for the following proof (of equivalence of 2 formulae) provide the justifications at each step, using the following equivalences. use the following key:

Answer:

Step-by-step explanation:

Correct answers only explained
------------------------------------------------------------------
We have the original equation as
72x + 12y = 60
If we multiply by 10 we get

720x + 120y = 600
First option

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

We can rewrite the original equation 72x + 12y = 60 as follows
Carry 72x to the right:
12y = 60 - 72x

Divide by 12
y = 5 - 6x
Second option

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

Rewrite  72x + 12y = 60 as

12y + 72x = 60  (same thing)

Divide by 6:
2y + 12x = 10

Third option

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

Rewrite 72x + 12y = 60 as

72x = 60 - 12y

Divide by 72

x = 60/72 -12y/72

Reduce to lowest fraction
x = 5/6 - y/6
Fifth option
------------------------------------------------

From given pie chart, The percentage of students for 12th grade is 20%.

What is a pie chart?

The “pie chart” is also known as a “circle chart”, dividing the circular statistical graphic into sectors or sections to illustrate the numerical problems. Each sector denotes a proportionate part of the whole. A pie chart requires a list of categorical variables and numerical variables. To find out the composition of something, Pie-chart works the best at that time. In most cases, pie charts replace other graphs like the bar graph, line plots, histograms, etc.

The total value of the pie is always 100%.

Now

As

The total value of the pie is always 100%.

12th+9th+10th+11th=100

12th+30+27+23=100

12th=100-80

12th=20%

Hence,

                The percentage of students for 12th grade is 20%

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Answer: 50

Step-by-step explanation:

1 van = 11 campers

Number of vans that will be needed = 550/11

=50

The statements that are true regarding the areas are that each palette icon will always allow you to drag only one fill area onto the graph. Changing the position of the other objects on the graph may change the shape of the possible regions you may fill.

The statement "Each palette icon will always allow you to drag only one fill area onto the graph." is true.

The statement "Areas can be used to shade a region of any shade." is false. Areas can be used to shade a region in a specific colour or pattern, but not necessarily any shade.

The statement "Changing the position of the other objects on the graph may change the shape of the possible regions you may fill." is true.

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The probability that both chosen students are women is 0.3025 and the probability that at least one of the two students is a woman is 0.8075.

a) Probability of both chosen students being women = P(W1 ∩ W2) = P(W1) * P(W2)

= 0.55 * 0.55 = 0.3025

b) Probability of atleast one of the two students being a woman = P(W1 ∪ W2)

= P(W1) + P(W2) - P(W1 ∩ W2)

= 0.55 + 0.55 - 0.3025 = 0.8075

Therefore, the probability that both chosen students are women is 0.3025 and the probability that at least one of the two students is a woman is 0.8075.

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After 15 minutes of walking, Julia and Josie are facing each other at the same point (in distance).

Distance between Julia and Josie = 1,500 m

Julia's traveling rate (speed) per hour = 2,000 mph

Josie's traveling rate (speed) per hour = 4,000 mph

Walking time = 15 minutes

Distance formula = time x speed.

In 15 minutes, Julia's distance traveled = 500 m (2,000/60 x 15)

In 15 minutes, Josie's distance traveled = 1,000 m (4,000/60 x 15)

Thus, in 15 minutes, Julia and Josie have covered the 1,500 m distance separating them and will be at the same point.

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She can only invite a total of six individuals, and the inequality that best captures the circumstance is 13x ≤ 85.

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

Given, Alessandra is having a dinner party she calculates that each meal will cost 13.00$ a person she has an 85 dollar budget

Let "x" be the number of people she can invite to the party

Thus,

The total cost required for the party = 13x

Since her budget is $85.

Maximum people she can invite:

13x ≤ 85

x ≤ 85/13

x ≤ 6.53

therefore, she can maximum invite 6 people and the inequality that represents the given situation is 13x ≤ 85.

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Answer:

e

Step-by-step explanation:

The number of months before the cost is the same as Plan A is 25 months.

The linear equation that represents the cost of plan A = cost per month x number of months

$70 x m = $70m

The linear equation that represents the cost of plan B = (cost per month x number of months) + cost of the phone

($50 x m) + $500

= $50m + $500

When the costs are the same, the two equations would be equal

$70m = $50m + $500

Solve for m:

Combine similar terms: $70m - $50m = $500

Add similar terms: $20m = $500

Divide both sides of the equation by 20 = 500 / 20

m = 25 months

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The percent of increase from 60 to 70 rounded to the nearest percent is 17%.

Percent​ increase is simply the amount of increase from the initial value to the new value in terms of 100 parts of the initial value.

It is expressed as;

C = ((x₂ - x₁) / x₁)100%

Where x₁ is initial value and x₂ is new value

Given that;

Plug in the given values and solve for C.

C = ((x₂ - x₁) / x₁)100%

C = ((70 - 60) / 60) × 100%

C = ( 10 / 60) × 100%

C = 1/6 × 100%

C = 17%

Therefore, the percentage increase is 17%.

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Considering the data we have been provided, we can build a multiple regression model as follows.

a.) In MS Excel, we enter the data set and utilize the "Correlation" option under Data > Data Analysis to create the correlation matrix and answer the question. The correlation matrix may be seen below.

[Fig. 1]

Correlation coefficients for at least one of the independent variables are larger than 0.7.

b.) We must look at the column labeled "Won" in the correlation matrix. The variables are Runs, Hits, Earned Run Average (ERA) and Walks if the criteria are 0.4.

c.) In MS Excel, we enter the data set and utilize the "Regression" option under Data > Data Analysis to create the regression model and answer the question. The result is shown below.

[Fig. 2,3,4]

Runs, ERA, and SO are all significant, with p-values less than 0.05. As a result, we recreate the regression model with these three independent variables.

[Fig. 5,6,7]

The right answer is Won = 80.321 + (0.101) X1 + (-14.276) X3 + (-0.011) X4.

The R2 value of the model is 0.948. This suggests that these factors can predict 94.8% of the number of victories. This model does not make use of the same variables as the previous one (b).

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So, the area of the stripe is 394.25= 282.75 square feet.

The stripe is a rectangle, with a width of 3 feet and a length that is the circumference of the cylinder. The diameter of the cylinder is 30 feet, so the circumference is 30pi=94.25 feet. So, the area of the stripe is 394.25= 282.75 square feet.

The white cylindrical silo has a red stripe painted on it, which makes two complete revolutions around the silo. The stripe is a horizontal rectangle with a width of 3 feet and a length equal to the circumference of the cylinder, which is calculated by multiplying the diameter of 30 feet by pi. The area of the stripe is the width of 3 feet multiplied by the length of 94.25 feet, which equals 282.75 square feet.

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The  most likely the next step in the series wil be heptagon, the correct option is B.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Given;

Figure 1 has 4 sides

Figure 2 has 5 sides

Figure 3 has 6 sides

Now, from the three given figures;

The next figure will have 7 sides

Therefore, by algebra the next figure will be heptagon.

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A graph is a visual representation of data or information using points, lines, or bars.

How to plot the Graph?

To plot a graph, you need to have a set of x and y values that correspond to points on the graph. Once you have the data, you can use a tool such as a graphing calculator, spreadsheet software or specialized graphing software to plot the points and create the graph.

This sequence appears to be a geometric sequence. In a geometric sequence, the ratio between any two consecutive terms is always the same. In this case, the ratio between consecutive terms decreases by a factor of 1/4 each time.

The first five terms of the sequence are: (64,1), (16,2), (4,3), (2,4), (0,5)

A recursive definition of the sequence is a definition that expresses each term of the sequence in terms of one or more of the previous terms.

This definition says that each term of the sequence is the previous term divided by 4.

It's important to note that the graph you provided does not have a clear representation of the sequence, the points (64,1) (16,2) (4,3) (2,4) (0,5) does not represent a sequence as the x-coordinate does not represent the nth term of the sequence. The graph does not provide enough information to determine if it's arithmetic or geometric, or to list the first five terms of the sequence, or to write a recursive definition of the sequence.

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Answer:

The statement "The series converges by the Integral Test" is true. The Integral Test is a method used to determine the convergence or divergence of a series. The test states that if the series is of the form:

∑(f(n))

where f(n) is a positive and continuous function defined for n ≥ 1 and is decreasing for n ≥ 1, then if the integral of f(n) from 1 to infinity converges, the series also converges. If the integral diverges, the series diverges.

It is important to note that the Integral Test is only one method of determining the convergence or divergence of a series and that it has some limitations such as it only works when the function f(n) is positive and decreasing. Also, the test is only inconclusive if the necessary conditions are not met, so statement 4 and 5 are not true.

Answer:

Step-by-step explanation:You should notice because you're in the class you should notice because the teachers are obviously teaching this because they wouldn't just give you something that they didn't cheat so if you sleep in class or like not paying attention speak into a friend or like something like doing something in my pay attention you ain't getting no you ain't getting nothing.

Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.

What is deviation ?

Deviation refers to how far a value or set of values is from the mean or average. In statistics, the standard deviation is a measure of the spread of a dataset, calculated as the square root of the variance. It represents the average distance of each data point from the mean. A low standard deviation indicates that the data points tend to be close to the mean.

To compute the probabilities for a standard normal random variable, we can use a standard normal table or a calculator with standard normal distribution functions.

P(z ? -1.0) = P(z < -1.0) = 0.1587

P(z ? -1.0) = P(z > -1.0) = 1 - 0.1587 = 0.8413

P(z ? -1.5) = P(z < -1.5) = 0.0668

P(z ? -2.5) = P(z < -2.5) = 0.0062

P(-3 < z ? 0) = P(-3 < z < 0) = P(z < 0) - P(z < -3) = 0.5 - 0.0013 = 0.4987,

Computed the probabilities P(z < -1.0)=0.1587, P(z > -1.0)=0.8413, P(z < -1.5)=0.0668, P(z < -2.5)=0.0062, P(-3 < z < 0)=0.4987.

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In the simplest rational exponent form of "square root of x times the fourth root of x" is [tex]x^{1/6}[/tex].

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a time to itself.

So, a is the exponent of m.

Given:

We have a phrase:

Square root of x times the fourth root of x.

In numerator form:

(√x)[tex]\sqrt[1/4]{x}[/tex]

Simplifying,

(√x)[tex]\sqrt[1/4]{x}[/tex],

= [tex]x^{1/2} x^{1/4}[/tex]

= [tex]x^{1/2+1/4}[/tex]

= [tex]x^{1/6}[/tex]

Therefore, [tex]x^{1/6}[/tex]the required simple rational form.

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Answer:

parallel

Brief explanation:

Well parallel lines have the same slopes sooo

these two lines are parallel

hence the answer

study hard

The number of students from given linear equation after 6 weeks will be 45.

What is a linear equation ?

A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form

Ax + B = 0

e.g. x-10=0. Here, x is a variable, A is a coefficient and B is constant.

The standard form of a linear equation in two variables is of the form

Ax + By = C

e.g. 2x-4y=10. Here, x and y are variables, A and B are coefficients and C is a constant.

Now,

As given linear equation for students is

y=-2.5t + 60

where where t is the number of weeks her students have been taking

the class and y = no. of students.

To find students after 6 weeks put y=6

Therefore, y=-2.5*6+60

y=45

Hence,

         The number of students from given linear equation after 6 weeks will be 45.

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Right question:-

Alexis is working with her English classes to make sure they are

all able to pass the upcoming state exam. From last year's data,

she predicts the number of students that will not pass the exam

is modeled by the linear equation:

y=-2.5t + 60,

where t is the number of weeks her students have been taking

the class and y = no. of students.

Find mo. of students after 6 weeks.

Probability of waiting between 15 and 30 seconds and probability of waiting for more than 2 minutes are 0.2462 and 0.0099 respectively.

Given that,

Do you find lines to be tedious? The grocery store chain Kroger has reduced the average wait time for customers at 2300 locations by using computer modeling and information technology. Kroger was able to reduce the typical customer wait time to to 26 seconds thanks to a new system called QueVision that helps the retailer to better anticipate when customers would be checking out.

P(Wait between 15 and 30 seconds)

= [tex]\int{15}{30} \frac{e^{-x/26}}{26} dx[/tex]

= 0.2462

P(wait for more than 2 minutes)

= 1 - P(Wait for less than or equal to 120 seconds)

= 1 - [tex]\int{0}{120} \frac{e^{-x/26}}{26} dx[/tex]

= 0.0099

As a result, the probabilities of waiting between 15 and 30 seconds and longer than 2 minutes are, respectively, 0.2462 and 0.0099.

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13 c is equal to 48.775 L.

Equality in math is a concept that states that two expressions, equations, or values are equal to each other. Equality is symbolized by the equals sign “=.” Equality is a fundamental law of mathematics, and it is used in a variety of contexts and equations. Equality can be used to compare two different objects, or to set a value for a single object. Equality can also be used to determine if two equations are equivalent. Equality is an important concept in mathematics, as it allows us to find solutions to difficult problems.

5 gallons (gal) is equal to 18.925 liters (L). Therefore, 13 c is equal to 48.775 L.

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Since dy/dx > 0 for x = -7 and dy/dx < 0 for x = -9 , So this is a turning point.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables and

constants.

So, the given expression ,

y = 2x^2 + 32x -4

So, first we have to find the derivative dy/dx

and than solve for dy/dx = 0

The derivative of any term x^n is equals to n*x^n-1 so for this polynomial

2x^2 + 32x - 4

The derivative could be

2.2x+1.32+0.-4

dy/dx = 4x+32

To calculate the turning points

let this equals to 0.

4x+32 = 0

x = -32/4

x = -5

By substituting this into the original equation, the turning point is at (-8,-137).

Therefore, Since dy/dx > 0 for x = -7 and dy/dx < 0 for x = -9 , So this is a turning point.

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You worked for 8 hours.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, You are getting paid $50 per hour and at the end of the day, you earned $400.

Unit rate for working an hour = $50

We will calculate the number of hours of work by dividing total earning by its unit rates.

= 400 / 50

= 8

Hence, You worked for 8 hours.

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The  the length and width of the rectangular field are respectively; 15 yards and 11 yards

The perimeter of a rectangle is given by the formula;

Perimeter = 2(Length + width)

We are given;

Perimeter = 52 yards

Length(L) = W + 4

Width = W

Thus;

2(W + W + 4) = 52

2W + 4 = 52/2

2W + 4 = 26

2W = 22

W = 11 yards

L = 11 + 4

L = 15 yards

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Answer:

C

Step-by-step explanation:

If two lines are parallel, then corresponding angles are congruent.

OR

If two lines are NOT parallel, then corresponding angles are NOT congruent.

So compare these 2 to the answers.  Only C is right.

The customer purchased 14 face masks and 8 hand sanitizers.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, Maleri Designs sells cartons of cloth face masks ($12) and cartons of hand-sanitizer ($6) on eBay.

Let the number of face masks be f an the number of hand-sanitizers be h.

One of their customers, Mod World, purchased 22 cartons for $216.

Now, f+h=22 --------(I) and

12f+6h=216 --------(II)

f=22-h

Substitute f=22-h in equation (II), we get

12(22-h)+6h=216

264-12h+6h=216

264-216=6h

6h=48

h=8

Substitute h=8 in equation (I), we get

f+8=22

f=14

Hence, the customer purchased 14 face masks and 8 hand sanitizers.

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Answer:

6, 8

Step-by-step explanation:

2  and 3 are factors of 6. So, if number is divisible by 6, then the same number is divisible by 2 and 3.

Eg: 12 is divisible by 6. So, 2 and 3 will divide 12.

4 and 2 are factors of 8.  if number is divisible by 8, then the same number is divisible by 4 and 2.

Eg: 48 is divisible by 8. So, 4 and 2 will divide 48.

So, to find the least number that is divisible by 2, 3, 4, 6 and 8, then the only two factors that we need to use are 6 and 8.

The standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

In order to use the formula sigma x = sigma/ to calculate the standard deviation of the sampling distribution of the sample mean, all three conditions must be met. The first condition is that n must be greater than or equal to 30. This is because the larger the sample size, the more likely it is that the population's distribution is approximately normal. The second condition is that the population's distribution is approximately normal. This is because the Central Limit Theorem states that when the sample size is large enough (usually n ≥ 30) the sample means will have an approximately normal distribution. The third condition is that the sample size is less than 10% of the population size. This is because samples that are too large can lead to sample means that are not representative of the population.

To calculate the standard deviation of the sampling distribution of the sample mean, we can use the following formula:

σx = σ/√n

Where σ is the population standard deviation, and n is the sample size. For example, if the population standard deviation is 5, and the sample size is 30, then the standard deviation of the sampling distribution of the sample mean would be 5/√30, or 0.87.

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The reciprocal of that fraction is 2/21.

The inverse of a value or a number is how reciprocal is commonly used in mathematics. The reciprocal of n will be 1/n if n is a real number. In other words, we must change the number to be inverted. One divided by nine, or 1/9, is the reciprocal of nine, for instance. A value of one is produced when we multiply a number by its reciprocal. The term multiplicative inverse is another name for it.

reciprocal is simply defined as the inverse of a value or a number. If n is a real number, then its reciprocal will be 1/n. It means that we have to convert the number to the upside-down form.

Using the given functions to set up and simplify 1-2

10=1-2=-1

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The win percentage is 79%

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

[tex]\dfrac{a}{100} \times b[/tex]

Given;

Number of games won=52

Number of games lost=14

Now, total games played= 14+52=66

Percentage of games won;

=(games won/total games)x100

= 52x100/66

=78.78

Therefore, the win percent will be 79%

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