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raketka [301]
3 years ago
13

An alloy is composed of nickel, zinc, and copper in a 7:2:9 ratio. How many kilograms of each metal is needed to make 3.8 kg of

this alloy?
Mathematics
1 answer:
Tamiku [17]3 years ago
6 0
Ni : Zn: Cu = 7:2:9 =7x : 2x : 9x

7x+2x+9x = 3.8
18x=3.8
x=3.8/18=1.9/9≈0.21

Ni:   7x=7*0.21=1.47 ≈1.5 kg
Zn:  2x=2*0.21=0.42≈0.4 kg
Cu: 9x=9*0.21=1.89 ≈1.9 kg

Check 1.5+0.4+1.9 =3.8 True
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&&x_1&&y_1&&x_2&&y_2\\
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%  (c,d)
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3 years ago
Recall from Intermediate Algebra that two non-vertical lines are perpendicular if and only if they have negative reciprocal slop
OLEGan [10]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The line is y  =  -4 x

Step-by-step explanation:

From the question we are told that

The line is y  =  \frac{1}{4} x  + 8

The point is P(0,0 )

Generally the equation for a line is yn =  mx  + c

Now comparing this with the given equation we see that

m  =\frac{1}{4} =  slope

C  =8  =  intercept

Generally the slope of the perpendicular to the given line is mathematically evaluated as

m_1  = -  \frac{1}{m}

=> m_1  = -  \frac{1}{ \frac{1}{4}}

=> m_1  = -4

Generally from the univesal equation of a line and the given point we have that

y = mx + c at p(0,0) and m_1 =  -4 is

0 = -4 (0 ) + c

=> c = 0

Hence the equation perpendicular to the line given at the point given is

y  =  -4 x

8 0
3 years ago
sanjay hockey team played 25 games each season they won 80% of there game. How many games did they lose
Contact [7]

Answer:

5 games

Step-by-step explanation:

Do 80% of 25 which would be 20 and then you can determine how many they lost so if they won 20 games and they have 25 games total then they lost 5 games.

3 0
3 years ago
Which expression is equivalent to (81x4y16)12 for all positive values of x and y?<br> 40.5x4y16
IrinaVladis [17]

Answer:

(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8

Step-by-step explanation:

Given

(81x^4y^{16})^{\frac{1}{2}}

Required

Determine an equivalent expression

Express 81 as 9^2

(9^2x^4y^{16})^{\frac{1}{2}}

Apply law of indices

9^2^{\frac{1}{2}} * x^4^{\frac{1}{2}} * y^{16}^{\frac{1}{2}}

9^{\frac{2*1}{2}} * x^{\frac{4*1}{2}} * y^{\frac{16*1}{2}}

9^{\frac{2}{2}} * x^{\frac{4}{2}} * y^{\frac{16}{2}}

9^1 * x^2 * y^8

9 * x^2 * y^8

9 x^2 y^8

Hence:

(81x^4y^{16})^{\frac{1}{2}} = 9 x^2 y^8

4 0
3 years ago
We're testing the hypothesis that the average boy walks at 18 months of age (H0: p = 18). We assume that the ages at which boys
marusya05 [52]

Answer:

II. This finding is significant for a two-tailed test at .01.

III. This finding is significant for a one-tailed test at .01.

d. II and III only

Step-by-step explanation:

1) Data given and notation    

\bar X=19.2 represent the battery life sample mean    

\sigma=2.5 represent the population standard deviation    

n=25 sample size    

\mu_o =18 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)    

p_v represent the p value for the test (variable of interest)    

2) State the null and alternative hypotheses.    

We need to conduct a hypothesis in order to check if the mean battery life is equal to 18 or not for parta I and II:    

Null hypothesis:\mu = 18    

Alternative hypothesis:\mu \neq 18    

And for part III we have a one tailed test with the following hypothesis:

Null hypothesis:\mu \leq 18    

Alternative hypothesis:\mu > 18  

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:    

z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}} (1)    

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".    

3) Calculate the statistic    

We can replace in formula (1) the info given like this:    

z=\frac{19.2-18}{\frac{2.5}{\sqrt{25}}}=2.4    

4) P-value    

First we need to calculate the degrees of freedom given by:  

df=n-1=25-1=24  

Since is a two tailed test for parts I and II, the p value would be:    

p_v =2*P(t_{(24)}>2.4)=0.0245

And for part III since we have a one right tailed test the p value is:

p_v =P(t_{(24)}>2.4)=0.0122

5) Conclusion    

I. This finding is significant for a two-tailed test at .05.

Since the p_v. We reject the null hypothesis so we don't have a significant result. FALSE

II. This finding is significant for a two-tailed test at .01.

Since the p_v >\alpha. We FAIL to reject the null hypothesis so we have a significant result. TRUE.

III. This finding is significant for a one-tailed test at .01.

Since the p_v >\alpha. We FAIL to reject the null hypothesis so we have a significant result. TRUE.

So then the correct options is:

d. II and III only

6 0
3 years ago
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