Three students in the Math Club are analyzing 1/410 x+8) and -(1/2 x +13)+3(x +5), for all the values of x. Each student claims the expressions are related according to the results shown in the table. Which student is correct?

The height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.

According to the question,

We have the following information:

A cereal company packs cereal boxes into large cardboard boxes. The large boxes are 12 inches long and 8 inches wide.

Volume of box = 3456 cubic inches

We know that the box is in the shape of cuboid.

Following formula is used to find the volume of cuboid:

Volume = length*width*height

12*8*height = 3456

96*height = 3456

Dividing both sides by 96:

Height = 3456/96

Height of the box = 36 inches

Hence, the height of the large boxes is 36 inches when the volume of box is 3456 cubic inches.

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Answer: Yes

Step-by-step explanation:

An equilateral triangle has three equal sides and angles, therefore all of the sides are congruent.

The interior angles of the triangle are 43°, 43° and 94°. The exterior angle of the triangle is 86°.

A triangle is polygon with three sides. The sum of angles in a triangle is 180 degrees.

The triangle above is an isosceles triangle. The base angles of a triangle is congruent.

Therefore, the base angles are 5x - 12 and 5x  -12.

The sum of the remote interior angles is equal to the opposite exterior angles.

5x - 12 + 5x - 12 = 8x - 2

10x - 24 = 8x - 2

10x - 8x = -2 + 24

2x = 22

x = 22 / 2

x = 11

Therefore,

5x - 12 = 5(11) - 12 = 43°

Third angle = 180 - 43 - 43 = 94°

Exterior angle =  8x - 2 = 8(11) - 2 = 86°

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Answer:

Hundreds: 6 Tenths: 2 Ten Thousands: 5

Step-by-step explanation:

Hundreds are 2 decimal places (0.02)

Tenths are 1 decimal place (0.1)

Ten Thousands are 4 decimal places (0.0004)

Hope this helped!

Robert can read 180 pages in [tex]1\frac 12[/tex] hours

The given parameters in the question are:

Speed = 2 pages per minute

Number of hours = [tex]1\frac 12[/tex] hours

The number of pages to read in this time can be calculated using the following equation

Number of pages = Speed * Number of hours

Substitute the known values in the above equation So, we have the following equation

Number of pages = 2 * [tex]1\frac 12[/tex]

Convert the units

Number of pages = 2 * [tex]1\frac 12[/tex] * 60

Evaluate

Number of pages = 180

Hence, the number of pages is 180 pages

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Answer:

Step-by-step explanation:

You want a system of equations for the width (x) and length (y) of a rectangle with a perimeter of 40 feet and length 2 more than 4 times the width.

One equation can give the relation for the perimeter:

  2(x +y) = 40

The other can express the relation between width and length:

  y = 2 +4x

Your system of equations is 2(x+y) = 40, and y = 2+4x.

__

Additional comment

The solution is (x, y) = (3.6, 16.4) feet.

Jim ate 3/4 part of his lunch is in fraction form then the left part of his lunch is a fraction equal to 1/4 .

Fraction : A fraction represents a part of whole . It is a numerical value. It is evaluated by dividing a whole into number of parts . It has two parts one is called numinator (dividend) and other one is denominator ( divisor) . Denominator tells you how many part of lunch is divided into.

Types : Three types are

We have given in question that,

Jim ate 3/4 of his lunch .

let his lunch be x as a whole number .

Now , 3/4 part of x is ate by Jim i.e 3x/4

left part of x = x - 3x/4 = x/4

so, 1/4 part of x i.e lunch is left .

Hence, after eating the 3/4 of lunch by Jim the left part of lunch is 1/4 .

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the matrix has one real eigenvalue of algebraic multiplicity.

[1-λ     k

1        -7-λ]     =(1-λ)(-7-λ)-(1)(k) = λ² +6λ -(k+7)

Mathematics has several different subfields, including algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.

Since many applications of mathematics include the manipulation of variables, which are frequently represented by Roman letters, elementary algebra is a prerequisite. For the most part in education, the study of algebraic structures like groups, rings, and fields is referred to as abstract algebra (the term is no more in common use outside the educational context). In contemporary presentations of geometry, linear algebra—which deals with linear equations and linear mappings—is used.

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Answer:

You can FACTOR x^2-12x+35 by using the AC method

This means the answer will be:

(x-7)(x-5)

I hope this helps!

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Given a budget of $25, the whole pounds of chocolate chips that Malik can order is 11 pounds of chocolate.

For up to 3 pounds, the supplier will charge Malik $4 per pound. This means that after buying 3 pounds of chocolate chips, the amount Malik would be left with it:
= Malik budget -  (Price of 4 pounds x 4 pounds)

=  25 - (4 x 3)

= $13

The number of pounds of chips that Malik an buy at $1.50 per pound is:

= 13 / 1 .50

= 8 whole pounds

The total number of whole pounds that Malik can order is:

= 3 + 8

= 11 pounds

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Refer to the attachment for figure:

The height of the rectangle = 11 inches

What is rectangle?

A rectangle is a type of quadrilateral with parallel sides equal to each other and four equal 90-degree vertices. Because of this, it is also known as an equiangular quadrilateral. Because the opposite sides of a rectangle are equal and parallel, it can also be referred to as a parallelogram.

Let x= height

Width becomes x+49

Diagonal BD=61 inches

By pythagoras theorem,

BD²=BC²+CD²

61²= (x+49)²+x²

3721=x²+98x+2401+x²

On simplification,

x²+49x-660=0

Find the factors

(x+60)(x-11)=0

x=-60, x=11

Consider positive value for height

height = 11 inches

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By using Binomial Distribution  of probability, it is obtained that

Probability  that the number of heads is 13 or more =  [tex]137980(\frac{1}{2})^{20}[/tex]

What is Binomial Distribution?

Binomial distribution is a discrete type probability distribution whose probability mass function is

P(X = k) = [tex]{n \choose k} p^k(1 - p)^{n-k}[/tex]

p is the probability of success.

Here Binomial distribution of probability is used

P(X [tex]\geq[/tex] 13) = P(X = 13) + P(X = 14) + ........ + P(X = 20)

P(X = 13) = [tex]{20 \choose 13} (\frac{1}{2})^{13}( 1 - \frac{1}{2}})^{20-13}[/tex]

              = [tex]{20 \choose 13} (\frac{1}{2})^{13}( \frac{1}{2}})^{7}[/tex]

              =[tex]{20 \choose1 3} (\frac{1}{2})^{20}[/tex]

P(X = 14) = [tex]{20 \choose14} (\frac{1}{2})^{20}[/tex]

P(X = 20) = [tex]{20 \choose20} (\frac{1}{2})^{20}[/tex]

Total Probability = [tex]({20 \choose 13} + {20 \choose 14} + .... {20 \choose 20})(\frac{1}{2})^{20}[/tex]

                  = (77520 + 38760 + 15504 + 4845 + 1140 + 190 + 20 + 1)[tex](\frac{1}{2})^{20}[/tex]

                   = [tex]137980(\frac{1}{2})^{20}[/tex]

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Answer: 50%

Hope this helps!

Answer:

Step-by-step explanation:

answer = company b

The number represented on number line by (A) -13   (B) 26   (C) 65

According to the number line given in part a

there are for parts in between 0 to 52

To find the numbers in one part = 52/4

                                                     = 13

Therefore,

For (A)

0 - 13 = -13

For (B)

0 + 2*13 = 26

For (C)

52 + 13 = 65

Hence, A is -13, B is 26 and C is 65.

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Answer:

====================

Triangle inequality theorem states that the sum of any two sides must be greater than the remaining side.

We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.

We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.

Given,

The lengths of triangle is given as:

10 , 10 and 20

To check the following three lengths form a right triangle.

Now, According to the question:

What is triangle inequality theorem ?

The triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.

So, The length of triangle are 10, 10, 20

10 + 10 = 20

We see 10 + 10 = 20, so this is contradicting the mentioned theorem, therefore these lengths are not good to form a triangle.

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The value of the angle ∠2 = 32° using angle bisector.

What is angle bisector?

In geometry, the ray, line, or segment that divides a given angle into two equal pieces is known as the angle bisector. For instance, a 60-degree angle will be split into two angles of 30 degrees each by an angle bisector. It splits one angle into two smaller congruent angles, to put it another way.

An angle in a triangle is divided into two equal or congruent angles by a straight line known as the angle bisector. Each triangle can have one angle bisector for each of its three vertices. The intersection of these three angle bisectors in a triangle is referred to as the triangle's incenter.

The given angle ∠XVW = 64°

VP is a bisector,

So the angle ∠XVW will be divided equally.

So ∠2 = 32°

Hence the angle of the bisector ∠2 = 32°.

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The number of dimes and nickels that Johnny has are 6 and 3 respectively.

The following should be noted:

Nickel = 5 cent = 0.05

Dime = 10 cents = 0.10

Let the number of nickels = n

Let the number of dimes = 2n

Total worth = $0.75

This will be illustrated as:

0.05(n) + 0.10(2n) = 0.75

0.05n + 0.20n = 0.75

0.25n = 0.75

Divide

n = 0.75/0.25

n = 3

Number of nickels = 3

Number of dimes = 2n

= 2 × 3

= 6

Number of dimes = 6

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Leroux can reduce the costs of regular health care without driving up the price of their health acre plan by : (c) Reducing the co-pay amounts but increase the annual deductible so that the monthly premium can stay the same.

Since the customers are complaining that the cost of regular visits and prescriptions ($15) are too expensive for them based on the plan they choose, this means that the purpose of the health insurance plan which is to reduce the overwhelming cost burden on individuals when trying to access proper healthcare is not be implemented successfully.

The co-pay amount which is usually known as the out-of-pocket amount that insurers pay whenever they go for regular doctor visits ( covered service in the insurance package ) and reducing this amount will reduce the immediate cost which makes the customers to complain about how expensive assessing a doctor on regular visits are.

The effect of the increased annual deductible is one way to push the immediate burden of paying a higher co-pay amount by the customer.

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Answer:

-1/8

Step-by-step explanation:

-2³/2⁶ negative exponents go in the denonimator

-1/2³ subtract exponents since the denonimator is larger

-1/8 simplify

Answer:

$306

Step-by-step explanation:

we know that

Erika earns 9$ per hour

so

By proportion

Find how much she earn during the total hours of two weeks

The total hours of two weeks is equal to

[tex]14+20=34 hours[/tex]

[tex]\frac{9}{1} \frac{money}{hour} = \frac{x}{34} \frac{money}{hours}[/tex]

[tex]x =34[/tex]×[tex]9[/tex]

x = 306$

therefore

the answer is

$306

Answer:

the correct answer is A. y = - x - 4

Step-by-step explanation:

Just insert the graph into a calculator and solve.

every time x goes up two, so does y. except the y is 4 units lower than the x.

Answer:

x-intercept: -([tex]\frac{35}{9}[/tex],0)

y-intercept: (0,-3)

Step-by-step explanation:

Answer:

(x-5)(x+8)

Step-by-step explanation:

Factors of -40:

-1, 40

-2, 20

-4, 10

-5, 8

-5 + 8 =3

x^2+3x-40

x^2 -5x +8x -40

=(x-5)(x+8)

The function that represent the given table is f(x) = 2n+1.

In the given question we have to write the correct function for the table given below.

The given table is

x                      y

0                      3

1                       5

2                      7

3                      9

We can write it as

x                      y

0                      3=1+2

1                       5=3+2

2                      7=5+2

3                      9=7+2

So we can see that in each odd number we are adding 2.

So the function should be

f(x) = (2n−1)+2

f(x) = 2n−1+2

f(x) = 2n+1

Hence, the function that represent the given table is f(x) = 2n+1.

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The measure that will be captured by approximately 9000 of the confidence intervals is given as follows:

(E) The Population Median.

The interpretation of a x% confidence interval is that it is x% likely that the population parameter(mean/proportion/standard deviation/median) is between a and b, which are the bounds of the confidence interval.

The bounds of the confidence interval are obtained by the estimate plus/minus the margin of error.

The measure for which the confidence intervals are calculated in this problem is given by:

Median.

The sample median for each sample is used for the estimes, and then these estimates are inferred for the population median, which is the population parameter, hence option e is correct.

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The intensity of the sound that is 88 decibels of the blender is 6.3×10⁻⁴ W/m².

Decibels:

Decibel is unit used to measure the intensity of a sound or the power level of an electrical signal by comparing it with a given level on a logarithmic scale.

Given,

Your parent promises to make you a smoothie using the blender while you're mowing the lawn. The blender makes a sound that is 88 decibels

Here we need to find the intensity of the sound of the blender

In order to find the intensity, we have to do the following steps,

First, we have to divide the decibel level by 10.

=> 88/10 = 10/10 log (x / 1 x 10⁻¹²)

Now, we have to use that value as the exponent of the ratio.

=> 8.8 = log (x / 1 x 10⁻¹²)

Finally, we have to use that power of ten to find the intensity in Watts per square meter.

=>  6.3×10⁻⁴ .

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