For St. Patrick's day, Mrs. G's sixth grade class was given a choice of four different drinks. One quarter of the class chose green milkshakes, one third of the class chose green ginger ale, one eighth of the class chose the green milk and one sixth of the class chose green juice. How many students did not have a drink?

Answer:

D

Step-by-step explanation:

the slope is 12/10 which simplifies to 6/5 and the y intercept is 2

The answer is 645,000

Answer:

C. asymptotes

Step-by-step explanation:

In the figure attached, a sign chart is shown. To fill it out you need to find the function's zeros and asymptotes. The zeros are those x values that makes the function equal to zero, in the example, those are the x values that make the denominator equal to zero (x = -1 and x = 5). In a rational function, the asymptotes are those x values that make the numerator equal to zero (x = -9 in the example)

Function in the example:

[tex]\frac{(-2x-2)(2x-10)}{-9x-81} [/tex]

Final answer:

To complete a sign chart accurately, one needs to use test numbers surrounding each of the function's zeros and asymptotes, determining the sign of the function in those intervals. This helps in understanding the behavior of the function and solving inequalities.

Explanation:

To fill out a sign chart, you will need to use test numbers before and after each of the function's zeros and C. asymptotes which fills the blank correctly. When you're dealing with functions, especially rational functions, the sign of the function can change around its zeros and asymptotes. Zeros are the points where the function crosses the x-axis, and the function's value is zero. Asymptotes, on the other hand, are lines that the function approaches but never touches; the function's value heads towards positive or negative infinity as it gets close to an asymptote.

When creating a sign chart, you select test numbers from intervals between these critical points -- zeros and asymptotes -- to determine if the function is positive or negative in those intervals. This process helps to understand the behavior of the function across its domain and is essential in solving inequalities.

Here's an example:

Identify the zeros and asymptotes of the function.

Place these values in increasing order on a number line to define test intervals.

Choose a test number from each interval and substitute it into the function to check the sign.

Fill in the sign chart with the corresponding signs for each interval.

"The correct operation to perform is the subtraction of the two given polynomial terms:

[tex]\[ \frac{4}{7}x^2 - \frac{3}{2}x^3 \][/tex]

To subtract these terms, we simply combine them, keeping in mind that subtraction requires us to change the sign of the term being subtracted and then add the terms together. Since the terms are already in descending powers of \( x \), we do not need to rearrange them. The subtraction then yields:

[tex]\[ -\frac{3}{2}x^3 + \frac{4}{7}x^2 \][/tex]

This is the simplified expression after performing the indicated operation. There are no like terms to combine further, so this is the final answer.

The answer is: [tex]\[ -\frac{3}{2}x^3 + \frac{4}{7}x^2 \]"[/tex]

Answer:

85

Step-by-step explanation:

15 times 6 is 90. This is how much money he spends on 6 DVDs if they're all $15. 90 subtracted by 5 (remember - he gets $5 off his entire purchase, not just each individual DVD) would be 85!

Answer:

g(x) is the image of f(x) after translated horizontally 2 units to the right

Step-by-step explanation:

∵ f(x) = √x

∵ g(x) = √(x - 2)

∴ The x-coordinate of f(x) becomes (x - 2)

∴ f(x) translated horizontally 2 units to the right

the answer is 12 place 2 , 4.5,12 In place of X and solve

Answer:   x = 12

Step-by-step explanation:

[tex].\qquad \qquad \qquad \qquad \qquad \sqrt{2x+1}-4=1\\\\\text{Add 4 to both sides:}\quad \sqrt{2x+1}=5\\\\\text{Square both sides:}\quad \quad 2x+1=25\\\\\text{Subtract 1 from both sides:}\quad 2x=24\\\\\text{Divide both sides by 2:}\qquad \quad x = 12[/tex]

Answer:

(2x + 3)(2x + 1)

Step-by-step explanation:

2(2x^2 + 4x) + 3

Distribute.

4x^2 + 8x + 3

Put this in factored form.

(2x + 3)(2x + 1)

Answer:

This would be an inequality. They use greater than (>) and less than (<) signs.

Step-by-step explanation:

A Mathematical sentence that compares expressions that are not equal is an inequality.

An inequality is a mathematical sentence that compares the value of two expressions using a inequality symbol.

An inequality is a relationship between two different quantities or expressions.

An inequality may be expressed by a mathematical sentence that uses the following symbols:

< is less than

> is greater than

≤ is less than or equal to

≥ is greater than or equal to

≠ is not equal to

Hence, a mathematical sentence that compares expressions that are not equal is an inequality.

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Answer:

a) 20 ways

b) 10 ways

Step-by-step explanation:

When the order of selection/choice matters, we use Permutations to find the number of ways and if the order of selection/choice does not matter, we use Combinations to find the number of ways.

Part a)

We have to chose 2 objects from a group of 5 objects and order of choice matters. This is a problem of permutations, so we have to find 5P2

General formula of permutations of n objects taken r at time is:

[tex]nPr=\frac{n!}{(n-r)!}[/tex]

Using the value of n=5 and r=2, we get:

[tex]5P2=\frac{5!}{(5-2)!} =20[/tex]

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice matters.

Part b)

Order of choice does not matter in this case, so we will use combinations to find the number of ways of choosing 2 objects from a group of 5 objects which is represented by 5C2.

The general formula of combinations of n objects taken r at a time is:

[tex]nCr=\frac{n!}{r!(n-r)!}[/tex]

Using the value of n=5 and r=2, we get:

[tex]5C2=\frac{5!}{2!(5-2)!} =10[/tex]

Therefore, we can choose 2 objects from a group of 5 given objects if the order of choice does not matters.

Answer:

20

10

Step-by-step explanation:

just took the test

Answer:

292

Step-by-step explanation:

The block is a rectangle with 80 yd length and 66 yd width. We need the perimeter of the block, which is the perimeter of the rectangle.

P = 2L + 2W

P = 2(80 yd) + 2(66 yd)

P = 160 yd + 132 yd

P = 292 yd

To calculate the distance of one lap around Danny's rectangular block (66 yards wide and 80 yards long), we find the perimeter, which is 292 yards.

The question asks about finding the distance Danny must run when doing a lap around his block, which is shaped as a rectangle. To find the distance around a rectangular path, we calculate the perimeter. The formula for the perimeter of a rectangle is 2 * (length + width). Given that the block is 66 yards wide and 80 yards long, the perimeter is 2 *(66 + 80) yards.

First, we add the length and width: 66 + 80 = 146 yards. Then, we multiply by 2: 2 * 146 = 292 yards. Therefore, one lap around Danny's block is 292 yards.

Answer:

Step-by-step explanation:

[tex](-4a^2)(2a^{-3})^{-4}\qquad\text{use}\ (xy)^n=x^ny^n\ \text{and}\ (x^n)^m=x^{nm}\\\\=(-4a^2)\bigg(2^{-4}a^{(-3)(-4)}\bigg)\qquad\text{use}\ 4=2^2\\\\=(-2^2a^2)(2^{-4}a^{12})\\\\=-(2^2)(2^{-4})(a^2a^{12})\qquad\text{use}\ x^nx^m=x^{n+m}\\\\=-2^{2+(-4)}a^{2+12}\\\\=-2^{-2}a^{14}\qquad\text{use}\ x^{-n}=\dfrac{1}{x^n}\\\\=-\dfrac{1}{2^2}a^{14}\\\\=-\dfrac{a^{14}}{4}[/tex]

Answer:

first one is D

second is B

third is B

Step-by-step explanation:

Answer:

0.5

Step-by-step explanation:

0.47058824

the 4 is in the tenths place

the 7 makes it turn to a 5

the answer would be 0.5 :)

Answer:

[tex]486\ toy\ boxes[/tex]

Step-by-step explanation:

we know that

[tex]1\ ft=12\ in[/tex]

step 1

Convert the dimensions of the boxes to feet

[tex]4\ in=4/12=(1/3)\ ft[/tex]

step 2

Find the volume of the toy boxes

[tex]V=b^{3}[/tex]

[tex]V=(1/3)^{3}=(1/27)\ ft^{3}[/tex]

step 3

Find the volume of the crate

[tex]V=LWH[/tex]

[tex]V=(3)(3)(2)=18\ ft^{3}[/tex]

step 4

Divide the volume of the crate by the volume of the toy boxes to find the number of toy boxes

[tex]\frac{18}{(1/27)}= 486\ toy\ boxes[/tex]

Answer: Your answer would be A. inherited

The behavior described in this scenario is most likely an inherited behavior.

The innate behaviors that are passed to offspring from parents is called as  Inherited behaviour

Earthworms are sensitive to light and often seek refuge in soil or other dark environments.

The response to light which is likely an innate behavior that has evolved over time in response to environmental pressures, such as predation risk from exposure to sunlight.

The earthworm's instinctive behavior to get shelter with response to light is likely a result of its genetic programming and not a learned, mimicked, or imprinted behavior.

Hence, the behavior described in this scenario is most likely an inherited behavior.

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To find the largest of two numbers when given their product and sum, we can use the quadratic formula.  Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation.  Solving the quadratic equation, we find that the larger of the two numbers is 6.

To find the largest of two numbers when given their product and sum, we can use the quadratic formula. Let's denote the numbers as 'a' and 'b'. We know that 'a * b = 24' and 'a + b = 10'. We can rewrite the second equation as 'b = 10 - a' and substitute it into the first equation.

Substituting 'b' into the equation 'a * b = 24', we get 'a * (10 - a) = 24'. Expanding and rearranging the equation, we have 'a^2 - 10a + 24 = 0'. Solving this quadratic equation, we find that the values of 'a' are 4 and 6. Therefore, the larger of the two numbers is 6.

Here is your answer

B) [tex]\huge{10}^{-2}[/tex]

REASON:

0.01

=1/100

=1/

[tex] {10}^{2} [/tex]

=

[tex] {10}^{ - 2} [/tex]

HOPE IT IS USEFUL

Answer: 10 to the negative second power

Step-by-step explanation: To write 0.01 as a power of 10, first notice that 0.01 is a decimal which means that the exponent on our power of 10 will be negative.

To determine the value of the exponent, count the number of places we would need to move the decimal point in order to get 1.0.

In this problem, we would need to move the decimal point 2 places to get 1.0 which means that the exponent on our power of 10 will b -2.

Therefore, 0.01 can be written as 10 to the negative 2nd power.

Answer:

140 ft²

Step-by-step explanation:

The figure is composed of a rectangle and a triangle

note triangle has a base = 16 - 12 = 4 ft

Area = area of rectangle + area of triangle

        = (16 × 8) + ([tex]\frac{1}{2}[/tex] × 4 × 6)

        = 128 + 12

        = 140 ft²

Answer:

get it down to a unit rate firstt by dividing the 129.5 by 7 dvds

$18.50

18.5x2=37

the 2 dvds were 37 dollars

Step-by-step explanation:

The basic operation that is used in finding the cost of n number of products is multiplication, if we know the cost of 1 article then we can find the cost of n numbers of articles by multiplying it with the cost of one article. Therefore, the cost price of 2 DVD's is $37.

Amee buys 7 DVDS for $129.50.

Thus,

The cost price of 7 DVDs is $129.50

We need to find the cost price of 2 DVDs.

First let us find the cost price of 1 DVD.

Therefore,

[tex]7 \;\rm{DVD's}= \$129.50\\1 \; \rm{DVD}=\frac{129.50}{7}\\1 \; \rm{DVD}=\$18.5[/tex]

Therefore, the cost price of 2 DVDs is $37.

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Answer:

B

Step-by-step explanation:

Expand the right side of the equation

5x² - 3x + 10 = 9x² + 24x + 16

Subtract 5x² - 3x + 10 from both sides

0 = 4x² + 27x + 6 ← in standard form

with a = 4, b = 27, c = 6

Answer:

Step-by-step explanation:

The catch is to put this into the quadratic and solve for a b and c in three equations.

x = 1

a(1)^2 + b(1) + c= 0            

a + b + c + 0                (1)

x = - 1

a(-1)^2 + b(-1) + c = 2

a - b + c = 2                 (2)

x = 2

a(2)^2 + b(2) + c = 8

4a + 2b + c = 8            (3)

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

Add 1 and 2 together

a + b + c = 0

a - b + c = 2

2a + 2c = 2           Divide by 2

a + c = 1                       (4)  

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

Multiply (2) by 2

2a - 2b + 2c = 4          (5)

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

Add (5) + (3)

2a - 2b + 2c = 4

4a + 2b + c = 8

6a + 3c = 12               (6)

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

Multiply (4) by 3

3a + 3c = 3                 (7)

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

Subtract (7) from (6)

6a + 3c = 12

3a + 3c =  3

3a = 9                      Divide by 3

3a/3 = 9/3

a = 3

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

Use (4) to find c

a + c = 1

3 + c = 1                  Subtract 3 from both sides

3-3 + c = 1-3

c = - 2

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

Use 1 to find b

3 + b - 2 = 0          Combine 3 and -2

1 + b = 0                Subtract 1 from both sides

b = - 1              

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

Answers

a = 3

b = - 1

c = - 2

Answer:

B .22

Step-by-step explanation:

The number of people who are male and attended an action movie is 105

There were 479 people who attended

P(male and attended an action movie) = male and attended an action movie

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

                                                                       attended

P(male and attended an action movie)=105/479

                                                               =.219206681

Rounded to two decimal places

                                                               =.22

there is no help!!!!!!!!!!!!!!!!!!!!!!!!!!!!

For this case we must resolve the following expression:

[tex]9 ^ {\sqrt {3}}[/tex]

We have to, by definition:

[tex]\sqrt {3} = 1.732050808[/tex]

So:

[tex]9 ^ {1.732050808} =[/tex]

Evaluating in a calculator we have to:

[tex]9 ^ {1.732050808} = 44.95691576[/tex]

Rounding the obtained expression:

[tex]9 ^ {\sqrt {3}} = 44.9569[/tex]

Answer:

Option C

Answer:

The central angle ADC = 81°

Step-by-step explanation:

From the figure we can see a circle with circumference = 200 cm and arc ABC length = 45 cm

To find the central angle ADC

Circumference = 200 cm

Length of arc ABC = 45

we have

arc length = circumference * (central angle /360)

central angle = (arc length * 360)/circumference

   = (45 * 360)/200

   = 81 cm

Therefore the central angle ADC = 81°

Answer:

ADC=81

Step-by-step explanation:

Answer: 62 in²

Step-by-step explanation:

You must apply the formula for calculate the surface area of a rectangular prims, which is shown below:

[tex]SA=2(wh+lw+lh)[/tex]

Where w is the width, l is the lenght and h is the height.

Based on the information given in the problem, you know that:

[tex]l=5in\\w=3in\\h=2in[/tex]

Therefore, when you substitute these values into the formula, you obtain that the surface area of the rectangular prism is:

[tex]SA=2[(3in*2in)+(5in*3in)+(5in*2in)]\\SA=62in^2[/tex]

Answer:the distance to work is 1 mile and you can walk at 4 miles per hour, then you can walk 1 mile in ¼ hr = 15 minutes

Step-by-step explanation:

Dylan,

If the distance to work is 1 mile and you can walk at 4 miles per hour, then you can walk 1 mile in ¼ hr = 15 minutes.

To set up the "equation" think about it this way:  (1 mile/ t) = (4 mile/ 1 hr)

so 1/t = 4/1 hr  

now multiply both sides by t to get 1 = t·(4/1 hr), next divide both sides by (4/1 hr)

t = 1/(4/ 1 hr) = 1 hr/4 = ¼ hr = 15 min.

The answer is 15 minutes because if he can walk 4 miles for only an hour and we know that an hour is 60 minutes

4. 60m

1. 15m

So what I have done there is just divide it by 4 to get one mile and divide 60 by 4 to get the 15 minutes

Answer:

50 tiles

Step-by-step explanation:

The area of a square is the square of the side. The area of each tile is

a = (20 cm)^2 = 20 cm * 20 cm = 400 cm^2

Now we convert 2 square meters into square centimeters.

2 m^2 * (100 cm)/m * (100 cm)/m = 20,000 cm^2

2 m^2 = 20,000 cm^2

Now we divide the total area by the area of one tile.

(20,000 cm^2)/(400 cm^2) = 50

Answer: 50 tiles

Answer:  $183.71

Step-by-step explanation:

Original amount is $5,175.00

1st year: Increase of 9%

→  $5175(1 + 0.09)

=   $5175(1.09)

=  $5640.75

                                       2nd year: Decrease of 5%  

                                       → $5640.75(1 - 0.05)

                                       =  $5640.75(0.95)

                                       = $5358.71

                                                                              Gain: 2nd year - Original  

                                                                               → $5358.71 - $5175.00

                                                                               = $183.71

Answer:

$183.7

Step-by-step explanation:

We know that $5,175.00 was invested in a stock plan.

It increased by 9% in the first year:

[tex] 9% \times 5175.00 = 465.75 [/tex]

So value reached to (5175 + 465.75 = ) $5640.75

Then it second year, it lost 5% of its value:

[tex] 95% \times 5640.75 = $5358.7 [/tex]

Therefore, the gain compared to the initial original investment will be:

$5358.7 - $5175.0 = $183.7