Triangle A B C is shown. Angle A C B is a right angle. The length of the hypotenuse is 20.

What additional information would be necessary to determine sin(A) without using the Pythagorean theorem? Explain.


The length of AC is needed because it is the side adjacent to ∠A.

The length of AC is needed because it is the side opposite ∠A.

The length of BC is needed because it is the side opposite ∠A.

The length of BC is needed because it is the side adjacent to ∠A.

Step-by-step explanation:

RAGL is a rhombus.

[tex] \therefore RA = AG..

(sides\: of\: rhombus) \\

\therefore m\angle ARG = m\angle AGR... (1)[/tex]

(Angles opposite to equal sides are equal)

[tex] In\:\triangle RAG, \\

m\angle ARG +\bold{ m\angle AGR} + {m\angle RAG} = 180°\\

m\angle ARG +\bold {m\angle ARG} + 58° = 180°\\

[From\:equation \: (1)]\\

2m\angle ARG = 180°-58° \\

2m\angle ARG = 122° \\

m\angle ARG =\frac{122°}{2} \\

\huge \red {\boxed {m\angle ARG = 61°}} [/tex]

Hence, option A is the correct answer.

Answer: it will take 9 hours to empty the pool.

Step-by-step explanation:

The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is

30 × 18 × 4 = 2160 ft³

If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as

Tn = a + d(n - 1)

Where

a represents the first term of the sequence(initial amount of water in the pool when completely full).

d represents the common difference(rate at which it is being pumped out)

n represents the number of terms(hours) in the sequence.

From the information given,

a = 2160 degrees

d = - 216 ft3

Tn = 0(the final volume would be zero)

We want to determine the number of terms(hours) for which Tn would be zero. Therefore,

0 = 2160 - 216 (n - 1)

2160 = 216(n - 1) = 216n + 216

216n = 2160 - 216

216n = 1944

n = 1944/216

n = 9

Step-by-step explanation:

Answer: it will take 9 hours to empty the pool. Step-by-step explanation: The pool is shaped like a rectangular prism with length 30 feet, wide 18 ft, and depth 4ft. It means that when the pool is full, its volume is 30 x 18 x 4 = 2160 ft3 If water is pumped out of the pool at a rate of 216ft3 per hour, then the rate at which the water in the pool is decreasing is in arithmetic progression. The formula for determining the nth term of an arithmetic sequence is expressed as Tn = a + d(n - 1) Where a represents the first term of the sequence(initial amount of water in the pool when completely full). d represents the common difference(rate at which it is being pumped out) n represents the number of terms(hours) in the sequence. From the information given, a = 2160 degrees 216 ft3 d = Tn = 0(the final volume would be zero) We want to determine the number of terms(hours) for which Tn would be zero.

We want to determine the number of terms(hours) for which Tn would be zero. Therefore,

O = 2160 - 216 (n - 1) 2160 = 216(n - 1) = 216n + 216 216n = 2160 - 216 216n = 1944 %3D n = 1944/216 n = 9

Answer:

C, 288 square yards

Step-by-step explanation:

The first step is to find the area of the triangular base. [tex]\frac{6\cdot 8}{2}=24[/tex]. Now you can multiply by the length of the prism, 12, to find the volume. 12*24=288, or option C. Hope this helps!

Answer:

b

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation

hope it helps!

Answer:

Yes if [3,5] is a set of integers then it contains elements 3,4,5

As Closed bracket denotes that extreme points are also included and 4 is mid element in between 3 and 5

Answer:

2 and 14?

Step-by-step explanation:

Multiplied together they are 28, but I don't know if that's what you were asking

Answer:

A shirt cost £5 while the hat cost £2.

Step-by-step explanation:

What I did was guess and check until i found the amount of each item. You can also use a table to this.

Answer: If you round it, should be about 5 hours.

The actual distance from Sandpoint to Grangeville would be 248 miles. If Joaquin's mother drives an average of 50 miles per hour, the trip will take almost 5 hours without any stops.

To solve this problem, we need to calculate the actual distance and then the time it will take. As it is mentioned that 1 inch on the map represents 62 miles in reality, if Joaquin measures the distance on the map to be 4 inches, then the actual distance will be 4 inches * 62 miles per inch = 248 miles. Then, if Joaquin's mother drives at a speed of 50 miles per hour, the time it will take to travel that distance can be calculated by dividing the total distance by the speed. So, 248 miles / 50 mph = 4.96 hours. It means that their trip will take almost 5 hours without any stops.

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Answer:

B.

Step-by-step explanation:

Answers A, D, C dont make any sense to me

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Answer: Diameter = 7.06 cm

Step-by-step explanation:

The formula for determining the volume of a cone is expressed as

Volume = 1/3πr²h

Where

h represents the height of the cone

r represents the radius of the cone

π is a constant whose value is 3.14

From the information given

Volume = 157 cubic centimeters

Height = 12cm

Therefore,

157 = 1/3 × 3.14 × r² × 12

157 =12.56r²

r² = 157/12.56

r² = 12.5

Taking square root of both sides of the equation, it becomes

r = √12.5

r = 3.53 cm

Diameter = 2 × radius = 2 × 3.53

Diameter = 7.06 cm

Answer:

    2          |   1 |     3  8

  3 0         |  2 |     5

9  8   2     |  3 |    6

3   3  1       | 4  |     1  5  5  

9  5 2   1   |  5 |     0  3  7  9  

                | 6  |    2  2

Step-by-step explanation:

Answer:

The probability that the customer is charged incorrectly on at least 3 items is 88.11%

Step-by-step explanation:

For each item, there are only two possible outcomes. Either they are charged correctly, or they are not. The probability of an item being charged incorrectly is independent of other items. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

A survey finds customers are charged incorrectly for 4 out of every 10 items.

This means that [tex]p = \frac{4}{10} = 0.4[/tex]

Suppose a customer purchases 11 items.

This means that [tex]n = 11[/tex]

Find the probability that the customer is charged incorrectly on at least 3 items.

Either he is charged incorrectly on less than 3 items, or at least 3. The sum of the probabilities of these events is decimal 1. So

[tex]P(X < 3) + P(X \geq 3) = 1[/tex]

We want [tex]P(X \geq 3)[/tex]. So

[tex]P(X \geq 3) = 1 - P(X < 3)[/tex]

In which

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{11,0}.(0.4)^{0}.(0.6)^{11} = 0.0036[/tex]

[tex]P(X = 1) = C_{11,1}.(0.4)^{1}.(0.6)^{10} = 0.0266[/tex]

[tex]P(X = 2) = C_{11,2}.(0.4)^{2}.(0.6)^{9} = 0.0887[/tex]

[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0036 + 0.0266 + 0.0887 = 0.1189[/tex]

[tex]P(X \geq 3) = 1 - P(X < 3) = 1 - 0.1189 = 0.8811[/tex]

88.11% probability that the customer is charged incorrectly on at least 3 items

Final answer:

To determine the probability that a customer is charged incorrectly on at least three items out of 11, we use the binomial probability formula, summing up probabilities from 3 to 11 incorrect charges.

Explanation:

Probability of Being Charged Incorrectly on At Least 3 Items

To solve the problem of finding the probability that a customer is charged incorrectly on at least three items when they purchase 11 items, we use the binomial probability formula. Given that the probability of being charged incorrectly for one item is 0.4 (4 out of 10), we denote this as p=0.4. The probability of being charged correctly is q=1-p=0.6. The total number of items, n, is 11.

The binomial probability P(X ≥ k) for at least k successes out of n trials is calculated by summing up the probabilities of having k, k+1,..., n successes.

To find P(X ≥ 3) we calculate:

This calculation involves using the binomial formula which is:

P(X=k) = C(n,k) × p^k × q^(n-k)

Where C(n,k) is the combination of n items taken k at a time.

Once each individual probability is calculated, add them up to find the total probability of being charged incorrectly on at least 3 items. Remember, it is not possible to have a probability greater than 1, as this would imply certainty beyond the maximum possible (100%).

Final answer:

The circumference of a circle with a given radius can be calculated using the linear equation C = 6.3r. Two examples of solutions to this equation are C = 12.6 units when r = 2, and C = 31.5 units when r = 5.

Explanation:

The circumference of a circle with a radius of r units is given by the linear equation C = 6.3r. To find two solutions of this function, we can substitute different values for r into the equation.

For example, if we let r = 2, then the circumference C is calculated as C = 6.3 * 2 = 12.6 units.

Another solution is when r = 5. In this case, the circumference C is C = 6.3 * 5 = 31.5 units.

Answer:

None of the given points lies on the circle.

Step-by-step explanation:

The circle is represented by the following formula:

(x - xc)² + (y - yc)² = r²

Where (xc,yc) are the coordinates of the center and r is the radius of the circle. In the case we have:

(x+5)² + (y-9)² = 82

If a point belongs to this circumference, then the results of applying the points to the equation should be valid. To test all the points we are going to apply each to the equation as shown below:

A.

(0 + 5)² + (8-9)² = 82

5² + (-1)² = 82

25 + 1 = 82

26 = 82 (invalid)

The point does not lies on the circle.

B.

(13 + 5)² + (-9-9)² = 82

(18)² + (-18)² = 82

324 + 324 = 82

648 = 82 (invalid)

The point does not lies on the circle.

C.

(-5 + 5)² + (1 - 9)² = 82

0² + (-8)² = 82

64 = 82 (invalid)

The point does not lies on the circle.

D.

(3 + 5)² + (17-9)² = 82

8² + 8² = 82

64 + 64 = 82

128 = 82 (invalid)

The point does not lies on the circle.

Answer:

c

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

the dependent variable is the amount of time she spends driving around.

Final answer:

In the scenario, the independent variable is the amount of gasoline used, and the dependent variable is the distance traveled. The domain is 0 to 2.5 gallons and the range is 0 to 162.5 miles, hence statement 2 is false regarding the dependent variable.

Explanation:

For the given situation, the independent variable is the amount of gasoline she'll use. This is because it is the variable that can be changed freely and does not depend on the other variables in the situation. In contrast, the dependent variable is the distance that can be traveled with the scooter, as it depends on the amount of gasoline used.

The domain for this situation would be the amount of gasoline available for use, which is between 0 gallons (an empty tank) and 2.5 gallons (a full tank). The range would be the distance the scooter can travel on that gasoline, from 0 miles (no gasoline) to 162.5 miles (2.5 gallons at 65 miles per gallon).

Therefore, statement 2 "The dependent variable is how many hours she will spend shopping in the stores" would have to be false given the situation and its parameters, because the dependent variable is actually the distance that can be traveled, not the time spent shopping.

Answer:

1. 70% of 7 = 4.9

2. 30% of 134 =  40.2

3. 100% of 109 =  109

4. 60% of 112 =  67.2

5. 40% of 142 =  56.8

6. 20% of 89 =  17.8

7. 10% of 127 =  12.7

8. 80% of 7 =  5.6

9. 90% of 95 =  85.5

10. 90% of 7 =  6.3

11. 80% of 154 =  123.2

12. 10% of 2 =  0.2

13. 100% of 2 =  2

14. 30% of 76 =  22.8

15. 70% of 43 =  30.1

Step-by-step explanation:

1. I

2. USED

3. GOOGLE

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Answer: the sale price of one hammer is $6.8

the sale price of one nail is $0.16

Step-by-step explanation:

Let x represent the sale price of one hammer.

Let y represent the sale price of one nail.

His first customer bought 3 hammers and 16 nails for $22.96. It means that

3x + 16y = 22.96- - - - - - - - -1

His last customer bought 2 hammers and 20 nails for $16.80. It means that

2x + 20y = 16.8- - - - - - - - - 2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 32y = 45.92

6x + 60y = 50.4

Subtracting, it becomes

- 28y = - 4.48

y = - 4.48/- 28

y = 0.16

Substituting y = 0.16 into equation 2, it becomes

2x + 20 × 0.16 = 16.8

2x + 3.2 = 16.8

2x = 16.8 - 3.2

2x = 13.6

x = 13.6/2

x = 6.8

Answer:

y = 1/4x -8

Step-by-step explanation:

First find the slope of the line

x-4y =3

Subtract x from each side

x-4y -x = -x+3

-4y = -x+3

Divide each side by -4

-4y/-4 = -x/-4 +3/-4

y = 1/4 x -3/4

This is in the form y= mx+b where the slope is m and the y intercept is b

The slope is 1/4

We want the same slope

y = 1/4x +b

we know the y intercept is -8

y = 1/4x -8

Answer:(-4,-9)

Step-by-step explanation:

Final answer:

After rotating the point (4,9) 180° about the origin, the new coordinates would be (-4, -9).

Explanation:

To determine the new coordinates of a point after a 180° rotation about the origin, you can apply the rules of rotation in a coordinate plane.

For a 180° rotation, each coordinate (x, y) becomes (-x, -y).

Therefore, if we rotate the point (4,9) 180° about the origin, we change the sign of both coordinates.

The new point after rotation would be (-4, -9).

Answer: [tex]r=3[/tex]

Simplify both sides of the equation

[tex]r+12/5=27/5[/tex]

Subtract 12/5 from both sides

[tex]r+12/5-12/5=27/5-12/5[/tex]

[tex]r=3[/tex]

The solution to the equation 2 2/5 + r = 5 2/5 is r = 3, which is found by subtracting 2 2/5 (converted to 12/5) from 5 2/5 (converted to 27/5).

The solution to the equation 2 2/5 + r = 5 2/5 is found by isolating the variable r.

First, convert the mixed numbers to improper fractions.

We have 12/5 (equivalent to 2 2/5) and 27/5 (equivalent to 5 2/5).

Now, subtract 12/5 from both sides of the equation to get r on one side:

After subtraction, we find that:

Thus, the solution to the equation is r = 3.

Answer: [tex]x=-3\\y=8[/tex]

Step-by-step explanation:

[tex]3x+y=-1\\2x+3y=18[/tex]

Multiply by -3 the upper equation to make y equal in value but with opposite signs.

[tex](-3)(3x+y=-1)\\-9x-3y=3[/tex]

Now add equation 1 and 2.

[tex]-9x-3y=3\\2x+3y=18[/tex]

--------------------------

[tex]-7x=21[/tex]

Solve for x;

To isolate x, divide by -7

[tex]\frac{-7x}{-7}=\frac{21}{-7}[/tex]

[tex]x=-3[/tex]

Now use one of the equations above and replace the value of x.

[tex]3x+y=-1\\3(-3)+y=-1\\-9+y=-1\\y=-1+9\\y=8[/tex]

To prove if it's correct, take either equation and replace both x and y values, if the results are equal to each other, it is correct.

[tex]2x+3y=18\\2(-3)+3(8)=18\\-6+24=18\\18=18[/tex]

The question keeps telling me to STOP!  Never mind.

The octagon is 8 isosceles triangles.  Each has common side r and base 10.  The central angle is 360/8 = 45°.  By the Law of cosines,

10² = r² + r² - 2 r² cos 45° = 2r²(1 - √2/2) = r²(2-√2)

r² = 100/(2-√2)

The area of a triangle with sides a,b and included angle C is (1/2)ab sin C. Our 8 octagon isosceles triangles each have sides r and r and included angle 45° so our total area, 8 triangles, is

A = 8(1/2) r² sin 45° = (400/(2-√2)) (√2/2) × (2+√2)/(2+√2) = 200(1+√2)

A ≈482.84271

Answer: 482.8 sq cm

Final answer:

To find the area of a regular octagon with a side length of 10 cm, use the formula: Area = 2 * (1 + √2) * side length². Substitute the given side length and round the answer to the nearest tenth.

Explanation:

To find the area of a regular octagon with a side length of 10 cm, we can use the formula:

Area = 2 * (1 + √2) * side length²

Substituting the given side length into the formula:

Area = 2 * (1 + √2) * (10)²

Area = 2 * (1 + √2) * 100

Area ≈ 414.2 cm² (rounded to the nearest tenth)

After further computation, the area approximates 414.2 cm², rounded to the nearest tenth. This formula captures the geometric intricacies of a regular octagon, demonstrating a concise method to calculate its area based on the given side length. This formula encapsulates the unique characteristics of a regular octagon, providing a streamlined approach to computing its area and showcasing the elegant relationship between side length and the polygon's spatial coverage.

Answer:

1

Step-by-step explanation:

9-8=1

since it is on the same y coordinate it doesn't move much

Answer:

5 yeet

Step-by-step explanation:

Answer:

x = 52

y = 38

Step-by-step explanation:

Angle x is supplementary to a 128º angle.

Supplementary angles add to 180

x+128 = 180

Subtract 128 from each side

x+128-128 = 180-128

x =52

Angle x and y are complementary.  

Complementary angles add to 90

x+y =90

52+y =90

Subtract 52 from each side

52-52 +y = 90-52

y = 38

Answer:

x = 52°

y = 38°

Step-by-step explanation:

x = 180 - 128

x = 52

y = 90 - 52 = 38

The total shaded area is four times the area of the inner shaded square. If the side length of the inner square is [tex]\(a\) units, the total shaded area is \(4a^2\)[/tex]square units. This is derived by adding the area of the inner square to the outer shaded region's area.

To find the total area shaded, we need to calculate the combined area of the inner shaded square and the outer shaded region.

Let's denote the side length of the inner square as a units and the side length of the outer square as b units. Since the design consists only of squares, the outer square will have sides twice as long as the inner square, so [tex]\(b = 2a\).[/tex]

The area of the inner shaded square is [tex]\(a^2\)[/tex] square units, and the area of the outer shaded region is the difference between the area of the outer square and the area of the inner square, which is[tex]\(b^2 - a^2\).[/tex]

Substituting [tex]\(b = 2a\), we get the area of the outer shaded region as \((2a)^2 - a^2 = 4a^2 - a^2 = 3a^2\)[/tex] square units.

Therefore, the total shaded area is the sum of the area of the inner square and the area of the outer shaded region: [tex]\(a^2 + 3a^2 = 4a^2\).[/tex]

So, the total area shaded is [tex]\(4a^2\) square units, where \(a\)[/tex] is the side length of the inner shaded square.

complete question

Diane made a design using only squares she shaded the inner square and outer region find the total area that is shaded explain how you found your answer.

The required probability of the selected letter was either an a or an n is 0.5.

Given that,

One letter was selected at random from the words San Antonio.  The probability that the selected letter was either an a or an n is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total letters = 10
Total a and n = 2 and 3
The probability is given as = 2 / 10 + 3 / 10
                                            = 5/10 = 1/2 = 0.5

Thus,  the required probability of the selected letter was either an a or an n is 0.5.

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Answer:

Darnell will do 75 knee lifts

Step-by-step explanation:

in two minutes he did 50. So that means that in one minute he did 25. add 50 and 25 together and you get 75 for your answer

Answer:75 knee lifts

Step-by-step explanation:2 mins       50 knee lifts

                                            1 min          25 knee lifts