Sophie is playing a game called circles and stars. Sophie rolls one number cube and gets the number six. Sophie draws six circles on her paper. Sophie rolls the number cube again and gets the number three. Sophie draws three stars in each of the six circles. Sophie writes 6×3 on her paper. Sophie plays the game again. Sophie rolls one number cube and gets the number. Sophie draws three circles on her paper. Sophie tools the number cube again and gets the number six. Sophie draws six stars in each of the three circles. Sophie writes 3×6 on her paper. Sophie says she got the total number of stars both times! Is Sophie correct?

Answer:  She needed 128 cm of ribbon.

Step-by-step explanation:

Since we have given that

Length of yellow ribbon needed to be cut = 1 meter

Length of blue ribbon needed to be cut = 28 cm

We need to find the number of centimeters she needed to be cut.

First of all, we convert meter into centimeter.

As we know that

1 meter = 100 centimeter

So, Total number of centimeters of ribbon she needed is given by

[tex]100+28\\\\=128\ cm[/tex]

Hence, She needed 128 cm of ribbon.

Final answer:

There are 209 numbers among the first 10,000 positive integers that contain the digit pair '43' in that order, when considering the different placements of the digit pair in a four-digit number.

Explanation:

To find out how many of the first 10,000 positive integers contain the digit pair "43" in that order, let's consider the different places this pair can occur. The '43' pair can be in the units and tens place, the tens and hundreds place, or the hundreds and thousands place.

For the units and tens place, we have '43' fixed and two remaining places that can be any digit from 0 to 9, so there are 10 times 10 = 100 possibilities. However, we need to exclude the combination '043' as it is not a four-digit number but rather '43', giving us 100 - 1 = 99 combinations.

For the tens and hundreds place, we again have 10 possibilities for the other two places (thousands and units). We do not need to exclude any numbers here because even '043x' represents a valid four-digit number. Thus, we have 10  imes 10 = 100 combinations.

For the hundreds and thousands place, there are only 10 possibilities for the units place, as '430x' represents a valid four-digit number, which results in 10 combinations.

Adding them up, we have a total of 99 + 100 + 10 = 209 numbers that contain the '43' pair in the first 10,000 positive integers.

The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].

Given:

An expression : [tex]\frac{3}{8}.(\frac{-3}{6})[/tex]

To find:

The product of the given expression of fractions in simplified form.

Solution:

[tex]\frac{3}{8}.(\frac{-3}{6})\\\\= \frac{3}{8}\times (\frac{-3}{6})\\\\=\frac{-9}{48}\\\\=\frac{-3}{16}[/tex]

The product of the given expression of a fraction is [tex]\frac{-3}{16}[/tex].

Learn more about the simplest form of fraction here:

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Answer:

B) -x-3

Step-by-step explanation:

If I read and did the math correctly, this should be the answer.  :)

Answer:

21

Step-by-step explanation:

hard wok

talent

Answer:

Length of Marliens house = [tex](\frac{7}{2}x-4)\text{ or }(\frac{9}{2}x-18)[/tex] .

Width of Marliens house = [tex](2x-2)[/tex].

Step-by-step explanation:

We need to find the length and width of Marlien's home in algebraic expressions.

Add length of living room, hallway and kitchen, to find the length of Marlien's home.

Length of Marlien's home = [tex](2x+2)+(\frac{1}{2}x-4)+(x-2)=\frac{7}{2}x-4[/tex]

Or we can add Master bedroom,guest room, hallway and bathroom, to find the length of Marlien's home.

Length of Marlien's home = [tex](2x-10)+(x-2)+(\frac{1}{2}x-4)+(x-2)=\frac{9}{2}x-18[/tex]

Add width of living room and Master bedroom to find the width of Marlien's home.

Width of Marlien's home = [tex]x+(x-2)=2x-2[/tex]

Hence, the length of Marliens house is either [tex](\frac{7}{2}x-4)\text{ or }(\frac{9}{2}x-18)[/tex]  and width of Marliens house is [tex](2x-2)[/tex].

Answer: 862

Step-by-step explanation:

Let the third digit of Y be x .

Then , the first digit will be 4x and the second digit will be 3x.

Since , the digits of Y add to 16.

Then we have

[tex]3x+4x+x=16\\\\\Rightarrow\ 8x=16\\\\\Rightarrow\ x=\dfrac{16}{8}=2[/tex]

Thus , the third digit of Y = 2

Then the first of Y digit will be [tex]4(2)=8[/tex]

The second digit of Y will be  [tex]3(2)=6[/tex]

Hence, the  digits of Y must be 862

The answer choices are:

A. h= m -2

B. h=m -10

C. h= m/5

D. h= m-10/5

Answer:

Option B is the correct answer.

Step-by-step explanation:

We need to find  the value of Sin 21° using calculator and round to four decimal places.

Using calculator

             Sin 21° = 0.358367949

Rounding the value of Sin 21° to four decimal places.

            Sin 21° = 0.3584

Option B is the correct answer.

The concept of linear equation and ratios is used to solve for the price of radios. The price of two radios are [tex]x=\pounds 80[/tex] and [tex]y=\pounds 20[/tex].

Given information:

The ratio of prices of two radios is [tex]x:y[/tex].

If the price of both the radios is increased by [tex]\pounds20[/tex], the ratio of price would become 5:2.

The above condition can be written mathematically as,

[tex]\dfrac{x+20}{y+20}=\dfrac{5}{2}\\2x+40=5y+100\\2x-5y=60.........(1)[/tex]

If the prices are both reduced by [tex]\pounds 5[/tex], the ratio will become 5:1.

The above condition can be written mathematically as,

[tex]\dfrac{x-5}{y-5}=\dfrac{5}{1}\\x-5=5y-25\\x-5y=-20\\-x+5y=20.........(2)[/tex]

Add equation (1) and (2), to get the value of [tex]x[/tex] and [tex]y[/tex] as,

[tex]2x-x=60+20\\x=80[/tex]

Solve for [tex]y[/tex] as,

[tex]2x-5y=60\\2\times 80-5y=60\\5y=100\\y=20[/tex]

Therefore, the price of two radios is [tex]x=\pouns 80[/tex] and [tex]y=\pounds 20[/tex].

For more details, refer the link:

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To find when the job cost is the same for both companies, equate their cost equations. By solving 100 + 15h = 75 + 17h, we find that at 12.5 hours the job would cost the same no matter which company is used.

To determine when a job costs the same for both landscape companies, we need to equate the two cost equations they offer and solve for the number of hours.

Let h be the number of hours the job takes. The first company's cost can be represented as C1 = 100 + 15h, and the second company's cost as C2 = 75 + 17h. To find the number of hours when both companies charge the same amount, we set C1 = C2:
100 + 15h = 75 + 17h.

Rearrange the equation to solve for h:
100 - 75 = 17h - 15h
25 = 2h
h = 12.5 hours.

So, a job that takes 12.5 hours would cost the same amount whether it is done by the first company or the second company.

Answer:

No, the expression 65-(45-20) is not equal to (65-45)-20.

Step-by-step explanation:

Consider the provided expression.

Consider the expression: 65-(45-20)

Solve the above expression as shown.

65-(45-20)

65-(25)

65-25

40

Now consider the second expression.

(65-45)-20

20-20

0

Now compare both the result.

40≠0

Hence, the expression 65-(45-20) is not equal to (65-45)-20.

Using the function p(t) = -8t + 100, where t is time and p(t) is the amount of paper left, we set p(t) to 0 and solve for t. This reveals that it will take 12.5 minutes for the printer to use all 100 sheets of paper.

In this problem, we're told that the printer uses paper according to the function p(t) = -8t +100, where t is the time it takes to print and p(t) is the amount of paper left in the printer. We want to find how much time it will take for the printer to use all the 100 sheets of paper, meaning we need to set p(t) to 0 and solve for t.

Therefore, we set up and solve the equation as follows: 0 = -8t + 100. If we solve this equation for t, we get t =100/8, which simplifies to t = 12.5 minutes.

This means it will take the printer 12.5 minutes to use all the 100 sheets of paper. The previous suggestions about other solutions and negative time are not applicable in the context of this problem because time cannot be negative in this instance, and this equation yields only one solution.

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Answer:

15 and 9 are the correct answers.

Step-by-step explanation:

The numbers that are at a distance of 3 units from 12 on a number line are given as:

We will add 3 to 12 and also subtract 3 from 12 to get both numbers on the left side an right side on the number line.

[tex]12+3 = 15[/tex]

[tex]12-3 = 9[/tex]

So, the correct answers are 15 and 9.

make 1 3/4 an improper fraction:

1 3/4 = 7/4

 now you have 4/7 divided by 7/4

now reverse the 7/4 and multiply:

4/7 x 4/7 = 16/49