Carlos is making goodie bags for a party. Every goodie bag has exactly the same treats in it. Carlos has 72 granola bars and 48 small popcorn balls. What is the greatest umber of identical goodie bags Carlos can make? How many of each kind of treat is in each goodie bag?

According to the volume of cylinder formula, an aluminum can with a 2 3/5 diameter and 5 1/4 in height are in 27.86 cubic inches.

Volume of Cylinder

The formula to calculate the volume of the cylinder is

Volume of a cylinder = πr²h cubic units.

where

r refers the radius

h refers the height.

Given,

Here we have an aluminum can with a 2 3/5 diameter and 5 1/4 in height and now we have to find the volume in cubic inches.

While we looking into the given question, we know the following values,

Diameter = 2 3/5

When we simplify it, then we get the value of diameter as

d = 13/5 or 2.6

Similarly, the value of height is rewritten as,

h = 5.25

So, based on the formula of volume of cylinder,

We get the value as,

=> V = π x (2.6/2)² x 5.25

Apply the value of π as 3.14, then we get,

=> V = 3.14 x (1.3)² x 5.25

=> V = 16.485 x 1.69

Therefore, the volume in cubic inches is 27.86 cubic inches.

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The selling price of the two washing machies are

I will buy the first because it has a lower selling price

The question is a percentage problem

The first washing machine has a mark down by ​40%

= 40 percent

= 40 / 100

= 0.4

marked down factor = 1 - 0.4 = 0.6

selling price of the first machine = 550 * 0.6 = 330

the second washing machine has mark down of 30%

30% = 0.3

marked down factor = 1 - 0.3 = 0.7

selling price of the second washing machine at first mark down

= 550 * 0.7 = 385

marked down again

10% = 0.1

the  factor here is = 1 - 0.1 = 0.9

selling price of the second washing machine at second mark down

= 385 * 0.9 = 346.5

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The polynomial function that has the degree of 5 is written as f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

Polynomial function:

The equations formed with variables, exponents and coefficients are known as the polynomial equations. And it can have different exponents, where the higher one is called the degree of the equation.

Given,

Here we have the following things,

Degree = 5

Root of multiplicity 2 is x = -4

Root of multiplicity 1 at x = -1

Root of multiplicity 2 at x = -2

y-intercept of (0, 128)

Here we need to find the polynomial equation of the function.

According to the given roots of multiplicity, we have the factors of the polynomials are,

=> (x + 4)² (x + 1) (x + 2)²

So, the general form of the polynomial function can be written as,

=> f(x) = A (x + 4)² (x + 1) (x + 2)²

In order to find the 5 degree polynomial function, we have to calculate the value of A.

To Find the value of A, we have to apply the y - intercept point on the equation then we get,

=> 128 = A (0 + 4)² (0 + 1) (0 + 2)²

=> 128 = A (4)² (1) (2)²

=> 128 = A (16 x 1 x 4)

=> 128 = 64A

=> A = 2

Now, the polynomial function is written as,

=> f(x) = 2 (x + 4)² (x + 1) (x + 2)²

When we expand this one then we get,

=> f(x) =2 [x⁵ + 13x⁴ + 64x³ + 148x² + 160x + 64]

Therefore, the resulting polynomial function is,

=> f(x) = 2x⁵ + 26x⁴ + 128x³ + 296x² + 320x + 128

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Answer:

A. (10x^2) / (5x + 4y)

B. (8xy) / (4y + 5x)

Step-by-step explanation:

A. Factor the numerator and denominator, then cancel out like terms

(10x^2(2a + 3b)) / (2a(5x + 4y) + 3b(5x + 4y))

(10x^2(2a + 3b)) / ((2a + 3b)(5x + 4y))

(10x^2) / (5x + 4y)

B. Factor the numerator and denominator, then cancel out like terms.

(8xy(3p - 4q)) / (3p(5x + 4y) - 4q(4y + 5x))

(8xy(3p - 4q)) / ((3p - 4q)(4y + 5x))

(8xy) / (4y + 5x)

The slope for the following question is = 4.

acc to our question-

hence the value of slope=4

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The equvalent fractions of 5/7 using 35 as a common denominator is 25/35.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, it should be noted that the fraction given is 5/7.

The equivalent fraction will be:

= 5/7 × 5/5

= 25/35

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Complete question

Write the equvalent fraction of 2/5 using 35 as a common denominater

Answer:

z=38

Step-by-step explanation:

Using the fact that angles on a straight line add to 180°, the interior angles of the triangle are 86°, (180-3z)°, and (180-4z)°.

Angles in a triangle add to 180°, so:

[tex]86+180-3z+180-4z=180 \\ \\ 86-3z+180-4z=0 \\ \\ 266-7z=0 \\ \\ 7z=266 \\ \\ z=38[/tex]

Answer:

slope = (1/3)

Step-by-step explanation:

(-8, 2), (-11, 3)

(x₁, y₁)   (x₂, y₂)

m = slope

        y₂ - y₁          3 - 2              1              1

m = ------------ = -------------- = ----------- = -------

        x₂ - x₁         -11 - (-8)       -11 + 8        3

I hope this helps!

The expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

In this question, we have been given a synthetic division of x^2 + 5x and x

We need to find the quotient.

    x  + 1  + 1 + 1 + 1 + 1        

x) x^2    x   x   x   x   x

 - x^2                                  

    0      x

         -  x                            

            0   x

             -  x                    

                  0  x

                  -  x                

                      0    x

                       -    x            

                             0  x

                             -    x      

                                   0

Therefore, the expression that represents the quotient of given model is x + 5

The correct answer is an option (C)

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Answer:

$205.6

Step-by-step explanation:

20.56hours × $10/hour = $205.6

The amount his account will have after 3 months be $ 759.38.

Given, Angel Garcia deposited his $750 federal income tax refund check into his savings account. The account pays 5% and he made no other deposits or withdrawals.

we have to find the amount in the account after 3 months,

So, the amount he made is,

Amount = 750(1 + 5/100)^0.25

Amount = 759.38

So, the amount his account will have after 3 months be $ 759.38.

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Applying the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

There are 4 different pairs of lines given to us.

We have to find out the pair of lines that are perpendicular to each other.

We know that the general equation of a line in slope-intercept form is represented as -

y = mx + c --- (1)

where

(x, y) = coordinates of the lines

m = slope of the line

c = y-intercept

It is also known to us that for two lines to be perpendicular the product of their slope must be equal to -1.

A. y = -8 and y = 2

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

B. x = 4 and y = -1

Comparing these two lines to the general equation of a line in equation (1), we see that the slope of both these lines is equal to 0.

So, these two pair of lines are not perpendicular.

C. x - y = 7 and y = x + 3

Now, x - y = 7

=> -y = 7 - x

=> y = x - 7

Comparing this to the equation (1), we have slope of the line, m = 1.

Also, y = x + 3

Comparing this to the equation (1), we have slope of the line, m = 1.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

D. y = -4x + 1 and 8x + 2y = -10

Now, y = -4x +1

Comparing this to the equation (1), we have slope of the line, m = -4.

Also, 8x + 2y = -10

=> 2y = -8x - 10

=> y = -4x - 10

Comparing this to the equation (1), we have slope of the line, m = -4.

We see that the product of the slope of these pair of lines is not equal to -1.

So, these two pair of lines are not perpendicular.

Thus, according to the slope-intercept form for perpendicular lines, we find out that no given pair of lines are perpendicular.

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Answer:

y-intercept (0,-3)

x-intercept (3,0)

Step-by-step explanation:

Let x = 0

-y =3

y = -3

(0,-3)

Let y = 0

x = 3

(3,0)

The sales tax rate of the cocktail table is 0.055

A sales tax is a consumption tax imposed by the government on the sale of goods and services

The cocktail table sold for $250 and the sales tax amount was $13.75. The sales tax rate can be calculated as follows:

Sales tax = list price * sales tax rate

Therefore,

sale tax rate = sales tax / list price

sales tax = $13.75

list price = $250

sale tax rate = 13.75 / 250

sales tax rate = 0.055

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The number of highway routes from A to D is 560

Number of highway routes from A to B = 7 highways

Number of highways routes from B to C = 8 highways

Number of highways routes from C to D = 10 highways

Number of routes from A to D = Number of highway routes from A to B × Number of highways routes from B to C × Number of highways routes from C to D

Here we have to use multiplication

Substitute the values in the equation

Number of routes from A to D = 7 × 8 × 10

= 560 highways

Hence, the number of highway routes from A to D is 560

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The percent increase in the median monthly rent prices is 14.3%

From the information, the median monthly rent in 2005 was $694 and $810 in 2010.

The increase in the amount will be:

= $810 - $694.

= $116

The percent increase in the median monthly rent prices from 2005 to 2010 will be:

= Increase in amount / Old rent × 100

= 116/810 × 100

= 14.3%

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Answer:

NOT CONGRUENT

Step-by-step explanation:

There are several types of congruence:

ASA - Angle Side Angle

AAS - Angle Angle Side

HL - Hypotenuse Leg

This image shows two triangles which have 2 congruent sides and one congruent angle.

Is it ASA?

There is only one congruent angle, so this cannot be congruent by ASA

Is it AAS?

By the same reasoning, it cannot be congruent by AAS.

Is it HL?

Although there are 2 congruent sides, neither one is the hypotenuse. Is is not congruent by HL.

There is no such thing as SSA congruence, because it is actually possible to have 2 non-congruent triangles who have 2 congruent sides and 1 congruent angle. Therefore, these are NOT CONGRUENT

Answer:

Step-by-step explanation:

Point- slope form:

Given:

Substitute into equation to get the line:

77 is 0.7% of 11000

this number is a lot greater than 77.

Let 77 is 0.7% of m

0.7 percent of m = 77

(0.7/100) * m = 77

m = 77 * (100/0.7)

m = 11000

Therefore, 77 is 0.7% of 11000

this number is a lot greater than 77.

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Answer: 5 is the ancer

Step-by-step explanation:!

Answer: School is 10 blocks north and 2 blocks west of Megan's house. A straight line from Megan's house to school is 10.2 blocks long, Northwest

Step-by-step explanation:

5 blocks north, then 4 east, then 5 north is a total of 10 blocks north.  The last turn is 6 blocks west. So she walks 4 blocks west to get her back to due north of her house then an additional 2 more blocks west.

Use the pythagorean theorem to calculate the straight line if Megan were able to take a straight path there:

slope= -3/2, y-intercept=8

y=mx+b m is the slope while b is the y-inteecept

The value of f(x+h)-f(x)  = h.

Given function:

f(x) = x + 7

difference quotient = f(x+h) - f(x)

= (x+h) - 7 - (x - 7)

= x + h - 7 - x + 7

= x - x + 7 - 7 + h

= 0 + 0 + h

= h

Therefore the value of f(x+h)-f(x)  = h.

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For give expression Ben's work is correct.

In this question, Ben and Jerry both simplified the expression √24x⁵y³

where x > 0, y > 0

We need to determine which student is correct.

First we simplify given expression.

√24x⁵y³

= √(2)(2)(2)(3)(x)(x)(x)(x)(x)(y)(y)(y)

= √(2²)(2)(3)(x²)(x²)(x)(y²)(y)

= √(2²) * √(2) * √(3) * √(x²) * √(x²) * √(x) * √(y²) * √(y)    ...(seperate the radical symbol)

= 2 * √(2) * √(3) * x * x * √(x) * y * √(y)            ...........exponent rule

= 2x²y√(2)(3)(x)(y)                     ........(combine terms with same powers)

= 2x²y √6xy

So, Ben's work is correct.

We observe that by rule of exponents, the fourth step in Jerry's work is incorrect.

Therefore, Ben's work is correct.

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Answer:

x^25

Step-by-step explanation:

The simplified expression is x²⁵.

Given is an expression (x⁵)⁵, we need to simplify the expression.

To simplify the expression (x⁵)⁵, we need to apply the exponentiation rules.

The exponent outside the parentheses should be distributed to each term inside the parentheses.

In this case, the exponent outside is 5, and the term inside the parentheses is x⁵.

To distribute the exponent, we multiply the exponents together.

Applying the rule, we get:

(x⁵)⁵ = x⁵⁽⁵⁾ = x²⁵

Therefore, the simplified expression is x²⁵.

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Answer:

[tex] \huge{ \bold{y = - 43x - 25}}[/tex]

Step-by-step explanation:

Equation of a line in slope-intercept form is given by

[tex]y = mx + c[/tex]

where

m is the slope

c is the y intercept

From the question

m = - 43

In order to find c we substitute the point (0,−25) into the equation y = mx + c

That's

[tex] - 25 = - 43(0) + c \\ - 25 = 0 + c \\ c = - 25[/tex]

We now substitute m and c into the equation

We have the final answer as

[tex] \bold{y = - 43x - 25}[/tex]

Hope this helps you

Answer:

46.9

Step-by-step explanation:

sin54=x/58

58sin54=46.922

The simple interest owned for the use of the money is $2625.

What is Simple Interest?

Simple interest is a quick and simple way to figure out how much money has accrued interest. Interest is always applied to the original principal amount and is calculated at the same rate for each period of time. Any bank where we deposit money will pay us interest on that amount. Simple interest is one of many forms of interest that banks charge. Now, let's first clarify what a loan is before delving further into the idea of simple interest. A loan is a sum of money that someone borrows from a bank or other financial institution to cover expenses. Home loans, auto loans, student loans, and personal loans are a few instances of loans.

In the given question we have:

Principal amount  = ​7000$​,

Rate of interest r​ = ​7.5%,

Time t​ =  15 months;

So, applying the formula to calculate simple Interest:

S.I = [tex]\frac{PRT}{100}[/tex]

S.I = [tex]\frac{7000 \times 7.5 \times 15}{ 12 \times 100}[/tex]

S. I =  $2625;

Hence, The Simple Interest owed for the use of the money.  is $ 2625.

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Answer:

Below

Step-by-step explanation:

x^2 + 32 + 116 = 12x         1st intermediate step: put everything on one side

x^2 -12x + 148 = 0      2nd intermediate step : re-arrange with constant on R

x^2 -12x = -148            3 rd intermediate step : take 1/2 of the 'x' coefficient

                                            square it and add to both sides

x^2 -12x + 36 = -148 + 36    4th intermediate step :   simplify

(x-6)^2  = -112

Answer:

150

Step-by-step explanation:

I had this on one of my quizzes, hope this helps :D