a warehouse 40 yards long, and 25 yards wide, and it is piled with cartons to a height of 3 yards. what is the area of the warehouse floor? what is the total volume of the cartons? (assume there is no space between cartons.)

The given expression is undefined when x = 5 OR x = -5

From the question, we are to determine the value of x for which the given expression is undefined

The given expression is

x-4/3x²-75

An expression is undefined when the denominator equals zero

Thus, the expression is undefined when

3x² - 75 = 0

Now, we will determine the values of x in the equation above

3x² - 75 = 0

3x²  = 75

x² = 75/3

x² = 25

x = ±√25

x = ±5

Hence, the given expression is undefined when x = 5 OR x = -5

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Answer:

a) [tex]f(x) = x + 3[/tex]

b) [tex]f(x) = -x - 5[/tex]

c) [tex]f(x) = 2x + 6[/tex]

Step-by-step explanation:

To determine the equation of a straight line, we need two things:

1. two known points (coordinates) on the line, used to calculate the gradient

2. the y-intercept of the line (the y-coordinate of the point at which the line crosses the y-axis)

Then we can use the equation:

[tex]\boxed {f(x) = ax + q}[/tex]

where a is the gradient and q is the y-intercept, to determine the equation of the line.

a) known points: (0, 3), (-4, -1)

y-intercept: 3

gradient = [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]

             ⇒ [tex]\frac{3 - (-1)}{0 - (-4)}[/tex]

             ⇒ [tex]\bf 1[/tex]

∴ a = 1 , q = 3

∴ equation:

[tex]{f(x) = ax + q}[/tex]

[tex]f(x) = 1x + 3[/tex]

⇒ [tex]\bf f(x) = x + 3[/tex]

b) known points: (-7, 2) , (0, -5)

y-intercept = -5

gradient = [tex]\frac{2 - (-5)}{-7 - 0}[/tex]

             ⇒ [tex]\bf -1[/tex]

∴ equation:

[tex]f(x) = -1x + (-5)[/tex]

⇒ [tex]\bf f(x) = -x - 5[/tex]

c) known points: (-3, 0), (0, 6)

y-intercept = 6

gradient = [tex]\frac{6 - 0}{0 - (-3)}[/tex]

             ⇒ [tex]\bf 2[/tex]

∴ equation:

[tex]\bf f(x) = 2x + 6[/tex]

Answer:

7 14/45

Step-by-step explanation:

9 1/9 - 1 4/5

82/9 - 9/5

410/45 - 81/45

329/45

7 14/45

Answer:

●7.31

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Answer:

17 & 26

Step-by-step explanation:

The equation

[tex]x+(x+9)=43\\2x+9=43[/tex]

[tex]2x=43-9\\2x=34[/tex]

[tex]x=34/2=17[/tex]

One number is 17

The other number is:

[tex]x+9=17+9=26[/tex]

Hope this helps

Using proportions, it is found that a force of 22 lb stretches the spring 18 inches.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The measures are direct proportional, hence the rule of three is:

11 lb - 9 inches

22 lb - n inches

Applying cross multiplication:

11n = 9 x 22

n = 9 x 2

n = 18 inches.

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The value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

The question has to do with definite integrals

Definite integrals are integrals obtained within a range of values (or limits) of the independent variable.

Given that

For any integral  [tex]\int\limits^a_c {g(x)} \, dx = \int\limits^a_b {g(x)} \, dx + \int\limits^b_c {g(x)} \, dx[/tex]

So,  [tex]\int\limits^{10}_3 {g(x)} \, dx = \int\limits^5_3 {g(x)} \, dx + \int\limits^{10}_5 {g(x)} \, dx[/tex]

So,   [tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

Since

Substituting the values of the variables into the equation, we have

[tex]\int\limits^{10}_5 {g(x)} \, dx = \int\limits^{10}_3 {g(x)} \, dx - \int\limits^5_3 {g(x)} \, dx[/tex]

[tex]\int\limits^{10}_5 {g(x)} \, dx = 36 - 18 \\\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

So, the value of the definite integral [tex]\int\limits^{10}_5 {g(x)} \, dx = 18[/tex]

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Answer:

{-5,-2,0,2,5,-1,1,8}

Step-by-step explanation:

The union of two sets contains all elements that are in set A or in set B (possibly both).

{-5,-2,0,2,5} ∪ {-5,-1,1,5,8} = {-5,-2,0,2,5,-1,1,8}

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

An equation is an expression that shows the relationship between two or more variables and numbers.

A geometric sequence is in the form aₙ = ar⁽ⁿ⁻¹⁾, where a is the first term and r is the common ratio.

The geometric sequence 81, 27, 9, 3, … has common ratio:

r = 27/81 = 1/3

The explicit formula for this  geometric sequence 81, 27, 9, 3, … is aₙ = 81(1/3)ⁿ⁻¹. It has common ratio of 1/3 and first term of 81.

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The two colors can be chosen in 3 different ways.

If we have a set of N elements, the number of different sets of K elements (such that the order of the K elements does not matter) is:

[tex]C(N, K) = \frac{N!}{(N - K)!*K!}[/tex]

In this case, we have 3 colors, so N=3, and we want to choose 2, then K=2.

Replacing that we get:

[tex]C(3, 2) = \frac{3!}{(3- 2)!*2!} = \frac{3*2*1}{1*2*1} = 3[/tex]

The two colors can be chosen in 3 different ways.

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Using simple interest, it is found that the APR is of 4.472%.

Simple interest is used when there is a single compounding per time period.

The amount of money after t years in is modeled by:

[tex]A(t) = A(0)(1 + rt)[/tex]

In which:

The parameters are given as follows:

A(t) = 6 x 511.18 = 3067.08, A(0) = 3000, t = 0.5.

Hence the APR is found as follows:

[tex]A(t) = A(0)(1 + rt)[/tex]

[tex]3067.08 = 3000(1 + 0.5r)[/tex]

[tex]1 + 0.5r = \frac{3067.08}{3000}[/tex]

1 + 0.5r = 1.02236

r = (1.02236 - 1)/0.5

r = 0.04472.

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Answer:

slope is -1

Step-by-step explanation:

Slope of the line is changes in y over changes in x. It can also be referred as rise over run.

We can express mathematically as:

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

where m is slope.

Let (-2,5) be [tex]\displaystyle{(x_2,y_2)}[/tex] and (6,-3) be [tex]\displaystyle{(x_1,y_1)}[/tex]. Hence, apply the slope formula:

[tex]\displaystyle{m=\dfrac{5-(-3)}{-2-6}}\\\\\displaystyle{m=\dfrac{5+3}{-8}}\\\\\displaystyle{m=\dfrac{8}{-8}}\\\\\displaystyle{m=-1}[/tex]

Therefore, the slope is -1

Answer:

√2² cannot be answer yesah

Answer:

it's answer came 20000o

-13, or +11, because they are both 12 places away from -1.

Using the normal distribution, the probability that x is of at most 40, represented by option B, is given as follows:

[tex]P(X \leq 40) = 0.1587[/tex]

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation of the distribution are given, respectively, by:

[tex]\mu = 51, \sigma = 11[/tex]

The probability that x is of at most 40 is the p-value of Z when X = 40, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{40 - 51}{11}[/tex]

Z = -1

Z = -1 has a p-value of 0.1587.

Hence the probability is:

[tex]P(X \leq 40) = 0.1587[/tex]

Which is the part to the left of X = 40 of the distribution, hence option B is correct.

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Answer:

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Step-by-step explanation:

Solution Given:

To find the inverse we need to exchange Domain to Range and vice-versa.

so

[tex]R^{-1}[/tex]={(2,1), (3,2), (9,3), (5,4)}

Answer:

its -14

Step-by-step explanation:

The total number of servings Stephen can achieve with 1/10 kilograms of tofu at 2/25 kilograms per serving is 5/4 servings

Number of servings = Total tofu Stephen has ÷ Tofu per serving

= 1/10 ÷ 2/25

= 1/10 × 25/2

= (1×25) / (10 × 2)

= 25/20

= 5/4 servings

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These are the laws of indices. You just have to memorise it, sorry : (

Hope it helps : )

Answer:

c

Step-by-step explanation:

because I had a test on these

66.90% of the total bankruptcy fillings are not chapter 13 fillings.

What is bankruptcy?

This is a situation where the management of a company declares that it could no longer pay its debt obligations as it does have the cash resources to do so.

In this case, the total number of bankruptcy fillings is 936,795, out of which 310,061 are chapter 13 filings

fillings that were not chapter 13=936,795-310,061

fillings that were not chapter 13=626,734

fillings that were not chapter 13 as % of total fillings=626,734/936,795

fillings that were not chapter 13 as % of total fillings=66.90%

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Step-by-step explanation:

the equation of a circle centered at the origin is

x² + y² = r²

r being the radius (the distance of the center to every point on the circle's arc).

so, we get a point on the arc : (0, -5).

what is its distance to the origin ?

the origin is (0, 0).

we see, both points have the same x coordinates. they are therefore on the same vertical line going through x=0.

that means there is no distance between them in x direction.

the only distance is in y direction : 0 to -5.

a distance is always positive (no matter in what direction).

so, the distance from 0 to -5 is : 5 units.

that means r = 5.

and our equation is

x² + y² = 5² = 25

The experiment is not a binomial experiment.

A binomial experiment is an experiment where there is a fixed number of trials, and the results are usually between two options- a yes or a no.

The conditions for a binomial experiment include:

1. Each trial should be classified either as a success or a failure.

2. There are a fixed number of observations

3. The trials are independent.

4. The number of trials are fixed.

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Answer:

62 inches

Step-by-step explanation:

Since we need to leave 2 cm of room on both sides, the maximum width of TV is 136 - 2 - 2 = 132 cm. Next, use the Pythagorean Theorem, a^2 + b^2 = c^2, to find the diagonal.

132^2 + 86^2 = c^2

c^2 = 17424 + 7396

c^2 = 24820

c = 157.543644746 cm

Finally, convert the value to inches using the given conversion factor.

157.543644746/2.54 = 62.0250569868 inches

Answer:

68

Step-by-step explanation:

Lets first find the quantity of tape the computing center is purchasing/month.

3/5 Of their 1600 dollar spending is on the heavy duty tapes, meaning they are spending 960 dollars/month on heavy duty tape, if we divide that by the original price, 40, it will give us the original quantity of heavy tape they are purchasing, 24/month.

The other 2/5 of their money, 640 dollars, are spent on regular tape, meaning they purchase 20 rolls of regular tape/month.

Given they are purchasing 24 rolls of heavy tape and 20 rolls of regular tape every month, we can simply multiple those by the new prices and sum the results.

24*38=912

20*31=620

912+620=1532

Then to find the money they are saving we subtract the new price from the original price.

1600-1532=68

Answer:

Step-by-step explanation:

x is the number of students

(x+5) is the number of students and chaperons

$2.50·(x+5) is the amount of money the number of students and chaperons will pay for the trip, and that number should be less or equal than $90 because those are all the money they have

2.50(x+5) ≤ 90 which is the same as 90 ≥ 2.50(x+5)

The inequality "90 greater-than 2.50 (x + 5) "

90 > 2.50(x+5) is an error becase it excludes the possibility that the trip can cost exact $90 so we need not just greater than > , yet greater and equal than ≥ sign

90 ≥ 2.50(x+5)