Answer:
Step-by-step explanation:
i believe it is nearly as hard as my usual amount of challenge
The angles are supplementary angles. Determine the
measures of angles 1 and 2.
Answer: ∡1 = 153°
∡2 = 27°
Step-by-step explanation:
Answer:
angle 2=27°
angle 1= 153°
Step-by-step explanation:
6x-9+x=180
7x-9=180
7x=189
x=27
angle 2=27°
angle 1= 27×6-9=153°
angle 1= 153°
simplify the expression ^4√16x^12y^16
(show explanation please).
Answer: 2x^3y^4
Step-by-step explanation:
The expression ^4√16x^12y^16 can be simplified as follows:
^4√16 = 2, since 2^4 = 16
x^12 can be written as (x^3)^4, and ^4√(x^3)^4 = x^3
y^16 can be written as (y^4)^4, and ^4√(y^4)^4 = y^4
Therefore, ^4√16x^12y^16 simplifies to:
2x^3y^4
Zoey is buying 6 pairs of work gloves.
She has a coupon for $2 off the regular
price of each pair. After using the
coupon, the total cost was $47.94.
Which equation can be used to find the
original cost of a pair of gloves?
The original cost of a pair of gloves is 3.9
Find the volume of this sphere.
Use 3 for TT.
-d=6in
V ≈ [?] in ³
V = πr³
Enter
Answer: Spheres aren’t three-dimensional—they are two-dimensional. This is evident from the fact that in order to specify a point on a sphere, you only need two pieces of information, such as latitude and longitude.
If you include the interior of the sphere, this is instead called a closed ball, and that is three-dimensional. You can specify a point in the closed ball in all sorts of different ways; one of the most convenient would be latitude, longitude, and distance from the center. However, other than convenience, there is no reason to prefer one coordinate system over any other.
(This fact has nothing to do with spheres or closed balls—that is just a statement that is generally true. People who insist that “the three dimensions” are length, width, and height don’t know what they are talking about.)
Step-by-step explanation:
A housewife along with group of ladies sold bags of different sizes. She earns a profit of 25 rupees on a purce and incures a loss of Rs 20 on a vanity bag sold
how many purces must she sell to have neither profit nor loss if the number of vanity bags sold is 750
pls answer quickly
whoever answers first will be marked brainliest
In linear equation, Her profit is rupees 4000.
No. of purses she must sell to have neither profit nor loss is 600 nos.
She made loss of rupees 2135.
What is a linear equation in mathematics?
A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables.
The housewife earns,
Profit on 1 purse = 25 rupees
Loss on 1 vanity bag = 20 rupees
So,
Profit on 1000 purses = 25*1000 rupees
= 25000 rupees
Loss on 1050 purses = 20*1050 rupees
= 21000 rupees
Here, Profit > Loss
So,
Total profit = 25000-21000 rupees
= 4000 rupees
i) Her profit is 4000 rupees.
If no. of vanity bags sold = 750 nos.
She made loss of = 750*20 rupees
= 15000 rupees
ii) No. of purses she must sell to have neither profit nor loss
= 15000/25 nos.
= 600 nos.
Profit on selling 325 purses = 325*25 rupees
= 8125 rupees
Loss on selling 513 vanity bags = 513*20 rupees
=10260 rupees
Here, Profit < Loss
So,
iii) She made loss of = 10260-8125 rupees
= 2135 rupees
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The complete question is -
A housewife along with a group of ladies sold bags of different sizes. She earns a profit of 25 on a purse and a loss of 20 on a vanity bag sold. i. She received an order of 1050 vanity bags and 1000 purses. What is her profit or loss? ii. How many purses must she sell to have neither profit nor loss, if the number of vanity bags sold is 750? iii. How much profit/loss did she make in selling 325 purses and 513 vanity bags?
The scale factor for sizing up rectangle A to the size of rectangle B is 52. The length of rectangle A is 6 m and the width is 4 m. Find the area of rectangle B. (A=l∙w) pls i need help
The area of rectangle B is 64,896 square meters.
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
To find the area of rectangle B, we need to first determine the dimensions of the rectangle after it has been scaled up from rectangle A using a scale factor of 52.
To do this, we can multiply the length and width of rectangle A by the scale factor of 52:
Length of rectangle B = Length of rectangle A x Scale factor = 6m x 52 = 312m
Width of rectangle B = Width of rectangle A x Scale factor = 4m x 52 = 208m
Now that we know the dimensions of rectangle B, we can find its area by using the formula:
Area of rectangle B = Length x Width
Area of rectangle B = 312m x 208m
Area of rectangle B = 64,896 square meters
Therefore, the area of rectangle B is 64,896 square meters.
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The number of people,y , leaving on cruises from a certain state from to can be approximated by , where is the number of years after
Therefore, we can predict that approximately 5,845,200 people left on cruises from this state in the year 2010.
What in mathematics is a linear equation?A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included.
This linear equation depicts the number of passengers embarking on cruises from a certain state between 2005 and 2009.
It goes like this:
y = 117,000x + 4,919,200
For example, if x = 0, which represents the year 2005, then y = 4,919,200. If x = 1, which represents the year 2006, then y = 4,919,200 + 117,000 = 5,036,200. Similarly, if x = 2, which represents the year 2007, then y = 4,919,200 + 2(117,000) = 5,153,200.
y = 117,000(5) + 4,919,200
y = 5,845,200
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Question:
The number of people, y, leaving on cruises from a certain state from 2005 to 2009 can be approximated by y=117,000x+4,919,200, where x is the number of years after 2005.
2. center (5, -6), radius 4
Answer:
(x - 5)² + (y + 6)² = 16
Step-by-step explanation:
assuming you require the equation of the circle
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r is the radius
here (h, k ) = (5, - 6 ) and r = 4 , then
(x - 5)² + (y - (- 6) )² = 4² , that is
(x - 5)² + (y + 6)² = 16
speed of both traveling east that was 112 mile wide and 8 mile per hour. North wind current is 5 miles per hour. what is speed of boat
Answer: the speed of the boat is approximately 9.43 miles per hour.
Step-by-step explanation: To find boat speed, add vectors. Boat goes east at 8 mph, with 5 mph north wind. Boat velocity is a vector eastward and current velocity is a vector northward. To combine velocities, use vector addition. Use Pythagorean theorem to find resultant velocity: resultant speed = √89 ≈ 9.43 mph.
Create a Truth Table for
(A ⋀ B) → C
The truth table is given above for (A ⋀ B) → C.
What is the logical statement?
A logical statement, also known as a proposition or a statement of fact, is a declarative sentence that is either true or false, but not both. It is a statement that can be evaluated based on the available information or evidence to determine its truth value. In other words, a logical statement is a statement that can be either true or false, but not both.
To create a truth table for the logical statement (A ⋀ B) → C, we need to consider all possible combinations of truth values for propositions A, B, and C.
There are 2 possible truth values (true or false) for each proposition, so there are 2³ = 8 possible combinations.
We can organize these combinations into a table as follows:
| A | B | C | (A ⋀ B) | (A ⋀ B) → C |
|---|---|---|---------|-------------|
| T | T | T | T | T |
| T | T | F | T | F |
| T | F | T | F | T |
| T | F | F | F | T |
| F | T | T | F | T |
| F | T | F | F | T |
| F | F | T | F | T |
| F | F | F | F | T |
In this table, the column labeled (A ⋀ B) represents the truth value of the conjunction of A and B (i.e., A AND B), and the column labeled (A ⋀ B) → C represents the truth value of the conditional statement (A ⋀ B) → C.
The symbol "T" represents "true" and the symbol "F" represents "false".
Hence, The truth table is given above for (A ⋀ B) → C.
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what is the range of the function in the graph?
A. 6≤e≤12
B. 40≤f≤100
C. 6≤f≤12
D. 40≤e≤100
The range of the function in the graph is 6≤e≤12. So correct option is A.
Describe Range?In mathematics, range is a term used to refer to the set of all possible output values of a function. It is the set of values that the function can take as its input varies over its entire domain. In other words, the range of a function is the set of all output values that can be obtained by evaluating the function for all possible input values.
For example, consider the function f(x) = x². The domain of this function is all real numbers, but the range is only non-negative real numbers, since x² is always non-negative for any real number x.
The range of a function can be determined by analyzing its graph, which is a visual representation of the function. The range corresponds to the set of all y-values that appear on the graph. For instance, the range of the function f(x) = sin(x) is the closed interval [-1, 1], since the sine function oscillates between -1 and 1 as its input varies over all real numbers.
Sometimes, it is useful to restrict the domain of a function in order to obtain a specific range. This process is called domain restriction or range selection. For example, the inverse function of f(x) = x² can be obtained by restricting the domain of f to non-negative real numbers, which ensures that the inverse function is also a function. The resulting function is f^-1(x) = √x, whose domain is non-negative real numbers and range is the same as the domain of f.
The range of the function in the graph is 6≤e≤12. So correct option is A.
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When I divide an integer by 15, the remainder is an integer from 0 to 14. When I
divide an integer by 27, the remainder is an integer from 0 to 26.
For instance, if the integer is 100 then the remainders are 10 and 19, which are
different.
How many integers from 1 to 1000 leave the same remainders after division by 15
and after division by 27?
Answer: 119
Step-by-step explanation:
We know that we must find the least common multiple of 15 and 27 in order to solve the problem because when we are finding remainders that are the same, there must be some relationship between the integer and the two dividing numbers.
Thus, we have the least common multiple 135 and its multiples which will all have a 0 remainder when divided by 15 and by 27.
We can take each of the numbers (7) and the 15 consecutive numbers after each of them, because of modulo becoming the same after 15. If we take the total of all these numbers, which will have the same remainder after division by 15 and 27, we are left with:
15 * 8 - 1 = 119
Can you find X? Show how did u find
Answer:
x=90°
Step-by-step explanation:
As in the angle, there is a box giving us info that x has to be 90°.
But to be sure that there is no mistake we have to do the following:
Look at all the other angles (see what kind of angles they are).Add all the angles up to 360°( in this case as the angle we are looking for is on a straight line which gives straight line=180°).Checking and comparing the two answers.So we are looking at the surroundings of angle x (which is on a straight line) we see that it is a right angle and look at the angle on the same line is a right angle too.
The equation right angle=90° helps us see that because there are two right angles on a 180° line (90°+90°+180°).
Therefore the answer is:
x=90°
Prove that
sin 2x
1+ cos2x
= tan x
The statement that (sin 2x) / (1 + cos 2x) = tan x can be proven.
How to prove the mathematical statement ?To prove that (sin 2x) / (1 + cos 2x) = tan x, we will use trigonometric identities.
(sin 2x) / (1 + cos 2x)
(2sin x × cos x) / (1 + (cos²x - sin²x))
(2sin x × cos x) / (cos²x + 2sin x × cos x + sin²x)
We can rewrite the denominator using the Pythagorean identity sin²x + cos²x = 1:
(2sin x × cos x) / (1 + 2sin x × cos x)
(2sin x × cos x) × (1 - 2sin x × cos x) / (1 - (2sin x × cos x)²)
((2sin x × cos x) - (4sin²x × cos²x)) / (1 - 4sin²x × cos²x)
(2sin x - 4sin²x) / (1/cos²x - 4sin²x)
Since tan x = sin x / cos x, we can rewrite the expression:
(2tan x - 4tan²x) / (sec²x - 4tan²x)
(2tan x - 4tan²x) / (1 + tan²x - 4tan²x)
(2tan x - 4tan²x) / (1 - 3tan²x)
2tan x × (1 - 2tan²x) / (1 - 3tan²x)
tan x
So, we have proved that (sin 2x) / (1 + cos 2x) = tan x.
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Will mark brainliest if answer is correct
The x⁶y³ term in the expansion will be: 35 x⁶y³.
The x⁸y² term in the expansion will be: 21x⁸y².
What is the binomial expansion?The binomial expansion of (x + y)ⁿ is given by the binomial theorem, which states:
(x + y)ⁿ = C(n, 0) * xⁿ * y⁰ + C(n, 1) * xⁿ⁻¹ * y¹ + C(n, 2) * xⁿ⁻² * y² + ... + C(n, k) * xⁿ⁻ᵏ * yᵏ + ... + C(n, n) * x⁰ * yⁿ
where;
C(n, k) is the binomial coefficient, defined as C(n, k) = n! / (k! * (n - k)!), and n! represents the factorial of n.Given that the term 210x⁴y⁶ appears in the expansion, we can infer that it corresponds to C(n, k) * x⁴ * y⁶, where k is the number of times y appears in the term, and (n - k) is the number of times x appears in the term.
Comparing this with the given term, we can deduce the values of n, k, and x in the following way:
C(n, k) = 210
x⁴ = x⁴
y⁶ = y³ * y³
Comparing the exponents on x and y, we can set up the following equations:
n - k = 4 (1)
k = 3 (2)
Solving equation (2) for k, we get:
k = 3
Substituting this value of k into equation (1), we can solve for n:
n - 3 = 4
n = 7
So, the value of n is 7.
Now, we can use the binomial coefficient formula to calculate C(n, k):
C(n, k) = C(7, 3) = 7! / (3! * (7 - 3)!) = 35
Finally, substituting the values of n, k, and C(n, k) into the general term of the expansion, we can find the specific terms:
The x⁶y³ term in the expansion will be:
C(7, 3) * x⁶ * y³ = 35 * x⁶ * y³
The x⁸y² term in the expansion will be:
C(7, 2) * x⁸ * y² = 21 * x⁸ * y²
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What are the trig ratios for the angle 7π/4 rad?
Sin 7π/4 is the value of sine trigonometric function for an angle equal to 7π/4 radians. The value of sin 7π/4 is -(1/√2) or -0.7071 (approx).
How many degrees does 74 radians equal?
315° is comparable to 7 / 4 radians. In general, we multiply the angle measurement in radians by 180/ to translate an angle measurement given in radians to degrees. Therefore, we multiply 7 / 4 by 180 / to convert to radians. We discover that 7/4 radians equals 315 degrees.
We can first convert the angle to degrees as follows:
7π/4 radians = (7/4) × 180 degrees/π ≈ 315 degrees
The trigonometric ratios for 315 degrees (or 7/4 radians) can therefore be calculated using the reference angle of 45 degrees (which is /4 radians), as shown below.
sin(7π/4) = -sin(π/4) = -1/√2
cos(7π/4) = -cos(π/4) = -1/√2
tan(7π/4) = tan(π/4) = 1
csc(7π/4) = csc(-π/4) = -√2/2
sec(7π/4) = sec(-π/4) = -√2/2
cot(7π/4) = cot(-π/4) = 1
Therefore, the trigonometric ratios for the angle 7π/4 radians are:
sin(7π/4) = -1/√2
cos(7π/4) = -1/√2
tan(7π/4) = 1
csc(7π/4) = -√2/2
sec(7π/4) = -√2/2
cot(7π/4) = 1
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help with statistics
Statistics is a branch of mathematics that involves the collection, analysis, interpretation, presentation, and organization of data. It is used in a wide range of fields such as science, engineering, social sciences, business, economics, and more.
What is statistics?In statistics, data is collected through various methods such as surveys, experiments, and observations. This data is then analyzed using statistical methods to extract meaningful insights, identify patterns and relationships, and make informed decisions.
Some common statistical techniques include descriptive statistics, inferential statistics, hypothesis testing, regression analysis, and probability theory. These techniques are used to help researchers and analysts to understand and draw conclusions about data, and to test whether their conclusions are statistically significant.
Statistics has many practical applications, such as market research, medical research, quality control, risk assessment, and many others. It plays a critical role in modern society, helping individuals and organizations make informed decisions based on data-driven insights.
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What is the meaning of [tex]s_{i-j}[/tex]?
This expression [tex]s_{i-j}[/tex] describes the distance between two points i and j in a geometric object
Explaining the meaning of the expressionIn the context of symmetry and rotations, [tex]s_{i-j}[/tex] typically refers to the distance between two points i and j in a geometric object, such as a crystal lattice or a molecule.
It is a vector that points from point i to point j, and its magnitude is the distance between the two points.
The distance vector [tex]s_{i-j}[/tex] is also used to describe the position of a point in the crystal lattice relative to the rotation axis.
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About 5% of the population of a large country is hopelessly romantic. If two people are randomly selected, what is the probability both are hopelessly romantic? What is the probability at least one is hopelessly romantic? Assume the events are independent.
The probability that both people are hopelessly romantic is 0.0025 and the probability that at least one person is hopelessly romantic is 0.0975
Let's denote the event of being hopelessly romantic as "H".
Given that 5% of the population is hopelessly romantic, we have P(H) = 0.05.
Since the events of selecting two people are independent, we can use the multiplication rule of probability to calculate the probability that both people are hopelessly romantic:
P(H and H) = P(H) x P(H) = 0.05 x 0.05 = 0.0025
To calculate the probability that at least one person is hopelessly romantic, we can use the complement rule of probability.
P(neither H nor H) = P(not H) x P(not H) = (1 - P(H)) x (1 - P(H)) = 0.95 x 0.95 = 0.9025
So, the probability that at least one person is hopelessly romantic is:
P(H or H) = 1 - P(neither H nor H) = 1 - 0.9025 = 0.0975
Therefore, the probability that at least one person is hopelessly romantic is 9.75%.
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what is the quotient and remainder of 39 divided by 8
Answer:
39 divided by 8 is equal to 4 with a remainder of 7.
The quotient is the number of times the divisor goes into the dividend. In this case, 8 goes into 39 4 times with a remainder of 7.
The remainder is the number that is left over after the divisor has been divided into the dividend. In this case, 7 is left over after 8 has been divided into 39.
Here is the long division of 39 by 8:
```
39 / 8
4
32
7
```
Step-by-step explanation:
The quotient of 39 divided by 8 is 4, and the remainder is 7.
We have,
When performing long division, we divide the dividend (39) by the divisor (8) to find the quotient and remainder.
4
--------
8 | 39
- 32
---
7
Here's how the long division process works for 39 divided by 8:
-We start by dividing the first digit of the dividend (3) by the divisor (8). Since 3 is less than 8, we can't divide it evenly, so we move to the next digit (9).
- We now have 39 as the remaining portion of the dividend. We divide 39 by 8. The largest multiple of 8 that fits into 39 is 4. We place the quotient, which is 4, above the line.
- We multiply the quotient (4) by the divisor (8), which gives us 32. We subtract 32 from 39, which leaves us with a remainder of 7.
- Since there are no more digits to bring down from the dividend, and the remainder (7) is less than the divisor (8), we stop the division process.
Therefore,
The quotient of 39 divided by 8 is 4, and the remainder is 7.
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Jackson had $104,292.12 in a savings account with simple interest. He had opened the
account with $80,040 exactly 3 years earlier. What was the interest rate?
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r
is the interest rate expressed as a decimal, and t is the time in years.
Answer: Using the formula i = prt, we have:
i = (104292.12 - 80040) = 24252.12
p = 80040
t = 3
Substituting these values, we get:
24252.12 = 80040 * r * 3
Solving for r, we get:
r = 0.101 or 10.1%
Therefore, the interest rate is 10.1%.
Step-by-step explanation:
Suppose that the functions fand g are defined as follows.
f(x)=2x-1
g(x)=√3x-5
a. i. The function f(x)/g(x) = (2x - 1)/√(3x - 5)
ii. The domain is x > 5/3
b. i. The function f(x) - g(x) = (2x - 1) - √(3x - 5)
ii. The domain is x > 5/3
What is a function?A function is a mathematical relation ship between two variables.
Since we have the functions f and g defined as follows
f(x) = 2x-1
g(x) = √3x-5
a. i To find f/g we note that
(f/g)(x) = f(x)/g(x)
So, substituting the values of the variables into the equation, we have that
f(x)/g(x) = (2x - 1)/√(3x - 5)
ii. The domain of f(x)/g(x) = (2x - 1)/√(3x - 5) is the value for which the denominator g(x) > 0.
So,g(x) > 0
⇒ √(3x - 5) > 0
⇒ 3x - 5 > 0²
⇒ 3x > 5
⇒ x > 5/3
So, the domain is x > 5/3
b. i. to find f - g, we note that
f - g = f(x) - g(x)
So, substituting the values of the variables into the equation, we have that
f(x) - g(x) = (2x - 1) - √(3x - 5)
ii. The domain of f(x) - g(x) is the value of x at which g(x) > 0
So. g(x) > 0
⇒ √(3x - 5) > 0
⇒ [√(3x - 5)]² > 0
⇒ 3x - 5 > 0
⇒ 3x > 5
⇒ x > 5/3
So, the domain is x > 5/3
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Find the polynomial function of lowest degree with only real coefficients and having the zeros √7. -√7, and 5.
Choose the correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5.
OA. f(x)=x³-7x²2 -5x+35
OB. f(x)=x³-5x² - 7x+35
OC. f(x)=x4 -8x³ - 7x²+3x+5
OD. f(x)=8x³+3x²-9x-9
The correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:
OB. f(x) = x³ - 5x² - 7x + 35
What is polynomial?
A polynomial is a mathematical expression that consists of variables and coefficients, which are combined using arithmetic operations such as addition, subtraction, multiplication, and non-negative integer exponents.
The polynomial function of lowest degree with only real coefficients and having the given zeros can be obtained by multiplying the factors (x - √7), (x + √7), and (x - 5) since the zeros are √7, -√7, and 5.
Expanding the product, we get:
(x - √7)(x + √7)(x - 5) = (x² - 7)(x - 5) = x³ - 5x² - 7x + 35
Therefore, the correct polynomial function of lowest degree with only real coefficients and having the zeros √7, -√7, and 5 is:
OB. f(x) = x³ - 5x² - 7x + 35
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Write the following expression without negative exponents.
[tex]\cfrac{5^7}{5^{-13}}\times\left( \cfrac{4^3}{7^{-2}} \right)^{-2}\implies 5^7\cdot 5^{13}\times \left( \cfrac{7^{-2}}{4^3} \right)^{+2}\implies 5^7\cdot 5^{13}\times\left( \cfrac{7^{-4}}{4^6} \right) \\\\\\ 5^{7+13}\times\left( \cfrac{1}{4^6\cdot 7^4} \right)\implies \cfrac{5^{20}}{4^6\cdot 7^4}\implies \cfrac{95367431640625}{9834496}[/tex]
How to solve for m? 2=8m
Answer:
2=8m
divide both sides by 8
the 8 cancels out
and your answer is
m= 2/8
Step-by-step explanation:
hope it helped have a nice day!
The wire attached to a radio station tower in Westlake Hills is placed at a 74º angle with the ground. The wire is attached 30 ft from the station. If Ryan wants to try to walk the wire, how long is the wire he wants to walk? (round to the nearest tenth)
HELP GIVING 25 POINTS AND BRAINLIST
Therefore, the wire Ryan wants to walk is approximately 107.9 ft long.
What are trigonometric functions?Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine, cosine, and tangent, often abbreviated as sin, cos, and tan respectively.
The sine function (sinθ) gives the ratio of the length of the side opposite an angle θ in a right triangle to the length of the hypotenuse (the longest side). The cosine function (cosθ) gives the ratio of the length of the adjacent side to θ to the length of the hypotenuse, while the tangent function (tanθ) gives the ratio of the length of the opposite side to θ to the length of the adjacent side.
Other trigonometric functions include cosecant (cscθ), secant (secθ), and cotangent (cotθ), which are the reciprocals of the sine, cosine, and tangent functions, respectively.
A represents the top of the tower, B represents the point where the wire is attached 30 ft away from the tower, and the wire itself is represented by the line segment AB. The angle between the wire and the ground is θ, and we want to find the length of the wire, which is represented by y.
We can use the trigonometric function tangent to relate the angle θ to the sides of the triangle:
tan(θ) = y/x
Solving for y, we get:
y = x * tan(θ)
We know that x = 30 ft, and θ = 74º, so we can plug those values in and calculate y:
y = 30 ft * tan(74º) = 107.9 ft (rounded to the nearest tenth)
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What is the measure of <×?
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Explanation:
Focus on triangle BDH
The three inside angles of any triangle always add to 180 degrees.
B+D+H = 180
47+31+H = 180
78+H = 180
H = 180-78
H = 102
Angle BHD is 102 degrees.
It adds to angle x, aka angle BHC, to get 180 degrees. These two adjacent angles combine to a straight line.
(angle BHD) + (angle BHC) = 180
102 + x = 180
x = 180-102
x = 78--------------
Shortcut:
Focus on triangle BDH.
Use the remote interior angle theorem to add the given interior angles.
B+D = 47+31 = 78
This is equal to the exterior angle that is not adjacent to either interior angle mentioned. This refers to angle BHC, aka angle x.
bers
Write the decimal
0.685
0.685 is a decimal that equals 68.5%.
Suppose a shipment of 160 electronic components contains 4 defective components. To determine whether the shipment should be accepted, a quality-control engineer randomly selects 3 of the components and tests them. If 1 or more of the components is defective, the shipment is rejected. What is the probability that the shipment is rejected
Please help asap!
Answer: To calculate the probability that the shipment is rejected, we need to find the probability that at least one of the three components selected is defective.
First, we can find the probability that none of the three components selected is defective, which would mean the shipment is accepted. To do this, we use the hypergeometric distribution formula:
P(X = k) = (C(N-k,n-K) * C(K,k)) / C(N,n)
where:
N = total number of components in the shipment (160)
K = number of defective components in the shipment (4)
n = number of components selected for testing (3)
k = number of non-defective components among the selected components (i.e., all 3 components are non-defective)
Plugging in the values, we get:
P(all 3 components are non-defective) = (C(160-4-3,3-0) * C(4,0)) / C(160,3)
= (C(153,3) * C(4,0)) / C(160,3)
= (22,446 * 1) / 6,384,320
= 0.00352
Therefore, the probability that the shipment is accepted is 0.00352.
To find the probability that the shipment is rejected, we can subtract this probability from 1, since the probabilities of all possible outcomes must add up to 1:
P(at least one component is defective) = 1 - P(all 3 components are non-defective)
= 1 - 0.00352
= 0.99648
Therefore, the probability that the shipment is rejected is 0.99648, or approximately 99.65%.
Step-by-step explanation:
find the value for each variable in simplest radical form
The values are;
1. x = 6 ,y = 6√2
2. x = 9√2, y = 18
3. x = y = 9
4. x = 12, y = 12√2
5. x = y = 4√2
6. x = y =( 3√2)/2
What trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
There are some special angles , in which 45 is part of them.
sin 45 = 1/√2
cos 45 = 1/√2
tan 45 = 1
1. x = 6 ( isosceles triangle)
y = 6 × √2 = 6√2
2. x = 9√2 ( isosceles triangle)
y = 9√2 × √2 = 9×2 = 18
3. x = 9√2/√2 = 9
x = y = 9 ( isosceles triangle)
4. x = 12 ( isosceles triangle)
y = 12×√2 = 12√2
5. x = 8/√2 = 8√2/2 = 4√2
x = y = 4√2( isosceles triangle)
6. x = 3/√2 = (3√2)/2
x = y =( 3√2)/2 ( isosceles triangle)
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