1. There are 65 adults and 15 children in a movie theater. Of these people, 41 adults and 6 children bought popcorn.


a) What is the probability that a randomly selected person in the theater is a child or someone who bought popcorn.


b) What is the probability that a randomly selected person is an adult or someone who did not buy popcorn.

My answers are 0.70 and 0.925 respectively. My friends believe otherwise.

Answer:

Height of the cone = 4 m

Step-by-step explanation:

Given:

Volume of a cube = (12π) m^3

Radius of the cone = (6/2) m = 3 m

We have to find the value of "x".

And "x" is the height of the cone from the figure shown.

Formula to be used:

Volume of the cone:  1/3(πr^2h)

Here height = "x"

⇒ [tex]V_c_o_n_e=\frac{\pi r^2 h}{3}[/tex]

⇒ [tex]V_c_o_n_e=\frac{\pi r^2 x}{3}[/tex]

⇒ [tex]3\times V_c_o_n_e=\frac{\pi r^2 x}{3}\times 3[/tex]

⇒ [tex]3\times V_c_o_n_e=\pi r^2 x[/tex]

⇒ [tex]\frac{3\times V_c_o_n_e}{\pi r^2} =\frac{\pi r^2\times x}{\pi r^2}[/tex]

⇒ [tex]x=\frac{3\times V_c_o_n_e}{\pi r^2 }[/tex]

⇒ [tex]x=\frac{3\times 12\pi }{\pi (3)^2 }[/tex]

⇒ [tex]x=\frac{36\pi }{9\pi }[/tex]

⇒ [tex]x=\frac{36}{9}[/tex]

⇒ [tex]x=4[/tex] meters.

The height of the cone "x" = 4 meters option A is the right choice.

1. 130 2/3 ft3

2. 226 in.3

3. 33 cm3

4. 4 m

5. 15 m

Answer:

The p-value of her test is 0.15386.

Step-by-step explanation:

We are given that a buyer for a grocery chain inspects large truckloads of apples to determine the proportion p of apples in the shipment that are rotten.

She selects a simple random sample of 200 apples from the over 20000 apples on the truck and the sample contains 9 rotten apples.

Let p = proportion of of apples in the shipment that are rotten.

SO, Null Hypothesis, [tex]H_0[/tex] : p = 0.06   {means that the proportion of apples in the shipment that are rotten is equal to 0.06}

Alternate Hypothesis, [tex]H_A[/tex] : p < 0.06   {means that the proportion of apples in the shipment that are rotten is less than 0.06}

The test statistics that will be used here is One-sample z proportion statistics;

                               T.S.  = [tex]\frac{\hat p-p}{{\sqrt{\frac{\hat p(1-\hat p)}{n} } } } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = proportion of apples that are rotten in a sample of 200 apples = [tex]\frac{9}{200}[/tex]  = 0.045  

           n = sample of apples = 200

So, test statistics  =  [tex]\frac{0.045 -0.06}{{\sqrt{\frac{0.045(1-0.045)}{200} } } } }[/tex]

                              =  -1.02

The value of the test statistics is -1.02.

Now, P-value of the test statistics is given by;

        P-value = P(Z < -1.02) = 1 - P(Z [tex]\leq[/tex] 1.02)

                                            = 1 - 0.84614 = 0.15386

Hence, the p-value of her test is 0.15386.

Using the z-distribution, it is found that the p-value for her test is of 0.1867.

The null hypothesis is:

[tex]H_0: p = 0.06[/tex]

The alternative hypothesis is:

[tex]H_a: p < 0.06[/tex]

The test statistic is given by:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

In which:

For this problem, the parameters are:

[tex]p = 0.06, n = 200, \overline{p} = \frac{9}{200} = 0.045[/tex]

Hence, the value of the test statistic is:

[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

[tex]z = \frac{0.045 - 0.06}{\sqrt{\frac{0.06(0.94)}{200}}}[/tex]

[tex]z = -0.89[/tex]

The p-value is found using a z-distribution calculator, with a left-tailed test, as we are testing if the proportion is less than a value, with z = -0.89, and is of 0.1867.

You can learn more about the use of the z-distribution for an hypothesis test at https://brainly.com/question/25912188

Step-by-step explanation:

Given

Now arranging in ascending order

7 , 12 , 13, 24 , 24

No of data (N) = 5

Now

Position of Median

= ( N+1) / 2 th item

= (5+1)/2 th item

= 3rd item

So Now

Exact Median = 13

Answer:in 2 + in a - in b

Step-by-step explanation: edge 2021

The expanded form is ln(2) + ln(a) - ln(b) of the expression  ln(2a/b).

An expression is combination of variables, numbers and operators.

Using the properties of logarithms

log(a/b)=loga-logb

we can expand ln(2a/b) as follows:

ln(2a/b) = ln(2a) - ln(b)

Now we use the property log(ab)=loga+logb

ln(2a) = ln(2) + ln(a)

we can substitute this in the above equation:

ln(2a/b) = ln(2) + ln(a) - ln(b)

Therefore, the expanded form of expression ln(2a/b) is ln(2) + ln(a) - ln(b).

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Answer:

6, 27, 45, 279.

Based on arranging the height of candles in ascending order are:

The correct order of the candles from shortest to tallest would be:

6 in.

27 in.

45 in.

279 in.

Answer:

A = 9.9648

Step-by-step explanation:

if the triangle is equilateral =>

P = 3L => L = 14.4/3 = 4.8

A = L²√3/4

= (4.8)²√3/4

= 23.04√3/4

= 5.76×1.73

= 9.9648

Answer:

The coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is (6.5, 4)

Step-by-step explanation:

Here we have the points on the line given as

(5, -5)  and  (7, 7)

Therefore to the distance between the x and y coordinates are;

x-coordinate difference,  7 - 5 = 2 and

y-coordinate difference,  7 - (-5) = 12 and

The required ratio is 3:1, that is 3 portions on one side and 1 portion on the other.

Therefore, the total portion of the line is 3 + 1 = 4

So we divide each of the differences between x and y by 3/4 and add it to the coordinate of the first point on the line as follows

x-coordinate difference × 3/4 = 2×3/4 =1.5

y-coordinate difference × 3/4 = 12×3/4 = 9

Therefore, the coordinate of the point on the line segment from (5, -5) to (7, 7) that partitions the segment into a ratio of 3 to 1 is

x-coordinate = 5 + 1.5 = 6.5

y-coordinate = -5 + 9 = 4

or (6.5, 4).

Answer:

(6.5,4)

Step-by-step explanation:

It looks a little sketchy but its correct

To find out the amount of milliliters from liters, multiply the value by 1000. This would give us 1250 mL of soap. Divide this by 50 to figure the amount of money it would take. 25, so multiply that by $0.19, $4.75 per bottle, and then multiply that by two.

Answer: $4.75 for one bottle and $9.50 for both bottles

Answer:

-10

Step-by-step explanation:

9^-8 x 9^-2 = a^b

We know that x^y * x^z = x^(y+z)

9^-8 x 9^-2 = 9^(-8+-2) = 9^(-10)

a= 9  

b = -10

Answer:

Step 1

Step-by-step explanation:

Trent multiplied one side of the equations by 3 but multiplied the other side of the equation by 1/3.  

Trent should have multiplied both sides of the equation by 3 to isolate g.

Trent's mistake is in step 2 of their solution where they incorrectly multiplied by different values.

Trent's mistake lies in step 2 of their solution. They incorrectly multiplied the numerator and denominator of &frac43 by &frac13. To solve the equation correctly, the numerator and denominator of &frac43 should be multiplied by the same value, which in this case is 3. The correct step would be to multiply &frac43 by 3, resulting in &frac49.

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the giraffe is 18 feet tall.

Answer: The test statistic is 1.75.

Step-by-step explanation:

Since we have given that

n = 47

First mean difference = 1

and second mean difference = 1.2

Standard deviation = 0.78

So, the value of test statistic would be

[tex]t=\dfrac{\bar{x_1}-\bar{x_2}}{\dfrac{\sigma}{\sqrt{n}}}\\\\t=\dfrac{1.2-1}{\dfrac{0.78}{\sqrt{47}}}\\\\t=\dfrac{0.2}{0.114}\\\\t=1.754[/tex]

Hence, the test statistic is 1.75.

The test statistic for the sample showing the difference between reported and actual height, with a mean difference of 1.2 inches, standard deviation of 0.78, and sample size of 47, is 1.96 when rounded to two decimal places.

The test statistic for a sample where the population standard deviation is unknown and the sample size is small can be calculated using a t-test. The formula for the test statistic in a one-sample t-test is t = (\bar{X} - \mu) / (s/\sqrt{n}), where \bar{X} is the sample mean, \mu is the population mean under the null hypothesis, s is the sample standard deviation, and n is the sample size.

In this case, we are testing the claim that the mean difference in reported and actual height is greater than 1 inch. The null hypothesis (H0) is that the mean difference is less than or equal to 1 inch, and the alternative hypothesis (H1) is that the mean difference is greater than 1 inch. Given a sample mean difference of 1.2, a sample standard deviation of 0.78, and a sample size of 47, the test statistic is calculated as follows:

t = (1.2 - 1) / (0.78/\sqrt{47})

After calculating and rounding to two decimal places, the test statistic is approximately 1.96

Answer:

27

Step-by-step explanation:

please tell me if i am wrong

Answer:

X = 48

Step-by-step explanation:

When you type sin(42) in your calculator it will give you something around 0.669.

If you try reverse sinus sin-1(0.669) it will give you 42.

Therefore you can say that:

Cos(x) = 0.669

So you can reverse the cos to get your answer

Cos-1(0.669) = 48

Or

Cos-1 (sin(42))

The domain is the set of all possible input values for the function. In this case, the realistic domain for this situation would be 0 ≤ t ≤ 25, indicating the number of years from the time the motorcycle is purchased up to 25 years later.

The domain of a function in mathematics defines the set of input values for which the function is defined. In this case, the function  [tex]v(t) = 7000 \times 0.91^t[/tex]is used to calculate the value of a motorcycle, where t is the number of years after the motorcycle was bought.

As time can't be negative in this real-world scenario, the smallest value for t is 0, representing the moment the motorcycle is bought. Theoretically, t can be any positive number, although it may not be practical to consider values of t that are too large, because the value of the motorcycle will decrease significantly after several years due to depreciation.

Again, if we assume that the motorcycle will be completely worthless after 25 years, a realistic domain would be 0 ≤ t ≤ 25, that is, from the year the motorcycle is bought to 25 years afterward.

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The population proportion [tex]\( p \)[/tex] is estimated to be between 0.224 and 0.276 based on the given sample data.

To construct a confidence interval estimate for a population proportion [tex]\( p \),[/tex] you can use the following formula:

[tex]\[ \text{Confidence Interval} = \hat{p} \pm Z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \][/tex]

where:

[tex]- \( \hat{p} \)[/tex]is the sample proportion.

[tex]- \( Z \)[/tex] is the Z-score corresponding to the desired confidence level.

[tex]- \( n \)[/tex] is the sample size.

In this case:

[tex]\( n = 840 \)[/tex]

[tex]\( \hat {p} = 0.25 \)[/tex]

The confidence level is not specified, so let's assume a common confidence level of 95%. For a 95% confidence level, the Z-score is approximately 1.96.

Substitute these values into the formula:

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \sqrt{\frac{0.25(1-0.25)}{840}} \][/tex]

Now, calculate the values:

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \sqrt{\frac{0.25(0.75)}{840}} \][/tex]

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \sqrt{\frac{0.1875}{840}} \][/tex]

[tex]\[ \text{Confidence Interval} = 0.25 \pm 1.96 \times 0.0132 \][/tex]

Now, compute the upper and lower bounds of the confidence interval:

[tex]\[ \text{Lower Bound} = 0.25 - (1.96 \times 0.0132) \][/tex]

[tex]\[ \text{Upper Bound} = 0.25 + (1.96 \times 0.0132) \][/tex]

Finally, round the values to an appropriate number of decimal places. The confidence interval for the population proportion p  is:

[tex]\[ \text{Confidence Interval} = (0.224, 0.276) \][/tex]

So, with 95% confidence, the population proportion [tex]\( p \)[/tex] is estimated to be between 0.224 and 0.276 based on the given sample data.

Answer:

Area of the shaded region= 80.4 cm²

Step-by-step explanation:

Area of the square = 10×10 cm² = 100cm²

Area of the circle= πr²=π(2.5)²=3.14 ×6.25cm²

= 19.625 cm ²

Area of the shaded region= 100cm²-19.625cm²

= 80.375cm²

Final answer:

Volume of a prism is represented in cubic units as length x width x height. The SI unit of volume is cubic meter (m³) and a common unit is the liter (L), equivalent to a cubic decimeter (dm³).

Explanation:

Volume is defined as the amount of space occupied by a solid in cubic units, and for a prism that is length x width x height. In the case of volume, it goes like length cubed, represented as V = L³.

The SI unit of volume is cubic meter (m³), equal to the space occupied by a cube of 1m on each edge. A more commonly used unit of volume is the liter (L), which is equivalent to a cubic decimeter (dm³).

Answer: A, because the equation of a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex]. So, if the point of the center is [tex](5,7)[/tex] and the radius [tex]2[/tex] , then on the equation should be changed as negative and the radius should be multiplied as [tex]4[/tex], which is [tex](x-5)^2+(y-7)^2=4[/tex]

Answer:

27

Step-by-step explanation:

When looking for the volume of a prism you multiply the base and height to get the volume. When looking for the volume of a pyramid of the same base and height all you need to do is multiply .333 or 1/3 in decimal form to get the correct answer.

The volume of the prism: (3)(3)(9) = 81

The volume of the pyramid: (1/3 or .333)(3)(3)(9) = 26.973 = 27

Answer: 625

Step-by-step explanation:

Do 5 to the third power, get the answer, and then multiply times 5 to get 625. Please mark this as the brainliest answer <3

Answer:

0.035714285714286

Step-by-step explanation:

is the decimal form

Answer:

9/100

Step-by-step explanation:

It would be 9/100 as a fraction if thats what your asking!

Answer:

the first part is distant outlier, i got the other two wrong tho :,(

Answer:

spread out from and larger

Step-by-step explanation:

hope it helps

Answer:

C. 5

Step-by-step explanation:

Find the factors of 10 and 35

Factors of 10:

1,2, 5, 10

Factors of 35:

1,5,7, 35

The greatest common factor between both is 5, so C is correct

[tex]\dfrac{1}{4} =0,25\\\dfrac{7}{10} =0,7\\\dfrac{1}{4} +\dfrac{7}{10}=0,25+0,7=0,95[/tex]

Answer:

(x-1)(x+6)

Step-by-step explanation:

Answer:

What is the correct factorization of x2 + 5x – 6?

A.) (x – 1) (x + 6)

Complete the factorization shown: 3 then 2 are the blank numbers

Step-by-step explanation:

Answer:

50

Step-by-step explanation:

divide 20 girls by 2 girls to get 10.

multiply 5 by 10 to get 50 boys.

Answer:

It's false, this number is a rational number.

Step-by-step explanation:

It's false, the kind of decimal where the same digits repeats forever are known as periodic decimals and they can be represented with fractions therefore they are a part of the rational numbers. To represent this number in a fraction form we need to first identify the part that repeats, in this case it's 7, since it's only one number we can insert it in the numerator and the denominator will have a 9, if it were two numbers the denominator would have a 99 and so on. So in this case:

7/9 = 0.7777...

The statement is false. The number 0.7777 repeating is not an irrational number, but a rational number, as it can be expressed as the fraction 7/9.

The statement is false. The number 0.7777 repeating is not an irrational number. An irrational number is a number that cannot be expressed as a/b, where a and b are integers and b ≠ 0. However, the number 0.7777 repeating can be expressed as a fraction, specifically, as 7/9. Therefore, it does not meet the definition of an irrational number and is, in fact, a rational number.

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Final answer:

The probability that both marbles chosen are blue is 1/6. This is calculated by multiplying the probability of drawing a blue marble on the first and second draws consecutively (4/9 × 3/8).

Explanation:

To calculate the probability that Lena chooses two blue marbles in a row from a bag containing 3 green, 2 red, and 4 blue marbles without replacement, we must consider two consecutive events. The probability of pulling one blue marble on the first draw is 4 out of 9, since there are 4 blue marbles out of a total of 9. After the first blue marble is drawn, there are now only 3 blue marbles left out of a total of 8 marbles (since one was not replaced). The probability of drawing a blue marble on the second draw is therefore 3 out of 8.

These two probabilities must be multiplied together to find the overall probability of both events occurring in sequence:

Probability of first blue marble = 4/9

Probability of second blue marble after the first is drawn = 3/8

Overall probability = (4/9) × (3/8) = 1/6

So, the probability that both marbles Lena chooses are blue is 1/6, which is already in its simplest form.