.
\(4t=15\\t=3.75\)
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Solve for x.
5 1/2≥1.6x
x≥3 7/16
x≤3 7/16
x≥8 4/5
x≤8 4/5
Answers
The values of x when solved;
a. x≥ 3. 44
b. x≥3. 44
c. x ≤ 8. 8
What are inequalities?Inequalities are simply described as relations that makes a non-equal comparison between two numbers, variable or other mathematical expressions.
They are used to compare numbers on the number line on the basis of size
From the information given, we have to determine the value of x in the inequality given;
a. 5 1/2≥1.6x
convert to improper fraction
11/2 ≥1.6x
divide both sides by 1. 6
x≥ 3. 44
b. x≥3 7/16
convert to improper fraction
x≥ 55/ 16
x≥3. 44
c. x≤8 4/5
convert to improper fraction
x≤ 44/ 5
x ≤ 8. 8
Hence, the value are x≥ 3. 44, x≥3. 44 and x ≤ 8. 8
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I need help with #47 ASAP please and thank you. It is due tomorrow
Answers
Sides of hexagon = 6
Hexagon
1
1 + 5 = 6
1 + 5 + 9 = 15
1 + 5 + 9 + 13 = 27
1 + 5 + 9 + 13 + 17 = 45
Use the Pythagorean Theorem to solve for the missing side of the right triangles.
Answers
The functions f and g are defined by f: x = 4 - x and g: x = hx² + k. If the composite function gf is given by gf: x + 2x² - 16x + 26, find
(a) the value of h and of k,
Answers
Answer:
Step-by-step explanation:
f(x) = 4-x
g(x) = h\(x^{2}\)+k
g(f(x)) = 2\(x^{2}\)-16x+26
so put f(x) in g(x)
h\((4-x)^{2}\)+k
h((4-x)(4-x) + k
h(\(x^{2}\)-8x+16)+k
if h = 2 , then
2\(x^{2}\)-16x+32 + k
and we want 26 instead of 32 so subtract 6 so K = (-6)
2\(x^{2}\)-16x+32 + (-6)
2\(x^{2}\)-16x+32 - 6
2\(x^{2}\)-16x+26
h=2
k=(-6)
Can a/the variable in a algebraic expression be a base?
Answers
Answer:
yes
Step-by-step explanation:
yes
yes
yes
yes
yeyed
yes
Write an expression that is the product of two factors and is equivalent to - 2x - 12.
Answers
Answer:
\(-2(x+6)\rightarrow(D)\)Explanation: We need to simply factorize the given to get the expression that is the product of two factors, this is done as follows:
\(\begin{gathered} -2x-12\rightarrow-2(x+6) \\ \text{ We factored out -2} \\ \therefore\rightarrow \\ -2(x+6)\rightarrow\text{ (D) Option} \end{gathered}\)Note! The resulting expression s indeed a product of two factors!
an insurance company checks police records on 582 accidents selected at random and notes that teenagers were at the wheel in 91 of them. (a) (8 pts) find the 95% confidence interval for , the true proportion of all auto accidents that involve teenage drivers. (note: for full credit, show all your work. no credit
Answers
The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).
To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.
The formula for the confidence interval is:
CI = p1 ± Z * √((p1 * (1 - p1)) / n)
Where:
CI is the confidence interval,
p1 is the sample proportion (proportion of accidents involving teenage drivers),
Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),
n is the sample size (number of accidents checked).
Given:
Number of accidents checked (sample size), n = 582
Number of accidents involving teenage drivers, x = 91
First, we calculate the sample proportion:
p1 = x / n = 91 / 582 ≈ 0.1566
Now we can calculate the confidence interval:
CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)
Calculating the standard error of the proportion:
SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184
Substituting the values into the formula:
CI = 0.1566 ± 1.96 * 0.0184
Calculating the values:
CI = 0.1566 ± 0.0361
Finally, we can simplify the confidence interval:
CI = (0.1205, 0.1927)
Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).
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2 × (5 + 5)
Which of the following describes (5 + 5) in the expression above?
Answers
Answer:
20
Step-by-step explanation:
the answer your looking for is 20
3). A cylindrical tank, 5 m in diameter, discharges through a horizontal mild steel pipe 100 m long and 225 mm in diameter connected to the base. Find the time taken for the water level in the tank to drop from 3 to 0.5 m above the bottom.
Answers
The time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom cannot be determined without additional information.
To calculate the time taken, we need to know the flow rate or discharge rate of the water from the tank. This information is not provided in the question. The time taken to drain the tank depends on factors such as the diameter of the outlet pipe, the pressure difference, and any restrictions or obstructions in the flow path.
If we assume a known discharge rate, we can use the principles of fluid mechanics to calculate the time. The volume of water that needs to be drained is the difference in the volume of water between 3 meters and 0.5 meters above the bottom of the tank. The flow rate can be determined using the pipe diameter and other relevant factors. Dividing the volume by the flow rate will give us the time taken.
However, since the discharge rate is not given, we cannot perform the calculation and determine the time taken accurately.
Without knowing the discharge rate or additional information about the flow characteristics, it is not possible to calculate the time taken for the water level in the tank to drop from 3 to 0.5 meters above the bottom.
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Chandler wants to raise 200$ to buy a new gaming system. He already has 80$ and plans to save 40$ a week. How many weeks will it take chandler to raise enough money to buy his gaming system?
Answers
Answer:
3 weeksStep-by-step explanation:
Step one:
given data
expected amount =$200
cash already at hand=$80
savings per week=$40
let the number of weeks be x
Step two:
the linear function for the situation is the same as the equation of a straight line
y=mx+c------1
200=4x+80
solve for x
200-80=40x
120=40x
divide both sides by 4
x=120/40
x= 3 weeks
Chandler will save for 3 weeks
Leslie is buying donuts for all her friends. Donuts cost 85 cents each. He has $20. What is the maximum number of donuts she can buy?
Answers
First, we need to convert Leslie's dollars to cents, since the cost of each donut is given in cents. We can do this by multiplying the dollars by 100:
$20 * 100 = 2000 cents
Now we can divide the total amount of money (in cents) by the cost of each donut (85 cents) to find the maximum number of donuts Leslie can buy:
2000 cents ÷ 85 cents/donut ≈ 23.53 donuts
Since Leslie cannot buy a fraction of a donut, we will round down to the nearest whole number. Therefore, the maximum number of donuts Leslie can buy with $20 and with each donut costing 85 cents is 23 donuts.
Answer:
23
Step-by-step explanation:
$20/$.85 ≈ 23.5294
Since Leslie cannot buy half a donut, she can buy 23.
An employee is 25 years old and starting a 401k plan. The employee is going to invest $150 each month. The account is expected to earn 5.5% Interest, compounded monthly.
What is the account balance, rounded to the nearest dollar, after two years?
A spreadsheet was used to calculate the correct answer. Your answer may vary slightly depending on the technology used.
O$3,976
O$3,796
O $6,675
O$6,765
Answers
The account balance (future value) of the employee's investment in a 401k plan, rounded to the nearest dollar, after two years is B. $3,796.
What is the future value?The future value refers to the compounded present value.
Compounding involves charging interest on accumulated interest and principal over the periods.
The future value can be determined using an online finance calculator.
N (# of periods) = 24 months (2 years x 12)
I/Y (Interest per year) = 5.5%
PV (Present Value) = $0
PMT (Periodic Payment) = $150
Results:
Future Value (FV) = $3,796.28
Sum of all periodic payments = $3,600 ($150 x 24)
Total Interest = $196.28
Thus, the employee's balance (future value) in the 401k plan after two years is Option B.
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What is the value of the expression 1 2 3 4 5?
Answers
The value of the given and completed expression in this problem is
-1
What are combined operations?Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.
In this case we have an arithmetic polynomial.
We complete the expression as follows:
1 + 2 - 3 + 4 - 5
We group the positive terms on one side and negative terms on the other:
(1 + 2 + 4) - (3 + 5)7 - (8)-1The value of the expression (1 + 2 - 3 + 4 - 5) is -1
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Find the area of a circle with a diameter of 16 units.
Exact Area:
Approx Area (use 3.14 for pi):
Approx Area (use 22/7 for pi):
Answers
Answer:
exact: 64π square units3.14 for π: 200.96 square units22/7 for π: 201 1/7 square unitsStep-by-step explanation:
You want the area of a 16-unit circle using different values for pi.
AreaThe formula for the area of a circle is ...
A = πr² . . . . . . where r is half the diameter
For the different values of pi, this will be (in square units) ...
π(8²) = 64π . . . . exact
3.14(8²) = 200.96 . . . . using 3.14 for π, slightly low
22/7(8²) = 201 1/7 . . . . using 22/7 for π, slightly high
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Cora is wrapping a ribbon around a cylinder-shaped gift box. The box has a diameter of 15 inches and the ribbon is 60 inches long. Cora is able to wrap the ribbon all the way around the box once, and then continue so that the second end of the ribbon passes the first end. What is the central angle formed between the ends of the ribbon? Round your answer to the nearest tenth of a degree.
Answers
The central angle formed between the ends of the ribbon is 98.6°.
How to illustrate the angle?The circumference will be:
= πd
= 3.14 × 15 = 47.1
Ribbon = 60 - 47.1 = 12.9
Length of arc = x/360 × πd
12.9 = x/360 × 3.14 × 15
x = 98.6°
The angle is 98.6°
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