6. At what position on the number line is the red dot located?
A:1/2
B:2/5
C:4/9
D:5/9

The average rate of change over is 1.

Given that;

the function is,

⇒ g (t) = - (t - 1)² + 5

Hence, We need to determine the average rate of change over the interval - 4 ≤ t ≤ 5.

The value of G(-4):

The value of G(-4) can be determined by substituting t = -4 in the function

⇒ g (t) = - (t - 1)² + 5

Thus, we have,

⇒ g (t) = - (-4 - 1)² + 5

⇒ g (t) = - 20

Thus, the value of G(-4) = -20

The value of G(5):

The value of G(5) can be determined by substituting t = 5 in the function , we get,

⇒ g (t) = - (t - 1)² + 5

⇒ g (t) = - (5 - 1)² + 5

⇒ g (t) = - 11

Thus, the value of G(5) is, -11

Now, Average rate of change:

The average rate of change can be determined using the formula,

⇒ G(b) - G (a) / (b - a)

where, a = - 4 and b = 5

Substituting the values, we get,

⇒ G(5) - G (-4) / (5 - (-4))

⇒ ( - 11 - (- 20)) / 9

⇒ 9/9

⇒ 1

Thus, the average rate of change over the interval is. 1.

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Answer:

Its normal value would be 50 beats per minute.

Step-by-step explanation:

20% = 10bpm

40% = 20bpm

60% = 30bpm

80% = 40bpm

100% = 50bpm

Answer:

x = 26

Step-by-step explanation:

sum of consecutive interior angles is 180

2(x + 15) + (3x + 20) = 180

2x + 30 + 3x = 160

5x = 130

x = 26

Answer:

value of x is 26.

Step-by-step explanation:

Given:

2(x+15)°+(3x+20)°=180°

Since the sum of angle of co interior angle is supplementary.

Solving for x.

2(x+15)°+(3x+20)°=180°

2x+30+3x+20=180

5x+50 =180

5x=180-50

5x=130

x=130/5

x=26

Therefore value of x is 26.

Hello there. To solve this question, you will need to conclude what happens when you multiply the fraction by the factor sqrt(7)/sqrt(7), it is, rationalizing with this factor (instead of the conjugate of the denominator expression)

We'll get:

5/(1+sqrt(7)) * sqrt(7)/sqrt(7)

Apply the foil

5sqrt(7)/(sqrt(7) + 7)

As you can see, you wouldn't be able to find a neat expression to this.

The right way is: multiply the fraction by the conjugate of the denominator expression, it is (sqrt(7) - 1)/(sqrt(7) - 1)

5/(1+sqrt(7)) * (sqrt(7) - 1)/(sqrt(7) - 1)

Apply the foil and remember (a + b)(a - b) = a² - b²

(5sqrt(7) - 5)/(7 - 1)

(5sqrt(7) - 5)/6

This is the expression we would be looking for. Note that the rationalizing process refers to getting rid of the square root (to be fair, any kind of root) of the denominator.

First case: a square root on the denominator;

Second case: another type of root on the denominator;

Third case: a sum of terms involving a root of any type.

It follows the same process we did to solve the question, but sometimes we'll need to use one of the other cases.

The conclusion that they would arrive at based on the rejection region would be to reject the null hypothesis.

This is the region that tells us that we are not to accept the null. The conclusion would be to reject the null.

This happens when the rejection region is found to be around the area that is in the critical value.

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The volume of the hexagonal prism is 212.4 unit square

Prism is three-dimensional solid which has identical faces at both ends. It is a polyhedron, which means all faces are flat.

How to determine this

When an hexagonal prism has a base area = 36 units

Height = 5.9 units

Volume of Prism = Base area * Height

Volume of prism = 36 units * 5.9 units

Volume = 212.4 units square

Therefore, the volume of the hexagonal prism is 212.4 units square

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Answer:

-0.55

Step-by-step explanation:

Use trig identity:

\(1+ cot^2t = \frac{1}{sin^2t}\)

\(1+2.25 = \frac{1}{sin^2t}\)

\(sin^2t = \frac{1}{3.25}\)

\(sin t = + \frac{1}{1.80}\)

Since t is in quadrant III, then sin t is negative

\(sint = - \frac{1}{1.8} =-0.55\)

Answer:

You need to simplify 0.3(12x + -16) = 0.4(12 + -3x)

Step-by-step explanation:

Reorder the terms:

0.3(-16 + 12x) = 0.4(12 + -3x) (-16 * 0.3 + 12x * 0.3) = 0.4(12 + -3x) (-4.8 + 3.6x) = 0.4(12 + -3x) -4.8 + 3.6x = (12 * 0.4 + -3x * 0.4) -4.8 + 3.6x = (4.8 + -1.2x)

Solving -4.8 + 3.6x = 4.8 + -1.2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1.2x' to each side of the equation. -4.8 + 3.6x + 1.2x = 4.8 + -1.2x + 1.2x

Combine like terms: 3.6x + 1.2x = 4.8x -4.8 + 4.8x = 4.8 + -1.2x + 1.2x

Combine like terms: -1.2x + 1.2x = 0.0 -4.8 + 4.8x = 4.8 + 0.0 -4.8 + 4.8x = 4.8 Add '4.8' to each side of the equation. -4.8 + 4.8 + 4.8x = 4.8 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0 0.0 + 4.8x = 4.8 + 4.8 4.8x = 4.8 + 4.8

Combine like terms: 4.8 + 4.8 = 9.6 4.8x = 9.6 Divide each side by '4.8'. x = 2

Simplifying x = 2

Answer:  C

Step-by-step explanation:

1. We can see that the number in the bottom box is: 13.5yd.

2. The number in the top box is: 7.5yd.

3. The area of the table = 78.75yd²

A trapezoid, also known as a trapezium in some countries, is a quadrilateral shape that has only one pair of parallel sides. The parallel sides of a trapezoid are called the bases of the trapezoid, and the non-parallel sides are called the legs.

We see here that in order to get the number in the bottom box, we discover that the number in the top box is a square which means that all the sides are equal to 7.5yd.

Thus, the number in the bottom box = 3 + 7.5 + 3 = 13.5yd.

Thus, the area of the table, a trapezoid = 1/2(a + b)h

Where a = 7.5yd

b = 13.5yd

height, h = 7.5yd.

Thus, A = 1/2(7.5 + 13.5) 7.5 = 157.5/2 = 78.75

∴ Area of the table, A = 78.75yd²

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The vertices of the reflected square.

Let's calculate them:

A' = (-0.914, 3.914)

B' = (-2.828, 5.828)

C' = (-0.086, 7.086)

D' = (1.828, 5.172)

The vertices of the image of the square ABCD after reflecting it about the line through (0, 0) and (-2, 2), we can use the following steps:

Find the equation of the reflection line:

The reflection line passes through (0, 0) and (-2, 2).

We can calculate the slope (m) of the line using the formula (y2 - y1) / (x2 - x1):

m = (2 - 0) / (-2 - 0) = 2 / -2 = -1.

Using the point-slope form of a line (y - y1) = m(x - x1), we can use either of the given points to write the equation of the line:

y - 0 = -1(x - 0)

y = -x.

Find the midpoint of each side of the square:

The midpoints of the sides of a square are also the midpoints of its diagonals.

The midpoint of AB is ((4+6)/2, (3+4)/2) = (5, 3.5).

The midpoint of BC is ((6+5)/2, (4+6)/2) = (5.5, 5).

The midpoint of CD is ((5+3)/2, (6+5)/2) = (4, 5.5).

The midpoint of DA is ((3+4)/2, (5+3)/2) = (3.5, 4).

Reflect the midpoints about the line:

To reflect a point (x, y) about the line y = -x, we can find the perpendicular distance (d) from the point to the line and use it to determine the reflected point.

The perpendicular distance d from the line y = -x to a point (x, y) is given by the formula:

d = (y + x) / √(2).

The coordinates of the reflected points can be found using the formula for reflection across a line:

x' = x - 2d / √(2)

y' = y - 2d / √(2).

Calculate the reflected vertices:

The coordinates of the reflected vertices are as follows:

A' = (4 - 2(3.5 + 5) / √(2), 3 - 2(3.5 - 5) / √(2))

B' = (6 - 2(5 + 5) / √(2), 4 - 2(5 - 5) / √(2))

C' = (5 - 2(5.5 + 5) / √(2), 6 - 2(5.5 - 5) / √(2))

D' = (3 - 2(4 + 5) / √(2), 5 - 2(4 - 5) / √(2))

Now we can plot the original square ABCD and its image A'B'C'D' on the same graph to visualize the reflection.

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The domain of the relation of the graph representing a relation where x represents the independent variable and y represents the dependent variable is {−4, −2, 0, 3, 5}.

The domain of a relation is the set of all possible input values (independent variable) for which the relation is defined.

Looking at the given points, the x-coordinates are -4, -2, 0, 3, and 5. So, the possible input values are -4, -2, 0, 3, and 5.

Therefore, the domain of the relation is {−4, −2, 0, 3, 5}.

Hence, the correct option is {−4, −2, 0, 3, 5}.

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The value of function f (4) is,

⇒ f (4) = 19

We have to given that;

The function is,

⇒ f (x) = x² + 3

Now, WE can find the value of f (4) by substitute x = 4 in above function as,

⇒ f (x) = x² + 3

Plug x = 4;

⇒ f (4) = 4² + 3

⇒ f (4) = 16 + 3

⇒ f (4) = 19

Thus, The value of function f (4) is,

⇒ f (4) = 19

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\((\stackrel{x_1}{3}~,~\stackrel{y_1}{6})\qquad \qquad \stackrel{slope}{m}\implies 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{6}=\stackrel{m}{7}(x-\stackrel{x_1}{3})\)

Answer:

\(y=7x-15\)

Step-by-step explanation:

Given the following question:

Point A = (3, 6) = (x1, y1)
m (slope) = 7

We will find the equation of this line by finding the slope intercept.

\(y=mx+b\)
\(y=6\)
\(m=7\)
\(x=3\)
\(6=7(3)+b\)
\(7\times3=21\)
\(21-21=0\)
\(6-21=-15\)
\(b=-15\)
\(y=7x-15\)

Hope this helps.

Let R be the radius in millions of miles and let t be the time in days. Assume that when t = 0 the radius is 20 million miles and increasing then  R(t) = 20 + 1.6sin(2πt/5.2).

The equation for a sine wave is y = A sin (Bx + C) where A is the amplitude, B is the frequency and C is the phase shift.

In this case, the amplitude is 1.6.

Since the radius changes by a maximum of 1.6 million miles.

The frequency is 2π/5.2 (one full cycle of the sine wave in 5.2 days)

The phase shift is 0, since when t = 0 the radius is increasing.

The equation then becomes R(t) = 20 + 1.6sin(2πt/5.2)

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Answer:

16m 24m and 24m

Step-by-step explanation:

Given the fact that it's a rectangle, and 1 side is 16m, we know that 1 of the other sides will be 16m. After that and some simple subtraction, we get the other 2 sides are 24m.

Answer:

0

Step-by-step explanation:

There are no scores that are much higher or lower than the others

Answer:

B

Step-by-step explanation:

There are several ways to find the vertex of function such as formula, completing the square or differential.

I will use the formula to find the vertex.

We are given the function:

\( \displaystyle \large{f(x) = - {x}^{2} + 4x - 3}\)

Vertex Formula

Let (h,k) = vertex

\( \displaystyle \large{ \begin{cases} h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} \end{cases}}\)

From the function, compare the coefficients:

\( \displaystyle \large{a {x}^{2} + bx + c = - {x}^{2} + 4x - 3}\)

Therefore:-

\( \displaystyle \large{ \begin{cases} h = - \frac{4}{2( - 1)} \\ k = \frac{4( - 1)( - 3)- {4}^{2} }{4( - 1)} \end{cases}}\)

Then evaluate for h-value and k-value.

\( \displaystyle \large{ \begin{cases} h = - \frac{4}{ - 2} \\ k = \frac{4( 3)- 16}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2 \\ k = \frac{12 - 16}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2 \\ k = \frac{ - 4}{ - 4} \end{cases}} \\ \displaystyle \large{ \begin{cases} h = 2\\ k = 1\end{cases}}\)

Therefore the vertex is (h,k) = (2,1)

Answer:

B (2.1)

Step-by-step explanation:

it was on a test i got it right

Answer: no

Step-by-step explanation:

Answer:

14 oz

Step-by-step explanation:

A week has 7 days and you need to ration your bread over them.

98 / 7 = 14

Answer:

Linear Function: f(x) = mx + b where m and b are real numbers.

Constant Function: f(x) = b where b is a real number.

Identity Function: f(x) = x.

Square Function: f(x) = x2.

Cube Function: f(x) = x3.

Square Root Function:

Reciprocal Function: f(x) = 1/x.

Absolute Value Function: f(x) = |x|

(1) p value is 0.234. So the 4th option is correct.

(2) p value grater that any alpha values so we fail to reject the null. So the 4th option is correct.

(3) The outcome is significant if the null hypothesis is rejected. So the third option is the correct choice.

4) We lack sufficient data to claim that UF students who are Florida residents differ from non-Florida residents in the average number of cities they have lived in since we are unable to reject the null hypothesis.

We consider the following hypothesis-

H0: µ1 = µ2 vs H1: µ1 ≠ µ2

Where µ1 is the population mean of the non FL res

µ2 is the population mean of the FL res

1) p value = 0.234

(Obtained by p value calculator corresponding to the test statistic at 0.05 significance level with degrees of freedom 232+1224-2 = 1454)

Hence the 4th option is correct.

2) We know if p value ≤ α we reject the null.

Here since p value grater that any alpha values so we fail to reject the null.

Hence the 4th option is correct i.e, t none of the usual α.

(3) The outcome is significant if the null hypothesis is rejected. This conclusion is neither statistically nor practically significant because we are unable to reject the null hypothesis. The third option is the correct choice.

(4) We lack sufficient data to claim that UF students who are Florida residents differ from non-Florida residents in the average number of cities they have lived in since we are unable to reject the null hypothesis.

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The right question is given below:

The rate (in km/h) at which the distance from the plane to the radar station is increasing a minute later is 0 km/h (rounded to the nearest whole number).

To solve this problem, we can use the concepts of trigonometry and related rates.

Let's denote the distance from the plane to the radar station as D(t), where t represents time. We want to find the rate at which D is changing with respect to time (dD/dt) one minute later.

Given:

The plane is flying with a constant speed of 360 km/h.

The plane passes over the radar station at an altitude of 1 km.

The plane is climbing at an angle of 30°.

We can visualize the situation as a right triangle, with the ground radar station at one vertex, the plane at another vertex, and the distance between them (D) as the hypotenuse. The altitude of the plane forms a vertical side, and the horizontal distance between the plane and the radar station forms the other side.

We can use the trigonometric relationship of sine to relate the altitude, angle, and hypotenuse:

sin(30°) = 1/D.

To find dD/dt, we can differentiate both sides of this equation with respect to time:

cos(30°) * d(30°)/dt = -1/D^2 * dD/dt.

Since the plane is flying with a constant speed, the rate of change of the angle (d(30°)/dt) is zero. Thus, the equation simplifies to:

cos(30°) * 0 = -1/D^2 * dD/dt.

We can substitute the known values:

cos(30°) = √3/2,

D = 1 km.

Therefore, we have:

√3/2 * 0 = -1/(1^2) * dD/dt.

Simplifying further:

0 = -1 * dD/dt.

This implies that the rate at which the distance from the plane to the radar station is changing is zero. In other words, the distance remains constant.

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The alternative hypothesis is Ha : μa ≠ μb Ha : μa - μb ≠ 0

Since they want to find out if the difference in the mean times spent studying by the students of the two schools is statistically significant, it means that it is a two directional test. Also called a two tailed test. The hypothesis would be as follows:

Null Hypothesis: There is no difference in the mean times spent by the schools' students.

Alternative Hypothesis: There is at least some difference in the mean times spent by the schools' students.

By using the appropriate symbols, it becomes

The null hypothesis is

H0 : μa = μb H0 : μa - μb = 0

The alternative hypothesis is

Ha : μa ≠ μb Ha : μa - μb ≠ 0

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Answer: B(t) = 16*(1.2)t

Step-by-step explanation:

The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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Answer:

\(area = (7 \times 1) + (5 \times 1) + (8 \times 1) \\ = 7 + 5 + 8 \\ = 20 \: {m}^{2} \)

Answer:

QUESTION:

which one is it?

ANSWER:

Okay, so everyone knows that a straight angle/ full triangle equals up to the sum of 180°, right?

So you take the 180° and subtract the 51°. And you should be getting 129°.

But, since this is a right triangle all I did was subtract 51° from 90° (a right triangle). In the end, the final answer is 39°

Step-by-step explanation:

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