Ask question

Ask question

All categories

1 year ago

15

Sue had finished three Christmas gifts before the first of December. After that she finished one gift each day. Which equation d

escribes her work if G = gifts and D = days?

1 answer:

Verdich [7]1 year ago

6 0

Xxxxxxxxxxxxxxxxxxxx

You might be interested in

What is the value of n in the equation –negative StartFraction one-half EndFraction left-parenthesis 2 n plus 4 right-parenthesi

fgiga [73]

Answer:

Solution to equation: $n = 1$

Step-by-step explanation:

We are given the following equation:

$-\dfrac{1}{2}(2n + 4) + 6 = -9 + 4(2n + 1)$

We have to solve the equation to find the value of n.

Solving the equation, we get,

$-\dfrac{1}{2}(2n + 4) + 6 = -9 + 4(2n + 1)\\\\-\dfrac{1}{2}(2n + 4)-4(2n+1) = -9-6\\\\-n-2-8n-4 = -15\\\Rightarrow -9n = -15 + 6\\\Rightarrow -9n = -9\\\Rightarrow n = 1$

Thus, value of n is 1.

4 0

1 year ago

Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-directi

miss Akunina [59]

Answer:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

Step-by-step explanation:

1st boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=1\\ \\b=-2a$

Equation:

$y=ax^2 -2ax+c$

The y-coordinate of the vertex:

$y_v=a\cdot 1^2-2a\cdot 1+c\Rightarrow a-2a+c=10\\ \\c-a=10$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-2a\cdot (-8)+c\\ \\80a+c=1$

Solve:

$c=10+a\\ \\80a+10+a=1\\ \\81a=-9\\ \\a=-\dfrac{1}{9}\\ \\b=-2a=\dfrac{2}{9}\\ \\c=10-\dfrac{1}{9}=\dfrac{89}{9}$

Parabola equation:

$y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}$

2nd boat:

Parabola equation:

$y=ax^2 +bx+c$

The x-coordinate of the vertex:

$x_v=-\dfrac{b}{2a}\Rightarrow -\dfrac{b}{2a}=0\\ \\b=0$

Equation:

$y=ax^2+c$

The y-coordinate of the vertex:

$y_v=a\cdot 0^2+c\Rightarrow c=-7$

Parabola passes through the point (-8,1), so

$1=a\cdot (-8)^2-7\\ \\64a-7=1$

Solve:

$a=-\dfrac{1}{8}\\ \\b=0\\ \\c=-7$

Parabola equation:

$y=\dfrac{1}{8}x^2 -7$

System of two equations:

$\left\{\begin{array}{l}y=-\dfrac{1}{9}x^2 +\dfrac{2}{9}x+\dfrac{89}{9}\\ \\y=\dfrac{1}{8}x^2 -7\end{array}\right.$

7 0

2 years ago

Read 2 more answers

The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for adm

Nat2105 [25]

Answer:

a) 16% of GMAT scores are 647 or higher.

b) 2.5% of GMAT scores are 647 or higher.

c) 34% of GMAT scores are between 447 and 547.

d) 81.5% of GMAT scores are between 347 and 647.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 547

Standard deviation = 100

a. What percentage of GMAT scores are 647 or higher?

The Empirical rule states that 68% of the scores are within 1 standard deviation of the mean, that is, from 547 - 100 = 447 to 547 + 100 = 647. So 32% of the scores are outside the interval. Since the distribution is symmetric, 16% of them are lower than 447 and 16% of them are higher than 647.

So

16% of GMAT scores are 647 or higher.

b. What percentage of GMAT scores are 747 or higher (to 1 decimal)?

The Empirical rule states that 95% of the scores are within 2 standard deviations of the mean, that is, from 547 - 2*347 = 347 to 547 + 2*100 = 747. So 5% of the scores are outside the interval. Since the distribution is symmetric, 2.5% of them are lower than 347 and 2.5% of them are higher than 757

So

2.5% of GMAT scores are 647 or higher.

c. What percentage of GMAT scores are between 447 and 547?

447 is one standard deviation below the mean. The Empirical rule states that 68% of the scores are within 1 standard deviation of the mean, and since the distribution is symmetric, 34% are within one standard deviation below the mean and the mean, and 34% are within the mean and one standard deviation above the mean.

547 is the mean

447 is one standard deviation below the mean

So 34% of GMAT scores are between 447 and 547.

d. What percentage of GMAT scores are between 347 and 647 (to 1 decimal)?

The easist way is adding the percentage of scores from 347 to the mean(547) and the mean to 647.

Between 347 and 547

347 is two standard deviations below the mean. The Empirical rule states that 95% of the scores are within 2 standard deviations of the mean, and since the distribution is symmetric, 47.5% are within two standard deviation below the mean and the mean, and 47.5% are within the mean and two standard deviations above the mean.

So 47.5% of the scores are between 347 and 547

Between 547 and 647

447 is one standard deviation above the mean. The Empirical rule states that 68% of the scores are within 1 standard deviation of the mean, and since the distribution is symmetric, 34% are within one standard deviation below the mean and the mean, and 34% are within the mean and one standard deviation above the mean.

So 34% of the scores are between 547 and 647.

Between 347 and 647

47.5 + 34 = 81.5% of GMAT scores are between 347 and 647.

7 0

1 year ago

The graph of which function passes through (0,3) and has an amplitude of 3? f (x) = sine (x) + 3 f (x) = cosine (x) + 3 f (x) =

Cloud [144]

Answer:

$f(x)=3*cosine(x)$

Step-by-step explanation:

We are looking for a trigonometric function which contains the point (0, 3), and has an amplitude of 3.

We know that for a sine function $f(x)=sin(x)$ , $f(0)= 0$ ; therefore the function we a looking for cannot be a sine function because it is zero at $x=0$ .

However, the cosine function $f(x)=cos(x)$ gives non-zero value at $x=0:$

$f(0)=cos(0)=1$

therefore, a cosine function can be our function.

Now, cosine function with amplitude $a$ has the form

$f(x)=a*cos(x)$

this is because the cosine function is maximum at $x= 0$ and therefore, has the property that

$f(0)=a*cos(0)= a$

in other words it contains the point $(0, a)$ .

The function we are looking for contains the point $(0, 3)$ ; therefore, its amplitude must be 3, or

$f(x)=3cos(x)$

we see that this function satisfies our conditions: $f(x)$ has amplitude of 3, and it passes through the point (0, 3) because $f(0)=3$

8 0

2 years ago

Read 2 more answers

Heights of adult males are known to have a normal distribution. a researcher claims to have randomly selected adult males and me

8090 [49]

Answer:

The sum of the probabilities is greater than 100%; and the distribution is too uniform to be a normal distribution.

Step-by-step explanation:

The sum of the probabilities of a distribution should be 100%. When you add the probabilities of this distribution together, you have

22+24+21+26+28 = 46+21+26+28 = 67+26+28 = 93+28 = 121

This is more than 100%, which is a flaw with the results.

A normal distribution is a bell-shaped distribution. Graphing the probabilities for this distribution, we would have a bar up to 22; a bar to 24; a bar to 21; a bar to 26; and bar to 28.

The bars would not create a bell-shaped curve; thus this is not a normal distribution.

3 0

1 year ago

Read 2 more answers