Nasim invests money in an account paying a simple interest of 1. 3% per year. If he invests $70 and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?

Answer:

121-129 F is in between

Step-by-step explanation:

Answer:

A yes, B no

Step-by-step explanation:

The triangle inequality states that the sum of any 2 sides of the triangle must be greater than the third side.

A Given 21, 18, 17 , then

21 + 18 = 39 > 17

21 + 17 = 38 > 18

18 + 17 = 35 > 21

Thus the triangle could exist

B Given 3, 12, 8 , then

3 + 12 = 9 > 8

3 + 8 = 11 < 12 ← fails the test

Thus the triangle does not exist

Answer:

Step-by-step explanation:

A. 2x = -6

    x = -3

 3 + y = 5

   y = 2

(-3, 2)

-9 - 2 = -11

 -11 = -11

3 + 2 = 5

5 = 5

B. 4x + 2y = 1

    6x + 4y = 1

-8x - 4y = -2

 6x + 4y = 1

-2x = -1

x = 1/2

4(1/2) + 2y = 1

2 + 2y = 1

2y = -1

y = -1/2

-2(-1/2) + 3 = 4(1/2) + 2

1 + 3 = 2 + 2

4 = 4

6(1/2) + 4(-1/2) = 1

3 - 2 = 1

1 = 1

C.

-x + 32y = -25

4x + 8y = 100

-4x + 128y = -100

136y = 0

y = 0

-x = -25

x = 25

(25, 0)

32(0) - 25= -25

-25= -25

5(25) = 100 + 25 - 8(0)

125 = 125

D.

3x + 2y = 6

4x + 5y = -20

-12x - 8y = -24

12x + 15y = -60

7y = -84

y = -12

2(-12) + 3x = 6

-24 + 3x = 6

3x = 30

x = 10

(10, -12)

2(-12) + 3(10) = 6

-24 + 30 = 6

6 = 6

4(10) + 5(-12) + 20 = 0

40 - 60 + 20 = 0

 -20 + 20 = 0

0 = 0

Answer:

The last choice

Step-by-step explanation:

So, - 5 1/2 is negative so it's on the left side of 0. 2 is a positive number so it's on the right side of the 0.

The last choice shows one blue dot on -5 1/2 and the other on 2, so it is correct

There are 126 number of ways for 8 men and 5 women to stand in a line such that no two women stand next to each other.

To determine the number of ways for 8 men and 5 women to stand in a line such that no two women stand next to each other, we can use the concept of permutations.

First, let's consider arranging the 8 men in a line. There are 8! (8 factorial) ways to arrange them.

Next, let's create spaces between the men where the women can stand.

Since no two women can stand next to each other, we need to distribute these spaces among the 8 men.

There are 9 spaces available: one at the beginning of the line, one at the end, and seven spaces between the men.

To ensure that no two women stand next to each other, we can choose 5 spaces out of the 9 available spaces for the women to occupy.

We can do this in (9 choose 5) ways, which is denoted as C(9, 5) or binomial coefficient.

The formula for the binomial coefficient is:

\(\[C(n, k) = \frac{{n!}}{{k! \cdot (n-k)!}}\]\)

In this case, we have:

\(\[C(9, 5) = \frac{{9!}}{{5! \cdot (9-5)!}} = \frac{{9!}}{{5! \cdot 4!}} = \frac{{9 \cdot 8 \cdot 7 \cdot 6}}{{4 \cdot 3 \cdot 2 \cdot 1}} = 126.\]\)

Therefore, there are 126 ways.

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Answer:

C) 7 minutes

Step-by-step explanation:

start with formula

g(x) = x^4 - 3x^2 + 4x - 5

substitute x with number of stops (2)

g(2) = 2^4 - 3(2^2) + 4(2) - 5

simplify using p.e.m.d.a.s: start with exponents

g(2) = 16 - 3(4) + 4(2) - 5

multiply

g(2) = 16 - 12 + 8 - 5

subtract/add

16 - 12 = 4

4 + 8 = 12

12 - 5 = 7

input: 2

output: 7

ordered pair: (2,7)

Expression for the nth term of the sequence: (n + 1) / (n + 3).The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.

To find the expression for the nth term of the sequence, we observe that each term can be expressed as (n + 1) divided by (n + 3), where n represents the position of the term in the sequence.

Let's verify this formula with the given terms:

For n = 1: (1 + 1) / (1 + 3) = 2 / 4 = 1/2 (first term of the sequence)

For n = 2: (2 + 1) / (2 + 3) = 3 / 5 (second term of the sequence)

For n = 3: (3 + 1) / (3 + 3) = 4 / 6 (third term of the sequence)

For n = 4: (4 + 1) / (4 + 3) = 5 / 7 (fourth term of the sequence)

For n = 5: (5 + 1) / (5 + 3) = 6 / 8 = 3 / 4 (fifth term of the sequence)

Therefore, the first five terms of the given sequence are: 1/2, 3/5, 4/6, 5/7, 3/4.

The expression for the nth term of the sequence is (n + 1) / (n + 3). Using this formula, we found the first five terms of the sequence, which are 1/2, 3/5, 4/6, 5/7, and 3/4.

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y = -9

Ok so to write the equation of the line you will need the slope and y-intercept. Since we are given two-point we can easily find the slope by using this equation for slope formula:

\(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

So now that we have our equation we can just plug in the numbers:

\(\frac{(-9)-(-9)}{5-(-3)}\)

After subtracting you should get:

0/8

Since zero is in the numerator and you can't divide zero by anything, the slope is 0. We still need the y-intercept for the equation however since the slope is 0 there is no need to put anything else.

Then to find the y-intercept all you have to do is plug in one of the coordinatines into the slope equation to solve, for example, using the point (5,-9):

\((-9) = 5(0) + b\)

B is the variable for the y-intercept. Also notice how I put 0 as our slope into the equation. Now all you have to do is solve for b. Which you would get b = -9. Since you have your slope and your y-intercept now you just write out your equatoin for the line which is:

y = 0x - 9

**Just write it as

y = -9

Answer:

Y = -9

Step-by-step explanation:

You're welcome and have a nice day

Answer:

x=-3 and the graph is A since x>-3

The shorter side of the rectangle is approximately 237.25 millimeters, and the diagonal makes angles of approximately 41 degrees and 49 degrees with the longer and shorter sides, respectively.

Let us denote the shorter side of the rectangle as x. We can use the Pythagorean theorem to relate the length of the diagonal to the two sides of the rectangle:

diagonal^2 = longer side^2 + shorter side^2

Substituting in the given values, we get:

450^2 = 393^2 + x^2

Solving for x, we get:

x = √(450^2 - 393^2) ≈ 237.25 mm

To find the angles that the diagonal makes with each side of the rectangle, we can use trigonometry. Let θ be the angle between the diagonal and the longer side, and let φ be the angle between the diagonal and the shorter side. Then we have:

sin(θ) = shorter side / diagonal

sin(φ) = longer side / diagonal

Substituting in the given values and solving for θ and φ, we get:

θ ≈ 41 degrees

φ ≈ 49 degrees

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Answer:

Z= 180 X = 95   y= 147

Step-by-step explanation:

Z=180 because it is a line and when it is a line it = 180 degrees

for X you want to first find the angle of the other triangle and when you do you subtract that # from 180 because those 2 angles make a line

to find that angle next to X is...

180- (the other 2 angles in the triangle)

180- 45- 50

180-95

85 degrees

now do

180-85

95 degrees   -- this is what X =

now you want to find the angle that is left in one triangle

so do

180- 95- 52

180- 147

33 degrees -- the angle that was missing

to find Y do...

180- 33

147 degrees -- this is what Y =

The condition for the equation (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 to be true is that the system described must be in a state of mechanical, thermal, and chemical equilibrium.

Let's break down the conditions for each partial derivative:

1. (∂U/∂V)T = 0: This condition implies that the internal energy of the system does not change with respect to volume at constant temperature.

It indicates mechanical equilibrium, where the system is in balance and no work is being done on or by the system due to volume changes.

2. (∂U/∂P)T = 0: This condition suggests that the internal energy of the system does not change with respect to pressure at constant temperature.

It indicates thermal equilibrium, where the system is in balance and there is no transfer of energy as heat due to pressure changes.

3. (∂H/∂V)T = 0: This condition implies that the enthalpy of the system does not change with respect to volume at constant temperature.

It also indicates mechanical equilibrium, where the system is in balance and there is no work being done on or by the system due to volume changes.

In summary, the condition (∂U/∂V)T = (∂U/∂P)T = (∂H/∂V)T = 0 is true when the system is in a state of mechanical, thermal, and chemical equilibrium, where there are no changes in internal energy, pressure, and enthalpy with respect to volume at constant temperature.

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\(x=5\sqrt{2}\)

Main concepts

1. Isosceles Triangles

2. Pythagorean theorem

1. Isosceles Triangles

For this triangle to be an isosceles triangle, two sides must be congruent (the same length).

As a consequence, the two angles across from those two congruent sides must be congruent angles (have the same measure).

Our triangle

We are given the hypotenuse (side across from the right angle) is 10, and one side is length x.  In order for the triangle to be isosceles, the unlabeled side must either be length x or length 10.

For any triangle, the increasing measure of the angles corresponds with the increasing lengths of the sides across from those angles, meaning that the smallest angle in a triangle always has the smallest side of that triangle as the side across from that smallest angle, and the largest angle of the triangle has the longest side as the side across from that largest angle.

In a right triangle, the right angle is always the largest angle, so the hypotenuse (the side across from the right angle), is always the longest side in a right triangle.

Since the angle across from the unlabeled side cannot also be 90 degrees (if it were, the sum of the angles of the triangle would be more than 180 degrees), the unlabeled side must be length "x"

2. Pythagorean Theorem

For any right triangle, requiring side "c" to be the length of the hypotenuse, and sides a & b to be the other two sides (legs -- the two sides touching the right angle) of the triangle, the lengths of the sides of the right triangle must obey the equation: \(a^2+b^2=c^2\)

Since, we have determined that the length of both legs is "x", we can substitute the quantities into the equation:

\((x)^2+(x)^2=(10)^2\)

\(2x^2=100\)

divide both sides by 2...

\(x^2=50\)

Apply a square root to both sides...

\(x=\sqrt{50}\)

Factor the radical

\(x=\sqrt{25*2}\)

Since the factors are all positive, the radical of a product is the product of radicals...

\(x=\sqrt{25}*\sqrt{2}\)

\(x=5*\sqrt{2}\)

\(x=5\sqrt{2}\)

Answer:

Vertex:(0,8)     Axis of Symmetry: x=0

Step-by-step explanation:

At x=0, we can say that the series ∑\(Cn(X - 3)^n\) converges, as the given condition for convergence is satisfied at x=7, x=10, and x=0 is between the two values.  

At x=11, we can say that the series ∑\(Cn(X - 3)^n\) converges, as the given condition for convergence is satisfied at x=7 and x=11 is between the two values. At x=5, we can say that the series ∑\(Cn(X - 3)^n\) diverges, as the given condition for convergence is not satisfied at x=5.

The theory behind the question is the idea of a power series, which is an infinite series of terms where each term is a power of a variable raised to a constant. In this case, we have a series of the form:

\(Cn(X - 3)^n\)

here Cn is a constant. The question is asking about the behavior of this series as a function of the variable x, specifically whether it converges or diverges. The condition for convergence of a power series is that the absolute value of the coefficients (i.e., the absolute value of Cn) must be less than or equal to 1 for all values of x in the interval where the series is defined. If this condition is satisfied, then the series converges.

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Answer:

option C.

Step-by-step explanation:

option C is the correct answer.

Direct variation: y = kx .........where k is constant.

10 = k * -5

k = -2

Then check if all are linear and matches.

y = -2 * -4

y = 8 ...matches.

then

y = -2 * -3

y = 6 ........matches

then

y = -2 * -2

y = 4 ........matches

then

y = -2*-1

y = 2 ......matches as well. so direct variation.

Answer:

$0.31

Step-by-step explanation:

$2.48/8 = $ 0.31

Answer: between $1.00 and $1.99

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since one side of the square is 16 cm, the diameter of the circle is also 16 cm. Which means that the radius is 8. the area of a circle is pi times radius square. so it is pi times 8 squared, which is 64pi

The volume of the solid here which is enclosed by paraboloids is 81π.

Use cylindrical coordinates.

z = x² + y² ==> z = r²

z = 18 - (x² + y²) ==> z = 18 - r².

Curve of intersection:

r² = 18 - r² ==> r = 3, a circle.

So, the volume ∫∫∫ 1 dV equals

∫(θ = 0 to 2π) ∫(r = 0 to 3) ∫(z = r² to 18 - r²) 1 * (r dz dr dθ)

= 2π ∫(r = 0 to 3) rz {for z = r² to 18 - r²} dr

= 2π ∫(r = 0 to 3) r(18 - 2r²) dr

= π ∫(r = 0 to 3) (36r - 4r³) dr

= π(18r² - r⁴) {for r = 0 to 3}

= 81π.

The intersecting curves that are transversally intersecting make up an intersection curve in most cases, which means that the surface normals are never parallel at any common point. This limitation does not apply in situations when the surfaces touch or share surface elements. The intersections of two revolution cylinders form the bicylindrical curves.

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Answer:

option c

might not be congruent

Step-by-step explanation:

as the triangles that have three pairs of congruent angles i.e. AAA might not have the sides of the same length.

so, AAA is not a congruence rule or congruent postulate

Answer:

here is your answer

Answer:hey guys just saying its 1/52

Step-by-step explanation:

We can make predictions about the cost of fire damage based on the distance from the house to the nearest fire station. This information can be useful to insurance companies, fire departments, and homeowners in determining the risk of fire damage and the appropriate level of insurance coverage needed.

In this particular study, the insurance company has determined that a linear relationship exists between the cost of fire damage in major residential fires and the distance from the house to the nearest fire station. The cost of fire damage is the dependent variable, while the distance from the house to the nearest fire station is the independent variable.
For this study, a sample of 20 recent fires in a large suburb of a major city was selected. For each fire, the following variables were recorded:
- the cost of fire damage in thousands of dollars (the dependent variable)
- the distance from the house to the nearest fire station in miles (the independent variable)
It is expected that the cost of fire damage increases as the distance from the house to the nearest fire station increases. This is because, as the distance from the fire station increases, the response time also increases, which can result in more damage being done to the property.
To analyze this data, a linear regression model can be used. The model will help to determine the nature and strength of the relationship between the two variables. The model will generate an equation in the form of y = mx + b, where y is the cost of fire damage, x is the distance from the house to the nearest fire station, m is the slope of the line, and b is the y-intercept.

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The variance of the total weight of flour sacks purchased is 36.

Since the moment generating function of a random variable uniquely determines its moments, we can use the moment generating function MW(t) to find the mean and variance of the weight of one sack of flour.

The first derivative of the moment generating function is:

MW'(t) = 6t/(1 - 3t)³

Setting t = 0, we get the mean:

MW'(0) = 6(0)/(1 - 3(0))³ = 0

So the mean weight of one sack of flour is zero.

The second derivative of the moment generating function is:

MW''(t) = 54t²/(1 - 3t)⁴ + 18/(1 - 3t)³

Setting t = 0, we get the second moment:

MW''(0) = 54(0)²/(1 - 3(0))⁴ + 18/(1 - 3(0))³ = 18

So the variance of the weight of one sack of flour is 18.

Now, let X and Y denote the weights of the first and second sacks of flour, respectively. Since the weights are independently distributed, the variance of the total weight of flour sacks purchased is the sum of the variances:

Var(X + Y) = Var(X) + Var(Y) = 18 + 18 = 36

Therefore, the variance of the total weight of flour sacks purchased is 36.

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We need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit which is compounded semi-annually.

To solve this problem, we can use the formula for the future value of an annuity:

\(FV = P * ((1 + r)^n - 1) / r\)

Where:

FV is the future value of the annuity

P is the periodic payment or deposit amount

r is the interest rate per period

n is the number of periods

In this case, the deposit amount is $726.56, the interest rate is 6.45% compounded semi-annually, and the future value is $31,300. We need to find the number of deposits (n).

We can rearrange the formula and solve for n:

n = log((FV * r) / (P * r + FV)) / log(1 + r)

Substituting the given values:

n = log((31,300 * 0.03225) / (726.56 * 0.03225 + 31,300)) / log(1 + 0.03225)

Using a calculator or software, we find that n ≈ 9.989.

Therefore, we need approximately 10 deposits to reach a balance of $31,300 four years after the last deposit.

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Answer:

13.2 gallons

Step-by-step explanation:

286/260 *12 = 13.2

Answer:

about 13.2 gallons

Step-by-step explanation:

Easy way to calculate.

12 gallons divided by 260 miles

Take that answer and multiply it by 286.

Answer: 88

Step-by-step explanation:

First, separate into familiar shapes

The area of the triangles at each side is 10 because the formula is length times times width divided by 2, when you plug the numbers in, 5 times 4 divided by two, times 2 because there are two triangles which equals 20.

That leaves the rectangle and the formula for the area of a rectangle is length times width, 17 times 4 which equals 68.

Add them, 20 plus 68 equals 88.

If machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

Given that machine a can make 350 widgets in 1 hour, and machine b can make 250 widgets in 1 hour.

How much time will both machines take to make 1000 widgets?

Suppose the time taken by both machines be x hours. Time is equal because both the machines need to work together.

According to the question the equation will be as under:

350x+250x=1000

600x=1000

x=1000/600

x=10/6

x=5/3

x=1.67

Converting 0.67 to minutes 0.67*60=40.2

Adding will result 1 hour and 40 minutes.

Hence if machine a can make 350 widgets in 1 hour and machine b can make 250 widgets in 1 hour then by forming equation we will get that both machines have to work for one hour and 40 minutes to make 1000 widgets.

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