When 12.393 and t are added together, the result is 20.463. What is the value of t?

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.

Answer:

B) -x-3

Step-by-step explanation:

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

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

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.

Answer:

21

Step-by-step explanation:

hard wok

talent

The solution is Option A.

The distance between the base of the ladder and the wall is 9 feet

What is a Triangle?

A triangle is a plane figure or polygon with three sides and three angles.

A Triangle has three vertices and the sum of the interior angles add up to 180°

Let the Triangle be ΔABC , such that

∠A + ∠B + ∠C = 180°

The area of the triangle = ( 1/2 ) x Length x Base

For a right angle triangle

From the Pythagoras Theorem , The hypotenuse² = base² + height²

Given data ,

Let the triangle be represented as ABC

Now , the height of the wall = 12 feet

The measure of AB = 12 feet

The length of the ladder = 15 feet

The measure of AC = 15 feet

Now , the distance between the base of the ladder and the wall = BC

The measure of BC is given by the Pythagoras Theorem , where

Hypotenuse² = base² + height²

AC² = AB² + BC²

Substituting the values in the equation , we get

15² = 12² + BC²

Subtracting 12² on both sides of the equation , we get

BC² = 15² - 12²

BC² = 225 - 144

BC² = 81

Taking square roots on both sides of the equation , we get

BC = 9 feet

Therefore , the value of BC is 9 feet

Hence , the distance is 9 feet

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Amy's class saw a total of 40 horses and ponies and 55 rabbits and hares at the fair,

The question involves comparing the numbers of two sets of animals seen at the fair: horses and ponies versus rabbits and hares. To solve this, we will first add the number of horses and ponies together and then do the same for rabbits and hares.

Number of horses and ponies combined:
22 horses + 18 ponies = 40

Number of rabbits and hares combined:
18 rabbits + 37 hares = 55

Comparing the two totals:
40 horses and ponies is less than 55 rabbits and hares. Therefore the class saw more rabbits and hares combined than horses and ponies combined at the fair

The answer choices are:

A. h= m -2

B. h=m -10

C. h= m/5

D. h= m-10/5

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.

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].

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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].

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

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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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].

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Final answer:

The area per person served by a 12-inch quiche, it was determined that a 10-inch quiche can indeed feed 4 people with the same serving size, as the area available per person in the 10-inch quiche is sufficient.

Explanation:

To determine whether a quiche with a diameter of 10 inches can feed 4 people at the same serving size as a 12-inch quiche that feeds 6 people, we need to compare the areas of the two quiches. The area of a circle is calculated using the formula A = πr² where A is the area and r is the radius. Since the radius is half of the diameter, the 12-inch quiche has a radius of 6 inches and the 10-inch quiche has a radius of 5 inches.

For the 12-inch quiche:
A12 = π(6²) = 36π

For the 10-inch quiche:
A10 = π(5²) = 25π

So, the 12-inch quiche has an area of 36π square inches and the 10-inch quiche has an area of 25π square inches. To find out if the smaller quiche can serve 4 people, we calculate the area per person for the larger quiche: 36π/6 = 6π square inches per person.

Now, we check to see if the 10-inch quiche provides at least that much area for 4 people: 25π/4 ≈ 6.25π square inches per person. Since 6.25π is greater than 6π, we can conclude the 10-inch quiche can indeed feed 4 people with the same serving size as the 12-inch quiche fed 6 people.

To find the side of the original square, we can set up an equation and solve for x.

To solve this problem, let's assume that the side length of the original square is 'x'. If we double it, the new side length would be '2x'. Adding 7 to it gives us '2x + 7'.

The new perimeter of the square is 8 more than 3 times the old perimeter, so we can set up the equation: 2(2x + 7) = 3(4x).

Simplifying this equation, we get 4x + 14 = 12x. By rearranging the equation, we find that 8x = 14, which leads to x = 1.75.

Therefore, the side length of the original square is 1.75 units.

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