The length of one leg of a right triangle is 2 times the length of the other, and the
length of the hypotenuse is 12. What is the length of the longest leg?

Answer:

That's Thomas the Train, but someone edited him with glowing red eyes

Step-by-step explanation:

The value of z-stat is -0.6721.

What is z stat?

The relationship between a value and the mean of a group of values is quantified by a Z-stat. The Z-stat is calculated using standard deviations from the mean. When a data point's Z-stat is 0, it means that it has the same score as the mean.

One standard deviation from the mean would be indicated by a Z-stat of 1.0. Z-stats can be positive or negative; a positive value means the score is above the mean, while a negative value means it is below the mean.

Solution Explained:

We use the formula,

\(z = \frac{P - \pi }{\sqrt{\frac{\pi (1-\pi )}{200} }}\), where P is the observed proportion, π is the hypothesized proportion

Therefore, P = 42/200 = 0.21 & π = 23/100 = 0.23

Putting the values in

\(z = \frac{0.21 - 0.23 }{\sqrt{\frac{0.23 (1-0.23)}{200} }}\)

After calculating, z-stat is therefore equal to -0.6721

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If 5 wholes are divided into pieces that are each \($\frac{1}{4}$\) start fraction, 1, divided by, 4, end fraction of a whole, there are 20 pieces.

In mathematics, a fraction represents a part of a whole or a collection of equal parts. It is a way of representing a number as a ratio of two integers, where the top number is called the numerator and the bottom number is called the denominator.

If 5 wholes are divided into pieces that are each \($\frac{1}{4}$\) of a whole, we can find the total number of pieces by multiplying the number of pieces in one whole by the number of wholes:

Number of pieces in one whole=

\($\frac{1}{\frac{1}{4}} = 4$\)

Number of pieces in 5 wholes = 5 x 4 = 20

Therefore, there are 20 pieces.

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Answer:

y <  \(\frac{1}{3}\) x - 2

Step-by-step explanation:

Slope of the line m = \(\frac{-4+1}{-6-3}\) = \(\frac{1}{3}\)

y + 1 = \(\frac{1}{3}\) (x - 3)

y = \(\frac{1}{3}\) x - 2

Points (9, 1) and (- 4, 7) are not solutions, then

1 < \(\frac{1}{3}\) (9) - 2

7 < \(\frac{1}{3}\) (- 4) - 2

Thus, the inequality is y <  \(\frac{1}{3}\) x - 2  

The tensions in each side of the rope will be the same when Nellie Newton hangs at rest in the middle of a clothesline and the lengths of each rope are the same.

When Nellie Newton is in equilibrium, meaning she is at rest and not experiencing any acceleration or movement, the forces acting on her must be balanced. In the case of a clothesline, the tension in each side of the rope contributes to the balancing of forces.

For the tensions to be the same in each side of the rope, the lengths of the ropes must also be the same. This ensures that the forces applied to each side are equal and balanced, resulting in Nellie Newton remaining in a stable position without any net force acting on her.


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The value of the definite integral \(\int [0, 1] x\sqrt{(1 - x^2)} dx\) is 1. Rounded to three decimal places, the answer is 1.000. The integral is a mathematical operation that finds the area under a curve or function.

For the definite integral \(\int [0, 1] x\sqrt{(1 - x^2)} dx\), we can use the substitution u = 1 - x².

First,
du/dx: du/dx = -2x.

Rearranging, we get dx = -du / (2x).

When x = 0, u = 1 - (0)² = 1.

When x = 1, u = 1 - (1)² = 0.

Now we can rewrite the integral in terms of u:

\(\int\)[0, 1] x√(1 - x²) dx = -\(\int\)[1, 0] (√u)(-du / (2x)).

Since x = √(1 - u), the integral becomes:

-\(\int\)[1, 0] (√u)(-du / (2√(1 - u))) = 1/2 \(\int\)[0, 1] √u / √(1 - u) du.

Next, we can simplify the integral:

1/2 \(\int\) [0, 1] √u / √(1 - u) du = 1/2 \(\int\)[0, 1] √(u / (1 - u)) du.

While evaluating this integral, we can use the trigonometric substitution u = sin²θ:

du = 2sinθcosθ dθ,

√(u / (1 - u)) = √(sin²θ / cos²θ) = tanθ.

When u = 0, θ = 0.

When u = 1, θ = π/2.

The integral becomes:

\(1/2 \int [0, \pi /2] tan\theta (2sin\theta \,cos\theta \,d\theta) = \int[0, \pi /2] sin\theta d\theta\).

Integrating sinθ with respect to θ gives us:

cosθ ∣[0, π/2] = -cos(π/2) - (-cos(0)) = -0 - (-1) = 1.

Therefore, the value of the definite integral \(\int [0, 1] x\sqrt{(1 - x^2)} dx\) is 1. Rounded to three decimal places, the answer is 1.000.

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Complete Question:

Find the following definite integral, round your answer to three decimal places.

\(\int\limits_{0}^{1} x \sqrt{1-x^{2} } dx\)

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

(1,0)

Step-by-step explanation:

\(\boxed{midpoint = ( \frac{x1 + x2}{2}, \frac{y1 + y2}{2}) }\)

Thus, midpoint of the line segment is

\( = ( \frac{3 - 1}{2} , \frac{1 - 1}{2} ) \\ = ( \frac{2}{2} , \frac{0}{2} ) \\ = (1,0)\)

Answer:

- 5

Step-by-step explanation:

Substitute x = - 2 into f(x)

f(- 2) = 2(- 2) - 1 = - 4 - 1 = - 5

Answer:

Step-by-step explanation:

Solve x² = 25.

x= 12.5

x = ±5

x = 5

x = ±12.5

x² = 25

x = √25

x = ±5

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

check with 5

5² = 25

check with -5

-5² = 25

Answer:

B is the answer your looking for

Step-by-step explanation:

Answer:  5346

Step-by-step explanation:

Let x = Total votes.

Given : The  ratio of yes votes to no votes was 4 to 5 i.e. The number of no votes = \(\dfrac{5}{5+4}\times x=\dfrac59x\)

Number of no votes = 2970

\(\Rightarrow\ \dfrac59x= 2970\\\\\Rightarrow\ x=\dfrac95\times2970\\\\\Rightarrow\ x=5346\)

Hence, total votes = 5346

The expression r(x) = \(tan^2x\) can be described in its fundamental algebraic structure by the function option A. A composition of f(g(x)).

We can describe the function  \(tan^2x\) as a composition of f (g(x)) of basic functions.

We will obtain the r(x) by using the function g(x) = \(tan(x)\) for the input variable x.

Now we will square on both sides to write the function as

r(x) = f(g(x))

Here, f(u) = \(u^2\) and also g(x) = \(tanx\).

The \(tanx\) represents tangent of an angle.

Whereas if we see the other options in the question we don't require the sum of two terms to obtain \(tan^2x\).

So options B, C, and D are rejected and the answer is the option A.

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The expression \(\(r(x) = \tan^2(x)\)\) can be described in its fundamental algebraic structure by the function option A. A composition of f(g(x)).

In this case, the function \(\(f(x)\) is \(f(x) = \tan(x)\)\), and the function \((g(x)\) is \(g(x) = x\)\).

So, \(\(r(x) = f(g(x)) = \tan^2(x)\)\).

To further explain, the function \(\(g(x)\)\)  represents the input of the function, which is \(\(x\)\).

The function \(\(f(x)\)\) is then applied to the output of \(\(g(x)\),\) which is \(\(\tan(x)\)\). Finally, the result is squaring the value obtained from \(\(f(x)\)\), giving us \((\tan^2(x)\)\).

Therefore, the correct answer is A. A composition \(\(f(g(x))\)\) of basic functions.

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The correct statement is that F(x) < 0 over the intervals (-0.7, 0.76) and (2.5, ∞).

Value of subjective concept that refers to the word of important that an individual group of people places on the something it is often associated with principal beliefs and the standard that are accepted by society when you can be seen as a matter of how important something is true person of organization it is often seen as a reflection of funds for view and can help to save decision.

This can be seen by looking at the function's minimum and maximum values and its points of intersection with the x- and y-axes. The minimum value of (1.9, negative 5.7) is to the left of the x-axis, indicating that the function is negative over the interval (-0.7, 0.76). The maximum value of (0, 2) is above the x-axis, indicating that the function is negative over the interval (2.5, ∞).

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If this is a sample of 6 scores, then  SS using the definitional formula would equal 17.5.

To find the SS (sum of squares) using the definitional formula, you need to first calculate the mean of the scores. Here's

1. Calculate the mean (µ) using ∑x and the number of scores (n):
Mean (µ) = (∑x) / n
µ = 39 / 6
µ = 6.5

2. Use the computational formula for SS:
SS = ∑x² - ( (∑x)² / n )
SS = 271 - (39² / 6)
SS = 271 - (1521 / 6)
SS = 271 - 253.5

3. Calculate sample score SS:
SS = 17.5

So, the answer is 17.5.

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x + y = 150

x - y = 100

______

x = hoodie

y = shoes

x = 150 - y

150 - y = 100 + y

50 = 2y

y = 25

x = y + 100

x = 25 + 100

x = 125

please give brainliest

Answer:

125

Step-by-step explanation:

it's unequal sharing

150-100=50

50/2=25

hoodie=100+25=$125

hope it helps

The point is where the vertex is situated \((2.5, 100)\).

A vertex, which is a unique point on a mathematical object, is often where 2 or more lines or edges come together. The shapes that include vertices most frequently are graphs, polygons, polyhedra, and angles. Vertices in a graph are sometimes called nodes.

A parabola's vertex is the location where its symmetry line and parabola intersect. The vertices of a parabola which equation is provided in standard form will be the lowest (lowest point) and highest (highest point) points on the graph, respectively.

To graph the equation \(h(t) = -16t^2 + 80t\) from \(t=0\) to \(t=5\) seconds, we can create a table of values by plugging in values of t and calculating the corresponding values of \(h(t)\):

t                   h(t)

0                      0

1                    64

2                   128

3                   144

4                   128

5                     80

To find the vertex, we can use the formula \(t = -b/(2a)\), where \(a = -16\) and \(b = 80\).

\(t = -b/(2a) = -80/(2(-16)) = 2.5\)

So the vertex occurs at \(t = 2.5\) seconds.

Now we can plot the points from the table and graph the equation,

Graph of \(h(t)=-16t^2+80t\) from \(t=0\) to \(t=5\) seconds

The vertex is located at the point \((2.5, 100)\).

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Answer:

62.8

Step-by-step explanation:

3.14 times 2 times 10

I hope this helps!

The expression for the difference of two linear functions is (f - g)(x) = 4x - 6.

A linear function is a type of function in mathematics that has the form f(x) = mx + b, where x is the independent variable, f(x) is the dependent variable, m is the slope of the line, and b is the y-intercept.

To find the expression for the difference of two linear functions, f(x) and g(x), denoted by (f - g)(x).

The expression for (f - g)(x) can be found by subtracting g(x) from f(x):

(f - g)(x) = f(x) - g(x)

Substituting the given functions f(x) = x - 2 and g(x) = -3x + 4, we get:

(f - g)(x) = f(x) - g(x)

= (x - 2) - (-3x + 4) [Substitute the given values of f(x) and g(x)]

= x - 2 + 3x - 4 [Distribute the negative sign in front of (-3x + 4)]

= 4x - 6 [Combine like terms]

Therefore, (f - g)(x) = 4x - 6.

Option D (-3x² - 2x - 8) is incorrect as it involves squaring a linear expression, which would result in a quadratic expression. Option A (which has no operation between 3 and 22) is not a valid expression. Option B (-3x - 8) and C (3x3x22 or 198) do not take into account the fact that each sundae can be made using one of 3 syrups and one of 3 candy toppings.

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Answer:

not sure but i think its B

Answer: the answer is f(x) = −4x + 200

Answer:

-4 + 200

Step-by-step explanation:

-4 x 2 + 200 = 192

-4 x 4 + 200 = 184

Answer with Step-by-step explanation:

a) 2 3/4 ÷ 3 = 11/12 feet

11/12 + 11/12 = 1 5/6

Or, you could write an algebraic equation:

 2 3/4 ÷ 3 = x.  (3x = 2 3/4)

x = 11/12

The height of the brick proportion of the wall is 1 5/6

b)

You know that 8 x 2 is 16. Well, you already know that the whole total of fractions, multiplied together, would probably be less that 1 and less than 1/2.

So, your rounded answer should be 16. Or 16 1/2

c)  

Area = 8 1/2 x 2 3/4.

Use Distributive Property to solve the area.

(8 x 2) + (3/4 x 1/2) = x

8 x 2 = 16

3/4 x 1/2 = 3/8

16 + 3/8 = 16 3/8

x = 16 3/8

I think my answer is reasonable because I estimated 16, and 1/2. 3/8 is close to 1/2. That's why my answer is reasonable.

-kiniwih426

The correct equations are: x = sin–1y = cos–1Sin–1 (also called arcsin) is the inverse trigonometric function of sine.

The equations for the measures of the unknown angles x and y are correct when x = sin–1 and y = cos–1.

It takes the ratio of a right-angled triangle's opposite side to its hypotenuse as its input and returns the angle whose sine is that ratio.

The answer will be given in radians.

Cos–1 (also called arccos) is the inverse trigonometric function of cosine. It takes the ratio of a right-angled triangle's adjacent side to its hypotenuse as its input and returns the angle whose cosine is that ratio.

The answer will be given in radians.

Tan–1 (also called arctan) is the inverse trigonometric function of tangent. It takes the ratio of a right-angled triangle's opposite side to its adjacent side as its input and returns the angle whose tangent is that ratio. The answer will be given in radians.

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The equations for the measures of the unknown angles x and y are x = cos-1 and y = sin-1.

For the unknown angles x and y, the correct equations are:

To find the measure of angle x, we can use the inverse cosine function because x is the adjacent side to the right triangle. And to find the measure of angle y, we can use the inverse sine function because y is the opposite side to the right triangle. The inverse trigonometric functions allow us to find the angles given their respective sides.

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Answer:

sum

multiple

Please mark me as brainlist answer.

I am in search of 2 brainlist answer.

Answer:

sum, multiple

Step-by-step explanation:

A number is divisible by 9 if the sum of digits is a multiple of 9

Answer:

firstly read the length of the arc then

center angle=l/r

=1/6

=6

Answer:

2. 13

Step-by-step explanation:

The least number of classes need for all of the students to be registered in a class is 13 since you want all of the stuednts to be registered so no one should be left out. If we do 12*12 (12 students in each class and there are 12 classes), that would only let 144 students take the swimming classes and 8 students would be left out. We don't want that though since we want all of the students to be registered. So let's go to 12*13 (12 students in each class and  there are 13 classes), that would let 156 students take the swimming class. 156>152 so therefore, 13 classes would allow for all 152 students to be registered and it is the least number of classes needed for all the students to be registered in a class (plus you would have 4 seats left for anyone who wants to register in the future but the remainder doesn't matter).  

Answer:

Step-by-step explanation:

You are given a right triangle. The square in the  corner of the triangle tells you that that angle = 90°.  Also the sum of all three angles in a triangle = 180°.

Sum of the angles in the triangle = 40° + 90° + y = 180°

                                                              130° + y = 180°

                                                                       y = 180° - 130°  

                                                                       y = 50°

Second way:

The acute angles of a right triangle = 90°. Therefore  40° + y =  90°

                                                                                                 y = 90° - 40°

                                                                                                 y = 50°