PLEASE HELP MEEEEEEEEEEEEEEE

The equation y = 9x represents a situation where there is a direct proportional relationship between two variables, where y is equal to 9 times x.

The equation y = 9x represents a linear relationship between two variables, y and x. In this situation, the value of y is directly proportional to the value of x, with a constant of proportionality equal to 9.

This means that for every increase in x by 1 unit, y will increase by 9 units. Similarly, for every decrease in x by 1 unit, y will decrease by 9 units. The equation describes a straight line that passes through the origin (0,0) and has a slope of 9. It implies that as x increases, y increases at a consistent rate.

For example, if x represents the number of hours worked and y represents the earnings in dollars, the equation y = 9x indicates that the earnings are $9 per hour. As the number of hours worked (x) increases, the earnings (y) increase at a rate of $9 for each additional hour.

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Answer: 17/20

Step-by-step explanation:

It's quite simple to solve this. Convert all of the fractions into decimal form:

21/25 = 0.84 (84%)

0.8 = 80%

82% (already in %)

17/20 = 0.85 (85%)

Therefore, the largest percentage, which is 17/20 in this situation, is Erin's highest score.

Answer:

the domain is -2 and the range is 0

Step-by-step explanation:

Answer:

Step-by-step explanation:

The domain of the graphed function is any value and the range is all positive numbers:

Answer:Perhaps you made a typo because there is no solution to this problem.

Step-by-step explanation:

We know one of the numbers is negative and one is positive since when multiplied the output is negative. And the negative number will be the smaller of the two since the sun is positive. So the factors of -20 are:

-1•20 -1+20=19

-2•10 -2+10=8

-4•5 -4+5=1

None of those equal 6 so i apologise but it seems this equation has no answer.

Answer:

d= negative 16

Step-by-step explanation:

Answer:

0.1(d-6)=0.15d+2.5-1.5+0.05d

Step-by-step explanation:

The equation for temperature change is T = -1.5t + 29 and the number line is plotted.

What is a number line?

A picture of numbers on a straight line is called a number line. It serves as a guide for contrasting and arranging numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

Let T represent the temperature in degrees Celsius, and let t represent the time in hours after lunchtime.

Then write an expression for the situation as follows:

T = -1.5t + 29

Here, -1.5t represents the decrease in temperature per hour, since the temperature is dropping at a rate of 1.5 degrees Celsius per hour.

Adding 29 to -1.5t gives the initial temperature of 29 degrees Celsius at lunchtime.

To illustrate this situation on a number line diagram, we can plot the temperature T as a function of time t.

The diagram would have time t on the horizontal axis and temperature T on the vertical axis.

Label the point (0, 29) on the diagram to represent the temperature at lunchtime, and the point (x, 16) to represent the temperature at sunset, where x is the number of hours after lunchtime.

Then draw a straight line connecting these two points to represent the linear relationship between temperature and time.

The line slopes downward from left to right, indicating that the temperature is decreasing over time.

Therefore, the number line diagram is plotted.

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On Tuesday at lunchtime, it was 29 degrees Celsius. By sunset, the temperature had dropped to 16 degrees Celsius. Please write an expression for the situation, and draw a number line diagram.

Answer:

One with a slope of -2 and different y-intercept

e.g. y = -2x + 3

Answer:

$14.92

Step-by-step explanation:

To find the sales tax, you would multiply $14.08 by 6%.

6% = 0.06

0.06*14.08 =  0.8592

Then add the sales tax to the original price to find how much the total costs.

0.8592 + $14.08 = $15.1792

Round $15.1792 to the nearest cent since its money.

So its $14.92

Answer:

Step-by-step explanation:

87 = x + 90

Isolate the variable by subtracting 90 on both sides

87 = x + 90

-90      -90

x=-3

-4x = 16

Isolate the variable by dividing by -4 on both sides

-4x=16

/-4   /-4

x = -4

43 = 6x - 5

Answer:

sin c - 25/7

cos c - 7/24

tan c - 25/24

Step-by-step explanation:

If for her party, Carla bought a 5-pound bag of candy to give as party treats. She invited 15 people. The amount of candy that each of the 15 people get is: A) 15 ÷ 5 = 15/5 = 3 pounds.

Given data:

Candy bought = 5

Number of people invited = 15

Now let find the amount of candy to gives as party treats

Number of candy = Number of people invited / Candy bought

Number of candy = 15/5

Number of candy = 3 pounds

Therefore we can conclude that the correct option is A.

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Answer:

1,723,176

Step-by-step explanation:

By plugging this into a calculator, you will receive 1,723,176.

Answer: 234 x 7364 = 1,723,176

The 3x3 matrix representing the composite 2D transformation of translating by (5,9) and then rotating 45° about the origin using homogeneous coordinates is: [ cos(45°) -sin(45°) 5  sin(45°) cos(45°) 9  0 0 1 ]

To find the matrix that represents the composite transformation, we first need to construct the individual transformation matrices for translation and rotation.

Translation Matrix:

The translation matrix for translating by (5,9) is:

[ 1 0 5

0 1 9

0 0 1 ]

Rotation Matrix:

The rotation matrix for rotating 45° about the origin is:

[ cos(45°) -sin(45°) 0

sin(45°) cos(45°) 0

0 0 1 ]

To obtain the composite transformation matrix, we multiply the translation matrix by the rotation matrix. Matrix multiplication is performed by multiplying corresponding elements and summing them up.

The resulting composite transformation matrix, accounting for translation and rotation, is:

[ cos(45°) -sin(45°) 5

sin(45°) cos(45°) 9

0 0 1 ]

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We need to find the function f(n) whose terms are the same as the series in question. We can then integrate this function from n=1 to infinity and determine if the integral is convergent or divergent. If it is convergent, then the series is convergent. If it is divergent, then the series is also divergent.

To determine whether a series is convergent or divergent using the integral test, we need to first check if the series satisfies three conditions:

1) The terms of the series are positive.

2) The terms of the series are decreasing.

3) The series has an infinite number of terms.

Assuming these conditions are satisfied, we can use the integral test which states that if the integral of the function f(x) from n=1 to infinity is convergent, then the series with terms a_n = f(n) is also convergent. Conversely, if the integral is divergent, then the series is also divergent.

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we have shown that E[X] = 1/√(2π) * e^(-a^2/2) for the given random variable X.

What is the equivalent expression?

Equivalent expressions are expressions that perform the same function despite their appearance. If two algebraic expressions are equivalent, they have the same value when we use the same variable value.

To show that E[X] = 1/√(2π) * \(e^{(-a^2/2)}\), where X is defined as X = {Z if Z > a, 0 otherwise}, we need to calculate the expected value of X.

The expected value (E) of a random variable X is given by:

E[X] = ∫(x * f(x)) dx

where f(x) is the probability density function (PDF) of X.

For the given random variable X, we have two cases:

Case 1: X = Z if Z > a

Case 2: X = 0 otherwise

Let's calculate the expected value of X by considering both cases separately.

Case 1: X = Z if Z > a

In this case, the PDF of X is given by the PDF of the standard normal distribution, which is:

f(x) = 1/√(2π) * \(e^{(-x^2/2)}\)

Since X = Z if Z > a, we need to calculate the expected value of X when Z > a. This can be expressed as:

E[X] = ∫(x * f(x) | x > a) dx

= ∫(x * (1/√(2π) * \(e^{(-x^2/2)}\)) | x > a) dx

= ∫(x * (1/√(2π) * \(e^{(-x^2/2)}\)) | x = a to ∞) dx

= 1/√(2π) * ∫(x * \(e^{(-x^2/2)}\)| x = a to ∞)

Now, let's perform a u-substitution, where u = -x²/2. Then du = -x dx.

When x = a, u = -a²/2, and when x approaches ∞, u approaches -∞.

Therefore, the integral becomes:

E[X] = 1/√(2π) * ∫(\(e^u\) du | u = -a²/2 to -∞)

= 1/√(2π) * [\(e^u\)| u = -a²/2 to -∞]

= 1/√(2π) * (\(e^{(-\infty)} - e^{(-a^2/2)}\))

Since \(e^{(-\infty)}\) approaches 0, we have:

E[X] = 1/√(2π) * (0 - \(e^{(-a^2/2)}\))

= 1/√(2π) * (-\(e^{(-a^2/2)}\))

= -1/√(2π) * \(e^{(-a^2/2)}\)

Now, we consider Case 2: X = 0 otherwise. In this case, the PDF of X is simply 0, as X is always 0 when Z ≤ a.

Therefore, the expected value of X for Case 2 is 0.

To calculate the overall expected value, we need to consider the probabilities of each case. In Case 1, X takes the value of Z with probability P(Z > a), and in Case 2, X takes the value of 0 with probability P(Z ≤ a).

Since Z is a standard normal random variable, P(Z ≤ a) = Φ(a), where Φ denotes the cumulative distribution function (CDF) of the standard normal distribution.

Therefore, the expected value of X can be calculated as:

E[X] = P(Z > a) * E[X | X = Z] + P(Z ≤ a) * E[X |

X = 0]

= (1 - Φ(a)) * (-1/√(2π) * \(e^{(-a^2/2)}\)) + Φ(a) * 0

= -1/√(2π) * \(e^{(-a^2/2)}\) + 0

= -1/√(2π) *\(e^{(-a^2/2)}\)

= 1/√(2π) * \(e^{(-a^2/2)}\)

Hence, we have shown that E[X] = 1/√(2π) * \(e^{(-a^2/2)}\) for the given random variable X.

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The percentage of calories that comes from saturated fat in each serving of these crackers is 0.4%

To calculate the percentage of calories that come from saturated fat, we need to first determine how many calories come from saturated fat in one serving of crackers.

We know that each serving of crackers provides 120 calories, and 0.5 grams of saturated fat. We can convert the amount of saturated fat from grams to calories by multiplying it by 9 (since 1 gram of fat provides 9 calories).

0.5 grams of saturated fat x 9 calories per gram = 4.5 calories from saturated fat

Therefore, out of the 120 total calories in one serving of crackers, 4.5 calories come from saturated fat.

To find the percentage of calories that come from saturated fat, we can divide the number of calories from saturated fat by the total number of calories in one serving of crackers, and then multiply by 100.

(4.5 calories from saturated fat / 120 total calories) x 100 = 0.0375 x 100 = 0.4%

Therefore, each serving of crackers provides 0.4% of calories from saturated fat.

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Answer:

No. It is not possible to construct a triangle with lengths of its sides 4cm, 5cm and 9cm because the sum of two sides is not greater than the third side:

5 + 4 is not greater than 9.

Step-by-step explanation:

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Answer:

x = 6

Step-by-step explanation:

7x = 42

To solve the equation, divide each side by 7.

7x/7 = 42/7

x = 6

Answer:

im pretty sure it would be 15%

Step-by-step explanation:

so A

Answer:

x greater than or equal to 3

x greater than or equal to -8/3

Step-by-step explanation:

Answer:

x = 1

Step-by-step explanation:

Here is what you need to know:

f(x) represents the y-value.

The x in the parenthesis represents the x-value.

Another way to write f(x) = 1 is y = 1.

So now you are just finding the x-value for when y = 1. Looking at the graph, when y is 1 ( 1 on the y-axis), x has to be 1! This is because when you go up one, the only value that matches that point is 1!

Hope this helps :)

(sorry if my explanation was a bit confusing)

Answer:

6.7ft

Step-by-step explanation:

190÷28=6.7 is correct

If the stiffness of the cord is no less than 28 pounds per foot, the cord stretch will be approximately 7 feet long

Given the equation that related the stiffness of the cord is expressed as:

\(K=\frac{(2W(S+L))}{S^2}\) where:

W is the weight

K = cord stiffness (pounds per foot)

L = free length of cord (feet)

S = stretch (feet)

Given the following parameters

W = 190 pounds

L = 52 feet

k = 28 pounds per foot

Required

Stretch S

Substitute the given expressions into the equation above to have:

\(28=\frac{(2(190)(S+52))}{S^2}\\28S^2=380(S+52)\\28S^2 = 380S+19,760\\28S^2 - 380S-19,760=0\\\)

On factorizing the result

The stretch is approximately 7 feet long

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To estimate the number of households in the sample that lost electricity, we can use the mean of the relevant distribution,

A) The relevant random variable is the number of households in the sample that lost electricity. Since we know that 7% of households in the city lost electricity, we can use this as the probability of any one household in the sample losing electricity. Therefore, the mean of the relevant distribution is:

Mean = np = 50 * 0.07 = 3.5 households

B) To find the standard deviation of the distribution, we use the formula:

Standard deviation = √(np(1-p))

where n is the sample size and p is the probability of success (in this case, the probability of a household losing electricity). Plugging in the values, we get:

Standard deviation = √(50 * 0.07 * (1 - 0.07)) = 1.51 households

Therefore, our estimate is that the sample will have an average of 3.5 households that lost electricity, with a standard deviation of 1.51 households.

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Answer:

(-3,-4,-2)

Step-by-step explanation:

You are given the y-values and want to find the x-values.

1 = 2x +7

-6 = 2x

-3 = x

-1 = 2x +7

-8 = 2x

-4 = x

3 = 2x +7

-4 = 2x

-2 = x

In quadrant IV, \(\cos(A)\) is positive. So

\(\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258\)

Then by the definition of tangent,

\(\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}\)

Answer:

\(\\ \frac{1}{8} e^{4a}-\frac{3}{4}e^{2a}+e^{a} -\frac{3}{8} \\\\or\\\\ \frac{e^{4a}-6e^{2a}+8e^{a}-3}{8}\)

Step-by-step explanation:

\(\\ \int\limits^{a}_{0} \int\limits^{x}_{0} \int\limits^{x+y}_{0} {e^{x+y+z}} \, dzdydx \\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [\int\limits^{x+y}_{0} {e^{x+y}e^z} \, dz]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}\int\limits^{x+y}_{0} {e^z} \, dz]dydx\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}e^z\Big|_0^{x+y}]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} [e^{x+y}e^{x+y}-e^{x+y}]dydx \\\\\\=\int\limits^{a}_{0} \int\limits^{x}_{0} e^{2x+2y}-e^{x+y}dydx \\\\\\\)

\(\\=\int\limits^{a}_{0} [\int\limits^{x}_{0} e^{2x}e^{2y}-e^{x+y}dy]dx \\\\\\=\int\limits^{a}_{0} [\int\limits^{x}_{0} e^{2x}e^{2y}dy- \int\limits^{x}_{0}e^{x}e^{y}dy]dx \\\\\\u=2y\\du=2dy\\dy=\frac{1}{2}du\\\\\\=\int\limits^{a}_{0} [\frac{e^{2x}}{2}\int e^{u}du- e^x\int\limits^{x}_{0}e^{y}dy]dx \\\\\\=\int\limits^{a}_{0} [\frac{e^{2x}}{2}\cdot e^{2y}\Big|_0^x- e^xe^{y}\Big|_0^x]dx \\\\\\=\int\limits^{a}_{0} [\frac{e^{2x+2y}}{2} - e^{x+y}\Big|_0^x]dx \\\\\)

\(\\=\int\limits^{a}_{0} [\frac{e^{4x}}{2} - e^{2x}-\frac{e^{2x}}{2} + e^{x}]dx \\\\\\=\int\limits^{a}_{0} \frac{e^{4x}}{2} -\frac{3e^{2x}}{2} + e^{x}dx \\\\\\=\int\limits^{a}_{0} \frac{e^{4x}}{2}dx -\int\limits^{a}_{0}\frac{3e^{2x}}{2}dx + \int\limits^{a}_{0}e^{x}dx \\\\\\u_1=4x\\du_1=4dx\\dx=\frac{1}{4}du_1\\\\\u_2=2x\\du_2=2dx\\dx=\frac{1}{2}du_2\\\\\\=\frac{1}{8}\int e^{u_1}du_1 -\frac{3}{4}\int e^{u_2}du_2 + \int\limits^{a}_{0}e^{x}dx \\\\\\\)

\(\\=\frac{1}{8}e^{u_1}\Big| -\frac{3}{4}e^{u_2}\Big| + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4x}\Big|_{0}^a -\frac{3}{4}e^{2x}\Big|_{0}^a + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4x} -\frac{3}{4}e^{2x} + e^{x}\Big|_0^a \\\\\\=\frac{1}{8}e^{4a} -\frac{3}{4}e^{2a} + e^{a}-\frac{1}{8} +\frac{3}{4} -1\\\\\\=\frac{1}{8}e^{4a} -\frac{3}{4}e^{2a} + e^{a}-\frac{3}{8}\\\\\\\)

Sorry if that took a while to finish. I am in AP Calculus BC and that was my first time evaluating a triple integral. You will see some integrals and evaluation signs with blank upper and lower boundaries. I just had my equation in terms of u and didn't want to get any variables confused. Hope this helps you. If you have any questions let me know. Have a nice night.

The force readings from the right side of a sphere are inaccurate due to differences in diameters, as Coulomb's law states that force between charged objects is directly proportional to the product of their charges and inversely proportional to the square of their distance. To ensure even distribution of charges, spheres are coated with conductors, which distribute excess charges uniformly over their surfaces. This uniform distribution ensures a constant electric field and predictable and measurable forces.

1) There would indeed be a problem with taking readings from the right side of a sphere if the diameters of the spheres were different. This is because Coulomb's law states that the force between two charged objects is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. In the case of spheres, if the diameters are different, the distances between the right side of each sphere and the point of measurement would not be the same. As a result, the force readings obtained from the right side of each sphere would not accurately reflect the interaction between the charges, leading to inaccurate results.

2) The spheres are coated with a conductor to ensure that the charges applied to them are evenly distributed on their surfaces. A conductor is a material that allows the easy flow of electric charges. When a conductor is used to coat the spheres, any excess charge applied to them will distribute itself uniformly over the surface of the spheres. This uniform distribution of charge ensures that the electric field surrounding the spheres is constant and that the electric forces acting on the charges are predictable and measurable. Coating the spheres with a conductor eliminates any localized charge concentrations and provides a controlled environment for conducting accurate experiments based on Coulomb's law.

3) Charge tends to 'leak' away from the charged conducting spheres due to a phenomenon known as electrical discharge or leakage. Conducting materials, such as the coating on the spheres, allow the movement of charges through them. When the spheres are charged, the excess charges on their surfaces experience a repulsive force, leading to a tendency for these charges to move away from each other. This movement can result in the charges gradually dissipating or leaking away from the spheres. The leakage can occur due to various factors, such as the presence of moisture, impurities on the surface of the conductor, or the influence of external electric fields. To minimize this effect, it is important to conduct experiments in a controlled environment and ensure that the conducting spheres are properly insulated to reduce the chances of charge leakage.

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Answer:

so here 25%=5

25×2=50, 5×2=10

50%=10

50%+50%=10+10

100%=20

baker makes total 20 cakes

A discrete probability distribution is a statistical distribution that relates to a set of outcomes that can take on a countable number of values, whereas a continuous probability distribution is one that can take on any value within a given range.Therefore, the main difference between the two types of distributions is the type of outcomes that they apply to.

An example of a discrete probability distribution is the probability of getting a particular number when a dice is rolled. The possible outcomes are only the numbers one through six, and each outcome has an equal probability of 1/6. Another example is the probability of getting a certain number of heads when a coin is flipped several times.

On the other hand, an example of a continuous probability distribution is the distribution of heights of students in a school. Here, the range of heights is continuous, and it can take on any value within a given range.

The expected value of a probability distribution measures the central tendency or average of the distribution. In other words, it is the long-term average of the outcome that would be observed if the experiment was repeated many times.

For a discrete probability distribution, the expected value is computed by multiplying each outcome by its probability and then adding the results. In mathematical terms, this can be written as E(x) = Σ(xP(x)), where E(x) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome.

For example, consider the probability distribution of the number of heads when a coin is flipped three times. The possible outcomes are 0, 1, 2, and 3 heads, with probabilities of 1/8, 3/8, 3/8, and 1/8, respectively. The expected value can be computed as E(x) = (0*1/8) + (1*3/8) + (2*3/8) + (3*1/8) = 1.5.

Therefore, the expected value of the distribution is 1.5, which means that if the experiment of flipping a coin three times is repeated many times, the long-term average number of heads observed will be 1.5.