John goes to the bank to get a $15,000 loan.The loan has a simple interest rate of 6% and is 4 years long.What is the TOTAL amount John has to pay?

The inequality for the statement:-2/7 is at most the product of a number and -4/5. is --4x/5 ≤ -2/7

Information from the question

the statement: -2/7 is at most the product of a number and -4/5

Inequality is a means of representing the relationship existing between the positive and negative parts of equations, using other terms aside exactly using equal to

at most means the highest value hence the answer is either the number or less.

let the number be x

x * -4/5 ≤ -2/7

--4x/5 ≤ -2/7

Learn more about inequality:

brainly.com/question/29244324

#SPJ1

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationships between sides and trig functions. The relevant relations here are ...

  Sin = Opposite/Hypotenuse

  Cos = Adjacent/Hypotenuse

In your diagram, leg 'a' is opposite angle α and adjacent to angle β. Similarly, leg 'b' is opposite angle β and adjacent to angle α. The hypotenuse is 'c' in all cases.

So, filling the table is a matter of identifying adjacent and opposite legs. You will notice that the sine of α is the cosine of β and vice versa.

Answer:

14

Step-by-step explanation:

Substitute -2 for x in the two places where x occurs:

              8

(-2)^2 - ------- + 6    =    4 + 4 + 6  =  14

              -2

The probability that on exactly 3 of these occasions the voters approve the Mayor's work is 0.089 .

Given that 70% of all voters approve of the mayor's work, then 30% of all voters disapprove of the mayor's work

The number of successes in a large number of observations n drawn under replacement from a single population of size n is frequently simulated using the binomial distribution.

Drawings are not independent if sampling is done without replacement, hence a hypergeometric model rather than a binomial one is used as the generative model. Nevertheless, for N far bigger than n, the binomial distribution is still a reliable approximation and is frequently utilised.

using binomial distribution formula

\(^nCx\cdot P^x \cdot(1-P)^{n-x}\)

we find the number of ways only 1 person approves (nCx) of the mayor multiplied by the probability 1 person approves(\(P^x\)) and 2 people disapprove \((1-P)^{n-x}\).

Now we will use this binomial distribution to calculate the required probability.

Hence the number of ways only 1 person approve, x = 1

= \(^3C1\cdot (0.7)^1 \cdot(1-0.7)^{3-1}\\\)

= 0.089

Hence the required probability is 0.089

To learn more about probability visit:

https://brainly.com/question/16484393

#SPJ4

The numerical length of the line segment FG is 10 units.

An equation is an expression that shows the relationship between two or more numbers and variables. An independent variable is a variable that does not depend on other variables while a dependent variable is a variable that depends on other variables.

Point G is on FH, hence:

FH = FG + GH

Given that GH = 8, FH = 3x + 3, FG = 2x, hence:

3x + 3 = (2x) + 8

x = 5

FG = 2x = 2(5) = 10

The numerical length of the line segment FG is 10 units.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Given:

The value of n and v(n) are tabulated.

Therefore, the function is

Answer:

b^20

Step-by-step explanation:

(b^4)^5 = b^4*5

\(\huge\text{Hey there!}\)

\(\mathtt{(b^4)^5}\\\mathtt{\rightarrow b^{4\times5}}\\\mathtt{\rightarrow b^{4 + 4 + 4 + 4 + 4}}\\\mathtt{\rightarrow b^{8 + 8 + 4}}\\\mathtt{\rightarrow b^{16 + 4}}\\\mathtt{\rightarrow b^{20}}\\\\\\\\\huge\text{Therefore your answer should be:}\\\huge\boxed{\mathtt{Option\ D. b^{20}}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer:

The Mean is 6.

Step-by-step explanation:

Answer:

70

Step-by-step explanation:

You know the fourth number in this pattern is 15, and that they are all consecutive. With this information you know that the fifth number will be 16, and by counting backwards from 15 you can figure out all of the numbers are 12, 13, 14, 15, and 16. Now, to find the sum of these numbers you must add them together.

This is what it could look like: 12+13+14+15+16

Now to find the answer you need to calculate what the addition would equal, which is 70.

The coordinates of the centroid are the average values of the \(x\)- and \(y\)-coordinates of the points \((x,y)\) that belong to the region. Let \(R\) denote the bounded region. These averages are given by the integral expressions

\(\dfrac{\displaystyle \iint_R x \, dA}{\displaystyle \iint_R dA} \text{ and } \dfrac{\displaystyle \iint_R y \, dA}{\displaystyle \iint_R dA}\)

The denominator is just the area of \(R\), given by

\(\displaystyle \iint_R dA = \int_0^8 \int_{\min(8\sin(2x), 8\cos(2x))}^{\max(8\sin(2x),8\cos(2x))} dy \, dx \\\\ ~~~~~~~~ = \int_0^8 |8\sin(2x) - 8\cos(2x)| \, dx \\\\ ~~~~~~~~ = 8\sqrt2 \int_0^8 \left|\sin\left(2x-\frac\pi4\right)\right| \, dx\)

where we rewrite the integrand using the identities

\(\sin(\alpha + \beta) = \cos(\alpha)\cos(\beta) + \sin(\alpha)\sin(\beta)\)

Now, if

\(8(\cos(2x) - \sin(2x)) = R \sin(2x + \alpha) = R \sin(2x) \cos(\alpha) + R \cos(2x) \sin(\alpha)\)

with \(R>0\), then

\(\begin{cases} R\cos(\alpha) = 8 \\ R\sin(\alpha) = -8 \end{cases} \implies \begin{cases}R^2 = 128 \\ \tan(\alpha) = -1\end{cases} \implies R=8\sqrt2\text{ and } \alpha = -\dfrac\pi4\)

Find where this simpler sine curve crosses the \(x\)-axis.

\(\sin\left(2x - \dfrac\pi4\right) = 0\)

\(2x - \dfrac\pi4 = n\pi\)

\(2x = \dfrac\pi4 + n\pi\)

\(x = \dfrac\pi8 + \dfrac{n\pi}2\)

In the interval [0, 8], this happens a total of 5 times at

\(x \in \left\{\dfrac\pi8, \dfrac{5\pi}8, \dfrac{9\pi}8, \dfrac{13\pi}8, \dfrac{17\pi}8\right\}\)

See the attached plots, which demonstrates the area between the two curves is the same as the area between the simpler sine wave and the \(x\)-axis.

By symmetry, the areas of the middle four regions (the completely filled "lobes") are the same, so the area integral reduces to

\(\displaystyle \iint_R dA \\\\ ~~~~ = 8\sqrt2 \left(-\int_0^{\pi/8} \sin\left(2x-\frac\pi4\right) \, dx + 4 \int_{\pi/8}^{5\pi/8} \sin\left(2x-\frac\pi4\right) \, dx \right. \\\\ ~~~~~~~~~~~~~~~~~~~~ \left. - \int_{17\pi/8}^8 \sin\left(2x-\frac\pi4\right) \, dx\right)\)

The signs of each integral are decided by whether \(\sin\left(2x-\frac\pi4\right)\) lies above or below axis over each interval. These integrals are totally doable, but rather tedious. You should end up with

\(\displaystyle \iint_R dA = 40\sqrt2 - 4 (1 + \cos(16) + \sin(16)) \\\\ ~~~~~~~~ \approx 57.5508\)

Similarly, we compute the slightly more complicated \(x\)-integral to be

\(\displaystyle \iint_R x dA = \int_0^8 \int_{\min(8\sin(2x), 8\cos(2x))}^{\max(8\sin(2x),8\cos(2x))} x \, dy \, dx \\\\ ~~~~~~~~ = 8\sqrt2 \int_0^8 x \left|\sin\left(2x-\frac\pi4\right)\right| \, dx \\\\ ~~~~~~~~ \approx 239.127\)

and the even more complicated \(y\)-integral to be

\(\displaystyle \iint_R y dA = \int_0^8 \int_{\min(8\sin(2x), 8\cos(2x))}^{\max(8\sin(2x),8\cos(2x))} y \, dy \, dx \\\\ ~~~~~~~~ = \frac12 \int_0^8 \left(\max(8\sin(2x),8\cos(2x))^2 - \min(8\sin(2x),8\cos(2x))^2\right) \, dx \\\\ ~~~~~~~~ \approx 11.5886\)

Then the centroid of \(R\) is

\((x,y) = \left(\dfrac{239.127}{57.5508}, \dfrac{11.5886}{57.5508}\right) \approx \boxed{(4.15518, 0.200064)}\)

A geometry constructions packet is a collection of exercises that require the student to create geometric figures

A Geometry constructions packet is a collection of activities or exercises that focus on the art of creating geometric figures using only a straightedge and a compass. In geometry, construction refers to the process of drawing or creating geometric figures using specific rules and procedures.

Some examples of construction tasks that might be included in a geometry constructions packet are:

Bisecting an angle

Constructing a perpendicular bisector of a line segment

Constructing a triangle given three sides

Constructing a square given one side

Constructing a regular hexagon

Constructing a regular pentagon

Learn more about Geometry here

brainly.com/question/29477789

#SPJ4

Answer:

hdjhdhdhdjdvdvddiwhegwiwiwhegeeuui

The distance between the points (0, 10) and (–9, 1) is 12.73 units.

Given the following data;

Points (\(x_1, x_2\)) = 0, -9

Points (\(y_1, y_2\)) = 10, 1

To find the distance between the points;

In Mathematics, the distance between two points on a plane is calculated by using the formula;

\(Distance = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2 }\)

Substituting the points into the formula, we have;

\(Distance = \sqrt{(0 - [-9])^2 + (10 - 1)^2} \\\\Distance = \sqrt{(0 + 9)^2 + (9)^2}\\\\Distance = \sqrt{9^2 + 9^2}\\\\Distance = \sqrt{81 + 81}\\\\Distance = \sqrt{162}\)

Distance = 12.73 units

Therefore, the distance between the points is 12.73 units.

Find more information: https://brainly.com/question/13272812

Answer:

\(9(7 + 9)\)

Step-by-step explanation:

To factor an expression you have to first find the highest common factor (HCF) of the numbers in the expression. You divide them by their HCF, bracket it and place the HCF outside the bracket.

\(63 + 81 = \\ 9(\frac{63}{9} + \frac{81}{9}) = \\ 9(7 + 9)\)

To check if it is factored properly you can do the opposite of what you just did by clearing the bracket.

9 (7 + 9)

(9 x 7) + (9 x 9)

= 63 + 81

It is claimed that the sample of participants is generalizable since it reflects the characteristics of the population.

To learn more about generalizable, refer to:

https://brainly.com/question/28237221

#SPJ4

Answer:

place it 2 3 4 5 6 7 8 9 10 1 then is come 18

Answer:

2 3 4 5 6 7 8 9 10 1 then come 18

Answer:

1. How to Solve using Algebra

Make both equations into "y =" format.

Set them equal to each other.

Simplify into "= 0" format (like a standard Quadratic Equation)

Solve the Quadratic Equation!

Use the linear equation to calculate matching "y" values, so we get (x,y) points as answers.

Algebraic method is more easy to do

2. linear functions have constant first differences. quadratic functions have constant second differences. exponential functions have a constant ratio.

Step-by-step explanation:

according to the property of the parallelogram m(OPE)=m(OHE), then  2x+25=3x-15, then (after calculation the 'x'):

1. x=40;

2. m(OHE)=2*40+25=105°;

3. m(OPE)=3x-15=3*40-15=105°;

4. m(HOP)=180-m(OPE)=180-105=75°;

5. m(HEP)=m(HOP)=75°.

Answer:

Because she found it improves division.

Step-by-step explanation:

Answer:

B'(5,-9)

Step-by-step explanation:

When reflecting across the x-axis, the "x" coordinate stays the same, and the "y" coordinate just becomes the opposite. So, the opposite of 9 is -9!

Therefore, B' is (5,-9), or "D"

Hope this helps!

The correct option is: a tabular summary of a set of data showing sums of frequencies.

A cumulative frequency distribution is a tabular summary of a set of data showing the sums of frequencies or relative frequencies of values at or below a given level.

A cumulative frequency distribution is a term used to describe the pattern of a dataset.

It shows the number of observations or occurrences in a cumulative frequency distribution.

In other words, the frequency of each observation is added to the frequency of the preceding observation in a cumulative frequency distribution until the cumulative frequency distribution is complete.

This results in a frequency distribution that shows the number of values that are less than or equal to the given values.

Know more about tabular summary here:

https://brainly.com/question/30671485

#SPJ11

The answer is E) a spreadsheet is not a component of a linear programming model

A spreadsheet is a tool or software used for organizing and analyzing data, but it is not a component of a linear programming model itself. In linear programming, the main components are:

A) Constraints: These are the limitations or restrictions that define the feasible region of the problem.

B) Decision variables: These are the variables that represent the quantities to be determined or optimized.

C) Parameters: These are the known values that influence the problem, such as coefficients in the objective function or constraints.

D) An objective: This is the goal or objective that is to be maximized or minimized.

While spreadsheets can be used to implement and solve linear programming models, they are not an inherent part of the model itself.

Know more about linear programming model here:

https://brainly.com/question/28036767

#SPJ11

Let be x the initial number of cups of punch. Then, we can write in algebraic language the word problem: x/2 because her guests drank 1/2 of punch.

And we can write the equation:

Because there was an initial amount of cups of punch, and then this amount decreased until there were 10 cups of punch left.

Now, we can write the equation for x:

Therefore, the initial number of cups that she started with was 60.

Answer:

thvsjz sjvsvvsvsgvg jso ski and snowboard and the world. how t, and the first thing I did was to you sir are always smart enough to know that the government is a joke. K the first thing I did t

So, the probability of ending up with a three-digit number that is divisible by 4 is 1/24.

To find the probability of ending up with a three-digit number that is divisible by 4 when spinning the spinner three times, we need to consider the possible outcomes that satisfy this condition and divide it by the total number of possible outcomes. Let's analyze the given spinner and its possible outcomes:

Spinner: [1, 2, 3, 4, 5, 6]

To form a three-digit number, the hundreds digit will be determined by the first spin, the tens digit by the second spin, and the units digit by the third spin. A number is divisible by 4 if the last two digits (tens and units digits together) form a number divisible by 4. Therefore, we need to find the number of possible outcomes for the tens and units digits that satisfy this condition.

Possible outcomes for the tens digit: [2, 4, 6]

Possible outcomes for the units digit: [2, 4, 6]

Combining the possible outcomes for the tens and units digits, we have a total of 9 (3 possibilities for the tens digit multiplied by 3 possibilities for the units digit) favorable outcomes. The total number of possible outcomes for each spin is 6 (since there are 6 numbers on the spinner). Since we are spinning the spinner three times independently, the total number of possible outcomes for spinning it three times is 6^3 = 216. Therefore, the probability of ending up with a three-digit number divisible by 4 is:

Probability = favorable outcomes / total outcomes

Probability = 9 / 216

Probability = 1 / 24

To know more about probability,

https://brainly.com/question/21467996

#SPJ11

The area enclosed in one loop of the curve r = cos2θ will be π/8.

Any function between the dependent and independent variables can be represented in a graph diametrically.

For instance, if y = x2 forms a parabola, we may infer from the graph alone that it will always have a positive value, regardless of the range of x.

As per the given curve,

r = cos2θ

Since |cos2θ| ranges between 0 and 1.

At r = 1

cos2θ = 1 ⇒ θ = 0

At r = 0

cos2θ = 0 ⇒ θ = π/4

The area of one loop will be as,

A = 1/2∫r²dθ

A = (1/2)∫cos²2θ dθ

A = (1/2)∫(1 + cos4θ)/2  dθ

A = π/8

Hence" The area enclosed by the given function will be π/8".

To learn more about graphs,

brainly.com/question/16608196

#SPJ1

Answer:

4725 pesos

Step-by-step explanation:

The price p of an aluminum tube is jointly proportional to its radius r and the length l.

For joint variation, we have the expression:

p ∝rl

Hence

p = krl

Step 1

Solving for k

if a 12-foot pipe with 5-inch radius costs 5250 pesos,

5250 = k × 12 × 5

5250 = 60k

k = 5250/60

k = 87.5

Step 2

how much will be the cost of a 9-foot pipe with a 6-inch radius

We make use of the expression:

p = krl

p = 87.5 × 9 × 6

p = 4725 pesos

Therefore, the cost is = 4725 pesos

If the area of rectangle abcd is 16in² and the area of the rectangle a’b’c’d’ is 64in², the scale factor used to dilate the rectangle was 2.

When a rectangle is dilated, its dimensions are multiplied by a common factor known as the scale factor. The scale factor is the ratio of the corresponding sides of the original rectangle and the dilated rectangle.

Let the scale factor be represented by k. The area of the original rectangle is 16 in², so we can write:

length x width = 16

Let L and W represent the length and width of the original rectangle, respectively. Therefore, we have:

LW = 16

After dilation, the area of the new rectangle is 64 in². The length and width of the new rectangle are kL and kW, respectively. Therefore, we can write:

(kL)(kW) = 64

Simplifying the above equation, we get:

k²LW = 64

Substituting the value of LW from the first equation, we get:

k²(16) = 64

Solving for k, we get:

k = √4 = 2

This means that the length and width of the new rectangle are twice the length and width of the original rectangle.

To learn more about scale factor click on,

https://brainly.com/question/15001483

#SPJ4

The weights in a weighted moving average are selected by: Trial and error, Fitting to a regression line, Guessing, Experience.

The methods for selecting weights in weighted moving averages are trial and error, fitting to a regression line, and experience.

When selecting weights for weighted moving averages, the following methods can be used:
Trial and error:

Testing different weight combinations to find the best fit for the data.
Fitting to a regression line:

Analyzing the relationship between the data points and assigning weights accordingly.
Experience:

Using prior knowledge and understanding of the data or similar situations to determine appropriate weights.

For similar question on average.

https://brainly.com/question/29219210

#SPJ11

 Trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

With weighted moving averages, the weights can be selected using various methods. Here are the applicable methods from your given options:

1. Trial and error fitting: Weights can be selected by testing different combinations of weights and observing their impact on the accuracy of the model.

2. Fitting to a regression line: Weights can be determined by fitting a regression line to the data and using the coefficients of the regression line as the weights.

3. Experience: Domain knowledge or past experience with similar data can help in selecting appropriate weights.

In summary, trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.

to learn more about regression line click here:

https://brainly.com/question/17731558

#SPJ11