Jake and Blake began their journey from the same location at the same time. Jake's rate is 50 mph and Blake's rate is 60 mph. How many hours will it take for Blake to get 70 miles ahead of Jake

Answer: $133.10.

Step-by-step explanation:

Answer:

To calculate the monthly payment for a loan, you can use the following formula:

Monthly payment = (APR/12) * loan amount / (1 - (1 + APR/12)^(-number of payments))

In this case, the loan amount is $6,000, the APR is 3.11%, and the loan is for 4 years, or 48 months. Plugging these values into the formula, we have:

Monthly payment = (0.0311/12) * $6,000 / (1 - (1 + 0.0311/12)^(-48))

Calculating, we find that the monthly payment is approximately $147.26. Rounded to the nearest cent, the monthly payment is $147.26.

Step-by-step explanation:

In the given arithmetic progression Common difference is 14.

An arithmetic progression is a set of integers with a fixed difference between any two succeeding numbers (A.P.).

Given, the n term of ap is Sₙ = 3n² + 5n

Where n is the number of terms

S₁ = 3* 1 + 5*1

S₁ = 8

S₂ = 3 * 4 + 5*2

S₂ = 22

common difference = 22-8

Common difference = 14

therefore, the Common difference in the given AP is 14.

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The cleaning company would charge $150 for cleaning two rooms according to the fixed charges.

A fixed amount is a fixed amount or amount established by agreement or contract. This amount is usually a specified amount, does not change over time, and is usually paid on demand or by a certain date. Fixed amounts are commonly used in loans, insurance, and other financial contracts.

This cost is calculated by dividing the difference between the total cost of 6 and 8 rooms by the number of rooms cleaned (6 - 2 or 4).

= ($250 - $320)/4

= $40

This will give you a price of for each additional room.

To calculate the cost of two rooms, simply add the fixed amount of the home visit and double the cost ($40) for each additional room. That's a total of $150 for two rooms.

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Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to a humorous effect.

Oscar Wilde wrote a play titled The Importance of Being Earnest, A Trivial Comedy for Serious People.

It is a farcical farce that was first presented on February 14, 1895, at the St James's Theatre in London.

The characters maintain false personae to avoid onerous social duties.

The play's main themes, which are based on late Victorian London social customs, are the triviality with which it treats institutions as important as marriage and the satire that results.

In "The Importance of Being Earnest," Oscar Wilde employs the literary devices of irony and hyperbole to hilarious effect as he criticizes upper-class Victorian society.

Therefore, Oscar Wilde mocks upper-class Victorian society in "The Importance of Being Earnest" by using the literary devices of irony and hyperbole to humorous effect.

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Because two triangles are said to be congruent when all three of their corresponding sides and all three of their corresponding angles have the same measure, the right answer is SSS.

Three sides and three vertices make up a triangle, which is a polygon. It is among the fundamental forms in geometry. Triangle ABC is the name given to a triangle with vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are found.

In the order below, beginning with triangles DAB and BCD, write the names of the vertices.

AB = CD

DA = BC

Since both triangles' BD sides are the same, BD = BD.

The SSS feature of a congruent triangle allows us to conclude that the triangles DAB and BCD are congruent since they share the same three sides.

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Answer:

Step-by-step explanation:

Answer: y ≥ −3/2x − 3

Step-by-step explanation:

Graph the inequality by finding the boundary line, then shading the appropriate area.

Hope this helps!

The ratio of surface area to volume is 6:s

A cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

Given that, A cube has an edge length given by the variable “s”. It’s surface area and volume can be given in terms of the edge length by: surface area= 6s² volume= s³

The ratio = 6s² / s³

= 6 / s

Hence, the required ratio is 6:s

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The expression (1/4 - 3/5) is equivalent to the following expressions -

Given is the expression as -

(1/4 - 3/5)

The given expression is -

(1/4 - 3/5)

1/4 - 3/5

(5 - 12)/20

-7/20

We can write the fraction : -7/20 in many ways as given below -

-7/20 = (3/20 - 10/20) = (1/4 - 3/5)

-7/20 = (13/20 - 1) = (1/4 - 3/5)

-7/20 = (23/20 - 3/2) = 1/4 - 3/5)

Therefore, the expression (1/4 - 3/5) is equivalent to the following expressions -

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The number of students who will not be able to ride on the bus for the school trip is given by the equation A = 15 students

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The total number of students for the trip = 235 students

The number of buses = 5 buses

The number of students in a bus be = B

Now , each seat on the bus can occupy = 2 students

So , 22 seats can occupy = 22 x 2 students

22 seats in the bus can occupy = 44 students

So , the number of students in a bus B = 44 students

And , the total number of students in 5 buses = 5 x number of students in a bus B

Substituting the values in the equation , we get

The total number of students in 5 buses = 5 x 44

The total number of students in 5 buses = 220 students

So , the remaining number of students A = total number of students for the trip - total number of students in 5 buses

Substituting the values in the equation , we get

The remaining number of students A = 235 - 220

The remaining number of students A = 15 students

Therefore , the value of A is 15 students

Hence , the number of students is 15 students

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Answer: 4 times

Step-by-step explanation: I got 4 times. Here's how to solve it:

Set up a proportional relationship, but first, we need to convert 10 hrs into mins:

1 hour = 60 mins

To find how many minutes are in 10 hours, we multiply 60 by 10, which equals 600.

So, therefore there are 600 mins in 10 hours. Now, we can set up our proportional relationship:

[tex]\frac{200}{60} = \frac{?}{12}[/tex]

So, if we know 12 is a factor of 60, we should divide 60 by 12, and we should get 5. So, now we do the same with the 200. We do 200 / 50, and we get 4. I hope this helps!

The sum of the sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] is 1

Consider given sequence [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex]

here, the dots . . . means that there are 21 numbers being added, one for each integer from −10 to 10.

We need to find the sum.

We can observe that the above sequence is a geometric sequence with the common ratio r = -1 and the first term a1 = [tex](-1)^{-10}[/tex] i.e., a1 = 1

We know that the formula of the sum of n-terms of a geometric sequence is:

[tex]S_n= a_1 \times (\frac{1-r^n}{1 -r} )[/tex]

For n = 21, r = -1 and a1 = 1

[tex]S_{21}=1 \times (\frac{1-(-1)^{21}}{1-(-1)} )\\\\S_{21 }= 1\times (\frac{1-(-1)}{1 +1} )\\\\S_{21 }=\frac{1+1}{2} \\\\S_{21 }= \frac{2}{2} \\\\S_{21 }= 1[/tex]

Therefore, [tex](-1)^{-10} +(-1)^{-9} +(-1)^{-8} +\cdots+ (-1)^9+ (-1)^{10}[/tex] = 1

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Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the laset day of the billing cycle instead of on the first day

Two or more expressions with an Equal sign is called as Equation.

The billing cycle for the month = 28 days

Current beginning balance = x

Annual percentage rate (APR) = 24%

Monthly percentage rate (MPR) = 2% (24% ÷ 12)

Purchase on the last day = $1,400

Total finance charge for the month = $51

Finance charge for the last-day purchase = $1 ($1,400 x 2% x 1/28)

Finance charge for the beginning balance = $50 ($51 - $1)

The current beginning balance, x = $2,500 ($50 ÷ 2%)

Equation for current beginning balance, x = 51 - 1 ÷ 0.02

Total finance charge for the last-day purchase = $28 ($1,400 x 2%)

Savings in finance charge by purchasing on the last day = $27 ($28 - $1)

Hence, Rebecca can save $27 in finance charge when she purchases the $1,400 gift for her friend on the last day of the billing cycle instead of on the first day.

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Answer:

x=3

Step-by-step explanation:

Since the altitude of this triangle is at the midpoint of the base,

It is a isosceles triangle making MJ=MK

9x-18=3x

6x-18=0

6x=18

x=3

The length of the arc of the sectored watered is 27.9 feets

length of arc is the distance between two points along a section of a curve.In other words, it's the distance from one point on the edge of a circle to another, or just a portion of the circumference

The length of an arc is given by :

L = theta/360 × 2πr

where tetha is the angle substends

r is the radius

Here the radius is the length at which water is sprayed = 20 ft

tetha = 80°

therefore l = 80/360 × 2×3.14 × 20

L = 29feets

Therefore the length of the arc formed by the water is 27.9 feets

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The linear equation 3x – 2y = 6 has one real solution. To find it, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable.

For example, you can solve for y to get y = (6 + 3x)/2, and then substitute this into the equation to get 3x – 2((6 + 3x)/2) = 6, which you can then solve for x. Doing this will give you x = 3, which means that the solution is (3, 3).

The linear  equation 3x – 2y = 6 has infinitely many solutions. To find them, you can solve the equation for one of the variables (either x or y) and then substitute the result into the equation to find the other variable

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Answer: $3.06

Step-by-step explanation: In order to get $3.06, you will have to find half $2.04 and then add that number to the price of 12 eggs.

The vertex and axis of symmetry of the graph is shown in image.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Now,

Since, The function is,

⇒ f (x) = 1/4 (x + 6)² - 5

Hence, The points corresponds to x = - 2 and - 4 are;

For x = - 2;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-2 + 6)² - 5

⇒ f (x) = 1/4 (4)² - 5

⇒ f (x) = 4 - 5

⇒ f (x) = - 1

For x = - 4;

⇒ f (x) = 1/4 (x + 6)² - 5

⇒ f (x) = 1/4 (-4 + 6)² - 5

⇒ f (x) = 1/4 (2)² - 5

⇒ f (x) = 1 - 5

⇒ f (x) = - 4

Thus, The points are;

⇒ (- 2, - 1) , (- 4, - 4)

And, The vertex of the function is,

⇒ ( - 6, - 5 )

And, The axis of symmetry of the graph is,

⇒ x = - 6

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If Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. His monthly payment is $87.31.

Monthly payment can be defined as the amount a person received on a monthly basis.

Now let find the monthly payment

Monthly payment = 7900 (0.0429/12) ( 1+ 0.0429/12)^12×10 ÷  ( 1+ 0.0429/12)^12×10 -1

Monthly payment = 7900 (0.003575) ( 1+ 0.003575)^120÷  ( 1+ 0.003575)^120 -1

Monthly payment =7900 (0.003575) ( 1.003575)^120 ÷  ( 1.003575)^120 -1

Monthly payment = $87.31

Therefore the monthly payment is $87.31.

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The complete question is:

Rich is going to a 4-year college. He was given a 10-year, unsubsidized student loan for $7,900 at 4.29%. He has to option of beginning to repay the loan in 4.5 years. He also knows that during the time he is not making payments, interest will be charged at 4.29%. If Rich decides to make no payments during the 4.5 years, the interest will be capitalized at the end of that period.  Suppose that Rich had decided to apply for a private loan rather than a federal loan. He is considering a 10-year lo"an with an interest rate of 5.9% .What will his monthly payments be?

Answer:

8.5 hrs? direct variation

Step-by-step explanation:

60 per hour is 600 for 10 hours so 70 per hour to go 600 miles is 8.57142857143 in the calculator

600/60 =10

600/70 = 8.5

and its direct variation because on a graph 8.5 8.5 squares up for ever 1 square going over every time and the graph does curve but I haven't learned this stuff in years so I'm not 100% sure

Answer:

The area of the windflower garden that is enclosed by a circular fence of 400 yards length is equal to 12732.39 square yards.

The measurement of the circle's perimeter, also known as its circumference, is called the circle's border. It is the length around the border of the circular object or the circle itself.

The formula for calculating the perimeter of a circle is ,

Perimeter/ Circumference of a circle = 2 * pi * r, where pi = 3.14 and r is the radius of the circle.

Taking the given information in the question, i.e circumference of the circular fencing wire , i.e C = 400 yards

                                         or , 2 * pi * r = 400

                                         or , r = 400/(2* 3.14)

                                                 r = 63.66 yards

Now the area of the circular fence is given by,

Area = pi * r^2

Area = 3.14 * 63.66^2

Area = 12732.39 square yards

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Answer: 1/2

Step-by-step explanation:

( see image ) ( Keep Change Flip )

The total surface area of the cuboid is 2 (lh + lw+ hw) square units.

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The side lengths measuring 4 units , 5 units and 6 units does not make a Right Triangle as they do not satisfy the condition of the Pythagoras Theorem that the square of the longest side is equal to the sum of square of other two side .

The Pythagoras Theorem states that the square of the lonest side (hypotnuse) is equal to the sum of the square of the other two sides ,.

The side lengths of the triangle are given as 4 units , 5 units and 6 units ,

According to the condition , [tex]6^{2} = 4^{2} + 5^{2}[/tex]

On simplifying ;

we get ;

[tex]36 = 16 + 25[/tex] ;

[tex]36 \neq 41[/tex]

that means the given side do not form a right triangle .

Therefore , the side 4 units , 5 units and 6 units do not make a right triangle .

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Answer:

( - 7, - 1, 1, 4 )

Step-by-step explanation:

( x, y )

where,

x is Domain

y is Range

Hence,

Domain is ( - 7, - 1, 1, 4 )

The expression determines the quantity of water leaving the tank per hour is (18 1/2 gallons)/(4 1/4 hours)

Rate is the ratio of a certain number of units of one quantity to units of another quantity. Mathematically, rate is one quantity divided by the other quantity.

If a total of 18 and one-half gallons flowed out of the tank in 4 and one-fourth hours. We can write that the rate as follows:

rate = (18 1/2 gallons)/(4 1/4 hours)

rate = 4 6/17 gallons per hour

Thus, the expression determines the quantity of water leaving the tank is (18 1/2 gallons)/(4 1/4 hours)

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If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

If the confidence interval for a difference between groups includes zero, that means that if you run your experiment again you have a good chance of finding no difference between groups.

If the confidence interval for a correlation or regression includes zero, that means that if you run the experiment again there is a good chance of finding no correlation in the data.

In both of these cases, you will also find a high p-value when you run the statistical test, meaning that the results could have occurred under the null hypothesis of no relationship between variables or no difference between groups.

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Distance of 2/3 from the horizontal axis is 2 for a cartesian plane.

The coordinate system in where the location of a point is identified by a pair of numerical terms and that has two reference axis is termed as cartesian coordinate system.

In cartesian plane the reference axis are named as X - axis and Y -axis.

In this system, location of a point p is identified by p (x, y) that means x is the x coordinate of point p and y is the y coordinate of point p. Generally, X-axis is horizontal, and Y-axis is vertical. Both axes are intersected at the origin.

The point coordinate 2/3 denotes the location of a point with respect to a reference direction in the polar coordinate system. In the polar coordinate system, the angle between horizontal axis and a reference point is called polar angle. we know tan angle = vertical coordinate / horizontal coordinate.

hence, tan angle = 2/3

for this reason, if we imagine a cartesian coordinate system 2 is the y coordinate and 3 is the x coordinate.

Finally, the distance of 2/3 from the horizontal axis is 2.

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The temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C.

To work out the temperature at the summit of Ben Nevis, we can use the formula:

Temperature at summit = Sea level temperature - (Altitude above sea level / 100) ×Temperature change per 100 metres

We are given that the sea level temperature is 5°C and the height of Ben Nevis is 1300 metres above sea level, and the temperature decreases by 1°C for every 100 metres above sea level.

So, after putting the values into the formula:
Temperature at summit = 5 - (1300/100) × 1 = -15°C

Therefore, the temperature at the summit of Ben Nevis, when the sea level temperature is 5°C is -15°C

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