Answer:
x = 23.6°
Step-by-step explanation:
The given diagram shows a right triangle with an unknown angle, x.
We have been given the measures of the hypotenuse of the triangle and the measure of the side opposite unknown angle. Therefore, we can use the sine trigonometric ratio to find the value of x.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Sine trigonometric ratio} \\\\$\sf \sin(\theta)=\dfrac{O}{H}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
The unknown angle is x, so θ = x.
The side opposite the angle measures 6 units, so O = 6.
The hypotenuse of the triangle measures 15 units, so H = 15.
Substitute the values into the ratio and solve for x:
[tex]\sin x=\dfrac{6}{15}[/tex]
[tex]x=\sin^{-1}\left(\dfrac{6}{15}\right)[/tex]
[tex]x=23.5781784...[/tex]
[tex]x=23.6^{\circ}\; \sf (nearest\;tenth)[/tex]
Therefore, the value of x is 23.6°.
The appropriate equation to solve for the missing angle is sin(x) = 6/15
Setting up the appropriate equation to solve for the missing angle.From the question, we have the following parameters that can be used in our computation:
The right triangle
From the triangle, we have
Angle x
Also, we have the following sides in relation to x
Opposite = 6
Hypotenuse = 15
This means that we make use of the sine ratio
i.e. sin = opposite/hypotenuse
Using the above as a guide, we have the following:
sin(x) = 6/15
Hence, the equation is sin(x) = 6/15
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b) In a certain weight lifting machine, a weight of 1 kN is lifted by an effort of 25 N. While the weight moves up by 100 mm, the point of application of effort moves by 8 m. Find mechanical advantage, velocity ratio and efficiency of the machine
The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.
The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.
The problem has provided the following information:
Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m
We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage
The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;
Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;
Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5
Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.
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A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t^2−16t+55
Rewrite the formula in factored form and select each true statement below.
The swimmer reaches a maximum depth of 16 feet.
The swimmer reaches a maximum depth of 16 feet.
The swimmer dives into the water 5 seconds after the timer is started.
The swimmer dives into the water 5 seconds after the timer is started.
The swimmer comes back up 16 seconds after the timer is started.
The swimmer comes back up 16 seconds after the timer is started.
The swimmer comes back up 11 seconds after the timer is started.
The swimmer comes back up 11 seconds after the timer is started.
This function shows that the swimmer dives into the water two separate times.
(sorry the answers duplicated themselves)
Answer: The formula in factored form is h(t) = (t - 5)(t - 11). The true statements are B and D.
Step-by-step explanation: To rewrite the formula in factored form, we need to find two numbers that multiply to 55 and add to -16. These numbers are -5 and -11. So, we can write:
h(t) = t^2 - 16t + 55 h(t) = (t - 5)(t - 11)
This means that the swimmer’s depth is zero when t = 5 or t = 11. These are the times when the swimmer dives into the water and comes back up, respectively. So statement B and D are true.
To find the maximum depth of the swimmer, we need to find the vertex of the parabola. The x-coordinate of the vertex is given by:
x = -b/2a x = -(-16)/2(1) x = 8
The y-coordinate of the vertex is given by:
y = h(8) y = (8 - 5)(8 - 11) y = (-3)(-3) y = 9
So the maximum depth of the swimmer is 9 feet, not 16 feet. Therefore, statement A is false.
Statement C is also false because the swimmer comes back up at t = 11, not t = 16.
Statement E is also false because the function shows that the swimmer dives into the water only once, not twice. The function has only two zeros, which correspond to the times when the swimmer enters and exits the water.
Hope this helps, and have a great day! =)
Find the exact value of sin
Answer:
the exact value of a sin is god
find the exact values of the following 3^-2 4^-3
The exact values of 3^-2 and 4^-3 are 1/9 and 1/64, respectively.
To find the exact values of 3^-2 and 4^-3, we must first understand the concept of exponents. Exponents are a shorthand way of representing repeated multiplication of the same number.
For example, 2^3 means 2 multiplied by itself three times: 2 × 2 × 2 = 8. Similarly, 3^4 means 3 multiplied by itself four times: 3 × 3 × 3 × 3 = 81.
3^-2 can be written as 1/3^2. Using the concept of exponents, 3^2 means 3 multiplied by itself two times: 3 × 3 = 9. Therefore, 3^-2 can be rewritten as 1/9.
4^-3 can be written as 1/4^3. Using the concept of exponents, 4^3 means 4 multiplied by itself three times: 4 × 4 × 4 = 64. Therefore, 4^-3 can be rewritten as 1/64.
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Water usage varies greatly in different countries, from as little as 20 liters a day
Answer: 287.1 billion liters
Step-by-step explanation:
Water usage per person: 30 liters/day
World population: 9.57 * 10^9
Total water needed = Water usage per person * World population
Total water needed = 30 liters/day * 9.57 * 10^9
To simplify the calculation, we can express 9.57 * 10^9 in scientific notation:
Total water needed ≈ 30 liters/day * 9.57 * 10^9
To multiply the two values, we multiply the numbers and add the exponents:
Total water needed ≈ (30 * 9.57) * 10^(0 + 9)
Total water needed ≈ 287.1 * 10^9
Now, we can convert the result back to standard notation:
Total water needed ≈ 287,100,000,000 liters
Therefore, if every person in the world used 30 liters of water a day, the total amount of water needed for one day would be approximately 287.1 billion liters.
A man receives 6% commission on all sales excluding the first R10 000. If he made R70 000 in sales, how much commission would he get?
The man would receive a commission of R3,600 on sales totaling R70,000, with a 6% commission rate excluding the first R10,000.
How to Calculate the Commission Received?To calculate the commission, we first need to determine the sales amount on which the commission applies.
In this case, the first R10,000 is excluded from the commission calculation.
Therefore, the commission would be calculated on the remaining amount of R70,000 - R10,000 = R60,000.
To find the commission, we multiply the sales amount by the commission rate of 6%:
Commission = R60,000 * 6% = R3,600.
Therefore, the man would receive R3,600 in commission.
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Please help I need help urgently
9. How does g(x) differ from the graph of f(x): A. the graph translates to the right 1 unit.
10. How does g(x) differ from the graph of f(x): A. the graph translates up 1 unit.
What is a translation?In Mathematics and Geometry, the translation of a graph to the right adds a number to the numerical value on the x-coordinate of the pre-image:
g(x) = f(x - N)
Conversely, the translation of a graph up adds a number to the numerical value on the y-coordinate of the pre-image:
g(x) = f(x) + N
Question 9.
The graph of the parent exponential function [tex]f(x) = 6^x[/tex] is shifted to the right by 1 unit, in order to produce the graph of this transformed exponential function [tex]g(x) = 6^{x-1}[/tex].
Question 9.
The graph of the parent exponential function [tex]f(x) = 2^x[/tex] is shifted to the up by 1 unit, in order to produce the graph of this transformed exponential function [tex]g(x) = 2^{x}+1[/tex].
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An equation is shown below: 5x + 3(x- 5) =6x + 2x- 15 What is the solution to this equation?
Answer:
All Real Number
Step-by-step explanation:
5x + 3(x - 5) = 6x + 2x - 15
5x + 3x - 15 = 8x - 15
8x - 15 = 8x - 15
-15 = -15
Since the -15 = -15, the equation will always be true for any value of x.
So, the answer is All Real Number.
Select the correct answer from each drop-down menu.
An axiom in Euclidean geometry states that in space, there are at least
Reset
points that do
Next
The axiom in Euclidean geometry states that in space, there are at least four points that do not lie in the same plane.
Why important to have at least four non-coplanar points?Having at least four points that do not lie in the same plane is important in concept of Euclidean geometry because it allows for the construction of a three-dimensional coordinate system.
These non-coplanar points together with the three coordinate axes, form a basis for describing and analyzing spatial relationships and measurements. With a three-dimensional coordinate system, geometric figures and their properties are represented and enables the development of various mathematical principles and theorems in three-dimensional space.
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What is the equation of the straight line shown below? Give your answer in the form y = mx + c, where m and c are integers or fractions in their simplest forms.
PLEASE HELP!ASAP!
(Photo given below.)
Answer:
y = 2x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 4, 0) and (x₂, y₂ ) = (0, 8) ← 2 points on the line
m = [tex]\frac{8-0}{0-(-4)}[/tex] = [tex]\frac{8}{0+4}[/tex] = [tex]\frac{8}{4}[/tex] = 2
the line crosses the y- axis at (0, 8 ) ⇒ c = 8
y = 2x + 8 ← equation of line
how to solve for s in P=b+2s
To solve for s in P = b + 2s, we need to isolate s on one side of the equation.
We can do this by subtracting b from both sides of the equation:
P - b = 2s
Then, we can divide both sides by 2:
(P - b) / 2 = s
Therefore, s = (P - b) / 2.
There are five boys to every seven girls in an introductory geology course. If there are 408
students enrolled in the course, how many are boys?
Answer:
170 boys
Step-by-step explanation:
If there are five boys to every seven girls, then one group will have a total of 12 students.
Since there are 408 total students enrolled, then there would be 408/12 = 34 groups.
Therefore, there are 5*34 = 170 boys
 Miguel deposited a certain amount of money in the bank. The bank paid him interest after one year at which point he had $757.12. After the next year he had $787.40. How much money did Miguel originally put into the bank? (Answer to the nearest dollar.)
Miguel originally put $728 into his bank account at a rate of 4% annually
What is an equation?An equation is an expression that shows how numbers and variables are related to each other.
Let r represent the interest rate. Between successive years, Miguel money increased from $757.12 to $787.40. Hence:
Interest rate = $787.40 / $757.12 = 1.04
The interest rate = 4% annually.
Let x represent the money Miguel had initially, hence:
x * 1.04 = $757.12
x = $728
Miguel originally put $728 into his bank account
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standard form of x^2 - 3 = 4x^2 + 6
Answer: x^4 - 2x^2 - 24
If 20% of a number is 72 and 50% of the same number is 180, find 30% of that number.
Answer:
.20x = 72, so x = 360
.30(360) = 108
If y=3x−2 and x=6 , find the value of y .
Answer:
y = 16
Step-by-step explanation:
y = 3x - 2 ← substitute x = 6
y = 3(6) - 2 = 18 - 2 = 16
When Boris had 3 years left in college, he took out a student loan for $15,485. The loan has an annual interest rate of 6.6%. Boris graduated 3 years after acquiring the loan and began repaying the loan immediately upon graduation.
According to the terms of the loan, Boris will make monthly payments for 10 years after graduation. During the 3 years he was in school and not making payments, the loan accrued simple interest.
Let's break down the calculation into several steps.
1. First, we will calculate the amount of interest that accrued over the 3 years that Boris was in school. This will be calculated using the formula for simple interest, which is:
I = PRT,
where:
I is the interest,
P is the principal amount (the initial amount of money),
R is the rate of interest per period, and
T is the time the money is invested for.
2. Next, we will add this accrued interest to the initial loan amount to find out how much Boris owes when he starts repaying the loan.
3. Finally, we will calculate the monthly payments Boris has to make. This will be calculated using the formula for an amortizing loan, which takes into account both the principal and the interest on the loan. The formula for the monthly payment of an amortizing loan is:
M = P[r(1 + r)^n] / [(1 + r)^n – 1],
where:
M is your monthly payment,
P is the principal loan amount,
r is your monthly interest rate (annual interest rate divided by 12),
n is the number of payments (the number of months you will be paying the loan).
Let's do these calculations.
1. Calculate the accrued interest over the 3 years in school:
I = PRT
I = $15,485 * 6.6/100 * 3
I = $3060.57
2. Calculate the total amount owed at the start of repayment:
Total = Principal + Interest
Total = $15,485 + $3060.57
Total = $18,545.57
3. Calculate the monthly payments:
First, convert the annual interest rate to a monthly rate:
r = 6.6% / 12 / 100 = 0.0055 per month
Then, use the formula for the monthly payment of an amortizing loan:
M = $18,545.57 * [0.0055(1 + 0.0055)^120] / [(1 + 0.0055)^120 – 1]
M = $210.83
So, Boris will have to make monthly payments of approximately $210.83 for 10 years after he graduates.
In the space provided below, state whether or not the condition is deducible (valid). If it is not,
comment on the error in the reasoning.
a) If a student has room 303 as his or her homeroom, the student is a freshman. Joe is a student of the
school and has room 303 as his homeroom. Therefore, Joe is a freshman.
b) If the three angles of a triangle are acute, then the triangle is acute. In triangle ABC, angles A and B
are acute. Therefore, triangle ABC is acute.
c) All school buses stop at railroad crossings. A vehicle stopped at the Santa Fe railroad crossing.
Therefore, that vehicle is a school bus.
d) All cloudy days are depressing. Therefore, since I was depressed on Thursday, Thursday was cloudy.
a) The condition is deducible (valid). Joe having room 303 as his homeroom confirms he is a freshman.
b) The condition is deducible (valid). If angles A and B in triangle ABC are acute, then triangle ABC is acute.
c) The condition is not deducible (invalid). A vehicle stopped at a railroad crossing does not necessarily mean it is a school bus.
d) The condition is not deducible (invalid). Being depressed on Thursday does not imply that Thursday was cloudy.
a) The condition is valid. The reasoning is correct because it follows a valid logical form of "If A, then B." In this case, if a student has room 303 as their homeroom (A), then the student is a freshman (B). Joe is a student with room 303 as his homeroom, so it can be deduced that Joe is a freshman.
b) The condition is valid. The reasoning is correct because it follows a valid logical form of "If A, then B." In this case, if the three angles of a triangle are acute (A), then the triangle is acute (B). Given that angles A and B of triangle ABC are acute, it can be deduced that triangle ABC is acute.
c) The condition is not valid. The error in reasoning is called "affirming the consequent." While it is true that all school buses stop at railroad crossings, it does not necessarily mean that any vehicle stopped at the Santa Fe railroad crossing is a school bus. There could be other vehicles, such as cars or trucks, stopped at the crossing for various reasons.
d) The condition is not valid. The error in reasoning is similar to affirming the consequent. Just because all cloudy days are depressing does not mean that all instances of being depressed imply a cloudy day. There could be various reasons for feeling depressed on Thursday, unrelated to the weather conditions.
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Simplify i10
Enter the power that is a multiple of 4 first
The mathematical term 'i' is the imaginary unit which is defined by its property i²=-1. The powers of 'i' follow a pattern that repeats every 4 numbers, so i¹⁰ is the same as i², which is -1.
Explanation:In mathematics, i is the imaginary unit, which is defined by the property that i2 = -1. When raising i to a power, there's a pattern that repeats every 4 numbers. Specifically, i1 = i, i2 = -1, i3 = -i, and i4 = 1. This pattern starts over with i5 = i, i6 = -1, etc.
Given this, to find i10, you can realize that 10 is a multiple of 4 (2*4) plus 2. So i10 is same as i2, which is -1.
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Which two points on the number line represent numbers that can be combined to make zero?
A
OB and D
A and B
C and D
OA and C
B
-9-8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8 9
Mark this and return
CD
Save and Exit
The two points on the number line that represent numbers that can be combined to make zero are point A (-1) and point B (1).
To find two points on the number line that can be combined to make zero, we need to look for two numbers that have opposite signs.
Looking at the number line:
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
We can see that the numbers -1 and 1 are located on opposite sides of zero. When combined, they add up to zero:
-1 + 1 = 0
Therefore, the two points on the number line that represent numbers that can be combined to make zero are point A (-1) and point B (1).
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17. Diane is making a quilt. She needs three
pieces with a yellow undertone, two pieces
with a blue undertone, and four pieces with
a white undertone. If she has six squares
with a yellow undertone, five with a blue
undertone, and eight with a white undertone
to choose from, in how many ways can she
choose the squares for the quilt?
There are 14,000 different ways for Diane to choose the squares for her quilt.
In how many ways can she choose the squares for the quilt?we want to find the number of ways Diane can choose the squares for her quilt, we can use the concept of combinations.
Diane needs to choose three squares with a yellow undertone, two squares with a blue undertone, and four squares with a white undertone. She has six squares with a yellow undertone, five squares with a blue undertone, and eight squares with a white undertone to choose from.
The number of ways to choose the squares for each color can be calculated using combinations:
Number of ways to choose yellow squares = C(6, 3) = 6! / (3! * (6 - 3)!) = 20Number of ways to choose blue squares = C(5, 2) = 5! / (2! * (5 - 2)!) = 10Number of ways to choose white squares = C(8, 4) = 8! / (4! * (8 - 4)!) = 70To calculate the total number of ways to choose the squares for the quilt, we multiply the number of ways for each color together:
Total number of ways = 20 * 10 * 70 = 14,000
there are 14,000 ways for Diane to choose the squares for her quilt.
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nine balls marked1 to 9 are placed in a box. if you pick one ball at random. what is the probability that an 8 is taken out
Answer:
P(8) = 1/9
Step-by-step explanation:
There are 9 balls, 1,2,3,4,5,6,7,8,9
We want to get ball 8
P(8) = number of balls marked 8/ total number of balls
= 1/9
Answer:
P = 1/9
Step-by-step explanation:
In this scenario, there are a total of nine balls in the box, numbered from 1 to 9 (1,2,3,4,5,6,7,8,9). We are interested in finding the probability of selecting the ball marked with the number 8.The probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.In this case, the number of favorable outcomes is 1 because there is only one ball marked with the number 8.The total number of possible outcomes is 9 since there are nine balls in total.Probability of selecting the ball marked with 8
[tex]\sf Probability = \dfrac{Number\: of \:favorable\: outcomes }{ Total \:number\: of\: possible\: outcomes}\\\\\sf Probability = \dfrac{1 }{9}[/tex]
The scatter plot below shows the number of pizzas sold during weeks when different numbers of coupons were issued. The equation represents the linear model for this data. y = 3.4x + 43 According to the model, what is the average number of pizzas sold in one night if no coupons are issued? Responses 0 pizzas 0 pizzas 21 pizzas 21 pizzas 43 pizzas 43 pizzas 60 pizzas 60 pizzas 70 pizzas
Answer: 43
Step-by-step explanation:
Look at the graph when 0 coupons are sold - the line is at about 45. The closest answer to that is 43.
A coffee shop serves an average of 75 customers per hour during the morning rush. Find the probability that 80 customers arrive in an hour during tomorrow's morning rush. Round answer to 4 decimal places.
The probability that 80 customers will arrive during tomorrow's morning rush is approximately 0.0629, rounded to 4 decimal places.
To find the probability that 80 customers will arrive during tomorrow's morning rush, we can use the Poisson distribution. The Poisson distribution is commonly used to model the number of events that occur in a fixed interval of time or space.
In this case, the average number of customers per hour is given as 75. The Poisson distribution is defined by a single parameter, λ (lambda), which represents the average rate of the event occurring in the given interval.
To calculate the probability, we can use the formula:
P(x; λ) = (e^(-λ) * λ^x) / x!
where P(x; λ) represents the probability of x events occurring given the average rate λ.
In this case, x = 80 and λ = 75. Plugging these values into the formula, we get:
P(80; 75) = (e^(-75) * 75^80) / 80!
Calculating this expression using a calculator or software, we find that P(80; 75) ≈ 0.0629.
The probability that 80 customers will arrive during tomorrow's morning rush is approximately 0.0629, rounded to 4 decimal places.
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15. Jonas played 9 holes of golf
and received the following
scores. Positive scores indi-
cate that Jonas was above
par. Negative scores indicate
that he was below par. Find
Jonas's total after 9 holes. Is
his score above or below par?
+2, +1,-1, 0, 0, -1, +3,
+4, -1
Answer:
Step-by-step explanation:
To find Jonas's total score after 9 holes of golf, we add up all the individual scores:
+2 + 1 - 1 + 0 + 0 - 1 + 3 + 4 - 1 = 7
Jonas's total score after 9 holes is 7.
Since the total score is positive (above zero), Jonas's score is above par.
Which list includes three processes that are represented in the rock cycle
diagram and lists them in the correct order, starting with x ?
A. Reaction with chemically active fluids, melting, uplift
B. Melting, uplift, reaction with chemically active fluids
OC. Uplift, melting, reaction with chemically active fluids
D. Uplift, reaction with chemically active fluids, melting
In the rock cycle diagram, these three processes occur in a specific order as D. Uplift, reaction with chemically active fluids, melting
Uplift: Uplift refers to the movement of rocks from deep within the Earth's crust towards the surface. This can occur due to tectonic forces, such as plate collisions or volcanic activity. Uplift exposes rocks to the Earth's surface, where they can undergo further processes.
Reaction with chemically active fluids: Once rocks are uplifted and exposed to the surface, they come into contact with chemically active fluids, such as water or magma. These fluids can infiltrate the rocks, leading to chemical reactions and alteration of their composition. This process is commonly observed in hydrothermal systems or areas of volcanic activity.
Melting: The last step in the sequence is melting. When rocks are subjected to intense heat and pressure, either due to tectonic forces or proximity to a magma source, they can undergo partial or complete melting. This molten rock, called magma, can then solidify and form igneous rocks through processes like cooling and crystallization.
Option D correctly represents the order of these processes in the rock cycle diagram. It starts with uplift, followed by the reaction with chemically active fluids, and concludes with melting. Understanding the sequence of these processes is crucial for comprehending the dynamic nature of Earth's geology and the continuous transformation of rocks throughout geological time. Therefore, Option D is correct.
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A binomial experiment is conducted with n = 32, p = 0.34, and x = 10. Copmpute the probability of x successes in
the n independent trials.
Round your answer to four decimal places.
P(x = 10) is
The probability of having exactly 10 successes in 32 independent trials, with a success probability of 0.34, is approximately 0.0122 (rounded to four decimal places).
To compute the probability of having exactly x successes in a binomial experiment, we can use the binomial probability formula:
[tex]P(x) = C(n, x) \times p^x \times (1 - p)^{(n - x)[/tex]
where:
P(x) is the likelihood that x successes will occur.
n is the total number of trials
P is the likelihood that a trial will be successful.
C(n, x) is the binomial coefficient, which represents the number of ways to choose x successes out of n trials.
In this case, n = 32, p = 0.34, and x = 10. Let's calculate the probability:
P(10) = C(32, 10) * (0.34)^10 * (1 - 0.34)^(32 - 10)
The binomial coefficient C(32, 10) can be calculated as:
C(32, 10) = 32! / (10! * (32 - 10)!)
Now, let's compute the value:
C(32, 10) = 32! / (10! * 22!)
= (32 * 31 * 30 * 29 * 28 * 27 * 26 * 25 * 24 * 23) / (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= 57,032,707,456 / 3,628,800
= 15,504
Now, substitute the values back into the binomial probability formula:
P(10) = 15,504 * (0.34)^10 * (1 - 0.34)^(32 - 10)
P(10) ≈ 0.0122
Therefore, the probability of having exactly 10 successes in 32 independent trials, with a success probability of 0.34, is approximately 0.0122 (rounded to four decimal places).
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Consider the system of equations (see attached)
The given system of equations is represented as: 2x - 3y + z = 0-2x - y + 4z = 7x + 2y - 5z = -5
The solution of the given system of equations is x = 2, y = -1, z = 3, which can be verified by substituting these values of x, y and z in each equation of the given system of equations, respectively.
The given system of equations is a consistent system of equations, which means it has a unique solution.
The unique solution is found by solving the equations simultaneously using different methods such as substitution method, elimination method or matrix method.
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Conduct a survey based on one of the topics below and write a research report. You are required to collect, represent, analyse, interpret and report the data. The topics are as follows: • The number of coins that teachers carry with them • The distance between a teacher's place of residence and her/his place of employment (school) • The school shoe sizes of grade 4 learners Follow these steps: Step 1: Collecting and organising data 1. Select one of the topics above and formulate it into a researchable title. (2) 2. Write down the main research question that will guide your investigation. (2) 3. What will be the source(s) of data for the topic you have selected? (2) 4. What data collection instrument will you use for your investigation? (2) 5. State whether you will obtain categorical data or numerical data. If the data will be numeric, state whether it will be discrete or continuous. (3) 6. Write down the question(s) that you would include in the instrument of your choice to help you get the information (data) necessary to answer the main research question. (2) 7. Gather data from a sample of 20–25 respondents using the instrument you designed. Attach one of the completed instruments to your solution. (10) 8. Use tally marks and a table to record the data in question 7. (7) [30] Step 2: Representing data 9. Which graph best represents the data that you sorted or organised in question 8? Explain your answer. (6) 10. Draw the graph that best represents the data you sorted in question 8. (5) 11. Write down two questions that will assist you in interpreting the graph that you drew in question 9.
Title: The Number of Coins That Teachers Carry with Them
Research Report
1. Research Question: What is the average number of coins carried by teachers?
2. Data Source: The data will be collected directly from teachers in a sample group.
3. Data Collection Instrument: A survey questionnaire will be used to collect the necessary data. The questionnaire will contain questions about the number of coins carried by teachers on a regular basis.
4. Data Type: Numerical data will be obtained, specifically discrete data.
5. Instrument Questions:
a) How many coins do you carry with you on a daily basis?
b) What is the highest number of coins you have carried with you?
6. Completed Instrument: Please find the attached completed survey questionnaire.
7. Data Collection: Data will be gathered from a sample of 20-25 respondents using the survey questionnaire.
8. Tally Marks and Data Table:
Number of Coins Tally
1
2
3
4
5
6
7
8
9
10
Step 2: Representing Data
9. The graph that best represents the data collected would be a bar graph. A bar graph is suitable for displaying discrete numerical data, such as the number of coins carried by teachers. It allows for easy visualization and comparison of the frequencies of different coin quantities.
Graph:
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1 5 10 15 20
10. Questions for Interpreting the Graph:
a) What is the most common number of coins carried by teachers?
b) How many teachers carry more than five coins with them?
11. Interpretation:
Based on the bar graph, it can be observed that the most common number of coins carried by teachers is around 4. Additionally, approximately 10 teachers carry more than five coins with them. This information provides insights into the typical coin-carrying habits of teachers within the sample group.
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a translation to the right has been applied to triangle ABC such that side AB coincides with side DE and side BC coincides with side EF, thus demonstrating that angle b and angle e have the same measure.
what is true about side AC?
thank you in advance!!!
Since the translation moved the entire triangle ABC to the right without rotating it, the length of side AC remains the same. Therefore, side AC is congruent to side DF.