What is the solution to this equation:
X+7=-8

The smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

What is the intermediate value theorem?

Intermediate value theorem is theorem about all possible y-value in between two known y-value.

x-intercepts

-x^2 + x + 2 = 0

x^2 - x - 2 = 0

(x + 1)(x - 2) = 0

x = -1, x = 2

y intercepts

f(0) = -x^2 + x + 2

f(0) = -0^2 + 0 + 2

f(0) = 2

(Graph attached)

From the graph we know the smallest positive integer value that the intermediate value theorem guarantees a zero exists between 0 and a is 3

For proof, the zero exists when x = 2 and f(3) = -4 < 0 and f(0) = 2 > 0.

Your question is not complete, but most probably your full questions was

Given the polynomial f(x)=− x 2 +x+2 , what is the smallest positive integer a such that the Intermediate Value Theorem guarantees a zero exists between 0 and a ?

Thus, the smallest positive integer that the intermediate value theorem guarantees a zero exists between 0 and a is 3.

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The height of the building is 8 units if a girl is standing 8 units away from the building at point P.

To solve this problem, we'll use the tangent function. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side.

In this case, the opposite side is the height of the building, which we want to find, and the adjacent side is the distance between the girl (point P) and the building. Since the angle of elevation is 45°, we can write the equation:

tan(45°) = height of the building / 8

Now, let's solve for the height of the building. We can start by finding the value of the tangent of 45°, which is 1.

1 = height of the building / 8

To isolate the height of the building, we multiply both sides of the equation by 8:

8 * 1 = height of the building

Simplifying the equation:

height of the building = 8

Therefore, the height of the building is 8 units.

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Complete Question:

1. Design a pole-placement controller to satisfy the following problem using angle of elevation use Matlab to aid in your calculations.

If a girl is standing at point P, which is 8 units away from a building, making an angle of elevation of 45° with point Q, find the height of the building.

Answer:9 hours

Step-by-step explanation:

when rounding to the nearest tenth, you use the number behind the decimal to determine which way you go. if it's below five(.1, .2, .3, .4) then you go down, if its above five(.6, .7, .8, .9) you would up. in this case, it's above fine, so we round up, which would make the total hours Andreas spent on the project 9 hours.

Answer:

She should walk at a rate of 16 km/hr

Step-by-step explanation:

At a rate of 12 km/hr, she would have traveled 4 km in 20 minutes. This can be calculated by finding the ratio of 20 minutes to 1 hour which is 1/3. We then multiply this ratio by the rate to find the distance Shalu needs to walk to school.

We then need to find the necessary km/hr in order for Shalu to travel 4 km in 15 minutes. 15 minutes is a quarter of 1 hr. Therefore a rate of 4 km/15 minutes is equal to a rate of 16 km/hr. This means that the average speed Shalu would have to walk is 16 km/hr.

Answer:

Divide the number of events by the number of possible outcomes. After determining the probability event and its corresponding outcomes, divide the total number of ways the event can occur by the total number of possible outcomes. For instance, rolling a die once and landing on a three can be considered one event.

Step-by-step explanation:

for more information check the above attachment

Answer:

Three Hundred Seventy-Five Million Dollars

Step-by-step explanation:

The Laplace equation is defined as Au=0. The aim is to solve analytically Laplace's equation in the square [0, 1]²2 with boundary conditions u(x,0) = 0 = u(0, y), u(x, 1) = u(1, y) = 1.

Let's consider the Laplace equation as followsAu = ∂²u/∂x² + ∂²u/∂y²= 0Given boundary conditions areu(x, 0) = 0u(0, y) = 0u(x, 1) = u(1, y) = 1The solution of the Laplace equation is as followsu(x,y) = X(x).Y(y)Let's find the boundary conditionsu(x, 0) = 0

Let's substitute the value of Y(0) in the solution to get X(x).Y(0) = 0, which implies Y(0) = 0Similarly, u(0, y) = 0 => X(0).Y(y) = 0 => X(0) = 0Now, let's find the remaining boundary conditionsu(x, 1) = 1X(x).Y(1) = 1 => Y(1) = 1/X(x)u(1, y) = 1 => X(1).Y(y) = 1 => X(1) = 1/Y(y)Now, let's put the values of X(0) and X(1) in the below equationX(0) = 0, X(1) = 1/Y(y)X(x) = x

Now, let's put the values of Y(0) and Y(1) in the below equationY(0) = 0, Y(1) = 1/X(x)Y(y) = sin(n.π.y) /sinh(n.π)Therefore, the solution of Laplace's equation u(x, y) is as follows;u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π)Answer:Therefore, the solution of Laplace's equation u(x, y) is u(x,y) = Σ(n=1 to ∞)sin(n.π.y).sinh(n.π.x) /sinh(n.π).

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The figure that represents the image of P is given as follows:

Figure A.

The rotation rules are defined as follows:

The vertices of figure P are given as follows:

(-2, -2), (-6,-2) and (-3,-7).

The rule for a rotation of 90º degrees counterclockwise about the origin is given as follows:

(x,y) -> (-y,x).

Meaning that the vertices of the image of P are given as follows:

(2,-2), (2,-6) and (7,-3).

Meaning that Figure A is the image of P.

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The standard deviation of a larger sample will be closer to the standard deviation of the population than the standard deviation of a smaller sample, making it a better estimate of the population standard deviation.

In order to measure the variability or spread of a population, a population standard deviation is utilized. This is frequently unknown and estimated using the standard deviation of a random sample taken from the population. The sample standard deviation is the measure of variability for a set of data values obtained from a sample.The sample standard deviation is preferable to the population standard deviation for samples, particularly large samples. The sample standard deviation, abbreviated as "s", is used to estimate the population standard deviation, represented by the Greek letter sigma, which is unknown in this situation. The sample standard deviation is more likely to accurately reflect the true population standard deviation when it is calculated from a large sample size.Samples from populations that have a normal distribution provide the most precise estimate of the population standard deviation. If the population distribution is not normal, the sample size should be at least 30. However, for smaller samples, it is impossible to estimate the population standard deviation using the sample standard deviation. This is particularly true when the population has an atypical or unusual distribution.

In conclusion, the sample standard deviation (s) is a better estimate of the population standard deviation for large samples.

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The results are as follows:

Mean (μ) = μ

Variance = 50

ACF at lag 1 (ρ(1)) = 0

ACF at lag 2 (ρ(2)) = -0.7071

ACF at lag 3 (ρ(3)) = 0

PACF at lag 1 (ψ(1)) = -0.7071

PACF at lag 2 (ψ(2)) = 0

PACF at lag 3 (ψ(3)) = 0

To find the mean, variance, autocorrelation functions (ACF), and partial autocorrelation functions (PACF) for the given MA(2) process, we need to follow a step-by-step approach.

Step 1: Mean

The mean of an MA process is equal to the constant term (μ). In this case, the mean is μ + 0, which is simply μ.

Step 2: Variance

The variance of an MA process is equal to the sum of the squared coefficients of the error terms. In this case, the variance is 5^2 + 5^2 = 50.

Step 3: Autocorrelation Function (ACF)

The ACF measures the correlation between observations at different lags. For an MA(2) process, the ACF can be determined by the coefficients of the error terms.

ACF at lag 1:

ρ(1) = 0

ACF at lag 2:

ρ(2) = -5 / √(variance) = -5 / √50 = -0.7071

ACF at lag 3:

ρ(3) = 0

Step 4: Partial Autocorrelation Function (PACF)

The PACF measures the correlation between observations at different lags, while accounting for the intermediate lags. For an MA(2) process, the PACF can be calculated using the Durbin-Levinson algorithm or other methods. Here, since it is an MA(2) process, the PACF at lag 1 will be non-zero, and the PACF at lag 2 onwards will be zero.

PACF at lag 1:

ψ(1) = -5 / √(variance) = -5 / √50 = -0.7071

PACF at lag 2:

ψ(2) = 0

PACF at lag 3:

ψ(3) = 0

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If Pham burgers has beginning net fixed assets of $684218 , ending net fixed assets of $679426 and depreciation expense of $48859 , then the net capital spending for the year is $44067  .

For the Pham burgers , the Beginning Net Fixed Assets is = $684218 ;

the ending net fixed assets for Pham burgers is = $679426  ;

the depreciation expense for Pham burgers is = $48859 ;

the tax rate is 21% , which is not relevant for this question ;

The Net capital Spending for the year can be calculated using the formula :

\((Ending \; Net \; Fixed \;Assets - Beginning \; Net\; Fixed \; Assets) + Depreciation\) ;

substituting the required values ,

we get ;

Net Capital Spending for year is = ($679426 - $684218) + $48859 ;

On simplifying ,

we get ;

= $44067 .

Therefore , the Net Capital Spending for the year is $44067  .

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Outcome 1 2 3 4 5 6 7 8

Probability 1/28 1/14 3/28 1/7 5/28 3/14 1/4 2/7

Since the die is weighted such that each number is k times more likely to land facing up than the previous number, we can set up the following probability distribution:

Outcome 1 2 3 4 5 6 7 8

Probability k 2k 3k 4k 5k 6k 7k 8k

To find the value of k, we know that the probabilities must add up to 1:

k + 2k + 3k + 4k + 5k + 6k + 7k + 8k = 1

28k = 1

k = 1/28

Thus, the probability distribution for the face landing up is:

Outcome 1 2 3 4 5 6 7 8

Probability 1/28 2/28 3/28 4/28 5/28 6/28 7/28 8/28

Simplifying, we get:

Outcome 1 2 3 4 5 6 7 8

Probability 1/28 1/14 3/28 1/7 5/28 3/14 1/4 2/7

Therefore, the probability of rolling each number on the octahedral die is as shown in the table above.

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Answer:

Problem 1:  1/64x^8

Problem 2: y^8/9x^2

Step-by-step explanation:

In the first problem, you first need to multiply the -2 exponent to everything in the parenthesis. This is equal to 1/64x^4*-2, simplified to be 1/64x^-8. Finally you simplify the x to 1/64x^8.

For the second problem, you do the same in the first one, getting x^-2/9y^4*-2. This can be simplified to be 3x^-2/y^-8. Finally you make sure there is no negative exponents, so you do y^8/9x^2.

Answer:

1/64x^8 and y^8/9x^2

Step-by-step explanation:

hope this helps have a good night :)

Answer:

The volume of the triangular prism is 677.6 cubic meters.

Step-by-step explanation:

The formula for the volume of a triangular prism is:

\(\sf\qquad\dashrightarrow Volume \: (V) = \dfrac{1}{2} \times b\times h \times l \)

where:

Substituting the given values, we have:

\(\sf:\implies Volume \: (V) = \dfrac{1}{2} \times 11 \times 11 \times 11.2\)

\(\sf:\implies \boxed{\bold{\:\:Volume \: (V) = 677.6\: meters^3\:\:}}\:\:\:\green{\checkmark}\)

Therefore, the volume of the triangular prism is 677.6 cubic meters.

Greetings! ZenZebra at your service, hope it helps! <33

There are 9 possible schedules to play basketball such that dave can play on monday or wednesday or both which is union of two set .

so this question seems like we have to take union of ways of palying on monday or wednesday

let n(m) be number of ways of playing on monday

n(w) be number of ways of playing on wednesday

we have to find n(m∪w)

n(mUw) = n(m) +n (w) - n(m∩ w)

so n(m) = \(4_C__2\) as one day is now fixed which is monday so we have 4 available days and 2 days to play.

n(m) = \(4_C__2\)  = 6

similary n(m) = n(w) = 6

now  n(m∩w) = \(3_C__1\) as now we have  2 fixed day and we have 3 day remaining and only one day to play.

n(m∩w) = \(3_C__1\) =3

now n(mUw) = n(m) +n (w) - n(m∩ w)

=> 6 + 6 -3

=> 12 - 3

so n(mUw) = 9

so we have 9 schedules to paly keeping condition given in the question.

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Answer:

212

Step-by-step explanation:

Basically mean is calculated by adding up the pages of the 4 different books and dividing the total by the number of books.

First you add: 186+210+246+206= 848.

Then you divide 848 by the number of books (4).

848/4 = 212.

Answer:

Step-by-step explanation:

By triangle sum theorem,

73°+ 39° + m∠1 = 180°

m∠1 = 180° - 102°

m∠1 = 78°

Since, m∠1 = m∠2 [Vertically opposite angles]

m∠2 = 78°

Sum of interior angles of a polygon = (n - 2)×180°

Where n = number of sides of the polygon

Sum of the interior angles of a quadrilateral = (4 - 2)×180°

= 360°

Therefore, 77° + m∠3 + 90° + m∠2 = 360°

77° + m∠3 + 90° + 78° = 360°

m∠3 = 360° - 245°

m∠3 = 115°

The measure of each angle formed by the three support beams for a bridge is 45 degrees.

The question states that three support beams for a bridge form a pair of complementary angles. Complementary angles are two angles that add up to 90 degrees.

Let's denote the angles as Angle A and Angle B. Since the angles are complementary, we can set up the following equation:

Angle A + Angle B = 90 degrees.

To find the measure of each angle, we need to divide 90 degrees by 2 since there are two angles.

Angle A = Angle B = 90 degrees / 2 = 45 degrees.

Therefore, each angle measures 45 degrees.

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The measure of each angle is 45 degrees.

To find the measure of each angle, we need to understand what complementary angles are. Complementary angles are two angles that add up to 90 degrees.

In this case, we have three support beams for a bridge that form a pair of complementary angles. Since the angles are complementary, their sum is 90 degrees.

Let's assume the measure of one angle is x degrees. The other angle will be (90 - x) degrees, as their sum is 90 degrees.

Since the three support beams form a pair of complementary angles, we can set up the equation:

x + (90 - x) = 90

By simplifying the equation, we have:

90 - x + x = 90

90 = 90

This equation is true for any value of x. Therefore, the measure of each angle can be any value, as long as their sum is 90 degrees.

So, the measure of each angle is not fixed, but it will always add up to 90 degrees.

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Answer:

Below.

Step-by-step explanation:

Total marbles = 16

(a)  Replacing the first marble:

Probability = 5/16 * 3/16

= 15/256

Not replacing the first marble:

Probability = 5/16 * 3/15

= 5/16 * 1/5

= 5/80

= 1/16.

Comparing the 2 values:

Probability of   Not replacement /  Replacement = 1/16 / 15/256

= 256 / 15* 16

= 16/15

Thus you are 16/15 = 1.0667 times more likely to pick a blue then a red when you do not replace the first marble.

Answer:

Height of cylinder = 12 cm

Step-by-step explanation:

Given:

Radius of cylinder = 6 cm

Curved surface area of cylinder = [2/3][Total surface area of cylinder]

Find:

Height of cylinder

Computation:

Curved surface area of cylinder = [2/3][Total surface area of cylinder]

2πrh = [2/3][2πr(h + r)]

h = 2h/3 +[2/3][6]

h - 2h/3 = 4

[3h - 2h] / 3 = 4

h = 12

Height of cylinder = 12 cm

Answer:

Option B (16 cm³)

Step-by-step explanation:

GIVEN :-

TO FIND :-

FACTS TO KNOW BEFORE SOLVING :-

Hence ,

Volume of cylinder = Thrice the volume of cone

[OR]

Volume of cone = One third of volume of cylinder

PROCEDURE :-

Volume of cone = \(\frac{1}{3} (Volume \: of \: cylinder) = \frac{48}{3} = 16cm^3\)

Answer:

-3/100

Step-by-step explanation:

Used gogle

a) We have a translation of 2 units to the right and 4 units up, and this is written as:

b) g(x) = ∛(x - 2) + 4

The turning point for the cubic root is at the point (0, 0), while on the given graph we can see that the turning point is at (2, 4), then we have a translation of 2 units to the right and 4 units upwards.

To write this function we will have:

g(x) = f(x - 2) + 4

replacing f(x) by the cubic root function we will get:

g(x) = ∛(x - 2) + 4

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The exact value of cos(tan^(-1)(8/3)) is (3/√73).This expression represents the cosine of the angle u, where u is the inverse tangent of 8/3.

To calculate cos(tan^(-1)(8/3)), we start by considering an angle u = tan^(-1)(8/3). We can draw the angle u on the coordinate axes and construct a right triangle to represent it. Let's label the sides of the triangle as follows:

Opposite side: 8

Adjacent side: 3

Hypotenuse: h (unknown)

We know that tan(u) = opposite/adjacent, so tan(u) = 8/3. By using the Pythagorean theorem, we can find the value of the hypotenuse:

h^2 = (opposite)^2 + (adjacent)^2

h^2 = 8^2 + 3^2

h^2 = 64 + 9

h^2 = 73

Taking the square root of both sides, we find h = √73. Now, we can calculate cos(u) using the adjacent side and the hypotenuse:

cos(u) = adjacent/hypotenuse

cos(u) = 3/√73

The exact value of cos(tan^(-1)(8/3)) is (3/√73). This expression represents the cosine of the angle u, where u is the inverse tangent of 8/3.

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Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.

An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.

An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"

2x + y = 4

now, putting the values in the equation (6,-8)

2(6) + (-8) = 4

or, 12 - 8 = 4

or, 4 ≡ 4

This equation, point IS a solution to the system.

x + 3y = - 20

or, 6 + 3(-8) = -20

or, 6 - 24 = -20

or, - 18 ≠ - 20

So, for this equation the result is not identity.

Thus, option A is the correct answer.

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