Rob runs at a constant speed of 3.4 meters per second for one half hour.​ Then, he walks at a rate of 1.5 meters per second for one half hour. How far did Rob run and walk in 60 ​minutes?

The amount of the principal investment is, $1200. So option A is correct

Simple interest is an amount which is calculated for a certain period of time and for a certain rate, in simple interest calculation there are three factors which we consider: principal amount(P), rate(R) and time(T).

Every time we calculate simple interest the principal values will be the same unlike compound interest.

Formula;    Simple Interest(I) =  P × R × T/100

A = P(1 + RT)

Given that,

A = $1422

R =  3.7%

T =  5 year

P  = ?

After 5 year total amount

1422 = P ( 1 + 0.037 × 5)

P  =   1422/( 1 + 0.037 × 5)

   =    1422/1.185

P  =    1200

Hence, the principal amount is $1200

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The angle whose supplement is 30 degrees greater than 4 times the supplement is 30°

Two angles are called supplementary when their measures add up to 180 degrees.

For example:- 120° and 60°, 110° and 70°, 140° and 40°, 90° and 90°, 20° and 160°, 135° and 45° are some example of supplementary angles.

Given that, an angle whose supplement is 30 degrees greater than 4 times the supplement.

Let the angle asked be x,

Therefore, the supplement of x, will be = 180°-x

According to the question, Its supplement is 30 degrees greater than 4 times the supplement.

Therefore, establishing the equation,

So, for solving for x, we have,

180°-x = 30°+4x

4x+x = 180°- 30°

5x = 150°

5x/5 = 150°/5

x = 30°

As, we considered the angle asked be x,

Hence, the angle whose supplement is 30 degrees greater than 4 times the supplement is 30°

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The sampling used in this situation is Stratified sampling
In the question, students are selected from subgroups of Sophomore, Junior, and Senior classes.

We are told that 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively.

This means that the sample numbers of 49, 34 and 48 students were selected in proportion to the subgroup sizes of 496, 348, and 481 students respectively.

Thus, due to the fact that subgroups were selected & that sample number of students were also selected in proportion to their respective subgroup sizes.

This is, therefore, a stratified sampling.

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Q: 49, 34, and 48 students are selected from the Sophomore, Junior, and Senior classes with 496, 348, and 481 students respectively. Identify which type of sampling is used and why?

The total cost of materials for one candle is $2 and she pays $40 for the booth for the day.

Therefore, the total cost for making and selling one candle is $2 + $12 + $40 = $54

To cover all her expenses, Leila must sell enough candles to make $54 from each candle.

She must sell 54/$12 = 4.5 candles

Therefore, Leila needs to sell at least 5 candles to cover all her expenses.

At that point, her sales and expenses will be 5 candles x $12/candle = $60

Therefore, Leila's sales and expenses will be $60 at that point.

We have to find solutions for the given differential equation when

y = 0,  y = 1/(k-x) and y(a) = b using ordinary differential equations.

We have dy / dx = y^2

a. let's define the given y = 1/(k-x)

derive the above equation with respect to x :

                                  dy / dx = y' = 1/(k-x)^2

So this is the general solution.

b) We would want a singular solution that is not included in the general form. Here we could use y = 0

dy / dx = 0 = 0^2

so,this is a trivial singular solution.

c) If we have y(a) = b,

then, y = 1(k-a) = b

To find the value of k we use the other condition: y'(^2) = 4 x y(2)

           1/(k-a)^2 = 4 x  1/(k-a)

              k - 2 = 1/4

              therefore, k = 9/4

hence we got, y = 1/(9/4 - a) = b

So the points (a, b) are of the form: (a, 1/(9/4 - a))

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The complete question is :

Find a general solution of the differential equation dy/dx=y2

b. Find a singular solution that is not included in the general solution.

c. Inspect a sketch of typical solution curves to determine the points (a,b) for which the initial value problem (y′)2=4y,y(a)=b

Answer: [tex]2\sqrt{13}-\sqrt{697}[/tex]

Step-by-step explanation:

Since ABD is a right triangle, 14^2 = 12^2 + BD^2

196 = 144 + BD^2

52 = BD^2

BD = [tex]\sqrt{52} = 2\sqrt{13}[/tex]

ADC is also a right triangle, so 29^2 = 12^2 + DC^2

841 = 144 + DC^2

DC^2 = 697

DC = [tex]\sqrt{697}[/tex]

Since x = BD + DC,

x = [tex]2\sqrt{13} +\sqrt{697}[/tex] :>

The sample has 3.33% of defective bulbs so, B. The shipment will not be replaced.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, If a shipment has at least 5% defective light bulbs, it will be replaced.

Now, A sample of 60 light bulbs has 2 that are defective.

Therefore, The percentage of defective bulbs is,

= (2/60)×100%.

= (1/30)×100%.

= 3.33%, So, the shipment will not be replaced.

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a) The probability of a student living within walking distance of campus is 0.1521.

To find the probability of a student living within walking distance of the campus, we can use the formula for conditional probability:

P(A and B) = P(A) * P(B|A).

For this situation, An is "living within walking distance to campus" and B is "living with parents."

Thus, P(A and B) = (0.23)(0.67) + (0.06)(0.33) = 0.1521.

Hence, the probability of a student living within walking distance of campus is 0.1521.

b)  The probability given a student living within walking distance of campus they experience with their parents is 0.67.

To find the probability given a student day to day routines within walking distance to campus they experience with their parents, we can use the formula for conditional probability:

P(A|B) = P(A and B)/P(B).

In this situation, A is "living with parents" and B is "living within walking distance to campus."

Thus, P(A|B) = P(A and B)/P(B) = (0.23)(0.67)/0.1521 = 0.67.

Subsequently, the probability gave a student living within walking distance of campus experience with their parents is 0.67.

c) Living with parents and living within walking distance are independent events.

To decide whether living with parents and living within walking distance are independent events, we can analyze P(A|B) with P(A).

On the off chance that P(A|B) = P(A), the events are independent. For this situation, P(A|B) = 0.67 and P(A) = 0.67, so living with parents and living within walking distance are independent events.

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Answer:

x = -2

y = -5

Step-by-step explanation:

5x - y = -5

3x - 6y = 24

First, multiply the first equation by -6

-30x + 6y = 30

3x - 6y = 24

-27x = 54

x = -2

Now, put in -2 for x and solve for y

5(-2) - y = -5

-10 - y = -5

-y = 5

y = -5

Let's Check

5(-2) -(-5) = -5

-10 + 5 = -5

-5 = -5

So, x = -2   y = -5  is the correct answer.

there exists an integer that is greater than 5 and whose square is smaller than 40, express as a mathematical quantifiers ∃x∈ℤ: x > 5 ∧ x² < 40

1.  Start by writing down the equation: x² < 40

2.  Take the square root of both sides of the equation to isolate the variable x: √x² < √40

3.  Simplify both sides of the equation: x < √40

4.  Check that the result makes sense: x < 6.3

5.  Take the integer part of the result: x < 6

6.  Since the requirement is that x is greater than 5, the answer is x = 6.

We start by writing the equation x² < 40 and then take the square root of both sides to get x < √40. We check that the result is reasonable and then take the integer part of the result to get x < 6. Since the requirement is that x is greater than 5, the answer is x = 6. To confirm, we can calculate that x² = 36 which is smaller than 40, and indeed, 6 is greater than 5. Therefore, the integer that is greater than 5 and whose square is smaller than 40 is 6. This can be expressed mathematically as ∃x∈ℤ: x > 5 ∧ x² < 40 which translates to: There exists an integer x such that x is greater than 5 and the square of x is smaller than 40.

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The surface area of the container is 62 square inches.

The correct option is D.

In three-dimensional space,

a prism is a polyhedron where two ends are similar.

Given:

A student draws the net below to show the dimensions of a container that is shaped like a right rectangular prism.

We have H = 2 inches

L = 5 inches

W = 3 inches

Surface area of the rectangular prism,

A = 2(W×L + H×L + H×W)

A = 2(3×5+2×5+2×3)

A = 2(15+10+6)

A = 2(31)

A = 62 square inches

Therefore, the surface area is 62 square inches.

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Arithmetic mean deals will middle number while geometric mean deals with typical value

From the question, we have

Arithmetic mean and Geometric mean

The arithmetic mean is the sum of a set of numbers divided by the number of items in the set, and is often used to find the "middle" value of a dataset.

On the other hand, the geometric mean is the nth root of the product of a set of numbers and is often used to find the "typical" value of a dataset when dealing with quantities that can increase or decrease exponentially.

The above definitions imply that the difference between the arithmetic mean and geometric mean can be significant when dealing with sets of numbers that have large variations in values.

In general, the geometric mean will be less than or equal to the arithmetic mean.

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The constants a and b can be found by ensuring the function is continuous and that the limits at each point match. This can be done by setting the values of a and b so that the function and its derivative are equal at each point.

To find the constants a and b for the given piece-wise cubic function, we must consider the definition of continuity and limits. Firstly, for the function to be continuous, the function and its derivative must be equal at each point. Thus, we need to set the values of a and b so that the function and its derivative are equal at the points x=1, x=2 and x=3. We can use this to create a system of equations to solve for a and b. Once we have determined the values of a and b, we can then check that the limits at each point match. This can be done by computing the left and right hand limits at each point, and ensuring they are equal. If the limits are equal, then the function is continuous and the constants a and b are correct.

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Yes, it is possible to offer a discount to customers who order two dozen cookies.

What is Discount ?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

1 dozen=12 pieces

Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to consider the cost of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.

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Yes, it is possible to offer a discount to customers who order two dozen cookies.

What is Discount ?

The discount equals the difference between the price paid for and it's par value. Discount is a kind of reduction or deduction in the cost price of a product.

1 dozen=12 pieces

Yes, it's possible to offer a reduction to guests who order two dozen eyefuls. Depending on the capacity of the company, offering a reduction could help to increase the number of orders and potentially increase the company's capacity. still, it's important to cocost nsider the of offering a reduction and the implicit increase in profit that could be generated from the fresh orders.

So ,Yes it is possible to offer a discount to customers who order two dozen cookies.

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The linear equation for the cost of lemonades is 1.50*x+6 where x=5 i.e. A   and he spends $54.75 in total.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

Cost of lemonade=$1.5, number of lemonades=5

Cost of hamburger=$8.25, number of hamburgers=5

Tip=$6

Hence,

        Total cost=5*1.5+5*8.25+6

          Total cost =$54.75

Cost of lemonades only = 5*1.5+6

In type of linear equation  1.50*x+6 where x=5

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{19})\hspace{10em} \stackrel{slope}{m} ~=~ 7 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{19}=\stackrel{m}{ 7}(x-\stackrel{x_1}{2}) \\\\\\ y-19=7x-14\implies {\Large \begin{array}{llll} y=7x+5 \end{array}}[/tex]

The speed of the bicycle is 381 meters per minutes

we know that,

revolutions per minute = speed in meters per minute / circumference in meters.

Diameter = 32 inches

Circumference of the wheel = 2πr

r = Diameter/2 = 32/2 = 16

Circumference = 2 × π × 16

=  100.5714 inches

Approximately = 100 inches

we know that,

1 inch = 0.0254 meter

100 inches = x

x = 100 × 0.0254 meters

x = 2.54 meters

Hence:

Revolutions per minute = Speed in meters per minute / circumference in meters.

Speed = Revolutions per minute × circumference in meters.

Speed = 150 RPM × 2.54 meters

Speed = 381  meters per minutes

so, the speed of the bicycle is 381 meters per minutes.

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Analyze the diagram of the trapezoid gives BA = 10.5 units

A trapezoid (also known as a trapezium) is a four-sided geometric shape that has two parallel sides (the bases) and two non-parallel sides (the legs). The bases of a trapezoid can have different lengths, but the legs must be congruent and parallel to each other.

Let's analyze the diagram below and complete the instructions:

Since CB / CA = DE / DF

where CB = 6, DE = 4, EF = 7

We can say:

DF = DE + EF = 4 + 7 = 11

CA = CB + BA = 6 + BA

CB / CA = DE / DF

6/(6 + BA) = 4/11

6 × 11 = 4(6 + BA)

66 = 24 + 4BA

24 + 4BA = 66

4BA = 66 - 24

4BA = 42

BA = 42/4

BA = 10.5 units

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Answer: 3 + y = 24

Step-by-step explanation: Hello!

If she rode 3 miles one day and y miles the other 6 days of the week, and in total that adds up to 24 miles, that means the equation should be addition.

3 miles + y miles = 24 miles
Monday, other 6 days, total seven days

The equation should be:
3 + y = 24

As per the cone surface, the general direction in which the shatter cone ridges converge is south.

The term cone in math is defined as a three-dimensional shape in geometry that narrows smoothly from a flat base  to a point called the apex or vertex.

Here we have given that Shatter cones are key features that uniquely characterize impact structures

In this one their presence provides evidence that an impact occurred. Here we also know that the Shatter cone surfaces exhibit a texture with a series of intersecting ridges that produce its conical geometry.

Based on the definition of cone surface we have identified that the the correct  option is (a) that is the south.

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Answer:

1.7320508075689

The measures of the angles are Z = 146 degrees, X and W = 34 degrees and B = 119 degrees

Question 4

From the question, we have

<Y = 146 degrees

Because the lines XY and WZ are equal, it means that

<Z = 146

So, we have

X = W = (180 - 146)

Evaluate

X = W = 34

Question 6

Here, we have

Sum of the angles = 180 degrees

This gives

9x + 2 + 5x - 4 = 180

Evaluate the like terms

14x = 182

Divide by 14

x = 13

So, we have

B = 9 * 13 + 2

B = 119 degrees

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The value of 3h(2) + 4g(1) is 39

You can simply replace those variables in function with the value you know of them and then operate on those values to get a final value. This is the result of that expression at those values of the considered variables.

Given;

h(x)= 3x        x<2

     = 4x+1     x>2

g(x)= x^2+2   x<3

     = x^3        x>3

Now, substituting the values;

3h(2)= 3*(4*2+1)

=3*9

=27

4g(1)= 4(1^2 + 2)

=4(3)

=12

3h(2)+4g(1)=27+12

=39

Therefore, the answer of the function will be 39

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Answer:

it is easy to add all the numbers up then you will get 77 then tell me how many number should you add to get to 100 it is easy trust me

Step-by-step explanation:

Applying the linear pair definition, m<KGH = 60°.

In geometry, a linear pair is a pair of adjacent angles that are supplementary, meaning that their measures add up to 180 degrees. The two angles must be adjacent, meaning that they share a common side or vertex, and they must be linear, meaning that they are formed by two intersecting lines.

Therefore:

m<FGK + m<KGH = 180

Substitute

120 + m<KGH = 180

m<KGH = 180 - 120

m<KGH = 60°

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The reflection of point G across the x-axis would be at (-3, 2).

A point is transformed when it is moved from where it was originally to a new location. Translation, rotation, reflection, and dilation are examples of different transformations.

The coordinates of point G in the question are (-3,-2)

When a point is reflected across the x-axis, the x-coordinate remains the same, but the sign of the y-coordinate is changed.

Therefore, the reflection of point G, which is located at (-3, -2), across the x-axis would be at (-3, 2).

The x-coordinate is the same, but the y-coordinate has changed from negative to positive.

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The question seems incomplete, the completed question would be as:

The coordinates of point G are (-3,-2)

What would be the reflection point G across the x-axis?

This problem is designed to minimize the cost of feeding students in the dorms while providing a minimum of 1800 calories. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost and adding them together. The constraints of the problem are that A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75.

1. 2.25A + 2B + 3C

2. A >= 0

3. B >= 2

4. C <= 0.75

The objective of this problem is to minimize the cost of feeding students in the dorms, while the diet must contain a minimum of 1800 calories. To achieve this, three decision variables were defined: A, B, and C, which represent the pounds of food A, B, and C respectively. The objective function is to minimize the cost of the diet, which is calculated by multiplying the pounds of each food by its cost, and adding them together. There are three constraints in the problem: A must be greater than or equal to 0, B must be greater than or equal to 2, and C must be less than or equal to 0.75. These constraints ensure that the diet contains the desired amount of each food and that the total calories meet the minimum requirements.

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Use the intercepts to graph the equation y = 18-2x

What is meant by graph ?

Interpret What real-life quantities do the x- and y-intercepts

represent in this situation:

when x = 0, y = 18,  when y = 0 x = 9

The x intercept is 9,  y intercept is 18.

After 9 hours the gas is run not .

The amount of gas in a car when it is not running

18 × 1/4 = 4.5

4.5 = 18-2x

x= 6.75 hours

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