What is the distance between the points (-7,-8) and (2,-8)?

\( \sqrt{8} + \sqrt{11} \\ = 2.8 + 3.3 \: (approximately) \\ = 6.1\)

Step-by-step explanation:

360÷100×20

=72

so 360+72

=432

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Given a relative frequency histogram for the systolic blood pressure readings.

We will find the percentage of the people who had a systolic blood pressure reading between 110 and 139

As shown:

The percentage of people who had a systolic blood pressure reading between 110 and 119 = 0.35

The percentage of people who had a systolic blood pressure reading between 120 and 129 = 0.25

The percentage of people who had a systolic blood pressure reading between 130 and 139 = 0.15

So, the answer will be = 0.35 + 0.25 + 0.15 = 0.75

So, the answer will be option 3) 75%

The circumference of the circle is 62.8cm.

The Circumference of the circle is given by the formula,

Circumference = 2*\(\pi\)*r cm.........equation 1

Given, r = 10cm

On substituting the radius value in equation 1

Circumference = 2*\(\pi\)*10

Circumference = 62.8 cm

Therefore, the circumference of the circle is 62.8cm.

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Answer: did you get a answer yet?

Step-by-step explanation:

Let x be the weight of the candy in pounds, then 0.9x is the weight of the milk chocolate in pounds

The weight of the caramels in the candy is 3 pounds, so

An equation that can be used find the total number of pounds of milk chocolate and caramels in the candy is

0.9x + 3 = x ⇒ x = 30

So there are 0.9(30) = 27 pounds of milk chocolate in the candy.

hope this helps

the x-coordinate of the point that is 2/5 of the way from V to W on this line segment is approximately 8.08.

A coordinate is a number or set of numbers that specifies the position of a point in a space. Coordinates are used to describe the position of objects in various mathematical systems, including two-dimensional and three-dimensional Euclidean spaces, as well as non-Euclidean spaces like spherical or hyperbolic geometries.

by the question.

The x-coordinate of the point that is 2/5 of the way from V to W can be found by first determining the x-coordinate of the point that is 2/5 of the way from V to W and then using the formula for finding the x-coordinate of a point on a line given its y-coordinate.

To find the point that is 2/5 of the way from V to W, we need to first find the distance between V and W. Using the distance formula:

d =\(\sqrt{11-(-4)^{2} }\) + (2 - \((-4)^{2}\)) = \(\sqrt{225+36}\)= \(\sqrt{261}\)

Then, the distance between V and the point we're looking for is (2/5) * \(\sqrt{261}\), and the distance between the point we're looking for and W is (3/5) * \(\sqrt{261}\).

To find the x-coordinate of the point we're looking for, we can use the formula:

x = (distance from V to point we're looking for)/ (total distance) * x

coordinate of W + (distance from point we're looking for to W)/(total distance) * x-coordinate of V.

Substituting the values, we found:

x = (2/5 *\(\sqrt{261}\))/\(\sqrt{261}\)) * 11 + (3/5 * \(\sqrt{261}\))/\(\sqrt{261}\)) * (-4) = 8.08

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Answer: 26 people

Step-by-step explanation: For the boys, there are 40 boys and only 35% of them are wearing sunglasses. To find how many boys are wearing sunglasses, you have to find 35% of 40. 0.35 • 40 is 14. So 14 boys are wearing sunglasses. Now for the girls, there are 20 girls and 60% of them are wearing sunglasses. So, you find 60% of 20. 0.6 • 20 is 12. 12 girls are wearing sunglasses. However, since we want to know how many people are wearing sunglasses altogether, we need to add up the number of boys that are wearing sunglasses to the number of girls that are wearing sunglasses. 14 boys + 12 girls = 26.

So your final answer is: 26 people are wearing sunglasses altogether.

**Hope this helps (I tried)**

For the 4-hour infusion, 1500ml of the 20% acetylcysteine solution must be made up and combined with 500ml of glucose.

To calculate the volume of acetylcysteine that needs to be added to the glucose, we can use the following formula:

The volume of acetylcysteine (in ml) = (Total amount of acetylcysteine needed in mg / Concentration of acetylcysteine in mg/ml) x 100

We have been asked to add 3000mg of acetylcysteine to 500 ml of glucose. If the concentration of the ampoule containing acetylcysteine is 20%, this means that there are 20g of acetylcysteine in 100 ml of solution, or 200mg/ml.

Using the formula above, we can calculate the volume of acetylcysteine that needs to be added as follows:

Volume of acetylcysteine = (3000mg / 200mg/ml) x 100 = 1500ml

Therefore, 1500ml of the 20% acetylcysteine solution needs to be drawn up and added to the 500ml of glucose to make the 4-hour infusion.

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f(0) = 0, f(1) = 2, f(3) = 486, f(5) = 6250

The given function is:

To get the value of f(x) for x = 0, 1, 3, and 5, it means we are going to find f(0), f(1), f(3), and f(5).

The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

Given two equations  1)6x-10<8 and 2) \(\frac{x}{3}\)+6 > 12

Solving the above equations

1) 6x-10≤8

⇒6x ≤ 18

⇒X≤ 3

⇒x ≤ 3 i.e.  x ∈ (-infinity,3]

2)\(\frac{x}{3}\)+6 > 12

⇒\(\frac{x}{3}\) > 6

⇒x>18

⇒ x > 18 i.e.  x ∈ (18,infinity)

Therefore,The value of x in 1st equation is x ≤ 3 i.e.  x ∈ (-infinity,3] and the value of x in 2nd equation is x > 18 i.e.  x ∈ (18,infinity)

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When it comes to medication or medical care, the person who would usually face the greatest impact from a discrepancy in dosage is the individual who is undergoing the treatment.

Insufficient dosage may result in a lack of intended therapeutic effects and failure to improve the patient's condition as anticipated. Also, if the amount administered is excessive, the individual may suffer from negative consequences or possible injury.

It should be noted that the effects of a difference in medication dosage can differ based on the type of medicine, the condition being treated, and personal characteristics like age, weight, general health, and specific reactions or sensitivities.

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The standard deviation for the given data set is 1.78 minutes.

Standard deviation is a measure of the spread of the data. It is calculated by taking the square root of the variance.

The variance is calculated by finding the mean of the squared differences between each data point and the mean.

Let's calculate the standard deviation of the given data set:

1. Calculate the mean of the data, which is given by

mean = (3+6+20+8)/4 = 15/4 = 3.75

2. Calculate the squared differences between each data point and the mean

For 0 up to 2 minutes: (2-3.75)^2 = 0.56

For 2 up to 4 minutes: (4-3.75)^2 = 0.06

For 4 up to 6 minutes: (6-3.75)^2 = 1.56

For 6 up to 10 minutes: (10-3.75)^2 = 10.56

3. Calculate the sum of all the squared differences

0.56+0.06+1.56+10.56 = 12.75

4. Calculate the variance by dividing the sum of the squared differences by the number of data points

Variance = 12.75/4 = 3.19

5. Calculate the standard deviation

Standard deviation = √3.19 = 1.78

Therefore, the standard deviation for the given data set is 1.78 minutes.

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The null hypothesis is that there is no discernible difference among the 5 treatments. The alternative hypothesis is that there is a discernible difference among the 5 treatments

Degree of freedom between groups is nothing but the number of treatments-1 i.e. 5-1=4 and degree of freedom within groups is nothing but total number of subjects- number of treatments i.e. 5*10-5=50-5=45

Mean squares between groups is calculated as follows:

Mean squares between groups= Sum of squares between groups/degrees of freedom between groups= 232/4=58

Mean squares within groups is calculated as follows:

Mean squares within groups= Sum of squares within groups/degrees of freedom within groups= 400/45= 8.89 rounded off to two decimal places

F ratio is calculated as follows:

F= Mean squares between groups/Mean squares within groups

= 58/8.89

= 6.524184477

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In order to explain why -4 - 2 equals -8, let's start with the equation 0.2 = 0. By analyzing this equation, we can uncover the reason behind this seemingly counterintuitive result.

1. Begin with the equation 0.2 = 0.

2. Subtract 0.2 from both sides of the equation to isolate the variable: 0.2 - 0.2 = 0 - 0.2.

  This simplifies to 0 = -0.2.

3. Observe that the right side of the equation, -0.2, is a negative number.

4. Recall that subtracting a negative number is equivalent to adding its positive counterpart. Therefore, -0.2 is the same as +0.2.

5. Rewrite the equation as 0 = +0.2.

6. Notice that 0 on the left side of the equation is equal to 0 + 0, since any number added to zero remains unchanged.

7. Substitute 0 + 0 for 0 in the equation: 0 + 0 = +0.2.

8. Simplify the equation to 0 = +0.2.

9. Finally, recognize that a positive number cannot equal zero. Hence, the equation 0 = +0.2 is false.

10. As a result, the original equation 0.2 = 0 is invalid.

11. Therefore, the logical consequence is that any subsequent deductions based on this invalid equation would also be incorrect.

12. Consequently, -4 - 2 does not equal -8, as per the explanation derived from the flawed equation.

To summarize, by analyzing the equation 0.2 = 0, we can determine that subsequent deductions based on this equation are incorrect. Hence, -4 - 2 does not equal -8.

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Answer:

x

Step-by-step explanation:

When a quadratic equation is given in the form y = ax^2 + Bx + C the easily seen features are

Equation of a parabola is the equation used to trace the path of a parabola. this equation is a quadratic equation

The formula for the roots of the quadratic equation is derived from the equation of the form y = ax^2 + Bx + C to be

-b ± √{(b² - 4ac)2a)

the y intercepts is gotten by equating x = 0

The axis of symmetry refers to the axis where the parabolic curve can be bisected. this is in the y axis

"a" shows if the curve opens upwards or downwards.

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Answer:

F(-x) = 0

Step-by-step explanation:

What is F(-x)?

F(-x) = F(-1)

F(x) = x³ + 1                              F(-1)

F(-1) = -1³ + 1

F(-1) = -1 + 1

F(-1) = 0

So, F(-x) = 0

Answer:

f(-1) = 0

Step-by-step explanation:

Evaluating a function for f(-x) is the same as evaluating it for f(-1).

So we plug in -1 instead.

f(-1) = x³ + 1  

      = (-1)³ + 1 (here we cube -1)

      = -1 + 1     (here we subtract)

      = 0           (and, this is the answer)

\(\therefore\) The answer is f(-1) = 0

Answer:

Step-by-step explanation:

To solve the equation (3x + 20)^2 = 125 using the square root method, we start by taking the square root of both sides:

√[(3x + 20)^2] = √125

3x + 20 = ± 5

Next, we subtract 20 from both sides:

3x = -20 ± 5

Finally, we divide both sides by 3:

x = -8 or x = 3/3

So, the two solutions to the equation (3x + 20)^2 = 125 are x = -8 and x = 1. These solutions are in radical form and are already simplified.

Answer:

your answer is 7,15,60

Step-by-step explanation:

15-8=7

15*4=60

7+15+60=82

Hope it helps u

The simplified expression of (4⁴)⁻¹  is one over four raised to the fourth power

The expression can be simplified as follows:

(4⁴)⁻¹

Therefore, the expression can be simplified using laws of indices.

\((a^{c} )^{b} = a^{cb}\)

and

\((a^{-b} )^{c} = \frac{1}{a^{bc} }\)

Therefore, using the laws of indices, the expression can be simplified below:

(4⁴)⁻¹  = 4⁻⁴

Hence,

4⁻⁴ = 1 / 4⁴ = (1 / 4)⁴

Hence,

(4⁴)⁻¹  = 1 / 4⁴ = (1 / 4)⁴

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The ordered triple representing \(3u - 2v\) is \((13, -8, 5)\).

To find an ordered triple representing \(3u - 2v\),

where \(u = (5, -2, 3)\) and \(v = (1, 1, 2)\),

we can perform the following operations:

\(3u = 3(5, -2, 3)\)

\(3u = (15, -6, 9)\)

\(2v = 2(1, 1, 2)\)

\(2v = (2, 2, 4)\)

Now, subtracting 2v from 3u gives:

\(3u - 2v = (15, -6, 9) - (2, 2, 4)\)

\(3u - 2v = (15-2, -6-2, 9-4)\)

\(3u - 2v = (13, -8, 5)\)

Therefore, the ordered triple representing 3u - 2v is (13, -8, 5).

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Answer:

Step-by-step explanation:

Step 1: Identify the GCF of the polynomial.

Step 2: Divide the GCF out of every term of the polynomial. ...

Step 1: Identify the GCF of the polynomial. ...

Step 2: Divide the GCF out of every term of the polynomial.

Step 1: Identify the GCF of the polynomial. ...

Step 2: Divide the GCF out of every term of the polynomial .

Answer:

work is shown and pictured

Exactly 5/12 of a full rotation is 150, where full rotation is 360.

A "full rotation," "revolution," "whole turn," or "full circle" describes this. It entails spinning around till you are once again pointing in the same direction. a rotational movement. In rotation, there is a fixed central point around which everything else revolves in a circle. 360° is a "Full Rotation." Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Given,

Number = 5/12

Full rotation = 360

5/12 of full rotation

5/12 × 360

5 × 30

150

Exactly 5/12 of a full rotation is 150, where full rotation is 360.

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We have the next information

In total, we have 231 students

van--- 7 students

bus - 25 students

in total, we have 15 vehicles

So our first equation is

x+y=15

where

x is the number of vans

y is the number of buses

The second equation is

7x+25y=231

so we will isolate the x of the first equation

x=15-y

then we substitute this equation in the second equation

7(15-y)+25y=231

105-7y+25y=231

then we sum like terms

18y=126

then we isolate the y

y=126/18

y=7

Then for the value of x we use the equation with the x isolate and we substitute the value of y

x=15-7=8

Therefore the answer is 8 vans and 7 buses

Answer:

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \(\pi\), and a confidence level of \(1-\alpha\), we have the following confidence interval of proportions.

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

In which

z is the zscore that has a pvalue of \(1 - \frac{\alpha}{2}\).

In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.

This means that \(n = 42, \pi = \frac{26}{42} = 0.619\)

95% confidence level

So \(\alpha = 0.05\), z is the value of Z that has a pvalue of \(1 - \frac{0.05}{2} = 0.975\), so \(Z = 1.96\).

The lower limit of this interval is:

\(\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 - 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.472\)

The upper limit of this interval is:

\(\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.619 + 1.96\sqrt{\frac{0.619*0.381}{42}} = 0.766\)

The 95% confidence interval for the proportion of water specimens that contain detectable levels of lead is (0.472,0.766).