In an introductory psychology class with n = 50 students, there are 9 freshman males, 15 freshman females, 8 sophomore males, 12 sophomore females, and 6 junior females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
a. 8/14
b. 12/20
c. 20/44
d. 20/50

Answer:

0.25

Step-by-step explanation:

Answer:

1/12

Step-by-step explanation:

To solve this expression, we need to remember that division should be done before multiplication or addition/subtraction.

So we first simplify the expression by dividing 1/2 by 6:

1/2 ÷ 6 = 1/2 × 1/6

Next, we multiply the two fractions by multiplying their numerators and denominators:

1/2 × 1/6 = (1 × 1)/(2 × 6) = 1/12

Therefore, the value of the expression 1/2 ÷ 6 is equal to 1/12.

Answer:

x = -5

y = -2

Step-by-step explanation:

-5x + 3y = 19

-5x + 7y = 11

Time the first equation by -1

5x - 3y = -19

-5x + 7y = 11

4y = -8

y = -2

Now put -2 in for y and solve for x

-5x + 3(-2) = 19

-5x - 6 = 19

-5x = 25

x = -5

Let's Check

-5(-5) + 3(-2) = 19

25 - 6 = 19

19 = 19

So, x = -5 and y = -2 is the correct answer.

30% percent of the students passed both Mathematics and English.

A rate, number, or amount in each hundred is known as a percentage

Let's use a Venn diagram to represent the information given in the problem. Let M be the set of students who passed Mathematics, E be the set of students who passed English, and F be the set of students who failed both.

We know that there are 40 students in the class, and 90% passed Mathematics, so the number of students who passed Mathematics is 0.9 × 40 = 36. Similarly, 75% passed English, so the number of students who passed English is 0.75 × 40 = 30.

We also know that 2 students failed both Mathematics and English, so we can label the F section with 2.

where the number in each section represents the number of students who passed the respective exam.

To find the percentage of students who passed both examinations (i.e., the intersection of M and E), we need to add the number of students in the M and E intersection to the F section, then subtract that from the total number of students (40), and finally divide by 40 to get the percentage. That is:

percentage of students who passed both exams = (M ∩ E + F) / 40 × 100%

= (28 + 2) / 40 × 100%

= 30%

Therefore, 30% of the students passed both Mathematics and English.

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The amount of daily daylight is unrelated to levels of depression in older adults. The hypothesis "The amount of daily daylight is unrelated to levels of depression in older adults" is an example of the null hypothesis.

A null hypothesis is a statement that there is no significant difference between two variables or a relationship between them.The null hypothesis assumes that the observed results or changes in the experiment or data are due to random fluctuations or errors in the measurement process. It is the default hypothesis that is typically tested against an alternative hypothesis.

A researcher tries to disprove or reject the null hypothesis by conducting experiments or collecting data to support the alternative hypothesis. If the null hypothesis is rejected, then the alternative hypothesis is accepted as true. However, if the null hypothesis cannot be rejected, then it remains as the plausible explanation for the observations or outcomes in the experiment.

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Answer: 139.4

Step-by-step explanation:

a supplementary angle is equal to 180 so all we have to do is subtract 40.6 from 180

180 - 40.6 = 139.4

There are a total of 27 combinations that give a sum of 10 when rolling three dice.

We have,

The possible outcomes in the sample space for rolling three dice:

S = {(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6),

(1, 2, 1), (1, 2, 2), (1, 2, 3), (1, 2, 4), (1, 2, 5), (1, 2, 6),

(1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6),

(1, 4, 1), (1, 4, 2), (1, 4, 3), (1, 4, 4), (1, 4, 5), (1, 4, 6),

(1, 5, 1), (1, 5, 2), (1, 5, 3), (1, 5, 4), (1, 5, 5), (1, 5, 6),

(1, 6, 1), (1, 6, 2), (1, 6, 3), (1, 6, 4), (1, 6, 5), (1, 6, 6),

(2, 1, 1), (2, 1, 2), (2, 1, 3), (2, 1, 4), (2, 1, 5), (2, 1, 6),

(2, 2, 1), (2, 2, 2), (2, 2, 3), (2, 2, 4), (2, 2, 5), (2, 2, 6),

(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5), (2, 3, 6),

(2, 4, 1), (2, 4, 2), (2, 4, 3), (2, 4, 4), (2, 4, 5), (2, 4, 6),

(2, 5, 1), (2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6),

(2, 6, 1), (2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5), (2, 6, 6),

(3, 1, 1), (3, 1, 2), (3, 1, 3), (3, 1, 4), (3, 1, 5), (3, 1, 6),

(3, 2, 1), (3, 2, 2), (3, 2, 3), (3, 2, 4), (3, 2, 5), (3, 2, 6),

(3, 3, 1), (3, 3, 2), (3, 3, 3), (3, 3, 4), (3, 3, 5), (3, 3, 6),

(3, 4, 1), (3, 4, 2), (3, 4, 3), (3, 4, 4), (3, 4, 5), (3, 4, 6),

(3, 5, 1), (3, 5, 2), (3, 5, 3), (3, 5, 4), (3, 5, 5), (3, 5, 6),

(3, 6, 1), (3, 6, 2), (3, 6, 3), (3, 6, 4), (3, 6, 5), (3, 6, 6),

(4, 1, 1), (4, 1, 2), (4, 1, 3), (4, 1, 4), (4, 1, 5), (4, 1, 6),

(4, 2, 1), (4, 2, 2), (4, 2, 3), (4, 2, 4), (4, 2, 5), (4, 2, 6),

(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6),

(4, 4, 1), (4, 4, 2), (4, 4, 3), (4, 4, 4), (4, 4, 5), (4, 4, 6),

(4, 5, 1), (4, 5, 2), (4, 5, 3), (4, 5, 4), (4, 5, 5), (4, 5, 6),

(4, 6, 1), (4, 6, 2), (4, 6, 3), (4, 6, 4), (4, 6, 5), (4, 6, 6),

(5, 1, 1), (5, 1, 2), (5, 1, 3), (5, 1, 4), (5, 1, 5), (5, 1, 6),

(5, 2, 1), (5, 2, 2), (5, 2, 3), (5, 2, 4), (5, 2, 5), (5, 2, 6),

(5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6),

(5, 4, 1), (5, 4, 2), (5, 4, 3), (5, 4, 4), (5, 4, 5), (5, 4, 6),

(5, 5, 1), (5, 5, 2), (5, 5, 3), (5, 5, 4), (5, 5, 5), (5, 5, 6),

(5, 6, 1), (5, 6, 2), (5, 6, 3), (5, 6, 4), (5, 6, 5), (5, 6, 6),

(6, 1, 1), (6, 1, 2), (6, 1, 3), (6, 1, 4), (6, 1, 5), (6, 1, 6),

(6, 2, 1), (6, 2, 2), (6, 2, 3), (6, 2, 4), (6, 2, 5), (6, 2, 6),

(6, 3, 1), (6, 3, 2), (6, 3, 3), (6, 3, 4), (6, 3, 5), (6, 3, 6),

(6, 4, 1), (6, 4, 2), (6, 4, 3), (6, 4, 4), (6, 4, 5), (6, 4, 6),

(6, 5, 1), (6, 5, 2), (6, 5, 3), (6, 5, 4), (6, 5, 5), (6, 5, 6),

(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)}

Now,

The combination where the sum is 10 is 27.

ie.

{(1, 3, 6), (1, 4, 5), (1, 5, 4), (1, 6, 3), ........, (6, 1, 3), (6, 2, 2,), (6, 3, 1)}

Thus,

There are 27 ways of combination where the sum is 10.

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the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]

What is quadratic equation?

A quadratic equation is a type of polynomial equation of degree two, meaning it contains one or more terms that involve x raised to the power of two (i.e., x²

The equation of a quadratic function is generally given by:

[tex]y = a(x - h)^2 + k[/tex]

where (h, k) is the vertex of the parabola and "a" determines the shape of the parabola.

To move the function to the left by three units, we need to replace "x" with "(x + 3)" inside the parentheses:

[tex]y = a(x + 3 - h)^2 + k[/tex]

To move the function up by four units, we need to add four to the value of "k":

[tex]y = a(x + 3 - h)^2 + (k + 4)[/tex]

To stretch the function by a scale factor of two, we need to multiply "a" by two:

[tex]y = 2a(x + 3 - h)^2 + 2(k + 4)[/tex]

Combining these transformations, we get the final equation:

[tex]y = 2(x + 3 - 0)^2 + (0 + 4)[/tex]

[tex]y = 2(x + 3)^2 + 4[/tex]

Therefore, the equation of the quadratic function that is moved to the left three, up four, and stretched by a scale factor of two is [tex]y = 2(x + 3)^2 + 4.[/tex]

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Answer:

1034 x 10⁷

Step-by-step explanation:

the seven just means to multiply by 10 seven times

Let me know if this helps.

Answer:

Step-by-step explanation:

9m = 7m + 4

9m - 7m = 4

2m = 4

m = 2

----------------------------------

check

9 x 2 = 7 x 2 + 4

18 = 18

this answer is good

n + 6 = 2n - 1

n + 7 = 2n

7 = n

-----------------------------------

7 + 6 = 2 x 7 - 1

13 = 13

this answer is good

Answer:

answer will be my albert enistein calculation is 4500000⁹7765⁵44³=6425786

The equation [tex]x^2-4x+y^2=0[/tex] can be rewritten as [tex]x^2-4x+4+y^2=4[/tex], which is equivalent to [tex](x-2)^2 + y^2 = 2^2[/tex]. This is the equation of a circle centered at (2,0) with a radius of 2.

To graph this equation, you could plot the center point (2,0) and then draw a circle with a radius of 2 around that point. Alternatively, you could find a few points on the circle by plugging in values for x and solving for y (or vice versa), and then plot those points to sketch the circle.

If Rose found the correct equation but incorrectly graphed it, she could try using the correct center point and radius to sketch the circle more accurately. Alternatively, she could check her work to see where she made a mistake in graphing the equation.

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Answer:

To determine which test Elena got a higher ratio of correctly spelled words to total words, we need to calculate the ratio of correctly spelled words to total words for each test and compare them.

For last week's test, the ratio of correctly spelled words to total words is:

16/20 = 0.8

For this week's test, the ratio of correctly spelled words to total words is:

13/15 ≈ 0.867

Since 0.867 is greater than 0.8, Elena got a higher ratio of correctly spelled words to total words on this week's test. Therefore, the new studying method appears to be working better for Elena. However, it is important to note that a single comparison is not sufficient to draw a definitive conclusion about the effectiveness of the studying method, and it would be beneficial for Elena to continue tracking her performance over a longer period of time.

The discount percentage is different, the amount that Lisa pays will also be different.

The act of estimating the present value of a future payment or series of cash flows that will be received in the future is referred to as discounting. A discount rate (also known as a discount yield) is the rate at which future cash flows are discounted back to their present value.

We need to know what percentage of the regular ticket price Lisa saves with her railcard. We cannot calculate the exact amount Lisa pays for the ticket without this information.

Assuming Lisa receives a 1/3 discount with her railcard, we can calculate the cost of her ticket as follows:

Discounted price = Regular price minus discount amount

Normal price x Discount percentage = Discount amount

Discount rate = 1/3 = 33.33% (rounded to two decimal places)

Discount amount = £24.90 multiplied by 33.33% = £8.30 (rounded to two decimal places)

Price after discount = £24.90 - £8.30 = £16.60 (rounded to two decimal places)

As a result, if Lisa receives a 1/3 discount with her railcard, she will pay£16.60 for the ticket. However, if the discount percentage is different, Lisa's payment will be different as well.

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Lisa uses her railcard to buy a ticket.

She gets off the normal price of the ticket.

The normal price of the ticket is £24.90

Work out how much Lisa pays for the ticket.

Answer:

y = -3(x - 2)^2 + 1. Explanation: x-coordinate of vertex: x = -b/(2a) = -12/-6 = 2 y-coordintae of vertex: y(2) = -12 + 24 - 11 = 1

Step-by-step explanation:

Answer:x-coordinate of vertex:

x = -b/(2a) = -12/-6 = 2

y-coordinate of vertex:

y(2) = -12 + 24 - 11 = 1

Vertex form:

y = -3(x - 2)^2 + 1

Check.

Develop y to get back to standard form:

y = -3(x^2 - 4x + 4) + 1 = -3x^2 + 12x - 11.

Step-by-step explanation:

The volume of the rectangular box is given by using the Lagrangian multiplier theorem is 172.435 cubic units.

It states that any local maxima or any local minima of the function are calculated under the equality constraints.

The equation of ellipsoid is given as,

[tex]\frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} =1[/tex]

Let the edges of the required rectangular box be x, y, and z.

Then, the volume of the box in the first quadrant is V = xyz

Then we have,

[tex]\phi(x,y,z) = \frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} -1[/tex]  

By the Lagrange multiplier,

[tex](V_x,V_y,V_z) = \lambda (\phi_x, \phi_y,\phi_z)\\\\(yz,xz,xy)=\lambda(\frac{2x}{4},\frac{2y}{64},\frac{2z}{49} )\\\\xyz = \lambda\frac{x^2}{2},xyz =\lambda\frac{y^2}{32} ,xyz=\lambda\frac{2z^2}{49} \\\\x^2 = 2k, y^2=32k,z^2=49k/2[/tex]

Solving for k we have the value of k as k = 2/3.

Put k=2/3 in equation 2, we have

x² = 2*2/3 , y² = 32*2/3, z² = 49/2*2/3

x =±2/√3 , y= ±8/√3 , z = ±7/√3

Then the volume of the rectangular box will be

Volume  = [tex]\frac{2}{\sqrt{3} } \frac{8}{\sqrt{3} } \frac{7}{\sqrt{3} }[/tex]

Volume  = 172.435 cubic units.

Therefore, the value of  volume of the rectangular box is  172.435 cubic units.

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Answer:

AC<BC = 30+60=90 < 60+90= 150

Step-by-step explanation:

AC>AB 30+90= 120 > 30+60=90
AC<BC 30+60=90 < 60+90= 150

The feature vector that generates the kernel K(x, x) = (x) - (x') is given by (x) = [x1, x2 + x3].

The formula for kernel is K(x, y) = φ(x) · φ(y) and the dot product of two vectors is defined as (x) · (y) = x^Ty where x^T denotes the transpose of x.

Therefore, we can expand the given kernel to: K(x, x') = φ(x) · φ(x')= [x1, x2 + x3] · [x1, x2 + x3]'= [x1, x2 + x3] · [x1, x2 + x3]= x1x1 + (x2 + x3)(x2 + x3) The correct option is (x) = [x1, x2 + x3]

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Answer:

C. 15m^3-6m=3m(5m^2 -6m) is true.

D. 6m^2+18m=6m^2(1+3m) is true.

A. 40m^6 -4=4(10m^6-1) is not true.

B. 32m^4 +12m^3 =4m^3(8m +3) is not true.

Answer:

C. 15m^3-6m=3m(5m^2 -6m) is true.

D. 6m^2+18m=6m^2(1+3m) is true.

Step-by-step explanation:

The amplitude of the model is 3.0 meters.

The amplitude of a harmonic oscillator represents the maximum displacement from the equilibrium position. In the case of tidal oscillations, the equilibrium position is the average water level.

The amplitude of the model can be determined by considering the difference between the high and low tide water depths, which represents the maximum displacement of the water from the average level. Dividing this difference by two gives us the amplitude of the model.

The amplitude of the model can be found using the formula:

Xm = (H - L)/2

where H is the high tide water depth, L is the low tide water depth, and Xm is the amplitude of the model.

Substituting the given values, we get:

Xm = (9.0 - 3.0)/2

Xm = 3.0 meters

Therefore, the amplitude of the model is 3.0 meters.

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Answer:

104.7% to the nearest tenth.

Step-by-step explanation:

Multiply the fraction by 100:

= (45 x 100) / 43

= 104.651.

Confidence in math is the belief in one's ability to understand and solve mathematical problems. Developing confidence in math is important because it can help individuals overcome anxiety and fear of math, which can limit their performance and success in the subject.

1) {Bread} -> {Milk}:
Support: 5/10
Confidence: 5/7
Lift: 5/2.4

2) {Beer} -> {Eggs}:
Support: 4/10
Confidence: 4/9
Lift: 4/3

3) {Beer, Bread} -> {Milk}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8

4) {Bread, Eggs} -> {Diapers}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6

5) {Milk, Bread} -> {Eggs, Coke}:
Support: 4/10
Confidence: 4/7
Lift: 4/2.6

6) {Beer, Milk} -> {Bread, Diapers}:
Support: 3/10
Confidence: 3/6
Lift: 3/1.8

7) {Bread, Milk, Eggs} -> {Diapers}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2

8) {Bread, Eggs, Coke} -> {Diapers, Beer}:
Support: 2/10
Confidence: 2/5
Lift: 2/2.2

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Based on the image given, the height of the parallelogram can be expressed as 2 units.

Parallelograms are two-dimensional figures that include four sides as rectangles. However, in parallelograms, the opposite sides are parallel and the vertical or horizontal sides are diagonal. Due to this, the height in a parallelogram can be determined by measuring the distance between the top and bottom lines. Based on this principle, the height of the parallelogram would be 2.

Note: Below I attach the missing image in this question:

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Answer: the angle opposite the side length 9 is 74.62 degrees I think .

Step-by-step explanation:

The given function is cos(α+20°) and its cofunction can be expressed as cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).

Therefore cos(α+20°) in terms of its cofunctions, we need to use the formulas for sin and cos of complementary angles.

The complementary angle of 20° is 70° because 20° + 70° = 90°.

So, we can rewrite cos(20°) as sin(70°) and sin(20°) as cos(70°).

Using the formula for the cosine of the sum of two angles, we can then substitute these values to get:

cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°)

Therefore, expression of cos(α+20°) in terms of its cofunctions is cos(α+20°) = cos(α)sin(70°) - sin(α)cos(70°).

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The area of 5feet 12feet and 13feet, 30 square feet

the formula 4(bxh) is used to calculate the area of a rectangle, not a triangle. However, the dimensions 5 feet, 12 feet, and 13 feet are actually the sides of a right triangle (known as a Pythagorean triple), so we can use the formula for the area of a right triangle:

Area = 1/2 x base x height

where the base and height are the two legs of the right triangle.

Using the Pythagorean theorem, we can determine that the legs of the triangle are 5 feet and 12 feet, and the hypotenuse is 13 feet. Therefore, the area of the triangle is:

Area = 1/2 x 5 feet x 12 feet

Area = 30 square feet

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Answer:

x = [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

[tex]\frac{x+1}{3}[/tex] - [tex]\frac{x-1}{2}[/tex] = [tex]\frac{1+2x}{3}[/tex]

multiply through by 6 ( the LCM of 2 and 3 ) to clear the fractions

2(x + 1) - 3(x - 1) = 2(1 + 2x) ← distribute parenthesis on both sides

2x + 2 - 3x + 3 = 2 + 4x

- x + 5 = 2 + 4x ( subtract 4x from both sides )

- 5x + 5 = 2 ( subtract 5 from both sides )

- 5x = - 3 ( divide both sides by - 5 )

x = [tex]\frac{-3}{-5}[/tex] = [tex]\frac{3}{5}[/tex]

Answer:

x = -2 ,  y = 2

Step-by-step explanation:

hope this helps :)

The correct statement regarding where the graph of h(x) = x³ has positive signal is given as follows:

x > 0.

The graph of a function is positive in the regions where the function values are greater than zero, and negative in the regions where the function values are less than zero.

The comparisons to zero are given as follows:

Hence, considering the function defined by the rule y = x³, the graph of the function is classified as positive or negative as follows:

The function is h(x) = x³, and it's graph is given by the image presented at the end of the answer.

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