PLEASE HELP ME!!
The QUADRATIC curve-of-best-fit for the data in the table is given by the equation
A) y = 0.8x2 + 1.7x - 1.4.
B) y = 1.1x2 + 2.2x - 1.2.
C) y = 1.4x2 - 2.9x + 1.0.
D) y = 2.3x2 - 2.4x + 3.5

Answer:

D)

\(5 \times {10}^{ - 12} \)

Step-by-step explanation:

velocity(v) = distance/time

but distance =

\(3 \times {10}^{ - 4} \)

and velocity =

\(6 \times {10}^{7} \)

\(6 \times {10}^{7} = \frac{3 \times {10}^{ - 4} }{time} \)

\(time = \frac{3 \times {10}^{ - 4} }{6 \times {10}^{7} } \)

\(time = 5 \times {10}^{ - 12} \)

Answer:

b

Step-by-step explanation:

Answer:

B. 0.06, 0.05, 0.4

Step-by-step explanation:

Use a decimal chart it can be very helpful

(a) i. (T – R)(2) = 3, ii. 2T(3) – 4R(1) = -14, iii. (T/R)(3) = Undefined, iv. T(R(3)) = 5.

(b) Vertical intercept of T(x): (0, 5).

(c) Horizontal intercept of R(x): (3, 0).

(d) \([T(R(2))]^{-1} + R^{-1}(2) = 1/3\).

(a) Find the value of each of the following expressions:

i. (T – R)(2):

To find the value of (T – R)(2), we subtract the corresponding values of R(x) from T(x) at x = 2:

(T – R)(2) = T(2) - R(2) = 2 - (-1) = 3.

ii. 2T(3) – 4R(1):

To find the value of 2T(3) – 4R(1), we substitute the values of T(3) and R(1) into the expression:

2T(3) – 4R(1) = 2(1) – 4(4) = 2 - 16 = -14.

iii. (T/R)(3):

To find the value of (T/R)(3), we divide the value of T(3) by R(3):

(T/R)(3) = T(3) / R(3) = 1 / 0 (Since R(3) = 0) = Undefined.

iv. T(R(3)):

To find the value of T(R(3)), we substitute the value of R(3) into T(x):

T(R(3)) = T(0) = 5.

(b) Find the vertical intercept of T(x):

The vertical intercept of a function occurs when x = 0. From the given table, we can see that T(0) = 5. Therefore, the vertical intercept of T(x) is (0, 5).

(c) Find a horizontal intercept of R(x):

The horizontal intercept of a function occurs when the function's output is zero. From the given table, we can see that R(x) = 0 when x = 3. Therefore, the horizontal intercept of R(x) is (3, 0).

(d) Evaluate \([T(R(2))]^{-1} + R^{-1}(2)\):

To evaluate \([T(R(2))]^{-1} + R^{-1}(2)\), we need to find the compositions T(R(2)) and \(R^{-1}(2)\) separately and then add them.

T(R(2)) = T(1) = 3.

To find \(R^{-1}(2)\), we need to determine the input value that results in R(x) = 2. Looking at the given table, we can see that R(x) = 2 when x = 0. Therefore, \(R^{-1}(2) = 0\).

Thus, \([T(R(2))]^{-1} + R^{-1}(2) = (3)^{-1} + 0 = 1/3 + 0 = 1/3.\)

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The function for the arithmetic sequence (fn) = 8n

The domain is {1,2,3,…10}

An arithmetic sequence is a series of numbers in which each term (save the first) is obtained by adding a constant number to the preceding term. For example, 2, 4, 6, 8,... is an arithmetic sequence because each term is created by adding 2 (a constant integer) to the previous term.

Given that

The arithmetic sequence is 8, 16, 24, 32, 40, 48, 56

Common difference = 16-8 = 8

The sequence is increasing so the common difference is positive 8

fn = 8 + (n-1)d

fn = 8 + (n-1)8

fn = 8 + 8n – 8

fn = 8n

So the function for the arithmetic sequence (fn) = 8n

b. The points to the graph are represented by (nfn). So the points are (1,8);(2,16);(3,24);(4,32);(5,40);(6,48);(7,56)

The domain of the function is the number 10

So, the domain is {1,2,3,…10}

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Answer:

Value of tan( π/3 ):

\({ \tt{ \frac{\pi}{3} = \frac{180}{3} = 60 \degree }}\)

60° lies within the first quadrant.

\({ \sf{ \tan( \frac{ \pi}{3} ) = ( \frac{1}{2} , \: \frac{ \sqrt{3} }{2}) }}\)

Since it's a half:

\({ \boxed{ \sf{ \tan( \frac{\pi}{3} ) = \sqrt{3} }}}\)

Length of hypotenuse:

\({ \bf{ \sin(31 \degree) = \frac{16.5}{h} }} \\ { \sf{h = 32.04}}\)

Hypotenuse = 32.0

Answer:(x+3)(x-8)=0

Step-by-step explanation:

Harriette has 58 songs in her playlist.

No of the songs in Lashondra's playlist = Nine times Harriette's playlist

No of the songs in Velora's playlist = Seven times Harriette's playlist

Total number of songs combined by all = 986

Let the number of songs in Harriette's playlist be x.

According to the problem,

9x + 7x + x = 986

⇒ 17x = 986

⇒ x = 58

Answer) Harriette's playlist has 58 songs.

         We have taken the number of songs in Harriette's playlist as x as the other numbers were given in relation to this playlist. Thus, the variable is used to create a generalized formula.

         Since the total number of songs is given, we can carry out simple algebraic addition and simplification to find out the answer.

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The entire question is given below:

Lashondra's playlist has 9 times as many songs as Harriette's playlist.-Velora-has 7 times as many songs on her playlist as Harriette does. If they combined their playlists, they would have 986 songs. How many questions does Harriette have in her playlist?

The probability that a three-  number integer is separable by 7 is 3/20or 0.15.

To determine the probability that a three-  number number is separable by 7, we need to count the number of three-  number integers that are separable by 7 and  also divide that number by the total number of three-  number integers.

First, we need to find the lowest three-  number integer that's separable by 7. We know that 14 is the  lowest two-  number integer separable by 7, so the  lowest three-  number integer that's separable by 7 will be the coming multiple of 7, which is 105.    

Next, we need to find the largest three-  number integer that's separable by 7. The largest three-  number integer is 999, and the largest multiple of 7 that's  lower than or equal to 999 is 994.    So, we need to count the number of integers that are separable by 7 between 105 and 994.

We can do this by using the formula for the number of integers in an  computation sequence  

number of integers = ( last term-first term)/ common difference  

In this case, the first term is 105, the last term is 994, and the common difference is 7, so we have  

number of integers = ( 994- 105)/ 7 1 =  135  

Thus, there are 135 three-  number integers that are separable by 7.    

The total number of three-  number integers is 900( from 100 to 999). So, the probability that a three-  number integer is separable by 7 is    probability =  number of integers that are separable by 7/ total number of three-  number integers  probability

=  135/ 900  probability =  3/ 20

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We would expect two real roots when the discriminant is positive (like in the previous question).

The discriminant can be positive, zero, or negative, and this determines how many solutions there are to the given quadratic equation. A positive discriminant indicates that the quadratic has two distinct real number solutions. A discriminant of zero indicates that the quadratic has a repeated real number solution.

It determines the number and the type of solutions that a quadratic equation has. If the discriminant is positive, there are 2 real solutions. If it is 0, there is 1 real repeated solution. If the discriminant is negative, there are 2 complex solutions (but no real solutions).

Hence, we would expect two real roots when the discriminant is positive (like in the previous question).

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Step-by-step explanation:

'a' region is    53  out of (53+81+106+85 + 64 = 389)

53/389 ths of the 360 degree circle would be the  a's

53/389  * 360 =    49 degrees

The answer is option b) 1.420, the particle's velocity is decreasing

To find the value of t at which the particle's velocity is decreasing most rapidly, we need to determine the maximum value of the acceleration function a(t) = (t - 8)sin(t) within the given interval.

To do this, we can analyze the critical points and endpoints of the acceleration function.

Critical Points:

To find the critical points, we need to find the values of t for which the derivative of the acceleration function is zero or undefined.

Taking the derivative of a(t), we get:

a'(t) = sin(t) + (t - 8)cos(t)

Setting a'(t) = 0, we solve for t:

sin(t) + (t - 8)cos(t) = 0

This equation does not have a simple algebraic solution, so we can approximate the values of t using numerical methods or graphing software.

The critical points within the interval 0 ≤ t ≤ 8 are approximately t ≈ 1.420 and t ≈ 4.439.

Endpoints:

We also need to evaluate the acceleration function at the endpoints of the interval.

a(0) = (0 - 8)sin(0) = 0  (velocity is not changing at t = 0)

a(8) = (8 - 8)sin(8) = 0  (velocity is not changing at t = 8)

Based on the analysis, the particle's velocity is decreasing most rapidly at the critical point t ≈ 1.420. Therefore, the answer is option b) 1.420.

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Answer:

x = 1 \(\frac{1}{2}\)

Step-by-step explanation:

make equal equations first

\(\frac{3/4}{1 and 1/8}\)  =  \(\frac{1}{x}\)

cross multiply to get: 3/4x = 1 \(\frac{1}{8}\)  

divide by 3/4 on both sides: x = 1 \(\frac{1}{2}\)

Axis of symmetry: x = -3

Vertex:  (-3,3)

Y intercept: 12

As x increases  ⇒ y increases

As x decreases  ⇒ y increases

In the given graph,

Since we know that,

The axis of symmetry is a hypothetical line that splits a figure into two identical portions, each of which is a mirror reflection of the other. The two identical pieces superimpose when the figure is folded along the axis of symmetry.

Hence,

The line x = -3 is the axis of symmetry for the given parabola.

From figure we can see that,

The vertex point is (-3, 3)

The point at which the curve intercept with Y axis be (0, 12)

For end behavior of the curve is,

We can see that,

As x increases  ⇒ y increases

And when,

As x decreases  ⇒ y increases

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Answer:

2

Step-by-step explanation:

Look at the graph, f(4) is at 3. So what is g(3)? it is 2.

The value of function g (f (4)) is 2.

Here,

Graph of f (x) and g (x) are shown.

We have to find the value of g (f (4)).

What is Composite function?

Composition  function is an operation of two functions f and g which produces a function J such that J (x) = g (f(x)).

Now,

The value of f (4) in graph is 3.

Hence,

g (f (4)) = g (3)

And, the value of g (3) is 2.

So, g (f (4)) = g (3) = 2

Hence, The value of function g (f (4)) is 2.

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Answer:

answer

Step-by-step explanation:

Simplifying

4y = 4x + -28

Reorder the terms:

4y = -28 + 4x

Solving

4y = -28 + 4x

Solving for variable 'y'.

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

Divide each side by '4'.

y = -7 + x

Simplifying

y = -7 + x

The solution of the system of equation are (1,8) and (0, 6)

-2x² + y = 6

4x² + 3y = 28

Therefore,

-4x² + 2y = 12

4x² + 3y = 28

5y = 40

y = 40 / 5

y = 8

Therefore,

-2x² + 8 = 6

-2x² = -2

x² = 1

x = 1

2(0)² + y = 6

y = 6

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Answer:

D. (-1, 8) and (1,8)

Step-by-step explanation:

I took the math exam

Answer:

(-5,-13)

Step-by-step explanation:

Find the vertex of the parabola y=1/5x^2+2x−8.  

In this equation a=15  and b = 2.  

x= -2/2(1/5) = -2/2/5 = -2/1 * 5/2 = -5

Substitute −5 into the equation y=1/5x^2+2x−8

y=1/5(−5)^2+2(−5)−8

y=5−10−8

y=−13

The vertex is (−5 , −13)

Answer:

0.9

Step-by-step explanation:

Y = B0 + B1X

B1 is the slope an from the question the slope estimate is 0.5

S.E= standard error at 0.2

At 5percent Level of significance, the z value for the test is equal to 1.96

We are required to find out the largest value of b for which the null hypothesis would be accepted.

0.5 + 1.96 x 0.2

= 0.892

Approximately 0.9

Answer:

420 is the answer

Step-by-step explanation:

15/2 * 56L =

l = 15/2 = 7.5

7.5 * 56 = 420

Answer:

420

Step-by-step explanation:

Attached below

The coordinate of points B, C, and D are B(3,-5), C(3,5), and D(0,-1).

A pair of numbers that employ the horizontal and vertical distinctions from the two reference axes to represent a point's placement on a coordinate plane.

As per the given coordinate A(-2,-5).

Since, AB = 5 and horizontal thus B(-2 + 5,-5) = B(3,-5)

Since, BC = 10 and the vertical line thus, C(3,-5+10) = C(3,5)

The equation of line AC will be as follows,

y + 5 = [(5 + 5)/(3 + 2)](x + 2)

y + 5 = 2(x + 2)

y = 2x - 1

At x = 0

y = -1 so D(0,-1)

Hence "The coordinate are B(3,-5), C(3,5), and D(0,-1)".

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53 inches is the mean height of the students in the group.

Given data: \(54,48,52,56,55\)

We know that mean of the heights =  \(\frac{Sum of all the heights}{No. of students}\)

                                                         \(= \frac{54+48+52+56+55}{5}\)

                                                         \(= \frac{265}{5}\)

                                                         \(= 53\) inches

Thus, the mean height of the students is 53 inches

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678.987Answer:

Step-by-step explanation:

Answer:

290

Step-by-step explanation:

210 x 2 = 420

420 - 130 = 290

The upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

To determine the upper and lower control limits for the sample means, we can use the formula:

Upper Control Limit (UCL) = Mean + (Z * Standard Deviation / sqrt(n))

Lower Control Limit (LCL) = Mean - (Z * Standard Deviation / sqrt(n))

In this case, we want to include roughly 95.5 percent of the sample means, which corresponds to a two-sided confidence level of 0.955. To find the appropriate Z-value for this confidence level, we can refer to the standard normal distribution table or use a calculator.

For a two-sided confidence level of 0.955, the Z-value is approximately 1.96.

Given:

Mean = 2.0 litres

Standard Deviation = 0.01 litres

Sample size (n) = 5

Using the formula, we can calculate the upper and lower control limits:

UCL = 2.0 + (1.96 * 0.01 / sqrt(5))

LCL = 2.0 - (1.96 * 0.01 / sqrt(5))

Calculating the values:

UCL ≈ 2.0018 litres

LCL ≈ 1.9982 litres

Therefore, the upper control limit (UCL) is approximately 2.0018 litres, and the lower control limit (LCL) is approximately 1.9982 litres, which would include roughly 95.5 percent of the sample means.

Now let's check if the process is in control using the given sample means:

Mean of the sample means = (2.005 + 2.001 + 1.998 + 2.002 + 1.995 + 1.999) / 6 ≈ 1.9997

Since the mean of the sample means falls within the control limits (between UCL and LCL), we can conclude that the process is in control.

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Answer:

C

Step-by-step explanation:

based in the graph if x=2 then y=4

Answer:

9

Step-by-step explanation:

this is the other answer if 4 isn't listed

Answer:

31.1

Step-by-step explanation:

Answer:

31.1

Step-by-step explanation:

124.4 / 4

= 0.1 * (1244/4)

= 0.1 * 311

= 31.1.

The next step of marshall should be divide both sides of the equation by 5.

Given:

Marshall is writing an equivalent equation to solve for x. what should be his next step.

5 + 4 y = 8.

5+4y-4y = 8-4y

5x = 8 - 4y

To solve for x:

The correct step is:

divide by 5 on both sides

5x/5 = 8-4y / 5

x = 8/5 - 4y/5

x = 1/5(8-4y).

Therefore The next step of marshall should be divide both sides of the equation by 5.

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Alexa landed right below the helicopter, which means she landed 3.4 kilometers away from the skydiving center.

To solve the problem, we need to use trigonometry. We know that the helicopter traveled 3.4 kilometers, and it ascended at an angle of 20°.

We can use this information to find the height of the helicopter above the ground using the trigonometric function tangent:

tan(20°) = height / 3.4 km

Solving for height, we get:

height = 3.4 km * tan(20°) ≈ 1.16 km

Now we can use the height to find the distance from the skydiving center to Alexa's landing spot. We know that Alexa fell in a straight line perpendicular to the ground, so we have a right triangle where the height of the helicopter is the opposite side, and the distance we're looking for is the adjacent side.

We can use the trigonometric function tangent again:

tan(90°) = distance / height

Solving for distance, we get:

distance = height * tan(90°) = 1.16 km * 0 = 0 km

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Complete question is:

Alexa's friends got her a skydiving lesson for her birthday. her helicopter took off from the skydiving center, ascending in an angle of 20°, and traveled a distance of 3.4 kilometers before she fell in a straight line perpendicular to the ground. How far from the skydiving center did Alexa land?

Answer and Step-by-step explanation:

1a. The work is NOT correct.

1b. The mistake was keeping the 2 with the \(\frac{12}{15}\), in which this number was found by multiplying the denominator 5 by the whole number 2, then adding it to the numerator 2, resulting in \(\frac{12}{15}\).

1c. Multiply the denominator 5 by the whole number 2, then add it to the numerator 2, which results in \(\frac{12}{15}\). When you add \(\frac{1}{15}\), you get the answer to be \(\frac{13}{15}\).

Have a good day!