A division of a ———ends?

Using the scale factor 1/4 inch equals 1 foot to convert Julie's actual bedroom dimensions to the blueprint scale, the bedroom measures 3 inches by 4 inches on the blueprint.

To find the dimensions of Julie's bedroom on the architect's blueprint when the scale drawing is 1/4 inch equals 1 foot, we first need to establish the unit scale as a ratio. Given that the actual dimensions of her bedroom are 12 feet by 16 feet, we convert these measurements to inches on the blueprint using the provided scale.

We use the ratios:

By cross-multiplying and dividing, we can find the blueprint measurements:

For length:

For the width:

Therefore, the dimensions of her bedroom on the blueprint are 3 inches by 4 inches.

To find the blueprint dimensions of Julie's bedroom using the scale 1/4 inch = 1 foot, the actual dimensions of 12 ft by 16 ft are converted to 48 inches by 64 inches respectively by multiplying each dimension by the inverse of the scale ratio (4 feet / 1 inch).

To find the dimensions of Julie's bedroom on the blueprint, we must use the scale given which is 1/4 inch = 1 foot. This means that for every foot in actual size, it is represented by 1/4 inch on the blueprint. To convert Julie's actual bedroom dimensions, 12 feet by 16 feet, to blueprint dimensions, we multiply each by the inverse of the given scale.

Calculation steps for the length:

For the width, follow the same steps:

Therefore, the dimensions of Julie's bedroom on the blueprint should be 48 inches by 64 inches.

Answer:

  9/10 hours

Step-by-step explanation:

You want the total of 1/2 hours and 2/5 hours.

Addition of fractions is accomplished by converting them to values that have a common denominator.

  1/2 = 5/10

  2/5 = 4/10

Then the sum is ...

  1/2 +2/5 = (5/10) +(4/10) = (5 +4)/10 = 9/10

Manuel spent 9/10 hours on the two assignments.

__

Additional comment

Equivalently, you can convert the fractions to decimals and add them that way:

  1/2 +2/5 = 0.5 +0.4 = 0.9 . . . . . 9/10 hours

Your calculator can tell you what the sum is.

Answer: 100 cents making it 1 dollar

Answer:

91 Cents

Step-by-step explanation:

The next and lowest coin is a penny.

90 + 1 = 91

Final answer:

After calculating the cost per ounce for both packages, the 10.5-ounce package, with a unit price of $0.284 per ounce, is the better deal compared to the 27.8-ounce package, which has a unit price of $0.323 per ounce.

Explanation:

To determine which package has the better unit price, you calculate the cost per ounce for each package and compare them. First, divide the total cost of each package by the number of ounces it contains.

For the 10.5-ounce package at $2.98:

$2.98 ÷ 10.5 ounces = approximately $0.284 per ounce

For the 27.8-ounce package at $8.99:

$8.99 ÷ 27.8 ounces = approximately $0.323 per ounce

Now, compare the unit prices. The 10.5-ounce package has a lower unit price of $0.284 per ounce compared to the 27.8-ounce package with a unit price of $0.323 per ounce, making the 10.5-ounce package the better deal based on unit price.

Answer:B

Step-by-step explanation:

The statement is true. Amir did indeed drive from Jerusalem to the Dead Sea, which holds the distinction of being the lowest point on Earth in terms of land elevation.

True. Amir drove from Jerusalem to the Dead Sea, which is indeed the lowest place on Earth in terms of land elevation. The Dead Sea is a remarkable geographical feature located in the Jordan Rift Valley and is renowned for its extreme salinity, making it one of the saltiest bodies of water on Earth. The surface of the Dead Sea lies approximately 430 meters (1,410 feet) below sea level, and its shores border both Jordan to the east and Israel and the West Bank to the west.

Jerusalem, on the other hand, is situated on a plateau in the Judaean Mountains, and the drive from Jerusalem to the Dead Sea involves descending from higher elevations down to the low-lying area where the Dead Sea is located. This journey provides travelers with a striking transition from the elevated terrain around Jerusalem to the uniquely low and buoyant waters of the Dead Sea.

The Dead Sea's remarkable location and its high salinity levels have made it a popular destination for tourists seeking the therapeutic benefits of its mineral-rich mud and the sensation of effortlessly floating on its surface. This natural wonder's status as the lowest place on Earth is well-documented and contributes to its global renown.

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The question probable may be:

Amir drove from Jerusalem to the lowest place on earth, the Dead Sea.   True or false.

Answer:

13.1

Step-by-step explanation:

yes

Answer:

I would combine like terms

Step-by-step explanation:

2/3x + 1/3x + =5

The first step would be to combine like terms

2/3 x + 1/3 x  = x

The problem is that Bob cannot evenly distribute his 24 fish and 18 plants across 5 tanks due to left over quantities when the numbers are divided.

The problem presented is a math problem requiring the use of division and balance. It involves Bob trying to evenly distribute his 24 fish and 18 plants across 5 tanks. An effective way is to divide the quantities of fish and plants by the number of tanks. Therefore, if there are 5 tanks, 24 fish would be divided by 5, giving 4 fish with 4 left over, and 18 plants divided by 5 gives 3 plants each with 3 left over. This indicates that an even distribution is not possible with these numbers, because there would always be a excess quantity of fish and plants beyond what can be put in the 5 tanks.

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To distribute the fish and plants without any leftover, divide the total number of fish and plants by the number of tanks.

To distribute the fish and plants without any leftover, Bob needs to divide them equally among the tanks. To find out how many fish and plants should be in each tank, we need to divide the total number of fish and plants by the number of tanks.

Number of fish in each tank = 24 fish / 5 tanks = 4 fish per tank.

Number of plants in each tank = 18 plants / 5 tanks = 3.6 plants per tank. Since we can't have a fraction of a plant, we can round it up to 4 plants per tank or distribute the leftover plant evenly among the tanks.

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Answer:

y = -3x-9

Step-by-step explanation:

To solve for y, we need to subtract 7 from each side

7-7 + y = -2-7 -3x

y = -3x-9

For x:

[tex]-2-3x=7+y[/tex]             add 2 to both sides

[tex]-3x=9+y[/tex]          divide both sides by (-3)

[tex]\boxed{x=-3-\dfrac{1}{3}y}[/tex]

For y:

[tex]7+y=-2-3x[/tex]      subtract 7 from both sides

[tex]\boxed{y=-9-3x}[/tex]

Answer:

first, you add the hours driven then you divide.

2+1.4+1.25=4.65

336/4.65=72.3

Step-by-step explanation:

Answer:

x= 60.1 degrees

Step-by-step explanation:

The triangle forms a right angle triangle

Opposite side of angle x = 13 ft

Hypotenuse of the triangle = 15

We know the opposite side and the hypotenuse

So we use trigonometric formula sin(x)

[tex]sin(x) = \frac{opposite}{hypotenuse}[/tex]

[tex]sin(x) = \frac{13}{15}[/tex]

When we move 'sin' to the other side it becomes 'sin^-1'

[tex]x=sin^{-1}(\frac{13}{15})[/tex]

x = 60.073565

Answer:x = 60.073565

Step-by-step explanation:

Answer:

Take wholesale cost and multiply it by 95%, then add to the original value

another way, just multiply by 1.95

Retail cost:  1.95*($99.50) = $194.03

ANSWER: [tex]y=9x-23[/tex]

EXPLANATION:

We can use the slope-formula to find the slope.

[tex]\text{Slope Formula:} \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\\frac{4+5}{3-2} =m\\\\\frac{9}{1} = m\\\\9=m[/tex]

Now that we have the slope, we can plug in one of the x and y values into the slope-intercept formula to find b.

[tex]\text{Slope-Intercept Formula}:y=mx+b\\\\4=9(3)+b\\\\4=27+b\\\\-23=b[/tex]

The equation of the line that passes through (3, 4) and (2, -1) is [tex]y=9x-23[/tex]

Answer:

4 hours

Step-by-step explanation:

6.25X4=25 so he'll have an extra dollar

The formula of a distance between two points:

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have the points (7, -1) and (9, -9). Substitute:

[tex]d=\sqrt{(9-7)^2+(-9-(-1))^2}=\sqrt{2^2+(-8)^2}=\sqrt{4+64}=\sqrt{68}\\\\=\qrt{4\cdot17}=\sqrt4\cdot\sqrt{17}=\boxed{2\sqrt{17}}[/tex]

The distance between the points (7, -1) and (9, -9) is calculated using the distance formula and simplifies to [tex]2\sqrt{17}[/tex] units.

To find the distance between two points in simplest radical form, we can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is [tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]. For the points (7, -1) and (9, -9), the calculation is as follows:

First, find the difference in the x-coordinates: 9 - 7 = 2.

Next, find the difference in the y-coordinates: -9 - (-1) = -8.

Now, square each difference: (2)^2 = 4 and (-8)^2 = 64.

Add these squares together: 4 + 64 = 68.

Finally, take the square root of the sum: [tex]\sqrt{68}[/tex].

This radical simplifies to [tex]\sqrt{4 * 17} = 2\sqrt{17}[/tex], which is in simplest radical form.

Therefore, the distance between the points (7, -1) and (9, -9) is [tex]2\sqrt{17}[/tex] units.

Answer:

c -2 -1 0 1 and 2

Step-by-step explanation:

abs (x) < 3

Absolute value equations have 2 solutions, one positive and one negative ( remember to flip the inequality when taking the negative solution).

x<3 and x>-3

-3 <x<3

The integer solutions are -2,-1,0,1-2

We do not include 3 because there is no equals sign on the inequality.

The green square is the larger square, the total area for the target would be 8 x 8 = 64 square units.

The area of the smaller yellow square would be 4 x 4 = 16 square units.

The green area would be the difference between the total target area and the yellow area: 64 - 16 = 48 square units.

The probability of hitting the green area = 48 / 64 = 0.75

The answer is C.

let's say that number is "x", so that is then the 100%.

if 150 is 25%, what is "x"?

[tex]\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 150&25 \end{array}\implies \cfrac{x}{150}=\cfrac{100}{25}\implies \cfrac{x}{150}=4\implies x=600[/tex]

Answer:  a) 278382 oz

b) 43 oz

c) 64.1 oz

Step-by-step explanation:

a) 8 T. 1,398 lb. 14 oz. × 6

First we need to change it in 'oz'.

As we know that

[tex]1\ ton=32000\ oz\\\\1\ lb=16\ oz[/tex]

so, it becomes,

[tex]8\times 32000+1398\times 16+14\ oz\\\\=278382\ oz[/tex]

8 T. 1,398 lb. 14 oz. × 6 becomes

[tex]278382\times 6\\\\=1670292\ oz[/tex]

b) 349 lb. 6 oz. ÷ 130

It becomes,

[tex]349\times 16+6\ oz\\\\=5590\ oz\\\\\text{ at last it becomes}\\\\=\frac{5590}{130}\\\\=43\ oz[/tex]

c) 6 T. 294 lb. ÷ 3,071

First it becomes,

[tex]6\times 32000+294\times 16\ oz\\\\=196704\ oz[/tex]

At last it becomes,

[tex]\frac{196704}{3071}\\\\=64.1\ oz[/tex]

Hence, a) 278382 oz

b) 43 oz

c) 64.1 oz

Answer:

A. 278382 ounces

B. 43 ounces

C. 64.1 ounces

Answer:

The equation of the  line has a slope of -5 and passes through the point (2, 2) is  y = -5x + 12 .

Option (D) is correct.

Step-by-step explanation

The equation of the line

y = mx + c

where m is the slope and c is the y - intercept .

As given

A line has a slope of -5 and passes through the point (2, 2).

The slope of the line is -5.

m = -5

Put in the equation of the line

y = -5x + c

Put x = 2 and y = 2

2 = -5 × 2  + c

2 = - 10  + c

2 + 10 = c

12 = c

Put the value of c in the y = -5x + c

y = -5x + 12

Therefore the equation of the  line has a slope of -5 and passes through the point (2, 2) is  y = -5x + 12 .

Option (D) is correct.

To find the equation of the line with slope -5 passing through (2, 2), use the point-slope form and simplify to get y = -5x + 12. Therefore, the correct answer is option D.

To find the equation of the line with a slope of -5 that passes through the point (2, 2), we can use the point-slope form of the equation of a line:

y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passes through.

Substituting the given values:

y - 2 = -5(x - 2)

Simplify this equation:

Therefore, the equation of the line is y = -5x + 12, so the correct answer is option D.

Answer:

x = 4 1/2 or 4.5 cm

Step-by-step explanation:

We know the perimeter of the rectangle is given by the formula

P =2(l+w)

19 = 2(2.5 + (2.5+x))

Simplifying

19 = 2( 5+x)

Distribute

19 = 10 + 2x

Subtract 10 from each side

19-10 = 10-10 + 2x

9 = 2x

Divide each side by 2

9/2 = 2x/2

4.5 = x

Answer:

32291999

Step-by-step explanation:

Step 1

We will use the fundamental counting principle to work out the total number of possible plates. The fundamental principle of counting states that if a process can be completed in k steps, and that there are [tex]n_1[/tex] steps to complete the first step, [tex]n_2[/tex] steps to complete the second step and [tex]n_k[/tex] stepts to finish the kth step, then there are [tex]n_1\times n_2 \times ....\times n_k[/tex] ways to complete the steps.

Step 2

In this step we figure out the number of ways to complete each step given that no repetitions are allowed. Note that this will include the plate that has I,O,W,A.

The first step can be carried out in 10 ways because there are 10 digits.

The second step can be carried out in 9 ways because we are not allowed to repeat any digits.

The third step can be carried out in 26 ways as there are 26 letters of the alphabet.

The fourth step can be carried out in 25 ways because no repeats are allowed.

the fifth step can be carried out in 24 ways because two of the letters will already have been used.

The sixth step can be carried out in in 23 ways because three letters have been used already.

Step 3

The third step is to use the fundamental counting principle with the values listed in step 3. We will also subtract 1 from whatever value we get because we would have counted the combination with I,O,W,A in it. This calculation is shown below,

[tex]10\times 9\times 26\times 25\times 24\times 23-1=32291999[/tex]

To calculate the total number of available license plates in Iowa based on specific formats and restrictions.

License Plate Combination Calculation:

Since the format is 2 numbers followed by 4 letters, with restrictions on certain letters and repeat use, we calculate the possibilities step by step:

For numbers: 10 choices for each position, so 10×10 = 100 possibilities.

For letters: After considering the restrictions, we have 22 choices for the first letter, 21 for the second, 20 for the third, and 19 for the fourth, resulting in 22×21×20×19 = 155,760 possibilities.

Finally, multiplying the possibilities for numbers and letters gives us the total number of available license plates: 100 × 155,760 = 15,576,000.

Answer:

$27.83

Step-by-step explanation:

26.50 x .05 = 1.325  (round up to 1.33 since the 5 is 5 or greater)  

26.50 + 1.33 = 27.83  

Amount of tax will be 1.33

Answer:

27.83

Step-by-step explanation:

Answer:

3. aₙ = -9n +7

4. d = -2.4

5. a₆ = 45

6. aₙ = 133 + 4n

Step-by-step explanation:

Question 3.

a₁ = -2; aₙ = aₙ₋₁ - 9

The explicit rule for an arithmetic sequence is

        aₙ = a₁ + d(n -1 )

         d = aₙ - aₙ₋₁

        aₙ = aₙ₋₁ - 9     Subtract aₙ₋₁ from each side

aₙ - aₙ₋₁ = -9

         d = -9

For this sequence,  

aₙ = -2 – 9(n - 1)     Remove parentheses

aₙ = -2 - 9n + 9      Combine like terms

aₙ = -9n + 7

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

Question 4

d = aₙ - aₙ₋₁

a₂ - a₁ = 6.2 – 8.6 = -2.4

a₃ - a₂ = 3.8 – 6.2 = -2.4, etc.

The common difference is

d = -2.4

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

Question 5

aₙ = 8n – 3     Substitute the value of n

a₆ = 8×6 – 3

a₆ = 48 - 3

a₆ = 45

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

Question 6

a₁ = 137; d = 4

aₙ = a₁ + d(n -1 )

aₙ = 137 + 4(n -1 )

aₙ = 137 + 4n -4

aₙ = 133 + 4n

Answer:

associative property of multiplication

Step-by-step explanation:

Associative property of multiplication states that (a x b) x c = a x (b x c).

5 * (sqrt(9) *4) = (5* sqrt(9) ) *4

Answer:

When dealing with the area of ANY geometric shape the rule is, an increase that doubles one dimension, will equal an increase of 4 in area.

Basically, this is because 2² = 4

So, the larger cake will serve 6 * 4 = 24 people.

Step-by-step explanation:

Answer:

12 people

Step-by-step explanation:

rachel has 2 hexagonally shaped birthday cakes

Let A and B represent the two hexagonally shaped cakes.

the smaller of which serves six people.

Oh!, so Let A represent the Bigger cake;     &

B to represent the smaller cake;

SO, B serves ------- 6 people

The question proceeds by stating it that ;

If one length of one side of the larger cake is twice that of the smaller cake

If the smaller cake side B is x

and the larger cake A be 2x

An hexagonally shaped cake is definitely going to have 6 sides

So;

For B

6x = 6

x = 1

Since x =6 , For A

2x = 2(1)

= 2

Therefore, the cake is going to serve 2 × 6 people

= 12 people

Final answer:

To solve 8(5x+9x+6)=160, we first combine like terms to simplify the expression within the parentheses to 14x+6, and then use the distributive property to further simplify and solve the equation. This order of operations ensures clarity and accuracy in solving the equation.

Explanation:

The question involves solving the algebraic expression 8(5x+9x+6)=160. The first step in simplifying and solving an equation like this is to combine like terms within the parentheses. Combining like terms (5x+9x) simplifies the expression inside the parentheses to 14x+6. This simplification makes the equation easier to manage and understand. The next step is to use the distributive property which allows us to multiply the number outside the parenthesis (in this case, 8) by each term inside the parenthesis individually (14x and 6). After distributing, we get 112x + 48 = 160, from which we can solve for x by isolating the variable.

The order of operations is crucial here; combining like terms before using the distributive property ensures the equation remains manageable and reduces the potential for errors. After these steps, we can subtract 48 from both sides and divide by 112 to find the value of x that satisfies the equation.

Answer:

(x, y) = (- 3, 3)

Step-by-step explanation:

given the 2 equations

- x + 3y = 12 → (1)

y = 6x + 21 → (2)

Substitute y = 6x + 21 into (1)

- x + 3(6x + 21) = 12 ← distribute

- x + 18x + 63 = 12

17x + 63 = 12 ( subtract 63 from both sides )

17x = - 51 ( divide both sides by 17 )

x = - 3

Substitute  x = - 3 into (2) for y

y = (6 × - 3 ) + 21 = - 18 + 21 = 3

solution is (- 3, 3 )

Answer: [tex]w=-\frac{1}{5}[/tex]

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have the following equation given in the problem above:

[tex]5 -5w= 6[/tex]

2. Then, you need to solve for [tex]w[/tex], as you can see in the following steps:

[tex]5-5w=6\\-5w=6-5\\-5w=1\\w=-\frac{1}{5}[/tex]

3. Therefore, as you can see, the value of [tex]w[/tex] is:

[tex]w=-\frac{1}{5}[/tex]