A trough is 12 feet long and 3 feet across the top (see figure). Its ends are isosceles triangles with altitudes of 3 feet.

Answer:

28.875

Step-by-step explanation:

you would just multiply the three together

Answer:

A

Step-by-step explanation:

Answer:

Easy B                  

Step-by-step explanation: srry If It's Wrong

9514 1404 393

Answer:

  (x, y) = (452.5, -986)

Step-by-step explanation:

Dividing the first equation by 300 gives the standard form equation ...

  12x +5y = 500

Dividing the second equation by 180 gives the standard form equation ...

  22x +10y = 95

Subtracting the second of these equations from twice the first gives ...

  2(12x +5y) -(22x +10y) = 2(500) -(95)

  2x = 905 . . . . . simplify

  x = 452.5 . . . . .divide by 2

The second equation tells us ...

  y = (95 -22x)/10 = (95 -9955)/10 = -9860/10 = -986

The solution is (x, y) = (452.5, -986).

Given:

Function interval

Find-: Average rate of change.

Sol:

The average rate of change is:

Choose any two-point.

So average rate of change is:

The average rate of change is -9.

graphing

then,

vertex: (0,5)

the coordinate is a maximum

equation of axis of symmetry:

therefore,

axis of symmetry is at: x = 0

We have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

To prove that the Newton-Raphson method for solving the equation \(x^k e^x = 0\), where k is a constant, is given by the formula

\(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n,\)

we can start by considering the iterative process of the Newton-Raphson method.

Given an initial guess \(x_n\), we want to find a better approximation \(x_{n+1}\)that is closer to the root of the equation \(x^k e^x = 0.\)

The Newton-Raphson method involves the following steps:

Calculate the function value \(f(x_n) = x_n^k e^x_n\) and its derivative \(f'(x_n) = k x_n^(k-1) e^x_n.\)

Find the next approximation x_{n+1} by using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Let's apply these steps to our equation \(x^k e^x = 0\):

Calculate the function value and its derivative:

\(f(x_n) = x_n^k e^x_n\\f'(x_n) = k x_n^(k-1) e^x_n\)

Find the next approximation x_{n+1} using the formula:

\(x_{n+1} = x_n - f(x_n) / f'(x_n)\)

Substituting the function value and its derivative:

\(x_{n+1} = x_n - (x_n^k e^x_n) / (k x_n^(k-1) e^x_n)\\= x_n - (x_n^k / k)\)

Simplifying the expression by combining like terms:

\(x_{n+1} = x_n - (x_n^k / k)\\= x_n - x_n^k / k\\= (k - 1) x_n + x_n^2 / k + x_n\)

Therefore, we have proved that the Newton-Raphson iteration formula for solving the equation\(x^k e^x = 0\) is given by \(x_{n+1} = (k - 1) x_n + x_n^2 / k + x_n.\)

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The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

8x² + 16x + 3 = 0

using Quadratic formula

The following steps are involved

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)

\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)

\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)

\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)

\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)

\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

\(x = -0.209431\)

or

\(x = -1.79057\)

Therefore, the steps peter could follow will give the result

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

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The solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

To determine which value is included in the solution set for the inequality statement -3(x-4) > 6(x-1), we need to solve the inequality for x.

Starting with the given inequality:

-3(x - 4) > 6(x - 1)

First, distribute -3 and 6 to the terms inside the parentheses:

-3x + 12 > 6x - 6

Next, combine like terms by subtracting 6x from both sides and adding 6 to both sides:

-3x - 6x > -6 - 12

-9x > -18

To isolate x, divide both sides of the inequality by -9. Remember that when dividing by a negative number, we need to reverse the inequality sign:

x < (-18) / (-9)

x < 2

Therefore, the solution set for the inequality is x < 2. Among the given options, the value that is included in the solution set is 0.

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Answer:

The answer is B) g(x) is shift 5 units to the right and 2 units up from f(x).

Step-by-step explanation:

The equation that is given in this item can be written for clarity as follows:

                       g(x) = 1/(x - 5)  + 2

It can be seen that the x-component is subtracted with 5 and the g(x) which would lie in the y-axis is added with two. This suggests that the graph of this equation is shifted to the right by 5 units and upwards by 2 units compared to the graph of the parent function.

The Graph for both function is attached below.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.

Given:

g(x) = - 1/x

and, f(x) = 1/x

The Graph shown below.

From the Graph we can see that the graph of g(x)= -1/x and f(x)= 1/x

shows the same graph but the position is changed in opposite of each other.

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The solution is:

If my parents are going to pay the 5%, then, they will pay: $2979.

I will need to save $62.06 each month to accomplish my goal.

Here,

I'm going to a 4-year college that will cost $14895/year.

It means that I will need to pay: 14895*4 = $59.580

If my parents are going to pay the 5%, then, they will pay: $2979.

Now, if I want to save my total contribution for all four years, and I have four years to accomplish  the goal, then:

Then, if I have 4 years to pay it. It means I have 4*12 = 48 months.

Then I will need to save $2979./48 = $62.06 each month to accomplish my goal.

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complete question:

You are going to a 4-year college in 4 years that will cost $14,895.00/yr. Your parents expect you to pay 5% of the total cost.

How much do you need to pay for each year of attending?

If you want to save your total contribution for all four years before you start attending college, how much do you need to save each month if you have four years to accomplish your goal?

Given statement solution is :- The manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

To determine if the manager will have enough funds to cover the nightly payroll for the next four weeks, we need to calculate the total cost for four weeks and compare it to the amount set aside.

The nightly payroll has a mean of $2200 and a standard deviation of $300. Since there are seven nights in a week, the weekly payroll can be calculated as:

Weekly Payroll = Nightly Payroll * Number of Nights in a Week

= $2200 * 7

= $15,400

To calculate the total cost for four weeks, we multiply the weekly payroll by four:

Total Cost for Four Weeks = Weekly Payroll * Number of Weeks

= $15,400 * 4

= $61,600

Now, let's calculate the z-score using the formula:

z = (X - μ) / σ

Where:

X = Total Cost for Four Weeks

μ = Mean of the distribution

σ = Standard deviation of the distribution

z = ($61,600 - $2200) / $300

z = $59,400 / $300

z ≈ 198

To determine if the manager will have enough funds to cover the payroll, we need to find the proportion of the distribution that is less than or equal to the z-score. This can be done by consulting a standard normal distribution table or using statistical software.

For a z-score of 198, the proportion in the tail of the distribution is essentially 1 (or 100%). This means that the manager is virtually guaranteed to have enough funds to cover the payroll for the next four weeks.

Since the manager has set aside $10,000, which is less than the calculated total cost of $61,600, he will indeed have enough funds to cover the payroll.

Therefore, the manager will have enough funds, and the amount set aside ($10,000) is sufficient to cover the payroll for the next four weeks.

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Answer:

hhhhhhhhhhhhhhhhhhhiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Step-by-step explanation:

The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

Given that;

The sequence is,

11, 13, 15, 17, ....

Here, Common difference is,

13 - 11 = 2

15 - 13 = 2

Hence, Sequence is in Arithmetic sequence.

So, the nth term of 11,13,15,17 is,

⇒ T (n) = a + (n - 1)d

⇒ T (n) = 11 + (n - 1) 2

⇒ T (n) = 11 + 2n - 2

⇒ T (n) = 9 + 2n

Thus, The nth term of 11,13,15,17 is,

⇒ T (n) = 9 + 2n

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Answer:

1716.

Step-by-step explanation:

52 x 33 = 1716

The expression to represent Rodney's salary at his new job is

\(S(t) = 35,700*(1 + 0.025)^t\)

Rodney's income can be expressed using this formula:

\(S(t) = 35,700*(1 + 0.025)^t\)

Where :

S( t) represents Rodney's salary at his new job

$ 35 700 is Rodney starting salary and

0.025 denotes annual increase (2.5% expressed as decimals is 0.025 )

t = number of years later.

The function assumes that Rodney will receive an annual increase in salary of 2.5% growth rate annually and and the initial function is $ 35,700

This is an exponential function having a growth rate of 2.5%

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Answer: See below

Step-by-step explanation:

Event 1:

There are 13 diamond cards in total

A standard deck of cards has a total of 52 cards

Probability = 13/52

P = 1/4 or 25%

Event 2:

There are a total of 6 sides on a standard dice

Probability = 4/6

P = 2/3 or 66.67%

Event 3:

There are 3 blue marbles in a bag of 18 marbles

Probability = 3/18

P = 1/6 or 16.67%

Answer: a) 1/4     b) 2/3     c) 1/6

Step-by-step explanation:

All of these are probability problems. They have this trick.

First, the trick. The chance of taking an x amount of blue marbles out of a bag of y marbles is x/y. Now using this…

a) there are 13 diamonds and 52 total. 13 is x, and 52 is y. It is 13/52 = 1/4

b) There are 4 numbers you need to get, and 6 in total. Therefore; there is a 4/6 chance which simplifies to 2/3.

c) There are 3 marbles you need, and 18 of them in total. It is 3/18 which is 1/6.

I once struggled on these problems, for they can be difficult.

Answer:

D  \(\sqrt{x} +11=15\)

Step-by-step explanation:

Edge 2020

For the given expression √x + 11 = 15 the value of x will be equal to 16.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression √x + 11 =15. The expression will be solved as below,

√x + 11 =15

√x = 15 - 11

√x = 4

Squaring on both sides of the equation,

x = 4²

x = 16

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Answer:

the probability of rolling a sum of 6 with these dice is 1/6.

Step-by-step explanation:

To find the probability of rolling a sum of 6 with the given pair of dice, we can first list all possible pairs of outcomes that add up to 6:

(2,4)

(3,3)

(4,2)

For each of these pairs, we need to find the probability of rolling each number on its respective die and then multiply those probabilities together. The probability of rolling a particular number on one die is the number of times that number appears on that die divided by the total number of outcomes on that die.

For the first pair (2,4), the probability is:

(2 appears twice on one die out of six possible outcomes) × (4 appears once on the other die out of six possible outcomes) = (2/6) × (1/6) = 1/18

For the second pair (3,3), the probability is:

(3 appears twice on one die out of six possible outcomes) × (3 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

For the third pair (4,2), the probability is:

(4 appears twice on one die out of six possible outcomes) × (2 appears twice on the other die out of six possible outcomes) = (2/6) × (2/6) = 4/36

The total probability of rolling a sum of 6 is the sum of the probabilities of each possible pair:

1/18 + 4/36 + 4/36 = 1/6

Therefore, the probability of rolling a sum of 6 with these dice is 1/6.

We have 12 puppies where we have 5 poodles (P), 3 terriers (T) and 4 retreivers (R).

If the selection is with replacement, the probabilities of the two events (Rebecka selection and Aaron selection) are independent.

The probability that Rebecka selects a terrier is 3 in 12, as there are only 3 terriers between the 12 puppies.

In the same way, and as the puppy selected by Rebecka is replaced with the same type, the probability that Aaron selects a retriever is 4 in 12.

Then, the probability of the two events is equal to the product of the probabilities of each event:

Answer: the probability that Rebecka selects a terrier and Aaron selects a retriever is P=1/12.

Answer:

.aabc=amn0#1211

Step-by-step explanation:

nosascoOsasco n=12.8

Answer:

20

Step-by-step explanation:

lol

The time that it will take, to the nearest year, for the value of the account to reach $2,310 for this case is 20 years.

If the initial amount (also called as principal amount) is P, and the interest rate is R% per unit time, and it is left for T unit of time for that compound interest, then the interest amount earned is given by:

\(CI = P(1 +\dfrac{R}{100})^T - P\)

The final amount becomes:

\(A = CI + P\\A = P(1 +\dfrac{R}{100})^T\)

For this case, we're provided that:

Let the time be 'T' years after which this investment becomes $2310

Then, by the formula stated above, we get:

\(A = P\left(1 +\dfrac{R}{100}\right)^T\\\\2310 = 920\left(1 +\dfrac{4.7}{100}\right)^T\\\\\\2310 = 920\times(1.047)^T\\\\(1.047)^T = \dfrac{2310}{920}\\\\\\T = \log_{1.047}\left( \dfrac{2310}{920} \right)\\\)

Using calculator, we get:

\(T \approx 20.0446 \approx 20 \: \rm years\) (as unit of time in rate of interest was assumed to be yearly)

Thus, the time that it will take, to the nearest year, for the value of the account to reach $2,310 for this case is 20 years.

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Answer:

5/28.

Step-by-step explanation:

3/7 * 5/12

= (3*5) / (7*12)

= 15/84

= 5/28.

The domain of a function is all the possible input values for which the function is defined.

Function is a block of code that performs a specific task. It is a reusable piece of code that can be called from other parts of the code, reducing the amount of code that needs to be written and making the code easier to read and maintain. Functions can take in parameters and return values, allowing for increased flexibility and reusability. Functions can also be used to break up large programs into smaller, more manageable pieces.

In this case, the reasonable domain for the function f(x) = 4x³-50x²+150x would be all real numbers. This is because the function is a polynomial, which is continuous, meaning that it is defined for all real numbers.

The input of the function is a width, and the output is a volume. Therefore, the domain of the function should include all reasonable widths that could produce a volume. This means that the domain should include all positive real numbers, as any negative value would produce a negative volume, which is not reasonable. Thus, the reasonable domain for the function f(x) = 4x³-50x²+150x is all positive real numbers.

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Answer:

4

Step-by-step explanation:

Answer:

CDBE

Step-by-step explanation:

If you add angle CD and BE together it would be CDBE

Answer:

b=7 & c=7√2

Step-by-step explanation:

b=7 as it is an isosceles triangle

now using Pythagoras theorem,

(c)^2= (7)^2+(7)^2

⇒(c)^2= 49+49

⇒(c)^2= 98

⇒c= √98

⇒c=7√2

Answer:

Step-by-step explanation:

You want the missing side lengths in an isosceles right triangle with one side given as 7.

The two congruent acute angles tell you this right triangle is isosceles. That means sides 7 and b are the same length:

  b = 7

The hypotenuse of an isosceles right triangle is √2 times the side length:

  c = 7√2

__

Additional comment

You can figure the hypotenuse using the Pythagorean theorem if you haven't memorized the side relations of this "special" right triangle.

  c² = 7² + b²

  c² = 7² +7² = 2·7²

  c = √(2·7²) = 7√2

The side length ratios for an isosceles right triangle (angles 45°-45°-90°) are 1 : 1 : √2.

The other "special" right triangle is the 30°-60°-90° triangle, which has side length ratios 1 : √3 : 2.

Answer:

x < 2 is the answer oh and do the 3rd line option

B.

Explanation:

1.5+1.5=3+1.5= 4.5+1.5= 6

(How much 1.5 is there?) (1.5=1 1/2 btw)

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

∆ABC ~ ∆QPR by SSS since 6/8 = 9/12.