if you’re good with probability in math 30 please help and answer the question below!!


A six-sided number cube has faces with the numbers 1 through 6 marked on it. What is the probability that a number less than 3 will occur on one toss of the number cube?

a) 1/6

b) 1/2

c) 1/3

d) 2/3

Answer:

a) The equation of Z and C is Z =K C

b) K = 2

Step-by-step explanation:

Explanation :-

Given data Z is directly proportional to C

              ⇒   Z ∝ C

               ⇒  Z = K C

The equation of relating Z and C    

               Z = K C

Given Z = 20 and C =10

              20 = K ( 10)

          ⇒ K = 2

Answer:

C is the correct answer.

Step-by-step explanation:

The reason it is C is because pi/the symbol on top is irrational.

Hope you have a good rest of your day :)

Answer:

  B.  135

Step-by-step explanation:

For ...

f(5) = 3·5^2 -5

   = 3·25 -5 = 75 -5 = 70

Then g(f(5)) is ...

  g(f(5)) = g(70) = 2·70 -5 = 140 -5

  g(f(5)) = 135 . . . . . matches choice B

Answer:

The best data collection method or sampling method to provide an unbiased sample is the random sampling method.

Step-by-step explanation:

There are 5 popular known sampling methods or data collection methods.

1) Random Sampling

In random sampling, each member of the population would have an equal chance of being surveyed. One of the best ways to use random sampling is to give all the members of the population numbers and then use computer to generate random numbers and pick the members of the population with those random numbers.

2) Systematic sampling is easier than random sampling. In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.

3) Convenience Sampling

This is the worst sampling technique. It is also the easiest. In Convenience sampling, the surveyor just picks the first set of members of the population that they find and surveys.

4) Stratified Sampling

Stratified sampling divides the population into groups called strata. A sample is taken from each of these strata using either random, systematic, or convenience sampling.

5) Cluster sampling

Cluster Sampling divides the population into groups which are called clusters or blocks. The clusters are selected randomly, and some members or every element/member in the selected clusters is surveyed.

Hope this Helps!!!

Answer:

B

The mode is 11 and 3

The Median is 10

The mean is 12

Answer:

-8.5

Step-by-step explanation:

-4x+8=42

-4x=42-8

-4x=34

x=34/-4

x=-8.5

Answer:

The recoil velocity of the gun is [tex]0.72\,\,\frac{km}{h}[/tex]  and is pointing in opposite direction to the velocity of the bullet.

Step-by-step explanation:

Use conservation of linear momentum, which states that the momentum of the bullet (product of the bullet's mass times its speed) should equal in absolute value the momentum of the recoiling gun (its mass times its recoil velocity).

We also write the mass of the bullet in the same units as the mass of the gun (for example kilograms). Mass of the bullet = 0.010 kg

In mathematical terms, we have:

[tex]5\, kg * v= 0.01 \,kg\,* 360\,\frac{km}{h} \\v=\frac{0.01\,*360}{5} \,\,\frac{km}{h}\\v=0.72\,\,\frac{km}{h}[/tex]

Answer:

a). r = [tex]\frac{6}{7}[/tex]

b). At least 5 terms should be added.

Step-by-step explanation:

Formula representing sum of infinite geometric sequence is,

[tex]S_{\inf}=\frac{a}{1-r}[/tex]

Where a = first term of the sequence

r = common ratio

a). If the sum is seven times the value of its first term.

    [tex]7a=\frac{a}{1-r}[/tex]

    [tex]7=\frac{1}{1-r}[/tex]

    7(1 - r) = 1

    7 - 7r = 1

    7r = 7 - 1

    7r = 6

    r = [tex]\frac{6}{7}[/tex]

b). Since sum of n terms of the geometric sequence is given by,

    [tex]S_{n}=\frac{a(1-r^{n})}{1-r}[/tex]

If the sum of n terms of this sequence is more than half the value of the infinite sum.

[tex]\frac{a[1-(\frac{6}{7})^{n}]}{1-\frac{6}{7}}[/tex] >  [tex]\frac{7a}{2}[/tex]

[tex]\frac{1-(\frac{6}{7})^{n}}{1-\frac{6}{7}}> \frac{7}{2}[/tex]

[tex]\frac{1-(\frac{6}{7})^{n}}{\frac{1}{7}}> \frac{7}{2}[/tex]

[tex]1-(\frac{6}{7})^{n}> \frac{7}{2}\times \frac{1}{7}[/tex]

[tex]1-(\frac{6}{7})^{n}> \frac{1}{2}[/tex]

[tex]-(\frac{6}{7})^{n}> -\frac{1}{2}[/tex]

[tex](\frac{6}{7})^{n}< \frac{1}{2}[/tex]

[tex](0.85714)^{n}< (0.5)[/tex]

n[log(0.85714)] < log(0.5)

-n(0.06695) < -0.30102

n > [tex]\frac{0.30102}{0.06695}[/tex]

n > 4.496

n > 4.5

Therefore, at least 5 terms of the sequence should be added.

Answer:

81%

Step-by-step explanation:

22+5=27

22/27

Answer:

By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

What minimum percentage of commuters in Boston has a commute time within 2 standard deviations of the mean

By the Chebyshev Theorem, at least 75% of commuters in Boston has a commute time within 2 standard deviations of the mean

95% of commuters in Boston has a commute time within 2 standard deviations of the mean

Empirical rule states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.

Hence, 95% of commuters in Boston has a commute time within 2 standard deviations of the mean

Find out more on Empirical rule at: https://brainly.com/question/10093236

Answer:

Step-by-step explanation:

20 sin^4x

=5(4sin^4 x)

=5(2sin²x)²

=5(1-cos 2x)²

=5(1-4cos2x+cos²(2x))

=5[1-4cos(2x)+{1+cos (4x)}/2]

=5/2[2-8cos(2x)+1+cos(4x)]

=5/2[3-8cos (2x)+cos (4x)]

Answer:

the loan was 1000

Step-by-step explanation:

Take the tuition and multiply by 5/6

1200 *5/6

1200/6 *5

200 *5

1000

Answer:

$1000

Step-by-step explanation:

In order to find 5/6 of the tuition, we just need to multiply the 2 values together.

5/6*1200

Note that 1200 = 1200/1

5/6*1200/1

When multiplying fractions, we can multiply the numerators together, and the denominators together.

5*1200/6*1

6000/6

Divide.

1000

Therefore, the loan was $1000.

Answer: To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93

Step-by-step explanation:

Answer:

An acute angle is open

Step-by-step explanation:

An acute angle is an angle that is less than [tex]90^{0}[/tex]. Two or more acute angles are set to be complementary if their sum equals a right angle.

Clara's diagram involves two acute angles JLK and KLM with both sharing the side LK.

If the acute angles are complementary angles, then JLM would be a right angle.

If the acute angles are not complementary angles, then JLM would be less than a right angle.

So the appropriate choice to select is an acute angle is open. Which implies that JLM may be a right angle or not depending on the degrees of the acute angles involved.

Answer:

Option C.

Step-by-step explanation:

The given logarithmic equation is

[tex]\log_2(x+11)=4[/tex]

It can be written as

[tex](x+11)=2^4[/tex]     [tex][\because log_ax=y\Leftrightarrow x=a^y][/tex]

[tex]x+11=16[/tex]

[tex]x=5[/tex]

Now, to check whether [tex]x=5[/tex] is a true solution or not. Substitute [tex]x=5[/tex] in the LHS of given equation.

[tex]LHS=\log_2(5+11)[/tex]

[tex]LHS=\log_2(16)[/tex]

[tex]LHS=\log_22^4[/tex]

[tex]LHS=4[/tex]     [tex][\because log_aa^x=x][/tex]

[tex]LHS=RHS[/tex]

Hence, [tex]x=5[/tex] is a true solution because [tex]\log_2(16)=4[/tex].

Therefore, the correct option is C.

Answer:

C on edge2021

Step-by-step explanation:

Answer: The answers are in the steps hopes it helps.

Step-by-step explanation:

40% * x = 23   convert 40% to a decimal

0.4 * x = 23     multiply 0.4 is by x

0.4x = 23    divide both sides by 0.4

x= 57.5  

Check:  

57.5 * 40% = ?

57.5 * 0.4 = 23

Multiply 2 by 1/2 to get 1.

Multiply 1 by 2/3 to get 2/3.

Multiply 2/3 by 3/4 to get 6/12 = 1/2.

Multiply 1/2 by 4/5 to get 4/10 = 2/5.

Multiply 2/5 by 5/6 to get 10/30 = 1/3.

Multiply 1/3 by 6/7 to get 6/21 = 2/7. (I suspect there's a typo in the question.)

And so on, so that the nth term in the sequence is multiplied by n/(n + 1) to get the (n + 1)th term.

Recursively, the sequence is given by

[tex]\begin{cases}a_1=2\\a_n=\dfrac{n-1}na_{n-1}&\text{for }n>1\end{cases}[/tex]

We can solve this exactly by iterating:

[tex]a_n=\dfrac{n-1}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}na_{n-1}=\dfrac{n-1}n\dfrac{n-2}{n-1}\dfrac{n-3}{n-2}a_{n-3}=\cdots[/tex]

and so on down to

[tex]a_n=\dfrac{(n-1)\cdot(n-2)\cdot(n-3)\cdot\cdots\cdot3\cdot2\cdot1}{n\cdot(n-1)\cdot(n-2)\cdot\cdots\cdot4\cdot3\cdot2}a_1[/tex]

or

[tex]a_n=\dfrac{(n-1)!}{n!}a_1[/tex]

and with lots of cancellation, we end up with

[tex]a_n=\dfrac{a_1}n=\boxed{\dfrac2n}[/tex]

Answer:

Divide 2 by n.

Step-by-step explanation:

Answer:

The number of students reporting readings between 87 g and 89 g is 61

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 88g

Standard deviation = 1g

Percentage of students reporting readings between 87 g and 89 g

87 = 88-1

So 87 is one standard deviation below the mean.

89 = 88+1

So 89 is one standard deviation above the mean.

By the Empirical Rule, 68% of students are reporting readings between 87 g and 89 g.

Out of 90 students:

0.68*90 = 61.2

Rounding to the nearest whole number:

The number of students reporting readings between 87 g and 89 g is 61

Answer:

P(M > 260.2-cm) = 0.702

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

[tex]\mu = 260.5, \sigma = 1.6, n = 8, s = \frac{1.6}{\sqrt{8}} = 0.5657[/tex]

P(M > 260.2-cm)

This is 1 subtracted by the pvalue of Z when X = 260.2. So

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

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{260.2 - 260.5}{0.5657}[/tex]

[tex]Z = -0.53[/tex]

[tex]Z = -0.53[/tex] has a pvalue of 0.298.

1 - 0.298 = 0.702

So

P(M > 260.2-cm) = 0.702

Answer:

The range of p-values

0.01 < p < 0.025

Step-by-step explanation:

Explanation:-

Given random sample size 'n' = 7

Assume that the populations are normally distributed

Null Hypothesis :H₀:μd=0.

Alternative Hypothesis:H₁:μd<0.

Degrees of freedom

ν = n-1 =7-1 =6

given the test statistic  t = - 3.201

we will use single tailed test in t-distribution table

The test statistic t= 3.201 is lies between the critical values is 0.01 and 0.025

The range of p-values

0.01 < p < 0.025  (check t- distribution table single tailed test)

Final answer:-

The range of p-values

0.01 < p < 0.025

Answer:

To the nearest hundredth of a percentage= 0.03

Step-by-step explanation:

Formula for compound interest

A= p(1+r/n)^nt

A= $330

P= $210

n = 356

t= 17

r = ?

330 = 210(1+r/356)^(356*17)

330 = 210(1+r/356)^(6052)

330/210 = (1+r/356)^6052

(6052√(330/210) - 1 )356 = r

(1.000074686-1)356= r

0.02658 = r

To the nearest hundredth of a percentage= 0.03

Answer:

2.66

Step-by-step explanation:

Answer:

1) The normal distribution should be used for the sample mean because the population distribution is known to be normal (answer b).

2) C. H0: mu = 519, H_1: mu not equal to 519, reject if z> 1.96 or z< -1.96.

3) Yes. There is enough evidence to support the claim that the true mean is not 519 ml.

Step-by-step explanation:

1) When the population follows a normal distribution, it is correct to assume a normal distribution for the sample mean.

2) As it is a two-tailed decision rule, we are interested in detecting a significant difference below and above the mean. This is why we use the unequal sign in the alternative hypothesis.

The null hypothesis state that there is not significant difference from 519.

The critical value for a significance level of 5% is z=1.96.

[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]

3) The claim is that the true mean is not 519 ml.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=519\\\\H_a:\mu\neq 519[/tex]

The significance level is 0.05.

The sample has a size n=16.

The sample mean is M=522.

The standard deviation of the population is known and has a value of σ=6.

We can calculate the standard error as:

[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{6}{\sqrt{16}}=1.5[/tex]

Then, we can calculate the z-statistic as:

[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{522-519}{1.5}=\dfrac{3}{1.5}=2[/tex]

This test is a two-tailed test, so the P-value for this test is calculated as:

[tex]\text{P-value}=2\cdot P(z>2)=0.046[/tex]

As the P-value (0.046) is smaller than the significance level (0.05), the effect is significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the true mean is not 519 ml.

Answer:

Aisha is shorter than 43 inches.

Step-by-step explanation:

[tex]x+5=48[/tex]

[tex]x=48-5[/tex]

[tex]x=43[/tex]

[tex]x >43[/tex]

Answer:

The answer is B!

Step-by-step explanation:

Test taking! <3

Answer:

 3x ≤ -6

Step-by-step explanation:

"At most" means "less than or equal to." If x represents the number, then you have ...

  (three) times (a number) (is at most) negative 6 . . . . . English

      3       ·         x                ≤           -6 . . . . . . . . . . . . . . . . Math

__

  3x ≤ -6

Answer:

3x ≤ -6

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

Because the slope is -0.09 the answer is the second option. A negative slope means a decrease.

Answer:

A.

Step-by-step explanation:

Density = Mass / Volume

D = 3/0.2

D = 15 kg/m³

Answer:

density=mass/volume

d=3kg/0.2m3

=15kgm-3

Answer:

Check Explanation

Step-by-step explanation:

In finding the public's view on pollution, the researchers waited outside a car dealership they had randomly selected from a list of such establishments. They stopped every 10th person who came out of the dealership and asked whether he or she thought pollution was a serious problem.

A) The population

The population is the sum total of every member of the public whose opinions on pollution, the researchers are interested in.

B) The population parameter of interest

Since the researchers stopped every member of the sample to ask them whether they thought pollution was a serious problem or not, it follows that the population parameter of interest is the proportion of the population who think that pollution is a serious problem.

C) The sampling frame

The sampling frame is defined as the source material where the sample is drawn from. And for this question, the sampling frame is the population of people leaving car dealership establishments.

D) The sample

The sample is the set of people that were asked the question of whether population was a serious problem or not. The sample includes every 10th person that came out of the chosen car dealership establishments.

E) The sampling method

Note that

- In random sampling, each population member would have an equal chance of being surveyed.

- Stratified sampling divides the population into groups called strata. A sample is taken from some or all of these strata using either random, systematic, or convenience sampling.

- In systematic sampling, a particular number, n, is counted repeatedly and each of the nth member is picked to be sampled.

Hence, this stratified sampling method uses random sampling technique to pick the strata where the samples will be obtained from and systematic sampling is now used for the picking of the members of the sample.

F) Any potential sources of bias you can detect and any problems you see in generalizing to the population of interest.

This survey only limits the members of the sample to those who visit a car dealership, and this cuts out a large percentage of the total population of humans.

Mostly men visit car dealership establishments, Hence, women, children, old people are at a disadvantage as they do not all have an equal chance of being surveyed.

Infact, only a financial class of the population visits car dealership establishments, so, it would be very wrong with all of this bias to use the results of this surveyor generalize for the whole population of people.

Hope this Helps!!!

Answer:

C

Step-by-step explanation:

-8 14 = 42 (He subtracted 14 from 42)

-8p = 28 (Which is how he got 28)

p = -3.5 (He took 28 divide by -8 which got him -3.5)

Answer:

C

Step-by-step explanation:

C

Answer:

5x^3(to the power of 3)

Step-by-step explanation:

10x^5/2x^2

divide the 10/2 like normal to get 5

x^5/x^2 (subtract the powers 5-2 when dividing powers)

you would get 5x^3

Answer:

The sample size must be greater than 37 if we want to reject the null hypothesis.

Step-by-step explanation:

We are given that someone claims that the breaking strength of their climbing rope is 2,000 psi, with a standard deviation of 10 psi.

Also, we are given a level of significance of 5%.

Let [tex]\mu[/tex] = mean breaking strength of their climbing rope

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 2,000 psi       {means that the mean breaking strength of their climbing rope is 2,000 psi}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 2,000 psi      {means that the mean breaking strength of their climbing rope is lower than 2,000 psi}

Now, the test statistics that we will use here is One-sample z-test statistics as we know about population standard deviation;

                         T.S.  =  [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex]  ~ N(0,1)

where, [tex]\bar X[/tex] = ample mean strength = 1,997.2956 psi

            [tex]\sigma[/tex] = population standard devaition = 10 psi

            n = sample size

Now, at the 5% level of significance, the z table gives a critical value of -1.645 for the left-tailed test.

So, to reject our null hypothesis our test statistics must be less than -1.645 as only then we have sufficient evidence to reject our null hypothesis.

SO,  T.S. < -1.645   {then reject null hypothesis}

         [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < -1.645[/tex]

         [tex]\frac{1,997.2956-2,000}{\frac{10}{\sqrt{n} } } < -1.645[/tex]

         [tex](\frac{1,997.2956-2,000}{10}) \times {\sqrt{n} } } < -1.645[/tex]

          [tex]-0.27044 \times \sqrt{n}< -1.645[/tex]

               [tex]\sqrt{n}> \frac{-1.645}{-0.27044}[/tex]

                 [tex]\sqrt{n}>6.083[/tex]

                  n > 36.99 ≈ 37.

SO, the sample size must be greater than 37 if we want to reject the null hypothesis.