please help and explain with words please
find the roots of the polynomial
8t^2-2t-3 ​

Answer:

The answer would be 2000

Step-by-step explanation:

Knowing that there are 1000 milliliters in 1 liter, you can multiply that by 2 to get 2000. I hope this helps! :)

Answer:

-2/3 stays the same and -7/4 goes to -1  3/4

Step-by-step explanation:

Answer: -29/12            

= -2.41667  

 12          

Step-by-step explanation:

Answer:

\( - \frac{18}{ {b}^{4} } \)

Step-by-step explanation:

\( - 18b {}^{ - 4} \)

express b^-4 with a positive exponent using:

\(a {}^{ - n} = \frac{1}{ {a}^{n} } \)

\( - 18 \frac{1}{ {b}^{4} } \)

\( - \frac{18}{ {b}^{4} } \)

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

least common multiple: 1000

greatest common factor is 50

least common factor would be 1, but that isn't really a common thing to calculate

Step-by-step explanation:

The length of the boundary of any closed figure is called its perimeter.

Perimeter is calculated only of 2-dimensional shape, or a 1-dimensional length. This means that shapes like cubes, cones, and cylinders don't have a perimeter.

The perimeter of any shape is calculated by adding up the length of all its sides. A side is referred to as any continuous uninterrupted length of the shape between two points.

A point to be noted is that the perimeter of a circle is calculated by its radius and a mathematical number called pi. This is denoted by π. All other curved sides are calculated in a similar manner as well.

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Given:

The point is (-5,7).

To find:

The image of the given point after 90 degrees counter clockwise rotation.

Solution:

If a point rotated 90 degrees counter clockwise, then

\((x,y)\to (-y,x)\)

Let the given point is P(-5,7). Using the above rule, we get

\(P(-5,7)\to P'(-7,-5)\)

Therefore, the image of the given point after 90 degrees counter clockwise rotation is (-7,-5).

(a) A temperature of -2 °C is warmer than a temperature of -5 °C as the temperature on the graph decreases.

(b)The inequality -2>-5 will be used to illustrate the connection between -2 and -5.

A diagram depicting the relationship between two or more variables, each measured along with one of a pair of axes at right angles.

On a number line, graph all the temperature that are warmer than -2°C.

(a)-2 °C  temperature is warmer,As the temperature in the graph is decreasing,-2 °C temperature is warmer than -5 °C.

The inequality to express the relationship between -2 and -5 will be -2>-5.

Hence,temperature of -2 °C is warmer than a temperature of -5 °C as the temperature on the graph decreases.

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Answer:

ejekkeifjejejrjjdjejejeiriririrj

Answer:

c i think

Step-by-step explanation:

Answer:

5.3

Step-by-step explanation:

a^2+b^2=c^2

a^2+36=48

subtract 36 from each side

a^2=28

square root; a=5.5~

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance is 10.76.

The critical value can be determined using a statistical table.

The degrees of freedom for the blocks is 4 (df_b = 5 - 1 = 4) and for the treatments is 2 (df_t = 3 - 1 = 2).

The critical value for a 5% level of significance is 10.76.

This value can be found in the statistical table given in the textbook.

The critical value used to test if there is evidence of an effect due to blocks at the 5% level of significance can be calculated by using the F-test statistic.

The F-test is used to compare the variance between the blocks (SSBL) and the variance between the groups (SSB).

The F statistic is calculated by dividing the variance between the blocks (SSBL) by the variance between the groups (SSB).

In this case,

The F statistic is 3738/1048.93 = 3.56.

The critical value for a 5% level of significance can be found using a statistical table.

According to the table,

The critical value for an F statistic of 3.56 with four degrees of freedom in the numerator and four degrees of freedom in the denominator is 10.76

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Answer:

  2153 meters

Step-by-step explanation:

You want to know the distance to a source of sound if it is heard through a medium with a speed of sound of 5030 m/s 6 seconds before it is heard through a medium with a speed of sound of 335 m/s.

The relation between time, speed, and distance is ...

  time = distance/speed

For some distance d in meters, the two times are d/335 seconds and d/5030 seconds. The time difference is 6 seconds, so we have ...

  d/335 -d/5030 = 6

Multiplying by 337010, we have ...

  1006d -67d = 2022060

  939d = 2022060 . . . . . simplify

  d ≈ 2153.42 . . . . . meters

The source of sound is about 2153 meters away.

__

Additional comment

The distance might rightly be rounded to 2150 meters, since the given numbers are 3 significant figures each.

\(~~~\sqrt{144 x^{12} y^{20}}\\\\=\left(144 x^{12} y^{20} \right)^{\tfrac 12}~~~~~~~~~~~~~~~~~~~~~~~;\left[\sqrt a = a^{\tfrac 12 } \right]\\\\=\left(144 \right)^{\tfrac 12} \cdot \left(x^{12 \right)^{\tfrac 12} \cdot \left(y^{20} \right)^{\tfrac 12}\\\\=\left(12^2 \right)^{\tfrac 12} \cdot x^{\tfrac{12}2} \cdot y^{\tfrac{20}2}\\\\=12 x^6y^{10}\)

Answer:

12x⁶y¹⁰

Step-by-step explanation:

√144x¹²y²⁰

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

12 × 12 = 144

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

12√x¹²y²⁰

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

xx

xx

xx

xx

xx

xx

six sets of two equals x⁶

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

12x⁶√y²⁰

yy

yy

yy

yy

yy

yy

yy

yy

yy

yy

ten sets of two equals y¹⁰

12x⁶y¹⁰

I hope this helps!

The estimated mean lifetime of a bulb of 154.69

The table is given as:

Lifetime                Frequency

25 < t ≤ 50             47

50 < t ≤ 100            86

100 < t ≤ 150          45

150 < t ≤ 200         36

200 < t ≤ 250        0

250 < t ≤ 300       37

300 < t ≤ 350      50

Calculate the midpoint using:

x = (Lower +Upper)/2

So, we have:

Lifetime                Frequency

37.5                        47

75                           86

125                        45

175                        36

225                        0

275                       37

325                      50

The mean value is calculated as:

\(\bar x = \frac{\sum fx}{\sum f}\)

So, we have:

\(\bar x = \frac{37.5 * 47 + 75 * 86 + 125 * 45 + 175 * 36 + 225 * 0 + 275 * 37 + 325 * 50}{47 + 86 + 45 + 36 + 0 + 37 + 50}\)

Evaluate

\(\bar x = \frac{46562.5}{301}\)

Divide

\(\bar x = 154.69\)

Hence, the estimated mean lifetime of a bulb of 154.69

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Answer:

$13.26

Step-by-step explanation:

12.75 × 0.04 = 0.51

0.51 + 12.75 = 13.26

Answer:

$12.75 cupcakes

Multiply the $12.75 x .04 = .51

$12.75 + .51 = $13.26 total

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Let's first write the possible function described.

The roots are:

-5 with a multiplicity of 3.

1 with a multiplicity of 2.

And 3 with a multiplicity of 7.

And the leading coefficient is negative.

Therefore:

\(f(x)=-a(x+5)^3(x-1)^2(x-3)^7\)

Where a is a positive value.

We want to know which statement is true about the graph.

First, since the second root is squared, it will always be positive. And since the leading coefficient is negative, our function is now negative.

So, we will only need to test the first and third root, as only they can alter the sign of our function.

Choice A)

(-∞, -5).

Pick any point within this interval. We can use -6 for simplicity. As stated previously, we only need to test the first and third root. We can ignore the exponents as well, since they do not alter signs. Therefore:

\((-6+5)(-6-3)=(-1)(-9)=9>0\)

Since the result is positive, and our function is already negative, our function is negative for (-∞, -5).

A is not correct.

Choice B)

(-5, 3)

Choosing 0:

\((0+5)(0-3)=-15<0\)

Negative times negative is positive. So, f(x) will be positive for (-5, 3).

B is not correct.

Choice C)

(-∞, 1).

Choosing 0, we can see that:

\((0+5)(0-3)=-3<0\)

Negative times a negative is positive. So, it seems that C is correct.

However, notice that the domain (-∞, 1) contains two roots: x = -5 and x = 1.

In reality, we only tested (-5, 1). We have yet to test (-∞, -5). So, by using -6 again:

\((-6+5)(-6-3)=(-1)(-9)=9\)

Positive times negative is negative.

So, f(x) is both positive and negative for (-∞, 1).

C is not correct.

Note: We did not need to double-check for B since it was already false.

Choice D)

(3, ∞)

This only has one root.

And using 4, we see that:

\((4+5)(4-3)=1>0\)

Positive times a negative will be negative.

Hence, f(x) will be negative for (3, ∞).

Choice D is the correct answer.

The function f is a one-to-one function,

a. \(f^{-1}\)(5) = 9.

b. f(–3) = -18.

(a) Since f(9) = 5, we know that \(f^{-1}\)(5) = 9. Therefore, \(f^{-1}\)(5) = 9.

(b) Since f '(-6) = -3, we can use the definition of the derivative to write:

f '(x) = lim h->0 [f(x + h) - f(x)]/h

Plugging in x = -6 and f '(-6) = -3, we get:

-3 = lim h->0 [f(-6 + h) - f(-6)]/h

Multiplying both sides by h and rearranging, we get:

f(-6 + h) - f(-6) = -3h

Adding f(-6) to both sides, we get:

f(-6 + h) = f(-6) - 3h

Now, we can plug in h = 9 to find:

f(-6 + 9) = f(3) = f(-6) - 3(9) = f(-6) - 27

We don't have enough information to find f(-6) directly, but we do know that f is one-to-one, which means that it has an inverse function. So we can find \(f^{-1}\)(-6) and use it to find f(-6). To do this, we use the fact that:

f(\(f^{-1}\)(x)) = x

Plugging in x = -6, we get:

f(\(f^{-1}\)(-6)) = -6

Since \(f^{-1}\) undoes the action of f, we can also write this as:

\(f^{-1}\)(f(\(f^{-1}\)(-6))) = \(f^{-1}\)(-6)

Using the fact that f(\(f^{-1}\)(x)) = x again, we get:

\(f^{-1}\)(-6) = \(f^{-1}\)(f(\(f^{-1}\)(-6)))

Since f is one-to-one, its inverse function \(f^{-1}\) is also one-to-one, which means that \(f^{-1}\)(f(x)) = x. Therefore, we can simplify the expression above to get:

\(f^{-1}\)(-6) = \(f^{-1}\)(f(\(f^{-1}\)(-6))) = \(f^{-1}\)(-6)

This tells us that \(f^{-1}\)(-6) is equal to itself, which means that \(f^{-1}\)(-6) is -6.

Finally, we can use \(f^{-1}\)(-6) = -6 to find f(-6) using the fact that f(\(f^{-1}\)(x)) = x:

f(-6) = f(\(f^{-1}\)(-6)) = f(-6) = -6 - 3 = -9

Therefore, f(-3) = f(-6 + 3) = f(-6) + 3(-3) = -9 - 9 = -18.

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The question is -

Assume that the function f is a one-to-one function. (a) If f(9) = 5, find f-'(5). Your answer is (b), lf f '(- 6) = – 3, find f( – 3).

Answer:

Step-by-step explanation:

If angle 2 is 75, the other angles that are also 75 are angles 4 (it's vertical to angle 2), angle 6 (it's corresponding to angle 2), angle 8 (it's alternate exterior to angle 2). All the other angles measure 180 - 75 which is 105.

Answer:

The Coefficients in this expression are 10 and 3, while the constants are 5 and 1.

Step-by-step explanation:

Coefficients = The number that is in front of the variable.

Constant = Any number without a variable.

(Variables are the letters that you may find in an equation or function.)

Hope this helps you :)

Answer:

The coefficient are 10 and  3

The constants are 5 and 1

Step-by-step explanation:

A coefficient is the number in front of any known term.

A constant is a number by itself.

So the coefficient are 10 and  3

The constants are 5 and 1

The correct statement regarding the variation of the two measures is given as follows:

C. Yes, they vary directly. When one quantity increases, the other quantity also increases.

For this problem, we have that when the number of correct answers on the test increases, the score also does, hence the two quantities vary directly, and option c is the correct option for this problem.

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Answer:

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g. 4 in 4x y).

Answer:

A coefficient is a numerical or constant quantity placed before and multiplying variable.

Step-by-step explanation:

For example, 4x+8=12. 4 is the coefficient.

The day of the week with the most crime is [insert the day with the highest crime rate]. The day of the week does have an effect on the crime rate, as certain days may exhibit higher crime rates compared to others.

The analysis of crime data reveals patterns and trends that can help identify the day of the week when crime incidents are most prevalent. Law enforcement agencies and researchers often analyze crime statistics to understand the dynamics of criminal activity. By examining crime rates across different days of the week, they can identify any correlations or trends.

Factors such as social behaviors, economic conditions, and routine activities can influence crime rates on specific days. For example, weekends might see higher crime rates due to increased social gatherings and leisure activities, while weekdays may experience different patterns driven by work schedules and routines.

Additionally, factors like alcohol consumption, events, or cultural practices can also contribute to variations in crime rates on specific days.

Understanding the relationship between the day of the week and crime rate can inform law enforcement strategies, resource allocation, and community safety initiatives. By focusing resources and efforts during periods of heightened crime rates, authorities can work towards crime prevention and reduction.

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the turning point(s) of a polynomial function by using below steps

To find the turning point of a polynomial function, follow these steps:

1. Determine the degree of the polynomial. The turning point will occur in a polynomial of odd degree (1, 3, 5, etc.) or at most one turning point in a polynomial of even degree (2, 4, 6, etc.).

2. Write the polynomial function in the form f(x) = axⁿ + bxⁿ⁻¹ + ... + cx + d, where n represents the degree of the polynomial and a, b, c, d, etc., are coefficients.

3. Find the derivative of the polynomial function, f'(x), by differentiating each term of the function with respect to x. This will give you a new function that represents the slope of the original polynomial function at any given point.

4. Set f'(x) equal to zero and solve for x to find the x-coordinate(s) of the turning point(s). These are the values where the slope of the polynomial function is zero, indicating a potential turning point.

5. Substitute the x-coordinate(s) obtained in step 4 into the original polynomial function, f(x), to find the corresponding y-coordinate(s) of the turning point(s).

6. The turning point(s) of the polynomial function is given by the coordinates (x, y), where x is the x-coordinate(s) found in step 4 and y is the y-coordinate(s) found in step 5.

By following these steps, you can find the turning point(s) of a polynomial function.

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The blood test for determining coagulation activity defects is called the Prothrombin Time (PT) test.

The blood test for determining coagulation activity defects is called the Prothrombin Time (PT) test. This test measures the time it takes for blood to clot and is used to assess the functioning of the clotting factors in the blood. It is commonly used to evaluate the extrinsic pathway of the coagulation cascade, which involves factors outside of the blood vessels.

The PT test is an important diagnostic tool in hematology and is used to diagnose or monitor conditions that affect blood clotting, such as bleeding disorders or the effectiveness of anticoagulant medications. By measuring the PT, healthcare professionals can determine if there are any abnormalities in the coagulation process and make appropriate treatment decisions.

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(A x B) - (A x C) is perpendicular to A and lies in the same plane as A, B, and C., Hence we prove the theorem.

We start by expanding the left-hand side of the equation, using the distributive property of multiplication over subtraction:

This equation is now in the form we want to prove, so we just need to show that it is true. To do this, we can use the distributive property of cross product over subtraction. Recall that the cross product of two vectors A and B is given by:

where |A| and |B| are the magnitudes of the vectors, θ is the angle between them, and n is a unit vector perpendicular to both A and B (according to the right-hand rule).

Using this formula, we can write:

where ϕ is the angle between A and C. We can factor out |A| and n from this expression:

Now, we need to show that this expression is equal to A x (B-C), which we can do by showing that the magnitudes and directions are the same. Let's start with the magnitudes:

where α is the angle between A and B-C. Using the distributive property of vector subtraction, we can write:

and since the magnitude of the negative of a vector is the same as the magnitude of the original vector, we have:

Substituting this into the previous equation, we get:

Now, let's look at the directions. Recall that the direction of the cross product is perpendicular to both vectors being crossed, according to the right-hand rule. The direction of A x B is perpendicular to both A and B, and the direction of A x C is perpendicular to both A and C.

Since B-C is a linear combination of B and C, its direction is somewhere in between the directions of B and C. Specifically, it is perpendicular to A and lies in the plane defined by A, B, and C. Therefore, the direction of A x (B-C) is also perpendicular to A and lies in the same plane as A, B, and C.

Putting it all together, we have shown that:

This is exactly what we need to show in order to prove the theorem, since the right-hand side of the equation we are trying to prove also has the same magnitude and direction:

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Microeconomics is a branch of economics that focuses on the behavior of individuals and firms in making decisions regarding the allocation of limited resources

Microeconomics is a branch of economics that studies the behavior of individuals and firms in making decisions about the allocation of limited resources, specifically focusing on the interaction of supply and demand in specific markets and how different factors influence the behavior of individuals and firms. It is concerned with the study of how people and firms make decisions about production, consumption, and distribution of goods and services.

Microeconomics analyzes how supply and demand in specific markets interact to determine the prices of goods and services. It also examines how different factors, such as taxes, government regulations, and technological changes, affect the behavior of individuals and firms.

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Answer:

Obj B, by 1 g/cm^3

Step-by-step explanation:

Obj A = 12g / 8cm^3 = 3g / 2cm^3 = 1.5 g/cm^3

Obj B = 20g / 8cm^3 = 5g / 2cm^3 = 2.5 g/cm^3

2.5 - 1.5 = 1 g/cm^3

Answer:

C. Object B, by 1 gram per cubic centimeter.

Step-by-step explanation:

Density = \(\frac{Mass}{Volume}\)

Volume x Density = \(\frac{Mass}{Volume}\) x Volume (cross both of volumes out)

Volume x Density = Mass

So, what you would do is divide the Mass and Volume, and the density would be the outcome.

Since we see it has a mass of 12g and a volume of \(8 cm^{3}\)

We would then do \(\frac{12 g}{8cm^{3}}\), this gives us 1.5, and \(\frac{20g}{8cm^{3}}\) gives us 2.5, so that would give us the answer C.