The largest possible number of red socks in the drawer that is consistent with this data is 990.
To solve the given question, we will form equations according to the given data including a known and an unknown variable.
Let r be the number of socks that are red, and t be the total number of socks.
We get,
2(r(r-1)+(t-r)(t-r-1))=t(t-1)
Expanding the left hand side and the right hand side
we get,
4r^2-4rt+2t^2-2t = t^2-t
moving the terms, we will get that
4r^2-4rt+t^2 = t
We notice that the left side is a perfect square.
(2r-t)^2 = t
Thus t is a perfect square.
And, the higher t is, the higher r will be. So, we should set
t = 44^2
= 1936
we see, 2r-1936 = 44
We will use the positive root, to get that
2r-1936 = 44,
2r = 1980
r = 990
Therefore, we can conclude that the largest possible number of red socks in the drawer that is consistent with this data is 990.
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What is the slope of the line that passes through the points (-4, 2)(−4,2) and (-5, 0)(−5,0)? Write your answer in simplest form.
Answer: 2
Step-by-step explanation:
We will use the slope formula to find the slope of the line going through these two points.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]
[tex]\displaystyle \frac{0-2}{-5--4} =\frac{-2}{-5+4} =\frac{-2}{-1} =2[/tex]
The slope of this line is 2.
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assume that all the lines that appear tangent are tangent. Find the perimeter.
We have that the tangents which meet at the same point outside the circle have the same length:
Tangents in this caseThen, in this case:
PerimeterNow that we have all the measures, we find the perimeter just by adding them:
6 + 6 + 9 + 9 + 12+ 12 = 54
Answer: the perimeter of the figure is 54
Please help ASAP, will mark brainliest!
These triangles are congruent by the triangle congruence postulate:
Answer:
SAS
Step-by-step explanation:
SAS is side, angle, side so two sides are congruent and one angle is congruent.
If you look at the picture the side that is shared by both triangles is equal.(side)
The two sides with the line through them means they're equal.
(side)
The picture shows the two angles are equal.
(angle)
=SSA or SAS
There are integers that are not rational
numbers. (True or false)
There are whole numbers that are not rational
numbers. (True or false
There are integers that are not whole numbers.(true or false)
All rational numbers are integers. (True or false)
A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043
Explain about the integers?Integers, as opposed to fractions or decimals, are all whole numbers plus their antipodes. For instance, numbers include -3, -2, -1, 0, 1, 2, 3,... On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.
False. An integer is a whole number.
False. For instance, 1/2 is not a whole number but is a rational number.
False. For instance, -3 is not a whole number but is an integer.
True. Rational numbers include all integers.
Answers:
False
False
False
True
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suppose the side length of a cube is measured to be 9 cm with an accuracy of 0.03 cm. use differentials to estimate the error in the computed volume of the cube.
By using differentials the error in the volume estimation is 7.29 cubic centimeters.
What is the error of the computed volume of the cube?
The volume of a cube (V), in cubic centimeters, is equal to the cube of the side length (L), in centimeters, whose formulas are:
V = L³
Now we proceed to estimate the volume differential by using first derivatives:
dV = 3 · L² · dL
Where dL is the length differential, in centimeters.
If we know that L = 9 cm and dL = 0.03 cm, then the error in the computed volume of the cube is:
dV = 3 · (9 cm)² · (0.03 cm)
dV = 7.29 cm³
The error in the volume estimation is 7.29 cubic centimeters.
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suppose that your boss must choose three employees in your office to attend a conference in jamaica. because all 18 of you want to go, he decides that the only fair way is to draw names out of a hat. what is the probability that you, sharon, and robert are chosen? enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that I, Sharon, and Robert are chosen is 0.0012
What is the formula for calculating combinations?
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.
The total number of employees=18
The Boss must choose 3 employees to attend the conference.
The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.
So, [tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}[/tex]
[tex]^{18}C_{3}=\frac{18!}{(15)! 3!}[/tex]
[tex]^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]
[tex]^{18}C_{3} =816[/tex]
The probability that I, Sharon, and Robert are chosen is [tex]\frac{1}{816}[/tex] = 0.0012
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The probability that I, Sharon, and Robert are chosen is 0.0012
What is the formula for calculating combinations?
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations, where n is the overall number of things and r is the number of items that are being chosen at a time.
The total number of employees=18
The Boss must choose 3 employees to attend the conference.
The number of possible ways to choose 3 employees from the total of 18 employees is [tex]^{18}C_{3}[/tex] .
The equation [tex]^{n}C_{r}=\frac{n!}{(n-r)! r!}[/tex] will be used to calculate combinations,.
So,
[tex]^{18}C_{3}=\frac{18!}{(18-3)! 3!}^{18}C_{3}=\frac{18!}{(15)! 3!}^{18}C_{3}=\frac{18 \times 17 \times 16 \times 15}{3 \times 2}[/tex]
[tex]^{18}C_{3}=816[/tex]
The probability that I, Sharon, and Robert are chosen is = 0.0012
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What is the value of this expression when x = -4 and y = 64?
-4+x²
A.
B. -8
C. -16
D. -48
Answer:
it's 0
Step-by-step explanation:
i hope this helps you
Please help I'm struggling and this is due tomorrow morning
Explain how to solve this equation I know it's 16 but I don't know how to solve it
In picture
Answer: to solve this equation, multiply both sides of the equation by 2.
Step-by-step explanation: by multiplying both sides of the equation by 2, you are effectively eliminating the fraction on the left, making the answer x = 16.
Lilly has a bag only containing blue beads and purple beads.
3/8 of the beads are blue.
If there are 9 blue beads in the bag, how many beads are purple?
Answer:
15 purple beads
Step-by-step explanation:
Calculate total beads
[tex]\frac{9}{\frac{3}{8} } =\frac{72}{3} =24[/tex]
Calculate how many beads are purple
[tex]24-9=15[/tex]
Hope this helps
There are total 15 purple beads.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
These values are frequently represented in algebra by symbols such as x, y, z, p, or q, and these symbols are known as variables.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
given:
Fraction of blue beads = 3/8
Total blue beads = 9
let the total number of beads be x.
So, 3/8x = 9
x= 9. 8/3
x= 72/3
x= 24
So, number of purple beads = 24 -9= 15 beads
Hence, there total 15 purple beads.
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Which ratios have the unit rate less than 1?choose all the apply
2 feet : 12/5 minutes
1/8 foot: 1 2/3 minutes
3 feet : 4 2/3 minutes
1 5/8 feet :2 minutes
A ratio displays the multiplicity of two numbers. For instance, if a dish of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. Similarly, the ratio of oranges to the overall amount of fruit is 8:14, whereas the ratio of lemons to oranges is 6:8. Ratios contrast two figures by typically dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
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after cynthia microwaves her bowl of morning porridge, it is either too cold, just right, or too hot. she estimates that there is a 35\55, percent chance that it will be too cold and a 50\pp, percent chance that it will be too hot. what is the probability that cynthia's morning porridge will be just right?
The probability that Cynthia's morning porridge will be just right is 15%.
Probability is defined as the likeliness of an event to happen. It can be determined by dividing the total number of the desired outcome by the total number of samples.
The sum of the probabilities in a probability distribution is always 1.
If there are three outcomes: too cold, just right, and too hot, then the sum of their probabilities is equal to 1 or 100%.
P(too cold) + P(just right) + P(too hot) = 100%
35% + P(just right) + 50% = 100%
P(just right) = 100 - (35 + 50)
P(just right) = 100 - 85
P(just right) = 15%
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A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go 1 mile
Answer:
525 miles is that was what was being asked
Step-by-step explanation:
sorry I don't know the quest but the car can travel a total of 525 miles with 15 gallons in the tank
15 times 35=525
HELP PLEASE!!!!
10 points!!
Mayumi rides her bike around a park. Each lap around the park is 2/3 mi. Mayumi rides a total of 3 mi. how many laps around the park does Mayumi ride?
Mayumi took 4.5 laps by riding her bike around the park
Distance of each lap around the park = 2/3 miles
Distance covered by Mayumi = 3 miles
Fractions: The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It specifies the number of equal portions of the whole or collection that are taken.
Laps took by Mayumi:
Distance covered by Mayumi on her bike/Distance of each lap around the park
= 3/(2/3)
= 3*3/2
= 9/2 or 4.5 laps
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There are 8 batteries in a package of AA batteries, and 12 batteries in
a package of AAA batteries. If you buy 10 packages of AA batteries and
6 packages of AAA batteries, how many batteries would you have?
A- 156 batteries
B- 36 batteries
C- 152 batteries
Answer:
C. 152
Step-by-step explanation:
8 × 10 + 6 × 12 = 80 + 72 = 152
Three students have summer jobs. The proportional relationship between their pay and the hours they work is shown.
Student A:
Time (hours) 5 13
Pay (dollars) 67.50 175.50
Student B: $189.00 for 14 hours
Student C: The equation p = 13.5h, where p represents total pay and h represents hours worked
Which student is paid the most for 20 hours of work?
All the students are paid equal amount of $270. Therefore, no oneis paid more.
How to illustrate the information?For student A, the amount paid for 20 hours will be:
= (67.50 / 5) × 20
= 13.50 × 20
= $270
For student B, the amount paid for 20 hours will be:
= (189/14) × 20.
= $270
For Student C, the amount paid for 20 hours will be:
p = 13.5h
where h = number of hours
p = 13.5 × 20 = $270
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Answer:
D yeyeyeye! <3
2
Write the decimal as a percent. .065
A
65%
B
650%
C
6.5%
D
.65%
The value of percent of the decimal .065 is 6.5 %.
We are provided with the value .065 .
The ratio or a number expressed as a fraction of 100 is referred to as percentage. It is denoted using the percent sign % .
We have, .065 . We need to convert this value in the percentage. certain steps need to be followed to convert this value in the percentage. These steps are mentioned below;
.065
Multiply this above mentioned value by 100 to convert it into percent.
.065 × 100
= 6.5 %
So, percent of the decimal value is 6.5 %.
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7 more than half on Eli's age is Sydney's age, 11. How old is Eli?
Answer:
8 years8 years
Explanation:
Let Eli's age be represented as x
Sydney's age = 11
half on Eli's age = x/2
7 more than half on Eli's age = x/2 + 7
If 7 more than half on Eli's age is Sydney's age, then;
x/2 + 7 = 11
Subtract 7 from both sides
x/2 + 7 - 7 = 11-7
x/2 = 4
Multiply both sides by 2;
x/2 * 2 = 4 * 2
x = 4 * 2
x = 8
Hence Eli is 8 years old
A coin box contains $26.50 in dimes and quarters. There are 157 coins altogether. How many of each
type of coin are in the box?
======================================================
Work Shown:
x = number of dimes
y = number of quarters
x+y = 157 coins total
-------------------------------
$26.50 = 2650 cents
1 dime = 10 cents
x dimes = 10x cents
1 quarter = 25 cents
y quarters = 25y cents
total value = 10x+25y = 2650 cents
-------------------------------
We have this system of equations
x+y = 157
10x+25y = 2650
Let's solve for y in the first equation
x+y = 157
y = 157-x
Then plug this into the second equation and solve for x.
10x+25y = 2650
10x+25(157-x) = 2650
10x+25(157)+25(-x) = 2650
10x+3925-25x = 2650
-15x+3925 = 2650
-15x = 2650-3925
-15x = -1275
x = -1275/(-15)
x = 85 is the number of dimes
Then use this to find the value of y
y = 157-x
y = 157-85
y = 72 is the number of quarters
-------------------------------
Check:
85 dimes + 72 quarters = 157 coins total
85 dimes = 85*10 = 850 cents
72 quarters = 72*25 = 1800 cents
850 cents + 1800 cents = 2650 cents = $26.50
This confirms the answers.
Answer:
so 85 dimes and 72 quarter coins are in the box
Step-by-step explanation:
Given; Total number of coin =1557 Total amount money =26.50 To find Number of dimes and quarters in the box. In order to find the solution, make equation of number of coin and amount money. solve for unknown.Let, Number of dimes = x Number of quarters = y As, it is given that total number of coin is 157. x + y = 157 ......(a) Also, the total money is $ 26.50. .. 0.10x+0.25y = 26.50 ..(b)To, solve equation (a) & (b), put value of y from (a) to (b); From (b); From (a); y= 157 0.10x+0.25(157 - x) = 26.50 0.10x+39.25 - 0.25x = 26.50 0.15x+39.25 = 26.50 39.25 26.50 = 0.15x 12.75 = 0.15x 12.75 0.15 = x 85 = x Now, put value of x in equation (a); x + y 85+ y = y= 72
State the law of logic that is illustrated.
4
Statement: If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20.
The given statement " If x > 12, then x +9>20. The value of x is 14. Therefore, x +9>20" is Hypotesis of a true conditional statement is true, so the conclusion is also true. This is Law of Detachment.
What is the hypothesis and conclusion of a conditional statement?The Hypothesis is the first or “If” portion of the conditional statement or p. The Conclusion is the second or “then” part of the conditional statement or q.
What is the truth of the conditional statement when the hypothesis true and the conclusion in true?If the hypothesis is true and the conclusion is true, the conditional statement if p, then q is true. If the hypothesis is true but the conclusion is false, the statement is false.
The following assertion "X + 9 > 20 if x > 12. X has a value of 14. Thus, x + 9 > 20 "The conclusion follows logically from the hypothesized truth of the conditional statement. This is the Detachment Law.
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The figures below are congruent. Name the corresponding sides.
The figures are congruent and the corresponding sides are AC = KM, AB = KL and BC = LM
How to find congruent figures?Congruent figures in geometry are identical in shape and size.
In other words, congruent figures are geometric figures that have the same shape and size.
If the figures are polygons, then they are congruent if all the corresponding sides and corresponding angles are congruent.
Therefore, the polygons above are triangles, they are congruent if the corresponding sides and angles are equal.
Therefore, the figures(triangles) are congruent by the following rules:
Side AC is congruent to side KMSide AB is congruent to side KLSide BC is congruent to side LMlearn more on congruent figures here: https://brainly.com/question/3453193
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Question 2 of 10Classify the following triangle. Check all that apply.
Given -
To Find -
Type of Triangle =?
Step-by-Step Explanation -
As we can see we have an obtuse angle in the triangle and also, the two sides are equal.
So,
It is an Obtuse angle triangle.
It is also an isosceles triangle
Final Answer -
B. Obtuse
E. Isoseceles
I need help with this.
The approximate length and width of this rectangle to the nearest tenth are 15.6 feet and 31.2 feet respectively.
How to calculate the area of a rectangle?Mathematically, the area of a rectangle can be calculated by using this formula:
A = LW
Where:
A represents the area of a rectangle.
W represents the width of a rectangle.
L represents the length of a rectangle.
Making length (L) the subject of formula, we have:
L = A/W
Substituting the given parameters into the formula, we have;
3x = 489/6x
3x × 6x = 489
18x² = 489
x² = 489/18
x² = 27.2
x = √27.2
x = 5.2
Now, we can determine the length and width of this rectangle as follows:
Width = 6x
Width = 6 × 5.2
Width = 31.2 feet.
Length = 3x
Length = 3 × 5.2
Length = 15.6 feet.
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Q.4 Find the median class.
Size of the shoe No. of pair sold
3 4
4 18
5 25
6 12
7 5
8 1
Answer: Median = 5
=====================================================
Explanation
Given Table of Data
[tex]\begin{array}{|c|c|} \cline{1-2}\text{Size of the shoe} & \text{No. of pair sold}\\\cline{1-2}3 & 4\\\cline{1-2}4 & 18\\\cline{1-2}5 & 25\\\cline{1-2}6 & 12\\\cline{1-2}7 & 5\\\cline{1-2}8 & 1\\\cline{1-2}\end{array}[/tex]
The second column is the set of frequencies. Adding up those frequencies gets us
4+18+25+12+5+1 = 65
There are 65 total shoes.
Divide this in half
65/2 = 32.5
There are 32 values below the median, and 32 values above it. That's 32+32 = 64 values so far. When including the median value itself we have 32+1+32 = 65 values total. This only works when the sample size is odd.
---------------------------
What we'll do is add up the partial sums of the frequency values.
The goal is to get to a sum of 33, or larger, because the median is in the 33rd slot.
Adding the first two frequencies gets us 4+18 = 22. This is not 33 or larger, so we move on.
Adding the first three frequencies gets us 4+18+25 = 22+25 = 47 which is 33 or larger.
What this tells us is that the median corresponds to the third row of the table, since we added the first three frequencies to get to 33 or larger.
The median must be 5.
PLS HELP!!!!!
31 POINTS
A car’s velocity increases from 4.2m/s to 14.8 m/s, E, in 2.5 sec. What is its acceleration?
Answer:
4.24ms-²
Step-by-step explanation:
S: x. write suvat and sub in values
u:4.2
v:14.8
a:?
t:2.5
use correct equation
v=u+at
sub values in
14.8=4.2+2.5a
rearrange to get a
10.6/2.5= a
a=4.24
The first of two numbers is twice the second. Seven more than the second number is equalto 6 less than the first number. Find the numbers.
Let's call x to the first number ans y to the second number.
The first of two numbers is twice the second:
x = 2y
Seven more than the second number is equal to 6 less than the first number:
7 + y = x - 6
Isolating x:
7 + y + 6 = x
13 + y = x
Combining last equation with first equation:
2y = 13 + y
2y - y = 13
y = 13
Then:
x = 2*13
x = 26
Find x so that q || r.
X =
Answer:
x = 12
Step-by-step explanation:
To justify q || r :
11x - 28 + 7x - 8 = 180 because they would be supplementary angles and their sum would be equal to 180°
add like terms
18x - 36 = 180 add 36 to both sides
18x = 216 divide both sides by 18
x = 12
please help quickly.
Answer:
Step-by-step explanation:
5) Domain: -3<=x<=2
Range: 4<=y<=-3
6) Domain: {-3,-2,-1,0,1,2}
Range: {4,3,2,1,0,-1,-2,-3}
Do you need number 7 too?
:]
You bring 1.5 dozen bagels to school.
A dozen bagels cost $5.98.
You used a coupon that took $1.00 off the total.