A person starts walking from home and walks:
2 miles East
3 miles Southeast
6 miles South
7 miles Southwest
3 miles East
This person has walked a total of
miles

Find the total displacement vector for this walk:


If this person walked straight home, they'd have to walk
miles

Given statement solution is :- It takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

To determine the number of months it takes to pay off the credit card and the total amount paid, including interest, we can follow these steps:

Step 1: Calculate the monthly interest rate.

The APR (Annual Percentage Rate) is given as 9.5%. To find the monthly interest rate, we divide this by 12 (the number of months in a year):

Monthly interest rate = 9.5% / 12 = 0.0079167

Step 2: Determine the monthly payment.

The monthly payment is given as $400.

Step 3: Calculate the interest and principal paid each month.

The interest paid each month can be calculated by multiplying the monthly interest rate by the current balance.

Principal paid = Monthly payment - Interest paid

Step 4: Track the remaining balance each month.

Starting with the initial balance of $1,367.90, subtract the principal paid each month to determine the new balance.

Step 5: Repeat Steps 3 and 4 until the balance reaches zero.

Continue calculating the interest and principal paid each month, updating the balance, until the remaining balance becomes zero.

Step 6: Determine the total number of months and the total amount paid.

Count the number of months it takes to reach a balance of zero. Multiply the number of months by the monthly payment ($400) to find the total amount paid.

Let's calculate the number of months and the total amount paid, including interest:

Month 1:

Interest paid = 0.0079167 * $1,367.90 = $10.84

Principal paid = $400 - $10.84 = $389.16

New balance = $1,367.90 - $389.16 = $978.74

Month 2:

Interest paid = 0.0079167 * $978.74 = $7.75

Principal paid = $400 - $7.75 = $392.25

New balance = $978.74 - $392.25 = $586.49

Month 3:

Interest paid = 0.0079167 * $586.49 = $4.64

Principal paid = $400 - $4.64 = $395.36

New balance = $586.49 - $395.36 = $191.13

Month 4:

Interest paid = 0.0079167 * $191.13 = $1.51

Principal paid = $400 - $1.51 = $398.49

New balance = $191.13 - $398.49 = -$207.36 (Paid off)

It takes 4 months to pay off the credit card. Now, let's calculate the total amount paid, including interest:

Total amount paid = 4 * $400 = $1600

Therefore, it takes 4 months to pay off the card, and the total amount paid, including interest, is $1600.

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Answer:

Volume of sphere = 1.3 * 10^-7 cubic meters.

Step-by-step explanation:

Given the following data;

Diameter, D = 6.4 mm to meters = 6.4/1000 = 0.0064 meters.

But, Radius = diameter/2

Radius = 0.0064/2 = 0.0032 meters.

π = 3.14

To determine the volume of sphere, we would use the formula;

\( Volume \; of \; a \; sphere = \frac {4}{3} \pi r^{3} \)

Substituting into the equation, we have;

\( V = \frac {4}{3} * 3.14 * 0.0032^{3} \)

\( V = 4.186666667 * 3.2768 * 10^{-8} \)

Volume of sphere = 1.371886933 * 10^-7 cubic meters.

To the nearest tenth;

Volume of sphere = 1.3 * 10^-7 cubic meters.

Answer:

need more info

Step-by-step explanation:

what are we sloving

The expression that represents the month of the year, in which months will the temperature be 17°C is x = 2π

The function is given as:

f(x) = 5sin(x/12) + 14.5

When the temperature is 17°C, the equation becomes

5sin(x/12) + 14.5 = 17

Subtract 14.5 from both sides

5sin(x/12) = 2.5

Divide both sides by 5

sin(x/12) = 0.5

Take the arc sin of both sides

x/12 = π/6

Multiply both sides by 12

x = 2π

Hence, the expression that represents the month of the year, in which months will the temperature be 17°C is x = 2π

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Answer:

m ≤ 5

Step-by-step explanation:

I will begin by assuming m to be the number.

Then, the sum of m and 3 is: m + 3.

The symbol for "less than or equal to" is ≤.

So we form an inequality, like this :

m + 3 ≤ 8

To find m subtract 3 on each side:

m ≤ 5

Therefore, m ≤ 5.

Answer:

Reflexive

Step-by-step explanation:

Because C and D are right angles. That’s def of perpendicular. I’m not sure about the vertical angles but it’s shown in the proof

Answer:

Reflexive

Step-by-step explanation:

The given function y = sec⁻¹(x³) is differentiated as dy/dx = 3x/√(x² - 1).

The differentiation of a function is defined as rate of change of its value at a point. It can be written as f'(x) = Lim h --> 0 (f(x + h) - f(x)) /(x + h - x).

Its geometric meaning is the slope of tangent of the function at a given point.

The given function is as below,

y = sec⁻¹(x³)

The given function is a composite function of sec⁻¹x and x³.

In order to differentiate it, first differentiate x³ and then sec⁻¹x as follows,

dx³/dx = 3x²

And, dsec⁻¹x /dx = 1/x√(x² - 1)

Now, differentiation of sec⁻¹(x³) is given as,

d sec⁻¹(x³)/dx = 3x²/(x√(x² - 1))

                      = 3x/√(x² - 1)

Hence, the differentiation of the given function is 3x/√(x² - 1).

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Answer:

five almost 6 weeks

Step-by-step explanation:

brady is saving up to 245 but he already has 98 which means he needs to save 147 more dollars. Brady is making 25 a week so if you divide 147 by 25 you get 5.88 so in 6 weeks he can have a new skateboard with a couple extra doll hairs.

The placement results provided, the student should start with Math 100.

The placement results indicate that the student has placements for Math 111, Math 100, and Math 102+. Math 111 typically corresponds to a higher-level course than Math 100, and Math 102+ implies a placement beyond Math 102.

To progress towards Math 103E, it is essential to follow the recommended course sequence. Usually, Math courses are designed to build upon previously learned concepts and skills. Starting with Math 100 would provide the foundational knowledge necessary to succeed in subsequent courses.

Therefore, the student should first start with Math 100, and upon successful completion, they can proceed to Math 103E. It is important for the student to consult with their academic advisor or the mathematics department at their institution for specific course placement and sequencing information to ensure they are following the appropriate path.

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Based on the data, the estimated number of lemon candies in the bag of 100 assorted candies is about 19.

In mathematics, proportion refers to the relationship between two quantities that are equivalent or have a constant ratio. It is usually expressed as a fraction or a ratio. For example, if a recipe calls for 2 cups of flour and 1 cup of water, the proportion of flour to water is 2:1 or 2/1. Proportions are used in a variety of mathematical and real-world situations, such as solving problems involving ratios, rates, and percentages.

In the given question,

We can use a simple proportion to estimate the number of lemon candies in the bag. We know that Ridgette handed out a total of 6 lemon candies out of a total of candies. Therefore, the proportion of lemon candies in the bag is:

6/total candies = number of lemon candies/100

We can cross-multiply to solve for the number of lemon candies:

number of lemon candies = 6 x 100 / total candies

We can also use the information about the other flavors to estimate the total number of candies in the bag. The total number of candies is:

total candies = lemon + orange + grape + cherry

Using the information from the table, we can estimate the total number of candies:

total candies = 6 + 5 + 8 + 13 = 32

Therefore, the estimated number of lemon candies in the bag is:

number of lemon candies = 6 x 100 / 32 = 18.75

We can round this to the nearest whole number to estimate that there were about 19 lemon candies in the bag of 100 assorted candies.

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The triangle for which angle a =30\degree, angle b=45\degree, and a=20, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636

Two angles (a and b) and one side (a) are provided for us to solve the triangle. Let's call the side across from angle a side A, the side across from angle b side B, and the side across from the final angle (angle c) side C.

Here, it is given that,

angle a = 30 degrees

angle b = 45 degrees

side a = 20

angle c = 180 - (angle a + angle b)

angle c = 180 - (30 + 45)

angle c = 180 - 75

angle c = 105 degrees

We know that, a/sin(A) = b/sin(B) = c/sin(C)

a/sin(A) = b/sin(B) = c/sin(C)

20/sin(30) = b/sin(45) = c/sin(105)

b/sin(45) = 20/sin(30)

b = (sin(45) * 20) / sin(30)

b ≈ (0.7071 * 20) / 0.5

b ≈ 14.142 / 0.5

b ≈ 28.284

Now,

c/sin(105) = 20/sin(30)

c = (sin(105) * 20) / sin(30)

c ≈ (0.9659 * 20) / 0.5

c ≈ 19.318 / 0.5

c ≈ 38.636

Thus, side a ≈ 20, side b ≈ 28.284, and side c ≈ 38.636.

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Answer:

He would weigh 218.5 pounds on Jupiter

Step-by-step explanation:

If objects weigh 2.3 times as much on Jupiter then you multiply Joey's weight by 2.3.

Answer: 218.5 pounds

Step-by-step explanation: If objects on Jupiter weigh 2.3 times their weight on Earth and if Joey weighs 95 pounds on Earth, he would weigh 2.3 times of his weight on Earth on Jupiter. 2.3 times 95 pounds would be 218.5 pounds. Joey would weigh 218.5 pounds on Jupiter.

f (x) = -3x + 2

then

Dilation is 3

Horizontal shift , find 0= -3x +2, x = 2/3

Vertical shift , x= 0 , y=+2

Reflection , find slope m' = -1/m = -1/-3= 1/3

Answer:

x = - \(\frac{3}{4}\) , x = 1

Step-by-step explanation:

4x² = x + 3 ← subtract x + 3 from both sides

4x² - x - 3 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 4 × - 3 = - 12 and sum = - 1

the factors are - 4 and + 3

use these factors to split the x- term

4x² - 4x + 3x - 3 = 0 ( factor the first/second and third/fourth terms )

4x(x - 1) + 3(x - 1) = 0 ← factor out (x - 1) from each term

(x - 1)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

4x + 3 = 0 ( subtract 3 from each side )

4x = - 3 ( divide both sides by 4 )

x = - \(\frac{3}{4}\)

x - 1 = 0 ( add 1 to both sides )

x = 1

solutions are x = - \(\frac{3}{4}\) , x = 1

Answer:

Step-by-step explanation:

A number cube has six sides so that would work rolling a die.. Also six pieces of paper drawn randomly without looking would work.

The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.

To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.

Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π

The length of the 45° arc is approximately 3.14 miles.

Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.

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The two different trinomials that have a greatest common factor of  \(5x^{2} y^{3}\) are:

a) \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\)

b) \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\\)

Let us verify,

a)  Consider the trinomial   \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\),

The Greatest Common Factor  of 35, 5, 15 is 5

The Greatest Common Factor  of  \(x^{2} ,x^{4} ,x^{3} =x^{2}\)

The Greatest Common Factor  of  \(y^{5} ,y^{9} ,y^{3} = y^{3}\)

There is no G.C.F for z because it is missing in the 3rd term.

So, the G.C.F  of the trinomial   \(35x^{2} y^{5}z^{2} +5 x^{4}y^{9}z +15x^{3} y^{3}\) =  \(5x^{2} y^{3}\)

b) Consider the trinomial   \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z\\\),

The Greatest Common Factor  of 25, 5, 10 is 5

The Greatest Common Factor  of \(x^{4} ,x^{7} ,x^{2} =x^{2}\)

The Greatest Common Factor  of \(y^{3} ,y^{8} ,y^{4} = y^{3}\)

There is no G.C.F for z because it is missing in the 2nd term.

So, the G.C.F of the trinomial  \(25x^{4} y^{3} z+5x^{7}y^{8} +10x^{2}y^{4} z = 5x^{2} y^{3}\)

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Answer:

1st one is: 1/125

2nd one is: 1/16

Answer:

23n=65

Step-by-step explanation:

Answer:

x = sqrt(17)

Step-by-step explanation:

Angle B is 90 degrees; the line BC is a radius of circle C and line AB is a tangent line of BC. Since they must be perpendicular, angle B is 90 degrees.

Now use the pythagorean theorem to solve for x.

c=9, a = 8, b= x

a^2+b^2=c^2

8^2+x^2=9^2

x=sqrt(81-64)

x=sqrt(17)

The required length of the base of the triangular pane of glass is 22 inches.

We know that the formula for the area of a triangle is:

Area = 1/2 * base * height

We are given that the height of the triangular pane of glass is 32 inches and the area is 352 square inches. Substituting these values into the formula, we get:

352 = 1/2 * base * 32

Multiplying both sides by 2 and dividing by 32, we get:

base = 22

Therefore, the length of the base of the triangular pane of glass is 22 inches.

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Answer: 16

Step-by-step explanation:

-24-64 / (-1.6)

-24-64 / (-8/5)

-24 + 64 x 5/8

-24 + 8 x 5

-24 + 40

= 16

The probability of 1. Favorite fruit is apple: 25/120 2. Favorite fruit is orange or grapes is 0. 458 3. Favorite fruit is apple and orange is 0.026 4. Favorite fruit is banana is 1/3.

Probability is a way to gauge how likely something is to happen. It is stated as a number between 0 and 1, with 0 denoting impossibility and 1 denoting certainty of the event.

The probability of an occurrence can be determined by dividing the number of possible outcomes by the number of ways the event could occur.

From the given bar graph we see that the total number of fruits are:

25 + 15 + 20 + 40  = 120

Now,

1. Favorite fruit is apple:

25/120

2. Favorite fruit is orange or grapes:

15/120 + 40/120 = 0.125 + 0.333 = 0. 458

3. Favorite fruit is apple and orange:

(25/120) (15/120) = 0.026

4. Favorite fruit is banana:

40/120 = 1/3

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Answer:

3.875 pizzas

Step-by-step explanation:

31/8=3.875

(a) The standard deviation of the large wild cats is 25.5 (b)  The standard deviation of the birds in flight is 33 (c) The standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate  more from the mean than the fastest recorded speeds of birds in flight . Option A

We should understand that standard deviation looks at the amount of deviation from the means of the set of data.

(a) (70+45+25+45+35+35+40+40+25)÷9 = 40

mean is = 40

(x-m) =30+5+-15+5+-5+-5+0+0+-15)

(x-m)²=(900+25+225+25+25+25+0+0+225)=1450/9

Standard deviation = √650

Standard deviation = 25.5

(b) x= (216+103+96+56+63+35+50+32+55+25+25+20)=776

Mean(m)=776/12=65

(x-m)=151+38+31+-9+-2+-30+-15+-33+-10+-40+-40+-45

Now the square of the deviations from the mean is

(x-m)²=(7396+1444+961+81+4+900+225+1089+100+1600+1600+2025)÷12

=1452

Standard deviation = √1452=33

(c) Therefore, from the calculations, the standard deviations of the two data sets show that the fastest recorded speeds of large wild cats deviate more from the mean than the fastest recorded speeds of birds in flight

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Answer:

A population is the entire group that you want to draw conclusions about. A sample is the specific group that you will collect data from. The size of the sample is always less than the total size of the population

Answer:

$499

Step-by-step explanation:

He payed at first a down payment = 250

and 20.75 a month for a year

and there is 12 months in a year which means he payed 20.75 12 times multiply these numbers 12x20.75

=$249

Plus the down payment

=249+250

=$499

Answer:

X= 30

Step-by-step explanation:

96-3x=6

first move all terms not containg x to the right side of the Equation

Subtract 96 from both sides of the equation.

-3x = 6 - 96

subtract 96 from 6 and u will get

-3x= -90

Then u will have to divide each term by -3 and simplify which will get u

-3x/-3 when u divide from that u should get -90/-3

Then divide x by 1 and itll equal

x= -90/-3

Then divide -90 by -3 and you will get

x= 30

I hope this is good  

Answer: Shade 6 pieces

Step-by-step explanation:

Because 2/5 of 15 is 6