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Teegan likes to play golf. He has budgeted $60 next month for the driving range. It costs him $10.55 for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?

gaby131o 2022-09-20

Consider the following function
$r (x) = - (x + 5)^{2} + 2$

Ignacio Casey 2022-09-20

Alonzo works as a car detailer. He charges $175 per car. He is planning to move out of his parents’ house and rent his first apartment. He will need to pay $120 for application fees, $950 for security deposit, and first and last months’ rent at $1,140 per month. He has $1,810 in savings. How many cars must he detail to have enough money to rent the apartment?

easternerjx 2022-09-20

What is the mean value of 1 and 5

gemauert79 2022-09-20

You can get a car loan with a term of three years at an APR of 6%. If you can afford a monthly payment of $350, how much can you borrow?

ye1neh4 2022-09-20

If $\frac{1}{2}$ is a root of the equation $x^{2} + k x - (\frac{5}{4}) = 0$ , then find the value of k

imchasou 2022-09-20

Why does $\int_{a}^{a b} \frac{1}{x} d x = \int_{1}^{b} \frac{1}{t} d t$ ?
I can't understand how the integral having limits from $a$ to $a b$ in Step 1 is equivalent to the integral having limits from $1$ to $b$ . I'm a beginner here. Please explain in detail.
$\begin{aligned} \ln (a b) = \int_{1}^{a b} \frac{1}{x} d x & = \int_{1}^{a} \frac{1}{x} d x + \int_{a}^{a b} \frac{1}{x} d x \\ = \int_{1}^{a} \frac{1}{x} d x + \int_{1}^{b} \frac{1}{a t} d (a t) \\ = \int_{1}^{a} \frac{1}{x} d x + \int_{1}^{b} \frac{1}{t} d t \\ = \ln (a) + \ln (b) . \end{aligned}$

Jazmyn Pugh 2022-09-20

Question releating to the $\int_{1}^{x} \frac{\ln (t)}{t + 1}$
If $f (x) = \int_{1}^{x} \frac{\ln (t)}{t + 1} d t$ if $x > 0$ . Compute $f (x) + f (1 / x)$ . As a check, you should obtain $f (2) + f (1 / 2) = (\ln 2)^{2}$
I have tried evaluating the integral $\int_{1}^{x} \frac{\ln (t)}{t + 1} d t$ by parts, but it turns out to be futile as $\int \frac{\ln (t)}{t + 1} d t = \ln (t) \ln (t + 1) - \int \frac{\ln (t + 1)}{t} t$ and $\int \frac{\ln (t + 1)}{t} = \ln (t) \ln (t + 1) - \int \frac{\ln (t)}{t + 1} d t$ which leads to $\int \frac{\ln (t)}{t + 1} d t = \int \frac{\ln (t)}{t + 1} d t$
Is there any other way to evaluate this integral?

likovnihuj 2022-09-20

A regression between foot length (Y variables in cm) and height (X variables in inches) for 33 students resulted in the following regression equation:
$y = 10.9 + 0.23 x$
One student in the sample was 73 inches wall with a foot length of 29cm.
a) The predicted foor length for this student is cm
b) Residual for this student's cm

mangicele4s 2022-09-20

1. Provide a rigorous definition of a lower bound of a subset of real numbers.
2. Provide a rigorous definition of a infimum of a subset of real numbers.
3. Show that an infimum of a subset of real numbers is unique.
4. Show that a subset E of R has an upper bound only if inf $λ E = λ sup E$ for any negative $r \in R$

Joyce Sharp 2022-09-20

Solve the equation.
$30^{13 x + 20} + 2 = 5$

ye1neh4 2022-09-20

The sum of two numbers is 88. The difference of the two numbers is 48. What are the two numbers? Let x be the larger number and y be the smaller number.

Colten Andrade 2022-09-20

Simplify the following expressions, free of negative exponents. Show all necessary work.
$(\frac{6 x^{- 7} y^{4}}{5 x^{2} y^{- 5} z^{4}})^{3}$

Raina Gomez 2022-09-20

Solving $e^{4 x} + 3 e^{2 x} - 28 = 0$
How to solve this equation:
$e^{4 x} + 3 e^{2 x} - 28 = 0$
I don't know how to solve this problem. I read over another example, $e^{2 x} - 2 e^{x} - 8 = 0,$ and it said that $e^{2 x}$ is $e$ to the $x$ squared, so $e^{2 x} = e^{x^{2}}$ . Why is this so? So $e^{4 x} = e^{x^{4}}$ ?
Please help me to solve it.

Daniella Reyes 2022-09-19

Find the equation of a line perpendicular to $y = - 3 x - 1$ that contains the point (-1,1). Write the equation in slope-intercept form.

Altenbraknz 2022-09-19

A boat going upstream on The River averages 5 mph. Going downstream, the boat averages 10 mph. Find the speed of the current and the speed of boat in still water.

zapri4j 2022-09-19

How do you graph $f (x) = \frac{x^{2} + 3 x + 2}{- 3 x - 12}$ using holes, vertical and horizontal asymptotes, x and y intercepts?

Chelsea Lamb 2022-09-19

Cephalexin is an antibiotic that frequently is prescribed in 500 mg tablets. A doctor prescribes 2 grams of cephalexin per day for a patient with a skin access. How many 500 mg tablets would have to be taken in order to achieve this daily dosage?

Seamus Mcknight 2022-09-19

Describe how synthetic division can be used to factor a polynomial.

imchasou 2022-09-19

Is the function $m (x) = 26 (8 x)^{2}$ a power function? If it is, write it in the form $m (x) = k x p$ and enter exact values for k and p.

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