You would like to have $41,000 in 5 years for the down payment on a new house
following college graduation by making deposits at the end of every three months in
an annuity that pays 4.25% compounded quarterly. How much should you deposit at
the end of every three months? How much of the $41,000 comes from deposits and
how much comes from interest?

Answer:

-4 < x ≤ 1.5

Step-by-step explanation:

First we will need to determine what signs to use for our inequality:

According to the picture, we have one of each

So we need to write an equality for each point and then combine them

The first inequality will be x > -4 because here the shading is "pointing" to the right just as the inequality sign >

The second inequality will be x ≤ 1.5 because here the shading is "pointing" to the left just as the inequality sign ≤

Now to combine, we arrange the two number values that we have from least to greatest with the smallest number being on the leftmost side of the inequality and the larger number being on the rightmost side of the inequality.

Then we put x in the middle and add the signs that we have

So our complete inequality will read -4 < x ≤ 1.5

Answer: 0.0898

Step-by-step explanation:

Probability = \(\dfrac{favorable\ outcomes}{Total\ outcomes}\)

Given : Sample size : 528

Number pf customers say they are happy = 237

Probability of getting one happy customer= \(\dfrac{237}{528}\)

Probability of getting second happy customer= \(\dfrac{236}{527}\)  [subtract 1 from both numbers]

Probability of getting third happy customer= \(\dfrac{235}{526}\)  

If 3 customers are elected without replacement

The probability they will all say they are happy with the service  = \(\dfrac{237}{528}\times\dfrac{236}{527}\times\dfrac{235}{526}\)  

\(\approx0.0898\)

Hence, the required probability = 0.0898

a. Assuming no additional restrictions, there are  800 possible three-digit area codes.

b. Considering ERCs, there are  80 ERCs.

c. For the seven digits after the area code, there are \(8 \times 10^6 = 8,000,000\)  possible seven-digit phone numbers.

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers is 800 \(\times\) 8,000,000 = 6,400,000,000.

a. For three-digit area codes, the first digit cannot be 0 or 1.

Assuming no additional restrictions, there are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining two digits (0-9). Therefore, the total number of three-digit area codes possible under this plan is \(8 \times 10 \times 10 = 800.\)

b. For an ERC (Easily Recognizable Code), the second and third digits of the area code must be the same, and the first digit cannot be 0 or 1. There are 8 possibilities for the first digit (2-9) and 10 possibilities for the third digit (0-9).

Since the second digit must be the same as the third digit, there is only 1 possibility.

Therefore, the total number of ERCs is \(8 \times 1 \times 10 = 80.\)

c. For the seven digits after the area code, the first digit of the three-digit local prefix cannot be 0 or 1.

There are 8 possibilities for the first digit (2-9) and 10 possibilities for each of the remaining six digits (0-9).

Therefore, the total number of seven-digit phone numbers possible is 8 * \(10\times 10 \times 10 \times 10 \times 10 \times 10 = 8,000,000.\)

d. Assuming only the 0 and 1 restrictions from parts a and c, the number of possible ten-digit phone numbers can be calculated by multiplying the number of possibilities for each digit position.

For the area code (part a), there are 800 possibilities.

For the seven digits after the area code (part c), there are 8,000,000 possibilities.

Therefore, the total number of ten-digit phone numbers possible is 800 * 8,000,000 = 6,400,000,000.

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Since we do not know the value of u, we cannot find the time taken by the basketball to travel a distance of 8.5 meters. We cannot find the height of the basketball at its highest point.

Given that n(x) = 3 for 8 < x < 8.5.It is impossible to determine whether the shot will be made or not based solely on this information. Winning the playoffs depends on various factors, such as the score, time remaining, and the overall performance of the team.

Therefore, additional information is required to determine the outcome of the playoffs.However, to find the height of the basketball at its highest point, we need to know the equation of the trajectory of the basketball.

Assuming that the basketball follows a parabolic path, we can use the formula:

y = ax² + bx + c,

where y is the height of the basketball, and x is the horizontal distance traveled by the basketball.

To find the values of a, b, and c, we need to know three points on the trajectory of the basketball. Let's assume that the basketball is thrown from a height of 1.5 meters and lands on the floor after traveling a horizontal distance of 8.5 meters.

Therefore, the points on the trajectory of the basketball are:

(0, 1.5), (8.5/2, h), and (8.5, 0),

where h is the height of the basketball at its highest point.Substituting these values in the equation of the trajectory,

we get:

1.5 = a(0)² + b(0) + c...(1)0 = a(8.5)² + b(8.5) + c...(2)h = a(8.5/2)² + b(8.5/2) + c...(3)

Simplifying equations (1) and (2),

we get:

c = 1.5...(4)b = -a(8.5)²/8.5...(5)

Substituting equation (4) in equation (3), we get:

h = a(8.5/2)² + b(8.5/2) + 1.5h = a(8.5/2)² - a(8.5)²/8.5 + 1.5h = -29.375a + 1.5

Substituting the value of a from equation (5) in the above equation,

we get:

h = -29.375(-a(8.5)²/8.5) + 1.5h = 0.5a(8.5)² + 1.5

Therefore, to find the height of the basketball at its highest point, we need to find the value of a. Since we know that the basketball lands on the floor after traveling a horizontal distance of 8.5 meters,

we can use the formula:

x = ut + 0.5at²,

where u is the initial horizontal velocity of the basketball, and t is the time taken by the basketball to travel a distance of 8.5 meters.

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Answer:

Step-by-step explanation:

To calculate the circumference of a circle, you can use the formula:

\(\displaystyle C=2\pi r\)

Where \(\displaystyle C\) represents the circumference and \(\displaystyle r\) represents the radius of the circle.

Given that the radius \(\displaystyle r\) is 8 inches, we can substitute this value into the formula:

\(\displaystyle C=2\pi (8)\)

Simplifying the expression:

\(\displaystyle C=16\pi \)

Thus, the circumference of a circle with a radius of 8 inches is \(\displaystyle 16\pi \) inches.

Note: \(\displaystyle \pi \) represents the mathematical constant pi, which is approximately equal to 3.14159.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

  an infinitely long time

Step-by-step explanation:

You want to know the time it takes for a kitten running 20 ft/s to catch a puppy running 25 ft/s when they start 180 ft apart and the puppy runs away from the kitten.

The kitten runs slower than the puppy, so can never catch up to it.

<95141404393>

Answer:

f(4) = 1612

Step-by-step explanation:

using the recursive formula and f(1) = 3 , then

f(2) = f(1)² + 3 = 3² + 3 = 9 + 3 = 12

f(3) = f(2)² + 3 = 144 + 3 = 147

f(4) = f(3)² + 3 = 147² + 3 = 1609 + 3 = 1612

\(1.4 < \sqrt{2} < 1.5\hspace{5em}1.7 < \sqrt{3} < 1.8 \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{lllll} 1.7& < &\sqrt{3}& < &1.8\\\\ 1.7-\sqrt{2}& < &\sqrt{3}-\sqrt{2}& < &1.8-\sqrt{2}\\\\ 1.7-1.5& < &\sqrt{3}-\sqrt{2}& < &1.8-1.4\\\\ 0.2& < &\sqrt{3}-\sqrt{2}& < &0.4 \end{array}\)

we're subtracting the upper-bound of √2, so is the most we can subtract from 1.7, and we're subtracting the lower-bound of √2 from 1.8, that way the resultant is within range.

If s and t are integers greater than 1 and each is a factor of the integer n, then the product nst must be divisible by both s and t. This is because s and t are factors of n, which means that n is divisible by s and t.

The product of two integers is divisible by the factors of each of those integers. Therefore, since n is divisible by s and t, and nst is the product of n, s, and t, nst must also be divisible by s and t. This can be proven by the definition of divisibility: if a number, in this case n, is divisible by an integer, in this case s or t, then the product of that number and another integer, in this case t or s, is also divisible by the initial integer.

For example, if n = 24, s = 4, and t = 3, we can see that 4 and 3 are factors of 24, since 24 is divisible by 4 and 3. The product of 24, 4 and 3 is 2443 = 288. 288 is also divisible by 4 and 3.

In summary, if s and t are integers greater than 1 and each is a factor of the integer n, then s and t must be factors of nst.

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Answer:

97.7

Step-by-step explanation:

1. so first find the area of the rectangle:

A= 13 * 9

A= 117

2. then find the area of the semicircle

A= \(\pi r^{2}\)/2

A= \(\pi (3.5)^{2}\)/2

A= 19.242255

finally, subtract the semicircle from the rectangle

117-19.242255≅ 97.7

To find the values of x and z, apply the opposite angles theorem.

Opposite angles are angles that can be said to be non-adjacent angles formed by two intersecting lines.

Opposite angles are congruent.

• Measure of angle Z:

∠z and 110 are opposite angles.

Thus, we have:

m∠z = 110°

• Value of x:

Given that total measure of angles = 360

We have:

Let's solve for x:

Divide both sides by 5:

ANSWER:

x = 18

z = 110°

The number of each type of ad that the department can run each month are:

TV Ads = 32

Radio Ads = 12

News Ads =  20

x = number of tv ads

y = number of radio ads

z = number of news ads

Two formulas are indicated.

x + y + z = 64

1000x + 200y + 600z = 46400

they want as many tv ads as radio and news ads combined.

equation for that is x = y + z

since x = y + z, replace x with y + z in both equations to get;

y + z + y + z = 64

1000 * (y + z) + 200 * y + 600 * z = 46400

combine like terms and simplify to get:

2y + 2z = 64

1000y + 1000z + 200y + 600z = 46400

combine like terms again to get:

2y + 2z = 64

1200y + 1600z = 46400

Solving simultaneously gives:

y = 12

z = 20

Thus:

x = 12 + 20

x = 32

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Answer:

you could do 3 tens and 1 ones or 2 tens and 11 ones

Step-by-step explanation:

hope this helps!

Answer: 3266.528

Step-by-step explanation:

The number 531.775197122 is rounded to the nearest ten thousandth place by 531.7752

What is rounding up numbers?

There are basically two rules while rounding up numbers

If the number you are rounding is followed by 0, 1, 2, 3, or 4, round the number down and if the number you are rounding is followed by 5, 6, 7, 8, or 9, round the number up.

Given data ,

Let the number be = A

Let the rounded number be = B

The value of A is given by

A = 531.775197122

Now , the number A can be rounded of to the nearest ten thousandth place by rounding to the nearest 0.0001 or the Ten Thousandths Place

So , the number will be

The 1 in the ten thousandths place rounds up to 2 because the digit to the right in the hundred thousandths place is 9

When the digit to the right is 5 or greater we round away from 0

Therefore , the number 531.775197122 is rounded to 531.7752

Therefore , the value of B is 531.7752 after rounding up

Hence , The number 531.775197122 is rounded to the nearest ten thousandth place by 531.7752

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(i)  \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) \(\lim_{x \to \frac{\pi^-}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^-}{2}}\) (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) \(\lim_{x \to \frac{\pi^+}{2}}\) h(x) = \(\lim_{x \to \frac{\pi^+}{2}}\) (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

\(\lim_{x \to 0}\) h(x) = h(0)

\(\lim_{x \to 0}\) x cos x/sin λx = 1/7

\(\lim_{x \to 0}\) cos x.\(\lim_{x \to 0}\) 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Therefore, it is not even chance, but it is also not very unlikely. It is moderately likely that a yellow marble will be selected on the first draw.

Probability is a branch of mathematics that deals with the study of random events and their likelihood of occurring. It is a measure of the likelihood or chance of an event happening. Probability is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain.

In other words, probability is a way of quantifying uncertainty. It is used in various fields, such as statistics, physics, finance, engineering, and more, to help make predictions and decisions based on uncertain information. Probability theory provides a set of rules and tools for analyzing and manipulating random variables and events, and for calculating the probability of complex events.

The likelihood of a yellow marble being selected on the first draw can be calculated by dividing the number of yellow marbles by the total number of marbles in the bag:

likelihood of selecting a yellow marble = number of yellow marbles / total number of marbles

So, in this case, the likelihood of selecting a yellow marble on the first draw is:

likelihood of selecting a yellow marble = 2 / (3 + 2 + 1) = 2/6 = 1/3

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Answer:

The height is 1.25m.

Step-by-step explanation:

Volume = 1/3 πr²h

Given:

V = 13.4 m³

r = 3.2 m

Asked: height (h)

Substitute the formula with the given values then solve

13.4m³ = 1/3π(3.2m)²h

13.4(3) = 10.24πh

40.2 = 10.24πh

h = 40.2/10.24π

h = 1.25m

The height of the cone is 1.25 meters.

We know that the volume of the cone is given by

V = (1 / 3) * π * r ^2 * h................equation 1

where,

V is the volume of the cone.

r is the radius of the cone's base

h is the height

The volume and radius of the cone are given,

V = 13.4 m

r = 3.2m

substituting these values in equation 1 we get,

13.4 = (1 / 3) * 3.14 * 3.2 ^ 2 * h

on simplifying further

13.4 = 10.717  * h

h = 1.25m

The height of the cone is 1.25 meters.

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The values of the trigonometric ratios are: a) - 7/5, b) -75 c ) -1/5  d ) -25/12

Trigonometric ratios are measurements of the lengths of two sides of a triangle. There are three basic trigonometric ratios: sine, cosine, and tangent.  Sine ratios are the ratios of the length of the side opposite the angle they represent over the hypotenuse

the give parameters are:

tanα = -4/3 where π/2 <α<π and sinβ = √3/2, 0<β<π/2

a)  sin(α+β)

Using the trig ratios tan = opp/adj

but from pyth. rule, 4² + 3² = h²

16+9 = h²

h = √25 = 5

Now from trig Sin(α+β)

4/5 + 3/5

=- 7/5

b) cos(α+β)

cos = ad/hypo

4/5 + 3/5

= -7/5

c) Sin(α-β)

4/5 - 3/5

-1/5

d) tan(α-β)

= -4/3 - 3/4

= (-16 - 9)/ 12

-25/12

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Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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let

width = w

length = 4w + 11

2(length) + 2(width) = perimeter

2(4w + 11) + 2(w) = 162

8w + 22 + 2w = 162

10w + 22 = 162

10w = 140

w = 14 cm (WIDTH)

length = 4w + 11

length = 4(14) + 11

length = 56 + 11

LENGTH = 67 cm

The length is 4(14)+ 11 = 67 cm and width is 14 cm.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values. We frequently observe constant change in specific values in our day-to-day situations.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Perimeter of rectangle = 162 cm

let the width be x .

then, the length is 4x+ 11

Thus, Perimeter of rectangle= 2(l + w)

162 = 2( 4x + 11 + x)

162 = 2( 5x +11)

81 = 5x+ 11

5x= 70

x= 14

Hence, the length is 4(14)+ 11 = 67 cm and width is 14 cm.

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Answer:

Step-by-step explanation:

Answer:

  18 cubic inches

Step-by-step explanation:

The formulas for the volumes of a cone and a cylinder can be used to answer this question.

The volume of a cone is given by ...

  V = 1/3πr²h . . . . . volume of cone with radius r and height h

The volume of a cylinder is given by ...

  V = πr²h . . . . . volume of a cylinder with radius r and height h

Comparing the formulas, we see that the volume of a cone is 1/3 the volume of a cylinder with the same radius and height.

  (cone volume) = 1/3(cylinder volume)

Multiplying this equation by 3 gives ...

  3×(cone volume) = (cylinder volume)

Using the given value for cone volume, we have ...

  cylinder volume = 3×(6 in³) = 18 in³

The volume of the cylinder is 18 cubic inches.

Answer:

Se pueden hacer 5040 permutaciones con la palabra COLUMNA.

Explanation:

La palabara COLUMNA posee 7 letras, por lo que debemos hacer permutación sin repetición.

La formula es:

P_^{n}: n!

Donde n son todos los elementos.

The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

3x^2-10x+6=0

Step-by-step explanation:

3x^2-10x+6=0

Δ=10^2-4*3*6=100-72=28

V28=V4*7=2V7

x1=(10+2V7)/6=2(5+V7)/6=(5+V7)/3

x2=(5-V7)/3

Answer:

d

Step-by-step explanation:

edge

This is an arithmetic sequence with a first term of 1, a common difference of 1, and a last term of 499. We can use the formula for the sum of an arithmetic series to find the sum of the numbers:

S = (n/2)(a1 + an)

where:

S = sum of the series

n = number of terms

a1 = first term

an = last term

Substituting the given values, we get:

S = (499/2)(1 + 499)

S = (249.5)(500)

S = 124,750

So the sum of the series 1 + 2 + 3 + 4 + ... + 498 + 499 is 124,750.

He made a mistakes on solving the division of fractions, he did not use the law of extremes and means, at least, he did not do it properly.