What is 30 1/4% as a fraction in simplest form

Let us say that:

x = pounds of $7 coffee

So that:

7 x + 2 * 20 = 5 * (x + 20)

7x + 40 = 5x + 100

2x = 60

x = 30 pounds

Therefore 30 pounds should be added.

To get a mixture of coffee worth $5 a pound, you should add 30 pounds of coffee worth $7 a pound to 20 pounds of coffee worth $2 a pound.

To solve this problem, we can use the method of mixtures. Let's assume that x pounds of coffee worth $7 a pound is added to 20 pounds of coffee worth $2 a pound. The total weight of the mixture will be (x + 20) pounds. The total value of the mixture will be the sum of the values of the two types of coffee.

The value of the 20 pounds of coffee worth $2 a pound is 20 * 2 = $40. The value of the x pounds of coffee worth $7 a pound is 7x. So, the total value of the mixture will be $40 + 7x.

Since we want the mixture to be worth $5 a pound, we can set up the equation:

(40 + 7x) / (20 + x) = 5

To solve this equation, we can cross-multiply:

(40 + 7x) = 5(20 + x)

Expanding the right side of the equation, we get:

40 + 7x = 100 + 5x

Subtracting 5x from both sides, we get:

2x = 60

Dividing both sides by 2, we get:

x = 30

Therefore, 30 pounds of coffee worth $7 a pound should be added to 20 pounds of coffee worth $2 a pound to get a mixture worth $5 a pound.

Answer: C)coordinate plane with two coinciding lines  has infinitely many solution.

Step-by-step explanation:

Since, By option A) If there is a coordinate plane with two parallel lines.

Then, It has no solution ( because, we get the solution at the the intersection point of the two lines but parallel lines do not intersect each other).So, it does not have infinite many solution.

By Option B) If there are two intersecting lines then we can get only one solution. So, it does not have infinite many solution.

By Option C) If there are two coinciding lines then we can get infinite number of intersection points therefore the system must have infinite number of solution.

Note: here, Option D) is same as Option B)

Therefore Only option C) is correct.

Answer: The value of x is 70.52°.

Step-by-step explanation:

Since we have given that

Length of ladder = 12 foot

Length of base = 4 feet

We need to find the value of 'x'.

We will use "Cosine of triangle":

[tex]\cos x=\dfrac{4}{12}\\\\x=\cos^{-1}(\dfrac{1}{3})\\\\x=70.52^\circ[/tex]

Hence, the value of x is 70.52°.

The inverse of this function is f(x) = [tex] \sqrt[3]{x - 6} [/tex]

You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.

f(x) = x^3 + 6 ----> Switch f(x) and x

x = f(x)^3 + 6 ----> Subtract 6 from both sides

x - 6 = f(x)^3 ----> Take the cube root of both sides

[tex] \sqrt[3]{x - 6} [/tex] = f(x) ----> Switch the order for formatting purposes

f(x) = [tex] \sqrt[3]{x - 6} [/tex]

And that would be your new inverse function.

7.88 units is the distance between points T(13, 1.6) and V(5.4, 3.7).

To find the distance between the points T(13, 1.6) and V(5.4, 3.7), we can use the distance formula:

Distance formula:

For two points [tex](x_1, y_1)[/tex]and [tex](x_2, y_2)[/tex], the distance between them is [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}.[/tex]

Let's plug in the coordinates of points T and V:

Distance = [tex]\sqrt{(5.4 - 13)^2 + (3.7 - 1.6)^2}[/tex]

= [tex]\sqrt{(-7.6)^2 + (2.1)^2}[/tex]

= √(57.76 + 4.41)

= √62.17

= 7.88.

So, the distance between points T(13, 1.6) and V(5.4, 3.7) is approximately 7.88 units.

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Answer:

B

Step-by-step explanation:

b is the closest answer to th actual aswer ad the most reasonable

Final answer:

The first sequence is arithmetic with an explicit formula of a_n = 10 + (n - 1) × 5 and recursive formula a_n = a_(n-1) + 5, a_1 = 10. The second sequence is geometric with an explicit formula of a_n = 2 × 3^(n-1) and recursive formula a_n = a_(n-1) × 3, a_1 = 2.

Explanation:

Analysis of Sequences

The first sequence: 10, 15, 20, 25, 30... increases by a constant amount of 5 which is an indication of an arithmetic sequence. The explicit formula for an arithmetic sequence is a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference between the terms. In this case, a_1 = 10 and d = 5. Hence, the explicit formula is a_n = 10 + (n - 1) × 5. The recursive formula for an arithmetic sequence is a_n = a_(n-1) + d, which would translate to a_n = a_(n-1) + 5 with a_1 = 10.

The second sequence: 2, 6, 18, 54, 162... multiplies by a common ratio of 3 which classifies it as a geometric sequence. The explicit formula for a geometric sequence is a_n = a_1 × r^(n-1), where a_1 is the first term and r is the common ratio. For this sequence, a_1 = 2 and r = 3, so the explicit formula is a_n = 2 × 3^(n-1). The recursive formula for a geometric sequence is a_n = a_(n-1) × r, which for this sequence is a_n = a_(n-1) × 3 with a_1 = 2.

Same girl can be chosen for both jobs, is the probability with replacement. Multiply the individual probabilities.

(6/20) * (6/20) = 9/100

The probability of a girl being selected to do both jobs on Monday will be 3 / 38. Then the correct option is D.

Its basic premise is that something will almost certainly happen. The percentage of favorable events to the total number of occurrences.

There are 14 boys and 6 girls in Emily’s class.

One student in Emily’s class is chosen each day to hand out calculators to all the students.

Also, one student in Emily’s class is chosen each day to collect calculators at the end of class.

The same student can be chosen for each job.

Each student is equally likely to be chosen.

Then the total number of the students will be

Total students = 14 + 6

Total students = 20

Then the probability a girl is selected to do both jobs on Monday will be

P = ⁶C₂ / ²⁰C₂

P = 15 / 190

P = 3 / 38

Then the correct option is D.

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The car will travel 300 miles while the bicycle travels 40 miles

Let's first calculate the ratio of distances traveled by the bicycle and the car in the given scenario:

Ratio of distances = Distance traveled by car / Distance traveled by bicycle

Ratio of distances = 30 miles / 4 miles = 7.5

This ratio represents the speed ratio between the car and the bicycle. Now, we can use this ratio to find the distance the car will travel while the bicycle travels 40 miles:

Distance traveled by car = Ratio of distances * Distance traveled by bicycle

Distance traveled by car = 7.5 * 40 miles = 300 miles

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The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months can be calculated using the formula: Total Finance Charge = Total Amount Repaid - Principal Amount.

The total finance charge for a $4,250 loan at 13.25% interest compounded monthly for 24 months can be calculated using the formula:

Total Finance Charge = Total Amount Repaid - Principal Amount

First, calculate the total amount repaid:

Now, calculate the principal amount:

Principal Amount = Loan Amount = $4,250

Finally, substitute the values into the formula and calculate the total finance charge:

Total Finance Charge = Total Amount Repaid - Principal Amount

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Answer:

The correct answer is D, "x − 2y = −1."

Step-by-step explanation:

I just completed the test.

39/4=9.

59/4=14.

add 14.+9.=23

now divide 23/4=5

40 is the first number evenly divided by 4 and is the 10th multiple of 4 (4*10=40)

56 is the last number evenly divisible by 4 and is the 14th multiple of 4 ( 4*14 =56)

14-10 = 4 +1 = 5

 there are 5 numbers evenly divisible by 4

The expression that can be used to represents the number of vehicles remaining in the bin is (b + c) - 1/3(b + c)

Total vehicles = b + c

Number of vehicles sold = 1/3 of total vehicles

= 1/3(b + c)

Number of vehicles remaining = (b + c) - 1/3(b + c)

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The expression that represents the number of vehicles remaining in the bin is 2/3 (b + c).

To determine the number of vehicles remaining in the bin after selling 1/3 of them, we start by calculating the total number of vehicles initially present. This total number is represented by b + c, where b is the number of bikes and c is the number of cars.

If the store sells 1/3 of the vehicles, the number sold can be represented as:

(b + c) / 3

The number of vehicles remaining in the bin would be the original total minus the number sold:

(b + c) - (b + c) / 3

We can simplify this expression by finding a common denominator:

(b + c) - (b + c) / 3 = 3(b + c)/3 - (b + c) / 3 = (3(b + c) - (b + c)) / 3 = (2(b + c)) / 3

Therefore, the expression that represents the number of vehicles remaining in the bin is 2/3 (b + c).

Answer:

When x = –5, y =

3.

When x = –1, y =

-2.

When x = 3, y =

-4

310/5 = 62

60 +61 +62 +63 +64 = 310

 3rd number is 62

Answer:

f/2=186 fish

186 x 2 = 372

372 fish left in the tank

Step-by-step explanation:

The center of the rail would rise approximately 0.06 meters above the ground.

The expansion of the railroad rail is given as 12 centimeters. To convert centimeters to meters, you divide by 100 since there are 100 centimeters in a meter.

So, the expansion in meters is  12/100 meters.

Now, the center of the rail would rise approximately half of this expansion because the rail expands equally on both sides. Therefore, the rise in the center of the rail above the ground would be

=1/2 × 12/ 100.

Let's calculate that:

Rise in the center= 1/2 × 12/100

​Rise in the center=6/100

Now, to express this fraction in decimal form, you divide the numerator by the denominator:

Rise in the center= 0.06

So, the center of the rail would rise approximately 0.06 meters above the ground.

Answer:

the answer is

Step-by-step explanation:

skewed left and 220

divide total cost by ticket price

972/27 = 36 tickets

The given functions f(x) and g(x) are not exceeding each other at any point as they are same function.

Both the graphs of these functions have same y-intercept of 0.

A function is the relation between two sets. A function relates the domain to the range.

Here,  f(x) = 5x and g(x) = 5x.

Therefore, both functions are equal and their graph will be same.

Hence, none of them exceeding the other one.

If we compare both functions with standard form: y = mx + c, it is clear that both functions have same y-intercept of 0.

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