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Reika [66]
3 years ago
15

Please help! Giving Brainliest for the best answer!

Mathematics
1 answer:
klasskru [66]3 years ago
8 0

Answer:

  • D. A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin

Step-by-step explanation:

<em>See the picture for better visual</em>

Take segments ST and S'T'. If we extend them they will intersect at right angle.

It is the indication that the rotation is 90° or 270° but not 180°, when the corresponding segments come parallel.

The QRST is in the quadrant IV and Q'R'S'T' is in the quadrant III, which mean the rotation is 90° clockwise or 270° counterclockwise.

<u>This rotation rule is:</u>

  • (x, y) → (y, -x)

We also see the points S and T have x-coordinate of 5 but their images have y-coordinates of -6. It means the translation to the right by 1 unit was the step before rotation.

<u>We now can conclude the correct choice is D:</u>

  • A translation 1 unit to the right followed by a 270-degree counterclockwise rotation about the origin

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Write a ratio for the following word phrase. Write fractions in lowest terms.42 in. to 6 ft
ollegr [7]
42 feet to 6 feet can be written as both ratio and a fraction:

42:6
42/6

If we look at the fraction, we can clearly see that we can simplify it:

42/6 = 7/1 = 7

So we can write the ratio in its lowest terms as 7:1.
6 0
3 years ago
In a process that manufactures bearings, 90% of the bearings meet a thickness specification. A shipment contains 500 bearings. A
vredina [299]

Answer:

c) P(270≤x≤280)=0.572

d) P(x=280)=0.091

Step-by-step explanation:

The population of bearings have a proportion p=0.90 of satisfactory thickness.

The shipments will be treated as random samples, of size n=500, taken out of the population of bearings.

As the sample size is big, we will model the amount of satisfactory bearings per shipment as a normally distributed variable (if the sample was small, a binomial distirbution would be more precise and appropiate).

The mean of this distribution will be:

\mu_s=np=500*0.90=450

The standard deviation will be:

\sigma_s=\sqrt{np(1-p)}=\sqrt{500*0.90*0.10}=\sqrt{45}=6.7

We can calculate the probability that a shipment is acceptable (at least 440 bearings meet the specification) calculating the z-score for X=440 and then the probability of this z-score:

z=(x-\mu_s)/\sigma_s=(440-450)/6.7=-10/6.7=-1.49\\\\P(z>-1.49)=0.932

Now, we have to create a new sampling distribution for the shipments. The size is n=300 and p=0.932.

The mean of this sampling distribution is:

\mu=np=300*0.932=279.6

The standard deviation will be:

\sigma=\sqrt{np(1-p)}=\sqrt{300*0.932*0.068}=\sqrt{19}=4.36

c) The probability that between 270 and 280 out of 300 shipments are acceptable can be calculated with the z-score and using the continuity factor, as this is modeled as a continuos variable:

P(270\leq x\leq280)=P(269.5

d) The probability that 280 out of 300 shipments are acceptable can be calculated using again the continuity factor correction:

P(X=280)=P(279.5

8 0
3 years ago
Solving Exponential and Logarithmic Equation In exercise,solve for x or t.See example 5 and 6.
Aloiza [94]

Answer:

0.70275

Step-by-step explanation:

Data provided in the question:

4e²ˣ⁻¹ -1 = 5

now solving for 'x'

⇒ 4e²ˣ⁻¹ = 5 + 1

or

⇒ 4e²ˣ⁻¹ = 6

or

⇒ e^{(2x-1)} =\frac{6}{4}

or

⇒ e^{(2x-1)} =\frac{3}{2}

now,

taking natural log both sides, we get

⇒ 2x - 1 = \ln(\frac{3}{2})

also,

we know

⇒ \log(\frac{A}{B}) = \log(A)+\log(B)

thus,

⇒ 2x - 1 = ln(3) - ln(2)

or

⇒ 2x - 1 = 1.0986 - 0.6931

or

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or

⇒ 2x = 0.4055 + 1

or

⇒ 2x = 1.4055

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⇒ x = 0.70275

3 0
3 years ago
X+y = 8 and 2x-y=7 <br>Anyone can help​
stiks02 [169]

Step-by-step explanation:

x=8-y

2x-y=7

2(8-y)-y=7

16-2y-y=7

-3y=-9

y=3

x=8-y

x=8-3=5

4 0
1 year ago
Read 2 more answers
5•7/8= multiply then reduce the answer to lowest terms
swat32
The answer is 35/8. 5*7 is 35 and 35/8 cannot be reduced more
6 0
3 years ago
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