I really need some help

Answer:

C

Step-by-step explanation:

Given

4\(x^{4}\) - 20x³ + 12x² ← factor out 4x² from each term

= 4x² (x² - 5x + 3) → C

Answer:

7/4 inches

Step-by-step explanation:

Longest bean sprout = 8/8 + 8/8

Longest bean sprout = 1 + 1

Longest bean sprout = 2

Shortest bean sprout = 2/8

Difference = 2 - 2/8

Difference  = (16-2)/8

Difference  = 14/8

Difference = 7/4

Hence the distance is 7/4 inches

Answer:

12.5

Step-by-step explanation:

7x + 20 +5x +10 = 180

12x +30= 180

12x = 180-30

12x = 150

x = 150/12

x = 12.5

On solving the provided question, we can say that the probability of guessing the sequence 2^99 possible combinations.

Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true.

As soon as you realize there are more heads than tails, you realize you require at least 50 of them, and you ask 100 people to select 50 locations for them to go.

Considering that you have 250 options for the remaining coins, there are a total of (100 pick 50) + 250 combinations that are feasible.

There are 299 potential options if you simply inquire as to whether the first coin will land on heads.

Asking whether there are more heads than tails is preferable because, according to Wolfram Alpha, 299 is larger than (100 pick 50) + 250.

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The surface area of the given rectangular prism with Height = 12 in, Length = 7 in, Width = 6 in is 396 square inches.

To find the surface area of a rectangular prism, we need to add up the areas of all six faces. The formula to find the surface area of a rectangular prism is:

Surface area = 2lw + 2lh + 2wh

Where l, w, and h are the length, width, and height of the rectangular prism, respectively.

Substituting the given values into the formula, we get:

Surface area = 2(7)(6) + 2(7)(12) + 2(6)(12)

Surface area = 84 + 168 + 144

Surface area = 396 square inches

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The Cartesian equation of the line that contains the points A and B, where A is the intersection point of the given plane with the x-axis and B is the intersection point with the z-axis, is x = 1 and z = 3.

To find the Cartesian equation of the line, we need to determine the values of x and z while allowing y to vary freely. Since point A lies on the x-axis, its y-coordinate is 0, so we have x = 1 and y = 0 for point A. Similarly, since point B lies on the z-axis, its y-coordinate is also 0, so we have z = 3 and y = 0 for point B.

Thus, the equation x = 1 represents the line that contains point A, and the equation z = 3 represents the line that contains point B. Since y can vary freely, we do not include it in the equations. Therefore, the Cartesian equation of the line that contains points A and B is x = 1 and z = 3.

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The OLS assumption most likely violated by omitted variables bias is: E(μ₁|X₁) = 0.

Omitted variables bias occurs when a relevant variable is left out of the regression model, leading to biased and inconsistent estimates. This violates the OLS assumption that the expected value of the error term, given the independent variable (E(μ₁|X₁)), is equal to zero.

When omitted variables bias is present, the error term captures the effect of the omitted variable, resulting in a non-zero expected value of the error term conditional on the independent variable. This can cause misleading inferences and incorrect conclusions about the relationships between the variables in the model.

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The value of g(1) is 4 because  (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

As we know if the f(x) has inverse function g(x)

Let (x, y) satisfy the function f(x) then (y, x) must satify the function g(x)

f(x) has ordered pair = (4, 1)

Then g(x) has (1, 4)

g(1) = 4

Thus, the value of g(1) is 4 because  (x, y) satisfy the function f(x) then (y, x) will satify the function g(x) option (D) 4 is correct.

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(-9, 2)

Note that the coordinates of the center of a line are given by the formulae:

The center of the line (a, b) = (-4, 2)

The first point on the line (x₁, y₁) = (1, 2)

The other end of the line = (x₂, y₂)

The point also located on the circle W is (-9, 2)

Answer:

LO  is parallel to MN

Step-by-step explanation:

Here we have a parallelogram, and we want to identify two segments that are parallel.

We can see that ON is parallel to LM

And LO is parallel to MN

Because this is a parallelogram (we know this because there is a 90° angle at N), the opposite sides are parallel.

So from this, we can see that sides ON and LM are opposite, then ON is parallel to LM

With the same reasoning, LO is parallel to MN.

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Answer:

Given a relationship between two quantities, determine whether the relationship is a function. ... If each input value leads to only one output value, classify the relationship as a function. If any input value leads to two or more outputs, do not classify the relationship as a function.

Step-by-step explanation:

hope it helps

The sum of Peter, Richard, and John's ages is 191.

We know that the ratio of Peter's age to Richard's age is = 5/8 --(i)

The ratio of John's age to Peter's age is = 7/12 --(ii)

Similarly, the ratio of John's age to Richard's age is = (5*7)/(8*12)= 35/96 -(iii)

Using the value of (i),(ii),(iii), we get -

Age of Peter = (5*12)/(8*12) = 60/96

= 60 years of age

Age of John = (7*5)/(12*5) = 35/60

=35 years of age

From the value of (iii), since no one is over 100 years of age, the age of Richard= 96 years of age

Hence the sum of their ages is = 96+35+60

= 191

Therefore, we know that the sum of their ages is 191.

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The current ratio for 2018 is approximately 3.02, and the current ratio for 2019 is approximately 2.97.

To calculate the current ratio for 2018 and 2019, we divide the current assets by the current liabilities for each year.

For 2018:

Current Ratio = Current Assets / Current Liabilities

Current Ratio = $101,600 / $33,650

Current Ratio ≈ 3.02

For 2019:

Current Ratio = Current Assets / Current Liabilities

Current Ratio = $97,350 / $32,800

Current Ratio ≈ 2.97.

Therefore, the current ratio for 2018 is approximately 3.02, and the current ratio for 2019 is approximately 2.97.

The current ratio is a financial metric that indicates a company's ability to cover its short-term liabilities with its short-term assets.

A higher current ratio generally suggests a better ability to meet short-term obligations.

Please note that the calculated current ratios are approximations, rounded to two decimal places, based on the given data.

For precise analysis, it's important to consider additional financial information and trends over time.

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The wheel will travel 131.8cm in 3 rotations.

The radius of the wheel, r = 7cm

Number of rotations, n= 3

distance covered in 1 rotation= circumference of circle=2πr

distance covered in 3 rotation= 2πr x 3

where π=3.14(fixed)

=2 x 3.14 x 7 x 3

Distance=131.88cm

Therefore, the distance covered in 3 rotations is 131.88cm

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Answer:

132cm

Step-by-step explanation:

use formula 22/7 *diameter which is 7*2 getting the answer as 44.For three rotations multiply the answer by three

The probability that the total sum of all rolls does not exceed 375 is approximately 0.7165

Assuming the die is a fair six-sided die, the possible outcomes for each roll are numbers 1 through 6, each with a probability of 1/6.

Let X be the total sum of all rolls. Then X follows a discrete uniform distribution with parameters n = 104 (number of rolls) and a = 1 (minimum value of each roll). The expected value of X is:

E(X) = n × (a + b) / 2 = 104 × (1 + 6) / 2 = 365

The variance of X is

Var(X) = n × (b - a + 1)^2 / 12 = 104 × 6^2 / 12 = 312

The standard deviation of X is

SD(X) = sqrt(Var(X)) = sqrt(312) = 17.67

To calculate the probability that the total sum of all rolls does not exceed 375, we need to calculate the cumulative distribution function (CDF) of X and evaluate it at 375

P(X <= 375) = F(375)

where F(x) = P(X <= x) is the CDF of X.

Using the normal approximation to the binomial distribution, we can approximate X as a normal distribution with mean E(X) = 365 and standard deviation SD(X) = 17.67

Z = (X - E(X)) / SD(X)

Z follows a standard normal distribution with mean 0 and standard deviation 1.

P(X <= 375) = P(Z <= (375 - E(X)) / SD(X))

= P(Z <= (375 - 365) / 17.67)

= P(Z <= 0.566)

Using a standard normal distribution table or a calculator, we can find that P(Z <= 0.566) is approximately 0.7165.

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The given question is incomplete, the complete question is :

A die is continuously rolled 104 times. what is the probability that the total sum of all rolls does not exceed 375 ?

Step-by-step explanation:

x² - 49 = 0

or, x² - (7²) = 0

or, ( x + 7 ) ( x - 7 ) = 0

hope this answer will help you.

Given:

The graphs of f(x) and g(x).

The function f(x) is given by:

\(f(x)=x^2\)

The graph of g(x) passes through the point (2,12).

To find:

The function g(x).

Solution:

From the given graph it is clear that the vertex of both function f(x) and g(x) is at (0,0). It means the graph of f(x) is not translated. It means the graph of f(x) is only vertically stretched to get the graph of g(x). So,

\(g(x)=kf(x)\)

Where, k is the stretch factor.

\(g(x)=kx^2\)               ...(i)

The graph of g(x) passes through the point (2,12). Putting \(x=2, g(x)=12\), we get

\(12=k(2)^2\)

\(12=k(4)\)

\(\dfrac{12}{4}=k\)

\(3=k\)

Putting \(k=3\) in (i), we get

\(g(x)=3x^2\)

Therefore, the correct option is A.

We have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\). This is the linearized equation.

To linearize the given ordinary differential equation (ODE) \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\), we need to rewrite it in a linear form. One common approach is to introduce a new variable that relates to the derivative of \(\( y \)\).

Let's define a new variable \(\( v = \sqrt{x} \)\). Taking the derivative of both sides with respect to \(\( t \)\), we have:

\(\[ \frac{{dv}}{{dt}} = \frac{{d}}{{dt}} \left( \sqrt{x} \right) \]\)

Using the chain rule, we can express \(\( \frac{{dv}}{{dt}} \)\) in terms of \(\( \frac{{dx}}{{dt}} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \frac{{dx}}{{dt}} \]\)

Now, we need to substitute \(\( \frac{{dx}}{{dt}} \)\) using the given equation \(\( \frac{{dy}}{{dt}} = 5 \sqrt{x} \)\):

\(\[ \frac{{dv}}{{dt}} = \frac{1}{{2 \sqrt{x}}} \cdot \left( 5 \sqrt{x} \right) \]\)

Simplifying the right-hand side:

\(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

Thus, we have linearized the given ODE to: \(\[ \frac{{dv}}{{dt}} = \frac{5}{2} \]\)

The linearized equation is much simpler compared to the original non-linear equation.

Note: The complete question is:

Linearize the ODE below;

\(\(\frac{{dy}}{{dt}} = 5\sqrt{x}\)\)

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Answer:  b

Step-by-step explanation:

I think

The representation which is most appropriate for showing the change in the average hourly wage is: A. scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 9, 1 comma 9 and a half, 2 comma 10, 3 comma 11, 4 comma 12, 5 comma 13, and 6 comma 14.

In this scenario, the years would be plotted on the x-axis (x-coordinate) of the scatter plot while the hourly wage would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the years and hourly wage, an equation for the line of best fit is given by:

y = 0.8571x + 8.6429

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Answer:

A = 576 square inches

Step-by-step explanation:

s = 2⁴ inches

A (Area) = s²

A (Area) = (2⁴)²

A = 2^8

A = 576

Answer:

About 4%

Step-by-step explanation:

6x10=60

52x20=1040

5x30=150

5x40=200

1x60=60

Total Points available:1510

Final Exam is 60 points

60/1510=0.0397

The distance that she runs from one corner of the field to another is given as follows:

147.1 yards.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

The distance in this problem is the diagonal of a rectangle, which is the hypotenuse of a right triangle in which the length and the width are the sides, hence:

d² = 85² + 120²

d = sqrt(85² + 120²)

d = 147.1 yards.

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Given:

Simplife:

The given simplifies equation is:

After the compare the both inequality:

a=2

b=2

c=2

d=6

e=1

f=9

As given by the question , so here the vertical and horizontal asymptotes are at x = -12 and y = 1.5.

On a function graph, a vertical asymptote represents the point at which the function is undefined. Take the formula f(x) = 1/x as an illustration. This function's graph exhibits a vertical asymptote at x = 0 since the function is undefined at this value (division by 0 is undefined).

A function's horizontal asymptote is a horizontal line on the function graph that the function approaches as the input (x-value) increases or decreases dramatically. Consider the function f(x) = x2 as an illustration. Because the y-values of the function do not converge to a fixed value as x grows very big, the graph of this function lacks a horizontal asymptote.

We must identify the values of x at which the function is undefined in order to determine the vertical asymptotes of the function 3x/(2x+24).So, to find the vertical asymptotes of the function, we need to solve the equation 2x + 24 = 0 for x. so x = -12.

Similarly, To find the horizontal asymptote in case of equal degrees of numerator and denominator i.e 1 in this case, we need to take the ratio of the first coefficients of numerator and denominator respectively which is 3/2 = 1.5.

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The inequality that represents the greatest number of boxes he can move in one trip is 255 + 50b ≤ 4000.

The solution of the inequality is 74.

The number of trips he would make to deliver 310 boxes is 5.

Here are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The inequality sign that would be used is ≤

The form of the inequality is:

Weight of the worker + weight of the cart + (weight of the boxes x number of boxes) ≤ 4000

160 + 95 + (50 x b) ≤  4000

255 + 50b ≤ 4000

In order to determine the value of b, take the following steps:

Combine similar terms:

50b ≤ 4000 - 255

50b ≤ 3745

b ≤ 3745 / 50

b ≤ 74.9

The number of boxes he can carry is 74

Number of trips = total number of boxes / number of boxes he can carry in one trip

= 310 / 74

= 4.1

= 5 trips

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The quantity that is unknown in this situation is the rental fee for one locker, or "r" and the equation is as follows: 50 * ($6 + r) = $475

To write an equation that represents the situation, you can use the information given in the problem. The total cost of the field trip, $475, covers the rental fees for 50 students, and the rental fee for one pair of skates is $6. Since the cost of the field trip is the sum of the rental fees for one pair of skates and one locker for each student, you can write an equation as follows:

50 * ($6 + r) = $475

This equation represents the situation in which the Student Council is organizing a field trip for 50 students, and the total cost of the field trip is the sum of the rental fees for one pair of skates and one locker for each student. The unknown quantity, "r", represents the rental fee for one locker.

Therefore, The quantity that is unknown in this situation is the rental fee for one locker, or "r" and the equation is as follows: 50 * ($6 + r) = $475

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