Find the missing length for the highlighted variable.


T=?

Complete question :

WNAE, an all-news AM station, finds that the distribution of the lengths of time listeners are tuned to the station follows the normal distribution. The mean of the distribution is 15.0 minutes and the standard deviation is 3.5 minutes. What is the probability that a particular listener will tune in:

a. More than 20 minutes? b. For 20 minutes or less

Answer: 0.0764 ; 0.9236

Step-by-step explanation:

Mean (m) = 15 minutes

Standard deviation (sd) = 3.5

Z - score :

Z = (x - m) / sd

A) more than 20 minutes

P(X > 20) ; x = 20

Z > (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z > 1.429) = 0.5 - P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 - 0.4236 = 0.0764

2) 20 minutes or less :

P(X <= 20) ; x = 20

Z < (20 - 15) / 3.5 = 5/3.5 = 1.429

P(z < 1.429) = 0.5 + P(0<z<1.43)

Using the z-table: 1.43 = 0.4236

0.5 + 0.4236 = 0.9236

The given expression in postfix notation is: x = a b * c * d * e f g * - * h i * j * k * l - /

To convert the given expression into postfix (reverse Polish) notation, we follow the rules of postfix notation where the operators are placed after their operands. The expression is:

x = (a * b * c * d * (e - f * g)) / (h * i * j * k - l)

To convert this expression into postfix notation, we can use the following steps:

Step 1: Initialize an empty stack and an empty postfix string.

Step 2: Read the expression from left to right.

Step 3: If an operand is encountered, append it to the postfix string.

Step 4: If an operator is encountered, perform the following steps:

a) If the stack is empty or contains an opening parenthesis, push the operator onto the stack.

b) If the operator has higher precedence than the top of the stack, push it onto the stack.

c) If the operator has lower precedence than or equal precedence to the top of the stack, pop operators from the stack and append them to the postfix string until an operator with lower precedence is encountered. Then push the current operator onto the stack.

d) If the operator is an opening parenthesis, push it onto the stack.

e) If the operator is a closing parenthesis, pop operators from the stack and append them to the postfix string until an opening parenthesis is encountered. Discard the opening and closing parentheses.

Step 5: After reading the entire expression, pop any remaining operators from the stack and append them to the postfix string.

In postfix notation, the operands are listed first, followed by the operators. The expression is evaluated from left to right using a stack-based algorithm. This notation eliminates the need for parentheses and clarifies the order of operations.

By converting the original expression to postfix notation, it becomes easier to evaluate the expression using a stack-based algorithm or calculator.

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B) Extreme values on the right side are less likely compared to a normal distribution (same mean and variance as the skewed distribution).

When a distribution has negative skewness, it means that the tail of the distribution is stretched towards the left side. This indicates that there is a longer and potentially more extreme tail on the left side compared to a normal distribution.

In a normal distribution, extreme values are equally likely on both sides of the mean. However, in a distribution with negative skewness, the tail on the left side is longer and contains more extreme values. This means that extreme values on the right side are less likely compared to a normal distribution with the same mean and variance as the skewed distribution.

Option B correctly states that extreme values on the right side are less likely. This is because the negative skewness causes the distribution to be more concentrated towards the right side, leading to fewer extreme values in that region.

Therefore, option B is the correct statement about the extreme values of a distribution with negative skewness.

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If ∆PQR≅∆ XYZ

that means PQ≡XY;QR≡YZ;PR≡XZ

The total distance traveled by the particle over the time interval 0 ≤ t ≤ 3 is approximately 3.95 units.(a) The acceleration of a particle is the derivative of its velocity function. Given the velocity function v(t) = 1 + e^(-t), we find the acceleration by differentiating with respect to time:

a(t) = dv(t)/dt = -e^(-t)

At t = 3, the acceleration is a(3) = -e^(-3) ≈ -0.05.

(b) To determine if the speed of the particle is increasing at t = 3, we need to examine the relationship between the velocity and acceleration at that time. If their signs are the same, the speed is increasing. At t = 3, v(3) = 1 + e^(-3) ≈ 1.05 (positive) and a(3) ≈ -0.05 (negative). Since the signs are different, the speed is not increasing at t = 3.

(c) A particle changes direction when its velocity changes sign. To find the values of t when this occurs, we must solve the equation v(t) = 1 + e^(-t) = 0 for t. Rearranging, we get e^(-t) = -1, which has no real solutions since e^(-t) is always positive. Therefore, the particle never changes direction.

(d) To find the total distance traveled over the interval 0 ≤ t ≤ 3, we must integrate the speed function, which is the absolute value of the velocity function: |v(t)| = |1 + e^(-t)|. Since the particle never changes direction, the absolute value is unnecessary:

Distance = ∫(1 + e^(-t)) dt from 0 to 3

Evaluating this integral, we get [t - e^(-t)] from 0 to 3. Plugging in the limits, we obtain:

Distance = (3 - e^(-3)) - (0 - e^(0)) = 3 - e^(-3) + 1 ≈ 3.95.

So, the total distance traveled by the particle over the time interval 0 ≤ t ≤ 3 is approximately 3.95 units.

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Answer:15(6)+15=13

Step-by-step explanation:

Answer:

96Km

Step-by-step explanation:

l wrote 90/60 because the speed is given in hours.

so I had to deal with hours only not hours and minutes.

that's why I wrote 90/60 .

you can also choose to divide.

I mean to change the minutes to hours so that the formula can work.

good day.

Answer:

x = 3

Step-by-step explanation:

\({ \rm{5x + 2 = 7x - 4}}\)

- First, using equality order by collecting like terms of x together and constants together;

\({ \rm{(5x + 2) { \green{- 2}} + = (7x- 4){ \green{ - 2}}}} \\ { \rm{5x = 7x - 6}}\)

\({ \rm{5x - { \blue{7x}} = (7x - 6) - { \blue{7x}}}} \\ { \rm{ - 2x = - 6}}\)

- Using division property of equality, by dividing -2 on both sides;

\({ \rm{ \frac{ - 2x}{ \orange{ - 2}} } = \frac{ - 6}{ \orange{ - 2}} } \\ \\ { \rm{x = 3}}\)

\({ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: \: creed}}}\)

Answer:

Step-by-step explanation:

What’s x??

Solve for x

5x+2=7x-4

2 + 4 = 7x - 5x

6 = 2x

x = 6 : 2

x = 3

--------------

check

5 * 3 + 2 = 7 * 3 - 4

17 = 17

Answer:

Step-by-step explanation:

7 students have cats only

6 students have dogs only

9 students have dogs and cats

3 students don't have cats or dogs

+ -----------------------------------------------------

25 students in total

The length of side LJ as shown in the similar shapes is 12.92.

Similar shapes are enlargements of each other using a scale factor.

To calculate the length of side LJ, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1 and solve for KL

Hence, the right option is 12.92.

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Answer:

"sixty-three hundredths of a Kilometer"

Step-by-step explanation:

Decimal measurements are read based on the place of their digits. In this case, Ajay would read this measurement as "sixty-three hundredths of a Kilometer". This is because the final digit of the decimal form measurement is in the "hundredths" position. One more to the right and it would be in the "thousandths" while one more to the left would be the "tenths"

Answer:

?

Step-by-step explanation:

54,675+33,548,000x^1+a^2=

get rid of ^1 cuz that doesn't change the value

a^2 can be written as 2a because a^2= a*a and 2a= a*a

54,675+33,548,000x+2a

54,675+33,548,000x= -2a-54675

33,548,000x=-2a-54675

16774000x=-a-27337.5

x=-a - 27337.5

x=-a-27337.5/ 16774000

I obviously know this isn't a real question but here

Answer:

Step-by-step explanation:hey Karlie

Answer:

230,300 different selections.

Step-by-step explanation:

If the order does not matter, the number of possible different selections is determined as the combination of choosing four numbers out of 50:

\(n=\frac{50!}{(50-4)!4!}\\\\n=\frac{50*49*48*47}{4*3*2*1} \\\\n=230,300\ combinations\)

There are 230,300 possible different selections.

Answer:

??????????????

Step-by-step explanation:

The maximum acceleration attained on the interval 0 ≤ t ≤ 3 by the particle is equal to 21 m/s².

Acceleration is a physical quantity that measures the rate of change of velocity over time. It is usually denoted by the symbol "a" and its unit is meters per second squared (m/s²).

In this case, the maximum acceleration attained by the particle on the interval 0 ≤ t ≤ 3 is given as 21 m/s². This means that at some point during this interval, the particle's velocity changed by 21 meters per second (m/s) every second of time.

So, in this case, the acceleration of the particle is 21 m/s².

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Step-by-step explanation:

\(1 + 34x = 45 - 32x \\ 34x + 32x = 45 - 1 \\ 66x = 44 \\ x = \frac{44}{66} \\ x = \frac{4}{6} \\ x = \frac{2}{3} \)

And pls go for the 2nd pfp cuz it's beautiful as well as meaningful :D

Answer:

7r is the correct answer

Step-by-step explanation:

7 x 8 = 56

Answer:

a) 3 b) y = 3x + 11

Step-by-step explanation:

a)

In order to find the gradient (slope), find the change in y or change in x (rise/run).

-2 - 2 / 7 - (-5)

-2 - 2 / 7 + 5

-4/12 = -1/3

Now that we know the gradient of line AB is -1/3, take the opposite reciprocal of that to find the gradient perpendicular to line AB.

-1/3 ⇒ 3

b)

Take point C's values and the perpendicular gradient found earlier and substitute them into the point-slope form equation.

y - 5 = 3(x - (-2))

y - 5 = 3(x + 2)

y - 5 = 3x + 6

y = 3x + 11

To write y as the sum of two orthogonal vectors, one in Span fu and one orthogonal to u, we first need to find a vector in Span fu.

Let's call this vector v. Since u is a 1x2 matrix, we can think of it as a vector in R^2. To find v, we need to find a scalar c such that cv = u.

We can do this by solving the equation cv = u for c:

c * [a,b] = [2,-6]

This gives us two equations:

ca = 2

cb = -6

Solving for c, we get:

c = 2/a

c = -6/b

Equating the two expressions for c, we get:

2/a = -6/b

Cross-multiplying, we get:

2b = -6a

Dividing both sides by 2, we get:

b = -3a

So we can choose v = [a,-3a], for any non-zero value of a. For simplicity, let's choose a = 1, so v = [1,-3].

Now we need to find a vector w that is orthogonal to u. The dot product of u and w should be 0:

[u1, u2] · [w1, w2] = u1w1 + u2w2 = 0

We know that u = [2,-6], so we can choose w = [3,1], which is orthogonal to u.

Now we can write y as the sum of two vectors, one in Span fu and one orthogonal to u:

y = (y · v/||v||^2) v + (y · w/||w||^2) w

where · denotes the dot product, ||v|| is the norm of v, and ||w|| is the norm of w.

Plugging in the values, we get:

y = ((41 + 3(-3))/10) [1,-3] + ((43 + 31)/(3^2 + 1^2)) [3,1]

y = (-2/5) [1,-3] + (15/10) [3,1]

y = [-2/51 + 15/103, -2/5*(-3) + 15/10*1]

y = [23/10, 7/10]

So we can write y as the sum of [-6/5, 9/5] (which is in Span fu) and [23/10, 7/10] (which is orthogonal to u).

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Answer:

The marginal cost is the additional cost added by increasing the quantity. This is also known as the additional cost “at the margin.” The marginal revenue is the additional revenue added by increasing the quantity. This is also known as the additional revenue “at the margin.”

Step-by-step explanation:

Please mark as brainlist

Answer:

B) Reflect triangle ABC across line BC

and the 2nd one is also B

Step-by-step explanation:

Hope this helps! Pls give brainliest!

Answer:

\(k<1, k>5\)

Step-by-step explanation:

\(3x+1=x^2+kx+2 \\ \\ x^2+x(k-3)+1=0 \\ \\ \Delta>0 \implies (k-3)^2-4(1)(1)>0 \\ \\ (k-3)^2-2^2>0 \\ \\ (k-1)(k-5)>0 \\ \\ k<1, k>5\)

128 = 2^7 is a power of 2

27 = 3^3 is a perfect cube

=======================================================

Explanation:

This is something you'd find through trial and error.

The powers of 2 are

2, 4, 8, 16, 32, 64, 128, 256, ...

We double each value to get the next one.

The largest power of 2 that is smaller than 155 is 128

155-128 = 27 which is a cube number since x^3 = 3^3 = 27 as you've shown in the screenshot.

If the result of 155-128 wasn't a perfect cube number, then you'd have to try the next largest power of 2 (which is 64) and work your way down the list.

----------------------

Or you could work with the list of perfect cubes

1, 8, 27, 64, 125, 216, ...

Each value is of the form x^3 where x is a whole number.

Let's pick the largest perfect cube that is under 155, and subtract it

155-125 = 30 which isn't a power of 2 (refer to the list above)

Then try 155-64 = 91 which isn't a power of 2 either

Keep moving down the list until reaching 155-27 = 128 which is a power of 2 since 2^7 = 128

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The combination of fiber alignment, bonding between fibers, and the presence of lignin and hemicellulose in wood contribute to its high strength in the longitudinal direction compared to the transverse direction.

The critical stages of a pavement's life reflected in the performance grading system are as follows:

1. Construction: During this stage, the pavement is built, and factors such as material selection, thickness, and compaction are crucial for ensuring its long-term performance. Adequate preparation of the subgrade and proper placement of the asphalt layers contribute to the durability and strength of the pavement.

2. Traffic Loading: Once the pavement is constructed, it is subjected to various traffic loads, including vehicles of different weights and frequencies. The performance grading system considers the ability of the pavement to withstand these loads without significant distress, such as cracking, rutting, or fatigue.

3. Aging: Over time, the pavement undergoes natural aging due to exposure to environmental factors like sunlight, moisture, and temperature variations. The performance grading system takes into account the pavement's ability to resist aging and maintain its structural integrity over an extended period.

4. Maintenance and Rehabilitation: As the pavement ages, it may require maintenance and rehabilitation to address any distress or damage that has occurred. The performance grading system considers the effectiveness of these interventions in restoring the pavement's performance and extending its service life.

From a molecular standpoint, the high strength of wood in a tree's longitudinal direction compared to the transverse direction can be attributed to the structure and arrangement of wood fibers.

In the longitudinal direction, the wood fibers run parallel to the tree trunk, providing a continuous and unbroken path for load transmission. This arrangement allows for efficient stress transfer and results in high tensile and compressive strength along the length of the tree.

In contrast, in the transverse direction, the wood fibers are arranged perpendicular to the tree trunk. This arrangement leads to weaker bonding between the fibers, making the wood more susceptible to shearing forces and limiting its strength in this direction.

Furthermore, the presence of lignin and hemicellulose in the wood cell walls contributes to its overall strength. These polymers provide rigidity and resistance to deformation, enhancing the wood's ability to withstand applied forces.

Overall, the combination of fiber alignment, bonding between fibers, and the presence of lignin and hemicellulose in wood contribute to its high strength in the longitudinal direction compared to the transverse direction.

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The equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x

The attached table of values represents the missing piece in the question.

Start by calculating the rate of change using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (14.77 - 10.55)/(7- 5)

Evaluate

m = 2.11

The equation is then calculated using:

y = m(x - x1) + y1

This gives

y = 2.11(x - 5) + 10.55

Evaluate

y = 2.11x - 10.55 + 10.55

y = 2.11x

Hence, the equation that represents the relationship between the number of liters, x, and the number of liquid pints, y is y = 2.11x

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Answer:

the correct answer is b

Step-by-step explanation:

i just took a quiz on ap3x, i hope this helped! have a blessed day! :))

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped. The correct option is graph B.

A parabola is a mirror-symmetrical planar curve that is nearly U-shaped.

y = a(x-h)² + k

where,

(h, k) are the coordinates of the vertex of the parabola in the form (x, y);

a defines how narrower is the parabola, and the "-" or "+" that the parabola will open up or down.

Given that the function f(x)=x², which represents a parabola, therefore, the function of g(x) can be represented as,

\(g(x)=\dfrac13 f(x)\\\\g(x)=\dfrac13 x^2\)

Now, if we compare the function g(x) with the general equation of a parabola, therefore, the value of 'a' will be 1/3 which means that the function will open wider than f(x).

Thus, the correct option is graph B.

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