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2 years ago

If trapezoid JKLM with vertices) (3, 4), K (6,4), L (8, 1) and M (1,1) is rotated 270 degrees counterclockwise, what are the

Mathematics

1 answer:

Stels [109]2 years ago

7 0

Answer:

$J' = (4,-3)$

Step-by-step explanation:

Given

$J = (3, 4)$

$K =(6,4)$

$L = (8, 1)$

$M = (1,1)$

$Rotation = 270CCW$

Required

Determine the new coordinate of J

From rules of rotation,

When a point (x,y) is rotated 270 degrees CCW;

The new point becomes (y,-x)

Considering point J

$J = (3, 4)$

This means

$(x,y) = (3,4)$

Where $x = 3$ and $y = 4$

Using the above rotation rule of

$(x,y) -> (y,-x)$

The coordinates of J' becomes

$J' = (4,-3)$

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) Tara earns twice as much per hour as Kayte.

Cerrena [4.2K]

Answer:

Austin's hourly wage is $8.

Step-by-step explanation:

This question can be solved using a system of equations.

I am going to say that:

Tara's hourly wage is x.

Kayte's hourly wage is y.

Austin's hourly wage is z.

Tara earns twice as much per hour as Kayte.

This means that $x = 2y$

Kayte earns $3 more per hour than Austin.

This means that $y = z + 3$

As a group, they earn $41 per hour.

This means that $x + y + z = 41$

What is Austin's hourly wage?

This is z.

$x + y + z = 41$

$y = z + 3$ and $x = 2y$ , so $x = 2(z + 3) = 2z + 6$

$x + y + z = 41$

$2z + 6 + z + 3 + z = 41$

$4z + 9 = 41$

$4z = 32$

$z = \frac{32}{4}$

$z = 8$

Austin's hourly wage is $8.

5 0

2 years ago

Read 2 more answers

Aubrey and Charlie are driving to a city that is 120 mi from their house. They have already traveled 20 mi, and they are driving

sineoko [7]

<span>D=20+50t 120=20+50t 50t=100 t=2 hours Domain of t from t=-(2/5)hr to t=2hr. Since they already drove 20 miles. [-2/5,2]</span>

5 0

2 years ago

The value of good wine increases with age. Thus, if you are a wine dealer, you have the problem of deciding whether to sell your

Katyanochek1 [597]

Answer: 64 years

Step-by-step explanation:

Let assume the dealer sold the bottle now for $P, then invested that money at 5% interest. The return would be:

R1 = P(1.05)^t,

This means that after t years, the dealer would have the total amount of:

$P×1.05^t.

If the dealer prefer to wait for t years from now to sell the bottle of wine, then he will get the return of:

R2 = $P(1 + 20).

The value of t which will make both returns equal, will be;

R1 = R2.

P×1.05^t = P(1+20)

P will cancel out

1.05^t = 21

Log both sides

Log1.05^t = Log21

tLog1.05 = Log21

t = Log21/Log1.05

t = 64 years

The best time to sell the wine is therefore 64years from now.

7 0

2 years ago

Bodhi has a collection of 175 dimes and nickels. The collection is worth $13.30. Which equation can be used to find n, the numbe

Ede4ka [16]

Answer:

N + D = 175

.05N + .10D = $13.30

Step-by-step explanation:

You need a system of equations to get the correct answer that applies to both constraints.

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2 years ago

Read 2 more answers

It is believed that as many as 23% of adults over 50 never graduated from high school. We wish to see if this percentage is the

JulijaS [17]

Answer:

1) n=48

2) n=298

3) n=426

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$p$ represent the real population proportion of interest

$\hat p$ represent the estimated proportion for the sample

n is the sample size required (variable of interest)

$z$ represent the critical value for the margin of error

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

Part 1

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.90=0.10$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=-1.64, z_{1-\alpha/2}=1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.1$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

We can assume that the estimated proportion is 0.23 for the 25 to 30 group. And replacing into equation (b) the values from part a we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.1}{1.64})^2}=47.63$

And rounded up we have that n=48

Part 2

The margin of error on this case changes to 0.04 so if we use the same formula but changing the value for ME we got:

$n=\frac{0.23(1-0.23)}{(\frac{0.04}{1.64})^2}=297.7$

And rounded up we have that n=298

Part 3

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by $\alpha=1-0.95=0.05$ and $\alpha/2 =0.025$ . And the critical value would be given by: