If right will give brainiest

On two​ examinations, you have grades of 87 and 89. There is an optional final​ examination, which counts as one grade. You decide to take the final in order to get a course grade of​ A, meaning a final average of at least 90.

What must you get on the final to earn an A in the​ course?

a) The PDF of X is f(X) = 2 \(e^{(-2X)\) for X > 0

b) P(X ≥ 1) is 0.135.

c)  P(X > 2 | X ≥ 1) is 0.1357.

d) The expected value of X (lifetime) is 0.5 years, and the variance of X is 0.25 years²

a. For the defective devices (0-year lifetime), the probability is given as 2% or 0.02.

So, the PDF for this case is:

f(X) = 0.02 for X = 0

For the non-defective devices (exponentially distributed lifetime with λ = 2 years), the PDF is given by the exponential probability density function:

f(X) = λ  \(e^{(-\lambda X)\) for X > 0

Substituting λ = 2, the PDF for non-defective devices is:

f(X) = 2 \(e^{(-2X)\) for X > 0

b. To find P(X ≥ 1), we need to integrate the PDF of X from 1 to infinity:

P(X ≥ 1) = \(\int\limits^{\infty}_1\) f(X) dX

For the non-defective devices, the integration can be performed as follows:

\(\int\limits^{\infty}_1\) 2  \(e^{(-2X)\) dX = \(\int\limits^{\infty}_1\)[-\(e^{(-2X)\)]

                          = (-\(e^{(-2\infty)\)) - (-\(e^{(-2(1))\)))

                          = -0 - (-\(e^{(-2)\))

                          = 0.135

Therefore, P(X ≥ 1) is 0.135.

c. To find P(X > 2 | X ≥ 1), we can use the conditional probability formula:

P(X > 2 | X ≥ 1) = P(X > 2 and X ≥ 1) / P(X ≥ 1)

For the non-defective devices, we can calculate P(X > 2 and X ≥ 1) as follows:

P(X > 2 and X ≥ 1) = P(X > 2) = \(\int\limits^{\infty}_2\) 2  \(e^{(-2X)\) dX

Using integration, we get:

\(\int\limits^{\infty}_2\) 2  \(e^{(-2X)\) dX = \(\int\limits^{\infty}_2\)[-\(e^{(-2X)\)]

                          = (-\(e^{(-2\infty)\)) - (-\(e^{(-2(2))\)))

                          = -0 - (-\(e^{(-4)\))

                          = 0.01832

Now, let's calculate the denominator, P(X ≥ 1), which we found in the previous answer to be approximately 0.135.

P(X > 2 | X ≥ 1) = P(X > 2 and X ≥ 1) / P(X ≥ 1)

                 = 0.01832 / 0.135

                 ≈ 0.1357

So, P(X > 2 | X ≥ 1) is 0.1357.

d. For an exponentially distributed random variable with parameter λ, the expected value is given by E(X) = 1 / λ, and the variance is given by Var(X) = 1 / \(\lambda^2\).

In this case, λ = 2 years, so we have:

E(X) = 1 / λ = 1 / 2 = 0.5 years

Var(X) = 1 / λ² = 1 / (2²) = 1 / 4 = 0.25 years²

Therefore, the expected value of X (lifetime) is 0.5 years, and the variance of X is 0.25 years².

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Answer:

y = 50

Step-by-step explanation:

y = 2x^2

Let x= -5

y = 2(-5)^2

Power first

y = 2(25)

Then multiply

  = 50

Answer:

The second option

Step-by-step explanation:

the range is all the y vaules

Answer:

Equation of a circle:

Substitute the given values to get the equation of this circle:

Answer:

Solution given:

Centre(h,k)=(-5,-9)

radius (r)=7

we have

Equation of a circle is;

(x-h)²+(y-k)²=r²

Substituting value;

(x+5)²+(y+9)²=7²

(x+5)²+(y-9)²=49 is a required equation of a circle.

Answer:

w/4 is less than or equal to -24

The formula for Integration of UV:

f the two functions are of the type u,v then the formula for the Integration of u and v may be written as follows: ∫ uv dx = u ∫ v dx – ∫ (u' ∫ v dx) dx.

Integration of Trigonometric functions involves basic simplification techniques. These techniques use different trigonometric identities which can be written in an alternative form that are more amenable to integration.

Identify the integral of the form ∫u.vdx. Choose u(x) using the LIATE rule and differentiate it. Choose v(x) and Integrate dv. Then plug in all the values obtained so far, in the formula ∫u.v = u. ∫v.dx- ∫( ∫v.dx.u'). dx and evaluate the integral.

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The sampling interval is calculated by dividing the digital sampling frequency by the number of samples taken per second.

The sampling interval refers to the time interval between each consecutive sample in a digital signal. It is determined by dividing the digital sampling frequency by the number of samples taken per second. The sampling frequency represents the number of samples captured in one second, while the number of samples per second represents the rate at which the samples are taken. By dividing the sampling frequency by the number of samples per second, we can determine the time interval between each sample.

This is crucial in accurately representing and reconstructing the original analog signal from the digital samples. Therefore, the sampling interval is calculated by dividing the digital sampling frequency by the number of samples taken per second.

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1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline is dynamic stretching.

2. The stretching technique emphasized in the scenario of a runner performing various stretches for 30 seconds on each side after a run is static stretching.

1. The stretching technique emphasized in the scenario of a tennis player running up to the net and shuffling back to the baseline five times is dynamic stretching. Dynamic stretching involves performing controlled movements that mimic the motions of the activity or sport being performed. In this case, the tennis player is incorporating dynamic movements to warm up and prepare their muscles for the specific demands of playing tennis.

2. The stretching technique emphasized in the scenario of a runner performing a quadriceps stretch, gastrocnemius stretch, and a runner's stretch for 30 seconds on each side of the body after a run is static stretching. Static stretching involves holding a stretch in a stationary position for a certain period of time. In this case, the runner is holding each stretch for 30 seconds, which is a characteristic of static stretching. Static stretching is commonly used to improve flexibility and promote muscle relaxation after exercise.

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In the given scenario, the type of stretching technique being emphasized is Dynamic Stretching.

Dynamic stretching is a type of stretching technique that involves active movements to improve flexibility and range of motion. It is typically performed as part of a warm-up routine before engaging in physical activity. Unlike static stretching, which involves holding a stretch for an extended period, dynamic stretching incorporates dynamic movements that mimic the actions performed during the activity. This helps to warm up the muscles, increase blood flow, and prepare the body for the upcoming exercise or sports activity.

In the given scenario, the type of stretching technique being emphasized is Static Stretching.

Static stretching, on the other hand, is a stretching method where a stretch is held in a fixed position for a prolonged period of time, typically ranging from 15 to 60 seconds. This technique is often used to improve flexibility and increase the length of muscles and tendons. Static stretching is commonly performed during the cooldown phase after exercise or physical activity. It helps to relax the muscles, reduce muscle soreness, and improve overall flexibility and joint mobility.

Both dynamic stretching and static stretching have their benefits and serve different purposes in a fitness or sports routine. Dynamic stretching is effective for warming up the body and preparing it for physical activity, while static stretching is useful for improving flexibility and promoting relaxation in the muscles. It's important to choose the appropriate stretching technique based on your specific goals and the context of your exercise or sports regimen.

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The Discriminant of the quadratic equation "2x + 5x² = 1" is 24  .

The Discriminant(D) of the Quadratic Equation ax² + bx + c can be calculated using the formula ; D = b² - 4ac .

the quadratic equation is given as 2x + 5x² = 1 ;

after rearranging the terms ,

the equation can be written as :

⇒ 5x² \(+\) 2x - 1 = 0  ;

Substituting the values in the discriminant formula ,

we get ;

D = (2)² - 4×5×(-1)

Simplifying further ,

we get ;

D = 4 + 20

D = 24 .

Therefore , the value of the Discriminant is 24 .

The given question is incomplete , the complete question is  

What is the discriminant of the quadratic equation 2x + 5x² = 1  ?

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Answer:

Mya’s equation

Step-by-step explanation:

Given that:

Detergent left in bottle after a certain number of washes x

Dexter’s equation,

y= -1.6x+50

Mya’s equation,

y = 50(.75)x

y = Detergent left in bottle.

Given that amount of Detergent left is about 1/2 ounces = y

For Dexter’s equation,

y= -1.6x+50

0.5 = 1.6x + 50

0.5 - 50 = 1.6x

-45.5 = 1.6x

x = 28.4375

For Mya’s equation :

y = 50(0.75)x

0.5 = 37.5x

0.5 / 37.5 = x

0.0133333 = x

Hence, Mya’s equation

Answer:

D

Step-by-step explanation:

Sin(x)=25/35=5/7

=> x = 45.6

A list of 6 one digit whole numbers with an average of 5, a median of 6, a range of 9, and no mode is

since the numbers will have no mode so they are all different

Assuming the numbers are: a, b. c. d. e. and f

The average is 5

(a + b + c + d + e + f ) / 6 = 5

a + b + c + d + e + f = 30

The median is 6

(c + d)/2 = 6

c + d = 12  (assume c = 5 and d = 7)

range is 9

f - a = 9, since it is a one digit number a range of 9 is possible for 9 - 0

hence a = 0 and f = 9

substituting assumed values to the average

0 + b + 5 + 7 + e + 9 = 30

b + e + 21 = 30

b + e = 9 (let b = 8and e = 1)

hence the numbers are

0, 1, 5, 7, 8, and 9

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Answer:

what are the shipping costs?

Answer:

the answer is A. 4.50

Step-by-step explanation:

The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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There are 15 ways for Minnie to select the 4 subjects and decide the order of doing homework. Minnie has 6 subjects to finish homework for including calculus and statistics.

Out of these 6 subjects, she wants to finish homework for 4 subjects.

Since she wants to finish statistics before calculus, there are only 2 ways to select the subjects to do first i.e. either statistics or calculus.

Statistics must be one of the subjects selected to finish homework for today and hence there are only 5 subjects left to choose from for the other 3 subjects.

So, Minnie has to select 3 subjects from a total of 5 subjects which can be done in 5C3 ways.

5C3 = 10

There are 10 ways for Minnie to choose the remaining 3 subjects.

Now, since Minnie wants to finish statistics before calculus, there is only one possible way to arrange these two subjects in the order she wants.

Hence, there are only 2 possible ways to arrange these two subjects for doing homework.

To arrange the remaining 2 subjects,

Minnie has 2 options.

Hence, there are 2 ways to arrange the last 2 subjects.

So, total number of ways to select the 4 subjects and then decide the order of doing homework is:

10 × 2 × 2 = 40.

Therefore, there are 15 ways for Minnie to select the 4 subjects and decide the order of doing homework.

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Answer:

Here is what I think the answer is.

n+2n+8 = 5n-10

3n+8 = 5n-10

    -8         -8

3n = 5n-18

-5n  -5n

-2n = -18

----      -----

-2         -2

n = 9

Step-by-step explanation:

It would be 8 + 2 = 10 - 5n I think.

The dimensions that will result in a solid with maximum volume are approximately x = 12.02 centimeters and h = 5.01 centimeters.

Let the side of the square base be x, and let the height of the rectangular solid be h. Then, the surface area of the solid is given by:

Surface area = area of base + area of front + area of back + area of left + area of right

Surface area = x² + 2xh + 2xh + 2xh + 2xh = x² + 8xh

We are given that the surface area is 433.5 square centimeters, so we can write: x² + 8xh = 433.5

We want to find the dimensions that will result in a solid with maximum volume. The volume of the solid is given by:

Volume = area of base × height = x² × h

We can use the surface area equation to solve for h in terms of x:

x² + 8xh = 433.5

h = (433.5 - x²)/(8x)

Substituting this expression for h into the volume equation, we get:

Volume = x² × (433.5 - x²)/(8x) = (433.5x - x³)/8

To find the maximum volume, we need to find the value of x that maximizes this expression. To do this, we can take the derivative of the expression with respect to x, set it equal to zero, and solve for x:

d(Volume)/dx = (433.5 - 3x²)/8 = 0

433.5 - 3x² = 0

x² = 144.5

x = sqrt(144.5) ≈ 12.02

We can check that this is a maximum by computing the second derivative of the volume expression with respect to x:

d²(Volume)/dx² = -3x/4

At x = sqrt(144.5), this is negative, which means that the volume is maximized at x = sqrt(144.5).

Substituting x = sqrt(144.5) into the expression for h, we get:

h = (433.5 - (sqrt(144.5))²)/(8×sqrt(144.5))

h = 433.5/(8×sqrt(144.5)) - sqrt(144.5)/8

h = 5.01

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The dimensions of the rectangular solid that will result in a maximum volume are approximately.\(6.34 cm \times 9.03 cm \times 9.03 cm.\)

Let's assume that the length, width, and height of the rectangular solid are all equal to x, so the base of the solid is a square.

The surface area of the rectangular solid can be expressed as:

\(SA = 2xy + 2xz + 2yz\)

Substituting x for y and z, we get:

\(SA = 2x^2 + 4xy\)

We are given that the surface area is 433.5 square centimeters, so:

\(2x^2 + 4xy = 433.5\)

Simplifying, we get:

\(x^2 + 2xy - 216.75 = 0\)

Using the quadratic formula to solve for y, we get:

\(y = (-2x\± \sqrt (4x^2 + 4(216.75)))/2\)

\(y = -x \± \sqrt (x^2 + 216.75)\)

Since the base of the rectangular solid is a square, we know that y = z. So:

\(z = -x \± \sqrt(x^2 + 216.75)\)

The volume of the rectangular solid is given by:

\(V = x^2y\)

Substituting y for\(-x + \sqrt (x^2 + 216.75),\) we get:

\(V = x^2(-x + \sqrt(x^2 + 216.75))\)

Expanding and simplifying, we get:

\(V = -x^3 + x^2\sqrt(x^2 + 216.75)\)

The dimensions that will result in a solid with maximum volume, we need to find the value of x that maximizes the volume V.

We can do this by taking the derivative of V with respect to x, setting it equal to zero, and solving for x:

\(dV/dx = -3x^2 + 2x\sqrt(x^2 + 216.75) + x^2/(2\sqrt (x^2 + 216.75)) = 0\)

Multiplying both sides by \(2\sqrt (x^2 + 216.75)\) to eliminate the denominator, we get:

\(-6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) + x^3 = 0\)

Simplifying, we get:

\(x^3 - 6x^2\sqrt (x^2 + 216.75) + 4x(x^2 + 216.75) = 0\)

We can solve this equation numerically using a graphing calculator or computer software.

\(The solution is approximately x = 6.34 centimeters.\)

Substituting x = 6.34 into the expression for y and z, we get:

\(y = z \approx 9.03 centimeters\)

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Answer:

Comparing means from dependent samples.

Step-by-step explanation:

In the scenario described above, the 25 sampled individuals were used to test the effect of weightlifting on alleviating back pain. The samples used were not changed nor altered during the study as the same subjects who were tested to measure their level of pain before lifting weight were the same group subjected to the actual weight lifting test and again had their level of pain tested. Since only one group was involved in the study ( a single group was tested on neutral and actual treatment). Hence, the study used dependent samples to compare the average level of pain.

On solving the provided question, we can say that - y proportional to  as the cube of s, y = ks3, then  \(y = 1 * 53 = 125\)

If two numbers are directly proportional, then as one quantity grows by a specific percentage, so does the other quantity by the same percentage. As an illustration, as gas costs rise, the price of food may also increase. If the ratio of two values x to y never changes, then x and y are said to be directly proportional to one another. example: Let's say you spend Rs. 50 on two pens. 4 pens cost 100 rupees each. If the ratio of two numbers, x and y, is greater than 1, then the two values The value of y1 is constant.

Since y proportional to  as the cube of s, y = ks3.

\(8 = k*23 = > k = 1\)

\(Then y = 1 * 53 = 125\)

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Answer:

C

Step-by-step explanation:

\(A. 20 - 6x = 4(1-x) -4 \\=>20 - 6x = 4-4x -4\\=>20-6x=-4x\\=> 20=2x\\=> x=10\)

\(B. 6x-2x = 4(1-2)+4\\=> 4x = 4(-1) +4\\=> 4x =0\\=>x=0\)

\(C.2x-6x=4(1-x)+4\\=> -4x = 4 - 4x +4\\=>-4x + 4x = 8\\=> no solution\)

\(D.6x-2x =4(1-2) +4\\=> 4x = 4(-1) +4\\=> 4x = 0\\=> x=0\)

\((7 \times 8 - 4) + (6 - 2) \\ (56 - 4) + (6 - 2) \\ 52 + (6 - 2) \\ 52 + 4 \\ 56\)

Answer:

Solution given;

P:parenthesis

E:exponents

M: multiplication

D: division

A:addition

S:subtraction

Now

(7×8-4)+(6-2)

According to PEMDAS rule doing calculation inside a bracket.

(7×8-4)+(6-2)

1st doing multiplication inside a bracket

(56-4)+(6-2)

2nd subtracting inside a bracket

(52)+(4)

3rd open bracket

52+4

4th add

56

56 is a required answer.

Answer:

shshjshshsbs

Step-by-step explanation:

shzjshsjjsisjs

The number of seconds, it takes for the balloon to drop below 310 feet is 1.25 seconds

To find out how many seconds it will take for the balloon to drop to below 310 feet, we need to use the information provided and some basic algebra.

Given the starting altitude of the balloon, we know:

h(0) = 1200 feet

The rate of change of the altitude, or the speed at which the altitude is changing, is given as:

dh/dt = −712 feet/second

This tells us that the altitude of the balloon is decreasing at a rate of 712 feet per second. To find out how long it will take for the altitude to drop to 310 feet or less, we can set up the following equation:

h(t) = h(0) + dh/dt * t

We know that h(t) must be less than or equal to 310 feet, so we can substitute this value in for h(t) and solve for t:

310 = 1200 + (−712) * t

This equation can be solved for t by isolating t on one side and then dividing both sides by −712:

t = (1200 - 310) / −712

t = (890) / (−712)

t = 1.25 seconds.

So it will take 1.25 seconds for the balloon to drop below 310 feet.

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If φ = arccos(-5/13), then cos(φ) = -5/13. Since this is negative, you know φ is an angle that terminates either the second or third quadrant.

arctan(x) has a range of -π/2 < arctan(x) < π/2, which is to say that arctan(x) is an angle that terminates in either the first or fourth quadrant.

These quadrants don't overlap, so there is no solution to the equation.

Answer: 182 pounds.

Step-by-step explanation:

170+25= 195 195-10=185 185-3=182

Answer:

182 pounds

Step-by-step explanation:

170+25=195

195-10= 185

185-3=182

Answer:

Step-by-step explanation:

(2, -5)   ; (-6 , -11)

Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

              \(=\sqrt{(-6-2)^{2}+(-11-[-5])^{2}}\\\\=\sqrt{(-6-2)^{2}+(-11+5)^{2}}\\\\=\sqrt{(-8)^{2}+(-6)^{2}}\\\\=\sqrt{64+36}\\\\=\sqrt{100}\\\\=10\)

Answer:

Step-by-step explanation:

One fourth times one fourth can be represented as (1/4) * (1/4) in fraction form.

To multiply fractions, we need to multiply the numerators (top numbers) together and the denominators (bottom numbers) together.

In this case, the numerator is 1 * 1, which equals 1. The denominator is 4 * 4, which equals 16.

So, (1/4) * (1/4) is equal to 1/16.

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Answer: 604.30

Step-by-step explanation:

You round it two to the right and add the number to the left by one every time the number is over 5.

Answer:

SA = 189 cm^2

Step-by-step explanation:

What you're going to want to do is calculate the surface area of each type of side (triangle or rectangle) then add them up accordingly!

Starting with triangles: area = 1/2 * l * h

So, in this scenario its (1/2) * 6 * 4 , or half of 24, which is 12 cm^2

Since we have two triangular sides, that totals to 24 cm^2.

Then the rectangular sides: area = l*h

so, 5*11 = 55 cm^2

We have three rectangular sides, totalling 165 cm^2

165+24 = 189 cm^2

Answer:

200 \(cm^{2}\)

Step-by-step explanation:

SA = LA + 2B     where LA is the lateral area and B is the area of the base(triangle)

LA = ph     p = perimeter of base and h = distance between bases

LA = (5 + 5 + 6)11 = 176

B = bh/2 = 6(4)/2 = 12

SA = 176 + 2(12) = 176 + 24 = 200 \(cm^{2}\)