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stepladder [879]
3 years ago
14

Lucas' mom is eight years older than twice his age. The sum of their ages is 77. How old are Lucas and his mom?

Mathematics
1 answer:
Rudiy273 years ago
3 0

Answer:

Age of Lucas = 23 years

Age of Lucas Mom = 54 Years

Step-by-step explanation:

In this question we have to find the age of Lucas and his Mom

Let the age of Lucas be x

According to given condition

Twice of his age 2 * x =2x

Eight years older means age + 8x

So

Age of his mom = Twice of his age + 8

                           = 2x + 8               .................(ii)

now according to second condition

Age of Lucas + Age of his mom = 77

Put the values in the condition above

x + (2x + 8) = 77

x + 2x + 8 =77

3x + 8 = 77

subtracting 8 from both sides

3x + 8 - 8 = 77 -8

3x = 69

Dividing both sides by 3

x = 69 / 3

x = 23 years

Age of Lucas = 23 years

Now from equation (i)

Age of Lucas Mom = 2(x) + 8

putting in the value we get

Age of Lucas Mom = 2 ( 23) + 8

                               =46 + 8

                               =54 Years

Age of Lucas Mom = 54 Years

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At the beginning of football season, Coach Carnes takes inventory of the team equipment to see what he needs. He counts 24 footb
Leviafan [203]

Answer:

13

Step-by-step explanation:

To solve this, lets first find the number of footballs he still needs:

75-24 = 51

Now to find the number of packages, divide by 4, since there are 4 balls per package:

51/4 = 12 Remainder 3

Since there is a remainder, and the Coach MUST have at least 75, then we need to add a package to include the remainder:

12 + 1 = 13 Packages

6 0
3 years ago
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time
kvasek [131]

Answer:

z(s) is in the acceptance region. We accept H₀  we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

Step-by-step explanation:

We must evaluate the differences of the means of the two machines, to do so, we will assume a CI  of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).

New machine

Sample mean                  x₁ =    25

Sample variance               s₁  = 27

Sample size                       n₁  = 45

Old machine

Sample mean                    x₂ =  23  

Sample variance               s₂  = 7,56

Sample size                       n₂  = 36

Test Hypothesis:

Null hypothesis                         H₀             x₂  -  x₁  = d = 0

Alternative hypothesis             Hₐ            x₂  -  x₁  <  0

CI = 90 %  ⇒  α =  10 %     α = 0,1      z(c) = - 1,28

To calculate z(s)

z(s)  =  ( x₂  -  x₁ ) / √s₁² / n₁  +  s₂² / n₂

s₁  = 27     ⇒    s₁²  =  729

n₁  = 45    ⇒   s₁² / n₁    = 16,2

s₂  = 7,56   ⇒    s₂²  = 57,15

n₂  = 36     ⇒    s₂² / n₂  =  1,5876

√s₁² / n₁  +  s₂² / n₂  =  √ 16,2  + 1.5876    = 4,2175

z(s) = (23 - 25 )/4,2175

z(s)  =  - 0,4742

Comparing z(s) and  z(c)

|z(s)| < | z(c)|  

z(s) is in the acceptance region. We accept H₀  we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean

3 0
3 years ago
-3x - 3y = 3 <br> y= -5x - 17
Kruka [31]

you first plug (substitute) in y

-3x - 3(-5x-17)=3

then distribute

-3x+15x+51=3

now combine like terms

12x+51=3

subtract to get 12x by itself

12x=3-51 or 12x=-48

lastly divide by 12 to find x

12x/12=-48/12

x=-4

now find y by plugging x into the other equation

y=-5(-4)-17

y=3

(-4,3)

4 0
3 years ago
How many centimeters are in 32 inches?
Anettt [7]

Step-by-step explanation:

12 inches = 30cm.

12 inches = 30cm.

8 inches = 20.3 cm

32 inches = 80.3 cm.

5 0
3 years ago
How do I solve without s calculator?
baherus [9]
You could solve it ( without a graph) in 2 easy ways :

1 use the equation that you have written in pencil and solve for y

y=3=-x+4
y=-x +1

Or you could use the point slop form after you find the y intercept y=mx+b


-3=4(-1)+b
b= 1

So the answer would be y= -x +1


Hope this help of it does feel free to give the brainliest

5 0
3 years ago
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