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2 years ago

3 Ximena draws an X shape in the coordinate plane as shown. Draw the images of

Mathematics

1 answer:

VARVARA [1.3K]2 years ago

3 0

When a shape is rotated, it must be rotated around a point.

<em>See attachment for the image of each rotation.</em>

To do this, the top coordinates of the X shape will be transformed using the appropriate rotation rule; the same rule will then be applied to the other parts of the X shape.

The top coordinates of the X shape are:

$A = (0,0)$

$B = (1,0)$

$C = (3,0)$

$D =(4,0)$

For 90 degrees counterclockwise rotation, the rule is:

$(x,y) \to (-y,x)$

So, we have:

$A' = (0,0)$

$B' = (0,1)$

$C' = (0,3)$

$D' = (0,4)$

For 180 degrees rotation, the rule is:

$(x,y) \to (-x,-y)$

So, we have:

$A' = (0,0)$

$B' = (-1,0)$

$C' = (-3,0)$

$D' = (-4,0)$

For 270 degrees counter rotation, the rule is:

$(x,y) \to (y,-x)$

So, we have:

$A' = (0,0)$

$B' = (0,-1)$

$C' = (0,-3)$

$D' = (0,-4)$

See attachment for the image of each rotation

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While sitting on a rooftop 95 feet off the ground Mary flicks a twig up and off of the ledge with the initial vertical velocity

cestrela7 [59]

Answer:

The maximum height of the twig is 96.6 feet off the ground

Step-by-step explanation:

To determine the maximum height of the twig,

First, we will determine the height distance covered by the twig after Mary flicks the twig up.

From the question,

Mary flicks a twig up and off of the ledge with the initial vertical velocity of 10 feet per second, that is

the initial velocity of the twig is 10 feet/second

At maximum height, the final velocity is 0

From on the equations of motions for bodies moving upwards,

v² = u² - 2gh

Where v is the final velocity

u is the initial velocity

g is the acceleration due to gravity (Take g = 9.8m/s² = 32.17 ft/s²)

and h is the height

From the question

u = 10 feet/second

and v = 0 feet/second

Putting the values into the equation

v² = u² - 2gh

0² = 10² - 2(32.17)h

0 = 100 - 64.34h

64.34h = 100

h = 100/64.34

h = 1.6 feet

This is the height distance covered by the twig after Mary flicks it up.

Now, the maximum height of the twig will be the sum of the height of the rooftop from the ground and the height distance covered by the twig.

That is,

Maximum height = 95 feet + 1.6 feet

Maximum height = 96.6 feet

Hence, the maximum height of the twig is 96.6 feet off the ground.

7 0

3 years ago

Eric and Mark were at a ball game and visited the concession stand. They each got a hamburger, and Mark got lemonade and some co

EastWind [94]

So here is the answer. Given that both Eric and Mark got a hamburger which is $4 each. Mark got a lemonade and some cotton candy which costs $5.
So this gives them a total of $4, $4, $5, $?(lemonade). Partial sum is $13 without the lemonade. Since Eric got a $2, the total bill was deducted with $2 and the rest of the amount is $14.50. Therefore, the total bill would have been $16.50. So $16.50 minus $13 (partial sum) is $3.50. So the lemonade costs $3.50. Hope this helps.

3 0

3 years ago

In a random sample of males, it was found that 28 write with their left hands and 210 do not. In a random sample of females, it

Drupady [299]

Answer:

a) Null hypothesis: $p_{M} \geq p_{W}$

Alternative hypothesis: $p_{M} < p_{W}$

b) $z=\frac{0.118-0.125}{\sqrt{0.122(1-0.122)(\frac{1}{238}+\frac{1}{497})}}=-0.271$

c) $p_v =P(Z$

d) If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of men that write with their left hand is NOT significant lower than the proportion of female that write with their left hand

Step-by-step explanation:

1) Data given and notation

$X_{M}=28$ represent the number of men that write with their left hand

$X_{W}=62$ represent the number of women that write with their left hand

$n_{M}=210+28=238$ sample of male selected

$n_{W}=62+435=497$ sample of female selected

$p_{M}=\frac{28}{238}=0.118$ represent the proportion of men that write with their left hand

$p_{W}=\frac{62}{497}=0.125$ represent the proportion of women that write with their left hand

$\alpha=0.05$ represent the significance level

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the rate of left-handedness among males is less than that among females , the system of hypothesis would be:

Null hypothesis: $p_{M} \geq p_{W}$

Alternative hypothesis: $p_{M} < p_{W}$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{M}-p_{W}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{M}}+\frac{1}{n_{W}})}}$ (1)

Where $\hat p=\frac{X_{M}+X_{W}}{n_{M}+n_{W}}=\frac{28+62}{238+497}=0.122$

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.118-0.125}{\sqrt{0.122(1-0.122)(\frac{1}{238}+\frac{1}{497})}}=-0.271$

4) Statistical decision

We have a significance level provided $\alpha=0.05$ , and now we can calculate the p value for this test.

Since is a one left side test the p value would be:

$p_v =P(Z$

If we compare the p value and the significance level given $\alpha=0.05, 0,1,0.15$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can say the the proportion of men that write with their left hand is NOT significant loer than the proportion of female that write with their left hand .

6 0

2 years ago

ericka, a realestate agent, specializes in leasing apartments. her commision is 150% of her clients monthly rent. last week, she

Viefleur [7K]

Probably Erica is charging 150% of the first month of rental/leasing an apartment.

$850 being 150% of the rental/ lease for a month

the amount Erica's fee is based is $850×100:150=$566.(6)

5 0

2 years ago

Im dum on this but smart on other things look at points too...

Over [174]

Step-by-step explanation:

Whole numbers = Natural numbers + "0"

Integers = Whole numbers + Negative counterparts

Since the set do contains negative numbers, only Rational numbers and Integers are correct. (D)

4 0

2 years ago