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iragen [17]
3 years ago
6

What is the equation of a line that is perpendicular to y=3x-2 and passes through the point (6 8) ?

Mathematics
1 answer:
Scrat [10]3 years ago
8 0
The result is a line perpendicular to y=3x-2
This line has the following equation: y =mx + b, where m = slope

Remember that the product of the slopes of two perpendicular lines is always = -1 (or in other term one is the reciprocal inverse of the other) so the
first slope = 3 and the sope perpendicular to 3 will be - 1/3.
Then the new equation is y = - 1/3(x) + b
How to calculate b? This line passes through (6, 8), that
means (x=6 and y=8) . Plug these values in y = -1/3 (x)+b:3
 8=(-1/3)(6) + b; 
8= - 2 + b and b = 10
Te final equation is y = - 1/3.x+10 (answer A)
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which container hold the most? a. cylinder with a radius of 5 in and a height of 15 in b. sphere with a radius 6in c. come with
stepan [7]
Vcylinder=hpir^2 Vsphere=(4/3)pir^3 Vcone=(1/3)hpir^2 Vcylinder=15*pi*5^2=375pi in^3 Vsphere=(4/3)*pi*6^3=288pi in^3 Vcone=(1/3)*15*pi*8^2=320pi in^3 greatest is Vcylinder at 375pi in^3 answer is A (cylinder)
8 0
3 years ago
If Siobhan hits a 0.25 kg volleyball with 0.5 N of force, what is the acceleration of the ball?
krek1111 [17]

Answer:

Force = mass x acceleration

Therefore,

acceleration = Force / mass

Acceleration = 0.5 / 0.25

Acceleration = 2 m/s²

Step-by-step explanation:

Force = mass x acceleration

Therefore,

acceleration = Force / mass

Acceleration = 0.5 / 0.25

Acceleration = 2 m/s²

5 0
3 years ago
Neil has 3 partially full cans of white paint.They contain 1/3 gallon, 1/5, gallon, and 1/2, gallons of paint About how much pai
stepan [7]

Answer:

1 and 1/30 gallons

Step-by-step explanation:

First, convert all the fractions to a common denominator. I'm choosing 30.

1/3=10/30  1/5=6/30  1/2=15/30

Now, you can add them together to get 31/30, so a little more than a gallon

7 0
3 years ago
1).Calculate T, when sample mean is 120, population mean is 100, standard deviation is 20 and smaple size is 10 using levels of
Sonbull [250]

Answer:

t=\frac{120-100}{\frac{20}{\sqrt{10}}}=3.16  

p_v =2*P(t_{9}>3.16)=0.012  

If we compare the p value and a significance level assumed \alpha=0.05 we see that p_v so we can conclude that we can reject the null hypothesis, and the true mean is significantly different from 100 at 5% of significance.  

Step-by-step explanation:

Data given and notation

\bar X=120 represent the sample mean  

s=20 represent the standard deviation for the sample

n=10 sample size  

\mu_o =100 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)  

State the null and alternative hypotheses to be tested  

We need to conduct a hypothesis in order to determine if the mean is different from 100, the system of hypothesis would be:  

Null hypothesis:\mu = 100  

Alternative hypothesis:\mu \neq 100  

Compute the test statistic  

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:  

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)  

t-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".  

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

t=\frac{120-100}{\frac{20}{\sqrt{10}}}=3.16  

Now we need to find the degrees of freedom for the t distirbution given by:

df=n-1=10-1=9

Conclusion

Since is a tao tailed test the p value would be:  

p_v =2*P(t_{9}>3.16)=0.012  

If we compare the p value and a significance level assumed \alpha=0.05 we see that p_v so we can conclude that we can reject the null hypothesis, and the true mean is significantly different from 100 at 5% of significance.  

8 0
3 years ago
Read 2 more answers
Verify each of the following by evaluating the logarithms.<br> log10(103) + log10(104) = log10(107)
ioda

Answer:

log₁₀(10³) + log₁₀(10⁴)

= log₁₀( 10³ × 10⁴ )

= log₁₀( 10³⁺⁴)

= log₁₀( 10⁷)

Step-by-step explanation:

Given:

log₁₀(10³) + log₁₀(10⁴) = log₁₀(10⁷)

Now,

we know the property of log function that

log(A) + log(B) = log(AB)

therefore,

applying the above property on the LHS, we get

log₁₀(10³) + log₁₀(10⁴) = log₁₀( 10³ × 10⁴ )

also,

xᵃ + xᵇ = xᵃ⁺ᵇ

therefore,

log₁₀( 10³ × 10⁴ ) = log₁₀( 10³⁺⁴)

= log₁₀( 10⁷)

Hence,

LHS = RHS

Hence proved

7 0
3 years ago
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