Solve the inequality

2/7 > b + 5/7

After half an hour the two boats will be at a distance of 68 mph

Given,

Both boats are moving in a direction that creates a right angle triangle. The lengths of the triangle's legs are the distances that both boats travelled going straight south and straight east. The hypotenuse of a right angle triangle is the distance between them after t hours.

Let x stand for the length of the triangle's shorter south leg.

Let y stand for the length of the right angle triangle's longer (east) leg.

Assume that z is the hypotenuse.

Using the Pythagorean theorem

Hypotenuse² = opposite side² + adjacent side²

Therefore

z² = x² + y²

We would discriminate with regard to t in order to ascertain the speed of the distances' alterations.

It develops,

2zdz/dt = 2xdx/dt + 2ydy/dt- - - -- - -1

One travels south at 32 mi/h and the other travels east at 60 mi/h. It means that

dx/dt = 32

dy/dt = 60

Distance = speed × time

Since t = 0.5 hour, then

x = 32 × 0.5 = 16 miles

y = 60 × 0.5 = 30 miles

z² = 16² + 30² = 256 + 900

z = √1156z = 34 miles

Substituting these values into equation 1, it becomes

2 × 34 × dz/dt = (2 × 16 × 32) + 2 × 30 × 60

68dz/dt = 1024 + 3600

68dz/dt = 4624

dz/dt = 4624/68

dz/dt = 68 mph

Therefore,

The distance between the boats after half an hour is 68 mph

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Completed question is given below with missing parts.

Two boats leave a dock at the same time. One boat travels south at 32 mi divided by hr32 mi/hr and the other travels east at 60 mi divided by hr60 mi/hr. After half an​ hour, how fast is the distance between the boats​ increasing?

The probability of getting a total of 8 when two dice are rolled is 0.139.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Probabilities can be represented by proportions on a 0–1 scale.

A single die will have six sides with the numbers: 1, 2, 3, 4, 5, and 6. Each of these events is equally likely to occur if the dice are rolled fairly. So the probability of getting any side of the number is 1/6. Therefore, the probability of getting 1 in dice is 1/6, 2 is 1/6, and so on.

Therefore, the total possible outcomes are the multiplication of the total possible outcomes on dice 1 and dice 2, which is 36.

This possible outcome of rolling two dice is given by,

[tex]\left\{\begin{array}{ccccccc}(1, 1)&(1, 2)& (1, 3)&(1, 4)&(1, 5)&(1, 6)\\(2, 1)&(2, 2)&(2, 3)&(2, 4)&(2, 5)&(2, 6)\\(3, 1)&(3, 2)&(3, 3)&(3, 4)&(3, 5)&(3, 6)\\(4, 1)&(4, 2)&(4, 3)&(4, 4)&(4, 5)&(4, 6)\\(5, 1)&(5, 2)&(5, 3)&(5, 4)&(5, 5)&(5, 6)\\(6, 1)&(6, 2)&(6, 3)&(6, 4)&(6, 5)&(6, 6)\end{array}\right\}[/tex]

The probability of getting a total of 8 from both dice is given by, (2, 6) (3, 5) (4, 4) (5, 3) (6, 2). So the number of favorable outcomes is 5 and the total outcome is 36. The probability is P(getting a total of 8 from both dices)=5/36= 0.139.

The answer is 0.139.

The complete question is -

Consider rolling dice and getting a total of 8. Find the probability of two dice are rolled. (Enter the value of probability in decimals. Round the answer to three decimal places).

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The minimum number of different rooms that will be needed = 18

We know that the Pigeonhole Principle states that if N objects are placed into k boxes, then at least one box contains at least N/k objects.

In this question, we have been given there are 38 different time periods during which classes at a university can be scheduled.

if there are 677 different classes, we need to find the minimum number of different rooms that will be needed.

There exists a time period will have at least 677/38 = 18 classes during

it.

Therefore, 18 different rooms will be needed.

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Answer:

a. 15 days

b. 704 days

Step-by-step explanation:

a.264+88+88=440

b.It takes mercury 264 days to orbit the sun 3 times which means all you have to do is

264+264=528+264=792-88=704

3 + 3 = 6 + 3 = 9- 1 = 8

Answer:

220.25

Step-by-step explanation:

881 divided by 4 is 220.25

Answer:

575 empty spaces

Step-by-step explanation:

If 625 --> 100% then

    X   --> 92%

X= (625 * 92)/100

X= 575

Archie will get $84.

We have given that,

archie and bijjan share some money in the ratio 7:11 and bijjan get $132.

We have to find how much money will archie get.

Let us consider x as a money

i.e. 7x:11x

bijjan gets $132

means 11x = 132

             x  = [tex]\frac{132}{11}[/tex]

             x = 12

Therefore archie's money,

7x=7(12) = 84

Hence archie get $84.

A ratio can be defined as the relationship or comparison between two numbers of the same unit to check how bigger is one number than the other one. The concept of ratio defines us to compare two quantities while the proportion is an equation that shows that two ratios are equivalent.

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C

Step-by-step explanation:

add x on both sides

-5y=10+x

divide both sides by -5

y=-1/5x-2

(iv) set A₄ holds well ordering property.

(v) set A₅ does not hold well ordering property.

(vi) set A₆ holds well ordering property.

(iv) A₄ = {5i+1/i I i ∈ N}

         = { 5(1) + 1/1, 2(2)+1/2, 5(3)+1/3, 5(4)+1/4, .....}

         = {5+1, 10+1/2, 15+1/3, 20+1/4, ....}

Elements of the set A₄ are distinct and increasing and 6 is the least elements of A₄.

set A₄ holds well ordering property.

(v) A₅ = { 1/n I n ∈ ZI }

        = {1,1/2,1/3,1/4,1/5,....}

A₅ does not hold well ordering property.

(vi) A₆ = {-5,7,10,13}

A₆ is the finite set and all elements are distinct .

For any sub sets of A₆ there exists a dense elements.

A₆ holds well deseriving property.

Hence we get the required answer.

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tasmanian license plates are 8,000,000 combinations possible

In probability, what do combination and permutation mean?

Combinations and permutations may appear to be synonyms. However, they are defined differently in probability theory. Combinations: The sequence of results is irrelevant. Permutations: The sequence of events matters.

If an event is made up of numerous other events (i.e., when it is a list), we may calculate the probability that it will occur with the help of permutations and combinations. If the sequence of the events doesn't matter, we have a combination; if it does, we have a permutation. A permutation can be defined as an ordered combination.

An ordered combination is what is meant by a permutation.

The number of permutations of n objects, taken r at a time, is calculated using the formula below:

P(n,r)=n!(n-r)!

The following formula calculates the number of combinations of n objects taken r at a time: C(n,r)=n!/(n-r)!r!

there are 26^3 combinations of letters. And 10^3 combinations of numbers.

So the total combinations is 26^3 x 10^3 = 17,576,000

Many license plates don’t allow vowels a,e,i,o,u,and y which would accidentally form some awkward words…

Then you’d have 20^3 x 10^3 = 8,000,000 combinations.

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Nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.

What is birth weight?

The body weight of a newborn is referred to as birth weight. Infants of European descent typically weigh between 2.5 and 4.5 kilogrammes at birth, with an average of 3.5 kilograms. South Asian and Chinese babies weigh about 3.26 kilogrammes on average.

Babies born to nonsmokers typically weighed between 1,000 and 5,000 grammes. Babies born to smokers often ranged in weight from 500 to 4500 grammes.

However, we also notice some significant variations between the two groups' normal ranges of birth weights. With fewer infants in the lower weight ranges, nearly half of the newborns among nonsmokers (56 out of 115, 48.7%) have birth weights between 3,000 and 4,000 grammes. 40 of 74, or 54%, of the infants born to smokers have birth weights between 2,000 and 3,000 grammes, with fewer infants in the larger weight groups.

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We may determine that the triangles are congruent based on the (B) HL criterion right away.

According to the HL Postulate, a right triangle's hypotenuse and leg are congruent if they are also congruent with the hypotenuse and leg of another right triangle.

So, we can see from the accompanying figure that these two triangles share a center line that is parallel to the base.

The two triangles are therefore right-angled triangles.

The hypotenuse of two triangles being congruent is then mentioned as a further argument.

Triangle congruence according to the HL criterion allows for a quick determination of congruence.

Therefore, we may determine that the triangles are congruent based on the (B) HL criterion right away.

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Complete question:
Which criteria for triangle congruence allows you to immediately conclude that the triangles are congruent without any extra steps?

A) SAS

B) HL

C) AAS

D) none

536.2  cubic inches  is the volume of a cube with surface area of 396.

a three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

Given,

[tex]A=6V^{\frac{2}{3}}[/tex]

A is surface Area ‘A’, in square units, of a cube

V is  volume of cube in cubic units.

We need to find the volume, in cubic inches, of a cube with surface area of 396.

A=396

We need to find V

[tex]V^{\frac{2}{3} } =A/6[/tex]

=396/6

=66

[tex]V=66^{\frac{3}{2} }[/tex]

V=536.2  cubic inches

Hence, 536.2  cubic inches  is the volume of a cube with surface area of 396.

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The number of elements that are common to S and T are 668 elements ,

the correct option is (d) .

In the question ,

it is given that ,

the set S is the set of 2005 positive multiple of 4

that is S = {4,8,12,16,....}

and the set T is the set of 2005 positive multiple of 6

that is T = {6,12,18,24,....}

and since the least common multiple , LCM of 4 and 6 is = 12,

So , elements that are common to set  S and T must be multiples of 12.

Since,  4 × 2005 = 8020 and 6 × 2005 = 12030,

the several multiples of 12 that are in set T won't be in set S,

but all multiples of 12 that are in set S will be in set T.

So we have to find the number of multiples of 12 that are in set S.

and since 4 × 3 = 12, that means every 3rd element of set S will be a multiple of 12.

which is = 2005/3 = 668 .

Therefore , there are 668 elements that are common .

The given question is incomplete , the complete question is

Let S be the set of the 2005 smallest positive multiples of 4, and let T be the set of the 2005 smallest positive multiples of 6. how many elements are common to S and T ?

(a) 166 (b) 333 (c) 500 (d) 668 (e) 1001

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Answer:The degree of the product is equal to the sum of the degrees of the factors.

Step-by-step explanation:

Answer: 8.4

Step-by-step explanation: 5.25 divided by 5 is 1.05. So 1.05 x 8 is 8.4

Two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.

In the given question, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7.

We have to find the ratio of their areas, a1/a2.

As we know that, the measurement of the area that a polygon encloses serves as its definition. The area of a polygon is the space that it takes up in a two-dimensional plane since polygons are closed plane structures.

As given that, two polygons are similar.

The ratio of their corresponding sides are

s1/s2 = 8/7

According to properties of similar polygon, the ratio of the areas of the two polygons is the square of the ratio of the sides. Hence,

a1/a2 = (s1/s2)^2

a1/a2 = (8/7)^2

a1/a2 = 64/49

Hence, two polygons are similar, and the ratio s1/s2 of their corresponding sides is 8/7 then the ratio of their areas, a1/a2 = 64/49.

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Answer:

Step-by-step explanation:

no

0.6% of the people had a mild allergic​ reaction

percentage, a relative value indicating hundredth parts of any quantity.

Given,

A company that makes​ hair-care products had 8000 people try a new shampoo.

In the 8000 people, 48 had a mild allergic reaction.

We need to find the percent of the people had a mild allergic​ reaction

We have to find what is 48 percent in 8000.

x×8000=48

Divide both sides by 8000

x=48/8000

x=0.006

Now we need to multiply by 100 as it is a hundredth part.

0.006×100

0.6

Hence, 0.6% of the people had a mild allergic​ reaction

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A function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .

We provided Cost C. ( in thousand of dollar)

And a company's revenue R (in thousands of dollars).

C is the cost function.

The value t = 9 is 9 years.

If P is the Annual profit. Then,

Profit = Revenue − Cost

P = R - C

P = 341 - (3.2)t - 254 - 9t + (1.1)t²

= (1.1)t² - (12.2)t + 87

Thus, a function P is provided that represents the company's annual profit: P = (1.1)t² - (12.2)t + 87 .

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Complete Question:

The annual cost C in thousands of dollars and revenue R in thousands of dollars for a company each year from 2010 through 2016 can be approximated by the models C = 254 − 9t + 1.1t2 and R = 341 + 3.2t where t is the year, with t = 10 corresponding to 2010.

(a) Write a function P that represents the annual profit of the company.

The Standard error of the estimate is 11.6985

The standard error of estimate is the measure of variation of an observation made around around the regression line

Simply, It is used to check the accuracy of prediction made with the regression line. A standard deviation which measures the variation in the set of data from its mean, the standard error of estimate also measured the variation in actual values of Y from the computed values of Y on the regression line.

Given in the question,

coefficient of y-intercept = -12.8094

Coefficient of x = 2.1794

N-1 = 9

=> N = 10

SSE = 1094.842

Standard error of estimate = √SSE(N-2)

where , SSE is sum of square of error

S.E = √(1094.842)/ (10-2)

=> √(1094.842)/8

=> √136,855

=> 11.6985 is standard error

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Answer:

Step-by-step explanation:

All units of a physical measure are linked via a conversion factor. On this web page for every unit you can find the conversion factor compared to the base unit (SI unit).

To do a conversion (or equivalent) you must multiply the value to be converted by the conversion factor of the start unit and then divide the result by the conversion factor of the destination unit.

For example, we want to know how many centimeters equals 12 yards?

# convert the units in meters (which is the SI base unit for the lengths)

# 1 yard = 0.9144 meters

# 1 centimeters = 0.01 meters

# derive the conversion factor between the yard and centimeters by dividing the factors found

# 0.9144/0.01 = 91.44

# 1 yd = 91.44 cm

# now we multiply the amount to be converted by the conversion factor found

# 12 * 91.44 = 1097.28

# result: 12 yd equals 1097.28 cm

Unit conversion tool implements this simple algorithm.

The value of 'k' will be;

⇒ k = - 12

What is Equation of line?

The equation of line in point-slope form passing through the points (x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

The graph of the equation has the given y-intercept are;

⇒ Y= -1/3x + 5/6k;  b= -10

Now,

Since, The equation of line in point-slope form will be;

⇒ y = mx + b

Here, The equation is,

⇒ Y= -1/3x + 5/6k

Hence, The y - intercept (b) = 5/6k

But here, b = - 10

So, We get;

⇒ 5/6 k = - 10

Solve for k as;

⇒ 5k = - 10 × 6

⇒ 5k = - 60

⇒ k = - 12

Thus, The value of 'k' will be;

⇒ k = - 12

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The number of ways can the selection be made is 84.

Given:

an executive hires 3 office workers from 8 applicants.

a ) .

Number of ways = C ( 8 , 3 )

C ( n , r ) = n! / ( n - r ) ! r!

C ( 8 , 3 ) = 8! / ( 8 - 3 ) ! 3!

= 8! / 5! * 3 !

= 8 * 7 * 6 * 5! / 5! * 3!

= 56 * 6 / 3!

= 56 * 6 / 3 * 2 * 1

= 56 * 3 / 2 * 1

= 28 * 3 / 1

= 28 * 3

= 84 ways

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36% of the variability equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).

Given:

Correlation value: 0.6

The amount of variation in the dependent variable that can be predicted from the independent variable is shown by the coefficient of determination.

The correlation coefficient is equal to;

Since the correlation in this instance is equal to 0.6, our coefficient is 0.36. Therefore, the age of the home can account for 36% of the variation in equation to predict income (y) in thousands of dollars from age (x1) and educational status (x2) found a significant interaction between age and educational status (x3).

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The type of sampling used to sample the class split into girls and boys is stratified sampling.

As given in the question,

Sample the class to split into guys and girls

Select at random 3 guys and 3 girls.

Types of sampling :

A simple random : Chances of selection is equally likely. Randomly choose the data.

False

B systematic: Samples are collected from large data so that it can systematically arranged.

False

C convenience : In this sample or data collection is done as per convenience.

False

D cluster : It divides the group into multiple group or clusters.

False

E stratified : This represents the division of heterogeneous group into fairly homogeneous group in form of strata.

True.

Therefore, the stratified sampling represents the splitting of class into guys and girls.

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Answer:

[tex](-4,-5)[/tex]

Step-by-step explanation:

When reflecting over [tex]y=-x[/tex], [tex](x,y) \longrightarrow (-y, -x)[/tex].

Gavin worked 7 hours tutoring and 3 hours landscaping.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Gavin is working for making $14 per hour tutoring and $13 per hour landscaping.

And, Last week Gavin worked a total 10 hours and earned $137.

Now,

Let number of hour for tutoring = x

And, Number of hour for landscaping = y

Since,  Gavin is working for making $14 per hour tutoring and $13 per hour landscaping and earned $137.

So, We can formulate;

⇒ 14x + 13y = 137  ..(i)

And, Last week Gavin worked a total 10 hours.

So, We get;

⇒ x + y = 10  ..(ii)

Multiply by 13 in equation (ii) and subtract from (i0, we get;

⇒ 14x + 13y - 13x - 13y = 137 - 130

⇒ x = 7

And, x + y = 10

⇒ 7 + y = 10

⇒ y = 10 - 7

⇒ y = 3

Thus, Gavin worked 7 hours tutoring and 3 hours landscaping.

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Answer:

The slope is -2/3

Step-by-step explanation:

2x + 3y = -6

We want to find the slope, so we need to get the equation in slope intercept form y = mx+b  where m is the slope and b is the y intercept

Subtract 2x from each side

3y = -2x+6

Divide each side by 3

y = -2/3x +2

The slope is -2/3