A smaller number is 3 less than half a larger number. The larger number is 10 times 1 less than the smaller number. Let x represent the smaller number, and let y represent the larger number. Which equations can be used to model the situation? Check all that apply.

Answer:

1. 5

2. 8

3. 40

Step-by-step explanation: So rounding the factors is an easy way to estimate the product of 5.3 and 7.9.

The real answer is 41.87 and 40 is a reasonable approximation, Your welcome.

Answer:

x ≥0.5

Step-by-step explanation:

Given : 2(4x-3)≥-3(3x)+5x.

To find : solve this inequality.

Solution : We have given that

2(4x-3)≥-3(3x)+5x.

Distributes 2 over (4x-3) and -3 over 3x.

8x - 6 ≥ -9x + 5x .

8x - 6 ≥ -4x .

On adding both side by 4x

8x + 4x - 6 ≥ 0 .

12 x - 6 ≥ 0

On adding both sides by 6.

12 x ≥ 6.

On dividing both sides by 12.

x ≥ [tex]\frac{6}{12}[/tex] .

x ≥ [tex]\frac{1}{2}[/tex] .

x ≥0.5.

Therefore, x ≥0.5

Answer:

Step-by-step explanation:

y = x - 4

there are so many ordered pairs which are the solution of the given equation.

for example,

x = 0, y = -4

x = 1 , y = -3

x = 2, y = -2

x = 3, y = -1

x = 4, y = 0

x = - 1, y = - 5

x = - 2, y = - 6

x = - 3, y = - 7

x = - 4, y = - 8

A) 17000*(1+(0.05*3) = 19550

19550-1700 = $2,550 total interest

B)  $19,550 total amount

C) multiply 5 by 3  = 15 than multiply by 17 = 17 * 15 = 255 , then make it a thousands amount by adding a zero at the end

Answer:

A)

p = 17000

r = 5% or 0.05

t = 3

Simple interest formula = p x r x t

Interest paid in 3 years = [tex]17000\times0.05\times3=2550[/tex] dollars

B)

Total amount to be paid = [tex]17000+2550=19550[/tex] dollars

C)

You can first multiply the years and rate that is 5 and 3 to make 15. Then you can multiply by 17. Then put proper decimals as per the values.

First of all, stop thinking on the number 10001000 and turn your attention to the number 990990 instead. If you solve the problem for 990990 you just have to add 993,995,996993,995,996 & 999999 to it for the final answer. This sum is (a)=3983(a)=3983

Count all the #s divisible by 33: From 33... to 990990 there are 330330 terms. The sum is 330(990+3)/2330(990+3)/2, so (b)=163845(b)=163845

Count all the #s divisible by 55: From 55... to 990990 there are 198198 terms. The sum is 198(990+5)/2198(990+5)/2, so (c)=98505(c)=98505

Now, the GCD (greatest common divisor) of 33 & 55 is 11, so the LCM (least common multiple) should be 3×5=153×5=15.

This means every number that divides by 1515 was counted twice, and it should be done only once. Because of this, you have an extra set of numbers started with 1515 all the way to 990990 that has to be removed from (b)&(c).

Then, from 1515... to 990990 there are 6666 terms and their sum is 66(990+15)/266(990+15)/2, so (d)=33165(d)=33165

The answer for the problem is: (a)+(b)+(c)−(d)=233168(a)+(b)+(c)−(d)=233168

Simple but very fun problem.

Answer: [tex]\dfrac{3}{10}[/tex]

Step-by-step explanation:

Given : Each of ten tickets is marked with a different number from 1 to 10 and put in a box.

i.e. The total number of outcomes : 10

Favorable outcomes : 2, 8, or 4

i.e. Number of favorable outcomes = 3

Now, the probability that you will draw 2, 8, or 4 is given by :-

[tex]=\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}\dfrac{3}{10}[/tex]

Answer:

Nicholas, Zachary, Chloe, Alyssa.

Step-by-step explanation:

Given that Four people are painting a house. Zachary paints 1/5 of the house, Alyssa paints 33% of the house, Chloe paints 0.3 of the house, and Nicholas paints 0.17 of the house.

As such we cannot compare their works to order from least to greatest

Hence we can convert each portion into a decimal thus enabling comparison easier.

Zachary paints [tex]\frac{1}{5} =0.20[/tex] of the house

Alyssa paints [tex]33%=\frac{33}{100} =0.33[/tex] of the house

Chloe paints 0.3 of the house and

Nicholas paints 0.17 of the house.

In ascending order these can be written as

0.17, 0.2, 0.3, 0.33

Hence Nicholas, Zachary, Chloe, Alyssa.

Notice that the above sequence is arithmetic because the common difference: d is constant.

d = second term - first term.

= 15 - 9

= 6

The general term of an arithmetic sequence is,

a_{n} =a_{1} +(n-1)d

Where , nth term = [tex] a_{n} [/tex]

[tex] a_{1} [/tex] = First term

and d = common difference.

The given sequence is: 9, 15, 21, ...

Here a_{1} = 9,

d = 6

We need to find the 31st term. So, n = 31.

Next step is to plug in these values in the above formula. Therefore,

[tex] a_{31} =9 +(31-1)*6 [/tex]

= 9 + 30* 6

= 9 + 180

= 189

So, 31st term of this sequence is 189.

Hope this helps you.

Answer:

189

Step-by-step explanation:

Answer:

Option B. $878.28

Step-by-step explanation:

On Monday, Elsbeth's bank account balance was =  $-16.75

She deposited a check = $5.72

On Thursday, she deposited = $16.75

Her new balance = -16.75+( 5.72 + 16.75)

                            = $5.72

On Friday Elsbeth deposited her pay check for = $872.56

The account's final total = 872.56 + 5.72 = $878.28

Elsbeth's account's final total was $878.28.

Option B. $878.28.

The calculated volume is 2284.886 cubic centimeters.

The volume of a rectangular prism (or box) is calculated using the formula:

Volume = length x width x height

For the given measurements:

Plug the values into the formula:

Volume = 6.2 cm x 13.7 cm x 26.9 cm

First, calculate the product of the length and width:

6.2 cm x 13.7 cm = 84.94 cm²

Next, multiply this result by the height:

84.94 cm² x 26.9 cm = 2284.886 cm³

Therefore, the volume of the object is 2284.886 cubic centimeters.

Answer: Distributive property

Step-by-step explanation:

Associative property states that either in addition or multiplication we can changes the position of parenthesis.

That is, a.(b.c) = (a.b).c  or  a+(b+c) = (a+b)+c

Commutative property states that in addition or multiplication we can change the order.

That is, a.b = b.a or a+b = b+a

Multiplicative identity is an element that gives the same number after multiplication.

That is, a × 1/a = 1 ⇒ 1/a is the multiplicative identity of a.

Distributive property lets us multiply a sum by multiplying each addend separately and then add the products.

That is, a(b+c) = a.b + a.c

Thus, it is clear that ,

5(3 + 2) = 5× 3+ 5×2 = 15 + 10  is the example of distributive property.

Answer:

Hence, the length of board is:

6.5 feet

Step-by-step explanation:

Merry and pippin were working on a project in carpentry class.

They needed to cut 4 lengths of 1 5/8 feet from a board.

That means each of the  piece  is of length 1 5/8 feet which could be written in fraction as:

[tex]1\frac{5}{8}=\dfrac{13}{8} feet[/tex]

Hence, the otal length of the board is addition of length of each board.

i.e.

[tex]\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}+\dfrac{13}{8}=4\times \dfrac{13}{8}=\dfrac{13}{2}feet=6.5feet[/tex]

Hence, the length of board is:

6.5 feet