what is the ratio of the area of a square inscribed in a semicircle with radius $r$ to the area of a square inscribed in a circle with radius $r$? express your answer as a common fraction.

The probability of scoring exactly​ 80%  is  0.04395  as per the given data.

Given: 10 true-false questions

So, we will have 50% chances (probability = 0.5) of being correct.

P( 80% score) = P( 8 answers correct)

As we observe, if X= number of correct answers, then X~ Binomial (n=10, p=0.5)

So, P(  80% score) = P( 8 answers correct)

= 0.0439453125

= 0.04395

Potential is described by probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events.

Probability basically refers to the degree to which something is likely to occur. With the help of this fundamental theory of probability, which is also used to describe the probability distribution, you will discover the possible results for a random experiment. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The areas are

(a) 0.2743

(b) 0.1587

(c) 0.8413

(d) 0.0548

(e) 0.8274

What is standard deviation ?

The standard deviation is a statistic that expresses how much variation or dispersion there is in a set of values. While a high standard deviation suggests that the values are dispersed over a wider range, a low standard deviation suggests that the values tend to be close to the set mean.

Use TI 84 plus calculator to find the following areas

(a) Entering the values

    Lower : -999999999

    Upper : 16

    Area (probability): 0.2743

(b) Entering the values

     Lower : -999999999

    Upper : 14

    Area (probability): 0.1587

(c) Entering the values

     Lower : 15

    Upper : 999999999

    Area (probability): 0.8413

(d) Entering the values

     Lower : 27

    Upper : 999999999

    Area (probability):  0.0548

(e) Entering the values

     Lower : 14

    Upper : 30

    Area (probability):  0.8274

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Answer:

3/4 = 12/16, y = 2, w = 2.5, 20/2.5 = x/9

Step-by-step explanation:

The first question is asking which is proportional.

B. 3/4 = 12/16

We know this is proportional because 4 can be multiplied by 4 to get 16, and the same can be applied to 3 to get 12.

The second question is asking for the missing value of y.

3/12 = y/8

y = 2

We can solve this by looking at the 12 and the 8.

8 is 2/3 of 12.

2/3 of 3 is 2

The third question is asking for the missing value of w.

5/w = 8/4

w = 2.5

We can solve this by looking at the 8/4.

8/4 is the same as 2/1.

Using this, we can conclude that w = 2.5

The fourth question is asking for the correct proportion.

If Mr. Argo can go 20 miles on 2.5 gallons of gas:

20/2.5

And he wants to know how many miles he can go with 9 gallons:

x/9

We can use the equation: C. 20/2.5 = x/9

Hope this helps!!

The step which Sammy should complete first in a bid to solve the equation is; subtraction 8 from both sides of the equation.

It follows from the task content that the step which Sammy should complete first in a bid to solve the equation.

Since the given equation is;

x/2 + 8 = -24

Therefore, in a bid to solve the equation; the first step which Sammy must complete first in a bid to solve the equation is;

Subtract 8 from both sides of the equation; so that we have;

x/2 = -24 -8

x/2 = -32

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Answer:

C -5 + (-15)

Step-by-step explanation:

-5 - 15 = -20

A -15 - (-5) = -15 + 5 = -10

B -5 + 15 = 10

C -5 + (-15) = -20

D -15 + 5 = -10

Answer:

c; -5+(-15)

Step-by-step explanation:

-5-15=-20

adding a negative number is subtraction, which means;

-5+(-15)=-20

therefore

-5-15=-20=-5+(-15)

With 98% confidence interval, all teenagers' mean number of hours watching TV per week will be (26.6,29.4).

98% confidence interval can be calculated as

Point estimate± Error margin

Point estimate=mean number of hours watching TV

students=28.

Error margin=1.4.

As per given data, the 98% confidence interval for all teenagers is

=28± 1.4

=(28-1.4,28+1.4)

=(26.6,29.4)

Statisticians use confidence intervals to assess the level of uncertainty in a sample variable. For instance, a researcher may select numerous samples at random from the same population and compute a confidence interval for each sample to estimate how each sample may correctly reflect the true value of the population variable. With certain intervals including the true population parameter and others not, each produced dataset is distinct. Confidence intervals are a set of values that are constrained by the mean of the statistic and are likely to include an unidentified population parameter. The confidence level is the proportion of likelihood, or certainty, that, after multiple draws from a random sample, the confidence interval would contain the true population parameter.

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Answer:

85%

Step-by-step explanation:

Hope it helps!

Answer:

85%

Step-by-step explanation:

51/60=.85=85%

Number of cups of milk that will you need to use is 2.001 cups

Total quantity of milk needed for the cake = 472 milliliter

we know

1 liter = 1.06 quarts

1 quart = 4 cups

Convert the given quarts to cups

Then 1.06 quarts = 4 × 1.06

Multiply the numbers

= 4.24 cup

Here the total quantity of milk needed for the cake is 472 milliliter

We have to use the unitary method here

1 liter = 4.24 cups

472 milliliter = 4.24 × 0.472

Multiply the numbers

= 2.001 cups

Therefore, he need 2.001 cups of milk to make a cake

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The inequality which can be used to determine x, the number of 60 kilogram crates that can be loaded into the shipping container is

60x ≤ 9900 where x is less than or equal to 165

What is an Inequality?

Inequalities are the mathematical expressions in which both sides are not equal.

In inequality, unlike in equations, we compare two values.

The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

According to the given question:

The greatest weight that can be loaded into the container is 24500 kilograms.

Other shipments weighing 14600 kilograms have already been loaded into the container.

24500 - 14600 = 9900 kg can be the weight of 60 kg containers

Now, the number of 60 kilogram crates that can be loaded into the shipping container can be represented as

                                            60x ≤ 9900

where x is number of 60 kg containers

Solving for x we get

x ≤ 165

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Total 504 three digit numbers can be formed if no digit appear twice

What is Permutation?

The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.

Solution:

Total Numer of Digits = 9

Number of Characters in the number = 3

Total Numbers = 9P3 = 9! / 6!

9P3 = 504

Total 504 three digit numbers can be formed

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Step-by-step explanation:

If there are 2 points (a,b) and (c,d),

then the slope = (d - b)/(c - a) = (b - d)/(a - c)

Therefore slope = (10 - 4)/(4 - 2) = 6/2 = 3

The point-slope form of a line is

y = mx + b, where m is the slope and b is the y-intercept Substituting either point (2,4) or (4,10) into the equation is fine.

(4) = (3)(2) + b

4 = 6 + b

b = 4 - 6 = -2

y = 3x - 2

Or

(10)=(3)(4) + b

10 = 12 + b

b = 10 - 12 = -2

y = 3x - 2

Answer:

1.07 maybe... don't trust me on that

Answer:

x = -6

Step-by-step explanation:

The sum of two interior angles in a triangle is equal to an exterior angle that is supplementary to the third interior angle.

We can write the following equation based on this information to calculate value of x:

64 + 27 = 97 + x

91 = 97 + x

91 - 97 = 97 - 97 + x

-6 = x

An equilateral △ABC with a side length of 2 cm is placed on top of a square BCDE to form a pentagon. A circle is drawn including points A, D, and E. And the radius of this circle is found to be 2 cm.

A triangle is said to be equilateral if all three of its sides are the same length and each of its three angles measures 60 degrees.

The given triangle is equilateral with a side length of 2cm. This triangle is on the top of a square BCDE. The circle circumscribes through the A, D, and E of the given shapes.

Using the given details, first, draw the diagram. Let H is the circumcenter of ADE. In the diagram, draw the altitude of AG passing through the circumcenter and square as GF.

From the diagram, let GH be x.  The side of the triangle is 2 cm and the altitude cut it into two equal halves. Then, BG=EF=1 cm, HF=2-x, and HE=x+√3

[tex]\begin{aligned}\sin \theta &= \frac{AG}{AB}\\\sin 60^{\textdegree} &=\frac{AG}{2}\\\frac{\sqrt{3}}{2}&=\frac{AG}{2}\\AG&=\sqrt{3}\end{aligned}[/tex]

By Pythagoras' theorem, from ΔHEF,

[tex]\begin{aligned}HE^{2}&=HF^{2}+EF^{2}\\\left(x+\sqrt{3}\right)^2&=(2-x)^2+1^2\\x^2+3+2\sqrt{3}x&=4-4x+x^2+1\\(4+2\sqrt{3})x&=5-2\\x&=\frac{2}{4+2\sqrt{3}}\\&=\frac{2}{2(2+\sqrt{3})}\times\frac{2-\sqrt{3}}{2-\sqrt{3}}\\&=\frac{2-\sqrt{3}}{4-3}\\&=2-\sqrt{3}\end{alinged}[/tex]

The radius of the circle (HE) is 2-√3+√3=2.

The answer is 2 cm.  Therefore, option C is correct.

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The COUNTIF function is used to compute the number of times a particular condition is satisfied within a given range of cells.

It is an excel statistical function, which is used to count the number of cells that meet a criterion. To determine how many cells in the worksheet contain a number higher than or less than the one specified, the countif formula is used.

It is typed =COUNTIF

1. Select a cell

2. Type =COUNTIF

3. Double-click the COUNTIF command

4. Select a range

5. Type

,6. Select a cell (the criteria, the value that you want to count)7.

Hit enter Hence the answer is COUNTIF

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If a four digit personal identification number is selected, then the probability that there are no repeated digits is 0.504

Number of digits in the identification number = 4

0, 1, 2, 3, 4, 5, 6, 7, 8 and 9

There are 10 digits

The probability = Number of favorable outcomes / Total number of outcomes

Total number of outcomes = 10 × 10 × 10 × 10

= 10000

Number of outcomes that digits wont repeat = 10 × 9 × 8 × 7

= 5040

Substitute the values in the equation of probability

The probability = 5040 / 10000

= 0.504

Therefore, the probability there are no repeated digits is 0.504

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Answer:

x3=5x+e3x+2−17

This is the best I can do :D

We will reject the H0 as there sufficient evidence is obtained that the percentage of people who believe that there is life on planets differs from 50%.

It is given that the sample size, (N) is 125

Probability (P)= 0.50 or 50%

P'= 50/120= 0.4166

Significance level ([tex]\alpha[/tex])=0.10

If we consider the null and alternative hypotheses, they are:

H0= 0.50

H1≠ 0.50

For conducting the test statistics:

Z= [tex](P'-P)/\sqrt{P*(1-P)/N}[/tex]

Z= [tex](0.41-0.50)/\sqrt{0.50*0.50/125}[/tex]

Z= -2.01

The critical value of Z at [tex]\alpha[/tex]=0.10 is 1.645 or -1.645

And the P- value at Z= 2.01 is 0.04

Decision Criteria: If the P-value is less than the significance level, we reject the H0. Also, if the Z is found to be greater than the critical value, we will reject H0.

Thus, in this case, we see that, the P-value, 0.04 is less than the significance level, i.e., 0.10, we will reject the H0.

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A gas station is open 365 day a year, 24 hours a day. If the gas station served 40,000 cups of coffee last year, then it served an average of 5 cups of coffee per hour.

The problem can be solved using the average value approach.

Average value = total amount or sum of data / number of data

In the given problem,

total amount = total coffee served last year

total amount = 40,000

number of data = number of hours in a year

number of data = 365 day/year x 24 hours/day = 8760 hours

Hence,

Average value = total amount or sum of data / number of data

                         = 40000 / 8760

                         = 4,6 ≈ 5 (round to the nearest whole cup)

Hence, the average coffee served is 5 cups per hour.

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7/11 is the probability of choosing a blue block.

Given:

a child has a box full of colored building blocks. he will choose one block without looking.

the odds against choosing a blue block are 47.

We need the probability of choosing a blue block,

Odds:

The odds of an event is the ratio of the probability of an event to the probability of its complement. In other words, it is the ratio of favorable outcomes to unfavorable outcomes.

The odds against choosing a blue block are 4/7 means. In 11 chances, 4 events will happen in which blue block will not be chosen and 7 events will happen in which blue blocks will be chosen.

So, the probability of not choosing the blue block is 4/11.

Probability of choosing blue block: complement of 4/11 which is equal to 7/11.

Hence we get the required answer.

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Answer: 12

Step-by-step explanation:

Convert both mixed numbers to improper fractions:

7 1/12= 85/12

1 3/5= 8/5

Multiply:

84 x 8 = 680

12 x 5 = 60

As a fraction:

680/60

Simplified:

11 1/3 ft. of paper needed

For FCFS (First Come, First Served):The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65.

SSTF (Shortest Seek Time First):

The requests will be serviced in the following order: 39, 22, 65, 69, 94, 133, 135, 169

SCAN:

The requests will be serviced in the following order: 39, 65, 69, 94, 133, 135, 169, 22

C-SCAN:

The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65

LOOK:

The requests will be serviced in the following order: 39, 65, 69, 94, 133, 135, 169, 22

C-LOOK:

The requests will be serviced in the following order: 94, 169, 39, 135, 22, 133, 69, 65

In FCFS and C-SCAN, the requests are serviced in the same order as they were received. In SSTF and LOOK, the requests are serviced in an order that minimizes the seek time of the disk head. In SCAN and C-LOOK, the requests are serviced in an order that moves the disk head in one direction (towards higher numbered cylinders in this case) until the end of the disk is reached, and then moves the disk head in the opposite direction to service the remaining requests.

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Since, it is observed that z = -2.74 < [tex]Z_{\alpha} = -2.33[/tex], it is then concluded that the null hypothesis is rejected.

What is a left-tailed test?

When the alternative hypothesis asserts that the true value of the parameter indicated in the null hypothesis is lower than the null hypothesis indicates, a left-tailed test is utilized.

This is a left-tailed test.

Test statistics

[tex]z = (\hat p - p_{0} ) / \sqrt{} p_{0}*(1-p_{0}) / n[/tex]

=  [tex]\sqrt{} (0.4*0.6) / 45[/tex][tex]= ( 0.2 - 0.4) \div \sqrt{} (0.4*0.6) / 45[/tex]

= -2.74

The critical value of the significance level is α = 0.01, and the critical value for a left-tailed test is:

[tex]Z_{\alpha} = -2.33[/tex]

Hence, it is observed that z = -2.74 < [tex]Z_{\alpha} = -2.33[/tex], it is then concluded that the null hypothesis is rejected.

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The standard deviation of the sampling distribution of sample proportions is 0.21

Given,

Number of people living in Miami  = 459,000

Sample size, n = 490 people

Population proportion, p = 68% = 68

We have to find the standard deviation for the sampling distribution of the sample proportions;

Here,

Standard deviation of the sampling distribution of sample proportions is

σpˆ=√p(1−p)/n

σpˆ=√.68(1-.68)/490

σpˆ= .021

That is,

0.21 is the standard deviation of the sampling distribution of sample proportions.

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The farm's 11 tons of watermelon will have a 92% confidence interval mean cash value of $148.89, which is within the margin of error.

In a random survey sample, a margin of error is a statistical measurement that takes into account the discrepancy between actual and anticipated findings. Simply said, you may determine the degree of unpredictability in data and study results using the margin of error. Your findings will vary from the actual population figure by how many percentage points, as shown by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.

Here,

n = 38

x = 6.88

= 1.86

= 1-.90

= .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

P(-1.645 < z < 1.645) = .90

Margin of error= z(/2)(/√n)

= 1.645(1.86/√38)

= $.4963(300)

= $148.89  

The margin of error for a farm brings 11 tons of watermelon to market with 92% confidence interval for the population mean cash value of this crop will be $148.89.

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Answer:x=6

Step-by-step explanation:You can simplify as 0 is worh nothing so it would be just 6

Answer:

72.13

Step-by-step explanation:

If you bought a stock last year for a price of $79, and it has gone down 8.7% since then, how much is the stock worth now, to the nearest cent?​

As there is no variables, so the given expression 9 + 10 is the numerical expression.

An object can be counted, measured, or labelled using a number, which is a mathematical value. Arithmetic calculations are often done with numbers. Natural numbers, whole numbers, rational and irrational numbers, among other types of numbers, are examples. A null value is also represented by the integer zero, or 0.

Numerical expression is a combination of the words numerical, which refers to numbers, and expression, which denotes a statement. Consequently, it is a statement that uses numbers.

Mathematical operations like add, subtract, multiply, and divide can be used to mix integers with numbers to create a numerical expression.

Given Expression 9 + 10

As it contains only numbers and mathematical operators,

So, it is the numerical expression.

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