The total number of socks are n, 3 of which are red. when 2 socks are chosen randomly from the box, the probability of both socks being red is 1/2 so the value of n is 4.
The information given by question is
Total number of socks = n
Number of red socks = 3
when 2 socks are chosen randomly from the box
Probability of both socks being red = 1/2
Ways of choosing 2 socks from n = [tex]_nC_2[/tex]
Ways of choosing 2 red socks from 3 = [tex]_3C_2[/tex]
Probability of both socks being red = [tex]\frac{_3C_2}{_nC_2}[/tex]
[tex]\frac{6}{n(n-1)}[/tex] = [tex]\frac{1}{2}[/tex]
12 = n² - n
n² - n -12 = 0
n² - 4n + 3n - 12 = 0
n(n - 4) + 3(n - 4) = 0
(n - 4)(n + 3) = 0
n = 4 or -3
Ignore negative value, therefore n = 4
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The Smith family will drive 240 miles round-trip to visit a relative. Mr. Smith, Mrs. Smith, and their 20 -year old son, James, will share the driving. Determine whether each statement is correct by selecting True or False. A If Mrs. Smith and Mr. Smith drive 80 miles each, then James will drive for 13 of the round-trip distance. True False B If Mrs. Smith and Mr. Smith drive 90 miles each, then James will drive for 12 of the round-trip distance. True False C If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then James will drive for 512 of the round-trip distance. True False D If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then James will drive for 712 of the round-trip distance. True False
The correct answers is (a). False (b). False (c). False (d).True
(A). False
If Mrs. Smith and Mr. Smith drive 80 miles each, then the total miles they drive is 80 + 80 = 160 miles. That means James will have to drive 240 - 160 = 80 miles, which is 1/3 of the round-trip distance, not 13/3.
(B). False
If Mrs. Smith and Mr. Smith drive 90 miles each, then the total miles they drive is 90 + 90 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{1}{4})[/tex] of the round-trip distance, not [tex]\frac{12}{4}[/tex].
(C). False
If Mrs. Smith drives 90 miles and Mr. Smith drives 50 miles, then the total miles they drive is 90 + 50 = 140 miles. That means James will have to drive 240 - 140 = 100 miles, which is [tex](\frac{1}{2} )[/tex] of the round-trip distance, not [tex](\frac{5}{12} )[/tex].
(D). True
If Mrs. Smith drives 60 miles and Mr. Smith drives 120 miles, then the total miles they drive is 60 + 120 = 180 miles. That means James will have to drive 240 - 180 = 60 miles, which is [tex](\frac{7}{12} )[/tex] of the round-trip distance.
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Answer:
Your answer should be: TRUE FALSE TRUE FALSE
At the Piedmont Middle School baseball game last Friday, the Piedmont Ravens hit 3 times as many foul balls as the other team, the Rossville Crows.
Step-by-step explanation:
jaubslsjsolqmaiBaokmaalo
The perimeter of a rectangular cocoa farm is 497 km. The length of the farm is 2½ times the width. Find the: (1) (ii) width; length of the farm.
Answer:
width=71km, length=177.5km
Step-by-step explanation:
Let x be the width of the farm.
Then the length of the farm will be 2.5x.
perimeter of farm in terms of x=2.5x+2.5x+x+x=7x
perimeter of farm in terms of x=perimeter of farm
7x=497
x=71
width=71km
length=71×2.5=177.5
How do you solve arithmetic overflow error converting numeric to data type numeric?
Arithmetic overflow error converting numeric to data type numeric can be solved by increasing the precision and the scale, storing number in different data type or use user-defined datatype.
An "arithmetic overflow error converting numeric to data type numeric" error occurs when you try to store a number in a numeric column that is too large to be represented by the specified precision and scale. To resolve this error, you have a few options:
Increase the precision and scale of the numeric column, you can increase the precision and scale of the numeric column so that it can store larger numbers.
Store the number in a different data type:If you don't need the precision and scale of a numeric column, you can store the number in a different data type, such as float or big int.
Round the number to a smaller value:If the number is too large to be represented in the numeric column, you can round it to a smaller value before inserting it into the database.
Use a user-defined data type:If the number is still too large to be represented in a numeric column or a different data type, you can create a custom data type in SQL Server to store the number.
It's important to choose the right solution based on your requirements and the specific use case. You may also need to consider the performance implications of each solution, especially if the data being stored is very large or complex.
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A slow 24-hour clock loses 25 minutes a day. At noon on the first of October, it is set to show the correct time. When will this clock next show the correct time?
Answer:
Nov 27 at 14:24 hours
Step-by-step explanation:
First let's figure out exactly when the slow clock will synchronize with a correct clockAt the rate of loss of 25 minutes per day, let x be the number of days when the two clocks coincideThe total time lost in x days = 25x minutesThe clocks will synchronize when the total time lost is exactly 24 hours.57.6 days equates to 57 days, 14 hours, 24 minutes (using a calculator)
Adding to Oct 1 at 12:00:00 we get this as Nov 27 at 14:24 hours
calculate x in the diagram
please help
Answer:
[tex]\frac{x}{x+(x-2)}[/tex] = [tex]\frac{10}{16}[/tex]
[tex]\frac{x}{2x-2}[/tex] = [tex]\frac{5}{8}[/tex]
5(2x-2) = 8x
10x - 10 = 8x
2x = 10
x = 5
Calculate 12% of 14=______
we are interested in testing to see if the variance of a population is less than 7. the correct null hypothesis is
The test is determined whether the population variance is less than 7.
The hypothesis formulation-
‘H0: σ² ≥ 7’
‘H1: σ² < 7’
Now let us solve this question options-wise:
Option a is incorrect because we should always contain the ‘=’ or ‘≥’ or ‘≤’ sign, and in the null hypothesis, and also this option denotes the standard deviation, not the variance.
Option b is correct because it contains a ‘≥’ sign and it is the right complement to the alternative hypothesis.
Option c is incorrect because it measures the standard deviation instead of the variance.
Option d is incorrect because it has the lower limit of the variance as 49 instead of 7
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full question:
We are interested in testing to see if the variance of a population is less than 7. The correct null hypothesis is
a. σ< 7.
b.σ^2≥7.
c. σ< 49.
d.σ^2≥ 49
Ella writes the sequence:
2, 0.2, 0.02, 0.002…
Describe the rule she used to write the next number in this sequence
Answer:
0.0002
Step-by-step explanation:
She divides by 10.
Find the value of the indicated trigonometric ratio:
Answer:
[tex] \sin( \alpha ) = \frac{16}{ \sqrt{281} } [/tex]
Step-by-step explanation:
Greetings!!!
Firstly, remember the sin trigonometric equation
[tex] \sin( \alpha ) = \frac{opposite}{hypotenuse} [/tex]
Assuming the image as this question and solve
If you have any questions or unclear ideas tag on comments
Hope it helps!!!
The value of the indicated trigonometric ratio sin( α ) is (16√281 )/281.
What is the value of sin(α)?
The figure in the image is a right triangle.
Angle ∠A = αAdjacent to angle ∠A = 5Opposite to angle ∠A = 16Hypotenuse = √281To find sin(α), we use trigonometric ratio.
Sine = Opposite / Hypotenuse
Plug in the values
sin( α ) = 16/√281
To simplify further, we rationalize the denominator
Multiply both the numerator and denominator by √281
sin( α ) = (16 × √281 ) /(√281 × √281 )
sin( α ) = (16 × √281 ) / 281
sin( α ) = (16√281 )/281
Therefore, the value of sin( α ) is (16√281 )/281.
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which equation does the graph of the systems of equations solve
Answer:
(a) -1/2x +3 = 3x -4
Step-by-step explanation:
Given a graph of two lines, you want to know which equation it is showing the solution for.
LinesThe blue line has a slope of -3/6 = -1/2, and a y-intercept of +3, so its slope-intercept equation is ...
y = -1/2x +3
This expression is seen on the left side of the equal sign for the first choice, and is not seen anywhere else.
By way of confirmation, the red line has slope 3/1 = 3 and a y-intercept that is a negative value less than -2. It is reasonable to say its slope-intercept equation is ...
y = 3x -4
This expression matches the right side of the equal sign for the first choice.
SolutionThe solution to the system of these two equations might reasonably be found by equating the expressions for y:
-1/2x +3 = 3x -4
Which expression represents the amount of money John has collected?
John collects $5 for club dues from each member. Use the variable
m
for the number of members in the club.
Answer: The expression that represents the amount of money John has collected is:
5 * m
This expression calculates the amount of money John collects by multiplying the number of members (m) by the amount of money collected per member ($5).
Step-by-step explanation:
5- A rectangle that has a perimeter of 16 cm has been dilated with a scale factor of 3. What is the perimeter of the new shape?
6- A triangle that has an area of 36 squared cm has been dilated with a scale factor of 0. 5.
Find the area of the new triangle.
CAN I PLEASE GET SOME HELP ON THIS. THANK YOU
5- Perimeter of the new rectangle is 48 cm.
6- Area of the new triangle is 9 cm².
5- A rectangle that has a perimeter of 16 cm has been dilated with a scale factor of 3. To find the perimeter of the new shape, we need to multiply the original perimeter by the scale factor:
16 cm * 3 = 48 cm
So the perimeter of the new shape is 48 cm.
6- A triangle that has an area of 36 squared cm has been dilated with a scale factor of 0.5. To find the area of the new triangle, we need to multiply the original area by the square of the scale factor:
36 cm² * (0.5)²
= 36 cm² * 0.25
= 9 cm²
So the area of the new triangle is 9 cm².
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Could someone please answer for this section I will give 20 points for all of it
Answer:
1) 2/5
2) 4/13
3) 1/8
4) 25/4 or 6 + 1/4
Step-by-step explanation:
1) 5/2 * x = 1
x = 1 / (5/2)
x = 2/5
2) (3 + 1/4) * x = 1
13/4 * x = 1
x = 1 / (13/4)
x = 4/13
3) 8 * x = 1
x = 1/8
4) (2/5)^2 * x = 1
2^2 / 5^2 * x = 1
4/25 * x = 1
x = 1 / (4/25)
x = 25/4
x = 6 + 1/4
of six letters (a, b, c, d, e, and f), two letters are to be selected at random. how many outcomes are possible?
Answer:
Below
Step-by-step explanation:
6 C 2 = 6! /(4! 2!) = 15 outcomes
A team of dogs in Alaska can run 4.3 miles per hour. There is approx. 1.61 kilometers in a mile. How many kilometers per hour can they run each hour?
Imagine this:
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending.
y = -10x + 1500
This means y is the altitude with -10ft decent every x minutes when the initial altitude is 1500Ft
Part A: Create a table for the values when x = 0,5,8,10,10
Show your work with the equation used to identify the values you put in the table when X = 0,5,8,10 and 30.
Part B: identify the altitude after 5 minutes and after 30 minutes. use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals. Starter: The plane's altitude after 5 minutes would be _________. After 30 minutes, the plane's altitude would be ________.
Then describe if the plane is in the air or on the ground at those times.
The table for the values when x = 0,5,8,10, will be:
x (minutes) y (altitude in feet)
0 1500
5 1450
8 1420
10 1400
30 1200
How to explain the equationAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
When x = 0, y will be:
-10x + 1500
= -10(0) + 1500
= 1500
When x = 5 y will be:
= -10(5) + 1500
= 1500 - 50
= 1450
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what is the highest number obtainable if you multiple the numbers 1-9? however you can only use each number once.
The highest number obtainable by multiplying the numbers 1-9 is 40,320. To obtain this result, you need to arrange the numbers in a specific order.
The problem is to find the highest number that can be obtained by multiplying the numbers 1-9, where each number can only be used once. To obtain the highest possible number, it's important to arrange the numbers in a specific order. One possible arrangement is 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1. This arrangement results in the highest product of 40,320. It's worth mentioning that different arrangements of the numbers may result in different products, but the arrangement mentioned above gives the highest possible product. Understanding the order of operations and how to manipulate the numbers is key to solving this problem and finding the highest number.
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Find each exact value if 0
Sin (x - y) if cos x = 8/17 and cos y = 3/5
Work Shown:
If cos(x) = 8/17, then sin(x) = 15/17. Use the identity [tex]\sin^2(\text{x}) + \cos^2(\text{x}) = 1[/tex] to determine this.
If cos(y) = 3/5, then sin(y) = 4/5 using that same identity.
So,
sin(x-y) = sin(x)cos(y) - cos(x)sin(y)
sin(x-y) = (15/17)*(3/5) - (8/17)*(4/5)
sin(x-y) = 45/85 - 32/85
sin(x-y) = (45 - 32)/85
sin(x-y) = 13/85
1.) The ( ) means that all of the points on the line will satisfy the inequality.
2.) The solution set for the inequality is the entire ( ) shown in the graph
1.) The "(≠)" means that all of the points on the line will satisfy the inequality.
2.) The solution set for the inequality is the entire region (shaded or unshaded portion) shown in the graph. The shaded region represents the set of all points that satisfy the inequality, while the unshaded region represents the set of all points that do not satisfy the inequality.
What is linear inequality?
A linear inequality is an equation that represents a linear relationship between two variables and is used to describe a region of the coordinate plane that satisfies a given set of conditions.
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do you think this model satisfies assumptions for multiple regression? list 4 of the assumptions and next to each one tell why you do or do not think it is valid.
In multiple regression, we have 4 assumptions listed and explained below. They are valid.
Following are assumptions for multiple regression model:
1. Linear connection: Each predictor variable and the responder variable have a linear relationship.
Making a scatter plot of each predictor variable and the response variable is the simplest technique to check if this premise is true.
2. Lack of Multicollinearity: There is no significant correlation between any of the predictor variables.
Calculating the VIF value for each predictor variable is the quickest approach to see if this premise is true.
3. Independence: Each observation has its own validity.
The Durbin-Watson test, a formal statistical test that informs us whether or not the residuals (and consequently the observations) exhibit autocorrelation, is the easiest approach to find out if this assumption is true.
4. Homoscedasticity: At every point in the linear model, the residuals' variance is constant.
The simplest technique to check if this premise is true is to plot the standardized residuals against the expected values.
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Evaluate the expression.
5
−
3
=
Value of expression 5 - 3 is 2
Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.
Given expression,
5 - 3 = ?
we need the difference of 5 and 3
5 - 3 = 2
Hence, 2 is value of expression 5 - 3
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3 ( n -5 ) = 21 integers answers pls
Answer:
n = 12
Step-by-step explanation:
Solve for n
3 ( n -5 ) = 21
Divide each side by 3.
3/3 ( n -5 ) = 21/3
n-5 = 7
Add 5 to each side.
n-5+5 = 7+5
n = 12
If y varies directly with x and y= – 93 when x= – 3, find y when x=2.
Answer:
Below
Step-by-step explanation:
y varies directly with x means
y = k x
now with y = -93 and x = -3
-93 = k (-3) shows k = 30
so y = 30 x
now with x = -2
y = 30 (-2) = -60
In a right triangle, a and b are the lengths of the legs and c is the length of the hypotenuse.
If a = 6 yards and c = 7 yards, what is b? If necessary, round to the nearest tenth.
yards
Answer:
Step-by-step explanation:
The Pythagorean Theorem will be applied:
[tex]c^{2} = a^{2} + b^{2}[/tex]
Substituting the values provided in the question:
[tex]7^{2} = 6^{2} + b^{2}[/tex]
[tex]= 49 = 36 + b^{2}[/tex]
[tex]= 49 - 36 = b^{2}[/tex]
[tex]= b^{2} = 13[/tex]
Taking the square root on both sides to get rid of the square:
[tex]= \sqrt{b^{2}} = \sqrt{13}[/tex]
[tex]= b = \sqrt{13}[/tex] yards
= b = 3.6 yards (Rounded to the nearest tenth)
help????????????????
The result is obtained by using the formula for a triangle.
How to find an area in coordinate system?Simply we count the number of grids representing a certain unit.
We have a flag in coordinate system can be seen in the picture.
Each grid represents a foot. Kenna will make five flags.
Find the area of material for one flag!Find the area of material for five flags!The flag is a triangle with the base at y-axis.
The base length is 3 ft and the height is 2. The area of the triangle is
Area of a flag = ½ bh
Area of a flag = ½(3)(2)
Area of a flag = 3 ft²
Area of five flags = 5(3 ft)
Area of five flags = 15 ft²
Hence, Kenna will need the material of 3 ft² for one flag and 15 ft² for five flags.
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help. need answer asap help.help.help.help.help.help.help.help.help.help.help.help.help.help.
The area of the triangle is calculated to be equal to 7.5 square inches.
How to evaluate for the area the triangleFor any triangle, the area is calculated as half the base multiplied by the height of the triangle, that is;
Area of triangle = 1/2 × base × height
we have the base of the triangle to be 6 inches and the height as 2.5 inches, so we solve for the area as follows:
1/2 × 6 inches × 2.5 inches
6 inches can be divided by 2 to give;
3 inches × 2.5 inches
7.5 square inches
Therefore, the area of the triangle is calculated to be equal to 7.5 square inches
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Malia was cutting out shapes from a rectangular piece of construction paper in art class.
The first shape Malia cut out was a circle from a piece of construction paper that
measured 8 inches by 10 inches, as shown in the diagram above. After Malia finished
cutting out the circle, what was the area of the piece of paper that was left after she
cut out the circle? Use 3.14 form.
The area of the piece of paper left after cutting out the circle is 29.76 in².
Area of a figure:
The amount of unit squares that completely encircle the surface of a closed figure is its area. Area is measured in square units like cm² and m². A shape's area is a two-dimensional measurement. The term “area” refers to the space inside the boundary or perimeter of a closed shape.
You need to first determine the rectangle's area.
8x10=80 in²
determine the circle's overall area.
The diameter is 8 in so you would use 4 as the radius
A=πr²
A=3.14x4²
A=3.14x16
A=50.24 in²
The area of the circle must then be subtracted from the area of the rectangle.
80-50.24=29.76
The area of the piece of paper is 29.76 in ².
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1. The simple interest due on a 2.5-year loan of $8, 500 is $1,062.50. Find the monthly payments on the loan.
-$825.50
- $1,062.50
- $3, 825
-$318.75
a regular hexagon is shown below O is the centre of the hexagon
AO in terms of P and/or Q is OA = Q = Q
OB in terms of P and/or Q is OB = P =Q
EB in terms of P and/or Q is EB = 2P =2Q
What is a Hexagon?A hexagon, also known as a sexagon, is a six-sided polygon that forms the shape of a cube in geometry. Any basic hexagon has a total internal angle of 720°.
In a regular hexagon, all sides are equal
Which means:
AB= BC
5p + q -5p = 6p-5p
q = p
So, every side of the hexagon is p = q
Which means that AB = BC = CD = DE = EF = FA = p =q
Recall that at the center, each side forms an angle
There are six sides in a hexagon.
Total angle = 360°
6x= 360°
x= 60°.
By the symmetry of regular hexagon, OA = OB
<OAB = <OBA
<AOB = x = 60°
Sum of all angles in a triangle is 180°
We add the values
<OAB = 60°.
<OAB is an equilateral triangle, thus every side is equal
Hence,
a. OA = Q = Q
b. OB = P =Q
c. EB = 2P =2Q.
From the figure, <BOE= 180° which makes it a straight line.
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