Find the value of x in the triangle shown below

Answer:

\(\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.\)

Step-by-step explanation:

System of Equations

Let's call:

x = number of nickels in the student's pocket

y = number of dimes in the student's pocket

Each nickel has a value of $0.05, so x nickels have a value of 0.05x

Each dime has a value of $0.10, so y dimes have a value of 0.10y

The student has a total of 10 coins, thus:

\(x+y=10\)

The total value of the coins is $0.85, thus

\(0.05x+0.10y=0.85\)

The system of linear equations that represents this scenario is:

\(\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.\)

Answer:

f(g(x)) = 6x3 + 4 dollars over hour

Step-by-step explanation:

got it right on the test

f(g(x)) is the amount of money earned in x number of hours.

f(g(x)) is 6\(x^6\) + 4.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(x) = 2x² + 4

g(x) = √3x³

f(g(x)):

= f(√3x³)

= 2(√3x³)² + 4

= 2 x 3 x \(x^6\) + 4

= 6\(x^6\) + 4

Thus,

f(g(x)) represents the amount of money earned in x hours.

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The required type ii error probability of the test using is 0.085.

It is determined by duplicating the pretest chances by the probability of a positive or negative test (as we will show). Post-test  probability  is characterized, as the likelihood of the objective problem after a symptomatic experimental outcome is known.

We have,

standard deviation = 7, mean = 6, size of the sample = 23.

P(type II error) = P(Xbar >=8 given mean =6)

=P(Z>(8-6)×√(23)/7) =P(Z>1.37)=1-P(Z<1.37)

=1-0.9147=0.0853 =0.085

Thus, required probability is 0.085

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{f(x) ∈ ℝ | f(x) ≥ 3}  is the range of f(x) = |x| + 3

When graphing the following equation shown below:

Answer:

{f(x) ∈ ℝ | f(x) ≥ 3}

Step-by-step explanation:

The range of a function is the output values (y-values).

Absolute value is the distance of x from zero, so it is never negative.  It is denoted by a bar on either side of the term.

Therefore, as |x| ≥ 0 then |x| +3 ≥ 3

Therefore, the range of the function is {f(x) ∈ ℝ | f(x) ≥ 3}

Answer:

-12

Step-by-step explanation:

I believe they multiply each term by -3/1

4/1 * -3/1 = -12/1 = -12

Answer:

There are 21 emperor penguins at the zoo

Step-by-step explanation:

The total number of penguins in the zoo \(= 60\)

The percentage share of emperor penguin in the total population of penguin \(= 35\) %

Number of emperor penguins at the zoo

\(\frac{35}{100} * 60\)

\(0.35 * 60\)

\(= 21\)

There are 21 emperor penguins at the zoo

Scenario 2 Magnifi Co. produces a high-end amplifier for musical aficionados. Historically, only 85% of the 200 amplifiers produced per month on average have met the company's demanding standards for quality control. Suppose a random sample of 50 amplifiers is taken from a month's production..

What is the probability that less than 40 of the amplifiers will meet the company's quality standards? b) What is the probability that between 40 and 45 inclusive of the amplifiers will meet the company's quality standards? c) What is the probability that more than 45 of the amplifiers will meet the company's quality standards? a) In order to solve for the probability that less than 40 amplifiers will meet the company's quality standards, we can use the binomial distribution formula: P(X < 40) = Σi=0^39 C(50, i) (0.85)i(1-0.85)50-i

This can be solved using a computer, calculator, or by using a binomial probability table. Using a binomial table, we can find that P(X < 40) = 0.024. Therefore, there is a 0.024 probability that less than 40 amplifiers will meet the company's quality standards. b) To solve for the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards, we can use the binomial distribution formula again. We need to solve for P(40 ≤ X ≤ 45): P(40 ≤ X ≤ 45) = Σi=40^45 C(50, i) (0.85)i(1-0.85)50-i This can also be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(40 ≤ X ≤ 45) = 0.435. Therefore, there is a 0.435 probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards. c) To solve for the probability that more than 45 amplifiers will meet the company's quality standards, we can use the binomial distribution formula one more time. We need to solve for P(X > 45): P(X > 45) = Σi=46^50 C(50, i) (0.85)i(1-0.85)50-i Once again, this can be solved using a computer, calculator, or binomial table. Using a binomial table, we can find that P(X > 45) = 0.056. Therefore, there is a 0.056 probability that more than 45 amplifiers will meet the company's quality standards.Overall, it can be concluded that the probability that less than 40 amplifiers will meet the company's quality standards is low, the probability that between 40 and 45 amplifiers inclusive will meet the company's quality standards is relatively high, and the probability that more than 45 amplifiers will meet the company's quality standards is relatively low.

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Step-by-step explanation:

line n (and if it is parallel or not) has nothing to do with this solution. it is only there to confuse us.

the sum of all angles around a single point on one side of a line is 180° (because the line can act as the diameter of a circle with the point being is center, and a half-circle stands for 180°).

so,

180 = (6x - 19) + (8x + 3)

180 = 6x - 19 + 8x + 3 = 14x - 16

90 = 7x - 8

98 = 7x

x = 98/7 = 14

The reason why product rule works is because the derivative of a product is not simply the product of the derivatives of the two functions as one might initially think.

In calculus, the rule helps to find derivative of the product of two functions and states derivative of product of 2 functions is = [First function * derivative of the second function} +  [Second function * derivative of the first function}.

When we have 2 functions f(x) and g(x) and need find the derivative of their product, we use the product rule. Its takes into account the fact that when we differentiate a product, we need to account for both functions changing at the same time.

By breaking the product down into two parts and taking the derivative of each part separately, we can then add them together using the product rule to get the overall derivative of the product.

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The polygons are similar with similarity ratio of 1.5, respectively

To check if the polygons are similar, we divide corresponding sides and check if the ratios are equal

So, we have

Rectangle

So, the similarity ratio is 1.5

Triangle

So, the similarity ratio is 1.5

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(a) You are approximately 11.79 meters East (-x) of the town center and 2.98 meters South (-y) of the town center.

(b) You are approximately 13.00 meters away from the center of town at an angle of -67.38°.

(c) You are approximately 57.45 meters away from the center of town at an angle of 3° North of East.

(d) You walked approximately 45.28 meters away from the center of town in a direction of 33° North of West (-x).

(a) Given:

Distance from the center of town = 14.2 meters

Angle North of East = 190°

(i) To find how far East (+x) of the town center you are, we can use trigonometry. The horizontal component (East) is given by:

Distance East = Distance from center * cos(Angle)

Distance East = 14.2 * cos(190°) ≈ -11.79 meters

(ii) To find how far North (+y) of the town center you are, we can use trigonometry. The vertical component (North) is given by:

Distance North = Distance from center * sin(Angle)

Distance North = 14.2 * sin(190°) ≈ -2.98 meters

Therefore, you are approximately 11.79 meters East (-x) of the town center and 2.98 meters South (-y) of the town center.

(b) Given:

Distance North (+y) of the center = 12.00 meters

Distance East (+x) of the center = -5.00 meters

(i) To find the distance from the center of town, we can use the Pythagorean theorem:

Distance from center = √((Distance North)² + (Distance East)²)

Distance from center = √((12.00)² + (-5.00)²) ≈ 13.00 meters

(ii) To find the angle, we can use trigonometry. The angle is given by:

Angle = atan(Distance North / Distance East)

Angle = atan(12.00 / -5.00) ≈ -67.38°

Therefore, you are approximately 13.00 meters away from the center of town at an angle of -67.38°.

(c) Given:

Distance from the center of town = 44.0 meters

Angle North of East = 23°

Distance walked = 30.0 meters

Angle of walking North of East = 160°

(i) To find the new distance from the center of town, we can use the Law of Cosines:

New distance from center = √((Distance from center)² + (Distance walked)² - 2 * Distance from center * Distance walked * cos(Angle of walking))

New distance from center = √((44.0)² + (30.0)² - 2 * 44.0 * 30.0 * cos(160°)) ≈ 57.45 meters

(ii) To find the new angle, we can use the Law of Sines:

New angle = Angle + Angle of walking - 180°

New angle = 23° + 160° - 180° ≈ 3°

Therefore, you are approximately 57.45 meters away from the center of town at an angle of 3° North of East.

(d) Given:

Distance from the center of town = 22.0 meters

Angle North of East = 123°

Distance walked = 40.0 meters

Direction = West (-x)

(i) To find the new distance from the center of town, we can use the Pythagorean theorem:

New distance from center = √((Distance from center)² + (Distance walked)²)

New distance from center = √((22.0)² + (40.0)²) ≈ 45.28 meters

(ii) To find the new direction, we can subtract the angle of walking from the original angle:

New angle = Angle - 90°

New angle = 123° - 90° ≈ 33°

Therefore, you walked approximately 45.28 meters away from the center of town in a direction of 33° North of West (-x).

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Answer:

what is the complete question?

The known solutions to f(x) = g(x) are given as follow:

x = 1 and x = 9.

When a system of equations is plotted on graph, the solutions are the intersection points of all the functions that compose the system.

At these intersections point, the functions have the same numeric value, which are the points looked at to find the solution on a table.

Hence the solutions are given as follows:

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Answer:

My answer is 1170 but the way I figured out the problem was by listing numbers 1-30. the problem state that the 1st row had 10, 2nd row had 12, and 3rd row had 14 and so forth. So I basically did the same method till I got to 30 and then add up all the numbers which gave me the answer of 1170.

Step-by-step explanation:

Answer:

1170

Step-by-step explanation:

hey there,

(the other person just calculated each number themselves then added them up which i guess is okay but not in the long term for when you're taking a test for example or your teacher asks you this kind of question so it's better to memorize a formula.)

< There are two types of sequences: arithmetic and geometric. So also two formulas for finding sums of each. This situation is an arithmetic sequence.

Formula for the sum of an arithmetic sequence: \(S_n=\frac{n}{2} (a_1+a_n)\)

We know there are 30 total rows so n = 30. a1 is the very first term of a sequence so this is 10 in this situation. Before we fill in the formula, we should find what an is equal to.

For this, we will use the basic formula you learned previously: \(a_n=dn+c\)

d (the common difference) = a2-a1 = 12-10=2

c (the common ratio) = a1-d = 10-2 = 8

an = dn + c = 2(30) + 8 = 68

Now that we have found what a_n is equal to, we can plug everything into the sum equation.

\(S_n = \frac{30}{2} (10+68)=1170\)

So 1170 is your final answer. >

Hope this helped! Feel free to ask anything else.

Answer:

x = 53°

Step-by-step explanation:

alternate exterior angles are equal

Answer:

Step-by-step explanation:

Two lines are parallel.

x = 53  

Alternate exterior angles are equal

꒷꒦꒷‧˚₊‧꒦꒷꒦ ꒷꒦‧˚.⁺꒷꒦꒷‧˚꒦

Question Given →

↪6x + 14x - 9 = 4(5x + 1) is x = 13.

Lets solve to see if the "friend" was correct!

↪ 6x + 14x - 9 = 4 (5x + 1)  

‣ Add like terms > 6x + 14x = 20x, 4(5x + 1) = 20x + 4

‣ Rewrite > 20x - 9 = 20x + 4

‣ Add *9* to both sides > 20x - 9 (+9) = 20x + 4 (+9)

‣ Rewrite > 20x = 20x + 13

‣ Subtract 20x from both sides > 20x (-20x) = 20x + 13 (-20x)

‣ Rewrite > 0 = 13

꒷꒦꒷‧˚₊‧꒦꒷꒦ ꒷꒦‧˚.⁺꒷꒦꒷‧˚꒦

Hope this helps you answer your question!

Notes ↠ Hey there! Just asking for brainiest :) It really helps me rank up! Thank you <3

Answer:

multiply both sides by 8

Step-by-step explanation:

I don't really know why I just know lol hope this helps

The interval of convergence is (-3,3) is for this limit exists for all x, so the series converges for |x|^2/9 < 1, or |x| < 3.

To find the power series for f(x) centered at c=0, we can use the formula:
f(x) = Σ[n=0 to infinity] (f^(n)(c)/n!)*(x-c)^n
where f^(n)(c) denotes the nth derivative of f evaluated at c.
In this case, f(x) = 7/(9-x^2), so we need to find the derivatives of f and evaluate them at c=0:
f'(x) = 14x/(9-x^2)^2
f''(x) = (126x^2-126)/(9-x^2)^3
f'''(x) = (6804x^3-2268x)/(9-x^2)^4
and so on.Since f^(n)(0) is equal to 0 for all odd values of n, we only need to compute the even derivatives:
f^(2n)(x) = (2n)!*7*(x^(2n+1))/(9-x^2)^(2n+2)
Plugging this into the power series formula, we get:
f(x) = Σ[n=0 to infinity] ((2n)!*7/(2^(2n)*(n!)^2))*x^(2n)
This is the power series for f(x) centered at c=0.
To determine the interval of convergence, we can use the ratio test:
lim[n→∞] |a(n+1)/a(n)| = lim[n→∞] |(2n+2)/(2n+1)*x^2/(9-x^2)| = |x|^2/9
This limit exists for all x, so the series converges for |x|^2/9 < 1, or |x| < 3. Therefore, the interval of convergence is (-3,3).

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This problem implies more cases to solve as well as the use of other formulas that we can use in the subject of free fall, if we read our exercise again, we will realize that we only have a height of 150 meters from where it is dropped freely a ball. To proceed to resolve, we collect the data.

Data:

h = 150 m

g = 9.8 m/s²

In order to obtain the distance traveled in 4 seconds, we can use the following formula:

\(\bf{\displaystyle h={{v}_{0}}t+\frac{g{{t}^{2}}}{2} }\)

Remember, that as it is a free fall, the initial speed is null, that is, zero. So the formula reduces:

\(\bf{\displaystyle h=\frac{g{{t}^{2}}}{2} }\)

We are going to place the 4 seconds in the “t” of time. Thus:

\(\bf{\displaystyle h=\frac{g{{t}^{2}}}{2}=\frac{\left( 9.8\frac{m}{{{s}^{2}}} \right){{\left( 4s \right)}^{2}}}{2} }\)

Carrying out the indicated operations:

\(\bf{\displaystyle h=\frac{g{{t}^{2}}}{2}=\frac{\left( 9.8\frac{m}{{{s}^{2}}} \right)16{{s}^{2}}}{2}=\frac{156.8m}{2}=78.4m }\)

That is to say that the height at 4 seconds is 78.4 meters.

For the velocity at 4 seconds, we use the following formula:

\(\bf{\displaystyle {{v}_{f}}={{v}_{0}}+gt}\)

Remember, that since there is no initial speed because it is free fall, then the formula is reduced:

\(\bf{\displaystyle {{V}_{f}}=gt }\)

Substituting our data and calculating:

\(\bf{\displaystyle {{v}_{f}}=gt=\left( 9.8\frac{m}{{{s}^{2}}} \right)\left( 4s \right)=39.2\frac{m}{s} }\)

So the speed at 4 seconds is 39.2 m/s.

Although it seems difficult to solve this section, it is not. It's very easy, let's remember that after 4 seconds it has traveled 78.4 meters and that the height from where the ball was dropped is 150 meters, so the difference is the amount that remains to reach the ground, that is:

\(\bf{\displaystyle {{h}_{T}}={{h}_{1}}+{{h}_{2}}}\)

It is as if we had:

\(\bf{\displaystyle 150=78.4+{{h}_{2}} }\)

Clearing "h2" what would be the distance to reach the ground.

\(\bf{\displaystyle {{h}_{2}}=150-78.4=71.6m }\)

In other words, we need to travel 71.6 meters to reach the ground.

Answer:

(4,-2)

Step-by-step explanation:

Start off by doing everything in the parenthesis which is everyone of them so 2x-1=-2 , your problem then should look like this:

-2(3x2-5x+2) carry the 2 over so multiply the 2 to everything so

(-6x-4+10x+2) add like numbers

10x+-6=4

-4+2=-2

(4,-2)

Answer:

Han had a stronger orange flavor

Step-by-step explanation:

Because he put less water in the mixture.

Answer:

I believe Han's orange juice has a stronger taste of the orange itself. Even though 1/4 is less than 1/3, the amount of water that has been mixed in with the amount of orange juice is less than the 2 1/2. Therefore Clare's is much more diluted with a weaker taste.

Step-by-step explanation:

Hope this helped! <3

Answer:

C

Step-by-step explanation:

She earns $3,567 and spends $2,895.  That means that $2,895 is taken away from how much she earns each month.  Subtraction is the correct operation, cancelling out choices B and D

$3,567 - $2,895

Now, you need to figure out the answer to the above problem.  Choice C is your answer.

$3,567 - $2,895 = $672

Answer:

the difference is 25.4 degrees.

Step-by-step explanation:

inventor

inventions led to great feats of engineering ..like great canal

Based on the limited information, it can be deduced that 1/5 of the ribbon is not in view.

In order to show the complete ribbon, we need to understand that in mathematical terms:

Since 4/5 of the ribbon is showing

This means that about 1- 4/5

= 1/5 of the ribbon is not in view.

With this knowledge, you can go ahead to complete your drawing, knowing that a full ribbon has a rectangular shape.

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Answer:

Figure C

Step-by-step explanation:

Beucase it does a reflection across the y axis

Answer:

Step-by-step explanation:

when x=means that you have to put your x into your f(x).

So f(5)=9(5)+3

= 45+3

=48

So f(5)=48

Given:-

\( \: \)

Solution:-

\( \: \)

now put the value of x = 5 in equation :

\( \: \)

\( \: \)

\( \: \)

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps:)

According to the general equation for conditional probability if P(A∩B)=4/7 and P(B)=7/8, then P(A | B) = 32/49.

We have the general equation of conditional probability as,

P(A | B) = P(A ∩ B) / P(B)

Here it is given that,

P(A ∩ B) = 4/7

P(B) = 7/8

Substituting the given values,

P(A | B) = 4/7 ÷ 7/8

            = 4/7 × 8/7

            = 32/49

Hence the required probability is 32/49.

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The equation of the line shown has a slope (m) = 1/4.

To find the slope of a line, we can use the ratio of the rise of the line over its run.

Referring to the image attached below, we have the following:

The blue line represents the rise of the line = 2 units

The red line represents the run of the line = 8 units

Therefore:

The slope (m) of the line = rise/run = 2/8

Simplify by dividing the numerator and the denominator by 2

The slope (m) of the line = 1/4.

Thus, the equation of the line shown has a slope (m) = 1/4.

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Answer:

40 feet

Step-by-step explanation:

24^2+32^2=x^2

solve for x

x=40 feet