Given that $a$ is an odd multiple of $7767$, find the greatest common divisor of $6a^2+49a+108$ and $2a+9$.

Determine the input value for which the statement f(x) = g(x) is true. From the graph, the input value is approximately_______ .

Julli [10]

In this question , we have a graph given, and we have to find the x coordinate of the intersection point .

From the graph , the input value is approximately 3.3 .

In the graph,

$f(x) =3$

And for g(x), we need the slope and y intercept .

Slope is the ratio of rise and run .

Here rise equals 3 units and run equals 2 units. And the graph touch the y axis at -2 .

So the equation of g(x) is

$g(x) = \frac{3}{2}x -2$

We need to do

$f(x)= g(x)$

Substituting the values of the two functions, we will get

$3 = \frac{3}{2}x -2$

Adding 2 to both sides

$5 = \frac{3}{2}x$

Cross multiplication

$10 =3x
\\
x = \frac{10}{3}$

$x = 3.3$

So the input value is 3.3 approx

6 0

1 year ago

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Which data sets have outliers? Check all that apply.

Alex Ar [27]

Answer:

(B), (D) and (E)

Step-by-step explanation:

An outlier is an observation which is quite different or very far from the rest of the given values of the data set.

(A) The given data set is:

14, 21, 24, 25, 27, 32, 35

Since, in the given data set, the values ranges from 14 to 35 in which no outlier is present, thus this data set does not contain any outlier.

thus, this option is incorrect.

(B) The given data set is:

15, 30, 35, 41, 44, 50, 78

In this data set, 78 is an outlier since it is quite far from the rest of the given data values, thus this option is correct.

(C) The given data set is:

16, 32, 38, 39, 41, 42, 58

In the given data set, there is no outlier present, thus this option is incorrect.

(D) The given data set is:

17, 23, 28, 31, 39, 45, 75

In this data set, 75 is an outlier since it is quite far from the rest of the given data values, thus this option is correct.

(E) The given data set is:

18, 30, 34, 38, 43, 45, 68

In this data set, 68 is an outlier since it is quite far from the rest of the given data values, thus this option is correct.

7 0

2 years ago

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Last year your professor wanted to study the pattern in class grades. The following table contains a sample of grades collected

Maslowich

Answer:

mean = 78.4

median = 77.5

mode = 75

This is Right - skewed (positive skewness) distribution

Step-by-step explanation:

Mean:-

The mean (average) is found by adding all of the numbers together and dividing by the number of items and it is denoted by x⁻

mean = $\frac{64+80+75+98+75}{5}$

mean (x⁻ ) = 78.4

The mean of the given data = 78.4

Median:

The median is found by ordering the set from lowest to highest and finding the exact middle.

64 ,75, 80, 98

The middle term of the given data set = $\frac{75+80}{2} =77.5$

Mode :

The mode is the most common repeated number in a data set.

64 ,75, 75, 80, 98

in data the most common number = 75

Conclusion:-

mean = 78.4

median = 77.5

mode = 75

This is Right - skewed (positive skewness) distribution

8 0

1 year ago

Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 1

BigorU [14]

Answer:

a: Sample mean: 20, Sample standard deviation: 1.732

b: 19.13 <µ < 20.87

c: 18.84< µ < 21.16

d: as the confidence level increases, the interval becomes wider

Step-by-step explanation:

a: Sample mean is found by adding up all the individual values of the sample, then dividing by the total number of values in the sample.

Sample standard deviation is the square root of the variance

See the first attached photo for the calculations of these values.

We need to create a 80% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.

Look for the column on the t-distribution chart that has "area in two tails" of 0.20 (80%), and row 7 (degree of freedom)

The t-value is 1.415

See the second attached photo for the construction of the confidence interval

We need to create a 90% confidence interval for the population. Since n < 30, we will use a t-value with degree of freedom of 7 (the degree of freedom is always one less than the sample size.

Look for the column on the t-distribution chart that has "area in two tails" of 0.10 (90%), and row 7 (degree of freedom)

The t-value is 1.895

See the third attached photo for the construction of the confidence interval

3 0

2 years ago

Grandpa ernie is shrinking! Over the past 4 years, his hight decressed by a total of 2.4cm. It decresed by the same amount each

dolphi86 [110]

Answer: 0.6 cm

Step-by-step explanation:

Given : Over the past 4 years, Grandpa Ernie's height decreased by a total of 2.4 cm.

If the height is decreased by the same amount each year.

Then, the change in Grandpa Ernie's height each year will be =

Total decrease in height ÷ 4

= 2.4 cm ÷ 4 = 0.6 cm

Hence, the change in Grandpa Ernie's height each year = 0.6 cm

4 0

1 year ago

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