write a word problem that involves dividing by a decimal .include a picture of solution using a model

Final answer:

To find out how much money Mr. Gaster will have after any number of days, we create an equation based on his initial savings and weekly contributions. For 28 days, the equation is T = ($45 × (28/7)) + $5, which simplifies to T = $185. Therefore, Mr. Gaster will have $185 in his piggy bank after 28 days.

Explanation:

To determine how much money Mr. Gaster will have in any number of days, we need to create an equation that accounts for the initial amount and the weekly savings. Because there are 7 days in a week, Mr. Gaster will save $45 for every 7 days. Therefore, to find the total amount in the piggy bank after a certain number of days (d), we divide the number of days by 7 (to get the full weeks), multiply it by the weekly saving amount, and then add the initial amount.

Forming the Equation

Let T be the total amount, and the equation representing the situation is:
T = ($45 \times \frac{d}{7}) + $5

Solving for 28 Days

To solve for the total amount in 28 days:

T = ($45 \times \frac{28}{7}) + $5

T = ($45 \times 4) + $5

T = $180 + $5

T = $185

Hence, after 28 days, Mr. Gaster will have $185 in his piggy bank.

23 is approximately 25 percent of 92.

To determine the percentage, we need to find what portion of 92 is represented by 23. We can set up a proportion to solve for the percentage.

Let's assume the unknown percentage is 'p'. We can write the proportion as:

23 is to 92 as p is to 100.

This can be expressed mathematically as:

23/92 = p/100

To solve for 'p', we can cross-multiply:

23 x 100 = 92 x p

2300 = 92p

To isolate 'p', we divide both sides of the equation by 92:

2300/92 = p

Simplifying, we find:

25 = p

Therefore, 23 is approximately 25% of 92. This means that 23 is 25% of the whole value of 92. To verify this, we can calculate 25% of 92:

(25/100) x 92 = 0.25 x 92 = 23

Hence, 23 is indeed 25% of 92.

To learn more about the percentage;

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[tex]\( \frac{40}{8} \)[/tex] simplified as a mixed number is 5.

To convert the improper fraction [tex]\( \frac{40}{8} \)[/tex] to a mixed number, we divide the numerator (40) by the denominator (8) to find the whole number part and the remainder.

[tex]\[ \frac{40}{8} = 5 \frac{0}{8} \][/tex]

So, [tex]\( \frac{40}{8} \)[/tex] as a mixed number is [tex]\( 5 \frac{0}{8} \)[/tex].

However, we can simplify the mixed number because the numerator and denominator have a common factor of 8.

[tex]\[ 5 \frac{0}{8} = 5 \][/tex]

So, [tex]\( \frac{40}{8} \)[/tex] simplified as a mixed number is 5.

The pair of numbers with 4 and 6 as common factors is option D) 36, 48.

To determine which pair of numbers have 4 and 6 as common factors, we need to find the factors of each pair of numbers and see if both 4 and 6 are factors.

A) Factors of 12: 1, 2, 3, 4, 6, 12

  Factors of 18: 1, 2, 3, 6, 9, 18

  Common factors: 1, 2, 3, 6

  Both 4 and 6 are common factors.

B) Factors of 20: 1, 2, 4, 5, 10, 20

  Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

  Common factors: 1, 2, 4

  Both 4 and 6 are not common factors.

C) Factors of 28: 1, 2, 4, 7, 14, 28

  Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30

  Common factors: 1, 2

  Both 4 and 6 are not common factors.

D) Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

  Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

  Common factors: 1, 2, 3, 4, 6, 12

  Both 4 and 6 are common factors.

Therefore, the pair of numbers with 4 and 6 as common factors is option D) 36, 48.

The probable question may be:

Which pair of numbers below have 4 and 6 as common factors?

A) 12, 18 B) 20, 24 C) 28, 30 D) 36, 48

The sum of the interior angles in any quadrilateral is always 360 degrees.

The sum of the interior angles in a quadrilateral is always 360 degrees. This is a fundamental concept in geometry that applies to all quadrilaterals, regardless of their shape. To understand why this is the case, one can consider dividing a quadrilateral into two triangles. Since the sum of the angles in a triangle is always 180 degrees, adding the angles from both triangles within the quadrilateral gives us a total of 360 degrees. This rule is crucial when solving various geometrical problems involving quadrilaterals. For example, if a quadrilateral ABCD has an extended line CE creating two angles on a straight line, angles ACD and ACE would sum up to 180 degrees because angles on a straight line always sum up to 180 degrees.

It is also worth noting that if a quadrilateral has three right angles, the properties of the sides relative to the fourth angle can be determined based on whether that angle is right, acute, or obtuse. These principles are derived from the fundamental properties of angles in polygons and are used to deduce further geometric relationships.

Answer:

Slope is 15 and y-intercept is 35.

Step-by-step explanation:

Given : The lake side marina charges a $35 rental fee for a boat in addition to charging $15 an hour for usage.

The total cost y of renting a boat for x hours can be represented by the equation [tex]y=15x+35[/tex]

To find : Graph the equation and interpret the slope and the y-intercept?

Solution :

The general slope form is [tex]y=mx+c[/tex]

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

On comparing the equation [tex]y=15x+35[/tex]

The slope is m=15.

The y-intercept is c=35.

Now we plot the equation [tex]y=15x+35[/tex] in graphing tool.

The equation is in green line passing thorough (35,0) and (-2.333,0).

Refer the attached figure below.

Answer:

y=15x+35

Step-by-step explanation:

Answer: the answer is 20

Step-by-step explanation:

Answer:

Step-by-step explanation:

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By adding the 14 bees in the hive to the 17 bees in the garden, we determine there are a total of 31 bees.

To find out how many bees there are in total, we need to add the number of bees in the hive to the number of bees in the garden. The problem states that there are 14 bees in the hive and 17 bees in the garden. Adding these two quantities together gives us:

14 bees in the hive + 17 bees in the garden = 31 bees in total.

So, there are 31 bees altogether.

Final answer:

To find the total number of bees, you need to add the number of bees in the hive to the number of bees in the garden. The total number of bees is 31.

Explanation:

To find the total number of bees, you need to add the number of bees in the hive to the number of bees in the garden. In this case, there are 14 bees in the hive and 17 bees in the garden.

To find the total number of bees, add the number of bees in the hive and the number of bees in the garden: 14 + 17 = 31.

Therefore, there are 31 bees in total.

Answer:

a. [tex]9\frac{3}{4}[/tex], from which he can make 9 loaves.

b. [tex]\frac{3}{4}[/tex] is the remaining part.

Step-by-step explanation:

Givens

To find then number loaves that Paul can make, we just need to divide the number of cups of raising he has, and the cups of raisins need it according to the recipe.

[tex]3\frac{1}{4} \div \frac{1}{3}[/tex]

But, we first need to transform the mixed numero into a fraction, then we solve

[tex]3\frac{1}{4} \div \frac{1}{3}=\frac{13}{4} \div \frac{1}{3}=\frac{13}{4} \times \frac{3}{1}= \frac{39}{4}[/tex]

If we divide this fraction, we obtain a mixed number, becuase the division is not exact

[tex]\frac{39}{4}= 9\frac{3}{4}[/tex]

So, Paul can make [tex]9\frac{3}{4}[/tex] number of loaves. But, he cannot make an incomplete loaf, that means Paul can only make 9 loaves, and the remaining is 3/4, that's the "excess". You can get this answer by subtracting

[tex]9\frac{3}{4} - 9= \frac{39}{4}-9=\frac{39-36}{4}=\frac{3}{4}[/tex]

Therefore, the answers are

a. [tex]9\frac{3}{4}[/tex]

b. [tex]\frac{3}{4}[/tex]

Mrs. Chang's truck runs at a unit rate of $3.75 per gallon of gas and 24 miles per gallon. These rates are found by dividing the total cost by gallons for the cost rate, and total miles by gallons for the efficiency rate.

To find the unit rates of dollars per gallon and miles per gallon for Mrs. Chang's truck, we can use the ratios provided by the information given. First, to find the cost per gallon of gas, we divide the total amount spent by the number of gallons:

Cost per gallon = Total cost / Number of gallons = $75 / 20 gallons = $3.75 per gallon

To calculate the miles per gallon, we divide the number of miles driven by the number of gallons it took to fill the tank when it was empty again:

Miles per gallon = Total miles driven / Number of gallons = 480 miles / 20 gallons = 24 miles per gallon

By calculating these unit rates, drivers can determine both the price efficiency of their gasoline purchases and the fuel efficiency of their vehicle.

Jeandre is correct because the absolute value of a number represents its distance from zero on a number line. Both |3| and |-3| are three units away from zero, therefore they have the same value of 3.

Jeandre is correct when he says that |3| equals |-3|. In mathematics, the absolute value of a number is the distance of that number from zero on a number line, regardless of direction. Both 3 and -3 are three units away from zero. Therefore, the absolute value of 3 is 3, and the absolute value of -3 is also 3.

To visualize this on a number line: if you start at zero and move three units to the right, you reach +3. If you move three units to the left of zero, you reach -3. Since absolute value is concerned with distance only and not direction, both |3| and |-3| represent a distance of 3 units from the origin, hence both have a value of 3.

The equals sign is used to indicate that both expressions are the same in value. Additionally, the rules of algebraic signs help to understand that the negative sign indicates direction on a number line, but does not affect the absolute value.

Answer: An increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.

Step-by-step explanation: In a linear model of this situation, the y-intercept represents the temperature at the base of the troposphere, 15°C.

The rate of change, or slope, can be determined using two values: temperature at the base, (0 , 15), and temperature at the top, (11 , −56.5).

The linear model of this situation is y = 15 − 6.5x, where x represents the height of the troposphere, in kilometers.

The rate of change, or slope, indicates that an increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature. Hope this helps

Final answer:

In the troposphere, an increase of 1 km in altitude corresponds to a temperature decrease of 6.5°C, based on the given data of 15°C at sea level and -56.5°C at the top of the troposphere (11 km).

Explanation:

The question concerns the change of air temperature with altitude in the troposphere. From the information provided, we know that the temperature at the base of the troposphere (0 km) is 15°C and at the average top (11 km), it's -56.5°C. To find the rate at which temperature decreases with altitude, we can use the given temperatures at two different altitudes to calculate the lapse rate.

The difference in temperature from the base to the top is 15°C - (-56.5°C) = 71.5°C. Over a distance of 11 km, this gives us a lapse rate of 71.5°C / 11 km = 6.5°C/km. Therefore, an increase of 1 km in altitude corresponds to a decrease of 6.5°C in temperature.

Answer:WHY U LOOK AT ME THERE IS AN EXPERT

Step-by-step explanation:

The correct set of favorable outcomes for rolling a sum of seven with two dice is Option C: (1-6) (2-5) (3-4) (4-3) (5-2) (6-1), as each of these pairs adds up to the target sum of seven.

The student is asking which of the given sets of pairs (representing the outcomes of rolling two dice) would result in a sum of seven. The correct choice is:

Option C: (1-6) (2-5) (3-4) (4-3) (5-2) (6-1)

Each pair of numbers in Option C adds up to seven, which are the favorable outcomes for rolling a sum of seven with two dice. The sum of the numbers in each pair from the other options does not equal seven. Therefore, the favorable outcomes for rolling a sum of seven on two dice are those where the first and second numbers add up to seven, as correctly listed in Option C.