Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.
what is statistical data ?The term "statistical data" refers to numerical data that is gathered from a sample or population in order to characterise or draw conclusions about a larger group. Observational studies, surveys, experiments, and other techniques can all be used to gather statistical data, as can data from already-existing records and databases. Many approaches and methodologies, including data visualisation, inferential statistics, and descriptive statistics, can be used to examine statistical data. Measures of central tendency (mean, median, mode), indicators of dispersion (standard deviation, range, interquartile range), and graphical representations are some examples of the key characteristics of a dataset that are summarised and described using descriptive statistics (histograms, box plots, scatter plots). A bigger population can be inferred from a sample of data using inferential statistics, on the other hand.
given
The stem-and-leaf plot that depicts the data set accurately is as follows:
Season Points for the 2021 Riverside Red Dragon Football
0 0 3
1 1 7 7 7 7
2 0 0 0 2 4 8 8
3 1 3
Key 1|1 = 11
This stem-and-leaf plot depicts the frequency distribution of the data set in an accurate manner.
Each data point's ones digit is displayed in the second column, while its tens digit is displayed in the first column. Each "1|1" in the key denotes the value "11" in the data collection.
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A car dealership pays a wholesale price of $12,000 to purchase a vehicle. This car dealership pays the salesperson commission for selling the car equal to 6.5% of the sale price. How much commission did the salesperson make when they decided to offer a 10% discount on the price of the car?
Math practice complete all this for 15 pts⬇️
The values of the lengths of the sides and segments obtained using the equivalent ratios of the sides of similar triangles are;
1. AA
2. AA
3. 200 ft
4. 21 feet
5. 37.5 meters
6. 4.2 meters
7. 6 feet
What are similar triangles?Similar triangles are triangles that posses similar shape, but may have varied sizes.
1. Two angles in triangle ORS are congruent to two angles in triangle VUT, therefore, the triangles are similar by the Angle-Angle, AA similarity postulate
2. Whereby the angle ∠ABC is congruent to the angle ∠ADF, and the angle ∠ABC and ∠ADGF are corresponding angles, we get by the conversed of the corresponding angles theorem;
BC ║ DF
However, angle A is congruent to itself, by reflexive property, therefore;
Triangle ABC is similar to triangle ADF, according to the AA similarity postulate.
3. Using the proportional sides relationship between similar triangles or the definition of the tangent of an angle, we get;
50/12.5 = h/50
h = 50 × 50/12.5 = 200
The height of the building is 200 ft
4. Using similar triangles relationship, we get;
7/2 = h/6
h = (7/2) × 6 = 21
The height of the taller flagpole is 21 ft
5. Using the equivalent ratio of the sides of similar triangles, we get;
x/25 = 12/8
x = 25 × (12/8) = 37.5
The distance is 37.5 meters
6. The equivalent ratio of the sides of similar triangles indicates;
h/7 = 9/15
h = 7 × (9/15) = 4.2
The height of the brace is 4.2 meters
7. The ratios of the sides of similar triangles indicates that we get;
136/34 = h/(1 1/2)
h = 1 1/2 × (136/34) = 6
The height of the man is 6 feet
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Identify the key features of the exponential function f(x) = 5x and its graph by completing each sentence. please, i have a test tomorrow
The graph of the exponential function f(x) = [tex]5^{x}[/tex] is an upward-sloping curve that starts at (0, 1) and gets steeper and steeper as x increases. It never touches or crosses the x-axis, but it gets arbitrarily close to it as x approaches negative infinity.
EquationsAs we may raise 5 to any power, all real numbers (-∞,∞ ) are the function's domain (positive, negative, or zero).
Range: The range of the function is all positive real numbers (0, ∞), since the exponential function always gives a positive result.
Asymptote: The graph of the function approaches the x-axis as x approaches negative infinity. Therefore, the x-axis is the horizontal asymptote.
Y-intercept: The y-intercept of the function is (0, 1), since[tex]5^{0}[/tex] = 1.
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Find the length x.
4
3.5
2
O
X
so we have two triangles touching each other at a point on that vertical line, and the angles on either side of the vertical line are vertical angles and thus congruent, which means both triangles are similar by AA.
[tex]\cfrac{4}{2}=\cfrac{x}{3.5}\implies 2=\cfrac{x}{3.5}\implies 7=x[/tex]
Need help on this as soon as possible I’ve been stuck for awhile
Answer:
[tex]\textsf{(C)} \quad -\dfrac{1}{4}[/tex]
Step-by-step explanation:
To differentiate an equation that contains a mixture of x and y terms, use implicit differentiation.
To find dy/dx for x² + 3y² = 8 + 2xy, differentiate each term with respect to x.
Begin by placing d/dx in front of each term of the equation:
[tex]\dfrac{\text{d}}{\text{d}x}x^2+\dfrac{\text{d}}{\text{d}x}3y^2=\dfrac{\text{d}}{\text{d}x}8+\dfrac{\text{d}}{\text{d}x}2xy[/tex]
Differentiate the terms in x only (and constant terms):
[tex]\implies 2x+\dfrac{\text{d}}{\text{d}x}3y^2=0+\dfrac{\text{d}}{\text{d}x}2xy[/tex]
Use the chain rule to differentiate terms in y only.
In practice, this means differentiate with respect to y, and place dy/dx at the end:
[tex]\implies 2x+6y\dfrac{\text{d}y}{\text{d}x}=0+\dfrac{\text{d}}{\text{d}x}2xy[/tex]
[tex]\implies 2x+6y\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}2xy[/tex]
Use the product rule to differentiate the term in x and y.
[tex]\textsf{Let}\;u(x)=2x \implies u'(x)=2[/tex]
[tex]\textsf{Let}\;v(x)=y \implies v'(x)= 1\dfrac{\text{d}y}{\text{d}x}[/tex]
Therefore:
[tex]\implies \dfrac{\text{d}}{\text{d}x}[u(x) \cdot v(x)]=u(x) \cdot v'(x)+v(x) \cdot u'(x)[/tex]
[tex]\implies \dfrac{\text{d}}{\text{d}x}2xy=2x \cdot 1 \dfrac{\text{d}y}{\text{d}x}+y\cdot 2[/tex]
[tex]\implies \dfrac{\text{d}}{\text{d}x}2xy=2x \dfrac{\text{d}y}{\text{d}x}+2y[/tex]
So the final differentiated equation is:
[tex]\implies 2x+6y\dfrac{\text{d}y}{\text{d}x}=2x \dfrac{\text{d}y}{\text{d}x}+2y[/tex]
Rearrange the resulting equation to make dy/dx the subject:
[tex]\implies 2x+6y\dfrac{\text{d}y}{\text{d}x}=2x \dfrac{\text{d}y}{\text{d}x}+2y[/tex]
[tex]\implies 6y\dfrac{\text{d}y}{\text{d}x}-2x \dfrac{\text{d}y}{\text{d}x}=-2x+2y[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}(-2x+6y)=-2x+2y[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-2x+2y}{-2x+6y}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{2(-x+y)}{2(-x+3y)}[/tex]
[tex]\implies \dfrac{\text{d}y}{\text{d}x}=\dfrac{-x+y}{-x+3y}[/tex]
To find d²y/dx², differentiate again using the quotient rule and implicit differentiation.
[tex]\textsf{Let}\;u(x)=-x+y \implies u'(x)=-1+1\dfrac{\text{d}y}{\text{d}x}[/tex]
[tex]\textsf{Let}\;v(x)=-x+3y \implies v'(x)=-1+3\dfrac{\text{d}y}{\text{d}x}[/tex]
Therefore:
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{\text{d}}{\text{d}x}\left[\dfrac{u(x)}{v(x)}\right]=\dfrac{v(x)\cdot u'(x)-u(x) \cdot v'(x)}{[v(x)]^2}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{\text{d}}{\text{d}x}\left[\dfrac{-x+y}{-x+3y}\right]=\dfrac{(-x+3y) \cdot \left(-1+1\dfrac{\text{d}y}{\text{d}x}\right)-(-x+y) \cdot \left(-1+3\dfrac{\text{d}y}{\text{d}x}\right)}{(-x+3y)^2}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{(3y-x)\left(\dfrac{\text{d}y}{\text{d}x}-1\right)-(y-x)\left(3\dfrac{\text{d}y}{\text{d}x}-1\right)}{(-x+3y)^2}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{\left(3y\dfrac{\text{d}y}{\text{d}x}-3y-x\dfrac{\text{d}y}{\text{d}x}+x\right)-\left(3y\dfrac{\text{d}y}{\text{d}x}-y-3x\dfrac{\text{d}y}{\text{d}x}+x\right)}{(-x+3y)^2}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{-2y+2x\dfrac{\text{d}y}{\text{d}x}}{(-x+3y)^2}[/tex]
Substitute in dy/dx:
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{-2y+2x\left(\dfrac{-x+y}{-x+3y}\right)}{(-x+3y)^2}[/tex]
To find d²y/dx² at (2, 2), substitute x = 2 and y = 2 into the second derivative:
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{-2(2)+2(2)\left(\dfrac{-2+2}{-2+3(2)}\right)}{(-2+3(2))^2}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{-4+4\left(\dfrac{0}{4}\right)}{(4)^2}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=\dfrac{-4}{16}[/tex]
[tex]\implies \dfrac{\text{d}^2y}{\text{d}x^2}=-\dfrac{1}{4}[/tex]
HELP What is the correct numerical expression for "12 times the sum of 5 and 25 minus 2?"
(12 x 5) + 25 − 2
12 x (5 + 25) − 2
12 x (5 + 25 − 2)
12 x 5 + (25 − 2)
Answer:
12×(5+25)-2
this is the answer to the question
Please help!
Today, the temperature in Boston
is -1 degrees and it is expected to rise
3 degrees each day.
It's 6 degrees in San Francisco and is
expected to fall 1 degree every two
days.
After how many days will the
two temperatures be the same?
Equation 1:
Equation 2:
Answer:
Answer:
The temperature will be the same in two days
Step-by-step explanation:
We can set up two equations to represent the temperatures in Boston (B) and San Francisco (SF) after a certain number of days (d):
B = -1 + 3d
SF = 6 - (d/2)
To find the number of days when the two temperatures will be the same, we can set the equations equal to each other and solve for d:
-1 + 3d = 6 - (d/2)
Multiplying both sides by 2 to eliminate the fraction:
-2 + 6d = 12 - d
Combining like terms:
7d = 14
Dividing both sides by 7:
d = 2
Therefore, the two temperatures will be the same after 2 days.
Find the surface area of a storage container with dimensions 24 feet long, 18 feet wide, and 8 feet high.
The surface area of the storage container is 1536 square feet. To find the surface area of a storage container with dimensions 24 feet long, 18 feet wide, and 8 feet high, we need to calculate the area of each of its six faces and then add them together.
The front and back face each have an area of 24 feet x 8 feet = 192 square feet.
The top and bottom faces each have an area of 18 feet x 24 feet = 432 square feet.
The left and right faces each have an area of 8 feet x 18 feet = 144 square feet.
Adding these areas together, we get:
Surface area of the container = 2(192 sq. ft.) + 2(432 sq. ft.) + 2(144 sq. ft.)
The surface area of the container = 384 sq. ft. + 864 sq. ft. + 288 sq. ft.
The surface area of the container = 1536 square feet
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Among all right circular cones with a slant height of , what are the dimensions (radius and height) that maximize the volume of the cone? The slant height of a cone is the distance from the outer edge of the base to the vertex
The radius and height that maximize the volume of the cone with a slant height of 12 are both 6√2.
To maximize the volume of a cone with a slant height of 12, we need to find the dimensions (radius and height) that give the maximum volume. Use this formula to get the volume of a cone:
[tex]V = 1/3 * \pi * r^2 * h[/tex]
where r and h represents radius ad height respectively.
From the problem statement, we know that the slant height s of the cone is 12. We can use the Pythagorean theorem to relate the height h, radius r, and slant height s:
[tex]s^2 = r^2 + h^2[/tex]
Substituting s = 12, we get:
[tex]12^2 = r^2 + h^2[/tex]
[tex]144 = r^2 + h^2[/tex]
We want to maximize the volume V, so we need to express it in terms of just one variable. We can use the equation relating r, h, and s:
[tex]s^2 = r^2 + h^2[/tex]
Solving for [tex]h^2[/tex], we get:
[tex]h^2 = s^2 - r^2[/tex]
Substituting s = 12, we get:
[tex]h^2 = 144 - r^2[/tex]
Now we can express the volume V as a function of just one variable, r:
[tex]V = 1/3 * \pi * r^2 * h[/tex]
[tex]V = 1/3 * \pi * r^2 * \sqrt{(144 - r^2)[/tex]
To find the maximum volume, we need to take the derivative of V with respect to r, set it equal to zero, and solve for r:
[tex]dV/dr = 1/3 * \pi * (2r * \sqrt{(144 - r^2)} - 2r^3 / \sqrt{(144 - r^2)})[/tex]
[tex]dV/dr = \pi r / 3 * (2\sqrt{(144 - r^2)} - 2r^2 / \sqrt{(144 - r^2)})[/tex]
Setting dV/dr = 0, we get:
[tex]2\sqrt{(144 - r^2)} - 2r^2 / \sqrt{(144 - r^2)} = 0[/tex]
[tex]2(144 - r^2) - 2r^2 = 0[/tex]
[tex]288 - 4r^2 = 0[/tex]
[tex]r^2 = 72[/tex]
So the radius that maximizes the volume is [tex]r = \sqrt{(72)} = 6\sqrt{(2)[/tex]. To find the height h, we can use the equation [tex]h^2 = 144 - r^2[/tex]:
[tex]h^2 = 144 - (6\sqrt{(2)})^2 = 72[/tex]
[tex]h = \sqrt{(72)} = 6\sqrt{(2)[/tex]
Therefore, the dimensions (radius and height) that maximize the volume of the cone with a slant height of 12 are [tex]r = 6\sqrt{(2)[/tex] and [tex]h = 6\sqrt{(2)[/tex].
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The complete question is:
What are the dimensions (radius and height) of all right circular cones with a slant height of 12 that maximize the cone's volume? The cone's slant height is the distance from the outer edge of the base to the vertex.
Find the value of x. 25 X 10.5, 12 Gina Wilson (Al Things Algebro. LLC, and
The value of x using Pythagoras Theorem on the triangle is: 27.741
How to use Pythagoras theorem?Pythagoras Theorem is defined as the manner in which we find the missing lengths of a right angled triangle.
The triangle has three sides, namely the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras theorem is in the form of;
a² + b² = c²
Using Pythagoras Theorem, we can find the smaller side of the triangle as:
y² = 12² - 10.5²
y = √(12² - 10.5²)
y = √33.75
y = 5.809
From the other triangle, we have:
x' = √(25² - 12²)
x' = √481
x' = 21.932
Thus:
x = 21.932 + 5.809
x = 27.741
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10. Alicia rides her bike 8 miles south of her house. Then she turns east for 15 miles. If she takes the short cut back home, how long will her ride by back home?
Answer:
8 miles i think
Step-by-step explanation:
i hope this helps
Rajah wanted to go to the amusement park and needed to determine how much money he would need based on how many friends he brought.
Help Rajah create an equation to represent the least amount of money (M=Money) he would need if the tickets coast $12 per person, food is approximately $11per person and he would buy one large Kettle corn at $15.00 to share with everyone.
The equation representing the least amount of money needed is 23x + 15.
What is an equation?
An equation is a statement stating the equality of two expressions containing variables and/or numbers. The attempts to logically resolve equations, which are essentially questions, have been the basic driving forces behind the development of mathematics.
Let the number of people be x.
Cost of tickets = $12x
Cost of food = $11x
Cost of large kettle corn = $15
Now, on adding all the values, we get the equation as
M = 12x + 11x + 15
M = 23x + 15
Hence, the equation representing the least amount of money needed is 23x + 15.
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Serenity buys milk and potatoes at the
store.
•She pays a total of $31.69.
• She pays a total of $4.09 for the milk.
• She buys 4 bags of potatoes that each
cost the same amount.
Write and solve an equation which can be
used to determine x, how much each bag
of potatoes costs.
Answer:
Let the cost of each bag of potatoes be x.
Then, the total cost of 4 bags of potatoes would be 4x.
According to the problem, Serenity pays a total of $31.69.
This can be written as:
4x + 4.09 = 31.69
Subtracting 4.09 from both sides, we get:
4x = 27.60
Dividing both sides by 4, we get:
x = 6.90
Therefore, each bag of potatoes costs $6.90.
Step-by-step explanation:
suppose i have a cabbage, a goat and a lion, and i need to get them across a river. i have a boat that can only carry myself and a single other item. i am not allowed to leave the cabbage and lion alone together, and i am not allowed to leave the lion and goat alone together. how can i safely get all three across?
This is a classic river crossing puzzle. To safely get all three across take the goat across, leave the goat, take the lion across, take the cabbage across, return with the empty boat, Take the goat across to reunite with the cabbage and lion
Here's one possible solution:
First, take the goat across the river, leaving the cabbage and lion on the original side.Next, leave the goat on the other side and return to the original side with the empty boat.Then, take the lion across the river, and leave it on the other side with the goat.Return to the original side with the empty boat, and take the cabbage across the river.Finally, leave the cabbage on the other side and return to the original side with the empty boat.Take the goat across the river to reunite with the cabbage and lion on the other side.By following these steps, you will have successfully transported all three items across the river without violating the rules.
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a sample of 5 months of sales data provided the following information. month 1 2 3 4 5 units sold 99 100 87 92 92 (a) develop a point estimate of the population mean number of units sold per month. (b) develop a point estimate of the population standard deviation. (round your answer to two decimal places.)
Answer:
The answer would be
Step-by-step explanation:
A. develop a point estimate of the population mean number of units sold per month.
I must say, I do hope this helps so good luck dude
Help please. It’s urgent
For the given equation of function, the production is equal when x = 1/3 and x = 3.
What is an equation?A relationship between a group of inputs and one output each is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function. y = f is how functions are typically represented (x).
The equation of the functions are:
A(x) = 3x²
B(x) = 8x + 3
The production when the functions are equal is given by:
3x² = 8x + 3
3x² - 8x - 3 = 0
3x² - 9x + x - 3 = 0
3x (x - 3) + 1 (x - 3) = 0
(3x + 1) (x - 3) = 0
x = 1/3 and x = 3
Thus, the production is equal when x = 1/3 and x = 3.
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5. At a carnival cotton candy and hot dogs are two different prices. Adam buys one cotton candy and one hot dog for $5. Shannon buys 3 cotton candies and one hot dog for $11. How
much is one hot dog? How much is one cotton candy?
if i roll a 6 sided dye, what is P(even)?
Pls help I’m in a hurry please
(1) The probability of getting tails and a 3 is the probability of following the path T-3, which is 1/2 x 1/4 = 1/8.
(ii) The probability of getting heads and an even number is the probability of following the path H-2 or H-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.
(iii) The probability of not getting heads and an even number is the probability of following the paths T-2 or T-4, which is 1/2 x 1/2 + 1/2 x 1/2 = 1/2.
Tom, Fred, and Rhoda combine their apples to sell at a fruit stand. Fred and Rhoda together have 35 more apples than Tom
If Fred and Rhoda together had 97 more apples than Tom, then the number of apples that Fred has is 105 apples.
Let the number of apples Fred had be denoted by variable "F".
We know that, Rhoda had 17 apples and Tom had 25 apples. We also know that Fred and Rhoda had 97 more apples than Tom.
We can write this information in equation as :
⇒ F + 17 = 97 + 25,
Simplifying this equation:
We get,
⇒ F + 17 = 122
Subtracting 17 from both sides:
⇒ F = 105
Therefore, Fred had a total of 105 apples.
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The given question is incomplete, the complete question is
Tom, Fred, and Rhoda combined their apples for a fruit stand. Fred and Rhoda together had 97 more apples than Tom. Rhoda had 17 apples. Tom had 25 apples. How many apples did Fred have?
Of the 36 people attending a lecture, each only have one pen that is either blue, red, or black.
If 9 people have a blue pen, is the probability 1/4 that a randomly selected person will have blue pen?
A True
B) False
If a randomly selected person is considered, and the probability of them having a blue pen is 1/4.
What is probability?Probability is a fundamental concept in mathematics and statistics that allows us to quantify uncertainty and make predictions based on available information Probability can range from 0 to 1, where 0 means the event is impossible and 1 indicates a certain event
Equation:We need to know the total number of people with pens as well as the number of people with blue pens to calculate the probability of a randomly selected person having a blue pen.
According to the assumption that each person has a single pen, and that the only colors available are blue, red, and black, a randomly selected person is likely to have a blue pen:
The number of people with blue pens divided by the total number of people gives P(blue)
P(blue) = 9 / 36
P(blue) = 1/4
Out of all the pens that this person has, the probability of selecting a blue pen is 1/4.
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the percentage of a Technology stock was $9.80 yesterday. today the price fell the $9.71. find the percentage decrease. round your answer to the nearest tenth of a percent.
[tex]\text{Yesterday} = \$9.80[/tex]
[tex]\text{Today} = \$9.71[/tex]
[tex]\% \ \text{Increase} = ((9.71 - 9.80) \div 9.80) \times 100\%[/tex]
[tex]= (-0.09\div9.80) \times 100%[/tex]
[tex]\thickapprox -0.0092 \times 100%[/tex]
[tex]\thickapprox -0.92\%[/tex]
[tex]\thickapprox \bold{-0.9 \%}[/tex] [tex]\bold{to \ the \ nearest \ tenth.}[/tex]
2 A pizza company bakes about 5565 pizzas over a 21-day period. If an equal number of pizzas
are baked each day, how many pizzas does the pizza company bake daily?
A 265 pizzas
B. 398 pizzas
c. 1855 pizzas
D. 2783 pizzas
Answer: "A 265 pizzas"
Step-by-step explanation:
STEP 1: Divide the number of pizzas by the number of days (5565/21).
This should give you the answer 265.
which angle of rotation would carry a regular dodecagon onto itself?
1. 36
2. 45
3. 330
4. 216
Answer:
A regular dodecagon has 12 sides and rotational symmetry. This means that if you rotate it by a certain angle about its center, it will look the same as before the rotation. The angle of rotation that would carry a regular dodecagon onto itself is equal to 360 degrees divided by the number of sides.
In this case, 360 degrees / 12 sides = 30 degrees.
So a regular dodecagon can be rotated onto itself by any multiple of 30 degrees. Out of the options you provided, only option 3 (330 degrees) is a multiple of 30 degrees. Therefore, an angle of rotation of 330 degrees would carry a regular dodecagon onto itself.
Anna borrowed 20000 at 5% for half year. She want to pay 8000 on maturity. To achieve this she is planning to pay 2000 in 10 months, 5000 in 16 months from now. How much should she pay in 2 and a half years from now to meet her obligation
Anna should pay £3666.67 in 2 and a half years from now to meet her obligation. It means simple interest is £3666.67.
To solve this problem, we can use the formula for simple interest:
I = Prt
where I is the interest, P is the principal, r is the interest rate, and t is the time in years.
Given that Anna borrowed 20000 at 5% for half a year, we can calculate the interest as:
I = Prt = 20000 x 0.05 x 0.5 = 500
So, the total amount Anna needs to pay at maturity is 20000 + 500 = 20500.
Anna plans to pay 8000 on maturity, 2000 in 10 months, and 5000 in 16 months. Therefore, the remaining amount she needs to pay is:
20500 - 8000 - 2000 - 5000 = 5500
To find out how much she needs to pay in 2 and a half years from now, we need to first calculate the time in years:
2 and a half years = 2.5 years
The total time elapsed from the time of borrowing is:
0.5 year (at borrowing) + 2.5 years = 3 years
Using the formula for simple interest, we can calculate the principal amount that will accrue an interest of 5500 in 3 years at 5% per annum:
I = Prt
5500 = P x 0.05 x 3
P = 3666.67
Therefore, Anna should pay £3666.67 in 2 and a half years.
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what is the expected value and standard deviation of the number of small aircraft that arrive during a 75-min period?
For the number of small aircraft that arrive during a 75-min period, the expected value if 10 and standard deviation is 3.17.
The expected value of the number of small aircraft that arrive during a 75-minute period is ⇒ E[X] = μ = 8t.
We need to convert the time period to hours,
So, t = 75/60 = 1.25 hours.
So, the expected number of small aircraft arrivals during a 75-minute period is ⇒ E[X] = μ = 8(1.25) = 10,
To find the standard deviation, we know that for a Poisson distribution, the standard deviation(σₓ) is the square root of mean.
So, σₓ = √μ = √8t,
Substituting t = 1.25,
We get,
⇒ σₓ = √8(1.25) = √10 ≈ 3.17,
Therefore, the expected value for number of aircraft is 10, and standard deviation is 3.17.
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The given question is incomplete, the complete question is
Suppose small aircraft arrive at a certain airport according to a Poisson process with rate α =8 per hour, so that the number of arrivals during a time period of t hours is a Poisson rv with parameter μ = 8t.
What are the expected value and standard deviation of the number of small aircraft that arrive during a 75-min period?
Help I'm lost, I can't manage to answer this question.
The simplified expression is [tex]\frac{1-4i\sqrt3}{7}[/tex].
What is simplification?
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do. For example, take this expression: 4 + 6 + 5.
Here the given expression is
=> [tex]\frac{2-i\sqrt3}{2+i\sqrt3}[/tex]
Multiply and divide by [tex]2-i\sqrt3[/tex] then
=> [tex]\frac{2-i\sqrt3}{2+i\sqrt3}\times\frac{2-i\sqrt3}{2-i\sqrt3}[/tex]
=> [tex]\frac{(2-i\sqrt3)^2}{2^2-(i\sqrt3)^2}[/tex]
=> [tex]\frac{4+i^2\sqrt3^2-4i\sqrt3}{4-i^2\sqrt3^2}[/tex]
=> [tex]\frac{4-3-4i\sqrt3}{4+3}[/tex]
=> [tex]\frac{1-4i\sqrt3}{7}[/tex]
Hence the simplified expression is [tex]\frac{1-4i\sqrt3}{7}[/tex].
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f(x)=x^4+3x^3-8x^2+5x-25
find total surface area
Answer:
Step-by-step explanation:
2 triangles on either side = 4*3/2 = 6 * 2 = 12
rectangle on the back = 4*8 = 32
rectangle on top = 5*8 = 40
rectangle on bottom = 3*8 = 24
12 + 32 + 40 + 24 = 108 cm
Hope this is correct
Tell me if im wrong
elect all of the situations that contain independent events. a. drawing an ace and then drawing a spade from a standard deck of 52 cards without replacement b. training as a long-distance runner and winning a marathon c. the destinations of 3 randomly selected travelers at an airport d. flipping a coin and getting heads twice in a row
The situation representing independent events are ,
Drawing an ace and spade from a deck of 52 cards.
Choosing a destination by 3 randomly selected travelers.
Representing the dependent and the independent events,
Drawing an ace and then drawing a spade from a standard deck of 52 cards without replacement.
The probability of drawing a spade is not affected by whether or not an ace was drawn first,
This is independent event .
Training as a long-distance runner and winning a marathon.
The probability of winning a marathon depends on various factors such as training, skill, and the competition.
These factors are not independent.
so these events are dependent.
The destinations of 3 randomly selected travelers at an airport.
The choice of destination for each traveler is independent of the choices made by the other travelers.
so these events are independent.
Flipping a coin and getting heads twice in a row.
The probability of getting heads on the second flip depends on the outcome of the first flip.
If the first flip resulted in tails, then the probability of getting heads on the second flip is 1/2.
However, if the first flip resulted in heads, then the probability of getting heads on the second flip is still 1/2.
This events are dependent.
Therefore, the independent events are drawing an ace and spade from deck of cards and selecting destination of 3 randomly selected travelers.
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