The value of the right triangle cos d = 15/17 and cos c = 8/17.
What are trigonometric functions?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.
Given that, the value of tan c = 15/8 and the value of sin d = 8/17.
From the trigonometric functions we can conclude that:
Opposite side to c = 15
Adjacent side to c = 8
Hypotenuse = 17
Opposite side to d = 8
Adjacent side to d = 15
The values of cos d is:
cos d = Adjacent side to d / Hypotenuse = 15/17
cos c = Adjacent side to c / Hypotenuse = 8/17
Hence the value of the right triangle cos d = 15/17 and cos c = 8/17.
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dave wants to buy a new collar for each of his 5 cats. the collars come in a choice of 9 different colors. step 1 of 2 : how many selections of collars for the 5 cats are possible if repetitions of colors are allowed?
If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:
9 x 9 x 9 x 9 x 9 = 59,049
In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:
Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
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You and your friend just finished playing a game. Your final score was 24 and her final score was -13. By how many points did you win
Answer: 37 points
Step-by-step explanation:
Which one of the following points lies on the line 3x=2x-1
The point (-1, 2) lies on the line 3x = 2x - 1.
The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.
So the line passes through the point (-1, y) for any value of y.
To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.
a) (0, -1)
3(0) = 2(0) - 1
0 = -1
This point does not lie on the line.
b) (-1, 2)
3(-1) = 2(-1) - 1
-3 = -3
This point does lie on the line.
c) (1, -4)
3(1) = 2(1) - 1
3 = 1
This point does not lie on the line.
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A figure is dilated by a scale factor of 3 and is rotated 90° clockwise.
Complete the description of the transformations that will transform the image back into the original figure. Drag and drop each choice into the correct boxes to complete the sentences below.
Answer:
Answer is Below ------v
1. clockwise
2. 3
1. (y, -x)
2. (3x,3y)
at the grocery store, caleb has narrowed down his selections to 5 vegetables, 8 fruits, 3 cheeses, and 7 whole grain breads. he wants to use the express lane, so he can only buy 20 items. in how many ways can he choose which 20 items to buy if he wants all 3 cheeses?
Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.
To choose 20 items at the grocery store, Caleb has narrowed down his selections to 5 vegetables, 8 fruits, 3 cheeses, and 7 whole grain breads. Since he wants all 3 cheeses, he only needs to choose 17 more items.
The number of ways he can choose these 17 items from the remaining vegetables, fruits, and breads is given by the combination: C(5+8+7, 17) = C(20, 17) = 1140.
This formula means that there are 20 items to choose from, and Caleb wants to choose 17. The order doesn't matter, so we use a combination.
Therefore, Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.
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Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given 2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent. 3. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Answer:
The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.
This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.
Answer:
Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Step-by-step explanation:
In this question that you have put:
7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =
Vertical Angles Theorem ( Or in similar terms VAT )
Make sure that you remember the following:
vertical angles are the angles that are opposite each other when the two line " meet together "
Thus, your answer to your questions is.
D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
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6.RP.3d-2016 (#39) Fei Yen's dog eats 8 ounces of dog food each day. Fei Yen bought a 28-pound bag of dog
food. How many 8-ounce servings are in a 28-pound bag of dog food?
A 14
B 56
C 224
D 448
There are 56 servings in a 28 pound bag of dog food.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each day Fei yen's dog eat dog food = 8 ounces
Fei yen bought a 28 pound bag of dog food.
And we know that 1 pound = 16 ounces
Then ,the food in ounces
= 28 x 16
= 448 ounces
Now, the number of 8 ounces servings are in a 28 pound bag of dog food
= 448 / 8
= 56
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0/1
12. Ashton picked 6 pounds of pecans. He used of the pecans in a soup recipe. Ashton then
splits the pecans that are left in pound bags. How many bags of pecans does he have?
Ashton has 4.5 bags of pecans. since you can't have half a bag, he might need to round up to 5 bags
What is Fraction?A fraction represents a part of a whole.
If Ashton used 1/4 of the pecans in a soup recipe, he has 3/4 of the pecans left.
To find out how many pounds of pecans he has left.
we can multiply the original amount of pecans by 3/4:
3/4 x 6 pounds = 4.5 pounds
So Ashton has 4.5 pounds of pecans left to split into bags.
If he splits the remaining pecans into 1-pound bags, then he has:
4.5 pounds ÷ 1 pound/bag = 4.5 bags
Therefore, Ashton has 4.5 bags of pecans. However, since you can't have half a bag, he might need to round up to 5 bags
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The complete question
Ashton picked 6 pounds of pecans. He used 1/3 of the pecans in a soup recipe. Ashton puts the pecans that are left in 1/4 pound bags. How many bags of pecans does he have
Find (1/3x−3)+(−3/4x−5)
Answer:
-5x-96/12
Step-by-step explanation:
Firstly we want ot combine the multiplied terms into one fraction:
(1x/3-3)+(-3/4 x-5)
Then we multiply by 1:
(x/3-3)+(-3/4 x-5)
Find common denominator:
(x/3+3(-3)/3)+(-3/4 x-5)
Combine fractions with common denominator:
(x+3(-3)/3)+(-3/4 x-5)
Multiply the numbers:
(x-9/3)+(-3/4 x-5)
Combine multiplied terms into a single fraction:
x-9/3+(-3x/4 -5)
Find common denominator:
x-9/3+(-3x/4 + 4(-5)/4)
Combine fractions with common denominator:
x-9/3+(-3x + 4(-5)/4)
Multiply the numbers:
x-9/3 + (-3x-20/4)
Find common denominator:
4(x-9)/12 + 3(-3x-20)/20
Combine fractions with common denominator:
4(x-9)+3(-3x-20)/12
Distribute:
4x-36+3(-3x-20)/12
Distribute:
4x-36-9x-60/12
Subtract the numbers:
4x - 96 - 9x/12
Combine like terms:
-5x - 96/12
Answer: -5x-96/12
Point D is the centroid of ABC, BD = 4x + 2 and DF = 3r. Find the value of x
Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and the value of x is -1
Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.
Given point D is the centroid of triangle ABC, BD = 4x + 2 and DF = 3x and Centroid is a term used in triangles and it is equals to the reciprocal of three-second of the distance from each midpoint of the given triangle to each vertices.
we know that,
BD = 4x+2
DF = 3x
So by the given formulae, we used to solve the x value as,
BD = (1/(3/2)) [DF]
BD = (2/3)[DF]
4x+2 = (2/3)(3x)
4x+2 = 2(x)
4x+2 = 2x
4x-2x = -2
2x = -2
x = -1
Therefore, the value of x is x = -1
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b³+b²+4b factorize this
Answer: b (b²+b+4)
Step-by-step explanation:
b²=bb
b³=b²b
=b²b+bb+4b
=b(b²+b+4)
Select the correct answer.
Consider this function.
f(x) = 6log₂x - 3
Over which interval is function f increasing at the greatest rate?
OA. [2, 6]
OB. [1/8, 1/2]
OC. [1, 2]
OD. [1/2,1]
The function f(x) = 6log₂x - 3 increasing at the greatest rate in the interval [1/8, 1/2].
What are maxima and minima?The maxima and minima of a function are the extreme values within the range; in other words, they are the maximum and minimum values of a function, respectively, at a given position.
Let the function be f(x) = 6log₂x - 3
For the interval x ∈ [2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased most rapidly in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
Therefore, the range [1/8, 1/2] is where the function f(x) = 6log₂x - 3 increases at the fastest pace.
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Luis wants to buy a skateboard that usually sells for $79.86. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 8.25%. Round your intermediate calculations and answer to the nearest cent.
The total cost of the skateboard is $
The total cost of the skateboard is $76.07.
What is the total cost of the skateboard?The first step is to determine the price of the skateboard after the 12% discount. A discount reduces the price of an item.
Price after discount = price before discount x (1 - percent discount)
$79.86 x (1 - 12/100)
$79.86 x (1 - 0.12)
$79.86 x 0.88
= $70.28
Price after the sales tax = (1 + sales tax) x price after discount
= (1 + 8.25/100) x $70.28
(1 + 0.0825) x $70.28
1.0825 x $70.28 = $76.07
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D. A car dealer purchased 40 new cars at
$6500 each. He sold 40% of them at
$8000 each and the rest at $9000 each.
What was his total profit?
40%=
5
2
5
2
⋅40=16 cars at 8000 each =128,000 in sales
40−16=
24 cars at 9000 each
=216,000 in sales
Total sales: 128,000+216,000=344,000
Total expense: 6500⋅40=260,000
Total profit: 344,000−260,000=84,000
Answer:
$84000
Step-by-step explanation:
40% of the cars would be 16 cars that are sold for $8000 each.
16×$8000=$128000
The remaining 60% of cars would be 24 cars to be sold at $9000 each.
24×$9000=$216000
The total profit = the sum - the amount he paid for all cars.
total profit = ($128000+$216000) - (40×$6500)
total profit = $344000 - $260000
total profit = $84000
There were 230,600 jobs available in the field of radiology in the year 2014. Each year, that number is expected to grow by 0.9%.
Write a function that gives the expected number j(t) of jobs in radiology t years from the year 2014.
Answer:
J(t) = 230,600(1.009)^t
Step-by-step explanation:
J(t) = 230,600(1 + 0.009)^t, or
J(t) = 230,600(1.009)^t If this is Wrong ill do. it again!!
Pleaseeee help needddd done asappppp
8 is (6x^2-7x-5)/(2x + 1)
If f(x) = 2x - 9 and g(x) = x² + 3, what is (f + g)(4)?
a radioactive substance decays exponentially. a scientist begins with 100 milligrams of a radioactive substance. after 29 hours, 50 mg of the substance remains. how many milligrams will remain after 38 hours?
After 38 hours, there will be 43.1 mg of the radioactive substance remaining.This means that the amount of a radioactive substance decreases exponentially over time
Radioactive decay follows an exponential decay curve. This means that the amount of a radioactive substance decreases exponentially over time. The equation for this is: [tex]A(t) = A0*e^(-λ*t\\[/tex])Where A(t) is the amount of substance at time t, A0 is the initial amount of substance, and λ is the decay constant. In this problem, A0 = 100 mg, t = 29 hours, and A(t) = 50 mg. We can use this to solve for λ:50 mg = 100 mg * [tex]e^(-λ*29)λ =[/tex] -0.027Now that we have the decay constant, we can calculate the amount of substance remaining after 38 hours:A(38) = 100 mg * [tex]e^(-0.027*38[/tex]).A(38) = 43.1 mg.Therefore, after 38 hours, there will be 43.1 mg of the radioactive substance remaining.
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pls help me i need now and if the answer is correct i give free BRAINLIEST HERE!!!!
THANK YOU
The measures of the angles formed by the cords and secant in the circle are found using circle theorems and presented as follows;
m∠1 = 47.5°[tex]m\widehat{BD}[/tex] = 110°m∠COD = 55°[tex]m\widehat{CD}[/tex] = 20°m∠AOC = 100°m∠APB = 25°m∠ADB = 25°[tex]m\widehat{CD}[/tex] = 90°[tex]m\widehat{AB}[/tex] = 70°[tex]m\widehat{CD}[/tex] = 100°What is a secant of a circle?A secant is a line that has two points of intersection on a circle.
The specified parameters are;
1. The measure of arc [tex]m\widehat{AB}[/tex] = 80°, and the measure of [tex]m\widehat{CD}[/tex] = 15°
Angle at the center of the circle = 2 × Angle at the circumference
Angle at the center of the circle = The arc angle of the circle
Therefore;
m∠DAC = 15°/2 = 7.5°
m∠ACO = 80°/2 = 40°
The external angle of a triangle theorem, indicates that we get;
m∠1 = 40° + 7.5° = 47.5°
m∠1 = 47.5°
2. m∠BOD = 100°, [tex]m\widehat{AC}[/tex] = 90°
The intersecting chords theorem indicates that we get;
m∠BOD = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; 100° = (1/2)×(90° + [tex]m\widehat{BD}[/tex])
[tex]m\widehat{BD}[/tex] = 2 × 100° - 90° = 110°
[tex]m\widehat{BD}[/tex] = 110°
3. [tex]m\widehat{AB}[/tex] = 90°, [tex]m\widehat{CD}[/tex] = 20°
Therefore; m∠ACO = 90°/2 = 45°
m∠DAC = 20°/2 = 10°
The external angle theorem indicates that we get;
m∠COD = 45° + 10° = 55°
m∠COD = 55°
4. m∠1 = 35°, [tex]m\widehat{AB}[/tex] = 50°, therefore;
m∠ACO = 50°/2 = 25°
m∠CAO = 35° - 25° = 10°
[tex]m\widehat{CD}[/tex] = 2 × m∠CAO
Therefore; [tex]m\widehat{CD}[/tex] = 2 × 10° = 20°
[tex]m\widehat{CD}[/tex] = 20°
5. m∠AOC = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; m∠AOC = (1/2)×(90° + 110°) = 100°
m∠AOC = 100°
6. [tex]m\widehat{CD}[/tex] = 20° and [tex]m\widehat{AB}[/tex] = 70°
The external secant, tangent theorem, indicates that we get;
m∠APB = (1/2) × ([tex]m\widehat{AB}[/tex] - [tex]m\widehat{CD}[/tex])
m∠APB = (1/2) × (70° - 20°) = 25°
m∠APB = 25°
7. [tex]m\widehat{AB}[/tex] = 50°,
The angle at the center of a circle is twice the angle subtended at the circumference, therefore;
m∠ADB = 50°/2 = 25°
m∠ADB = 25°
8. m∠CAD = 45°
The angle formed by an arc at the center of a circle theorem, indicates that we get;
[tex]m\widehat{CD}[/tex] = 2 × m∠CAD
[tex]m\widehat{CD}[/tex] = 2 × 45° = 90°
[tex]m\widehat{CD}[/tex] = 90°
9. m∠ACB = 70°
m∠ACB is the angle subtended by the arc [tex]m\widehat{AB}[/tex] on the circumference
Therefore;
[tex]m\widehat{AB}[/tex] = 2 × m∠ACB
[tex]m\widehat{AB}[/tex] = 2 × 70° = 140°
[tex]m\widehat{AB}[/tex] = 70°
10. m∠AOB = 80°, [tex]m\widehat{AB}[/tex] = 60°
m∠(AOB) = (1/2) × ([tex]m\widehat{AB}[/tex] + [tex]m\widehat{CD}[/tex])
Therefore; m∠(AOB) = 80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
[tex]m\widehat{CD}[/tex] = 2 × 80° - 60° = 100°
[tex]m\widehat{CD}[/tex] = 100°
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Find the simplified product:^3sqrt2x^5 x ^3sqrt64x^9
The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.
[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]
[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]
[tex]3.8\sqrt{2}x^{5+3+9}[/tex]
[tex]3.8\sqrt{2}x^{17}[/tex]
[tex]24\sqrt{2}x^{17}[/tex]
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which expression is equivalent to 5^6
a.125 x 125 b. 6 x 5 c. 35 x 6 x 6 x 6 d. 25 x 5 x 5 x 5
The expression that is equivalent to 5^6 is A.125 x 125
What are index forms?Index forms are defined as mathematical forms of writing numbers that are too large or small in more convenient forms.
Other terms for index forms are called standard forms or scientific notations.
They are also described as numbers or variables that are raised to an exponent.
From the information given, we have that;
5⁶
This is replicating 5 in 6 places, we have the representation as;
5 × 5 × 5 × 5 × 5 × 5
Hence, the expression is 125 x 125
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s this true or false? fraction numerator n squared plus 2 n space plus 5 over denominator n end fraction space element of space capital omega (n squared )true
The given expression is a fraction in the form of[tex](n^2 + 2n + 5)/n[/tex], which is an element of the set Omega ([tex]n^2[/tex]). This expression is true.
The given expression is a fraction in the form[tex](n^2 + 2n + 5)/n[/tex], which belongs to the set Omega[tex](n^2).[/tex] This statement is valid, as the fraction is simply a simplified form of a polynomial, which is an element of the Omega set. The numerator of the fraction is [tex]n^2 + 2n + 5[/tex], which is a quadratic equation in n. The denominator is n, which is a linear equation in n. As the numerator and denominator are both polynomials of n, the fraction is an element of the Omega set. Therefore, the statement is true.
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question 8
help me asap
The sector area of the sector defined by the minor arc CB is given as follows:
7.5 cm².
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
We have that the radius is half the diameter, hence it's measure is given as follows:
r = 3 cm.
The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.
CB + 84º = 180º.
CB = 96º.
An entire circle has an angle of 360º, hence the area of the sector is given as follows:
A = 96/360 x π x 3²
A = 7.5 cm².
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Kashif and ali invested equal sum in two different banks at 9% and 10% interest compound annually. In 6 years how much will kashif can more than ali
If Kashif and Ali invested equal sums in the two different banks at 9 % and 10% , then in 6 years Ali will have $0.0945 more than Kashif .
We use the formula for compound interest, to calculate the amount that each person will have after 6 years ;
Amount after 6 years for Kashif is :
⇒ A = P(1 + r/n[tex])^{nt}[/tex]
where A = (amount after 6 years) ; P = (initial investment)
r = interest rate = 9% ; n = 1 ; t = time period (6 years) ;
So, A = P(1 + 0.09/1)⁶ ⇒ P(1.09)⁶ ;
Amount after 6 years for Ali is :
⇒ A = P(1 + 0.10/1)⁶ = P(1.10)⁶ ;
So , difference in the amounts that Kashif has compared to Ali after 6 years is ⇒ P(1.09)⁶ - P(1.10)⁶ ;
Simplifying this expression, we get:
⇒ P(1.09⁶ - 1.10⁶) ;
≈ -$0.0945 ;
Since the value is negative, it means that after 6 years, Ali will have more money than Kashif and difference between their amounts is approximately $0.0945 .
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Compare the experimental and theoretical probabilities of each outcome.
Getting two tails
Getting two heads
Getting one heads and one tails
The theoretical probability of getting two tails is 1/4 = 0.25 = 25%. The experimental probability of getting two tails will change for every experiment.
The theoretical probability of getting two heads is 1/4 = 0.25 = 25%.
The theoretical probability of getting one head and one tail is 2/4 = 0.50 = 50%.
What is experimental probability?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Given that two coins flip together. The outcomes of a coin is {H,T}.
The outcomes after flipping of two coins are
{HH, HT, TH, TT}
The total number of outcomes is 4.
The number of outcomes to get two tails is 1.
The probability of getting two tails is 1/4 = 0.25 = 25%.
The number of outcomes to get two heads is 1.
The probability of getting two heads is 1/4 = 0.25 = 25%.
The number of outcomes to get one head and one tail is 2
The probability of getting one head and one tail is 2/4 = 0.50 = 50%.
The theoretical probabilities will change for every experiment.
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Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
The solution is Option E.
The solution to the system of equations is the point of intersection of line and the lines intersect at the point A ( 3 , 2 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , -4 )
Let the second point be Q ( 7 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = 10 / 10 = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 6 = 1 ( x - 7 )
y - 6 = x - 7
y = x - 1 be equation (1)
Now , the point of intersection of lines is at ( 3 , 2 )
Substitute the value of x and y in the equation , we get
when x = 3 , y = 2
2 = 3 - 1
2 = 2
Hence , the solution to the equation is ( 3 , 2 )
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Please help me by finding the degree measure of angle x
We can say in this triangle by Pythagorean theorem A2 = B2 + C2 => AC = sqrt115 after answering the provided question.
What exactly is a triangle?Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Pythagorean theorem applies here, in this triangle
[tex]A^2 = B^2 + C^2[/tex]
[tex]AC = \sqrt{14^2 - 9^2}[/tex]
[tex]AC = \sqrt{196 - 81}[/tex]
[tex]AC = \sqrt{115}[/tex]
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3, -24, 192, ... Find the 19th term:
Answer:
Step-by-step explanation:
a
n
=ar
n−1
a
3
=ar
2
=24...(1)
a
6
=ar
5
=192...(2)
dividing (2) by (1) we get
ar
2
ar
5
=
24
192
r
3
=8⇒r=2
From (1)
ar
2
=24
a=
2
2
24
=6
∴a
10
=(6)(2)
10−1
=3072
Y-1= -1/3(x-6) in standard form
Answer:
x + 3y = 9
Step-by-step explanation:
A ladder leans against the side of a house. The angle of elevation of the ladder is 68° when the bottom of the ladder is 7 ft from the
is the top of the ladder from the ground? Round your answer to the nearest tenth.
Check
68°
O
X
Save-
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T
Answer:
17.3 feet
Step-by-step explanation:
We can use the tangent function to evaluate the height of the building.
The definition of the tangent function is
[tex]\tan x=\frac{O}{A}[/tex]
Where
[tex]A[/tex] is the side adjacent to the angle
[tex]O[/tex] is the side opposite to the angle
In this example we are given values of the adjacent side and the angle.
Knowing that we can evaluate the side opposite to the angle.
Numerical Evaluation
We are given
[tex]x=68\\A=7[/tex]
Substituting these values into the equation for the tangent function yields[tex]\tan 68=\frac{O}{7}[/tex]
Lets solve for [tex]O[/tex].
Multiply both sides by [tex]7[/tex].
[tex]O=7*\tan 68[/tex]
Evaluate [tex]\tan 68[/tex].
[tex]O=7*2.47508685[/tex]
[tex]O=17.325608[/tex]
Rounding to the nearest tenth gives us
[tex]O=17.3[/tex]
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