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3 years ago

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The kids in Mrs. B's class did a survey about their favorite flavors of ice cream. One-fourth of the class likes strawberry the

best. One-half of the class likes chocolate the best. The rest of the class, 7 kids, said vanilla is their favorite ice cream flavor. How many kids are in Mrs. B's class?

1 answer:

irga5000 [103]3 years ago

7 0

Answer:

28 Students

Step-by-step explanation:

Let's break down all of our variables.

$\dfrac{1}{4}$ likes strawberry

$\dfrac{1}{2}$ likes chocolate

7 likes vanilla

First we need to combine the number of students that like strawberry and chocolate.

$\dfrac{1}{4}+\dfrac{1}{2}=\dfrac{3}{4}$

This then tells us that the 7 kids that like vanilla are the remaining $\dfrac{1}{4}$ of the class.

Let's use ratio to find out how many students there are in total.

$\dfrac{1}{4}=\dfrac{7}{x}$

Let x = number of student in Mrs. B's class.

We need to multiply 4 to 7 and x to 1.

So that leave us with:

x = 28

There are 28 students total in Mrs. B's class.

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Find a set of parametric equations for y= 5x + 11, given the parameter t= 2 – x

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Answer:

$x = 2-t$ and $y = -5\cdot t +21$

Step-by-step explanation:

Given that $y = 5\cdot x + 11$ and $t = 2-x$ , the parametric equations are obtained by algebraic means:

1) $t = 2-x$ Given

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4) $y = 5\cdot \left[(-1)^{-1} \cdot (-1)\right]\cdot x +11$ Existence of multiplicative inverse/Commutative property

5) $y = [5\cdot (-1)^{-1}]\cdot [(-1)\cdot x]+11$ Associative property

6) $y = -5\cdot (-x)+11$ $\frac{a}{-b} = -\frac{a}{b}$ / $(-1)\cdot a = -a$

7) $y = -5\cdot (-x+0)+11$ Modulative property

8) $y = -5\cdot [-x + 2 + (-2)]+11$ Existence of additive inverse

9) $y = -5 \cdot [(2-x)+(-2)]+11$ Associative and commutative properties

10) $y = (-5)\cdot (2-x) + (-5)\cdot (-2) +11$ Distributive property

11) $y = (-5)\cdot (2-x) +21$ $(-a)\cdot (-b) = a\cdot b$

12) $y = (-5)\cdot t +21$ By 1)

13) $y = -5\cdot t +21$ $(-a)\cdot b = -a \cdot b$ /Result

14) $t+x = (2-x)+x$ Compatibility with addition

15) $t +(-t) +x = (2-x)+x +(-t)$ Compatibility with addition

16) $[t+(-t)]+x= 2 + [x+(-x)]+(-t)$ Associative property

17) $0+x = (2 + 0) +(-t)$ Associative property

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In consequence, the right answer is $x = 2-t$ and $y = -5\cdot t +21$ .

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irina1246 [14]

Answer:

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Step-by-step explanation:

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Using the equation and plugging in the values, you get

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Step-by-step explanation:

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Read 2 more answers

A sample survey is designed to estimate the proportion of sports utility vehicles being driven in the state of California. A ran

mart [117]

Answer:

a) The 95% confidence interval would be given (0.070;0.121).

b) "increase the sample size n"

"decrease za/2 by decreasing the confidence"

Step-by-step explanation:

Notation and definitions

$X=48$ number of vehicles classified as sports utility.

$n=500$ random sample taken

$\hat p=\frac{48}{500}=0.096$ estimated proportion of vehicles classified as sports utility vehicles.

$p$ true population proportion of vehicles classified as sports utility vehicles.

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

(a) Use a 95% confidence interval to estimate the proportion of sports utility vehicles in California. (Round your answers to three decimal places.)

The confidence interval would be given by this formula :

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 95% confidence interval the value of $\alpha=1-0.5=0.05$ and $\alpha/2=0.025$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=1.96$

And replacing into the confidence interval formula we got:

$0.096 - 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.070$

$0.096 + 1.96 \sqrt{\frac{0.096(1-0.096)}{500}}=0.121$

And the 95% confidence interval would be given (0.070;0.121).

We are confident (95%) that about 7.0% to 12.1% of vehicles in California are classified as sports utility .

(b) How can you estimate the proportion of sports utility vehicles in California with a higher degree of accuracy? (HINT: There are two answers. Select all that apply.)

For this case we just have two ways to increase the accuracy one is "increase the sample size n" since if we have a larger sample size the estimation would be more accurate. And the other possibility is "decrease za/2 by decreasing the confidence" because if we decrease the confidence level the interval would be narrower and accurate

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What is the discriminant <br><br> 3g^2+10= -15g

Ilia_Sergeevich [38]

$\bf 3g^2+10=-15g\implies 3g^2+15g+10=0
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\begin{array}{llcccll}
& 3g^2& +15g& +10\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\\\\\\
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