Which fraction is less then 1/3 or 1/5

The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

Answer:Any equation that when solved will be y=(number)

Step-by-step explanation:

Well you didn't add any "equations below" so I can't help too much bite you need to solve the equations they listed and the result of the equation must be y=(number), there cannot be any other variable in the equation when simplified if that makes sense. Sorry i can't help more.

To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

How to determine the appropriate graph?

The graphs that complete the question are added as an attachment

From the attached graph, we have the following highlights:

The data points on the y-axis of graph A are in an arithmetic sequence i.e. 30, 60, 90, 120....

The data points on the y-axis of graph B are not in an arithmetic sequence i.e. 60, 20, 40, 80....

The above means that graph B is a misleading graph

Hence, Benjamin should use graph A for his report

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The positive square root of 57.27 is approximately 7.5726, with further decimal places available through iterative approximation methods.

To find the positive square root of the number 57.27, we can use a calculator or mathematical operations.

Taking the square root of a number involves finding a value that, when multiplied by itself, gives the original number. In this case, we want to find the value that, when squared, equals 57.27.

Using a calculator, we can find the square root of 57.27 as approximately 7.5726. However, it's important to note that this is an approximation and may not be completely accurate due to rounding errors.

If we want to find a more precise answer manually, we can use iterative approximation methods. One such method is the Newton-Raphson method, which involves repeatedly refining an initial guess.

Starting with an initial guess of, let's say, 7, we can use the formula:

x(n+1) = (x(n) + (57.27/x(n)))/2,

where x(n) is the current approximation and x(n+1) is the next approximation. Iterating this formula a few times will converge to a more accurate value.

After a few iterations, we find that the positive square root of 57.27 is approximately 7.572615. This value can be further refined by performing more iterations or using more advanced numerical methods.

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Answer:

72.1

Step-by-step explanation:

G(x) =19.60 + 1.75x

Let x = 30

G(30) =19.60 + 1.75*30

          =19.60 +52.5

            72.1

The number of days which it would take 1000 people to sign the petition as required in the task content is; 4.35 days.

It follows from the task content that the number of days which it would take Jan to get 1000 signatures on the petition be determined.

Since it is given in the task content that 230 people sign the petition each day.

It therefore follows from proportion that the number of days needed for 1000 people to sign the petition is;

= 1000/230

= 4.3478 days.

Hence, the number of days which it would take 1000 people to sign the petition is approximately; 4.35 days.

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Answer:

The set D has 5 elements - 3, 6, 9, 12, and 15, all of which are multiples of 3.

Answer:

936

Step-by-step explanation:

1. <C= 90 degree

AC =  13.25 unit

<B= 60 degree

2.  <C= 90 degree

AC =  13.

<B= 60 degree

1. Using Sine law

sin C/4 = sin 30/2 = sin B/ AC

so, sin C/4 = 1/4

sin C = 1

C= 90 degree

and, <B= 180 - 30- 90= 60 degree

So, sin 30/2 = sin 60/ AC

1/4 AC = √3/2

AC = 2√3

2. Using Sine law

sin 30/ 7.65 = sin B / 15.3

1/15.3 = sin B/15.3

sin B= 1

B = 90 degree

and, <C= 180 - 90 - 30 = 60

So, 1/15.3 = sin 60/ C

C = 13.25

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Answer:

3.6 in³

This should be the correct answer, good luck!

Answer:

Step-by-step explanation:

The null and the alternative hypothesis are:

\(\mathbf{ H_o: \rho = 0} \\ \\ \mathbf{H_1: \rho \ne 0}\)

The test statistics is as follows:

\(t = \dfrac{r\sqrt{n-2} }{\sqrt{1-r^2}}\)

\(t = \dfrac{0.4 \sqrt{30-2} }{\sqrt{1-0.4^2}}\)

\(t = \dfrac{0.4 \sqrt{28} }{\sqrt{0.84}}\)

t = 2.3094

The critical value

\(t_{\alpha/df} = t_\ \{0.05/2 \ , \ 30-2 \} } \\ \\ = t_{0.025,28} = \pm 2.048 ( from \ the \ t-tables)\)

Decision rule:

To reject \(H_o\) if t > \(t_{\alpha/df}\).

So since t > \(t_{\alpha/df}\). we reject \(H_o\) at ∝ = 0.05

Conclusion: There is sufficient evidence to conclude that blood pressure and patient calcium are linearly related.

Answer:

12 million

Step-by-step explanation:

Answer:

47400000

Step-by-step explanation:

12 million * 79/20 = 47400000

Answer:

the answer is b, c, d, a, respectively

Answer:

Okay I gotcha one sec

You add all the angles to 180

and solve from there

180 is what a triangle measures up to be

48 + (6x -28) + (2x)= 180

20 + 8x = 180

-20 on both sides

8x = 160

160/8

x=20

In statistics, the risk of making an error is referred to as a significance level. A significance level represents the probability of making a Type I error, which occurs when a null hypothesis is rejected even though it is true.

The most common significance level used in statistical analyses is 0.05 or 5%. This means that there is a 5% chance of rejecting a true null hypothesis.

In general, the choice of significance level depends on the specific application and context of the statistical analysis.

The 5% significance level is commonly used in scientific research, particularly in the fields of medicine and psychology.

The choice of this level is based on a balance between the risk of making a Type I error and the risk of making a Type II error, which occurs when a null hypothesis is not rejected even though it is false.

A Type II error is often more serious than a Type I error since it may lead to incorrect conclusions about the relationship between variables or the effectiveness of a treatment or intervention.

A 5% significance level provides a reasonable balance between these two types of errors. However, in some situations, a higher or lower significance level may be more appropriate.

For example, in a clinical trial where the consequences of a Type II error are severe, a lower significance level may be used to reduce the risk of this type of error.

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Answer:

4s

Step-by-step explanation:

Equate the equations and solve for x:

\(-3x^2 + 24x + 3=-4x^2 + 25x + 15\)

\(\implies x^2 -x -12=0\)

\(\implies x^2 -4x+3x -12=0\)

\(\implies x(x-4)+3(x-4)=0\)

\(\implies (x+3)(x-4)=0\)

\(\implies x=-3, x=4\)

As time is positive, x = 4

The time at which the water balloons collided at their highest point is 7 seconds after the launch.

To find the time at which the two water balloons collided at their highest point, we need to determine the time at which the sum of their heights is maximized. The sum of the heights is represented by the sum of the two quadratic functions.

Given the functions:

y = -3x² + 24x + 3

y = -4x² + 25x + 15

The sum of the heights, S(x), is:

S(x) = (-3x² + 24x + 3) + (-4x² + 25x + 15)

Combine like terms:

S(x) = -7x² + 49x + 18

To find the time when the sum of the heights is maximized, we need to find the x-coordinate of the vertex of the parabolic function S(x). The x-coordinate of the vertex of a quadratic function in the form ax² + bx + c is given by:

x vertex = -b / (2a)

In this case, for S(x) = -7x² + 49x + 18:

a = -7

b = 49

Calculate the x-coordinate of the vertex:

x vertex = -49 / (2 * -7)

x vertex = 7

Now that we have the x-coordinate of the vertex, we can find the corresponding time by plugging it into either of the original functions. Let's use the first function for simplicity:

y = -3x² + 24x + 3

When x = 7:

y = -3(7)² + 24(7) + 3

y = -147 + 168 + 3

y = 24

Therefore, the time at which the water balloons collided at their highest point is 7 seconds after the launch.

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Answer:

Hello There. ☆~\---___`:•€`___---/~☆ The correct answer is C. Both (1,3) and (-2,-4).

To check whether (-2,-4) is a solution of the equation let's substitute x= -2 and y= -4 into the equation:

-7x+3y=2

-7*(-2)+3*(-4)=2

14-12=2

2=2

Do the same thing with (1,3)

-7x + 3y = 2

-7 * 1 + 3 * 3 = 2

-7 + 9 = 2

2 = 2.

Hope It Helps!~ ♡

ItsNobody~ ☆

Answer:

HUH

Step-by-step explanation:

Question 1.

Given the solution in set notation:

Here, the solution is all real numbers.

Hence, we have:

Inequality notation:

Thus, we have:

• Inequality: -∞ < x < ∞

• Interval notation: (-∞, ∞)

ANSWER:

• Inequality: -∞ < x < ∞

• Interval notation: (-∞, ∞)

Answer:

-1

Step-by-step explanation:

I solved it the way one-variable equations are solved.

Answer:

-1 is ur answer

Step-by-step explanation:

Answer:  (NO)

1.43,

0.46,

2/3,

-0.09,

1.43,

0.09,

-1/4,

0.02​

Step-by-step explanation:

Probability is a number between 0-1.

The graph of g(x) will have the same shape as f(x) = |x|, but it will be shifted 12 units to the right and 9 units down.The fomula is g(x) = |x - 12| - 9

To obtain the function g(x) by shifting the graph of f(x) = |x| down 9 units and to the right 12 units, we can use the following formula:

g(x) = |x - 12| - 9.Let's break down the formula:

|x - 12| represents the absolute value function shifted 12 units to the right. This shift ensures that any point (x, y) on the original graph f(x) is now located at (x - 12, y) on the new graph.

Subtracting 9 from |x - 12| shifts the entire graph 9 units down, resulting in the desired vertical shift.

By combining these two operations, we obtain the formula g(x) = |x - 12| - 9, which represents the function obtained after the specified shifts.

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Answer:

35

Step-by-step explanation:

23,125/185= 125

125-90 = 35

$35 less amount  school district pay in salary by paying a substitute teacher instead of paying Mrs. Cook for that day

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:

Mrs. Cook is a teacher whose salary is $23,125 for a 185-day school year.

Mrs. Cook per day salary= 23125/ 185 = $125

Now,  substitute teachers are paid at a rate of $90 per day.

So, if  substitute teachers take class instead of Mrs. Cook, then school will pay

= 125-90

=$35 less amount.

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