Assignment: Counting Investigation Dakota and Karen noticed that there were a bunch of combinations available in their school cafeteria. Think about a meal at your school, or maybe a favorite restaurant. How many combinations of choices do you have? Create a tree diagram listing the possible combinations, and count the results. 1. For what will you find the number of combinations? ______________________________________________________________________________________________________________________ 2. List at least three categories to consider. ______________________________________________________________________________________________________________________ 3. List the choices within each category. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 4. Assign each choice a symbol. Ex. juice = (diamond shape) ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 5. Create a tree diagram to determine the number of combinations available. 6. List all possible combinations and count the total number of possibilities. ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Answer:

Jim's claim is correct

Step-by-step explanation:

Total survey=100 people

Morning exercise=35 people

Afternoon exercise=45 people

Night exercise=20 people

Morning exercise : Total survey

=35 : 100

Afternoon exercise : Total survey

=45 : 100

Night exercise : Total survey

=20 : 100

Jim's claim is correct because in finding the ratio, one has to relate it with the total people involved in the survey.

Tara's claim however seems to relate one variable with two other variables

Example:

35 : 55

Morning exercise : (morning exercise + night exercise)

35 : (35+20)

35 : 55

Answer:

Sample Response: Jim is correct because 35:100, 45:100, and 20:100 are part-to-whole comparisons. There are other possible part-to-part ratios from the data.

Answer:

[tex]\large \boxed{\mathrm{B. \ 84}}[/tex]

Step-by-step explanation:

[tex]LU[/tex] bisects [tex]RU[/tex] and [tex]UA[/tex].

[tex]RU=UA[/tex]

[tex]3m+21=6m[/tex]

Solve for m.

Subtract 3m from both sides.

[tex]21=3m[/tex]

Divide both sides by 3.

[tex]7=m[/tex]

Calculate [tex]RA[/tex].

[tex]RA=3m+21+6m[/tex]

[tex]RA=9m+21[/tex]

Put m = 7.

[tex]RA=9(7)+21[/tex]

[tex]RA=63+21[/tex]

[tex]RA=84[/tex]

Answer:

B) 84

Step-by-step explanation:

ΔLRU ≅ ΔLAU   {SAS congruent}

Therefore, UA = UR    {CPCT}

 6m = 3m +21

Subtract 3m from both sides

6m - 3m = 3m + 21 -3m

        3m = 21

Divide both sides by 3

    3m/3 = 21/3

m = 7

RA = RU + UA

    = 3m + 21 + 6m {add like terms}

    = 9m + 21   {Plug in m =7}

    = 9*7 + 21

    = 63 + 21

RA = 84 units

Answer:

1/2b*h

1/2 6*27

162/2

81 is the answer

Answer:

1306.90≅  1307 rounded to the nearest tens

Step-by-step explanation:

r= radius = 13 cm

l is the slant height =19 cm

surface area of the cone= area of the circle + area of the curved of the cone

SA=πrl +πr²

SA=π(13)(19) +169π

SA= 247π +169π= 416π=1306.90≅  1307 rounded to the nearest tens

The monthly income is $844.

Given:

To find: The monthly income

The monthly income refers to the amount of money left over each month after paying all expenses.

Evaluating, we have,

The total monthly expense = $([tex]725 + 125 + 120 + 35 + 48 + 78 + 600 + 225[/tex])

That is, the total monthly expense is $1956.

It is given that weekly earning after taxes is $700. Since a month contains 4 weeks, we can say that monthly earning after taxes is $([tex]700 \times 4[/tex]), that is, $2800.

Then, monthly income is given by the difference between the monthly earnings and the monthly expenses. So, monthly income is $([tex]2800-1956[/tex]), that is, $844.

The monthly income is $844.

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Answer:

$240 extra

Step-by-step explanation:

1/3(7200) + 12(420) = 2400 + 5040 = 7440

7440 - 7200 = 240

The customer had to pay 1720 extra.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

A car is priced at $7200.

If the deposit is one third = 7200/3

                                          = 240

The amount after 12 payments will be

= 240 x 12

= 2880

total cost will be

= 2880 + 2400

= 5280

and, The customer had to pay extra amount

= 7200 - 5280

= 1720

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Answer:

centre = (11, 0 ), radius = 3

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - h)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Given

(x - 11)² + y² = 9 ← in standard form

with (h, k ) = (11, 0 ) and r² = 9 ⇒ r = [tex]\sqrt{9}[/tex] = 3

centre = (11, 0 ) and r = 3

Answer:

365.7 km²

hopefully this answer can help you to answer the next question.

The vertical lines on each side of the x mean it is the absolute value of x.

Replacing x with -x would make no change on the graph, because the absolute value is always a positive number.

The answer is B.

There will be no change on the graph of y = |x| if x is replaced with -x. Option B is correct.

A function is defined as the expression that set up the relationship between the dependent variable and independent variable.

The vertical lines on each side of the x mean it is the absolute value of x. Replacing x with -x would make no change on the graph because the absolute value is always a positive number.

Therefore, there will be no change on the graph of y = |x| if x is replaced with -x. Option B is correct.

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Answer:

-7

Step-by-step explanation:

*Two negatives will cancel out and turn into addition.

-12 - (-5)

Subtract 12 from 5 and add the negative sign:

-12 + 5 =

  -7

The answer would be -7

Hope this helped.

Answer:

52°

Step-by-step explanation:

360 - 33 - 165 - 20 - 90 = x

x = 52

Answer:

Step-by-step explanation:

Let's find the size of angle x

The angle in a complete turn add up to 360°

[tex] \mathsf{x + 20 + 165 + 33 + 90 = 360}[/tex]

Add the numbers

[tex] \mathsf{x + 308 = 360}[/tex]

Move constant to R.H.S and change it's sign

[tex] \mathsf{x = 360 - 308}[/tex]

Calculate the difference

[tex] \mathsf{x = 52}[/tex] °

Hope I helped!

Best regards!

Step-by-step explanation:

x= 9

[tex] {x}^{2} + 9 \div x + 1[/tex]

[tex] {9 }^{2} + 9 \div 9 + 1[/tex]

[tex]81 + 9 \div 10[/tex]

[tex]90 \div 10[/tex]

[tex]9[/tex]

Answer:

Hello,

None !!!

Step-by-step explanation:

[tex]f(x)=x(x+5)(x+2)\\=x(x^2+5x+2x+10)\\\\=x^3+7x^2+10x\\[/tex]

Answer:

-17.3

Step-by-step explanation:

To solve for x, we can divide both sides by -3:

x = -52 / 3 which = -17.3

Answer:

Step-by-step explanation:

[tex] \sf{ - 3x = 52}[/tex]

Divide both sides of the equation by -3

⇒[tex] \sf{ \frac{ - 3x}{ - 3} = \frac{52}{ - 3} }[/tex]

Calculate

⇒[tex] \sf{x = - 17.33}[/tex]

Hope I helped!

Best regards!!

Answer:

d.13 the measure of eg that's the answer

Answer:

Step-by-step explanation:

Domain of a function represents the set of x-values (input values) and y-values (output values) of the function represent the Range of the function.

Given function is,

[tex]y=-\frac{2}{3}x+7[/tex]

If Domain (input values) of this function is,

{-12, -6, 3, 15}

Table for the input-output values of this function,

x        -6         3        15       -12

y        11         5         -3        15

Answer:

Step-by-step explanation:

Answer:

C. 2 [tex]\frac{1}{4}[/tex]

Step-by-step explanation:

First, calculate the amount of clay that both groups used in total. We can find this by multiplying the amount by the number of students.

Used 3/4 of a pound:

3/4(4) = 3 pounds

Used 1/4 of a pound:

1/4(3) = 3/4 pound

Now, subtract:

3 - 3/4 = 2 and 1/4

Answer

i got it right

C. 2

Answer:

6. No. See explanation below.

7. 18 months

8. 16

Step-by-step explanation:

6. To rewrite a sum of two numbers using the distributive property, the two numbers must have a common factor greater than 1.

Let's find the GCF of 85 and 99:

85 = 5 * 17

99 = 3^2 + 11

5, 3, 11, and 17 are prime numbers. 85 and 99 have no prime factors in common. The GCF of 85 and 99 is 1, so the distributive property cannot be used on the sum 85 + 99.

Answer: No because the GCF of 85 and 99 is 1.

7.

We can solve this problem with the lest common multiple. We need to find a number of a month that is a multiple of both 6 and 9.

6 = 2 * 3

9 = 3^2

LCM = 2 * 3^2 = 2 * 9 = 18

Answer: 18 months

We can also answer this problem with a chart. We write the month number and whether they are home or on a trip. Then we look for the first month in which both are on a trip.

Month                Charlie          Dasha

1                          home             home

2                          home             home

3                          home             home

4                          home             home

5                          home             home

6                         trip                home

7                          home             home

8                          home             home

9                          home             trip

10                         home             home

11                         home             home

12                         trip               home

13                         home             home

14                         home             home

15                         home             home

16                         home             home

17                         home             home

18                         trip                 trip

Answer: 18 months

8.

First, we find the prime factorizations of 96 an 80.

96 = 2^5 * 3

80 = 2^4 *5

GCF = 2^4 = 16

Answer: 16

Answer:

Step-by-step explanation:

One pump will fill 200l in 20 minutes

So the rate of filling per pump will be 10l/minute (200/20)

Let the number of minutes it will take to fill the 600l be x minutes

Now, since the rate of filling per pump is 10 l/minute

Then in x minute, they would have filled 10l/minute * x = 10x liters

So it is now this 10x liters that will be equal to 600

To find x, we simply divide

10x = 600

x= 600/10

x = 6 minutes

Answer:

She borrowed 4000 from bank.

Step-by-step explanation:

Let 'y' be the amount borrowed from bank. Then 10000-y is the amount borrowed from her mother-in-law.

Let x= interest amount gained by bank . Then 1080- x = interest gained by mother-in-law

I1= interest rate by bank= 9%

I2= interest rate by mother-in-law=12%

Time(T) = 1 year

Now, By Simple Interest formula:

x=PTR/100

Or, x=(y*1*9)/100

Or,100x=9y

or,9y-100x=0...........................Equation (i)

Again 1080-x= ((10000-y)*1*12)/100

Or, 108000-100x=120000-12y

Or, 12y-100x=12000.................Equation(ii)

Solving equation (i) and (ii), we get

y= 4000, which the amount borrowed from bank.

y=-1.4x

Step-by-step explanation:

divide the change in y by the change in x to find the gradient,

7 divided by -5 [as the translation is to the left].

there might be a y intercept value, c as in

y=mx + c but with the given information without  thee starting points it is hard to find

The required equation of the graph that results from the translation is y = √(x + 5) + 7.

Translation on a coordinate plane is a transformation that moves an object or figure from its original position to a new position in a straight line. It is also called a "slide." In translation, all points of the object are moved by the same distance in the same direction.

Here,
To shift the graph of the function y = √x to the left by 5 units, we need to replace x with x + 5 in the equation. This will give us the graph of y = √(x + 5).

To shift the graph 7 units up, we need to add 7 to the entire function. This will give us the final equation of the translated graph:

y = √(x + 5) + 7.

Therefore, the equation of the graph that results from the translation is y = √(x + 5) + 7.

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Answer:

Step-by-step explanation:

The cross-section is an 8”×13” rectangle.

Area = 104 square inches

Answer:

D

Step-by-step explanation:

The slope of the line is - 1/4. The equation of the line is y=(-1/4x)+5

Answer:

[tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}=\dfrac{-13}{8}[/tex]

Step-by-step explanation:

We need to find the value of expression [tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}[/tex].

Firstly solving the second term as :

[tex](2-\dfrac{3}{8})=\dfrac{16-3}{8}=\dfrac{13}{8}[/tex]

Now the above expression becomes,

[tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}\\=\dfrac{-3}{2}-\dfrac{13}{8}+\dfrac{3}{2}[/tex]

-3/2 and +3/2 equals 0.

It means that, [tex]\dfrac{-3}{2}-(2-\dfrac{3}{8})+\dfrac{3}{2}=\dfrac{-13}{8}[/tex]

Answer:

x = 10

Step-by-step explanation:

5x - 6 = 44

Add 6 on both sides of the equation.

5x = 50

Divide by 5 on both sides of the equation.

x = 10

So, the value of x is equal to 10

Answer:

x=10

Step-by-step explanation:

5x-6=44

grouping constants and numbers with coefficient of x we get

5x=44+6

5x=50

5x/5=50/5

x=10

Answer:

Step-by-step explanation:

Given her total cost of ride tickets modeled by the equation c = 3.5t where c is the total cost of tickets and t is the number of tickets, If Stacy bought 15 tickets, to know the amount she would spend on 15 tickets, we will substitute t = 15 into the modeled equation as shown;

[tex]c = 3.5t\\when t = 15\\\\c = 3.5(15)\\\\c = \frac{35}{10} * 15\\ \\c = \frac{5*7}{5*2} * 15\\\\[/tex]

[tex]c = \frac{7}{2} * 15\\ \\c = \frac{105}{2}\\ \\c = \ 52.2[/tex]

Hence Stacy would spend $52.2 on 15 tickets

Answer:

I hope this helps!

Step-by-step explanation:

Answer:

Top circle:

A=25pi or 78.54 sq cm  

P = 10pi or 31.42 cm

Bottom circle(assuming D is 13 m):

A= 42.25pi or 132.73 sq m  

P = 13pi or 40.84 m

Step-by-step explanation:

[tex]\\ \sf\longmapsto 7x-27=1[/tex]

[tex]\\ \sf\longmapsto 7x=1+27[/tex]

[tex]\\ \sf\longmapsto 7x=28[/tex]

[tex]\\ \sf\longmapsto x=\dfrac{28}{7}[/tex]

[tex]\\ \sf\longmapsto x=4[/tex]

Answer:

The 100 students who are asked questions.