A triangle has a side that is 5 inches long that is adjacent to an angle of 61. In addition, the side oppositethe 61 angle is 4,8 inches long. There are two triangles with these measurements. For each one,determine the other two angles of the triangle and the length of the third side..acute:(a) The triangle in which the angle opposite the 5-inch side-The angle between the two given sides measuresnearest tenth of a degree.)The third angle measuresThe remaining side is approximatelyan inch.)(b) The triangle in which the angle opposite the 5-inch side is obtuse:The angle between the two given sides measuresnearest tenth of andegree.)WThe third angle measuresThe remaining side is approximatelyan inch.)degrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)Ainches long. (Round to the nearest tenth ofdegrees. (Round to thedegrees. (Round to the nearest tenth of a degree.)inches long. (Round to the nearest tenth of an inch

Answer:

(c) is correct.

Step-by-step explanation:

(c) 9 + 2(4) = 9 + 8 = 17

Answer:

160 / 5 = 32 miles

Step-by-step explanation:

Step-by-step explanation:

First, we need to find out the total number of people who will be attending the party.

There are 23 guests, plus 7 family members, so there are 23 + 7 = 30 people attending.

Each person will get 2 cupcakes, so:

30 * 2 = 60 cupcakes

Therefore, Mom likely needs to make 60 cupcakes.

60

Step-by-step explanation:

first 23+7=30

each needs=2

so take 30×2=60

Answer:

I think the first quartile is 30

Step-by-step explanation:

To find the quartiles you would look at the end points of the box.

Answer:

number of apples he originally had in each bag was 14 apples

Step-by-step explanation:

We are told that he had 3 bags of apples.

Now, let amount of apples in one bag be x.

Thus, total amount of apples is 3x.

We are told he gave 2 apples to his best friend, he gave 3 to his brother, and he fed 1 to his horse.

This means total given out = 2 + 3 + 1 = 6 apples.

Then, on the way home, he was chased by some dogs and dropped 1 bag.

Thus, amount of apples dropped is 1x = x

Thus;

Amount left on getting home after the entire giving and dropping is;

3x - 6 - x = 2x - 6

Now,we are told that he had 22 apples left when he got home.

Thus;

2x - 6 = 22

2x = 22 + 6

2x = 28

x = 28/2

x = 14 apples

Thus, number of apples he originally had in each bag was 14 apples

Answer:

Linear pair angle of 136 degree =180-136

=44

Therefore angle y is alternate angle of 44

Therefore angle y=44

Answer:

44

Step-by-step explanation:

180 - 136 = 44

(A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.

An angle is formed when two straight lines or rays meet at a single terminal.

The place where two points converge is known as an angle's vertex. The name "angle" comes from the Latin word "angulus," which means "corner."

Two lines that meet at the same point or two planes that meet at the same line form a geometric figure.

The angle in degrees separates these lines or planes.

So, we know that:

The side opposite to the largest angle is also the largest side of the triangle and vica-versa.

Remembering this we can easily conclude that ∠X is the largest angle as the largest is 9 units and X is opposite of the side YZ which measures 9 units.

Therefore, (A) ∠X is the largest angle in the given triangle as the side opposite is also the largest.

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Correct question:

Which angle in AXYZ has the largest measure?

A. ∠X

B. ∠Y

C. ​∠Z

D. Cannot be determined

The theta notation for the expression n+2 (n+1)(n+3) is Θ(\(n^3\)).

Here's how we determine the theta notation:

1. Simplify the expression:

  n+2 (n+1)(n+3) = n(n+1)(n+3) + 2(n+1)(n+3)

                 = \(n^3 + 4n^2\) + 5n + 6n + 6

                 = \(n^3 + 4n^2\) + 11n + 6

2. Identify the highest order term: The highest order term in this expression is\(n^3\).

3. Remove any lower order terms and coefficients: We ignore all lower order terms and coefficients.

4. Apply the theta notation: Since the highest order term is \(n^3,\) we can express the expression as Θ(\(n^3\)).

The theta notation for the expression n+2 (n+1)(n+3) is Θ(\(n^3\)).

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The trigonometric ratios of angle C are sin C = 15/17, cos C = 8/17, and tan C = 15/8.

Since triangle ABC is a right triangle with a right angle at B, and we know AC = 17 units (hypotenuse) and BC = 8 units (adjacent side to angle C), we can use the Pythagorean theorem to find the length of the remaining side, AB (opposite side to angle C).

The Pythagorean theorem states: AB² + BC² = AC²

Plugging in the values we know:
AB² + 8² = 17²
AB² + 64 = 289

To find AB:
AB² = 289 - 64 = 225
AB = √225 = 15 units

Now we can determine the trigonometric ratios of angle C:

1. sine (sin C) = opposite/hypotenuse = AB/AC = 15/17
2. cosine (cos C) = adjacent/hypotenuse = BC/AC = 8/17
3. tangent (tan C) = opposite/adjacent = AB/BC = 15/8

So the trigonometric ratios of angle C are:
sin C = 15/17, cos C = 8/17, and tan C = 15/8.

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Answer:

c and d

Step-by-step explanation:

when cut in half, both shapes are the same

Calvin's investment need to be increased by a factor of 115.9% to equal Marquez's investment at any time after Calvin's investment is made.

An exponential function is in the form:

y = abˣ

Where a is the initial value of y and b is the multiplication factor.

Let v represent the value of the account after y years. Hence:

For Juana:

\(v=1500(1.03)^y\)

Marquez invests three years before Juana,  Hence:

\(v'=1500(1.03)^{y+3}=1500(1.03)^y(1.03)^3=(1.03)^3*v=1.092727v\)

Calvin invests two years after Juana. Hence:

\(v"=1500(1.03)^{y-2}=1500(1.03)^y*(1.03)^{-2}=(1.03)^{-2}v\)

v' / v" = ((1.03)³ * v) / ((1.02⁻²) * v) = 1.159 = 115.9%

Calvin's investment need to be increased by a factor of 115.9% to equal Marquez's investment at any time after Calvin's investment is made.

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the coordinates of point c is (9/2, -3/2)

The original coordinate = C(6, -2)

scale factor r =3/4

New coordinate (c) = scale factor × the original coordinate

c = 3/4(6, -2)

c = (3/4×6, -2×3/4)

c = (18/4, -6/4)

c = (9/2, -3/2)

Hence, the coordinates of point c is (9/2, -3/2)

At least 11 students must take the quiz to assure that at least two have exactly the same answers to all five questions.

Determining the minimum number of students required to guarantee that at least two students have the same answers to all five questions on a multiple choice quiz. Under the area of probability and combinatorics.

There are 4 possible answers for each of the 5 questions, so there are a total of \(4^5 = 1024\) possible sets of answers.

Let's consider the opposite scenario where no two students have exactly the same answers to all five questions. In this case, the first student can choose any of the 1024 possible sets of answers. The second student must choose a different set of answers from the first student, so there are 1023 possible sets of answers for the second student. Similarly, the third student must choose a different set of answers from the first two students, so there are 1022 possible sets of answers for the third student. Continuing in this way, the nth student has 1025-n possible sets of answers to choose from.

Therefore, the total number of possible sets of answers for n students is the product of the number of possible sets of answers for each student:

1024 × 1023 × 1022 × ... × (1025-n)

We want to find the minimum value of n such that this product is less than 1024, because that is the maximum number of sets of answers possible. That is, we want to solve the inequality:

1024 × 1023 × 1022 × ... × (1025-n) < 1024

To simplify this expression, notice that each term in the product is very close to 1024, which suggests that we can approximate the product as \(1024^n\). This approximation is valid when n is much smaller than 1024, which is the case here.

Using this approximation, we can rewrite the inequality as:

\(1024^n\)< 1024

Taking the logarithm base 2 of both sides, we get:

n < log2(1024) = 10

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The calculated correlation coefficient (r) is approximately -0.291.

To calculate the correlation coefficient between telomere length and chronicity, we can utilize the given summary data. The correlation coefficient, often denoted as r, measures the strength and direction of the linear relationship between two variables.

Let's denote the sum of products as Σxy, the sum of squares for chronicity as Σx², the sum of squares for telomere length as Σy², and the total sample size as n.

From the given data, we have the following values:

Σxy = -8.822

Σx² = 318.817

Σy² = 2.868

n = 38

The correlation coefficient (r) can be calculated using the following formula:

r = Σxy / √(Σx² * Σy²)

Substituting the given values into the formula:

r = -8.822 / √(318.817 * 2.868)

Now, let's solve this equation step by step:

First, multiply the values inside the square root:

r = -8.822 / √(913.350956)

Next, calculate the square root:

r = -8.822 / 30.219307

Finally, divide Σxy by the square root of the product of Σx² and Σy²:

r ≈ -0.291

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Answer:

amar makes 8 dollars per hour

Step-by-step explanation:

to find the number of hours of work amar does you have to divide the total amount earned by the number of hours worked

64/8 = 8

every hour amar makes 8 dollars, $8 x 8 hours = $64

Answer:

D

I believe the second one is none of the above

Step-by-step explanation:

61-27

Answer:

34 degrees.

Step-by-step explanation:

m<AOC - m<BOC = <AOB = 61 - 27 = 34

for the second one i think it's none.

The graph shows the relationship between the number of students who attend a homecoming dance and the amount of money raised. The graph is a straight line with a slope of $10, passing through the point (0, $80) and another point on the line. The fixed cost for decorations is $80, which is a constant cost that does not depend on the number of students attending the dance. For each additional student that attends the dance, the amount of money raised will increase by $10.

Answer:

y = 10x - 80

Therefore your answer is B, hope this helps! :)

To calculate the cost price of each 500g bag, we need to consider the following steps: Step 1: Determine the number of 500g bags that can be made from a 10kg bag of potatoes.

10kg is equivalent to 10,000g, and since each smaller bag weighs 500g, we divide 10,000g by 500g: 10,000g ÷ 500g = 20.So, 20 bags of 500g can be made from the 10kg bag. Step 2: Calculate the cost price of each 500g bag. To find the cost price of each bag, we divide the total cost of the 10kg bag by the number of smaller bags: R62.00 ÷ 20 = R3.10. Therefore, the cost price of each 500g bag would be R3.10.

This means that Sameer would need to sell each 500g bag for more than R3.10 in order to make a profit. The selling price would depend on factors such as overhead costs, desired profit margin, and market demand.

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Answer:

h

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

If each side of tangle is increased by 25 %, then find the percentage increase or decrease in area

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

-30

Step-by-step explanation:

The product of M x N is {4a + 8b + 12c}.

Given are the matrices as -

M = {a, b, c} and N = {4, 8, 12}

We can write the product as -

M x N = {4a + 8b + 12c}

Therefore, the product of M x N is {4a + 8b + 12c}.

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{

Question in english -

Establishes the cartesian product; represents in sagittal diagram and cartesian plane M={a, b, c} N={4,8,12}

}

W is the set of all vectors in R3 with nonnegative components.

W is not a subspace of the vector space R3.

To verify that W is not a subspace of the vector space R3, we will check if it satisfies the conditions from Theorem 4.5. The theorem states that a set W is a subspace if:

1. The zero vector is in W.
2. If u and v are elements of W, then u+v is in W (closed under addition).
3. If u is an element of W and c is a scalar, then cu is in W (closed under scalar multiplication).

W is the set of all vectors in R3 with nonnegative components. Let's examine each condition:

1. The zero vector (0, 0, 0) is in W because its components are nonnegative.

Now, let's check if W is closed under addition and scalar multiplication. We will do this by providing a specific example that violates either condition 2 or 3:

2. Consider the vectors u = (1, 0, 0) and v = (0, 1, 0), both of which are in W. However, if we add them, we get u+v = (1, 1, 0), which is still in W.

3. Let's use vector u = (1, 0, 0) again, and let c = -1 be our scalar. Now, if we multiply u by c, we get cu = (-1, 0, 0). This result is not in W, as the first component is negative.

Since the third condition is violated, we can conclude that W is not a subspace of the vector space R3.

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The values of the unknown variables in the given figure are :

a = 20, b = 140°, x = 120° and y = 60°.

Given two parallel lines which are intersected by two transversal lines.

Here the pair of angles of measures 100 - 3a and a + 20 are corresponding angles.

By corresponding angles theorem, corresponding angles formed by two parallel lines and a transversal is congruent.

So,

100 - 3a = a + 20

-4a = -80

a = 20

So, a + 20 = 20 + 20 = 40°

Now, b and a + 20 are linear pair of angles and are thus supplementary.

b + a + 20 = 180

b = 180 - 40 = 140°

Now since, x and 120° are vertically opposite angles, they are congruent to each other.

So, x = 120°

Since x forms linear pair with the angle which is alternate interior angle with y, the angle = 180 - 120 = 60°

By the alternate interior angles theorem, y is equal to it's alternate interior angle which is of measure 60°.

So, y = 60°

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Step-by-step explanation:

If son present age is x then

father present age=4x+4

so the equation is

(4x+4)-x=28

3x=24

x=8

Let S = Sum after 13 years

     So = amount invested

     t = time in years

     i = annual interest rate = .0325

The S = So(1+i)t = $2,200(1.0325)13 = $3,334.21

The average productivity of the workforce, A(x), is given by

A(x) = p(x)/x,

where p(x) is the total value of the production when there are x workers in the plant.

A'(x) is the derivative of A(x) with respect to x.

A'(x) = (p(x)/x)' = (p'(x)x - p(x))/x^2.

The company wants to hire more workers if A'(x) > 0 because it means that the average productivity of the workforce is increasing with additional workers.

A'(x) > 0 if p'(x) is greater than the average productivity, which is p(x)/x.

Therefore, A'(x) > 0 if p'(x) > p(x)/x.
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Answer: lol why so expensive.