We know that :
\(\color{hotpink} \tt \: circumference \: of \: a \: circle\color{plum} = 2\pi r\)
So, let the diameter of this circle be x.
Which means :
\( =\tt2 \times \pi \times r\)
\( =\tt 2 \times x \times \pi = 12\pi\)
\( =\tt 2x\pi = 12\pi\)
\( =\tt x = \frac{12}{2} \)
\( = \tt \: x = 6 \: m\)
Thus, the radius of the circle Robert drew = 6 m
Since the circle in option B has a radius of 6 m, it is the circle Robert drew.
▪︎Therefore, the correct option is (B)
Can someone help me with the questions in the picture?
Answer:
\( y = 8 \)
Step-by-step explanation:
Equation of the line that passes through (-2, 8) with a slope of 0, can be written in point-slope form, \( y - y_1 = m(x - x_1) \) and also in slope-intercept form, \( y = mx + b \).
Using a point, (-2, 8) and the slope (m), 0, substitute x1 = -2, y1 = 8 and m = 0 in \( y - y_1 = m(x - x_1) \).
Thus:
\( y - 8 = 0(x - (-2)) \)
\( y - 8 = 0 \)
Rewrite in slope-intercept form
\( y - 8 + 8 = 0 + 8 \) (addition property of equality)
\( y = 8 \)
(a) A = = (b) A = 2 2 4 1 -2 -2 -7] -4
By multiplying matrices B and A, we obtain the product BA. Using BA, we can solve the system of equations y + 2z = 7, x - y = 3, and 2x + 3y + 4z = 17.the values of x, y, and z are -1, 2, and 1 respectively
To find the product BA, we multiply matrix B with matrix A. The resulting matrix will have the same number of rows as B and the same number of columns as A. The product BA will be used to solve the given system of equations.
The product BA can be computed by multiplying each row of matrix B by each column of matrix A and summing the results. The resulting matrix will be:
Now, we can use the product BA to solve the system of equations:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.
1 -1 2
2 3 1
0 4 2
We can rewrite this system of equations as:
-10x - 10y + 6z = 7,
3x - 8y + 2z = 3,
-6x - 16y + 15z = 17.
By comparing the coefficients of x, y, and z in the system of equations with the entries in the matrix BA, we can determine the values of x, y, and z.
Solving the system of equations using matrix BA, we get:
x = -1,
y = 2,
z = 1.
Therefore, the values of x, y, and z are -1, 2, and 1 respectively.
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The complete question is:
Given A=
⎣2 2 -4|
|-4 2 -4|
|2 -1 5|
, B=
⎣1 -1 0|
⎢2 3 4|
⎢0 1 2|
, find BA and use this to solve the system of equations y+2z=7, x−y=3, 2x+3y+4z=17.
What is the effect on the graph of the function f(x) = x2 when f(x) is changed to f(5x)?
Answer:
Step-by-step explanation:
If the parent function is f(x) = x² and the transformed function is g(x) = a(x)²
For a > 1, then the transformed function g(x) will be vertically stretched by a factor of 'a'
For 0 < a < 1, then the transformed function will be vertically compressed or shrink by a factor of 'a'
For a function f(x) = x² when transformed to f(5x) = (5x)²
g(x) = 25x²
Therefore, graph of the parent function f(x) will be vertically stretched by 25 units.
Solve the given initial-value problem for y0 > 0. dy dx = y , y(x0) = y0 y(x) = find the largest interval i on which the solution is defined. (enter your answer using interval notation.)
The largest interval I on which the solution is defined.
\(y(x)=\left(\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2}\right)^{2}\)
This is further explained below.
Find the largest interval I on which the solution is defined. ?Generally, the equation for is mathematically given as
\(\frac{d y}{d x}=\sqrt{y}\)
Separating variables and integrating
\(\begin{aligned}&\Rightarrow \int \frac{d y}{\sqrt{y}}=\int d x \\&\Rightarrow 2 \sqrt{y}=x+c \\&\text { Put } y\left(x_{0}\right)=y_{0} \\&\Rightarrow 2 \sqrt{y_{0}}=x_{0}+c \\&\Rightarrow c=2 \sqrt{y_{0}}-x_{0}(2) \\&\text { Put }(2) \text { in } \\&\Rightarrow 2 \sqrt{y}=x+2 \sqrt{y_{0}}-x_{0} \\&\Rightarrow \sqrt{y}=\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2} \\&\Rightarrow y(x)=\left(\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2}\right)^{2} \end{aligned}\)
In conclusion, the largest interval I on which the solution is defined.
\(y(x)=\left(\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2}\right)^{2}\)
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Paula bought a ski jacket on sale for $4 less than half its original price. She paid $86 for the jacket. What was the original price? The original price was $
Answer:
$180
Step-by-step explanation:
step one 86+4 =90
step two 90×2=180
F(x)=2/3x+3 find the value of x, such that f(x)=-15
Answer:
\(x=-27\)
Step-by-step explanation:
\(f(x)=\frac{2}{3} x+3\)
Substitute -15 for \(f(x)\):
\(-15=\frac{2}{3} x+3\)
Subtract \(3\) from both sides of the equation:
\(-18=\frac{2}{3} x\)
Rewrite the equation:
\(-\frac{18}{1} =\frac{2}{3} x\)
Find the cross product:
\(-54=2x\)
Divide by the coefficient of \(x\), which is \(2\):
\(-27=x\)
I'm going to flip the equation so my variable is on the left:
\(x=-27\)
Solve the simultaneous equation.
The value of a = -2 and b = 3.
What is a system of equations?
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
Here, we have
Given: 3a - 5b = -26, a + 2b = 6
We have to solve this equation.
3a - 5b = -26...(1)
a + 2b = 6...(2)
Now we multiply equation (1) by 2 and equation (2) by 5 and we get
6a - 10b = -52....(3)
5a + 10b = 30....(4)
After solving equations (3) and (4), we get
11a = -22
a = -2
Now we put the value of 'a' in equation(3) and we get
6(-2) - 10b = -52
-10b = -52 + 12
-10b = -30
b = 3
Hence, the value of a = -2 and b = 3.
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. Simplify 4x 2/3when x = 25. Write answer in radical form.
Use a ratio box to solve this problem. If Mrs. C can wrap
12 packages in 5 minutes, how many packages can she
wrap in 1 hour?
PLEASE HELP
Answer: 12:1
Step-by-step explanation:
So how u start is they give you five minutes right
So then you divide 60min by 5. Which is 12.
and then you multiply 12*12
and that would be 144
so then 144:12 would simplify to 12:1 as your ration
water is being drained from a container which has the shape of a right circular cone. the cone has a radius of 3 inches at the top and a height of 6 inches. when the water is 3 inches deep, the surface level is falling at a rate of 2 inches per second. find the rate at which the water is being drained from the container.
The rate at which the water is being drained from the container is -12.56 cubic inches per second.
Given that the water is being drained from a container which has the shape of a right circular cone. The cone has a radius of 3 inches at the top and a height of 6 inches. When the water is 3 inches deep, the surface level is falling at a rate of 2 inches per second. We need to find the rate at which the water is being drained from the container.
Step 1: Calculate the volume of the cone. Consider the cone with the height h = 6 inches and radius of the base r = 3 inches. Let H be the height of the water and V be the volume of the water in the cone. Let V0 be the volume of the cone.
Cone Volume formula: $V=\frac{πr^{2}h}{3}$V0 = πr²h/3 = (3.14) (3²) (6)/3 = 56.52 cubic inches
Step 2: Find the rate at which the water level is falling. Let the rate at which the water level is falling be dh/dt. When the water is 3 inches deep, the surface level is falling at a rate of 2 inches per second. Thus, dh/dt = -2.
Step 3: Find the rate at which the water is being drained from the containerLet dv/dt be the rate at which the water is being drained from the container. To find this rate we need to differentiate the volume of water with respect to time V = (1/3)πr²H.H²dv/dt = (2/3)πr² dh/dtdv/dt = (2/3)π(3²)(-2) = -12.56 cubic inches per second.
Hence, the rate at which the water is being drained from the container is -12.56 cubic inches per second.
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Which option best compares the two equations? A. The solution set of the second equation is a line parallel to the line that is the solution set of the first equation. B. The solution set of the second equation is a plane perpendicular to the line that is the solution set of the first equation. C. The solution set of the second equation is a plane parallel to the line that is the solution set of the first equation. D. The solution set of the second equation is a plane parallel to the plane that is the solution set of the first equation.
The option best compares the two equations is C. The solution set of the second equation is a plane parallel to the line that is the solution set of the first equation
The two given equations are $y=2x+3$ and $z=-4$,
The equation $y=2x+3$ is a linear equation which represents a straight line on the Cartesian plane.
This line passes through $(0,3)$ and $(1,5)$ and continues in both directions infinitely.
The equation $z=-4$ is an equation of the form $z=k$ which represents a plane that is parallel to the $xy$-plane and lies at a distance of $k$ units below the $xy$-plane.
From the two given equations, it can be seen that the solution set of the first equation is a straight line.
In contrast, the solution set of the second equation is a plane parallel to the $xy$-plane, hence, option C is the correct option. A plane is a flat two-dimensional surface that extends infinitely far, it has no thickness. It is often described as a "flat" surface because it has the same properties as a flat surface in Euclidean geometry. Therefore, the correct option that compares the two equations is C. The solution set of the second equation is a plane parallel to the line that is the solution set of the first equation
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Caleb an investment banker sold his shares for $18,189.27 when there was a boom in the stock market. Calculate the amount he paid for the shares if his selling price was 130% of the amount he paid for the shares.
Therefore, Caleb paid approximately $14,067.90 for the shares.
Let's assume the amount Caleb paid for the shares is represented by the variable "x". According to the given information, his selling price was 130% of the amount he paid.
Selling price = 130% of the amount paid
$18,189.27 = 1.3 * x
To find the amount he paid for the shares, we can solve the equation for "x" by dividing both sides by 1.3:
x = $18,189.27 / 1.3
Calculating this, we find:
x ≈ $14,067.90
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help me with this question please
Answer:
N+1
Step-by-step explanation:
It begins with = 2
then n+1=3
then n+2=4 and so on it is n+1
Solve the equation. 8,000g = 48,000
60
600
6
40,000
Answer:
6 or C
Step-by-step explanation:
Answer:
60=460
600=4600
6=46
40000=80000
what is the answer to
f(x)=-3x^2-20
\( \huge \boxed{\mathfrak{Question} \downarrow}\)
What is the answer to \(\sf \: f ( x ) = - 3 x ^ { 2 } - 20\)\( \huge \boxed{\mathfrak{Answer} \downarrow}\)
\( \large \boxed{ \bf \: - 6x}\)
\( \huge \boxed{\mathfrak{Explanation} \downarrow}\)
\( \large \sf \: f ( x ) = - 3 x ^ { 2 } - 20\)
The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of \(\sf \: ax^{n}\) is \(\sf \: nax^{n-1}\).\( \large \sf \: 2\times ( -3x)^{2-1} \)
Multiply 2 times - 3.\( \large \sf \: - 6x^{2-1} \)
Subtract 1 from 2.\( \large \sf \: - 6x^{1} \)
For any term t, t¹ = t.\(\large \boxed{ \bf \: - 6x}\)
Solve the quadratic F(x)=x^2+10x-1
Please explain.
The solutions to the quadratic equation f(x) = x² + 10x - 1 are x = -5 + √26 and x = -5 - √26
To solve the quadratic equation f(x) = x² + 10x - 1
we can use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
For the given equation, a = 1, b = 10, and c = -1.
Substituting these values into the quadratic formula:
x = (-(10) ± √((10)² - 4(1)(-1))) / (2(1))
= (-10 ± √(100 + 4)) / 2
= (-10 ± √104) / 2
Simplifying further:
x = (-10 ± 2√26) / 2
= -5 ± √26
Therefore, the solutions to the quadratic equation f(x) = x² + 10x - 1 are:
x = -5 + √26 and x = -5 - √26
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Find a formula for the nth partial sum of the series and use it to determine if the series converges or diverges. If a seres converges, find its sum
[infinity]
Σ (In √n+1 - in √n)
n = 1
Sn=
(type an exact answer, using radicals as needed)
The sum of the series is____
(type an integer or a fraction.)
The formula for the nth partial sum of the series is equal to Sn = ln √(n+1), and the series diverges.
Get a formula for the nth partial sum of the series, by writing out the first few terms,
S₁ = (ln √2 - ln √1)
= ln √2
S₂ = (ln √3 - ln √2) + (ln √2 - ln √1)
= ln √3 - ln √1
S₃= (ln √4 - ln √3) + (ln √3 - ln √2) + (ln √2 - ln √1)
= ln √4 - ln √1
Pattern here expressed the nth partial sum is equal to
ln √(n+1) - ln √1.
Simplify this to,
ln (√(n+1)/√1)
= ln √(n+1).
nth partial sum is equal to,
Sn = ln √(n+1)
Series converges or diverges,
Take the limit of the nth partial sum as n approaches infinity we have,
\(\lim_{n \to \infty}\) ln √(n+1)
= ln ∞
= ∞
Here, the limit of the nth partial sum diverges to infinity, the series itself diverges.
⇒the series does not have a sum.
Therefore, the nth partial sum of the series is Sn = ln √(n+1), and the series diverges.
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A soccer team has 18 players. 5 of the players have scored at least 4 goals this season. Approximately what percent of the players have scored
at least 4 goals?
Select the best answer from the choices provided.
O A. 1596
OB.
30%
Ос.
6096
D
7596
Answer:30%
Step-by-step explanation:you divide 18 by 100 and then multiply that by 30 and it gives you 5.4 which is close to 5 players. So 30% is the answer
38) Paula is making a pair of drapes for her dining room. Each of the four drapery panels, when completed, measures 8 feetlang by 4 feet wide. What is the total area of the four drapery panels?
pls help if I see a off topic answer or a silly joke I will report and make sure u get in trouble so do not joke around.
Answer:
128 ft^2
Step-by-step explanation:
each drapery has an area of 8*4 feet^2 and there are four panes so the total area is 8*4*4= 128
If Cos A = 9/41 and tan B = 28/45 angle A and B are in quadrant I find the value of Tan(A+B)
Find the value of X.
Answer:
im not sure but I think its 8.3
The table shows the speeds Y in miles per hour of a car after X seconds of braking. write an equation of the line that passes through the points in the table
Answer:
y = 10x + 70
slope of 10
y-intercept of 70
Step-by-step explanation:
y = - 10x + 70.
The slope of - 10 represents the decrease in car speed in miles per hour each second after braking.
The y-intercept of 70 represents the initial speed of the car before braking.
What are lines and their slopes?We know lines have various types of equations, the general type is
Ax + By + c = 0, and the equation of a line in slope-intercept form is
y = mx + b.
Where slope = m and b = y-intercept.
the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects the y-axis at x = 0.
We know slope(m) of a line is (y₂ - y₁)/(x₂ - x₁).
Therefore, Slope of this line is (60 - 70)/(1 - 0).
= - 10/1.
= - 10.
Now, 60 = - 10(1) +b.
60 = - 10 + b.
b = 70.
So, The required equation of the line is y = - 10x + 70.
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A probability distribution must sum up to a) 100 b) 1 0 d) total number of events Question 2:- The random variables X and Y are said to be independent if a) when standard deviations are equal b) Cov (X,Y) = 0 mean of X is equal to Mean of Y d) Their probability distribution is same. Question 3:- The standard normal distribution has a) O mean = 1 and sd = 0 b) O mean = 1 and sd =1 c) O mean = 0 and sd = 0 d) mean = 0 and sd = 1
1) A probability distribution must sum up to 1. 2) The random variables X and Y are said to be independent if Cov (X,Y) = 0. 3) The standard normal distribution has a mean = 0 and sd = 1.
In probability theory and statistics, a probability distribution is the mathematical function that describes the likelihood of a random variable taking different values. The probability distribution of a random variable, X, describes the probabilities of the outcomes of a random experiment.A probability distribution must sum up to 1. The sum of the probabilities of all possible outcomes in a sample space is equal to 1.
Random variables X and Y are independent if the distribution of one variable is not affected by the presence of another. In other words, two variables X and Y are said to be independent if the value of one does not affect the probability distribution of the other. The Covariance of X and Y should be zero for independence.
The standard normal distribution, also known as the Gaussian distribution or Z distribution, is a continuous probability distribution that has a mean of 0 and a standard deviation of 1. A standard normal distribution is a normal distribution with a mean of zero and a standard deviation of 1. The notation for a standard normal variable is Z.
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What is the remainder when the function, f(x)=x²-2x² -5x+16, is divided by (x+3)
O-32
O-14
O 10
022
Answer:
14/x+3
Step-by-step explanation:
1. Simplify the expression. 3[(11–6)2+5]
A 5
B 3
C 15
D 6
Answer:
3 is the answer
mutiply and open bracket minus each other
You work for a packaging company. The total weight of a container and its contents is 48 pounds. The contents of the container account for 13/16 of the total weight.Which fraction represents the ratio of the weight of the container to the weight of the contents?
The fraction 3/13 represents the ratio of the weight of the container to the weight of the contents.
How to Solve Fractions?Let C be the weight of the container, and let X be the weight of the contents. We know that:
C + X = 48 (the total weight of the container and its contents is 48 pounds)
We also know that the contents account for 13/16 of the total weight:
X = (13/16)(48) = 39
To find the fraction representing the ratio of the weight of the container to the weight of the contents, we need to express C/X as a fraction. Substituting X = 39 into the first equation, we get:
C + 39 = 48
Solving for C, we get:
C = 9
Therefore, the ratio of the weight of the container to the weight of the contents is:
C/X = 9/39 = 3/13.
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The doors at a local school have windows in them as shown in the diagram below. The window and the face of the door are similar rectangles. Find the value of x. Note: Images are not to scale.
Answer:
106 cm
Step-by-step explanation:
Given that the rectangles are similar, therefore the ratio of their corresponding sides will be equal. So , we can say that;
53cm/100cm = x/200 cm
Simplify and solve for "x" , as ;
x = 53/100 *200 cm
x = 53*2 cm
x = 106 cm
Hence the value of x is 106cm .
Find the slope of the line graphed below
*there are no answer choices please help!
Answer:
-3/5
Step-by-step explanation:
rise/run
since its a negative slope, you count down three and to the right 5. -3/5 is the slope
Answer:
-3/5
Step-by-step explanation:
Equation for slope of a line is:
(y₂-y₁)÷(x₂-x₁)
In your example:
-4-(-1)÷4-(-1)
(-4+1)÷(4+1)=
-3/5
4/6 x 3/5 in the simplest form.
Answer:
Step-by-step explanation:
2/5
Is the image an example of an angle?
B
65°
A
C
O No; AB and BC intersect in more than one point.
O Yes; AB and BC do not form a line and share an endpoint.
O No; AB and BC form a line.
O Yes; AB and BC are perpendicular to each other.
Yes, the image an example of an angle AB and BC do not form a line and share an endpoint.
What is an angle ?An angle is formed when two lines are extending from a point .
Using this Knowledge it can be deduced from the figure that line BA and BC are extending from point B. Hence forming an angle of 65 degrees
Analyzing the options
option A is wrong as line AB and BC intersected only on one point. formation of a line do not typically say if an angle is formed or not hence making option c incorrect. There is no perpendicular line formed in th figure .
This leaves option B as the correct option
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