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frosja888
6 days ago
15

23. Find the value of x. (5x + 4)' X (8x - 71)

Mathematics
1 answer:
Zina [9.1K]6 days ago
8 0

Answer:

x = 71/8

Step-by-step explanation:

To find x:

5 X (8 x - 71) = 0

Divide both sides by 5 X:

8 x - 71 = 0

Add 71 to both sides:

8 x = 71

Divide both sides by 8:

Answer:  x = 71/8

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136 = x. In detail: When an angle is presented, the angle opposite corresponds to the first equation. The angles at the bottom equal a total of 360, so calculating 46 x 2 = 92. Subtracting 92 from 360 gives 268. Dividing that by 2 yields one of the larger angles as 134 degrees. The upper angle correlates to the lower one, therefore, 136 = x.
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10 days ago
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Aaron draws a segment in his notebook. What is the minimum number of points through which the segment is drawn?
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Answer:

The result is 2

Step-by-step explanation:

A segment requires at least 2 points for its construction.

In geometry, a line segment refers to a section of a line defined by two unique endpoints, encompassing all points located along the line segment between these endpoints.

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Upgrading a certain software package requires installation of 68 new files. Files are installed consecutively. The installation
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Answer:

The chance of completing the entire package installation in under 12 minutes is 0.1271.

Step-by-step explanation:

We define X as a normal distribution representing the time taken in seconds to install the software. According to the Central Limit Theorem, X is approximately normal, where the mean is 15 and variance is 15, giving a standard deviation of √15 = 3.873.

To find the probability of the total installation lasting less than 12 minutes, which equals 720 seconds, each installation should average under 720/68 = 10.5882 seconds. Thus, we seek the probability that X is less than 10.5882. To do this, we will apply W, the standard deviation value of X, calculated via the formula provided.

Utilizing \phi, we reference the cumulative distribution function of the standard normal variable W, with values found in the attached file.

P(X < 10.5882) = P(\frac{X-15}{3.873} < \frac{10.5882-15}{3.873}) = P(W < -1,14)

Given the symmetry of the standard normal distribution density function, we ascertain \phi(-1.14) = 1-\phi(1.14) = 1-0.8729 = 0.1271.

Consequently, the probability that the installation process for the entire package is completed within 12 minutes is 0.1271.

Download pdf
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19 days ago
A mirror is made of two congruent parallelograms as shown in the diagram. The parallelograms have a combined area of 9 1/3 squar
AnnZ [9099]
Given:
Two identical parallelograms total area = 9 1/3 yd²
Each parallelogram has height 1 1/3 yd

Area formula: area = base × height

Split the total area equally to find each parallelogram's area.

Convert 9 1/3: (9*3)+1 = 28/3

Divide by 2: 28/3 × 1/2 = 28/6 yd², which is 4 4/6 yd² → 4 2/3 yd²

So each parallelogram's area is 4 2/3 yd²

Set up base × 1 1/3 yd = 4 2/3 yd²

Convert and divide: 14/3 yd² ÷ 4/3 yd = base

Multiply: 14/3 × 3/4 = base
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42 / 12 = base
Which simplifies to 3 6/12 yd = base
or 3 1/2 yd = base

a) Each parallelogram has a base of 3 1/2 yards
b) If the two parallelograms form a rectangle:
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Length = 3 1/2 yd × 2 = 7 yds
Width = 3 1/2 yds

Area = 7 yd × 3 1/2 yd
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Area = 24 1/2 yd²


8 0
4 days ago
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Value of sec Square 26 degrees - cot square 64 degrees is
Leona [9271]

Answer:

The value equals 1

Step-by-step explanation:

Consider the expression

sec^{2}(26\°)-cot^2(64\°)

Recall that

cot^2(64\°)=\frac{cos^2(64\°)}{sin^2(64\°)}

sec^{2}(26\°)=\frac{1}{cos^2(26\°)}

For two complementary angles A and B (where A+B=90°),

the identity is

cos(A) = sin(B)

Here, 26° and 64° are complementary angles, so

\frac{1}{cos^2(26\°)}=\frac{1}{sin^2(64\°)}

Substituting values,

\frac{1}{sin^2(64\°)}-\frac{cos^2(64\°)}{sin^2(64\°)}

\frac{1-cos^2(64\°)}{sin^2(64\°)}

From this, we find

1-cos^2(64\°)=sin^2(64\°)

By substitution,

\frac{sin^2(64\°)}{sin^2(64\°)}=1

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