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3 years ago

A choreographer uses a number line to position dancers for a ballet. Dancers A and B

Mathematics

2 answers:

vovangra [49]3 years ago

8 0

Answer:

the coordinates of dancer c = 15

Step-by-step explanation:

the coordinates of dancer A is 5 and the coordinate of dancer B is 23

the distance between dancer A and dancer B is

distance = 23 -5

= 18

so,

as dancer C is 5/9 of the distance from dancer A to dancer B, find the 5/9 of the distance .

5/9 of distance = 5/9(18)

= 10

add the above value to coordinates of dancers A to find the coordinates dancer C

coordinate of dancer c = 10 + 5

= 15

hence , the coordinates of dancer c = 15

kenny6666 [7]3 years ago

5 0

First we will calculate the distance AB.
$AB=B-A=23-5=18.$
If C is 5/9 of the distance, mathematically speaking that means:
$C= \frac{5}{6} *AB= \frac{5}{6} *18=15.$
R: The coordonate of C is 15.

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What is the equation of this graph

Gekata [30.6K]

Answer:

y = (1/2)(x + 4)(x + 1)(x - 3)

Step-by-step explanation:

Since this graph begins in Quadrant III and continues growing in Quadrant I, and has three roots/zeros, we know immediately that it's a cubing function and can confidently write out

y = d(x - a)(x - b)(x - c) as one general form of the cubing function.

In this particular case we have:

y = d(x + 4)(x + 1)(x - 3) (where the '4' comes from the x-intercept (-4, 0) )

From the graph we know that y = -6 when x = 0, and therefore:

-6 = d(0 + 4)(0 + 1)(0 - 3), or -6 = d(-12), leading to d = 1/2

Then our tentative equation (above) becomes y = (1/2)(x + 4)(x + 1)(x - 3)

5 0

3 years ago

The sum of the edged of a cube is 24 inches. Find the length of each edge

sertanlavr [38]

24 divided by 12 is 2

4 0

4 years ago

Eliza started her savings account with $100. Each month she deposits $25 into her account. Determine the average rate of change

Afina-wow [57]

First, lets create a equation for our situation. Let $x$ be the months. We know four our problem that Eliza started her savings account with $100, and each month she deposits $25 into her account. We can use that information to create a model as follows:
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We want to find the average value of that function from the 2nd month to the 10th month, so its average value in the interval [2,10]. Remember that the formula for finding the average of a function over an interval is: $\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1} }$ . So lets replace the values in our formula to find the average of our function:
$\frac{25(10)+100-[25(2)+100]}{10-2}$
$\frac{350-150}{8}$
$\frac{200}{8}$
$25$

We can conclude that the average rate of change in Eliza's account from the 2nd month to the 10th month is $25.

6 0

3 years ago

A psychologist has designed an index to measure the social perceptiveness of elementary school children. The index is based on r

Zanzabum

Complete Question

A psychologist has designed an index to measure the social perceptiveness of elementary school children. The index is based on ratings of a child's responses to questions about a set of photographs showing different social situations. A random sample of 16 elementary school children was chosen, and their index measurements were recorded. Assume that the index measure in the population is normally distributed. The 95% confidence interval created from this data is (56.29, 65.09). This interval indicates:__________.Choose one or more:

a. The average index of elementary school children must be 60.69.

b. The standard deviation of the sample is about 10% smaller than the population standard deviation.

c. That if we take many samples from this population 95% of them will have a sample mean between 56.29 and 65.09.

d. 95% of all elementary school children in this district have indices between 56.29 and 65.09.

e. 4.40 is 95% of the true average of the index for all elementary school children.

f. We are 95% confident that the average index for all elementary school children is between 56.29 and 65.09.

Answer:

The correct option is a and f

Step-by-step explanation:

From the question we are told that

The sample size is n = 16

The 95% confidence interval is (56.29, 65.09)

Generally the sample mean(average index of elementary school children) is mathematically represented as

$\= x = \frac{65.09 + 56.29}{2}$

=> $\= x = 60.69$

5 0

4 years ago

The steps to derive the quadratic formula are shown below:

insens350 [35]

Answer:

$x^{2} +\frac{b}{a} x+(\frac{b}{2 a} )^{2} = \frac{-c}{a} + (\frac{b}{2 a}) ^{2}$

Step-by-step explanation:

Step(i):-

Given quadratic equation ax² + bx + c = 0

step(ii):-

ax² + bx = -c

Step(iii):-

Dividing 'a' on both sides , we get

$\frac{ax^{2} +bx }{a} = \frac{-c}{a}$

$x^{2} + \frac{bx}{a} = \frac{-c}{a}$

Step(iv):-

Adding $(\frac{b}{2 a} )^{2}$ on both sides , we get

$x^{2} +\frac{b}{a} x+(\frac{b}{2 a} )^{2} = \frac{-c}{a} + (\frac{b}{2 a}) ^{2}$

8 0

4 years ago