The distance between points A and B is approximately 170.4 ft.
How to find the distance between point a and point bTo solve the problem, we can use the law of cosines. Let's call the angle between points A and B "x". Then we have:
cos(x) = (150^2 + 210^2 - 2(150)(210)cos(180°-76°-32°))/ (2(150)(210))
Simplifying this expression, we get:
cos(x) = 1/2
To solve for x, we take the inverse cosine of both sides:
x = cos^(-1)(1/2)
Using a calculator, we find that:
x ≈ 60°
Now we can use the law of sines to find the distance between points A and B:
sin(76°) / 210 = sin(60°) / d
where d is the distance between points A and B.
Simplifying this expression, we get:
d = 210sin(60°) / sin(76°)
Using a calculator, we find that:
d ≈ 170.4 ft
Therefore, the distance between points A and B is approximately 170.4 ft.
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On a standardized test with a normal distribution, the mean was 64.3 and the standard deviation was 5.4.
Approximately what percent of those taking this exam had scores between 58.9 and 69.7?
Responses
A 68.3%
B 38.2%
C 60.0%
D 34.1%
The percent of those taking this exam had scores between 58.9 and 69.7 is 34.1%
What is standardized test?To find the number of standard deviations 58.9 and 69.7 are above and below the mean, find the difference between these two numbers and the mean, then divide by the standard deviation 5.4:
z1 = (58.9 - 64.3) / 5.4 = -0.996
z2 = (69.7 - 64.3) / 5.4 = 1.004
Since the absolute values of the z-scores are almost equal, we can approximate the area between them as half of the total area between -1 and 1 standard deviations.
Therefore, the approximate percentage of those taking the exam with scores between 58.9 and 69.7 is:
68% / 2 = 34%
Therefore, the correct option is D 34.1%.
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A rectangular pyramid is shown in the figure.
A rectangular pyramid with a base of dimensions 7 centimeters by 5 centimeters. The two large triangular faces have a height of 7.6 centimeters. The two small triangular faces have a height of 8 centimeters.
What is the surface area of the pyramid?
The surface area of the pyramid is 113 cm².
What is rectangular pyramid?A rectangular pyramid is a type of pyramid where the base is a rectangle and the triangular faces meet at a single point called the apex or vertex. It has five faces, including a rectangular base and four triangular faces, and it is a polyhedron with five vertices and eight edges.
The rectangular pyramid has a base of dimensions 7 cm by 5 cm, and the two large triangular faces have a height of 7.6 cm, while the two small triangular faces have a height of 8 cm.
To find the surface area of the pyramid, we need to find the area of each face and then add them up.
Area of the base:
The base of the pyramid is a rectangle with dimensions 7 cm by 5 cm, so its area is:
Area of base = length × width = 7 cm × 5 cm = 35 cm²
Area of the four triangular faces:
Each of the four triangular faces has a base of 5 cm (the width of the rectangle) and a height of either 7.6 cm or 8 cm. Using the formula for the area of a triangle, we can find the area of each face:
Area of each large triangular face = 1/2 × base × height = 1/2 × 5 cm × 7.6 cm = 19 cm²
Area of each small triangular face = 1/2 × base × height = 1/2 × 5 cm × 8 cm = 20 cm²
There are two large triangular faces and two small triangular faces, so the total area of the four triangular faces is:
Total area of four triangular faces = 2 × area of large triangular face + 2 × area of small triangular face
= 2 × 19 cm² + 2 × 20 cm²
= 78 cm²
Total surface area:
Finally, we can find the total surface area of the pyramid by adding the area of the base to the total area of the four triangular faces:
Total surface area = area of base + total area of four triangular faces
= 35 cm² + 78 cm²
= 113 cm²
Therefore, the surface area of the pyramid is 113 cm²
.
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The product of two numbers is 2420 and their LCM is 110.Find the HCF
of the two numbers.
Answer: Let the two numbers be x and y. We know that:
x*y = 2420 ---(1)
LCM(x, y) = 110 ---(2)
We can write the LCM as:
LCM(x, y) = (x*y)/HCF(x, y)
Substituting the given values, we get:
110 = (x*y)/HCF(x, y)
Multiplying both sides by HCF(x, y), we get:
HCF(x, y) * 110 = x*y
Substituting equation (1), we get:
HCF(x, y) * 110 = 2420
Dividing both sides by 110, we get:
HCF(x, y) = 2420/110
HCF(x, y) = 22
Therefore, the HCF of the two numbers is 22.
Step-by-step explanation:
Throughout the day, the water level, h(t), at Sunny Beach varies with the tides. Joe, a frequent visitor of Sunny Beach, arrived at the beach at 12:00 p.m., and collected the following data, where t represents the number of hours since Joe arrived at the beach.
t 0 1 2 3 4 5
h(t) 5 4.41 3 1.59 1 1.59
Joe lost some of his data, but he knows that the highest tide occurs at 12:00 p.m., and he was able to use a trigonometric function to model the height of the tide at any time.
What is the period of the function that can be used to model the height of the tide?
A.
5 hours
B.
More information is needed to solve this problem.
C.
8 hours
D.
12 hours
the answer to the question is A. 5 hours. This information is essential for accurately modeling the tide using a trigonometric function and predicting the water level at any time in the future or past within the 5-hour cycle
How to solve the question?
The given data represents the variation of water level at Sunny Beach over a period of 5 hours. As Joe arrived at 12:00 p.m., we can assume that the highest tide occurred at that time, and the water level started to decrease until it reached its lowest point after 3 hours. Then, the water level started to increase again until it reached its highest point after 5 hours, completing one full cycle of the tide.
To model this variation of water level over time, we can use a trigonometric function, specifically a sine or cosine function. These functions have a repeating pattern over a fixed period, which makes them suitable for modeling cyclic phenomena such as tides.
The period of a sine or cosine function represents the length of one complete cycle. In this case, the period of the function that models the tide is 5 hours because the tide completes one cycle over a 5-hour period, as observed from the given data.
Therefore, the answer to the question is A. 5 hours. This information is essential for accurately modeling the tide using a trigonometric function and predicting the water level at any time in the future or past within the 5-hour cycle
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Sarah wants to save $1600 so she can spend it on a summer vacation. She plans to work no more than 20 hours per week. Her budget for April, 2023 is shown below.
a) What advice would you give her if her goal is to save this amount of money by the end of June, 2023?
b) List below her adjusted income and expenses over this period of time.
what is the base 8 representation of 1100111 base 2
Answer:
147
My teacher has been trying to help me learn this and it has been working.
You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble. What is the probability of drawing a red marble out of the bag?
Answer:
40%
Step-by-step explanation:
We Know
You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble.
4 + 3 + 2 + 1 = 10 marbles total
What is the probability of drawing a red marble out of the bag?
We Take
(4 ÷ 10) x 100 = 40%
So, 40% of drawing a red marble out of the bag.
how long does it take for a deposit of $1300 to double at 9% compounded continuously?
how many years does it take to double? years _ days _
What is M in triangle properties
I hope this helps you.
In triangle AB, let the angle bisectors be BY and CZ. Given AB = 16, AY = 16, and CY = 16, find BC and BZ.
We know that the angle bisector theorem and the specified requirements are satisfied if BC = 16, CZ = 8, and BZ = 24. The angle bisector theorem is also satisfied if BC = 8, which also makes CZ = 16/3 and BZ = 112/9.
What is angle bisector theorem?The opposite side of a triangle is divided into two portions that are proportional to the sides they are on if the angle is bisected by a line, according to the angle bisector theorem.
The angle bisector theorem, which asserts that if a line bisects a triangle's angle, it divides the opposite side into two segments that are next sides to each other, can be used to solve this problem.
Let BC and BZ both equal x. The angle bisector theorem provides us with:
AC/AB = CZ/BZ
16/(16+x) = 16/y
We solve y in terms of x, and as a result,
y = 16(16+x)/16 = x+16
Upon substitution, we discover—
16/(16+x) = 16/(x+16)
If we cross-multiply, we obtain:
16(x+16) = 16(16+x)
Simplifying, we get:
16x + 256 = 256 + 16x
In light of the fact that 16x cancels on both sides, we are left with:
256 = 256
As a result, there exist an endless number of BC and BZ values that could satisfy the requirements.
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How is this solved? how does this even work
Part a: The Weight corresponding to the given z score: z = -1 is 2.4 kilograms.
Part b: The Weight corresponding to the given z score: z = 1.34 is 3.921 kilograms.
Define about the z score:The relationship between a value and a group of values' mean is described by the Z score or standard score. It gauges how far a data point deviates from the mean.
the procedure of standardising or normalising a raw score to get a standard score. The most popular name for the standard scores is Z Scores.
Given that for the normal distribution.
mean weight of the new born babies μ = 3.05 kilogramsstandard deviation σ = 0.65 kilogramsLet the weight for the given z scores be x.Weight corresponding to the given z score-
Part A: z = -1
Z score :
z = (x - μ)/σ
-1 = (x - 3.05)/0.65
x - 3.05 = -0.65
x = -0.65 + 3.05
x = 2.4
Thus, the Weight corresponding to the given z score: z = -1 is 2.4 kilograms.
Part b: z = 1.34
z = (x - μ)/σ
1.34 = (x - 3.05)/0.65
x - 3.05 = 1.34*0.65
x = 0.871 + 3.05
x = 3.921
Thus, the Weight corresponding to the given z score: z = 1.34 is 3.921 kilograms.
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An insurance company reported that 70% of all automobile damage claims were made by people under the age of 25. If 5 automobile damage claims were selected at random, determine the probability that exactly 4 of them were made by someone under the age of 25.
I need the method more than the answer, as detailed as possible, please.
There is a 0.00567 percent chance that 4 out of the 5 auto damage claims were submitted by individuals under the age of 25.
what is a binomial theorem?An expression that has been raised to any finite power can be expanded using the binomial theorem. A binomial theorem is a potent expansionary technique with uses in probability, algebra, and other fields.
A binomial expression is an algebraic expression with two terms that are not the same. For instance, a+b, a3+b3, etc.
Let n = N, x, y, R, then the binomial theorem holds.
(x + y)n = nΣr=0 where, nCr xn - r yr
what is a probability?The likelihood of an event happening is gauged by probability. Several things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty. A crucial subject for pupils in class 10, probability explains all the fundamental ideas of the subject. A sample space has an overall probability of 1 for all events.
This is a binomial probability problem, where each automobile damage claim is a Bernoulli trial with a probability of success (a claim made by someone under the age of 25) of p=0.70. We want to find the probability of getting exactly 4 successes out of 5 trials.
The probability of getting exactly k successes out of n trials in a binomial experiment with probability of success p is given by the binomial probability formula:
P(k successes out of n trials) = (n choose k) * [tex]p^k[/tex] * [tex](1-p)^(n-k)[/tex]
where (n choose k) = n! / (k! * (n-k)!) is the number of ways to choose k items out of n items.
In this case, we have n=5 and p=0.70. So, the probability of getting exactly 4 successes out of 5 trials is:
P(4 out of 5 claims made by someone under 25) = (5 choose 4) * [tex]0.70^4[/tex] *[tex](1-0.70)^(5-4)[/tex]
P(4 out of 5 claims made by someone under 25) = 5 * [tex]0.70^4[/tex] *[tex]0.30^1[/tex]
P(4 out of 5 claims made by someone under 25) = 0.00567 (rounded to 5 decimal places)
Therefore, the probability that exactly 4 of the 5 automobile damage claims were made by people under the age of 25 is approximately 0.00567.
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60°
y
Find the value of y.
A. y = 2
B.
4√√3
3
y = 4
C.
D. y = 4√3
8
30°
The value of y is 4, so the answer is option A: y = 4.
What is trigonometric ratios ?
Trigonometric ratios are mathematical relationships between the angles and sides of a right triangle. There are three primary trigonometric ratios: sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
Using the given diagram, we can use the trigonometric ratios to find the value of y.
First, we can find the length of the side opposite the 30-degree angle by using the sine ratio:
sin(30°) = opposite/hypotenuse
sin(30°) = y/8
y/8 = 1/2
y = 8/2
y = 4
Therefore, the value of y is 4, so the answer is option A: y = 4.
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What is the approximate distance from the origin to the point (-2, -7, -4)? Round to the nearest tenth
O 3.6 units
O 7.6 units
O 8.3 units
O 9.4 units
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
Distance between two points formula:In three-dimensional space, the distance formula is used to calculate the distance between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) in a three-dimensional coordinate system.
The formula is given by:
d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²]
Here we have
The point (-2, -7, -4)
We need to find the distance between the origin to the point
Let (x₁, y₁, z₁) = (-2, -7, -4) and (x₂, y₂, z₂) = (0, 0, 0)
Using the distance formula,
d = √ [(x₂ - x₁)² + (y₂ - y₁)²+ (z₂ - z₁)² ]
d = √ [(0 - (-2))² + (0 - (-7))²+ (0 - (-4))² ]
d = √ [(2)² + (7)²+ (4)² ]
d = √ [4 + 49 + 16 ]
d = √69 = 8.3066
d = 8.3
Therefore,
The approximate distance from the origin to the point (-2, -7, -4) is 8.3 units.
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PLEASE HELP !!
(Do not guess please and thank you )
Step-by-step explanation:
A = π r²
r = 3 inches
A = 3.14 × (3)²
A = 3.14 × 9
A = 28.29 square inches
If you are performing a right-tailed z-statistic test with a sample size n = 100 and a 0.01 significance level, what is the critical value?
If your calculated value of the z-statistic is z = 2.88, what is your conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis)?
1. The critical value, according to the z-table, is roughly 2.33. 2. There is enough data to support the alternative hypothesis and reject the null hypothesis.
What is null hypothesis?A null hypothesis is a claim that assumes there is no meaningful difference between two or more variables in a population or that any difference that is detected is the result of chance in statistical hypothesis testing. Typically, it is indicated by H0. A statement that rejects the null hypothesis and assumes that the variables being compared have a substantial difference is known as an alternative hypothesis, or Ha. In contrast to the null hypothesis, which the researcher is attempting to refute, the alternative hypothesis is what the researcher is attempting to prove.
1. We can use a z-table or a calculator to determine the critical value for a right-tailed z-statistic test with a sample size of 100 and a significance level of 0.01. The z-score that equates to the 0.99 probability level, which is the complement of the 0.01 significance level, is the critical value. The crucial value, according to the z-table, is roughly 2.33.
2. We compare the estimated z-statistic value, z = 2.88, to the crucial value, 2.33. The estimated value of z falls in the rejection zone of the null hypothesis because it exceeds the crucial value. As a result, we find that there is enough data to support the alternative hypothesis and reject the null hypothesis.
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Calculate Volume of Air passing through Filter HEPA Filter 100ft/min *- Airflow 4ft 2ft Volume = Filter Area x Airflow Velocity
The volume of air passing through the filter is 800 cubic feet per minute. It is calculated by multiplying the air flow speed (100ft/min) by the area of the filter (8ft²).
Explanation:The volume of air passing through the HEPA filter can be calculated using the formula for the speed of air flow multiplied by area. The speed of the air flow is given as 100ft/min and the area of the filter is given as 4ft x 2ft, which equals 8 square feet. Therefore, the volume of the air passing through the filter can be calculated as 8ft2 x 100ft/min = 800 cubic feet per minute.
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In 1991, the moose population in a park was measured to be 4330. By 1999, the population was measured again to be 5850. Assume population continues to change linearly.
A)find a formula for the moose population,P since 1991.
B)what does your model predict the moose population to be in 2002?
Answer:
a) Let’s assume that the moose population, p, changes linearly with time t (in years since 1991). We can use the given data to find the slope of the line that represents the population change. The slope is (5850-4330)/(1999-1991) = 190 moose/year. The equation of the line is p = 190(t) + 4330.
b) According to this model, the moose population in 2002 would be p = 190(2002-1991) + 4330 = 6490 moose.
Step-by-step explanation:
please help fill in these..
Answer:
Vertex: (-2, -1)
Axis of Symmetry: x = -2
Y-intercept: (0, 3)
Min/Max: Min
Domain: All Real
Range: y ≥ -1
Step-by-step explanation:
Given the graph:
Vertex is the intersection of the axis of symmetry and the max/min value.Axis of Symmetry is the line that equally divides an object into two halves.Y-intercept is when the line crosses the y-axis and can be found when x is equal to zero.Min is the lowest value and max is the highest value.Domain is all of the x-values that work in the function.Range is all of the y-values that work in the function.Answer:
So, the answers to the question is:
Vertex: (-2, -1)
Axis of Symmetry: x = -2
Y-intercept: (0, 3)
Min/Max: Min
Domain: All Real
Range: y ≥ -1
What is the volume of a cube with a length of 11 meters? Volume V = $³ V = /w/z V = Bh V=²h Cube Rectangular prism Triangular prism Cylinder OA) 33 m³ B) 121 m³ C) 1,221 m² D) 1,331 m³ or V = Bh
Answer:
The volume of a cube with a length of 11 meters is 33 m³.
Spencer is working with his finande advisor to create some personal financial goals for the next year. One of his goals is to reduce the amount of debt
he has. Which statement could
his goal specific and timely?
He should focus intust his student loan debt and give himself a deadline of five years.
B. He should ask
end to be his accountability partner and remind him of his goal every two weeks.
le should review.
current finances to determine how much he can allocate to his goal.
He should pay
the minimum payment on his credit card statement each month.
Answer: A. He should focus on his student loan debt and give himself a deadline of five years. This statement specifies a particular type of debt and sets a time-bound goal, making it both specific and timely.
Step-by-step explanation:
can anyone help me with this?
Answer:
The surface area is 65.94 ft
3. Find the probability of randomly entering each room in the maze shown at right.
a. P(A)
b. P(B)
The probabilities of randomly entering each room in the maze shown at right are:
P(A) = 5/18
P(B) = 1
What is the probability?The probabilities can be determined from the formulas below:
P(A) = 1/3 * 1/2 * 1 + 1/3 * 1/3
P(B) = 1/3 * 1 + 1/3 * 1 + 1/3 *1
To calculate the probabilities, we need to simplify the expressions and do the arithmetic.
Using the formulas you provided:
P(A) = (1/3 * 1/2 * 1) + (1/3 * 1/3) = 1/6 + 1/9 = 5/18
P(B) = (1/3 * 1) + (1/3 * 1) + (1/3 * 1) = 1
Therefore, the probabilities, evaluated to their simplest form, are:
P(A) = 5/18
P(B) = 1
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Create a Truth Table for
A ⋀ ~B
By answering the presented question, we may conclude that Finally, the expressions fourth column represents the value of the expression A ⋀ ~B for each possible combination of truth values of A and B.
how can we create truth table?To create a truth table for A ⋀ ~B, we first need to list all possible combinations of truth values for A and B, and then calculate the value of the expression A ⋀ ~B for each combination.
A B ~B A ⋀ ~B
True True False False
True False True True
False True False False
False False True False
In the above truth table, the first column lists all possible truth values of A, and the second column lists all possible truth values of B. The third column represents the negation of B, which is denoted as ~B. Finally, the fourth column represents the value of the expression A ⋀ ~B for each possible combination of truth values of A and B.
Therefore, the truth table for A ⋀ ~B is:
A B A ⋀ ~B
True True False
True False True
False True False
False False False
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PLEAE HELP ME!!! I need this quickly!
Find the exact value of the expressions cos(alpha + beta) sin(alpha + beta) and tan(alpha + beta) under the following conditions. sin(alpha) = 24/25 a lies in quadrant I, and sin(beta) = 15/17 B lies in quadrant II.
We can use the trigonometric identities to find the exact values of the expressions.
First, we can find cos(alpha) and cos(beta) using the Pythagorean identity:
cos(alpha) = sqrt(1 - sin^2(alpha)) = sqrt(1 - (24/25)^2) = 7/25
cos(beta) = -sqrt(1 - sin^2(beta)) = -sqrt(1 - (15/17)^2) = -8/17 (since beta is in quadrant II, where cosine is negative)
Next, we can use the sum formulas for sine and cosine to find sin(alpha + beta) and cos(alpha + beta):
sin(alpha + beta) = sin(alpha)cos(beta) + cos(alpha)sin(beta) = (24/25)(-8/17) + (7/25)(15/17) = -117/425
cos(alpha + beta) = cos(alpha)cos(beta) - sin(alpha)sin(beta) = (7/25)(-8/17) - (24/25)(15/17) = -24/85
Finally, we can use the quotient identity for tangent to find tan(alpha + beta):
tan(alpha + beta) = sin(alpha + beta) / cos(alpha + beta) = (-117/425) / (-24/85) = 39/85
Therefore, cos(alpha + beta) sin(alpha + beta) = (-24/85)(-117/425) = 936/7225, and tan(alpha + beta) = 39/85.
What is the average of these numbers?
45 46 50 52 51 59 55 51 42 44
51 55 60 62 52 54 47 74 52 52
59 52 65 45 58 59 59 52 54 65
Landon and Maria are meeting at the library to work on their history project. Maria walks 9 blocks east and 3 blocks north to get to the library from her house. Landon walks 5 blocks south and 7 blocks west to get to the library from his house. The map below shows the location of the library and Landon's and Maria's houses. To the nearest block, how far is Landon's house from Maria's house if Maria could walk in a straight line?
To the nearest block, Landon's house is at distance of 12 blocks away from Maria's house if Maria could walk in a straight line.
What is Pythagoras theorem?A basic mathematical theorem relating to the sides of a right-angled triangle is known as Pythagoras' theorem. The square of the length of the hypotenuse, the side that faces the right angle, is said to be equal to the sum of the squares of the lengths of the other two sides, known as the legs, in a right triangle.
This can be written in mathematical notation as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the legs of the right triangle.
In this case, we can consider the straight line between Maria's house and Landon's house as the hypotenuse of a right triangle, with the distances they walked as the other two sides. We can use the distance formula to find the lengths of those sides:
Distance walked by Maria = √(9² + 3²) = √90 ≈ 9.49 blocks
Distance walked by Landon = √(5² + 7²) = √74 ≈ 8.60 blocks
Now we can use the Pythagorean theorem to find the distance between their houses:
Distance between houses = √(9.49² + 8.60²) ≈ 12.46 blocks
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solve for r if $425.83=400(1+r)^5 ? (show explanation please)
Answer: 0.0295
Step-by-step explanation: To solve for r in the equation $425.83=400(1+r)^5$, we can rearrange the equation to isolate the variable.
Dividing both sides by 400 gives $(1+r)^5=1.064575$, and taking the fifth root of both sides gives:
$1+r=\sqrt[5]{1.064575}$.
Subtracting 1 from both sides gives $r\approx 0.0295$.
Therefore, your answer would be 0.0295.
A pair of dice are tossed twice. Find the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10.
Answer: 0.0972
Step-by-step explanation:
To find the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10, we need to find the probabilities of each event separately and then multiply them together.
First, let's find the probability of the first roll being a total of at least 7. There are a total of 36 possible outcomes when rolling a pair of dice (6 sides on each die, so 6 x 6 = 36). To get a total of at least 7, the following outcomes are possible:
7: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
8: (2, 6), (3, 5), (4, 4), (5, 3), (6, 2)
9: (3, 6), (4, 5), (5, 4), (6, 3)
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)
12: (6, 6)
There are 21 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 7 in the first roll is:
P(at least 7) = 21/36
Next, let's find the probability of the second roll being a total of at least 10. The following outcomes are possible:
10: (4, 6), (5, 5), (6, 4)
11: (5, 6), (6, 5)
12: (6, 6)
There are 6 successful outcomes out of the total 36 possibilities. So, the probability of getting a total of at least 10 in the second roll is:
P(at least 10) = 6/36
Now, to find the probability that both events happen, we multiply the probabilities of each event:
P(first roll at least 7 and second roll at least 10) = P(at least 7) * P(at least 10) = (21/36) * (6/36)
P(first roll at least 7 and second roll at least 10) = 126/1296
So, the probability that the first roll is a total of at least 7 and the second roll is a total of at least 10 is 126/1296, or approximately 0.0972 (rounded to four decimal places).
What is the perimeter of the triangle?
Answer:
40 units
Step-by-step explanation:
a = 8
b = 15
To find c, we can use the formula: [tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]8^{2} +15^{2} =x^{2}[/tex]
64 + 225 = c^2
289 = c^2
c = 17
a + b + c = perimeter
8 + 15 + 17 = 40
Answer:
40 units
Step-by-step explanation:
You want the perimeter of the triangle shown in the graph.
DimensionsYou can count the grid squares to find the horizontal and vertical dimensions of the triangle. You find they are 8 units and 15 units, respectively.
The length of the slant side is the hypotenuse of a right triangle with sides 8 and 15. If you don't recognize this {8, 15, 17} Pythagorean triple, you can find the hypotenuse using the Pythagorean theorem:
c² = a² +b²
c² = 8² +15² = 64 +225 = 289
c = √289 = 17
The long side of the triangle is 17 units.
PerimeterThe perimeter of the triangle is the sum of the lengths of its sides:
P = 8 + 15 + 17 = 40
The perimeter is 40 units.
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Additional comment
A "Pythagorean triple" is a set of three integer side lengths that form a right triangle. The triple is "primitive" if the numbers have no common factor. There are a few Pythagorean triples that regularly show up in algebra, trig, and geometry problems. Some of them are ...
{3, 4, 5}, {5, 12, 13}, {7, 24, 25}, {8, 15, 17}, {9, 40, 41}
You will also see multiples of these, for example, 2·{3, 4, 5} = {6, 8, 10}.
The smallest is {3, 4, 5}, and it is the only set that is an arithmetic sequence (has constant differences between lengths). In every case, the sum of the numbers is even. (A right triangle cannot have integer side lengths and an odd perimeter value.)