select the number and name of the degree of :4x^8+5x^2+9x-7

If the distribution of observations were perfectly symmetrical and unimodal, option B) The mean, median, and mode would be the same.

In a perfectly symmetrical and unimodal distribution, the mean, median, and mode would be equal. This is because in such a distribution, the data would be evenly spread around a central value. The mean is calculated by summing all the observations and dividing by the total number of observations. Since the distribution is symmetrical, the sum of the observations on one side of the central value would be equal to the sum on the other side, resulting in a balanced mean.

The median is the middle value when the observations are arranged in ascending or descending order. In a symmetrical distribution, the middle value would be the same as the central value, leading to the median being equal to the mean.

The mode represents the value that appears most frequently in the distribution. In a perfectly symmetrical and unimodal distribution, all values would occur with the same frequency, resulting in multiple modes. However, since the distribution is unimodal, meaning it has only one peak, all the modes would coincide, and the mode would also be equal to the mean and median. Therefore, in a perfectly symmetrical and unimodal distribution, the mean, median, and mode would all be the same value, leading to answer B) The mean, median, and mode would be the same.

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Answer:

x = 8 degrees ; y= 12 degrees

Step-by-step explanation:

According to the information, the null hypothesis is that 70% or fewer of the instructor's students have improved their driving distance by at least 20 yards. The alternative hypothesis is that more than 70% of the instructor's students have improved their driving distance by at least 20 yards. Based on the data provided, we can evaluate whether the instructor's claim is valid.

Accordign to the information we have to consider that the null hypothesis states that 70% or fewer of the instructor's students have improved their driving distance by at least 20 yards, while the alternative hypothesis suggests that more than 70% have seen such improvement.

According to the above, the claim's validity is assessed by comparing the observed data with the expected outcome under the null hypothesis. In this case, 138 out of 180 viewers reported an improvement. Statistical tests can be conducted to determine if this observed proportion significantly differs from the hypothesized proportion of 70% or fewer.

To conclude, if the test results reject the null hypothesis, there is evidence to support the claim; otherwise, the claim cannot be validated.

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No, the instructor's claim is NOT valid. See   the explanation below.

To   test the hypothesis, we can use a z- test.

z = (p - p₀) / σ

Where

σ = √(p₀(1 - p₀) / n)

where:

Since p  =138/180

= 0.7667.

p₀=0.7. The sample size is n=180.

z = (0.7667 - 0.7) / √(0.7(1 - 0.7) / 180)

= 1.95277604597

≈ 1.92

Since the p-value for a z-score of 1.92 is 0.054, we can reject the null hypothesis.

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Answer:

Here is your answer

((10 * 10) ^ 4) ^ 4 =

(100 ^ 4) ^ 4 =

100000000 ^ 4 = 100000000000000000000000000000000

Step-by-step explanation:

\(\huge\text{Hey there!}\)

\(\mathsf{((10 * 10) ^ 4) ^ 4}\)

\(\mathsf{= (10 \times 10^4)^4}\)

\(\mathsf{= (10 \times 10 \times 10 \times 10 \times 10)^4}\)

\(\mathsf{= (10 \times 100 \times 100)^4}\)

\(\mathsf{= (10 \times 10,000)^4}\)

\(\mathsf{= (100,000)^4}\)

\(\mathsf{= 100,000^4}\)

\(\mathsf{= 100,000 \times 100,000 \times 100,000 \times 100,000}\)

\(\mathsf{= 10,000,000,000 \times 10,000,000,000}\)

\(\mathsf{= 100,000,000,000,000,000,000}\)

\(\huge\text{Therefore, your answer should be: }\)

\(\huge\boxed{\mathsf{100,000,000,000,000,000,000}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

Answer: For number 8 it is 2  For number 9 it is confusing

Step-by-step explanation:

Answer:

21.7 cm²

Step-by-step explanation:

Given:

Right ∆BCD,

<D = 60°

adjacent length = 5 cm

Required:

Area of ∆BCD

SOLUTION:

Step 1: find the height (opposite side length) of ∆BCD

\( tan(D) = \frac{opp}{adj} \)

\( tan(60) = \frac{h}{5} \)

Multiply both sides by 5

\( tan(60)*5 = \frac{h}{5}*5 \)

\( tan(60)*5 = 8.7 cm \) (approximated)

Step 2: find the area of ∆BCD

Area = ½*base*height

Area = ½*5*8.7 = 21.7 cm² (nearest tenth)

Provided in the question, total number of people that can be accommodated in the theatre are 471.

Then, according to the question there are two possibilities. The number of people is less than the total number of People who can be accommodated.

\(1) \: p + 254 < 471\)

Or, they can be equal to the number of people.

\(2) \: p + 254 = 471\)

Combining both the inequations, We get

\( \boxed{ p + 254 \leqslant 471}\)

So, the correct option is Option D

━━━━━━━━━━━━━━━━━━━━

Answer:

3 1/8

Step-by-step explanation:

6 1/4 ÷ 2

~Turn each number into an improper fraction

25/4 ÷ 2/1

~Copy Dot Flip

25/4 * 1/2

~Multiply

25/8 or 3 1/8

Best of Luck!

When the mixed number i.e. \(6\frac{1}{4}\) is divided by 2 so the answer is \(3 \frac{1}{8}\)

Given that,

Based on the above information, the calculation is as follows:

\(= 6\frac{1}{4} \div 2\\\\= \frac{25}{4} \div 2\\\\= \frac{25}{4} \times \frac{1}{2} \\\\= \frac{25}{8}\\\\= 3 \frac{1}{8}\)

Therefore we can conclude that when the mixed number i.e. \(6\frac{1}{4}\) is divided by 2 so the answer is \(3 \frac{1}{8}\)

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The response y(t) graphically, we can first plot the individual functions h(t) and x(t) on a graph, and then determine their convolution to obtain y(t). Let's go step by step:

Plotting h(t):

The function h(t) is defined as h(t) = [u(t-1) - u(t-4)].

The unit step function u(t-a) is 0 for t < a and 1 for t ≥ a. Based on this, we can plot h(t) as follows:

For t < 1, h(t) = [0 - 0] = 0

For 1 ≤ t < 4, h(t) = [1 - 0] = 1

For t ≥ 4, h(t) = [1 - 1] = 0

So, h(t) is 0 for t < 1 and t ≥ 4, and it jumps up to 1 between t = 1 and t = 4. Plotting h(t) on a graph will show a step function with a jump from 0 to 1 at t = 1.

Plotting x(t):

The function x(t) is defined as x(t) = t[u(t) - u(t-2)].

For t < 0, both u(t) and u(t-2) are 0, so x(t) = t(0 - 0) = 0.

For 0 ≤ t < 2, u(t) = 1 and u(t-2) = 0, so x(t) = t(1 - 0) = t.

For t ≥ 2, both u(t) and u(t-2) are 1, so x(t) = t(1 - 1) = 0.

So, x(t) is 0 for t < 0 and t ≥ 2, and it increases linearly from 0 to t for 0 ≤ t < 2. Plotting x(t) on a graph will show a line segment starting from the origin and increasing linearly with a slope of 1 until t = 2, after which it remains at 0.

Obtaining y(t):

To obtain y(t), we need to convolve h(t) and x(t). Convolution is an operation that involves integrating the product of two functions over their overlapping ranges.

In this case, the convolution integral can be simplified because h(t) is only non-zero between t = 1 and t = 4, and x(t) is only non-zero between t = 0 and t = 2.

The convolution y(t) = h(t) * x(t) can be written as:

y(t) = ∫[1,4] h(τ) x(t - τ) dτ

For t < 1 or t > 4, y(t) will be 0 because there is no overlap between h(t) and x(t).

For 1 ≤ t < 2, the convolution integral simplifies to:

y(t) = ∫[1,t+1] 1(0) dτ = 0

For 2 ≤ t < 4, the convolution integral simplifies to:

y(t) = ∫[t-2,2] 1(t - τ) dτ = ∫[t-2,2] (t - τ) dτ

Evaluating this integral, we get:

\(y(t) = 2t - t^2 - (t - 2)^2 / 2,\) for 2 ≤ t < 4

For t ≥ 4, y(t) will be 0 again.

Maximum value of y(t):

To find the value of t at which y(t) reaches its maximum value, we need to examine the expression for y(t) within the valid range 2 ≤ t < 4. We can graphically determine the maximum by plotting y(t) within this range and identifying the peak.

Plotting y(t) within the range 2 ≤ t < 4 will give you a curve that reaches a maximum at a certain value of t. By visually inspecting the graph, you can determine the specific value of t at which y(t) reaches its maximum.

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The function is not one to one function.

What is one to one function?

A function f(x) is sait to be one to one function if it satisfies the following two conditions:

(1) \(f(x_1)=f(x_2)\) implies \(x_1=x_2\).

(2) ∀\(x_1\), ∀\(x_2\), \(x_1\ne x_2\) implies that \(f(x_1) \ne f(x_2)\).

It means that there is only one value for each value of the variable x.

Now, consider the given function.

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

If it is one to one function then it must satisfy the above two conditions.

Lets check the first condition. Substitute 3 for x.

\(2(3-1)^2+3=f(3)\\11=f(3)\)

Again, substitute -1 for x.

\(2(-1-1)^2+3=f(-1)\\11=f(-1)\)

Hence at two different values of x the function have the same value.

In this case, f(-1)=f(3) but \(-1 \ne 3\). Hence, it do not satisfy the first condition.

Hence, the given function is not one to one function.

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Answer:

(1, 6).

Step-by-step explanation:

The reflection of  the x coordinate of (1, 2) creates a point with y -coordinate

-1 - 3 = -4 while the x-coordinate  remains 1.

The point (1, -4) is now reflected about  y = 1, so  -4 translates to 1 + 5 = 6. and x stays at 1.

Answer is (1, 6).

In the given point (2,1/4), 2 is on the x axis and 1/4 represent the y axis. The point (2,1/4) on the coordinate plane is given below;

In the given question we have to represent the given point in the coordinate plane.

The given coordinate is (2, 1/4).

Firstly we learn about the coordinate.

The coordinate are the points that shows the position of point on the x axis and y axis.

The first point shows the x axis and second point shows the y axis.

So in the given point 2 is on the x axis and 1/4 represent the y axis.

We can write 1/4 as 0.25.

The point (2,1/4) on the coordinate plane is given below;

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Answer:

I

Step-by-step explanation:

graph is not provided

Answer: We may utilize the characteristics of related triangles to determine the breadth of the river.

Step-by-step explanation:

Let's write "x" for the river's breadth.

Triangle RQS has RS = 42 feet.

ST = 28 ft

SQ = RS + ST = 42 + 28 feet equals 70 feet.

Triangle TSU has TU = 68 feet.

Triangles RQS and TSU can be compared to one another since points U, S, and Q are collinear.

The following ratio can be established using the comparable triangles property:

RQ / TS equals RS / TU.

By replacing the specified numbers, we get (x / 70 ft) = (42 ft / 68 ft).

Now, we may multiply by x to find the answer:

x = (42 ft * 70 ft) / 68 ft, rounded to the nearest two decimal places, equals 43.23529411764706 ft.

As a result, the river is roughly 43.24 feet wide.

a. Since the vertical component of velocity v' = 241.05 mph > v" = 229.43 mph, the first plane is rising faster

b. I would change the angle of elevation of both planes

Two planes at started to take off at the same time. Plane One took off from the tarmac going 375 mph at an angle of elevation of 40° and Plane Two took off from the tarmac going 400 mph at an angle of elevation of 35°, to fidn which plane is rising faster, we compute their vertical component of velocity of the plane .

The vertical component of velocity is v' = vsinФ where

For the first plane

So, v' = vsinФ

= (375 mph)sin40°

= (375 mph) × 0.6428

= 241.05 mph

For the second plane

So, v" = vsinФ

= (400 mph)sin35°

= (400 mph) × 0.5736

= 229.43 mph

Since v' = 241.05 mph > v" = 229.43 mph

So, the first plane is rising faster

To make both planes rise at the same rate, I would change the angle of elevation of both planes

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The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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Larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

For a population that is not normally distributed, the distribution of the sample means will approach a normal distribution as the size of the sample increases.

This is known as the Central Limit Theorem, which states that as the sample size increases, the distribution of sample means becomes more normal regardless of the shape of the population distribution.

Therefore, larger sample sizes provide more accurate estimates of the population mean, even if the population is not normally distributed.

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Answer:

2x+3=4

2x=1

x=0.5

.....

Answer:

x-y

-18-(-15)

-18+15

-3

The graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

Here we have:

\(f(x) = x^3\\\\g(x) = (x - 2)^3 + 6\)

You can notice that if we take f(x), and we shift it 2 units to the right, we have:

g(x) = f(x - 2)

Then if we apply a shift upwards of 6 units, then we have:

g(x) = f(x - 2) + 3

Replacing f(x) by the cubic parent function, we have:

\(g(x) = (x - 2)^3 + 6\)

So we conclude that the graph of g(x) is the graph of f(x) translated 2 units to the right and 6 units up.

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A line segment of length 8.6 cm, when bisected the length of each half is  4.3cm.

Draw a straight line and mark two points A and B that are 8.6 cm apart.

With A as centre and radius more than half of AB, draw arcs on both sides of AB.

With the same radius and B as centre, draw arcs on the both sides of AB, cutting the previous two arcs.

Label the intersection points of the two arcs as E and F.

Draw a straight line connecting points E and F. This is the line of symmetry and bisects the line segment AB.

The length of each part of the bisected line segment is equal. To measure the length of each part, we can use a ruler to measure the distance from point A to the intersection point C and from point B to the intersection point D. Each of these distances should be approximately 4.3 cm, which is half the length of the original segment.

we get: AC=BC=4.3 cm.

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____The given question is incomplete, the complete question is given below:

Draw a line segment of length 8.6 cm. Bisect it and measure the length of each part.  

The equation of the line is y = 13/6x - 5

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

Points: (0, -5) and (6, 8)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

This means that

c = -5

So, we have

y = mx - 5

Also, we have

(x, y) = (6, 8)

This means that

8 = m x 6 - 5

So, we have

6m = 13

This gives

m = 13/6

So, we have

y = 13/6x - 5

Hence, the equation is y = 13/6x - 5

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Answer:

The diameter would be 12.

The coordinates of the vertices of the resulting image A'B'C'D'E' is A'(-2,2), B'(-4, 2), C'(-6,4), D'(-4,6) and E' (-2,6) when ABCDE

is rotated 90° counterclockwise about the origin.

When point M (h, k) is rotated through 90 degrees in a clockwise direction around the origin O, the rotation of the point occurs. M' will represent the updated location of point M (h, k) will become M'(k, -h).

In 90° counterclockwise rotation,

(x, y) becomes (-y, x)

A(2, 2) becomes A (-2, 2)

B (2, 4) becomes B' (-4,2)

C(4,6) becomes C (-6, 4)

D (6,4) becomes D' (-4,6)

E (6, 2) becomes E' (-2, 6)

Answers:

A'(-2,2)

B'(-4, 2)

C'(-6,4)

D'(-4,6)

E' (-2,6)

Hence there are the answers for the given question.

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He received: (180 × 5/6) votes

= 150 votes

Answer:

150 votes

Step-by-step explanation:

We require to calculate

\(\frac{5}{6}\) of 180 , that is

\(\frac{5}{6}\) × 180 ( divide 180 by 6, then multiply answer by 5 ) , so

5 × 30

= 150

The function f(x) = 2x³ - 6x² + 90x is increasing on the intervals (-∞, -5) and (3, ∞), and decreasing on the interval (-5, 3). The local minimum value of f is -162, and the local maximum value of f is 350.

To find the intervals on which f is increasing or decreasing, we can use the derivative of f. The derivative of f is f'(x) = 6(x + 5)(x - 3). f'(x) = 0 for x = -5, 3. Since f'(x) is a polynomial, it is defined for all real numbers. Therefore, our critical points are x = -5 and x = 3.

f'(x) is positive to the left of x = -5 and to the right of x = 3, and it is negative between x = -5 and x = 3. This means that f is increasing on the intervals (-∞, -5) and (3, ∞), and decreasing on the interval (-5, 3).

To find the local minimum and maximum values of f, we can look for the critical points and the endpoints of the function's domain. The critical points are x = -5 and x = 3. The endpoints of the function's domain are x = -∞ and x = ∞.

f(-5) = -162 and f(3) = 350. Therefore, the local minimum value of f is -162, and the local maximum value of f is 350.

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Answer:

x < 12/7

Step-by-step explanation: