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2 years ago

Which represents the solution set of 5 (x + 5) less-than 85

Mathematics

1 answer:

lapo4ka [179]2 years ago

5 0

Answer:

x < 12

Step-by-step explanation:

Step 1: Write out expression

5(x + 5) < 85

Step 2: Solve

5x + 25 < 85

5x < 60

x < 12

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A baker determined the annual profit in dollars from selling pies using p n( ) = 52n − 0.05n2 , where n is the number of pies so

miss Akunina [59]

Answer:

<u>The annual profit if the baker sells 400 pies would be US$ 12,800</u>

Step-by-step explanation:

1. Let's review the information provided to us to answer the question correctly:

Annual profit in dollars from selling pies using p n( ) = 52n − 0.05n² , where n is the number of pies sold

Annual sales of the baker = 400 pies

2. Let's solve p for 400 pies

p n( ) = 52n − 0.05n²

p (n₄₀₀) = 52 * 400 − 0.05 * 400²

p (n₄₀₀) = 20,800 − 0.05 * 160,000

p (n₄₀₀) = 20,800 − 8,000

p (n₄₀₀) = 12,800

<u>The annual profit if the baker sells 400 pies would be US$ 12,800</u>

Note: Same answer to question 14179960, answered by me today.

3 0

2 years ago

A random sample of 28 statistics tutorials was selected from the past 5 years and the percentage of students absent from each on

Zielflug [23.3K]

Answer:

The 90% confidence interval using Student's t-distribution is (9.22, 11.61).

Step-by-step explanation:

Since we know the sample is not big enough to use a z-distribution, we use student's t-distribution instead.

The formula to calculate the confidence interval is given by:

$\bar{x}\pm t_{n-1} \times s/\sqrt{n}$

Where:

$\bar{x}$ is the sample's mean,

$t_{n-1}$ is t-score with n-1 degrees of freedom,

$s$ is the standard error,

$n$ is the sample's size.

This part of the equation is called margin of error:

$s/\sqrt{n}$

We know that:

$n=28$

$\bar{x}=10.41$

degrees of freedom $= 27$

$1-\alpha = 0.90 \Rightarrow \alpha = 0.10$

$t_{n-1} = 1.703$

$s = 3.71$

Replacing in the formula with the corresponding values we obtain the confidence interval:

$\bar{x}\pm t_{n-1} \times s/\sqrt{n} = 10.41 \pm 1.70 \times 3.71/\sqrt{28} = (9.22, 11.61)$

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8 0

2 years ago

Read 2 more answers

If g (x) = StartFraction x + 1 Over x minus 2 EndFraction and h(x) = 4 – x, what is the value of (g circle h) (negative 3)? Eigh

brilliants [131]

Answer:

Step-by-step explanation:

Given g (x) = $\frac{x+1}{x-2}$ and $h(x) = 4-x$ , we are to find $(goh)(-3)$

First we need to get $(goh)(x)$

$(goh)(x) = g(h(x))\\g(h(x))= g(4-x)\\g(4-x) = \frac{(4-x)+1}{(4-x)-2}\\ g(4-x) = \frac{5-x}{2-x}\\substitute \ x = -3 \ into \ resulting \ function\\ g(4-x) = \frac{5-x}{2-x}\\(goh)(-3) = \frac{5-(-3)}{2-(-3)}\\\\(goh)(-3) = \frac{8}{5}\\$

Hence $(goh)(x)\ is \ Eight-fifths$

Also given f(x) = x and g(x) = 1/x, we are to find $(fog)(x)$

$(fog)(x) = f(g(x))\\f(g(x)) = f(\frac{1}{x} )\\ since \ f(x) = x^2, we\ will \ repalce\ x \ with \ \frac{1}{x} \ to \ have;\\ f(\frac{1}{x} ) =( \frac{1}{x})^2\\\\$

$f(\frac{1}{x} ) = \frac{1}{x^2}$

For the pair of function f(x) = 2/x and g(x) = 2/x

f(g(x)) = f(2/x)

f(2/x) = 2/(2/x)

f(2/x) = 2*x/2

f(2/x) = x

Hence f(g(x)) = x

For the pair of function f(x) = x-2/3 and g(x) = 2-3x

f(g(x)) = f(2-3x)

f(2-3x) = (2-3x-2)/3

f(2-3x) = -3x/3

f(2-3x) = -x

f(g(x)) = -x for the pair of function

For the pair of function f(x) = x/2 - 2 and g(x) = x/2 + 2

f(g(x)) = f(x/2 + 2)

f(x/2 + 2) = f((x+4)/2)

f((x+4)/2) = [(x+4)/2]/2 - 2

f((x+4)/2) = (x+4)/4 - 2

find the LCM

f((x+4)/2) = [(x+4)-8]/4

f((x+4)/2) = (x-4)/4

Hence f(g(x)) for the pair of function is (x-4)/4

8 0

2 years ago

Consider the graph of Bx + Cy = A where A, B, and C are all positive constants. Find the coordinates of the x-intercept. Use upp

timofeeve [1]

That is where the line crosses the x axis or where y=0
set y=0
Bx=A
find x value
divie both sides by B
x=A/B
the x intercept is x=A/B

3 0

2 years ago

Read 2 more answers

The triangles in the diagram are congruent. If mF = 40°, mA = 80°, and mG = 60°, what is mB?

maria [59]

Answer:

The answer is 40 degrees.

Step-by-step explanation:

Since the two triangles are congruent, which means they are the same shape and size, they share the same angle measures. Since angle B is the same as angle F, it equals 40 degrees.

I hope this helped! :-)

5 0

2 years ago

Read 2 more answers