Find the value of x in the triangle shown below.
Find the value of x in the triangle shown below. - 1

Answers

Answer 1
Answer:

Answer:

x=8

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2+b^2 = c^2  where a and b are the legs and c is the hypotenuse

6^2 + x^2 = 10^2

36 + x^2 = 100

Subtract 36 from each side

36-36 +x^2 = 100-36

x^2 = 64

Take the square root of each side

sqrt(x^2) = sqrt(64)

x = 8

Answer 2
Answer:

Answer:

x = 8

Step-by-step explanation:

According to Pythagorean Theorem

AB {}^(2)  + BC {}^(2)  = AC {}^(2)

here

AB = x \n BC = 6 \n AC = 10

Now,

{x}^(2)  +  {6}^(2)  = 10 {}^(2)  \n  {x}^(2)  =  {10}^(2)  -  {6}^(2)  \n x {}^(2)  = 100 - 36 \n  {x}^(2)  = 64 \n x =  √(64)  \n x = 8

AB =x =8


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Create an expression without parentheses that is equivalent that is equivalent to 4(6x+x)

Answers

This is what the distributive property is all about.
  4(6x +x) = 4*6x +4*x = 24x +4x
Of course, this can be simplified further by combining the terms.
  24x +4x = (24 +4)x = 28x

Equivalent expressions without parentheses are ...
  24x +4x
  28x

Polygraph lie-detector machines are commonly used in criminal investigations. The device measures nervous excitement, operating on the idea that if a person is telling the truth they will remain calm. The American Polygraph Association claims that polygraphs accurately identify liars 90% of the time. In other words, if a person lied the test results will be positive 90% of the time. Although the polygraph test is good at identifying liars, there is a 50% chance that the polygraph test will say a truthful person is lying. A police force wants to predict the accuracy of lie-detector tests for 1,000 suspected criminals. Assume that 700 per 1,000 suspected criminals tell the truth during polygraph tests. Lie Truth Row Totals Test result: negative P Test result: postive Q Column Totals 1,000 Barber, N. (2013). Do Lie Detectors Work? Psychology Today . What is the value of Q?

Answers

Answer:

The value of Q is 350.

Step-by-step explanation:

Denote the events as follows:

X = the test is positive

Y = the test is negative

A = the person is telling the truth

B = the person is telling a lie.

It is provided that:

P (B ∩ X) = 0.90

P (A ∩ Y) = 0.50

Then:

P (B ∩ Y) = 1 - P (B ∩ X) = 1 - 0.90 = 0.10

P (A ∩ X) = 1 - P (A ∩ Y) = 1 - 0.50 = 0.50

To test the accuracy of lie-detector a police officer tests 1000 suspected criminals.

It is assumed that 700 per 1,000 suspected criminals tell the truth during polygraph tests.

The table needed to be completed is:

                       Truth (A)        Lie (B)         TOTAL

Positive (X)           Q                 __               __

Negative (Y)         __                 P                __

TOTAL                   __                __               __

For the 1000 suspected criminals selected complete the table as follows:

Given:

                       Truth (A)        Lie (B)         TOTAL

Positive (X)           Q                 __               __

Negative (Y)         __                 P                __

TOTAL                  700              300           1000

n (A ∩ X) = P (A ∩ X) × n (A)

               = 0.50 × 700

               = 350

n (A ∩ Y) = P (A ∩ Y) × n (A)

               = 0.50 × 700

               = 350

n (B ∩ X) = P (B ∩ X) × n (B)

               = 0.90 × 300

               = 270

n (B ∩ Y) = P (B ∩ Y) × n (B)

               = 0.10 × 300

               = 30

n (X) = n (B ∩ X) + n (A ∩ X)

        =  270 + 350

        = 620

n (Y) = n (B ∩ Y) + n (A ∩ Y)

        =  30 + 350

        = 380

Complete table is:

                         Truth (A)        Lie (B)        TOTAL

Positive (X)       Q = 350           270            620

Negative (Y)        350             P = 30          380

TOTAL                  700               300            1000

Thus, the value of Q is 350.

A distribution of measurements is relatively mound-shaped with a mean of 60 and a standard deviation of 14. Use this information to find the proportion of measurements in the given interval. between 46 and 74

Answers

Approximately 68.26% of the measurements fall between 46 and 74 in this distribution.

To find the proportion of measurements between 46 and 74 in a normal distribution with a mean (μ) of 60 and a standard deviation (σ) of 14, we can use the standard normal distribution (z-score) and the cumulative distribution function (CDF).

First, we need to convert the interval endpoints to z-scores using the formula:

z = (x - μ) / σ

Where x is the value in the interval, μ is the mean, and σ is the standard deviation.

For x = 46:

z₁ = (46 - 60) / 14

z₁ = -1

For x = 74:

z₂ = (74 - 60) / 14

z₂ = 1

Using the Excel functions:

=NORM.S.DIST(-1) and =NORM.S.DIST(1)

The probabilities are 0.1587 and 0.8413 respectively.

Now, we want the proportion of measurements between z₁ and z₂, which is:

Proportion = 0.8413 - 0.1587

                  ≈ 0.6826

To learn more about the z-score;

brainly.com/question/15016913

#SPJ12

If 3 inches represents 90 miles on a scale drawing , how long would a line segment be that represents 240 miles?

Answers

Answer:

8 inches

Step-by-step explanation:

90 miles -------------> represented by 3 inches

1 mile -------------> represented by 3/90 inches

240 miles ----------> represented by 3/90 x 240 = 8 inches

Help please I don’t get this

Answers

Answer: 62.5 (assuming it flies straight up, because we don't know the speed of the bird going straight, left, right, or back.)

Step-by-step explanation:

They want to know how far the bird flies in a minute. What you do is you use the char to help you figure it out, by dividing the first row both by 2, so it would give the answer under the altitude column.

Consider the function f(x)=x3+15x2+74x+120. If f(x)=0 for x=−6, for what other values of x is the function equal to 0? List the values separated by commas.

Answers

Answer:

other x values are -5,-4

Step-by-step explanation:

f(x)=0 for x=−6

Apply synthetic division to get the quotient . using that we find other two values of x

-6                1           15             74          120

                   0          -6           - 54          -120                    

                  -------------------------------------------------

                    1           9             20         0

the quotient is x^2+9x+20=0

now factor the left hand side, product is 20 and sum is 9

x^2+9x+20=0\n(x+5)(x+4)=0\nx+5=0 , x=-5\nx+4=0, x=-4

So  other x values are -5,-4