the opposite of -2.25​

The random variable is 3×sigma²/4.

Since, X1, X2 & X3 are independent & identically distributed.

so we have,

var(X1) = var(X2) = var(X3) = \sigma².

And,[tex]cov(X1 , X2) = cov(X2 , X3) = cov(X1 , X3) = 0.[/tex]

Now,  [tex]var(Y1) = var(X2 + X3) = var(X2) + var(X3) + 2.cov(X2 , X3) = \sigma² + \sigma² + 0 = 2.\sigma²[/tex]

[tex]var[(Y1 + Y2 + Y3)/2] = (1/4). [var(Y1) + var(Y2) + var(Y3) + 2.cov(Y1 , Y2) + 2.cov(Y1 , Y3) + 2.cov(Y2 , Y3)] = (1/4). (\sigma² + \sigma² + \sigma² + 0 + 0 + 0) = 3.\sigma²/4[/tex]

The collection of potential outcomes for a random event is referred to as the sample space, which is the domain of a random variable. When a coin is tossed, for instance, there are only two possible outcomes: heads or tails. Read Related Links as well. Probability.

Different from an algebraic variable is a random variable. An algebraic equation's variable is an unknowable but calculable value. The formula [tex]10 + x = 13[/tex] demonstrates that we can determine the precise value of x, which is [tex]3.[/tex] As seen in the example of the dice above, a random variable has a set of values, and any of those values could be the outcome.

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Step 1) : We know that,

[tex]\begin{cases}P = 7000& \\r = 5.6 \% & \\ n = 4 & \\ t = 4 & \end{cases}[/tex]

Step 2) : Formulate and Substitute:

[tex]Substitute\begin{cases}P = 7000& \\ r = 5.6 \% & into \: formula \\ n = 4 & \\ t = 4 & \end{cases}[/tex]

[tex]\bf\longrightarrow{F = P * (1 + \frac{r}{n} )^{(n*t)}} [/tex]

Put the values according to the formula:

[tex]\bf\longrightarrow{F = 7000 * (1 + \frac{ \frac{5.67}{100} }{4} )^{(4*4)}}[/tex]

Step 3) : Evaluate the equation/expression:

[tex]\bf\longrightarrow{8768.1}[/tex]

Answer:

The "different" answer is BC-AC and AB

The "same" answer is AC+CB and CA+BC

Step-by-step explanation:

AC+CB and CA+BC if are rearranged wold be the same CA becomes AC and CB becomes BC

The critical number of the given function {g(t) = 3t ㏑t} is t = e⁻¹

Assume f(x) is a function with an open interval (a,b). If c is in the interval (a,b) and either f'(c) =0 or f'(c) does not exist, we say c is a critical number of f(x).

Each local minimum as well as maximum of f(x) must correspond to a critical number of f(x). The opposite is not truly the case: not all critical number of f(x) must correspond to a local maximum as well as minimum of f(x).

Now, as per the question;

It should be noted that the broadest possible domain of {g(t) = 3t ㏑t} is given in the set {t : t > 0} as ㏑t can not be defined for negative numbers of zero.

Now, differentiate the given function with respect to t.

[tex]g^{\prime}(t)=\frac{d}{d t}(3 t \ln t)[/tex]

Apply the product rule of differentiation;

[tex]\begin{aligned}&=\left[\frac{d}{d t}(3 t)\right] \ln t+3 t \frac{d}{d t}(\ln t) \\&=3 \ln t+3 t \frac{1}{t} \\&=3 \ln t+3 \\&=3(\ln t+1)\end{aligned}[/tex]

Now, put this value of g'(t) = 0 for finding the critical points.

0 = g'(t)

  = 3(㏑t + 1)

Divide equation by 3.

0 = ㏑t + 1

㏑t = -1

Taking anti log;

t = e⁻¹ (critical value)

Therefore, the critical value obtained for the given function is  t = e⁻¹.

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The complete question is-

how many critical numbers does {g(t) = 3t ㏑t} have? note: critical numbers must be within the domain of the function.

Answer:

Step-by-step explanation:

speed = distance/time

however speed is a compound measure

distance to school = speed x time

                               = 30mph x 1/3hr

                               = 10m

time =  10m / 45mph

       = 13.3 (recurring)

       = 13 mins

Answer:

16a

Step-by-step explanation:

14a+2=14+2+a=16a.

Answer:

m∠a = 100°

m∠b = 100°

m∠c = 110°

Step-by-step explanation:

Calculation of m∠a

∠a is an exterior angle of ΔPST .
Therefore m∠a  = sum of the interior angles of ΔPST
m∠a = 30 + 70 = 100°

Calculation of m∠c

∠c and ∠PST are supplementary so their measures must add up to 180°
m∠c + 70° = 180° so m∠c = 180 - 70 = 110°

Calculation of m∠b
QRST is a quadrilateral.
The sum of the interior angles of the quadrilateral = 360°
So m∠a + m∠b + 50 + m∠c = 360°
We have already computed ∠a = 100° and ∠c = 110°
So 100 + m∠b + 50 + 110 = 360°
260 + m∠b = 360
m∠b = 360 - 260 = 100°

We can understand dot plot by taking example of be the choice of foods that you and your friends ate for snacks.

Dot plots are used to represent small amounts of data. To analyze this chart, let's say four people are having a snack together. Snack selections are pizza, burgers, fries, and pasta. Using the dot plant, we can see that everyone chose pizza. Also, her 3 other people in your group added burgers to their snack plates. The graph also shows that two people in the group  added French fries and one person in the group added pasta to their meal.

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Answer:

1a. -( x + 1)² + 4

1b. y-intercept at y = 3

1c. x-intercepts at x = -3 and x = 1

Derivation of 1b and 1c below

Step-by-step explanation:

Question 1a

The vertex equation form of a parabola is given by

y = a(x-h)²  + k where (h, k) are the coordinates of the vertex

If a > 0 then the parabola is facing up(vertex is at a minimum)  and if a < 0 then parabola is facing down (vertex at a maximum)

From the graph we see that the parabola is facing down so a = -1

The vertex is at (-1, 4) so h = -1 and k = 4

Therefore the equation of the parabola is

y = -1(x - h)² + k = -1(x- (-1))² + 4 = -1(x + 1)² + 4

y = -( x + 1)² + 4   (Answer 1a)

Question 1b

The y-intercept is the y-value where the parabola crosses the y-axis. From the graph we see that the parabola crosses the y-axis at y = 3 and x = 0

So y-intercept from the graph is 3

To solve algebraically, set x = 0 in the parabola equation and solve for y

We get, for x = 0,

y = - (0 + 1)² + 4

y = -(1²) + 4 = -1 + 4 = 3

Hence verified

Question 1c

There will be two x-intercepts for a parabola. Looking at the graph we see that the parabola intersects the x-axis at two points (-3, 0) and (1, 0). So the two x-intercepts are -3 and 1

Algebraically we can determine the x-intercepts by setting y = 0 and solving for the two values of x

Setting y = 0 in the parabolic equation, we get
y = 0 = -(x + 1)² + 4

Switch sides
-(x + 1)² + 4 = 0

-(x + 1)² = -(x² + 2x + 1) = -x² -2x - 1

-(x + 1)² + 4 = 0
==> -x² -2x - 1 + 4 = 0

==> -x² - 2x +3 = 0

Multiply by -1 both sides
==> x² + 2x - 3 = 0

Solve this quadratic equation by factoring

x² + 2x - 3 = (x - 1)(x + 3) = 0

The solutions are
x - 1 = 0   ==> x = 1

x + 3 = 0 ==> x = -3

Hence verified

the value y = 0 does not belong to the range, that is why we need to use parenthesis next to the range.

When we write in interval notation, the parenthesis are used to denote that the "ends" of the interval don't belong to the interval.

This means that in (a, b).

a and b don't belong to that interval.

While if instead we wrote [a, b]

In that case, a and b belong.

For the case of the exponential function:

y = a^x

As x tends to really large negative values, the value of y will tend to zero asymptotically. This means that y is really close to zero, but it is never equal to zero.

Then the value y = 0 does not belong to the range, that is why we need to use parenthesis next to the range.

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Answer:

15 years old

Step-by-step explanation:

Answer: 22

Step-by-step explanation:

this problem is solved by a system of equations

Let Arthur’s current age be represented by:a

His brother’s current age will be represented by: b

The first equation will be:

a = 7 + b

The second equation will be:

a + 8 = 2b

now we solve for the equations. Plug in a = 7+b into a in the second equation.
So now we have

b+7+8=2b

Simplify:

B+15=2b

15=b

We aren’t done yet though

Arthur’s brother is 15 years old but since he is 7 years older we need to add 7 to 15

Hence, Arthur is 22 years old.

A. 130.4 pounds shows an appropriate level of precision for the scale

The quantity 0.2 pound represents readability of the digital scale. It is also known by the terms division size or resolution. The number indicates the division in digital scale. The scale division will be 20 in case 0.2 readability. Another example of readability can be understood by more simple divisions. For instance, 1 gram readability can be divided into divisions like 5 or 25 etc.

Capacity, is another term related to digital scale. It refers to the highest amount that can be weighed safely by the digital scale. Precision is defined as the total number of digits in any given number. Among the given options, the option with 4 digits will be the correct option. This is represented in option A. 130.4 pounds. Hence, it shows an appropriate level of precision.

The complete question is -

A digital scale measures weight to the nearest 0.2 pound. Which

measurement shows an appropriate level of precision for the scale?

A.130.4 pounds

B.124.75 pounds

C.125 pounds

D.120 pounds

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The expression of Mia's height in cm is 5 + x

The given parameters are

Mia's height = 5 cm taller than her sister

Her sister's height  = x

The parameter "Mia's height = 5 cm taller than her sister" means that

Mia's height = 5 cm + her sister's height

Substitute Her sister's height  = x in Mia's height = 5 cm + her sister's height

Mia's height = 5 cm + x

This means that the expression of Mia's height in cm is 5 + x

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The cost for 14 cranberry juice bottles would be $7.56

In this question, Sophia buys 13 bottles of cranberry juice at the corner store for a total cost of $7.02

If each bottle costs the same amount, we need to find the amount for 14 bottles of juice.

Let x be the cost of one bottle of cranberry juice.

13 bottles of cranberry juice costs $7.02

So, we get an equation,

13x = $7.02

We solve above equation to find the cost of 1 bottle of cranberry juice.

x = $0.54

By unitary method the cost for 14 cranberry juice bottles would be,

14 × 0.54 = $7.56

Therefore, the cost for 14 cranberry juice bottles would be $7.56

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Answer:

5,7 given point its korrect now

The perimeter of the sandbox is 2x+2y.

Therefore, the inequality is

[tex]\boxed{2x+2y \leq 20}[/tex]

The value of x from the given expression is 1

If the point M is on the line LN, then the equivalent addition postulate is expressed as;

LM+MN = LN

Given the following

LN=9,

MN =4x

LM=5x

Substitute

5x + 4x = 9

9x = 9

x =9/9

x = 1

Hence the value of x from the given expression is 1

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Answer:

it's -2/67x12w<3(xyz)

Answer: n>=10

Step-by-step explanation:

n=number

2(n-2)>=16

2n-4>=16

2n>=20

n>=10

Answer:

[tex]2(x-2)\geq 16[/tex]

[tex]2x-4\geq 16[/tex]

[tex]2x\geq 20[/tex]

[tex]x\geq 10[/tex]

Step-by-step explanation:

hi

1/3 =2 /6

so 1/6 +2/6 = 3/6

as 3/6 is half if his income, then he remains the other half

The erased value in the descending order series is 5.8 so option (C) will be correct.

A series follows some pattern for example if you take data set of natural numbers then there will be a sequence of that data and something will be due to that we can form that series.

Given the descending order series ;

31/5,---- 5 1/2, √26

Since the series is descending its means every next term must be smaller than the previous.

In the given option

6 1/4  = 6.25 and 31/5 = 6.2 so 6.25 > 6.2 so it will not the missing term.

60% refers to 0.60 but 5 1/2 > 0.60 so it is also no solution.

5.8 < 6.2 and 5 1/2 < 5.8 so it will be the solution.

Last √23 = 4.795 but 5 1/2 > 4.795 so it will also not solution.

Hence "The erased value in the descending order series is 5.8".

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The equation of the line passing through (14, 25) and (9, -10) is given by y = 7x - 73

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard equation of a line is:

y = mx + b

Where m is the rate of change and b is the y intercept

The equation of the line passing through the point (14, 25) and (9, -10) is:

y - 25 = [(-10 - 25)/(9 - 14)](x - 14)

y = 7x - 73

The equation of the line passing through (14, 25) and (9, -10) is given by y = 7x - 73

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The rope's diameter is 10⁻³ inches greater than that of the floss, for example.

The diameter of a stand of rope is 1.2 × 10⁻³ inch.

The diameter of a strand of floss is 2 × 10⁻⁴ inches.

Subtract the diameter of the floss strand from the diameter of the rope to determine how much longer the diameter of the rope is than the diameter of the floss.

Therefore, the length by which the diameter of the strand of rope is longer than the diameter of the strand of floss will be:

= 1.2 × 10⁻³ inch - 2 × 10⁻⁴ inches

Now,

= 12 × 10⁻⁴ inch - 2 × 10⁻⁴ inch

= 10 × 10⁻⁴ inch

= 10⁻³ inch

The diameter of the strand of rope is 10⁻³ inches longer than the diameter of the strand of floss.

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Since Barry is going to post-secondary school for three years, a personal line of credit is vital to pay for his education.

It should be noted that when a individual collects a loan, the person will have to pay it back with an extra amount as interest.

In this case, it's important for him to use his personal line or credit rather than collecting a student loan from people. This isn't good in this scenario.

Therefore, since Barry is going to post-secondary school for three years, a personal line of credit is vital to pay for his education.

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Answer:

-7

-48

Step-by-step explanation:

-2*2 = -4. -4-3=-7

-3*-3*-3=-27    -27*2=-54. -54+6=-48

Answer:

Step-by-step explanation:

Answer: 3.23

Step-by-step explanation:

Add 1/6 + 1/7 = 13/42 Take the reciprocal = 42/13 hrs ≈ 3.23 hrs

Answer:

Yes

Step-by-step explanation:

Imagine you have 1 cup. It’s 8 oz. Then imagine someone came up and doubled the # of ounces you have. Now you have 16 oz or 2 cups. 2 cups is double one.

This isn’t a good explanation, sorry lol

But honestly, just think of it as a fraction, what you do to the top, you do to the bottom. As long as you do the same thing to the cups that you did to the ounces, the cups and ounces will remain proportional.