The length of the long leg in a 30°-60°-90° triangle is 3√2 cm. What is thelength of the short leg?

The average rate of change f(x) on the interval -6 ≤ x ≥ 2 is; 5

Average rate of change is a measure of how much the function changed per unit, on average, over that interval. This is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Now, the formula for the average rate of change over the interval (a, b) is;

f'(x) = [f(b) - f(a)]/(b - a)

Now, we are given the interval as -6 ≤ x ≥ 2.

From the given polynomial graph, we see that;

f(2) = 0 and f(-6) = 40

Thus;

f'(x) = [f(-6) - f(0)]/(2 - (-6))

f'(x) = (40 - 0)/8

f'(x) = 5

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In population 1:

Pattern is changing by 13.5 to 11.5 to 8.3

Which is 2 then 3.2.

In population 2:

Population is decreasing by 2.

A recurring arrangement of numbers, forms, colors, and other elements constitutes a pattern in mathematics. The Pattern can be connected to any kind of occasion or thing. When a group of numbers are arranged in a particular way, the arrangement is referred to as a pattern. Patterns can also occasionally be referred to as a series.

Given.

Pattern in which population is changing are:

In population 1:

It is changing by 13.5 to 11.5 to 8.3

Which is 2 then 3.2.

In population 2:

Population is decreasing by 2.

Completing the table:

Population 1            Population 2

      42.8                             29

      38.6                              27

     33.4                              25

      27.2                              23

Graph is mentioned below.

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For the given values, the probability that a student watches TV news regularly is 0.833, the probability that a randomly selected college student reads internet news regularly is 0.240.

According to a survey, 83% of college students routinely watch the news on television, while 24% of college students read newspapers on a regular basis.

Additionally, the survey revealed that 20% of college students routinely read newspapers and watch TV news.

(A) Given that a student reads newspapers frequently,

The answer is [P(TV and newspapers)/P] where P(watches TV|reads newspapers) (newspapers)

= 0.20/0.24 = 0.833

(b) Given that a randomly chosen college student watches TV news frequently

The answer is that P(newspapers | watches TV) = [P(newspapers and TV)] / P. (TV)

= 0.20/0.83 = 0.240

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Graph 1: No, because it fails the vertical line test.

Graph 2: No, because it fails the vertical line test.

Graph 3: Yes, because it passes the vertical line test.

Graph 4: Yes, because it passes the vertical line test.

Graph 5: No, because it fails the vertical line test.

Graph 6: Yes, because it passes the vertical line test.

Using trigonometry we know that option (B) "cosθ < 0" is correct.

For a right-angle triangle, the sum of the square of the legs is equal to the hypotenuse side(longest side).

Therefore, for a right triangle

For the triangle that has a² + b² > c², it shows it is not a right triangle.

Cosine law:

Substitute the value then we get:

Subtracting c² on both sides of the inequality:

Adding 2abcosθ on both sides then we get:

cosθ is negative in the second quadrant and third quadrants.

Therefore, using trigonometry we know that option (B) "cosθ < 0" is correct.

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Using synthetic division, the solution to the polynomial fraction expression is; 2x² - 10 + 12/(x - 4)

We are given the polynomial fraction as;

(2x³ - 10x + 2)/(x- 4)

This means that we want to divide the polynomial (2x³ - 10x + 2) by (x - 4) using synthetic division.

For the divisor, we have x - 4, and that means x - 4 = 0, x = 4

So, we'll be using 4 for the synthetic division and we have;

-1  |   2     0    -10   2

     ×       0     0    10        

   -------------------------

     2      0    -10   12

Now we will form the expression in the form of fraction again;

2x² - 10 + (12/(x - 4))

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The graphic below includes the graph of the provided question.

The horizontal axis is x-axis

The vertical axis is y-axis.

Points that are situated along the same straight line but within a single line are known as collinear points. Two or more points in Euclidean geometry are said to be collinear if they are situated on a line that is either close to or far from one another.

All the points necessary to solve the equation will be positive and negative in turn, and that point will form a straight line through the origin, indicating that all the points are collinear.

You can change the value to fit your graph in the diagram that corresponds to the graph for the question that is attached below.

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Given the following expression:

a.) 8x - 1 = 3x + 4

Let's determine the value of x,

8x - 1 = 3x + 4

8x - 1 + 1 - 3x = 3x + 4 + 1 - 3x

8x - 3x = 4 + 1

5x = 5

5x/5 = 5/5

x = 1

Therefore, x = 1.

Answer:

It belongs to the sets of natural numbers, {1, 2, 3, 4, 5, …}.

It is a whole number because the set of whole numbers includes the natural numbers plus zero. It is an integer since it is both a natural and whole number.

Answer:  rational numbers if thats an answer

Step-by-step explanation:

Using the table, we have the following points:

(x1, y1) ==> (2.5, 3), (3.5, 4.5), (5, 4.8), (5.5, 5.2), (6, 5.5)

Let's find the correlation coefficient.

To find the correlation coefficient, apply the formula:

Where:

n = 5

Σx = 2.5 + 3.5 + 5 + 5.5 + 6 = 22.5

Σy = 3 + 4.5 + 4.8 + 5.2 + 5.5 = 23

Σxy = 2.5⋅3 + 3.5⋅4.5 + 5⋅4.8 + 5.5⋅5.2 + 6⋅5.5 = 108.85

Σx² = 2.5² + 3.5² + 5² + 5.5² + 6² = 109.75

Σy² = 109.6

Plug in values in the formula and solve for r.

We have:

Therefore, the coefficient is 0.94

ANSWER:

0.94

Area of a Rectangle

Given a rectangle of length L and width W, the area is calculated as follows:

A = L.W

We are given the area of A=135 square feet and the width is W= 9 ft. Solving for L:

The driveway is 15 feet long

Answer:

Is wolfgang Mozart's

Step-by-step explanation:

The central traits of the Classical style are all present in Mozart's music. Clarity, balance, and transparency are the hallmarks of his work, but simplistic notions of its delicacy mask the exceptional power of his finest masterpieces, such as the Piano Concerto No. 24 in C minor, K.

We have the following:

The general formula of a geometric sequence is:

where,

n = 6

a₁ = -8100

r = -0.1

Replacing on the formula:

When one fails to reject a null hypothesis that is actually wrong, this error is known statistically as a type II error. This term is used in the context of hypothesis testing.

A type II error, often called an error of omission, results in a false negative. When the patient is infected, a disease test, for instance, can return a negative result. This is a type II error because, despite being wrong, we accept the test's negative conclusion.

The difference between a type I and type II error is that a type I error refers to the failure to reject a valid null hypothesis, whereas a type II error refers to the failure to do so. Despite the fact that the error does not happen by accident, it rejects the alternative theory.

The likelihood of mistakenly failing to reject the null hypothesis when it does not apply to the entire population is known as a type II error.

In essence, a type II error is a false negative.

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Let the commission sales = X

Salary Plan 1

salary per week = $400

commission sales = 2%

Salary Plan 2

salary per week = $300

commission sales = 18%

Becky's salary for both plans (inclusive of commission sales) would be:

Plan 1:

Plan 2:

In order to find how much Becky needs to make in sales for salary to be the same from both plans would be:

Therefore, the commission sales should be $625

we have the sequence

1,790 2,555 3,320 4,085 4,850

so

a1=1,790 ----> first term

a2=2,555

a3=3,320

a4=4,085

a5=4,850

Find out the difference between consecutive terms

a2-a1=2,555-1,790=765

a3-a2=3,320-2,555=765

a4-a3=4,085-3,320=765

a5-a4=4,850-4,085=765

This is an arithmetic sequence

The common difference is d=765

so

we have

d=765

a1=1,790

substitute

Whole numbers are the numbers 0, 1, 2, 3, 4, etc. (the natural numbers and zero). Negative numbers are not considered whole numbers. All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.

For example.

- 2, - 10

Coordinates - A pair of integers that show the location of a point on a graph. The first number represents the x-axis, while the second represents the y-axis.

Other names for this type of pair are ordered pair and numbered pair. A proportionate connection is one in which the values are all connected by the same constant value. A proportionate connection is also known as a linear relationship in mathematics.

Assume f(x) and g(x) are two functions that accept a real number as input and return a real number as output.

The intersection points of f(x) and g(x) are then those x values for which f(x)=g(x).

The precise numbers can sometimes be discovered by algebraically solving the equation f(x)=g(x).

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Ratio:

cups of water / pancake mix = (1/2) / 2

For 1 pancake mix, x cups of water:

x / 1 = (1/2) / 2

Solve for x, cross multiply:

2x = ( 1/2) 1

2x = 1/2

Divide both sides by 2

2x/2 = (1/2) / 2

x = 1/4

Answer:

She would need 1/4 cups of water

Answer:

see my photo bro. hope it can help.

Answer:

[tex]\textsf{(a)} \quad \overline{v}=-8t-4h-2[/tex]

[tex]\textsf{(b)} \quad v(t)=-8t-2[/tex]

[tex]\textsf{(c)} \quad L(t)=-26t+41[/tex]  

(d)  See attachment.

Step-by-step explanation:

Given equation for displacement:

[tex]s(t)=-4t^2-2t+5[/tex]

Average velocity formula:

[tex]\boxed{\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}[/tex]

where:

To find the average velocity of s(t) between the inputs t and t+h:

Find expressions for s(t) at t₁ and t₂:

[tex]\implies s(t_1)=s(t)=-4t^2-2t+5[/tex]

[tex]\begin{aligned}\implies s(t_2)=s(t+h)&=-4(t+h)^2-2(t+h)+5\\&=-4(t^2+2th+h^2)-2t-2h+5\\&=-4t^2-8th-4h^2-2t-2h+5\end{aligned}[/tex]

Substitute the found values into the average velocity formula:

[tex]\begin{aligned}\implies \overline{v} =\dfrac{s(t_2)-s(t_1)}{t_2-t_1}}&=\dfrac{(-4t^2-8th-4h^2-2t-2h+5)-(-4t^2-2t+5)}{(t+h)-t}}\\\\&=\dfrac{-4t^2-8th-4h^2-2t-2h+5+4t^2+2t-5}{t+h-t}\\\\&=\dfrac{-8th-4h^2-2h}{h}\\\\ &=-8t-4h-2\\\\ \end{aligned}[/tex]

Therefore, the average velocity between the inputs t and t+h is:

[tex]\boxed{\overline{v}=-8t-4h-2}[/tex]

To find the equation for instantaneous velocity v(t), differentiate the equation for displacement:

[tex]\begin{aligned}\implies v(t)&=s'(t)\\&=2 \cdot -4t^{(2-1)}-1 \cdot 2t^{(1-1)}+0\\&=-8t-2\end{aligned}[/tex]

Find the value of s when t = 3:

[tex]\begin{aligned}\implies s(3)&=-4(3)^2-2(3)+5\\&=-4(9)-6+5\\&=-36-6+5\\&=-42+5\\&=-37\end{aligned}[/tex]

To find the gradient of s(t) at t = 3, substitute t = 3 into the differentiated function:

[tex]\begin{aligned}\implies s'(3)=v(3)&=-8(3)-2\\&=-24-2\\&=-26\end{aligned}[/tex]

Substitute the found gradient and found point (3, -37) into the point-slope form of a linear equation to find the equation of the tangent line L(t):

[tex]\begin{aligned}\implies s-s_1&=m(t-t_1)\\s-(-37)&=-26(t-3)\\s+37&=-26t+78\\s&=-26t+41\\\implies L(t)&=-26t+41\end{aligned}[/tex]

See attachment.

A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.

A quartic function is a quartic polynomial, which is an integer-coefficients polynomial with a four-degree maximum.

Quartic in mathematics refers to something that is of the "fourth order," such as a function. One of the following is possible: Quartic function, a fourth-degree polynomial function. Quartic polynomial, a polynomial equation of degree 4, where an is a nonzero polynomial that defines the quartic equation.

A quartic equation, also known as an equation of the fourth degree, is an equation of the form that reduces a quartic polynomial to zero. A quartic function's derivative is a cubic function.

Therefore, the correct answer is option a) quartic.

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Answer:

1 == B No Solutions

2 == A One Solution

3 == C Infinitely Many Solutions

Explanation:

We first find go through each system and see which has one solution, no solutions, and infinitely many solutions.

1.

x

Based on the given figure, you can conclude:

x-intercepts:

x = 0

x = number in between 100 and 125, approximately 105

x = number greater than 175, approximately 180

y-intercepts:

y = 0

For the second and third x-intercepts there is no possible to specifiy the exact numbers due to the scale units of the graph.

The roots of a prabola is where the function intersects the x-axis.

The inverse of the function y = 2 · x² - 4 is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4. (Correct choice: B)

In this problem we have a quadratic function, whose inverse has to be found. First, we make the following substitution on the function:

y = x

x = y⁻¹

Now we proceed to clear y⁻¹ by using algebra properties:

x = 2 · (y⁻¹)² - 4

x + 4 = 2 · (y⁻¹)²

(x + 4) / 2 = (y⁻¹)²

√[(x + 4) / 2] = y⁻¹

y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4

The inverse of the function is equal to y⁻¹ = √[(x + 4) / 2], such that x ≥ - 4.

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The area of a rectangle is calculated using the formula:

where l is the length and w is the width.

The functions for the length and width are given to be:

Therefore, the area of the rectangle will be:

We can apply the FOIL Method:

Therefore, we have:

Simplifying, the area is:

The SECOND OPTION is correct.

There is a 0.6915 = 69.15% probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l.

The z-score of a measure X of a normally distributed variable that has mean represented by [tex]\mu[/tex] and standard deviation represented by [tex]\sigma[/tex] is given by the rule presented below:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the albumin levels are given as follows:

[tex]\mu = 35, \sigma = 5[/tex]

The probability that a randomly selected adult has a serum albumin level greater than 32.5 g/l is one subtracted by the p-value of Z when X = 32.5, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (32.5 - 35)/5

Z = -0.5

Z = -0.5 has a p-value of 0.3085.

1 - 0.3085 = 0.6915 = 69.15% probability.

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The number of bags of oranges Noah used on Tuesday as required to be determined in the task content is; 11/20 bags of oranges.

It follows from the task content that Noah used 3 3/10 bags of oranges on Monday.

Hence, by expressing the mixed number, 3 3/10 as a fraction; we have; 33/10.

Therefore, since he uses 1/6 as many oranges as on Monday on Tuesday;

The number of bags of oranges used on Tuesday is; (1/6) × 33/10

= 33/60

= 11/20.

Therefore, the number of bags of oranges Noah uses on Tuesday is; 11/20.

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