The local pizzeria is charging $12.50 for a medium pizza with no toppings. Each topping costs $1.20 each. The variable, P, to represent the price and the variable, t, to represent the number of toppings. Which of the following models is correct?

a) P = 12.50t + 1.20

b) P = 1.20t + 12.50

c) t = 12.50P + 1.20

d) t = 1.20P + 12.50

Answer:

Rhombuses

Step-by-step explanation:

It has four vertical lines, then draw a Venn Diagram, opposite to opposite.

Order from Venn Diagrams:

Quadrilaterals

Rectangles

Squares

Rhombuses.

the first five nonzero terms of the power series solution of the initial value problem y' + 4xy - 4y = 0, y(2) = 2, y'(2) = 4 are:

y(x) = (x - 2)² - (2/3)(x - 2)³ + (2/3)(x - 2)⁴ + ...

What is series?

In mathematics, a series is the sum of the terms of a sequence. It is a way of representing the accumulation or total of an infinite or finite sequence of numbers.

To find the power series solution of the initial value problem y' + 4xy - 4y = 0 with the initial conditions y(2) = 2 and y'(2) = 4, we can use the method of power series expansion.

Let's assume that the solution can be represented as a power series of the form y(x) = ∑(n=0 to ∞) aₙ(x - 2)ⁿ.

First, we need to find the coefficients aₙ. Differentiating y(x) with respect to x, we have y'(x) = ∑(n=0 to ∞) n * aₙ(x - 2)ⁿ⁻¹.

Substituting y and y' into the differential equation, we get:

∑(n=0 to ∞) n * aₙ(x - 2)ⁿ⁻¹ + 4x * ∑(n=0 to ∞) aₙ(x - 2)ⁿ - 4 * ∑(n=0 to ∞) aₙ(x - 2)ⁿ = 0.

Next, let's combine the terms with the same powers of (x - 2). The coefficient of each power of (x - 2) should be zero. Thus, we can equate the coefficients of each power of (x - 2) to zero.

For the zeroth-order term, we have:

a₀ - 4a₀ = 0, which gives a₀ = 0.

For the first-order term, we have:

a₁ + 4a₀ = 0, which gives a₁ = 0.

For the second-order term, we have:

2a₂ + 4a₁ - 4a₀ = 0, which gives a₂ = 0.

For the third-order term, we have:

3a₃ + 4a₂ - 4a₁ = 0, which gives a₃ = -2a₂/3.

For the fourth-order term, we have:

4a₄ + 4a₃ - 4a₂ = 0, which gives a₄ = -a₃ = 2a₂/3.

Therefore, the first five nonzero terms of the power series solution are:

y(x) = a₂(x - 2)² - (2/3)a₂(x - 2)³ + (2/3)a₂(x - 2)⁴ + ...

To determine the coefficient a₂, we can use the initial condition y(2) = 2. Substituting x = 2 and y = 2 into the power series solution, we have:

2 = a₂(2 - 2)² - (2/3)a₂(2 - 2)³ + (2/3)a₂(2 - 2)⁴ + ...

Since all the terms after the second term are zero when x = 2, we have:

2 = a₂(2 - 2)², which simplifies to a₂ = 1.

Therefore, the first five nonzero terms of the power series solution of the initial value problem y' + 4xy - 4y = 0, y(2) = 2, y'(2) = 4 are:

y(x) = (x - 2)² - (2/3)(x - 2)³ + (2/3)(x - 2)⁴ + ...

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Since you're trying to find f(-3), your function that you have to plug -3 into will be f(x).

f(-3) = -2(-3)^2+(-3)+3

f(-3) = -2(9)+(-3)+3

f(-3) = -18-3+3

f(-3) = -18 is your final answer

Answer: Mean

Step-by-step explanation: the mean, is the average or the expected value that measures the central value of a data set. It is found by adding all of the values in the data set and dividing it by the number of values.

We have that the amount he will get back at the end of this period is

x=1080

From the question we are told that

Rs 6000

r=6\%

time t=3yrs

Generally

A=P(1+rt)

A=P(1+rt)A=7080

Therefore

The amount he will get back at the end of this period is

7080-6000

7080-6000x=1080

In conclusion

The amount he will get back at the end of this period is

x=1080

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The probability that the firm receives 2 or more complaints in a day is 0.33.

This can be calculated using the Poisson distribution formula. The Poisson distribution is a probability distribution used to calculate the probability of an event occurring a given number of times in a fixed interval of time or space.

It is based on the assumption that the rate of occurrence of an event is constant.

In this case, we are looking at the probability of the firm receiving 2 or more complaints in a day. Let x = 2, where x is the number of complaints in a day. Then, the Poisson distribution formula is: P(x) = (e-λ λx) / x!

Where e = 2.71828 and λ = 3 (the rate of complaints per day).

Plugging in the values, we get: P(2) = (2.71828-3 * 32) / 2! = 0.33. Therefore, the probability that the firm receives 2 or more complaints in a day is 0.33.

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Step-by-step explanation:

From the image, let Angle 1 be x, and angle 2 be 16°

\({ \tt{x + 16 = 180}} \\ { \tt{x = 164 \degree}}\)

Answer:

b.2/6.

Step-by-step explanation:

Simplify each fraction

a.3/3 =1

b.2/6. Divide the top and bottom by 2  1/3

c.3/12 Divide the top and bottom by 3  1/4

d.7/12 Does not simplify

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

I don't think that there are two answers. I think there's only one.

The student's exam grade was converted to a negative z-score, indicating that they scored below the mean

Therefore, option d is correct.

When a grade is transformed into a z-score, it represents how many standard deviations the grade is away from the mean. The mean is always set at a z-score of 0, and positive z-scores indicate that a grade is above the mean, while negative z-scores indicate that a grade is below the mean.

In this question, the student's exam grade was transformed into a negative z-score, which means that the grade is below the mean. This is because the negative sign in the z-score indicates that the grade is a certain number of standard deviations below the mean. The further the z-score is below 0, the further the grade is below the mean.

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Answer:

Step-by-step explanation:

The root is the fractional part of an exponent and the power is the upper part of the exponent fraction

1)    \(\sqrt{x^{3} } = x^{\frac{3}{2} }\)

2)    \(17^{\frac{1}{5} } =\sqrt[5]{17}\)

3)   \(\sqrt[5]{y^{3} } = y^{\frac{3}{5} }\)

4)   \(z^{\frac{2}{3} } =\sqrt[3]{z^{2} }\)

Answer: 2.2 mph

Step-by-step explanation:

there's 60 minutes in an hour so you multiply the 1.1 miles to get how many miles they would walk in an hour.

you will pay approximately $11,542 in interest over the life of the loan.

it will take approximately 82.3 months to pay off the loan.

To calculate the number of years, we divide the number of months by 12:

Years ≈ 82.3 / 12 ≈ 6.9 (rounded to one decimal place)

FV = P * [(1 + r)^n - 1] / r

Where:

FV = Future value of the annuity (total amount paid)

P = Monthly payment amount ($140)

r = Monthly interest rate (16% / 12 = 0.16 / 12 = 0.0133)

n = Number of periods (months)

We need to solve for n. Rearranging the formula, we have:

n = log((FV * r) / (P * r + P)) / log(1 + r)

Plugging in the given values:

FV = $3,400

P = $140

r = 0.0133

n = log(($3,400 * 0.0133) / ($140 * 0.0133 + $140)) / log(1 + 0.0133)

Calculating this expression:

n ≈ log(45.22) / log(1.0133)

Using a calculator, we find:

n ≈ 82.3

To calculate the number of years, we divide the number of months by 12:

Years ≈ 82.3 / 12 ≈ 6.9 (rounded to one decimal place)

So, it will take approximately 6.9 years to pay off the loan.

To calculate the total interest paid, we subtract the initial loan amount from the total amount paid:

Total interest = (P * n) - $3,400

Total interest = ($140 * 82.3) - $3,400

Total interest ≈ $11,542

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The exact value of the expression is 7√33/33

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given expression is sec[sin⁻¹(-4/7)]

We need to fine the exact value of the expression

sec[sin⁻¹(-4/7)]=√1-(-4/7)²/1-(-4/7)²

=√(1-16/49)/1-16/49

=√(1-16/49)/1-16/49

=√33/7/33/49

=√33/7×49/33

=7√33/33

Hence, the exact value of the expression is 7√33/33

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Answer:

20%

0.5

Step-by-step explanation:

There are 20 margins, so you have to count how many are 6.0 or higher. There are 4 margins that fit this so you divide the 4 margins by 20, then multiply the quotient by 100. That's how you get 20%.

The most common time was 0.5.

Answer: Each person gets 2.25 liters.

Step-by-step explanation:

Given: Total quantity of water = 9 liters

Number of persons = 4

Quantity of water each person get = \(\dfrac{\text{Total quantity of water }}{\text{Number of persons }}\)

\(=\dfrac{9}{4}\text{ liters}\\\\=2.25\text{ liters}\)

Hence, each person gets 2.25 liters.

The distance between the points (9, –6) and (–4, 7) is equal to 13√2 units..

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

By substituting the given end points into the distance formula, we have the following;

Distance = √[(7 + 6)² + (-4 - 9)²]

Distance = √[(13)² + (-13)²]

Distance = √[169 + 169]

Distance = √338

Distance = 13√2 units.

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A piecewise function is a function that is defined by different equations on different intervals.

Graphing a piecewise function on a graph is a great way to visualize its behavior and understand its properties. One of the most popular and user-friendly ways to graph piecewise functions is using the online graphing calculator Desmos.

Here is a step-by-step guide on how to graph a piecewise function on Desmos:

Go to the Desmos website

and click on the "Graphing Calculator" button.

On the left side of the screen, you will see a text box labeled "y=". This is where you will enter the equation of your piecewise function. You can enter multiple equations by separating them with commas.

To graph a piecewise function, you will need to enter different equations for different intervals.

For example, if you have a piecewise function that is defined by the equation y = x^2 for x < 0 and y = x + 2 for x ≥ 0, you would enter y = x^2, x < 0 and y = x + 2, x ≥ 0 in the "y=" text box.

Once you have entered your equations, press the "Graph" button to see the graph of your piecewise function on the screen.

If you want to adjust the graph, you can use the sliders on the left side of the screen to change the range of the x- and y-axis. You can also use the buttons at the top of the screen to zoom in and out or pan around the graph.

To see the graph of multiple piecewise functions at once you can use the "Add another equation" button under the "y=" text box to add additional equations.

You can also use the "Table" tab to see the values of the function at certain x-values and also can use the "Slider" tab to change the value of x and see how that effects the graph of the function.

By following these steps, you can easily graph piecewise functions on Desmos and visualize the behavior of the function. Desmos is a great tool that allows you to experiment with different equations and see how they affect the graph of the function.

It is a great way to understand the properties of piecewise functions and to visualize them in multiple ways.

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A-1. The expected value of the sample proportion is 0.1667, and the standard error of the sample proportion≈ 0.0335.

A-2. Yes, it is appropriate to use the normal distribution approximation for the sample proportion because:

np = (155)(1/6) ≈ 25.83 ≥ 5

n(1-p) = (155)(5/6) ≈ 129.17 ≥ 5

b. The probability that more than 21% of smartphone users in the sample have fallen prey to cyber-attack is approximately 0.0584 or 5.84%.

A-1. The expected value of the sample proportion can be calculated as:

E(p) = p = 1/6 = 0.1667 (rounded to 2 decimal places)

where p is the population proportion.

The standard error of the sample proportion can be calculated as:

\(SE(p) = \sqrt{{[p(1-p)]/n} }\)

\(= \sqrt{{[(1/6)(5/6)]/155} }\)

≈ 0.0335 (rounded to 4 decimal places)

where n is the sample size.

A-2. Yes, it is appropriate to use the normal distribution approximation for the sample proportion because:

np = (155)(1/6) ≈ 25.83 ≥ 5

n(1-p) = (155)(5/6) ≈ 129.17 ≥ 5

This means that both np and n(1-p) are greater than or equal to 5, which satisfies the condition for using the normal approximation.

b. Let X be the number of smartphone users in the sample who have fallen prey to cyber-attack.

Then X follows a binomial distribution with parameters n = 155 and p = 1/6.

We want to find P(X > 0.21n), which can be calculated using the normal approximation as:

\(P(X > 0.21n) = P(Z > (0.21n - np) / \sqrt{{np(1-p)}) }\)

\(= P(Z > (0.21*155 - 25.83) / \sqrt{{(155)(1/6)(5/6} )})\)

≈ P(Z > 1.57)

where Z is the standard normal random variable.

Using a standard normal distribution table or calculator, we can find that P(Z > 1.57) ≈ 0.0584 (rounded to 4 decimal places).

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Answer:

Step-by-step explanation:

This should help you :

Answer:

11,000

Step-by-step explanation:

You would multiply 1,500 by 7 and then add 500.

Answer:

NO children. Because too many kids could make me stressed out. and I dont wanna be stressed out. I may be able to handle 1 or 2 kids but 12? nah imma be stressed and may think suici.d.e thoughts.

Step-by-step explanation:

Answer:

never be able to have children at all

Step-by-step explanation:

Answer:

Substitute your answer for Step 1 into the second equation to solve for Z.

Answer:

1quarts = 4cups

12quarts = 48cups

20guests each get 2 cups =40cups

48-40=8

8cups =2quarts

Answer:

3.75 cubic centimeters

Step-by-step explanation:

\( {( \frac{1}{2}) }^{3} \times 2 \times 3 \times 5\)

\( \frac{1}{8} \times 30 = \frac{15}{4} = 3.75\)

Answer:

3 3/4cm^3

Step-by-step explanation:

The given hypothesis statement isH 0: μ1 − μ2 ≤ 8H 1: μ1 − μ2 > 8The level of significance α is 0.01.

Assuming equal population variances and the normality of the populations, the test statistic for the hypothesis test is given by Z=(x1 − x2 − δ)/SE(x1 − x2), whereδ = 8x1 = 65.3, s1 = 18.5, and n1 = 18x2 = 54.5, s2 = 17.8, and n2 = 22The formula for the standard error of the difference between means is given by

SE(x1 − x2) =sqrt[(s1^2/n1)+(s2^2/n2)]

Here,

SE(x1 − x2) =sqrt[(18.5^2/18)+(17.8^2/22)] = 4.8862

Therefore,

Z = [65.3 - 54.5 - 8] / 4.8862= 0.6719

The appropriate test statistic is 0.67.Critical value:The critical value can be obtained from the z-table or calculated using the formula.z = (x - μ) / σ, where x is the value, μ is the mean and σ is the standard deviation.At 0.01 level of significance and the right-tailed test, the critical value is 2.33.The calculated test statistic (0.67) is less than the critical value (2.33).Conclusion:Since the calculated test statistic value is less than the critical value, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the alternative hypothesis at a 0.01 level of significance. Thus, we can conclude that there is insufficient evidence to indicate that the population mean difference is greater than 8. Hence, the null hypothesis is retained. The hypothesis test is done with level of significance α as 0.01. Given that the population variances are equal and the population distributions are normal. The null and alternative hypothesis can be stated as

H 0: μ1 − μ2 ≤ 8 and H 1: μ1 − μ2 > 8.

The formula to calculate the test statistic for this hypothesis test when the population variances are equal is given by Z=(x1 − x2 − δ)/SE(x1 − x2),

where δ = 8, x1 is the sample mean of the first sample, x2 is the sample mean of the second sample, and SE(x1 − x2) is the standard error of the difference between the sample means.The values given are x1 = 65.3, s1 = 18.5, n1 = 18, x2 = 54.5, s2 = 17.8, and n2 = 22The standard error of the difference between sample means is calculated using the formula:

SE(x1 − x2) =sqrt[(s1^2/n1)+(s2^2/n2)] = sqrt[(18.5^2/18)+(17.8^2/22)] = 4.8862

Therefore, the test statistic Z can be calculated as follows:

Z = [65.3 - 54.5 - 8] / 4.8862= 0.6719

The calculated test statistic (0.67) is less than the critical value (2.33).Thus, we fail to reject the null hypothesis. Therefore, there is not enough evidence to support the alternative hypothesis at a 0.01 level of significance.

Thus, we can conclude that there is insufficient evidence to indicate that the population mean difference is greater than 8. Hence, the null hypothesis is retained.

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Answer:

point j is .55 because its .55

Step-by-step explanation:

Multiplying the entire expression by 100 gives us the percentage of peanut concentration in the final mix.

To find the percentage of peanut concentration in the final mix after Marshall adds x ounces of peanuts, we can use the following expression:

((0.3 * 32) + x) / (32 + x) * 100

Let's break down the expression:

0.3 * 32 represents the number of ounces of peanuts initially present in the mixed nuts. Since the mixed nuts are estimated to be 30% peanuts, multiplying 0.3 by the total weight of 32 ounces gives us the initial amount of peanuts

Adding x to this expression represents the additional ounces of peanuts that Marshall adds to the mix.

The denominator (32 + x) represents the total weight of the final mix, which includes both the initial mixed nuts (32 ounces) and the additional x ounces of peanuts.

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With a modified Wells score of 1 and a negative D-dimer, Ms. Rollo has a low post-test probability of having a DVT. The combination of these factors suggests a reduced likelihood of DVT.

Ms. Rollo has a modified Wells score of 1, which suggests a low probability of having deep vein thrombosis (DVT). Additionally, her D-dimer test results are negative, indicating a lower likelihood of DVT. Based on this information, her post-test probability of having a DVT would be further reduced.

While the specific numerical value of the post-test probability cannot be determined without additional information, the combination of a low Wells score and a negative D-dimer generally indicates a low probability of DVT.

It is important to note that medical professionals should interpret and assess the test results in conjunction with the patient's clinical presentation and other relevant factors to arrive at an accurate diagnosis.

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--The given question is incomplete, the complete question is given below "if ms. rollo has a modified wells score of 1 and a negative d-dimer, what is her post-test probability of having a dvt? give a genenral overview of scenario."--

To find a solution to the differential equation y'' - 10y' + 41y = 0, we can assume a solution of the form y = e^{rx}, where r is an unknown constant.

By substituting this into the differential equation and simplifying, we can find the characteristic equation and solve for the values of r. Once we have the values of r, we can construct the general solution by combining exponential terms.

Assuming a solution of the form y = e^{rx}, we can substitute it into the differential equation to get:

r^2e^{rx} - 10re^{rx} + 41e^{rx} = 0

Factoring out e^{rx}, we obtain:

e^{rx}(r^2 - 10r + 41) = 0

For this equation to hold, either e^{rx} = 0 or r^2 - 10r + 41 = 0. Since e^{rx} is never zero, we focus on solving the quadratic equation:

r^2 - 10r + 41 = 0

Using the quadratic formula, we find the roots:

r = (10 ± sqrt(10^2 - 4141)) / 2

r = 5 ± sqrt(-24)

r = 5 ± 2i√6

Since the roots are complex, the general solution will involve complex exponential terms. Therefore, a solution to the given differential equation is:

y = e^{5x}(C1cos(2√6x) + C2sin(2√6x))

where C1 and C2 are arbitrary constants.

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