MATHEMATICS
HIGH SCHOOL

B) (x + 4)2 + (y - 9)2 = 102

C) (x + 4)2 + (y + 9)2 = 1002

D) (x - 4)2 + (y - 9)2 = 1002

Answer: The circle of radius r centered at (h, k) has equation

.. (x -h)^2 +(y -k)^2 = r^2

Selection A is appropriate.

_____

It would be helpful if you would use appropriate math symbols. 102 is very different from 10^2. (Copying and pasting does not work--editing is needed.)

.. (x -h)^2 +(y -k)^2 = r^2

Selection A is appropriate.

_____

It would be helpful if you would use appropriate math symbols. 102 is very different from 10^2. (Copying and pasting does not work--editing is needed.)

COLLEGE

1. Popeye is lifting Olive Oyl off the ground by pulling her upward with a force of 108.1 N. She is pretty thin so she only weighs 10 kg. What is Olive Oyl’s acceleration as a result of this force?

Answer:

1 m/s2

Step-by-step explanation:

Olive Oyl's weight = 10 × 9.81 = 98.1 N

This weight is a force acting downward because it is due to gravity.

Popeye pulls Olive Oyl up with a force of 108.1 N. Both forces act vertically but in opposite directions. Hence their resultant, R, is their difference and is in the direction of the larger force.

R = 108.1 N - 98.1 N = 10 N

This force causes an acceleration, a, on the mass, m, of Popeye.

R = ma

a = R/m = 10 N/10 kg = 1 m/s2

Answer:

1.01 m/s²

Step-by-step explanation:

From Newton's law of motion,

ma = F-W................ Equation 1

Where m = mass of Olive Oyl, a = acceleration, F = Upward force, W = weight of Olive Oyl.

Also,

W = mg .................. Equation 2

Where g = acceleration due to gravity.

Substitute equation 2 into equation 1

ma = F-mg

make a the subject of the equation

a = (F-mg)/m............. Equation 3

Given: F = 108.1 N, m = 10 kg

Constant: g = 9.8 m/s²

Substitute into equation 3

a = [108.1-(10×9.8)]/10

a = (108.1-98)/10

a = 10.1/10

a = 1.01 m/s²

Hence, Olive Oyl's acceleration = 1.01 m/s²

COLLEGE

A researcher plants 22 seedlings. After one month, independent of the other seedlings, each seedling has a probability of 0.08 of being dead, a probability of 0.19 of exhibiting slow growth, a probability of 0.42 of exhibiting medium growth, and a probability of 0.31 of exhibiting strong growth. What is the expected number of seedlings in each of these four categories after one month? Calculate the probability that after one month:(a) Exactly three seedlings are dead, exactly four exhibitslow growth, and exactly six exhibit medium growth.(b) Exactly five seedlings are dead, exactly five exhibitslow growth, and exactly seven exhibit strong growth.(c) No more than two seedlings have died.

Answer:

E(X₁)= 1.76

E(X₂)= 4.18

E(X₃)= 9.24

E(X₄)= 6.82

a. P(X₁=3, X₂=4, X₃=6;0.08,0.19,0.42)= 0.00022

b. P(X₁=5, X₂=5, X₄=7;0.08,0.19,0.31)= 0.000001

c. P(X₁≤2) = 0.7442

Step-by-step explanation:

Hello!

So that you can easily resolve this problem first determine your experiment and it's variables. In this case, you have 22 seedlings (n) planted and observe what happens with the after one month, each seedling independent of the others and has each leads to success for exactly one of four categories with a fixed success probability per category. This is a multinomial experiment so I'll separate them in 4 different variables with the corresponding probability of success for each one of them:

X₁: "The seedling is dead" p₁: 0.08

X₂: "The seedling exhibits slow growth" p₂: 0.19

X₃: "The seedling exhibits medium growth" p₃: 0.42

X₄: "The seedling exhibits strong growth" p₄:0.31

To calculate the expected number for each category (k) you need to use the formula:

E(X

So

E(X₁)= n*p₁ = 22*0.08 = 1.76

E(X₂)= n*p₂ = 22*0.19 = 4.18

E(X₃)= n*p₃ = 22*0.42 = 9.24

E(X₄)= n*p₄ = 22*0.31 = 6.82

Next, to calculate each probability you just use the corresponding probability of success of each category:

Formula: P(X₁, X₂,..., Xk) =

a.

P(X₁=3, X₂=4, X₃=6;0.08,0.19,0.42)= = 0.00022

b.

P(X₁=5, X₂=5, X₄=7;0.08,0.19,0.31)= = 0.000001

c.

P(X₁≤2) = + + = 0.7442

I hope you have a SUPER day!

MIDDLE SCHOOL

A textbook store sold a combined total 402 of psychology and math textbooks in a week. The number of psychology textbooks sold was two times the number of math textbooks sold. How many textbooks of each type were sold?

Answer:

The number of textbooks of each type were sold is 134 math and 268 psychology books.

Step-by-step explanation:

Given:

Total number of math and psychology textbooks sold in a week is 402.

Now, let the number of math textbooks sold be .

And, the number of psychology textbooks be .

According to question:

Dividing both sides by 3 we get:

So, total number of math textbooks were 134 .

And, total number of psychology textbooks were

.

Therefore, the number of textbooks of each type were sold is 134 math and 268 psychology books.

HIGH SCHOOL

A tourist was planning a trip by car for travelling at some constant speed for 2.5 hours. However, he found that if he increases the speed by 20 km/h he can cover the same distance in 30 minutes less time than it was planned. What was the planned speed of the tourist, in km/h?

Answer:

The planned speed of the tourist is 80 km per hour.

Step-by-step explanation:

Let the constant speed of a tourist be v km per hour and distance covered be x km.

Now we will start forming the equations as per the direction given in the question.

Since tourist covers x km with a constant speed of v in 2.5 hours.

So the equation will be speed v = Distance covered (x)÷Time taken(2.5)hours

Therefore v = x÷2.5

⇒ x = 2.5v-------(1)

Now we form the second equation

With a new speed (v+20) = Distance (x)÷Time(2.5-0.5)

Or v+20 = x÷2

⇒ now we multiply 2 on both the sides of this equation

⇒ 2(v+20) = x-------(2)

Now we put the value of x from equation (2) to equation number (1)

⇒ 2(v+20) = 2.5v

⇒ 2v+40 = 2.5v

⇒ 2.5v-2v = 40

⇒ 0.5v = 40

⇒ v = 40÷(0.5) = 80 km/hr

MIDDLE SCHOOL

A quadratic equation is shown below: 9x^2 - 16x + 60 = 0

Part A: Describe the solution(s) to the equation by just determining the radicand. Show your work

Part B: Solve 4x^2 + 8x - 5 = 0 by using an appropriate method. Show the steps of your work, and explain why you choose the method used.

the solutions to a general quadratic equation is

X=-b±√b²-4ac/2a ,, When ax²+bx+c=0

the discriminant is the expression under the radical b²−4ac

Part A:

discriminant is (-16)² - 4(9)(60) = -1904

there are two complex solutions

Part B:

4x² + 8x − 5 = 0

4x² + 10x -2x - 5=0

2x ( 2x + 5) - 1(2 x + 5) =0

(2x + 5)(2x-1) = 0

/ \

/ \

2x+5 = 0 2x-1 =0

x = -5/2 x = 1/2

MIDDLE SCHOOL

Divide. −3/68 Enter your answer as a mixed number, in simplified form, in the box.

Answer:

-3/68

Step-by-step explanation:

This is a fraction. It cannot be changed to a mixed number since it is less than 1 and greater than -1

MIDDLE SCHOOL

(1,5)&(3,12) what’s the slope?

Answer:

7/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

MIDDLE SCHOOL

After dropping 5*F the temperature was 25*F. Create and solve an equation to show the starting temperature. Steps:

1. Variable-

2. Coefficient-

3. Constant-

4. Equation-

Answer:

30°F

Step-by-step explanation:

Let the starting temperature be: x°F

After dropping 5°F, the expression becomes.

The resulting temperature was 25°F

This means:

The variable is x.

The coefficient of the variable is 1.

The constants are -5 and 25

The equation is

We now add 5 to both sides to get:

Therefore the initial temperature is 30°F

COLLEGE

Which statements are true about the ordered pair (−4, 0) and the system of equations? {2x+y=−8x−y=−4 Select each correct answer. (A) The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.

(B) The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.

(C) The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.

(D) The ordered pair (−4, 0) is a solution to the system because it makes both equations true.

Answer:

(D) The ordered pair (−4, 0) is a solution to the system because it makes both equations true.

Step-by-step explanation:

Given:

The system of equations are given as:

Let us solve this system using elimination method.

Addin the two equations, we get:

Now, plug in -4 for in second equation and solve for .

Therefore, the solution to the given system of equations is (-4,0).

This means that the point (-4, 0) satisfies both the equations.

This can be verified as shown below:

Plug in -4 for and 0 for and check whether the left side equals right side or not.

Therefore, the option (D) is correct.