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Anettt [7]
2 years ago
4

Lance and alex have 70 pencils. Lance has 4 times as many pencils as alex. Alexs pencils are shared equally among 2 children. Ho

w many pencils does each child get?
Mathematics
1 answer:
Kamila [148]2 years ago
8 0
The total number of pencils that Lance and Alex have = 70
Let us assume the number of pencils that Alex has = x
Then
The number of pencils that Lance has = 4x
So, the equation can be written as
x + 4x = 70
5x = 70
x = 70/5
   = 14
So from the above deduction we can say that Alex has a total of 14 pencils. Now the number of pencils that Alex have is divided equally among two children.
Then
The number of pencils that each children has = 14/2
                                                                          = 7
So each child gets 7 pencils.
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23) An extension ladder forming a 60° angle with the ground is placed against
Pachacha [2.7K]

Answer: the length of the extended ladder is 8√3 feet or 13.9 feet

the distance between the wall and the bottom of the ladder is 4√3 feet or 6.9 feet

Step-by-step explanation:

The ladder forms a right angle triangle with the building and the ground. The length of the ladder represents the hypotenuse of the right angle triangle. The height from the top of the ladder to the base of the building represents the opposite side of the right angle triangle.

The distance from the bottom of the ladder to the base of the building represents the adjacent side of the right angle triangle.

To determine the extended length of the ladder h, we would apply

the Sine trigonometric ratio.

Sin θ = opposite side/hypotenuse. Therefore,

Sin 60 = 12/h

√3/2 = 12/h

h = 12 × 2/√3 = 24√3

h = 24√3 × √3/√3

h = 8√3

To determine the distance between the wall and the bottom of the ladder d, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse.

Therefore,

Cos 60 = d/8√3

0.5 = d/8√3

d = 0.5 × 8√3

d = 4√3

3 0
2 years ago
Alice has a 4-inch by 5-inch photo of your school’s championship girls’ ice hockey team. To celebrate their recent
Pachacha [2.7K]

Alice should pick the enlarged-photo with dimensions of 8-inch by 10-inch.

Step-by-step explanation:

Step 1:

In order for a part of the photo to not be cut off, the enlarged photo's dimensions should be of a constant ratio with the original photo's dimensions.

We divide the dimensions of the enlarged-photo with the dimensions of the original photo to check which has a constant ratio.

Step 2:

The original photo was a 4-inch by 5-inch photo.

Option 1 is 7-inch by 9-inch, so the ratios are

\frac{7}{4} = 1.75, \frac{9}{5} = 1.8. The ratios are different so this cannot be the enlarged photo's dimensions.

Option 2 is 8-inch by 10-inch, so the ratios are

\frac{8}{4} = 2, \frac{10}{5} = 2. The ratios are the same so this can be the enlarged photo's dimensions.

Option 3 is 12-inch by 16-inch, so the ratios are

\frac{12}{4} = 3, \frac{16}{5} = 3.2. The ratios are different so this cannot be the enlarged photo's dimensions.

So the enlarged-photo with dimensions of 8-inch by 10-inch should be picked.

7 0
2 years ago
A machine fills boxes weighing Y lb with X lb of salt, where X and Y are normal with mean 100 lb and 5 lb and standard deviation
Bas_tet [7]

Answer:

Option b. None is the correct option.

The Answer is 63%

Step-by-step explanation:

To solve for this question, we would be using the z score formula

The formula for calculating a z-score is given as:

z = (x-μ)/σ,

where

x is the raw score

μ is the population mean

σ is the population standard deviation.

We have boxes X and Y. So we will be combining both boxes

Mean of X = 100 lb

Mean of Y = 5 lb

Total mean = 100 + 5 = 105lb

Standard deviation for X = 1 lb

Standard deviation for Y = 0.5 lb

Remember Variance = Standard deviation ²

Variance for X = 1lb² = 1

Variance for Y = 0.5² = 0.25

Total variance = 1 + 0.25 = 1.25

Total standard deviation = √Total variance

= √1.25

Solving our question, we were asked to find the percent of filled boxes weighing between 104 lb and 106 lb are to be expected. Hence,

For 104lb

z = (x-μ)/σ,

z = 104 - 105 / √25

z = -0.89443

Using z score table ,

P( x = z)

P ( x = 104) = P( z = -0.89443) = 0.18555

For 1061b

z = (x-μ)/σ,

z = 106 - 105 / √25

z = 0.89443

Using z score table ,

P( x = z)

P ( x = 106) = P( z = 0.89443) = 0.81445

P(104 ≤ Z ≤ 106) = 0.81445 - 0.18555

= 0.6289

Converting to percentage, we have :

0.6289 × 100 = 62.89%

Approximately = 63 %

Therefore, the percent of filled boxes weighing between 104 lb and 106 lb that are to be expected is 63%

Since there is no 63% in the option, the correct answer is Option b. None.

3 0
2 years ago
Takuya's parents gave him $100dollar as a birthday gift. Since he loves board games, he spent $20dollar out of his present on bo
LUCKY_DIMON [66]

Answer:

To write a recursive formula you need to: First, determine if the sequence is geometric(For example, If your multiply, or divide, the same amount for one term or more). Next, Find the common ratio(In other words the number that you multiply or divide).

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Which of following lies between 0 and -1 ?
kogti [31]

Answer:

Step-by-step explanation:

There are many numbers that lie between 0 and -1

Some common numbers are -1/4 , -1/2 , -3/4 , etc.........

Other numbers can be found by multiplying the numerator and denominator by the same number for example, 10

0/1 × 10/10 = 0/10

-1/1 × 10/10 = -10/10

Now the numbers between 0/10 and -10/10 are :

-1/10, -2/10....................................-9/10 etc.

hope this helps

plz mark it as brainliest!!!!!!!

6 0
2 years ago
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