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3 years ago

Jennifer had a 7/8- foot board. She cut off a 1/4 foot piece that was for a project. In feet, how much of the board was left

Mathematics

1 answer:

Tems11 [23]3 years ago

7 0

Answer: There was 5/8 of a foot of board left.

Step-by-step explanation:

Step 1. We need to subtract 1/4 from 7/8. To do this make it where both fractions have the same denominator.

Step 2. The easiest way to do this is to multiply 1/4 by 2.

1/4*2/2=2/8.

Step 3. Now all you got to do is subtract 2/8 from 7/8.

7/8-2/8= 5/8.

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Explain how to use a horizontal number line<br> to order four fractions from least to greatest.

horsena [70]

Answer:

To order fractions from least to greatest, start by finding the lowest common denominator for all of the fractions. Next, convert each of the fractions by dividing the lowest common denominator by the denominator and then multiplying the top and bottom of the fraction by your answer.

Step-by-step explanation:

Solution for the above problem: We first find the least common denominator by finding the least common multiple for 4, 3, 2, 6, and 8. We find the LCM by the prime factorization method. Next, place the fractions in order from least to greatest.

4 0

2 years ago

In his first year, a math teacher earned $32,000. Each successive year, he

Ivan

Answer:

Step-by-step explanation:

Each successive year, he

earned a 5% raise. It means that the salary is increasing in geometric progression. The formula for determining the nth term of a geometric progression is expressed as

Tn = ar^(n - 1)

Where

a represents the first term of the sequence(amount earned in the first year).

r represents the common ratio.

n represents the number of terms(years).

From the information given,

a = $32,000

r = 1 + 5/100 = 1.05

n = 20 years

The amount earned in his 20th year, T20 is

T20 = 32000 × 1.05^(20 - 1)

T20 = 32000 × 1.05^(19)

T20 = $80862.4

To determine the his total

earnings over the 20-year period, we would apply the formula for determining the sum of n terms, Sn of a geometric sequence which is expressed as

Sn = (ar^n - 1)/(r - 1)

Therefore, the sum of the first 20 terms, S20 is

S20 = (32000 × 1.05^(20) - 1)/1.05 - 1

S20 = (32000 × 1.653)/0.05

S20 = $1057920

3 0

2 years ago

A teacher places n seats to form the back row of a classroom layout. Each successive row contains two fewer seats than the prece

Alex_Xolod [135]

Answer:

The number of seat when n is odd $S_n=\frac{n^2+2n+1}{4}$

The number of seat when n is even $S_n=\frac{n^2+2n}{4}$

Step-by-step explanation:

Given that, each successive row contains two fewer seats than the preceding row.

Formula:

The sum n terms of an A.P series is

$S_n=\frac{n}{2}[2a+(n-1)d]$

$=\frac{n}{2}[a+l]$

a = first term of the series.

d= common difference.

n= number of term

l= last term

$n^{th}$ term of a A.P series is

$T_n=a+(n-1)d$

n is odd:

n,n-2,n-4,........,5,3,1

Or we can write 1,3,5,.....,n-4,n-2,n

Here a= 1 and d = second term- first term = 3-1=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=1 and d=2

$n=1+(t-1)2$

⇒(t-1)2=n-1

$\Rightarrow t-1=\frac{n-1}{2}$

$\Rightarrow t = \frac{n-1}{2}+1$

$\Rightarrow t = \frac{n-1+2}{2}$

$\Rightarrow t = \frac{n+1}{2}$

Last term l= n,, the number of term $=\frac{ n+1}2$ , First term = 1

Total number of seat

$S_n=\frac{\frac{n+1}{2}}{2}[1+n}]$

$=\frac{{n+1}}{4}[1+n}]$

$=\frac{(1+n)^2}{4}$

$=\frac{n^2+2n+1}{4}$

n is even:

n,n-2,n-4,.......,4,2

Or we can write

2,4,.......,n-4,n-2,n

Here a= 2 and d = second term- first term = 4-2=2

Let $t^{th}$ of the series is n.

$T_n=a+(n-1)d$

Here $T_n=n$ , n=t, a=2 and d=2

$n=2+(t-1)2$

⇒(t-1)2=n-2

$\Rightarrow t-1=\frac{n-2}{2}$

$\Rightarrow t = \frac{n-2}{2}+1$

$\Rightarrow t = \frac{n-2+2}{2}$

$\Rightarrow t = \frac{n}{2}$

Last term l= n, the number of term $=\frac n2$ , First term = 2

Total number of seat

$S_n=\frac{\frac{n}{2}}{2}[2+n}]$

$=\frac{{n}}{4}[2+n}]$

$=\frac{n(2+n)}{4}$

$=\frac{n^2+2n}{4}$

4 0

2 years ago

Bettina spent $75 on 5 shirts that each cost the same price. Three of the shirts.were red. Wich expression represents the total

maw [93]

The answer is 75/5 * 1/3 because 75/5 is the price of 1 shirt, and 1/3 but I don't know how it's 1/3. I got 75/5 * 3 but the closest answer was C.

Hope this helped☺☺

7 0

2 years ago

HELP ME ASAP IF U CAN!!! a baker needs sugar syrup that is 40% sugar how many gallons of water shoud he add to 5 gallons of 70%

aleksley [76]

Answer:

15/4

Step-by-step explanation:

Equation: 40(5+x)=70*5+0x

Solve:

200+40x=350

40x=150

x = 15/4

15/4 gallons is the answer.

4 0

2 years ago

Read 2 more answers