0.442÷26.7812 pleaseeeeeeeeeeeeeeeee

The root of the polynomial equation x (x-2) (x + 3) = 18 is x = 3.

Concept: An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

Given:

x (x-2) (x + 3) = 18

Divide both sides of the equation by x:

x (x-2) (x + 3) / x = 18 / x

(x-2) (x) + 3) = 18 / x

You can use the following simultaneous equations.

(1) y = (x-2) (x + 3)

(2) y = 18 / x

Using a graphing calculator, we get:

x = 3, y = 6 → point = (x, y) = (3,6)

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0.2 / 0.22

it would've been 0.22222222 but if you cut it short its 0.2 or 0.22.

The correct option based on the hypothesis is that D. Proposition I is true and Proposition II is false.

The 5% significance level means that there is a 5% chance of making a Type I error. In other words, there is a 5% chance of rejecting the null hypothesis when it is actually true.

If the researcher rejects the null hypothesis, then they are making a Type I error. This means that they are concluding that vaccination causes a higher mean immunogenicity level when it actually does not.

Proposition I is true because there is a 5% chance of making a Type I error. Proposition II is false because the researcher has not yet made a decision. The researcher will only make a decision after they have calculated the p-value.

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Answer:

The value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

What is an integer exponent?

In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.

It is given that:

The equation is:

After solving:

(x + 9)³ = 4096

x + 9 = ∛4096

x + 9 = 16

x = 7

Thus, the value of x is 7 if the equation can be reduced to (x + 9)³ = 4096 after applying the properties of the integer exponent option (C) 7 is correct.

Answer:

12 miles

Step-by-step explanation:

Total miles = Length of trail ×

Number of times she rode

Total miles = 3 miles × 4 times

Total miles = 12 miles

Mika traveled a total of 12 miles.

Answer:

The circumcenter is the center of a triangle's circumcircle. It can be found as the intersection of the perpendicular bisectors.

Therfore ans is C

Answer:

hiiiiii

Step-by-step explanation:

Answer:

$18.4

Step-by-step explanation:

40oz=2.5lb

10lb=4*2.5lb=4*4.6=18.4

Test the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level. The p-value is 0.024.

The null and alternative hypotheses for the claim that the proportion of people who own cats is significantly different than 70% at the 0.02 significance level are:

H0: p = 0.7 (null hypothesis

)H1: p ≠ 0.7 (alternative hypothesis)

The test is a two-tailed test because the alternative hypothesis includes not equal to (<>) which means either p is less than 0.7 or greater than 0.7

Based on a sample of 500 people, 62% owned cats.

This means that the sample proportion, p = 0.62.

To calculate the p-value, we will use the z-test statistic.

The formula for calculating the z-test statistic is given as:

z = (p - P) / √(PQ/n) where P is the hypothesized proportion (P = 0.7), Q is the complement of P (Q = 1 - P), and n is the sample size.

Using the given values in the formula, we have; z = (0.62 - 0.7) / √(0.7 × 0.3 / 500) = -2.52

The p-value for a two-tailed test at 0.02 level of significance is obtained from the standard normal table.

The area in both tails beyond the z-score of 2.52 is 0.012.

Therefore, the p-value is:

p-value = 2 × 0.012 = 0.024

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Answer:

-3√5

Step-by-step explanation:

3√5-2√45

3√5-2•√9×√5

3√5-2•3√5

3√5-6√5

-3√5

Answer:

c. \( - 3 \sqrt{5} \)

Step-by-step explanation:

\(3 \sqrt{5} - 2 \sqrt{45} \)

\( - 2 \times 3 \sqrt{5} = - 6 \sqrt{5} \)

\(3 \sqrt{5} - 6 \sqrt{5} \)

\((3 - 6) \sqrt{5} = - 3 \sqrt{5} \)

\( \boxed{\green{= - 3 \sqrt{5} }}\)

a. The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes.

b. The probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20

What is Probability?

Probability is a field of mathematics that calculates the likelihood of an experiment occurring. We can know everything from the chance of getting heads or tails in a coin to the possibility of inaccuracy in study by using probability.

a. The mean of the sampling distribution of the difference in sample means, xF - xM, is equal to the difference of the population means, μF - μM = 8.8 - 7.3 = 1.5 minutes.

where σF and σM are the standard deviations of the populations of female and male students, respectively, and nF and nM are the sample sizes of female and male students, respectively.

\(Standard\ Deviation = \sqrt{3.3^2/8 + 2.9^2/8} \\\\Standard\ Deviation = \sqrt{{2.75} }\\\\Standard\ Deviation = 1.65\ minutes\)

So, the mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes, respectively.

b. The probability of getting a difference in sample means xF - xM that is less than 0 can be found using a standard normal distribution table. First, we need to standardize the difference in sample means xF - xM by subtracting the mean and dividing by the standard deviation:

z = (xF - xM - (μF - μM)) / standard deviation

z = (0 - 1.5) / 1.65 = -0.91

Looking up -0.91 in a standard normal distribution table, we find that the probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

So, there is a 20% probability of getting a difference in sample means xF - xM that is less than 0.

Hence, The mean and standard deviation of the sampling distribution of the difference in sample means xF - xM are 1.5 and 1.65 minutes and probability of getting a difference in sample means xF - xM that is less than 0 is approximately 0.20.

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Answer:

Yes.

Step-by-step explanation:

Straight lines can be linear

i hope this helps :)

Mae's walking speed is 10 miles per hour. This is calculated by considering the given information.

Let's assume Mae's walking speed is represented by the variable "x" (in miles per hour). According to the given information, her jogging speed would then be "x + 12.5" miles per hour.

To calculate Mae's exercise time, we can use the formula: time = distance / speed.

Mae jogs 27 miles at a speed of "x + 12.5" miles per hour, so her jogging time can be calculated as:

jogging time = 27 / (x + 12.5)

Mae walks an additional 3 miles at a speed of "x" miles per hour, so her walking time can be calculated as:

walking time = 3 / x

The total exercise time is given as 3 hours. Therefore, we can set up the equation:

jogging time + walking time = 3

Substituting the calculated values, we get:

27 / (x + 12.5) + 3 / x = 3

To solve this equation, we can start by multiplying all terms by x(x + 12.5) to eliminate the denominators:

27x + 27 * 12.5 + 3(x + 12.5) = 3x(x + 12.5)

Simplifying the equation:

\(27x + 337.5 + 3x + 37.5 = 3x^2 + 37.5x\)

Combining like terms:

\(30x + 375 = 3x^2 + 37.5x\)

Rearranging the terms to set the equation equal to zero:

\(3x^2 + 7.5x - 375 = 0\)

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(\(b^2\) - 4ac)) / (2a)

In this case, a = 3, b = 7.5, and c = -375. Substituting these values into the quadratic formula:

x = (-7.5 ± √(\(7.5^2\) - 4 * 3 * -375)) / (2 * 3)

x = (-7.5 ± √(56.25 + 4500)) / 6

x = (-7.5 ± √(4556.25)) / 6

Calculating the square root:

x = (-7.5 ± 67.5) / 6

Simplifying further:

x = (60 / 6) or x = (-75 / 6)

Since Mae's walking speed cannot be negative, the solution is x = 10.

Therefore, Mae's walking speed is 10 miles per hour.

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The complete question is:

For exercise, Mae jogs 27 miles then walks an additional 3 miles to cool down. If her jogging speed is 12.5 miles per hour faster than her walking speed and her total exercise time is 3 hours, what is her walking speed? The athlete's walking speed is

The length of the rectangle is 1 more than twice its width, the dimension of the square is approximately \((7 + \sqrt{673}) / 6\)meters.

Let's assume the side length of the square is represented by "x" meters.

The area of a square is given by the formula: \(A^2 = side^2.\)

So, the area of the square is \(x^2\)square meters.

The width of the rectangle is 2 meters less than the side length of the square. Therefore, the width of the rectangle is\((x - 2)\)meters.

The length of the rectangle is 1 more than twice its width. So, the length of the rectangle is 2(width) + 1, which can be written as \(2(x - 2) + 1 = 2x - 3\)meters.

The area of a rectangle is given by the formula: A_rectangle = length * width.

So, the area of the rectangle is \((2x - 3)(x - 2)\)square meters.

According to the problem, the total area of the square and rectangle combined is 58 square meters. Therefore, we can set up the equation:

A_square + A_rectangle = 58

\(x^2 + (2x - 3)(x - 2) = 58\)

Expanding and simplifying the equation:

\(x^2 + (2x^2 - 4x - 3x + 6) = 58\)

\(3x^2 - 7x + 6 = 58\)

\(3x^2 - 7x - 52 = 0\)

To solve this quadratic equation, we can factor or use the quadratic formula. Factoring doesn't yield simple integer solutions in this case, so we'll use the quadratic formula:

\(x = (-b + \sqrt{ (b^2 - 4ac)}) / (2a)\)

For our equation, a = 3, b = -7, and c = -52.

Plugging in these values into the quadratic formula:

\(x = (-(-7) + \sqrt{((-7)^2 - 4(3)(-52))} ) / (2(3))\)

\(x = (7 + \sqrt{(49 + 624)} ) / 6\)

\(x = (7 +\sqrt{673} ) / 6\)

Since the side length of the square cannot be negative, we take the positive solution:

\(x = (7 + \sqrt{673} ) / 6\)

Therefore, the dimension of the square is approximately \((7 + \sqrt{673} ) / 6\)meters.

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The values of \(\(x\)\) that represent the possible side lengths of the square are  \(\[x_1 = \frac{7 + \sqrt{673}}{6}\]\)  \(\[x_2 = \frac{7 - \sqrt{673}}{6}\]\) .

Let's assume the side length of the square is x meters.

The area of the square is given by the formula:

Area of square = (side length)^2 =\(x^2\)

The width of the rectangle is 2 meters less than the side length of the square, so the width of the rectangle is\((x - 2)\) meters.

The length of the rectangle is 1 more than twice its width, so the length of the rectangle is \((2(x - 2) + 1)\) meters.

The area of the rectangle is given by the formula:

Area of rectangle = length × width = \(2(x - 2) + 1)(x - 2)\)

Given that the total area of the square and rectangle is 58 square meters, we can write the equation:

Area of square + Area of rectangle = 58

\(x^2 + (2(x - 2) + 1)(x - 2) = 58\)

Simplifying and solving this equation will give us the value of x, which represents the side length of the square.

\(\[x^2 + (2(x - 2) + 1)(x - 2) = 58\]\)

To solve the equation \(\(x^2 + (2(x - 2) + 1)(x - 2) = 58\)\) for the value of \(\(x\)\), we can expand and simplify the equation:

\(\(x^2 + (2x - 4 + 1)(x - 2) = 58\)\)

\(\(x^2 + (2x - 3)(x - 2) = 58\)\)

\(\(x^2 + 2x^2 - 4x - 3x + 6 = 58\)\)

\(\(3x^2 - 7x + 6 = 58\)\)

Rearranging the equation:

\(\(3x^2 - 7x - 52 = 0\)\)

Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the values of \(\(x\)\).

To solve the quadratic equation \(\(3x^2 - 7x - 52 = 0\)\), we can use the quadratic formula:

\(\[x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\]\)

In this equation, \(\(a = 3\), \(b = -7\), and \(c = -52\).\)

Substituting these values into the quadratic formula, we get:

\(\[x = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(3)(-52)}}{2(3)}\]\)

Simplifying further:

\(\[x = \frac{7 \pm \sqrt{49 + 624}}{6}\]\)

\(\[x = \frac{7 \pm \sqrt{673}}{6}\]\)

Therefore, the solutions to the equation are:

\(\[x_1 = \frac{7 + \sqrt{673}}{6}\]\)

\(\[x_2 = \frac{7 - \sqrt{673}}{6}\]\)

These are the values of \(\(x\)\) that represent the possible side lengths of the square. To find the dimensions of the square, you can use these values to calculate the width and length of the rectangle.

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Hey there! I'm happy to help!

First, we'll want to find the vertex of this parabola.

Given the equation y=ax^2+bx+c, the formula for the x-coordinate of the vertex is always \(-\frac{b}{2a}\).

In our equation here, our a is 1 and our b is -2.

\(-\frac{-2}{2}=\frac{2}{2}=1\)

Now that we have our x-value of our vertex, we can plug it into our equation to find our y-coordinate.

y=1²-2(1)-5

y=1-2+5

y=-1+5

y=4

So, our vertex is at (1,4).

Vertex form is y=a(x-h)²+ k where (h,k) is our vertex. We know now that our vertex is (1,4) and we also know that our a is 1, so we can simply plug it in to this equation.

y=(x-1)²+4

Have a wonderful day and keep on learning! :D

Answer:

8.50f + 3.00h = 24

Step-by-step explanation:

Answer:

let M(-3,-4) be (x1, Y1)

    T(5,0) be (x2,y2)

m:n = 2 : 3

using section formula

Q(x,y) =  {mx2 + nx1/(m+n), my2 + ny1/(m+n)}

        { ( 10 -9)/5, (0 -12)/5}

         (1/5, -12/5)

This could be answer if internally

The line with slope m that contains the point (x1, y1) can be described by the equation

y − y1 = m(x − x1). In a real-world linear situation, you may have information that represents two points on the line. You can write an equation in point-slope form that represents the situation and use that equation to solve a problem.

Let x represent the number of days since the ship left port and y represent the number of gallons of water.

Two points on the line are (8,3240) and (1, 3555).

m =  

3555 − 3240

1 − 8

 =  

315

−7

 = −45

y − y1 = m(x − x1) Point-slope form.

y − 3555 = −45(x − 1) or y − 3240 = −45(x − 8)

y − 3555 = −45(60 − 1) Substitute for x.

y − 3555 = −2655 Simplify the right side.

y = 900 Solve for y.

900 gallons of water will be left after 60 days.

Hope this helped! (I didn't do it sooner cause I just did the quiz lol)

The equation of the function, in point-slope form, is given by:

\(y - 3555 = -45(x - 1)\)

The amount of water left in the ship after 60 days is of 900 cubic units.

A line, in point-slope form, is represented by the following equation:

\(y - y_0 = m(x - x_0)\)

In which:

We have two points: (1, 3555) and (8,3240).

\(m = \frac{3240 - 3555}{8 - 1} = -45\)

Then

\(y - y_0 = m(x - x_0)\)

\(y - 3555 = -45(x - 1)\)

The amount after 60 days is y when x = 60, thus:

\(y - 3555 = -45(60 - 1)\)

\(y = 900\)

The amount of water left in the ship after 60 days is of 900 cubic units.

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It is TRUE that If you want to calculate the total magnification, take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.

If you want to get the total magnification of a microscope, you need to multiply the magnification of the objective lens by the magnification of the eyepiece lens. The objective lens typically has a magnification of 4X, 10X, or 40X, and the eyepiece lens usually has a magnification of 10X. So, for example, if you are using a 10X objective lens and a 10X eyepiece lens, the total magnification would be 10 × 10 = 100X.

On the other hand, these numbers may be the total magnification for a lower powered stereomicroscope. 10X and 40X are achievable with 10X eyepieces and 1X or 4X objective lenses. Or it can be a zoom stereomicroscope with zoom set to 1X and 4X and 10X eyepieces. To get a total of 4X, you can use the 0.8X zoom setting (which is common) plus the 5X eyepiece. Or you can use the 0.5x auxiliary lens, 0.8x zoom and 10x eyepieces.

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Complete Question:

True, or False

To get the total magnification take the power of the objective (4X, 10X, 40x) and multiply by the power of the eyepiece, usually 10X.

tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

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Answer:

22 years old

Step-by-step explanation:

let the son's age be x then the father's age is x + 20 , so

x + x + 20 = 64

2x + 20 = 64 ( subtract 20 from both sides )

2x = 44 ( divide both sides by 2 )

x = 22

that is son is 22 years old

The expression for the amount received for the second donor will be d² + 8d.

From the information, Aditi is participating in a walkathon fundraiser. two anonymous donors agree to donate money according to the distance she walks. the money, a, in dollars, that she receives from the first donor for walking d kilometers is given by the formula a(d)=12d.

The total money, t, in dollars, that she receives from both donors for walking d kilometers is given by the formula t(d)=d^2+20d.

The amount received for the second donor will be:

d² + 20d - 12d

= d² + 8d

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Complete question

Aditi is participating in a walkathon fundraiser. two anonymous donors agree to donate money according to the distance she walks. the money, a, in dollars, that she receives from the first donor for walking d kilometers is given by the formula a(d)=12d. the total money, t, in dollars, that she receives from both donors for walking d kilometers is given by the formula t(d)=d^2+20d. Find the amount received for the second donor.

Answer:

Therefore D. 57 divided by 18 has a quotient greater than 3 as it has the highest remainder with quotient of 3. All others are equal or less than 3.

Explanation:

A. 32 divided by 15  - quotient: 2 remainder: 2  → 2.133

B. 45 divided by 22  -  quotient: 2 remainder: 1  →  2.045

C. 48 divided by 16  -  quotient: 3  →  3

D. 57 divided by 18  -  quotient: 3 remainder: 3  →  3.167

The height of the building is approximately 79.22 meters, rounded to the nearest meter.

To calculate the angle of elevation, we use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle.

We know that the pole is 3.5 meters tall, and its shadow is 1.77 meters long. We can use this information to calculate the angle of elevation of the sun's rays, which is the angle formed between the horizontal line and the line of sight from the top of the pole to the sun.

In this case, the opposite side is the height of the pole (3.5 meters), and the adjacent side is the length of the shadow (1.77 meters). Therefore, we have:

tan(angle of elevation) = opposite/adjacent = 3.5/1.77

Using a calculator, we can find that the angle of elevation is approximately 63.24 degrees.

Now, we can use this angle to find out the height of the building. We know that the shadow of the building is 43.5 meters long, and we want to find its height, which is the opposite side of the right triangle formed by the angle of elevation and the length of the shadow. Therefore, we have:

tan(63.24 degrees) = opposite/43.5

Solving for the opposite, we get:

opposite = 43.5 * tan(63.24 degrees) = 79.22 meters

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Answer:

See answers below (and image for functions)

Step-by-step explanation:

g(x) = (3)^5x is a horizontal compression

h(x) = 4(3)^x is a vertical stretch since |a|>1

p(x) = 1/2(3)^x is a vertical compression since 0<|a|<1

w(x) = 3^0.2x is a horizontal stretch