find the distance from the point (-2,6) to the line y=x-8

Answer:

x=110.6

Step-by-step explanation:

sin(19)=36/x. x=36/sin(19)=110.6

Answer:

4z²+4z-15 Square Metre  

Step-by-step explanation:

According To The Question,

Area Of Garden = Length × Breadth

Area Of Garden = (2z+5) × (2z-3)

Area Of Garden = 4z²-6z+10z-15

Area Of Garden=4z²+4z-15 Square Metre

Their boss should promote and facilitate open communication and understanding between Yan and Tracy to foster a more inclusive and collaborative work environment.

In a diverse workplace, it is crucial for the boss to encourage inclusivity and bridge the gap between individuals with different world views. By promoting open communication and understanding, the boss can create opportunities for Yan and Tracy to learn from each other and gain a broader perspective.

This can be achieved through team-building exercises, diversity training, or creating a supportive space for discussions on cultural differences. The goal is to foster a work environment where individuals feel comfortable expressing their views, learning from others, and working together towards common goals. By addressing the perceived distance between Yan and Tracy, the boss can help create a more inclusive and harmonious work atmosphere.

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The statement that the sum of any rational number and any irrational number will always be an irrational number is true.

The sum of any rational number and any irrational number will always be an irrational number. To prove this, let's consider a rational number, represented as a/b, where a and b are integers and b is not equal to 0. Additionally, let's consider an irrational number, represented as √2. When we add the rational number a/b and the irrational number √2, the result will be a + (√2)b, which is a combination of a rational number and an irrational number.

Since irrational numbers cannot be expressed as a ratio of two integers, the sum a + (√2)b cannot be simplified to a rational number. Thus, it is an irrational number. Therefore, the statement that the sum of any rational number and any irrational number will always be an irrational number is true.

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Answer:

7

Step-by-step explanation:

Answer:

We can call the numbers x and x + 1. Then we can write:

x + x + 1 = 113 which simplifies to 2x + 1 = 113.

Answer:

Hey there!

The correct answer would be x+x+1=113, or 2x+1=113.

Let the smaller number be x, then the larger number would be x+1

Thus, the sum of x and x+1 would be 2x+1.

We have that 2x+1=113.

Now, this is just a simple linear equation we have to solve.

Start by subtracting 1 to get 2x=112

Then, divide by 2 to get x=56

Since x=56, x+1 would be 57.

Thus, you would have the two numbers be 56 and 57, and use 2x+1 to solve.

Hope this helps :)

this number can be written as 3+0.242424

The equation in standard form for the circle with diameter endpoints (1,17) and (1,-1) is (x - 1)^2 + (y - 8)^2 = 81.

To write the equation of a circle in standard form, we need to use the formula: (x - h)^2 + (y - k)^2 = r^2 Where (h,k) is the center of the circle and r is the radius.

We can use the midpoint formula to find the center of the circle, which is the midpoint of the diameter: Midpoint = ((x1 + x2)/2 , (y1 + y2)/2) Substituting the given endpoints, we get: Midpoint = ((1 + 1)/2 , (17 + (-1))/2) = (1, 8) So the center of the circle is (1,8).

Now we need to find the radius, which is half the length of the diameter: Length of diameter = sqrt((1-1)^2 + (17-(-1))^2) = sqrt(18^2) = 18 Radius = 18/2 = 9 Substituting the center and radius in the standard form equation, we get: (x - 1)^2 + (y - 8)^2 = 9^2 Simplifying, we get: (x - 1)^2 + (y - 8)^2 = 81

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The simplified expression to represent the total amount in dollar Moxie makes on Monday is 14.75w + 21.75

The fixed salary per day = $40

The amount that he earn for every window he sells = $12.50

The amount that he earn for every window that includes a warranty = $2.25

The cost of renting a car = 18.25

Consider the number of window he sells x and windows that includes warranty is y

Then the total amount z = 40 + 12.50x + 2.25y - 18.25

On Monday she sells w windows that all include a warranty

Then the total amount = 40 + 12.50w + 2.25w - 18.25

= 14.75w + 21.75

Hence, the simplified expression to represent the total amount in dollar Moxie makes on Monday is 14.75w + 21.75

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Answer:

14.75x + 21.75

Step-by-step explanation:

Answer: 24 millimeters

the length of the other leg is x (x > 0)(millimeters)

using Pythagoras theorem with the right triangle, we have:

x² + 10² = 26²

⇔ x² = 26² - 10² = 576

=> x = 24 (mm)

Step-by-step explanation:

Step-by-step explanation:

(26)^2 = (10)^2 + BC^2

676 = 100 + BC^2

576 =BC^2

BC = 24 mm

100% humidity is very common in many coastal zones, near rivers or   lakes or in your bathroom when you take a shower, and possibly in  Alaska as well as UAE.

Relative humidity:

                             Relative humidity is the ratio of the current absolute humidity to the highest possible absolute humidity (which depends on the current air temperature). A reading of 100 % relative humidity means that the air is totally saturated with water vapor and cannot hold any more, creating the possibility of rain. This doesn't mean that the relative humidity must be 100 percent in order for it to rain — it must be 100 percent where the clouds are forming, but the relative humidity near the ground could be much less.

0% humidity means there is an absence of water vapor in the air.

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Answer: -35

Step-by-step explanation:

Answer:

The LCD is 6, I think.

Step-by-step explanation:

Answer:

21 cubed is 9261

55 cubed 166375

302 cubed 27543608

hope this helps

have a good day :)

Step-by-step explanation:

Answer:

6 yards

Step-by-step explanation:

a³ = 216

a = ∛ 216

    = 6 yards

Answer:

6 yards

Step-by-step explanation:

The volume of a cube can be found using the following formula.

\(v= s^3\)

We know the volume is 216 cubic yards, so we can substitute 216 yd³ in for v.

\(216 yd^3=s^3\)

We want to find the side length. Therefore, we must isolate the variable, s, on one side of the equation.

s is being cubed. The inverse of cubed is the cube root. Take the cube root of both sides of the equation.

\(\sqrt[3]{216 yd^3}=\sqrt[3]{s^3}\)

\(\sqrt[3]{216yd^3}=s\)

\(6yd=6\)

The side length of the cube is 6 yards.

The point (4,5)  would be on the line y = x + 1

A linear equation in two variables can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

So, we have

y = mx + c

Using the points, we have

5 = 4m + c

Let m = 1

So, we have

5 = 4 + c

Evaluate

c = 1

So, we have

y = x + 1

Hence, the equation is y = x + 1

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The simplified form of the given expression is (x-7)/3x.

The given expression is (2x²-8x-42)/6x² ÷ (x²-9)/(x²-3x)

Here, (x²-4x-21)/3x² ÷ (x-3)(x+3)/x(x-3)

= (x²-4x-21)/3x² ÷ (x+3)/x

= (x²-4x-21)/3x² × x/(x+3)

= (x²-4x-21)/3x × 1/(x+3)

= (x²-4x-21)/3x(x+3)

= (x²-7x+3x-21)/3x(x+3)

= [x(x-7)+3(x-7)]/3x(x+3)

= (x-7)(x+3)/3x(x+3)

= (x-7)/3x

Therefore, the simplified form of the given expression is (x-7)/3x.

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If a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The mean of the normal distribution = 4

Standard deviation of the normal distribution = 1.5

The value of x = 5.5

The z-score of the normal distribution = The mean of the normal distribution / Standard deviation of the normal distribution

Substitute the values in the equation

The z-score of the normal distribution  = (5.5 - 4) / 1.5

Substract the terms

= 1.5 / 1.5

= 1

Hence, if a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x= 5.5 is 1

The complete question is:

suppose a normal distribution has a mean of 4 and a standard deviation of 1.5. what is the z-score of x = 5.5

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The convergent series are (a) 1 + + 2 4 and (c) Σ5 (0.4") n=3. The sum of the series are 2 and 0.213333 respectively. The series that diverges is (b) 1.1 + 1.12 +1.13 +1.14 +... 8 and (d) (-1)" 32n+2 n=1.

(a) The series is 1 + 1/2 + 1/4 + ...
This is a geometric series with a common ratio of 1/2. Since the absolute value of the common ratio is less than 1 (|1/2| < 1), the series converges. To find the sum of this convergent series, we use the formula:

Sum = a / (1 - r)
where a is the first term (1) and r is the common ratio (1/2).

Sum = 1 / (1 - 1/2) = 1 / (1/2) = 2

(b) The series is 1.1 + 1.12 + 1.13 + 1.14 + ...
This is an arithmetic series with a common difference of 0.01. Arithmetic series do not converge, so this series diverges.

(c) The series is Σ(5 * (0.4)^n) from n=3 to ∞.
This is a geometric series with a common ratio of 0.4. Since the absolute value of the common ratio is less than 1 (|0.4| < 1), the series converges. To find the sum of this convergent series, we use the formula:

Sum = a / (1 - r)
where a is the first term (5 * (0.4)^3) and r is the common ratio (0.4).

Sum = (5 * (0.4)^3) / (1 - 0.4) = 0.128 / 0.6 ≈ 0.213333

(d) The series is Σ((-1)^n * 32n+2) from n=1 to ∞.
This is an alternating series. To determine its convergence, we can apply the Alternating Series Test. The test requires two conditions to be met:
1. The absolute value of the terms must be decreasing.
2. The limit of the terms must be 0 as n approaches ∞.

Taking the absolute value of the terms: 32n+2
As n increases, the terms increase, so condition 1 is not met. Therefore, this series diverges.

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the answer

155

324

5/9 (87/3(1/12)= 155/324

Answer:

the forth one is linear

Step-by-step explanation:

The probability of making it home for the holidays is 0.9582. The result is obtained by summing up probabilities of the two cases.

The condition shows that the probability of the flight cancelled is 22 percent. When it happens, there is a second option, a car seat with 81 percent probability.

Case 1: Making home by plane, the flight should not be cancelled.

P(flight not cancelled) = 1 - P(flight cancelled)

P(flight not cancelled) = 1 - 0.22

P(making home by plane) = 0.78

Case 2: Making home by car when the flight is cancelled.

P(making home by car) = P(flight cancelled) × P(car seat available)

P(making home by car) = 0.22 × 0.81

P(making home by car) = 0.1782

The probability of making home by either of the options is

= P(making home by plane) + P(making home by car)

= 0.78 + 0.1782

= 0.9582

Hence, the probability of making it home through the flight or by car is 0.9582.

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Answer:

see image

Step-by-step explanation:

Use new exponent rules like:

A power raised to a power is the product of the powers. (power to a power, times the exponents)

and,

Square root is a half power. (Converting radicals to fractional exponents)

Also, you can multiply in any order, like since you learned multiplying (example: 2×6 is the same as 6×2)

see image.

Here's the plan:

Change the radical to a 1/2 exponent. Now 3 and 1/2 are both exponents. Rearrange the order. Rewrite in radical form again.

see image.

The proof of the equation  (√5)³ = √(5³) is given below.

Exponentiation is one of the mathematics operation.

Let mᵃ, where m and a are the real numbers.

And m is multiplied by a times to itself.

So, a is the exponent of m.

Given:

A radical equation,

(√5)³ = √(5³).

LHS =  (√5)³

Simplifying,

(√5)³ = {(5\()^{1/2}\)}³

        = \(5^{3/2}\)

        = √(5³)

        = RHS.

Therefore,  (√5)³ = √(5³).

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The complete question:

Simplify and prove the equation (√5)³ = √(5³) by using exponent rules.

(0.82 , 3.38) is estimate of the population mean weight loss for this diet in standard deviation.

What is standard deviation in math?

mean weight loss = 2.1lb

standard deviation = 4.8lb

sample size n = 40

std error = stdev/sqrt(n) = 4.8/sqrt(40) = 0.76

degrees of freedom = n - 1 = 39

critical value for alpha 0.10 and df 39 = +1.68

margin of error = critical value * std error = +1.68 * 0.76 = +1.28

confidence interval = sample mean + margin of error = 2.1 +1.28 = (0.82 , 3.38)

Yes it is effective since the values > 0mean weight loss = 2.1lb

standard deviation = 4.8lb

sample size n = 40

std error = stdev/sqrt(n) = 4.8/sqrt(40) = 0.76

degrees of freedom = n - 1 = 39

critical value for alpha 0.10 and df 39 = +1.68

margin of error = critical value * std error = +1.68 * 0.76 = +1.28

confidence interval = sample mean + margin of error = 2.1 +1.28 = (0.82 , 3.38)

Yes it is effective since the values > 0

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The 70th percentile for these sample data is 27.6 pounds.

The 70th percentile for these sample data is 27.3 pounds.

To find the 70th percentile, we first need to order the weights from smallest to largest:

20.6, 21.2, 22.5, 23.4, 24.6, 25.9, 26.5, 27.3, 28.1, 29.7, 30.8

Next, we need to find the rank of the 70th percentile. We can do this using the formula:

Rank = (percentile / 100) * (sample size + 1)

Plugging in the values for the percentile and sample size, we get:

Rank = (70 / 100) * (11 + 1) = 8.4

Since the rank is not a whole number, we need to interpolate between the two nearest ranks. In this case, the two nearest ranks are 8 and 9.

To find the 70th percentile, we can use the following formula:

70th percentile = value at rank 8 + (value at rank 9 - value at rank 8) * (rank - 8)

Plugging in the values, we get:

70th percentile = 27.3 + (28.1 - 27.3) * (8.4 - 8) = 27.3 + 0.32 = 27.62

Rounding to the nearest tenth, we get 27.6.

Therefore, the 70th percentile for these sample data is 27.6 pounds.

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Answer:

Step-by-step explanation:

The area of the 7 cm by 11 cm rectangle is ...

  A = bh

  A = (7 cm)(11 cm) = 77 cm^2

The area of the circle of radius 2 cm is ...

  A = πr^2 = π(2 cm)^2 = 4π cm^2

If the shaded area lies between the circle and the rectangle, its area is the difference of these:

  shaded area = 77 cm^2 -4π cm^2

Using π = 3.14, this area is ...

  (77 -4·3.14) cm^2 = 64.44 cm^2

Using π = 3.141592, this area is ...

  (77 -4·3.141592) cm^2 ≈ 64.43 cm^2

The shaded area is 64.43 cm^2, (64.44 if you use π=3.14).

_____

Comment on π

Often, you are required to use a specific valued for π, even if that is inappropriate for the number of significant digits required in the answer. In recognition of that, we have offered both the correct answer (64.43) and the one associated with the value of π you may be expected to use.

Answer:

64.43cm ^2

Step-by-step explanation:

First, calculate the area of the whole figure, including the unshaded area.

The area of a rectangle is the length times the width.

7cm x 11cm = 77c\(m^{2}\)

Next, calculate the area of the inner figure.

The area of a circle is \(\pi\)\(r^{2}\)

\(\pi\) x 2cm x 2cm = 4\(\pi\) c\(m^{2}\)

Finally, subtract the area of the inner circle from the area of the outer rectangle.

77 c\(m^{2}\) - 4\(\pi\) c\(m^{2}\) ≈ 64.43 c\(m^{2}\)

To help you identify which correlation goes with which scatterplot, here's a brief explanation of the correlation coefficients provided:

1. 0.62: This positive correlation indicates a moderate, positive relationship between the two variables. As one variable increases, the other also tends to increase. In the scatterplot, you'll see a rough upward trend in the data points, but they might not be tightly clustered around a line.
2. -0.93: This strong negative correlation implies a significant, negative relationship between the two variables. As one variable increases, the other tends to decrease. In the scatterplot, you'll see a clear downward trend in the data points, closely clustered around a line.
3. -0.02: This near-zero correlation suggests that there is virtually no relationship between the two variables. The scatterplot will show a random distribution of data points without any apparent pattern.
To determine which correlation goes with which scatterplot, examine the scatterplots closely and identify the trends described above. Match each scatterplot to the corresponding correlation based on the strength and direction of the relationship between the variables.

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In statistical modeling, a dummy variable is used to represent categorical variables with two or more levels as binary variables (0 or 1).

The presence of a dummy variable in a model does not inherently indicate multicollinearity or singularity of the design matrix. Multicollinearity refers to a situation where two or more predictor variables in a regression model are highly correlated, making it difficult to distinguish their individual effects on the response variable. Multicollinearity can cause instability in the estimation of regression coefficients but is not directly related to the use of dummy variables.

Singularity of the design matrix, also known as perfect collinearity, occurs when one or more columns of the design matrix can be expressed as a linear combination of other columns. This can happen when, for example, a set of dummy variables representing different categories has one category that is completely determined by the others. In such cases, the design matrix becomes singular, and the regression model cannot be estimated.

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Answer:

The answer is -5<x

Step-by-step explanation:

-3<2x+7

Subtract 7 from both sides

-10<2x

Isolate x by divided both sides by 2

-5<x

a. D. magna is an effective grazer of the G. semen alga. b. a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

a. The scatterplot of the data shows a clear negative correlation between the number of D. magna grazers and the net growth rate of G. semen. As the number of grazers increases, the net growth rate of G. semen decreases. This suggests that D. magna is an effective grazer of the G. semen alga.

b. The correlation coefficient between the number of grazers and the net growth rate is -0.996. This indicates a strong negative correlation between the two variables, which supports the interpretation that D. magna is an effective grazer of G. semen. The closer the correlation coefficient is to -1, the stronger the negative correlation between the two variables. In this case, the correlation coefficient is very close to -1, which indicates a very strong negative correlation between the number of grazers and the net growth rate of G. semen.

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