A carpenter has several boards of equal length. He cuts 3/5 of each board. After cutting the boards, the carpenter notices that he has enough pieces left over to make up the same length as 4 of the original boards. How many boards did the carpenter start with?

Answer:

more

Step-by-step explanation:

i know because i took the test 4 seconds ago

Answer:

9.81

Step-by-step explanation:

:3

Answer:

Hence, the set of values that holds true is:

2-3-4

Hence, option: D is true.

Step-by-step explanation:

We are asked to find which set of the values make the following inequality:

2x-1<10 true.

i..e we will put the given set of value s in place of xx and check whether the value of 2x-1 is less than 10 or not.

If it is then the set of values hold true.

A)

10-15-20

put x=10

2x-1=2×10-1

      =20-1

        =19 which is not less than 10.

Hence, option: A is incorrect.

B)

5-7-9

when x=9

2x-1=2×9-1

     =18-1

     =17 which is not less than 10.

Hence, option: B is incorrect.

C)

4-6-8

when x=8

2x-1=2×8-1

     =16-1

     =15 which is again not less than 10

Hence, option: C is incorrect.

D)

2-3-4

when x=2

2x-1=2×2-1

     =4-1

    =3<10

when x=3

2x-1=2×3-1

     =6-1

     =5 < 10

when x=4

2x-1=2×4-1

     =8-1

     =7<10

Hence, option: D is true.

Hence, the set of values that holds true is:

2-3-4

Final answer:

Saul needs to sell $2,750 worth of electronics in 22 hours to earn $12.50 per hour from a 10% sales commission.

Explanation:

To calculate how much Saul has to sell in 22 hours to earn $12.50 per hour from commission at a rate of 10%, we first determine his total earnings from commission over the 22 hours. So we multiply $12.50 by 22 hours, which gives us $275. Now, because the commission is 10%, we can write a simple equation where the total sales (which we'll call S) multiplied by 10% (or 0.10) equals $275.

The equation looks like this: S × 0.10 = $275. To solve for S, we divide both sides of the equation by 0.10: S = $275 / 0.10, which results in S = $2,750. Therefore, Saul has to sell $2,750 worth of electronics in 22 hours to earn an hourly wage of $12.50 from commission.

The formula for compound interest is given by:

[tex] A = P (1+\frac{r}{n})^{nt} [/tex]

where ,

A= Amount,

P=Principal

r=rate of interest

n= number of times interest is compounded per year

t = time ( in years)

Plugging the values ,

P = $12,000

r=0.06

t=6 years

n=1(annually compounded)

Plugging these in the formula,

[tex] A = 12000 (1+\frac{0.06}{1})^{1*6} [/tex]

A =$17022.229 which is approximately 17022.23

Answer: Amount is option B. $17022.23

Answer:

The percent increase in value of the baseball card is 66.667%

Step-by-step explanation:

You must first determine the amount of money increased by the value of an autographed baseball card.  For this you must subtract the price with the applied increase and the original price of the card: $65-$39=$26

This will be the amount of increase. Then, one way to calculate the percentage increase in the value of the baseball card is through a direct rule of three.

The rule of three or is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them. That is, what is intended with it is to find the fourth term of a proportion knowing the other three. Remember that proportionality is a constant relationship or ratio between different magnitudes.

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other  (Or when one magnitude decreases, so does the other), the direct rule of three must be applied. To solve a direct rule of three, the following formula must be followed:

a ⇒ b

c ⇒ x

Then

[tex]x=\frac{c*b}{a}[/tex]

In this case, the rule of three applies as follows: If the original price ($ 39) represents 100%, what is the value of the percentage in the value of the baseball card when its value increases $ 26?

[tex]percentage=\frac{26*100}{39}[/tex]

percentage=66.667%

Another way of thinking about it is considering that:

change from the original price = percentage of change*original price

In this case: $26=percentage of change*$39

So, isolating the percentage of change you get:

[tex]percentage of change=\frac{26}{39} =0.66667[/tex]

This value is expressed in decimal, and for it to be expressed in fraction you must multiply it by 100 (100%). Then you get:

percentage of change=0.66667*100%

percentage of change=66.667%

Note that the value obtained is the same as in the previous case, so both ways of thinking the solution to this problem is correct

Finally, the percent increase in value of the baseball card is 66.667%

The image of the triangle undergoes a transformation: (x, y) ⇒ [-(1/2)y - 2, (1/2)x + 4]

Dilation is a process for creating similar figures by changing the size.

A graph can be defined as a pictorial representation or a diagram that represents data or values.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions on the actual figure or object.

Transformation is the movement of a point from its initial location to a new location. Types of transformation include translation, reflection, rotation and dilation.

If a point A(x, y) is dilated by a factor p, the new point is at A'(px, py).

If a point A(x, y) is reflected over the x-axis, the new point is at A'(x, -y).

If a point A(x, y) is translated a units left and b units up, the new point is at A'(x - a, y + b).

The image of the triangle undergoes a transformation: (x, y) ⇒ [-(1/2)y - 2, (1/2)x + 4]

Learn more about Dilation here :

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