g Assuming the probability of a single sample testing positive is 0.15​, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely​ necessary?

Step-by-step explanation:

Let adults = a and children = c,

(1) a + c = 1100

(2) 48a + 23c = 45300

From the (1) equation, a = 1100 - c

Then substitute a = 1100 - c into (2),

48(1100 - c) + 23c = 45300

52800 - 48c +23c = 45300

-25c = -7500

c = 300

Substitute c = 1500 into a = 1100 - c,

a = 1100 - 300

a = 800

Therefore, 800 adults and 300 children bought the tickets

Answer:

5+4 = 9

6+4 = 10

7+4 =11

Step-by-step explanation:

Answer:

(5,9)

(6,10)

(7,11)

Step-by-step explanation:

w = m + 4

when m = 5,

w = 5 + 4 = 9

when m = 6

w = 6 + 4 = 10

when m = 7

w = 7 + 4 = 11

Step-by-step explanation:

here's the answer to your question

Answer: Third Choice. 3i√3

Step-by-step explanation:

Concept:

Here, we need to know the idea of radical expression and an imaginary number.

A radical expression is any mathematical expression containing a radical symbol. If you need to multiply the number outside of radical back into the radical, then you need to square the number then multiply.

Imaginary numbers are the numbers when squared it gives the negative result. An imaginary number is a complex number that can be written as a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.

Solve:

3√3 = √(3 × 3²) = √27     FALSE

-3√(3i) = √(3i × (-3)²) = √27i     FALSE

3i√3 = √(3 × (3i)²) = √-27     TRUE

3√(3i) = √(3i × 3²) = √27i     FALSE

As we can see from above, only the third choice equals √-27.

Hope this helps!! :)

Please let me know if you have any questions

Answer:

150%

Step-by-step explanation:

is the correct answer

Answer:

-55.5+12.9c

Step-by-step explanation:

-55.5 — -8.55c +4.35c

Subtracting a negative is like adding

-55.5 +8.55c +4.35c

Combine like terms

-55.5          +8.55c +4.35c

-55.5          +12.9c

Step-by-step explanation:

angle of a triangle is 180, therefore to get the remaining one, subtract the sum of the two knows from 180, also for the second one; angle on a straight line is as well 180, since you have fine the interior one, subtract it from 180 to get the second answer

Answer:

so angles in a triangle add up to 180,

32+50+m<MQP=180

82+m<MQP=180

m<MQP=180-82

=98°

and angles on a straight line add up to 180 therefore

m<MQR=180-m<MQP

=180-98

=82

I hope this helps and if you don't understand feel free to ask

Answer:

(x-3)^2+(y+1/2)^2=3.25

Step-by-step explanation:

The radius of the circle would be the midpoint of diameter. Radius is (3,-1/2) and the length would be 1.8.

Answer:

c

Step-by-step explanation:

Answer:

The mean is the average number of a data set gotten by adding all the numbers then dividing by two.

the median is the middle number in a sorted set of data,either sorted in ascending order or descending order.

I hope this helps

To calculate mean:

• add up all the numbers,

• then divide by how many numbers there are.

Example:

Data: 5, 6, 10, 1

Add these all together, which is 22, then divide by 4 (because that is how many numbers there are), so:

the mean is 5.5

To calculate median:

Arrange your numbers in order.

Cross off numbers until you get to the middle.

If there is an even number of data, then find the two in the middle and find the middle of that.

Example:

Data: 5, 6, 10, 1

Arrange: 1, 5, 6, 10

So, the middle 2 are 5 and 6. In between these would be 5.5, so that is the median.

If the data was: 1, 5, 6, 8, 10,

then the median would be 6.

Answer:

9 − (3 x 2) ÷ 3 + 6 is the answer

According to the manufacturer's claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, we have that:

As the test involves a comparison of samples, it involves subtraction of normal variables, and for this, we need to understand the central limit theorem and subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Before:

Average of 0.250 in 56 at bats, so:

[tex]p_B = 0.25[/tex]

[tex]s_B = \sqrt{\frac{0.25*0.75}{56}} = 0.0579[/tex]

After:

Average of 0.44 in 25 at bats, so:

[tex]p_A = 0.44[/tex]

[tex]s_A = \sqrt{\frac{0.44*0.56}{25}} = 0.0993[/tex]

Test if there was improvement:

At the null hypothesis, we test if there was no improvement, that is, the subtraction of the proportions is 0:

[tex]H_0: p_A - p_B = 0[/tex]

At the alternative hypothesis, we test if there was improvement, that is, the subtraction of the proportions is positive, so:

[tex]H_1: p_A - p_B > 0[/tex]

The test statistic is:

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

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_B - p_A = 0.44 - 0.25 = 0.19[/tex]

[tex]s = \sqrt{s_A^2 + s_B^2} = \sqrt{0.0579^2 + 0.0993^2} = 0.1149[/tex]

Value of the test statistic:

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

[tex]z = \frac{0.19 - 0}{0.1149}[/tex]

[tex]z = 1.65[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a difference of at least 0.19, which is 1 subtracted by the p-value of z = 1.65.

Looking at the z-table, z = 1.65 has a p-value of 0.9505.

1 - 0.9505 = 0.0495.

The p-value of the test is of 0.0495 > 0.02, which means that there is not sufficient evidence to say that his batting average has improved at the 0.02 level of significance.

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Answer:

D

Step-by-step explanation:

since

cos(2x) = 1 - 2×sin²(x)

and for x near 0, sin(x) is very similar to x.

Answer:

y = 4x -1.5

Step-by-step explanation:

The slope intercept form of a line is given by

y = mx+b  where m is the slope and b is the y intercept

y = 4x -1.5

9514 1404 393

Answer:

  {x ∈ ℝ | x ≤ 3}

Step-by-step explanation:

Subtracting 5 from both sides, we see the solution is ...

  x ≤ 3

In set notation, this can be written ...

  {x ∈ ℝ | x ≤ 3}

Answer:

(-16, 17)

Step-by-step explanation:

The range of the function will be (-16, 17)

The range of function f(x) = 3x + 2 overthe interval -6 < x < 5 is (-13,14)

The difference between the highest and lowest values.

The given function is  f(x) = 3x + 2

f(x) equal tp three times of x plus two.

The given interval is minus six less than x less than five.

-6 < x < 5

Which means the x values are -5, -4, -3, -2, -1, 0, 1, 2,3,4

Plus in the function

f(-5)=-15+2=-13

f(-4)=-10

f(-3)=-9+2=-7

f(-2)=-6+2=-4

f(-1)=-3+2=-1

f(0)=0+2=2

f(1)=3+2=5

f(2)=6+2=8

f(3)=9+2=11

f(4)=12+2=14

Hence the range of function f(x) = 3x + 2 overthe interval -6 < x < 5 is (-13,14)

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Answer:

C

Step-by-step explanation:

the answer is C because only C contained it's correct root and power

Answer:

cannot understand the language man

but please follow

Answer:

5.3

Step-by-step explanation:

2×2×4/3

= 5.3 (rounded to the nearest tenth)

Answer.

ANSWER

.......

Equate what is inside cosine with [tex]2\pi[/tex], base period and solve for x,

[tex]2\pi=\frac{\pi}{3}x[/tex]

[tex]6\pi=\pi x[/tex]

[tex]\boxed{x=6}[/tex]

Hope this helps :)

Answer:

10 5/16

Step-by-step explanation:

2 2/5 x 4 1/8 = 10 5/16

Answer:

3043 (base 6)

Step-by-step explanation:

216      36    6    1

3           0      4  3

216* 3 = 648

6*4 = 24

1*3 = 3

648+24+3 = 675

Answer:

3 pants are $20.55

4 shirts are $47.9

Step-by-step explanation:

a pant is $6.85 × 3= $20.55

68.45 - 20.55 = $47.9

$47.9 ÷ 4 = $11.98 a shirt

Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing.

A control experiment can be defined as a type of experiment in which a condition assumed to be a probable cause of an effect is compared with the same situation without involving or using the suspected condition.

A treatment group refers to a group of participants in an experiment that are exposed to some manipulation in the independent variable such as an administration of medication to a particular group.

Thus, Janelle can conclude that the medication used in this experiment was effective and it decreases sneezing because the treatment group show reduced signs of sneezing.

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Answer:

The ratio of the perimeters of the first nonagon to the second is 3.6 to 1.

Step-by-step explanation:

Given that a regular nonagon has an area of 90 square feet, and a similar nonagon has an area of 25 square feet, to determine what is the ratio of the perimeters of the first nonagon to the second, the following calculation must be performed:

25 = 1

90 = X

90/25 = X

3.6 = X

Therefore, the ratio of the perimeters of the first nonagon to the second is 3.6 to 1.

Answer:

Surface area of prism is 48km^2

The two stem plots (with and without splitting the leaves) are plotted below using the data given in the attached picture :

The stem and leaf plots are given below:

Rounding the data to the nearest 10;

The values obtained are :

630, 670, 740, 650, 710, 740, 720, 700, 650, 600, 780, 780, 790, 810, 830, 860, 860, 900, 810, 790, 790, 960, 870

Ordering the data allows for easier generation of the plot.

Ordered data : 600, 630, 650, 650, 670, 700, 710, 720, 740, 740, 780, 780, 790, 790, 790, 810, 810, 830, 860, 860, 870, 900, 960

The stem plot without splitting :

STEM __ LEAF

6 ___ 00, 30, 50, 50, 70

7 ___ 00, 10, 20, 40, 40, 80, 80, 90, 90, 90

8 ___ 10, 10, 30, 60, 60, 70

9 ___ 00, 60

KEY :  6 | 00 = 600

The stem plot WITH splitting :

STEM __ LEAF

6 ___ 00, 30

6 ___ 50, 50, 70

7 ___ 00, 10, 20, 40, 40

7 ___ 80, 80, 90, 90, 90

8 ___ 10, 10, 30

8 ___ 60, 60, 70

9 ___ 00

9 ___ 60

KEY :  6 | 00 = 600

The stem plot with splitting gives a cleaner and more arranged output of the data as the values aren't congested on a single line.

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A quotient is found by dividing two numbers and a quotient with a denominator of zero is infinity which is not a real number

The word that complete the sentence is therefore;

Each quotient must have a nonzero denominator

The reason by which the above word is selected is as follows;

The set of Real Numbers include;

Rational numbers; a/b, where b = nonzero number

Integers; Positive and negative whole numbers, including zero

Whole numbers; 0, 1, 2

Natural numbers; Positive whole numbers excluding zero

Irrational number; Numbers that cannot be expressed as a/b

A quotient is the outcome of dividing two numbers, x by y

Therefore;

Quotient = x/y

A quotient can be a rational or irrational number, however, a quotient that has a denominator of zero (y = 0) is infinity, which is not a real number

When y = 0, x/y = x/0 = ∞ (∞ is not a real number)

Therefore, from the properties of Real Numbers,

Each quotient must have a nonzero denominator to be a Real Number

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