Yesterday, two friends went into a bank to open savings accounts. Megan started by putting $80 in her account, and she will deposit an additional $15 each week. Noah made no initial deposit, but he will add $25 more each week. In a few weeks, the friends will have the same account balance.

Answer:

The slope is just 1.

Step-by-step explanation:

Rise 1, up 1. so 1 over 1 just equals 1

Answer:

Wht question. don't see nothing

The sequence {20, 40, 60, 80, ...} is an infinite sequence.

To determine whether a sequence is finite or infinite, we need to examine if there is a clear pattern or rule that allows us to generate more terms indefinitely.

In this case, we can observe that each term in the sequence is obtained by multiplying the previous term by 2. Starting with 20, we multiply by 2 to get 40, then multiply by 2 again to get 80, and so on. This pattern continues indefinitely, with each term being twice the previous term.

Since there is a clear rule to generate more terms and there is no specific endpoint or limit, the sequence is infinite. We can continue generating terms by multiplying the last term by 2 repeatedly, resulting in an unending sequence of numbers.

It's important to note that even though we haven't listed out all the terms, we can still confidently conclude that the sequence is infinite based on the established pattern and rule.

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Answer:

4ac

Step-by-step explanation:

Assuming you're referring to the equation \(ax^2+bx+c=0\).

Since the discriminant \(D=b^2-4ac\) has to be equal to 0 in order for there to be exactly one real solution, then we have the following:

\(0=b^2-4ac\\b^2=4ac\)

Therefore, b² needs to be the same value as 4ac.

Answer:

b = - 12

Step-by-step explanation:

substituting m = \(\frac{4}{5}\) , x = 10, y = - 4 into y = mx + b , gives

- 4 = (\(\frac{4}{5}\) × 10) + b

- 4 = (4 × 2) + b

- 4 = 8 + b ( subtract 8 from both sides )

- 12 = b

Answer:

15 percent

Step-by-step explanation: You will substract the new value from the old value.

23-20

Now you will get the difference between them and divide that by the original amount.

3/20

This will equal 0.15 in which you now multiply by 100

15 percent

The actual factor of safety is 0.0874. a) One roof support load data: P = (600 × 100) / 4 = 150000 N

b) The value of z that corresponds to a reliability of 0.995 against compressive failure is 2.81.

c) The design factor associated with a reliability of 0.995 against compressive failure is 3.15.

d) The required diameter dowel for a reliability of 0.995 is calculated by:

\[d = \sqrt{\frac{4P}{\pi Su N_{d}}}\]

Where, \[Su\]-N[10.18, 0.4) ksi\[N_{d}\]= 0.2\[d

= \sqrt{\frac{4(150000)}{\pi (10.18) (0.2)}}

= 1.63 \,inches\]

The diameter of the dowel needed for a reliability of 0.995 is 1.63 inches.

e) A standard dowel with a diameter of at least 1.63 inches is required for a minimum reliability of 0.995 against failure. From the standard diameters given in the question, a 6-inch diameter dowel is the most suitable.

f) The actual factor of safety is the load that will cause the dowel to fail divided by the actual load. The load that will cause the dowel to fail is

\[P_{f} = \pi d^{2} Su N_{d}/4\].

Using the value of d = 1.63 inches,

\[P_{f} = \frac{\pi (1.63)^{2} (10.18) (0.2)}{4}

= 13110.35 \, N\]

The actual factor of safety is: \[\frac{P_{f}}{P} = \frac{13110.35}{150000} = 0.0874\]

Therefore, the actual factor of safety is 0.0874.

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The lateral surface area of the rectangular prism given in the picture is 36 cm ²

The lateral surface area of a rectangular prism can be found by the formula :

= 2 x height x ( Length + Breadth )

Height = 2 cm

Length = 3 cm

Breadth = 6 cm

The lateral surface area is therefore:

= 2 x 2  x ( 3 + 6 )

= 4 x 9

= 36 cm ²

In conclusion, the lateral surface area is 36 cm ².

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Answer:

linear

Step-by-step explanation:

the exponent of x is 1, so the function intercepts the x axis only one time

Answer:

15.5cm² for number one

Step-by-step explanation:

I will only do number one for you but here how you do it

1/2 (12+9) 10.  

The 12 and 9 come from the top and bottem number and 10 come from the total height

Then we need to calucate

1/2(12+9)+10

1/2*21+10

1/2*31

31/2

15.5

So 15.5cm² is the answer for the first one now I think you can do the rest!

The Area of Trapezoids are:

1. 105 cm²

2. 6.75 ft²

3. 150 mm²

4.  19 ft²

5. 19.6 cm²

6. 331.2 mm²

7.  270.6 ft²

8. 30.36 in²

9.  73.2 cm²

10. 136.17 mm²

The formula of Area of Trapezoids is:

= 1/2 x (Sum of bases) x height

1. Area of Trapezoids is:

= 1/2 x (12 + 9) x 10

= 1/2 x 21 x 10

= 105 cm²

2. Area of Trapezoids is:

= 1/2 x (1.5+ 3) x 3

= 1/2 x 4.5 x 3

= 6.75 ft²

3. Area of Trapezoids is:

= 1/2 x (12 + 18) x 10

= 1/2 x 30 x 10

= 150 mm²

4. Area of Trapezoids is:

= 1/2 x (3 + 6.5) x 4

= 1/2 x 9.5 x 4

= 19 ft²

5. Area of Trapezoids is:

= 1/2 x (9.2+ 2) x 7

= 1/2 x 11.2 x 7

=  19.6 cm²

6.  Area of Trapezoids is:

= 1/2 x (8 + 24) x 20.7

= 1/2 x 32 x 20.7

=  331.2 mm²

7. Area of Trapezoids is:

= 1/2 x (20.1 + 25) x 12

= 1/2 x 45.1

= 270.6 ft²

8. Area of Trapezoids is:

= 1/2 x (3.2 + 5.6) x 6.9

= 1/2 x 8.8 x 6.9

=  30.36 in²

9. Area of Trapezoids is:

= 1/2 x (4.5  + 7.5) x 12.2

= 1/2 x 12 x 12.2

= 73.2 cm²

10. Area of Trapezoids is:

= 1/2 x (14 + 3.8) x 15.3

= 1/2 x 17.8 x 10

= 136.17 mm²

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Answer:

\(\dfrac{2m -1}{5}\)

Step-by-step explanation:

Since we have common denominators inside the parentheses, we can combine the denominators. Then, we get the following expression:

\(2\huge\text{(}\dfrac{1}{5} m - \dfrac{2}{5} \huge\text{)} + \dfrac{3}{5}\)

\(2\huge\text{(}\dfrac{m - 2}{5} \huge\text{)} + \dfrac{3}{5}\)

Now, we can multiply the expression inside the parentheses by 2.

\(\huge\text{(}\dfrac{2m - 4}{5} \huge\text{)} + \dfrac{3}{5}\)

Since the expression inside the parentheses cannot be simplified further, we can open the parentheses and simplify the expression.

\(\dfrac{2m - 4}{5} + \dfrac{3}{5}\)

We can combine the denominators as the denominators are the same.

\(\dfrac{2m - 4 + 3}{5}\)

Finally, we can simplify -4 + 3.

\(\dfrac{2m -1}{5}\)

Therefore, the simplified expression is (2m - 1)/5.

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Answer:

The change in momentum is: 60 N.s

Step-by-step explanation:

By Newton's second law:

F = ∆p / ∆t

Given that

Using the formula to determine the change in momentum

F = ∆p / ∆t

∆p = F × ∆t

     = 12 × 5

      = 60 N.s

Therefore, the change in momentum is: 60 N.s

Answer:  A

Step-by-step explanation:

When multiplying: Numbers multiply with numbers and for the x's, add the exponents

If there is no exponent, you can assume an imaginary 1 is the exponent

2x⁴ (3x³ − x² + 4x)

= 6x⁷ -2x⁶ + 8x⁵

Answer:

A. \(6x^{7} - 2x^{6} + 8x^{5}\)

Label the parts of the expression:

Outside the parentheses = \(2x^{4}\)

Inside parentheses = \(3x^{3} -x^{2} + 4x\)

You must distribute what is outside the parentheses with all the values inside the parentheses. Distribution means that you multiply what is outside the parentheses with each value inside the parentheses

\(2x^{4}\) × \(3x^{3}\)

\(2x^{4}\) × \(-x^{2}\)

\(2x^{4}\) × \(4x\)

First, multiply the whole numbers of each value before the variables

2 x 3 = 6

2 x -1 = -2

2 x 4 = 8

Now you have:

6\(x^{4}x^{3}\)

-2\(x^{4}x^{2}\)

8\(x^{4} x\)

When you multiply exponents together, you multiply the bases as normal and add the exponents together

\(6x^{4+3}\) = \(6x^{7}\)

\(-2x^{4+2}\) = \(-2x^{6}\)

\(8x^{4+1}\) = \(8x^{5}\)

Put the numbers given above into an expression:

\(6x^{7} -2x^{6} +8x^{5}\)

distribution

variable

like exponents

(a) To show that F is conservative, we need to check if it satisfies the condition of being the gradient of a scalar function.

We can do this by taking the partial derivatives of the components of F with respect to x and y and checking if they are equal:

∂F/∂y = (1 + x^2y)e^xyi + (x^3y + 2xy)e^xyj

∂F/∂x = (1 + xy)e^xyi + (2xy + x^2)e^xyj

Since the mixed partial derivatives are equal (∂^2F/∂x∂y = ∂^2F/∂y∂x = (1+3xy)e^xy), F is conservative.

(b) To find f, we need to integrate the component functions of F with respect to the corresponding variables:

f(x,y) = ∫[(1 + xy)e^xy]dx = (x + 1)e^xy + g(y)

f(x,y) = ∫[x^2e^xy]dy = xe^xy + h(x)

where g(y) and h(x) are integration constants.

Taking the partial derivative of f with respect to x and y, we get:

∂f/∂x = (1 + xy)e^xy + yg'(y)

∂f/∂y = (1 + xy)e^xy + xg'(y) + xe^xyh'(x)

Comparing these with the components of F, we get:

β1 = 1 + xy, β2 = y, β3 = 0

β1 = 1 + xy, β2 = x^2, β3 = 0

Solving for g'(y) and h'(x), we get:

g'(y) = y

h'(x) = x

Integrating with respect to y and x, we get:

g(y) = 1/2 y^2 + C1

h(x) = 1/2 x^2 + C2

where C1 and C2 are integration constants.

Thus, the function f is:

f(x,y) = (x + 1)e^xy + 1/2 y^2 + C1 + 1/2 x^2 + C2

(c) Using the Fundamental Theorem of Line Integrals, we have:

∫CF.dr = ∫C(∇f).dr = f(r(2)) - f(r(0))

where r(0) and r(2) are the initial and final points of the curve C.

We have:

r(0) = cos(0)i + 2sin(0)j = i

r(2) = cos(2π)i + 2sin(2π)j = i

Substituting into the expression for f, we get:

f(r(0)) = (1 + 0)e^0i + 1/2(0)^2 + C1 + 1/2(1)^2 + C2 = C1 + C2 + 1/2

f(r(2)) = (1 + 0)e^0i + 1/2(0)^2 + C1 + 1/2(1)^2 + C2 = C1 + C2 + 1/2

Thus, the value of the line integral is:

∫CF.dr = f(r(2)) - f(r(0)) = (C1 + C2 + 1/2) - (C1 + C2 + 1/2) =

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Answer:

The length of the shortest side of the triangle is 10.

Step-by-step explanation:

Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :

6 = 15

4 = X

4 x 15/6 = X

10 = X

Therefore, the length of the shortest side of the triangle is 10.

We can use minus(-) sign i.e. -9 to represent loss of 9 yards.

The word “gain” implies “acquiring something”.

Gain means to acquire something one desires especially because of one’s efforts.

Gain means to get something additional, for example, to gain more speed, to gain more weight.

We can denote gain by using plus(+) sign before the given number.

“Loss” generally means “to lose something one already has.”

Loss means the deprivation from keeping something, for example, bearing the loss of a theft.

It refers to something which is lost, for example, the theft of jewelry was a great loss.

We can denote loss by using minus(-) sign before the number.

In the given question it is said that there is gain of 4 yards, loss of 9 yards and gain of 15 yards.

It is asked that how would we represent 9 yards loss.

We know that we use minus(-) sign to represent loss.

So we can represent loss of 9 yards by writing it as -9.

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The difference quotient of the function f(x) = 4x² - 5x is 8x + 4h - 5.

The formula for difference quotient is expressed as:

\(\frac{f(x+h)-f(x)}{h}\)

Given the function in the question:

f(x) = 4x² - 5x

To solve for the difference quotient, we evaluate the function at x = x+h:

First;

f(x + h) = 4(x + h)² - 5(x + h)

Simplifying, we gt:

f(x + h) = 4x² + 8hx + 4h² - 5x - 5h

f(x + h) = 4h² + 8hx + 4x² - 5h - 5x

Next, plug in the components into the difference quotient formula:

\(\frac{f(x+h)-f(x)}{h}\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - (4x^2 - 5x)}{h}\\\\Simplify\\\\\frac{(4h^2 + 8hx + 4x^2 - 5h - 5x - 4x^2 + 5x)}{h}\\\\\frac{(4h^2 + 8hx - 5h)}{h}\\\\\frac{h(4h + 8x - 5)}{h}\\\\8x + 4h -5\)

Therefore, the difference quotient is 8x + 4h - 5.

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To find a value of c such that P(z ≥ c) = 0.55, we need to use a standard normal distribution table or calculator.From the standard normal distribution table, we find that the z-score corresponding to a right-tailed area of 0.55 is approximately 0.126.

Therefore, we have:

P(z ≥ c) = 0.55

P(z ≤ c) = 1 - P(z ≥ c) = 1 - 0.55 = 0.45

Using the standard normal distribution table, we find that the z-score corresponding to a left-tailed area of 0.45 is approximately -0.126.

So, c = -0.126.

Therefore, the value of c that satisfies P(z ≥ c) = 0.55 is approximately -0.126.

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Answer:

Sin k jajs

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

Given data set have, Mean = 10.5, Median = 11, Mode = 11.

To find the mean, median, and mode of the given set of data after adding a constant value of 3 to each element, we need to follow these steps:

Step 1: Add 3 to each value in the data set:

2 + 3 = 5

10 + 3 = 13

9 + 3 = 12

8 + 3 = 11

8 + 3 = 11

8 + 3 = 11

The updated data set becomes: 5, 13, 12, 11, 11, 11

Step 2: Calculate the mean:

Mean = (sum of all values) / (number of values)

Mean = (5 + 13 + 12 + 11 + 11 + 11) / 6

Mean = 63 / 6

Mean = 10.5

The mean of the updated data set is 10.5.

Step 3: Calculate the median:

The median is the middle value in a sorted list of numbers.

First, let's sort the updated data set in ascending order: 5, 11, 11, 11, 12, 13

The median is the middle value, which in this case is the average of the two middle values:

Median = (11 + 11) / 2

Median = 22 / 2

Median = 11

The median of the updated data set is 11.

Step 4: Calculate the mode:

The mode is the value that appears most frequently in the data set.

In the updated data set: 5, 11, 11, 11, 12, 13, the mode is 11 since it appears three times, which is more than any other value.

Therefore, the mode of the updated data set is 11.

To summarize:

Mean = 10.5

Median = 11

Mode = 11

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Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.

Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):

AC² = AB² + BC²

Substituting the given values, we have:

(AC)² = (AB)² + (BC)²

(AC)² = 16² + (BC)²

(AC)² = 256 + (BC)²

Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.

AC = 2 * radius

To find the radius, we can use the formula for the area of a circle:

Area = π * radius²

Given that the area of the circle is 2897 units², we can solve for the radius:

2897 = π * radius²

radius² = 2897 / π

radius = √(2897 / π)

Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:

(2 * radius)² = 256 + (BC)²

4 * radius² = 256 + (BC)²

Substituting the value of radius, we have:

4 * (√(2897 / π))² = 256 + (BC)²

4 * (2897 / π) = 256 + (BC)²

Simplifying the equation gives:

(4 * 2897) / π = 256 + (BC)²

BC² = (4 * 2897) / π - 256

Now we can solve for BC by taking the square root of both sides:

BC = √((4 * 2897) / π - 256)

To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.

In summary:

BC = √((4 * 2897) / π - 256)

mBC = 90 degrees

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Answer:

4p+3

Step-by-step explanation:

4p+6+-3

[4p]+[6+-3]

4p+3

The statement is True only for independent events and False otherwise. The statement "p (A ∩ B) = p(A). p(B)" is not always true for any two events A and B defined on a sample space S of an experiment.

This equation only holds true if A and B are independent events, meaning that the occurrence of one event does not affect the probability of the other event happening. In other words, p(A|B) = p(A) and p(B|A) = p(B).

If A and B are dependent events, meaning that the occurrence of one event affects the probability of the other event happening, then the equation does not hold true. In this case, the probability of A and B occurring together (p(A ∩ B)) would be less than the product of the probabilities of A and B occurring separately (p(A).p(B)).

Therefore, the statement is not always true and depends on whether A and B are independent or dependent events.

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(a) The firm's output supply function is given by q = (p + 199) / 2.

(b) The market-equilibrium price is $32.56, and the equilibrium number of firms is 10.

(c) Each firm sells 70 computers in the long run.

(39 - 0.009q) = (2q - 2) / q

Simplifying the equation, we find:

q = (p + 199) / 2

This represents the firm's output supply function.

p = 39 - 0.009((p + 199) / 2)

Simplifying and solving for p, we get:

p ≈ $32.56

Substituting this price back into the output supply function, we find:

q = (32.56 + 199) / 2 ≈ 115.78

Given that each firm produces 70 computers in the long run, we can calculate the equilibrium number of firms:

Number of firms = q / 70 ≈ 10

70 * 10 = 700

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The formula to determine the  density of a liquid with cubes, a meterstick and stopwatch is density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)

Density is a measure of how much mass is contained in a given volume of a material. In order to determine the density of a liquid, you will need three things: cubes, a meterstick, and a stopwatch.

First, gather your materials and select a cube of known dimensions. Place the cube on the surface of the liquid and start the stopwatch. Observe how long it takes for the cube to sink to the bottom of the container. Let's call this time t.

Next, use the meterstick to measure the height of the liquid in the container

With these two pieces of information, you can calculate the density of the liquid using the formula:

=> density = mass / volume

The mass of the cube can be calculated as:

=> mass = volume * density of the cube

where the volume of the cube is given by

=> volume = s³, where s is the length of one side.

Since we know the length of one side (s = 1 cm), the volume of the cube is 1 cm³.

The density of the cube can be assumed to be a constant value (for example, if the cube is made of aluminum, the density is approximately 2.7 g/cm³).

So,

=> mass = volume * density of the cube = 1 cm³ * 2.7 g/cm³ = 2.7 g.

The volume of the liquid displaced by the cube can be calculated as:

volume = mass / density of the liquid = mass / (h/t²)

where h/t² is the acceleration due to gravity.

Finally,

density of the liquid = mass / volume = 2.7 g / (volume of liquid displaced by the cube)

Complete Question:

Determine the density of an unknown liquid with only a meterstick, stopwatch, and cubes that sink.

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The radius of the circle inscribed in a 9-12-15 triangle is 3 units

The radius of a circle inscribed in a 9-12-15 triangle can be found using the formula for the inradius (r) of a triangle:

r = A/s

where A is the area of the triangle, and s is the semi-perimeter of the triangle.

Step 1: Find the semi-perimeter (s)
s = (a + b + c) / 2
s = (9 + 12 + 15) / 2
s = 36 / 2
s = 18

Step 2: Find the area (A) of the triangle using Heron's formula:
A = √(s(s-a)(s-b)(s-c))
A = √(18(18-9)(18-12)(18-15))
A = √(18(9)(6)(3))
A = √(2916)
A = 54

Step 3: Find the inradius (r) using the formula r = A/s:
r = 54 / 18
r = 3

Therefore, the radius of the circle inscribed in a 9-12-15 triangle is 3.

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Answer:

D

Step-by-step explanation:

Using the formula of area of a circle, about 226.08in² has been eaten

The diameter of the pizza is given as 24 inches. To calculate the area of the entire pizza, we need to use the formula for the area of a circle:

Area = π * r²

where π is approximately 3.14 and r is the radius of the circle.

Given that the diameter is 24 inches, the radius (r) would be half of the diameter, which is 12 inches.

Let's calculate the area of the entire pizza first:

Area = 3.14 * 12²

Area = 3.14 * 144

Area ≈ 452.16 square inches

Now, if half of the pizza is consumed, we need to calculate the area of half of the pizza. To do that, we divide the area of the entire pizza by 2:

Area of half of the pizza = 452.16 / 2

Area of half of the pizza ≈ 226.08 square inches

Therefore, if half of the pizza is consumed, approximately 226.08 square inches of pizza would be eaten.

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