Find the measure of x in the right triangle.
X
21
2

Answer:

3-(-3) / -15-(-5)

= 3+3/-15+5

=6 /-10

= -3 /5

Hope it helps You

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a) Using a system of equations, the amount invested in the mutual fund that earned 6% was $1,600.

b) The amount invested in the mutual fund that earned 4% was $200.

A system of equations is two or more equations solved concurrently.

A system of equations is also called simultaneous equations.

Total investment = $1,800

Profit from investment A = 6%

Profit from investment B = 4%

The total investment profit = $76

Let A = Investment A and B = Investment B

A + B = 1,800

A = 1,800 - B

0.06A + 0.04B = 76

0.06(1,800 - B) + 0.04B = 76

108 - 0.06B + 0.04B = 76

108 - 0.02B = 76

-0.02B = -32

B = 1,600

A = 200 (1,800 - 1,600)

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\(\begin{cases} f(x)=4x-9\\\\ g(x)=x+1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ f(~~g(x)~~)=4[g(x)]-9\implies f(~~g(x)~~)=4[x+1]-9 \\\\\\ f(~~g(x)~~)=4x+4-9\implies \boxed{f(~~g(x)~~)=4x-5} \\\\[-0.35em] ~\dotfill\\\\ g(~~f(x)~~)=[f(x)]+1\implies g(~~f(x)~~)=[4x-9]+1 \\\\\\ g(~~f(x)~~)=4x-9+1\implies \boxed{g(~~f(x)~~)=4x-8}\)

Answer:

To calculate the mass of copper needed to make the cone, we can use the following formula:

Volume of Cone = (1/3) * π * r^2 * h

where r is the radius of the base of the cone and h is the height of the cone.

Given that Allen wants the cone’s base to have a diameter of 8 cm, we can calculate that the radius of the base is 4 cm. The height of the cone is given as 10 cm.

Substituting these values into the formula above, we get:

Volume of Cone = (1/3) * π * (4 cm)^2 * 10 cm = 167.55 cubic centimeters

The density of copper is given as 8.96 grams/cubic centimeter. Therefore, we can calculate the mass of copper needed to make the cone as follows:

Mass of Copper = Volume of Cone * Density of Copper

Mass of Copper = 167.55 cubic centimeters * 8.96 grams/cubic centimeter = 1500.98 grams

Therefore, Allen will need approximately 1500.98 grams of copper to make the cone.

The total number of the outcomes will be 12. The table is shown below with all the outcomes.

A sample is a group of clearly specified components. The number of items in a finite sample is denoted by a curly bracket.

Julie went to visit her aunt and uncle for the weekend.

She took the following clothes:

two pairs of slacks – one brown, one black;

three sweaters – one tan, one red and one white;

two shirts – one white and one gray.

Then the total number of the outcomes will be

Total outcomes = 2 x 3 x 2

Total outcomes = 12

The table is shown below with all the outcomes.

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In order to determine if a matrix is consistent or inconsistent, we need to analyze its augmented matrix in the context of a system of linear equations.

- If the system has a unique solution, the matrix is consistent.

- If there are no solutions or infinitely many solutions, the matrix is inconsistent.

In more detail, let's consider a system of linear equations represented by an augmented matrix [A|B], where A is the coefficient matrix and B is the constant matrix. We can perform row operations on the augmented matrix to determine its consistency. The row operations include swapping rows, multiplying a row by a nonzero scalar, and adding or subtracting rows.

1. Row Echelon Form: Transform the augmented matrix to row echelon form (REF) using row operations. The REF has the following properties:

  a) All rows with all zeros are at the bottom.

  b) The leftmost nonzero entry in each row, called a pivot, is to the right of the pivot of the row above.

  c) Any rows consisting only of zeros are at the bottom.

2. Row Reduced Echelon Form: Further transform the augmented matrix to row reduced echelon form (RREF). The RREF has the same properties as the REF, with additional properties:

  d) Each pivot is 1, and the entries above and below each pivot are zero.

  e) Each column containing a pivot has no other nonzero entries.

Now, based on the RREF, we can determine the consistency of the system:

  i) If there is a row in the RREF with only zeros on the left side and a nonzero entry on the right side, the system is inconsistent. There are no solutions.

  ii) If there are no rows in the RREF violating condition (i), the system is consistent.

     a) If the number of pivots (nonzero rows) equals the number of variables, the system has a unique solution.

     b) If the number of pivots is less than the number of variables, the system has infinitely many solutions.

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There are 96 ways for four people to sit in six chairs so that the leftmost chair is occupied and the rightmost is empty.

There are 4 guests and the leftmost seat is to be occupied, so there are 4  such ways to choose the occupant of that seat.

Then, for each of those 4 ways, there are 4 ways to decide the occupant for the second seat -- the remaining three people plus the possibility of that seat being empty, that makes a total of 16 ways to decide the configuration of the first two seats.

Then, for each of those 16 ways, there are 3 ways to choose the occupant for the third seat (either 3 remaining guests if the second seat was left empty, or the two remaining guests plus the possibility of leaving the 3rd seat empty). Hence, 16 times 3 is 48. For each of those ways, there are two choices for the next seat, i.e. 48 times 2 = 96, and finally one choice for the fifth seat. So in all, there are 96 ways.

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Based on the theory, the distance from the starting point to the return point = Arc length = 109.9 feet.

Using the formula for arc length, it is possible to determine the length of an arc that contains a circle by providing the radius and the central angle.

AL = ∅/360 × 2πr

Considering that the new area is a quarter circle in shape, then ∅ = 90°.

Raidus (r) = 70 ft

The distance between the point of departure to the place of departure again= arc length.

Al = ∅/360 × 2πr =  90/360 × 2π(70)

Al =  109.9 feet

In conclusion, According to the hypothesis, the distance from the point of departure to the point of arrival is equal to the length of the arc, which is equal to 109.9 feet.

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CQ

The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement of the handler as he moves the herd. The arc the handler makes from the starting point to the return point should be a quarter of a circle: A sector showing a quarter of a circle is drawn. The radius is marked as 70 feet. The endpoints of the arc of the sector are marked as Starting Point and Return Point. The sector is filled with cattle. Based on this theory, what distance will the handler move from the starting point to the return point if he creates an arc of a circle with radius 70 feet? 439.6 feet 3846.5 feet 109.9 feet 1758.4 feet

Answer:

44 div by 4 = 11

the answer is 11

Step-by-step explanation:

First we need to find the inverse function.  To do this, I'd put f(x) into vertex form:

    \(\begin{aligned}f(x) &= (x^2-4x)-6\\[0.5em] &= (x^2-4x+4)-6-4\\[0.5em] &= (x-2)^2-10\\[0.5em]\end{aligned}\)

Now, we can try to invert the function, keeping in mind this is only used when x≥2.

     \(\begin{aligned}y&= (x-2)^2-10\\[0.5em]y+10&= (x-2)^2\\[0.5em]\sqrt{y+10}&= x-2\\[0.5em]\sqrt{y+10}+2&= x\\[0.5em]\end{aligned}\)

(The fact that x ≥ 2 allowed us only keep the positive square root on the third line.)

So our inverse function is \(f^{-1}(y)=\sqrt{y+10}+2\).

Now, let's find the derivative of this function:

    \(\begin{aligned}\dfrac{df^{-1}}{dy}&= \dfrac{1}{2\sqrt{y+10}}\cdot\dfrac{d}{dy}[y+10]\\[0.5em] &= \dfrac{1}{2\sqrt{y+10}}\end{aligned}\\\)

(The chain rule was used, but the derivative of the inside function equals 1.)

So \((f^{-1})'(-6) = \dfrac{1}{2\sqrt{-6+10}} = \dfrac{1}{4}\)

Now having done all of that, it did cross my mind that since \(f\) and \(f^{-1}\) are simply reflections over the line y=x, if we had actually just found f'(4) and then used the reciprocal slope, we'd also get the same answer more quickly.

f'(x) = 2x - 4

when y = -6, then x = 4 (by solving f(x) = -6).

f'(4) = 4, so reflecting that slope of 4/1 over the line y=x, we'd get a slope of 1/4.

Answer:

B

Step-by-step explanation:

The points where f(x) intersects g(x) are - 4 and 2.5. These points are the solution of the equation f(x)=g(x)

Answer:

(-4,8) and ( 2.5, -8)

Step-by-step explanation:

The solutions are where the two graphs intersect

They intersect at x = -4  and y = 8   and at x = 2.5  and y = -8

(-4,8) and ( 2.5, -8)

F(x)= {0.29x, 0 <x ≤ 25 GB

{0.26x, 25 <x ≤ 50

{0.23x, 50 <x ≤ 75

{0.20x, x > 75

.23 x 75= 17.25

.20 x 75 +1= 15.2

The difference in price for storing just the 75 GB and for storing 75 GB plus a new music collection that is 1 GB or less is $0.06.

Mathematical expressions with inequalities are those in which the two sides are not equal. Unlike to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not is used in place of the equal sign.

we have,

Charges         Size

$0.29           0 < x ≤ 25

$0.26            25 < x ≤ 50

$0.23            50 < x < 75

$0.20                x > 75

Now, the charges for 75 GB is $0.23 and the charges for more than 75 GB plus a new music collection that is 1 GB or less is $0.29.

So, the difference in charges is

= 0.29- 0.23

= $0.06

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Answer:

3(x+y)=45

x+y=15

y=-1x +15

so

slope(m) = -1

Answer: 3 shirts

Step-by-step explanation:

so they are 20 a piece

5+45=50

they need to raise $50

1= 20

2=40

3=60

Answer:

Step-by-step explanation:

Answer:

8, 1, and 3

Step-by-step explanation:

Range is the y in (x, y)

Hope it helps

The value of the expression 3y²-8y+9 when y = 5 will be 44.

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given the expression,

3y²-8y+9

Now substitute y = 5

⇒ 3(5)² - 8(5) + 9

⇒ 3 × 25 - 40 + 9

⇒ 75 -31

⇒ 44

Hence "The value of the expression 3y²-8y+9 when y = 5 will be 44".

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Answer:

Option C.

Step-by-step explanation:

For a given set of N elements:

{x₁, x₂, ..., xₙ}

The mean is given by:

\(M = \frac{x_1 + x_2 + ... + x_n}{N}\)

And the variance is given by:

\(v = \frac{(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_n - M)^2}{N}\)

Then for our set:

{70, 80 ,75, 75, 80}

We have 5 elements, then N = 5

The first thing we need to find is the mean.

\(M = \frac{70 + 80 + 75 + 75 + 80}{5} = 76\)

Then the variance will be:

\(v = \frac{(70 - 76)^2 + (80 - 76)^2 + (75 - 76)^2 + (75 - 76)^2 + (80 - 76)^2}{5} = 14\)

The correct option is C, 14.

Answer:

2,4,6,8,10,12,14,16,18,20,22,24,26,28 for 2 3,6,9,12,15,18,21,24,27 for 3

Step-by-step explanation:

for both 6,12,18,24

Answer:

A its 10

Step-by-step explanation:

Okay, let's think this through step-by-step:

* Ms. Adami has 24 feet of fencing total

* She wants to use all 24 feet for the perimeter of the rectangle

* She needs to find length and width combinations that will make the perimeter = 24 feet

Here are the possible combinations:

1. Length = 12 ft, Width = 2 ft: perimeter = 2*12 + 2*2 = 24 ft

2. Length = 8 ft, Width = 3 ft: perimeter = 2*8 + 2*3 = 24 ft

3. Length = 6 ft, Width = 4 ft: perimeter = 2*6 + 2*4 = 24 ft

Therefore, the 3 possible length and width combinations that would give a perimeter of 24 ft using all the fencing are:

1. Length = 12 ft, Width = 2 ft

2. Length = 8 ft, Width = 3 ft

P (X)= \(x^3+4 x^2-3x+2\)  moreover, \(\frac{P(x)}{x - 1} = x^{2} + 5x +2\) as a result, the actual claim is  \($p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$\)

The likelihood of an event occurring is determined by probability:       P(A) = f / N. Probability and odds are related, but probability is necessary for odds to exist. Prior to calculating the likelihood that an event will occur, probability is required.

The steps listed below can be used to determine an event's likelihood: Step 1: Identify an event that has only one outcome. Step 2: Compile a list of all potential outcomes, including any positive ones. Step 3: Subtract the number of favourable outcomes from the total number of outcomes that are feasible. The probability of A or B is equal to p(A or B) = p(A) + p(B) if occurrences A and B are mutually exclusive (B). A probability is a number that expresses the possibility or likelihood that a specific event will take place.

Therefore the correct answer is option A ) \($p(x)=(x-1)\left(x^2+5 x+2\right)+\frac{4}{x-1}$\)

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Answer:

A = 2(7) + (1/2)(4)(4 + 9) = 14 + 26 = 40 m²

Answer:

yes

Step-by-step explanation:

:)

Answer:

  no

Step-by-step explanation:

The sides of the given lengths will form a right triangle if they satisfy the Pythagorean theorem.

  c² = a² + b²

  9² = 4² +6²

  81 = 16 +36 . . . . . not true

These side lengths do not form a right triangle. (They form an obtuse triangle.)

Answer:

The correct statements are:

* The scatter plot has a cluster with a span for variable A from 2 to 7.

* The scatter plot has an outlier at (15, 2).

A scatter plot is a graph that shows the relationship between two variables. The points on the graph are plotted by their coordinates. The independent variable is plotted on the x-axis, and the dependent variable is plotted on the y-axis.

In the scatter plot, the points are clustered around a line. The line represents the relationship between the two variables. The cluster of points means a strong correlation between the two variables. The outlier at (15, 2) indicates that one data point does not fit the general trend.

Step-by-step explanation:

This is a logical statement, of the form

where p is the statement "the test is today" and q is the statement "the party is tonight". The DeMorgan's Law indicates that:

Therefore the equivalent statement is " the test is not today and the party is not tonight".

The common risk-neutral price for both the down-and-in barrier option and the down-and-out barrier option is approximately $1.7036.

The risk-neutral price of both options can be determined by using the formula for European call options, adjusted for the barrier feature. Here's how we can calculate the common risk-neutral price:

1. Define the variables:

S = Initial price of the security = $25

K = Strike price of the options = $22

T = Time to expiration = 30 days (assuming 252 trading days in a year)

r = Risk-free interest rate = 0

σ = Volatility parameter = 0.2

2. Calculate the risk-neutral drift (μ):

The risk-neutral drift, μ, is calculated as (r - σ^2/2). Since r is 0, we have:

\(μ = -σ^2/2 = -0.2^2/2 = -0.02\)

3. Calculate the risk-neutral probability of hitting the barrier (p):

The risk-neutral probability, p, is calculated using the formula:

p = exp(-2μ√T)

Substituting the values, we get:

p = exp(-2*(-0.02)*√(30/252)) ≈ 0.9705

4. Calculate the common risk-neutral price:

To calculate the risk-neutral price, we need to consider both the down-and-in and down-and-out options.

The risk-neutral price of the down-and-in option is given by:

Price_DI = S * N(d1) - K * exp(-rT) * N(d2)

The risk-neutral price of the down-and-out option is given by:

Price_DO = Price_DI - (p^(T/252))

We need to calculate the values of d1 and d2, which are defined as follows:

d1 =\((ln(S/K) + (r + σ^2/2)T) / (σ√T)\)

d2 = d1 - σ√T

5. Calculate d1 and d2:

d1 = \((ln(S/K) + (r + σ^2/2)T) / (σ√T)\)

   = (ln(25/22) + (0 + 0.2^2/2)*(30/252)) / (0.2√(30/252))

   ≈ 0.3162

d2 = d1 - σ√T

   ≈ 0.3162 - 0.2√(30/252)

   ≈ 0.1933

6. Calculate the common risk-neutral price:

Price_DI = S * N(d1) - K * exp(-rT) * N(d2)

Price_DO = Price_DI - (p^(T/252))

Using the Black-Scholes formula, we can calculate the common risk-neutral price:

Price_DO = 25 * N(0.3162) - 22 * exp(0) * N(0.1933) - (0.9705^(30/252))

        ≈ 5.1722 - 2.5027 - 0.9659

        ≈ 1.7036

Therefore, the common risk-neutral price for both the down-and-in barrier option and the down-and-out barrier option is approximately $1.7036.

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Hello !

Answer:

\(\boxed{\sf C\approx62.8 ft}\)

Step-by-step explanation:

To find the circumference of a circle with its radius, we will apply the following formula:

\(\sf C=2\pi r\)

Where r is the radius of the circle.

Given :

We know that the diameter is equal to two times the radius, so \(r=10\) ft.

Let's substitute our value into the formula :

\(\sf C=2\times \pi\times 10\\\boxed{\sf C\approx62.8 ft}\)

Have a nice day !

Answer:

Step-by-step explanation:

We know that

So,

→ R = 20/2

→ R = 10

Now,

We know that,

Circumference of circle = 2πr

→ 2 × 22/7 × 10

→ 440/7

→ 62.8 ft

Hence ,

Answer:

\(d=\sqrt{73}\approx8.54\)

Step-by-step explanation:

So we have the two points (10,-4) and (2,-7).

And we want to find the distance between them using the Distance Formula and the Pythagorean Theorem. Let's do each one individually.

1) Distance Formula.

The distance formula is:

\(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2\)

Let's let (10,-4) be (x₁, y₁) and let's let (2,-7) be (x₂, y₂). So:

\(d=\sqrt{((2)-(10))+((-7)-(-4))^2\)

Simplify:

\(d=\sqrt{(2-10)^2+(-7+4)^2\)

Subtract:

\(d=\sqrt{(-8)^2+(-3)^2\)

Square:

\(d=\sqrt{64+9}\)

Add:

\(d=\sqrt{73}\)

Approximate:

\(d\approx8.54\)

So, the distance between (10,-4) and (2,-7) is approximately 8.54 units.

2) Pythagorean Theorem

Please refer to the graph.

So, we want to find the distance. This will be the length of the red line, or the hypotenuse.

First, let's find the length of the two legs.

The longer leg will be the difference between the two x-coordinates. So, the length of the longer leg is:

\((10-2)=8\)

Note: It doesn't matter if we do 2-10, which gives -8, since we are going to square anyways. Also, distance is always positive, so 8 would be our answer.

And the shorter leg is the difference between the two y-coordinates. Namely:

\((-7-(-4))=-3=3\)

So, the shorter leg is 3 units.

So now, we can use the Pythagorean Theorem, which is:

\(a^2+b^2=c^2\)

Substitute 8 for a and 3 for b. So:

\((8)^2+(3)^2=c^2\)

Square:

\(64+9=c^2\)

Add:

\(c^2=73\)

Take the square root:

\(c=\sqrt{73}\approx8.54\)

This is the same as our previous answer, so we can confirm that it's correct.

So, using both the distance formula and the Pythagorean Theorem, the distance between the two points is approximately 8.54.

And we're done!

Distance formula: d = √(x2-x1)²+(y2-y1)²

= √(2-10)²+(-7-(-4))²

= √-8²+(-3)²

= √64+9

= √73

≈ 8.54

Best of Luck!