Simplify 1/8 - 1/9 x+3/4-2/3x

The Present value is $6,139.132.

We have,

FV=100000, pmt = 4000, I =5%, n=10

So, The present value formula is

PV=FV / (1 + \(i)^n\)

So, PV =  100, 000 / (1+ 5/100\()^{10\\\)

PV = 100,000 / (1+ 0.05\()^{10\\\)

PV = 100, 000/ (1.05\()^{10\\\)

PV = 100,000 / 1.6288946

PV= $6,139.132

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Answer:

Left tailed.

Step-by-step explanation:

A claim (alternative hypothesis) is set against the null hypothesis.

The claim (alternative hypothesis) of the  golf analyst is that the standard deviation of the​ 18-hole scores for a golfer is  less than 2.1 strokes

Ha: Sd< 2.1

The null hypothesis will be opposite of the alternate hypothesis

H0: sd ≥ 2.1

A test for which the entire rejection region is located in only one of the two tails - either left or right- is called one tailed test.

In the given example the acceptance region is located in the area greater or equal to 2.1 . The rejection region lies to the left and the acceptance region lies to the right.

As the rejection region lies to the left, it is a left tailed test.

Also if the alternative hypothesis contains equality less than it is left tailed.

Answer: Choice C

9(51-12) = 9(51) - 9(12)

============================================

Explanation:

The distributive property is

a(b+c) = a*b + a*c

which can also be written as

a(b-c) = a*b + a*(-c) = a*b - a*c

In this case we're using

a(b-c) = a*b - a*c

where a = 9, b = 51, c = 12

Answer:

Step-by-step explanation:

$3,456.00 + $3,298.00 + $1,235.00 + $750.00 - $2,450.00 = $6,289.00

Answer: As a fraction: 1/2

              As a decimal: 0.005

Step-by-step explanation:

FRACTION:

To figure out how to write 0.5% as a fraction, all you need to know is that 0.5 = to a half, or 1/2 because 0.5 is half of 1.

DECIMAL:

0.5% as a decimal form is 0.005 because it is 1000 times less than 1, so you move the 0 3 times right.

Answer:

X=9

Step-by-step explanation:

Answer:

y+4=-3(x+1)

Step-by-step explanation:

Hope this helps may all your sweet dreams come true!

Answer:

y+4=-3(x+1)

Step-by-step explanation:

this is right im in the test

Answer:

Step-by-step explanation:

Let's call the number of hotdogs sold "x". According to the problem, the number of sodas sold is three times the number of hotdogs sold, or 3x.

We know that the total number of sodas and hotdogs sold is 136. So we can set up an equation:

x + 3x = 136

Simplifying this equation, we get:

4x = 136

Dividing both sides by 4, we get:

x = 34

This means that 34 hotdogs were sold. To find the number of sodas sold, we can multiply the number of hotdogs sold by 3:

3x = 3(34) = 102

So, 102 sodas were sold.

The measures of angle 4 (m<4) and angle 7 (m<7) are 42° and 96°, respectively.

To find the measures of angles 4 and 7, we need to apply some geometric principles. Since the top and bottom pieces of the crib are parallel to each other, we can use the property of alternate interior angles.

Angle 4 (m<4) is formed by a transversal (the line connecting the top and bottom pieces of the crib) intersecting two parallel lines. Given that angle m<2 is 42°, we know that angle 4 is congruent to angle 2. Therefore, m<4 = m<2 = 42°.

Angle 7 (m<7) is formed by a transversal intersecting two parallel lines as well. However, in this case, angle 7 is an exterior angle, which is equal to the sum of the two remote interior angles. The remote interior angles are angles 2 and 4. We know that m<2 = 42° (as given) and m<4 = m<2 = 42° (as explained above). Therefore, the sum of angles 2 and 4 is 42° + 42° = 84°. Since angle 7 is an exterior angle, it is equal to 180° minus the sum of the remote interior angles. Thus, m<7 = 180° - 84° = 96°.

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Answer:

\(\boxed{x=5},x=-9\)

Step-by-step explanation:

To rid the denominators, multiply both sides by \((x-3)(x+1)\).

We get:

\(6(x+1)-12(x-3)=(x-3)(x+1)\)

Simplifying, we have:

\(6x+6-12x+36=x^2-3x+x-3,\\-6x+42=x^2-2x-3,\\x^2+4x-45=0\)

Solving, we get:

\(x^2+4x-45=0,\\(x-5)(x+9)=0,\\x=5,x=-9\)

Therefore, the solution with the greatest value is \(x=\boxed{5}\)

Answer:

Where is the table?

Step-by-step explanation:

Answer:

Angle 2

Step-by-step explanation:

Find S and find X.

Then find U.

The angle at X connected to S and U is the angle number.

The laplace inverse transformation L−1{F(s)G(s)} =  5 \(\frac{2s}{s^{2} + 1^{2} }\)  

If L{f(t)} = F(s), then the inverse Laplace transform of F(s) is

L−1{F(s)} = f(t). (1)

The inverse transform L−1is a linear operator:

L−1{F(s) + G(s)} = L−1{F(s)} + L−1{G(s)}, (2)

andL−1{cF(s)} = cL−1{F(s)}, (3)

for any constant c

given functions are

f(t) =5t ,g(t) = sin(t)

L(f(t)) = F(s)

L{F(s)*G(s)} = L^-1{5tsin(t)}

   =5L^-1{tsin(t)}

   =5L^-1{\(\frac{d}{ds}\) tsin(t)}

    = 5 \(\frac{2s}{s^{2} + 1^{2} }\)  

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The measures of the non-right angles of each triangle are 40 degrees and 50 degrees.

The sum of the interior angles of a regular 18-gon can be found using the formula:

S = (n - 2) × 180 degrees

n is the number of sides of the polygon.

Substituting n = 18 we get:

S = (18 - 2) × 180 degrees

= 2880 degrees

The 18-gon into 36 right triangles need to draw 18 lines from the center of the polygon to its vertices dividing the polygon into 36 congruent sectors each with a central angle of 360 degrees / 18 = 20 degrees.

Each sector is an isosceles triangle with two sides of equal length radiating from the center of the polygon.

The vertex angle of each isosceles triangle is equal to twice the central angle or 40 degrees.

Since the vertex angle of a right triangle is 90 degrees the two non-right angles of each right triangle are 40 degrees and 50 degrees.

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The height of the hexagonal-based pyramid is approximately 101.61 inches.

To find the height of the hexagonal-based pyramid, we can use the formula for the volume of a pyramid:

Volume = (1/3) × Base Area × Height

In this case, the base of the pyramid is a regular hexagon, and we have the side length (s) and apothem (a) given.

The base area of a regular hexagon can be calculated using the formula:

Base Area = (3√3/2) × s²

Let's calculate the base area first:

Base Area = (3√3/2) × (6 in)²

Base Area = (3√3/2) × 36 in²

Base Area ≈ 93.53 in²

Now, we can rearrange the volume formula to solve for the height:

Height = Volume / ((1/3) × Base Area)

Height = 3168 in³ / ((1/3) × 93.53 in²)

Height = 3168 in³ / (31.177 in²)

Height ≈ 101.61 in

Therefore, the height of the hexagonal-based pyramid is approximately 101.61 inches.

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The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Answer : 30x=22y <= (less than or equal to) 130

Step-by-step explanation:

Answer  :      x= \(\sqrt{2wy}\)/ y

Step-by-step explanation:

9514 1404 393

Answer:

  60°

Step-by-step explanation:

The sum of angles in a quadrilateral is 360°. The interior angle adjacent to x will have measure 180°-x. So, the equation can be written ...

  100° +50° +90° +(180° -x°) = 360°

  420° -x° = 360° . . . . simplify

  x = 420 -360 . . . . . . divide by °, add x-360

  x = 60

The differential equation for the amount of salt in the tank is obtained as \(A = \frac{2000}{3} - \frac{2000}{3} \times e^{(\frac{-9t}{250})}\).

What is differential equation?

Any equation with one or more terms and one or more derivatives of the dependent variable with respect to the independent variable is referred to as a differential equation.

We can start by finding the rate of change of salt in the tank. Let's call this quantity dA/dt, where A is the amount of salt in the tank.

The salt that enters the tank at a rate of 10 grams per liter, so the amount of salt that enters the tank per minute is -

10 grams/liter × 6 liters/minute = 60 grams/minute

The salt that leaves the tank at a rate of 9 liters per minute, so the amount of salt that leaves the tank per minute is -

A/250 grams/liter × 9 liters/minute = 9A/250 grams/minute

Therefore, the rate of change of salt in the tank is -

dA/dt = 60 - 9A/250

This is a separable differential equation, which we can solve by separating the variables and integrating -

dA/(60 - 9A/250) = dt

Multiplying both sides by (250/9) and integrating, we get -

-250/9 × ln|60 - 9A/250| = t + C

where C is an arbitrary constant of integration.

Solving for A, we get -

\(A = \frac{250}{9} \times (60 - e^{(\frac{-9t}{250} + C)})\)

To find the value of C, we can use the initial condition that there are 11 grams of salt in the tank initially (when t = 0) -

A(0) = 11

Substituting t = 0 and A(0) = 11 into the equation above, we get -

\(11 = \frac{250}{9} \times (60 - e^C)\)

Solving for C, we get -

C = ln(60 - 9/250 × 11)

C = ln(57.28)

Therefore, the amount of salt in the tank as a function of time t is -

\(A = \frac{250}{9} \times (60 - e^{(\frac{-9t}{250} + ln(57.28))})\)

Simplifying this expression, we get -

\(A = \frac{2000}{3} - \frac{2000}{3} \times e^{(\frac{-9t}{250})}\)

Therefore, the differential equation is \(A = \frac{2000}{3} - \frac{2000}{3} \times e^{(\frac{-9t}{250})}\).

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Answer:

7

Step-by-step explanation:

First, this triangle is a 30-60-90 triangle, this means that the hypotenuse is 2x, the "bottom" is x, and the other side is \(x\sqrt{3}\).

For our purposes, we need to use the hypotenuse and the "bottom".

Since the hypotenuse is two times x, we can divide the hypotenuse to get x.

14/2 = 7

Therefore, x is equal to 7.

Answer:

the probability is 0.0202

Step-by-step explanation:

The computation is shown below:

Given that

The Average life span = 17 hours

Standard deviation = 0.8 hours

Sample = 30 batteries

Sample mean = 16.7 hours

Now based on the above information

The probability is

\(P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202\)

Hence, the probability is 0.0202

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

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a) The angles outside the side PQ measure 65° and 25°

The angles outside the side QR measure 85° and 95°

The angles outside the side PR measure 55° and 35°

b) The arc PR, PQ and PR measure 120°

a)

Let us assume that the inscribed square be ABCD and equilateral triangle is PQR.

Let side PR of triangle intersects the quadrilateral at points M and N.

So, we get a triangle DMN outside the equilateral triangle.

Here, ∠DMN = 55°, ∠D = 90°

So, ∠MND = 180 - (90 + 55)

                 = 35°

Similarly,  side PQ of triangle PQR intersects the quadrilateral at points X and Y.

So, we get a triangle AXY outside the equilateral triangle.

From triangle PXM we get the measure of angle PXM which is 65 degrees.

As angle PXM and angle AXY are opposite angles, the measure of angle AXY = 65°

∠A = 90°

So, ∠AYX = 180° - (∠A + ∠AXY )

                 = 180° - (90° + 65°)

                 = 25°

Let the side QR of triangle PQR intersects the quadrilateral at points L and K.

so we get new quadrilateral LKBC

In this quadrilateral ∠B = 90°, ∠C = 90°

From triangle QYL, we get the measure of angle QLY = 95°

So, the measure of ∠KLB = 95° .......(∠QLY and ∠KLB opposite angles)

So, the remaining angle LKC of quadrilateral LKBC would be,

∠LKC = 360° - (∠B + ∠C + ∠KLB)

∠LKC = 360° - (90 °+ 90° + 95°)

∠LKC = 85°

b)

We know that he angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

so, the measure of arc PR = 120°

the measure of arc PQ = 120°

the measure of arc RQ = 120°

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Answer:

258m

Step-by-step explanation:

This is a guess, if you could, please post your answer again, but this time click the paperclip icon, and add a screenshot of the figure!

Answer:

m = 2/3

Step-by-step explanation:

Answer:

\( \frac{2}{3} \)

Step-by-step explanation:

slope is

\( m = \frac{rise}{run} = \frac{y 2 - y1}{x2 - x1} \)

(0,0) & (3,2)

\( m = \frac{2 - 0}{3 - 0} = \frac{2}{3} \)

a. There were 93 inches of wood left after the cut

b. There were 31/4 feet of wood left after the cut

From the question, we are to determine how long of the wood was left after the cut

From the given information,

A carpenter cut 15 inches off a piece of wood measuring 9 feet long

First,

Convert 9 feet to inches

1 feet = 12 inches

Thus,

9 feet = 12 × 9 inches

9 feet = 108 inches

After the cut, the length of the wood in inches would be:

108 inches - 15 inches = 93 inches

b. To express the remaining length in feet, we can divide the total length in inches (93 inches) by the number of inches in a foot (12 inches/foot) and simplify the resulting fraction:

93 inches / 12 inches/foot = (31 * 3 inches) / (4 * 3 inches/foot) = 31/4 feet

Hence, there were 31/4 feet of wood left after the cut.

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