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2 years ago

Given the image below, what is the image of C after a dilation with a scale factor of 3

Mathematics

1 answer:

Ne4ueva [31]2 years ago

6 0

Answer: The coordinates of point C after the dilation are (-2, 5)

Step-by-step explanation:

I guess that you want to find where the point C ends after the dilation.

Ok, if we have a point (x, y) and we do a dilation with a scale A around the point (a,b), then the dilated point will be:

(a + A*(x - a), b + A*(y - b))

In this case we have:

(a,b) = (2,1) and A = 3.

And the coordinates of point C, before being dilated, are: (1, 2)

Then the new location of the point C will be:

C' = (1 + 3*(1 - 2), 2 + 3*(2 - 1)) = (1 -3, 2 + 3) = (-2, 5)

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The grade point average (GPA) of the students at Lakeview High School is normally distributed with a mean of 3.1 and a standard

Morgarella [4.7K]

Approximately 1718 have a score within that range.

We calculate the z-score for each end of this spectrum:

z = (X-μ)/σ = (2.5-3.1)/0.3 = -0.6/0.3 = -2

Using a z-table (http://www.z-table.com) we see that the area to the left of, less than, this z-score is 0.0228.

For the upper end:
z = (3.7-3.1)/0.3 = 0.6/0.3 = 2

Using a z-table, we see that the area to the left of, less than, this z-score is 0.9772.

The probability between these is given by subtracting these:
0.9772 - 0.0228 = 0.9544.

This means the proportion of people that should fall between these is 0.9544:
0.9544*1800 = 1717.92 ≈ 1718

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2 years ago

A standard weight known to weigh 10 grams. Some suspect bias in weights due to manufacturing process. To assess the accuracy of

notsponge [240]

Answer:

a) The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams

b) 49 measurements are needed.

Step-by-step explanation:

Question a:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1 - 0.98}{2} = 0.01$

Now, we have to find z in the Ztable as such z has a pvalue of $1 - \alpha$ .

That is z with a pvalue of $1 - 0.01 = 0.99$ , so Z = 2.327.

Now, find the margin of error M as such

$M = z\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 2.327\frac{0.0003}{\sqrt{5}} = 0.00031$

The lower end of the interval is the sample mean subtracted by M. So it is 10.0044 - 0.00031 = 10.00409 grams

The upper end of the interval is the sample mean added to M. So it is 10 + 0.00031 = 10.00471 grams

The 98% confidence interval for the mean weight is between 10.00409 grams and 10.00471 grams.

(b) How many measurements must be averaged to get a margin of error of +/- 0.0001 with 98% confidence?

We have to find n for which M = 0.0001. So

$M = z\frac{\sigma}{\sqrt{n}}$

$0.0001 = 2.327\frac{0.0003}{\sqrt{n}}$

$0.0001\sqrt{n} = 2.327*0.0003$

$\sqrt{n} = \frac{2.327*0.0003}{0.0001}$

$(\sqrt{n})^2 = (\frac{2.327*0.0003}{0.0001})^2$

$n = 48.73$

Rounding up

49 measurements are needed.

7 0

1 year ago

Mike has a net spendable income of $1,400. He decides to set up a budget before looking for an apartment or a car. He sets up hi

KATRIN_1 [288]

This budget might be a problem because Mike is using the minimum recommended percentages for food, housing, and transportation. He prepared the biggest sum for entertainment, putting the basic needs under the disadvantage and forgetting about medical emergencies. Therefore, in the end of month there is a strong possibility that he will find out he organized his budget in a wrong way.

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1 year ago

Modern Vehicles Company came up with two different plans for the next financial year. Plan Y: Increase vehicle production by 5%

ladessa [460]

Answer: plan Y will produce more vehicles after 4 years.

Step-by-step explanation:

1) Plan Y: Increase vehicle production by 5% every year. It means that the rate of production is in geometric progression. The formula for determining the sum of n terms, Sn of a geometric sequence is expressed as

Sn = (ar^n - 1)/(r - 1)

Where

n represents the number of term(years) in the sequence.

a represents the first term(number of vehicles in the present year) in the sequence.

r represents the common ratio.

From the information given,

a = 10000

r = 1 + 5/100 = 1.05

n = 4 years

Therefore, the sum of the vehicles produced in the first 4 years, S4 is

S4 = (10000 × 1.05^(4) - 1)/1.05 - 1

S4 = (10000 × 0.21550625)/0.05

S4 = 2155.0625/0.05

S4 = 43101 vehicles

2) Plan Z: Increase production by 300 vehicles every year. It means that the rate of production is in geometric progression. The formula for determining the sum of n terms of an arithmetic sequence is expressed as

Sn = n/2[2a + (n - 1)d]

Where

n represents the number of terms in the arithmetic sequence.

d represents the common difference of the terms in the arithmetic sequence.

a represents the first term of the arithmetic sequence.

From the information given,

n = 4 years

a = 10000

d = 300

Therefore, the sum of the first 4 terms, S4 would be

S4 = 4/2[10000 × 2 + (4 - 1)300]

S4 = 2[20000 + (3)300]

S4 = 2 × 20900

S4 = 41800 vehicles

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2 years ago

Which function represents g(x), a reflection of f(x) = On a coordinate plane, 2 exponential functions are shown. g (x) decreases

Vanyuwa [196]

Answer:

$g(x)=\frac{1}{2}(3^{-x})$

Step-by-step explanation:

Given:

The graph of function $f(x)\ and\ g(x)$ are given.

The equation for $f(x)$ is given as:

$f(x)=3^x$

Now, the graph of $g(x)$ is a reflection of $f(x)$ .

The graph of $g(x)$ passes through the point (-1, 1.5) [second quadrant] and crosses the y-axis at (0, 0.5).

As evident from the graph, the functions $f(x)\ and\ g(x)$ are reflections about the y-axis.

We know the transformation rule for reflection about the y-axis as:

$f(x)\to f(-x)\\\\\therefore 3^x\to3^{-x}....(\textrm{Reflection about y-axis})$

Now, the y-intercept of the function $y=3^{-x}$ is obtained by plugging in $x=0$ . This gives,

$y=3^0=1$

So, the y-intercept is at (0, 1). But the graph of $g(x)$ crosses the y-axis at (0, 0.5). As we observe, the coordinate rule for the transformation can be written as:

(0, 1) → (0, 0.5)

$(x,y)\to (x,\frac{1}{2}y)$

So, the reflected graph is compressed vertically by a factor of $\frac{1}{2}$ .

Therefore, the transformation is given as:

$y\to \frac{1}{2}y\\\\\therefore 3^{-x}\to \frac{1}{2}(3^{-x})$

Therefore, the equation for $g(x)$ is:

$g(x)=\frac{1}{2}(3^{-x})$

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2 years ago

Read 3 more answers