What is the slope for the graph of the line shown? Write your answer in the form a/b

Answer:

Step-by-step explanation:

4. a

x cannot be 0 because 2/0 cannot be calculated - we say that it is undefined.

b. x cannot be 1 as that would mke the denominator x - 1 = 0 which is undefined.

5 a. (9x - 5)(9x + 5)

b. (2x + 1)(x - 3).

6.

C.  (x + 7)/3

7.

a. (-5, ∝)

b. (-∝, 2]

c.(-3, 7].

8.

y = kx

24 = 16k

k = 1.5

So, y = 1.5x

When x = 50

y = 1.5*50 = 75.

Grayson measured the length of a pencil to be 18 centimeters. If he used meters instead of centimeters, he would need fewer than 18 meters to measure the length of the pencil.

The metric system is used for measuring length in most countries, and it has three basic units: meter, centimeter, and millimeter. These units are all interconnected and can be converted from one to another. Grayson measured the length of the pencil to be 18 centimeters, which is equal to 0.18 meters.

if he used meters instead of centimeters, he would need fewer than 18 meters to measure the length of the pencil. Since a meter is a larger unit of measurement than a centimeter, he would require fewer meters to measure the pencil's length.Consequently, it would be an inefficient way to measure the length of a pencil in meters, as this will result in a very long measurement with an unnecessarily large unit.  it is more appropriate to measure the length of a pencil in centimeters.

To know more about measuring visit:

https://brainly.com/question/28913275

#SPJ11

Work done by the person for the displacement of 100m along +x-axis with constant velocity and mass of 10kg is equal to 0Joule.

As given in the question,

Mass of a person 'm' = 10kg

Displacement of the person while walking along +x axis 'd'= 100m

Constant velocity = 2m/s

Let 'w' be the work done by the person

Work = Force × Displacement

Force = mass × acceleration

Acceleration = (final velocity - initial velocity)/ total time taken

Here, Constant velocity ⇒final velocity - initial velocity = 2- 2

                                                                                      = 0m/s

⇒Acceleration = 0m/s²

⇒Force = 10 × 0

             = 0Kgm/s²

⇒Work done = 0 × 100

                     = 0 Joule

Therefore, work done by the person for the given displacement, velocity, and mass is equal to zero Joule.

Learn more about work done here

brainly.com/question/16976412

#SPJ4

Answer:

925 marks.

Step-by-step explanation:

AS Biraj had 20 less marks then the  40% pass mark must be 350+20 = 370.

370  is equivalent to 40%

So 100% = 100*370 / 40

= 925 marks.

Answer:

\(\( \huge green[ \mid \underline \overline[ \tt BILLIE }} \mid]]\) \: sorry \: i \: m \: testing \: something\)

∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx equals approximately 1932.5

To evaluate the given integrals, let's first identify the functions f(x) and g(x) and their respective intervals.

f(x) = 4x^2 - 3x + 2

g(x) = 2x^3 - 5x + 1

Interval: [3, 8]

Now, let's evaluate the integrals step by step.

∫[3, 8] f(x) dx:

We integrate the function f(x) over the interval [3, 8].

∫[3, 8] (4x^2 - 3x + 2) dx

To find the integral, we can use the power rule for integration. For each term, we increase the exponent by 1 and divide by the new exponent.

= [4 * (x^3/3) - 3 * (x^2/2) + 2x] evaluated from 3 to 8

Now we substitute the upper and lower limits into the integral expression:

= [(4 * (8^3/3) - 3 * (8^2/2) + 2 * 8) - (4 * (3^3/3) - 3 * (3^2/2) + 2 * 3)]

Simplifying further:

= [(4 * 512/3) - (3 * 16/2) + 16 - (4 * 27/3) + (3 * 9/2) + 6]

= [(1706.67) - (24) + 16 - (36) + (13.5) + 6]

= 1683.17

Therefore, ∫[3, 8] f(x) dx equals approximately 1683.17.

∫[3, 8] g(x) dx:

We integrate the function g(x) over the interval [3, 8].

∫[3, 8] (2x^3 - 5x + 1) dx

Using the power rule for integration:

= [(2 * (x^4/4)) - (5 * (x^2/2)) + x] evaluated from 3 to 8

Substituting the upper and lower limits:

= [(2 * (8^4/4)) - (5 * (8^2/2)) + 8 - (2 * (3^4/4)) + (5 * (3^2/2)) + 3]

Simplifying further:

= [(2 * 4096/4) - (5 * 64/2) + 8 - (2 * 81/4) + (5 * 9/2) + 3]

= [(2048) - (160) + 8 - (162/2) + (45/2) + 3]

= 1932.5

Therefore, ∫[3, 8] g(x) dx equals approximately 1932.5

for such more question on integrals

https://brainly.com/question/12231722

#SPJ8

Answer:

It will take them 7.89 days

Traditionally, the spatial intervals between typographic elements are called "kerning" and "tracking."

1. Kerning: Kerning refers to the adjustment of space between individual pairs of characters.

It involves modifying the spacing between specific letter combinations to achieve better visual harmony and readability.

Kerning is particularly important when dealing with letter pairs that may appear awkward or visually unbalanced, such as "AV" or "To."

2. Tracking: Tracking, also known as letter-spacing, involves adjusting the overall spacing uniformly between all characters in a text block or a selected range of text.

It affects the spacing between all letters and can be used to create a more open or compact appearance of the text.

Increasing the tracking value creates more space between characters, while decreasing it brings the characters closer together.

Both kerning and tracking play crucial roles in typography to ensure legibility, readability, and overall visual appeal. Designers use these techniques to achieve optimal spacing between characters and create well-balanced and aesthetically pleasing typographic layouts.

To know more about typographic elements refer here:

https://brainly.com/question/30052783#

#SPJ11

Answer:

a) 71

b) an = a1 + (n-1)×7

c) the 37th term

Step-by-step explanation:

clearly, an+1 = an + 7

so, any new term is the previous term plus 7.

a1 = 8

and then the sequence goes on. starting with a2 we add 7 every time.

so, for an we added 7 n-1 times to a1. n-1 because for a1 we did not have to add 7.

therefore, the building function of this sequence to calculate the nth term is

an = a1 + (n-1)×7

a10 = a1 + 9×7 = 8 + 63 = 71

and

ax = 260 = a1 + (x-1)×7 = 8 + 7x - 7 = 1 + 7x

259 = 7x

x = 37

=> the 37th term of the sequence is 260

To solve the given problems, we'll use the properties of the normal distribution with mean μ = 100 and standard deviation σ = 10.

a. Probability that X > 85:

To find this probability, we need to calculate the area under the normal curve to the right of 85. We can use the standard normal distribution table or a calculator to find the corresponding z-score and then use the z-table to find the probability.

First, let's calculate the z-score:

z = (X - μ) / σ

z = (85 - 100) / 10

z = -15 / 10

z = -1.5

Using the z-table or a calculator, we find that the probability of Z > -1.5 is approximately 0.9332.

Therefore, the probability that X > 85 is 0.9332 (rounded to four decimal places).

b. Probability that X < 80:

Similarly, we'll calculate the z-score for X = 80:

z = (X - μ) / σ

z = (80 - 100) / 10

z = -20 / 10

z = -2

Using the z-table or a calculator, we find that the probability of Z < -2 is approximately 0.0228.

Therefore, the probability that X < 80 is 0.0228 (rounded to four decimal places).

c. Probability that X < 90 or X > 130:

To calculate this probability, we'll find the individual probabilities of X < 90 and X > 130, and then subtract the probability of their intersection.

For X < 90:

z = (90 - 100) / 10

z = -10 / 10

z = -1

Using the z-table or a calculator, we find that the probability of Z < -1 is approximately 0.1587.

For X > 130:

z = (130 - 100) / 10

z = 30 / 10

z = 3

Using the z-table or a calculator, we find that the probability of Z > 3 is approximately 0.0013.

Since these events are mutually exclusive, we can add their probabilities:

P(X < 90 or X > 130) = P(X < 90) + P(X > 130)

P(X < 90 or X > 130) = 0.1587 + 0.0013

P(X < 90 or X > 130) = 0.1600

Therefore, the probability that X < 90 or X > 130 is 0.1600 (rounded to four decimal places).

d. 99% of the values are between what two X-values (symmetrically distributed around the mean)?

To find the two X-values, we need to find the corresponding z-scores for the cumulative probabilities of 0.005 and 0.995. These probabilities correspond to the tails beyond the 99% range.

For the left tail:

z = invNorm(0.005)

z ≈ -2.576

For the right tail:

z = invNorm(0.995)

z ≈ 2.576

Now we can find the corresponding X-values:

X1 = μ + z1 * σ

X1 = 100 + (-2.576) * 10

X1 = 100 - 25.76

X1 ≈ 74.24

X2 = μ + z2 * σ

X2 = 100 + 2.576 * 10

X2 = 100 + 25.76

X2 ≈ 125.76

Therefore, 99% of the values are greater than 74.24 and less than 125.76 (rounded to two decimal places).

To learn more about probability : brainly.com/question/31828911

#SPJ11

(a) 1/2 (b) The expected time until all three customers have left the post office is 3/2 units of time , (c) we can show that X1A2P(C is not the last to leave) = 1 + A2 + d2.

(a) Since the service times of all customers are IID exponential random variables with mean 1/1, the memoryless property of exponential distributions implies that the remaining service time of person C is still exponential with mean 1/1, regardless of how long person A and person B have been serviced. Therefore, the probability that person C will be the last to leave is the same as the probability that person A or person B will be the last to leave, which is 1/2.

(b) Let T1, T2, and T3 be the service times of person A, person B, and person C, respectively. Since all service times are exponential with mean 1/1, we have E[T1] = E[T2] = E[T3] = 1. Therefore, the expected time until all three customers have left the post office is E[T1+T2+T3] = E[T1] + E[T2] + E[T3] = 3/2, by the result from problem P3(b) about the sum of exponential random variables.

(c) Let λ1 and λ2 be the service rates of clerk 1 and clerk 2, respectively. Since the service time of person C depends on which clerk is available when person C arrives, we need to consider two cases. If person C is serviced by clerk 1, then the remaining service time of person C is exponential with mean 1/λ1. If person C is serviced by clerk 2, then the remaining service time of person C is exponential with mean 1/λ2. Therefore, the probability that person C is not the last to leave the post office is given by:

P(C is not the last to leave) = λ1/(λ1+λ2) * (1 - exp(-(λ1+λ2)/λ1)) + λ2/(λ1+λ2) * (1 - exp(-(λ1+λ2)/λ2))

Using the result from problem P3(a), we can simplify this expression as:

P(C is not the last to leave) = 1/(1+λ2/λ1)

Therefore, we can show that X1A2P(C is not the last to leave) = X1A2/(1+λ2/λ1) = X1A2/(X1+X2) = 1 + A2 + d2, by the result from problem P3(a).

To learn more about mean click here, brainly.com/question/31101410

#SPJ11

Answer:

what you mean im confused

Step-by-step explanation:

Answer:

my school

Step-by-step explanation:

block me from sieng the image

Answer:

answer: Hi = 15

Step-by-step explanation:

the larger shape is the same as the smaller shape just flipped over and bigger of course so to find this out you have to take 2 simular angles and find out what multiplied by the small angle will get the big angle so I see angles gh and ba are simular I try 4.5 ÷ 1.5 = 3 so 3 is how much the shape is being multiplied by so bc is simular to hi so I do 5 x 3 = 15 and theres are answer 15 is the length of hi hope this helps you!

Answer: 150$

Step-by-step explanation:

60 minutes in an hour means you make 5$ * 6 = 30$ per hour.

For 5 hours would be 150$

Answer:

Please check the explanation.

Step-by-step explanation:

Given the table

Time, x(hours)             Number of Cells, y

0                                   100

1                                     200

2                                    400

h                                     6400

We know that the exponential function is of the form

A(b)ˣ = y

substituting x = 0 and y  = 100

A(b)⁰ = 100

A×1 = 100           ∵ (b)⁰ = 1

substituting x = 1 and y = 200

A(b)¹ = 200

Ab = 200

plug in A = 100

100×b = 200

b = 200/100

b = 2

So, the values of A and b are:

Thus, the equation of the exponential function becomes:

A(b)ˣ = y

substituting A = 100 and b = 2

100(2)ˣ = y

Thus, the equation of the exponential function becomes:

Given that we have to determine the value of 'h' hours at y = 6400

so substituting y = 6400

100(2)ˣ = y

100(2)ˣ = 6400

divide both sides by 100

\(\frac{100\cdot \:2^x}{100}=\frac{6400}{100}\)

Simplify

\(2^x=64\)

\(\:2^x=2^6\)              ∵ 2⁶ = 64

\(x=6\)

Therefore, in 6 hours i.e. x = 6 h, the number of cells present will be 6400.

Answer:

62,489

Step-by-step explanation:

60089

+  2400

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

62,489

Answer:

18n-42 should make it as simple as it can be.

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

The phasor form of a sinusoid represents the amplitude and phase angle of the sinusoid in complex number notation. In this case, the phasor form of \(8 sin(20t 57)\) would be 8 ∠57°. The amplitude, 8, is the magnitude of the complex number, and the phase angle, 57°, is the angle of the complex number in the complex plane.

In terms of amplitude and phase angle, a sinusoidal waveform is mathematically represented in phasor form. Electrical engineering frequently employs it to depict AC (alternating current) circuits and signals. A complex number that depicts the magnitude and phase of a sinusoidal waveform is called a phasor. The phase angle is represented by the imaginary component of the phasor, whereas the real part of the phasor represents the waveform's amplitude. Complex algebra can be used to analyse AC circuits using the phasor form, which makes computations simpler and makes it simpler to see how the circuit behaves.

Learn more about phasor here:
https://brainly.com/question/22970717

#SPJ11

Therefore, the probability that Smith wins 8 dollars before losing all of his money is approximately 0.0479.

To solve this problem, we can use a probability tree diagram to visualize the different possible outcomes.

At each stage, Smith either wins a dollars or loses a dollars, until he either reaches 8 dollars (and wins) or 0 dollars (and loses). We can calculate the probability of each outcome by multiplying the probabilities of the branches leading to that outcome.

Starting with 3 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 4 dollars.

Smith loses a dollar with probability 0.6, leaving him with 2 dollars.

From 4 dollars, there are three possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 5 dollars.

Smith loses a dollar with probability 0.6, leaving him with 3 dollars.

Smith wins 4 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 7 dollars.

From 5 dollars, there are two possible outcomes:

Smith wins a dollar with probability 0.4, leaving him with 6 dollars.

Smith wins 3 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

From 6 dollars, there are two possible outcomes:

Smith wins 2 dollars with probability 0.4 * 0.4 = 0.16, leaving him with 8 dollars.

Smith loses a dollar with probability 0.6, leaving him with 5 dollars.

From 7 dollars, there is one possible outcome:

Smith wins 1 dollar with probability 0.4, leaving him with 8 dollars.

Therefore, the probability that Smith wins 8 dollars before losing all of his money is the sum of the probabilities of the outcomes that lead to winning 8 dollars, which is:

0.4 * 0.6 * 0.4 * 0.4 + 0.4 * 0.6 * 0.4 * 0.6 * 0.4 + 0.4 * 0.6 * 0.4 * 0.4 * 0.6 * 0.16 + 0.4 * 0.6 * 0.4 * 0.4 * 0.4 * 0.4 * 0.16 = 0.047872

To know more about probability,

https://brainly.com/question/13690215

#SPJ11

Answer:

3

8

Step-by-step explanation:

probability= no. of blue marbles

total no. of marbles

= 3

8

Answer:

\(\pounds36\)

Step-by-step explanation:

Cost of one dress = \(\pounds40\)

Cost of one pair of shoes = \(\pounds32\)

Cost of one dress and a pair of shoes is \(40+32=\pounds72\)

They get half off the price because they buy both

\(\dfrac{72}{2}=\pounds32\)

The shipping and handling charge is \(\pounds4\).

So, the total amount Ruth has to pay is \(32+4=\pounds36\).

The 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

The following formula is used to calculate a confidence interval for the proportion of all American adults who support same-sex marriage

KI = p ± z*(√(p*(1-p)/n))

where:

p = percentage of respondents who support same-sex marriage

n = sample size (total number of respondents)

z = z-score for the desired confidence level

substitute all the values in the above formula,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/n))

To compute confidence intervals, we need to know the sample size (n). the sample size is large, so we can use the normal distribution.

the random sample size of 1000 is taken as no sample size is specified.

For n = 1000,

CI = 0.517 ± 1.96*(√(0.517*(1-0.517)/1000))

= 0.517 ± 0.032

Therefore, the 95% confidence interval for the proportion of all American adults who support same-sex marriage is 0.485 to 0.549.

learn more about normal distribution

brainly.com/question/29509087

#SPJ4

The reason why {[0]} and z/7z are the only subgroups of z/7z is because {[0]} is the trivial subgroup consisting only of the identity element.

And z/7z is a cyclic group of order 7, which means that it has no non-trivial proper subgroups other than {[0]}. This is because any subgroup of a cyclic group must also be cyclic, and the order of any subgroup must divide the order of the original group.

Since the only divisors of 7 are 1 and 7, the only possible subgroups of z/7z are {[0]} and the entire group z/7z itself.

the only possible subgroups are the trivial subgroup containing just the identity element {[0]}, and the entire group itself (Z/7Z). This is due to Lagrange's Theorem, which states that the order of a subgroup must divide the order of the group.

To know more about Lagrange's Theorem click here

brainly.com/question/13264870

#SPJ11

Answer:

To convert 15 inches to yards you need to divide 15 by 36 to get 41.67 yards tep-by-step explanation:

Answer:

14 blue

Step-by-step explanation:

3/2 = 21/b

3b = 42

b = 42/3

b = 14

The formula for allocation deviation is as follows:σA = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)σB = (w1σ1^2 + w2σ2^2 + … + wσn^2)^(1/2)

Here,

σ1 = 15%

σ2 = 10%

w1 = 50%,

w2 = 50%

Substituting the values in the above formula:

σA = (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158 = 1.58%σB

= (0.5 × 0.15^2 + 0.5 × 0.10^2)^(1/2)

= (0.0225 + 0.0100)^(1/2)

= 0.0158

= 1.58%

Hence, the correct option is

D. σ(A) = 14.14%;

σ(B) = 16.33%.

To know more about deviation visit:

https://brainly.com/question/31835352

#SPJ11

Answer:

length = 10.64 cm, width = 5.64 cm, and height = 5 cm.

Step-by-step explanation:

Total volume of dice that filled the box = (150 x 2) cm³

                                         = 300 cm³

Let the length, width and height of the box be represented by l, w and h respectively.

So that;

l = (w + 5) cm

w = w

h = 5 cm

volume of the box = length x width x height

                               = (w + 5) x w x 5

                               = (w + 5) x 5w

                               = 5\(w^{2}\) + 25w

volume of the box = 5\(w^{2}\) + 25w

Since the box was completely filled by 150 dice, then;

total volume of dice = volume of the box

300 = 5\(w^{2}\) + 25w

5\(w^{2}\) + 25w - 300 = 0

Divide through by 5 to have;

\(w^{2}\) + 5w - 60 = 0

Applying the quadratic expression,

w = (-b ± \(\sqrt{b^{2} - 4ac}\)) ÷ 2a

where: a = 1, b = 5 and c = -60

(-5 ± \(\sqrt{5^{2} - 4(1*-60)}\) ) ÷ 2

(-5 ± \(\sqrt{265}\)) ÷ 2

(-5 ± 16.28) ÷ 2

(-5 + 16.28) ÷ 2 OR (-5 - 16.28) ÷ 2

5.64 OR -10.64

Thus, w = 5.64 cm

So that, l = (w + 5) = 10.64 cm

The possible dimensions of the box are: length = 10.64 cm, width = 5.64 cm and height = 5 cm.

Answer:

x= 17

Step-by-step explanation:

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides adjacent to the right angle. The hypotenuse is the side of the triangle opposite the right angle.

Hope this helps.

The length of the side length x = 17 units, for the given right-angled triangle, was found using the Pythagoras Theorem.

In a right-angled triangle, the side opposite to the right angle is called the hypotenuse, and the other two sides are called the two legs (or, base and perpendicular respectively).

According to the Pythagoras theorem, in a right-angled triangle, the square of the hypotenuse is the sum of the squares of the two legs. This can be written as:

Hypotenuse² = Base² + Perpendicular².

In the question, we are given a right-angled triangle with lengths of the legs as 8 and 15 units respectively, and the length of the hypotenuse is x units.

We are asked to find the value of the x.

To find the value of x, we will use the Pythagoras Theorem, by which,

Hypotenuse² = Base² + Perpendicular².

or, x² = 8² + 15²

or, x² = 64 + 225

or, x² = 289 = 17²

or, x = 17.

∴ The length of the side length x = 17 units, for the given right-angled triangle, was found using the Pythagoras Theorem.

Learn more about the Pythagoras Theorem at

https://brainly.com/question/231802

#SPJ2