∠1 and ∠2 are a linear pair. m∠1 = x - 29, and m∠2 = x + 61. Find the measure of each angle.

To find the point closest to the origin on the plane with equation z = 2x + 3y + 3, an offset vector from the origin to a point on the plane is used. This vector's dot product with the plane's normal vector should be zero, since the shortest path to the plane will be perpendicular to it. This creates a system of equations that can be solved for x, y, and z.

To find the closest point (x, y, z) on the given plane to the origin in three-dimensional Cartesian axes, we can start by creating an offset vector from the origin to an arbitrary point on the plane. Let's use the equation of the plane, z = 2x + 3y + 3. Let's presume a point P(x, y, z) on this plane. The vector to this point from the origin is (x, y, z - 3).

Because we want the shortest distance to the origin, the dot product of this vector and the normal vector to the plane (2, 3, -1) should be zero, because the shortest path to the plane will be perpendicular to it. So, the formula for the dot product gives us:

2*x + 3*y - (z - 3) = 0

This simplifies to:

2x + 3y - z + 3 = 0

Which combined with the equation of the plane (z = 2x + 3y + 3), provides a system of equations that can be solved using methods like Gaussian elimination or substitution.

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Answer:

The required equation is [tex](x+4)^2=-36(y+6)[/tex].

Step-by-step explanation:

The standard form of the equation of the parabola is

[tex](x-h)^2=4p(y-k)[/tex]         .... (1)

where, (h, k) is vertex and  y = k - p is directrix.

It is given that vertex of parabola is (–4, –6) and the directrix is y = 3.

[tex](-4,-6)=(h,k)[/tex]

On comparing both the sides, we get

[tex]h=-4,k=-6[/tex]

Directrix of the parabola is

[tex]y=k-p[/tex]

Put y=3 and k=-6 in the above equation.

[tex]3=-6-p[/tex]

[tex]3+6=-p[/tex]

[tex]9=-p[/tex]

[tex]-9=p[/tex]

Substitute h=-4,p=-9 and k=-6 in equation (1).

[tex](x-(-4))^2=4(-9)(y-(-6))[/tex]

[tex](x+4)^2=-36(y+6)[/tex]

Therefore the required equation is [tex](x+4)^2=-36(y+6)[/tex].

The correct option is A. Gender and handedness are associated because men are more likely to be left-handed than women. This conclusion is drawn from the different probabilities of being left-handed based on gender, indicating an association rather than independence.

A. Gender and handedness are associated because men are more likely to be left-handed than women - - This statement is correct based on the given information. Men have a [tex]12\%[/tex] likelihood of being left-handed compared to women who have a [tex]10\%[/tex] likelihood. This difference shows an association between gender and handedness.

The other incorrect options are:

B. Gender and handedness are independent because all of the possible combinations of each exist - This option is incorrect because independence between two events means that the occurrence of one event does not affect the occurrence of the other. In this case, the probability of being left-handed depends on whether the person is male or female ([tex]12\%[/tex] for men and [tex]10\%[/tex] for women), indicating an association rather than independence.

C. Gender and handedness are associated because the percentage is an estimate - This option is incorrect because the percentages given ([tex]12\%[/tex]for men and [tex]10\%[/tex] for women) are specific probabilities based on data, not estimates. The difference in these probabilities reflects an association between gender and handedness.

D. Gender and handedness are independent because they are both comprised of mutually exclusive events - This option is incorrect because being male or female (gender) and being left-handed (handedness) are not mutually exclusive events. One can be male or female and still be left-handed or right-handed. Independence would require that the probability of being left-handed is the same regardless of gender, which is not the case here.

The complete Question is

About 12%  of men and 10%  of women are left-handed. If a person is selected at random, are the event that the person is male and the event that the person is handed independent or associated?

Choose the correct answer below.

A.  Gender and handedness are associated because men are more likely to be left handed than women

B.  Gender and handedness are independent because all of the possible combinations of each exist

C.  Gender and handedness are associated because the percentage is an estimate

D. Gender and handedness are independent because they are both comprised of mutually exclusive events

Answer:

D

Step-by-step explanation:

Final answer:

By dividing the total minutes (72) by the minutes per problem (6), we find that the student can solve 12 algebra problems in 72 minutes.

Explanation:

The student asking how many algebra problems can be solved in 72 minutes if each problem takes 6 minutes can be answered with a simple division operation. You divide the total available time by the time taken for each problem to find the number of problems that can be solved. In this case, 72 minutes ÷ 6 minutes per problem equals 12 problems.

Answer:

8.25 in.

Step-by-step explanation:

In order to solve this you just have to clear the equation that Kylie created to calcuate the diameter of the circle for diameter, in this case, you just need to do the next steps:

[tex]4(d+4)=7^{2} \\4(d+4)=49\\d+4=\frac{49}{4} \\d+4=12.25\\d=12.25-4\\d=8.25[/tex]

Now we know that the diameter of the circle is 8.25 inches.

Answer:

Monthly Payment = $2,286.85

Interest on first month payment = $1,793.75

Principal value on first month payment =  $493.10

Step-by-step explanation:

lars has been approved for $420,000 for loan.

Time for loan = 20-years

APR (Annual Rate of interest ) = 5.125%

We need to find monthly payment. First month interest and First month principle.

Formula for loan:

[tex]p=\dfrac{PV\cdot \frac{r}{n}}{1-(1+\frac{r}{n})^{-nt}}[/tex]

Where,

p is monthly payment.

PV = Loan Amount (PV=$420,000)

R = Rate of interest (R=0.05125)

t = Loan period ( t=30)

n = Mode of payment (n=12)

Substitute the value into formula and solve for p

[tex]p=\dfrac{420000\cdot \frac{0.05125}{12}}{1-(1+\frac{0.05125}{12})^{-12\cdot 30}}[/tex]

p=$2,286.85

Thus, Monthly Payment =$2,286.85

Interest for first month [tex]=420000\times \dfrac{0.05125}{12}=1793.75[/tex]

Interest pay on the loan in on month = $1,793.75

Principle value on first month payment = 2286.85 - 1793.75 = $493.10

The monthly payment will go towards the principal is $493.10

Reuben deposits $700 at a 5% annual interest rate for 3 years, using the simple interest formula, he will earn $105 in interest over that period.

The question deals with calculating the simple interest Reuben will receive by depositing $700 into an account at a 5% annual interest rate over 3 years. To calculate simple interest, the formula used is Interest = Principal × Rate × Time. In this scenario, the principal (P) is $700, the rate (R) of interest per year is 5% or 0.05 when expressed as a decimal, and the time (T) is 3 years.

Substituting these values into the formula provides us with: Interest = $700 × 0.05 × 3. Simplifying this gives us: Interest = $105.

Therefore, Reuben will be paid $105 in interest over the first 3 years.

Real Question:

You Make A Table To Use AS A Quick Reference Guide. [tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]

Use The Table Tool To Answer The Question:

[tex]\left[\begin{array}{ccc}-8&-104\\-9&-92\\-10&-80\\-11&-68\\-12&-56\end{array}\right][/tex]

What is the y-value when x equals -11?  

[tex]\left[\begin{array}{ccc}y = -200 -12 (x)\end{array}\right][/tex]

Step-By-Step Explanation:

Plug In The X-Value [tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\end{array}\right][/tex]

Then You'll Multiply [tex]\left[\begin{array}{ccc}-12(x) Or -12(-11)\\132\end{array}\right][/tex]

To Find The Y-Value Simplify [tex]\left[\begin{array}{ccc}y=-200+132\\y=-68\end{array}\right][/tex]

Answer:

[tex]\left[\begin{array}{ccc}y=-200-12(x)\\y=-200-12(-11)\\y=-200+132\\ y=-68\end{array}\right][/tex]

Answer with explanation:

it is given that ,6.8% of standard normal curve lies to left of z.

6.8% [tex]=\frac{6.8}{100}\\\\=0.068[/tex]

We will use z table to calculate the value of z.

First we will go on y axis in z table to see value of 0.06 and then on 0.08 on x axis.Their point of intersection will give value of z at 0.068, which is equal to 0.2483.

Value of Z ,at 6.8% ,when the curve is normal = 0.25

⇒0.25 represents area in the left of ,z=0.068.

The z-score corresponding to 6.8% in the standard normal distribution is approximately -1.48, rounding to two decimal places, ensuring 6.8% lies to the left.

To find the z-score such that 6.8% of the standard normal curve lies to the left of it,

use a standard normal distribution calculator.

For the z-score corresponding to the cumulative probability of 0.068 (6.8%).

Using a standard normal distribution calculator:

The cumulative probability of 0.068 (or 6.8%) in the standard normal distribution calculator.

find the z-score associated with this probability.

The z-score corresponding to a cumulative probability of 0.068 is approximately -1.48 (rounded to two decimal places).

Therefore, the z-score z such that 6.8% of the standard normal curve lies to the left of it is approximately -1.48.

Learn more about z-score here

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The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

The sum of the two numbers is 45. One number is 4 times as large as the other.

Let the two numbers be x and y. Then the equation is given as,

x + y = 45      ...1

y = 4x            ...2

From equations 1 and 2, then we have

x + 4x = 45

5x = 45

x = 9

Then the value of y will be

y = 4(9)

y = 36

The value of the variable x and y whose sum is 45 will be 9 and 36, respectively.

More about the solution of the equation link is given below.

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The expected value for the sampling distribution of the sample mean is -12.2. The standard error for the sampling distribution of the sample mean is 0.6250.

The expected value for the sampling distribution of the sample mean can be calculated using the formula µx = μ = -12.2. So, the expected value is -12.2.

The standard error for the sampling distribution of the sample mean can be calculated using the formula σx = σ/√n, where σ is the population standard deviation and n is the sample size.

Substituting the given values, we get σx = 5/√64 = 0.6250 (rounded to four decimal places).

The expected value and the standard error for the sampling distribution of the sample mean is 0.6250.

Expected Value: -12.2

Standard Error: 0.6250

1. The expected value (mean) of the sampling distribution of the sample mean is equal to the population mean, which is given as -12.2. Therefore, the expected value of the sampling distribution is also -12.2.

2. The standard error (SE) of the sampling distribution of the sample mean is calculated using the formula:

[tex]\[ SE = \frac{\sigma}{\sqrt{n}} \][/tex]

where [tex]\sigma[/tex] is the population standard deviation and n is the sample size.

Given [tex]\sigma[/tex] = 5 and n = 64, we can calculate the standard error as follows:

[tex]\[ SE = \frac{5}{\sqrt{64}} = \frac{5}{8} = 0.625 \][/tex]

Rounded to four decimal places, the standard error is 0.6250.