Find the probability that a randomly
selected point within the square falls in the
red-shaded triangle.
Enter as a decimal rounded to the nearest hundredth.
Enter

When we describe relationships between variables, a correlation nearer to 1.00 (plus or minus) indicates the relationship between variables is strong.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

When correlation is known, predictions can be made using it. Knowing a score on one measure helps us predict another that is closely related to it more accurately. The forecast will be more accurate the stronger the correlation between/among the variables.

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Answer: Plain:  the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

Step-by-step explanation: To multiply complex numbers in polar form, we multiply their magnitudes and add their angles. We can start by converting the given complex numbers from rectangular form to polar form:

6√5 - 6i = 6(√5 - i) = 12 ∠ -30°

(√3 + √3i) = √3(1 + i) = 2 ∠ 45°

where we have used the fact that ∠θ is the angle between the positive real axis and the line connecting the origin and the complex number a + bi, measured counterclockwise.

Now, we can multiply the two complex numbers in polar form:

(6√5 - 6i)(√3 + √3i) = 12 ∠ -30° * 2 ∠ 45°

= 24 ∠ 15°

Therefore, the product is 24 ∠ 15° in polar form. This means that the magnitude of the product is 24 and the angle between the positive real axis and the line connecting the origin and the product is 15°, measured counterclockwise.

To determine the quadrant of the complex plane in which the product lies, we note that the angle 15° is in the first quadrant (between 0° and 90°). Therefore, the product lies in the first quadrant of the complex plane.

The gambler's payoff has a standard deviation of $1. The gambler can expect to win or lose $1 on average for each coin flip, and there is a high degree of variability in the possible outcomes of the game.

The standard deviation of the gambler's payoff can be calculated using the following formula:

σ = √(Σ(xi - μ)^2 * P(xi))

where σ is the standard deviation, xi is the possible outcome of the game, μ is the expected value of the game, and P(xi) is the probability of each outcome.

In this case, there are two possible outcomes: winning $1 with probability 1/2 and losing $1 with probability 1/2. The expected value of the game is:

μ = (1/2 * $1) + (1/2 * -$1) = $0

To calculate the standard deviation, we need to determine the variance first. The variance can be calculated as:

σ^2 = Σ(xi - μ)^2 * P(xi)

= (1 - 0)^2 * 1/2 + (-1 - 0)^2 * 1/2

= 1

Therefore, the standard deviation is:

σ = √1 = 1

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Step-by-step explanation:

a) The test statistic is (4.4-4)/(1.3/sqrt(70)) = 2.83. The p-value is 0.0023. Since the p-value is less than 0.05, we reject the null hypothesis.

b) The test statistic is (5.3-4.4)/sqrt((1.4^2/106)+(1.3^2/70)) = 4.09. The p-value is less than 0.0001. Since the p-value is less than 0.05, we reject the null hypothesis.

In the circle, angle t is solved to be

The unknown angle labelled t is solved with the knowledge of the circle theorem which states that the angle subtended by an arc at the center is twice the angle subtended at the circumference.

Using this knowledge we have that

t = 2 * 24

t = 48 degrees

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We square the residuals when using the least-squares line method to find the line of best fit because we believe that huge negative residuals (i.e., points well below the line) are just as harmful as large positive residuals (i.e., points that are high above the line).

We treat both positive and negative disparities equally by squaring the residual values.  We cannot discover a single straight line that concurrently minimizes all residuals. The average (squared) residual value is instead minimized.

We might also take the absolute values of the residuals rather than squaring them. Positive disparities are viewed as just as harmful as negative ones under both strategies.

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Answer:

$33.60

Step-by-step explanation:

$32.50 + $9.50 = $42.00

20% is changed to .20

Multiply 42.00 x .20 = $8.40 percentage discount

$42.00 - $8.40 = $33.60 is how much he spent

Answer:

B

Step-by-step explanation:

B

The numerator is 10 + x.

The denominator is y - 3.

Answer: This is a binomial distribution problem with parameters n = 17 and p = 0.3, where n is the sample size and p is the probability of a defective bulb. We need to find the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective.

Let X be the number of defective bulbs in the sample. Then X has a binomial distribution with parameters n = 17 and p = 0.3, i.e., X ~ B(17, 0.3).

We want to find P(3 ≤ X ≤ 6). Using the binomial probability formula, we have:

P(3 ≤ X ≤ 6) = P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6)

= (17 choose 3)(0.3^3)(0.7^14) + (17 choose 4)(0.3^4)(0.7^13) + (17 choose 5)(0.3^5)(0.7^12) + (17 choose 6)(0.3^6)(0.7^11)

≈ 0.1566 (rounded to four decimal places)

Therefore, the probability that between 3 and 6 (both inclusive) bulbs from the sample are defective is approximately 0.1566.

Step-by-step explanation:

Answer:

185 and 1/3

Step by step explanation

Answer:

Step-by-step explanation:

Question 1: C

1 multiplied by 5 = 5

1 plus 5 = 6

So you get: (x+5)(x+1) which means x = -5 or -1

Question 2: B

2 multiplied by -4 = - 8

2 plus -4 = -2

So you get: (x-4)(x+2) which means x = 4 or -2

The expression can be expressed in the form of x².

The value of a is 2.

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is a number used before a phrase.

Given:

We have an expression,

\(x^{3/2}\)×√x.

Simplifying,

\(x^{3/2}\)×√x,

= \(x^{3/2} x^{1/2}\)

= \(x^{3/2+1/2}\)

=  \(x^{2}\)

Therefore, the value of a is 2.

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There is evidence to support the claim that the mean lifetime of a particular car engine is greater than 220,000 miles.

Based on the information given, we can use a one-sample t-test to test the claim that the mean lifetime of a particular car engine is greater than 220,000 miles.

The null hypothesis is that the true mean of the population is equal to or less than 220,000 miles, and the alternative hypothesis is that the true mean is greater than 220,000 miles.

Let's assume that the sample size is large enough for the Central Limit Theorem to apply. We can use a t-test with the following formula:

t = (X- μ) / (s / √n)

Where:

X = sample mean

μ = hypothesized population mean

s = sample standard deviation

n = sample size

From the sample data provided, we have:

X= 225,000 miles

s = 4,000 miles

n = 25

Using a significance level of α = 0.05, the critical value for a one-tailed t-test with 24 degrees of freedom is 1.711.

Plugging in the numbers, we get:

t = (225,000 - 220,000) / (4,000 / √25) = 2.50

Since the calculated t-value (2.50) is greater than the critical value (1.711), we reject the null hypothesis. This means we have sufficient evidence to conclude that the mean lifetime of a particular car engine is greater than 220,000 miles at the α = 0.05 level of significance.

Therefore, we can conclude that there is evidence to support the claim that the mean lifetime of a particular car engine is greater than 220,000 miles.

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Answer:

-232

Step-by-step explanation:

-5|+23|·|4-23|=-5|8|·|4-23|

-5|8|·|4-23|=-5|8|·|-4|

-5|8|·|-4|=-58·|-4|

-58·|-4|=-58·4

-58·4=-232

Answer:

The first answer is correct because the angle it gives you in the 3rd picture at the bottom left is congruent with X,  therefore makeing the X 100.

Step-by-step explanation:

We can simplify the expression by combining terms and simplifying further based on any specific values of u or 1.

To express the trigonometric expression cot(sin(1u)) cot(sin(1]) as an algebraic expression in u, we need to apply trigonometric identities and simplify it.

Let's start by using the identity cot(x) = 1/tan(x):

cot(sin(1u)) cot(sin(1]) = (1/tan(sin(1u))) (1/tan(sin(1]))

Next, we'll use the identity tan(x) = sin(x)/cos(x) to rewrite the tangents in terms of sine and cosine:

= (1/(sin(1u)/cos(1u))) (1/(sin(1)/cos(1]))

Simplifying further, we can multiply the reciprocals:

= (cos(1u)/sin(1u)) (cos(1)/sin(1))

Now, let's use the identity sin(2x) = 2sin(x)cos(x) to express the sines and cosines in terms of sine of half-angles:

= (cos(1u)/(2sin(1/2u)cos(1/2u))) (cos(1)/(2sin(1/2)cos(1/2)))

= (cos(1u)/2sin(1/2u)cos(1/2u)) (cos(1)/2sin(1/2)cos(1/2))

Since cos(x)cos(y) = (1/2)[cos(x+y)+cos(x-y)], we can use this identity to simplify the expression further:

= (cos(1u)/2sin(1/2u)(1/2)[cos(1/2+1/2u)+cos(1/2-1/2u)]) (cos(1)/2sin(1/2)cos(1/2))

= (cos(1u)/4sin(1/2u)[cos(1/2+1/2u)+cos(1/2-1/2u)]) (cos(1)/2sin(1/2)cos(1/2))

Now, we can simplify the expression by combining terms and simplifying further based on any specific values of u or 1.

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Answer:

77

Step-by-step explanation:

3.5 ( 11 ) = 38.5

1.9 ( 11 ) = 20.9

1.6 ( 11 ) = 17.6

38.5 + 20.9 + 17.6

= 77

hope this helps

Answer:

D.

Step-by-step explanation:

The answer is D. because the vicinity of the playing field can be associated with the bleachers.

Answer:

0.2266739274

Step-by-step explanation:

[√(150 + 214.9) ] / (9.85 - 0.4)²

Answer:

174

Step-by-step explanation:

All 3 angles in a triangle add up to 180.

So we are given 2 angles and we need to find angle 3. I am going to call the missing 3rd angle 'x'.

1 + 5 + x = 180.

Solve for x

6 + x = 180

Subtract 6 from both sides

x = 174

Answer:

79.7°

Step-by-step explanation:

You hava to do this =

\(180-100.3=79.7\)

Answer:

79.7°

Step-by-step explanation:

Supplementary angles add up to 180°

100.3 + x = 180

Subtract 100.3 from both sides

x = 79.7°

The value of e³/₂ is 4.4758

e in here is considered as Euler's number. Euler's number is a numerical constant which is often used in mathematical calculations. the value of e can be taken into consideration as 2.71828.

The given expression e⁽³÷²⁾ can also be written as √e³. First the cube of e is calculated which is then followed by finding the square root of the calculated value.e⁽³÷²⁾ = √e³. The value of e³ when calculated is 2.7182 x 2.7182 x 2.7182 = 20.0855

Now taking the square root of the calculated value is √20.0855 is 4.4816

Therefore the value of e⁽³÷²⁾ up to four decimal places is 4.4816

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The specific heat capacity of the metal sample is 0.416 cal/g·°C. This value represents the amount of heat energy required to raise the temperature of one gram of the metal by one degree Celsius.

To determine the specific heat capacity of the metal sample, we can use the equation:

q = m * c * ΔT

Where:

q is the heat energy absorbed by the metal sample,

m is the mass of the metal sample,

c is the specific heat capacity of the metal, and

ΔT is the change in temperature.

Given:

m = 25.0 g (mass of the metal sample)

ΔT = (72.5°C - 52.5°C) = 20.0°C (change in temperature)

q = 130.0 cal (heat energy absorbed by the metal sample)

Rearranging the equation, we can solve for c:

c = q / (m * ΔT)

 = 130.0 cal / (25.0 g * 20.0°C)

 ≈ 0.416 cal/g·°C

The specific heat capacity of the metal sample is approximately 0.416 cal/g·°C. This value represents the amount of heat energy required to raise the temperature of one gram of the metal by one degree Celsius.

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A fundamental identity is an equation that relates the values of the trigonometric functions for a given angle. The equation cot θ = cos θ/sinθ is an example of a fundamental identity.

This identity states that the cotangent of an angle is equal to the cosine of the angle divided by the sine of the angle. The equation sec θ = 1/cosθ is another example of a fundamental identity. This identity states that the secant of an angle is equal to the reciprocal of the cosine of the angle. The equation sec^2 + 1 = tan^2θ is also a fundamental identity. This identity states that the square of the secant of an angle plus one is equal to the square of the tangent of the angle. The equation 1 + cot^2θ = csc^2θ is not a fundamental identity. This equation states that one plus the square of the cotangent of an angle is equal to the square of the cosecant of the angle. This equation is not a fundamental identity because it does not relate the values of the trigonometric functions for a given angle.

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The angle x in the diagram is 98 degrees.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angle, alternate exterior angles, vertically opposite angles, same side interior angles etc.

Therefore, let's find the angle of x using the angle relationships as follows:

The size of the angle x can be found as follows:

82 + x = 180(same side interior angles)

Same side interior angles are supplementary.

Hence,

82 + x = 180

x = 180 - 82

x = 98 degrees

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Answer:

y= -2/3x+3

Step-by-step explanation:

Parallel lines have the same slope but different y-intercepts.

y=-2/3x is your original equation

Your slope is still -2/3

y=mx+b

y=-2/3x + b

Substitute the points from the coordinates

5 = -2/3(-3) + b

5 = 2 + b

-2   -2

b=3

Your parallel line equation is: y= -2/3x+3

Have a great day!

The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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1) isolate

2a) opposite

2b) sign

1) delete

2a) flip

2b) reciprocal

isolate

opposite

sign

Delete

flip

Reciprocal

Answer:

Negative

Step-by-step explanation:

Assume that you mean if c÷d is positive or negative when c > 0 and d < 0

c > 0 means that c is positive

d < 0 means that d is negative

positive divides negative is always negative.

Thus, c÷d is negative when c > 0 and d < 0

Answer:

7.2£

Step-by-step explanation:

I used pencil and paper for this so I am sure

Hope this helps!!! If so please give brainliest!!!