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IgorLugansk [536]

1 year ago

15

You could win a giant jar of jelly beans if only you could guess how many are in the jar. You find a smaller jar such that the g

iant one is exactly five times the smaller one in each dimension. If you count 83 jelly beans in your smaller jar, about how many should be in the giant jar?

2 answers:

Gennadij [26K]1 year ago

4 0

The giant jar of jelly beans is 5 times the size of the smaller jar. If there are 83 jelly beans in the smaller jar, the giant jar can be represented as 5(83).

5(83) = 415 jelly beans

KatRina [158]1 year ago

4 0

Answer: 415 jelly beans.

Step-by-step explanation:

Since, the ratio between the size of smaller jar and larger jar = 1 : 5

Thus, the ratio between the number of jellies contains by smaller and larger jar = 1 : 5

Let the jellies in smaller jar = x,

The jellies in larger jars = 5 x

Where x is any number.

According to the question,

The number of jellies in smaller jar = 83,

⇒ x = 83,

⇒ The number of jellies in larger jar = 5 x = 5 × 83 = 415

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1 year ago

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2 years ago

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Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6

lora16 [44]

Answer:

The answer is the option C

graph of $3x$ minus $3$ , with discontinuity at negative $2$ , negative $9$

Step-by-step explanation:

we have

$f(x)=\frac{9x^{2}+9x-18}{3x+6}$

Simplify

$f(x)=9\frac{(x^{2}+x-2)}{3(x+2)}$

$f(x)=3\frac{(x^{2}+x-2)}{(x+2)}$

Step 1

Convert to a factored form the numerator

$x^{2}+x-2=0$

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

$x^{2}+x=2$

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

$x^{2}+x+0.25=2+0.25$

$x^{2}+x+0.25=2.25$

Rewrite as perfect squares

$(x+0.5)^{2}=2.25$

Square root both sides

$x+0.5=(+/-)1.5$

$x=-0.5(+/-)1.5$

$x=-0.5+1.5=1$

$x=-0.5-1.5=-2$

so

$x^{2}+x-2=(x-1)(x+2)$

Step 2

Simplify the function f(x)

$f(x)=3\frac{(x^{2}+x-2)}{(x+2)}=3\frac{(x-1)(x+2)}{(x+2)}$

The domain of the function f(x) is all real numbers except the number $x=-2$

Because the denominator can not be zero

$f(x)=3\frac{(x-1)(x+2)}{(x+2)}=3(x-1)=3x-3$

$f(x)=3x-3$ ------> with a discontinuity at $x=-2$

$f(-2)=3(-2)-3=-9$

The discontinuity is at point $(-2,-9)$

the answer in the attached figure

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2 years ago

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2 years ago

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A member of a student team playing an interactive marketing game received the fol- lowing computer output when studying the rela

nirvana33 [79]

Answer:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case for the significance level assumed $\alpha=0.05$ we see that $p_v >\alpha$ so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares procedure.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

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In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level assumed on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The p value on this case would be given by:

$p_v = 2*P(t_{n-2} > |t_{calc}|)= 0.91$

So on this case for the significance level assumed $\alpha=0.05$ we see that $p_v >\alpha$ so then we can conclude that the result is NOT significant. And we don't have enough evidence to reject the null hypothesis.

So on this case is not appropiate say that :"the more we spend on advertising this product, the fewer units we sell" since the slope for this case is not significant.

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2 years ago