you have 3 bolts that are 3/8, 5/16 and 5/8 long. Which is the shortest?

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

There is the need for 4 vans.

To determine how many vans are needed for 29 students, with each van able to transport 8 students, we can use division and then round up, since you can't have a fraction of a van. We divide 29 students by 8 students per van, which gives us 3.625. Since we can't have 0.625 of a van, we need to round up to the next whole number to ensure all students have a seat. That means we need 4 vans to transport 29 students.

Divide the total number of students by the number of students each van can hold: 29 / 8 = 3.625.

Round this number up to the nearest whole number, because you need whole vans: This gives us 4.

Thus, you need 4 vans to transport 29 students.

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.

Final answer:

The volume of the square pyramid with a base length of 6 inches and a height of 8 inches is 96 cubic inches.

Explanation:

To find the volume of a square pyramid, you can use the formula V = (1/3) × base area × height, where the base area is the area of the square base. Since the base length is 6 inches, the area of the base is 6 in. × 6 in. = 36 in.². The height of the pyramid is 8 inches. So, the volume of the pyramid can be calculated as follows:

V = (1/3) × 36 in.² × 8 in. = 96 in.³

Therefore, the volume of the square pyramid is 96 cubic inches.

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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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.

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:

Option 1 - There is no extraneous solution i.e. 0.      

Step-by-step explanation:

Given : Expression [tex]\frac{9}{n^2+1}=\frac{n+3}{4}[/tex]

To find : How many extraneous solutions does the equation have ?

Solution :

First we solve to expression to determine the extraneous solution,

[tex]\frac{9}{n^2+1}=\frac{n+3}{4}[/tex]

Cross multiply,

[tex]9\times 4=(n+3)(n^2+1)[/tex]

[tex]36=n^3+n+3n^2+3[/tex]

[tex]n^3+3n^2+n-33=0[/tex]

An extraneous solution is defined as a solution, such as that to an equation, that emerges from the process of solving the problem but is not a valid solution to the problem.

The equation form is a cubic function so it has 3 solutions.

Therefore, There is no extraneous solution.

Numbers which have exactly 4 factors between 1 and 20 are 6, 8, 10, 14, 15 represented on number line.

" In mathematics factor is a number by which when we divides another number remainder is zero."

According to the question,

Factors of all the numbers between 1 and 20

2, 3, 5, 7, 11, 13, 17, 19 are prime number , so they have only two factors.

4 = 1, 2, 4

6 = 1, 2, 3, 6

8 = 1, 2, 4, 8

9 = 1, 3, 9

10 = 1, 2, 5, 10

12 = 1, 2, 3, 4, 6, 12

14 = 1, 2, 7, 14

15 = 1, 3, 5, 15

16 = 1, 2, 4, 8, 16

18 = 1, 2, 3, 6, 9, 18

Hence, we conclude that numbers which have exactly 4 factors between 1 and 20 are 6, 8, 10, 14, 15.

Learn more about factors here

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Try this explanation:

'y-interception' means x=0.

If x=0, then y=1.

answer: (0;1)

Answer:

D

Step-by-step explanation:

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.