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The correct option is B) 67.4%

A standard normal table (also called the unit normal table or z-score table) is a mathematical table for the values of ϕ, indicating the values of the cumulative distribution function of the normal distribution. Z-Score, also known as the standard score, indicates how many standard deviations an entity is, from the mean.

Given here, P(probability that a worker is a college graduate) = 32%

                                                                                                      = 0.32

q (probability that a worker is not a college graduate) is 1-0.32 = 0.68  

now μ(mean) = n×p

                      = 50×0.32

                      = 16

Again standard deviation σ = [tex]\sqrt{npq\\}[/tex]

                                           σ = [tex]\sqrt{50\cdot 0.32\cdot 0.68}[/tex]

                                           σ = 3.2985

now P(x<17.5) = P((x-μ)/σ <(17.5-16)/3.2985)

                      = P(z<0.45)  

                      = 0.674 [using z table]

                      = 67.4%

Hence option 2 is the correct answer

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Using the z-distribution, it is found that since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

At the null hypothesis, it is tested if the mean is not different to 16 ounces, that is:

[tex]H_0: \mu = 16[/tex]

At the alternative hypothesis, it is tested if the mean is different, hence:

[tex]H_1: \mu \neq 16[/tex]

The test statistic is:

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

In which:

The parameters for this problem are:

[tex]\overline{x} = 15.75, \mu = 16, \sigma = 1.46, n = 150[/tex].

Hence:

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

[tex]z = \frac{15.75 - 16}{\frac{1.46}{\sqrt{150}}}[/tex]

z = -2.1

Using a z-distribution calculator, for a two-tailed test, as we are testing if the mean is different of a value, with z = -2.1, the p-value is of 0.0357.

Since the p-value is less than 0.05, there is evidence that the mean amount of cereal in each box is different from 16 ounces at 0.05 significance.

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Answer:

1 13/30

Step-by-step explanation:

10/12 + 6/10 =

= 5/6 + 3/5

= 25/30 + 18/30

= 43/30

= 30/30 + 13/30

= 1 13/30

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Equation:}[/tex]

[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]

[tex]\huge\textsf{Solving:}[/tex]

[tex]\mathsf{\dfrac{10}{12} + \dfrac{6}{10}}[/tex]

[tex]\mathsf{= \dfrac{10\div2}{12\div2} + \dfrac{6\div2}{10\div2}}[/tex]

[tex]\mathsf{= \dfrac{5}{6} + \dfrac{3}{5}}[/tex]

[tex]\mathsf{= \dfrac{5\times5}{6\times5} + \dfrac{3\times6}{5\times6}}[/tex]

[tex]\mathsf{= \dfrac{25}{30} + \dfrac{18}{30}}[/tex]

[tex]\mathsf{= \dfrac{25 + 18}{30-0}}[/tex]

[tex]\mathsf{= \dfrac{25 + 18}{30}}[/tex]

[tex]\mathsf{= \dfrac{43}{30}}[/tex]

[tex]\approx\mathsf{1\dfrac{13}{30}}[/tex]

[tex]\huge\textsf{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\frak{1\dfrac{13}{30}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

wait ewiai twia it i ti i got this soon

(1+3) x (2 x 3)

Step-by-step explanation:

1/4×48

=12

So if 12people are out of state

48-12=36,is the number of people living in the state

Answer:30%

Step-by-step explanation:

10% of 50 is 50/10 so 10% is 5
15/5=3 so its three lots of 10%

3*10%=30%

The relationship between all pairs of special angles 1, 2, 3, and 4 created by transversal line b and parallel lines d and e include:

These are usually formed when two straight lines meet at a common endpoint or vertex.

Angles 3 and 4 are equal due to them being alternative interior angles and other relationships are mentioned above.

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The odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76.

An odds ratio is a measure of the strength of an association with the exposure and outcome.

The odds ratio can be calculated by dividing the odds of the first group (exposure) by the odds of the second group (outcome).

                             Flies      Does not fly     Total

Long beak               11               7                     19

Not a long beak      3              13                     15

Total                       14             20                    34

Probability of long beaks flying = 0.79 (1/14)

Probability of not having long beaks flying = 0.21 (3/14)

Odds ratio = 3.76 (0.79/0.21)

Thus, the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly is 3.76, showing greater odds of association.

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Complete question

Researchers wanted to study if having a long beak is related to flight in birds. They surveyed a total of 34 birds. The data are shown in the contingency table below. What is the odds ratio for birds having long beaks being able to fly against birds not having long beaks being able to fly? Round your answer to two decimal places.

Long beakNot a long beakTotalFlies11719Does not fly31315Total142034

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

The function is positive when g(x) > 0.

Then we need to solve:

∛(x - 3) > 0

We can directly remove the cubic root, because it does not affect the sign of the argument, then:

x - 3 > 0

x > 3

The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)

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The interval which the function is positive is (3, ∝)

The equation of the function is given as:

g(x) =∛x - 3

Set the radical greater than 0

x - 3 > 0

Add 3 to both sides of the inequality

x > 3

Express as an interval notation

(3, ∝)

Hence, the interval which the function is positive is (3, ∝)

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Triangle 1, triangle 3 and triangle 4 are congruent triangles bases on side-side-side and side-angle-side congruency.

Triangle is a polygon that has three sides and three angles. Types of triangles are isosceles, equilateral and scalene triangle.

Two triangles are said to be congruent if they have the same shape and their corresponding sides are congruent to each other. Also, their corresponding angles are congruent.

Triangle 1, triangle 3 and triangle 4 are congruent triangles bases on side-side-side and side-angle-side congruency.

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Step-by-step explanation:

Notice that the main vertices (-15,4) and (5,4) both have the same y coordinate. This means that the focal axis is horizontal so we have a horizontal ellispe.

Equation of a horizontal ellipse is

[tex] \frac{(x - h) {}^{2} }{ {a}^{2} } + \frac{(y - k) {}^{2} }{ {b}^{2} } = 1[/tex]

I'll explain the variables.

Step 1: Find the center.

The center (h,k) is the midpoint of either the main or co vertices. It doesn't matter because of the definition of an ellipse.

So using the midpoint formula, let find the midpoint of the main vertices.

[tex]( \frac{ - 15 + 5}{2} ) = - 5[/tex]

[tex] \frac{4 + 4}{2} = 4[/tex]

So our center is (-5,4) so as of right now we have

[tex] \frac{(x + 5) {}^{2} }{ {a}^{2} } + \frac{(y - 4) {}^{2} }{ {b}^{2} } = 1[/tex]

Step 2: The variable a represents the semi major axis. This

basically means what is the distance from the center to either main vertex.

Here, let use (5,4). Using (5,4), our main vertex and (-5,4), our center.

Use the distance formula

[tex]a= \sqrt{(5 - ( - 5) {}^{2} + (4 - 4) {}^{2} } [/tex]

[tex]a = \sqrt{100} [/tex]

[tex]a= 10[/tex]

So our distance is 10, this means a=10

Step 3: The variable b represent the semi minor axis. This basically the distance from the center to either co vertex.

Using the distance formula,

[tex]b = \sqrt{ (- 5 - ( - 5) {}^{2} + (4 - 11) {}^{2} } [/tex]

[tex]b = \sqrt{49} [/tex]

[tex]b = 7[/tex]

So b=7, so finally we plug a=10, b=7

[tex] \frac{(x + 5) {}^{2} }{100} + \frac{(y - 4) {}^{2} }{49} = 1[/tex]

The histogram that correctly shows the data in the table is the histogram number four.

This a type of graph that allows people to visually represent data by using bars and gathering the data they have in different categories.

This data can be represented using ranges of temperature and the number o elements or substances in these ranges.

This data matches the fourth graph

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The volume of the cone illustrated will be 117.2 unit³.

From the information illustrated, the glass inform of a the frustrum of a cone has the dimensions: radius 4cm and a height of 7cm.

It should be noted that the volume of a cone is calculated as:

= 1/3 πr²h.

where,

π = 3.142

r = radius = 4cm

h = height = 7cm

In this case, since we know the values of the dimensions, then we can calculate the volume. This will be:

= 1/3πr²h

= 1/3 × 3.14 × 4² × 7

= 117.2 unit³

Therefore, the volume of the shape is 117.2 unit³.

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Complete question:

A glass inform of a the frustrum of a cone has the following dimensions: radius 4cm and a height of 7cm. Calculate the volume of the shape.

Applying precedence of operations, the result of the expression is of 161.

Power operations are done before multiplication/division, which are also done before addition/subtraction.

Operations inside brackets or parenthesis also take precedence.

In this problem, the operation is:

[3 x 2^5 + 13 x (-2)] + 7[8 - (4 - 9)]

First the power:

[3 x 32 + 13 x (-2)] + 7[8 - (4 - 9)]

Now the multiplications on the first bracket, and the subtraction on the second:

[96 - 26] + 7[8 - (-5)]

Then, applying the parenthesis to the negative number, we have that:

[96 - 26] + 7[8 - (-5)] = 70 + 7 x 13 = 161.

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{3 \times 2^5 + 13(-2)] + 7[8 - (4 - 9)]}[/tex]

[tex]\mathsf{= 3\times32 + 13\times -2 + 7[8 - (4 - 9)] }[/tex]

[tex]\mathsf{= 96 + 13\times -2 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 96 - 26 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 70 + 7(8 - (4 - 9))}[/tex]

[tex]\mathsf{= 70 + 7(8 - (-5))}[/tex]

[tex]\mathsf{= 70 + 7\times13}[/tex]

[tex]\mathsf{= 70 + 91}[/tex]

[tex]\mathsf{= 161}[/tex]

[tex]\huge\text{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{161}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

40

Step-by-step explanation:

P=2(l+w)

2·(10+10)

          =40

The time at Sydney when Dan rings his friend is 1 : 30 am (option B).

The first step is determine the time difference between London and Sydney.

Time difference = time at Sydney - time at London

( 12 + 10pm) - 12pm

22pm - 12pm = 10 hours

The second step is to add the time difference to the time it was when Dan rang.

15 : 30 pm + 10pm = 25 : 30

We know that there are only 24 hours in day, so subtract 24 hours from 25 : 30

25 : 30 - 24 = 1 : 30 am

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There are 120 ways to color the 4 rectangles

The given parameters are:

Paints, n = 5

Rectangles, = 4

The number of ways to color the rectangles is

[tex]Ways = ^nP_r[/tex]

This gives

[tex]Ways = ^5P_4[/tex]

Apply the permutation formula

[tex]Ways = \frac{5!}{1!}[/tex]

Evaluate the expression

Ways = 120

Hence, there are 120 ways to color the 4 rectangles

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Answer:

-1/3

5

Step-by-step explanation:

We need to complete

y = mx + b

with a slope, m, and with the y-intercept, b.

From the graph, we see that the line intersects the y-axis at y = 5, so the y-intercept, b, is 5.

We now have y = mx + 5.

Now we need the slope.

We pick two points that are easy to read, (0, 5) and (3, 4).

m = slope = rise/run

To go from (3, 4) to (0, 5), we go up vertically 1 unit. The rise is 1.

Then we go left horizontally 3 units. The run is -3.

m = slope = rise/run = 1/(-3) = -1/3

Now we have the slope, so we can finish.

y = -1/3 x + 5

Answer:

-1/3

5

Step-by-step explanation:

Answer:

equation 1 has no solution

Step-by-step explanation:

when you compare each of the equations, all the equations gives a correct answer with the exception of equation 1

Answer:

Percent increase is 70%.

Step-by-step explanation:

The original price was $110. That will go on the bottom (denominator) in our calculation. On the top (numerator) we put the change in the dollar amount. The new price is $187. So we'll subtract:

187 - 110

= 77

The change in price was $77.

change/original

= 77/110

= 0.7

Change the decimal answer to a percent by multiplying by 100.

0.7 × 100

= 70%

The percent increase is 70%.

Using the normal distribution, there is a 0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

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

The proportion estimate and the sample size are given as follows:

p = 0.45, n = 437.

Hence the mean and the standard error are:

The probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3% is 2 multiplied by the p-value of Z when X = 0.45 - 0.03 = 0.42.

Hence:

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

By the Central Limit Theorem:

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

Z = (0.42 - 0.45)/0.0238

Z = -1.26

Z = -1.26 has a p-value of 0.1038.

2 x 0.1038 = 0.2076.

0.2076 = 20.76% probability that the proportion of persons with a college degree will differ from the population proportion by greater than 3%.

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Answer: 6.25

Step-by-step explanation: Here, you want to find how much of 6,298 pounds of food each person got. You can do this by dividing. 6,298/1,007 should get you the answer because it shows how the 6,298 pounds were distributed amongst the 1,007 people.

Answer:

Step-by-step explanation:

7/9 * 15/8 = 105/72 = 35/24

[tex](\stackrel{x_1}{-1.2}~,~\stackrel{y_1}{2.9})\qquad (\stackrel{x_2}{2.9}~,~\stackrel{y_2}{9.46}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{9.46}-\stackrel{y1}{2.9}}}{\underset{run} {\underset{x_2}{2.9}-\underset{x_1}{(-1.2)}}}\implies \cfrac{6.56}{2.9+1.2}\implies \cfrac{6.56}{4.1}\implies 1.6[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{2.9}=\stackrel{m}{1.6}(x-\stackrel{x_1}{(-1.2)}) \\\\\\ y-2.9=1.6(x+1.2)\implies y-2.9=1.6x+1.92\implies \boxed{y=1.6x+4.82} \\\\\\ \textit{when x = 115, what is "y"?}\qquad y=1.6(115)+4.82\implies y=188.82[/tex]

The inequalities are matched with the respective graphs as shown in the attached image.

In mathematics, inequality is the relationship between two non-equal expressions, denoted by a sign such as 'not equal to,' > 'greater than,' or 'less than.'

Roads feature speed limits, some movies have age limitations, and the time it takes to go to the park are all instances of inequalities in the real world.

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