Which of the following is a solution to z2 + 2 < 6?
0, 2, 4, -2, or -4

Answer:

11 and 12

Step-by-step explanation:

11^2<139

but

12^2>139

therefore

it lies between 11 and 12

The value of x is 24.

Pythagoras theorem states that for a right angled triangle, the square of the hypotenuse is the sum of the squares of base and altitude.

Given is a right angled triangle since one of the angle is 90 degrees.

Length of leg 1 = 12√2

Length of leg 2 = 12√2

Length of hypotenuse = x

By Pythagoras theorem,

Hypotenuse² = (leg 1)² + (leg 2)²

x² = (12√2)² + (12√2)²

x² = 2 × (12√2)²

   = 576

x = √576

x = 24

Hence the value of x is 24.

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Your question seems incomplete. Probably, the complete question is as follows.

What is the value of x in the triangle?

a 45-45-90 triangle with a leg of length 12 times the square root of 2 and hypotenuse of length x

The ordered pair that show a combination of 12 coins from the graph is (10, 2)

from the question, we have the following parameters that can be used in our computation:

The graph

The purple line represents the combination of 12 coine

Using the above as a guide, we have the following:

The equation is

x + y = 12

From the list of options, we have

(10, 2): 10 + 2 = 12

Hence, the ordered pair is (10, 2)

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a) An exponential growth function that models the tuition which increased from 1995 to 2005 by 7% annually, is y = 8,000 (1.07)^t.

b) If the trend of annual increase in tuition continues, the tuition in 2020 will be $43,419.20.

c) The tuition in 1995 was $8,000.

d)  If the trend of annual increase in tuition continues, the tuition in 2011 will be $23,617.28.

An exponential growth function is one of the two types of exponential functions.

The exponential growth function is marked by an increasing constant rate and modeled as f(x ) = a (1 + r)^x , where r is the growth rate.

The other exponential function is known as an exponential decay function because it shows a constant rate of decrease.

The tuition in 1995, y = $8,000

Annual increase = 7% = 0.07

Time from 1995 = t

Time from 1995 to 2020 = 25 years

Time from 1995 to 2011 = 16 years

y = 8,000 x (1 + 7%)^t

y = 8,000(1.07)^t

When t = 25 years, y = 8,000 x (1.07)^25 = 8,000 x 5.4274 = $43,419.20

When t = 16 years, y = 8,000 x (1.07)^16 = 8,000 x 2.95216 = $23,617.28

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Tuition in 1995 = $8,000

The note Micah made for the test on right triangles is correct by the Pythagoras rule.

The Pythagoras rule states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. 

so by Pythagoras rule we can write:

For the first right triangle;

(x/√2)² + (x/√2)² = x²...(1)

from the left hand side of equation (1): (x/√2)² + (x/√2)²

x²/2 + x²/2

2(x²)/2 = x² {the right hand side of equation (1)}

and for the second right triangle;

(x√3/2)² + (x/2)² = x²...(2)

from the left hand side of equation (2): (x√3/2)² + (x/2)²

x²(3)/4 + x²/4

3x²/4 + x²/4

(3x² + x²)/4

4x²/4 = x² {the right hand side of equation (2)}

Therefore by Pythagoras rule the note Micah made for the test on right triangles is correct

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it would end up by costing $0.55 cents a cup

Answer:

Below

Step-by-step explanation:

3 x^2 = 48      divide both sides of the equation by 3 to get

x^2 = 16         Now, sqrt both sides

x = + 4  or  -4

The standard form of the Polynomial would be [tex]x^{4}[/tex]  -x³ /2 -8

The term "polynomial" refers to a mathematical statement of one or more algebraic terms in which the variables are all of non-negative integer powers. Variables, fixed values, and exponents are all present in the terms. The degree 'n' standard form polynomial is Standard form is one method of expressing a polynomial.

We must consider each term's degree in order to write any polynomial in standard form.

Given the polynomial -8 -x³ /2 -xx³ with the highest degree comes first, followed by x raise to power 4, and then the constant, -8, comes last.

Thus, we would have:

[tex]x^{4}[/tex]  -x³ /2 -8

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Answer: The height of the  court is 93.75 feet.

Step-by-step explanation:

We know that the area of a rectangle is given by :-

Area = length x width/height                                 (1)

Given : A standard-size volleyball court has an area of 2,100 square feet.

The length of the court is 22.4 feet.

To find : The width of the court.

According to (1) , we have

[tex]2100=22.4*height[/tex]

Then,

[tex]Height=\frac{2100}{22.4} =93.75[/tex]

Hence, the height of the  court is 93.75 feet.

The midpoints of the given quadrilateral, AB = CD and AD = BC, are equal.

Let P represent the quadrilateral's vertices (-4,2) Q (2,6): Let A, B, C, and D be the midpoints of P(-4,2) and Q. R(8,5) and S (9,-7) (2,6)

Consequently, A's coordinates are

[tex]$\left(\frac{-4+2}{2}, \frac{2+6}{2}\right)=\left(\frac{-2}{2}, \frac{8}{2}\right)=(-1,4)$[/tex]

Coordinates of B are

[tex]$\left(\frac{2+8}{2}, \frac{6+5}{2}\right)=\left(\frac{10}{2}, \frac{11}{2}\right)=\left(5, \frac{11}{2}\right)[/tex]

Coordinates of c are

[tex]$\left(\frac{8+9}{2}, \frac{5-7}{2}\right)=\left(\frac{17}{2}, \frac{-2}{2}\right)=\left(\frac{17}{2},-1\right)[/tex]

coordinates of D are [tex]$\left(\frac{9-4}{2}, \frac{7+2}{2}\right)=\left(\frac{5}{2}, \frac{-5}{2}\right)$[/tex]

Distance between A and B

[tex]$& d(A, B)=\sqrt{(-1-5)^2+\left(4-\frac{11}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]

Simplify,

[tex]$& d(C, D)=\sqrt{\left(\frac{17}{2}-\frac{5}{2}\right)^2+\left(-1+\frac{5}{2}\right)^2}=\sqrt{36+\frac{9}{4}}=\sqrt{\frac{153}{4}} \\[/tex]

Then,

[tex]$& d(A, D)=\sqrt{\left(-1-\frac{5}{2}\right)^2+\left(4+\frac{5}{2}\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}} \\[/tex]

We get,

[tex]$& d(B, C)=\sqrt{\left(5-\frac{17}{2}\right)^2+\left(\frac{11}{2}+1\right)^2}=\sqrt{\frac{49}{4}+\frac{169}{4}}=\sqrt{\frac{218}{4}}[/tex]

As a result, the given quadrilateral's midpoints, AB = CD and AD = BC, are equal.

It is a parallel gramme as a result.

The complete question is :

A quadrilateral has the vertices at the point (−4,2),(2,6),(8,5) and (9,−7). Show that the mid-point of the sides of this quadrilateral are the vertices of a parallelogram.

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We have to find the area of a circle which has a diameter of 27.2 m

We know that the area of the circle is:

A = πr², where A = area of the circle and r = radius

Given Diameter = 27.2 m

We know that Radius = Diameter/2,

So, Radius = [tex]\frac{27.2}{2}[/tex]

Radius = 13.6 m

Now, area of circle = 3.14 * 13.6 * 13.6

Area = 580.77

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Answer:

11/27

Step-by-step explanation:

55/135 (divide by 5)

11/27

The first two digits represent hours, and the last two digits represent minutes. 00:00 is midnight and 12:00  is noon. 0001 to 1159 defaults to "A.M." hour.

11:30 PM in regular time on a 12-hour clock.

1. 23:30 represents afternoon time, so we add 12 hours to the given time.

2. 11 + 12 hours = 23 hours

3. minutes is always the same no matter which time format is used.

4. Remove PM and colon.

5. conversion 11:30 23:30 war time

Step 1

First divide the given time into hours and minutes. For wartime 2330, this is 23 hours and 30 minutes.

Step 2

Then check if the set time is greater than 1300. Since 2330 is greater than 1300, we use the hour subtraction rule (23 - 12 = 11 hours).

Step 3

Military time minutes are the same as standard time, so 30 minutes is still 30 minutes.

Step 4

Add a colon between the calculated hours and minutes, and the result is 11:30.

Step 5

2330 is greater than 1200, so according to the mentioned rules, adding the PM after the expected time gives 23:30 regular time.

The correct answer is 23:30 standard time.

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Residual sum of squares (RSS) is a measure of the total amount of variance in a given data set that is not explained by a model.

It is equal to the sum of squared differences between the observed data values and the predicted values from the model. This measure is commonly used in regression analysis to evaluate the performance of a model. The formula for RSS is  RSS = Σ(y_i - ȳ)², where y_i is the observed value and ȳ is the predicted value.For example, let's say we have a data set of 10 observations (y_1, y_2, ...,y_10). We fit a linear regression model to the data set which predicts a value ȳ_i for each observation. The RSS for this model is calculated by summing the squared differences between the observed values (y_i) and the predicted values (ȳ_i) for each of the 10 observations. This yields the RSS, which is a measure of how much of the variance of the data set is not explained by the model.

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The point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

The angle for this problem is given as follows:

-4pi/3.

Hence the sine and the cosine are given as follows:

Hence the point (-0.5, 0.866) represents the angle -4pi/3 graphed on the unit circle.

(the equation of the unit circle is x² + y² = 1).

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The number of freshmen that are students is 738

Let y represent the number of students that are freshmen

The freshmen class is made up of 480 female students

This number represents 65% of the freshmen class

Therefore the total number of students that are freshmen can be calculated as follows

y × 65/100= 480

65y/100= 480

Cross multiply both sides

65y= 480 × 100

65y= 48000

y= 48000/65

y= 738.4

≅ 738

Hence 738 students are freshmen

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[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{3}{4} + \dfrac{1}{2}}[/tex]

[tex]\mathsf{= \dfrac{3}{4} + \dfrac{1\times2}{2\times2}}[/tex]

[tex]\mathsf{= \dfrac{3}{4} + \dfrac{2}{4}}[/tex]

[tex]\mathsf{= \dfrac{3 + 2}{4 + 0}}[/tex]

[tex]\mathsf{= \dfrac{5}{4}}[/tex]

[tex]\mathsf{= 1 \dfrac{1}{4}}[/tex]

[tex]\huge\text{Therefore your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{5}{4}\ or \ 1 \dfrac{1}{4}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

See below

Step-by-step explanation:

[tex]I_1=[1],\, I_2=\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right],\,I_3=\left[\begin{array}{ccc}1&0&0\\0&1&0\\0&0&1\end{array}\right],\,...[/tex] and so on are examples of identity matrices.

The multiplicative inverse of a 2x2 matrix is [tex]\displaystyle A^{-1}=\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex] where ad-bc represents the determinant. Multiplying this with the original matrix will produce the identity matrix as described previously. Usually, you'll mostly deal with 2x2 matrices when it comes to this topic, but don't worry too much.

Answer:

No, Tony should have rounded up to 38.

Step-by-step explanation:

Tony solved the inequality correctly; however, he rounded incorrectly.

8c+200≥500

Subtract 200 from both sides

8c≥300

Divide each side by 8

c≥37.5

Tony cannot wash 37.5 cars, because in the context it is impossible to wash half of a car. We round the answer up because rounding down would give us a value less than $500 (the inequality is greater than or equal to).

Therefore, the answer is 38. Tony is incorrect.

The length of the diameter of the circle is 8 cm.

The diameter of a circle is the distance measured through its centre. The radius of a circle is the distance from the center to any point on the edge. The diameter is divided by the radius.

Given:

Radius = 4 cm

As, the radius is the point which starts from center  and reach to point on the surface of the Circle.

and, the Diamter is the two times of the radius.

So, Diameter = 2 x radius

D= 2 x 4

diameter = 8 cm

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Answer:

Step-by-step explanation:

wheres the worksheet...

By evaluating the linear equation we can see that the complete table is:

x|  -4   -2  0  2  4

y| 17    13  9   5  1

Here we have a linear function:

y = -2x + 9

And we want to complete the given table, to do so, we just need to evaluate the linear function in the given values of x.

if x = -2

y = -2*-2 + 9 = 4 + 9 = 13

if x = 0

y = -2*0 + 9 = 9

if x = 2

y = -2*2 + 9 = 5

if x = 4

y = -2*4 +9 = 1

Then the complete table is:

x|  -4   -2  0  2  4

y| 17    13  9   5  1

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The distance the cyclist travelled during the time are as follows;

4 meters, 18 m and 45 etc.

Speed can be calculated as the ratio of distance traveled to the time taken

Distance = speed x time

Distance = 5 x 0.8

= 4 meters

Distance = 10 x 1.8

= 18 meters

Distance = 15 x 3

= 45 meters.

Here Segment shows as time is increasing, distance is also increasing. Which means the cyclist is moving forward at a speed.

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Answer:

Step-by-step explanation:

A distribution is said to be skewed to the right (also known as positively skewed) if it has a longer tail on the positive side of the mean or median, indicating that the majority of the data values are on the lower end and there are a few large values on the higher end. This results in a mean that is larger than the median.

In other words, the right skew occurs when the tail of the distribution is located to the right side of the peak, which pulls the mean to the right as well. The presence of outliers or extreme values on the right side of the distribution can cause right skew.

Right-skewed distributions are common in data sets that represent measurements or quantities that have a minimum value of zero or a natural lower limit, but can increase without bound, such as income, wealth, and height.

In summary, when a distribution is skewed to the right, it has a higher mean and lower median compared to a symmetrical distribution, and the majority of the data is concentrated on the left side.

The solution is the median dress size = 12.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

here, we have,

given that,

from the given data we get,

dress sizes are, 10, 12 , 14, 16

no. of dresses,   16, 38, 27, 19

Hence, using the formula we get, the median dress size = 12.

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180 hours will it take them to consume 45 capsules.

What is least common multiple ?

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of all the given numbers. In other words, it is the smallest number that is divisible by all the given numbers without leaving a remainder.

To find the LCM of two or more numbers, you can list their multiples and look for the smallest number that appears in all the lists. However, this can become time-consuming for large numbers. There are various methods and algorithms to find the LCM efficiently, such as using prime factorization or the Euclidean algorithm.

According to the question:
Allergy Sufferer #1 takes 1 capsule every 6 hours, so in 45 capsules, they will need to take 45 * 6 = 270 hours.

Allergy Sufferer #2 takes 1 capsule every 12 hours, so in 45 capsules, they will need to take 45 * 12 = 540 hours.

To find the total time it will take them together to consume 45 capsules, we need to find the least common multiple (LCM) of 6 and 12.

The prime factors of 6 are 2 and 3.

The prime factors of 12 are 2, 2, and 3.

To find the LCM, we take the highest power of each prime factor that appears in either factorization. In this case, that's 2^2 * 3 = 12.

So, the LCM of 6 and 12 is 12.

This means that every 12 hours, Allergy Sufferer #1 will have taken 2 capsules (since 12/6=2), and Allergy Sufferer #2 will have taken 1 capsule.

Therefore, in 12 hours, they will have taken a total of 2+1=3 capsules.

So, to consume 45 capsules, it will take them 45/3 = 15 lots of 12 hours, which is 180 hours in total.

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The pool water will be 0.006% chlorine after approximately 236.5 minutes, and the percentage of chlorine in the pool after 1 hour (60 minutes) is approximately 0.674%.

Let C(t) be the amount of chlorine in the pool at time t in minutes, measured in gallons of chlorine. Since the volume of the pool is 10,000 gal and the initial concentration of chlorine is 0.01%, we have:

C(0) = 10,000 gal x 0.01% = 1 gal

As city water containing 0.003% chlorine is pumped into the pool at a rate of 6 gal/min and the pool water flows out at the same rate, the differential equation for C(t) is:

dC/dt = (0.003 - C(t)/10,000) x 6 - C(t)/10,000 x 6

Simplifying the right-hand side and solving the differential equation using separation of variables, we get:

C(t) = 30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7)

After 1 hour (60 minutes), we have:

C(60) = 30,000(1 - e^(-60/166.7)) - 180,000e^(-60/166.7) ≈ 0.0674 gal

The percentage of chlorine in the pool after 1 hour is:

0.0674 gal / 10,000 gal x 100% ≈ 0.674%

To find when the pool water is 0.006% chlorine, we set C(t) = 10,000 gal x 0.006% = 0.6 gal and solve for t:

30,000(1 - e^(-t/166.7)) - 180,000e^(-t/166.7) = 0.6

Using numerical methods, we find that t ≈ 236.5 minutes.

After roughly 236.5 minutes, the chlorine content of the pool will be 0.006%, and after an hour (60 minutes), it will be approximately 0.674%.

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The solution is Option A.

The transformed equation is y = -x - 8

The transformation of a function may involve any change.

Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs), etc.

If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:

Horizontal shift (also called phase shift):

Left shift by c units: y=f(x+c) (same output, but c units earlier)

Right shift by c units: y=f(x-c)(same output, but c units late)

Vertical shift:

Up by d units: y = f(x) + d

Down by d units: y = f(x) - d

Stretching:

Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given data ,

Let the parent function be represented as A

Now , the value of A is

f ( x ) = x or y = x

Now , when the function is reflected over the y-axis , the x coordinate of the function is changed to its additive inverse

So , reflected function is g ( x ) = -x

Now , when the function is translated down 8 units ,

It is a vertical shift of down by d units: y = f(x) - d

The new transformed function is h ( x ) = -x - 8

Hence , the transformed function is y = -x - 8

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