263 second grader and 198 third graders choose hot dogs to eat. How many hot dogs do the students eat choose to eat ?

Answer:

Yes

Step-by-step explanation:

You must use the quadratic formula

-b√b^2 -4ac/2a --> -8√-(-8)^2 -4(12)(1)/2(12)

8 +/- 4/24

(1/2, 1/6)

Yes, we can factor 12x²-8x+1=0 and the factors are x=1/6 and x= 1/2.

A factor in maths is one of two or more numbers that divides into a number without a remainder, making it a whole number.

In other words, a factor is a number that divides another number evenly.

   12x² -8x +1=0

⇒ 12x² -2x- 6x+1=0

⇒ 2x (6x-1) -1 (6x-1)=0

⇒ (2x-1) (6x-1)=0

⇒ 2x-1 = 0, 6x-1 = 0

⇒ x=1/2, x=1/6

Therefore, the factors of 12x²-8x+1=0 are 1/2, 1/6.

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Answer: For every 6 chairs sold they sell 1 table

Step-by-step explanation:

After some work this is my answer

Hope this helps :)

Alonzo invests 76,500 in each account.

What is simple interest?

Simple interest is calculated based on a loan's principal or the initial deposit into a savings account. Simple interest doesn't compound, therefore a creditor will only charge interest on the principal sum, and a borrower will never be required to pay further interest on the interest that has already accrued.

Here, we

Let x and y be the amounts invested at 7% and 5% respectively.

then,

x + y = 30,00  for the parts of the Principal

0.07x + 0.05y = 1680  For the rates and total Earnings

x + y = 30,00

y = 30,00 - x

y can be rewritten as 30,00 - x

Using the rates to total earnings we have

0.07x + 0.05(30,00 - x) = 1680

0.07x - 0.05x + 150 = 1680

0.02x = 1680 - 150

0.02x = 1530

x = 76,500

Hence, Alonzo invests 76,500 in each account.

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Slope of line will be 2 and both the variable quantity charge and time are positively related that means if time will increase cost will also increases.

Slope for two points:

                                   P(x1,y1)   and Q(x2,y2)

             slope of line PQ,

                               [tex]m_{pq}[/tex] = [tex]\frac{y2 - y1}{x2 - x1}[/tex]

while calculating the slope it may comes positive or negative,

              A positive slope means that two variables are positively related to each other.

  while,

            A negative slope means that two variables are negatively related.

from the given graph,

Part A :

              we have two points

                    A(1 , 60)

                    B(3,100)

slope of AB will be,

                               [tex]m_{AB}[/tex] = [tex]\frac{100 - 60 }{3 - 1}[/tex]

                                         = 40 / 2

                                        = 2

         slope of line in graph will be 2

Part B:

              Here slope of line is 2 which is positive, means both the variables charges and hours are positively related.

            that means, if time will increase the cost will also increases.

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By linear search, We discovered that element 9 is the seventh in the sequence, meaning that number 9 appears on the list in the sequence 1, 3, 4, 5, 6, 8, 9, 11.

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts.

Given,

Sequence = 1, 3, 4, 5, 6, 8, 9, 11

By linear search,

The first element is compared to 9 first. If the element's value is less than nine, we compare the subsequent element with nine, and so on.

Step 1: 9 is not the same as 1.

Step 2: 9 is not the same as 3.

Step 3: 9 is not the same as 4

Step 4: 9 is not the same as 5

Step 5: 9 is not the same as 6

Step 6: 8 and 9 are not the same.

Step 7: 9 equals 9.

We discovered that element 9 is the seventh in the sequence, meaning that number 9 appears on the list.

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The ratio of the distance the hare traveled to that of the tortoise is 9 : 2 and expressing it in the unit rate it will be 4.5 miles per miles

What is unit rate?

A unit rate is a cost for only one of anything. Unit rate is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Solution Explained:

For the ratio of the distance:
Try to reduce the ratio further with the greatest common factor (GCF).

The GCF of 315 and 70 is 35

Divide both terms by the GCF, 35:

315 ÷ 35 = 9

70 ÷ 35 = 2

The ratio 315 : 70 can be reduced to lowest terms by dividing both terms by the GCF = 35 :

315 : 70 = 9 : 2

Now, to express it as a unit rate

This is a fraction equal to

315 miles ÷ 70 miles

We want a unit rate where

1 is in the denominator,

so we divide top and bottom by 70

[tex]\frac{315}{70} / \frac{70}{70}[/tex]

= 4.5 miles per miles

Therefore, in unit rate the ratio of the distance the hare traveled to the tortoise is 4.5 miles per miles.

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Answer:

The equation of the line in fully simplified slope-intercept form is [tex]y=\frac{2}{3}x-6[/tex]

Step-by-step explanation:

The equation of the line in fully simplified slope-intercept form can be calculated as follows

The first step is to calculate the slope [tex]m[/tex] of the given line using the slope formula as follows

[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Take two coordinates on the given line

[tex](9, 0)~\text{and}~ (0, -6)[/tex]

Substitute [tex]-6[/tex] for [tex]y_{2}[/tex], [tex]0[/tex] for [tex]x_{2}[/tex] , [tex]0[/tex] for [tex]y_{1}[/tex], [tex]9[/tex] for  [tex]x_{1}[/tex] in the slope formula

[tex]m=\frac{-6-0}{0-9}[/tex]

Simplify the numerator and the denominator at the right side of the equation

[tex]m=\frac{-6}{-9}[/tex]

Simplify the equation

[tex]m=\frac{2}{3}[/tex]

The second step is to find the slope-intercept form of the given line by the point-slope form formula as follows

[tex]y-y_{1}=m(x-x_{1})[/tex]

Take any coordinates on the given line,  take [tex](9,0)[/tex]

Substitute [tex]0[/tex] for [tex]y_{1}[/tex],  [tex]9[/tex] for [tex]x_{1}[/tex], [tex]\frac{2}{3}[/tex]  for [tex]m[/tex]

[tex]y-0=\frac{2}{3}(x-9)[/tex]

Simplify the left side of the equation

[tex]y=\frac{2}{3}(x-9)[/tex]

Expand the right side of the equation

[tex]y=\frac{2}{3}x-\frac{2\times 9}{3}[/tex]

Simplify the right side of the equation

[tex]y=\frac{2}{3}x-6[/tex]

Hence the equation of the line in fully simplified slope-intercept form is

[tex]y=\frac{2}{3}x-6[/tex]

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The numbers would have to be added to complete the square is x = [tex]\frac{9+\sqrt{185} }{2}[/tex] and x = [tex]\frac{9-\sqrt{185} }{2}[/tex]

The quadratic equation is

[tex]x^2[/tex] - 9x - 26 = 0

Add both side of the equation by 26

[tex]x^2[/tex] - 9x - 26 + 26 = 26

[tex]x^2[/tex] - 9x = 26

[tex]x^2[/tex]  - 2(9/2)x = 26

Take the coefficient of x and take square of the term and add both side of the equation

[tex]x^2[/tex]  - 2(9/2)x + 81/4 = 81/4 + 26

Add the terms

[tex]x^2[/tex]  - 2(9/2)x + 81/4 = 185/4

Form the left side of the equation in the form of [tex](a-b)^2[/tex]

Then the equation will be

[tex](x-\frac{9}{2} )^2[/tex] = 185/4

x - 9/2 =± [tex]\frac{\sqrt{185} }{2}[/tex]

x =  [tex]\frac{\sqrt{185} }{2}[/tex] +  9/2

x = [tex]\frac{9+\sqrt{185} }{2}[/tex]

Then

x = - [tex]\frac{\sqrt{185} }{2}[/tex] +  9/2

x = [tex]\frac{9-\sqrt{185} }{2}[/tex]

Hence, the numbers would have to be added to complete the square is x = [tex]\frac{9+\sqrt{185} }{2}[/tex] and x = [tex]\frac{9-\sqrt{185} }{2}[/tex]

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The solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.

Given inequality is given as:

|x-1| ≤ 5

Simplifying this inequality we get,

-5  ≤  x-1  ≤ 5

Adding 1 on both sides, we get,

-5+1  ≤  x-1  ≤ 5+1

-4  ≤  x  ≤ 6

Therefore, the solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.

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NOTE: The given question is incomplete on the portal. Here is the complete question.

QUESTION: What is the solution set of the inequality |x-1| ≤ 5?

After solving the value of x = 1/2.

From the figure:

AB = 4 ,BD = 3,DE = 4

AD = AB + BD

= 4+3

= 7

ADE is a right angle triangle.

AE^2 = AD^2+DE^2

= 7^2 + 4^2

= 49 + 16

= 65

AE = [tex]\sqrt{65}[/tex]

AC = AE/2

= [tex]\sqrt{65}[/tex]/2

ABC is a right angle triangle.

AC^2 = AB^2+BC^2

[tex](\sqrt{65}/2)^2[/tex]= 4^2+x^2

65/4 = 16 + x^2

65/4 - 16 = x^2

65 - 16*4 / 4 = x^2

1/4 = x^2

x = [tex]\sqrt{1/4}[/tex]

x = 1/2

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The domain of the function shown on the graph is given by the following option:

B. All real numbers.

The domain of a function is the set composed by all the input values that are assumed by the function.

On a graph, the meaning of each variable is given as follows:

Hence, considering the graph of the function, the domain of the function is the set that contains all the values of x of the function.

From the image given at the end of the answer, the line continues to left and to right, meaning that it has no spaces in it's definition, and thus the function is defined for all real values and the correct option is given by option b.

The problem containing the graph of the function and the options is given by the image presented at the end of the answer.

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After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large, the best recommendation is c. Increase the sample size.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specific confidence level; the 95% confidence level is the most commonly used, but other levels, such as 90% or 99%, are also used.

Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. A researcher, for example, may randomly select different samples from the same population and compute a confidence interval for each sample to determine how well it may represent the true value of the population variable. The resulting datasets are all unique, with some intervals containing the true population parameter and others not.

In this case, the sample size should be increased when the results are meaningless because the width of the interval is too large.

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Complete questions

After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?

a. Increase the level of confidence for the interval

b. Decrease the sample size

c. Increase the sample size

d. Reduce the population variance

After solving the equation we get to know LHS = RHS

What is an equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

LHS

7 log(10/9) - 2log(25/24) + 3 log( 81/80)

= 7log{(2*5)/3²} - 2log{5²/ (2^3 *3)} + 3log{(3^4/(2^4*5)}

= 7( log 2 + log5 - 2log3) -2 (2log 5- 3log2-log3) + 3(4log3 - 4log2–log5)

= 7log2+ 7log5- 14log3 - 4log5 + 6log2 + 2log 3 + 12log3 - 12log2 - 3log 5

= (7log2+ 6log2 -12log2 ) + (7log5 - 4log5–3log5)

= 13log2 - 12 log2 + 3log5 - 3log5

= log2

= RHS

∴ LHS = RHS

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The price per gallon will be 2.4 at Miguel's gasoline center.

The slope of the line is represented as the rise of the line.

Here the price per gallon is equal to the slope of the given points

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)

we take the two points (4, 10) and (9, 22)

Let

x₁ = 4, y₁ = 10

x₂ = 9, y₂ = 22

∵ Slope m = (y₂ - y₁)/(x₂ -x₁  )

Substitute values in the formula

m = (22 - 10) / (9 - 4)

m = (12)/(5)

m = 2.4

Thus, the price per gallon will be 2.4 at Miguel's gasoline center.

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Answer:

reflection over the y-axis

Step-by-step explanation:

formula for reflection over y is (x,y) -> (x,-y)

Answer:

68.21 and 39.79

Step-by-step explanation:

When it says that they are going to "share" it means that the number  (108) is going to be divided amongst the two of them. So you are going to do an addition problem which is 12+7=19. So you are going to do 12/19*108=68.21.  Then to find the second number it's 7/19*108=39.79.

1326 divided by 41 is equivalent to 32.35.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is 1326 divided by 41.

Assume that 1326 divided by 41 is equivalent to [x].

[x] = 1326/41

[x] = 32.35

Therefore, 1326 divided by 41 is equivalent to 32.35.

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[Question translation in english -

How much is the result of 1326 divided by 41.]

We can convert a parabola equation from standard form to vertex form. This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)

Standard Form

A parabola's standard form is: y = ax2 + bx + c

Here, a, b, and c are real numbers (constants), with a = 0. x and y are variables, with (x, y) representing a parabola point.

Vertex Form

A parabola's vertex form is: y = a (x - h)2 + k

Here, a, h, and k are real numbers, with a = 0. x and y are variables, with (x, y) representing a parabola point.

There is a "whole square" in the vertex form, y = a (x - h)2 + k. To convert from standard to vertex form, we simply need to complete the square. Aside from that, we have a formula method for doing this. Let us investigate both methods.

By Finishing the Square

Consider the following standard-form parabola: y = -3x2 - 6x - 9 and complete the square to get the vertex form. First, we must ensure that the x2 coefficient is 1. If the coefficient of x2 is NOT 1, the number will be placed outside as a common factor. We'll get: y = 3x2 6x 9 = 3 (x2 + 2x + 3).

Now, the coefficient of x2 is 1. Here are the steps to convert the above expression into the vertex form.

Determine the x coefficient. 3 (x2 + 2x + 3)

Divide it in half and square the result.

(2/2)^2 = 1^2 = 1

Y= -3(x2+2x+1-1 +3)

Using the appropriate identity, factor the perfect square trinomial formed by the first three terms.

We can use x2 + 2xy + y2 = (x + y) in this case.

x2 + 2x + 1 = (x + 1) in this case.

The preceding expression becomes:

Y= -3 (x2 + 2x + 1-1 +3)

Y= -3(x+1)^2 – 1 +3

The last two numbers should be simplified, and the outside number should be distributed.

Here, -1 + 3 = 2. As a result, the preceding expression becomes:

Y= -3(x+1)^2 + 2

Y = -3(x+1)^2 - 6

This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)

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Answer:

m = -96/7

Step-by-step explanation:

5(m - 6) = 10 - 4[2(m - 7) - 5m]

5m - 30 = 10 - 4[2m - 14 - 5m]

5m - 30 = 10 - 4(-3m - 14)

5m - 30 = 10 + 12m + 56

-7m = 96

m = -96/7

The values of x, y and z are 74°, 37° and 17° respectively

What is Angles?

An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.

Given,

x°, (4z + 6)°, 2y° and 106°

Lets solve,

x° and 106°

From the co-interior  angle

x + y = 180°

x° + 106° = 180°

x = 180 - 106

x = 74°

by alternate exterior angle

x = 2y

Since we know about the value of x

we can write it as

74 = 2y

y = 74/2

y = 37°

Now by alternate interior angles

(4z + 6) = x

(4z + 6) = 74

4z = 74 - 6

4z = 68

z = 68/4

z = 17°

Hence, Value of x, y and z is 74°, 37° and 17° respectively

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The area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

In this question, we have been given the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)

We need to find the perimeter and area of the rectangle.

Using distance formula we find the length and width of the rectangle.

d1 = √(-2 - 7)² + (3 - 3)²

d1 = √(-9)²

d1 = 9

And d2 = √(-2 + 2)² + (-6-3)²

d2 = √(-9)²

d2 = 9

d3 = √(7 + 2)² + (-6 + 6)²

d3 = 9

This means, the length and width of rectangle are equal i.e., 9 units.

So, perimeter would be,

P = 4 * 9

P = 36 units

And the area would be,

A = 9 * 9

A = 81 square units

Therefore, the area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.

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x = 24

y = 58

Step-by-step explanation:

5x+20 = 6x-4 ( vertically opposite angles)

20+4 = 6x-5x(collect like terms)

x = 24

(y-18)+(5x+20) = 180 (sum of angles on a straight line)

(y-18)+(5×24+20) = 180

(y-18)+140 = 180

y-18 = 180-140(collect like terms)

y-18 = 40

y = 40+18

y=58

Cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.

As given in the question,

Cost of Thaddeus sports camp is equal to  $170.00

Money earned by Thaddeus while raking leaves = $58.35

Money earned by Thaddeus while shovels snow = $58.35

Total amount of money Thaddeus required to earn to pay sports camp fee

= $170 - $(58.35 + 58.35)

= $(170 - 116.7)

= $53.3

Therefore, cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.

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We can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

We have been given an expression  2x² + 12x + 8

We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.

2x² + 12x + 8

=  2x² + 12x + 18 - 18 + 8

= (√2x + 3√2)² - 10

= (√2)² (x + 3)² - 10

= 2(x + 3)² - 10

Comparing with a(a + b)² + c, where a, b and c are numbers.

a = 2, b = 3 and c = -10

Therefore, we can write given quadratic expression  2x² + 12x + 8 as  2(x + 3)² - 10

And a = 2, b = 3, c = -10

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13 72/99 is rational number.

A rational number is a number that can represented in the form p/q where p, q are integers and q ≠ 0. E.g. 3/1, 5/12.

An irrational number is the opposite of a rational number that cannot be represented in the form p/q where p, q are integers and q ≠ 0. E.g. √2

Given, number = 13 72/99

It is a mixed fraction. It can be converted into proper fraction :

(13×99 + 72)/99 = 1359/99

1359/99 is a rational number since numerator and the denominator are both integers.

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Control procedures are those that enable researchers to rule out specific causes for results other than the hypotheses they intend to test.

In a controlled experiment, every factor besides the independent variable is kept under control or constant to ensure that it has no impact on the dependent variable.

This experiment involves the systematic manipulation of an independent variable (the cause) and the measurement of the dependent variable (the effect). This ensures that any extraneous variables are controlled.

This experiment aids the researcher in determining whether the experimental group and control group differ from one another.

For example, during the medication effect test, the group that receives the medication is referred to as the experiment group. Those who don't get any medication are referred to as the control group.

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The amount is 20 more than 70 that will be 90.

An equation is an expression that shows the relationship between two or more numbers and variables.

A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.

We have been given that the statement is "20 more than 70"

WE are asked to find the amount of the given statement.

More means addition therefore,

20 more than 70 = 20 + 70

= 90

Therefore, the amount is 20 more than 70 that will be 90.

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The number of blue cars is 375.

What is a ratio?

Ratio is a relationship between two values, represented by numbers or percentage Which expresses which of the two value are bigger. And to find that we cancel the common factor between them.

We are given that the ratio of blue cars to red cars is 3:5

Also there are 600 cars in the parking lot

Now, Let the common factor between them be 'x'

Hence the number of red cars is 3x and number of blue cars is 5x

Hence the equation can be given as

3x+5x = 600

8x = 600

Dividing both sides by 8 we get

x= 75

Hence the number of blue cars is 5(75)= 375

The number of blue cars is 375

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