Answer:
[tex]\sf \dfrac{1}{4} \pi \quad or \quad \dfrac{7}{9}[/tex]
Step-by-step explanation:
The width of a square is its side length.
The width of a circle is its diameter.
Therefore, the largest possible circle that can be cut out from a square is a circle whose diameter is equal in length to the side length of the square.
Formulas
[tex]\sf \textsf{Area of a square}=s^2 \quad \textsf{(where s is the side length)}[/tex]
[tex]\sf \textsf{Area of a circle}=\pi r^2 \quad \textsf{(where r is the radius)}[/tex]
[tex]\sf \textsf{Radius of a circle}=\dfrac{1}{2}d \quad \textsf{(where d is the diameter)}[/tex]
If the diameter is equal to the side length of the square, then:
[tex]\implies \sf r=\dfrac{1}{2}s[/tex]
Therefore:
[tex]\begin{aligned}\implies \sf Area\:of\:circle & = \sf \pi \left(\dfrac{s}{2}\right)^2\\& = \sf \pi \left(\dfrac{s^2}{4}\right)\\& = \sf \dfrac{1}{4}\pi s^2 \end{aligned}[/tex]
So the ratio of the area of the circle to the original square is:
[tex]\begin{aligned}\textsf{area of circle} & :\textsf{area of square}\\\sf \dfrac{1}{4}\pi s^2 & : \sf s^2\\\sf \dfrac{1}{4}\pi & : 1\end{aligned}[/tex]
Given:
side length (s) = 6 inradius (r) = 6 ÷ 2 = 3 in[tex]\implies \sf \textsf{Area of square}=6^2=36\:in^2[/tex]
[tex]\implies \sf \textsf{Area of circle}=\pi \cdot 3^2=28\:in^2\:\:(nearest\:whole\:number)[/tex]
Ratio of circle to square:
[tex]\implies \dfrac{28}{36}=\dfrac{7}{9}[/tex]
A car travel 80km at 100km/h how long does it take
Answer:
0.8 hrs it take to drive 80 km at 100 km an hour
Step-by-step explanation:
Hello,
Answer:
48 min
Step-by-step explanation:
Cross product :
80 km ⇒ x h
100 km ⇒ 1 h
x = (1 × 80)/100 = 8/10 = 0,8 h
= 0,8 × 60 min
= 48 min
pls help with and pls explain
Answer:
3.) b) The straight line that divides the parabola into half.
4.) b) 1/11^4
Explanation:
3. The axis of the symmetry is the straight line that divides the parabola into half.
Note down: the image below which shows a parabola (red line) and axis of symmetry (blue line).
4. Formula's: [tex]a^{-1} = \dfrac{1}{a}[/tex] , same with [tex]a^{-4 } = \dfrac{1}{a^4}[/tex]
So here: [tex]11^{-4}[/tex] is equivalent to [tex]\dfrac{1}{11^4}[/tex] which later equals to [tex]\dfrac{1}{14641}[/tex]
In the following figure. Find the length of the unknown side of the triangle. Give an exact answer then an
answer correct to 5 decimal places.
Answer:
Step-by-step explanation:
Formula
c^2 = a^2 + b^2
Givens
a = 3b = 8c = ?Solution
c^2 = 3^2 + 8^2 Substitute givens
c^2 = 9 + 64 Combine
c^2 = 73 Take the square root of both sides
√c^2 = √73
c = √73 \
Exact answer
c = √73 73 is prime. It will break down no further
Approximate answer
c = 8.54400 Both zeros must be entered
Giving brainliest :)
The system of equation that will represent her situation is as follows:
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
How to represent system of equation?At store A she will pay a total sum of $50.73 for bread and milk.
At store B she will pay a total sum of $51.63 for bread and milk.
Therefore, the system of equation that will represent her situation is as follows:
where
b = number of breadm = number of milkTherefore,
1.39b + 2.49m = 50.73
1.29b + 2.69m = 51.63
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2. For the entire world's population, approximately 14% of all people speak Chinese as
their native language. Suppose four people are randomly selected from the Earth's
population, and define x to be the number of these who speak Chinese as their native
language. The probability distribution associated with this random variable is given below.
Complete the table to find the answer.
I don't know please help me
Find the height of the triangle by applying formulas for the area of a triangle and your knowledge about triangles.
This is a triangle. side a has a length of 12 inches. side b has a length of 12 inches. side c has a length of 8 inches. The altitude to side c has a length of X inches.
Using the Pythagorean Theorem, the altitude to side c has a length of 11.3 inches.
What is the Pythagorean Theorem?The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:
[tex]h^2 = l_1^2 + l_2^2[/tex]
To find the altitude relative to side c, we bisect this side, which cuts it's length into half(now of 4 inches), forming a right triangle in which:
The altitude is the other leg.The side of 12 inches is the hypotenuse.Hence:
[tex]x^2 + 4^2 = 12^2[/tex]
[tex]x = \sqrt{12^2 - 4^2}[/tex]
x = 11.3 inches.
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Abby can buy individual songs for $1.00 to download, or she can
download an entire album for $8.00. Abby can spend no more
than a total of $50. She wants to buy at least two albums, and no
more than 30 individual songs.
The following system of inequalities represents this situation,
where x is the number of individual songs and y is the number of
albums.
x + 8y ≤ 50
x ≤ 30
y22
Which yellow shaded region corresponds to Abby's possible
choices?
The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let x represent the number of individual songs and y represent the number of albums, hence:
x + 8y ≤ 50 (1)
x ≤ 30 (2)
y > 2 (3)
The solution to the inequalities x + 8y ≤ 50, x ≤ 30, y > 2 is the darker region shown on the graph.
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Our goal is to make add on during 85% of sales.If you make 35 sales how many add on do you need to make to meet the goal
To achieve the goals, he needs to make 29.75 sales and 30 sales as add-on sales.
Since we have given that,
A total number of sales = 35
According to the question, his goal is to make add-on sales during 85% of sales.
So, His added sales would be 85% of sales,
What is the percentage?A percentage calculator computes a number of values involving percentages, including the percentage difference between two given values.
85 percent of 35
[tex]=(\frac{85}{100}) \times 35\\[/tex]
=29.75
To achieve the goals, he needs to make 29.75 sales and 30 sales as add-on sales.
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Which of the following is a parent function?
O A. 1(x)=2*3^x
OB. 1(x)=x^4 +3
O C. 1(x)=e^x
OD. 1(x)=2x
The answer to this question is choice C
Problem
Using the following image, find the midpoint of the line by completing the problems below.
Solution
The midpoint is ( Answer
, Answer
).
Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).
What is the midpoint of the line in the graph?From the graph;
Point 1 : ( x₁ = 0, y₁ = 4 )Point 2: ( x₂ = 2, y₂ = -2 )Midpoint = ?Using midpoint formula;
[tex]( \frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
We substitute in our values
[tex]( \frac{0+2}{2},\frac{4+(-2)}{2}) \\\\( \frac{2}{2},\frac{4-2)}{2}) \\\\( \frac{2}{2},\frac{2}{2}) \\\\( 1, 1 )[/tex]
Given the initial point( x₁,y₁) and the final point( x₂,y₂ ), the midpoint of the line is ( 1, 1 ).
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A sample of size 50 will be drawn from a population with mean 73 and standard deviation 8. Find the 19th percentile of the sample mean.
Answer:
72
Step-by-step explanation:
Geometry
Does anyone know how to do this?
For all rectangles, the area is the length multiplied by the height. For squares (a special type of rectangle), the length and height are the same, so you just use [tex]s^2[/tex], where [tex]s[/tex] is the side length.
[tex]A=s^2=16^2=\boxed{256}[/tex]
(b) The circleThe formula for the area of the circle is [tex]\pi r^2[/tex], where [tex]\pi[/tex] is pi, a constant, and [tex]r[/tex] is the radius of the circle, or the length from the center point to the edge.
We're given the side length of the square, which is the same as the diameter of the circle (length from edge to edge going through the center point). Divide the diameter by [tex]2[/tex] to get the radius of [tex]8[/tex] kilometers.
[tex]A=\pi r^2=\pi8^2=\boxed{64\pi}\approx201.1[/tex]
(c) The blue sectionThe area of the blue section is simply the area of the square minus the area of the circle since we just want what's left over.
[tex]A=\boxed{256-64\pi}\approx54.9[/tex]
You can keep the answer exact (the boxed expression) or use the approximate value of 54.9, depending on the instructions for the assignment.
When asked to find the sum of two mixed numbers with different
denominators, you should
before you add.
о A. find the difference
O B. find a common denominator
OC. round each fraction
The solution to When asked to find the sum of two mixed numbers with different denominators, you should before you add, find a common denominator.
Addition of fractionmixed numbers are; 1 2/5, 2 1/3, 4, 4/5Numerator refers to the upper or top value of a fraction.Denominator refers to the bottom or down value of a fraction.For instance,
4 1/3 + 3 2/5
= 13/3 + 17/5
find common denominator
= (65+51) / 15
= 116/15
= 7 11/15
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factorize 3ac-6ad-2bc+4bd
Answer:
(c - 2d) (3a - 2b)
Step-by-step explanation:
if you need the steps just ask me in the comments and I’ll type them lol
For the given functions f and g find f•g and state it’s domain
f(x) = 3x - 6; g(x) = 8x +4
The function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers
How to determine the composite functions?The given parameters are:
f(x) = 3x - 6; g(x) = 8x +4
The composite function is calculated as:
(f.g)(x) = f(x) * g(x)
This gives
(f.g)(x) = (3x - 6) * (8x + 4)
Expand
(f.g)(x) = 24x^2 + 12x - 48x - 24
Evaluate the difference
(f.g)(x) = 24x^2 - 36x - 24
The above function is a quadratic function;
Quadratic functions have a domain of all set of real numbers
Hence, the function is (c) (f.g)(x) = 24x^2 - 36x - 24; domain of all set of real numbers
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The swimming pool at Spring Valley High School is a rectangle with a width of 70 meters and a length of 30 meters. Around the perimeter of the pool is a tiled floor that extends w meters from the pool on all sides. Find an expression for the area of the tiled floor.
The expression that can be used to find the area of the tiled floor is 4w² + 200w
Area of rectangleOriginal rectangle:Length = 70 Meters
Width = 30 meters
Area = length × width
= 70 × 30
= 2100
New rectangle(including tiled floor):Length = 70 + 2w meters
Width = 30 + 2w meters
Area = length × width
= (70+2w) (30+2w)
= 2100 + 140w + 60w + 4w²
= 4w² + 200w + 2100
Area of the tiled floor = Area of new rectangle - area of old rectangle
= (4w² + 200w + 2100) - 2100
= 4w² + 200w + 2100 - 2100
= 4w² + 200w
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Can you help me to create a histogram graph with the following data please?
The range data is 55
The attached graph represents a histogram that has a range of 55
How to create the histogram?The range is given as:
Range = 55
The range is calculated as:
Range = Maximum - Minimum
So, we have:
Maximum - Minimum = 55
Rewrite as:
Maximum = Minimum + 55
Let the minimum be 10.
So, we have:
Maximum = 10 + 55
Evaluate
Maximum = 65
The following dataset can be used to create the histogram
Score Frequency
10 2
15 5
45 3
65 1
This is so because it has a range of 55
See attachment for the histogram
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Equations in Iwo V Solve the system by the addition method. 3x+8y=6 3x-8y=6 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. There is exactly one solution. The solution set is ‹› (Simplify your answer. Type an ordered pair.) B. There are infinitely many solutions. The solution set is {(x,y)|3x + 8y = 6) or ((x,y)|3x - 8y = OC. The solution set is Ø.
Answer:
A. there is exactly one solution. the solution set is {(2, 0)}.
Step-by-step explanation:
3x + 8y = 6
3x - 8y = 6
when we add these 2 equations, we get
6x + 0 = 12
6x = 12
x = 2
now we use one of the original equations to get y :
3×2 + 8y = 6
6 + 8y = 6
8y = 0
y = 0
What is the value of x in the triangle
Answer:
[tex]5\sqrt{3}[/tex]
Step-by-step explanation:
the sides of a 30 60 90 triangle are x, 2x, and [tex]x\sqrt{3}[/tex], with [tex]x\sqrt{3}[/tex] being opposite to the 60 degree angle, and x being adjacent to the 60 degree angle. If [tex]x\sqrt{3}[/tex] = 15 (as given from the image), you can calculate x to be [tex]5\sqrt{3}[/tex].
a. Missing x:-6 Missing y:22 c. Missing x:-7 Missing y:20 b. Missing x:-7 Missing y:22 d. Missing x:-6 Missing y:21
This exercise is about Linear Functions. From the values given, we can state that:
The value of missing x = 6The value of missing y = 21 (Option D)What is the explanation for the above?Given that the table represents a linear function, so the function is a straight line.
Taking two points
(-12, 17)
(-10, 19)
To determine the slope between (-12, 17) and (-10, 19), we need to use the formula:
Slope = (y2-y1)/(x2 - x1)
Recall that:
(x1, y1) = (-12, 17); and
(x2, y2) = (-10, 19)
m = 19 -17/-10 -17
m = 1
Leveraging the point-slope to create the linear equation, we have:
y-y1 = m(x-x1)
where m is the slope of the line and (x₁, y₁) is the point substituting the values m = 1 and the point (-12, 17). Hence, we have:
y-y1 = m(x-x1)
→ y-17 = 1 (x-(-12))
→ y - 17 = x +12
y = x + 12 + 17
y = x + 29 ..................................Linear Equation
Next, we substitute x = -8 into the Linear Equation
y = (-8) + 29
y = 21
Hence, the missing y = 21; and
The missing x = -8
If we substitute y = 23 into the equation, we have:
y = x + 29
23 = x + 29
x = 29 - 23
x = 6
Thus, when the value of y = 23, the missing x is = 6
Conclusively,
The value of missing x = 6
The value of missing y = 21
Full Question
Determine any data values that are missing from the table, assuming that the data represent a linear function.
X Ix ly |-12 17 -10 19 -8 23
a. Missing x:-6 Missing y:22
b. Missing x:-7 Missing y:22
c. Missing x:-7 Missing y:20
d. Missing x:-6 Missing y:21
Please select the best answer from the choices provided.
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sec(x)- cos(x)=sin(x)tan(x)
Answer:
Step-by-step explanation:
What is the fourth rule of probability
Answer: Addition Rule
Step-by-step explanation:This is the probability that either one or both events occur. a. If two events, say A and B, are mutually exclusive - that is A and B have no outcomes
Find the equation of the graph
y=[tex]\sqrt{x}[/tex]
y=3[tex]\sqrt{x+1}[/tex]
y=[tex]\sqrt{x+7}[/tex]
y=[tex]\sqrt{x-7}[/tex]
Answer:
c
Step-by-step explanation:
y=[tex]\sqrt{x+7}[/tex]
Calculate the amount of money you'll have at the end of the indicated time period.
You invest $3000 in an account that pays simple interest of 3% for 10 years.
The amount of money you'll have at the end of 10 years is
The amount of money you'll have at the end of 10 years is $3900.
Given that, P=$3000, R=3% and T=10 years.
What is the formula to find the simple interest?The formula to find the simple interest is [tex]Interest=\frac{P \times T \times R}{100}[/tex].
Now, simple interest [tex]=\frac{3000 \times 10 \times 3}{100}=\$900[/tex].
Amount=Simple Interest+Principal
=900+3000=$3900
Therefore, the amount of money you'll have at the end of 10 years is $3900.
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a. In the general education course requirement at a college, a student needs to choose one each from social sciences, humanities, natural sciences, and foreign languages. There are 5 social science courses, 4 humanity courses, 4 natural science courses, and 3 foreign language courses available for general education. How many different ways can a student choose general education courses from these 4 areas?
Using the Fundamental Counting Theorem, there are 240 ways to choose general education courses from these 4 areas.
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
Considering the number of options for each course, the parameters are given as follows:
[tex]n_1 = 5, n_2 = 4, n_3 = 4, n_4 = 3[/tex].
Hence the number of ways is given by:
N = 5 x 4 x 4 x 3 = 240.
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Find the absolute maximum and absolute minimum values of f on the given interval.
f(x) = 4x³ - 18x² - 48x + 7, [-2, 5]
The first thing we need to do is evaluate the function at its endpoints.
[tex]f(-2)=-1\\\\f(5)=-183[/tex]
Then, we need to find the critical points to find if the stationary points give the absolute min/max values.
[tex]f'(x)=12x^2 - 36x-48=0\\\\x^2 - 3x-4=0\\\\(x-4)(x+1)=0\\ \\ x=-1, 4[/tex]
[tex]f(-1)=33\\\\f(4)=-217[/tex]
So, the absolute maximum is 33 and the absolute minimum is -217
Find 10 rational numbers between 2/5 and 3/2
[tex] \frac{2}{5} \: \: and \: \: \frac{3}{2} [/tex]
L.C.M. of 5 and 2 = 10
[tex] \frac{2 \times 2}{5 \times 2} = \frac{4}{10} \\ \\ \frac{3 \times 5}{2 \times 5} = \frac{15}{10} [/tex]
[tex] \frac{5}{10} , \frac{6}{10} , \frac{7}{10} , \frac{8}{10} , \frac{9}{10}, \frac{10}{10} , \frac{11}{10} , \frac{12}{10} , \frac{13}{10} , \frac{14}{10} [/tex]
The 10 rationals numbers are :
[tex] \frac{1}{2} , \frac{3}{5} , \frac{7}{10} , \frac{4}{5} , \frac{9}{10} , \frac{1}{1}, \frac{11}{10} , \frac{6}{5} , \frac{13}{10} , \frac{7}{5} .[/tex]
What is the coefficient of "y" after you multiply the following:
( -3 + 2 y) ( -6 + -4 )
answer using two decimal places.
Answer:
20
Step-by-step explanation:
-3(-6+4)+2y(-6+-4)
18 - 12 - 12y - 8y
6 +-20y
Find the vertex
f(x) = 2x²-x-10
Answer:
vertex = (1/4 , -81/8)
Step-by-step explanation:
f(x) = y
f(x) = 2x²-x-10
a= 2
b= -1
c = -10
-b/2a
-(-1)/(2(2))
1/4
x = 1/4
f(x) = 2x²-x-10
y = 2x²-x-10
y = 2(1/4)²-(1/4)-10
y = 2/16-1/4-10
y = 2/16-4/16-160/16
y = -2/16-160/16
y = -162/16
y = -81/8
Reflect (4, 1) over the y-axis. Then translate the result to the right 2 units. What are the coordinates of the final point?
Answer:
Step-by-step explanation:(-4, -1) --> (4, -1). Translating two units to the right means adding two units to the x-coordinate: (4, -1) --> (6, -1). This is our final point