During which one-day interval did she work the most hours?

Peter is reading a 193-page book. he has read three pages more than one-fourth of the number of pages he hasn't yet read. how ma

exis [7]

Let's call the number of pages we have read $m$ . To find the number of pages we have left to read, we'll need to subtract the number of pages we've read from the total number of pages in the book. Our total page count is 193, and the number of pages we've read is the unknown $m$ , so the number of pages we haven't read can be written as $193-m$ . With that knowledge, let's construct the rest of our equation.

"He has read three pages more than one-fourth of the number of pages he hasn't yet read." The first key phrase here is "he has read." What this means is that the number of pages he's read, which we've named $m$ , is equal to everything in the rest of the sentence. "Thee pages more than" means that we're going to be adding 3 to whatever the next quantity described is, which, in this case, is "one-fourth of the number of pages he hasn't yet read." We already established earlier that "the number of pages he hasn't yet read" is $193-m$ , so one-fourth of that would be $\frac{1}{4} (193-m)$ . Putting everything together, we get the following equation:

$m= \frac{1}{4} (193-m)+3$

To solve for $m$ , we might first want to eliminate the fraction 1/4 by multiplying both sides of the equation by 4, obtaining

$4m=193-m+12$

Solving for m, we get:

$4m=193+12-m\\5m=205\\m=41$

Now that we have m, it's a simple matter to solve for $193-m$ :

$193-41=152$

So, he has not yet read 152 pages.

6 0

3 years ago

Use a translation rule to describe the translation of ABC that is 6 units to the right and 10 units down.

vesna_86 [32]

Answer:

(x, y ) → (x + 6, y - 10 )

Step-by-step explanation:

6 units right is + 6 in the x- direction

10 units down is - 10 in the y- direction

the translation rule is

(x, y ) → (x + 6, y - 10 )

6 0

2 years ago

Maurice and Johanna have appreciated the help you have provided them and their company Pythgo-grass. They have decided to let yo

Colt1911 [192]

1.A triangular section of a lawn will be converted to river rock instead of grass. Maurice insists that the only way to find a missing side length is to use the Law of Cosines. Johanna exclaims that only the Law of Sines will be useful. Describe a scenario where Maurice is correct, a scenario where Johanna is correct, and a scenario where both laws are able to be used. Use complete sentences and example measurements when necessary.

The Law of Cosines is always preferable when there's a choice. There will be two triangle angles (between 0 and 180 degrees) that share the same sine (supplementary angles) but the value of the cosine uniquely determines a triangle angle.

To find a missing side, we use the Law of Cosines when we know two sides and their included angle. We use the Law of Sines when we know another side and all the triangle angles. (We only need to know two of three to know all three, because they add to 180. There are only two degrees of freedom, to answer a different question I just did.

2.An archway will be constructed over a walkway. A piece of wood will need to be curved to match a parabola. Explain to Maurice how to find the equation of the parabola given the focal point and the directrix.

We'll use the standard parabola, oriented in the usual way. In that case the directrix is a line y=k and the focus is a point (p,q).

The points (x,y) on the parabola are equidistant from the line to the point. Since the distances are equal so are the squared distances.

The squared distance from (x,y) to the line y=k is $(y-k)^2$

The squared distance from (x,y) to (p,q) is $(x-p)^2+(y-q)^2.$ 
These are equal in a parabola:


$(y-k)^2 =(x-p)^2+(y-q)^2$ 

 $y^2-2ky + k^2 =(x-p)^2+y^2-2qy + q^2$

$y^2-2ky + k^2 =(x-p)^2 + y^2 - 2qy+ q^2$

$2(q-k)y =(x-p)^2+ q^2-k^2$

$y = \dfrac{1}{2(q-k)} ( (x-p)^2+ q^2-k^2)$

Gotta go; more later if I can.

3.There are two fruit trees located at (3,0) and (−3, 0) in the backyard plan. Maurice wants to use these two fruit trees as the focal points for an elliptical flowerbed. Johanna wants to use these two fruit trees as the focal points for some hyperbolic flowerbeds. Create the location of two vertices on the y-axis. Show your work creating the equations for both the horizontal ellipse and the horizontal hyperbola. Include the graph of both equations and the focal points on the same coordinate plane.

4.A pipe needs to run from a water main, tangent to a circular fish pond. On a coordinate plane, construct the circular fishpond, the point to represent the location of the water main connection, and all other pieces needed to construct the tangent pipe. Submit your graph. You may do this by hand, using a compass and straight edge, or by using a graphing software program.

5.Two pillars have been delivered for the support of a shade structure in the backyard. They are both ten feet tall and the cross-sections of each pillar have the same area. Explain how you know these pillars have the same volume without knowing whether the pillars are the same shape.

5 0

3 years ago

In a study on the time that

krok68 [10]

The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

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To solve this question, we need to find the confidence interval for the amount of time it takes the students to get the degree.

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

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The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So

df = 80 - 1 = 79

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95% confidence interval

Standard level of confidence, we have to find a value of T, which is found looking at the t table, with 79 degrees of freedom(y-axis) and a confidence level of $1 - \frac{1 - 0.95}{2} = 0.975$ . So we have T = 1.9905.

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The margin of error is:

$M = T\frac{s}{\sqrt{n}} = 1.9905\frac{2.2}{\sqrt{80}} = 0.5$

In which s is the standard deviation of the sample and n is the size of the sample.

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The lower end of the interval is the sample mean subtracted by M. So it is 4.8 - 0.3 = 4.3 years.

The upper end of the interval is the sample mean added to M. So it is 4.8 + 0.3 = 5.3 years.

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The 95% confidence interval of the population mean, in years, is (4.3, 5.3). 4 years is not part of the confidence interval, which means that it contradicts the fact that 39% of students get their college degree in four years.

A similar question is given at brainly.com/question/24278748

6 0

3 years ago

Find the surface area of the cylinder. Type an exact answer in terms of pi.

weqwewe [10]

Answer:

154π cm²

Step-by-step explanation:

Radius (r) = 7 cm

Height (h) = 4 cm

Surface area of cylinder

= 2πr (h + r)

= 2π (7) (4 + 7)

= 2π (7) (11)

= 2π (77)

= 154π cm²

______

Hope it helps ⚜

8 0

2 years ago

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