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If 5 minus the reciprocal of 5 is x+1, what is the value of x?

Give your answer as a fraction.
$$S$$ is the sum of 50 different numbers of the form $$1+\frac{1}{n}$$, where $$n$$ takes on positive integer values.

Quantity A

$$S$$

Quantity B

51


$$4 < x < y < 8$$

The ratio of $$x$$ to $$y$$ is 4 to 7.

Quantity A

$$y-x$$

Quantity B

3


A farmer blended corn and wheat to make 40 pounds of chicken feed. If the blend consisted of 3 parts of corn and 5 parts of wheat, by weight, how many pounds of the blend was corn?
$$x$$ is an integer.

$$1 ≤ k < 10.$$

$$\frac{120,000}{0.006}=(k)(10^x)$$

Quantity A

$$x-k$$

Quantity B

5


Which of the following is an integer?

Which of thefollowing is equivalent to $$36^{-1}$$?

Quantity A

$$(-2)^{-5}$$

Quantity B

-1


A quadratic equation of the form $$x^2-cx+d=0$$, where $$c$$ and $$d$$ are constants, has solutions 2 and 7. What is the value of $$d$$?

_____
A lecture hall has 15 rows of seats. There are n-2 seats in the first row and n seats in each of the other rows. ff there are no other seats in the lecture hall and the total number of seats in the lecture hall is between 180 and 200, what is the total number of seats in the lecture hall?
$$x^{3} < -8$$

$$y^{2} > 16$$

Quantity A

x

Quantity B

y


The function $$f$$ is defined for all numbers $$x$$ by $$f(x) = 2+ 3x$$.

Quantity A

$$f(x+4)-f(x)$$

Quantity B

12




Quantity A

The length of line segment PQ

Quantity B

6


$$r$$, $$s$$, and $$t$$ are prime numbers such that $$r < s < t$$.

Quantity A

The number of positive factors of $$rs$$

Quantity B

The number of positive factors of $$st$$


On March 1, 2018, James deposited $12,000 in a new savings account, X, that earned interest at an annual rate of 6 percent, compounded annually. There were no other transactions in the account. On March 1, 2019, James withdrew the total amount of money in account X and deposited that money in a new savings account, Y, that earned interest at an annual rate of 7 percent, compounded annually. There were no other transactions in the account. How much more money did James have on March 1, 2020, in account Y than he would have had in account X if he had not withdrawn the money on March 1, 2019, assuming account X continued earning an annual rate of 6 percent, compounded annually, and there were no other transactions in the account?
The lengths of the sides of a right triangle are 5, 9, and x. The value of x could be between which of the following pairs of integers?

Indicate all such pairs.


What is the value of $$\frac{t}{u}$$?


The figure shows a rectangle where the line segment with length x is perpendicular to the diagonal of the rectangle. What is the value of x?
The author suggests which of the following about the "expansion of the electorate to include women" in eighteenth-century Britain?

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