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jasenka
2 months ago
12

Bob thought of an even and odd number, multiplies the numbers together, added 6, divided by 5, and subtracted 3 to give an answe

r of 1. What was the odd number he started with?
Mathematics
1 answer:
babunello [11.8K]2 months ago
7 0
7. Step-by-step explanation: By working backward, we determine Bob's initial product. Since we subtracted 3 to arrive at 1, his earlier total was 4. Dividing by 5 resulted in 4, indicating his original value was 20. Adding 6 to that gives us 14. We know that the multiplication of two numbers totals 14, specifically between 2 and 7, making the odd number 7.
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Ruben bought 6 new books for his collection. This increased his collection by 12%. How many books did he have before his purchas
tester [12383]

Response: Ruben initially possessed 50 books before making any purchases.

Explanation in steps: Ruben's acquisition of 6 new books led to a 12% increase in his collection.

We aim to determine the quantity of books Ruben had prior to his recent purchases.

Let x represent the original count of books Ruben held before buying more.

Based on the provided data, we derive the following equation:

x+6=x+12\%\times x\\\\\\\Rightarrow 6=\dfrac{12}{100}x\\\\\\\Rightarrow 6=\dfrac{3x}{25}\\\\\\\Rightarrow 3x=150\\\\\Rightarrow x=\dfrac{150}{3}\\\\\Rightarrow x=50.

Consequently, the original number of books Ruben had before making additional purchases equals 50.

4 0
2 months ago
One hundred teachers attended a seminar on mathematical problem solving. The attitudes of representative sample of 12 of the tea
Svet_ta [12734]

Answer:

a) 1.92

b) 3.25

c) 1.5

d) -5.23

Step-by-step explanation:

We are provided with the following in the question:

4, 7, -1, 1, 0, 5, -2, 2, -1, 6, 5, -3

a) mean change score

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle\frac{23}{12} = 1.92

b) standard deviation for the population

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n}}

where x_i represents data points, \bar{x} is the average, and n denotes the count of observations.

Sum of squared deviations = 126.92

\sigma = \sqrt{\frac{126.92}{12}} = 3.25

c) median change score

Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}

Arranged data: -3, -2, -1, -1, 0, 1, 2, 4, 5, 5, 6, 7

Median equal to

\dfrac{6^{th} + 7^{th}}{2} = \dfrac{1+2}{2} = 1.5

d) change score that is 2.2 standard deviations lower than the mean.

x = \mu - 2.2(\sigma)\\x = 1.92-2.2(3.25)\\x = -5.23

4 0
2 months ago
Find the inverse of y=x2-10x
AnnZ [12381]
<span>This is quite challenging, but here’s the solution:
</span>

y = x^2 - 10x + 25 - 25

<span> y = (x-5)^2 - 25</span>

<span> y + 25 = (x-5)^2</span>

<span> x - 5 = ±sqrt(y+25)</span>

 

<span> You will derive TWO inverses:</span>

 

<span> x = 5 + sqrt(y+25),</span> for x ≥ 5

<span> x = 5 - sqrt(y+25),</span> for x ≤ 5


5 0
3 months ago
Read 2 more answers
Karl records the number of city blocks from his house to each of his friends houses. which statement is supported by the data?
AnnZ [12381]

Response:

Thorough analysis:

I believe that option 4 is the right choice

5 0
3 months ago
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