Answers
The measure of arc BC is 40⁰.
The measure of angle BPE is 50⁰.
The measure of angle BAD is 55⁰.
The measure of angle AOP is 110⁰.
The measure of angle AFB is 70⁰.
The value of arc DE is 110⁰.
What is the measure of the angles?The measure of each angle is calculated as follows;
if arc BA = arc CD, then value of arc BC is calculated as follows;
BA + CD + BC = 180 (sum of angles of a semi circle)
arc CD = 70 (intersecting chord theorem)
70 + 70 + BC = 180
140 + BC = 180
BC = 180 - 140
BC = 40
Arc AE = 70⁰, since angle EOF = 70 (vertical opposite angles)
Arc AB = 180 - (AE + BC)
arc AB = 180 - (70 + 40)
arc AB = 70⁰
The value of angle P is calculated as follows;
arc EB = 70 + 70 = 140⁰
m∠BPE = ¹/₂ (140 - 40)
m∠BPE = 50⁰
m∠BAD = ¹/₂ (BC + CD) (intersecting chord theorem)
m∠BAD = ¹/₂ (40 + 70)
m∠BAD = 55⁰
m∠AOP = (AB + BC) (intersecting chord theorem)
m∠AOP = (70 + 40)
m∠AOP = 110⁰
m∠AFB = (AB) (intersecting chord theorem)
m∠AFB = 70⁰
The value of arc DE is calculated as follows;
DE = 360 - (180 + CD) (sum of angles of a circle)
DE = 360 - (180 + 70)
DE = 360 - 250
DE = 110⁰
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Related Questions
Find the GCF (Greatest common factor) for the following polynomial equation 24x ^ 9 + 21x ^ 6 = 0
Answers
The general common factor (GCF) of the polynomial equation [tex]24x^9 + 21x^6 = 0[/tex] is 3x6, which, after factoring, is the common factor of the coefficients and the terms enclosed in brackets.
We must factor out the common terms from both the coefficients and the exponents in order to determine the GCF (Greatest Common Factor) for the polynomial equation 24x9 + 21x6 = 0.
The first step is to determine the coefficients' common factor, which is 3. The equation can be changed to read:
3(8x^9 + 7x^6) = 0
We now need to determine which term the parenthesized terms have in common the most. Since x is raised to a power in both terms, we may factor out x^6 to obtain:
3x^6(8x^3 + 7) = 0
The greatest common factor of the polynomial equation 24x^9 + 21x^6 = 0 is 3x^6.
We can verify this by dividing both terms in the equation by 3x^6. Doing so gives us:
(8x^3 + 7) = 0
This equation has no common factors, and we cannot factor it further. Thus, the GCF of the original polynomial equation 24x^9 + 21x^6 = 0 is 3x^6
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How many different words consisting of four different letters a,b,c,d,e,p that do not start with the letter p and do not end with the letter b and include the letters c,e
Answers
First, we need to choose the positions for the letters c and e. Since we want the word to include both c and e, we have two choices for the position of c and one choice for the position of e, or vice versa. This gives us a total of 4 different ways to choose the positions for c and e.
Next, we need to fill in the remaining two positions with any of the remaining letters: a, b, d, or p. There are 4 choices for the first remaining position, and 3 choices for the second remaining position, since we cannot use the same letter twice.
Therefore, the total number of different words that meet the given conditions is:
4 (choices for the positions of c and e) x 4 (choices for the first remaining position) x 3 (choices for the second remaining position) = 48
So there are 48 different words consisting of the letters a,b,c,d,e,p that do not start with the letter p and do not end with the letter b and include the letters c,e.
A resort sells an all-included package for a week-long stay at $2000 per person. It costs $1600 for the resort to operate, so the profit is $400 per package. They sell 300 packages every month. The resort wants to increase the price and they estimate that the number of packages sold will decrease by 5 every time they increase the price by $100. What price will maximize the monthly profit? Find the maximal profit, the number of packages, and their price to get that profit.
Answers
The resort should sell a number of 255 packages at a price of $2400 per person to maximize their monthly profit and the maximal profit is $613,400.
What do you mean by maximal profit?Maximal profit refers to the highest level of profit that a business or organization can achieve given certain constraints such as cost, demand, or pricing. It is the point at which a company or business generates the most revenue after accounting for all expenses associated with production and distribution of goods or services. To determine the maximal profit, a business will need to find the optimal balance between costs and revenue, while also taking into account factors such as competition and market demand. This involves analyzing a variety of financial metrics such as revenue, cost of goods sold, gross profit margin, and net profit margin, among others.
Let's begin by defining some variables:
P = price of the package
Q = number of packages sold
R = revenue
C = cost
Profit = revenue - cost
Based on the information given, we can create the following equations:
R = P * Q
C = 1600 + 2000 * Q
Profit = R - C = P * Q - (1600 + 2000 * Q)
We want to find the price that will maximize the monthly profit. To do this, we need to find an expression for profit in terms of P only. We can use the equation for C to substitute Q in the expression for profit:
C = 1600 + 2000 * Q
Q = (C - 1600) / 2000
Profit = P * Q - (1600 + 2000 * Q)
Profit =
Profit = P * ((C - 1600) / 2000) - C + 1600
Now we can find the derivative of profit with respect to P:
dProfit/dP = (C - 1600) / 2000
To find the value of P that maximizes profit, we need to set the derivative equal to 0:
dProfit/dP = 0
(C - 1600) / 2000 = 0
C = 1600
This means that profit is maximized when revenue equals cost, which makes sense. Substituting C = 1600 into the expression for profit, we get:
Profit = P * ((1600 + 2000 * Q - 1600) / 2000) - 1600
Profit = P * Q - 1600
Now we need to find the corresponding values of P and Q. We know that for every increase of $100 in price, there will be a decrease of 5 in the number of packages sold. This means that:
Q = 300 - (P - 2000) / 100 * 5
Substituting this into the expression for profit, we get:
Profit = P * (300 - (P - 2000) / 100 * 5) - 1600
To find the maximum profit, we can take the derivative of this expression with respect to P and set it equal to 0:
dProfit/dP = 300 - (P - 2000) / 20 = 0
P = 2400
This means that the price that will maximize the monthly profit is $2400 per person. To find the corresponding number of packages sold, we can substitute this into the equation for Q:
Q = 300 - (2400 - 2000) / 100 * 5 = 255
Therefore, the resort should sell 255 packages at $2400 per person to maximize their monthly profit. To find the maximal profit, we can substitute these values into the expression for profit:
Profit = 2400 * 255 - 1600 = $613,400.
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15 POINTS!
Which retirement plan(s) is not considered a defined contribution plan?
I. Fixed Annuity
II. Pension Plan
III. Social Security
IV. Traditional IRA
II, IV
I, IV
I, II, III
I, III, IV
Answers
The options that are not seen as retirement plan(s) are: II, IV
II. Pension Plan
IV. Traditional IRA
What is the retirement plan?A defined contribution plan is a retirement plan in which the contributions made by or on behalf of the employee are defined, but the ultimate benefit depends on the performance of the investments made with those contributions.
Based on this definition, the retirement plans that are not considered defined contribution plans are:
II. Pension Plan - Pension plans are typically defined benefit plans, where the ultimate benefit is based on a formula that takes into account the employee's salary and years of service, rather than the contributions and investment returns.
IV. Traditional IRA - Traditional Individual Retirement Arrangements (IRAs) are also not defined contribution plans. While they do involve individual contributions, the ultimate benefit is not solely based on the contributions and investment returns, but rather on various factors, such as the individual's age, income, and tax deductions.
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solve this pleasee!!
Answers
Thus, the area of the given trapezium is found toe be 37.8 sq. cm.
Explain about the trapezium:A trapezium is a quadrilateral in two dimensions with one pair of parallel sides. The non-parallel sides of a trapezium are referred to as the trapezium's "legs," while the parallel sides are referred to as its "bases." The length of the legs or the measuring of their angles are used to categorise trapeziums.
Given data:
Height PA = 8 cmSide AR = 6.3 cmAs CA = AR; PQ = 6.3 / 2 = 3.15area of trapezium = 1/2(sum of parallel side) * height
area of trapezium = 1/2(PQ + CR)*PA
area of trapezium = 1/2*(3.15 + 6.3)*8
area of trapezium = 1/2*(9.45)*8
area of trapezium = 37.8 sq. cm
Thus, the area of the given trapezium is found toe be 37.8 sq. cm.
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Your lawnmower requires 1/3 gallon of gas to cut grass for one hour. you know it will take you 3/4 of an hour to mow the empty lot. You have 5/6 gallon of gas in a gas can in the garage. How long can you cut the grass with this amount of gas?
Answers
Therefore, the lawnmower can cut grass for 2.5 hours on 5/6 of a gallon of fuel in the gas can
To find out how long the lawnmower can cut grass with 5/6 of a gallon of gas, we first need to figure out how many gallons of gas the lawnmower will use per hour:
1 hour of grass cutting = 1/3 gallon of gas
1 gallon of gas = 3 hours of grass cutting
So the lawnmower uses 1/3 gallon of gas per hour, which means that 1 gallon of gas will last for 3 hours of grass cutting.
Now we can use this conversion factor to figure out how long 5/6 of a gallon of gas will last:
5/6 gallon of gas * 3 hours of grass cutting per 1 gallon of gas = 15/18 hours of grass cutting
Simplifying this fraction by dividing the numerator and denominator by 3:
15/18=3/6
So 5/6 of a gallon of gas will last for 5/6 of 3 hours, which is equal to 2.5 hours of grass cutting.
As a result, 5/6 of a gallon of gas will last for 5/6 of 3 hours, or 2.5 hours of mowing the lawn.
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1. A cart moving at 20 m/s is brought to a stop by the force plotted in the force-time graph shown here. Find the impulse and the approximate mass of the cart. Show all your work.
Answers
The required value of impulse is 88 N-s and the mass of the cart is 8.8 kg.
How to find the impulse?Newton's Second Law relates an object's acceleration as a function of both the object's mass and the applied net force on the object.
Given data:
The speed of cart is, v = 10 m/s.
We are given the Force-time graph for which the area of the force-time graph will provide the value of impulse. So from the graph, the maximum force is,
F = 22 N
And time interval is,
t = 4.5 s - 0.5 s
t = 4 s
So, the impulse is,
I = Area of graph
I = F × t
I = 22 × 4
I = 88 N-s
Now the standard expression for the impulse as per the impulse-momentum theorem is,
I = ΔP (Change in momentum)
I = m ×( v - u )
Here, u is the final velocity, and since the cart stops finally, then u = 0 m/s. And m is the mass of the cart.
Solving as,
88 = m ×( v - u )
88 = m ×( 10 - 0 )
m = 8.8 kg
Thus, we can conclude that the required value of impulse is 88 N-s and the mass of car is of 8.8 kg.
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Surface area of this trapezoid prism
Answers
The surface area of the trapazoid based prism is 289.6 ft². The right option is b. 289.6 ft².
What is a prism?A prism is a solid shape that is bound on all its sides by plane faces.
To calculate the surface area of the trapazoid based prism, we use the formula below.
Formula:
S.A = c(a+b)+L(a+b+c+d)..................... Equation 1Where:
S.A = Surface area of the trapazoid based prismc = Height of the base of the prismL = Length of the prisma,b,d = The remaining sides of the trapezium.From the diagram,
Given:
c = 5 ftL = 9 fta = 8 ftb = 6 ftd = 5.4 ftSubstitute these values into equation 1
S.A = 5(6+8)+9(8+6+5+5.4)S.A = 70+219.6S.A = 289.6 ft²Hence, the right option is b. 289.6 ft².
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Adeline earns $28 for mowing lawns for 7 hours. If Adeline charges at the same rate, how many hours will it take her to earn $40?
Answers
Answer:
10 hours
Step-by-step explanation:
[tex] \frac{28}{7} = \frac{40}{h} [/tex]
[tex]28h = 280[/tex]
[tex]h = 10[/tex]
A business owner wants to have the front window of his store painted and is considering two artists for the job. Pete has quoted a flat rate of $60 for the job. Reba's quote is $19 per hour, plus $41 to cover the cost of materials. Depending on how long it takes Reba to paint the window, these two could end up charging the same amount. How long would Reba have to take? How much would it cost?
If the job takes Reba ___hours, the cost would be ___$ with either artist.
HELPPP
Answers
If the job takes Reba 1 hours, the cost would be $ 19 with either artist
Given data ,
Let the equation be represented as A
Now , the value of A is
Substituting the values in the equation , we get
Let's assume the number of hours that Reba takes to paint the window is h. Then, the total cost of the job with Reba would be:
Total cost with Reba = $19 ( h ) + $41
The total cost with Pete is already given as a flat rate of $60.
We want to find the number of hours that Reba would have to take to charge the same amount as Pete, so we can set the two expressions for the total cost equal to each other and solve for "h":
$ 19 ( h ) + $ 41 = $ 60
Subtracting $41 from both sides, we get:
$ 19 ( h ) = $ 19
Dividing both sides by $ 19, we get:
h = 1
So Reba would have to take 1 hour to charge the same amount as Pete.
To calculate the cost of the job with either artist if it takes Reba 1 hour, we can substitute h=1 into the expression for the total cost with Reba:
Total cost with Reba = $ 19 ( 1 ) + $ 41 = $ 60
Hence , this is the same as the flat rate quoted by Pete, so the cost of the job would be $60 with either artist if it takes Reba 1 hour
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A ball is hit from the ground. When the ball has traveled a horizontal distance of d d meters, its height, h , h , in meters, can be modeled by the function h ( d ) = − 1 125 d 2 + d . h ( d ) = − 1 125 d 2 + d . What is the horizontal distance from the point where the ball is hit to the point where the ball lands on the ground? Enter your answer in the space provided.
Answers
Answer:
Step-by-step explanation:
when h=0
0=-1125d²+d
1125d²-d=0
d(1125d-1)=0
d=0
or 1125d-1=0
d=1/1125 meters
Note: Figure is not drawn to scale. If x = 12 units, y = 4 units, and h = 7 units, find the area of the rhombus shown above using decomposition. A. 112 square units B. 28 square units C. 84 square units D. 15 square units
Answers
The area of the rhombus is 84 square units . Option C
How to determine the areaThe formula that is used for calculating the area of a rhombus is expressed with the equation;
A = a × h
Given that the parameters are;
A is the area of the rhombusa is the length of the rhombush is the height of the rhombus.From the information given, we have that;
If x = 12 units, y = 4 units, and h = 7 units.
Then the area of the rhombus will be;
Substitute the values into the equation
A = 12 × 7
Multiply the values
A = 84 square units.
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which equation can be used to find the value of x x=60 + 40
Answers
Answer:
x = 50
Step-by-step explanation:
2x = 60+40
simply 60 + 40 to 100
so 2x = 100
and then divide 2 to get it to the other side.
like this = x = 100/2
then divide 100 by 2 and get 50
so x=50
How many ways can 5 different cards be dealt from a standard 52-card deck?
Answers
Answer:
there are 2,598,960 ways to deal 5 different cards from a standard 52-card deck.
Step-by-step explanation:
The number of ways 5 different cards can be dealt from a standard 52-card deck is given by the combination formula:
C(52,5) = 52! / (5! * 47!)
which simplifies to
C(52,5) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)
= 2,598,960
A tent is in the shape of a triangular prism whose base is an isosceles triangle find the area and volume of the tent
Answers
The surface area and volume of the tent are 213.5 ft² and 148?75ft³ respectively.
What is volume and area of prism?A prism is a solid shape that is bound on all its sides by plane faces.
The surface area of prism is expressed as ;
SA = 2B + ph. Where p is the perimeter and h is the height of the prism. B is the base area
Base area = 1/2 bh
= 1/2 × 7 × 5 = 35/2
= 17.5ft²
perimeter = 7+6+6 = 21ft
SA = 2 × 17.5 + 21 ×8.5
SA = 35+178.5
SA = 213.5 ft²
Volume of prism is expressed as;
V = base area × height
= 17.5 × 8.5
= 148.75 ft³
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Assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 70 beats per minute and 78 beats per minute
Answers
Answer:
We can use the Central Limit Theorem to solve this problem since we are dealing with a sample size greater than 30. The distribution of sample means will be approximately normal with a mean of 74 beats per minute and a standard deviation of 12.5 / sqrt(4) = 6.25 beats per minute.
To find the probability that the mean pulse rate of 4 adult females is between 70 and 78 beats per minute, we need to calculate the z-scores for both values and then use a z-table or calculator to find the area under the normal curve between those two z-scores.
The z-score for 70 beats per minute is:
z = (70 - 74) / 6.25 = -0.64
The z-score for 78 beats per minute is:
z = (78 - 74) / 6.25 = 0.64
Using a standard normal distribution table or calculator, the area between these two z-scores is approximately 0.4115.
Therefore, the probability that 4 adult females have pulse rates with a mean between 70 and 78 beats per minute is approximately 0.4115 or 41.15%.
Find the area of the composite figure(will mark brainliest)
Answers
The area of the composite figure is equal to 278 square inches
How to calculate for the area of the figureThe composite figure can be observed to be made up of two triangles, a rectangle and a parallelogram, so we shall calculate for the area and sum the results to get the total area of the composite figure as follows:
area of top triangle = 1/2 × 8 in × 11 in = 44 in²
area of the side triangle = 1/2 × 9 in × 4 in = 36 in²
area of the rectangle = 11 in × 9 in = 99 in²
area of the parallelogram = 11 in × 9 in = 99 in²
total area of the composite figure = 44 in² + 36 in² + 99 in² + 99 in²
total area of the composite figure = 278 in²
Therefore, the area of the composite figure is equal to 278 square inches
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Felipe the trainer has two solo workout plans that he offers his clients: Plan A and Plan B. Each client does either one or the other (not both). On Monday there were 6 clients who did Plan A and 5 who did Plan B. On Tuesday there were 2 clients who did Plan A and 3 who did Plan B. Felipe trained his Monday clients for a total of 7 hours and his Tuesday clients for a total of 3 hours. How long does each of the workout plans last?
Answers
Plan A lasts for 2/7 hours or approximately 17.14 minutes, and Plan B lasts for 9/7 hours or approximately 1 hour and 17.14 minutes.
What is an equation example?In algebra, the definition of an equation in its simplest form is a mathematical statement that shows that two mathematical expressions are equal. For example, 3x 5 = 14 is an equation where 3x 5 and 14 are two expressions separated by an equal sign.
Let's say plan A takes x hours and plan B takes y hours.
Based on the given data, we can create two equations:
Monday: 6x + 5y = 7
Tuesday: 2x + 3y = 3
We can solve this system of equations by elimination or substitution.
Eliminating, we can multiply the second equation by two and subtract it from the first equation:
(6x + 5 y) - 2 (2x + 3y) = 7 - 2 (3)
Simplifying this, we get:
2x - y = 1
Using substitution, we can solve an equation in one variable and replace it with another equation:
From the first equation we can solve for x:
6x + 5y = 7
6x = 7-5 years
x = (7-5 years) / 6
Substituting this into the second equation, we get:
2 ((7-5 years) / 6) + 3 y = 3
Simplifying this, we get:
7 y = 9
y = 9/7
Now that we know y, we can substitute it back into both equations to solve for x:
6 x + 5 (9/7) = 7
Simplifying this, we get:
x = 2/7
Therefore, Plan A takes 2/7 hours, or approximately 17.14 minutes, and Plan B takes 9/7 hours, or approximately 1 hour and 17.14 minutes.
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Pls help! Make up two data sets. List all the values in each data set and write a story to describe where they may have originated. The data sets should meet the following conditions:
- The means should be different
- The MADs should be similar
- The means should be more than one MAD apart
Pls show work for the data sets
Answers
Answer:
Here are two example data sets that meet the given conditions:
Data Set 1:
Values: 10, 12, 14, 16, 18, 20
Mean: (10+12+14+16+18+20) / 6 = 15
MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|10-15| + |12-15| + |14-15| + |16-15| + |18-15| + |20-15|)/6) = 2.5
Story: This dataset may have originated from measuring the time taken to complete a series of tasks by a group of skilled workers. The values represent the time taken in seconds, and the low MAD value indicates that the workers' performance was consistent. The mean value of 15 seconds suggests that the workers were efficient, completing the tasks quickly and accurately.
Data Set 2:
Values: 3, 5, 7, 9, 11, 13
Mean: (3+5+7+9+11+13) / 6 = 8
MAD: Mean Absolute Deviation = sum(abs(x - mean))/n = ((|3-8| + |5-8| + |7-8| + |9-8| + |11-8| + |13-8|)/6) = 2.5
Story: This dataset may have originated from measuring the height of a group of plants grown under different conditions. The values represent the height in inches, and the low MAD value indicates that the plants' growth was consistent across all conditions. The mean value of 8 inches suggests that the conditions were not optimal for plant growth, as the mean height is lower than the expected average for this type of plant.
Both data sets have a similar MAD value of 2.5, indicating that the variation in the data is relatively low, and the differences in the mean values suggest that they came from different sources. In both cases, the means are more than one MAD apart, indicating that there are significant differences between the values in each set.
Simplify (4x3y − 2xy2 + 3xy) + (2x3y − 5xy2 − 3xy).
6x3y − 7xy2
6x3y + 3xy2
6x3y − 7xy2 − xy
6x3y − 7xy2 + 2xy
Answers
The expression simplified can be written as:
6x³y -7xy²
The correct option is the first one.
How to simplify the expression?Here we have the following expression:
(4x³y - 2xy² + 3xy) + (2x³y - 5xy² - 3xy)
To simplify it, we need to group the like terms (this is terms with the same variables and correspondent exponents).
Then we can rewrite the expression as:
(4 + 2)x³y + (-2 - 5)xy² + (3 - 3)xy
6x³y -7xy²
That is the expression simplified.
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Answer:
A:6x3y − 7xy2
Step-by-step explanation:
i took the test and got it right
Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Axequals
b.
Then solve the system and write the solution as a vector.
Aequals
left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 7 3rd Column negative 6 2nd Row 1st Column negative 2 2nd Column negative 4 3rd Column 2 3rd Row 1st Column 4 2nd Column 3 3rd Column 5 EndMatrix right bracket,
bequals
left bracket Start 3 By 1 Matrix 1st Row 1st Column negative 3 2nd Row 1st Column 16 3rd Row 1st Column negative 29 EndMatrix right bracket
Question content area bottom
Part 1
Write the augmented matrix for the linear system that corresponds to the matrix equation Axequals
b.
Answers
The vector (3, 8, 1) provides the system's solution.
As a result, the system's vector solution is (3, 8, 1).
What is vector?A sort of data structure used in computer programming is the vector. It is a collection of data objects that can be any type, such as strings, numbers, or even other vectors. The storage and manipulation of collections of data elements, such as a list of numbers, words, or other data elements, is done using vector data structures. Sorting, searching, and data manipulation can all be done with vector data structures.
The matrix equation Axequalsb's augmented matrix for the linear system is as follows:
[tex]\left[\begin{array}{ccc}1&-2&4\\7&-4&3\\-6&2&5\\-3&16&-29\end{array}\right][/tex]
Part - 2:
Step 1: Write the system's solution as a vector after solving it.
We must first reduce the augmented matrix to its reduced row-echelon form in order to solve this system.
[tex]\left[\begin{array}{ccc}1&0&0\\0&1&0\\-5&2&0\\-3&8&1\end{array}\right][/tex]
Step 2: We can now quickly find solutions for the unknowns.
[tex]x_1[/tex] equals
3
[tex]x_2[/tex] equals
8
[tex]x_3[/tex] equals
1
Step 3:
The vector (3, 8, 1) provides the system's solution.
As a result, the system's vector solution is (3, 8, 1).
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An altitude divides the hypotenuse of a right triangle into two segments measuring 3.6 and 6.4 centimeters. What is the length of the altitude?
Answers
Therefore, the length of the altitude is 4.8 centimeters.
What is triangle?A triangle is a closed two-dimensional shape with three straight sides and three angles. It is one of the basic shapes in geometry and can be classified based on the length of its sides and the size of its angles. The sum of the angles of a triangle is always 180 degrees. Triangles are used in various fields of mathematics and science, including trigonometry, geometry, and physics. They also have practical applications in fields such as construction, engineering, and architecture.
Here,
Let the altitude of the right triangle be 'h' and the hypotenuse be 'c'.
We know that the altitude of a right triangle divides the triangle into two similar triangles, which are also similar to the original triangle.
Therefore, we can set up the following proportion:
h/3.6 = 6.4/h
Simplifying, we get:
h² = 3.6 x 6.4
h² = 23.04
Taking the square root of both sides, we get:
h= √23.04
h = 4.8 centimeters
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Binomial Random Variable where n = 10 and probability of success on one trial is 15%. Show formula used. a. Find the probability of exactly 4 successes. b. Find the probability of at most 1 success c. Find the probability of at least 1 success d. Find the probability of more than 1 success e. Find the probability of less than 1 success.
Answers
Considering the binomial random variable, the probabilities are:
a. 0.1611
b. 0.8915
c. 0.7588
d. 0.1085
e. 0.0576
How to find the probabilitiesThe binomial distribution formula is:
P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)
where:
P(X = k) is the probability of getting k successes
n is the number of trials
p is the probability of success on one trial
(n choose k) is the binomial coefficient, which is equal to n! / (k! * (n - k)!)
k is the number of successes we want to find the probability for
Using this formula, we can find the probabilities for the given scenarios:
a. P(X = 4) = (10 choose 4) * 0.15^4 * (1 - 0.15)^(10 - 4) = 0.1611
b. P(X <= 1)
= P(X = 0) + P(X = 1)
= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1)
= 0.8915
c. P(X >= 1)
= 1 - P(X = 0)
= 1 - (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)
= 0.7588
d. P(X > 1)
= 1 - P(X <= 1)
= 1 - (P(X = 0) + P(X = 1))
= 1 - ((10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0) + (10 choose 1) * 0.15^1 * (1 - 0.15)^(10 - 1))
= 0.1085
e. P(X < 1)
= P(X = 0)
= (10 choose 0) * 0.15^0 * (1 - 0.15)^(10 - 0)
= 0.0576
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Find the surface area of the figure (on photo)
Answers
Answer:
208
Step-by-step explanation:
4*4(2)+11*4(2)+11*4(2)=208
Find the small squares.
4^2+4^2=32
4*11*4=176
176+32=208
Vanessa invests $20,000 in an account at 9.1% interest compounded continuously. Find the total value of the investment after 19 years.
Answers
Answer:
Step-by-step explanation:
17.5
equivalent equation for (4x • 7)(5x • 9)
Answers
Another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.
What are Equivalent equations?Equivalent equations in algebra are those that have equivalent roots or solutions.
In order to produce an equivalent equation, the same quantity or expression must be added to or subtracted from both sides of the original equation.
If you multiply or divide an equation's two sides by the same non-zero number, the results are identical.
If x4=2x+7, we can add 4 to both sides to get the following equation, which is equivalent: x4+4=2x+7+4.
So, we have the equation:
(4x • 7)(5x • 9)
Then, another equation that will be equivalent to the given equation can be:
(4x • 7)(5x • 9)
(28x)(45x )
Then,
28x(45x)
So,
(4x • 7)(5x • 9) = 28x(45x)
Therefore, another equivalent equation to the equation (4x • 7)(5x • 9) is 28x(45x) respectively.
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23
A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.
Jake finds out that the track is 270 km long.
He assumes that the track has been measured correct to the nearest 10 km.
Could the average speed of the train have been greater than 160 km/h?
You must show how you get your answer.
Answers
Answer: To answer this question, we need to calculate the maximum possible speed of the train based on the given information and check if it is greater than 160 km/h.
First, let's use the given information to find the range of possible speeds of the train. The time taken by the train is given as 110 minutes, correct to the nearest 5 minutes. This means that the actual time taken by the train could be anywhere between 107.5 minutes and 112.5 minutes.
Converting the time to hours, we get:
Lower bound of time = 107.5 minutes = 107.5/60 hours = 1.792 hours
Upper bound of time = 112.5 minutes = 112.5/60 hours = 1.875 hours
Now, let's use the given distance of 270 km, correct to the nearest 10 km, to find the range of possible average speeds of the train. The lower bound of the distance is 265 km, and the upper bound is 275 km.
Lower bound of speed = 265 km / 1.875 hours = 141.3 km/h
Upper bound of speed = 275 km / 1.792 hours = 153.5 km/h
Therefore, based on the given information, the maximum possible speed of the train is 153.5 km/h, which is less than 160 km/h.
So, we can conclude that the average speed of the train could not have been greater than 160 km/h.
Step-by-step explanation:
Rewrite -3 to the -3 power without exponents
Answers
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
Explain about the exponents:A number's power or exponent, in other words, tells how many times it must be multiplied by itself. Any integer, fraction, or decimal can serve as the basis in this situation. Moreover, the exponent might have either a positive or negative value.
The exponent rules must be understood while performing mathematical calculations or when simplifying complex equations. There are numerous rules, including the multiplication rule, the rule of negative exponents, and the rule of fractional exponents.Given that-
-3 to the -3 power
This can written as:
= (-3)⁻³
Now using the property of exponents,taking reciprocal of the number will remove the negative number.
= (1 /-3)³
= (1)³ / (-3)³
= 1/(-27)
= - 1/ 27
Thus, the statement -3 to the -3 power written without using exponents is -1/27.
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what fraction is equivelent to - (7/8)
Answers
Answer: The negative sign in front of 7/8 indicates that the fraction is negative. To find an equivalent fraction, we can keep the same value but change the sign. Therefore, an equivalent fraction that is positive would be (-(7/8)) = (-7)/8.
Step-by-step explanation:
HELP!!!! 50 POINTS!!!!
Answers
Answer:sorryy if this is late but its 2
Step-by-step explanation: