Simplify the following expression 1^9

The solution to the inequality [tex]\( \frac{2}{3}x - \frac{5}{6} \geq \frac{1}{2} \)[/tex] is [tex]\( x \geq 2 \)[/tex].

Given inequality: [tex]\( \frac{2}{3}x - \frac{5}{6} \geq \frac{1}{2} \)[/tex]

Step 1: To simplify the equation, let's find a common denominator for the fractions. The least common multiple (LCM) of 3 and 6 is 6.

Step 2: Rewrite the fractions with the common denominator, which is 6.

So, [tex]\( \frac{2}{3}x - \frac{5}{6} \)[/tex] becomes [tex]\( \frac{4x}{6} - \frac{5}{6} \).[/tex]

Step 3: Now, we have the equation [tex]\( \frac{4x}{6} - \frac{5}{6} \geq \frac{1}{2} \).[/tex]

Step 4: Combine the fractions on the left side of the equation: [tex]\( \frac{4x - 5}{6} \geq \frac{1}{2} \)[/tex].

Step 5: To get rid of the denominator, multiply both sides of the equation by 6 to clear it.

[tex]\( 6 \times \frac{4x - 5}{6} \geq 6 \times \frac{1}{2} \)[/tex]

This simplifies to: [tex]\( 4x - 5 \geq 3 \)[/tex]

Step 6: Now, let's isolate [tex]\(x\)[/tex] by adding 5 to both sides:

[tex]\( 4x - 5 + 5 \geq 3 + 5 \)[/tex]

[tex]\( 4x \geq 8 \)[/tex]

Step 7: Finally, divide both sides by 4:

[tex]\( \frac{4x}{4} \geq \frac{8}{4} \)[/tex]

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

Complete correct question:

Solve: [tex]\frac{2}{3} x-\frac{5}{6} \geq \frac{1}{2}[/tex]

Answer:

0.3

Step-by-step explanation:

Given: The odds of winning a contest are 3:7

To find: probability of winning the contest

Solution:

Probability refers to chances of occurrence of an event.

Odds are defined as (chances for success) : (chances against success)

Probability of winning = (chances for success) : (chances for success + chances against success)  

As odds of winning a contest are 3:7,

(chances for success) : (chances against success) = 3:7

So,

Probability of winning the contest = [tex]\frac{3}{3+7} =\frac{3}{10}=0.3[/tex]

Final answer:

To find the probability of winning a contest when given odds, add the two parts of the odds together and divide the favorable outcome by the total outcomes. For odds of 3:7, the probability of winning the contest is 3/10.

Explanation:

The odds of winning a contest are 3:7. What is the probability of winning the contest?

To find the probability from odds, you need to add the two numbers together to get the total possible outcomes. In this case, 3 + 7 = 10. Then, divide the favorable outcome by the total outcomes, so 3/10. This gives a probability of winning the contest as 3/10.

Answer:

  n(A) = 2701

Step-by-step explanation:

If we subtract 299 from the numbers in the set, we get the counting numbers ...

  {1, 2, 3, ..., 2701}

The number of elements in the set is 2701:

  n(A) = 2701

n(A) is a notation used to denote the number of elements in a set. For the set A = {300, 301, 302, ..., 3000}, n(A) is calculated as 2701.

To find n(A) for the set A = {300, 301, 302, ..., 3000}, let's first understand that n(A) means. n(A) is a notation used in set theory to denote the number of elements in a set. In this case, it’s asking for the total number of integers from 300 to 3000.

You can calculate it by using the formula n = the last number - the first number + 1. Substituting the given values, we get n = 3000 - 300 + 1 = 2701. Therefore, n(A) for the set is 2701.

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Answer:

89.44%

Step-by-step explanation:

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.

In this question:

[tex]\mu = 45, \sigma = 5.6[/tex]

If you score 52 on the test, what percentage of test takers scored lower than you?

This is the pvalue of Z when X = 52.

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

[tex]Z = \frac{52 - 45}{5.6}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944.

So 89.44% of test takers scored lower than you.

Answer:

(D)117 Cubic Inches

Step-by-step explanation:

Dimensions of the box are:

Length[tex]=7\frac{1}{2}\:inch[/tex]

Width[tex]=4\frac{1}{3}\:inch[/tex]

Height[tex]=3\frac{3}{5}\:inch[/tex]

Volume of the Box =Length X Width X Height

[tex]=7\dfrac{1}{2}X4\dfrac{1}{3}X3\dfrac{3}{5}\\\\=\dfrac{15}{2}X\dfrac{13}{3}X\dfrac{18}{5}\\\\=\dfrac{15X13X18}{2X3X5}\\\\=\dfrac{3510}{30}[/tex]

=117 Cubic Inches

The volume of the box is 117 cubic inches.

Answer:

D) 117 cubic inches

Step-by-step explanation:

Have a wonderful day!

The product of each number and 3x in the set [-6, -11, -14, -9] is [-18x, -33x, -42x, -27x]. The term 'product' refers to the result of multiplication. This was calculated by individually multiplying each number in the set by 3x.

The question is asking what the product would be if you multiplied each number in the array by 3x. In mathematical terms, product refers to the result obtained from multiplying at least two numbers together.

Here's how we'd do this:

So, in conclusion, the set of numbers you get when you multiply the original set by 3x are: [-18x, -33x, -42x, -27x]. You calculate these one at a time, following the laws of multiplication. I hope that helps explain in detail what the term 'product' means in this mathematical context, and how to find it.

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Answer:

[tex]z = \frac{4-4.25}{\frac{1.5}{\sqrt{40}}}= -1.054[/tex]

And we can find the following probability:

[tex] P(z<-1.054) = 0.146[/tex]

And the last probability can be founded using  the normal standard distribution or excel.

Step-by-step explanation:

For this case we define the random variable X as the ages of vehicles. We know the following info for this variable:

[tex]\bar X = 4.25[/tex] represent the mean

[tex]\sigma =18/12=1.5[/tex] represent the deviation in years

They select a sample size of n=40>30. And they want to find this probability:

[tex] P(\bar X<40)[/tex]

Since the sample size is large enough we can use the central limit theorem and the distribution for the sample mean would be:

[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]

We can use the z score formula given by:

[tex] z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

And if we find the z score for 4 we got:

[tex]z = \frac{4-4.25}{\frac{1.5}{\sqrt{40}}}= -1.054[/tex]

And we can find the following probability:

[tex] P(z<-1.054) = 0.146[/tex]

And the last probability can be founded using  the normal standard distribution or excel.

Answer:

The answer would be 56.55ft please give brainliest :)

Answer:

55.65

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Because 9cm2 is 9 times 9 which equals 81 cm.

To find the length of one side of a cube with a surface area of 9 cm², set up the equation s² * 6 = 9. Simplify and solve for s to find that the length of one side is √(9/6) cm.

The question is asking about the surface area of a cube. The surface area of a cube can be found by multiplying the length of one side by itself, and then multiplying that result by 6 since a cube has 6 faces. So, if the surface area of a cube is 9 cm², you can set up the equation: 9 = s² * 6. Simplifying, you get s² = 9/6. Taking the square root of both sides, you find that s = √(9/6). Therefore, the length of one side of the cube is √(9/6) cm.

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Answer:

= 80y - 56 then it will be the answer, it may be incorrect so i apologize if it is.

Answer:

80y - 56

Step-by-step explanation:

Answer:

Step-by-step explanation:

a) A test of H0​: p = 0.6 vs. HA​: p < 0.6 fails to reject the null hypothesis. Later it is discovered that p = 0.7.

Answer: No error has been made since there is not enough statistical evidence to reject the null.

b) A test of H0​: μ = 30 vs. HA​: μ > 30 rejects the null hypothesis. Later it is discovered that μ = 29.9. ​

A type I error has been made. Rejecting the null hypothesis when it is actually true.

c) A test of H0​: p = 0.4 vs. HA​: p /= 0.4 rejects the null hypothesis. Later it is discovered that p = 0.55.

A type I error has been made since the p value was greater than 0.4, one will fail to reject the null but in the case the null was rejected.

d) A test of H0​: p = 0.7 vs. HA​: p < 0.7 fails to reject the null hypothesis. Later it is discovered that p = 0.6.

A type II error has been made since the p value is less than 0.7 and it was expected that the null should be rejected but that ws not the case.

In situation a and d, a Type II error was made as the null hypothesis was not rejected but it should have been. In situation b, a Type I error was made as the null hypothesis was rejected but it shouldn't have been. In situation c, neither error was made as the null hypothesis was correctly rejected.

In each of the following situations, different types of errors are made. A type I error is made when the null hypothesis is true, but it is rejected. A type II error is the opposite, when the null hypothesis is false, but it isn't rejected.

   d) Type II error: The null hypothesis was not rejected, although the actual population proportion (0.6) was less than the hypothesized proportion (0.7).    

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Answer:

27

Step-by-step explanation:

PEMDAS

Answer:8

Step-by-step explanation:

2x4=2x2x2

4x2=2x2x2

The greatest common factor is 2x2x2=8

Answer:

The mean of the total repair time is 150 minutes.

The variance of the total repair time is 725 minutes^2.

Step-by-step explanation:

To solve this problem, we have to use the properties of the mean and the variance. Our random variable is the sum of 3 normal variables.

In the case, for the mean, we have that the mean of the sum of 3 normal variables is equal to the sum of the mean of the 3 variables:

[tex]y=x_1+x_2+x_3 \\\\E(y)=E(x_1+x_2+x_3)=E(x_1)+E(x_2)+E(x_3)\\\\E(y)=50+60+40=150[/tex]

For the variance, we apply the property for the sum of independent variables (the correlation between the variables is 0):

[tex]V(y)=V(x_1)+V(x_2)+V(x_3)\\\\V(y)=s_1^2+s_2^2+s_3^2\\\\V(y)=15^2+20^2+10^2\\\\V(y)=225+400+100\\\\V(y)=725[/tex]

Answer:

The 95% confidence interval for the population proportion is (0.778, 0.884).

Step-by-step explanation:

We have to calculate a 95% confidence interval for the proportion.

The sample proportion is p=0.831.

The standard error of the proportion is:

[tex]\sigma_p=\sqrt{\dfrac{p(1-p)}{n}}=\sqrt{\dfrac{0.831*0.169}{195}}\\\\\\ \sigma_p=\sqrt{0.00072}=0.027[/tex]

The critical z-value for a 95% confidence interval is z=1.96.

The margin of error (MOE) can be calculated as:

[tex]MOE=z\cdot \sigma_p=1.96 \cdot 0.027=0.053[/tex]

Then, the lower and upper bounds of the confidence interval are:

[tex]LL=p-z \cdot \sisgma_p = 0.831-0.053=0.778\\\\UL=p+z \cdot \sisgma_p = 0.831+0.053=0.884[/tex]

The 95% confidence interval for the population proportion is (0.778, 0.884).

Answer:

[tex]z=\frac{0.537-0.531}{\sqrt{0.534(1-0.534)(\frac{1}{147}+\frac{1}{147})}}=0.103[/tex]    

Now we can calculate the p value with the following probability taking in count the alternative hypothesis:

[tex]p_v =2*P(Z>0.103) =0.918 [/tex]    

For this case since the p value is large enough we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that we have significant differences between the two proportions analyzed.

Step-by-step explanation:

Information provided

[tex]X_{1}=79[/tex] represent the number of New Yorkers familiar with the brand  

[tex]X_{2}=78[/tex] represent the number of Californians familiar with the brand  

[tex]n_{1}=147[/tex] sample of New Yorkers

[tex]n_{2}=147[/tex] sample of Californians

[tex]p_{1}=\frac{79}{147}=0.537[/tex] represent the proportion New Yorkers familiar with the brand  

[tex]p_{2}=\frac{78}{147}=0.531[/tex] represent the proportion of Californians familiar with the brand  

[tex]\hat p[/tex] represent the pooled estimate of p

z would represent the statistic

[tex]p_v[/tex] represent the value

System of hypothesis

We want to verify if the two proportions of interest for this case are equal, the system of hypothesis would be:    

Null hypothesis:[tex]p_{1} = p_{2}[/tex]    

Alternative hypothesis:[tex]p_{1} \neq p_{2}[/tex]    

The statistic would be given by:    

[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex]   (1)  

Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{79+78}{147+147}=0.534[/tex]  

Repalcing the info given we got:

[tex]z=\frac{0.537-0.531}{\sqrt{0.534(1-0.534)(\frac{1}{147}+\frac{1}{147})}}=0.103[/tex]    

Now we can calculate the p value with the following probability taking in count the alternative hypothesis:

[tex]p_v =2*P(Z>0.103) =0.918 [/tex]    

For this case since the p value is large enough we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that we have significant differences between the two proportions analyzed.

Answer:

e) None of the above

Step-by-step explanation:

We are in posession of the sample's standard deviation, so we use the student t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 43 - 1 = 42

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 42 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0181

The margin of error is:

M = T*s = 2.0181*11.3 = 22.80

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 77.86 - 22.8 = 55.06

The upper end of the interval is the sample mean added to M. So it is 77.86 + 22.8 = 100.66.

So the correct answer is:

e) None of the above

Answer:

[tex]77.86-2.02\frac{11.30}{\sqrt{43}}=74.38[/tex]    

[tex]77.86+2.02\frac{11.30}{\sqrt{43}}=81.34[/tex]    

And for this cae none of the options satisfy the result so then the best option would be:

e) None of the above

Step-by-step explanation:

Information given by the problem

[tex]\bar X= 77.86[/tex] represent the sample mean for the score

[tex]\mu[/tex] population mean  

s=11.30 represent the sample standard deviation

n=43 represent the sample size  

Calculating the confidence interval

The confidence interval for the true mean of interest is given by:

[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]   (1)

For this case the degrees of freedom are:

[tex]df=n-1=43-1=42[/tex]

The Confidence is 0.95 or 95%, the significance then is [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], the critical value for this case would be [tex]t_{\alpha/2}=2.02[/tex]

And replacing in equation (1) we got:

[tex]77.86-2.02\frac{11.30}{\sqrt{43}}=74.38[/tex]    

[tex]77.86+2.02\frac{11.30}{\sqrt{43}}=81.34[/tex]    

And for this cae none of the options satisfy the result so then the best option would be:

e) None of the above

Answer: C 5/16

stay safe !!!

The probability that a randomly selected player on Team C 10 years old is 5/16.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

According to the table the total number of 10 years old players on Team C is 5 and the total number of all ages players (8, 9 and 10 years old) on Team C is 16,

So the probability that a randomly selected player on Team C is 10 years old is 5/16.

Therefore, the probability that a randomly selected player on Team C 10 years old is 5/16.

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Answer:

The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the first five numbers are selected is not important, so we use the combinations formula to solve this question.

Combinations formula:

[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]

First five numbers:

Desired:

5 correct numbers, from a set of 5. So

[tex]D = C_{5,5} = \frac{5!}{5!(5-5)!} = 1[/tex]

Total:

5 numbers from a set of 69. So

[tex]T = C_{69,5} = \frac{69!}{5!(69-5)!} = 11238513[/tex]

Probability:

[tex]P_{5} = \frac{D}{T} = \frac{1}{11238513}[/tex]

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

Sixth number:

1 from a set of 26

Then

[tex]P_{6} = \frac{1}{26}[/tex]

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

Probability of winning the prize

[tex]P = P_{5} \times P_{6} = \frac{1}{11238513} \times \frac{1}{26} = \frac{1}{292201338}[/tex]

The probability that a player wins the jackpot is [tex]\frac{1}{292201338}[/tex]

To calculate the probability of winning the jackpot in the Powerball lottery, we need to consider the probability of choosing the first five numbers correctly and the probability of choosing the sixth number correctly. Multiply the probabilities from these two steps to find the overall probability.

To calculate the probability of winning the jackpot in the Powerball lottery, we need to consider two parts: the probability of choosing the first five numbers correctly (regardless of order) and the probability of choosing the sixth number correctly.

To find the overall probability, we multiply the probabilities from the two steps:

P(winning jackpot) = P(choosing first five numbers correctly) x P(choosing sixth number correctly) = [P(choosing one number correctly)]^5 x P(choosing one number correctly) = (5/69)^5 x 1/26

Calculating this expression gives us the probability of winning the jackpot in the Powerball lottery.

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Answer:

The total number of items to be counted each day ≈ 100

Step-by-step explanation:

Lindsay​ Electronics has 6,500 items in its inventory.

11​% of the items in inventory are A​ items

33% of the items in inventory are B items

56​% of the items in inventory are C items

A items are counted every 20 working​ days

B items are counted every 62 working​ days

C items are counted every 121 working​ days

How many items need to be counted each​ day?

First we will find the number of items of type A, B and C

Number of A​ items = 11​% of 6,500 = 0.11*6500 = 715

Number of B items = 33% of 6,500 = 0.33*6500 = 2145

Number of C items = 56% of 6,500 = 0.56*6500 = 3640

The number of A items to be counted each day is

A items = 715/20

The number of B items to be counted each day is

B items = 2145/62

The number of C items to be counted each day is

C items = 3640/121

The total number of items to be counted each day is

Total items = 715/20 + 2145/62 + 3640/121

Total items = 100.42

Rounding the answer to the nearest whole number yields,

Total items ≈ 100

Answer:

The amount of money he has in the account after 3 years:

A = Money x (1 + rate)^year

  = 2000 x (1 + 4.3/100)^3

  =2269.3 dollar

Hope this helps!

:)

Answer:

Amount of money in the account:   $2,269.25

Interest: $269.25

Step-by-step explanation:

John starts out with $2000 in savings.

(I can't be bothered to find the formula for annual compound interest, so we'll do it manually based on yearly calculations.)

Because it is calculated annually, we must do yearly calculations.

2,000 x 1.043 = 2,086.00

After the first year, at 4.3% John's $2000 Savings account would mature into $2,086.00. (earning him $86.00 interest for the year)

2,086.00 x 1.043 = 2,175.70

After, the second year at 4.3%,  $2,086.00 becomes $2,175.70.  (making his interest $175.70 total, and $89.70 for the year.)

2,175.70 x 1.043 = 2,269.25

After the third, and final year, at 4.3%, $2,175.70 becomes $2,269.25. (making the interest $269.25 or $93.56 for the year.)

1

2

0

x

+

120x+392

Step-by-step explanation:

Answer:

[tex]a_{n}[/tex] = 8 *[tex]0.5^{n-1}[/tex]

Step-by-step explanation:

First find the common ratio

r = 4/8 = 1/2

and first term is 8

a_n = a_1 * r^(n-1)

a_n = 8 * (1/2)^(n-1)

[tex]a_{n}[/tex] = 8 *[tex]0.5^{n-1}[/tex]

hi

Here is the answer :

0.25 *140 = 35

Answer: 35

Step-by-step explanation: Well percent means over 100 so we can set up an equation for this problem by reading it from left to right.

What means x, is means equals, 25% is 25/100,

of means times, and 250 means 250.

So we have the equation x = 25/100 · 40.

Simplifying on the right side of the equation,

notice that 25/100 reduces to 1/4.

So we have x = 1/4 · 40.

Think of the 40 as 40/1.

So we can cross-cancel 140 and 4 to 35 and 1

and we have x = (1)(35) over (1)(1) or x = 35.

Now let's check our answer back in the

original problem to see if it makes sense.

We have (35) is 25% of 140.

Well we know that 100% of 140 would be 140.

So 25% of 250 should be a lot less than 140.

So 35 seems to make sense as a pretty good answer.

I have shown my work in the image attached.

Answer:

I will answer a few questions so you can apply the same logic to the others

The volume of a sphere = [tex]\frac{4}{3}[/tex] π [tex]r^{3}[/tex]

1.

We can see that the radius of the sphere is 5cm

Substitute the value into the equation for volume and solve for V

V = [tex]\frac{4}{3}[/tex] * π * [tex]5^{3}[/tex]

V = 523.6 [tex]cm^{3}[/tex]

4.

The diameter is given to us as 6km. To find the radius we take half of this, 3km

Substitute the value into the equation for volume and solve for V

V = [tex]\frac{4}{3}[/tex] * π * [tex]3^{3}[/tex]

V = 113.1 [tex]km^{3}[/tex]

Hopefully that helps you with completing the rest!

Answer:

10

Step-by-step explanation:

When two numbers are placed together that close with parenthesis, you are most likely (99.9% of the time), going to be multiplying them.

Note that:

When you multiply two positive numbers, your result is positive.

When you multiply one negative and one positive number, your result will be negative.

When you multiply two negative numbers, your result will be positive.

Multiply -5 with -2: -5 * -2 = 10

10 is your answer.

~

Final answer:

No, the given probability experiment does not represent a binomial experiment because it does not meet the three conditions required for a binomial experiment.

Explanation:

No, the given probability experiment does not represent a binomial experiment. In order for an experiment to be considered a binomial experiment, it must meet three conditions:

1. There must be a fixed number of trials, denoted by 'n'. However, in the given experiment, the number of stocks that the investor purchases is not fixed.

2. There must be only two possible outcomes, called success and failure, for each trial. However, in the given experiment, the outcomes can have three possibilities: the stock can increase, decrease, or have no change in value.

3. The 'n' trials must be independent and repeated using identical conditions. However, in the given experiment, the success or failure of one stock can potentially influence the success or failure of another stock.

Answer:

[tex]90\pi[/tex]

Step-by-step explanation:

The first step is to find the slant height of the cone. Using the pythagorean theorem, you can find that [tex]\sqrt{12^2+5^2}=13[/tex] cm. Plugging this into the equation, you get [tex]\pi \cdot 5 \cdot 13=90\pi[/tex]. Hope this helps!

Phytagoras Theorem :

c² = a² + b²

c² = 9² + 2²

c² = 81 + 4

c² = 85

c = √85

So, the distance between the following points is √85

Hope it helpful and useful :)