On Saturday, some adults and some children were in a theatre.The ratio of the number of adults to the number of children was 7:2
Each person had a seat in the Circle or had a seat in the Stalls.
of the children had seats in the Stalls.
124 children had seats in the Circle.
There are exactly 3875 seats in the theatre.
On this Saturday, what percentage of the seats had people sitting on them?

Answer:

B

Step-by-step explanation:

Round 64.12 and 7.4 to whole numbers that divide nicely, and are CLOSE to the original numbers.

The equation of the line passing through the point (-1, -5) with slope = 6 is y = 6x - 1

The coordinates of the point = (-1, -5)

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The slope of the line m = 6

The slope intercept form is

y = mx + b

Where m is the slope of the line

b is the y intercept

Substitute the values in the slope intercept form

-5 = 6(-1) + b

-5 = -6 + b

b = -6+5

b = -1

The slope intercept form

y = 6x - 1

Therefore, the equation of the line is y = 6x - 1

I have answered the question in general, as the given question is incomplete

The complete question is:

Write the slope-intercept form of the equation of the line through the given point with the given slope. Through (-1,-5), slope =6

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The proportion should be sufficiently demonstrated to be lower than 49% at the 0.05 level.

Given,

Less than 49% of a newsletter publisher's subscribers, in their estimation, own a personal computer.

A potential advertiser wants to verify this claim for marketing purposes.

The marketer chooses to reject the null hypothesis after running a test with a 0.05 level of significance.

We have to determine the conclusion regarding the publisher's claim;

Here,

Null and Alternative hypothesis;

H₀ = P ≥ 0.49

H₁ = P < 0.49 (Left tailed test)

The significance level is 0.05

So,

0.05 < 0.49

Then,

At the defined meaning level, it is chosen to reject the null hypothesis.

Therefore,

There should be sufficient evidence that the proportion is lower than 49% at the 0.05 level.

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The sample space for the single digit even number = {2, 4, 6, 8}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space.

Events are the subset of possible experiment results. Depending on the experiment, a sample space could contain a variety of results.

Given that,

Layla thinks about a positive single digit even number.

There are four single digit even numbers 2, 4, 6 and 8.

The sample space for the single digit even number = {2, 4, 6, 8}

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Answer:

Step-by-step explanation:

if the null hypothesis is rejected in hypothesis testing the alternative hypothesis is true.

The relationship between important factors of interest and any apparent connection, according to a competing theory, is most certainly not accidental. The opposite of a null hypothesis is an alternative hypothesis. If we are able to rule out the null hypothesis, it signifies that we have enough data to support the alternative hypothesis. In one test, we cannot rule out both possibilities.

If one is disproven, it indicates that there is evidence to support the other. The opposing view is that a study's potential conclusion will materialize. It claims there is no coincidence in the relationship between important components of interest and the observed connection. As a result, the alternative hypothesis is true if the null hypothesis is disproved during hypothesis testing.

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Half-life of iodine-133 is 21.7 hours .

FR = 0.5n  (fraction remaining)

n = number of half lives that have elapsed.

FR = 4.7x102 / 5.5x102 = 0.8545

n = to find

0.8545 = 0.5n

log 0.8545 = n log 0.5

-0.0683 = -0.301 n

n = 0.227 half lives have elapsed

Since this is equal to 295 minutes, we can easily find what 1 half life is

0.227 / 295  = 1 / x

x = 1300 min = 21.7 hours

The amount of time it takes for the concentration of a given reactant to reach half of its initial concentration is known as the half-life of a chemical reaction  (i.e. the time taken for the reactant concentration to reach half of its initial value).

It is commonly expressed in seconds and is represented by the sign t1/2 .

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Answer:

97

Step-by-step explanation:

< LMN = 33

The sum of the interior angles equal 180

180 - 92 - 55 = 33

<QM (can't read the last letter 50

180 - 45 - 85 = 50

<LMQ This is a straight angle and straight angles are 180

180 - 33 -50 = 97

The number of men on the sight - seeing tour was  22 .

In the question ,

it is given that,

the ratio of women to children on the tour is = 5 : 2

let the number of men in the sight seeing tour =  m

let the number of women in the sight seeing tour =  w

let the number of children in the sight seeing tour =  c

So , w/c = 5x/2x

also the ratio of children to men is 5/11 ,

c = 5y and m = 11y

the number of women on the sight seeing tour is less than 30 ,

which is 5x < 30 ,

x < 6

but we have c = 2x and 5y ,

and since c is a multiple of 5 , 2x also has to be a multiple of 5 ,

earlier we got , x < 6 ,

Now using x =5 , we get c = 2*5 = 10

and so , 10 = 5y

y = 2 ,

So , the number of men = 11y = 11*2 = 22 men

Therefore , the number of men are 22 .

The given question is incomplete , the complete question is

On a certain sight-seeing tour, the ratio of the number of women to the number of children was 5 to 2. What was the number of men on the sight-seeing tour?

(1) On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.

(2) The number of women on the sight-seeing tour was less than 30.

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After 9 hours, Singer A and Singer B will both charge the same amount.

An equation in French is defined as having one or more variables, whereas an equation in English is any well-formed formula consisting of two expressions combined with an equals sign.

Solving a variable equation includes determining which variables' values result in equality. Unknowns are the variables for which the equation must be solved, while equation solutions are the unknown values that satisfy the equality. An equation is a mathematical phrase with two equal sides separated by an equal sign. An equation is 4 + 6 = 10. We can see 4 + 6 on the left side of the equal sign and 10 on the right.

The Singer A's initial fee is $50.

Singer A's hourly rate is $10.

Singer B's initial fee was $95

Singer B's hourly wage is $5.

Assume the duration after which both singers will charge the same amount = x.

Then 50 +10x =95+5x

10x-5x=95-50

5x=45

x=45/5

x=9 hours

So, after 9 hours, Singer A and Singer B will both charge the same amount.

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The minimum number of students required in a school are 102 , it can be calculated by multiplying the 2 quantities.

What is arithmetic?

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

Main body:

Total grades = 1 to 6 = 6

minimum students in each grade  required = 17

total students required = 6*17

                                       = 102

hence total minimum number of students required in a school are 102.

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The equation of the function is: B = -5x + 30

X-intercept is 6, which means after 6 hours, the battery is totally drained.

The x-intercept of a function is the point on the x-axis that the line intercepts, which is the value of x when y = 0.

Find the slope of the function (m):

Slope (m) = change in B / change in t = (20 - 10) / (2 - 4)

Slope (m) = 10/-2

Slope (m) = -5

The y-intercept (b) = 30.

Write the equation of the function by substituting m = -5 and b = 30 into B = mt + b:

B = -5x + 30

The x-intercept of the function is 6, which represents the hours it took for the whole battery to drain.

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The length and width of the rectangular poster are 23 inches and 7 inches respectively.

Here we have to find the dimensions of the length and width of the rectangular.

Data given:

length of the rectangular poster is 2 more than three times its width.

Let us assume that the width of the rectangular is x.

The area of the poster = is 161 inches²

So by this, we get the length 3x + 2.

width = x

length = 3x + 2

The formula of the area of the rectangular:

Area = length × width

161 = (3x+ 2) × x

161 = 3x² + 2x

3x² + 2x - 161 = 0

3x² + 23x - 21x - 161 = 0

x(3x + 23) - 7( 3x + 23) = 0

(3x + 23) ( x -7)= 0

x = -23/3, 7

As the length cannot be negative so we get the value of x as 7

width = 7 inches

length = 3x + 2

= 3×7 + 2

= 21 + 2

= 23inches

Therefore the length and width are 23 inches and 7 inches respectively.

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The set of inequalities formed for the bounce house of Natalie are-

200x + 80y ≤ 1200 and 3x + 2y ≥ 20.

The data for the people enrolled for the bounce house.

Let 'x' be the number of adults.

Let 'y' be the number of children.

Then,

Weight of adult = 200 pounds.

Weight of children = 80 pounds.

maximum weight = 1200 pounds

Then, equation becomes-

200x + 80y ≤ 1200

For the price.

adults -$3 each and

children - $2 each

Minimum profit at least $20

3x + 2y ≥ 20.

Thus, the set of inequalities are-

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The ball will land 67.381 feet away.

Thus, option (B) is correct.

Given:

v = 62 feet / second

[tex]\theta[/tex] = 15

h = 2.2 feet

Using the formula

Horizontal range = [tex]\dfrac{v \;cos\; \theta\; [v \;sin\;\theta + \sqrt{v^2\;sin\;\theta + 2gh]}}{g}[/tex]

Substituting the value back into the formula as

Horizontal range = [tex]\dfrac{62 \;cos\; (15)\; [62 \;sin\;(15)+ \sqrt{(62\;sin\;(15))^2 + 2g*2.2]}}{g}[/tex]

                            = 67.381 feet

Therefore, the distance is 67.381 feet.

Thus, option (B) is correct.

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The question attached here seems to be incomplete, the complete question is:

A tennis player hits the ball with an initial speed of 62 feet per second at an angle of 15", from a height of 2.2 feet. How far away does the ball land in feet? (5 points)

56.372 feet

67.381 feet

60.646 feet

47.293 feet

The value of the expression illustrated as 1.5(6t+2) is 9t + 3.

Expression is simply used in Mathematics to show the relationship between the variables that are illustrated. In this case, this depicts the information given.

Based on the information, the expression is illustrated as:

1.5(6t+2)

Open the parentheses

(1.5 × 6t) + (1.5 × 2)

= 9t + 3.

The value is 9t + 3.

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Complete question

Find the value of the expression given 1.5(6t+2) i

hence proved If number is 2t + 1 where t belongs to integer, then it is odd integer.

Odd number integers = 2k + 1, where k is integer

Even number integer = 2k

Odd integer + even integer

= 2k + 1 + 2k

= 4k + 1

= 2(2k) + 1

Let 2k = t, where t is integer

 = 2t + 1

= Odd integer by definition

If number is 2t + 1 where t belongs to integer, then it is odd integer.

Hence proved.

The question is incomplete. The complete question is :

Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2k+1, where k is an integer. An even integer is an integer that can be expressed as 2k, where k is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd

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Answer: x < 4

Step-by-step explanation: look at the link attached

The standard deviation of the sampling distribution is 0.03

Instructor number is calculated as - (failure /100)

Number of failures for instructor A = 13 = 0.13

Number of failures for instructor B = 0 = 0.

Number of failures for instructor C = 11 = 0.11

Number of failures for instructor D = 16 = 0.16

Calculating mean -

Mean(m)

= 0.13 + 0.11 + 0.16) / 3

= 0.4 / 3

= 0.13

Calculating the Standard deviation -

Σ(X - m)² / N - 1

Σ(0.13 - 0.1333)² + (0.11 × 0.1333)² + ( 0.16 - 0.1333)² = 0.001266

= 0.001266 / 2

= 0.00063343

= √0.00063343

= 0.025168

= 0.03

Complete question -

The chair of the operations management department at Quality University wants to construct a p-chart for determining whether the four faculty teaching the basic P/OM course are in control with regard to the number of students who fail the course. Accordingly, he sampled 100 final grades from last year for each instructor, with the following results: Instructor Number of Failures Prof. A 13 Prof. B 0 Prof. C 11 Prof. D 16 What is the estimate of the standard deviation of the sampling distribution for an instructor's sample proportion of failures?

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The number of ways would be 2.68367259e14 for selecting 15 candidates out of  66 candidates.

Generally speaking, an arrangement of objects is just a collection of them. The sequence of the n items has no bearing on the number of "arrangements" that can be made of them (order is significant).

Total Candidates for software engineer = 66

Total Short listed candidates = 15

To find:

Number of 15 Candidates set possible

  ⁶⁶C₁₅ = [tex]\frac{66!}{51! 15!}[/tex]

After Calculating from calculator we get,

2.68367259e14.

Hence the number of ways would be 2.68367259e14.

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The normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution.

The usual normal distribution is then followed by the z variable. A value of the x variable's z variable, also known as the z-score of the x variable, indicates how many standard deviations from the mean it is.

The area under the normal distribution curve must be calculated that lies between

z=−1.56 and z=1.56

Using the standard normal table, the area is calculated as:

P(−1.56<z<1.56)

=P(z<1.56)−P(z<−1.56)

=P(z<1.56)−(1−P(z<1.56))

=0.9406−(1−0.9406)

=0.8812

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The complete question is

if z is a standard normal variable, find the probability. the probability that z lies between -1.56 and 1.56 is

Answer:

y value , r i = y i − y i ^

Step-by-step explanation:

Residual = actual y value − predicted y value , r i = y i − y i ^ . Having a negative residual means that the predicted value is too high, similarly if you have a positive residual it means that the predicted value was too low. The aim of a regression line is to minimise the sum of residuals.

answer:

no, because 0+0≠1 and 100+-49≠1 so the values are not a part of the system.

step-by-step explanation:

for this question, plug in the x & y values into the equation x+y=1. if the values add up to be 1, then it's possible for the system to have those solutions. hope that helps!

The expression -5g + 15h - 25 can be simplified as -5(g + 3h - 5)

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

In the question given, the expression is -5g + 15h - 25;

We have to simplify this to by factoring the expression.

-5g + 15h - 25 = -5(g + 3h - 5)

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When the population starts out with 8 people and triples, it will take 5 years to reach 1,944.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here,

Initial population=8

Final population=1944

Rate of increment=3ˣ

1944=8*3ˣ

1944/8=3ˣ

243=3ˣ

3ˣ=3⁵

x=5

It will take 5 years for the population to reach 1,944 when started with with the population of 8 and increase by 3ˣ.

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Answer:

Leah runs:

400 meters per minute

Step-by-step explanation:

2000 meters ⇒ 5 minutes

A meters ⇒ 1 minute

A = 2000 meters * 1 minute / 5 minute

A = 400 meters

The speed of wind is 380 miles per hour.

What is speed?

Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is traveling along a path.

Here, we have

The plane has a cruising speed of 200 miles per hour when there is no wind. at this speed, the plane flew 500 miles with the wind in the same amount of time it flew 300 miles against the wind.

We have to find the speed of the wind.

Time = Distance/speed

Time = 500/200 = 2.5hrs

When the plane moves against the wind its effective speed reduces as it has to overcome the opposing force of the wind since it is given that it cover's a distance of 300 miles at the same time we can write

2.5 = 300/ V(plane) - v(wind)

2.5 = 300/500- v(wind)

v(wind) =380mph

Hence, the speed of the wind is 380mph.

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Answer:

60 minutes

Step-by-step explanation:

Saturday = 16 minutes

Sunday = 28 minutes + 16 minutes = 44 minutes

Saturday + Sunday = 44 + 16 = 60 minutes