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Kay [80]
2 years ago
14

Aa if #2 wasn't confusing enough, laura is now trying to come up with a number where three less than 8 times the number is equal

to half of 16 times the number after it was increased by 1
Mathematics
1 answer:
umka21 [38]2 years ago
4 0

Answer: Laura cannot find the number, as explained below.


Explanation:


1) The question is aimed to determine the number that Laura is trying to come up with.


Such question is solved by stating an algebraic equation from the word statement, which is done step by step.


2) Using the name x for the unknown, the expression "three less than 8 times the number" is translated to: 8x - 3


3) The expression "half of 16 times the number after it was increased by 1" is translated to: (1/2) (16x + 1)


4) Finally, since they are equal, you can set the equation:


8x - 3 =  (1/2) (16x + 1)


5) And solve for x in this way:


i) Distributive property:

8x - 3 = 8x + 1/2


ii) At this stage you can see that the both 8x terms (on the left and on the right) cancel each other, which leads to the impossibility to determine the value of the unknown:

-3 = 1/2 which is alwasy false, meaning that the equation has no solution.

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On a recent road trip, Mr. Yost drove 210 miles in 3 1/2 hours. Find both the miles driven per hour and the hours driven per mil
amid [387]

Miles driven per hour is 60 miles per hour

Hours driven per mile is 0.01667 hours per mile

<em><u>Solution:</u></em>

Given that,

On a recent road trip, Mr. Yost drove 210 miles in 3 1/2 hours

Therefore,

Miles driven = 210 miles

Time\ taken = 3\frac{1}{2}\ hour = \frac{7}{2} = 3.5\ hour

To find: miles driven per hour and the hours driven per mile

<h3><u>Miles driven per hour</u></h3>

\frac{miles}{hour} = \frac{210}{3.5}\\\\\frac{miles}{hour} = 60\ miles\ per\ hour

<h3><u>Hours driven per mile</u></h3>

\frac{hours}{miles} = \frac{3.5}{210}\\\\\frac{hours}{miles} = 0.01667\ hours\ per\ miles

Thus both the miles driven per hour and the hours driven per mile are found

7 0
2 years ago
A researcher evaluates the significance of a multiple-regression equation and obtains an F-ratio with df = 2,24. How many partic
alisha [4.7K]

Answer:

N=27 participants

Step-by-step explanation:

Analysis of variance (ANOVA) "is used to analyze the differences among group means in a sample".  

The sum of squares "is the sum of the square of variation, where variation is defined as the spread between each individual value and the grand mean"  

When we conduct a multiple regression we want to know about the relationship between several independent or predictor variables and a dependent or criterion variable.

If we assume that we have k independent variables and we have  j=1,\dots,j individuals, we can define the following formulas of variation:  

SS_{total}=\sum_{j=1}^n (y_j-\bar y)^2  

SS_{regression}=SS_{model}=\sum_{j=1}^n (\hat y_{j}-\bar y)^2  

SS_{error}=\sum_{j=1}^n (y_{j}-\hat y_j)^2  

And we have this property  

SST=SS_{regression}+SS_{error}  

The degrees of freedom for the model on this case is given by df_{model}=df_{regression}=k=2 where k =2 represent the number of variables.

The degrees of freedom for the error on this case is given by df_{error}=N-k-1=24. Sinc we know k we can find N.

N=24+k+1=24+2+1=27

And the total degrees of freedom would be df=N-1=27 -1 =26

On this case the correct answer would be N=27 participants

6 0
2 years ago
Subtract. (8u - 2v + 7w) and (5u + v + 6w)
KiRa [710]

Answer:

c)3u-3v-w

Step-by-step explanation:

5 0
2 years ago
A square rotated about its center by 360º maps onto itself at(1,2,3,4) different angles of rotation. You can reflect a square on
Sladkaya [172]

A square rotated about its center by 360º maps onto itself at 90°, 180°, 270° and 360° - 4 different angles of rotation.

You can reflect a square onto itself across two diagonals and two segments that connects the middlepoints of opposite sides - 4 different lines of reflection.

7 0
2 years ago
If i = StartRoot negative 1 EndRoot, what is the value of i 3? –1 i 1 –i
Annette [7]

Answer:

-i

Step-by-step explanation:

Our number is i = √-1, and we want to find i³, which is essentially just i * i * i, so:

i³ = i * i * i = √-1 * √-1 * √-1 = -1 * √-1 = -1 * i = -i

The answer is -i.

5 0
2 years ago
Read 2 more answers
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