33.2g of sugar is needed to make 4 cakes. How much sugar is needed for 6 cakes?

Answer:

[tex](x-1)(3x-5)[/tex]

Step-by-step explanation:

[tex]3x^2 - 8x + 5[/tex]

To factor it we use AC or splitting the middle term method

product is 3 times 5 is 15

Sum is -8

-3 times -5 is 15

-3 plus -5 is -8

Factors are -3 and -5

[tex]3x^2 -5x-3x+ 5[/tex]

Group first two terms and last two terms

[tex](3x^2 -5x)+(-3x+ 5)[/tex]

[tex]x(3x-5)-1(3x- 5)[/tex]

Factor out 3x-5

[tex](x-1)(3x-5)[/tex]

Answer: 51

Step-by-step explanation: A prime number is a number that is greater than 1 and it has two factors which are 1 and itself.

23 is a prime number because it has no other factors besides 1 and 23. In other words, there is no other number multiplied by a number than will equal 23 so we call it a prime number.

Gerry will spend $13.6 in two weeks

From the problem given:

Gerry spend $1.25/day on lunch

Fridays spend extra $0.55

How much Gerry will spend in two weeks?

In one week, there are 5 school days

4 days (Monday to Thursday) Gerry spend $1.25/day

1 day, Fridays, Gerry spends $1.25+$0.55 = $1.80

So, in one week Gerry will spend :

= [tex]\boxed {(1.25 \times4) + 1.80\ }\\ =\boxed {5+1.80\ }\\ =\boxed {6.8\ }[/tex]

In two weeks, Gerry will spend :

[tex]=\boxed {2 \times 6.8\ }\\ =\boxed {13.6\ }[/tex]

When we are multiplying decimal numbers, the process the same as multiplying whole numbers except for the placement of the decimal point in the answer. In multiplying we don't need to line up the decimal point.

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Keywords: multiplication, decimal number multiplication, additional, decimal number additional, standard algorithm

Answer:

A. 0.3 (With a line above the 3) ([tex]0.\overline{3}[/tex])

Step-by-step explanation:

The part of money used for the bus fare = [tex]\frac{1}{3}[/tex]

Upon division the value,

[tex]\frac{1}{3} = 0.33333333....333[/tex]

As this no. is a rational number with recurring decimal. It means that the number after the decimal repeats up to infinity.

Such recurring decimal numbers are represented with a bar or line over the recurring digits.

Thus the given number is represented as [tex]0.\overline{3}[/tex].

Answer: 6%

Step-by-step explanation:

If you turn 6% to a decimal (move it twice to the right) we get 0.06. If we multiply 0.06 and $750 we get $45, which is how much investment increased. Add $45 to $750 we get $795 ( which is the new value).

750×0.06= 45

45+ 750= 795

Final answer:

To make an equation with no solution, choose a constant for the question mark that, when combined with the existing terms, will create a contradiction when attempting to solve for x. For the equation 3(x - 4/3) = 3x + ?, placing the number 5 in the question mark will result in 3x - 4 = 3x + 5, which simplifies to a contradiction of -4 ≠ 5, meaning no solution exists.

Explanation:

To create an equation with no solution, you should first expand the expression on the left-hand side of the equation. When you distribute the 3 across (x - 4/3), you get 3x - 4. In order for the equation to have no solution, the right-hand side of the equation must be equal to 3x plus a constant value that is not -4.

By setting the equation to 3x + 5, for example, you ensure there can be no value of x that will satisfy the equation because when you attempt to solve it, you'll reach a contradiction.

Here's the detailed transformation:

Start with 3 (x - 4/3) = 3x + ?

Distribute the 3 to get 3x - 4 = 3x + ?

To ensure no solution, choose a constant that is not -4, for example, +5, to get 3x - 4 = 3x + 5

Subtract 3x from both sides to attempt to solve for x: -4 ≠ 5, which is clearly a contradiction, indicating no solution.

When the boat has made 35 tours, the train will have made 56 tours, based on the ratio 8 train tours for every 5 boat tours.

The question involves calculating the number of train tours when a given number of boat tours is reached, utilising basic multiplication and ratios. Since there are 5 boat tours and 8 train tours per day, for every boat tour, there are 8/5 train tours. To find out the number of train tours when there have been 35 boat tours, we multiply 35 by 8/5 which equals 56.

Here is the table showing the boat to train tour ratios:

Boat Tours  5,10,15,20,25,30,35

Train Tours 8,16,24,32,40,48,56

Therefore, when the boat has made 35 tours, the train will have made 56 tours.

The mini laptop is on sale for 40% off, the discount is 40% of the regular price then the discount could be 180 dollar.

Third party discount is the multiplication result of the maturity value of the original rate to the rate of interest and time period.

Thus, we get:

Third party discount = Maturity value × R × T (R in decimal form).

WE have been given that the laptop is on sale for 40% off, the discount is 40% of the regular price.

Since they are asking for the discount and not the discounted price.

Discount

= 40% ×$450

= ⅖ ×$450

= $180

Thus, the option c is correct.

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Answer:

The odds against winning the game is 3 to 1.

Step-by-step explanation:

*Probability states that it is the likelihood of something happening in the future.

*Its value lie between 0 and 1.

*complement of an event is that event that is not occurring .

Then, the probability of  Event A will not occur is denoted by P(A').

Given:

The probability of winning a particular game at game place is [tex]\frac{1}{4}[/tex]

or we can write this as P(X) = [tex]\frac{1}{4}[/tex] where X is winning a particular game  at game place.

To find the odds against winning the game:

P(X') = P(Not winning a game) = 1-P(X) = [tex]1-\frac{1}{4} = \frac{4-1}{4} =\frac{3}{4}[/tex]

Now, we have

the probability of winning is [tex]\frac{1}{4}[/tex] = 25%

and the probability of not winning is [tex]\frac{3}{4}[/tex] = 75%

Therefore, odds against winning is (chances against success) : (chances for success) =  3 to 1 or 3 : 1

The following best describes the location of lake Eyre as it relates to sea level is -50. Therefore, option D is the correct answer.

Given that, Lake Eyre in Australia is approximately 50 feet below sea level.

Mean sea level is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured.

Now, if the surface sea level is 0.

50 feet below sea level = 0-50=-50

The following best describes the location of lake Eyre as it relates to sea level is -50. Therefore, option D is the correct answer.

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Answer:

[tex]w=-1[/tex].

Step-by-step explanation:

We have been given an equation [tex]2w-5(w+1)=3w+1[/tex]. We are asked the equation for w.

Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:

[tex]2w-5w-5=3w+1[/tex]

[tex]-3w-5=3w+1[/tex]

Subtract 3w from both sides:

[tex]-3w-3w-5=3w-3w+1[/tex]

[tex]-3w-3w-5=1[/tex]

Combine like terms:

[tex]-6w-5=1[/tex]

Add 5 on both sides:

[tex]-6w-5+5=1+5[/tex]

[tex]-6w=6[/tex]

Divide both sides by -6:

[tex]\frac{-6w}{-6}=\frac{6}{-6}[/tex]

[tex]w=-1[/tex]

Therefore, our required equation would be [tex]w=-1[/tex].

vertical angles equal each other

 so you have

9x+12 = 3x +24

subtract 12 from each side:

9x = 3x+12

 subtract 3x from each side:

6x = 12

 divide both sides by 6

 x = 12/6

x = 2

Answer:

its a

Step-by-step explanation:

Barney should get 2 as his answer.Ana's result implies  N = 2.Therefore, when Barney multiplies the same numberN  by 8, he should get 16 as his answer.

Ana's result implies that [tex]\( N \div 8 = 0.25 \).[/tex] To find the original number N we can multiply both sides by 8:

[tex]\[ N = 0.25 \times 8 = 2 \][/tex]

Therefore, the original number Nis 2. Now, Barney is asked to multiply the same number N by 8.

[tex]\[ \text{Barney's result} = N \times 8 = 2 \times 8 = 16 \][/tex]

Hence, Barney should get 16 as his answer.

In summary, Ana's division of N  by 8 resulting in 0.25 implies that the original number  N  is 2. When Barney multiplies this number by 8, he should get 16 as the final answer.

It's important to note that Ana's division and Barney's multiplication are inverse operations. Ana divided by 8, and to undo that operation, we multiply by 8. This concept is fundamental in algebraic reasoning, where operations can be reversed by applying their inverse operations. In this case, understanding the relationship between division and multiplication allows us to determine the value of the original number and predict the outcome of Barney's multiplication.

The total length of string needed to decorate 17 identical decorative bottle is 3570 cm or 35.7 m

Given:

Question

Total length of string needed for 17 identical decorative bottle?

String A = 35

String B = 5 x string A

            = 5 x 35

            = 175 cm

String B = 175 cm

We need to calculate total string needed for 1 decorative bottle

= String A + String B

= 35 cm + 175 cm

= 210 cm

The total length to decorate one bottle is 210 cm

To decorate 17 identical bottles, it would need:

= 210 x 17

= 3570 cm

Here is to solve the multiplication in standard algorithm method:

   21

  17  x

 147

 21     +

357

then adding the zero = 3570

To simplify the multiplication we just do the two digit numbers and then adding the zero later in the answer,

So,  the total string needed for 17  identical decorative bottle is 3570 cm or 35.7 m

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