Solve the equation. And write all solutions in general form.

Answer:

if the sequence is:

12, 13, 13, 14, 14 etc, and each term keeps growing up, the sequence obviusly diverges.

Now, if the sequence is

1/2, 1/3, 1/3, 1/4, 1/4, 1/5 , 1/5

so the terms after the first one repeat, we could group the terms with the same denominator and get:

1/2, 2/3, 2/4, 2/5..... etc.

So the terms after the first one are aₙ = 2/n.

Now, a criteria to see if a sequence converges if seing if:

[tex]\lim_{n \to \infty} a_n = 0[/tex]

and here we have;

[tex]\lim_{n \to \infty} 2/n[/tex]

that obviusly tends to zero, so we can conclude that this sequence converges.

then the limit is:

There exist a n' such that for any n > n' then IL -aₙI < ε

where L is the limit

I2/n - 0I = I2/nI < ε

then this is true if n > 2/ε = n'

Answer:

x = 150°

Step-by-step explanation:

Start by cutting the shape into two triangles by bisecting the 30°

Now we have two triangles that have two angles 90° and 15°

Subtract 15° from 90°, you'll get 75°

Double 75° because x is split into 2

150° = x

Also, were given 3 angles, this is a quadrilateral.

90° + 90° +  30° = 210°

360° - 210° = 150°

Answer:

150°

Step-by-step explanation:

OA⊥AC and OB⊥BC

∠A+∠B+∠C+∠O=360°

90°×2+30°+x=360°

x=360°-210°=150°

Answer:

14

Step-by-step explanation:

Since sine and cosine are cofunctions of each other:

[tex]\sin (\theta)= \cos (90-\theta)[/tex]

and vice versa. Therefore:

[tex]18+x=90-58 \\\\18+x=32 \\\\x=32-18=14[/tex]

Hope this helps!

Answer:

D.

Step-by-step explanation:

One slope is positive and one negative, so one line should go up and one down. B or D.

y = 1/2 x - 1 line goes up and y-int. = - 1.  Answer D.

y = - 1/2 x + 3 line goes up and y-int. = 3.  Answer D.

Answer:

Step-by-step explanation:

You take 70.3m^3 multiple with 880kg /m^3 divide with 5300.kg will give you the answer cause I tried it and it worked 100% true.

I hope tis helps .

Answer:

[tex] P(X<12000)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]

Then we can conclude that the probability that your bid will be accepted would be 0.41

Step-by-step explanation:

Let X the random variable of interest "the bid offered" and we know that the distribution for this random variable is given by:

[tex] X \sim Unif( a= 10100, b =14700)[/tex]

If your offer is accepted is because your bid is higher than the others. And we want to find the following probability:

[tex] P(X<12000)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<12000)= \frac{12000-10100}{14700-10100}= 0.41[/tex]

Then we can conclude that the probability that your bid will be accepted would be 0.41

This is the steps for equation solving for the value of x,

x/3-7 = 11

now 7 goes to the other side of equation by changing the sign from - to +,

x/3 = 11 + 7

x/3 = 18

now when we multiply both sides of equation with 3 or 3 goes to the other side of equation and multiply with 18 leaving x alone here for finding the value of x,

and we get, x = 54

at the end of equation we get x = 54, if the equation was in the form 3x - 7 = 11, then we will get x = 6

Answer:

a. The distribution is bell-shaped and symmetric: True.

b. The distribution is bell-shaped and symmetric: True.

c. The probability to the left of the mean is 0: False.

d. The standard deviation of the distribution is 1: True.

Step-by-step explanation:

The Standard Normal distribution is a normal distribution with mean, [tex] \\ \mu = 0[/tex], and standard deviation, [tex] \\ \sigma = 1[/tex].

It is important to recall that the parameters of the Normal distributions, namely, [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] characterized them.

We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where [tex] \\ x[/tex] is the raw score that we want to standardize.

Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:

(a) True or False: The distribution is bell-shaped and symmetric

Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.

(b) True or False: The mean of the distribution is 0.

Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex]

If [tex] \\ x = \mu[/tex]

[tex] \\ z = \frac{\mu - \mu}{\sigma}[/tex]

[tex] \\ z = \frac{0}{\sigma}[/tex]

[tex] \\ z = 0[/tex]

Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.

(c) True or False: The probability to the left of the mean is 0.

Answer: False. The probability to the left of the mean is not 0. The cumulative probability from [tex] \\ -\infty[/tex] until the mean is 0.5000 or [tex] \\ P(-\infty < z < 0) = 0.5[/tex].

(d) True or False: The standard deviation of the distribution is 1.

Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.

In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, [tex] \\ x - \mu[/tex], by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, [tex] \\ \sigma[/tex].

In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.

Answer:

A: true

B: true

C: false

D: true

Answer:

  A.  The weekly usage of both coupons is decreasing and approaching a horizontal asymptote as x gets larger.

Step-by-step explanation:

You can see that f(x) is a decreasing exponential function because the base is 0.75, a value less than 1. The horizontal asymptote is 10, the constant added to the exponential term.

Obviously, g(x) is decreasing. If we assume it is an exponential function, we know there is a horizontal asymptote. (Every exponential function has a horizontal asymptote.)

__

If you use your graphing calculator's exponential regression function, you can find a good model for g(x) is ...

  g(x) = 950·0.7^x +12

That is, it is an exponential function that decays faster than f(x), but has a higher horizontal asymptote.

_____

Both functions are decreasing and approaching horizontal asymptotes.

Answer:

[tex]z=-1.49[/tex]

Step-by-step explanation:

[tex]\text{Standard Score, z} =\dfrac{X-\mu}{\sigma} $ where:\\\\Mean Pulse rate, \mu =67.3$ beats per minute\\Standard Deviation, \sigma = 10.3$ beats per minute.\\[/tex]

For a male student who has a measured pulse rate of 52 beats per  minute.

Raw Score, X =52 beats per  minute.

Therefore:

[tex]\text{Standard Score, z} =\dfrac{52-67.3}{10.3}\\z=-1.49[/tex]

Since the usual pulse rates are within 2 standard deviations of the mean, a z-score of -1.49 tells us that the selected student's pulse rate is within the usual pulse rates.

Answer:

6x(x - 6y +2)

Step-by-step explanation:

Step 1: Write out expression

6x² - 36xy + 12x

Step 2: Factor out x

x(6x - 36y + 12)

Step 3: Factor out 6

6x(x - 6y + 2)

That is the most we can do. We can only take GCF to factor. Since we don't have an y² term we do not have binomial factors.

Answer:

1.2kg

Step-by-step explanation:

6 identical toys weigh 1.8kg.

1 toy would weigh:

1.8/6 = 0.3

0.3 kg.

Multiply 0.3 with 4 to find how much 4 identical toys would weigh.

0.3 × 4 = 1.2

4 identical toys would weigh 1.2kg

Answer:

[tex]1.2kg[/tex]

Step-by-step explanation:

6 identical toys weigh = 1.8kg

Let's find the weight of 1 toy ,

[tex]1.8 \div 6 = 0.3[/tex]

Now, lets find the weigh of 6 toys,

[tex]0.3 \times 4 = 1.2kg[/tex]

Answer:

[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]

And we can find this probability using the normal standard table with this difference:

[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]

Step-by-step explanation:

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(1539,1580)[/tex]  

Where [tex]\mu=1400[/tex] and [tex]\sigma=\sqrt{10000}= 100[/tex]

We are interested on this probability

[tex]P(1539<X<1580)[/tex]

And we can solve the problem using the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we got:

[tex]P(1539<X<1580)=P(\frac{1539-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{1580-\mu}{\sigma})=P(\frac{1539-1400}{100}<Z<\frac{1580-1400}{100})=P(1.39<z<1.8)[/tex]

And we can find this probability using the normal standard table with this difference:

[tex]P(1.39<z<1.80)=P(z<1.80)-P(z<1.39)= 0.9641-0.9177=0.0464[/tex]

Answer:

Step-by-step explanation:

The equation of this circle is (x - 3)^2 + (y - 3)^2 = 12^2.

Let's substitute the coordinates of the given point and compare the results to the above equation:  do they produce a correct statement?

(-6 - 3)^2 + (-5 - 3)^2 = ?

9^2 + 8^2 = 145

Because r = 12, the above result would need to be 144, not 145, if the given point were actually on the circle.  We must conclude that (-6, -5) lies just outside the circle.

81 + 64 = 144  

Answer:

The x-coordinate is the solution to x - 4 = 0, which is x = 4 and the y-coordinate is 3 so the answer is (4, 3).

Answer:

Three: x = 400

Four : 9

Step-by-step explanation:

Three

a = 10*√2

2a = √(2x)                    Square both sides.

4a^2 = 2x                     Divide both sides by 2

2a^2 = x                       Put a = 10√2 into a^2

2(10√2)^2 = x               Square a

2(100*2) = x                 Multiply the result by 2.

2(200) = x

x = 400

Four

x^(a^2) / x ^(b^2) = x^36

Substitute a + b = 4 in for b.

x^(a^2) / x^(4 - a)^2 = x^36

Subtract powers

x^(a^2 - (4 - a)^2 = x^36

x^(a^2 - (16 - 8a + a^2) = x^36

Gather like terms

x^(8a - 16) = x^36

The powers are now equal

8a - 16 = 36      

Add 16 to both sides

8a = 36 + 16

8a = 52

Divide by 8

a = 6.5

Solve for b

a + b = 4

6.5 + b = 4

b = 4 - 6.5

b = - 2.5

a - b = 6.5 - (- 2.5) = 9

Answer:

0.495 probability that Jim and Molly take counters of different colours

Step-by-step explanation:

For each trial, there are only two possible outcomes. Either a blue counter is picked, or a red counter is picked. The counter is put back in the bag after it is taken, which means that we can use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The probability that the counter is red is 0.45

This means that [tex]p = 0.45[/tex]

Jim taken a counter, then Molly:

Two trials, so [tex]n = 2[/tex]

What is the probability that Jim and Molly take counters of different colours?

One red and one blue. So this is P(X = 1).

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{2,1}.(0.45)^{1}.(0.55)^{1} = 0.495[/tex]

0.495 probability that Jim and Molly take counters of different colours

Answer:

Minimum = 25

First quartile = 58

Second quartile = 72

Third quartile = 80

Maximum = 98

Step-by-step explanation:

Answer:

Mean: 94.5.

Median: 99.5

Standard deviation: 33.1

We can tell the owner that the applicants don't have a score significantly below from 100.

Step-by-step explanation:

First, we analize the sample and calculate the statistics (mean, median and standard deviation).

Mean of the sample:

[tex]M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{10}(95+105+120+81+90+115+99+100+130+10)\\\\\\M=\dfrac{945}{10}\\\\\\M=94.5\\\\\\[/tex]

The median, as the sample size is an even number, can be calculated as the average between the fifth and sixth value, sort by value:

[tex]\text{Median}=\dfrac{99+100}{2}=99.5[/tex]

The standard deviation is:

[tex]s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{9}((95-94.5)^2+(105-94.5)^2+(120-94.5)^2+. . . +(10-94.5)^2)}\\\\\\s=\sqrt{\dfrac{9834.5}{9}}\\\\\\s=\sqrt{1092.7}=33.1\\\\\\[/tex]

To tell if this sample has a value significantly lower than the expected score of 100, we should make a hypothesis test.

The claim is that the mean score is significantly lower than 100.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=100\\\\H_a:\mu< 100[/tex]

The significance level is 0.05.

The sample has a size n=10.

The sample mean is M=94.5.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=33.1.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{33.1}{\sqrt{10}}=10.467[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{94.5-100}{10.467}=\dfrac{-5.5}{10.467}=-0.53[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=10-1=9[/tex]

This test is a left-tailed test, with 9 degrees of freedom and t=-0.53, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-0.53)=0.306[/tex]

As the P-value (0.306) is bigger than the significance level (0.05), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that the mean score is significantly lower than 100.

Answer:

[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]

So the answer for this case would be n=183 rounded up to the nearest integer

Step-by-step explanation:

Information provided

[tex]\bar X[/tex] represent the sample mean

[tex]\mu[/tex] population mean (variable of interest)

[tex]\sigma = 0.143[/tex] represent the population standard deviation

n represent the sample size  

[tex] ME = 0.023[/tex] the margin of error desired

Solution to the problem

The margin of error is given by this formula:

[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]    (a)

And on this case we have that ME =0.023 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex]   (b)

The confidence level is 97% or 0.97 and the significance would be [tex]\alpha=1-0.97=0.03[/tex] and [tex]\alpha/2 = 0.015[/tex] then the critical value would be: [tex]z_{\alpha/2}=2.17[/tex], replacing into formula (5) we got:

[tex]n=(\frac{2.17(0.143)}{0.023})^2 =182.03 \approx 183[/tex]

So the answer for this case would be n=183 rounded up to the nearest integer

Answer:

C

Step-by-step explanation:

Answer:

[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]

Time for bacteria count reaching 8019: t = 2.543 hours

Step-by-step explanation:

To find the composite function N(T(t)), we just need to use the value of T(t) for each T in the function N(T). So we have that:

[tex]N(T(t)) = 22 * (8t + 1.7)^2 - 123 * (8t + 1.7) + 40[/tex]

[tex]N(T(t)) = 22 * (64t^2 + 27.2t + 2.89) - 984t - 209.1 + 40[/tex]

[tex]N(T(t)) = 1408t^2 + 598.4t + 63.58 - 984t - 169.1[/tex]

[tex]N(T(t)) = 1408t^2 - 385.6t - 105.52[/tex]

Now, to find the time when the bacteria count reaches 8019, we just need to use N(T(t)) = 8019 and then find the value of t:

[tex]8019 = 1408t^2 - 385.6t - 105.52[/tex]

[tex]1408t^2 - 385.6t - 8124.52 = 0[/tex]

Solving this quadratic equation, we have that t = 2.543 hours, so that is the time needed to the bacteria count reaching 8019.

Answer:

Step-by-step explanation:

the equation of a line is given as

[tex]y= mx+c[/tex]

where

m= is the slope

c= is the y intercept

their mistake is that they did not recall that if the "c" is not shown, it is assumed to be zero (0)

Answer:

You're pretty sure that your candidate for class president has about 55% of the votes in the entire school. but you're worried that only 100 students will show up to vote. how often will the underdog (the one with 45% support) win? to find out, you set up a simulation.

a. describe-how-you-will-simulate a component.

b. describe-how-you-will-simulate a trial.

c. describe-the-response-variable

Step-by-step explanation:

Part A:

A component is one voter's voting. An outcome is a vote in favor of our candidate.

Since there are 100 voters, we can stimulate the component by using two random digits from 00 - 99, where the digits 00 - 64 represents a vote for our candidate and the digits 65 - 99 represents a vote for the under dog.

Part B:

A trial is 100 votes. We can stimulate the trial by randomly picking 100 two-digits numbers from 00 - 99.

And counted how many people voted for each candidate.  Whoever gets the majority of the votes wins the trial.

Part C:

The response variable is whether the underdog  wins or not.

To calculate the experimental probability, divide the number of trials in which the simulated underdog wins by the total number of trials.

Answer: z = 55.

Step-by-step explanation:

we want to find values of k that make this inconsistent.

x - 2y + 4z = 3

4x + 5y + kz = 9

y + 3z = 2

First, can you can see that k never can make some of the equations linearly dependent because of how constructed is the set. Now, let's see if there are values of k that give problems to our system.

To see it, let's solve the system.

from the third equation we can write y = 2 - 3z, and we can replace it into the first two equations:

x - 2(2 - 3z) + 4z  = 3

4x + 5(2 - 3z) + kz = 9

simplify both equations and get

x  + 10z = 7

4x  + ( k - 15)*z = - 1

from the first equation, we have that:

x = 7 - 10z

we can replace it into the other equation:

4*(7 - 10z) + (k - 15)*z = -1

28 - 40z + (k -15)*z = -1

(k - 55)*z = -29

z = -29/(k - 55)

here you can see that the only value of z that has problems is z = 55, because we never can have a 0 in the denominator.

Answer:

6%

Step-by-step explanation:

We have to calculate the interest rate in the note, we must follow the following steps, calculate the amount of time remaining from the year 2021, as follows:

interest is for 5 months i.e. from Aug 01 to Dec 31 for year 2021 , so it means it would be 5/12 months.

We have to calculate the interest as follows:

I = P * R * T

We replace:

200 = 8000 * R * 5/12

we solve for R

200 * 12/5 = 8000 * R

R * 8000 = 480

R = 480/8000

R = 0.06

Which means that the interest rate on the note is 6%

Answer:

The value of 7.9-4.36 is 3.54

The value of 5.27 + 3.5 is 8.77

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Answer:

  x = -1

Step-by-step explanation:

The usual approach to these is to square the radicals until they are gone.

  [tex]\displaystyle\sqrt{3x+7}+\sqrt{x+1}=2\\\\(3x+7) +2\sqrt{(3x+7)(x+1)}+(x+1) = 4\qquad\text{square both sides}\\\\2\sqrt{(3x+7)(x+1)}=-4x-4\qquad\text{subtract $4x+8$}\\\\(3x+7)(x+1)=(-2x-2)^2\qquad\text{divide by 2, square again}\\\\3x^2+10x +7=4x^2+8x+4\qquad\text{simplify}\\\\x^2-2x-3=0\qquad\text{subtract the left expression}\\\\(x-3)(x+1)=0\qquad\text{factor}\\\\x=3,\ x=-1\qquad\text{solutions to the quadratic}[/tex]

Each time the equation is squared, the possibility of an extraneous root is introduced. Here, x=3 is extraneous: it does not satisfy the original equation.

The solution is x = -1.

_____

Using a graphing calculator to solve the original equation can avoid extraneous solutions. The attachment shows only the solution x = -1. Rather than use f(x) = 2, we have rewritten the equation to f(x)-2 = 0. The graphing calculator is really good at showing the function values at the x-intercepts.

Answer:

<XWZ is a right angle

Step-by-step explanation:

Since <YWZ and <XWY both equal 45 degrees, So, <XWZ is a right angle.

Given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,

Triangles that are similar possess equal corresponding angles.

We are given that:

ΔYWZ ~ ΔYXW

∠YWZ = ∠XWY = 45 degrees

∠YWZ + ∠XWY = ∠XWZ

45 + 45 = ∠XWZ

∠XWZ = 90 degrees (right angle).

Therefore, given that ΔYWZ and ΔYXW are similar triangles, the statement that is true about ΔYXW is: B. XWZ is a right angle,

Learn more about similar triangles on:

https://brainly.com/question/2644832