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Misha Larkins [42]
3 years ago
14

What is the constant of proportionality for the equation? y =1.5x

Mathematics
1 answer:
Kazeer [188]3 years ago
6 0

Answer:

1.5

Step-by-step explanation:

y=1.5x

y/x=1.5

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A thearte ticket costs £63 plus a booking fee of 3%<br> what is the total price of the ticket
ira [324]

Answer:

the total price is 64.89

Step-by-step explanation:

63 / 100 =

0.63 * 103 = 64.89

3 0
3 years ago
Read 2 more answers
which statements are true about the graph of the function f(x) = 6x – 4 x2? check all that apply. the vertex form of the functio
Brut [27]

Answer:

The vertex of the function is the point (-3,-13)

The graph increase over the interval--------> (-3,∞)

Step-by-step explanation:

we have

f(x)=6x-4+x^{2}

<u>1) Convert to vertex form</u>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

f(x)+4=x^{2}+6x

Complete the square. Remember to balance the equation by adding the same constants to each side

f(x)+4+9=x^{2}+6x+9

f(x)+13=x^{2}+6x+9

Rewrite as perfect squares

f(x)+13=(x+3)^{2}

f(x)=(x+3)^{2}-13 -----> function in vertex form

<u>2) Find the vertex</u>

The vertex of the function is the point (-3,-13)

<u>3) Find the axis of symmetry</u>

we know that

In a vertical parabola, the axis of symmetry is equal to the x-coordinate of the vertex

The x-coordinate of the vertex in this problem is equal to x=-3

therefore

the equation of the axis of symmetry is  x=-3

<u>4) Find the increase-decrease intervals</u>

The graph increase over the interval--------> (-3,∞)

The graph decrease over the interval--------> (-∞,-3)

see the attached figure to better understand the problem

<u>5) Find the x-intercepts of the function</u>

we know that

the x-intercepts are the values of x when the value of the function is equal to zero

In this problem the x-intercepts are  

(-6.61,0) and (0.61,0)

so

The function cross the x-axis twice

see the attached figure

5 0
3 years ago
Read 2 more answers
A​ 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense he
Orlov [11]

Answer:

We conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are​ effective.

Step-by-step explanation:

We are given that in a 9-year-old girl did a science fair experiment in which she tested professional touch therapists to see if they could sense her energy field.

Among 264264 ​trials, the touch therapists were correct 105105 times.

<u><em>Let p = proportion that touch therapists uses a random guess method.</em></u>

Here, random guess means; p = 50%

So, Null Hypothesis, H_0 : p = 50%     {means that the touch therapists use a method equivalent to random guesses}

Alternate Hypothesis, H_A : p \neq 50%     {means that the touch therapists does not use a method equivalent to random guesses}

The test statistics that would be used here <u>One-sample z proportion statistics</u>;

                         T.S. =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

where, \hat p  = sample proportion of touch therapists were correct = \frac{105}{264} = 0.39

            n = sample of trials = 264

So, <em><u>test statistics</u></em>  =  \frac{\frac{105}{264} -0.50}{\sqrt{\frac{\frac{105}{264}(1-\frac{105}{264})}{264} } }  

                                =  -3.395

The value of z test statistics is -3.395.

<em>Now, at 0.05 significance level the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>

Therefore, we conclude that the the touch therapists does not use a method equivalent to random guesses.

Yes, the results suggest that touch therapists are​ effective.

3 0
2 years ago
Write the equation of the line parallel to<br> y=-2/3x+4 and through the point (–3, 15)
MrRa [10]
Parallel = same slope
y = -2/3x + b
Plug in point
15 = -2/3(-3) + b
15 = 2 + b, b = 13
Solution: y = -2/3x + 13
6 0
2 years ago
Read 2 more answers
The volume of a sphere can be found using the formula V = πr . If the sphere has a diameter of 10x y z mm, what is the volume of
viva [34]

Answer:

<em>500πx³y³z³ </em>

Step-by-step explanation:

Volume of a sphere = 4πr³

r is the radius of the sphere

Given

Diameter of the sphere = 10xyz mm

Radius = diameter/2

Radius = 10xyz/2

Radius = 5xyz

Substitute the radius into the formula

Volume of the sphere = 4π(5xyz)³

Volume of the sphere = = 4π(125)x³y³z³

Volume of the sphere = 500πx³y³z³

<em>Hence the volume of the sphere is 500πx³y³z³ mm³</em>

8 0
2 years ago
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