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tiny-mole [99]
3 years ago
5

If y varies directly as x and inversely as z, and y = 32 whe x = 4 and z = 6, find y when x = 10 and z = 26

Mathematics
1 answer:
satela [25.4K]3 years ago
7 0

The value of y is 18.46 when x=10 and z = 26

Step-by-step explanation:

The direct proportion is denoted as:

y∝x

And the inverse proportion will be denoted as:

y∝1/z

combining both

y∝ x/z

When the symbol of proportionality is removed, the proportionality constant is introduced

y = k\frac{x}{z}

Given

y = 32 when x=4 and z = 6

Putting the values

32 = k * \frac{4}{6}\\k = 32 * \frac{6}{4}\\k = 8*6\\k = 48

So the equation will become:

y = 48* \frac{x}{z}

Putting x=10 and z= 26

y = 48 * \frac{10}{26}\\y = \frac{480}{26}\\y = 18.4615

Hence,

The value of y is 18.46 when x=10 and z = 26

Keywords: Proportion, variation

Learn more about proportion at:

  • brainly.com/question/4054269
  • brainly.com/question/4163549

#LearnwithBrainly

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32​% of college students say they use credit cards because of the rewards program. You randomly select 10 college students and a
Tems11 [23]

Answer:

a) P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

b) P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

c) P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=10, p=0.32)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

Part b

P(X> 2)=1-P(X\leq 2)=1-[P(X=0)+P(X=1)+P(X=2)]

P(X=0)=(10C0)(0.32)^0 (1-0.32)^{10-0}=0.0211  

P(X=1)=(10C1)(0.32)^1 (1-0.32)^{10-1}=0.0995

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

Part c

P(2 \leq x \leq 5)=P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X=3)=(10C3)(0.32)^3 (1-0.32)^{10-3}=0.264

P(X=4)=(10C4)(0.32)^4 (1-0.32)^{10-4}=0.218

P(X=5)=(10C5)(0.32)^5 (1-0.32)^{10-5}=0.123

P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

6 0
3 years ago
Solve the equation and find value of 'x' in 2x=(360/4)
uranmaximum [27]
2x = 360/4
x = 90 / 2
x = 45

Hope this is the answer you are looking for! 
8 0
3 years ago
According to an article in Newsweek, the natural ratio of girls to boys is 100:105. In China, the birth ratio is 100:114 (46.7%
mojhsa [17]

Answer:

z=\frac{0.42 -0.467}{\sqrt{\frac{0.467(1-0.467)}{150}}}=-1.154  

p_v =2*P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of girls born is not significantly different from 0.467

Step-by-step explanation:

Data given and notation

n=150 represent the random sample taken

X=63 represent the number of girls born

\hat p=\frac{63}{150}=0.42 estimated proportion of girls born

p_o=0.467 is the value that we want to test

\alpha=0.05 represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportion if girls is 0.467.:  

Null hypothesis:p=0.467  

Alternative hypothesis:p \neq 0.467  

When we conduct a proportion test we need to use the z statistic, and the is given by:  

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

The One-Sample Proportion Test is used to assess whether a population proportion \hat p is significantly different from a hypothesized value p_o.

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

z=\frac{0.42 -0.467}{\sqrt{\frac{0.467(1-0.467)}{150}}}=-1.154  

Statistical decision  

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level provided \alpha=0.05. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

p_v =2*P(z  

So the p value obtained was a very high value and using the significance level given \alpha=0.05 we have p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of girls born is not significantly different from 0.467

3 0
3 years ago
A line has this equation: y = -8x + 8,
DIA [1.3K]
Parallel lines have the same slope
Y = -8x + 8
The slope will be -8
Therefore: y = -8x + b
Plug in the point
7 = -8(9) + b
7 = -72 + b, b = 79

Solution: y = -8x + 79
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In triangle DEF, CG = (x + 5) units and DG = (3x – 2).<br><br><br><br> What is DG? ______units
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