The diagram shows a parallelogram.
4 cm
7 cm
100°
Work out the area of the parallelogram.
Give your answer to 2 significant figures.

Answer:

9x-1=26

Step-by-step explanation:

9(3) -1

27-1

26

We know that the point of intersection of the linear and quadratic functions lies on the xy-plane at coordinates ( ,v w). Since the vertex of the quadratic function is given as (4, 19), we can assume that the quadratic function is of the form

\(y = a(x-4)^2 + 19\)

To find the value of v, we need to find the x-coordinate of the point of intersection. Since the linear function is also given, we can set y = mx + b (where m is the slope of the line and b is the y-intercept) equal to the quadratic function and solve for x. Once we have the value of x, we can substitute it back into either equation to find the value of v.

Regarding the second question, we know that there are 78 students and the dig site has 24 sections. Each section can be studied by a group of 2 or 4 students. Let the number of sections studied by a group of 2 students be x, and the number of sections studied by a group of 4 students be y.

We know that x + y = 24 and 2x + 4y = 78. Solving these two equations simultaneously gives us x = 9 and y = 15, which means that 9 sections will be studied by a group of 2 students.

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Answer: 40 gallons for every 5 minutes.

In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n          

                                                                                                                        In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n            

In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n                                                                                                                                                                        we need to perform the inverse Z-transform. The inverse Z-transform converts a function in the Z-domain back into the time domain.

The general form of the inverse Z-transform is given by:

f(n)= \(\frac{1}{2\pi j}\) ∮ \(_{C}\) \(F(z)z^{n-1} dz\)

​ where

F(z) is the function in the Z-domain, f(n) is the corresponding time-domain sequence, j is the imaginary unit, and ∮\(_{c}\)

​represents integration around a closed path in the Z-plane.

In this case, the function F(z) is a rational function, and we can find its inverse Z -transform using partial fraction decomposition. Let's find the inverse Z-transform step by step:

Step 1: Express F(z) in partial fraction form.

\(F(z)=\frac{1}{z^2} + \frac{3}{z} +4\)

Step 2: Find the roots of the denominator The roots of \(z^{2} =0\) and

z=0 (a double pole at the origin).

Step 3: Perform partial fraction decomposition.

We can write \(F(z)=\frac{A}{z} +\frac{B}{z^2} ​\)

​Multiplying through by \(z^{2}\) to clear the fractions we get,\(1+3z^{-1} +4z^{-2} = A+Bz^{-1}\)                                                                                                        Comparing coefficients, we get:

A=1

B=4

Step4: Apply the inverse Z transform for each term

Inverse Z transform for A/z is \(a^{n}\), where a is the root of corresponding term in the denominator. In this case a=0, so the inverse Z transform of A/z=1

The inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\), where a is the root of the corresponding term in denominator. In this case a=0. So the inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\)=0

therefore the time domain of function f(z) is

f(n)=1+0=1

So the sampled time domain representation of the function F(z)=\(1+3z^{-1} +4z^{-2}\) is f(n)=1 for all the values of n

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Answer:

Step-by-step explanation:

To solve the expression (7.2×10^(-1))×(4×10^(-7)), you can multiply the numerical values and combine the exponents.

First, multiply the numerical values:

7.2 × 4 = 28.8

Next, add the exponents of 10:

10^(-1) × 10^(-7) = 10^(-1-7) = 10^(-8)

Putting it all together, the expression simplifies to:

28.8 × 10^(-8)

This is the final answer in scientific notation.

The height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.

Computed using differentiation.

We assume the radius of the can be r cm, and its height to be h cm.

We are given that the can is to hold 230 cm³ of liquid, thus the volume of the can is:

V = 230,

or, πr²h = 230 {Since, the volume of a cylinder is πr²h, where r is the radius, and h is the height},

or, h = 230/(πr²) ... (i) .

We are asked to find the height and radius that minimize the amount of the material.

To calculate the amount of the material, we calculate the surface area of the can (A).

The surface area of the can = area of the base + area of the side,

or, A = πr² + 2πrh = πr(r + 2h).

Substituting h = 230/(πr²), we get:

A = πr(r + 2{230/(πr²)}),

or, A = {πr(πr³ + 460)}/πr² = πr² + 460/r.

Differentiating both sides with respect to the radius r, we get:

dA/dr = 2πr - 460/r² ...(ii)

To find the point of inflection, we equate this to zero, to get:

2πr - 460/r² = 0,

or, 2πr = 460/r²,

or, r³ = 460/2π = 73.2113,

or, r = 4.18337 cm.

To check whether the point of inflection shows the point of maximum or minimum, we differentiate (ii) with respect to the radius r, to get:

d²A/dr² = 2π + 920/r³, which is always positive when the radius r is positive.

Thus, the area is minimum when the radius r = 4.18337 cm.

Height, h = 230/(πr²) = 4.18336 cm.

Thus, the height and the radius that minimize the material needed to manufacture the can is 4.18336 cm and 4.18337 cm respectively.

Computed using differentiation.

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Using Chebyshev's theorem, we can find the percentage of observations that fall within a certain number of standard deviations from the mean for any distribution, regardless of its shape.

Part 1 The formula for Chebyshev's theorem is: \(P(|X - μ| ≥ kσ) ≤ 1/k²\) The probability of a value falling within k standard deviations of the mean is greater than or equal to\((1 - 1/k²).\) To find the percentage of values that fall between 34 and 106, we first need to find the number of standard deviations away from the mean these values are. Using the formula, we have: \(k = |X - μ|/σ\) Let's first consider 34:34

\(= 70 - k(18)k\)

\(= (70 - 34)/18k\)

= 2At 34, the value is 2 standard deviations below the mean. Using the same formula for 106:106 = 70 + k(18)k

= (106 - 70)/18k

= 2At 106, the value is 2 standard deviations above the mean. To find the probability that a value falls within 2 standard deviations from the mean, we use Chebyshev's theorem: \(P(|X - 70| ≥ 2(18)) ≤ 1/2²P(|X - 70| ≥ 36) ≤ 0.25.\) This means that at least 75% of values must fall within 2 standard deviations from the mean, or between 70 - 2(18) and 70 + 2(18), which is 34 to 106. Since we want to find the percentage that falls between 34 and 106, we know it must be greater than 75%, but we can't know exactly what it is.

Part 2 We want to find the percentage of values that fall between 39 and 101. Using the formula for k again: \(k = |X - μ|/σ For 39:k\)

\(= (39 - 70)/18k\)

\(= -1.72 For 101:k\)

\(= (101 - 70)/18k\)

= 1.72 We want to find the probability that a value falls within 1.72 standard deviations from the mean: \(P(|X - 70| ≥ 1.72(18)) ≤ 1/1.72²P(|X - 70| ≥ 52.56) ≤ 0.3345\) We know that at least 66.55% of values will fall within 1.72 standard deviations from the mean. However, we want to find the percentage that falls between 39 and 101.

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Heritability is a statistic that quantifies the proportion of observed variance in a group of individuals that can be attributed to genetic variance.

Heritability is a fundamental concept in genetics and behavioral sciences that helps understand the extent to which genetic factors contribute to observed variations in a particular trait within a population. It measures the proportion of phenotypic variation (differences in traits) that can be explained by genetic variation. Heritability estimates range from 0 to 1, where a value of 0 indicates that all observed variation is due to environmental factors, and a value of 1 suggests that all observed variation is due to genetic factors.

To calculate heritability, researchers typically study populations with varying degrees of genetic relatedness, such as twins or family members. By comparing the similarity of traits between individuals with known genetic relatedness, it is possible to estimate the contribution of genetic factors to the observed variance. Environmental factors that contribute to phenotypic variation are considered as part of the non-genetic or "environmental" component.

It is important to note that heritability estimates are population-specific and apply only to the particular group being studied. Additionally, heritability does not provide information about specific genes or the precise mechanisms by which genetic factors influence traits. Nonetheless, heritability serves as a valuable tool in understanding the relative importance of genetic and environmental factors in shaping individual differences within a population.

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With a credit card balance of $17,426, a minimum monthly payment of $461, and an interest rate of 15.5%, we need to calculate the number of years it will take to pay off the card without adding any additional debt.

To determine the time required to pay off the credit card, we consider the monthly payment and the interest rate. Each month, a portion of the payment goes towards reducing the balance, while the remaining balance accrues interest.

To calculate the time needed for repayment, we track the decreasing balance each month. First, we determine the interest accrued on the remaining balance by multiplying it by the monthly interest rate (15.5% divided by 12).

We continue making monthly payments until the remaining balance reaches zero. By dividing the initial balance by the monthly payment minus the portion allocated to interest, we obtain the number of months needed for repayment. Finally, we divide the result by 12 to convert it into years.

In this scenario, it will take approximately 3.81 years to pay off the credit card (17,426 / (461 - (17,426 * (15.5% / 12))) / 12).

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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Answer:

The third answer is correct.

Step-by-step explanation:

You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral.  Then you need the scale factor from the smaller figure to the larger.  

Side EF times the scale factor will give you side AB.  Let's call the scale factor s then our equation would be:

EF x s = AB  To find s divide both sides by EF

\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)

s = \(\frac{AB}{EF}\)  This is our scale factor.

Helping in the name of Jesus.

Given:

Scatter plot shows the height x (in inches) and the weight y (in pounds) of 10 people.

To find:

The weight of the person who is 63 inches tall. Then find the height of the person who weighs 135 pounds.

Solution:

In the given scatter plot,

x = height (in inches)

y = weight (in pounds)

First we need to find the weight of the person who is 63 inches tall.

If height of a person is 63 inches, then x = 63.

From the given graph, it is clear that y = 110 at x = 63.

Therefore, the weight of the person who is 63 inches tall is 110 pounds.

Now, we need to find the height of the person who weighs 135 pounds.

If weight of a person is 135 pounds, then y = 135.

From the given graph, it is clear that x = 66 at y = 135.

Therefore, the height of the person who weighs 135 pounds is 66 inches.

Answer:

I think true im sorry if its not

The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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The equation −19/100 * (y - 3) models the shape of the arches in the loft, closely resembling parabolic curves.

The equation of the parabola that closely models the arches in the loft of Casa Batlló in Barcelona is −19/100 * (y - 3).

To understand the equation, let's break it down step by step:

1. The equation represents a parabola that closely resembles the shape of the arches.
2. The term "−19/100" is the coefficient that determines the steepness of the parabola. A negative value indicates that the parabola opens downwards.
3. The term "(y - 3)" represents the vertical displacement of the parabola. It indicates that the vertex of the parabola is at the point (0, 3).

So, the equation −19/100 * (y - 3) models the shape of the arches in the loft, closely resembling parabolic curves.

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Answer:

Option D is correct

Step-by-step explanation:

This is because 5 and 3 are odd numbers and a coefficient is a number next to a variable and both of those coefficients in Option D are odd. Therefore, Option D is correct.

Answer:

11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Plug in x and y values into the equation

Multiply

Add

Answer:

1234

Step-by-step explanation:

Answer:

the answer would be D) undefined

Step-by-step explanation:

above is what the graph should look like and in that graph there is no slope.

Answer:

5

Step-by-step explanation:

To evaluate (g ￮ h)(9), evaluate h(9) , then use this value to evaluate g(x)

h(9) = \(\sqrt{9}\) = 3, then

g(3) = 2(3) - 1 = 6 - 1 = 5

Answer: \(\frac{1}{3}\) or about 33%

Step-by-step explanation:

       We will divide the wanted outcomes by the possible outcomes.        

\(\displaystyle \frac{\text{wanted outcomes}}{\text{possible outcomes}} =\frac{\text{Number of numbers greater than 4}}{\text{number of numbers 1 through 6}} =\frac{2}{6}=\frac{1}{3}\;\; \text{or about 33\%}\)

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Answer: 1/3

Step-by-step explanation:

There are only 2 numbers greater than 4. 5 and 6.

2/6= 1/3 chance

These are the values of the step function for the given inputs:

A step function is a function that has constant values on given intervals, with the constant value varying between intervals. The name of this function comes from the fact that when you graph the function, it looks like a set of steps or stairs.

To find the value of a step function at a given input, find the interval that the input falls into. If the input is greater than or equal to the upper bound of the interval, then the value of the function is 1. If the input is less than the lower bound of the interval, then the value of the function is 0. If the input falls within the interval, then the value of the function is the constant value for that interval.

For the given inputs, the following intervals are used:

[7.8] falls within the interval [0, 10] so the value of the function is 1.

[0.75] falls within the interval [0, 1] so the value of the function is 0.75.

[-6.56] falls within the interval (-∞, 0] so the value of the function is 0.

[101.2] falls within the interval [0, 10] so the value of the function is 1.

[-93.6] falls within the interval (-∞, 0] so the value of the function is 0.

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The government agency that does not regulate banking or financial market is the The FCC. option C

The term FCC stands federal Communication Commission.  We should know that the duty of the federal communication Commission not to regulate finance in the society or regulate banking activities rather than to regulate Communication

It is the duty of the Commission to report on chain broadcasting, assign television stations to private and government individuals in the state.

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Answer:

a=3

Step-by-step explanation:

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Answer:

a = 3

Step-by-step explanation:

7a - 3 = 2a + 12

Add 3 to both sides of the equation:

7a - 3 + 3 = 2a + 12 + 3

7a = 2a + 15

Add 2a to both sides of the equation:

7a - 2a = 2a + 15 - 2a

5a = 15

Divide each side by 5:

5a ÷ 5 = 15 ÷ 5

a = 3

The point estimate, p, based on the given confidence interval (.688, .724), is .706.

To find the point estimate, p, we take the midpoint of the confidence interval.

In this case, the lower limit is .688 and the upper limit is .724.

To find the midpoint, we calculate the average of these two values.

Midpoint = (lower limit + upper limit) / 2

              = (.688 + .724) / 2

              = 1.412 / 2

              = .706

Therefore, the point estimate, p, is .706.

The point estimate represents our best estimate for the true population proportion based on the available sample data.

In this case, it suggests that the proportion, p, is most likely around .706.

However, it's important to note that the point estimate is subject to sampling variability and may not perfectly reflect the true population proportion.

706 is the correct answer as it represents the point estimate obtained from the confidence interval limits provided.

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Answer:

Part A: 5 miles per hour or 12 min per mile.

Part B: 30 min to get to his friends house.

Question 16 Part B: 30 minutes.

Step-by-step explanation:

Part A:

36 min for 3 miles so the unit is :

36/3 = 12 so: 1 mile per 12 min and 5 miles per hour.

Part B:

21/2 miles away so:

one mile per 12 min so 2.5 x 12 = he'll get there in 30 min.

Question 16 Part B:

just type in 30.

Answer:

171

Step-by-step explanation:

To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.