Joe borrowed $3,000 from the bank at a rate of 7% simple interest per year. How much interest did he pay in 6 years?

Answer:

a) 0.0031 = 0.31% probability of marking exactly 3 incorrect answers.

b) 0.0035 = 0.35% probability of passing.

Step-by-step explanation:

For each question, there are only two possible outcomes. Either the student chooses the correct answer, or he does not. Questions are independent of each other. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

In which \(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by the following formula.

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

And p is the probability of X happening.

10 multiple choice questions

This means that \(n = 10\)

4 answers that are equally likely to be the correct one. The quiz taker selects the answers randomly.

This means that \(p = \frac{1}{4} = 0.25\)

a) Probability of marking exactly 3 incorrect answers.

3 incorrectly = 7 correctly, so this is P(X = 7).

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031\)

0.0031 = 0.31% probability of marking exactly 3 incorrect answers.

b) Probability of passing

At least 7 correct, so

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)\)

\(P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}\)

\(P(X = 7) = C_{10,7}.(0.25)^{7}.(0.75)^{3} = 0.0031\)

\(P(X = 8) = C_{10,8}.(0.25)^{8}.(0.75)^{2} = 0.0004\)

\(P(X = 9) = C_{10,9}.(0.25)^{9}.(0.75)^{1} \approx 0\)

\(P(X = 10) = C_{10,10}.(0.25)^{10}.(0.75)^{0} \approx 0\)

\(P(X \geq 7) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0031 + 0.0004 + 0 + 0 = 0.0035\)

0.0035 = 0.35% probability of passing.

The equation that represent the number of penguins is (6 ×  4) + (3 × 6) + (3 × 6) = p.

A building has 6 homes per floor and 3 floors. On the first floor, there are 4 penguins per home. On the second and third floor, there are 3 penguins per home.

Therefore, the equation that can be used to find the total number of penguins living in the building is as follows:

Hence,

(6 ×  4) + (3 × 6) + (3 × 6) = p

where

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The expression that models the number of people attending concert 1 is given as follows:

512/6.

The number of people attending concert 1 is obtained applying the proportions in the context of the problem.

From the bar model, the fractions corresponding to each concert are given as follows:

The total number of people is given as follows:

512.

Hence the expression that models the number of people attending concert 1 is given as follows:

512/6.

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According to the Dietary Guidelines for American 2015, you should limit your fat intake to 25% - 35% of your total calories. The correct option is B.

Food-based dietary guidelines also known as dietary guidelines are intended to serve as a foundation for public food and nutrition policies, health and agricultural policies, and nutrition education programs aimed at promoting healthy eating habits and lifestyles.

Calories are the units of energy released by your body when it digests and absorbs food. The higher the calorie content of a food, the more energy it can provide to your body. When you consume more calories than you require, your body stores the excess calories as fat. Even fat-free foods can be high in calories. In this case, the fay should not be more than 35%.

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None of these options seem to be correct. You can check each result by differentiation:

\((e^x\sec^2x)'=e^x(\sec^2x+2\sec^2\tan x)=e^x\sec^2x(1+\tan x)\)

\((e^x\sec x)'=e^x(\sec x+\sec x\tan x)=e^x\sec x(1+\tan x)\)

\((e^x\tan^2x)'=e^x(\tan^2x+2\tan x\sec^2x)=e^x\tan x(\tan x+2\sec^2x)\)

\((e^x\tan x)'=e^x(\tan x+\sec^2x)\)

But none of these are equivalent to \(e^x(\sec x+\tan^2x)\)...

Answer:

A

Step-by-step explanation:

Answer:

m= -1

y intercept= 1

y= - x + 1

Step-by-step explanation:

Answer:

alternate interior angles

Step-by-step explanation:

Answer:

alternate interior angles

Answer:

17/30

Explanation:

m a t h

PS:

Can I have brainliest?

ANSWER:

4

___

15

STEP BY STEP:

Answer:

The length of CD is 6

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

Answer:

6 units.

Step-by-step explanation:

Got it correct on khan academy:

Answer: 70 cats

Step-by-step explanation:

add 2+7 = 9
90/9 = 10
multiply 2x10 = 20 dogs
10x7= 70 cats.

The intersection of sets M and F contains the elements "c" and "d".

To find the intersection of sets M and F, we need to identify the elements that are common to both sets.

M = {a, b, c, d}

F = {c, d, e, f}

The intersection of M

and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.

Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".

Therefore, the intersection of M and F can be expressed as:

M ∩ F = {c, d}

So, the intersection of sets M and F contains the elements "c" and "d".

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Answer:

the factor is 3/1

Step-by-step explanation:

2.5 goes into 7 3 times.

duh lol

Answer:

Step-by-step explanation:

Let the number of minutes in 6.1 hours be x. Remember that there are 60 minutes in one hour. Therefore,

If 60 minutes = 1 hour,

Then

x minutes = 6.1 hours

Cross multiplying, it becomes

x × 1 = 6.1 × 60 minutes

x = 6.1 × 60 minutes/1

Therefore, the correct ratio with which 6.1 hours would be multiplied is

60 minutes/1 hour

Answer: one hour/ sixty minutes

Step-by-step explanation: Just took the quiz

Answer:

Graph is attached below

Step-by-step explanation:

You first need to plot any two points on the coordinate plane(you can also do more than two points to make it more accurate). Then, using a ruler connect the points and extend the line outwards.

The plotted straight line is as shown in below graph.

Given straight line equation is y = x + 2

To plot a straight line, take two different values of x which output different values of y. Then plot those points in the graph.

After plotting those two points, you connect both dots with straight line and extend that line infinitely from both endpoints.

Example, take x = 1 and x = 2 for straight line y = x + 2

Then we get:

For x = 1, y = 1 + 2 = 3

For x = 2, y = 2 + 2 = 4

The plot of points (1,3) and (2,4) and the straight line y = x + 2 is shown below.

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Answer:

85+75+160=v

Step-by-step explanation:

correct answer

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

In other words, the collection of all feasible values for the parameters that satisfy the specified mathematical equation is the convenient storage of the bunch of equations.

The equations are given below.

6x = 52 - 2y

6x + 2y = 52

3x + y = 26                   ...1

5x + 7y = 70

(5/7)x + y = 10              ...2

Subtraction equation 2 from equation 1, then we have

3x - (5/7)x = 26 - 10

(16/7)x = 16

x = 7

Then the value of 'y' is given as,

3(7) + y = 26

21 + y = 26

y = 5

The solution of the equations 6x = 52 − 2y and 5x + 7y = 70 by elimination method will be (7, 5).

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The composition of transformation shown in the image attached is

In mathematics, a transformation refers to a change in the position, size, shape, or orientation of a geometric figure or mathematical function. Geometric transformations can be applied to shapes, such as

In the figure the first transformation is rotation about the origin 90 degrees clockwise

The second transformation, is reflection across the x axis

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slope-intercept equation:

y=mx+b

Where:

m= slope

b= y-intercept

Parallel lines have the same slope, so:

2x+y=5

y= -2x+5

m=-2

We have so far:

y=-2x+b

Replace x,y by the coordinates of the point given (-3,14) and solve for b:

14= -2(-3)+b

14 = 6+b

14-6=b

8=b

Final equation:

y= -2x+8

Answer:

The probability that there will be

(a) at least 2 such accidents in the next month?

= 0.864

(b) at most 1 accident in the next month?

= 0.136

Step-by-step explanation:

This is a Poisson Distribution question.

The formula is given as:

For X = x ,

= λ^x × e^-λ/x!

The monthly worldwide average number of air- plane crashes of commercial airlines is 3.5. What is the probability that there will be

(a) at least 2 such accidents in the next month?

= λ^x × e^-λ/x!

λ = 3.5

x = at least 2 such accidents

x ≥ 2

= 1 - [P(x = 0) + P(x = 1)]

= 1 - [(3.5^0 × e^-3.5/0!)+ (3.5^1 × e^-3.5/1!)]

= 1 - [ 1 × 0.0301973834 + 3.5 × 0.0301973834]

1 - [ 0.0301973834+ 0.105690842]

= 0.8641117746

≈ 0.864

(b) at most 1 accident in the next month?

= λ^x × e^-λ/x!

λ = 3.5

x = at most 1 such accidents

x ≤ 1

= [P(x = 0) + P(x = 1)]

= [(3.5^0 × e^-3.5/0!)+ (3.5^1 × e^-3.5/1!)]

= [ (1 × 0.0301973834) + (3.5 × 0.0301973834)]

[ 0.0301973834+ 0.105690842]

= 0.1358882254

≈ 0.136

The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

To solve this problem, we can use the concept of radioactive decay and the decay factor. Here's how we can calculate the required volume to correct the dose:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = Initial activity * Decay factor

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = Initial activity - 20 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = Remaining activity * Decay factor

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = Desired activity at 9:30 / Remaining activity at 9:30 * Volume at 9:30

Calculate the remaining volume at 9:30:

Remaining volume = Volume at 8 am - Volume withdrawn - Volume accidentally discharged

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume

Let's perform the calculations step by step:

Determine the initial activity of the kit:

Initial activity = 180 mCi

Calculate the decayed activity at 9:30 (after 1.5 hours):

Decay factor = 0.841

Decay activity = 180 mCi * 0.841 = 151.38 mCi

Calculate the remaining activity after withdrawing 20 mCi at 8 am:

Remaining activity = 180 mCi - 20 mCi = 160 mCi

Calculate the remaining activity at 9:30:

Remaining activity at 9:30 = 160 mCi * 0.841 = 134.56 mCi

Calculate the desired activity at 9:30 (20 mCi):

Desired activity at 9:30 = 20 mCi

Calculate the volume needed to achieve the desired activity:

Volume needed = (Desired activity at 9:30 / Remaining activity at 9:30) * Volume at 9:30

Volume at 9:30 = Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Volume needed = (20 mCi / 134.56 mCi) * 15 ml = 2.236 ml

Calculate the remaining volume at 9:30:

Remaining volume = 30 ml - (30 ml / 2) = 15 ml

Calculate the volume that needs to be added:

Volume to be added = Volume needed - Remaining volume = 2.236 ml - 15 ml = -12.764 ml

Since the calculated volume to be added is negative, it means that no additional volume is required. The remaining Kit volume in the syringe is sufficient to correct the dose to 20 mCi.

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Answer:

-2*-3*-2 =-12

then add the t or use it before

-12t

Answer:

I think it is 30 inches

Step-by-step explanation:

Answer: C

Step-by-step explanation: on edge 2023

Answer:

(2,-1)

Step-by-step explanation:

We can use substitution to solve this system of equations. Since x is already solved for in the second equation, we can substitute 2y + 4 for x in the first equation:

4(2y + 4) + 2y = 6

Simplifying the left side:

8y + 16 + 2y = 6

Combining like terms:

10y + 16 = 6

Subtracting 16 from both sides:

10y = -10

Dividing both sides by 10:

y = -1

Now that we know y, we can use the second equation to find x:

x = 2y + 4

x = 2(-1) + 4

x = 2

Therefore, the solution to the system of equations is (x, y) = (2, -1).

The correct answer choice is (2, -1).

Answer:

P( 44 < X < 56 ) =  0.12

Step-by-step explanation:

Number of seconds one gets to solve the puzzle ( X )

E( X ) = 100 + 0 ) / 2 = 50

Var ( X ) = 833.3333

бx = √833.3333  =  28.868

Determine The approximate probability

P( 44 < X < 56 ) = Δ time given / number of players selected

P( 44 < X < 56 ) = (56 - 44) / 100

                          = 12 / 100 = 0.12

Answer:

use a ruler to answer the question

Angles in a triangle add up to 180 degrees

The value of x is 85 degrees

A triangle is a polygon which has  three sides and three vertices. It is one of the normal shapes in geometry. A triangle with vertices A, B, and C has three sides & three angles A, B, C.

here, we have,

How to determine the value of x

The total  sum of angles for a triangle is 180 degrees.

So, we have:

x + 35 + 60 = 180

Evaluate the sum

x + 95= 180

Subtract 95 from both sides

x = 85

Hence, the value of x is 85 degrees

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Full question: (SAT Prep) Find the value of x. 35° 60° X

x=?​