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Ksivusya [100]
3 years ago
10

Students are given 3 minutes to complete each multiple-choice question on a test and 8 minutes for each free-response question.

There are 15 questions on the test and the students have been given 55 minutes to complete it. A Table titled Test Time, showing Number of Questions, Time per Item in minutes, and Total Time in minutes. The first row shows Multiple Choice, with m, 3, and 3 m. The second row shows Free Response, with 15 minus m, 8, and x. The third row shows Total, with 15, blank, and 55. Which value could replace x in the table? 7 – m 23 – m 8(15 – m) 8(15) – m

Mathematics
1 answer:
weqwewe [10]3 years ago
6 0

Answer:

8(15-m)

Step-by-step explanation:

By looking at the options, we can understand that the right one is 8(15-m), since we need to multiply the time by the number of question.

Also, we can check that result by arranging an equations usint the total time.

55 = 3m - 8(15-m)

55 = 3m - 120 + 8m

55 = 11m - 120

55 + 120 = 11m

175 = 11m

m = 175/11 = 15.91

55 = 3*15.91 - 8(15-15.91) = 47.73 - 120 + 127.28 = 55.01 ≈ 55

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Please provide an answer
Igoryamba

Answer:

Step-by-step explanation:

The opposite angles in a quadrilateral theorem states that when a quadrilateral is inscribed in a circle, the angles that are opposite each other are supplementary, their degree measures add up to 180 degrees. One can apply this here by using the sum of (<C) and (<A) to find the measure of the parameter (z). Then one can substitute in the value of (z) to find the measure of (<B). Finally, one can use the opposite angles in a quadrilateral theorem to find the measure of angle (<D) by using the sum of (<B) and (D).

Use the opposite angles in an inscribed quadrialteral theorem,

<A + <C = 180

Substitute,

14x - 7 + 8z = 180

Simplify,

22z - 7 = 180

Inverse operations,

22z = 187

z = \frac{187}{22}

Simplify,

z = \frac{17}{2}

Now substitute the value of (z) into the expression given for the measure of angle (<B)

<B = 10z

<B = 10(\frac{17}{2})

Simplify,

<B = 85

Use the opposite angles in an inscribed quadrilateral theorem to find the measure of (<D)

<B + <D = 180

Substitute,

85 + <D = 180

Inverse operations,

<D = 95

8 0
2 years ago
Read 2 more answers
Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were millio
JulijaS [17]

Answer:

The amount of oil was decreasing at 69300 barrels, yearly

Step-by-step explanation:

Given

Initial =1\ million

6\ years\ later = 500,000

Required

At what rate did oil decrease when 600000 barrels remain

To do this, we make use of the following notations

t = Time

A = Amount left in the well

So:

\frac{dA}{dt} = kA

Where k represents the constant of proportionality

\frac{dA}{dt} = kA

Multiply both sides by dt/A

\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}

\frac{dA}{A}  = k\ dt

Integrate both sides

\int\ {\frac{dA}{A}  = \int\ {k\ dt}

ln\ A = kt + lnC

Make A, the subject

A = Ce^{kt}

t = 0\ when\ A =1\ million i.e. At initial

So, we have:

A = Ce^{kt}

1000000 = Ce^{k*0}

1000000 = Ce^{0}

1000000 = C*1

1000000 = C

C =1000000

Substitute C =1000000 in A = Ce^{kt}

A = 1000000e^{kt}

To solve for k;

6\ years\ later = 500,000

i.e.

t = 6\ A = 500000

So:

500000= 1000000e^{k*6}

Divide both sides by 1000000

0.5= e^{k*6}

Take natural logarithm (ln) of both sides

ln(0.5) = ln(e^{k*6})

ln(0.5) = k*6

Solve for k

k = \frac{ln(0.5)}{6}

k = \frac{-0.693}{6}

k = -0.1155

Recall that:

\frac{dA}{dt} = kA

Where

\frac{dA}{dt} = Rate

So, when

A = 600000

The rate is:

\frac{dA}{dt} = -0.1155 * 600000

\frac{dA}{dt} = -69300

<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>

7 0
2 years ago
Find the point on the graph of the given function at which the slope of the tangent line is the given slope.
mezya [45]

Answer:

A ( -2 , 9 )

Step-by-step explanation:

<u>Idea:</u> You find the first derivative of f(x), and then set it equal to the desired slope. You'll find some x. That we will use to find the point.

f'(x) = 3x^2 + 12x + 20

f'(x) = 8

3x^2 + 12x + 20 = 8

3x^2 + 12x + 12 = 0

3 ( x^2 + 4x + 4 ) = 0

3 ( x + 2 )^2 = 0

x + 2 = 0

x = -2

So, the desired point is:

A ( -2, f(-2) ) --> A ( -2 , 9 )

3 0
3 years ago
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vodomira [7]

15/17. The value (ratio) of cos A is 15/17.

The trigonometric ratios of an acute angle are, basically, the sine, the cosine and the tangent. They are defined from an acute angle, α, of a right triangle, whose elements are the hypotenuse, the leg contiguous to the angle,  and the leg opposite the angle.

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-The tangent of the angle is the opposite leg divided by the adjacent leg or, which is the same, the sine of the angle divided by the cosine of the angle.

cos A = adjacent leg/hypothenuse = BC/AC = 15/17

4 0
3 years ago
Empirical generalization is known as reasoning from a large example to a basic conclusion based on a sample. a. True b. False
Taya2010 [7]

Answer:True

Step-by-step explanation:Empirical generalisation is the relationship between two variables that has been observed over a long period of time, science tries to show the interactions taking place between empirical Generalisation and theory,empirical Generalizations can also be seen as a pattern that repeats over different circumstances. Empirical Generalizations can also be said to be a reasoning from large example to basic conclusions which can be represented mathematically graphically or symbolically.

8 0
3 years ago
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