find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x

Answer:

6 put of 8, 3/4, or 75%

Step-by-step explanation:

Hope this helps ! :)  good luck

the coordinates of endpoint B are (7,7)

Answer:

Solution given:

M(x,y)=(2,-1)

A\((x_{1},y_{1})=(-3,5)\)

Let

B\((x_{2},y_{2})=(a,b)\)

now

by using mid point formula

x=\(\frac{x_{1}+x_{2}}{2}\)

$ubstituting value

2*2=-3+a

a=4+3

a=7

again

y=\(\frac{y_{1}+y_{2}}{2}\)

$ubstituting value

-1*2=5-b

b=5+2

b=7

the coordinates of endpoint B are (7,7)

The total distance traveled by the dust in 2.70 minutes is 345.96 m.

Given that the spin rate of the CD is 410 rpm and the piece of dust is 4.97 cm from the center. The first step in solving this problem is to determine the distance traveled by the dust in one revolution. It is known that the circumference of a circle is equal to 2πr, where r is the radius of the circle.

The circumference of the CD is given by: C = 2πr= 2π(4.97)= 31.27 cm The distance traveled by the dust in one revolution is equal to the circumference of the CD. It is, therefore, 31.27 cm. Next, we need to determine the total number of revolutions made by the dust in 2.70 minutes.

The number of revolutions per minute is given by the spin rate of the CD, which is 410 rpm. We can, therefore, calculate the total number of revolutions made by the dust in 2.70 minutes as follows: Number of revolutions in 2.70 minutes = 410 rpm × 2.70 min= 1107 revolutions Finally, we can calculate the total distance traveled by the dust in 2.70 minutes as follows: Total distance = Distance per revolution × Total number of revolutions= 31.27 cm/revolution × 1107 revolutions= 34595.89 cm= 345.96 m

Therefore, the total distance traveled by the dust in 2.70 minutes is 345.96 m.

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The amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

Given,

Two waves are described by:

3₁ (2, 1) = (0.30) sin(5z - 200t)] and

g (z,t) = (0.30) sin(52-200t)

+ =]

where OA A, 0.52 m and v= 40 m/s

OB A=0.36 m and

v= 20 m/s OC

A=0.60 m and

v= 1.2 m/s OD.

A = 0.24 m and

v= 10 m/s

DE A=0.16 m and

= 17 m/s

The amplitude of a wave is the distance from its crest to its equilibrium. The amplitude of the resultant wave is calculated by adding the amplitudes of the individual waves and is represented by A.

The expression for the resultant wave is given by f(z,t) = 3₁ (2, 1) + g (z,t)

= (0.30) sin(5z - 200t)] + (0.30) sin(52-200t)

+ =]

f(z,t) = (0.30) [sin(5z - 200t) + sin(52-200t)

+ =]

Therefore, A = 2(0.30) = 0.60 m/s

The speed of a wave is given by the product of its wavelength and its frequency. The wavelength of the wave is the distance between two consecutive crests or troughs, represented by λ. The frequency of the wave is the number of crests or troughs that pass through a given point in one second, represented by f.

Speed = λf

The wavelengths of the given waves are OA = 0.52 m,

OB = 0.36 m,

OC = 0.60 m,

OD = 0.24 m,

DE = 0.16 m

The frequencies of the given waves are OA :

v = 40 m/s,

f = v/λ

= 40/0.52

= 77.0 Hz

OB : v = 20 m/s,

f = v/λ

= 20/0.36

= 55.6 Hz

OC : v = 1.2 m/s,

f = v/λ

= 1.2/0.60

= 2.0 Hz

OD : v = 10 m/s,

f = v/λ

= 10/0.24

= 41.7 Hz

DE : v = 17 m/s,

f = v/λ

= 17/0.16

= 106.25 Hz

The speed of the resultant wave is the sum of the speeds of the individual waves divided by the number of waves. Therefore,

Speed of the resultant wave = (40 + 20 + 1.2 + 10 + 17)/5

= 17.64 m/s

Hence, the amplitude of the resultant wave is 0.60 m/s and its speed is 17.64 m/s.

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The amplitude of the resultant wave and its speed are to be determined.

Let's use the formula of the resultant wave, where,

A is amplitude, f is frequency, v is velocity and λ is wavelength of the wave.

A = \([(OA^2 + OB^2 + OC^2 + OD^2 + DE^2 + 2(OA)(OB)(cosθ) + 2(OA)(OC)(cosθ) + 2(OA)(OD)(cosθ) + 2(OA)(DE)(cosθ) + 2(OB)(OC)(cosθ) + 2(OB)(OD)(cosθ) + 2(OB)(DE)(cosθ) + 2(OC)(OD)(cosθ) + 2(OC)(DE)(cosθ) + 2(OD)(DE)(cosθ))]^{1/2\)

where, cosθ = [λ1/λ2] and λ1, λ2 are the wavelength of the two waves.

The velocity of the wave is given by the relation v = fλ

We can calculate the velocity of the resultant wave by using the above formula and calculating the value of wavelength of the wave.

Here, we are given λ for each wave. Speed = 40 m/s

Amplitude of the resultant wave= \([ (0.52^2 + 0.36^2 + 0.6^2 + 0.24^2 + 0.16^2 + 2(0.52)(0.36) + 2(0.52)(0.6) + 2(0.52)(0.24) + 2(0.52)(0.16) + 2(0.36)(0.6) + 2(0.36)(0.24) + 2(0.36)(0.16) + 2(0.6)(0.24) + 2(0.6)(0.16) + 2(0.24)(0.16) )]^{1/2\)

=\([ (0.2704 + 0.1296 + 0.36 + 0.0576 + 0.0256 + 0.3744 + 0.624 + 0.2496 + 0.1664 + 0.1296 + 0.0864 + 0.0576 + 0.144 + 0.096 + 0.0384) ]^{1/2\)

=\([ (2.2768) ]^{1/2\)

= 1.51 m/s

Therefore, the amplitude of the resultant wave is 1.51 m/s and the speed of the wave is 1.51 m/s.

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The bicycle manufacturer is studying the reliability of its models and analyzing the probability of defects. They found the probability of a brake defect is 4 percent and the probability of both brake and chain defects is 1 percent.

Given that the probability of a defect with brakes or chain is 6 percent, we can find the probability of a chain defect using the formula: P(A and B) = P(A|B) * P(B), where P(A and B) is the probability of both events A and B occurring, P(A|B) is the probability of event A occurring given that event B has occurred, and P(B) is the probability of event B occurring.

In this case, we want to find the probability of a chain defect given that there is a defect with either the brakes or the chain. Let's use the events: A = brake defect, B = chain defect, From the problem statement, we know that: P(A) = 0.04 (probability of a brake defect), P(A and B) = 0.01 (probability of both a brake defect and a chain defect)
P(A or B) = 0.06 (probability of a defect with the brakes or the chain).

To find P(B|A or B), we can use the formula: P(B|A or B) = P(A and B) / P(A or B) = 0.01 / 0.06, = 1/6, = 0.1667, So the probability of a chain defect given that there is a defect with either the brakes or the chain is 16.67%, or approximately 2/12 or 1/6.

Therefore, the correct answer is option 2: 2%, Solving for the probability of a chain defect, we get: P(chain defect) = 0.06 - 0.04 + 0.01 = 0.03, So, the probability of a chain defect is 3 percent.

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Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

Given that,

A fair coin is tossed 29 times.

We have to find what is the probability that at most 27 heads occur.

We know that,

A fair coin is tossed 29 times.

n=29

Probability of heads p=1/2

q= 1-p

q=1-1/2=1/2

We get

P (X=x) = ⁿCₓ qⁿ⁻ˣ pˣ

Now, the probability that at most 27 heads occurs is

P(X<27)

=1-[P(X=28)+ P(X=29)]

=1-[²⁹C₂₈(1/2)²⁹⁻²⁸(1/2)²⁸- ²⁹C₂₉(1/2)²⁹⁻²⁹(1/2)²⁹]

=1-[²⁹C₂₈(1/2)²⁹- ²⁹C₂₉(1/2)²⁹]

=1-[28+1](1/2)²⁹

=1-29×0.00000000186

=0.999999945

Therefore, Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

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Answer:

Correct ✅ answer ✅ - Danielle's retirement income is $90000. Assuming it is 70 % of his final salary, what was her final salary $63000 $90000 $128571 $14.

Answer:

1

Step-by-step explanation:

Simplify the following:

(44×10)^0

Hint: | Simplify (44×10)^0 by distributing exponents over products.

Multiply each exponent in 44×10 by 0:

Answer: 1

any number to the zero power always gives a one

To maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

To maximize the seating area, we need to determine the dimensions of the rectangular auditorium that will give us the largest possible area while using the given length of light strips.

Let the length of the rectangular auditorium be L, and its width be W.

The seating area consists of the rectangular portion minus the semicircular stage. So, the seating area's length is L - 2r (subtracting the semicircle's diameter) and the seating area's width is W - 2r.

The perimeter of the seating area is the sum of the lengths of its four sides, excluding the semicircular stage. The perimeter is given as 45π + 60 meters.

Perimeter = 2(L - 2r) + 2(W - 2r) + πr = 45π + 60

Simplifying: 2L + 2W - 8r + πr = 45π + 60

Rearranging: 2L + 2W = 8r + 44π + 60

The area of the seating area is given by A = (L - 2r)(W - 2r).

We want to maximize A, so we need to express it in terms of a single variable. Since we have an equation with two variables (L and W), we can rewrite one of the variables in terms of the other.

Rearranging the perimeter equation: 2L + 2W = 8r + 44π + 60

Solving for L: L = (8r + 44π + 60 - 2W) / 2

Substituting L in terms of W into the area equation: A = [(8r + 44π + 60 - 2W) / 2 - 2r] (W - 2r)

Simplifying: A = (4r + 22π + 30 - W) (W - 2r)

Now we have the area equation in terms of a single variable, W. To maximize A, we can take the derivative of A with respect to W, set it equal to zero, and solve for W.

dA/dW = 2(4r + 22π + 30 - W) - (W - 2r) = 0

Solving for W: 8r + 44π + 60 - W = W - 2r

Simplifying: 10r + 44π + 60 = 2W

W = 5r + 22π + 30

Now that we have W in terms of r, we can substitute this expression back into the area equation to get the area in terms of r only.

A = (4r + 22π + 30 - (5r + 22π + 30)) ((5r + 22π + 30) - 2r)

Simplifying: A = (r - 22π) (3r + 22π + 30)

Expanding: A = 3r² + 8rπ + 30r - 66πr - 660π

Now, to find the maximum area, we can take the derivative of A with respect to r, set it equal to zero, and solve for r.

dA/dr = 6r + 8π + 30 - 66π = 0

Simplifying: 6r - 58π + 30 = 0

6r = 58π - 30

r = (58π - 30) / 6

r ≈ 29π/3 - 5

Therefore, to maximize the seating area while using 45π + 60 meters of light strips, the radius of the semicircular stage should be approximately 29π/3 - 5 meters.

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The calculated value of the expression A + B is 60

From the question, we have the following parameters that can be used in our computation:

A - B = 56

B = 2

Substitute the known values of B in the above first equation

So, we have the following representation

A - 2 = 56

Evaluate the sum

A = 58

Add B to both sides

A + B = 58 + B

So, we have

A + B = 58 + 2

Evaluate

A + B = 60

Hence the solution is 60

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Answer:

The answer is 127.6

Step-by-step explanation:

To find the volume of something, you multiply.

So:5.5 times 3.2 times 7.25 is equal to 127.6

HOPE THIS HELPS YOU!!!!    :)

Answer:

127.60 square inches

Step-by-step explanation:

Multiply the diameters all together to get your answers.

5.5 x 3.2 x 7.25

Multiply

5.5 x 3.2 = 17.6

Multiply some more

17.6 x 7.25 = 127.6

You can also just multiply like this:

5.5 x 3.2 x 7.25 = 127.6

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Answer:

Solving:

\( \frac{x}{5} = - 2 \\ \\ x = - 2 \times 5 \\ { \boxed{x = - 10}}\)

Checking:

\( \frac{x}{5} = - 2 \\ when \: x \: is \: - 10 \\ \\ \frac{ - 10}{5} = - 2 \\ \\ - 2 = - 2\)

# since all sides are the same, the answer is consistent.

\(.\)

The required answer is  the tangent of angle T is 7/24.

The tangent of angle T can be found using the formula "tangent = opposite/adjacent". In this case, we don't have the lengths of the opposite and adjacent sides, but we do have the hypotenuse (c) and angle T. We can use trigonometric ratios to find the opposite and adjacent sides.

First, we can use the Pythagorean theorem to find the length of the missing side: a^2 + b^2 = c^2. Plugging in the values we have, we get:
a^2 + 24^2 = 25^2
a^2 + 576 = 625
a^2 = 625 - 576
a^2 = 49
a = 7
So the length of the opposite side is 7, and the length of the adjacent side is 24. Now we can plug these values into the formula for tangent:
Identify the opposite and adjacent sides.
tangent(T) = opposite/adjacent
tangent(T) = 7/24

Therefore, the tangent of angle T is 7/24.

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y=70+18(x)

y=70+18(12)

y=70+216

y=286

Step-by-step explanation:

since Tanya bakes 12 more cookies,

x=12

y= 70 + 18(12)

y=70 + 216

y= 286

therefore, she bakes 286 cookies with twelve more batches

π/32 is the area enclosed by the curve r= sin(8θ)

The given curve is polar curve and hence the area of the polar curve is given by:

Let A be the area of the curve so,

A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)

where a and b is the boundary at which r=0

so after equation r=0

sin(8θ) =0

=> sin(8θ) =0

=> 8θ = 0,π

=> θ = 0, π/8

so a=0 , b= π/8

now  

   A = \(\int\limits^a_b {\frac{1}{2} r^2 } \, d\theta\)    ------(i)

 so   \(r^2\) = (sin(8θ))^2

=>  \(sin^2\) ( 8θ )

ans we know that

cos(2α) = 1 -  2\(sin^2\) α

so   \(r^2\)  = (1- cos(16θ) )/2

putting the value of r in the equation (i) we get :-

A = \(\int\limits^a_b {\frac{1}{4} *(1-cos(16\alpha ) } \, d\alpha\)

=> 1/4* \(\int\limits^a_b {(1-cos(16\alpha ) } \, d\alpha\)

here a=0 and b=π/8

after putting the value and solving the integral

A = π/32

so A is the area enclosed by r=sin(8θ) is π/32

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The statement "The center of a trapezoid is the perpendicular distance between the bases" is false.

To make the statement true, we need to replace the underlined term. The correct term should be "midsegment" instead of "perpendicular distance between the bases."

The midsegment of a trapezoid is a line segment that connects the midpoints of the non-parallel sides. It is parallel to the bases and its length is equal to the average of the lengths of the bases.

Here's a step-by-step explanation:

1. A trapezoid is a quadrilateral with exactly one pair of parallel sides.

2. The bases of a trapezoid are the parallel sides.

3. The midsegment of a trapezoid connects the midpoints of the non-parallel sides.

4. The midsegment is parallel to the bases and its length is equal to the average of the lengths of the bases.

5. Therefore, the statement "The center of a trapezoid is the perpendicular distance between the bases" is false.

6. To make it true, we should replace "perpendicular distance between the bases" with "midsegment".

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Answer:

x = (√10  -3)/2  and (-√10  -3)/2

Step-by-step explanation:

(2x+3)^2 = 10

To solve the equation, take the square root of each side

sqrt((2x+3)^2) = ±√10

2x+3 = ±√10

Subtract 3 from each side

2x+3-3 = ±√10  -3

2x = ±√10  -3

Divide each side by 2

2x/2 = (±√10  -3)/2

x = (±√10  -3)/2

There are two solutions

x = (√10  -3)/2

and (-√10  -3)/2

Answer:

\(\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}\)

Step-by-step explanation:

Given: (2x + 3)² = 10

In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.

Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.

Step 1: Square both sides of the equation.

\(\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}\)

Step 2: Separate into possible cases.

\(\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}\)

Step 3: Solve for x in both cases.

\(\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\\)

\(\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}\)

Therefore, the solutions to this quadratic equation are: \(\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}\)

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The two numbers which when multiplied and added gives the same result is 2 and 2

To add two (or more) numbers is to calculate their sum (or total). To find the difference between two numbers, subtract one from the other. times when multiplied (or repeated addition). The outcome of multiplying two (or more) numbers is a product. Here are the guidelines when an expression only contains the four fundamental operations: Divide and multiply from left to right. tally up and down from left to right

The two numbers which when multiplied and added gives the same result is 2 and 2

For example; 2 + 2 = 4

and 2 multiplied by 2 is 4

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The single basic motion that will make the figures coincide are
1) a linear motion.

2) Linear motion

3) Rotational motion

4) Translational motion

5) Rotational motion

6) translational motion

Here are some basic motions in physics:

Linear motion: This is the motion of an object in a straight line, such as a car moving down a highway or a ball being thrown straight up.

Circular motion: This is the motion of an object moving in a circle, such as a car driving around a roundabout or a satellite orbiting the Earth.

Projectile motion: This is the motion of an object that is thrown, launched, or dropped and then moves under the influence of gravity alone. Examples include a cannonball being fired or a basketball being shot.

Oscillatory motion: This is the motion of an object that repeats the same motion over and over again, such as a pendulum swinging back and forth or a guitar string vibrating.

Rotational motion: This is the motion of an object that rotates around a fixed axis, such as a spinning top or a bicycle wheel.

Translational motion: This is the motion of an object that moves from one place to another, such as a train moving from one station to the next.

Wave motion: This is the motion of a disturbance that travels through a medium, such as sound waves or ocean waves.

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Answer:

x< -17/6

Step-by-step explanation:

This is actually quite easy

all you have to do is divide -6 from both sides to isolate X

-6x/-6 > 17/ -6 (but here is the thing, when it is an inequality and you are dividing by a negative number, you flip the sign, so ">" turns to "<."

so, the answer is x< -17/6 (you cannot simply it!)

After solving the given equations the answer is an Infinite solution. Hence, option A is correct

Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.

This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.

As per the given equation in the question,

8 + 4x = 2x + 8 + 2x

Firstly, let's write the given equation in a simplified manner,

8 + 4x = 8 + 4x  

As we can see that LHS = RHS, which means that both equations are the same then which means they will give infinite solutions.

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The answer is C - "Select a level for β". The five steps in the hypothesis testing procedure are:

State the null and alternative hypothesis.

Identify the level of significance (α).

Determine the appropriate test statistic and calculate its value.

Formulate a decision rule based on the test statistic and α.

Make a decision and interpret the results in the context of the problem.

The level of significance (α) is determined in step 2, not step 3. The level of significance is the probability of rejecting the null hypothesis when it is actually true. Typically, the level of significance is set to 0.05 or 0.01, which means there is a 5% or 1% chance of rejecting the null hypothesis when it is true.

Step 3 involves identifying the level of Type II error (β) that the researcher is willing to accept. β is the probability of failing to reject the null hypothesis when it is actually false. However, β is not always explicitly selected by the researcher and is often calculated after the sample size and effect size have been determined.

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Answer: Elevation is going to be greater than 5.71059°

Step-by-step explanation: 60/600 = tan∅ = 0=5.71059°,   so 0> 5.71059°

The correct option id D. There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than our sample's 36 working full-time

A study was conducted to determine if more than 30% of Cal State East Bay students work full-time.

The sample of Cal State East Bay students selected was random.

Out of 100 students, 36 were found to be working full-time.

The p-value was calculated to be 0.0952.

The probability of having more than 36 Cal State East Bay students working full-time out of a random sample of 100 students is 9.52% if exactly 30% of Cal State East Bay students work full-time.

Therefore, it is concluded that the null hypothesis cannot be rejected.

The p-value is greater than 0.05 which shows the significance level.

Hence, we accept the null hypothesis.

The null hypothesis states that the proportion of Cal State East Bay students who work full-time is not greater than 30%.

The alternate hypothesis states that the proportion of Cal State East Bay students who work full-time is greater than 30%.

The test is a right-tailed test.

The sample proportion is p = 0.36. The test statistic is given as Z = (p - P0) / √ [P0 (1 - P0) / n]Z = (0.36 - 0.30) / √ [(0.30) (0.70) / 100] = 1.76The p-value is given as 0.0392.

Since the p-value is less than 0.05, we can reject the null hypothesis.

Thus, we can conclude that more than 30% of Cal State East Bay students work full-time.

Hence, option D is the correct answer.

There is a 9.52% chance that a random sample of 100 Cal State East Bay students would have more than 30% working full-time.

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Answer: idk man

Step-by-step explanation: rg

Answer:iidk

Step-by-step explanation:

Answer:

PEMDAS

Step-by-step explanation:

P=Parenthesis

E=Exponent

M=Multiply

D=Division

A=Addition

S=Subtract

The first step you should perform is the exponent 3 of base 8.

BODMAS rule is the rule used when solving expressions involving more than one operations.

It is the abbreviation of Brackets, Order, Division, Multiplication, Addition, Subtraction, which is the order of the operations to be done.

The given expression is 8³ - 10 × 5 - 4.

We know the rule of BODMAS.

since the given expression includes more than one operations, we have to follow the rule of BODMAS.

There are no brackets in the expression.

There is a power of 3 for the base 8.

We should perform that in the first step.

8³ - 10 × 5 - 4 = 512 - 10 × 5 - 4

Next we do the operation of multiplication.

512 - 10 × 5 - 4 = 512 - 50 - 4

There is subtraction.

512 - 50 - 4 = 566

Hence the operation of the power is done first.

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To solve the expression (L-2L/3)^3, we will simplify it using the following steps:

Step 1: Simplify the expression inside the bracket.\((L-2L/3) = L(1-2/3) =\)\(L(1/3) = L/3\)

Step 2: Cube the simplified expression.\([L/3]^3 = L^3/27\)

The simplified form of the given expression is\(L^3/27.\)

To understand the above solution more easily, let us explain it in more than 100 words.

Let's start with the given expression:

\((L-2L/3)^3\)We can rewrite it as:\(L^3[-2/3+1]^3\)

Now, let's simplify the term inside the bracket:

-2/3+1 = 1/3

\(L-2L/3)^3\)can be rewritten as:\(L^3 (1/3)^3L^3 (1/27) = L^3/27\)Hence, the simplified form of the given expression is L^3/27.This is how we solve the expression

\((L-2L/3)^3\) and get the simplified form\(L^3/27.\)

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The point that lies in the fourth quadrant is (1, -2).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates are:

(1,−2), (1, 8), (-5, -4), and (-5, 2).

(1, -2) is in the fourth quadrant.

(1, 8) is in the first quadrant.

(-5, -4) is in the third quadrant.

(-5, 2) is in the second quadrant.

Thus,

(1, -2) lies in the fourth quadrant.

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Answer:   (5,−2) is the only point in the fourth quadrant.

Step-by-step explanation:

The change in profit (ΔP) when the number of units (Δx) increases by 5, based on the given marginal profit function, is -18331.50

To find the change in profit (ΔP) when the number of units (Δx) increases by 5.

we need to evaluate the marginal profit function and multiply it by Δx.

The marginal profit function is given by dP/dx = 12.1(60 - 3x).

We are given the value of x as 121, so we can substitute it into the marginal profit function to find the marginal profit at that point.

dP/dx = 12.1(60 - 3(121))

= 12.1(60 - 363)

= 12.1(-303)

= -3666.3

Now, we can calculate the change in profit (ΔP) by multiplying the marginal profit by Δx, which is 5 in this case.

ΔP = dP/dx×Δx

= -3666.3 × 5

= -18331.5

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One car was traveling at 42 mph and the other car was traveling at 43 mph (since we know one car was traveling 1 mph faster). So the average speed of each car was:  - Car 1: 42 mph and Car 2: 43 mph.

Let's call the speed of one car "x" and the speed of the other car "x+1" (since we know that one car travels 1 mph faster than the other).
We also know that they are 170 miles apart and meet in 2 hours. When two objects are moving towards each other, we can add their speeds together to find their combined speed.
So, using the formula: distance = speed x time
We can write:
170 = (x + x+1) x 2
Simplifying this equation:
170 = 2x + 2x + 2
170 = 4x + 2
168 = 4x
x = 42
Therefore, one car was traveling at 42 mph and the other car was traveling at 43 mph (since we know one car was traveling 1 mph faster).
So the average speed of each car was:
- Car 1: 42 mph
- Car 2: 43 mph

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