if integer polynomials p and q satisfy p(x)/q(x) is an integer for infinitely many integer inputs x, does it follow that q(x) divides p(x)?

If Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

So, the probability that the base construction company did not bid:

[tex]\begin{aligned}& P(A \mid B)=\frac{P(B \mid A) P(A)}{P(B \mid A) P(A)+P\left(B \mid A^{\prime}\right) P\left(A^{\prime}\right)} \\& P\left(B^{\prime} \mid O\right)=\frac{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)}{P\left(O \mid B^{\prime}\right) P\left(B^{\prime}\right)+P(O \mid B) P(B)} \\& P\left(B^{\prime} \mid O\right)=\frac{(0.5)(0.3)}{(0.5)(0.3)+(0.25)(0.7)} \\& P\left(B^{\prime} \mid O\right)=\frac{0.15}{0.15+0.175} \\& P\left(B^{\prime} \mid O\right)=0.4615\end{aligned}[/tex]

Therefore, if Olive Construction Company won the job, there is a 0.4615 (or 46.15%) probability that Base Construction Company would not have submitted a proposal.

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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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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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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 required evaluation to the given expression is 5/12.

A fraction is defined as a numerical representation of a part of a whole that represents a rational number.

The expression is given in the question as:

1 3/4  - 1/3 (4)(3) - 1/3

We have to determine the evaluation to the given expression

As per the given question, we have

⇒ 1 3/4  - 1/3 (4)(3) - 1/3

⇒ 7/4  - 1/3 (12) - 1/3

Apply the subtraction operation,

⇒ 7/4  - 4 - 1/3

Take the LCM in the above fractions,

⇒ (21 - 12 - 4)/12

⇒ 5/12

Thus, the required evaluation to the given expression is 5/12.

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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!!

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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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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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

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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The difference between the value of two signed numbers and the absolute value is that

Positive and negative numbers are referred to as signed numbers. The number is automatically regarded as positive if no sign is present.

On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0

Without taking direction into account, absolute value describes how far away from zero a certain number is on the number line.

A number can never have a negative absolute value.

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The measured height of the tree is found as 3.2 yards.

Let 'h' be the height of the three.

Let distance between student A and tree =  x.

Using trigonometric relation;

tan 57 = h/x

x = h/tan 57   ......eq 1

tan 46 = h/(x + 1)

x + 1 = h/tan 46   ......eq 2

Equation eq 1 and eq 2.

h/tan 57 + 1 = h / tan 46

h / tan 46 - h / tan 57 = 1

Further solving,

h(tan 57 - tan 46) = tan 46.tan 57

h = tan 46 tan 57 / (tan 57 - tan 46)

h = 3.2 yards

Thus, the measured height of the tree is found as 3.2 yards.

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The complete question is-

Two students stand 1 yard apart and measure their respective angles of elevation to the top of a tree. Student A measures the angle to be 57°, and Student B measures the angle to be 46°.

What is h, the height of the tree? Use the law of sines to first find AT. Then use that measure to find the value of h.

A) 3.0 yards

B) 3.2 yards

C) 3.8 yards

D) 4.4 yards

Answer: 3.2 is correct

Step-by-step explanation:

edge 2023

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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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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The statement that is true about the triangle ABC with vertices A(-6, 6), B(4, 2), and C(-4, 0) is C. Since two of the sides have slopes that are negative reciprocals, it is a right triangle.

Right triangles are triangles with have perpendicular relationships

The lines will be checked for perpendicularity by calculating the slopes, if any two slopes are negative reciprocals then they are perpendicular and the triangle is a right triangle'

the points A(-6, 6), B(4, 2), and C(-4, 0)

Using point A(-6, 6) and B(4, 2)

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - 6) / (2 - -6)

m = -1/2

Using point B(4, 2), and C(-4, 0)

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - -4) / (2 - 0)

m = 2

Comparing the slopes shows that slopes calculated are negative reciprocals

Therefore the triangle is a right triangle

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The probability flipping of four coin that will give head is 0.93

Probability:

In statistics, Probability defines the possible way of occurring a particular event.

Given,

A flipped coin can land in one of two states: heads or tails.

Here we need to find the probability while flipping four coins then  how many of these coins land in the heads state.

In order to calculate the probability of these event, we have to know the values of the sample space and the possible number of events,

Here the value of sample space is written as,

S = {HHHH, TTTT, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

So, the value of n(S) = 16

The possible number of way to obtain the head state is,

E = {HHHH, HHHT, HHTH, HTHH, THHH, HHTT, HTTH, HTHT, THHT, THTH, TTHH, HTTT, THTT, TTHT, TTTH}

the value of n(E) = 15.

Therefore, the probability of getting head state is

=> P(E) = 15/16

=> P(E) = 0.93

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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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The following ways of measuring weight loss are more appropriate than correlation, i.e.,Skin calipers, Impedance scales, DEXA scanning, Body measurements.

Calories factor into the equation while trying to maintain a healthy weight. The key to losing weight is to burn more calories than you consume. You may do this by consuming fewer calories than you need and increasing the number of calories you burn via physical exercise.

A realistic, efficient, and lasting weight loss plan might be difficult to follow even if it may appear straightforward.

You don't have to do it by yourself, though. Seek advice from your doctor, family, and friends. Consider whether this is the right time and whether you're prepared to make the essential changes. Plan wisely as well: Consider how you'll respond to circumstances that put your determination to the test and the inevitable slight setbacks.

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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 slope and intercept of the line will be 2 and 80 respectively.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

It is given that, the total amount of tourist spending in Florida from 2013 to 2017 can be predicted using the equation y=2x+80, where x is the number of years since 2013, to the tune of billions of dollars.

Compare the equation with the standard equation,

y=mx+ c

Where m is the slope and c is the intercept of the line.

Thus the slope and intercept of the line will be 2 and 80 respectively.

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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 social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

What is arithmetic?

Arithmetic is an elementary a part of arithmetic that consists of the study of the properties of the normal operations on numbers—addition, subtraction, multiplication, division, mathematical process, and extraction of roots

Main body:

Cumulative Earnings before this pay period = $128,300

pay amount this period = $3000

tax rate of 6.2% on social security = 6.2%

effective earning = 128300 = 3000

                           = 125300

social security deduction = 6.2 % of 125300

⇒ 6.2 *125300 /100

⇒$7768

Medicare deductions = 1.45%

⇒ 1.45*125300/100

⇒$1816

Hence , the social security and Medicare deductions for the following employee are  $7768 and $1816 respectively.

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Answer:

[tex]\huge\boxed{\sf 3}[/tex]

Step-by-step explanation:

y = 3x + 5

Comparing it with standard form of slope-intercept equation i.e. y = mx + b.

Where,

m = slope = 3

b = y-intercept = 5

A line that is parallel to this line will have the same slope as this line.

So, it will also have a slope of 3.

[tex]\rule[225]{225}{2}[/tex]

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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Answer:

No.

Step-by-step explanation:

Below I should you two ways to get the correct answer.

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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The required system of equation for the cost of shirt and tie are-

For the stated question-

Let 's' be the cost of each shirt.

Let 't; be the cost of each tie.

Then, the equations become-

4s + 2t = 95

3s + 3t = 84 are the required system of equation.

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