Answers
The value of length BD is 3.0 units
What is Pythagoras theorem?Pythagoras theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.
since AC is a radius that joins a tangent, the angle between them is 90°. Therefore ∆ABC is a right triangle and Pythagoras theorem can be applied.
therefore c² = a²+b²
c² = 4.5²+6²
c²= 20.25+36
c²= 56.25
c = √7.5
AC = CD(radii of a circle)
therefore BD = BC -CD
= 7.5-4.5
= 3.0units
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Related Questions
How do I find the quadratic formula?
Answers
Answer:
x = -31 maybe
Step-by-step explanation:
Use the drawing tool(s) to form the correct answers on the provided graph.
Graph the system of equations given below on the provided graph.
32+y
Then, use the Mark Feature tool to plot the solution to the system.
Drawing Tools
Select
Mark Feature
Line
Click on a tool to begin drawing.
=
-5
10-
80
92
3 Delete
Answers
The solution of the given system of equations is (-3, 4).
Given two linear equations.
2x - 3y = -18
3x + y = -5
Multiplying the first equation by 3 and the second equation by 2,
6x - 9y = -54
6x + 2y = -10
Subtracting the equations,
-11y = -44
y = 4
Substituting,
x = -3
The graph of the system of equations is given below.
Hence the solution is (-3, 4).
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A figure has a area of 25 units^2. what will the new area be after a dilation with a scale factor of 4 ?
Answers
The new area of the figure after the dilation with a scale factor of 4 will be 400 units²
We have,
When a figure is dilated by a scale factor of k, its area is multiplied by k².
So,
If the original area of the figure = 25 units²
Dilated by a scale factor = 4
The new area.
= (4²)(25 units²)
= 16(25 units²)
= 400 units²
Therefore,
The new area of the figure after the dilation with a scale factor of 4 will be 400 units².
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Assume that the speed of automobiles on an expressway during rush hour is normally distributed with mean of 62 mph and a standard deviation of 5 mph.
What percent of cars are traveling slower than 62 mph?
Write your percentage as a decimal (so 12% = 0.12)!
Answers
The percentage of cars traveling slower than 62 mph during rush hour is 0.5 or 50%.
Since the speed of automobiles on an expressway during rush hour is normally distributed with a mean of 62 mph and a standard deviation of 5 mph, we can use the cumulative distribution function (CDF) of the normal distribution to find the percentage of cars traveling slower than 62 mph.
Let X be the speed of an automobile on the expressway during rush hour. Then, X follows a normal distribution with mean (µ) = 62 mph and standard deviation (σ) = 5 mph.
We want to find P(X < 62), which represents the probability that a car is traveling slower than 62 mph.
Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find the z-score corresponding to the value X = 62, using the formula;
z = (X - µ) / σ
Plugging in the given values;
z = (62 - 62) / 5 = 0
Now, we can find the cumulative distribution function (CDF) of the standard normal distribution at z = 0, denoted as Φ(0), which represents the probability that a standard normal random variable is less than or equal to 0.
Using the standard normal distribution table or a calculator with built-in functions for the normal distribution, we can find Φ(0) to be approximately 0.5.
So, P(X < 62) = Φ(0)
= 0.5
Therefore, the percentage of car is 0.5 or 50%
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Apply the k-means algorithm on the following dataset (x,y):(-1,-0.75),(-1,-1),(-0.75,- 1.0), (- 0.25, - 0.25), (0.25, 0.25), (0.75, 1.0), (1.0, 1.0), (1.0, 0.75) and create two clusters. Let the initial cluster prototypes be located at (0.0, 0.0) and (0.75, 0.75) respectively.
Answers
1. Choose the number of clusters, k = 2, and the initial cluster prototypes: c1 = (0.0, 0.0) and c2 = (0.75, 0.75).
2. Assign each data point to the nearest cluster prototype based on the Euclidean distance:
- The distance between (-1, -0.75) and c1 is 1.3229, and the distance between (-1, -0.75) and c2 is 1.5033. Therefore, (-1, -0.75) is assigned to cluster 1.
- The distance between (-1, -1) and c1 is 1.4142, and the distance between (-1, -1) and c2 is 1.8028. Therefore, (-1, -1) is assigned to cluster 1.
- The distance between (-0.75, -1.0) and c1 is 1.1180, and the distance between (-0.75, -1.0) and c2 is 1.4765. Therefore, (-0.75, -1.0) is assigned to cluster 1.
- The distance between (-0.25, -0.25) and c1 is 0.3536, and the distance between (-0.25, -0.25) and c2 is 0.8839. Therefore, (-0.25, -0.25) is assigned to cluster 1.
- The distance between (0.25, 0.25) and c1 is 0.3536, and the distance between (0.25, 0.25) and c2 is 0.5303. Therefore, (0.25, 0.25) is assigned to cluster 2.
- The distance between (0.75, 1.0) and c1 is 1.1180, and the distance between (0.75, 1.0) and c2 is 0.3536. Therefore, (0.75, 1.0) is assigned to cluster 2.
- The distance between (1.0, 1.0) and c1 is 1.1180, and the distance between (1.0, 1.0) and c2 is 0.5303. Therefore
Can u mark my answer as the Brainlyest if it work Ty
Simplify the expression -2-17+12-(-14)
hurry 100 points and brainlyest
Answers
Step-by-step explanation:
k = a constant of proportionality
Putting m = 1kg, a = 1 ms-2
F becomes 1 N.
So, 1 N = 4 × 1kg × 1 ms-2
∴ k = 1
From equation (1), we have
F = ma
what type of number is 15/10?
Answers
Answer:
1.5
Step-by-step explanation:
its a decimal number
Answer: the number 15/10 is a fraction.
Step-by-step explanation:
any two numbers that have a slash in the middle are fractons. :)
Last week, the value of an investment changed at a rate of -\$ 3.15−$3.15 each day. After how many days was the total charge in $ 12.60?−$12.60?
Answers
Based on the rate of change, the total charge will be $ 12.60 in 4 days
After how many days was the total charge in $ 12.60?From the question, we have the following parameters that can be used in our computation:
Rate of change of investment = $3.15
Value of the investment = $12.60
Using the above as a guide, we have the following:
Number of days = Value of the investment/Rate of change of investment
Substitute the known values in the above equation, so, we have the following representation
Number of days = 12.60/3.15
Evaluate
Number of days = 4
Hence, the number of days is 4
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What is the answer to this question
Answers
The maximum profit that can be made is $1737.82
What is an equation?An equation is an expression showing the relationship between numbers and variables using mathematical operators.
The profit function is the difference between the revenue and cost of a commodity. Given that:
Revenue, R(x) = 700x - 11.3x²
Cost, C(x) = 8068 - 34.25x
Profit, P(x) = Revenue - Cost
P(x) = (700x - 11.3x²) - (8068 - 34.25x)
P(x) = 665.75x - 11.3x² - 8068
The maximum profit is at P'(x) = 0; hence:
P'(x) = 665.75 - 22.6x
665.75 - 22.6x = 0
22.6x = 665.75
x = 29.45
P(29.45) = 665.75(29.45) - 11.3(29.45)² - 8068
P(29.45) = 1737.82
The profit to be made is $1737.82
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You're trying to save to buy a new $160,000 Ferrari. You have $58,000 today that can be invested at your bank. The bank pays 6 percent annual interest on its accounts. How many years will it be before you have enough to buy the car? Assume the price of the car remains constant. explain
Answers
You need 9 years to buy the car.
Given that, you need to $160,000, you have $58,000, the bank pays 6 % annual interest on its accounts. we need to find the number of years will it be before you have enough to buy the car,
A = P(1+r)ᵇ
102000 = 58000(1+0.06)ᵇ
1.75 = 1.06ᵇ
log 1.75 = b log 1.06
b = 9.6
Hence, you need 9 years to buy the car.
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
Answers
The area of the composite figure is 13 ft².
How to find the area of a composite figure?The figure is a composite figure. The are of the composite figure is the sum of the individual areas.
The composite figure can be divided into two shapes namely rectangle and triangle.
Therefore,
area of the composite figure = area of the rectangle + area of the triangle
Hence,
area of the rectangle = 4.5 × 2
area of the rectangle = 9 ft²
area of the triangle = 1 / 2 bh
where
b = baseh = heightTherefore,
area of the triangle = 1 / 2 × 4 × 2
area of the triangle = 8 / 2
area of the triangle = 4 ft²
Therefore,
area of the composite figure = 9 + 4
area of the composite figure = 13 ft²
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The length of a rectangle is represented by the function L(x) = 6x. The width of that same rectangle is represented by the function W(x) = 4x2 − 5x + 12. Which of the following shows the area of the rectangle in terms of x? (L ⋅ W)(x) = 24x3 − 30x + 72 (L ⋅ W)(x) = 24x3 − 30x2 + 72x (L + W)(x) = 4x2 + x + 12 (L + W)(x) = 2x2 + x + 12
Answers
The area of the rectangle in terms of x can be represented as (L . W)(x) = 24x³ - 30x² + 72x.
Given a rectangle.
Length of the rectangle, L(x) = 6x
Width of the rectangle, W(x) = 4x² − 5x + 12
The formula to find the area of the rectangle is,
Area = Length × Width
Substituting the given length and width,
Area of the rectangle = L(x) . W(x)
= (L . W)(x)
= (6x) (4x² − 5x + 12)
= 24x³ - 30x² + 72x
Hence the area of the rectangle is represented as (L . W)(x) = 24x³ - 30x² + 72x.
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Answer:
(L . W)(x) = 24x³ - 30x² + 72x.
Step-by-step explanation:
One number is 10 more than fifteen times another. Their sum is 42. Find the numbers.
Answers
From the problem, we know that:
- x = 15y + 10 (since "One number is 10 more than fifteen times another")
- x + y = 42 (since "Their sum is 42")
We can use substitution to solve for one of the variables. Substituting the first equation into the second equation, we get:
(15y + 10) + y = 42
Simplifying the left side, we get:
16y + 10 = 42
Subtracting 10 from both sides, we get:
16y = 32
Dividing both sides by 16, we get:
y = 2
Now that we know y, we can use the first equation to solve for x:
x = 15y + 10
x = 15(2) + 10
x = 40
Therefore, the two numbers are 2 and 40.
Answer:
40, 2
Step-by-step explanation:
x = number 1
y = number 2
x = 15y + 10
x + y = 42
we use the first in the second equation and get
15y + 10 + y = 42
16y = 32
y = 32/16 = 2
x + y = 42
x + 2 = 42
x = 40
Need help pls and thank u!
Answers
Answer:
[tex]\sqrt[]{72}[/tex]
6.3141414141414...
[tex]\sqrt[4]{64}[/tex]
8.121 121 112 111...
Step-by-step explanation:
irrational numbers are real numbers that cannot be expressed as a ratio of integers.
example of irrational number [tex]\sqrt[]{2}[/tex]
example of rational number 2, 3, -4, etc.
Let the vector v have an initial point at (1,−1) and a terminal point at (7,2) what is the direction angle?
Answers
The direction angle of the vector with initial point (1, -1) and terminal point (7, 2) is approximately 26.57 degrees, found by calculating the arctangent of the ratio of the y and x components of the vector.
The direction angle of the vector v is the angle it makes with the positive x-axis, measured counterclockwise.
To find this angle, we need to calculate the difference between the y-coordinates and x-coordinates of the terminal and initial points of the vector, respectively. Then, we can use the arctangent function to find the angle.
Let's first find the components of the vector v
v = <7 - 1, 2 - (-1)> = <6, 3>
Now, we can find the direction angle as follows
θ = arctan(3/6)
θ = 0.4636 radians (in decimal form)
To convert this to degrees, we can multiply by 180/π
θ ≈ 26.57°
Therefore, the direction angle of the vector v is approximately 26.57 degrees.
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Select the correct answer. Determine which statement is true about the zeros of the function graphed below. An upward parabola f on a coordinate plane vertex at (1, 4) and intercepts the y-axis at 5 units. A. Function f has one real solution and one complex solution. B. Function f has exactly one real solution and no complex solutions. C. Function f has exactly two real solutions. D. Function f has exactly two complex solutions.
Answers
The correct option is D, the equation has two complex solutions.
Which is the correct statement about the quadratic equation?Here we can see that we have the graph of a quadratic equation.
It opens upwards, and we can see that it has a vertex at (1, 4), which intercepts the y-axis at y = 5.
Now, we say that the solutions of a quadratic are the values of x such that the function becomes zero.
Particualrly, in this graph we can see that the graph never intercepts the x-axis, that means that this equation has no real roots.
Then the correct option is:
"Function f has exactly two complex solutions."
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If the rate of inflation is 2.6% per year, the future price p (1) (in dollars) of a certain item can be modeled by the following exponential function, where t is the
number of years from today.
p(t)=1200 (1.026)
Find the current price of the item and the price 8 years from today.
Round your answers to the nearest dollar as necessary.
Current price ?$
Price 8 years from today?$
Answers
a) Based on the exponential function, p(t)=1200 (1.026)^t, the item's current price with a rate of inflation of 2.6% per year is $1,200.
b) In 8 years, the future price of the item would be $1,473.53.
What is an exponential function?An exponential function is a mathematical equation depicting the relationship between one variable and another with a periodic constant rate of growth or decline.
Exponential functions are classified into two:
Exponential growth functionExponential decay function.Let the number of years from today = t
Annual inflation rate = 2.6%
Current price = $1,200
Time in years = 8 years
Exponential function:p(t)=1200 (1.026)^t
p(8) = 1,200(1.026)^8
= $1,473.53
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The line plots show the history and mathematics grades for 20 students. What is
the degree of overlap of the two data sets?
Answers
The degree of overlap between the two data sets is said to be high degree of overlap
what is degree of overlap of data?Data overlap is a statistical term that analyzes the extent to which data points or distributions intersect.
It is often employed when comparing two or more datasets, determining how similar or dissimilar they are from each other.
A high degree of overlapping indicates an extensive similarity among shared values between multiple sets of data or distributions. Conversely, if there is a low level of overlapping observed between two datasets, it suggests complete distinctness and no sharing of common quantitative baseline measurements or metrics.
The domain of the overlap according to the plot is [55 85]
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Convert 300° to radians.
O A. 3T
7T
OB. T
O C.
11T
ike
O D. ST
3
Answers
A conversion of 300 degrees to radians is equal to 5.24 radians.
How to determine the angle in radians?In Mathematics and Geometry, you will have to divide the central angle that is subtended by the arc of a circle by 360 degrees if you want to calculate the arc length formed by a circle, and then multiply this fraction by the circumference of the circle.
Mathematically, the arc length formed by a circle can be calculated by using the following equation (formula):
Arc length = rθ
Where:
r represents the radius of a circle.θ represents the central angle measured in degrees.Next, we would convert degrees to radians;
300 = rads × 180/π
Radians = 300π/180 = 5.24 radians.
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What does f(t) + g(t) mean in this context?
Answers
The expression f(t) + g(t) in the context of composite functions mean (f + g)(t)
What does f(t) + g(t) meanFrom the question, we have the following parameters that can be used in our computation:
f(t) + g(t)
The above means that we add the functions f(t) and g(t) together to form another function i.e. a composite function (f + g)(t)
Another way to write the sum of the functions is (f + g)(t)
So, in this context; f(t) + g(t) means (f + g)(t)
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Find the mean absoulute deviation for the following data 6,7,10,12,13,4,8,12
Answers
Answer:
2.75
Step-by-step explanation:
To find the mean absolute deviation for a set of data, we first need to find the mean (average) of the data set. Then, for each data point, we find the absolute value of the difference between the data point and the mean. Finally, we take the mean of those absolute differences.
Step 1: Find the mean
Mean = (6+7+10+12+13+4+8+12)/8 = 72/8 = 9
Step 2: Find the absolute differences
|6-9| = 3
|7-9| = 2
|10-9| = 1
|12-9| = 3
|13-9| = 4
|4-9| = 5
|8-9| = 1
|12-9| = 3
Step 3: Find the mean of the absolute differences
Mean absolute deviation = (3+2+1+3+4+5+1+3)/8
Mean absolute deviation = 22/8
Mean absolute deviation = 2.75
Therefore, the mean absolute deviation for the given data set is 2.75.
Need help. This please
Answers
The domain of the quadratic function in this problem is given as follows:
All real values.
How to obtain the domain of the function?The domain of a function is the set of all the possible input values that can be assumed by the function.
On the graph, the domain of the function is given by the values of x of the function.
A quadratic function has no restrictions on the domain, hence it is defined by all the real values.
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It is well documented that a typical washing machine can last anywhere between 5 to 20 years. Let the life of a washing machine be represented by a lognormal variable, Y = eX where X is normally distributed. In addition, let the mean and standard deviation of the life of a washing machine be 5 and half years and 3 years, respectively. [You may find it useful to reference the z table.]
a. Compute the mean and the standard deviation of X. (Round your intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
b. What proportion of the washing machines will last for more than 11 years? (Round your intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
c. What proportion of the washing machines will last for less than 3 years? (Round your intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
d. Compute the 70th percentile of the life of the washing machines. (Round your intermediate calculations to at least 4 decimal places and final answer to the nearest whole number.)
Answers
b. We want to find P(Y > 11) = P(e^X > 11) = P(X > ln(11)) = P(Z > (ln(11) - ln(5.5) + 0.5 * ln(3/5.5)^2) / 0.7634) ≈ 0.0002, where Z is the standard normal distribution.
c. We want to find P(Y < 3) = P(e^X < 3) = P(X < ln(3)) = P(Z < (ln(3) - ln(5.5) + 0.5 * ln(3/5.5)^2) / 0.7634) ≈ 0.0001, where Z is the standard normal distribution.
d. The 70th percentile corresponds to a z-score of z = invNorm(0.7) ≈ 0.5244. Therefore, we want to find the value of y such that P(Y < y) = P(e^X < y) = 0.7. This implies that ln(y) = ln(5.5) - 0.8329 * 0.7634 + 0.5244 * 0.7634, so y ≈ 7.
mean(X) = ln(5.5) - (1/2) * ln(1 + (3/5.5)^2) ≈ 1.5041 years
std(X) = sqrt(ln(1 + (3/5.5)^2)) ≈ 0.8321 years
b. Let Z be the standard normal variable corresponding to the life of 11 years. Then:
Z = (ln(11) - ln(5.5)) / 0.8321 ≈ 0.9672
Using the z-table, we find that the proportion of the washing machines that will last for more than 11 years is:
P(Z > 0.9672) ≈ 0.1661
c. Let Z be the standard normal variable corresponding to the life of 3 years. Then:
Z = (ln(3) - ln(5.5)) / 0.8321 ≈ -1.4645
Using the z-table, we find that the proportion of the washing machines that will last for less than 3 years is:
P(Z < -1.4645) ≈ 0.0721
d. The 70th percentile of the life of the washing machines corresponds to the standard normal variable Z such that:
P(Z < z) = 0.70
Using the z-table, we find that z ≈ 0.5244. Then:
ln(Y) = mean(X) + z * std(X) ≈ 2.1629
Solving for Y, we get:
Y ≈ e^2.1629 ≈ 8.6913 years
Therefore, the 70th percentile of the life of the washing machines is about 9 years.
The area of a square table top can be represented by (9x^2-30x+25) square feet. The perimeter of the table top is 34 feet. What is the value of x? Explain ow you solved this problem.
Answers
The requried value of x that satisfies the problem is 4.5,
Let's start by finding the side length of the square tabletop, which is equal to the square root of its area. We have:
Area = 9x² - 30x + 25
Side length = √(Area) = √(9x² - 30x + 25)
To find x, we need to use the fact that the perimeter of the table top is 34 feet. The perimeter of a square is given by 4 times the length of one of its sides, so we can write:
Perimeter = 4 * Side length
34 = 4 * √(9x² - 30x + 25)
8.5 = √(9x² - 30x + 25)
9x² - 30x - 47.25 = 0
We can solve this quadratic equation by using the quadratic formula gives,
x = 4.5 and -1.16
Therefore, the value of x that satisfies the problem is approximately 4.5, since the other solution is negative and not meaningful in this context.
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Solitary Savings received an initial deposit of $2000. It kept a percentage of this money in reserve based on the reserve rate and loaned out the rest. The amount it loaned out was eventually all deposited back into the bank. if this cycle continued indefinitely and eventually the $2000 turned into $40,000, what was the reserve rate?
Answers
The value of reserve rate is 5%
Given that;
Solitary savings bank received initially amount of $2000.
Now, Let x% percent be kept as reserve then (100-x)% will be loaned out which would be deposited in other bank.
The other bank would keep x% of (100 - x) and again loan the remaining amount.
Thus the total deposits of this cycle would be a geometric series as
⇒ 2000[1 + (100 - x)% + (100 - x)²%+(100-x)² +...]
Here common ratio is,
(100 - x) / 100 = 1 - 0.01x <
for all possible x
This series is infinite and sum of this would be
= sum of geometric series
= 2000 (1/ (x/100)
= 200000/x
This is given as, 40000
Hence, equate and simplify to get;
⇒ x = 5%
So, The value of reserve rate is 5%
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I need these pages done quick! Can anyone give the answers?
Answers
Answer:
Step-by-step explanation:
3x+10<3 or 2x-5 ≥ 5 solve the inequality
Answers
Answer: x is greater than or equal to 5 (I can't put the symbol in)
Step-by-step explanation:
Add 5 to both sides then simplify, which will get you 2x is greater than or equal to 10, then divide by 2.
Answer:
Step-by-step explanation:
3x+10<3
3x<3-10
3x<-7
x<-7/3
2x-5≥5
2x≥5+5
2x≥10
x≥10/2
x≥5
so x<-7/3 or x≥5
PLEASE ANSWER
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
one half
3
one third
Answers
Answer: B) 1/2
Step-by-step explanation: Hope this helps! :)
The answer is 1/3. I looked it up on gpt and also got a 100 on this quiz
A beaker is shaped like a cylinder with a radius of 1.8 inches and a height of 4.6 inches. It is filled to the top with a solution. Caleb wants to pour it into a different beaker with a radius of 1.25 inches. What is the minimum height the second beaker must be so it does not overflow? Round to the nearest tenth.
Answers
The minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.
Now, For the minimum height of the second beaker, we need to find its volume first.
The volume of the first beaker is given by;
⇒ V₁ = πr₁²h₁
where r₁ is the radius and h₁ is the height.
Substituting the given values, we get:
V₁ = π(1.8)²(4.6)
V₁ ≈ 66.85 cubic inches
Since, the first beaker is filled to the top, its volume equals the volume of the solution.
Therefore, the volume of the solution is also 66.85 cubic inches.
To find the minimum height of the second beaker, we need to use the formula for the volume of a cylinder:
V₂ = πr₂²h₂
where r₂ is the radius and h₂ is the height of the second beaker.
We want to find h₂ such that V₂ is equal to 66.85 cubic inches.
Dividing both sides of the equation by πr₂², we get:
h₂ = V₂ / (πr₂²)
Substituting the given value for r₂, we get:
h₂ = 66.85 / (π(1.25)²)
h₂ ≈ 13.5 inches
Therefore, the minimum height of the second beaker must be approximately 13.5 inches to hold the solution without overflowing.
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Answers
Answer: 1/2 cup oats 2/3 cup flower
