Which of the following statement(s) is/are TRUE about the number of data values that lie over an interval for normal distribution by using the empirical rule ? There are 71.5% data values within 1 -- and u +20. There are 68% data values within y and pto. There are 50% data values within and o. There are 50% data values within u-30 and . There are 100% data values within 30 and + 30.

The solution of differential equation, y" + 4y' + 3y = 0, to = 1, is equals to y(t) = c₁e⁻ ᵗ + c₂e⁻³ᵗ.

19) y₁ = eᵗ , y₂ = eᵗ + teᵗ, are solutions of y" - 2y' + y = 0 and they form a fundamental set of solutions.

20) y₁ = e⁻ᵗ , y₂ = e²ᵗ, are solutions of y" - y' - 2y = 0 and they form a fundamental set of solutions.

21) y₁ = cos(2t) , y₂ = sin(2t), are solutions of y" + 4y = 0 and they form a fundamental set of solutions.

The general solution form of differential equation is, y = ceᵐᵗ. In case of second order differential equation, there are two constants and two values of m exist. We have a second order linear homogeneous ordinary differential equation is, y" + 4y' + 3y = 0, to = 1 --(1)

and we have to solve it. The auxiliary equation for equation (1) is, m² + 4m + 3

= 0 and we determine the value of m, for this using middle term splitting method,

=> m² + 3m + m + 3 = 0

=> m( m + 3) + 1( m+3) = 0

=> (m +1)(m+3) = 0

=> m + 1 = 0 or m + 3 = 0

=> m = -1 , -3

=> m₁ = -1 , m₂ = -3

So, the general solution of equation (1) is written as y(t) = c₁e⁻ ᵗ + c₂e⁻³ᵗ.

19) y" - 2y' + y = 0 --(2), y₁ = eᵗ , y₂ = eᵗ + teᵗ

For verification : drive first and second derivatives of y₁ and y₂. That is y₁' = eᵗ , y₁'' = eᵗ and y₂' = 2eᵗ + teᵗ , y₂'' = 3eᵗ + teᵗ

plug these values into above equation,

=> 0 = y₁''- 2y₁' + y₁ = eᵗ - 2eᵗ + eᵗ = 0

0 = y₂'' - 2y₂' + y₂ = 3eᵗ + teᵗ - 4eᵗ - 2 teᵗ + eᵗ + teᵗ = 0 , so, y₁ and y₂ are solution of equation (2). The solutions y₁ and y₂ form a fundamental set of solutions iff their wronskian is non-zero. Now, W(eᵗ , eᵗ + teᵗ) = y₁ y₂' + y₂ y₁' = eᵗ(2eᵗ + teᵗ) + eᵗ(eᵗ + teᵗ) ≠0. So, they form fundamental set of solutions.

20) y" - y' - 2y =0 --(3), y₁ = e⁻ᵗ , y₂ = e²ᵗ

For verification : drive first and second derivatives of y₁ and y₂. That is y₁' = -e⁻ᵗ , y₁'' = e⁻ᵗ and y₂' = 2e²ᵗ, y₂'' = 4e²ᵗ

plug these values into above equation,

=> 0 = y₁''- y₁' - 2y₁ = e⁻ᵗ - (-e⁻ᵗ) - 2e⁻ᵗ = 0

0 = y₂'' - y₂' - 2y₂ = 4e²ᵗ - 2e²ᵗ - 2e²ᵗ = 0

so, y₁ and y₂ are solution of equation (3).

y₁ and y₂ solutions form fundamental set of solutions iff their wronskian is non-zero

Now, W(e⁻ᵗ , e²ᵗ) = y₁ y₂' + y₂ y₁'

= 2e⁻ᵗe²ᵗ - e⁻ᵗe²ᵗ ≠0. So, they form fundamental set of solutions.

21) y" + 4y =0 --(4), y₁ = cos(2t) , y₂ = sin(2t)

For verification : drive first and second derivatives of y₁ and y₂. That is y₁' = - 2 sin(2t) , y₁'' = - 4 cos(2t) and y₂' = 2 cos(2t), y₂'' = -4 sin(2t)

plug these values into above equation,

=> 0 = y₁'' + 4y₁ = - 4 cos(2t) + 4 cos(2t) = 0

0 = y₂'' + 4y₂ = -4 sin(2t) + 4sin(2t) = 0

so, y₁ and y₂ are solution of equation (3).

y₁ and y₂ solutions form fundamental set of solutions iff their wronskian is non-zero

Now, W(cos(2t), sin(2t)) = y₁ y₂' + y₂ y₁'

= 2 cos²(2t) - 2 sin²(2t) ≠0. Hence, they form fundamental set of solutions.

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Complete question:

y" + 4y' + 3y = 0, to = 1 " In each of Problems 19 through 21, verify that the functions y₁, and y₂ are solutions of the given differential equation. Do they constitute a fundamental set of solutions?

19. y" - 2y' + y = 0 , y₁ = eᵗ , y₂ = eᵗ + teᵗ 20. y" - y' - 2y =0, y₁ = e⁻ᵗ , y₂ = e²ᵗ 21. y" + 4y =0, y₁ =cos(2t) , y₂ = sin(2t)

Answer:

Down below!!

Step-by-step explanation:

Exact Form:

27/10

Decimal Form:

2.7

Mixed Number Form:

2 7/10

Answer:

4 1/2 - 1 8/10 =  2 7/10

Step-by-step explanation:

Step 1 : Start by making the mixed fraction into improper fractions

4 1/2 = 9/2

(For the fraction 1 8/10,  make sure to simplify 8/10!)

9/2 - 1 4/5 = 9/2 - 9/5

Step 2: Next find a common denominator for both the improper fractions.

9/2 x 5/5 = 45/10

9/5 x 2/2 = 18/10

45/10 - 18/10 = 27/10

Step 3: Now, make the improper fraction into a mixed number

27/10 = 2 7/10

So this shows us that 4 1/2 - 1 8/10 =  2 7/10! Hope this helps! :D

Answer:

D) 2

Step-by-step explanation:

Use the following slope formula:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (4 , 1)

(x₂ , y₂) = (1 , -5)

Plug in the corresponding numbers to the corresponding variables:

m = (-5 - 1)/(1 - 4)

Simplify. Remember to follow PEMDAS. First subtract, then divide:

m = (-5 - 1)/(1 - 4)

m = (-6)/(-3)

m = 2

D) 2 is your answer.

~

Answer:

B: 12.5%

Step-by-step explanation:

You take the 20.000- 8.500 the number decreased with= 11.5.

You then round of your answer to the nearest 10th, the number 11,5 will change to 12,50.

Answer:

k

Step-by-step explanation:

2x+13<5x−20

Subtract 5x from both sides.

Combine 2x and −5x to get −3x.

Subtract 13 from both sides.

Subtract 13 from −20 to get −33.

Divide both sides by −3. Since −3 is negative, the inequality direction is changed.

​

x>11

By applying angle relationships theory, it can be concluded that BCE and CED are Alternate Interior angles.

When a transversal intersects two parallel lines, there will be some angle relationships:

Now we take a look at the picture given and use the angle types above to name the relationship between angles.

As we are asked to determine the relationship between angles BCE and CED, we can take a look at the above explanation.

Thus, the angle relationship describes angles BCE and CED as Alternate Interior angles.

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Answer:

m∠ABC = m∠BED; Corresponding Angles Theorem

Step-by-step explanation:

I took the test on FLVS and got it right

The relationship between tan A and tan B is: tan A * tan B = 1

From the question, we have the following parameters that can be used in our computation:

angle A + angle B = 90 deg

When angle A + angle B = 90 degrees,

The two angles are complementary, meaning they add up to 90 degrees.

In this case, the relationship between tan A and tan B is:

tan A * tan B = 1

This is known as the tangent addition formula.

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The answer is:

5/4

Work/explanation:

Let's work out the slope of the line.

The equation is in y = mx + b form where m = slope; b = y intercept.

Similarly, in y=5/4x - 7/4, the slope is 5/4.

The estimation of 0.000007328 is \(7\times10^{-6\).

Estimation is he ability to guess the amount of anything without actual measurement.

The number (n) is given as:

\(\text{n}=0.000007328\)

Multiply by 1

\(\text{n}=0.000007328\times1\)

The number is to be rounded to the nearest millionth.

So, we substitute \(\frac{1000000}{1000000}\) for 1

\(\text{n}=0.000007328\times1\)

\(\text{n}=0.000007328\times\dfrac{1000000}{1000000}\)

This becomes

\(\text{n}=7.328\times\dfrac{1}{1000000}\)

Express the fraction as a power of 10

\(\text{n}=7.328\times10^{-6\)

Approximate to a single digit

\(\rightarrow\bold{n=7\times10^{-6}}\)

Therefore, the estimation of 0.000007328 is \(7\times10^{-6}\).

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The degree of expression is one.

And, There are two terms in the expression.

Since, Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division

Given that;

The expression is,

⇒ 2x + 7

Now, We can see that,

The degree of expression is one because it is a linear equation.

And, There are two terms in the expression that is, 2x and 7

Thus, The degree of expression is one.

And, There are two terms in the expression.

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Therefore , the solution of the given problem of slope comes out to be

m =-1/5 and b =5 units.

The slope of a line determines how steep it is. A characteristic of a color filter equation is a gradient overflow. The horizontal distance disparities (run) between two points are divided by the average vertical differences (rise) between the exact two points to determine the slope. The equation y = mx + b, which is known as the hill type equation, is used to express the fixed path issue. If grading is m, a = b, and the line's y-intercept is located there (0, b).

Here,

Given :

From the given graph we get

Points(0,5)  and (1,0)

So,

Slope m = 1-0 /0-5

=> m= -1/5

and

For b

=> b = 5 units.

Therefore , the solution of the given problem of slope comes out to be

m =-1/5 and b =5 units.

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Answer:

put the yes in the second box, fourth box, and fifth box.

Step-by-step explanation:

trust me, your welcome

Answer:

10.95

Step-by-step explanation:

The square root of 120 is 10.95445. And if you want it to the nearest hundredth it would be 10.95 :)

Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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PQ→ can also be referred to as QP→ or line n, while plane R can also be called plane SVT or plane PTV.

Alternative names for PQ→:

1. QP→ (Reverse direction of the vector)

2. Line n (Referring to PQ as a line)

Alternative names for plane R:

1. Plane SVT (Using the points S, V, and T to define the plane)

2. Plane PTV (Using the points P, T, and V to define the plane)

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Answer:

Step-by-step explanation:

Answer:

2, 3, 5

Step-by-step explanation:

Because I said so

The diameter of a bicycle wheel is 24 inches. Around the wheel, there are 32 spokes that are spaced 48 meters away from one another.

The diameter of a circle is the distance measured through its center. The radius of a circle is the distance from the center to any point on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d . The simplest place to start would be to use a ruler to measure the distance between the circle's outside edges starting from its very center. The diameter would be that.

The diameter of the circle is the measurement at issue. The distance between the circle's center and its periphery can be measured.

far apart is each spoke (distance) = radius = diameter / 2

distance = 24/2

distance = 12

Since a wheel has 4 parts. so, 12*4 =  48 m

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Based on the terms of the invoice, the gross amount on the invoice and the date of payment, the cash discount is $19 and the net amount paid is $931.

The terms of the invoice are such that if the person pays within 10 days they get a 3% discount. If they pay in 15 days, they get a 2% discount.

The person paid on the 22nd after buying on the 8th so they qualify for the 2% for paying within 15 days.

The cash discount is:

= 2% x 950

= $19

The net amount paid is:

= 950 - 19

= $931

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Answer:

3.14 mph

Step-by-step explanation:

5.5 divided by 1.75

5.5 is the miles

1.75 is the hours

Answer: The average speed on the return trip is 2.44 miles/h

Step-by-step explanation:

Answer:

The answer should be 20,365.714 but I am not sure

Step-by-step explanation:

To calculate the present value of $51,270 payments to be made at the end of each period for 17 periods at a 9% interest rate, we need to find the discounted value of each payment and sum them up.

The present value (PV) is calculated by discounting each future payment back to its current value using the interest rate. The formula to calculate the present value of a series of payments is:

PV = Payment × [1 - (1 + interest rate)^(-number of periods)] / interest rate.

In this case, the payment is $51,270, the interest rate is 9% (or 0.09 as a decimal), and the number of periods is 17.

Using the provided formula and rounding the factor values to 5 decimal places, we can calculate the present value as follows:

PV = $51,270 × [1 - (1 + 0.09)^(-17)] / 0.09.

Evaluating this expression will give us the present value of the payments. It's important to round the final answer to 0 decimal places, as stated in the question.

By substituting the values and calculating the expression, we can determine the present value of the $51,270 payments made over 17 periods at a 9% interest rate.

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Answer:

the square root of five is irrational

Step-by-step explanation:

Answer:

A, I think

Step-by-step explanation:

Answer:

y = -3x - 1

Step-by-step explanation:

To find the slope, use the slope formula: \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

Plugging in the given values, we have: \(\frac{-4-2}{1-(-1)}\)

\(\frac{-4-2}{1-(-1)}\)

= \(\frac{-6}{2}\)

= -3

Now that we know that the slope is -3, we need to find the y-intercept. Anazlyzing the graph, we can see that the line passes through the point (0, -1) on the y-axis, therefore, that is our y-intercept.

Combining the information, the result is: y = -3x - 1

hope this helps!

A parking lot has 120 vehicles with motorcycles and cars in the ratio of 7:5. The number of motorcycles in the parking lot is 70 and the number of cars is 50.

Assume the number of motorcycles in the parking lot to be 7x and cars be 5x. Since there are 120 vehicles, we can write the equation as;7x + 5x = 12012x = 120x = 10Now, the number of motorcycles in the parking lot is 7x = 7 × 10 = 70 and the number of cars is 5x = 5 × 10 = 50.Therefore, there are 70 motorcycles and 50 cars in the parking lot. The total number of vehicles is 120. A parking lot has 120 vehicles with motorcycles and cars in the ratio of 7:5. The number of motorcycles in the parking lot is 70 and the number of cars is 50.

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There were 13 salmon fillets that the restaurant served.

The solution to this math problem involves fractions, especially percentage. A percentage is a fraction of a hundred. The literal meaning of percentage is "per 100". Percentage is often referred to as percent. The symbol or sign for percentage is %. The number beside the symbol/sign is the numerator, so for example, 10% can also be written as 10/100.

We're given that 25% of the dinner specials served by the restaurant were salmon fillets. In order to find out how many salmon fillets were served, we only need to multiply 52 by 25%.

52 × 25% =

52 × 25/100 =

(52 × 25)/100 =

1,300/100 = 13

There were indeed thirteen salmon fillets served by the restaurant.

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Answer: 60% or 0.6

Step-by-step explanation:

A discount simply means the amount that is deducted from the normal cost of a good or service.

In the question above, the store was offering 40% as discount, this means that he'll only pay 60% of the price of the good. Note that (100% - 40% = 60%).

Therefore, the number that he should multiply the prices on the tags by to find the price he would have to pay will be 60% = 0.6.

Answer:

The radius is 6

Step-by-step explanation:

Arc length ACB = 6 pi

The arc length = fraction of a circle times the circumference

6 pi = 180/360 * 2 * pi *r

6 pi = 1/2 * 2 * pi*r

6 pi =  pi r

The radius is 6

The equation that represents the graph is y equals negative three halves times x minus 3, and option A is correct.

The ratio of the change in y coordinate to the change in x coordinate is known as a line's slope.

y and x, respectively, stand for the net change in the y-coordinate and the net change in the x-coordinate.

Consequently, the connection between a change in y-coordinate and a change in x-coordinate

Given a graph,

from the graph, we find that when y is 0, x = -2

and when x is o, y = -3

so the line passes from (-2, 0) and (0, -3)

the slope of the line is (y₂-y₁)/(x₂-x₁)

m = (-3 - 0)/(0 - 2)

m = -3/2

and the y-intercept is -3

equation of line is y = mx + c

y = -3x/2 - 3

which is y equals negative three halves times x minus 3.

Hence option A is correct for the equation of the line,

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Answer:D

Step-by-step explanation:D