Simple interest, I, in dollars are calculated using the formula I=PT, where p represents the principle, or amount in dollars that is invested or borrowed, r represents the annual interest rate, expressed as a decimal, and t represents time in years, find the value of the variable t using the simple formula I=$210, p=$4000, r=3.5%

Step-by-step explanation:

-1/4, -1/5, -1/6, -1/7, -1/8, 1/8, 1/7, 1/6, 1/5, 1/4

Answer:

1) Option 3

2) Option 3

3) Option 3

4) Option 1

5) Option 2

6) Option 3

7) Option 1

Step-by-step explanation:

1) \(y = x^2 + 4x + 3\)

Lets split the middle term.

\(=> y = x^2 + 3x + x + 3\)

\(=> y = x(x+3) + 1(x + 3)\)

\(=> y = (x+1)(x+3)\)

∴ \(x = -3 , -1\)

2) \(y = 8x^2 - 22x + 5\)

Lets split the middle term.

\(=> y = 8x^2 - 20x - 2x + 5\)

\(=> y = 4x(2x - 5) - 1(2x - 5)\)

\(=> y = (2x - 5)(4x - 1)\)

∴ \(x =\frac{1}{4} , \frac{5}{2}\)

3) \(y = x^2 - 5x\)

\(=> y = x(x - 5)\)

∴ \(x = 0 , 5\)

4) \(y = 12x^2 + 18x\)

\(=> y = 6x(2x + 3)\)

∴ \(x = \frac{-3}{2} , 0\)

5) \(y = x^2 - 7x + 12\)

Lets split the middle term.

\(=> y = x^2 -3x - 4x + 12\)

\(=> y = x(x - 3) - 4(x - 3)\)

\(=> y = (x - 3)(x - 4)\)

∴ \(x = 3,4\)

6) \(y = 3x^2 + 10x + 8\)

Lets split the middle term.

\(=> y = 3x^2 + 6x + 4x + 8\)

\(=> y = 3x(x + 2) + 4(x + 2)\)

\(=> y = (x + 2)(3x + 4)\)

∴ \(x = -2 , \frac{-4}{3}\)

7) \(y = x^2 - 4x - 45\)

Lets split the middle term.

\(=> y = x^2 - 9x + 5x - 45\)

\(=> y = x(x - 9) + 5(x - 9)\)

\(=> y = (x - 9)(x + 5)\)

∴ \(x = -5 , 9\)

The convergence or divergence of an infinite geometric series depends on the common ratio (r) between consecutive terms.

If the absolute value of the common ratio (|r|) is less than 1, the series converges. In this case, as the series progresses, each term becomes smaller and smaller, approaching zero. The sum of all the terms in the series will have a finite value.

If the absolute value of the common ratio (|r|) is equal to or greater than 1, the series diverges. In this case, as the series progresses, the terms either increase indefinitely or oscillate without converging to a specific value. The sum of all the terms in the series will be infinite.

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Given a quadratic equation: y = ax² + bx + c, "a", "b" and "c" are the coefficients of the regression and can be estimated using the formulas below.

a = {[Σ x²y * Σ xx ] - [Σ xy * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}

b = {[Σ xy * Σ x²x² ] - [Σ x²y * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}

c = [Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x² / n ]}

Where:

Σ xx = [Σ x²] - [ ( Σ x )² / n]

Σ xy = [Σ x y] - [ ( Σ x * Σ y ) / n]

Σ xx² = [Σ x³] - [ ( Σ x² * Σ x ) / n]

Σ x²y = [Σ x²y] - [ ( Σ x² * Σ y ) / n]

Σ x²x² = [Σ x⁴] - [ ( Σ x² )² / n]

And:

x and y are the Variables.

n = Number of Values or Elements

Σ x = Sum of x Scores

Σ y = Sum of y Scores

Σ x² = Sum of Square of x

Σ x³ = Sum of Cube of x

Σ x⁴ = Sum of Power Four of x

Σ xy= Sum of the Product of x and y

Σ x²y = Sum of Square of x and y

To solve the problem, follow the steps below.

Step 01: Find n and the values of x and y.

n = 6.

x = 8, 10, 12, 14, 16, 18

y = 45.94, 56.84, 63.88, 67.07, 66.4, 61.87

Step 02: Find Σ x, Σ y, Σ x², Σx³, Σ x⁴, Σ xy, Σ x²y

* (,) represents a decimal point.

Step 03: Find Σ xx, Σ xy, Σ xx², Σ x²y, Σ x²x²

Substitute the values above in the equations for each variable:

Σ xx = [Σ x²] - [ ( Σ x )² / n]

Σ xy = [Σ x y] - [ ( Σ x * Σ y ) / n]

Σ xx² = [Σ x³] - [ ( Σ x² * Σ x ) / n]

Σ x²y = [Σ x²y] - [ ( Σ x² * Σ y ) / n]

Σ x²x² = [Σ x⁴] - [ ( Σ x² )² / n]

Doing the same for the other variables, you have the results:

* (,) represents a decimal point.

Step 03: Find "a".

a = {[Σ x²y * Σ xx ] - [Σ xy * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}

Step 04: Find "b".

b = {[Σ xy * Σ x²x² ] - [Σ x²y * Σ xx² ] } / { [ Σ xx * Σ x²x²] - [Σ xx² ]²}

Step 05: Find "c".

c = [Σ y / n ] - { b * [ Σ x / n ] } - { a * [ Σ x² / n ]}

Answer:

The equation is:

Answer:

2. 3/4, 50%, 1/4, 12.5%

Step-by-step explanation:

Work completed at the 4 sites = 1/4, 50%, 12.5%, 3/4

1/4 = 0.25

50%

= 50/100

= 0.5

12.5%

= 12.5/100

= 0.125

3/4

= 0.75

in order from greatest to least?

3/4, 50%, 1/4, 12.5%

1. 12.5%, 1/4, 50%, 3/4

2. 3/4, 50%, 1/4, 12.5%

3. 3/4, 12.5%, 1/4, 50%

4. 1/4, 50%, 3/4, 12.5%

Answer:

Step-by-step explanation:

5.33

Answer:

Food problems are fun  :D

Step-by-step explanation:

\(\frac{7}{2}\) = \(\frac{cheeseburgers}{chicken}\)

chicken =12  sooo..

\(\frac{7}{2}\) = \(\frac{x}{12}\)

and solve for x.... that is... get x by itself... "isolate x"

12 * \(\frac{7}{2}\) = x

6 * 7 = x

42 = x

the restaurant sold 42 cheeseburgers  :P  

If Mark has a container in the shape of a cube and he uses 64 cubes with sides length of 1 inch to completely fill the container, then the edge length of the container is 4 inches

The shape of  the container is cube

He uses 64 cubes with side length of 1 inch to completely fill the container

The volume of cube with side length of 1 inches = \(a^{3}\)

Where a is the side length of the cube

= \(1^{3}\)

= 1 cubic inches

The volume of 64 cubes = 64×1

= 64 cubic inches

The volume of the container in cub shape = The volume of the 64 cubes with side length of 1 inches

\(a^{3}\) = 64

a = 4 inches

Hence, if Mark has a container in the shape of a cube and he uses 64 cubes with sides length of 1 inch to completely fill the container, then the edge length of the container is 4 inches

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The inequality to find the possible widths of the roped-off section is: w ≤ 4.9.

We can make use of the fact that the manager can only use a rope that is 25 meters in length and that the section's length is fixed at 7.6 meters.

Let's write 'w' (in meters) to represent the width of the roped-off area.

If we assume that we must rope off all four sides, we may calculate the total length of rope required for the portion to be roped off:

Length of rope = 2 * (width + length)

Substituting the given values:

Length of rope = 2 * (w + 7.6)

According to the problem, the manager can use no more than 25 m of rope. Therefore, we can set up the following inequality:

2 * (w + 7.6) ≤ 25

Simplifying the inequality:

2w + 15.2 ≤ 25

Subtracting 15.2 from both sides:

2w ≤ 9.8

Dividing both sides by 2:

w ≤ 4.9

Therefore, the inequality to find the possible widths of the roped-off section is: w ≤ 4.9.

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The probability that a bottle selected at random will contain at least one defect can be found using the complement probability of having no defect.

Let us denote the probability of having at least one defect in a bottle as P(A). P(A') is the probability of not having any defect in the bottle. Since the probability of an event occurring plus the probability of it not occurring is equal to 1, then \(P(A') = 1 - P(A).\)

Thus, the probability of having no defect in a bottle is

\(P(A') = (1 - 0.00001) = 0.99999\)

.Since a bottle has either no defect or at least one defect,

\(P(A) = 1 - P(A') = 1 - 0.99999 = 0.00001.\)

Therefore, the probability that a bottle selected at random will contain at least one such defect is \(0.00001 or 1/100,000.\)

This means that on average, only 1 bottle in 100,000 will contain such a defect.

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Step-by-step explanation:

19 mm = 1.9 cm

4.1 cm = 41 mm

1.) mm²

19 × 41 = 779 mm²

2.) cm²

1.9 × 4.1 = 7.79 cm²

The area of rectangle in centimeters is 7.79 cm² and Area of rectangle in mm² is 779 mm²

The area of Rectangle is length times of width.

In the given rectangle length is 4.1 cm

Width is 19 mm

Let us convert 4.1 cm to millimeters

We know that 1 cm = 10 millimeters

4.1 cm =4.1×10 mm

=41 millimeters

Now convert 19 mm to centimeter

19 mm = 1.9 cm

Now let us find area of rectangle in cm²

Area of rectangle =4.1 cm×1.9 cm

=7.79 cm²

Area of rectangle in mm²

Area of rectangle =41 mm×19 mm

=779 mm²

Hence, the area of rectangle in centimeters is 7.79 cm² and area of Area of rectangle in mm² is 779 mm²

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Answer:

c

Step-by-step explanation:

In this case, the marked price of 220 is the cost price and discount of 20% is announced on sales, so the selling price is 176.

The t-shirt costs $166.5 to purchase. To do this, multiply the listed price (220) by the discount rate (20%) stated as a decimal. This will give you the amount of the discount (0.20).

220*0.20 =44

The selling price is then determined by deducting the discount (44) from the marked price (220):

220-44 =176

Before applying any markups or reductions, the retailer paid the item's cost price, commonly referred to as the wholesale price. The price a consumer pays to purchase an item is known as the selling price. The selling price will be less than the advertised price if a discount is being offered, and the difference between the two represents the discount.

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a. 5

b. 6

c. 8

d. 10

e. 12

f. 15

Answer:

a) 5

b) 6

c) 8

d) 10

e) 12

f) 15

Answer:

25 4-point questions and 75 2-point questions

Step-by-step explanation:

Let x = no. of 4-point questions

Then 3x = no. of 2-point questions

So, x + 3x = 100

4x = 100

x = 25 =  no. of 4-point questions

and 3x =  3(25) = 75 = no. of 2-point questions

Answer: $11.20

Step-by-step explanation:

Jade: 8+2*2.5=$12

Chet: 4*2.5+6=$16

12+16=$28

40% of 28=$11.20

Answer:

assuming that the problem was actually

-1/12 x ^ 2 + 2x + 4

height = 16

(12,16)

forty feet (40) feet

vertex = -b/2a = -2/(-1/6) = 12

f(12) = - 144/ 12 + 24 + 4 = -12+ 24 + 4   = 16

Step-by-step explanation:

Answer: The last one.

Step-by-step explanation:

Answer:

5 x 5 = 25

4 x 2 = 8

25 + 8 = 33 cm^2

Note: The second expression must be \([(-3)+(-7)]+(-6)\) instead of \([3+(-7)]+(6)\)

Given:

The given expression is:

\(-3+[(-7)+(-6)]\)

Rahal rewrites the expression as:

\([(-3)+(-7)]+(-6)\)

To find:

The property that Rahal use to rewrite the expression.

Solution:

According to the associative property of addition, if a, b and c are three real numbers, then

\(a+(b+c)=(a+b)+c\)

We have,

\(-3+[(-7)+(-6)]\)

Using the associative property of addition, we get

\(-3+[(-7)+(-6)]=[(-3)+(-7)]+(-6)\)

Therefore, the required property is associative property of addition.

The general solution of the equation is y = Cx^{-3}, where C is an arbitrary constant.

To find the general solution of the given equation, we need to solve for y in terms of x.

The equation x^3 y' + y = 0 is a first-order linear homogeneous ordinary differential equation. We can rearrange it as y' = -y/x^3.

To solve this differential equation, we can separate the variables and integrate both sides:

∫(1/y) dy = -∫(1/x^3) dx

Applying integration:

ln|y| = 1/(2x^2) + C₁

where C₁ is an arbitrary constant of integration.

Taking the exponential of both sides:

|y| = e^(1/(2x^2) + C₁)

Since y can be positive or negative, we remove the absolute value notation and consider both cases separately:

Case 1: y > 0

y = e^(1/(2x^2) + C₁) = e^(1/(2x^2)) * e^(C₁)

Let C be another constant, C = e^(C₁). Then we have:

y = C * e^(1/(2x^2))

Case 2: y < 0

y = -e^(1/(2x^2)) * e^(C₁) = -C * e^(1/(2x^2))

Combining both cases, the general solution is:

y = C * x^(-3)

where C is an arbitrary constant.

The general solution of the equation x^3 y' + y = 0 is y = Cx^(-3), where C is an arbitrary constant.

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Answer:

7.20

Step-by-step explanation:

I took 18/5 and got 3,60 and then multiplied that by 2.

Using translation concepts, it is found that the transformation used to create this frieze pattern is a 180º rotation.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.

In this problem, looking at each pair and imagining a coordinate plane, we can see that one image is on the second quadrant and the other in the fourth, that is, the following rule is applied:

(x,y) -> (-x,-y).

Which is a 180º rotation.

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Answer:

glide reflection

Step-by-step explanation:

Brian has  £63 Initially, by using the ratio and proportion method.

What are Ratio and Proportion?

In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Numerous examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.

An equation known as proportion shows that the two ratios presented are equal to one another. For instance, the time it takes a train to go 100 kilometers per hour is equal to the time it needs to travel 500 kilometers in five hours. Example: 100 km/hr = 500 km/5 hour. The division technique of comparing two amounts can be quite effective in some circumstances. We can argue that a ratio is a comparison or condensed form of two quantities of the same type. We may determine how many times one quantity is equal to another using this relationship. The ratio may be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects. A ratio is indicated by the symbol ":".

In the question, It is given that:

The ratio of money in Brian's wallet to Colin's wallet one day was 7:2.

Let 7x denotes the amount in Brian's wallet and 2x denote the amount in  Colin's wallet on that day.

we know that:

Brian spent £39 that day.

Amount left in Brian's wallet = 7x- 39

Brian now had £4 less than Colin.

⇒ 2x -4= 7x- 39

⇒  7x-2x=4+39

⇒  5x=35

⇒  x=7   [Divide both sides by 5 ]

So , The initial amount in Brian's wallet  = 7(7)= £49

The initial amount in Colin's wallet = 2(7)= £14

The amount they had together =  £49+£14 = £63

So, They had £63 altogether initially.

Therefore, Brian has  £63 Initially.

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Answer: £14

Using the Laplace transform to solve the given integral equation  f(t) = t, 0 ≤ t < 4 0, t ≥ 4 is \(\frac{4(1-2e^-5s)/}{s}\)

explanation is given in the image below:

Laplace remodel is an crucial remodel approach that's particularly beneficial in fixing linear regular equations. It unearths very wide programs in var- areas of physics, electrical engineering, manipulate, optics, mathematics and sign processing.

The Laplace transform technique, the function inside the time domain is transformed to a Laplace feature within the frequency area. This Laplace function could be inside the shape of an algebraic equation and it may be solved without difficulty.

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The sampling technique used in this scenario is a) random sampling. The researcher interviews all passengers on five randomly selected flights.

The sampling technique used in this scenario is random sampling. Random sampling involves selecting individuals from a population in such a way that each individual has an equal chance of being chosen. In this case, the researcher selects five flights at random, and then interviews all passengers on those selected flights.

Random sampling helps ensure that the sample is representative of the population and reduces the potential for bias. By randomly selecting flights, the researcher increases the likelihood of obtaining a diverse range of passengers, capturing a variety of opinions and experiences.

Other sampling techniques have different characteristics. Cluster sampling involves dividing the population into groups or clusters and randomly selecting entire clusters to be included in the sample. Stratified sampling involves dividing the population into subgroups or strata and then randomly selecting individuals from each stratum. Systematic sampling involves selecting every nth individual from a list. Convenience sampling involves selecting individuals based on their availability or accessibility, which may introduce bias into the sample.

In summary, the sampling technique used in this scenario is random sampling, as the researcher randomly selects five flights and interviews all passengers on those selected flights. This approach helps ensure a representative sample and reduces potential bias.

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Given that the second term a₂ = -4 and the seventh term a₇ = -128, we need to find the first term a₁ and the common ratio r for the geometric sequence.

Step 1: Find the common ratio Using the formula for the nth term of a geometric sequence, we can write:a₇ = a₂⋅r⁵Replacing the given values, we get:-128 = -4⋅r⁵Dividing both sides by -4, we get:32 = r⁵Taking the fifth root of both sides, we get:r = 2

Step 2: Find the first team to find the first term a₁, we can use the formula for the nth term again. This time we'll use n = 2 and r = 2:a₂ = a₁⋅r¹Replacing the values, we get:-4 = a₁⋅2¹ Simplifying, we get:-4 = 2a₁

Dividing both sides by 2, we get:-2 = a₁Therefore, the first term a₁ is -2 and the common ratio r is 2. Hence, the required geometric sequence is:-2, -4, -8, -16, -32, -64, -128And we can verify that this sequence satisfies both the given terms a₂ = -4 and a₇ = -128.

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Answer:

Use https://www.bartleby.com/  it has helped me out a lot . Its actual tutors/teachers who answer your questions in about 30 minutes :)

Step-by-step explanation:

Answer:

-3

Step-by-step explanation:

Answer:

\(-384\)

Step-by-step explanation:

n = 6 (6th term)

\(-3* 2^{6+1}\)

\(-3* 2^{7}\)

\(=-384\)