a magazine provided results from a poll of adults who were asked to identify their favorite pie. among the ​respondents, ​% chose chocolate​ pie, and the margin of error was given as percentage points. given specific sample​ data, which confidence interval is​ wider: the ​% confidence interval or the ​% confidence​ interval? why is it​ wider?

The required integral for the gasoline tank is [tex]V = \int\limits_{ - 5}^3 {20 \cdot \sqrt {16 - {x^2}} } dx[/tex]

For the given circular cylinder, the desired limit is determined by the depth and radius of the cylinder. And, the integral function is obtained by employing a Pythagoras theorem. The final set-up must be in the form of [tex]{eq}\int\limits_a^b {f\left( x \right)dx}[/tex]

Let x be the vertical distance up from the centre line of the tank.

The radius of the right circular cylinder is 4 ft

The length of the right circular cylinder is 10 ft

The volume of the strip is determined by the front view of the right circular cylinder as follows:

dV=(L+L)dx×14

=2L×10dx

=20Ldx

The front view of the right circular cylinder is

x^2 + L^2 = 4^2

[tex]L = \sqrt{16 - x^2}[/tex]

Substitute the value of L in the equation of dV.

[tex]dV = 20 \cdot \sqrt {16 - {x^2}} dx[/tex]

The integral required to set up the volume at a depth of 6 ft will be given by taking integrals limits from -5 to 3

[tex]V = \int\limits_{ - 5}^3 {20 \cdot \sqrt {16 - {x^2}} } dx[/tex]

This is the required integral

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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].

Answer:

220.25

Step-by-step explanation:

881 divided by 4 is 220.25

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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Nulls in a relationship should be avoided as much as possible because of the following reasons:-

• Memory space will be wasted at the storage level

• When aggregate operations such as SUM, AVG etc. are performed on the attribute which has

null value, the result will be incorrect

• When JOIN operation involves an attribute with null values, the result may be unpredictable

• The NULL value has a different meaning. It may be unknown, not applicable or absent

Spurious tuples are generated as the result of bad design or improper decomposition of the base

table.

• Spurious tuples are the tuples generated when a JOIN operation is performed on badly

designed relations. The resultant will have more tuples than the original set of tuples

• The main problem with spurious tuples is that they are considered invalid as they do not

appear in the base tables.

Spurious tuples can be avoided by taking care while designing relation schemas:

• The relations should be designed in such a way that when a JOIN operation is performed, the

attributes involved in the JOIN operation must be a primary key in one table and a foreign key in

another table

• While decomposing a base table into two tables, the tables must have a common attribute. The

the common attribute must be the primary key in one table and the foreign key in another table.

Hence the answer is given.

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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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C

Step-by-step explanation:

add x on both sides

-5y=10+x

divide both sides by -5

y=-1/5x-2

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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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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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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Answer:

575 empty spaces

Step-by-step explanation:

If 625 --> 100% then

    X   --> 92%

X= (625 * 92)/100

X= 575

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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5 - 3 (x - 1) = 4 - 7x, initial equation

5 - 3x + 3 = 4 - 7x, distributing 3 (x - 1) to get 3x + 3

8 - 3x = 4 - 7x, adding 3 to 5 to get 8

8 = 4 - 4x, subtracting 3x from both sides of the equation

x= -1, substituting x for the only possible value to make the equation true.

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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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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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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Given any set of seven numbers that should be at least 2 that must have the same remainder when divided by 6

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product since the product is divisible by them.

Step 1: factor the provided number into primes, or describe it as the product of primes.

Step 2: Write the prime factorization in exponent form in step three.

Step 3: Increase each exponent by one.

Step 4: Multiply each of the results.

There can only be a maximum of six different remainders when dividing by six: 0, 1, 2, 3, 4, and 5.

In any set of seven integers, two must have the same remainder when divided by seven according to the pigeon hole principle.

b) Consider set of integers 0, 1 ,2, 3, 4, 5 and 66. All these have different remainders upon division by 8 and hence the answer is no.

The interpretation is yes

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Answer:

the answer to that is 65.

Step-by-step explanation:

maths

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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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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Answer: 135

Step-by-step explanation:

Answer: 145

Step-by-step explanation:

100% of 90 is, welll 90, and 50% of 90 is 45, so 150% of 90 is 145

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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Answer:

Step-by-step explanation:

no

Answer:

The rates are equivalent.

Step-by-step explanation:

Liam practiced piano 24 times in 4 weeks. 1 week = 7 days. 4 weeks = 28 days.

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:

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

(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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The Reimann sum with n rectangle will be given as [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]

Let us suppose that f is a non-negative function, defined over a closed interval represented by [a, b].

The integral of f with respect to x signifies the area between the graph of f and X-axis. This area would be called definite integral of a function f from a to b. Then Riemannian method of determining this area is:

“if the area is divided into n rectangles of very small breadth, then it would be simpler to calculate the area of such rectangles and then we can add them up

(i ) The width of each rectangle will be denoted as Δx

Δx = b-a/n,

where , a is lower bound

b is upper bound of the integral

(ii) The right-hand endpoints of each rectangle are refer as [tex]x_i[/tex] and we can find the right endpoints by [tex]x_i[/tex] = a + Δx.i

(iii) The height of each rectangle is the value of the function at the upper point of the interval.

a + (b-a)/n for the first rectangle , a + 2(b-a)/n for the second rectangle and so on

(iv) The area of the each rectangle will be

Area = Width × height

=> A = (b-a)/2 × a + i(b-a)/2

(v) The Riemann sum with n rectangles is

Area of rectangle = [tex]\sum^{n-1}_{i = 0} f{(x_i)} \Delta x[/tex]

Which is also known as Reimann sum

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Step-by-step explanation:

a point on a coordinate grid always creates a right-angled triangle.

the straight distance from the origin (0, 0) is the Hypotenuse (the side opposite of the 90° angle).

the coordinate distances in x and y directions are the 2 legs.

Pythagoras :

c² = a² + b²

c being the Hypotenuse, a and b being the legs.

so,

(distance from origin)² = x² + y²

because the x, y coordinates are the coordinate distances from the origin in x and in y direction.

distance² = 8² + (-6)² = 64 + 36 = 100

distance = sqrt(100) = 10

the point is 10 units apart from the origin.

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?