5 gal × 20 mpg = ? how far can the driver travel with 5 gallons of gas

General Idea:

When we are working with word problems, we need to follow the below steps:

Step 1: Assign variable for the unknown that we need to find.

Step 2: Write a meaningful mathematical equation using the sentence given

Step 3: Solve the equation by Performing reverse operation by Undoing whatever is done to the variable. Solving means find the value of the variable which will make the equation TRUE.

Applying the concept:

Step 1: Let x be the number of books that Brett can afford without spending more than his gift voucher amount.

Step 2: Writing mathematical equation based on the given sentence "Brett has a $30 online gift voucher. He plans to buy as many books as he can. The cost of each book is $4. There is also a single shipping charge of $2"

[tex] Online \; Gift \; Voucher=Number \; of \; books \; \times \; Cost\;per \; Book \; + \; Single \; shipping \; charge [/tex]

[tex] 30=4x+2 [/tex]

Step 3: Solving equation

[tex] 4x+2=30\\ Subtract \; 2 \; on \; both \; sides\\ \\ 4x+2-2=30-2\\ Combine \; like \; terms\\ \\ 4x=28\\ Divide \; 4 \; on \; both \; sides\\ \\ \frac{4x}{4}= \frac{28}{4} \\ Simplifying \; fraction \; on \; both \; sides\\ \\ x=7 [/tex]

Conclusion:

The number of books that Brett can afford without spending more than his gift voucher amount is 7 !!

Answer:

Its K ≥ 12

Step-by-step explanation:

Hope this helps! Have a good day!:) and happy St. Patrick's day lol

To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we can use the equation a = 500 + 500t.

To model the relationship between the number of months, t, since opening the bank account and the total amount of money, a, deposited into the account, we need to find the pattern. According to the information given, Ms. Gibson made an initial deposit of $500 and then deposited the same amount each month. This means that the total amount of money, a, deposited after a certain number of months, t, can be represented by the equation:

a = 500 + 500t

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She can enjoy her original 3/4 brownie divided into six equal parts, each constituting 1/8 of the delectable treat.

Deb possesses 3/4 of a brownie and intends to partition it into smaller portions, each equivalent to 1/8 of a brownie, allowing her to savor it throughout the day.

To determine the number of 1/8 portions she'll obtain, we can perform a simple division.

By dividing 3/4 by 1/8, we essentially multiply the numerator of 3/4 by the reciprocal of 1/8, which is 8/1.

This multiplication yields (3 * 8) / (4 * 1) = 24/4.

Simplifying further, we find that Deb will have 6 portions of 1/8 of a brownie.

Consequently, she can enjoy her original 3/4 brownie divided into six equal parts, each constituting 1/8 of the delectable treat.

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Question

Deb has 3/4 of a brownie. She wants to divide it up into 1/8 of a brownie so she can have it throughout the day. How many 1/8s will she have's will she have?

Answer:

Step-by-step explanation: Add pic so ppl can help

Answer:

g3h

Step-by-step explanation:

I got it right

Answer:

Step-by-step explanation:

Here we have to use the rate of depreciation, the initial value and the total time to find the final value with this formula

[tex]A=A_{0}(1-r)^{t}[/tex]

Where [tex]A[/tex] is the final value, [tex]A_{0}[/tex] is the initial value, [tex]r[/tex] is the rate of depreciation and [tex]t[/tex] is the time.

Replacing all values, we have

[tex]A=20300(1-0.0875)^{12}[/tex]

[tex]A=6765.35[/tex]

Therefore, after 12 years the car will value $6,765.35.

Answer : The surface area of the package is, [tex]185.9inch^3[/tex]

Step-by-step explanation :

The given package is in cuboid shape. Now we have to calculate the surface area of the package by using volume of cuboid.

Formula used for volume of cuboid is:

[tex]V=2(lb+bh+hl)[/tex]

where,

V = volume of package

l = length of package = [tex]2\frac{1}{3}inch=\frac{7}{3}inch[/tex]

b = width of package = [tex]8\frac{1}{2}inch=\frac{17}{2}inch[/tex]

h = height of package = [tex]6\frac{3}{4}inch=\frac{27}{4}inch[/tex]

Now put all the given values in the above formula, we get:

[tex]V=2\times [(\frac{7}{3}\times \frac{17}{2})+(\frac{17}{2}\times \frac{27}{4})+(\frac{27}{4}\times \frac{7}{3})][/tex]

[tex]V=2\times [\frac{119}{6}+\frac{459}{8}+\frac{63}{4}][/tex]

[tex]V=185.9inch^3[/tex]

Therefore, the surface area of the package is, [tex]185.9inch^3[/tex]

The solution set is (9, ∞).

To solve the inequality 3.3x-11.6>18.1, we need to isolate the variable x.

First, we can add 11.6 to both sides of the inequality to get 3.3x>29.7.

Then, we can divide both sides by 3.3 to solve for x: x>9.

We can express the solution set using interval notation as (9, ∞).

Therefore, The solution set is (9, ∞).

The solution set for the inequality 3.3x - 11.6 > 18.1 is x > 9, meaning x is greater than 9.

To solve the inequality 3.3x - 11.6 > 18.1, you can follow these steps:

1. Add 11.6 to both sides to isolate the term with x:

3.3x - 11.6 + 11.6 > 18.1 + 11.6

3.3x > 29.7

2. Now, divide both sides by 3.3. Remember, when you divide by a positive number, the inequality sign remains the same:

[tex]\[ \frac{3.3x}{3.3} > \frac{29.7}{3.3} \][/tex]

[tex]\[ x > \frac{29.7}{3.3} \][/tex]

x > 9

So, the solution set for the inequality 3.3x - 11.6 > 18.1 is x > 9.

The reasonable estimate is 10.

We can approximate 915.25 to 900.

We can approximate 88.22 to 90.

Then we divide them: [tex]\frac{915.25}{88.22}\approx\frac{900}{90}=10[/tex].

So the reasonable estimate is 10.

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100 is not a reasonable estimate for the operation 915.25 divided by 88.22, as the actual answer is approximately 10.37. While estimates don't provide exact numbers, the difference here is too great for 100 to be considered reasonable, depending on the level of accuracy needed.

In mathematics, estimation is commonly used when you do not need the exact answer, but rather a ballpark number close to the actual value. The student's question revolves around whether 100 is a reasonable estimate for the operation 915.25 divided by 88.22. We can check this by performing the actual division: 915.25 / 88.22 equals approximately 10.37. Although this is not exactly 100, it is within an order of magnitude which might make the estimate reasonable depending on the context. Therefore, as a quick estimate, 100 might not be suitable for high-precision contexts.

It's important to understand how estimates work. Their value is not in providing exact numbers, but in giving a quick understanding of a situation, especially when the exact numbers are complex or cumbersome. Here, however, the difference between the actual result (10.37) and the estimate (100) is quite significant, which suggests that 100 might not be a reasonable estimate in this case, depending on the level of accuracy needed.

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After the simplification of the  given radial expression [tex]\sqrt{\frac{64}{16}(\frac{y^{10} }{y^{12} } )\frac{h^{5} }{h^{5} } }[/tex] we get [tex]\frac{2}{y}[/tex].

A radical expression is defined as any expression containing a radical ([tex]\sqrt{}[/tex]) symbol.

The term underneath the radical symbol is called the radicand.

To solve a radical expression, simply take the the square root of the radicand.

According to the given question, we have a radical expression

[tex]\sqrt{\frac{64y^{10}h^{5} }{16y^{12} h^{5} } }[/tex]

=[tex]\sqrt{\frac{64}{16}(\frac{y^{10} }{y^{12} } )\frac{h^{5} }{h^{5} } }[/tex]                           ([tex]\frac{x^{m} }{x^{n} } =x^{m-n}[/tex])

= [tex]\sqrt{4(\frac{1}{y^{2} })(1) }[/tex]

= [tex]\sqrt{\frac{4}{y^{2} } }[/tex]

= [tex]\frac{2}{y}[/tex]

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27/40 miles long was the bus ride.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

The store is 7⁄8 of a mile away from your house.

Distance covered by Walking = 1/5

and, the rest is covered by Bus.

So, the distance covered by Bus

= 7/8- 1/5

= 35/ 40- 8/40

= 27/40

Hence, 27/40 miles covered by Bus.

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