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3 years ago

10

Mathematics

1 answer:

Novay_Z [31]3 years ago

5 0

Answer:

The sequence of transformations that maps ΔABC to ΔA'B'C' is the reflection across the line y = x and a translation 10 units right and 4 units up, equivalent to T₍₁₀, ₄₎

Step-by-step explanation:

For a reflection across the line y = -x, we have, (x, y) → (y, x)

Therefore, the point of the preimage A(-6, 2) before the reflection, becomes the point A''(2, -6) after the reflection across the line y = -x

The translation from the point A''(2, -6) to the point A'(12, -2) is T(10, 4)

Given that rotation and translation transformations are rigid transformations, the transformations that maps point A to A' will also map points B and C to points B' and C'

Therefore, a sequence of transformation maps ΔABC to ΔA'B'C'. The sequence of transformations that maps ΔABC to ΔA'B'C' is the reflection across the line y = x and a translation 10 units right and 4 units up, which is T₍₁₀, ₄₎

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Part I: Marco rented a small moving van. The moving company charges $40 a day for up to 5 days. The input is the time, in days,

Snezhnost [94]

Given mapping is a function.

Domain: $\{1,2,3,4,5\}$

Range: $\{40,80,120,160,200\}$

Step-by-step explanation:

By observing Marco's mapping diagram we can see that every value in time is mapped to only one value in the cost. This means that there will be no repetition or same output to two different outputs so given mapping is a function.

Domain:

Domain is the set of all inputs of a function. Here time is input so domain of function is:

$\{1,2,3,4,5\}$

Range:

Range is the set of all outputs of the function on domain so the range of the given function is:

$\{40,80,120,160,200\}$

Hence,

Given mapping is a function.

Domain: $\{1,2,3,4,5\}$

Range: $\{40,80,120,160,200\}$

Keywords: Domain, range, function

Learn more about function at:

#LearnwithBrainly

7 0

3 years ago

.21 of what number is 7.98

AlladinOne [14]

.21 as a percentage is 21%
You can divide 7.98 by 21 then multiply by 100 which gives you an answer of 38.

Hope this helps :)

8 0

3 years ago

In a completely randomized experimental design, three brands of paper towels were tested for their ability to absorb water. Equa

arlik [135]

Answer:

Yes. At this significance level, there is evidence to support the claim that there is a difference in the ability of the brands to absorb water.

Step-by-step explanation:

The question is incomplete:

The significance level is 0.05.

The data is:

Brand X: 91, 100, 88, 89

Brand Y: 99, 96, 94, 99

Brand Z: 83, 88, 89, 76

We have to check if there is a significant difference between the absorbency rating of each brand.

Null hypothesis: all means are equal

$H_0:\mu_x=\mu_y=\mu_z$

Alternative hypothesis: the means are not equal

$H_a: \mu_x\neq\mu_y\neq\mu_z$

We have to apply a one-way ANOVA

We start by calculating the standard deviation for each brand:

$s_x^2=30,\,\,s_y^2=6,\,\,s_z^2=35.33$

Then, we calculate the mean standard error (MSE):

$MSE=(\sum s_i^2)/a=(30+6+35.33)/3=71.33/3=23.78$

Now, we calculate the mean square between (MSB), but we previously have to know the sample means and the mean of the sample means:

$M_x=92,\,\,M_y=97,\,\,M_z=84\\\\M=(92+97+84)/3=91$

The MSB is then:

$s^2=\dfrac{\sum(M_i-M)^2}{N-1}\\\\\\s^2=\dfrac{(92-91)^2+(97-91)^2+(84-91)^2}{3-1}\\\\\\s^2=\dfrac{1+36+49}{2}=\dfrac{86}{2}=43\\\\\\\\MSB=ns^2=4*43=172$