HERE
BD=4CD=3In. triangle BDC
Using Pythagorean theorem
\(\\ \sf\longmapsto CB^2=BD^2+CD^2\)
\(\\ \sf\longmapsto CB^2=3^3+4^2\)
\(\\ \sf\longmapsto CB^2=9+16\)
\(\\ \sf\longmapsto CB^2=25\)
\(\\ \sf\longmapsto CB=\sqrt{25}\)
\(\\ \sf\longmapsto CB=5\)
Step-by-step explanation:
Solution,
In triangle BCD
CD = b = 3
BD = p = 4
CB = h = ?
By using Pythagoras theorem,
h²=p²+b²
(CB)²=(BD)²+(CD)²
(CB)²=(4)²+(3)³
(CB)²=16+9
(CB)²=25
CB=√25
CB=5
A dishwasher has a mean lifetime of 14 years with an estimated standard deviation of 2.5 years. Assume the lifetime of a dishwasher is normally distributed. Identify the individual, variable, and type of variable in the context of this problem.
In this problem, the individual is the dishwasher. The variable is the lifetime of the dishwasher. The type of variable is quantitative, continuous.
Here's how to arrive at the answer:
Given the data, the mean lifetime of a dishwasher is 14 years and the estimated standard deviation is 2.5 years. This indicates that the lifetime of the dishwasher is normally distributed. In this context, the lifetime of the dishwasher is the variable. The type of variable is quantitative, continuous, as it can take any value within a specific range (0 - infinity).An individual is any object or person that data is collected on. In this case, the dishwasher is the individual being referred to because data is collected on its lifetime.
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The lifetime of a dishwasher is a continuous variable, as it can take on any value within a certain range, and it can be measured in decimal points (for example, a dishwasher could last for 14.6 years).
The individual in this problem would be a dishwasher, the variable would be the lifetime of the dishwasher, and the type of variable in the context of this problem would be a continuous variable.
A dishwasher has a mean lifetime of 14 years with an estimated standard deviation of 2.5 years.
Assume the lifetime of a dishwasher is normally distributed.
This is a normal distribution problem that contains the terms mean, standard deviation and variable.
The mean is given as 14 years, the standard deviation is given as 2.5 years and the variable is the lifetime of the dishwasher.
A normal distribution is a bell-shaped distribution that shows how data are distributed.
The Normal distribution is a continuous probability distribution. It is widely used in statistics due to its simplicity. It is used in cases where data follows a normal pattern.
The standard deviation is an important parameter in the distribution as it tells us how spread out the data is.
The lifetime of a dishwasher is a continuous variable, as it can take on any value within a certain range, and it can be measured in decimal points (for example, a dishwasher could last for 14.6 years).
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You want to endow a scholarship that will pay $5,000 per year forever, starting one year from now. If the school's endowment discount rate is 7%, what amount must you donate to endow the scholarship? How would you answer change if you endow it now, but it makes the first award to a student 10 years from today?
The amount required to endow the scholarship would still be approximately $71,428.57.
To calculate the amount needed to endow a scholarship that pays $5,000 per year forever, starting one year from now, we can use the concept of perpetuity and the formula for present value. The amount required to endow the scholarship can be calculated as follows:
Amount needed = Annual payment / Discount rate
Using the given values, the amount needed to endow the scholarship is:
Amount needed = $5,000 / 0.07 = $71,428.57
Therefore, you would need to donate approximately $71,428.57 to endow the scholarship.
If the scholarship makes the first award to a student 10 years from today, the calculation would be different. In this case, we need to account for the time value of money and discount the future payments to their present value. We can use the formula for the present value of an annuity to calculate the amount needed to endow the scholarship:
Present value = Annual payment / (Discount rate - Growth rate)
Assuming there is no growth rate mentioned, we can use the same discount rate of 7% for simplicity. The amount needed to endow the scholarship, in this case, would be:
Present value = $5,000 / (0.07 - 0) = $71,428.57
Even though the first award is made 10 years from today, the present value remains the same. This is because the discount rate is equal to the growth rate (0% in this case). Therefore, the amount required to endow the scholarship would still be approximately $71,428.57.
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The sum of two numbers is 25 one number is 5 less than the other number
NEED HELP ASAP 20POINTSS
Answer:
a) Low: 45 Q1=80 Q2=89 Q3=94 High=100 b) Look at attached image
Step-by-step explanation:
Organized numbers: 45,70,72|,80,|82,85,88|,89,|90,92,92|,94,|98,100,100
mark medians
Graph created in Desmos
Those activities that enable a person to describe in the detail the system that solves the need is called?
Those activities that enable a person to describe in the detail the system that solves the need is called "System design".
What is a system design?The method of defining the components of a system consists, modules, and components, the various interfaces of those components, and the data that flows through that system is known as system design.
Some key features regarding the system design are-
It is intended to meet unique objectives and needs of a company or group by creating a cohesive and well-functioning system.The systematic approach to system design is implied by the term systems design. It may take a bottom-up as well as top-down approach, but in either case, the process is systematic in that it considers all associated factors of the system that must be created—from the architecture to the necessary hardware and software, all the way down to the data and in how it travels as well as transforms throughout its journey through the system.To know more about the system design, here
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1) alice decides to take a trip from the east coast of the united states to the west coast. while planning, she chooses to drive, fly, and ride a train. her first leg of the trip is traveling by car, from sacramento, california to denver, colorado. along the way, she fills up her tank using regular unleaded gas, costing $4.65 per gallon, and premium gas, $4.95 per gallon. after driving for many hours, alice finally makes it to denver, colorado spending $874.80 in gas. a) let r represent gallons of regular unleaded gas and let p represent gallons of premium gas. create an equation that models the situation.
The equation will be: 4.65r + 4.95p = 874.80
The total cost of gas will be sum of the individual costs of both the types of gas. Firstly, calculating cost of regular and premium gas followed by forming the equation.
The total cost of regular gas = Amount of regular gas × Cost of regular gas per gallon
The total cost of regular gas = 4.65 × r
The total cost of premium gas = Amount of premium gas × Cost of premium gas per gallon
The total cost of regular gas = 4.95 × p
We are given overall spending = 874.80
Forming the equation -
Total cost of regular gas + total cost of premium gas = overall spending on gas
4.65r + 4.95p = 874.80
Hence, the equation that models the situation is 4.65r + 4.95p = 874.80.
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If the average value of the function f on the interval [1, 4] is 8, what is the value of
â« (3 f(x) + 2x) dx from 1 to 4 ?
The value of the integral you're looking for is 87. Given that the average value of the function f on the interval [1, 4] is 8, we can use this information to find the value of the integral you're looking for.
The average value of a function can be found by dividing the integral of the function over the interval by the length of the interval. In this case:
Average value = (1/(4-1)) * ∫f(x) dx from 1 to 4
Since the average value is given as 8, we have:
8 = (1/3) * ∫f(x) dx from 1 to 4
Now, we can find the integral of f(x) over the interval [1, 4]:
∫f(x) dx from 1 to 4 = 8 * 3 = 24
Now, we want to find the value of:
∫(3 f(x) + 2x) dx from 1 to 4
We can split this integral into two separate integrals:
∫(3 f(x) + 2x) dx from 1 to 4 = ∫(3 f(x)) dx from 1 to 4 + ∫(2x) dx from 1 to 4
We already found the integral of f(x) from 1 to 4, so the integral of 3 f(x) from 1 to 4 is:
3 * ∫f(x) dx from 1 to 4 = 3 * 24 = 72
Now, we need to find the integral of 2x from 1 to 4:
∫(2x) dx from 1 to 4 = x^2 | from 1 to 4 = (4^2 - 1^2) = 15
Finally, we can add these two integrals to find the value of the original integral:
∫(3 f(x) + 2x) dx from 1 to 4 = 72 + 15 = 87
So, the value of the integral you're looking for is 87.
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Marta used chalk to create a sequence of six numbers on the sidewalk outside her apartment building. After the first two numbers, each number in the sequence equals the sum of the previous two numbers. Marta started with the number 112 and ended with the number 2021. What are the other four numbers in her sequence?
The sequence is 112 , 337 , 449,786 , 1235 , 2021
What is an Equation ?An equation is a mathematical statement formed when two algebraic expressions re equated by an equal sign.
On the base of the given data
Let the first and second number is x and y
Then the third , fourth , fifth and sixth number is (x+y) , (x+2y) ,(2x+3y),(3x+5y)
The first term is 112
There are six numbers in the sequence
The last term is given by the equation
3x+5y = 2021
3* 112 +5y = 2021
5y = 1685
y = 337
Therefore the sequence is 112 , 337 , 449,786 , 1235 , 2021
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Nina owns a condominium where she paid $3,340 in maintenance fees this year. If her property taxes are 15% of this amount, how much did Nina pay in property taxes?
Nina pay in property taxes 501. or \(5.01*10^{2}\).
A property tax, often known as a millage rate, is an ad valorem tax based on a property's value. The tax is imposed by the administrative body of the region where the property is situated. This could be the federal government, a federated state, a county, a region of land, or a municipality. The average effective property tax rate in the Lone Star State is 1.60%, making Texas' property taxes the seventh-highest in the nation. Comparing that to the current 0.99% national average will help. Property taxes in Texas cost the average homeowner $3,797 a year. It is well known that British property owners do not pay property tax. But hold on, it's too soon to celebrate because there might still be taxes to pay.
Based on the given conditions, formulate:
3340*15%
Calculate.
501
Alternative forms.
\(5.01*10^{2}\)
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Please help with a rational functions equation question.
13. If B is the midpoint of AC and AC = 8x -20, find BC. AB= 3x-1
Answer:
\(\Huge \boxed{5x - 19}\)
\(\rule[225]{225}{2}\)
Step-by-step explanation:
A ——— B ——— C
AC = 8x - 20
AB = 3x - 1
BC = AC - AB
BC = (8x - 20) - (3x - 1)
Distributing negative sign.
BC = 8x - 20 - 3x + 1
Combining like terms.
BC = 5x - 19
\(\rule[225]{225}{2}\)
fifteen students are competing for 4 rotary scholarships, 1 in england, 1 in germany, 1 in brazil, and 1 in japan. in how many ways can the scholarships be awarded to different students?
The number of different ways of distributing the scholarships is 32,760.
consider the situation: fifteen students are competing for 4 Rotary scholarships.
consider each scholarship is to be a position In which a student assigned.
This is a permutation problem as:
A) each student selected from the same set.
b) No students can be selected twice.
c) The order in which students are assigned to three scholarships.
Four students are assigned in 4 activities For scholarships.
Activity A1: select a student from the set of 15 students for giving away the first scholarship.
Activity A2: select a student from remaining 14 students for giving away the second scholarship.
Activity A3: select a student from remaining 13 students for giving away the third scholarship.
Activity A4: Select a student from remaining 12 students for giving away the forth scholarship.
According to multiplication rule of accounting the number of different arrangements is A1 X A2 X A3 X A4
15 X 14 X 13 X 12=32760
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What is the solution of the proportion?
Step-by-step explanation:
by cross multiplication:
r=22×13/11
r=2×13
r=26.
hope this helps you.
simplify 2x-3(y-2x) 8x-3y
Answer:
16x - 6y
Step-by-step explanation:
Hope that helps you
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point
�
A, the boat’s crew measures the angle of elevation to the beacon, 12
∘
∘
, before they draw closer. They measure the angle of elevation a second time from point
�
B at some later time to be 20
∘
∘
. Find the distance from point
�
A to point
�
B. Round your answer to the nearest foot if necessary.
The distance between the points A and B is 209.4 feet
What is an equation?An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either be linear, quadratic, cubic, depending of the degree of the variable.
Trigonometric ratio is used to show the relationship between the sides and angles of a right triangle.
A boat is heading towards a lighthouse, whose beacon-light is 107 feet above the water. From point A, the boat’s crew measures the angle of elevation to the beacon, 12°. Let a represent distance from point A to light house:
tan(12) = 107/a
a = 503.4 feet
They measure the angle of elevation a second time from point B at some later time to be 20°. Hence, if b represent distance from point A to light house:
tan(20) = 107/b
b = 294 feet
Distance from point A to B = 503.4 feet - 294 feet = 209.4
The distance between the points is 209.4 feet
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IM GIVING BRAINLIEST!!PLEASE HELP!!I PROMISE!!
Answer:
i think it's b sorry if it's wrong
Step-by-step explanation:
A rectangle has an area of 96 in2. The rectangle's base is 4 in. What is the height of the rectangle?
A. 384in
b. 24in
c. 92in
d. 100in
Answer:
B
Step-by-step explanation:
please answer will give brainliest
Answer: 29152332 ≡ 0 (mod 3)
Step-by-step explanation:
In modular arithmetic, there is the form a ≡ b (mod m) where b is the remainder.
To solve this problem, we want to divide 29152332 by 3 and find the remainder.
29152332 ÷ 3 = 9717444
Since we get an integer with no remainder, we know the answer is 29152332 ≡ 0 (mod 3).
The ratio of students who wear glasses to the total class is 2: 5. If there
are 14 kids with glasses, how many students do not wear glasses?
Answer:
35
Step-by-step explanation:
If 14 kids wear glasses and all others do not and the ratio is 2:5
divide 14 by 2 the answer is 7 multiply it by 5 and you have your answer
At a basketball game, an air cannon launches T-shirts into the crowd. The function y=−18x2+4x
represents the path of a T-shirt. The function 3y=2x−14
represents the height of the bleachers. In both functions, y
represents vertical height (in feet) and x
represents horizontal distance (in feet). At what height does the T-shirt land in the bleachers?
The height that the T-short lands on the bleachers is x = 0.65.
What is quadratic formula?The quadratic equation may be solved by adding and subtracting the same number within the parenthesis to get a perfect square trinomial, which is how the quadratic formula is obtained. A version of the equation that can be solved using the square root function is the result of this method.
Given that it can be used to solve any quadratic equation regardless of the values of the variables a, b, and c, the quadratic formula is an effective tool for solving quadratic equations.
The equation of the path of T-shirt is y = -18x² + 4x and that of the height of bleachers is 3y=2x−14 or y = 2/3x - 14/3
To find the height of the T-shirt landing we find the intersection of the two equations as follows:
-18x² + 4x = (2x - 14)/3
-54x² + 12x = 2x - 14
54x² - 10x - 14 = 0
27x² - 5x - 7 = 0
Using the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Substitute the values;
x = (-(-5) ± √((-5)² - 4(27)(-7))) / 2(27)
x = (5 ± √(925)) / 54
x = (5 ± 5√37) / 54
x = (5 + 5√37) / 54 = 0.65 and
x = (5 - 5√37) / 54 = -0.47
Hence, the height that the T-short lands on the bleachers is x = 0.65.
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Find the next three terms in each geometric sequence.
3. 400,200,100,50, .......
4. 4,-12,36,-108, ........
Answer:
3) 25, 12.5, 6.25
4) 324, -972, 2916
Step-by-step explanation:
What is the area of this figure?
The area of the figure is given as follows:
100.56 mm².
How to obtain the area of the figure?The figure in this problem is composed as follows:
Rectangle of dimensions 4 mm and 12 mm.Rectangle of dimensions 2 mm and 7 mm.Rectangle of dimensions 4 mm and 12 - 7 = 5 mm.Rectangle of dimensions 3 mm and 2 mm.Semicircle of radius 2 mm.The areas for each region are given as follows:
Rectangle of dimensions 4 mm and 12 mm -> 4 x 12 = 48 mm²Rectangle of dimensions 2 mm and 7 mm -> 2 x 7 = 14 mm².Rectangle of dimensions 4 mm and 12 - 7 = 5 mm -> 4 x 5 = 20 mm².Rectangle of dimensions 3 mm and 2 mm -> 3 x 2 = 6 mm².Semicircle of radius 2 mm -> 3.14 x 2² = 12.56 mm².Hence the total area is of:
48 + 14 + 20 + 6 + 12.56 = 100.56 mm².
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Janelle wants to learn to play the piano. Her friends recommended two different music schools. Make Music charges $525 for 10 hours of lessons. Piano Play offers 12 hours of lessons for $540. Which school offers the better deal?
Answer:
Piano Play
Step-by-step explanation:
Answer:
Piano Play offers the better deal.
Step-by-step explanation:
If you divide $525 by 10 you will get $52.50 every hour for Make Music but if you divide $540 by 12 you will get $45 every hour for Piano Play so Piano Play offers the better deal.
Hope this helps!!
Please help me solve this Geometric Sequences problem and please show and explain all steps to solve, thank you for your help and time.
Identify the 10th term of the geometric sequence 2, 8, 32…
Answer:What is the next term in the geometric sequence 2 8 32?
If you notice in this sequence,the next number is a multiple of 4 of the previous number. 2 multiplied by 4 is 8,8 multiplied by 4 is 32. So, the geometric sequence is 2,8,32,128,512,2048,8192,32768. The sum of the sequence is 43,690.
Step-by-step explanation:
i hope this helps
What is the equation of the directrix for the parabola -8(y-3) = (x+4)^2?
I need a proper explanation for this pls
1) y = 5
2) y = 1
3) y = -2
4) y = -6
The equation of the directrix is y=5.
What is Directrix?All points in a plane that are equally spaced out from a given point and a given line make up a parabola. The line is known as the directrix, and the point is known as the parabola's focus. A parabola's axis of symmetry is perpendicular to the directrix, which does not touch the parabola.
Knowing the axis and vertex of a parabola allows one to determine the directrix of the curve.
Given:
-8(y-3) = (x+4)²
Now,
y - 3 = (-1/8)(x + 4)2
y = (-1/8)(x + 4)4 + 3
So,
y = k - p
y = 3 - p
Also, p = 1/ 4a
p = 1 / 4(-1/8)
p = -2
So,
y = 3 - p
y= 3-(-2)
y = 3+ 2
y= 5
Hence, the equation of the directrix is y=5.
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Let k ? R and f(x, y-x2 + y2 + kxy. If you imagine the graph changing as k increases, at what values of k does the shape of the graph change qualitatively? Justify your answer.
The shape of the graph changes qualitatively at k = ± 2 and
\(k=\sqrt{(2)\).
The given function is f(x,y) = y-x²+y²+kxy.
The critical points of the function are found by taking the partial derivatives and equating them to zero:
∂f/∂x = -2x + ky = 0
y = 2x/k
∂f/∂y = 2y + kx = 0
y = -kx/2
Substituting y from the first equation into the second equation gives
x = k²x/4, so k² = 4 and k = ± 2.
Therefore, the critical points are (0,0), (2,4), and (-2,4)
We will now examine the critical points to see when the shape of the graph changes qualitatively.
There are two cases to consider:
Case 1: (0,0)At (0,0), the Hessian matrix is
H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]
=[ -2 0;0 2].
The determinant of the Hessian matrix is -4, which is negative.
Therefore, (0,0) is a saddle point and the graph changes qualitatively as k increases for all values of k.
Case 2: (±2,4)At (2,4) and (-2,4), the Hessian matrix is
H = [∂²f/∂x² ∂²f/∂x∂y;∂²f/∂y∂x ∂²f/∂y²]
=[ -2k 2k;2k 2].
The determinant of the Hessian matrix is 4k²+8, which is positive when k is greater than √(2).
Therefore, the critical points (2,4) and (-2,4) are local minima when
k > √(2).
Thus, the shape of the graph changes qualitatively at k = ± 2 and
k = √(2).
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Two different families bought general admission tickets for a Reno Aces baseball game. One family paid $71 for 3 adult tickets and 5 children tickets, and the other family paid $31 for 2 adult tickets and 1 child’s ticket. How much less does the child ticket cost than an adult’s?
The child ticket costs $10 less than an adult ticket for the Reno Aces baseball game.
In the first scenario, the family paid $71 for 3 adult tickets and 5 children tickets. Let's assume the cost of an adult ticket is A and the cost of a child ticket is C. We can create an equation based on the given information:
3A + 5C = 71
In the second scenario, the family paid $31 for 2 adult tickets and 1 child's ticket. We can create a similar equation:
2A + C = 31
To find the difference in cost between an adult and a child ticket, we need to determine the values of A and C. We can solve these equations simultaneously to find the solution. Subtracting the second equation from the first equation eliminates the C term:
3A - 2A + 5C - C = 71 - 31
A + 4C = 40
Simplifying the equation, we get:
A = 40 - 4C
Substituting this value into the second equation:
2(40 - 4C) + C = 31
80 - 8C + C = 31
7C = 49
C = 7
Now that we have the value of C, we can substitute it back into the first equation to find A:
3A + 5(7) = 71
3A + 35 = 71
3A = 36
A = 12
Therefore, an adult ticket costs $12 and a child ticket costs $5. The child ticket is $10 less than an adult ticket.
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The parent function f(x) = x2 is reflected across the x-axis, vertically stretched by a factor of 5, and translated 3 units down to create g. Identify g in vertex form.
g(x) = −5(x − 3)2
g(x) = −5x2 − 3
g(x) = −5(x + 3)2
g(x) = −5x2 + 3
Answer:
g(x) = −5x2 − 3
Step-by-step explanation:
did the homework and this was the right answer.
The vertex form of the function g will be;
⇒ g (x) = - 5x² - 3
What is Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
The parent function is,
⇒ f (x) = x²
Now,
After the reflection across the x - axis, we get;
f (x) = - f (x)
Thus, The function is,
g (x) = - x²
And, Vertically stretched by a factor of 5, we get;
g (x) = - 5x²
And, Translated 3 units down, we get;
g (x) = - 5x² - 3
Thus, The vertex form of the function g will be;
⇒ g (x) = - 5x² - 3
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c. A 40-foot ladder reaches 38 feet up the side of a house. How far from the base of the
house is the foot of the ladder?
Answer: 12.48
Step-by-step explanation:
38x38+bxb=40x40
1444+b=1600
1600-1444=156
\(\sqrt156\)=12.48
The base of the house is 12.48 foot far from the foot of the ladder.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
|AC|^2 = |AB|^2 + |BC|^2
It is given that A 40-foot ladder reaches 38 feet up the side of a house.
We need to find that How far from the base of the house is the foot of the ladder.
Using Pythagoras theorem, we get;
\(38^2 + b^2 =40^2\\\\1444 + b^2 = 1600\\ \\b^2 = 1600 - 1444 \\\\b^2= 156\\\\b = 12.48\)
Therefore, the base of the house is 12.48 foot far from the foot of the ladder.
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There were 5 boys for every 7 girls at Rayville High School last year. If there were 420 students at the school, how many were girls?
Answer:
240
Step-by-step explanation: