(4√3+ 7√5) – (2√3 +3√5)

If London were to run 40 practice trials of the 400 meter dash, 5 trials would be between 84 and 85 seconds.

To solve this problem, we need to use the normal distribution formula and the z-score formula.

First, we need to calculate the z-scores for 84 and 85 seconds:

z₁ = (84 - 83) / 1 = 1

z₂ = (85 - 83) / 1 = 2

Next, we need to look up the area under the standard normal distribution curve between these two z-scores. We can do this using a standard normal distribution table.

we can find the area between these two z-scores by subtracting the area to the left of z₁ from the area to the left of z₂:

area = P(z₁ < Z < z₂) = P(Z < z₂) - P(Z < z₁)

area = P(Z < 2) - P(Z < 1)

area = 0.9772 - 0.8413

area = 0.1359

This means that approximately 13.59% of the practice trials will be between 84 and 85 seconds. To find the actual number of trials, we can multiply this percentage by the total number of trials:

number of trials = 0.1359 * 40

number of trials ≈ 5.44

Rounding to the nearest whole number, we get that about 5 of the 40 practice trials will be between 84 and 85 seconds.

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Answer:

THanks

Step-by-step explanation:

Answer:

What is the question??

Step-by-step explanation:

Answer:

x = 4

Step-by-step explanation:

If a line is parallel to a side of the triangle and intersects the other 2 sides then it divides those sides proportionally, that is

\(\frac{2}{4}\) = \(\frac{x-1}{6}\) ( cross- multiply )

4(x - 1) = 12 ( divide both sides by 4 )

x - 1 = 3 ( add 1 to both sides )

x = 4

a) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] b) The transition matrix from C to B is [1 0 0], [0 1 0], [0 0 1] c) p(x) = a + bx + cx² as a linear combination of the polynomials in C can be defined as p(x) = a + b + c(x - 1)²

(a) Finding the transition matrix from C to B

To find the transition matrix from C to B, we need to express the vectors in the basis C as linear combinations of the vectors in basis B.

Let's express each vector in basis C in terms of basis B

1 = 1(1) + 0(x) + 0(x²)

(2 - 1) = 0(1) + 1(x) + 0(x²)

(x - 1)² = 0(1) + 0(x) + 1(x²)

The coefficients of the linear combinations are the entries of the transition matrix from C to B. Thus, the transition matrix is

[1 0 0]

[0 1 0]

[0 0 1]

(b) Finding the transition matrix from B to C:

To find the transition matrix from B to C, we need to express the vectors in the basis B as linear combinations of the vectors in basis C.

Let's express each vector in basis B in terms of basis C

1 = 1(1) + 0(2 - 1) + 0((x - 1)²)

x = 0(1) + 1(2 - 1) + 0((x - 1)²)

x² = 0(1) + 0(2 - 1) + 1((x - 1)²)

The coefficients of the linear combinations are the entries of the transition matrix from B to C. Thus, the transition matrix is

[1 0 0]

[0 1 0]

[0 0 1]

(c) Writing p(x) = a + bx + cx² as a linear combination of the polynomials in C

To write p(x) = a + bx + cx² as a linear combination of the polynomials in C, we need to express the polynomial p(x) in terms of the basis C.

We have the basis C = {1, (2 - 1), (x - 1)²}

p(x) = a + bx + cx² = a(1) + b(2 - 1) + c((x - 1)²) = a + b(2 - 1) + c((x - 1)²)

Thus, the polynomial p(x) = a + bx + cx² can be written as a linear combination of the polynomials in C as

p(x) = a + b(2 - 1) + c((x - 1)²)

Simplifying further

p(x) = a + b + c(x - 1)²

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Answer:

460 yards

Step-by-step explanation:

3 feet are in a yard so 276 feet / 1 second * 1 yard / 3 feet=92 yards per second

92 * 5 = 460 yards

Unit rate is the quantity of an amount of something at a rate of one of another quantity.

If the car travels at a speed of 276 feet per second, the number of yards the race car travels in 5 seconds is 460 yards.

It is the quantity of an amount of something at a rate of one of another quantity.

Example:

A man can travel 3 miles in 60 minutes.

The man can travel 1 mile in 20 minutes.

We have,

A car travels 276 feet each second.

This can be written as:

276 feet = 1 second

Multiply both sides by 5 we get,

5 x 276 feet = 5 x 1 second

1380 feet = 5 second ____(1)

1 yard = 3 feet

Multiply both sides by 460.

460 x 1 yard = 460 x 3 feet

460 yard = 1380 feet ____(1)

From (1) and (2) we get,

460 yard = 5 seconds

Thus,

If the car travels at a speed of 276 feet per second, the number of yards the race car travels in 5 seconds is 460 yards.

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If a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75

The original price of the item = $825

The off offered by the store = 1/4

The off offered by the coupon = 1/5

Total off = 1/4 + 1/5

= 9/20

Then the selling price = The original price of the item - The original price of the item× (9/20)

= 825 - 825×9/20

= 825-371.25

= $453.75

Hence, if a store advertised a sale that gave customers a 1/4 off the original price of $825.00 he also wanted to use a coupon for 1/5 off the sale price, then he paid $453.75

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The rate of return in perpetuity on an asset is equal to the asset's cash flow divided by the share price. By dividing the cash flow by the share price,  we are calculating the proportion of the investment amount that is returned to the investor as income.

Let's assume you invest in a stock with an annual cash flow (dividend) of $10 and a share price of $100. To calculate the rate of return in perpetuity, you divide the cash flow by the share price: $10 / $100 = 0.1 or 10%. This means that for every dollar you invest, you receive a return of 10 cents annually. It represents the annual return on your investment as a percentage.

The rate of return in perpetuity is 10% because the cash flow is 10% of the investment amount. The reason the rate of return is equal to the cash flow divided by the share price is because it captures the income generated by the asset relative to the investment made in it.

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Answer:

answer :36

Step-by-step explanation:

opp exterior angles are equal............

To find the probability that someone who tests negative for opium use does not use opium, we need to use Bayes' theorem.

Let's assume that the prevalence of opium use in the population is 5%. This means that out of 100 people, 5 people use opium.

Now, let's say that the test for opium use has a sensitivity of 95% and a specificity of 98%. This means that out of 100 people who use opium, 95 will test positive, and out of 100 people who do not use opium, 98 will test negative.

Using Bayes' theorem, we can calculate the probability that someone who tests negative for opium use does not use opium as follows:

P(Not using opium | Negative test) = P(Negative test | Not using opium) * P(Not using opium) / P(Negative test)

P(Negative test | Not using opium) = 0.98 (specificity)
P(Not using opium) = 0.95 (complement of the prevalence)
P(Negative test) = P(Negative test | Not using opium) * P(Not using opium) + P(Negative test | Using opium) * P(Using opium)
P(Negative test | Using opium) = 1 - 0.95 = 0.05 (false negative rate)
P(Using opium) = 0.05 (prevalence)

P(Negative test) = 0.98 * 0.95 + 0.05 * 0.05 = 0.0935

P(Not using opium | Negative test) = 0.98 * 0.95 / 0.0935 ≈ 0.994

Therefore, the probability that someone who tests negative for opium use does not use opium is approximately 0.994, or 0.994 in decimal format rounded to three decimal places.
In this case, we want to find the probability of not using opium, given that someone tests negative.

Let's define the events as follows:
- A: Person does not use opium
- B: Person tests negative for opium

We want to find P(A|B), which is the probability of event A occurring given that event B has occurred. Using the conditional probability formula:

P(A|B) = P(A ∩ B) / P(B)

Unfortunately, without specific data on the probabilities of A, B, and A ∩ B (not using opium and testing negative), we cannot provide a numeric answer. However, if you have this information, you can simply plug the values into the formula and divide P(A ∩ B) by P(B) to obtain the probability in decimal format. Finally, round the result to three decimal places.

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Answer:

\(\frac{15}{25}\) ÷ \(\frac{5}{5}\) = \(\frac{3}{5}\)

Answer:

3/5

Step-by-step explanation:

Both of them are multiples of five by dividing them u get the answer

3/5

Answer:

388.8

Step-by-step explanation:

Thats correct i think

9514 1404 393

Answer:

  trisect the median. The centroid is 1/3 its length from the side.

Step-by-step explanation:

The centroid divides each median into parts with a ratio of 2:1. If you trisect the median, the centroid will be 1 unit from the side and 2 units from the vertex.

Answer:

0,3,1

Step-by-step explanation:

The probability that a student smokes but does not drink alcohol is 0.176, the probability that a student eats between meals and drinks alcohol but does not smoke is 0.062.

To find the probabilities in this scenario, we'll use the principle of inclusion-exclusion and the given information about the number of students engaging in different health practices.

Let's define the events:

S: Student smokes

D: Student drinks alcoholic beverages

E: Student eats between meals

We are given the following information:

P(S) = 210/500 = 0.42 (210 students smoke)

P(D) = 258/500 = 0.516 (258 students drink alcohol)

P(E) = 216/500 = 0.432 (216 students eat between meals)

P(S ∩ D) = 122/500 = 0.244 (122 students smoke and drink alcohol)

P(E ∩ D) = 83/500 = 0.166 (83 students eat between meals and drink alcohol)

P(S ∩ E) = 97/500 = 0.194 (97 students smoke and eat between meals)

P(S ∩ D ∩ E) = 52/500 = 0.104 (52 students engage in all three practices)

Now, we can calculate the probabilities:

(a) P(S and D') = P(S) - P(S ∩ D) = 0.42 - 0.244 = 0.176

This represents the probability that a student smokes but does not drink alcohol.

(b) P(E and D and S') = P(E ∩ D) - P(S ∩ D ∩ E) = 0.166 - 0.104 = 0.062

This represents the probability that a student eats between meals and drinks alcohol but does not smoke.

(c) P(S' and E') = 1 - P(S) - P(E) + P(S ∩ E) = 1 - 0.42 - 0.432 + 0.194 = 0.342

This represents the probability that a student neither smokes nor eats between meals.

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Answer:

3/2

Step-by-step explanation:

Answer:

The Slope is 3/2

Step-by-step explanation:

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\)

Option D is the correct answer.

We have,

In this equation, the variable x represents the number of times the square is cut in half, and y represents the surface area of the square.

As x increases, the exponent of 1/2 decreases, causing the value of y to decrease.

This exponential decay accurately represents the idea that the surface area becomes less and less but never reaches zero units²

Thus,

The equation that would help the mathematician model the surface area of a square piece of paper as it was repeatedly cut is \(y = 36 \times \frac{1}{2}^x\).

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The correct equation that would help model the surface area of a square piece of paper as it is repeatedly cut in half is:  \(\(y=36(\frac{1}{2})^x\)\)

As the square is cut in half, the side length of the square is divided by 2, resulting in the area being divided by \(\(2^2 = 4\)\).

Therefore, the equation \(y=36(\frac{1}{2})^x\)\)accurately represents the decreasing surface area of the square as it is repeatedly cut in half.

and, \(\(y=x^2+4x-16\)\)is a quadratic equation that does not represent the decreasing nature of the surface area.

and, \(\(y=-25x^2\)\) is a quadratic equation with a negative coefficient.

and, \(\(y=9(2)^x\)\)represents exponential growth rather than the decreasing nature of the surface area when the square is cut in half.

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Answer:

She sold 3 computer games and 4 board games.

Step-by-step explanation:

If I am doing this right you subtract 9 from 43 until you get the lowest number that you can subtract 9 from 43 thats goes into 4. You then subtract 4 until you get 0.

Sorry if this is confusing I didn't know how to explain it well.

Answer:

Step-by-step explanation:

find prime factorization of 6 and 9

6 = 2 x 3

9 = 3 x 3

Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the LCM:

LCM = 2 × 3 × 3

LCM = 18

Step-by-step explanation:

Make a line like that and add the numbers 6 and 9 ( order doesn't matter).

then look for a number that can divide both of them without a remainder first which is 3.

Divide 6 and write the Answer down under it

Divide name and write the answer under it.

look for another number that can divide those answers you got. but they aren't no numbers that can divide them without remainders anymore, so you divide 2 by 2 and write down 1 and just write down the 3 back .

then divide 3 by 3 and write down the answer which is one beneath it.

(you should keep dividing until you get everything to 1)

Then multiply together all the numbers used in dividing and that is your L.C.M.

Hope this helps.

Good luck ✅.

Answer:

7

Step-by-step explanation:

start by adding 3+ 11 in the parenthesis, that should give you 14. now you should have  7 + 14 over -5 + 8.  

-5 + 8 = 3  (another way to look at this problem is, 8 -5)

7+14 = 21

you should now have 21 over 3

to simplify this divide 21 by 3, this should give you 7  

Answer: 21 divided by 3

Step-by-step explanation:

If you solve the top and the bottom you get 21 for the top and 3 for the top and you can divide 21 by 3 and get 7. You can double check the math if you want, hope this helps!

According to the given information, the two equations that are true for  x=-2  and  x=2  are  4x²-16=0  and  2(x-2)²=0.

What is an equation?

An equation is a mathematical statement that shows that two expressions are equal. It consists of two sides separated by an equals sign (=). The expressions on both sides of the equation can contain numbers, variables, and mathematical operations such as addition, subtraction, multiplication, and division.

The values of  x=-2  and  x=2  satisfy the equation  4x²=16, so  4x²-16=0  is true for both  x=-2  and  x=2.

The equation  x²=-4  has no real solutions, so it is not true for either  x=-2  or  x=2.

The equation  3x²+12=0  is not true for either  x=-2  or  x=2 , because  3x²+12  is always positive for any real value of  x .

The equation  2(x-2)²=0  is only true for  x=2 , because plugging in  x=-2  gives  2(-4)² =32 ≠0.

Therefore, the two equations that are true for  x=-2  and  x=2  are  4x²-16=0  and  2(x-2)²=0 .

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The given linear regression model means that 90% of the variation in long jump distances is explained by the regression line. (Option C)

Linear regression refers to a basic and commonly used form of predictive analysis. It is used to determine the relationship between two quantitative variables. It is used to determine the strength of the relationship between two variables and the value of the dependent variable at a certain value of the independent variable. Regression models describe the relationship between variables by fitting a line to the observed data. Linear regression models use a straight line, while logistic and nonlinear regression models use a curved line. The regression model illustrates how a dependent variable changes as the independent variable(s) change.  The given linear regression model r2= 0.90, where r2 gives the proportion of the variation in the long jump explained by the change in years, the model means that 90% of the variation in long jump distances is explained by the regression line.

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Answer:

$0.90

Step-by-step explanation:

15 x 0.06 = 0.9

You paid tax $0.9 for an umbrella.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

You buy an umbrella for $15 with the tax rate of 6%.

The taxed amount = 15 x 6 / 100

= 90/100

= $0.9

Therefore, the tax amount is $0.9.

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An oak tree is located at the reflection of point B across the x-axis, what ordered pair describes the location of the oak tree.

The reflection of point B across the x-axis is (3, -7) which lies in the fourth quadrant. When an oak tree is located at the reflection of point B across the x-axis, then it means that it is present at the same distance from the x-axis as point B but in the opposite direction. So, it will be present at (-3, 7) in the first quadrant. Therefore, the ordered pair that describes the location of the oak tree is (-3, 7).This reflection across the x-axis is also known as the reflection in the x-axis. It can be seen as if you were to fold a piece of paper along the x-axis and look at the reflection of a point over the fold line, the coordinates of the point will change sign on the y-coordinate.

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Answer:11

Step-by-step explanation:

Answer:

Answer:

3/2 pi radians

Step-by-step explanation:

To change to radians. multiply by pi/180

270 * pi/180

3/2 pi

The law of mathematical logic that was used to derive the given conclusion is; Law of Syllogism

The law of syllogism is defined as a type of logical argument using deductive reasoning.

Now, In mathematical logic, the Law of Syllogism states that if the following two statements are true:

(1) If a , then b .

(2) If b , then c .

Then we can derive a third true statement:

(3) If a , then c .

Now, applying that law to our question, we see that;

1) If I'm a student, then I go to school.

2) If I go to school, then I learn.

Then we can derive a third true statement:

3)  If I'm a student, then I learn.

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