LN and OQ are parallel lines.Which angles are supplementary angles?

Answer:

129, because you split the shape into two find the area of them separately and then add them up

Solution :

Given :

The sample mean = 21.3

Standard deviation = 3.2

The null hypothesis is : \(H_0: \mu =20\)

The alternate hypothesis : \(H_a:\mu \neq20\)

This is a two tailed test, for which a \(\text{t-test for one mean}\) with an unknown population of a standard deviation is being used.

Now the significance level, \(\alpha = 0.1\), as well as the critical value for a two tailed test is \(t_c = 1.833\)

The rejection region is \(R = \{ t:|t| > 1.833 \}\)

The t-statistic is computed as follows :

\(t=\frac{\overline x - \mu_0}{s/ \sqrt n}\)

\(t=\frac{21.3-20}{3.2/ \sqrt{10}}\)

 = 1.285

Since it is observed that \(|t| = 1.285 \leq t_c=1.833\), it is then concluded that  \(\text{the null hypothesis is not rejected.}\)

The p-value is p=0.231 and since p 0.231 ≥ 0.1, it is concluded that \(\text{the null hypothesis is not rejected.}\)

Conclusion

Thus we concluded that \(\text{null hypothesis}\) \(H_0\) is not rejected. Therefore, the population mean \(\mu\) is different than 20, at the 0.1 significance level.

7 is not included and hence it is depicted on the number line using an open dot. Hence, solution to the inequality is option B.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign (≠)" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

The given inequality is:

x + 8 > 15

Subtracting 8 on both sides of the equation:

x + 8 - 8 > 15 - 8

x > 7

Here, 7 is not included and hence it is depicted using an open dot.

Hence, option B is the correct answer.

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None of the chosen pairs will be dependent as nothing is specified.

Independent events are those events whose occurrence does not have any effect on the events that may occur or occurred.

Dependent events are those vents whose occurrence either depends on some other event or has an effect on occurring or occurred vents.

Given, The top shelf of a bookcase holds 6 fiction and 4 nonfiction books. On the bottom shelf are 3 fiction and 5 nonfiction books.

As not mentioned that what kind of book he chooses first or types of book.

Also which shelf he chooses first choosing the first book is independent

and choosing the second book is also independent so none of the chosen pair will be dependent.

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Answer:

y+3=3/2(x-6)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-3)=3/2(x-6)

y+3=3/2(x-6)

Answer:

There are no solutions.

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

4x/5+2/3+1x/5=x

4/5x+2/3+1/5x=x

(4/5x+1/5x)+(2/3)=x(Combine Like Terms)

x+23=x

x+23=x

Step 2: Subtract x from both sides.

x+2/3−x=x−x

2/3=0

Step 3: Subtract 2/3 from both sides.

2/3−2/3=0−2/3

0=−2/3

Answer:

There are no solutions.

Let f(x) = lnx and g(x) = log₂x. for all 0 < x < 1, f(x) < g(x): True.

In this scenario and exercise, we would determine the corresponding output value for the functions f(x) and g(x) under the given mathematical operation and independent variables.

When x = 1, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(1) = ln(1).

f(1) = 0.

When x = 2, the output value for f(x) based on the table of values is given by;

f(x) = lnx

f(2) = ln(2).

f(2) = 0.69314718

When x = 1, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(1) = log₂(1)

g(1) = 0.

When x = 2, the output value for g(x) based on the table of values is given by;

g(x) = log₂x

g(2) = log₂(2)

g(2) = 1.

In this context, we can logically deduce that the function f(x) is less than function g(x) for all 0 < x < 1.

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Answer:

Step-by-step explanation:

inorder to solve the area of the shaded area;°/360ñRsquared

arc length you use ;°/360ñD

Answer:

5cm^3

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

Answer:

A ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.

Step-by-step explanation:

Let's use variables to represent the cost of each dinner. Let's say that the cost of a ribeye steak dinner is "r" and the cost of a grilled salmon dinner is "s".

From the first day's sales, we know:

From the second day's sales, we know:

We now have two equations with two variables, which we can solve using elimination or substitution.

Let's use elimination. If we multiply the first equation by 15 and the second equation by 11, we can eliminate the "r" variable:

Subtracting the second equation from the first, we get:

Dividing both sides by 133, we get:

So a grilled salmon dinner costs $14.04.

We can substitute this value back into one of the original equations to solve for "r". Let's use the first equation:

So a ribeye steak dinner costs $32.23.

Therefore, a ribeye steak dinner costs $32.23 and a grilled salmon dinner costs $14.04.

what is the value of b -a if a=18, b=27,and c= 11​

we have

(b-a)

so

For a=18 and b=27

substitutte in the given expression

(27-18)=9

therefore

The sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

To prove that m∠D + m∠F = 180∘, we can use the property of angles inscribed in a circle.

In a circle, an inscribed angle is equal to half the measure of its intercepted arc. Therefore, if we can show that arc DE + arc FG = 360∘, we can conclude that m∠D + m∠F = 180∘.

Let's start the proof:

1. Quadrilateral DEFG is inscribed in circle P. This means that all the vertices of the quadrilateral lie on the circumference of the circle.

2. Let's consider arc DE and arc FG. These arcs are intercepted by angles ∠D and ∠F, respectively.

3. By the property of angles inscribed in a circle, we know that the measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. Therefore, m∠D = 1/2(arc DE) and m∠F = 1/2(arc FG).

5. We want to prove that m∠D + m∠F = 180∘. This is equivalent to showing that 1/2(arc DE) + 1/2(arc FG) = 180∘.

6. Combining the fractions, we have 1/2(arc DE + arc FG) = 180∘.

7. Now, we need to show that arc DE + arc FG = 360∘.

8. Since quadrilateral DEFG is inscribed in circle P, the sum of the measures of all the arcs intercepted by the sides of the quadrilateral is equal to 360∘.

9. This means that arc DE + arc EF + arc FG + arc GD = 360∘.

10. However, we can observe that arc EF and arc GD are opposite sides of the same chord, so they have equal measures. Therefore, arc EF = arc GD.

11. Substituting arc GD with arc EF in the equation from step 9, we have arc DE + arc EF + arc FG + arc EF = 360∘.

12. Simplifying the equation, we get 2(arc DE + arc EF + arc FG) = 360∘.

13. Dividing both sides by 2, we have arc DE + arc EF + arc FG = 180∘.

14. Comparing this result with step 7, we can conclude that arc DE + arc FG = 180∘.

15. Finally, going back to our initial goal, we can now substitute arc DE + arc FG with 180∘ in the equation from step 6: 1/2(180∘) = 180∘.

16. Simplifying, we have 90∘ = 180∘, which is a true statement.

17. Therefore, we have proven that m∠D + m∠F = 180∘.

Thus, we have successfully proved that the sum of angles ∠D and ∠F in quadrilateral DEFG, inscribed in circle P, is equal to 180∘.

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Answer:

Step-by-step explanation:

RSB is a right angle

12. RSB is 90 degrees

13. A right angle is 90 degrees

H is between P and S

14. PS + PH = HS

15. Deductive Reasoning

The value of x in the interval 0 ≤x≤ pi is 2.083 so the graph f and g have parallel tangent lines

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation.  The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x) = tan x

and, g(x) = x²

Now, f(x) = t g(x)

and, g(x) = x²

On differentiating f(x) we get

f'(x) = t g²(x) + 1

and, g(x) = 2x

Now, the parallel tangent line

f' (x) = g'(x)

t g²(x) + 1 = 2x

since the interval for x is 0 ≤x≤ pi.

So, the value of x = 2.083

Hence, the value of x is 2.083.

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Answer:

4\(y^{\frac{3}{2} }\)

Step-by-step explanation:

using the rule of exponents/ radicals

\(\sqrt[n]{a^{m} }\) = \(a^{\frac{m}{n} }\)

then

4 \(\sqrt{y^{3} }\)

= 4\(y^{\frac{3}{2} }\)

Answer:

C. All real numbers

Answer:

Step-by-step explanation:

3244314 x 2 = 6,488,628

6,488,628 + 3242 = 6,491,870

The multiplication of 232 x 5 = 1,160

9514 1404 393

Answer:

Step-by-step explanation:

The sum of torques about the pivot point is zero when the system is in equilibrium. That means the total of clockwise torques is equal to the total of counterclockwise torques. For this purpose, torque can be modeled by the product of mass and its distance from the pivot. The uniform beam can be modeled as a point mass at its center.

__

a) Let E represent the location of the center of mass of the beam. So, AE = 1.5 m. Then the distance from C to E is AC-AE = AC -1.5 and the CCW torque due to the beam's mass is (16 kg)(AC -1.5 m).

The distance from B to C is 3 m - AC, so the CW torque due to the particle at B is (7 kg)(3 -AC m)

These are equal, so we have ...

  16(AC -1.5) = 7(3 -AC)

  16AC -24 = 21 -7AC . . . . . eliminate parentheses

  23AC = 45 . . . . . . . . . . . add 7AC+24

  AC = 45/23 ≈ 1.957 . . divide by the coefficient of AC

  AC ≈ 2.0 meters . . . . rounded to 1 dp

__

b) The torques in this scenario are ...

  M(0.7) = 16(0.8) +7(2.3) . . . . . . AD = 0.7 m, DE = 0.8 m, DB = 2.3 m

  M = 28.9/0.7 ≈ 41.286 . . . . simplify, divide by the coefficient of M

  M = 41.3 kg . . . . rounded to 1 dp

_____

Additional comment

Torque is actually the product of force and distance from the pivot. Here, the forces are all downward, and due to the acceleration of gravity. The gravitational constant multiplies each mass, so there is no harm in dividing the equation by that constant, leaving the sum of products of mass and distance.

Answer:

Multiply 2/3 by 4 to make it have the same denominator.

Step-by-step explanation:

This could work for all fractions, you just need to get them to have the same denominator.

Ps. If you were wondering, they are equivalent.

Answer:

Only 60 is an identified outlier

Step-by-step explanation:

Given

Age group: 40 to 50

\(Min = 60\)           \(Q_1 = 70\)           \(Median= 73\)

\(Q_3 = 76\)              \(Max = 85\)

Conditions for outlier

\(Value > Q_3 + 1.5 * IQR\)

\(Value < Q_1 - 1.5 * IQR\)

See attachment for complete question

Required

Which of 60, 62 and 84 is an outlier of age grout 40 to 50 years

First, calculate the IQR of group 40 to 50.

This is calculated as:

\(IQR = Q_3 - Q_1\)

Where:

\(Q_3 = 76\) and \(Q_1 = 70\)

So:

\(IQR = 76 - 70\)

\(IQR = 6\)

Next, is to test the outlier conditions on each value (i.e. 60, 62 and 84)

Testing 60

Condition 1

\(Value > Q_3 + 1.5 * IQR\)

\(60 > 76 + 1.5 * 6\)

\(60 > 76 + 9\)

\(60 > 85\) --- False

Condition 2

\(Value < Q_1 - 1.5 * IQR\)

\(60 < 70 - 1.5 * 6\)

\(60 < 70 - 9\)

\(60 < 61\) --- True

Because one of the conditions is true, then 60 is an outlier of group 40 - 50 years

Testing 62

Condition 1

\(Value > Q_3 + 1.5 * IQR\)

\(62> 76 + 1.5 * 6\)

\(62 > 76 + 9\)

\(62 > 85\) --- False

Condition 2

\(Value < Q_1 - 1.5 * IQR\)

\(62 < 70 - 1.5 * 6\)

\(62 < 70 - 9\)

\(62 < 61\) --- False

Because both conditions are false, then 62 is  not an outlier of group 40 - 50 years

Testing 84

Condition 1

\(Value > Q_3 + 1.5 * IQR\)

\(84> 76 + 1.5 * 6\)

\(84 > 76 + 9\)

\(84 > 85\) --- False

Condition 2

\(Value < Q_1 - 1.5 * IQR\)

\(84 < 70 - 1.5 * 6\)

\(84 < 70 - 9\)

\(84 < 61\) --- False

Because both conditions are false, then 84 is  not an outlier of group 40 - 50 years

Answer:

A. 3/12

Step-by-step explanation:

1/4 x 3 for the three different bags and each bag having 1 crayon that's the color green it's 1/4 however due to there being 4 crayons in each bag

the only other answer could be 1/4 when simplified

Answer:

Step-by-step explanation:

1 bag of crayons = 4 crayons = 100% (10/10)

1/4 bag of crayons = 1 crayon = 25% = 1 green crayon per bag

3 bags of crayons = 12 crayons (3 x 4)

if 1 bag has 1 green crayon and there are 3 bags then there are 3 green crayons

A. 3/12

EXPLANATION

Drawing given set data ni a graph, will give us:

As we can see in graph, this is a proportional relationship given by a straight line.

Answer:

167.6190 approximately 167.62 inches

Step-by-step explanation:

formula for surface area of a cone is 1/3πr×r×slant height. How this helps.

Answer:

it will be 12f

Step-by-step explanation:

since you told the wrong question

Encontrando un factor comun entre los 3 números dados, concluimos que cada pedazo de tronco debe medir 3 metros, y se obtendran 10 pedazos en total.

Sabemos que los troncos miden 15, 9, y 6 metros, si los queremos cortar en pedazos de igual longitud, de tal forma que nada se desperdicie, entonces debemos encontrar un factor comun entre esos 3 numeros.

Los podemos reescribir como:

15 = 3*5

9 = 3*3

6 = 2*3

Entonces el unico factor comun entre las 3 longitudes es 3.

El tronco de 15 metros dará:

15/3 = 5 pedazos de tronco.

El tronco de 9 metros dará:

9/3 = 3 pedazos de tronco.

El tronco de 6 metros dará:

6/3 = 2 pedazos de tronco.

Sumando eso obtenemos 5 + 3 + 2 = 10 pedazos en total.

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The side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

To order the side lengths IK, KL, IJ, IL, and LJ from least to greatest, we can analyze the given figure.

Since the figure is not drawn to scale, we cannot determine the exact lengths of the sides. However, we can make some observations based on the given angles.

Let's analyze the angles:

Angle L: Since angle L is marked as 47°, we know that side KL is the shortest side, as it is opposite to the smallest angle in a triangle.

Angle I: Since angle I is marked as 20°, we can infer that side IJ is longer than side IK, as it is opposite to a larger angle.

Angle LJ: Since angle LJ is marked as 89°, we can conclude that side LJ is the longest side, as it is opposite to the largest angle in the triangle.

Based on these observations, we can order the side lengths from least to greatest as follows:

IK < KL < IJ < IL < LJ

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