Is (22, 11) a solution to the following
system of equations: y 5 2x 2 5,
y 5 4x 2 3? Explain.

Answer:

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

The distance traveled in each minute is a speed.

Find the speed per min for each distance:

Since the speed is not same over the total distance, the first choice is correct.

Find the average speed over the given distance:

Find the predicted time to travel 30 km:

The inequality to represent this situation is 5 + 1.25x < 45.

Rob and Ahab are in Las Vegas for vacation. They get a taxi to drive

them around town. The taxi charges a flat fee of $5.00 plus $1.25 per

mile of traveling. They want to spend less than $45.00 for their taxi

fare. The inequality to represent the situation is as follows:

let

x = number of miles

Therefore, the inequality is as follows:

5 + 1.25x < 45

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Value of x is -6

According to question

(x/2)-6 = 2+(2x+1)

⇒x-12/2 = 3+2x

⇒x-12=2(3+2x)

⇒x-12=6+4x

⇒-3x=18

⇒x=18/-3

∴x=-6

The value of x is -6.

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Answer:

x = - 6

Step-by-step explanation:

(b)

[tex]\frac{1}{2}[/tex] x - 6 = 2 + (2x + 1) ← remove parenthesis

[tex]\frac{1}{2}[/tex] x - 6 = 2 + 2x + 1

[tex]\frac{1}{2}[/tex] x - 6 = 2x + 3 ( add 6 to both sides )

[tex]\frac{1}{2}[/tex] x = 2x + 9 ( multiply through by 2 to clear the fraction )

x = 4x + 18 ( subtract 4x from both sides )

- 3x = 18 ( divide both sides by - 3 )

x = - 6

Answer:

433 pizzas

Step-by-step explanation:

6062 / 14 = 433

The value of u.v is 32.

A vector is a quantity or phenomenon that has two independent properties: magnitude and direction.

Given are two vectors, u = ⟨2, –8⟩ and v = ⟨8, –2⟩,

We know, x.y = x₁.x₂+y₁+y₂

Therefore, u.v = 2×8+(-2)(-8)

= 16+16

= 32

Hence, The value of u.v is 32.

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By applying the concept of algebra, it can be concluded that the two cost plans will be the same after 125 minutes.

The use of algebra in everyday life.

Algebra is a branch of mathematics that uses numbers, symbols, or letters to solve a mathematical problem. In everyday life, algebra is often used for financial planning, plan or scheme comparison, and so on.

In the given problem, we are asked to compare the two calling plans.

Let's say the total cost for the first plan is P1, then:

P1 = monthly fee + total cost per minute

   = 20 + (0.08 x number of minutes)

The total cost for the second plan is P2, then:

P2 = monthly fee + total cost per minute

    = 25 + (0.04 x number of minutes)

Let's say the two total costs become equal after x minutes, then we can equate the two expressions given above as follows:

   20 + 0.08x = 25 + 0.04x

0.08x - 0.04x = 25 - 20

            0.04x = 5

                    x = 5 : 0.04

                       = 125 minutes

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This ratio is used to compare the variances of the two samples and determine if they are statistically equal.

The test for the equality of two population variances is a statistical test used to determine whether or not the variances of two populations are equal. This test is based on the ratio of the two sample variances, which is calculated by dividing the difference between the two sample variances by the difference between the two sample means. This ratio is then compared to the value of a critical statistic to determine whether or not the two population variances are statistically equal. If the ratio is greater than or equal to the critical statistic, then the two population variances are considered equal. If the ratio is less than the critical statistic, then the two population variances are considered unequal. This test is useful for determining if the two populations have similar amounts of variation or if one population has more variation than the other.

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A total discount of $18.6 and 1860 cents is availed by Amadou in buying pair of sunglasses after the final step of processing charge.

Given the intital price as $60 i.e cost price

given he had a coupon code to get discount of 40%

so after apply discount the price of pair of sunglasses is [tex]\frac{100-40}{100} *60[/tex]

=> 0.6 *60

=>36

so the current price of pair of sunglasses is $36

now we need to apply 15% processing fee after the discount so the current price of pair of sunglasses will increase from previous value and is given by:

[tex]36 + \frac{15}{100} *36[/tex]

=>36 + 5.4

=> 41.4

so the final price of pair of sunglasses is $ 41.4

Total discount = initial price - final price

=> 60- 41.4

=> $18.6

$1 = 100 cents

so total discount = 18.6 *100 = 1860 cents

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Answer: the right answer is D

Step-by-step explanation:

If you multiply 4 by 2 you get 8. If this goes on the answers are aways the same and it’s going to be proportional

Answer:

There are several equations or inequalities that could describe this situation. Here are a few examples:

- The total number of plants cannot exceed 60: c + t ≤ 60

- The total number of plants must be at least 60: c + t ≥ 60

- The total amount of growing space must not exceed 300 square feet: 6c + 4t ≤ 300

- The total amount of growing space must be at least 300 square feet: 6c + 4t ≥ 300

Step-by-step explanation:

Any equation or inequality that accurately represents the given constraints on the number and types of plants, and the amount of growing space available, could be used to describe this situation.

The number sentence to find how many people are on all the buses is 7 x10 = ?. (Option C)

A number sentence refers to an equation or inequality which expresses using numbers and mathematical symbols. Examples of number sentences include 32 + 57 = ? or 5 x 6 = ?. In the given situation, Jack sees 7 buses and each bus has 10 people on it. In order to determine the total number of buses on all the buses, multiplication operation is used. Multiplication, one of the four basic mathematical operations of arithmetic, refers to an operation that represents the basic idea of repeated addition of the same number. Hence, it is used to combine groups of equal sizes. As in the given case, the group of equal size i.e., the number of people on each bus is seen in 7 buses, the total number of people would be the product of two and would be represented by 7 x10 = ?.

Note: The question is incomplete. The complete question probably is: Jack sees 7 buses. Each bus has 10 people on it. Which number sentence can be used to find how many people are on all the buses? A. 7 + 10 = ? B. 10 – 7 = ? C. 7 x10 = ? D. 10 ÷ 7 = ?

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Answer: 30%

Step-by-step explanation:

First, take 300 divided by 1000, then times 100% = 30% for 6 years

If you want to find the rate for each year

The take 30% divided by 6

You get 5% each year

(1) We incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.

(2) The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.

1) Assume you predicted the variable "Number of Promotion Earned" by regressing it against just two other variables, "Income in $s" and "Years of Experience."

When compared to the beta for years of experience, the income beta is quite modest. You incorrectly interpret the beta number, compare the two, and draw the inference that because the beta for years is greater than the beta for income, the beta for years of experience is stronger.

But until we standardize the variables, this is incorrect. Then they can be put side by side.

2) As HR, I was questioned about whether employees who earn more money perform better. Do those with higher salaries complete the same task more quickly? I've been given data with two columns: "HIGH" salary people's income, and "LOW" salary people's income.

I conduct an ANOVA method test on two groups of individuals and track their typical completion time. The ANOVA will reveal who consistently does better in terms of the typical amount of time needed to finish a job.

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The complete question is:

First, how can graphics and/or statistics be used to misrepresent data? Where have you seen this done? Second, image that you are a human resources (HR) analyst reporting to a recently hired supervisor. Your supervisor has asked you to provide an example of data processed by HR. Describe one type of data that an HR department may process, and discuss a corresponding statistical method that may be used to summarize the data.

By solving the system of equation, length of flag = 1290ft and width = 1030 ft.

An equation is a mathematical statement that shows the equality of two expressions. An equation typically consists of two expressions separated by an equals sign (=), and it states that the expressions are equal in value.

The substitution method is a technique for solving a system of equations, which is a set of two or more equations that contain multiple variables. The goal of the substitution method is to find the values of the variables that make all of the equations in the system true simultaneously.

To solve a system of equations using the substitution method, you follow these steps:

Identify one of the equations that contains only one variable.

Solve that equation for that variable.

Substitute the expression you found for the variable into the other equation(s) in the system.

Solve the resulting equation(s) for the remaining variable(s).

Substitute the values you found for the variables back into one of the original equations to check your solutions.

To find the width and length of the flag, we can set up the following system of equations:

width + length = 2,320

length = width + 260

We can solve this system of equations by substitution. First, we can solve for width in the second equation by subtracting 260 from both sides:

length - 260 = width

Then, we can substitute this expression for width into the first equation:

(length - 260) + length = 2,320

2 * length - 260 = 2,320

2 * length = 2,580

length = 1,290

Now that we know the value of length, we can substitute it back into the second equation to find the value of width:

length = width + 260

1,290 = width + 260

width = 1,030

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The Density of object is 10,490 kg/m³

What is Density, Mass and Volume ?

Given,

Mass = 73,430 Kg

Volume = 7 m³

We know,

Density = Mass / volume

Now, plug in the values

Density = 73430/7

             = 10, 490 kg/m³

Hence, the Density of object is 10,490 kg/m³

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Based on their sides, the 3 triangles are classified as equilateral triangles, isosceles triangles, and scalene triangles.

Scalene-Triangle-1

In the figure, all three symbols that are given on each side are different, which denotes that all three sides are unequal.

One example of the angles of an isosceles acute triangle is 50°, 50°, and 80°.

The sum of all three angles of an equilateral triangle is equal to 180 degrees.  60° + 60° + 60° = 180°

the examples of acute angles are 25°, 36°, 47°, 64°, 55°, 72°, 80° and so on

Examples of right angles are all around us. We can see right angles in the corners of a room, book, cube, windows, and at several other places.

Examples of obtuse angles include 166°, 121°, 110°, 117°, and 91°.

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The solutions to the quadratic equation 8x² - 3x = 5 are x = 1 and x = -5/8

From the question, we have the following parameters that can be used in our computation:

8 x squared - 3 x = 5

Express properly

So, we have

8x² - 3x = 5

This gives

8x² - 3x - 5 = 0

The quadratic formula is represented as

x = (-b ± √[b² - 4ac])/2a

Substitute the known values in the above equation, so, we have the following representation

x = (3 ± √[(-3)² - 4 * 8 * -5])/(2 * 8)

Evaluate

x = (3 ± √169)/16

So, we have

x = (3 ± 13)/16

Expand

x = (3 + 13)/16 and x = (3- 13)/16

Evaluate

x = 1 and x = -5/8

Hence, the solution is x = 1 and x = -5/8

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In a lottery game, if a player picks 6 numbers then the total 9366819 different choices player have if order doesn't matter.

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items, regardless of the order of selection. Formula is

ⁿCᵣ = n! /r!(n-r)!

where n is total number of objects

r is total number of choosing objects

We have given that,

In a lottery game total number = 46 = { 1,2,...., 46}

A player can pick total number = 6 numbers

We have to calculate different choices does the player have if order doesn't matter.

Using Combination formula,

we have , n = 46 , r = 6

⁴⁶C₆ = 46!/6!(40!)

=> ⁴⁶C₆ = 46×45×44×43×42×41×40!/40!(6!)

= 46×45×44×43×42×41 /(6×5×4×3×2×1)

= 23×3×7×11×43×41

= 9366819

Hence, the required ways are 9366819..

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Answer:

angle 3 = 44 degrees

angle 2 = 136 degrees

angle 4 = 136 degrees

Step-by-step explanation:

angle 2 = angle 4

angle 1 = angle 3

angle 1 + angle 2 = 180 degrees

angle 3 +  angle 4 = 180 degrees

The distance between the two given points is 13 units.

Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal to the square of the sum of the other two sides. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.

The Pythagorean theorem is given by the following formula:

h² = a² + b²

Where h is the hypotenuse and a and b are the legs of the right triangle.

In the given image, when you construct a right triangle with the line of the two points as a hypotenuse, you have for a and b:

a = 5

b = 12

Replace the previous values of a and b in the formula for h:

h² = (5)² + (12)²

h² = 25 + 144

h² = 169

h = √169

h = 13

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Option A is the correct answer

A polynomial function is made up of terms called monomials; If the expression has exactly two monomials it’s called a binomial. A third-degree polynomial is of the form f(x) = ax³ + bx²+ cx + d where is not equal to zero. It is also called a cubic polynomial as it has a degree of 3.

Given here the polynomial as g(x) = f(2x)

                                                         =8ax³ + 4bx²+2cx + d

Both the polynomial have the same constant d and therefore the same y-intercept.

Hence, the correct option is B

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Answer: 114 red marbles

Step-by-step explanation:

We know that for every 20 marbles, there are 19 red and 1 black marble.

So to get from 20 to 120, we multiply by 6. So we take 19 times 6 = 114 red marbles and 6 black marbles,

324 miles can Mario drive with 9 gallons of gas.

The term "proportional" refers to any connection where the ratio and amount fluctuate directly with one another.

As per the details share in the above question we get,

The data are as follow,

Mario has a driving range of 18 miles  ½ gallon of gas.

Here we have to find how many miles can mario drive with 9 gallons of gas.

Thus we know that,

He can travel 18 miles on just half a gallon of fuel.

Let x be the amount of miles that 9 gallons of gas will cover.

Thus, if we use the notion of proportion, we obtain

⇒ 18 / (1/2) = x / 9

⇒ 18 × 2 = x / 9

⇒ 36 × 9 = x

⇒ x = 324 miles

Mario can travel 324 miles on 9 gallons of gas.

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The quadratic functions given are matched with the parameters as follows

f(x) = -0.3(x - 2)² + 5           f(x) = 0.2(x + 2)² - 5

vertex (-2, 5)                      

axis of symmetry, x = -2    axis of symmetry, x = 2

focus f (-2, 4 1/6)                focus f (2, -3 3/4)

Both the vertex form and the standard form of the quadratic equation are used in the axis of symmetry formula. Any geometric shape is divided into two equal halves by the symmetry.

Parabolic equation in vertex form is written as

f(x) = a (x - h)² + k

the vertex is v (h, k)

f(x) = -0.3(x - 2)² + 5, v (-2, 5)

f(x) = 0.2(x + 2)² - 5, v ( 2, -5)

The axis of symmetry formula is given as, x = h

f(x) = -0.3(x - 2)² + 5, x = -2

f(x) = 0.2(x + 2)² - 5, x = 2

the focus, f (h, k + 1/4a)

f(x) = -0.3(x - 2)² + 5, f (-2, 5 + 1/(4 * -0.3)) = f(-2, 5 - 5/6) = f (-2, 4 1/6)

f(x) = 0.2(x + 2)² - 5, f (2, -5 + 1/(4 * 0.2)) = f(2, -5 + 1/0.8) = f (2, -3 3/4)

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The value of the account to the nearest dollar in 2007 is $6,929.76

We should know that value is the amount left in an account at a particular time

The  given parameters are

In 1990 the value is = $4,800.

In 1998,  the value is =$6,300

From 1990 to 1998 there are 8 years

Increase in the investment

Using simple interest,

SI= (P*T*R)÷100

Applying the figures in the formula

1500=(4800*8*R)÷100

⇒ 15000=30400R

Making R the subject we have

R= 4.93%

⇒ 4.93% of 4800 *9 = $2129.76

Add initial cost of investment and the interest for 9 years

=$(4800+2129.76)

=$6929.73

In conclusion,  the value of the account would on the $6929.76

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The researcher can use two categorical variables or two values from a contingency table to perform chi - squared test.

A standard hypothesis test used to analyze contingency tables with large sample sizes is the chi-squared approach. This test is designed to examine if two categorical factors influence the test statistic independently. Pearson's chi-squared test and its variants are true when the test statistic equals chi-squared under the null hypothesis.

Pearson's chi-squared test is used to determine whether there is a statistically significant difference between expected and observed frequencies for one or more contingency table categories. For contingency tables with fewer samples, a Fisher's exact test is employed instead.

In the traditional application of this exam, observations are classified into mutually exclusive kinds. If the null hypothesis is correct and there are no variations in the population between classes, the test statistic generated by the data has a two-frequency distribution.

The test's purpose is to estimate how likely observed observed frequencies are if the null hypothesis is true.

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27  is the percentile score of 71 on this test score and 71 is the score of victor.

Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Given, the teacher recorded unit 4 test scores from class.

The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.

A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.

The percentile rank of a score of 71 on the test is find by formula.

[tex]R_{100} =\frac{100(N < )+\frac{1}{2}N }{N}[/tex]

=100×4+1/2(1)/15

=400+0.5/15

=400.5/15

=26.7=27th

Now we need to find the score of victor who has 60 th percentile.

[tex]R_{100} =\frac{100(N < )+\frac{1}{2}N }{N}[/tex]

60=Score/15

score=71

Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.

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In one well-developed paragraph with a topic sentence and supporting details, compare and contrast the experience of reading "The Highwayman" with listening to it. Explain, using examples from the text, how hearing the poem read aloud changes or increases your understanding of a poem.

On the 19th day, the lily pad covered half the pond.

The reason behind this is, If the lily pad doubles in size every day, then on the 20th day it will be twice as large as it was on the 19th day. That means it was already covering half the pond on the 19th day.

In this puzzle, the water lily is described as doubling in size every day. This means that on the first day, the lily pad is small, but by the second day, it has doubled in size. On the third day, it doubled in size again, and so on. By the 20th day, the lily pad has grown so large that it covers the entire pond.

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