Simplify to a single power of 6:​​

Part a: 0.75x + 0.15y = 90 is the equation that indicates how many club pens and pencils the glee club can purchase.

Part B: The maximum number of pens and pencils the club can purchase is 120 and 600 respectively.

The stated values in the questions are-

Cost of one pen = $0.75

Let total number of pens be x.

Cost of one pencil = $0.15

Let total number of pencils be y.

Total cost (pens and pencils) = $90

Total cost = (Cost of one pen) x (Number of pens)  +  (Cost of one pencil)x(Number of pencils)

The equation modelling number of club pens and pencils is:

0.75x  +  0.15y    =   90

For the greatest number of pens ;

0.75x  = 90

x  =  90/0.75

x  =  120

Thus, the greatest number of pens bought by club is 120.

For greatest number of pencils;

0.15y = 90

y  =  90/0.15

y  =  600

Thus, the greatest number of pencils bought by club is 600.

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The type of sampling required for this test is Independent sampling with quantitative data.

Randomly chosen samples are known as independent samples since their results are independent of other observations' values. The premise that samples are independent underlies many statistical analyses.

In the hypothetical situation, independent sampling is required since the researcher needs two distinct samples: one from freshmen and one from sophomores. These samples are independent since there would be no relationship between them.

The information would be quantitative in nature. Student GPAs are the dependent variable in this study. Since GPA is a qualitative indicator, the kind of data being collected is also quantitative.

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5.152 L volume will it occupy at STP.

What is ideal gas law?

The equation of state for an ideal gas, in theory, is known as the ideal gas law. Even though it has a number of shortcomings, it provides a good approximation of the behavior of several gases under various circumstances. Theoretical point particles that move randomly and only collide in elastic ways make up an ideal gas.

Using the ideal gas equation PV=nRT, where n is the number of moles, it is possible to determine the volume that will be present at STP as follows.

n= PV/RT

p=0.974 atm

V=6.0  L

R = 0.0821  L.atm/k.mol

T=  35 +273= 308k

n=  (0.974 atm  x  6.0 L)/( 0.0821 L.atm/k.mol  x 308 k)=  0.178 moles

STP  1 mole=  22.4 L  what obout  0.23 moles

=22.4  x0.178moles/ 1moles =5.152 L

Hence, 5.152 L volume will it occupy at STP

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The domain and the range of the functions are given by the images at the end of the answer.

The domain of a function is composed by the set that contains all possible values assumed by the input of the function. Hence, on the graph, it will be given by the values of x of the graph, the values assumed by the horizontal axis of the graph.

The range of a function is composed by the set that contains all possible values assumed by the output of the function. Hence, on the graph, it will be given by the values of y of the graph, the values assumed by the vertical axis of the graph.

The notations are given as follows:

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The scale factor of the figure of the two squares is 1.5

The scale factor is determine using division

The formula involve:

let the scale factor be r then we say

area of square A * r = area of square B

8 * 8 * r = 12 * 12

64r = 144

r = 144 / 64

r = 1.5

using the dimensions

8r = 12

r = 12 / 8

r = 1.5

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The number of terms that must be added together to achieve this series s is 5000.

Given that,

The remainder of the following convergent series must be less than 10 Superscript negative 5 in magnitude.

We have to calculate the number of terms that must be added together to achieve this.

Given

S= summation n=0 to infinity (-1)ⁿaₙ.

An upper bound for the error of the series Rₙ is aₙ₊₁ so

Rₙ=|s-sₙ|≤aₙ₊₁

In this case we have

1/2n+1≤1/10⁴

10⁴≤2n+1

(10⁴-1)/2≤n

(10⁴-1)/2 is approximately 5000.

Therefore, the number of terms that must be added together to achieve this series s is 5000.

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There's not enough evidence to refute the publisher's claim.

Here, we are given that a newsletter publisher believes that 29% of their readers own a personal computer.

The testing firm believes this is inaccurate and hence conducts hypothesis testing to verify the claim.

They take a significance level of 0.02 and fail to reject the null hypothesis.

The null hypothesis of the testing firm would be- 29% of the readers own a personal computer because this is what is established by the publisher.

They fail to reject this null hypothesis which means that there is not enough evidence at 0.02 significant level that the percentage is not 29%.

Thus, there's not enough evidence to refute the publisher's claim.

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As per the standard distribution, the lowest test score is 27.76%

Standard distribution:

In statistics, standard distribution means a normal distribution with a mean of zero and standard deviation of 1.

Given,

The top 5% of applicants on a test will receive a scholarship. if the test scores are normally distributed with a mean of 76 and a standard distribution of 12.

Here we need to find the lowest test score that still qualifies for a scholarship.

As per the given question, we have identified the value of

=> μ = 76 (mean)

=> σ = 12 (standard deviation)

Then we need to take the value of x as,

x < 5% (find the probability)

Now, converting the problem in standard form

=> Z = (5 − 76) / 12

=> Z = -5.91

Then as per the z table the value is 0.2786

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Answer: 220 meters in 1 minute

Step-by-step explanation:

if harper can run 2200 meters in 10 min then that means you can run 220 in 1 min

2200/10 = 220

Answer:

220

Step-by-step explanation:

2200/10 is 220

Answer:

  about 2.758 cm/s

Step-by-step explanation:

You want the rate of change of a cylinder's radius, when its height is 33 cm increasing at 2 cm/s, and its volume is 403 cm³ increasing at 1152 cm³/s.

The volume of a cylinder is given by the equation ...

  V = πr²h

Solving for the radius gives ...

  r = √(V/(πh))

Differentiating, we have ...

  [tex]r'=\dfrac{1}{\sqrt{\pi}}\left(\dfrac{1}{2}V^{-\frac{1}{2}}h^{-\frac{1}{2}}V'-\dfrac{1}{2}V^{\frac{1}{2}}h^{-\frac{3}{2}}h'\right)=\dfrac{hV'-Vh'}{2h\sqrt{\pi Vh}}[/tex]

Filling in the values V = 403, V' = 1152, h = 33, h' = 2, we have ...

  r' = (33·1152 -403·2)/(2·33·√(π·403·33)) = 37210/(66√(13299π))

  r' ≈ 2.758 . . . . . cm/s

The rate of change of the radius is about 2.758 cm/s.

Hence, the remainder is [tex]0[/tex] and the quotient is [tex]3x-y[/tex].

What is the polynomial?

A polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

Here given polynomial is

[tex]\frac{9x^4+3x^3y-5x^2y^2+xy^3}{3x^3+2x^2y-xy^2}[/tex]

                      [tex]3x-y[/tex]

[tex]\sqrt[3x^3+2x^2y-xy^2]{9x^4+3x^3y-5x^2y^2+xy^3} \\\\[/tex]

                  [tex]9x^4+6x^3y-3x^2y^2+0[/tex]

              -----------------------------------------

                         [tex]-3x^2y-2x^2y^2+y^3x[/tex]

                         [tex]-3yx^3-2y^2x^2+y^3x[/tex]

             ------------------------------------------

                                              [tex]0[/tex]

Hence, the remainder is [tex]0[/tex] and the quotient is [tex]3x-y[/tex].

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The equation form as per the statement in the question will be y = -200x - 2000.

Equations are mathematical expressions that have two algebras on either side of an equal (=) sign. The expressions on the left and right are shown to be equal to one another, demonstrating this relationship. L.H.S. = R.H.S. (left-hand side = right side) is a fundamental simple equation.

As per the given information in the question,

They spent $2,000 therefore that would be -2,000, and they make $200 per month selling brownies.

So simply add -2,000 each time on the chart under "Income made," and the final amount should be 600.

So, the equation will be,

y = -200x - 2000.

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Answer:

As a decimal:0.016

As a percentage:1.6%

Step-by-step explanation:

Answer: specific analyze is as it follows

Step-by-step explanation:

The appropriate statistic test should be ANOVA and The degree of freedom is 12.

What are Statistical tests?

An instrument for making quantitative judgments about a process or processes is a statistical test. The goal is to decide whether there is sufficient data to "reject" a theory or hypothesis on the process.

In the given problem the average age of the corporate executives at the three locations is being calculated, it means more than two groups are being compared. hence, The appropriate statistic test would be ANOVA.

In order to calculate the degree of freedom, we must know the no. of observations.

here,  no. of observations are 15 ( 3 × 5 ) and the no. of groups are 3.

∴ Degree of freedom = no. of observations - no. of groups

                                    = 15 - 3 = 12.

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The following are the amount each person receive:

a. 6 : 4

Total ratio = 6 + 4

= 10

6/10 × 500

= $300

4/10 × 500

= $200

b. 1 : 4 : 5

Total ratio = 1 + 4 + 5

= 10

1/10 × 500

= $50

4/10 × 500

= $200

5/10 × 500

= $250

c. 1 : 8 : 1

Total ratio = 1 + 8 + 1

= 10

1/10 × 500

= $50

8/10 × 500

= $400

1/10 × 500

= $50

d. 8 : 9 : 8

Total ratio = 8 + 9 + 8

= 25

8/25 × 500

= $160

9/25 × 500

= $180

8/25 × 500

= $160

e. 10 : 5 : 4 : 1

Total ratio = 10 + 5 + 4 + 1

= 20

10/20 × 500

= $250

5/20 × 500

= $125

4/20 × 500

= $100

1/20 × 500

= $25

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Jay is incorrect in doing addition first.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given the expression as;

3x (3 +12 divided by 3) -4.

To simplify this expression, then must follow PEMDAS.

3x(3+12÷3)

3x(3+4)

3x(7)

21x

Which means that Jay is incorrect in doing addition first.

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12 People plan to visit the art museum only.

What is Set Theory?

We study sets and their characteristics in the area of mathematical logic known as set theory. A set is a collection of things or a group of things. These things are frequently referred to as elements or members of a set. A set is, for instance, a group of cricket players. A set is a clearly defined collection of things or people, as we already learnt in the introduction. Numerous examples from everyday life, such as the number of rivers in India and the colors in a rainbow, can be used to relate sets.

Given,

Total no of people =116

No of people visiting any of the three places = total - people visiting none of the places

= 116 -14 = 102

No of people visiting only Gateway arch = total people visiting gateway arch - (people visiting all the three +  people visiting Gateway ans museum butnot zoo +people visiting gateway and zoo butnot museum)

= 66 - (18+9+14) = 25

Similarly, people visiting only zoo = 14

Total no of people plan to visit Art Museum only = 102 - (25+14+9+18+10+14) = 112

12 People plan to visit the art museum only.

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Answer: 32 every month or day. if its every month the answer is 384, if its every day it would be 11680

Step-by-step explanation:

Given:

Find the amount of interest:

Find the balance after one year:

The solutions are given below.

An angle is the formed when two straight lines meet at one point, it is denoted by θ.

Given that,

lines u and v are parallel,

And ∠ 9 = 80° and ∠ 5 = 68°

(a)

Angle 12 is supplementary angle of angle 9,

Therefore, ∠12 = 180 - 80 = 100

(b)

Angle 1 and angle 9 are corresponding angle and are equal.

∠ 1 = ∠ 9 = 80

(c)

Angle 1 is supplementary angle of angle 4,

Therefore, ∠ 4 = 180 - 80 = 100

(d)

Angle 3 and angle 1 are vertically opposite angles,

Therefore, ∠ 3 = ∠ 1 = 80°

(e)

Angle7 and angle 5 are vertically opposite angles,

Therefore, ∠ 7 = ∠ 5 = 68°

(f)

Angle 16 and 7 are supplementary angles,

Therefore,  ∠16 = 180 - 68 = 112

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The unit rate per batch of cookies is 2.75 as Lennon uses 5 1/2 cups of flour for every 2 batches of cookies she bakes.

To calculate the unit rate, divide the denominator by the numerator so that the denominator equals 1. For example, if 50 kilometers are reached in 5.5 hours, the unit rate is 50 kilometers/5.5 hours = 9.09 kilometers per hour.

When expressed as a fraction, a unit rate has a denominator of one unit. To write a rate as a unit rate, divide the rate's numerator and denominator by the rate's denominator.

Based on the given conditions, formulate:

(5 1/2)/2

We have to find the common denominator and write the numerators above the common denominator.

(((5×2)/2)+(1/2))/2

Now, we have to calculate the product or quotient:

((10/2)+(1/2))/2

Now, write the numerators over common  denominator,

((10+1)/2)/2

Then, calculate the sum or difference:

(11/2)/2

=11/4

=2.75 (or) 2 3/4

Therefore, the unit rate per batch of cookies is 2.75.

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When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape.

On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies.

Consider your square as being composed of smaller unit squares.

The number of unit squares necessary to completely cover the surface area of a specific 2-D shape is used to calculate the area of a figure. Some typical units for measuring area are square cms, square feet, square inches, square meters, etc.

Draw unit squares with 1-centimeter sides in order to calculate the area of the square figures shown below. The shape will therefore be measured.

Hence, When Chance stops feeding the beanstalk, it loses half its height every day. Chance's beanstalk grows to a height of 20 inches after he stops feeding it= 20.5^t

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Answer:

ITS A

Step-by-step explanation:

By definition of slope , we have seen that Slope = 4/3 and 4/3 = 16/12

The slope of a line is basically a measure of its steepness. Mathematically, the slope is calculated as rise over run.

To find the slope, we divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points. This is change in y divided by change in x.

From definition of slope, we know that;

Slope between line D and E is; Slope = 4/3

Similarly, by definition of slope, we know that;

Slope between line D and E is; Slope = 16/12

Now, 16/12 can be reduced to 4/3 and as such;

4/3 = 16/12

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There are 80 sundaes possible using one flavor of ice cream and three different toppings.

Here, we are given that a club is hosting an ice cream sundae party with four different flavors of ice cream and six different toppings.

For choosing 1 flavor of ice cream from 4, we have 4 ways.

Now, we need to choose 3 different toppings from the given 6.

This can be done in 6C3 ways

6C3 = 6! / (3! × 3!)

= (6 × 5 × 4) / (3 × 2)

= 120/ 6

= 20

Thus, we have 20 ways of choosing 3 different toppings.

Now, the number of ways of making the sundaes would be-

4 × 20

= 80

Thus, there are 80 sundaes possible using one flavor of ice cream and three different toppings.

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Answer:  9 hours

Step-by-step explanation:

here are a couple of things to notice here. You don’t have a starting temperature, so that will be an unknown. I will call it S.

The next thing to notice is that the current temperature (C) at any given time is just the starting temperature minus 4 times the number of hours (H) that have passed since 1 PM.

C = S – 4*H

We want to solve this for H when the current temperature (C) is -1.

-1 = S – 4*H

You can rearrange this by adding 4*H to both sides and adding 1 to both sides:

4*H = S + 1

Then you divide both sides by 4

H = (S+1)/4

This will tell you the number of hours PAST 1 PM that it takes to get to -1 degrees. Of course, you need to know the starting temperature, S, in order to get a numeric answer.

Let’s check this with an example. If the starting temperature were exactly 4 degrees above -1, then it should take exactly 1 hour. So let S = -1 + 4 = 3. If you plug 3 in for S, you do see that H becomes 1 hour PAST 1 PM (2 PM).

correlation coefficients most closely corresponds to the observed correlations between the intelligence scores of adopted children is a. child-adoptive: 0.20; child-biological: 0.40

Children for adoption

Adoption is the social, emotional, and legal process in which children who will not be raised by their birth parents become full and permanent legal members of another family while maintaining genetic and psychological connections to their birth family.

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y - 9 = 1(x - 15) is the required equation for the tangent.

Equations come in two varieties: identities and conditional equations.

All possible values of the variables result in an identity.

Only certain combinations of the variables' values make a conditional equation true.

Two expressions joined by the equals symbol ("=") form an equation.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

A formula would be 3x - 5 = 16, for instance.

When this equation is solved, we discover that the value of the variable x is 7.

So, the equation of the tangent is:

First, with respect to t, differentiate the function as follows:

dx/dt = d(9t² + 6)/dt

dx/dt = 18t

Like this, we have:

dy/dt = d(6t³ + 3)/dt

dy/dt = 18t²

Now, we will obtain:
dy/dx = 18t²/18t

dy/dx = t

We know that (15, 9) occurs on the curve, so we got:

d(9t² + 6)/dt and d(6t³ + 3)/dt ⇒ t = ±1 and t = 1 ⇒ t = 1

So, (15, 9) is the slope.

y - 9 = 1(x - 15) is the equation of the tangent.

Therefore, y - 9 = 1(x - 15) is the required equation for the tangent.

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Correct question:
Find the equations of the tangents to the curve x = 9t2 + 6, y = 6t3 + 3 that passes through the point (15, 9).

The statements that are true about the ordered pair (−1, 5) and the system of equations include the following;

A. The ordered pair (−1, 5) is a solution to the first equation because it makes the first equation true.

B. The ordered pair (−1, 5) is a solution to the second equation because it makes the second equation true.

D. The ordered pair (−1, 5) is a solution to the system because it makes both equations true.

In order to determine if this ordered pair is a true solution based on the given system of linear equations, we would have to test the ordered pair (-1, 5) by substituting it into each of the linear equation as follows;

For the first linear equation, we have the following:

x + y = 4

-1 + 5 = 4

4 = 4 (True).

For the first linear equation, we have the following:

x - y = -6

-1 - 5 = -6

-6 = -6 (True).

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