Answer:
1/2
Step-by-step explanation:
options in a 6 sided die= 1,2,3,4,5,6
greater than 3 = 4,5,6
so three sides out of a 6 sided die is greater than three
P(not greater than 3) = [tex]\frac{6-3}{6} = \frac{1}{2}[/tex]
Answer:
1/2 or 0.5
Step-by-step explanation:
The probability of rolling a number greater than 3 on a six-sided die is 3/6 or 1/2, since there are three numbers (4, 5, 6) out of six that are greater than 3.
To find the probability of not rolling a number greater than 3, we can subtract the probability of rolling a number greater than 3 from 1:
P(not greater than 3) = 1 - P(greater than 3)
P(not greater than 3) = 1 - 1/2
P(not greater than 3) = 1/2
Therefore, the probability of not rolling a number greater than 3 is 1/2 or 0.5.
there are 29 horses competing in a show. in how many ways can the blue, red, and yellow ribbons be awarded?
Answer:21924 different ways
Step-by-step explanation:
There are 29 choices for the blue ribbon, 28 for the red and 27 for the yellow. If you multiply 29x28x27 you get 21924
If there are 29 horses competing in the show. then there are 21,084 ways can the blue, red, and yellow ribbons be awarded.
Ribbons are awarded to horses. Therefore, we will use the multiplication rule of probability to find the total number of ways in which the blue, red, and yellow ribbons can be awarded.
Multiplication Rule of Probability If there are 'm' ways of doing one thing and 'n' ways of doing another thing, then there are 'm*n' ways of doing both things.
Multiplication Rule of Probability formula:
A total number of ways of doing both things = m*n
To find the total number of ways in which the blue, red, and yellow ribbons can be awarded to horses,
we need to multiply the number of ways of giving each ribbon.
Blue ribbons can be awarded to 29 horses.
Red ribbons can be awarded to 28 horses.
Yellow ribbons can be awarded to 27 horses.
The multiplication rule of the probability formula will be applied to get the total number of ways of awarding blue, red, and yellow ribbons to horses.
A total number of ways of awarding blue, red, and yellow ribbons = Number of ways of awarding blue ribbons × Number of ways of awarding red ribbons × Number of ways of awarding yellow ribbonsTotal number of ways of awarding blue, red, and yellow ribbons
= 29 × 28 × 27
The total number of ways of awarding blue, red, and yellow ribbons
= 21,084
Therefore, there are 21,084 ways in which the blue, red, and yellow ribbons can be awarded to horses.
Probability: In mathematics, the probability of an event is the extent to which it is likely to occur, measured by the ratio of the favorable cases to the whole number of cases possible.Permutation: In mathematics, a permutation of a set is an arrangement of its members into a particular sequence, or if the set is already ordered, a rearrangement of its elements.Learn more about horses are being awarded ribbons Probability at: https://brainly.com/question/28527510
#SPJ11
You measure 41 randomly selected textbooks' weights, and find they have a mean weight of 39 ounces. Assume the population standard deviation is 2.8 ounces. Based on this, construct a 99% confidence interval for the true population mean textbook weight. Give your answers as decimals, to two places afe
The 99% confidence interval for the true population mean textbook weight is (38.11, 39.89) ounces.
We can find the standard error (SE) by using the formula:
SE = σ/√n
Where
σ = population standard deviation = 2.8 ounces
n = sample size = 41
SE = 2.8/√41
SE = 0.436
Now we can find the confidence interval by using the formula:
CI = x ± z*SE
Where
x = sample mean = 39 ounces
z* = the z-value corresponding to the level of confidence of 99 percent
The z-value corresponding to the level of confidence of 99 percent can be found using the z-table or calculator. It is found to be 2.576.
CI = 39 ± 2.576*0.436
CI = (38.11, 39.89)
Therefore, we can say that we are 99% confident that the true population mean textbook weight is between the interval (38.11, 39.89) ounces.
Learn more about confidence interval here: https://brainly.com/question/17097944
#SPJ11
What is the measure of Angle X?
Answer:
x = 79
Step-by-step explanation:
the exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
∠ BHC = x is an exterior angle of Δ BHD , then
x = 33 + 46 = 79
Tell whether the given value is a solution of the inequality.
q/5 < q-20; q=15
Answer:
No, q=15 is not a solution to the inequality.
Step-by-step explanation:
As given, q=15. So, substituting is the best way to solve this problem.
Step 1: Substitute
[tex]\frac{15}{5}=3[/tex]
[tex]15-20=-5[/tex]
Step 2: Substitute values into inequality
[tex]3 < -5[/tex]
Equation is false since 3 is a bigger value than -5.
Hope this helps ya!
Solve: You have a machine with a screen and three buttons: red, green, and blue. If you press the red button, the number on the screen is doubled. If you press the green button, the number on the screen is tripled. If you press the blue button, the number on the screen is multiplied by itself. The number 1 is displayed on the screen. What is the least number of times you need to press a button to get the number 2592 on the screen.
Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.
Explain about the prime factorization?The technique of expressing all numbers as the product of primes is known as prime factorization. So, let's take something like the number 20 as an example. It can be divided into two components. "Well, that's 4 times 5," we can respond. Observe that 5 is a prime number.
Given data:
Red - The number displayed on the screen doubles if you hit the red button say (x²) green - The number displayed on the screen is tripled if you push the green button say (y³)blue- The number shown on the display is multiplied by itself when you hit the blue button say (z).The number formed as:
(x²) .(y³).(z) ...eq 1
Number appeared on screen - 2592
Find the prime factors of 2592.
2592 = 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3
This can be written as:
2592 = 4² x 3³ x 2 x 3
2592 = 4² x 3³ x 6¹ .....eq 2
comparing eq 1 and 2
(x²) .(y³).(z) = 4² x 3³ x 6¹
x = 4, y = 3 and z = 6
Thus, the least number of times the button need to be pressed is: red- 4 times, green 3 times and blue button 6 times.
Know more about the prime factorization
https://brainly.com/question/1911965
#SPJ1
f(x)=x^3 shifted right 4 units
Answer:
f(x) = x ³ shifted 4 units to the right will be g(x) = f(x-4) = (x - 4)³
Step-by-step explanation:
If a function f(x) is shifted right 4 units every x coordinate will become x - 4
g(x) = f(x - 4) = (x - 4)³
because we do not know if the population distribution is approximately normal. because the large sample condition is not met. they should proceed, all of the conditions are met. because the 10% condition is not met. because the random condition is not met.
To use the normal approximation for the confidence interval in the sampling distribution of the population proportion, the following conditions must be met:
The sample size should be large enough (np ≥ 10 and n(1-p) ≥ 10), where n is the sample size and p is the population proportion. The observations should be independent. The population size should be at least 10 times larger than the sample size.If these conditions are met, then the distribution of the sample proportion can be approximated by a normal distribution with a mean of p and a standard deviation of sqrt(p*(1-p)/n).
Learn more about population proportion
https://brainly.com/question/15087042
#SPJ4
Full Question ;
The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval?
n a survey given by camp counselors, campers were asked if they like to swim and if they like to have a cookout. The Venn diagram displays the campers’ preferences. A Venn Diagram titled Camp Preferences. One circle is labeled S, 0.06, the other circle is labeled C, 0.04, the shared area is labeled 0.89, and the outside area is labeled 0.01. A camper is selected at random. Let S be the event that the camper likes to swim and let C be the event that the camper likes to have a cookout. What is the probability that a randomly selected camper likes swimming or having a cookout, but not both?
Answer:
The probability that a randomly selected camper likes to have a cookout will be 0.93.
Step-by-step explanation:
did it already.
Answer: To solve this problem, we need to find the probability that a randomly selected camper likes swimming or having a cookout, but not both. We can do this by using the formula:
P(S or C, but not both) = P(S) + P(C) - 2P(S and C)
We are given the following probabilities from the Venn diagram:
P(S) = 0.06 (the proportion of the circle labeled S)
P(C) = 0.04 (the proportion of the circle labeled C)
P(S and C) = 0.89 (the proportion of the shared area)
Substituting these values into the formula, we get:
P(S or C, but not both) = 0.06 + 0.04 - 2(0.89)
= 0.10 - 1.78
= -1.68
This is not a valid probability, as probabilities cannot be negative. Therefore, there must be an error in the problem statement or the Venn diagram. Please check the values again and ensure they are correct.
Step-by-step explanation:
for what mileages will company a charge less than company b? use for the number of miles driven, and solve your inequality for .
For the number of miles driven, Company A will charge less than Company B if x<y, where x is the number of miles driven for Company A and y is the number of miles driven for Company B. Therefore, the inequality is x<y.
When comparing two companies for their charges for a specific service, it is necessary to obtain a basic understanding of the charges for each company. You can make use of the inequality operator to check when one company will charge less than the other company.
To use the inequality operator, you'll need to calculate the differences between the two companies for the specific mileage. Let's assume that the mileage is represented by "m" and that the charge for company A is "cA" and the charge for company B is "cB".
If the question only provides specific numerical values for these variables, you can substitute them into the inequality formula. If you're given algebraic expressions, you'll need to simplify them before substituting them into the inequality formula.
The inequality formula for comparing the charges is as follows: cA < cB.
To use this formula, substitute the expression for each variable.
For example: 4m + 20 < 3.5m + 35 Now, you'll need to simplify the inequality by performing algebraic operations on both sides of the inequality. Begin by subtracting 3.5m from both sides of the inequality: 0.5m + 20 < 35.
Next, subtract 20 from both sides of the inequality: 0.5m < 15 Finally, divide both sides of the inequality by 0.5: m < 30
Therefore, Company A will charge less than Company B for any mileage less than 30.
Know more about inequality here:
https://brainly.com/question/25275758
#SPJ11
an operation is performed on a batch of 100 units. setup time is 20 minutes and run time is 1 minute. the total number of units produced in an 8-hour day is:
The total number of units produced in an 8-hour day is approximately 22.86 units.
There are different ways to approach this problem, but one possible method is to use the concept of cycle time and the total available production time to determine the number of units produced in a day.
An operation is performed on a batch of 100 units.
Setup time is 20 minutes and run time is 1 minute.
The total number of units produced in an 8-hour day is:
Step 1: Find the cycle time per unitThe cycle time per unit is the sum of the setup time and the run time:
Cycle time = setup time + run time = 20 minutes + 1 minute = 21 minutes.
Step 2: Find the total available production time in a day
One day has 24 hours, but 8 hours are not available for production due to breaks, maintenance, and other factors. Therefore, the total available production time is:
Total available production time = 8 hours × (60 minutes per hour) = 480 minutes.
Step 3: Calculate the number of units produced in a day
The number of units produced in a day is the total available production time divided by the cycle time per unit:
Units produced = total available production time ÷ cycle time= 480 minutes ÷ 21 minutes≈ 22.86 units (rounded to two decimal places)
Therefore, the total number of units produced in an 8-hour day is approximately 22.86 units.
This assumes that there is no variability in the process, and that all units are of good quality.
If there are any defects, rework, or other disruptions, the actual production may be lower.
For similar question on approximately.
https://brainly.com/question/114935
#SPJ11
The voltage in an electrical circuit is multiplied by itself each time it is reduced. The voltage is 27/125 of a volt and it has been reduced three times. What is the voltage in exponential form?
Answer: x 3= 27/125
Step-by-step explanation:
h + i3 where i = 1 and h = 19 caculate
Answer:22
Step-by-step explanation:
h + i3 = ?
19 + 1X3 = 22
Answer:
h + i3 = 22
Step-by-step explanation:
Given expression,
→ h + i3
→ h + 3(i)
Now we have to use,
→ i = 1
→ h = 19
Let's simplify the expression,
→ h + 3(i)
→ 19 + 3(1)
→ 19 + 3
→ 22 => {final answer}
Hence, the solution is 22.
In an isosceles triangle, measure of one of the angles is 30o. What are the measures of the other two angles? Select all that apply. Note that more than one option may be correct.
A. 30o, 120o
B. 40o, 110o
C. 75o, 75o
D. 50o, 100o
Answer: A and C
Step-by-step explanation:
angles in a triangle add up to 180
180 - 30 = 150
other two angles must add up to 150 and two of the angles have to be the same.
Since one is already 30, one of the others have to also be 30 or both of the others have to be the same.
A and C both add up to 150 and both of them have one angle repeating
Distributive property applied to 7(2x+5) - 4(2x+5)
To implement the distributing principle to the phrase 7(2x+5) - 4(2x+5), we must first divide the 7 and 4 within the parenthesis to their respective terms:
7(2x+5) - 4(2x+5) = (72x + 75) - (42x + 45)
Within the parenthesis, each term is simplified:
= (14x + 35) - (8x + 20)
We may now reduce the phrase by grouping similar terms:
= 14x - 8x + 35 - 20
= 6x + 15
As a consequence, using the distributive property on 7(2x+5) - 4(2x+5) yields 6x + 15.
By expansion or multiplying, the distribution principle is frequently employed to compress statements and solve problems. It enables us to translate complicated statements into shorter language and conversely. The distributive principle is commonly utilized in mathematics, mathematics, as well as other mathematical subjects.
To know more about multiplying click here
brainly.com/question/25114566
#SPJ9
Salespersons at the Kings Park Auto Giant are paid a commission, c(p), based on the profit, p. The following piecewise function gives the commission rules.
a. If the profit is $1,500, what is the percent commission rate?
b. If the profit is $900, what is the percent commission rate?
c. What is the commission on a car sold for a $970 profit?
d. Kings Park Auto Giant purchases a car for $32,090 and sells it for $33,200. What commission is paid to the salesperson?
Based on the provided information The seller received a fee of $122.
How much does the term "commission" mean?The term "commission" describes the payment made to the staff member after they successfully complete a job, which is frequently marketing a predetermined quantity of goods or services. Selling goods or services is difficult. Sales and marketing professionals must contend with fierce rivalry.
The commission rules are defined by the following piecewise function:
c(p) = 0.10p, if p ≤ 1,000
c(p) = 0.15p - 50, if 1,000 < p ≤ 1,500
c(p) = 0.20p - 125, if p > 1,500
a. If the profit is $1,500, the commission rate is calculated using the second rule:
c(1,500) = 0.15(1,500) - 50 = 175
The commission rate is $175 / $1,500 = 0.1167, or approximately 11.67%.
b. If the profit is $900, the commission rate is calculated using the first rule:
c(900) = 0.10(900) = 90
The commission rate is $90 / $900 = 0.10, or 10%.
c. To find the commission on a car sold for a $970 profit, we need to determine which rule applies. Since 970 is less than 1,000, we use the first rule:
c(970) = 0.10(970) = 97
The commission on a car sold for a $970 profit is $97.
d. The profit on the car sale is calculated as follows:
profit = selling price - purchase price = $33,200 - $32,090 = $1,110
To determine the commission, we need to identify the appropriate rule based on the profit amount. Since $1,110 is greater than $1,500, we use the third rule:
c(1,110) = 0.20(1,110) - 125 = 122
The commission paid to the salesperson is $122.
To know more about Commission visit:
https://brainly.com/question/24951536
#SPJ1
what is the sum of 5 4/5 + 2 2/3
Answer:
8 7/15
Step-by-step explanation:
4/5 and 2/3 need to a a common denomenator
4/5*3 and 2/3*5 = 12/15 and 10/15 so 5 12/15 + 2 10/15= 7 22/15= 8 7/15
Select the statement that shows equivalent measurements.
5.2 meters = 0.52 centimeters
5.2 meters = 52 decameters
52 meters = 520 decimeters
5.2 meters = 5,200 kilometers
None of these options
Option A
Conversion of measurement of Metres to Centimetres can be done by multiplying the number by 100
1 metre = 100 centimetres
5.2 metres = 520 centimetres
Option B
Conversion of measurement of Metres to Decametres can be done by multiplying the number by 0.1
1 metre = 0.1 decametres
5.2 metres = 0.52 decametres
Option C
Conversion of measurement of Metres to Decimetres can be done by multiplying the number by 10
1 metre = 10 decimetres
5.2 metres = 52 decimetres
Option D
Conversion of measurement of Metres to Kilometres can be done by multiplying the number by 0.001
1 metre = 0.001 kilometres
5.2 metres = 0.0052 kilometres
Therefore,
5.2 metres = 520 centimetres
5.2 metres= 0.52 decametres
5.2 metres= 52 decimetres
5.2 metres= 0.0052 kilometres
To learn more about Measurements visit:
https://brainly.com/question/12652877
#SPJ1
which is an x-intercept of the graphed function?
The x-intercepts of the graphed function are:
(-2, 0), (-1, 0), (1, 0), and (2, 0)
How to identify the x-intercepts of the graphed function?For any function, we define the x-intercepts as the values of x such that y= 0, when we have a graph we can identify these values as the values of x at which the graph intercepts the x-axis.
Remember that the x-axis is the horizontal one, then, we can look at the graph and identifty the 4 x-intercepts, these are at the values of x:
x = -2
x = -1
x = 1
x = 2
Writting them in point notation, these are (-2, 0), (-1, 0), (1, 0), and (2, 0)
Learn more about x-intercepts at:
https://brainly.com/question/24363347
#SPJ1
is this right?.........
Answer:
yes you're right!
Step-by-step explanation:
-6 equals c because the quadratic formula is [tex]ax^2+bx+c=0[/tex].
to apply the formula, we would end up with [tex]\frac{-(-2)±\sqrt(-2)^2-4*3(-6)}{2(3)}[/tex] as our answer
once we simplify, we're left with [tex]x=\frac{2±2\sqrt{19}}{6}[/tex]
we break the equations into two to separate the positive sign's answer from the negative sign's answer, so we'll have [tex]x=\frac{2+2\sqrt{19} }{6}[/tex] and [tex]x=\frac{2-2\sqrt{19} }{6}[/tex]
isolate the variable to get our solution, [tex]x=\frac{1±\sqrt{19} }{3}[/tex]
The area of a rectangular pool is 5056 m². If the width of the pool is 64 m, what is its length?
Answer:
79
Step-by-step explanation:
Using the formula
A=wl
Solving forl
l=A
w=5056
64=79m
To find area, you multiply the width by the length [tex]( \text{A} = \text{L} \times \text{W})[/tex]. Here, it is asking for the length, giving the area of the pool and the width. With this information, you can inverse operation ( division) to find the length of the pool. So:
[tex]5056 \div 64 = 79[/tex]
This tells us that the length of the pool is 79 meters. To check this answer, multiply 64 and 79. If it's equivalent to 5056, the given area, then 79 is indeed the length of the pool.
[tex]64 \times79 = 5056[/tex].
Thus, the length of the pool is 79 m.
the letter t is formed by placing two $2\:\text{inch}\!\times\!4\:\text{inch}$ rectangles next to each other, as shown. what is the perimeter of the t, in inches?
The perimeter of the letter "T" is 22 inches.
Since the letter "T" is formed by placing two rectangles next to each other, its perimeter is the sum of the perimeters of the two rectangles minus the shared side.
The shared side will be the width of the rectangles, which is 2 inches.
The lengths of the rectangles are 4 inches each.
Let's calculate the perimeter:
Perimeter of the top rectangle = 2 * (length + width) = 2 * (4 + 2) = 12 inches
Perimeter of the bottom rectangle = 2 * (length + width) = 2 * (4 + 2) = 12 inches
Now, subtract the shared side (width) once:
Shared side = 2 inches
Total perimeter = (Perimeter of top rectangle + Perimeter of bottom rectangle) - Shared side
Total perimeter = (12 + 12) - 2 = 22 inches
So, the perimeter of the letter "T" is 22 inches.
Learn more about perimeter here:
brainly.com/question/397857
#SPJ12
2. a. There is a new family called the Grump family. Mr. Grump's rule is (x,y). Circle the rules that
his family members in red. Circle the imposters in blue.
(3x,3y)
(2x,y)
(x,4y)
(4x,4y)
(6x, 5y)
(9x, 9y)
(0.3x, 0.3Y)
which set of numbers can make the inequality below true? 26> n + 15
Answer:
[tex]26 > n + 15[/tex]
[tex]11 > n[/tex]
[tex]n < 11[/tex]
six distinct integers are picked at random from . what is the probability that, among those selected, the second smallest is ?
The probability that the second smallest integer from a set of six distinct integers is picked at random is the same as the probability that the first smallest is 1.
This can be expressed mathematically as:
P(second smallest) = P(first smallest).
The probability of the first smallest integer is the number of combinations that result in the first smallest number divided by the total number of possible combinations of six distinct integers.
For example, if we have six distinct integers in a set, A, B, C, D, E, and F, the probability of A being the first smallest is the number of combinations that result in A being the smallest divided by the total number of combinations.
The combinations that result in A being the smallest are {A, B, C, D, E, F}, {B, A, C, D, E, F}, {C, A, B, D, E, F}, and so on. That’s a total of 6 combinations out of the total possible number of combinations, which is 6 x 5 x 4 x 3 x 2 x 1 = 720.
Therefore, P(first smallest) = 6/720 = 1/120. Similarly, the probability of the second smallest number being the same is also 1/120.
To know more about probability refer here:
https://brainly.com/question/30034780
#SPJ11
You complete a hypothesis test using α = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis. If the treatment actually has no effect, which of the following is true?
Question 10 options:
You have made a Type II error.
You have made a Type I error.
You have made the correct decision.
You might have made a Type I error, but the probability is only 5% at most.
The probability of making a Type I error is represented by alpha (α), which is typically set to 0.05 in hypothesis testing. Therefore, if α = .05, the likelihood of making a Type I error is 5% at most.
What is hypothesis testing? Hypothesis testing, also known as statistical hypothesis testing, is a technique used to evaluate two hypotheses about a population using sample data. One hypothesis, known as the null hypothesis (H0), proposes that there is no significant difference between a population parameter and a sample parameter, whereas the other hypothesis, known as the alternative hypothesis (H1), suggests that there is a significant difference between a population parameter and a sample parameter.You might have made a Type I error, but the probability is only 5% at most is true if you complete a hypothesis test using α = .05, and based on the evidence from the sample, your decision is to reject the null hypothesis, but the treatment actually has no effect. In the given situation, if the treatment actually has no effect, you might have made a Type I error, but the probability is only 5% at most. When the null hypothesis is rejected when it should not be, a Type I error occurs. The probability of making a Type I error is represented by alpha (α), which is typically set to 0.05 in hypothesis testing. Therefore, if α = .05, the likelihood of making a Type I error is 5% at most.
Learn more about hypothesis testing here, https://brainly.com/question/29350481
#SPJ11
you flip a coin 12 times. it lands on tails 9 times. what is the experimental probability of landing on heads?
Answer:
25%
Step-by-step explanation:
U flipped a coin 12 times, it lands on tail 9 times. Now the probability of landing on head = 12-9
= 3
In percentage= 12\3 *100
=25%
Answer:
0.25%
Step-by-step explanation:
a playground 98 ft long and 56 ft wide is to be resurfaced at a cost of $3.75 per sq ft what will the resurfacing cost?
Answer:L x b
98ft x 56ft =5488
=5488 / $3.75= $1463.47
Step-by-step explanation: Play ground is more like a rectangle so we use the formula for the rectrectangle to get total area . A=Lxb
Divide the total with the cost since it say each per sqr feet
A=lxb
98x56=5488
5488/3.75= 1463.47
find the distance between (-8,-1) and (-8,4)
A. -5
B. 5
C. 11
D. 14
The distance between the two points (-8,-1) and (-8,4) is 5 units.
What is distance formula?The distance formula is a mathematical formula used to find the distance between two points in a two-dimensional or three-dimensional coordinate system.
According to question:The distance between two points (x1, y1) and (x2, y2) in a two-dimensional coordinate system can be found using the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
In this case, the two points are (-8, -1) and (-8, 4). Therefore, we can substitute the values into the formula:
d = √((-8 - (-8))² + (4 - (-1))²)
= √(0² + 5²)
= √(25)
= 5
Therefore, the distance between the two points is 5 units, so the answer is (B) 5.
To know more about distance visit:
https://brainly.com/question/25841655
#SPJ1
The angle of depression from a lightbouse that is 32 meters in height to the base of a ship at the water’s edge measures 26°. To the nearest meter, hkw far js the ship to the base of the lighthouse?
The ship is about 65.6 meters away from the base of the lighthouse.
What is tangent function ?
Tangent is one of the three primary trigonometric functions, along with sine and cosine. In a right triangle, the tangent of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.
The tangent function is denoted by "tan" and is defined mathematically as:
tan(theta) = opposite / adjacent
where theta is the angle, opposite is the length of the side opposite the angle, and adjacent is the length of the side adjacent to the angle.
According to the question:
We can use trigonometry to solve this problem. Let's draw a right triangle with the lighthouse at the top, the ship at the bottom, and the line connecting them as the hypotenuse. The angle of depression of 26° is the angle between the hypotenuse and the horizontal line passing through the lighthouse. We know the height of the lighthouse is 32 meters.
Let x be the distance between the ship and the base of the lighthouse, which is the adjacent side of the angle of depression. Then we can use the tangent function:
tan(26°) = opposite / adjacent
We know the opposite side is the height of the lighthouse, which is 32 meters. Solving for x:
x = opposite / tan(26°)
x = 32 / tan(26°)
x ≈ 65.6 meters
Therefore, the ship is about 65.6 meters away from the base of the lighthouse.
To know more about tangent function visit:
https://brainly.com/question/29305357
#SPJ1
I need some help please
Answer:
3(2c + d) - 4(c - d) + d² = 32
Step-by-step explanation:
Now we have to,
→ Simplify the given expression.
We have to use,
→ d = 3
→ c = 1
The given expression is,
→ 3(2c + d) - 4(c - d) + d²
Let's simplify the expression,
→ 3(2c + d) - 4(c - d) + d²
→ 3(2(1) + 3) - 4(1 - 3) + 3²
→ 3(2 + 3) - 4(-2) + 9
→ 3(5) + 8 + 9
→ 15 + 17
→ 32 => {final answer}
Therefore, the answer is 32.