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4 years ago

What is the equation of the line that passes through the point (6, 1) and is perpendicular to the line y = –3x + 2

1 answer:

4 0

The slope of the given equation of the line, y = -3x + 2 is equal to -3. The slope of the line perpendicular to it is 1/3. The equation of the line may be expressed in slope-point form which can generally be expressed as,
y - y1 = m(x - x1)
Substituting the values,
y - 6 = (1/3)(x - 1)
Simplifying,
y = x/3 +17/3
The answer is not among the choices.

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One bottle contains 341 ml of juice. Céline buys 2 cases of 24 bottles of juice. Nicole buys 3 cases of 12 bottles of juice. Who

Helga [31]

Answer: Celine, 4092 ml

Step-by-step explanation:

Given

1 bottle contains 341 ml Juice

Celine buys 2 cases of 24 bottles i.e. a total of 48 bottles

Nicole buys 3 cases of 12 bottles i.e. a total of 36 bottles

Amount of Juice Celine has

$\Rightarrow 48\times 341=16,368\ ml$

Amount of Juice Nicole has

$\Rightarrow 36\times 341=12,276\ ml$

Thus, Celine has more juice than Nicole

$\Rightarrow 16,368-12,276=4092\ ml$

Celine has 4092 ml more than Nicole

7 0

3 years ago

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to spli

Rudik [331]

Answer:

1) The equation 1/8(x+16)=76/8 represents the situation, where x is the food bill.

2) The solution x=60 represents the total food bill.

These both answers are correct.

Step-by-step explanation:

Since there are 8 group of friends, and the total amount spent by them is $76 including the tip i.e $16.

If x is the food bill our equation can be:

(x+16)/8 = 76/8

Solving the equation

(x+16)/8 = 9.5

x+16= 9.5*8

x= 76 -16

x= 60

The food bill is x=60.

6 0

3 years ago

Read 2 more answers

A nursery owner owner buys 8 panes they cost 19.60 she breaks 3 more how much do the 3 cost

shtirl [24]

Answer:

Step-by-step explanation:

6 0

3 years ago

Find a particular solution to the nonhomogeneous differential equation y'' + 4 y = cos(2x) + sin(2x).

alukav5142 [94]

The characteristic solution follows from solving the characteristic equation,

$r^2+4=0\implies r=\pm2i$

so that

$y_c=C_1\cos2x+C_2\sin2x$

A guess for the particular solution may be $a\cos2x+b\sin2x$ , but this is already contained within the characteristic solution. We require a set of linearly independent solutions, so we can look to

$y_p=ax\cos2x+bx\sin2x$

which has second derivative

${y_p}''=(-4ax+4b)\cos2x+(-4bx-4a)\sin2x$

Substituting into the ODE, you have

$y''+4y=\cos2x+\sin2x$
$\implies4b\cos2x-4a\sin2x=\cos2x+\sin2x$
$\implies\begin{cases}4b=1\\-4a=1\end{cases}\implies a=-\dfrac14,b=\dfrac14$

Therefore the particular solution is

$y_p=-\dfrac14x\cos2x+\dfrac14x\sin2x$

Note that you could have made a more precise guess of

$y_p=(a_1x+a_0)\cos2x+(b_1x+b_0)\sin2x$

but, of course, any solution of the form $a_0\cos2x+b_0\sin2x$ is already accounted for within $y_c$ .

6 0

3 years ago

Use the given information to bound the p-value of the F statistic for a one-tailed test with the indicated degrees of freedom. F

lianna [129]

Answer:

The range of the p-value is: 0.050 < p-value < 0.100.

Step-by-step explanation:

For checking the equivalence of two population variances of independent samples, we use the f-test.

The test statistic is given by:

$F=\frac{S_{1}^{2}}{S_{2}^{2}}\sim F_{\alpha, (n_{1}-1)(n_{2}-1)}$

It is provided that the hypothesis test is one-tailed.

The computed value of the test statistic is:

F = 4.23.

The degrees of freedom of the numerator and denominator are:

$df_{1}=4\\df_{2}=5$

Use MS-Excel to compute the p-value as follows:

Step 1: Select function fX → F.DIST.RT.

Step 2: A dialog box will open. Enter the values of f-statistic and the two degrees of freedom.

*See the attachment below.

Step 3: Press OK.

The p-value is, 0.0728.

The range of the p-value is:

0.050 < p-value < 0.100

4 0

4 years ago