Answer:
47 the answer is simply 47
Cookies are on sale! Today each cookie costs
$
0.75
$0.75dollar sign, 0, point, 75 less than the normal price. Right now if you buy
7
77 of them it will only cost you
$
2.80
$2.80dollar sign, 2, point, 80!
Write an equation to determine the normal price of each cookie
(c)
(c)left parenthesis, c, right parenthesis.
The correct answer is:
The equation is [tex]7(c-0.75) = 2.80[/tex], and the regular price of a cookie is [tex]c =\$1.15[/tex].
Explanation:
c is the regular price of a cookie. We know that today they are $0.75 less than the normal price; this is given by the expression [tex]c-0.75[/tex].
We also know if we buy 7 of them, the total is $2.80. This means we multiply our expression, [tex]c-0.75[/tex], by 7 and set it equal to $2.80:
[tex]7(c-0.75) = 2.80[/tex]
To solve, first use the distributive property:
[tex]7 \times c-7\times0.75 = 2.80[/tex]
[tex]7c-5.25 = 2.80[/tex]
Add 5.25 to each side:
[tex]7c-5.25+5.25 = 2.80+5.25[/tex]
[tex]7c = 8.05[/tex]
Divide each side by 7:
[tex]7c\div7 = 8.05\div7[/tex]
[tex]c = \$1.15[/tex].
An 8 foot long ladder is leaning against a wall. The top of the ladder is sliding down the wall at the rate of 2 feet per second. How fast is the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall.
"The rate at which the bottom of the ladder moving along the ground at the point in time when the bottom of the ladder is 4 feet from the wall is calculated to be 3.464 ft/s."
At a pace of 2 feet per second, the lower end of the ladder is being pulled away from the wall.
At a specific moment, when the lower end of the ladder is 4 feet from the wall, we should determine the rate at which the bottom of the ladder is lowering.
From the point t, the bottom of the ladder is x m, the top of the ladder is y m from the wall.
x² + y² = 64
Differentiating the given relationship with regard to t,
2x dx/dt + 2y dy/dt = 0
x dx/dt + y dy/dt = 0
We need to find out dx/dt at x = 4.
dy/dt = -2
At x = 4, we have,
x² + y² = 64
16 + y² = 64
y² = 48
y = 4√3
Put in the known values to find out dx/dt,
x dx/dt + y dy/dt = 0
4 dx/dt + 4√3 (-2) = 0
4 dx/dt = 8√3
dx/dt = 2√3 = 3.464
Thus, the bottom of the ladder is calculated to be moving at the rate 3.464 ft/s.
The figure can be drawn as shown in the attachment.
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The windows to a Tudor-style home create many types of quadrilaterals. Use the picture of the window below to answer the following questions.
Please help me I will give literally anything
a. Determine which type of quadrilaterals you see. Name these quadrilaterals using the labeled vertices.
b. What properties of quadrilaterals would you have to know to identify the parallelograms in the picture? Be specific as to each type of parallelogram by using the properties between sides, angles, or diagonals for each.
Answer:
I'd be happy to help!
a. From the picture of the window, we can identify the following quadrilaterals:
Rectangle: ABCD (all angles are right angles and opposite sides are parallel and congruent)
Parallelogram: EFGH (opposite sides are parallel and congruent)
Trapezoid: BCGH (at least one pair of opposite sides are parallel)
b. To identify the parallelograms in the picture, we would need to know the following properties of parallelograms:
Opposite sides are parallel and congruent
Opposite angles are congruent
Diagonals bisect each other
Using these properties, we can identify the following parallelograms in the picture:
Parallelogram EFGH: Opposite sides EF and GH are parallel and congruent, and opposite sides EG and FH are also parallel and congruent. Additionally, angles E and G are congruent, and angles F and H are congruent.
Rectangle ABCD: Opposite sides AB and CD are parallel and congruent, and opposite sides AD and BC are also parallel and congruent. Additionally, angles A and C are congruent, and angles B and D are congruent. The diagonals AC and BD bisect each other, meaning that they intersect at their midpoints.
Step-by-step explanation:
the position vector r describes the path of an object moving in the xy-plane. position vector point r(t)
a) Velocity vector v(t) = i - 2tj, Speed s(t) = sqrt(1 + 4t²), Acceleration vector a(t) = -2j. b) Velocity vector v(1) = i - 2j, Acceleration vector a(1) = -2j
This problem is about finding the velocity, speed, and acceleration vectors of an object moving in the xy-plane, described by a position vector r(t). We can find the velocity vector by taking the derivative of the position vector, and the speed by taking the magnitude of the velocity vector. The acceleration vector can be found by taking the derivative of the velocity vector. We can then evaluate the velocity and acceleration vectors at a given point by plugging in the coordinates of the point. This problem requires basic vector calculus and understanding of the relationship between position, velocity, speed, and acceleration vectors.
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Complete question is attached below
The five-number summary of a data set is given below.
Minimum: 3 Q1: 12 Median: 15 Q3: 16 Maximum: 20
Which of the following equals 1.5(IQR)?
The required value is 1.5(IQR) equals 6.
What is Data set?A dataset is a collection of facts that relates to a particular subject. The test results of each pupil in a particular class are an illustration of a dataset. Datasets can be expressed as a table, a collection of integers in a random sequence, or by enclosing them in curly brackets.
According to question:The IQR (interquartile range) is the difference between the third quartile (Q3) and the first quartile (Q1). So, we first need to calculate IQR:
IQR = Q3 - Q1 = 16 - 12 = 4
Now we can calculate 1.5 times the IQR:
1.5(IQR) = 1.5(4) = 6
Therefore, 1.5(IQR) equals 6.
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Complete question:
The five-number summary of a data set is given below.
Minimum: 3 Q1: 12 Median: 15 Q3: 16 Maximum: 20
Which of the following equals 1.5(IQR)?
Please help! 20 points
Order the simplification steps of the expression below using the properties of rational exponents.
Given: We have the expression [tex]\sqrt[3]{875x^5y^9}[/tex]
Step-1: [tex]\sqrt[3]{875x^5y^9}[/tex]
Step-2: [tex](875\times x^5 \times y)^{1/3}[/tex] [break the cube root as power [tex]1/3[/tex]]
Step-3: [tex](125.7)^{1/3}\times x^{5/3} \times y^{9/3}[/tex] [break [tex]875=125\times7[/tex]]
[tex]125=5^3[/tex]
Step-4: [tex](5^3)^{1/3}\times7^{1/3}\times x^{(1+2/3)}\times y^{9/3}[/tex] [ [tex]\frac{5}{3} =1+\frac{2}{3}[/tex] ]
Step-5: [tex]5^1\times7^{1/3}\times x^1\times x^{2/3}\times y^{3}[/tex] [break the power of [tex]x[/tex]]
Step-6: [tex]5\times x\times y^{3} \ (7^{1/3}\times x^{2/3})[/tex]
Step-7: [tex]5xy^3 \ (7x^2)^{1/3}[/tex]
Step-8: [tex]5xy^3\sqrt[3]{7x^2}[/tex]
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19. Hockey Game Two families go to a hockey game. One family purchases two adult tickets and four youth tickets for $28. Another family purchases four adult tickets and five youth tickets for $45.50. Let x represent the cost in dollars of one adult ticket and let y represent the cost in dollars of one youth ticket. a. Write a linear system that represents this situation. b. Solve the linear system to find the cost of one adult and one youth ticket. c. How much would it cost two adults and five youths to attend the game?
Could you please solve this one.
The proof that the lines CD and XY are parallel is shown below in paragraghs
How to prove the lines CD and XY are parallelGiven that
∠CAY ≅ ∠XBD
This means that the angles CAY and XBD are congruent angles
The above means that
The angles ∠AYX & ∠ACD correspond to the angle ∠CAYThe angle ∠BXY & ∠BDC corresponds to the angle ∠XBDBy the corresponding angles, we have
∠BXY = ∠AYX
∠ACD = ∠BDC
By the congruent angles above, the following lines are parallel
Line AC and BX
Line AY and BD
Line CD and XY
Hence, the lines CD and XY are parallel
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The events A and B are mutually exclusive. If P(A) = 0.2 and P(B) = 0.4, what is P(A or B)?
Round your answer to two decimal places.
5/9=
1/14=
12/13=
2/13=
9/11=
9/17=
To round each fraction
Answer:
Step-by-step explanation:
1. Rounded to 0.56
2. Rounded
A teacher has a large yellow bulletin board in her classroom. She decides to use purple paper to frame a smaller rectangle inside the original board. The paper will create a border that is x inches wide. The teacher's bulletin board plan and dimensions are shown below.
Look at the picture then choose the answer from the options below:
Select the true statement about the expression.
A.
The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
B.
The term 4x2 represents the area, in square inches, of the entire bulletin board.
C.
The factor (48 − 2x) represents the height, in inches, of the bulletin board including the decorative border.
D.
The term -288x represents the area, in square inches, of the decorative border.
Option A: The factor (96 − 2x) represents the length, in inches, of the uncovered portion of the bulletin board.
How to obtain the area of a rectangle?To obtain the area of a rectangle, you need to multiply the dimensions of the rectangle, which are the length and the width.
Hence the formula for the area of the rectangle is given as follows:
Area = Length x Width.
The area of the uncovered region is given by the total area subtracted by the area of the covered region.
Then the dimensions for the uncovered region are given as follows:
96 - 2x.48 - 2x.The area of the covered region is given as follows:
4x².
The area of the entire region is given as follows:
4x² - 288x + 4608.
Hence the correct statement is given by option A.
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The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5) calculate the corresponding z-scores for the following 6 American’s weekly beer intake.
The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.
1. 5 beers per week: z-score = -1
2. 8 beers per week: z-score = +1
3. 10 beers per week: z-score = +2
4. 4 beers per week: z-score = -2
5. 6 beers per week: z-score = -0.5
6. 12 beers per week: z-score = +3
To calculate a z-score, we need to know the mean (μ) and standard deviation (σ) of the population. In the given problem, the mean is 7 beers per week, and the standard deviation is 1.5.
A z-score is the number of standard deviations away from the mean. Therefore, to calculate the z-scores, we subtract the mean from the given data point and divide by the standard deviation.
For example, for 5 beers per week, the z-score is (-1). This is calculated by subtracting the mean (7) from the data point (5) and dividing by the standard deviation (1.5). Therefore, (5-7)/1.5 = -1.
Similarly, the z-score for 8 beers per week is (+1). This is calculated by (8-7)/1.5 = +1. The z-score for 10 beers per week is (+2). This is calculated by (10-7)/1.5 = +2. The z-score for 4 beers per week is (-2). This is calculated by (4-7)/1.5 = -2. The z-score for 6 beers per week is (-0.5). This is calculated by (6-7)/1.5 = -0.5.The z-score for 12 beers per week is (+3). This is calculated by (12-7)/1.5 = +3.
the complete question is :
The average American drinks approximately seven beers per week (mean = 7). Assuming a standard deviation of 1.5 (SD = 1.5), calculate the corresponding z-scores for the following 6 Americans’ weekly beer intake:
a) Bob drinks 9 beers per week
b) Sarah drinks 6 beers per week
c) John drinks 4 beers per week
d) Emily drinks 8 beers per week
e) Michael drinks 10 beers per week
f) Rachel drinks 5 beers per week
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Help me find the value of x
Answer:
x = 30
Step-by-step explanation:
We know
The three angles must add up to 180°. We know one is 20°, so the other two must add up to 160°.
2x + 3x + 10 = 160
5x + 10 = 160
5x = 150
x = 30
The pens in a box are repackaged equally into 9 packs. Each pack has more than 15 pens.
1. Find an inequality to represent n, the possible number of pens in the box.
2. Explain why you chose this inequality.
Therefore, the possible number of pens in the box is p, where p is greater than 135.
What is inequality?Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.
Inequalities are mathematical expressions that compare two values using the symbols < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to). To solve an inequality, you need to isolate the variable (the unknown quantity) on one side of the inequality symbol and determine the range of values for which the inequality holds true.
Here are some general steps to solve an inequality:
Simplify both sides of the inequality as much as possible. This may involve combining like terms, distributing terms, or factoring.Get all the variable terms on one side of the inequality symbol and all the constant terms on the other side. Remember that when you multiply or divide both sides of an inequality by a negative number, you must reverse the direction of the inequality symbol.Solve for the variable by isolating it on one side of the inequality symbol. If the variable has a coefficient, divide both sides of the inequality by that coefficient.Write down the solution as an inequality. If you have solved for x, the solution will be in the form of x < a or x > b, where a and b are numbers.Check your solution by testing a value in the original inequality that is within the range of the solution. If the inequality holds true for that value, then the solution is correct. If not, then you may need to recheck your work or adjust your solutionby the question.
Let's say there are 'p' pens in the box. Each pack has more than 15 pens, so we can write the inequality:
p/9 > 15
Multiplying both sides by 9, we get:
p > 135
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taking a whole number, how do you know if there is a number that you can multiply by itself to get it
If a whole number has a whole number square root, it means that there exists a number that you can multiply by itself to get that number.
Let us understand this statement by taking example, the whole number 9 has a whole number square root, which is 3. This means that 3 multiplied by itself gives 9: 3 x 3 = 9. Similarly, the whole number 16 has a whole number square root, which is 4. This means that 4 multiplied by itself gives 16: 4 x 4 = 16.
However, not all whole numbers have whole number square roots. For example, the whole number 2 does not have a whole number square root, which means that there is no whole number you can multiply by itself to get 2. In this case, we would say that 2 is an "irrational" number, because its square root is not a whole number or a fraction of whole numbers.
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HELP! I WILL AMKE YOU BRAINLIEST BC THIS IS DUE TODAY!!!
Answer: 27.3
Step-by-step explanation:
I took the outcomes of the Aces from the trial and found the average and the answer I got was 27.3%
Hope this helps.
PLS HELP I WILL MARK BRAINILEST
Answer:
Let's assume the original price of the stock was x.
When the company announced it overestimated demand, the stock price fell by 40%.
So, the new price of the stock after the first decline was:
x - 0.4x = 0.6x
A few weeks later, when the seats were recalled, the stock price fell again by 60% from the new lower price of 0.6x.
So, the new price of the stock after the second decline was:
0.6x - 0.6(0.6x) = 0.24x
Given that the current stock price is $2.40, we can set up the equation:
0.24x = 2.40
Solving for x, we get:
x = 10
Therefore, the stock was originally selling for $10.
Let X1, X2, ..., Xn denote n independent and identically distributed Bernoulli random vari- ables s.t. P(X; = 1) = p and P(Xi = 0) = 1 – p. for each i = 1, 2, ..., n. Show that __, Xi is sufficient for p by using the factorization criterion given in Theorem 9.4. THEOREM 9.4 Let U be a statistic based on the random sample Yı, Y2, ..., Yn. Then U is a sufficient statistic for the estimation of a parameter 0 if and only if the likelihood L(0) = L(y1, y2, ..., yn 10) can be factored into two nonnegative functions, L(y1, y2, ..., yn (0) = g(u,0) x h(yı, y2, ..., yn) where g(u,0) is a function only of u and 0 and h(y1, y2, ..., yn) is not a function of o.
The likelihood function can be factored using Theorem 9.4 as L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn), where g(Σⁿᵢ=1Xᵢ, p) = p^Σⁿᵢ=1Xᵢ (1-p)^(n-Σⁿᵢ=1Xᵢ) and h(X₁, X₂, ..., Xn) = 1. This satisfies the factorization criterion, and thus, Σⁿᵢ=1Xᵢ is a sufficient statistic for p.
To show that Σⁿᵢ=1Xᵢ is sufficient for p, we need to show that the likelihood function can be factored using Theorem 9.4 as:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
where g(Σⁿᵢ=1Xᵢ, p) is a function only of Σⁿᵢ=1Xᵢ and p, and h(X₁, X₂, ..., Xn) is not a function of p.
First, we can write the joint probability mass function of X₁, X₂, ..., Xn as:
P(X₁ = x₁, X₂ = x₂, ..., Xn = x_n) = p^Σⁿᵢ=1xᵢ (1-p)^Σⁿᵢ=1(1-xᵢ)
Taking the product of these probabilities for all i, we get:
L(p) = L(X₁, X₂, ..., Xn | p) = Πⁿᵢ=1P(Xᵢ = xᵢ) = p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ)
Using the factorization criterion given in Theorem 9.4, we need to find functions g(u, p) and h(X₁, X₂, ..., Xn) such that:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
Let's take g(u, p) = pᵘ(1-p)⁽ⁿ⁻ᵘ⁾, which only depends on u and p. Then:
L(p) = L(X₁, X₂, ..., Xn | p) = g(Σⁿᵢ=1Xᵢ, p) * h(X₁, X₂, ..., Xn)
= p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ) * h(X₁, X₂, ..., Xn)
We can see that the term Σⁿᵢ=1Xᵢ appears in the exponent of p, and Σⁿᵢ=1(1-Xᵢ) appears in the exponent of (1-p). Therefore, we can write:
L(p) = L(X₁, X₂, ..., Xn | p) = [p^Σⁿᵢ=1Xᵢ (1-p)^Σⁿᵢ=1(1-Xᵢ)] * [1]
where the second factor is a constant function of p. This satisfies the factorization criterion, with g(u, p) = pᵘ(1-p⁽ⁿ⁻ᵘ⁾ and h(X₁, X₂, ..., Xn) = 1.
Therefore, we have shown that Σⁿᵢ=1Xᵢ is a sufficient statistic for p.
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Complete question is in the image attached below
A company reported the following:
$275,270
Preferred dividends
$20,390
Shares of common stock outstanding
36,000
Market price per share of common stock
$118.87
Calculate the company's price-earnings ratio. Round your answer to two decimal places.
Net income
The company's price-earnings ratio for a company that reported net income of $275,270 with $20,390 for preferred dividends and 36,000 shares of common stock, is 16.79.
What is the price-earnings ratio?The price-earnings ratio represents the per-dollar amount that an investor can expect to invest in a company in order to receive $1 of that company's net earnings.
The price-earnings (P/E) ratio is also referred to as the price multiple.
The price-earnings (P/E) ratio compares the market price with the earnings per share.
Net income = $275,270
Preferred Dividends = $20,390
Net income available to Common Stockholders = $254,880 ($275,270 - $20,390)
Number of common stock outstanding = 36,000 shares
Market price per share of common stock = $118.87
Earnings per share (Common Stock) = $7.08 ($254,880/36,000)
Price-earnings ratio = Market price per share/Earnings per share
= 16.79 ($118.87/$7.08).
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In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s.
The index of refraction of the material used in double slit experiment is 1.36.
The distance between adjacent maxima on a screen in a double-slit experiment is given by:
d sinθ = mλ
where d is the slit separation, θ is the angle between the screen and the line connecting the slits and the maxima, m is the order of the maximum, and λ is the wavelength of light.
The distance between adjacent maxima changes from 1.0cm to 0.50cm when the slit separation is cut in half, which means that the wavelength of light is also halved. Therefore, the ratio of the two wavelengths is:
λ1/λ2 = 2/1 = 2
The speed of light in the material is given as 2.2x10^8 m/s. The speed of light in a vacuum is c, so the index of refraction of the material is given by:
n = c/v
where v is the speed of light in the material. Therefore:
n = c/2.2x10^8 m/s = 1.36
The index of refraction of the material is 1.36.
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_____The given question is incomplete, the complete question is given below:
In a double slit experiment, it is observed that the distance between adjacent maxima on a remote screen is 1.0cm. The distance between adjacent maxima when the slit separation is cut in half decreases to 0.50cm. The speed of light in a certain material is measured to be 2.2x10^8 m/s. what is the index refraction of this material?
4) 6 out of the 80 dogs in a shelter were adopted yesterday. Express adopted rate as a percent.
Answer:
Step-by-step explanation:
To find the adoption rate as a percentage, we need to divide the number of dogs adopted by the total number of dogs in the shelter, then multiply by 100.
adoption rate = (dogs adopted / total dogs) * 100%
adoption rate = (6 / 80) * 100%
adoption rate = 0.075 * 100%
adoption rate = 7.5%
Therefore, the adoption rate as a percent is 7.5%.
given the following limit lim(x;y)!(0;0) infinty y infinity y , show that the function f (x; y) does not have a limit as (x; y) ! (0; 0).
The limit of f(x, y) as (x, y) approaches (0, 0) depends on the path taken, the limit does not exist, and we can conclude that the function f(x, y) do not have a limit as (x, y) → (0, 0).
To show that the function f(x, y) does not have a limit as (x, y) → (0, 0), we need to show that the limit does not exist, either because the limit is infinite or because the limit does not exist.
We are given that the limit of f(x, y) as (x, y) → (0, 0) when y → infinity is infinity. This means that as y approaches infinity, the function f(x, y) becomes arbitrarily large, regardless of the value of x. However, this does not imply that the limit of f(x, y) exists as (x, y) → (0, 0).
To see why, consider the sequence of points (x_n, y_n) = (1/n, n) as n approaches infinity. As y_n → infinity, we have
lim (x_n, y_n) → (0, 0) f(x_n, y_n) = infinity.
However, if we consider the sequence of points (x_n, y_n') = (1/n, n^2) instead, as n approaches infinity, we have
lim (x_n, y_n') → (0, 0) f(x_n, y_n') = 0.
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Type the correct answer in each box. Assume π = 3.14. Round your answer(s) to the nearest tenth. 90° 30° In this circle, the area of sector COD is 50.24 square units. The radius of the circle is units, and m AB is units.
Therefore, the length of segment AB is approximately 7.4 units.
What is area?Area is a mathematical concept that describes the size of a two-dimensional surface. It is a measure of the amount of space inside a closed shape, such as a rectangle, circle, or triangle, and is typically expressed in square units, such as square feet or square meters. The area of a shape is calculated by multiplying the length of one side or dimension by the length of another side or dimension. For example, the area of a rectangle can be found by multiplying its length by its width.
Here,
To find the radius of the circle, we can use the formula for the area of a sector:
Area of sector = (θ/360) x π x r²
where θ is the central angle of the sector in degrees, r is the radius of the circle, and π is approximately 3.14.
We're given that the area of sector COD is 50.24 square units and the central angle of the sector is 90°. So we can plug in these values and solve for r:
50.24 = (90/360) x 3.14 x r²
50.24 = 0.25 x 3.14 x r²
r² = 50.24 / (0.25 x 3.14)
r² = 201.28
r = √201.28
r ≈ 14.2
Therefore, the radius of the circle is approximately 14.2 units.
Next, we need to find the length of segment AB. Since AB is a chord of the circle, we can use the formula:
AB = 2 x r x sin(θ/2)
where θ is the central angle of the sector in degrees, r is the radius of the circle, and sin() is the sine function.
We're given that the central angle of sector COD is 30°. So we can plug in this value and the radius we found earlier to solve for AB:
AB = 2 x 14.2 x sin(30/2)
AB = 2 x 14.2 x sin(15)
AB ≈ 7.4
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Product -72 and sum -6
The ordered pair that respect the given conditions are: (6,-12) and (-12,6).
System of Equations
A system of equations is the given term of math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.
You can solve a system of equations by substitution or adding methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.
You should convert the text of the question into equations. See below.
Product = -7 -> xy= -72 (1)Sum= -6 -> x+y=-6 (2)From equation 1, you have x=-72/y. Thus, applying the substitution method, you can solve this question by following the steps below:
1) Replace x=-72/y into equation 2. Then, you have:
[tex]\frac{-72}{y} +y=-6\\ \\[/tex]
-72+y²=-6y
y²+6y-72=0
2) Solving the quadratic equation y²+6y-72=0 for finding y:
Δ=b²-4ac
Δ=6²-4*1*(-72)
Δ=36+288
Δ=324
[tex]y=\frac{-b\pm \sqrt{\Delta} }{2a} =\frac{-6\pm \sqrt{324} }{2*1}=\frac{-6\pm18 }{2}[/tex]. Therefore,
y1=(-6-18)/2=-12
or
y2=(-6+18)/2=12/2=6
3) Finding x
If x=-72/y and y=-12 or y=6. You have
For y=-12, x=-72/-12, thus x=6
For y=6, x=-72/6, thus x=-12
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CDs are on sale for $5 each. Jennifer has $45 and wants to buy as many as she can. How many CDs can Jennifer buy?
Answer:
9 CDs
Step-by-step explanation:
r u d0mb? 45 divided by 5 = 5 10 15 20 25 30 35 40 45
count the numbers
BOOM ANSWER
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Answer:
See step by step.
Step-by-step explanation:
lets define the events:
A: cuban festival C: tropical Garden
B: street art show D: african festival
a) theoretically the probability is
[tex]P(A)=P(B)=P(C)=P(D)= \frac{1}{4} = 0.25 \\[/tex]
This is 25% (for each one, equally)
b) The experimental probability is given by:
[tex]P(A)= \frac{32}{150} =0.2133[/tex]
[tex]P(B)= \frac{38}{150} =0.2533[/tex]
[tex]P(C)= \frac{35}{150} =0.2333[/tex]
[tex]P(D)= \frac{45}{150} =0.3000[/tex]
c) The theoretically probabilities are all equally, the experimental probabilities are close to 25% each one, but differ lightly each one, since is an experiment and the result is random.
Subtract 1/9 - 1/14 and give answer as improper fraction if necessary.
Answer:
To subtract 1/9 - 1/14, we need to find a common denominator. The smallest number that both 9 and 14 divide into is 126.
So, we will convert both fractions to have a denominator of 126:
1/9 = 14/126
1/14 = 9/126
Now we can subtract them:
1/9 - 1/14 = 14/126 - 9/126
Simplifying the right-hand side by subtracting the numerators, we get:
5/126
Therefore, 1/9 - 1/14 = 5/126 as an improper fraction.
Answer:
1/9-1/14
=14-9/9*14
=5/126
= 25 1/5
Expand and simplify completely
[tex]x(x+(1+x)+2x)-3(x^2-x+2)[/tex]
Answer:
x² + 4x - 6
Step-by-step explanation:
x(x + (1 + x) + 2x) - 3(x² - x + 2) ← simplify parenthesis on left
= x(x + 1 + x + 2x) - 3(x² - x + 2)
= x(4x + 1) - 3(x² - x + 2) ← distribute parenthesis
= 4x² + x - 3x² + 3x- 6 ← collect like terms
= x² + 4x - 6
the temperature on monday was ₋7∝.
the temperature on tuesday was 5∝ lower than on monday.
the temperature on wednesday was 8∝ higher than on tuesday.
find the temperature on wednesday.
Answer:
пошел в
Step-by-step explanation:
Orders arriving at a website follows a Poisson distribution. Assume that on average there are 12 orders per hour. (a) What is the probability of no orders in five minutes? (b) What is the probability of 3 or more orders in five minutes? (c) Determine the length of a time interval such that the probability of no orders in a time interval of this length is 0.001.
a) The probability of no orders in 5 minutes is calculated to be 0.36788.
b) The probability of three or more orders in 5 minutes is calculated to be 0.08.
c) The length of the time interval such that the probability of no orders in a time interval of this length is 0.001 is calculated to be 34.5 min.
X is assumed to be the poisson's distribution where λ = 12 orders per hour.
a) At T = 1/12 hours which is 5 min, probability of no orders,
P (X = 0) = e^(-12/12) = 0.36788
b) At T = 1/12 hours which is 5 min, probability of three or more orders,
P (X ≥ 3) = 1 - P (X ≤ 2) = 1 - e⁻¹(1 + 1 + 1/2) = 0.08
c) Let us find the interval T for which:
P (X = 0) = 0.001
e^(-12T) = 0.001
Solving the equation for T we have,
T = -1/12 ln(0.001) = 0.5756 hours = 34.5 min
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