Answer:
There are 35 possible group of 3 socks from a total of 7
Step-by-step explanation:
Given
Number of unique socks = 7
Number of possible selection = 3
Required
Number of ways she can make her selection.
The question can be categorised as combination; reason being that words like "take" as used in the question points to combination or selection.
To solve this, we make use of combination formula.
nCr = nPr/r!
Where n = 7 and r = 3
By substitution, we have
7C3 = 7P3÷3!
Taking it one at a time
7P3 = 7!÷(7-3)!
7P3 = 7! ÷ 4!
7P3 = 7 * 6 * 5 * 4! ÷ 4!
7P3 = 7 * 6 * 5
7P3 = 210
3! = 3 * 2 * 1
3! = 6.
So,
7C3 = 210 ÷ 6
7C3 = 35.
Hence, there are 35 possible group of 3 socks from a total of 7
Find the volume of the regular hexagonal prism with side lengths of 4 ft, height of 3ft and apothem of approximately 3.5 ft
Answer:
A(p) = 84 ft³
Step-by-step explanation:
Volume of regular prism is equal to V(p):
V(p) = Area of the face * h
we know h = 3 ft
A regular hexagonal prism has 6 equal sides forming its face.
Finding the area (A₂) of a triangle formed by center of the prism, straight lines between the center and two adjacents vertex and side between these two vertex, and then multiply that area by 6 (number of equal triangles inside hexagonal prism) we get the area of the face, but we need further consideration, the triangle described above, has doble area of (A₁), the triangle formed by apothem, half side, and straight line between center of the face and the vertex, therefore.
Area of small triangle = base * height
A₁ = (1/2) * 4 * 3,5
A₁ = 2*3,5
A₁ = 7 ft²
A₂ = 2* 7
A₂ = 14 ft²
Finally volume of the hexagonal prism is:
V(p) = 6 * 14
A(p) = 84 ft³
Solve for x. 5 = − 3 9 x
Answer:
x = -5/27
Step-by-step explanation:
5 = − 3 · 9x; x = -5/27
Find the measure of
sorry been trying to find something to say but i don't have a answer for it wish i could help
Answer:
28 degrees
Step-by-step explanation:
since DBE is 90 degrees, ABE is 90 degrees as well
given that BEF is 62 degrees
you need to subtract 90 from 62
to get 28 degrees as your answer
You Are Planting a garden in the shape of an equilateral triangle as shown in the diagram. You want to find the area of the garden to determine how much topsoil you will need. Substitute the values of b and h in the formula A = 1/2 • b • h for the area of the garden.
The area of the garden 16√3 ft².
Given: garden base = 8 ft
Find:
Garden surface area =?
First, we must determine the height of the triangle.
82 42 = Height
Height = 64 - 16
Height = 48 cm
43 inches in height
Calculating the garden's area
Garden area = half of bxh
Garden surface area = 1/2 8 43
Garden surface area = 16v/3 ft2
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The value of the expression 2x + x(100 – 15x) when x = 5 is
119
129
135
145
Answer:
[tex]135[/tex]
Step-by-step explanation:
[tex]2(5) + 5(100 - 15(5))\\10 + 500-375\\135[/tex]
The value of the expression 2x + x(100 – 15x) when x = 5 is 135.
What is an expression?An expression is a number, a variable, or a combination of numbers and variables and operation symbols.
The given expression is,
2x + x(100 – 15x)
Now we have to find the value of expression when x = 5
Put the value of x in the given expression we get,
2(5) + 5(100 – 15*5)
solving the brackets we get,
10 + 5( 100 - 75)
10 + 5*25
10 + 125
135
hence, the value of the expression 2x + x(100 – 15x) when x = 5 is 135.
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Help please. Find the value of x in the isosceles triangle shown below
Answer:
A
Step-by-step explanation:
We need to use some properties of an isosceles triangle and the Pythagorean Theorem.
First, the vertical line down the middle of the triangle is the height, which means the angle is makes with the base is 90 degrees and it bisects the base. So, we have two right triangles, each with a height of 6 and with a base of 4/2 = 2.
We can now use the Pythagorean Theorem, which states that for a right triangle with legs a and b and hypotenuse c:
a² + b² = c²
Here, a = 6 and b = 2 and x = c, so:
a² + b² = c²
6² + 2² = x²
x² = 36 + 4 = 40
x = √40
Thus, the answer is A.
Answer:
A
Step-by-step explanation:
This triangle contains two congruent right angle triangles
x² = 6² + 2²
x² = 36 + 4
x² = 40
x = sqrt(40)
x = 4sqrt(10)
Does this graph represent a function? Why or why not?
10
8
8
+
-10-8-042
2
4
0
8
10
4
-8
-8
-10
O A. Yes, because it is a curved line.
O B. No, because it is not a straight line.
O C. No, because it fails the vertical line test.
O D. Yes, because it passes the vertical line test.
Answer:
Step-by-step explanation:
D.
No, basically because it fails the vertical line test. The correct option is C.
What is vertical line test?The vertical line test determines whether a relationship between two variables defines a function. If and only if vertical lines intersect the graph at least once, a relation is a function.
The graph fails the vertical line test because vertical lines intersect it at more than one point.
This means that some x-values correspond to multiple y-values, which violates the definition of a function.
In other words, for each x-value, there should be only one y-value, but this is not the case for all x-values. As a result, the graph does not depict a function.
Thus, the correct option is C.
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Please answer this question
Answer:
2 : 3
Step-by-step explanation:
There are 24 red and 24 black cards in the pack since ratio is 1 : 1
8 red cards are removed leaving 16 red cards, thus
ratio of red : black = 16 : 24 = 2 : 3 ← in simplest form
PLEASE HELP!!!
Adele is paid a weekly salary of $685. She is paid an additional $23.50 for every hour of overtime she works. This week her total pay, including regular salary and overtime was $849.50. how many hours of overtime did Adele work this week?
Answer:
7
Step-by-step explanation:
$849.50-$685=$164.50 which is less than 685 so it all had to be overtime hours then I did 164.50 ÷ $23.50 and got 7
What is the value of x ? Special right triangle
FOR BRAINLIEST BRAINLIEST!! EASY MATH, Give EXPLANATION with it.
Answer:
Just about 5-6-7. In that range
Step-by-step explanation:
you have to count up all the fully shaded in squares. And then what u have to do is try and put together the half of squares and so on while counting them up. It is an esta=mation question- mostly.
Answer:
you make squares around it to find the area
Step-by-step explanation:
hope this helps
The following data show the scores Gina obtained on 12 IQ tests:
93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86
The box plot below represents the data:
box plot has minimum value equal to 74, lower quartile equal to 83, median equal to 86.5, upper quartile equal to 89 and maximum value equal to 94
Which of the following is shown incorrectly in the box plot? (5 points)
Median
Lower quartile
Upper quartile
Maximum value
The upper quartile is shown incorrectly in the box plot. So, the third option is correct.
It is given that,
Data values are: 93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86.Box plot has a minimum value equal to 74, lower quartile equal to 83, median equal to 86.5, upper quartile equal to 89, and a maximum value equal to 94.Explanation:
Arrange the data values in ascending order.
74, 74, 83, 83, 83, 86, 87, 90, 92, 93, 93, 94
Divide the data in 4 equal parts.
(74, 74, 83), (83, 83, 86), (87, 90, 92), (93, 93, 94)
Now,
Minimum value: 74
First quartile: [tex]\dfrac{83+83}{2}=83[/tex]
Median: [tex]\dfrac{86+87}{2}=86.5[/tex]
Third quartile: [tex]\dfrac{92+93}{2}=92.5[/tex]
Maximum value: 94
The value of the upper quartile in the box plot is 89 which is not equal to 92.5. Thus, the third option is correct.
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There are 12 sixth graders, 14 seventh graders,
and 7 eighth graders in a gym class. The gym
teacher randomly selects one student to collect
balls. In how many ways can choosing not a
seventh grader occur?
The requried there are 19 ways to choose a student who is not a seventh grader.
What is arithmetic?Arithmetic is a branch of mathematics that deals with the study of numbers, their properties, and their operations. It involves the basic operations of addition, subtraction, multiplication, and division, as well as more advanced operations such as exponents, roots, logarithms, and trigonometric functions.
There are a total of 12 + 14 + 7 = 33 students in the gym class.
The number of ways to choose a student who is not a seventh grader is equal to the number of ways to choose a sixth grader or an eighth grader.
The number of ways to choose a sixth grader is 12, and the number of ways to choose an eighth grader is 7.
So the total number of ways to choose not a seventh grader is:
12 + 7 = 19
Therefore, there are 19 ways to choose a student who is not a seventh grader.
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Final answer:
The requried there are 19 ways to choose a student who is not a seventh grader.
Explanation:
In this scenario, we need to find the ways of choosing not a seventh grader from the gym class.
To do this, we calculate the total number of ways to select a student from the gym class and then subtract the ways of selecting a seventh grader.
The total number of ways to select a student from the gym class is 12 (sixth graders) + 14 (seventh graders) + 7 (eighth graders) = 33.
The number of ways of selecting a seventh grader is 14 (since there are 14 seventh graders).
Therefore, the number of ways of not choosing a seventh grader is 33 - 14 = 19 ways.
So, there are 19 ways to choose not a seventh grader.
Consider the system of equations.
y=-2x + 4
3y + x=-3
Which statement is true of this system of equations?
Both equations are in slope-intercept form.
The first equation converted to slope-intercept form is y + 2x = 4.
The second equation converted to slope-intercept form is.y =
Neither equation is in slope-intercept form.
Answer:
the second equation converted to slope-intercept form is y = -1/3x -1
Step-by-step explanation:
The formula for the volume of a cone is V= 1/3pir^2h where V represents the volume, r represents the radius of the base, h represents the height. What is the height of a cone with a volume of 66 cubic centimeters and a base with a radius of 3 centimeters?
The height of the cone is approximately 7.01 centimeters.
We know the volume (V) is 66 cubic centimeters and the radius (r) is 3 centimeters. Substitute these values into the formula:
V = 1/3πr²h
66 = 1/3 × π × 3² × h
Simplify the equation:
Multiply both sides by 3:
200 = π × 9 × h
Cancel out the common factor of 9:
200/9 = π × h
Solve for the height (h):
Divide both sides by π:
h = 200/9π
Then, we have that;
h ≈ 7.01 cm
Therefore, the height of the cone is approximately 7.01 centimeters.
The stock of Company A gained 5% today to $34.65. What was the opening price of the stock in the beginning of the day?
To find the opening price of the stock, we can subtract the 5% gain from the current price. The opening price of the stock in the beginning of the day was approximately $36.47.
Explanation:To find the opening price of the stock, we need to deduct the 5% gain from the current price of $34.65.
Let x be the opening price.
Since the stock gained 5%, the opening price minus 5% of the opening price equals the current price: x - 0.05x = 34.65.
Simplifying the equation, we get 0.95x = 34.65. To solve for x, divide both sides of the equation by 0.95.
The opening price of the stock in the beginning of the day was approximately $36.47.
(1, 13)
(-2,4)
O
A. y- 4 = 3(x+2)
B. y- 4 = 3 (x-2)
C. y-1 = 3(x - 13)
D. y- 2 = 3(x - 4)
D is the answer because the y =-2 so that's why that's the answer
You are asked to draw a triangle with side lengths of 10 inches, 7 inches, and 2 inches. How many triangles like this can you draw?
A- One
B- Three
C- Two
D- Zero
Solve 65x = 20.
Round to the nearest ten-thousandth.
Answer: 0.3076
Step-by-step explanation:
Answer:
0.307
Step-by-step explanation:
To get rid of the 65, simply divide both sides of the equation by 65. Thus, rounded to the nearest ten-thousandth, x = 0.307.
At McCain Middle School, approximately 10 out of every 14 students ride the bus to school each morning.McCain Middle School has 147 students.How many students can be expected to ride the bus to school?
Answer:
105
Step-by-step explanation:
set a ratio so
10/14=?/147
cross multiply
10*147=?*14
1470=14*?
divide 1470 by 14 and get 105
An
Step-by-step explanation:
Misha solves the equation 3 x minus 2 (x + 3) = 4 (x minus 2) minus 7 by applying the distributive property to each side of the equation. The result is 3 x minus 2 x minus 6 = 4 x minus 8 minus 7. Misha then wants to combine like terms. Which are the terms Misha should combine?
Answer:
2(x+3)=4
2x+6=4
2x=4-6
2x=-2
2x÷2
x=1
Answer:
The terms that Misha should combine are 3x – 2x and –8 – 7
Step-by-step explanation:
Misha have the equation : 3x-2(x+3) = 4(x-2)-7
After applying distributive property, a(b+c) = ab+ac
3x - 2x - 6 = 4x - 8- 7 ..............(1)
Now, we need to combine the like terms, like terms are the terms having the same coefficient and combining them means to combine their coefficients.
In equation (1), 3x and -2x are like terms as it have the same coefficient x
Hence we will solve them and get (3-2)x = x
Similarly, -8 and -7 can be solved and we get -7-8 = -15
Now, the equation becomes, x-6 = 4x-15
Then, again collecting the like terms on L.H.S and R.h.s and then solving, we get
4x - x = 15-6
3x = 9
x = 3
The graph of the parent function f(x) = x3 is transformed such that g(x) = f(–2x). How does the graph of g(x) compare to the graph of f(x)? g(x) is stretched horizontally and reflected over the y-axis. g(x) is stretched horizontally and reflected over the x-axis. g(x) is compressed horizontally and reflected over the y-axis. g(x) is compressed horizontally and reflected over the x-axis.
The correct answer is: g(x) is compressed horizontally and reflected over the y-axis.
To understand how the graph of [tex]\( g(x) = f(-2x) \)[/tex] compares to the graph of the parent function [tex]\( f(x) = x^3 \)[/tex], we need to analyze the effects of the transformations applied to [tex]\( f(x) \)[/tex].
1. The transformation [tex]\( f(-x) \)[/tex] would reflect the graph of [tex]\( f(x) \)[/tex] over the y-axis. This is because for every point [tex]\( (x, y) \)[/tex] on the graph of [tex]\( f(x) \)[/tex], there will now be a corresponding point [tex]\( (-x, y) \)[/tex] on the graph of .
2. The transformation [tex]\( f(2x) \)[/tex] would compress the graph of [tex]\( f(x) \)[/tex] horizontally by a factor of 2. This is because for every point [tex]\( (x, y) \)[/tex] on the graph of [tex]\( f(x) \)[/tex], there will now be a corresponding point [tex]\( \left(\frac{x}{2}, y\right) \)[/tex] on the graph of [tex]\( f(2x) \)[/tex]. The x-values are halved, which means the graph is compressed along the x-axis.
Combining these two transformations, [tex]\( g(x) = f(-2x) \)[/tex] indicates that the graph of [tex]\( f(x) \)[/tex] is first compressed horizontally by a factor of 2 and then reflected over the y-axis.
Therefore, the graph of [tex]\( g(x) \)[/tex] is compressed horizontally and reflected over the y-axis when compared to the graph of the parent function [tex]\( f(x) \)[/tex].
The ratio of red fish to yellow fish in the pond is 2:3. If there are 24 yellow fish, how many red fish are in the pond?
Answer:
16
Step-by-step explanation:
Since there are 24 yellow fish and the ratio of the yellow fish to the red fish is 3:2. Then we know that 24/3=8. This means that 1 is equal to 8 fish. Since there are 2 ones for the red fish, we times 8 by 2 to get 16.
probability: There are 11 shirts
in your closet, 6 blue and 5
green. You randomly select
one to wear on Monday and
then a different one on
Tuesday. You wear blue shirts
both days.
Answer:
There was a 54.5% probability of you getting a blue shirt on Monda and a 50% chance on Tuesday.
what is the volume of a cylinder with a height of 6 cm and a radius of 3 cm
Answer: 169.65 cm
Step-by-step explanation: I just put this into a calculator, hope this helps!
Answer:
169.64600329385
Step-by-step explanation:
Lindsay shot a model rocket over an area that consists of two grassy areas shown in green and an area without grass, shown in white. What is the probability that his rocket landed in the area WITHOUT grass?
A. 3/5
B. 4/5
C. 3/4
D.3/10
Answer: 3/5
Step-by-step explanation:
If 30 acres are without grass and 20 acres have grass then you set up a fraction with the area without grass on top and the total area on the bottom which would be 30/50 then simplify to get 3/5
Find the equation of the line that has a slope of 11 and passes through the point (-5,8). Help me please please do it right
Answer:
y=11x-47
Step-by-step explanation:
find the exact length of the third side
Answer:
[tex] \sqrt{74} [/tex]
Step-by-step explanation:
Use the Pythagorean theorem.
[tex] a^2 + b^2 = c^2 [/tex]
We are solving for the hypotenuse, c.
[tex] c^2 = a^2 + b^2 [/tex]
[tex] c^2 = 5^2 + 7^2 [/tex]
[tex] c^2 = 25 + 49 [/tex]
[tex] c^2 = 74 [/tex]
[tex] c = \sqrt{74} [/tex]
Answer: [tex] \sqrt{74} [/tex]
Simplify x^2+ 5x + 4 over
x+4
Answer:
x+1
Step-by-step explanation:
5,8,11,7? If the mean of the data set is 8 points, find the missing number of points.
Answer:
9
Step-by-step explanation:
if you add 5,8,9,11,and 7 you get 40 then you need to divide it by 5 because their are 5 numbers so then 40 divided by 5 is 8 so the number is 9
Final answer:
To determine the missing number in the data set with a mean of 8, we set up the equation 8 = (5 + 8 + 11 + x) / 4. Solving for x, we find that the missing number is 8.
Explanation:
To find the missing number in the data set 5, 8, 11, ?, where the mean is 8 points, we can use the formula for the mean of a data set. The mean is the sum of all data points divided by the number of points. Since we know the mean and three of the four numbers, we can create an equation to solve for the missing number:
Mean = (Sum of all data points) / (Number of data points)
8 = (5 + 8 + 11 + x) / 4
Now, solve for x:
8 * 4 = 5 + 8 + 11 + x
32 = 24 + x
x = 32 - 24
x = 8
Therefore, the missing number is 8.