If students get their assignments done on time there is an 80% chance of earning a good grade in the class. If the assignments are finished during class or late then there is only a 30% chance of earning a good grade in the class. If the assignments are not done at all then there is only a 5% chance of earning a good grade in the class. In a certain class, 50% of the students have the assignments completed on time, 40% finish during class, and 10% do not do their assignments. If a student from this class is selected at random, what is the probability that student has a good grade?

The rate of change of y with respect to x is approximately 0.475

To compute dy/dx, we need to take the partial derivative of P with respect to x and y and then evaluate it at the given values of x and y.

Taking the partial derivative of P with respect to x:

∂P/∂x = \(0.6x^{-0.4} y^{0.4\)

The partial derivative of P with respect to y:

∂P/∂y = \(0.4x^{0.6} y^{-0.6\)

Now, substituting x=100 and y=120,000, we get:

∂P/∂x = \(0.6(100)^{(-0.4)} (120,000)^{0.4\)

≈ 82.41

∂P/∂y = \(0.4(100)^{0.6} (120,000)^{(-0.6)\)

≈ 39.22

dy/dx when x=100 and y=120,000 is approximately:

dy/dx = (∂P/∂y)/(∂P/∂x)

≈ 39.22/82.41

≈ 0.475

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Answer:

1. B (40)

2. A (3 times a number)

3. 2x+1

Step-by-step explanation:

1. (3(5) +5) x 2

(15+5) x 2

20 x 2

40

Answer:

1. B. 40

2. A. 3 times the number

3. 2x + 1

Step-by-step explanation:

1.

2(3n + 5)

2(3(5) + 5)

2(15 + 5)

2(20)

40

2.

3(x)

- not adding or dividing or subtraction, and its not to the power of anything

3.

Rule is 2x + 1

2(1) + 1 = 3

2(2) + 1 = 5

2(3) + 1 = 7

2(4) + 1 = 9

(a) The number 72% is a D. statistic.

(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.

It is related to statistics and parameters.

(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.

A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.

(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.

A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.

In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.

The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.

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In (4, 1) 4 represents x, and 1 represents y

y = 3x + 1

1 = 3(4)+1

1 = 12 + 1

1 ≠ 13   ← sides are not equal so (4, 1) is not a solution to y=3x+1

Hiiiii.

How are you?

I like to be Friends.

We would expect the spinner to land on 2 approximately 20 times in 50 spins.

Let's denote the probability of landing on 2 as P(2) and the probability of landing on 3 as P(3).

Since the spinner is biased and lands on 2 twice as often as it lands on 3, we can write the relation as:

P(2) = 2 * P(3)

Now we know that the sum of the probabilities of all four numbers should be equal to 1. We already have the relative frequencies for numbers 1 and 4:

P(1) = 0.1

P(4) = 0.3

So, the sum of probabilities for numbers 2 and 3 is:

P(2) + P(3) = 1 - P(1) - P(4) = 1 - 0.1 - 0.3 = 0.6

Now, we can rewrite the relation between P(2) and P(3) as:

P(3) = P(2) / 2

Substitute P(3) into the sum equation:

P(2) + P(2) / 2 = 0.6

Multiply both sides by 2 to get rid of the fraction:

2 * P(2) + P(2) = 1.2

Combine like terms:

3 * P(2) = 1.2

Now, solve for P(2):

P(2) = 1.2 / 3

P(2) = 0.4

Now that we have the probability of the spinner landing on 2, we can find out how many times we would expect it to land on 2 in 50 spins:

So, we would expect the spinner to land on 2 approximately 20 times in 50 spins.

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Answer:

5

Step-by-step explanation:

Answer:

\( \boxed{0.76} \: is \: correct.\)

Step-by-step explanation:

\( let \: the \: unknown \: ounce \: be \to \: u_{kn}\\ if \: 1 \: ounce \: is = 23.8 \: grams \\ then \to \: u_{kn} = \frac{18 \: grams \times 1 \: ounce}{23.8 \: grams } \\ u_{kn} = \frac{18}{23.8} (1 \: ounce \:) = 0.756302521 \times 1 \: ounce \\ \boxed{u_{kn} = 0.756302521 \: ounce }\)

♨Rage♨

Answer:

the solution points for the system of equations are (3, 25) and (-7/2, -7).

Step-by-step explanation:

We can solve this system of equations using substitution or elimination. Here, we will use the substitution method:

Substitute y = 2x^2 + 5x - 10 into the second equation:

4x - (2x^2 + 5x - 10) = -11

Simplifying the left side of the equation:

4x - 2x^2 - 5x + 10 = -11

Rearranging the terms:

2x^2 - x + 21 = 0

Using the quadratic formula:

x = (-(-1) ± sqrt((-1)^2 - 4(2)(21))) / 2(2)

x = (1 ± sqrt(169)) / 4

x = (1 ± 13) / 4

Simplifying:

x = 3 or x = -7/2

Now, substitute each value of x back into one of the original equations to find the corresponding value(s) of y:

For x = 3:

y = 2(3)^2 + 5(3) - 10 = 25

So one solution point is (3, 25).

For x = -7/2:

y = 4(-7/2) + 11 = -7

So the other solution point is (-7/2, -7).

Therefore, the solution points for the system of equations are (3, 25) and (-7/2, -7).

Using Normal distribution,

Z-test statistic value for given sample is 1.92..

and there is no evidence to support the rejection of the null hypothesis at 1% significance level.

The Z-test is a statistical test performed on approximately normally distributed data..

We have given that

Sample mean (X) = 144

Standard deviations (σ) = 28

Sample size (n) = 80

population mean (μ) = 150

we want to calculate z statistic value for the provided data .

using formula, z = (X- μ)/σ/√n

z = (-150 +144)/28/√80 = 6/28/2√20

= - 1.9166 ~ - 1.92

Now we were asked that it gives us enough evidence to reject the null hypothesis. So we checking to look what the critical value is for rejecting. No hypothesis at alpha equals 0.01, so that would be the value such that the area under the curve right here is 0.01, and if we look up the z table and find out z critical value for alpha = 0.02 is - 2.32.. The negative 1.92 is not passing that threshold, which means that, since it is not less than the significance level z value negative 1.92 is not less than the negative 2.32, which is a significance, level z, value. So, we can't reject the null hypothesis.

Hence, the Z-test statistic value is -1.92 and no evidence to support the rejection of null hypothesis.

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Complete question

Consider the following hypotheses: H0: μ ≥ 150 HA: μ < 150 a sample of 80 observatoins results in a sample mean of 144. the population standard deviation is known to be 28.

calculate the value of the test statistic. does the above sample evidence enable us to reject the null hypothesis at 1% significance level?

The type of graph that groups data values into classes is a histogram.

A histogram is used to represent data graphically. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class. The frequency is usually on the vertical axis while the class is usually on the horizontal axis. The class is a group assigned to numbers that are similar.

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Answer:

You only have to sort (numbers with numbers and variables with variables) then do the operations (+/-).

Step-by-step explanation:

\(5 + 9f - 10 + 5 \\ - 5 + 9f + 5 \\ 0 + 9f \\ 9f\)

Answer:

A. Sample space = 6

B. 0.17

C. No

D. Yes

Step-by-step explanation:

A. The sample space of an experiment is the set of all possible outcomes of that experiment.

since there are three colours and 2 outcomes for a coin toss,

sample space = 3 * 2 = 6

B. Probability of picking a green first = 4/12 = 1/3

probability of a tail = 1/2

Probability of a green and a tail, P(A) = 1/3 * 1/2 = 0.17

C. No.

Considering the two events;

A; green card is picked first

C ; a green or red card is picked

There is an intersection point for the two events.  Therefore, they are not mutually exclusive.

D. Yes.

Considering the two events;

A; green card is picked first

B ; a blue or red card is picked

There is no intersection point for the two events. Therefore, they are mutually exclusive.

Answer:

square is a geometrical figure have all side equal .

The equation for the cartesian form of representation of a plane is given by ax + by + cz = d.

The cartesian form is a mathematical model which is used for the graphical representation of either a point, line, or plane in a two-dimensional (2D) or three-dimensional (3D) plane.

Mathematically, the cartesian form of representation of a plane is given by this equation:

ax + by + cz = d.

Where:

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Answer:

11 weeks

Step-by-step explanation:

340 - 120 = 220

220/20=11

The type of sampling being used when 5% of the registered voters from each county in a state are drawn at random separately is a stratified sampling.

Stratified sampling is the type of probability sampling that is used when the population being sampled has different groups or strata with varying characteristics. A sample is then drawn from each group to make sure that each stratum or group is represented.The samples can be of equal sizes or can be proportionate to the size of the group. The idea behind stratified sampling is to increase the representativeness of the sample by reducing the variability of the data obtained from the sample.

The advantages of using stratified sampling are that it reduces the variability of the data obtained and ensures that every group or stratum is represented. It also makes it possible to identify any differences between the groups and analyze them independently of the others.In summary, when 5% of the registered voters from each county in a state are drawn at random separately, it is an example of a stratified sampling.

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Answer:

42

Step-by-step explanation:

3x + 12 + x = 180

4x  + 12 = 180

4x = 168

x = 42

Answer:

216 students played i struments

B 216

1080×20%=216

F'(8) = 450 and G²(8) = 202,500.

To find F'(8) and G²(8), we need to apply the chain rule and use the given information about f(x). Let's start with F(x) = f(f(z)). Since F(x) is composed of nested functions, we can use the chain rule to find its derivative. Applying the chain rule, we have:

F'(x) = f'(f(z)) * f'(z)

Now, we need to find F'(8). From the information given, f'(8) = 15. To find f'(z), we can use f'(5) = 5, since f(5) = 3. Using the chain rule, we can calculate f'(z) as follows:

f'(z) = f'(5) * f'(z)

      = 5 * f'(z)

Since f'(8) = 15, we can substitute these values into the equation for F'(x) to find F'(8):

F'(8) = f'(f(z)) * f'(z)

     = f'(f(8)) * f'(8)

     = f'(3) * 15

     = 5 * 15

     = 75

Thus, F'(8) = 75.

Next, we need to find G²(8). Given that G(x) = F²(x), we can express G²(8) as (F²(8)). Using the chain rule, we can calculate (F²(x))' as follows:

(F²(x))' = 2 * F(x) * F'(x)

Substituting F(x) = f(f(z)) and F'(x) = F'(8) = 75, we can find (F²(8))':

(F²(8))' = 2 * F(8) * F'(8)

        = 2 * f(f(8)) * F'(8)

To find f(f(8)), we can substitute f(8) = -5 into f(x):

f(f(8)) = f(-5)

       = 5(-5)²(1-4(-5))³

       = 5 * 25 * 9

       = 1125

Plugging in the values, we can calculate (F²(8))':

(F²(8))' = 2 * 1125 * 75

        = 2250 * 75

        = 168,750

Finally, to find G²(8), we square (F²(8))':

G²(8) = (F²(8))'²

      = 168,750²

      = 202,500

Therefore, G²(8) = 202,500.

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The type of transformation and scale factor as required are;

16) Rotation

17) Reflection

18) Dilation

19) n = 5

20)P = r = 4

There are different types of transformation as follows;

1) Translation: This type of translation is defined as moving the object in space by keeping its size, shape or orientation constant. In a translation, each point of the shape must be moved in the same direction and for the same distance

2) Dilation: This type of translation expands or contracts the object by keeping its orientation or shape the same. This is also known as resizing.

3) Rotation: This type of transformation has an object about a fixed point without changing its size or shape.

4) Reflection: This type of translation is called reflection because it flips the object across a line by keeping its shape or size constant.

16) This transformation is rotation based on the definitions above.

17) This type of transformation is a reflection as it is like the image was flipped across a line more like a mirror image.

18) This called dilation as the scale factor was adjusted to produce the new image.

19) Scale Factor = 6/3 = 2

Thus;

n = 10/2 = 5

20) Scale factor = 12/9 = 4/3

Thus;

P = r = 3 * 4/3

= 4

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Answer:

n = 4

Step-by-step explanation:

1/2(n + 2) + 4 = 3n - 5

1/2n + 5 = 3n - 5

- 5 | - 5

1/2n = 3n - 10

- 3n | - 3n

-5/2n = -10

* 2 | * 2

-5n = -20

/5 | /5

n = 4

---

Hope this helps!

Answer:

y=5x+19

Step-by-step explanation:

Answer:

A = 32 m²

Step-by-step explanation:

The figure is composed of 2 rectangles, The base one and the vertical one on the right.

The area (A) is the sum of the areas of the 2 rectangles

A = (2 × 6 ) + (2 × 10) = 12 + 20 = 32 m²

Pasos

5

3

​

k+

10

7

​

=

15

11

​

k−

5

2

​

Resta  

15

11

​

k en los dos lados.

5

3

​

k+

10

7

​

−

15

11

​

k=−

5

2

​

Combina  

5

3

​

k y −

15

11

​

k para obtener −

15

2

​

k.

−

15

2

​

k+

10

7

​

=−

5

2

​

Resta  

10

7

​

 en los dos lados.

−

15

2

​

k=−

5

2

​

−

10

7

​

El mínimo común múltiplo de 5 y 10 es 10. Convertir −

5

2

​

 y  

10

7

​

 a fracciones con denominador 10.

−

15

2

​

k=−

10

4

​

−

10

7

​

Como −

10

4

​

 y  

10

7

​

 tienen el mismo denominador, reste sus numeradores para restarlos.

−

15

2

​

k=

10

−4−7

​

Resta 7 de −4 para obtener −11.

−

15

2

​

k=−

10

11

​

Multiplica los dos lados por −

2

15

​

, el recíproco de −

15

2

​

.

k=−

10

11

​

(−

2

15

​

)

Multiplica −

10

11

​

 por −

2

15

​

 (para hacerlo, multiplica el numerador por el numerador y el denominador por el denominador).

k=

10×2

−11(−15)

​

Realiza las multiplicaciones en la fracción  

10×2

−11(−15)

​

.

k=

20

165

​

Reduzca la fracción  

20

165

​

 a su mínima expresión extrayendo y anulando 5.

k=

4

33

​

Answer:

33/4

Step-by-step explanation:

3k/5 +7/10 = 11k/15 - 2/5

11k/15 - 3k/5 = 7/10 +2/5

11k/15 - 9k/15 = 7/10 + 4/10

2k/15 = 11/10

2k = 165/10

2k = 33/2

k = 33/4

For  triangle EFD, the value of x is 24 units.

We know that the side-splitting theorem states that, 'if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.'

For  triangle EFD we can obaserve that GH is parallel to side ED.

By applying the side-splitter theorem to triangle EFD,

⇒ FG/GE = FH/HD

Here, FG = 18 units, GE = 6 units, HD = 8 units

substituting values,

⇒ 18/6 = x/8

⇒ 3 = x/8

⇒ x = 3 × 8

⇒ x = 24 units

Therefore, the value of x is 24 units.

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How many meters is the peak of Orizaba higher than Popocatepetl?

Answer:

Popocatépetl: 5426 m and 17,802 ft

Orizaba: 18,491 meters

Step-by-step explanation:

How long does it take to climb Pico de Orizaba?

about 15 hours

Most ascents of Pico de Orizaba will take about 15 hours from the mountain hut to the summit and back. You will usually wake up and begin climbing by 1 a.m. to reach the summit by 10 a.m. and return to the starting mountain hut by 4 p.m.

How long does it take to climb Popocatépetl?

4 hours

What is Popocatépetl?

Popocatepetl is currently a very active volcano with forested slopes and a large crater. It is the second-highest peak in Mexico, behind Pico de Orizaba (5636 meters/18,491 feet), and is generally considered to be the fifth highest mountain in North American. The name Popocatepetl is Aztec for Smoking Mountain; it is often shortened to Popo. Popo and its neighboring volcano Iztaccihuatl (17,343 ft) dominate the sky east of Amecameca. They are located less than 80 km from Mexico City and are separated from each other by ten miles of high grounds referred to as Paso de Cortes. I had the pleasure of climbing the mountain on December 18, 1992, when the volcano was still considered dormant. This is no longer the case. In the 20th century, Popo had an eruption in 1947, but on December 21, 1994, it awakened from dormancy, spewing gas and ash, which was carried by the wind as far as Puebla, 25 miles east. Surrounding towns were evacuated, and scientists have since been closely monitoring Popo for signs of a possible eruption. Ever since then the mountain has been closed to climbing. In December 2000, the mountain came alive with the biggest eruption in 1200 years and with the biggest display of "fireworks" (lava shot ~400 meters/1300 feet into the air) that has been. 30,000 people were evacuated. The first documented ascent of Popocatepetl was by the Tecuanipas tribe in 1289, but this ascent has been disputed by historians. The first Spanish ascent of the mountain was an expedition led by Diego de Ordaz in 1519. Emperor Montezuma sent ten warriors to climb the mountain sometime between 1502 and 1519. Only two of these warriors survived the climb.

The clinic should hire at least 7 doctors in order to serve 122 patients per day.

To determine how many doctors the clinic should hire in order to serve 122 patients per day, we need to calculate the number of patients each doctor can see within their working hours.

Let's start by calculating the total number of minutes each doctor works per day. Since each doctor works 8 hours per day and there are 60 minutes in an hour, the total minutes worked by a doctor per day would be 8 hours × 60 minutes = 480 minutes.

Next, we need to find out how many patients a doctor can see within their working hours. Given that each patient requires an average of 27 minutes with a doctor, the number of patients a doctor can see per day would be 480 minutes ÷ 27 minutes per patient = 17.7778 patients.

Since we can't have a fractional number of patients, we need to round this number up to the nearest whole number to ensure that each patient gets the required attention. Therefore, each doctor can see approximately 18 patients per day.

To serve 122 patients per day, we divide the total number of patients by the number of patients each doctor can see per day: 122 patients ÷ 18 patients per doctor = 6.7778 doctors.

Again, we can't have a fractional number of doctors, so we need to round this number up to the nearest whole number. Therefore, the clinic should hire at least 7 doctors to serve 122 patients per day.

In summary, the clinic should hire at least 7 doctors in order to serve 122 patients per day.

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Answer:

The numbers are 16 and 25

Answer:

x + 2y = -8

Step-by-step explanation:

In the standard form you want the x and the y on one side of the equation. So, lets add 1/2x to both sides. We then get 1/2x + y = -4. However, we want the x coefficient to be an integer. So, lets multiply the entire equation by 2, and we get x + 2y = -8, and that is our answer.

Answer:

y = 150x

Step-by-step explanation:

If y = savings and they save $150 each month then you can just multiply $150 by each month to get the total savings

Answer:

7.55 miles

Step-by-step explanation:

Given that :

Distance of descent = 1.5 miles

New elevation point after descent = 6.05 miles

The initial elevation of the plane before descent will be :

New elevation point after descent + Distance of descent

(6.05 miles + 1.5 miles)

= 7.55 miles