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marshall27 [118]
2 years ago
15

Jen and Ariel are reading a 400 page novel for their literature class. Jen decides to read 100 pages the first day and 50 pages

each day thereafter. Ariel's progress on reading the book is represented by the linear function y = 40x + 80, where y is the total number of pages read after x days. Which statement BEST compares Jen's reading rate each day to Ariel's daily reading rate?
A) Jen reads 20 pages per day more than Ariel.
B) Ariel reads 10 pages per day less than Jen.
C) Ariel read 20 pages less the first day than Jen read.
D) The reading rate each day for Jen and Ariel is the same.
Mathematics
2 answers:
Furkat [3]2 years ago
6 0

Answer:

Option B is the correct answer.

Step-by-step explanation:

Jen decides to read 100 pages the first day and 50 pages each day thereafter.

Number of pages read by Jen per day = 50

Number of pages read by Jen on first day = 100

Ariel's progress on reading the book is represented by the linear function y = 40x + 80, where y is the total number of pages read after x days.

Number of pages read by Ariel per day = 40

Number of pages read by Ariel on first day = 40 + 80 = 120

Option A:

Jen reads 20 pages per day more than Ariel

Wrong

Option B:

Ariel reads 10 pages per day less than Jen.

Correct

Option C:

Ariel read 20 pages less the first day than Jen read.

Wrong

Option D:

The reading rate each day for Jen and Ariel is the same.

Wrong

Option B is the correct answer.

Vilka [71]2 years ago
6 0

Answer:

b

Step-by-step explanation:

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A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past
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Answer: We reject the null hypothesis, and we use Normal distribution for the test.

Step-by-step explanation:

Since we have given that

We claim that

Null hypothesis : H_0:\mu\geq 50000

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There  is 5% level of significance.

\bar{X}=46800\\\\\sigma=9800\\\\n=29

So, the test statistic would be

z=\dfrac{\bar{X}-\mu}{\dfrac{\sigma}{\sqrt{n}}}\\\\z=\dfrac{46800-50000}{\dfrac{9800}{\sqrt{29}}}\\\\z=-1.75

Since alternate hypothesis is left tailed test.

So, p-value = P(z≤-2.31)=0.0401

And the P-value =0.0401 is less than the given level of significance i.e. 5% 0.05.

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Which statements about the local maximums and minimums for the given function are true? Choose three options.
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Answer:

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.

Step-by-step explanation:

The true statements are:

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.  

Lets discuss each option one by one:

Over the interval [1, 3], the local minimum is 0

This is a false statement. Look at the graph. The minimum point given is (3.4,-8). Therefore the local minimum is -8 not 0

Over the interval [2, 4], the local minimum is –8.

This statement is true because the given minimum point is(3.4, -8). Thus the  local minimum is -8 which is true

Over the interval [3, 5], the local minimum is –8.

According to the given minimum point, the local minimum  is -8 which is true

Over the interval [1, 4], the local maximum is 0.

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Over the interval [3, 5], the local maximum is 0.

This is a false statement because there is no maximum point

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Anton will be constructing a segment bisector with a compass and straightedge, while Maxim will be constructing an angle bisecto
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The similarities are;

  • Compass and a straight edge required for both construction
  • Both construction includes a line drawn from the intersection of arcs to bisect a segment or an angle
  • The bases for the construction of both bisector are the ends of segment and the angle to be bisected
  • The width of the compass when drawing intersecting arcs, is more than half the width of the segment or angle being bisected

The differences are;

  • Two points of intersection of arcs are used in the segment bisector while only one is requited in an angle bisector
  • The bisecting line crosses the segment in a segment bisector, while it stops at the vertex of the angle being bisected in an angle bisector

The sources of the above equations are as follows;

The steps to construct a segment bisector are;

  • Place the needle of the compass at one of the ends of the line segment to be bisected
  • Widen the compass so as to extend more than half of the length of the segment to be bisected
  • Draw two arcs, one above, and the other below the line
  • Place the compass needle at the other end and with the same compass width draw arcs that intersects with the arcs drawn in the above step
  • Draw a line segment by placing the ruler on the points of intersection of the arcs above and below the line

The steps to construct an angle bisector are;

  • With the compass needle at the vertex, open the pencil end such that arcs can be drawn on the rays (lines) forming the angle
  • Draw an arc on both lines forming the angle
  • Place the compass needle at one of the intersection points and draw an arc in between the lines forming the angle
  • Repeat the above step with the same compass width from the other intersection point with the rays forming the angle
  • Join the point of intersection of the two arcs to the vertex of the angle to bisect the angle

Therefore, we have;

The similarities are;

  • A compass and a straight edge can be used for both construction
  • A straight line is drawn from the point of intersection of arcs to bisect the segment or the angle
  • The arcs are drawn from the ends of the segment or angle to be bisected
  • The width of the compass is more than half the width of the line or angle when drawing the arcs

The differences are;

  • In a segment bisector, the intersection point is above and below the line, while in an angle bisector only one pair of arcs are drawn to intersect above the line
  • The bisecting line passes through the segment being bisected, while the line stops at the vertex in an angle bisector

Learn more about the construction of segment and angle bisectors here;

brainly.com/question/17335869

brainly.com/question/12028523

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