rn for some constant r, r must be a root of the characteristic equation p2 - C1p - C2 = 0. That is, r must satisfy the characteristic equation.
To prove this, first assume an = rn for a constant r. Plugging this into a given recurring relation gives:
rn = C1rn-1 + C2rn-2
Expanding the right-hand side, we get:
rn = C1r(n-1) + C2r(n-2)
Simplifying by combining equal terms, we get:
rn - C1rn-1 - C2rn-2 = 0
This is a linear homogeneous recurrence relation of degree 2 with constant coefficients. In general, solutions to such recurrence relations are of the form an = ar1n + br2n. where r1 and r2 are the roots of the characteristic equation p2 - C1p - C2 = 0.
Therefore, if an = rn for some constant r, r must be a root of the characteristic equation p2 - C1p - C2 = 0. That is, r must satisfy the characteristic equation. This completes the proof.
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A submarine is 975 meters below sea level. It had to change its depth and is now 315 meters below sea level. Write an equation to show how much the submarine's depth changed.
Answer: You simply subtract 315 from 975
Step-by-step explanation:
4p2 divided by 2! - 4c2
Answer:
Step-by-step explanation:
12.5663706144
4. The top of a desk is shaped like the trapezoid shown, which has an area of 792 square inches. Each triangular section has an area of 216 square inches. What is the height of the trapezoid?
Height of the trapezoid is 18 inches
What do you mean by trapezoid?
A quadrilateral with at least one pair of parallel sides is called a trapezoid
The parallel sides are called the base of the trapezoid. The other two sides are called legs (or sides) if they are not parallel. Otherwise, the trapezoid is a parallelogram and has two base pairs.) A scalene trapezoid is a trapezoid without equal sides
It is given that the area of the trapezoid is 792 square inches and area of each triangular section is 216 square inches.
Area of trapezoid = area of 2 triangle + area of rectangle
792 = 2 × 216 + (length × breadth)
792 = 432 + (length × breadth)
792 - 432 = length × 20
360 = length × 20
length = 360/20
length = 18
Therefore, height of the trapezoid is 18 inches
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Each of the 9 reindeer have 8 jingle bells on their collar. There are 12 more bells on the reins. How many bells in all?
Answer: 84 bells
Step-by-step explanation:
12 + 9x8
84
use the intermediate value theorem to show that there is a root of the given equation in the specified interval.
To use the intermediate value theorem to show that there is a root of the given equation in the specified interval, we first need to find the values of the function at the two endpoints of the interval. Let's say the function is denoted by f(x) and the interval is [a, b].
If f(a) and f(b) have opposite signs (one is positive and the other is negative), then by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [a, b]. This is because the intermediate value theorem states that if a function is continuous on a closed interval and the function takes on different values at the endpoints of the interval, then there must be at least one point in the interval where the function takes on the value of the intermediate value between the two endpoints.
For example, suppose we have the equation f(x) = x^2 - 3 and we want to show that there is a root of the equation in the interval [1, 2]. We can evaluate the function at the two endpoints of the interval:
f(1) = 1^2 - 3 = -2
f(2) = 2^2 - 3 = 1
Since f(1) and f(2) have opposite signs, by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [1, 2]. To find the root, we can use a root-finding algorithm such as bisection or Newton's method.
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Does the histogram appear to depict data that have a normal distribution? O A. The histogram appears to depict a normal distribution. The frequencies generally decrease to a minimum and then increase. O B. The histogram does not appear to depict a normal distribution. The frequencies generally increase and the histogram is roughly symmetric. O C. The hidtogram does not appear to depict a normal distribution. The frequencies generally decrease to a minimum and then increase, and the histogram is roughly symmetric. OD. The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Frequency Weight (g) 6.000-6.049 6.050-6.099 6.100-6.149 6.150-6.199 6.200-6.249 6.250 6.299 6.300-6.349 6.350-6.399 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?
The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then decrease, and the histogram is symmetric.
The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.
For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.
The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.
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how do you
graph y= -3x-10
Answer:
slope: -3
Y- intercept: (0,10)
WILL MAKE BRAINLIEST Your classmate is starting a new fitness program. He is planning to ride his bicycle 50 minutes every day. He burns 5 calories per minute bicycling at 11 mph and ! minute bicycling at 15 mph. How long should he bicycle at each speed to burn 400 calories?
He should bicycle for ———— minutes at 11 mph and ______ minutes at 15 mph
Hello,
I hope you and your family are doing well!
The classmate should bike for 50 minutes at 11 mph and at 150 minutes for 15 mph. (See explanation below)
First, let's find how many calories your classmate burns while biking at 11 mph:
calories burned = time * rate of calorie burn
Since your classmate bikes at 11 mph for 50 minutes, the number of calories he burns at this speed is:
calories burned = 50 minutes * 5 calories/minute = 250 calories
Now, let's find how many calories your classmate burns while biking at 15 mph:
calories burned = 400 calories - 250 calories = 150 calories
Since your classmate burns 1 calorie per minute while biking at 15 mph, he needs to bike at this speed for 150 minutes to burn the remaining calories:
time = calories burned / rate of calorie burn
time = 150 calories / 1 calorie/minute = 150 minutes
Please rate this answer 5 stars and brainliest if you find it helpful.
Happy Holidays!
A fair coin is tossed 10 times. Find the probability of satisfying the condition that that the coin does not land on tails twice in a row
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
When a fair coin is tossed 10 times, the sample size (n) is:
n = [tex]2^{10}[/tex]
This is so because a fair coin has 2 sides.
So, we have:
n = 1024
There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.
So, the probability is:
P = [tex]\frac{1}{1024}[/tex]
Therefore,
The probability of tossing 10 tails in a row is [tex]\frac{1}{1024}[/tex]
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What term encompasses a variety of people and requires an openness and willingness to accept and appreciate that which is different?
O A.
OB
О с. work ethic
OD. productivity
diversity
team-building
The term that encompasses a variety of people and requires an openness and willingness to accept and appreciate that which is different is diversity.
What is diversity?The world by its very nature is diverse. The meaning of this is that there are a lot of people that can be found in the world and all of them do come from different walks of life and speak different languages and are from different races.
It is expected that we must be able to embrace people that are coming from so many different backgrounds so that we can be able to live a productive life and thereby contribute meaningfully to the society.
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Hailey went to Frank's Market and bought 1 3/4 pounds of coffee at $13 a pound and 8 1/2 pounds of rice at $0.40 per pound. Hailey paid for her purchase with a $50 bill. How much change did Hailey receive?
Answer:
$23.85
Step-by-step explanation:
1 3/4 = 1.75 pounds of coffee
8 1/2 = 8.5 pounds of rice
1.75 x 13= 22.75
8.5 x 0.4= 3.4
22.75 + 3.4 = 26.15
50-26.15=23.85
Which model shows the problem 1 divided by 1/6 ?
The model that shows the problem 1 divided by 1/6 is option 1.
What is meant by circle?Every point in a plane that is at a specific distance from the center, or the circle's center, forms a shape. To put it another way, it is the curve that a moving point in a plane draws to keep a constant distance from another point. The radius of a circle is the separation of any point from the center. A positive integer is typically necessary for the radius. Except as specifically stated, this article discusses circles in the Euclidean plane and other aspects of Euclidean geometry.
In particular, a circle is a straight, closed curve that separates the plane into its inner and exterior.
Therefore, The model that shows the problem 1 divided by 1/6 is option 1.
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Refer to the above diagram. Economies of scale: A) are evident over the entire range of output. B) occur over the OQ range of output. C) begin at output 03. D) occur only over the
Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.
Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.
The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.
The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.
Minimum efficient scale is the level of output where economies of scale have been fully exploited.
A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.
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A cube with side length s has volume s3. Matt has a cube-shaped wooden box that he uses to store his marble collection. It has 8-inch sides. What is the volume of the cube?
The volume of the cube with side length 8 inches is 512 inches cube.
How to find the volume of a cube?The cube with side length s has volume s³. Matt has a cube-shaped wooden box that he uses to store his marble collection. It has 8-inch sides.
The volume of the cube can be calculated as follows:
A cube has all side length equal to each other.
Therefore,
volume of the cube = s³
where
s = side lengthTherefore,
s = 8 inches
Hence,
volume of the cube = 8³
volume of the cube = 8 × 8 × 8
volume of the cube = 512 inches cube
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Complete the equation of the line through (-10,3 and (-8,-8)
Answer:
y=-5.5x-52
Step-by-step explanation:
Your input: find the equation of a line given two points P = (-10 , 3) and Q = (-8 , -8). The slope of a line passing through the two pointsP=(x1,y1) and Q=(x2,y2) is given byWe have that x1 = -10 , y1 = 3, x2 = -8 , y2 = -8Step 2:Plug the given values into the formula for slope:Step 3:Now, the y-intercept is b=y1−m⋅x1 (or b=y2−m⋅x2, the result is the same).b = 3 - (-5.5) ⋅ (-10) = -52Step 4:Finally, the equation of the line can be written in the form y=mx+b.y = -5.5x -52The equation of the line in the slope-intercept form is:y = -5.5x -52The equation of the line in the point-slope form is:y - (3) = -5.5 ⋅ ( x - (-10))The equation of the line in the point-slope form is:y - (-8) = -5.5 ⋅ ( x - (-8))The general equation of the line is:-5.5x - y -52 = 0
the winch on the truck is used to hoist the garbage bin onto the bed of the truck. if the loaded bin has a weight of 8500 lb and center of gravity at g, determine the force in the cable needed to begin the lift. the coefficients of static friction at a and b are ma
The coefficients of static friction at a and b are T = 3600 lb and N_b = 2882 lb.
Given:
Coefficient of static friction at a u_a = 0.2
Coefficient of static friction at b u_b = 0.3
Weight of the loaded bin W = 8500 lb
Find:
Find the force in the cable needed to begin the lift.
Solution:
Draw the forces on the diagram. see attachment.
Take the sum of moments about point B as zero:
(M)_b = W*12 - N_a * 22 = 0
N_a = W*12 / 22 = 8500*12 / 22
N_a = 4636.364 lb
Compute friction force F_a at point A:
F_a = u_a*N_a = 4636.364*0.2
F_a = 927.2727 lb
Take the sum of moments about point A as zero:
-W*10 - F_b*sin(30)*22+ 22*N_b*cos(30) + 22*T*sin(30) = 0
Where, F_b = u_b*N_b = N_b*0.3
Hence, -85000 - 3.3*N_b + 11sqrt(3)*N_b + 11 T = 0
15.753*N_b + 11*T = 85000 ...... (1)
Take the sum of forces in the x-direction equal to zero:
T*cos(30) - N_b*sin(30) - u_b*N_b*cos(30) - F_a = 0
T*cos(30) - 0.75981*N_b = 927.2727 ..... (2)
Solve two equations simultaneously:
T = 3600 lb , N_b = 2882 lb
Refer to this complete question:
The winch on the truck is used to hoist the garbage bin onto the bed of the truck. If the loaded bin has a weight of 8500 lb and a center of gravity at G, determine the force in the cable needed to begin the lift. The coefficients of static friction at A and B are MuA = 0.2 And MuB = 0.3 respectively. Neglect the height of the Support at A.
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let w represent the number of attempted experiments to get one experiment that is not successful. the random variable w has a geometric distribution with mean 4 and standard deviation 3.5. which of the following is the best interpretation of the standard deviation? responses a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selecte
The best interpretation of the standard deviation on this problem is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
How to interpret the standard deviation?The standard deviation of a data-set is calculated as the square root of the sum of the differences squared between each observation of the data-set and the mean, divided by the number of observations in the data-set.
The interpretation of this calculation is that the standard deviation represents by how much each value of the distribution is expected to vary from the mean, on average.
This means that the correct statement is given as follows:
A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.
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Find the midpoint of the line segment with the given endpoints.
Answer
2x73
Step-by-step explanation:
Answer:
(11.5, 7.5)
Step-by-step explanation:
17 + 6 / 2 = 11.5
2 + 13 / 2 = 7.5
Look at the meaning of “frail” on the chart. Which clues help you understand what “frail” mean?
Answer:
fragile breakable
Step-by-step explanation:
basically the meaning of frail is anything that can be broken easily for example the glass was frail therefore meaning of dropped of damaged it could break extremely easily and if your describing a person think of someone who's old of sick they can be described as weak or in other words not strong. I hope this helped
Two sides of a triangle are 17 and 53. The third side is?
Answer:
the answer would be e because you can't determine the side length
Answer: (B)
Step-by-step explanation:
Step 1: Find minimum values of the third side.
53-17 = 36
Step 2: Find maximum values of the third side.
17+53 = 70
Step 3: Find equation
36 < x < 70
A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the village and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree, and let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree. What is the p-value?
.32
.16
.07
.18
The value of p is 0.16. So the option b is correct.
A local entrepreneur takes a random sample of 100 people.
Of the urban participants, 22 buy a real tree.
Of the rural participants, 28 buy a real tree.
Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.
Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.
We have to find the p-value
p1 = X1/N1
p1 = 28/100
p1 = 0.28
p2 = X2/N2
p2 = 22/100
p2 = 0.22
p = (X1 + X2)/(N1 + N2)
p = (28+22)/(100+100)
p = 0.25
Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 > p2
Test statistic
z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))
z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))
z = 0.9798
P-value Approach
P-value = 0.16
Hence, the option A is correct. 0.16 is the p-value.
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Which expression is equivalent to (m−2n−4)−4? m8n16 m−8n−16 m−6n−8 1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
Answer: C m-6n-8
Step-by-step explanation:
Which expression is equivalent to (m−2n−4)−4?
A m8n16
B m−8n−16
C m−6n−8
D 1 over the quantity m raised to the sixth power times n raised to the eighth power end quantity
(m-2n-4)-4
(2n-4)
(2x-4)
(n-8 )
(m- 4)-4
4+4
m-6
which = C m−6 n−8
If sin =−0.093 and 00 ≤ <3600, then what is to the nearest tenth of a degree?
A. 5.3⁰ or 174.7⁰
B. 185.3⁰ or 354.7⁰
C. 174.7⁰ or 185.3⁰
D. 2.2⁰ or 0.9⁰
There are two angles for the sine function such that sin θ = - 0.093: (i) 185.3°, (ii) 354.7°.
What are the approximate values of a trigonometric function?
In this problem we must determine two values of the angle of the sine function such that its result is - 0.093. According to the features of the trigonometric function, sine is negative for angles between 180° and 360°.
Since trigonometric functions are trascendent functions, we can only obtain approximate values of the angle by means of inverse trigonometric functions and numerical methods. There are two possible solutions:
sin⁻¹ - 0.093
θ₁ ≈ 185.336° or θ₂ ≈ 354.664°
θ₁ ≈ 185.3° or θ₂ ≈ 354.7°
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Please help me with this!
1) express the original claim in symbolic form
2) identify the null and the alternative hypotheses
The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < o
What is hypothesis?
A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientists typically build their scientific ideas on prior observations that cannot be adequately explained by the current body of knowledge.
In statistics, the null hypothesis is usually denoted by letter H with subscript '0' (zero), such that H0. It is pronounced as H-null or H-zero or H-nought
At the same time, the alternative hypothesis expresses the observations determined by the non-random cause.It is represented by H1 or Ha.
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1) En la figura que se muestra, si las rectas que están cortadas por la transversal son paralelas, entonces podemos concluir que las medidas de los ángulos 1 y 4 son iguales por el A) Teorema de los ángulos consecutivos internos B) Teorema de los ángulos alternos internos C) Teorema de los ángulos alternos externos D) Teorema de los ángulos correspondientes
En la figura que se muestra, La respuesta correcta es la opción B: Teorema de los ángulos alternos internos.
Qué es líneas?Generalmente, Cuando dos rectas son paralelas y son cortadas por una transversal, los ángulos alternos internos (es decir, los ángulos que están en posiciones opuestas en relación a la transversal y están en el mismo lado de la transversal) son congruentes. En este caso, los ángulos 1 y 4 son ángulos alternos internos y, por lo tanto, tienen la misma medida.
El teorema de los ángulos consecutivos internos se refiere a ángulos que están en posiciones opuestas en relación a la transversal y están en lados opuestos de la transversal.
El teorema de los ángulos alternos externos se refiere a ángulos que están en posiciones opuestas en relación a la transversal y están en el mismo lado de la transversal, pero están en el exterior de los dos pares de paralelas. El teorema de los ángulos correspondientes se refiere a ángulos que están en la misma posición en relación a las dos pares de paralelas.
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A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?
1. The domain is distance (d) and the range is time (t).
2. The domain is time (t) and the range is distance (d).
3. The domain is time (t) and the range is 80.
4. The domain is 80 and the range is time (t).
The domain and range of such equation in which case the distance travelled d is dependent on the time, t is best described by the answer choice; 2. The domain is time (t) and the range is distance (d).
What is the domain and range of the equation?It follows from the task content that the domain and range of the function as described in the task content is to be determined.
According to the task content; A train travels at 80 miles per hour.
On this note, the equation that compares the time (t) with the distance (d) as required is;
d = 80 t
On this note, the dependent and independent variables are d and t respectively.
Consequently, the domain is time which is the set of all possible inputs while the range is distance which is the set of all possible output values.
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3. "Seventeen less than twice a number is -49."
Answer: the number is -16
Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.
Answer: -16
Step-by-step explanation: So, to solve, we should write an equation. It should look like this:
2x - 17 = -49
So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!
P.S. our new equation would look like 2(16) - 17 = -49
32-17 = 49
32 + -17 = 49
49 = 49
It checks out.
Can you help me with this
2. Natalie is selling candles to raise money for her softball team. The team has two different options for selling the candles. The first option is to sell a package of 5 candles for $18. The second option is to sell individual candles for $4 each.
(a) The team wants to earn $1404. How many candles do the members need to sell if they sell candles only in packages? How many candles do they need to sell if they sell only single candles? Explain your answer using an equation for each situation.
(b) Describe at least one advantage of selling the candles in packages. Describe at least one disadvantage of selling the candles in packages
a) The amounts that the team needs to sell is given as follows:
Packages: 390 candles.Single candles: 351 candles.b) The advantage and disadvantage is given as follows:
Advantage: Better opportunity cost when a person needs one candle, the person will have to purchase the entire package.Disadvantage: Lower revenue per candle.How to obtain the amounts?The amounts needed are found applying the proportion, considering the costs and the number of candles.
A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:
5 candles - $18
n candles - $1404
Applying cross multiplication, we have that:
18n = 5 x 1404
n = 5 x 1404/18
n = 390 candles.
With a single candle, the number of candles is calculated as follows:
1404/4 = 351 candles.
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can someone help me with this pre calc question? and show work so I know how to do it please :)
[tex]$$(x-h)^2+(y-k)^2=r^2$$[/tex]
This is the general standard equation for the circle centered at (h, k)
with radius r.
Circles can also be given in expanded form, which is simply the result of expanding the binomial squares in the standard form and combining like terms.
For example, the equation of the circle centered at (1,2) with radius 3 is [tex]$(x-1)^2+(y-2)^2=3^2$[/tex]. This is its expanded equation:
[tex]$$(x-1)^2+(y-2)^2=3^2$$[/tex]
[tex]\begin{array}{r}\left(x^2-2 x+1\right)+\left(y^2-4 y+4\right)=9 \\x^2+y^2-2 x-4 y-4=0\end{array}[/tex]
We know that the general equation for a circle is[tex]( x - h )^2 + ( y - k )^2 = r^2[/tex], where ( h, k ) is the center and r is the radius.
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Write the complex equation 8 + 3; in trigonometric form.
The complex equation 8 + 3; in trigonometric form is z = 8.544[cos(20.6) + isin(20.6)}.
What is trigonometric form ?
Here, we'll utilize that fundamental transformation to recast z = a + bi in a different (sometimes more practical) form that is based on the polar transformation. The trigonometric form of a complex number is the name of this new representation.
Given
8 + 3i
Required
Rewrite in trigonometric form.
The trigonometric form of a complex equation is
z = r[cosθ + isinθ]
Let a = 3 and b = 8
Where
r is calculated by
r² = b² + a²
And
θ is calculated by
θ = arctan(a/b)
Substituting 3 for a and 8 for b
r² = a² + b² becomes
r² = 3² + 8²
r² = 9 + 64
r² = 73
√r² = √73
r = √73
r = 8.544
Calculating θ
θ = arctan(a/b) becomes
θ = arctan(3/8)
θ = arctan(0.375)
θ = 20.556°
θ = 20.6 --- Approximated
Hence, z = r[cosθ + isinθ] becomes
z = 8.544[cos(20.6) + isin(20.6)}
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