A building with a height of 14 m casts a shadow that is 16 m long while a taller building casts a 24 m long shadow. What is the height of the taller building?

Sandy's total earnings before taxes for the two weeks will be $769.70, which includes $518 from her hourly wages and $251.70 from her sales commission.

To solve how much Sandy will earn in hourly wages and commission over two weeks of work at a clothing store, where she makes $7 per hour and earns a 15% commission on her sales of $1,678, we first calculate her hourly wages: Sandy worked 74 hours, and at $7 per hour, her earnings from hours worked are 74 hours x $7/hour = $518.

Next, we calculate her commission earnings: 15% of $1,678 in sales is 0.15 x $1,678 = $251.70.

Adding both earnings gives us Sandy's total earnings before taxes, which is $518 + $251.70 = $769.70.

Answer: YES

Step-by-step explanation: yes it is proportional because ut is a linear equation and you know where to set the y and the x

When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation.

In simpler terms, that means if A is always twice as much as B, then they directly vary. If a gallon of milk costs $3, and I buy 1 gallon, the total cost is $3. If I buy 10 gallons, the price is $30. In this example the total cost of milk and the number of gallons purchased are subject to direct variation -- the ratio of the cost to the number of gallons is always 3.

To be more "geometrical" about it, if y varies directly as x, then the graph of all points that describe this relationship is a line going through the origin (0, 0) whose slope is called the constant of variation. That's because each of the variables is a constant multiple of the other.Hope I helped

An equation in the slope-intercept form represents a direct variation only when the y-intercept is zero. For instance, y=3x is a direct variation while y=3x+9 isn't due to having y-intercept 9. The differentiation between a direct variation and a simple linear equation helps understand the relationship in algebra.

In mathematics, the slope-intercept form of an equation can represent a direct variation, but it's only sometimes true. An equation in the slope-intercept form represents a direct variation only when the y-intercept (the 'b' in the equation y=mx+b) is zero.

For example, the equation y = 3x represents a direct variation because the y-intercept is 0. Here, the value of y changes proportionately with x, which denotes a direct variation. However, in the equation y=3x+9 (represented in Figure A1), it does not represent a direct variation since the y-intercept is 9 (b ≠0).

Therefore, the direct variation depends on whether the y-intercept is zero or not in a slope-intercept equation. This relationship between the x and y variables in algebra helps scholars understand the difference between a direct variation and a simple linear equation.

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To find the value of x in the equation 50 - 10x = 20, we subtract 50 from both sides and then divide by -10, leading to x = 3.

To solve the equation 50 - 10x = 20 for the value of x, we need to isolate x on one side of the equation. First, we subtract 50 from both sides, which gives us -10x = -30. Next, we divide both sides by -10 to solve for x, resulting in x = 3. This process demonstrates the systematic approach to solving linear equations, ensuring accurate determination of unknown variables and facilitating problem-solving in various mathematical contexts. Once simplified, the equation x=3 represents the solution where the given expression is true, providing clarity on the value of x that satisfies the equation.

All the solution of the expression are,

⇒ 223.6 ÷ 40 = 5.59

⇒ 8.14 ÷ 20 = 0.407

⇒ 361.5 ÷ 12 = 30.125

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications.

For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

All the expressions are,

⇒ 223.6 ÷ 40

⇒ 8.14 ÷ 20

⇒ 361.5 ÷ 12

Now, We can divide all the expressions as;

⇒ 223.6 ÷ 40

⇒ 223.6 / 40

⇒ 5.59

⇒ 8.14 ÷ 20

⇒ 8.14 / 20

⇒ 0.407

⇒ 361.5 ÷ 12

⇒ 361.5 / 12

⇒ 30.125

Thus, All the solution of the expression are,

⇒ 223.6 ÷ 40 = 5.59

⇒ 8.14 ÷ 20 = 0.407

⇒ 361.5 ÷ 12 = 30.125

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The previous number is multiplied by 10 to get the next number.

We have numbers [tex]\frac{1}{1000} ,\frac{1}{100},\frac{1}{10}[/tex]

Here first number is [tex]\frac{1}{1000}[/tex]

Second number is [tex]\frac{1}{100}[/tex]

Third number  is [tex]\frac{1}{10}[/tex]

So ratio is [tex]\frac{ \frac{1}{100}}{ \frac{1}{1000}}=10[/tex]

And [tex]\frac{ \frac{1}{10}}{ \frac{1}{100}}=10[/tex]

As the ratio between each number is 10.

Therefore the previous number is multiplied by 10 to get the next number.

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To obtain a high score of 1500 points in the video game, you must beat at least 5 levels.

To find the number of levels you must beat in order to obtain the high score of 1500 points, we can set up an inequality. Let's denote the number of levels as 'x'. Each level gives you 300 points, so the total number of points you will earn is 300x. The inequality will be:

300x >= 1500

To solve this inequality, divide both sides by 300:

x >= 5

So, you must beat at least 5 levels to obtain the high score of 1500 points.

The mass of ether considering its density as 713 kg/m³ will be 0.09 kg.

Density or mass density is the mass of any object per volume.

For example, if the metal has a 100 kg mass and an area of 10-meter square then 100/10 = 10 kg/meter square will be the density of the given object.

Given the volume (V) of ether = 130 mL = 130 × 10⁻³ L

Since 1000 L = 1 m³

1 L =  10⁻³ m³

So, V = 130 × 10⁻³ × 10⁻³ m³

V = 130 × 10⁻⁶ M³

Now density of ether is 713 kg/m³

Thus, 713 = Mass / 130 × 10⁻⁶

Mass = 0.09 kg

Hence "The mass of ether considering its density as 713 kg/m³ will be 0.09 kg".

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The number of cups of flour required to make 1 dozen muffin is 2 1/3 cups.

To find out how many cups of flour are needed for every dozen muffins made, we'll use the information given that 3 1/2 cups of flour make 1 1/2 dozen muffins. We need to set up a proportion to scale the amount of flour down to the amount needed for 1 dozen muffins. First, we know that 1 1/2 dozens equals 18 muffins (since a dozen is 12), so we can express the known ratio as:

3 1/2 cups of flour / 18 muffins

To find out how many cups of flour make 12 muffins, we set up the proportion:

(3 1/2 cups / 18 muffins) = (x cups / 12 muffins)

We then cross-multiply and solve for x, which represents the cups of flour:

3 1/2 * 12 = 18 * x

7/3 or 2 1/3 = x

Answer:

8$

Step-by-step explanation:

No, the flour is not enough to make the recipe; Katrina will still need 6/35 kilograms of flour.

To get the amount of kilogram that Katrina will still need, you should subtract the amount of flour Katrina needed from the amount she had.

This implies 3/5-3/7.

You have to find the smallest number that can divide the denominators (5 and 7) and since 35 is the smallest number that can divide both denominators, then it is the lowest common denominator or LCD.

You should now divide the denominators with 35, and also multiply the answer you get with the numerators.

This implies 3/5-3/7 = 21/35-15/35

= 6/35kg.

The final answer is 6/35, which means Katrina will still need 6/35 kilograms more of flour.

As you can see, we arrived at the final answer by subtracting the numerators (21-15) to have 6, and the lowest common denominator remains 35.

If you are faced with questions that require you to find the smallest number or LCD for large numbers, what you should do is to multiply the denominators together and reduces it if necessary.

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The first digit of the quotient for 18.88 divided by 4 will be the ones place.

When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division, thus, can be interpreted as equally dividing the number that is being divided in total x parts, where x is the number of parts the given number is divided.

WE need to find the first digit of the quotient for 18.88 divided by 4.

18.88 / 4 = 4.72

We know that Quotients are the number that is obtained by dividing one number by another number.

Dividend ÷ Divisor = Quotients

Therefore, the first digit of the quotient for 18.88 divided by 4 will be the ones place.

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The solution is, The blank is 1/2.

Here, we have,

given that,

if 4/5 times blank equals 2/5

Let x be the unknown

4/5 x = 2/5

Multiply each side by 5

4/5x * 5 = 2/5*5

4x = 2

Divide each side by 4

4x/4 = 2/4

x = 1/2

so, The blank is 1/2.

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