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PIT_PIT [208]
1 year ago
6

You and your friend drive toward each other. The equation 50h=190−45h, h represents the number of hours until you and your frien

d meet. When will you meet? Solve for h

Mathematics
2 answers:
Ksivusya [100]1 year ago
8 0

Answer:

You meet with your friend after 2 hours.

Step-by-step explanation:

Consider the provided equation.

50h=190-45h

Where, h represents the number of hours until you and your friend meet.

We need to solve the equation for h.

Add 45h to both the sides of the equation.

50h+45h=190-45h+45h

95h=190

Now divide both the sides by 95.

\frac{95h}{95}=\frac{190}{95}

h=2

Hence, you meet with your friend after 2 hours.

AlladinOne [14]1 year ago
5 0
Here you go, hope it helps! :)

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Step-by-step explanation:

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Have you ever been frustrated because you could not get a container of some sort to release the last bit of its contents? The ar
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Answer:

Yes. There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.

Step-by-step explanation:

The sample of the remaining toothpaste is: [.53, .65, .46, .50, .37].

This sample has a size n=5, a mean M=0.502 and standard deviation s=0.102.

M=\dfrac{1}{5}\sum_{i=1}^{5}(0.53+0.65+0.46+0.5+0.37)\\\\\\ M=\dfrac{2.51}{5}=0.502

s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{5}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.53-(0.502))^2+...+(0.37-(0.502))^2]}\\\\\\s=\sqrt{\dfrac{1}{4}\cdot [(0.001)+(0.022)+(0.002)+(0)+(0.017)]}\\\\\\            s=\sqrt{\dfrac{0.04188}{4}}=\sqrt{0.01047}\\\\\\s=0.102

The 10% of the advertised content is:

0.10\cdot 6.0\;oz=0.6\:oz

Hypothesis test for the population mean:

The claim is that the remaining toothpaste is significantly is less than 10% of the advertised net content.

Then, the null and alternative hypothesis are:

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The significance level is 0.05.

The estimated standard error of the mean is computed using the formula:

s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.102}{\sqrt{5}}=0.046

Then, we can calculate the t-statistic as:

t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{0.502-0.6}{0.046}=\dfrac{-0.098}{0.046}=-2.148

The degrees of freedom for this sample size are:

df=n-1=5-1=4

This test is a left-tailed test, with 4 degrees of freedom and t=-2.148, so the P-value for this test is calculated as (using a t-table):

P-value=P(t

As the P-value (0.049) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the remaining toothpaste is significantly is less than 10% of the advertised net content.

7 0
2 years ago
Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned by 10x2+4xâ1, 3xâ4x2+3, and
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I suppose

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The vectors that span H form a basis for P_2 if they are (1) linearly independent and (2) any vector in P_2 can be expressed as a linear combination of those vectors (i.e. they span P_2).

  • Independence:

Compute the Wronskian determinant:

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The determinant is non-zero, so the vectors are linearly independent. For this reason, we also know the dimension of H is 3.

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which is equivalent to the system

\begin{bmatrix}10&-4&5\\4&3&1\\-1&3&-1\end{bmatrix}\begin{bmatrix}k_1\\k_2\\k_3\end{bmatrix}=\begin{bmatrix}a\\b\\c\end{bmatrix}

The coefficient matrix is non-singular, so it has an inverse. Multiplying both sides by that inverse gives

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Answer:the uncle is 54 years old.

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Let x represent the age of the uncle.

Let y represent the age of the woman that he married.

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He wittily replies, "Ah, but in 18 years time I shall only be twice her age. It means that

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Substituting x = 3y into equation 1, it becomes

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y = 18

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x = 54

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1 year ago
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