Jessica wrote a computer program to create colored shapes. The shapes are either squares or circles and both are equally likely. The colors are either blue, red, or green, and each is equally likely. What is the probability the computer program will create a green circle?

Answer:

  C = (-1, -2)

  D = (2, 0)

Step-by-step explanation:

You want the coordinates of points C and D in parallelogram ABCD such that point E(0, 2) is the intersection of the diagonals. Given points are A(1, 6) and B(-2, 4).

The diagonals of a parallelogram bisect each other. This means the point of intersection of the diagonals is the midpoint of each:

  E = (A +C)/2 . . . . . . . . . . . . . . . E is the midpoint of AC

  C = 2E -A = 2(0, 2) -(1, 6)

  C = (-1, -2)

and

  D = 2E -B = 2(0, 2) -(-2, 4) . . . . . using the same pattern

  D = (2, 0)

340=10f.

frequency=34hertz.

Step-by-step explanation:

We have the wavelength which is 10,speed/velocity=340 and frequency=?.

The formula is velocity=frequency × wavelength.

340=f × 10.

340=10f.

frequency=34hertz.

Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.

Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.

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a) The range is 14.

b) The sample variance is 20.78.

c) The sample standard deviation is 4.56.

a) Range

The range of a given set of data values is the difference between the maximum and minimum values in the set. In this case, the maximum value is 15 and the minimum value is 1. So, the range is:

Range = maximum value - minimum value

Range = 15 - 1

Range = 14

b) Sample variance

To calculate the sample variance, follow these steps:

1. Calculate the sample mean (X). To do this, add up all of the data values and divide by the total number of values:

n = 9

∑x = 7 + 4 + 6 + 12 + 8 + 15 + 1 + 9 + 13 = 75

X = ∑x/n = 75/9 = 8.33

2. Subtract the sample mean from each data value, square the result, and add up all of the squares:

(7 - 8.33)² + (4 - 8.33)² + (6 - 8.33)² + (12 - 8.33)² + (8 - 8.33)² + (15 - 8.33)² + (1 - 8.33)² + (9 - 8.33)² + (13 - 8.33)² = 166.23

3. Divide the sum of squares by one less than the total number of values to get the sample variance:

s² = ∑(x - X)²/(n - 1) = 166.23/8 = 20.78

Therefore, the sample variance is 20.78 (rounded to two decimal places).

c) Sample standard deviation

To calculate the sample standard deviation, take the square root of the sample variance:

s = √s² = √20.78 = 4.56

Therefore, the sample standard deviation is 4.56 (rounded to two decimal places).

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Although part of your question is missing, you might be referring to this full question: If the 1st person saves 1/4 of total, 2nd person saves 2/3 of total, and 3rd person saves 1/10, which fraction left to pay for the birthday party?

The fraction left to pay for the birthday party is 17/30.

The calculation is as follows:

1 * 1/4 = 1/4 … (1)

1/4 * 2/3 = 2/12 … (2)

2/12 * 1/10 = 2/120 … (3)

Fraction left to pay:

= 1 - (1/4 + 2/12 + 2/120)

= 1 - (30/120 + 20/120 + 2/120)

= 1 - (52/120)

= 1 - 13/30

= 30/30 - 13/30

= 17/30

Thus, the fraction left to pay for the birthday party is 17/30.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, where the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

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The capacity of fish tank in quarts is 246.

Therefore the answer is 246.

A pint is a unit of volume in the US customary system of measurement and is equal to 16 fluid ounces. A quart is also a unit of volume in the US customary system of measurement and is equal to 32 fluid ounces or 2 pints.

There are 2 pints in 1 quart, so to convert from pints to quarts, we need to divide by 2.

The capacity of the fish tank in pints is 492.

Therefore, the capacity of the fish tank in quarts is

= 492 pints / 2 pints per quart

= 246 quarts

So, the capacity of the tank in quarts is 246 quarts.

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Since the calculated t-value (0.876) is less than the critical value (1.895), we do not reject the null hypothesis that is µ1= µ2. So, the correct answer is option 3

Using the data below from a simple random paired sample from two (2) populations under consideration, at the 10% significance level, use the paired t-test to determine if the mean of population one is not equal to that of population 2:

Pair Population 1 Population 21 10 122 8 73 13 114 13 165 17 156 12 97 12 128 11

Here,Paired t-test

Null Hypothesis, H0: µ1= µ2 (There is no significant difference between the mean of population one and population two)

Alternative Hypothesis, H1: µ1 ≠ µ2 (There is a significant difference between the mean of population one and population two)

At 10% significance level, the degree of freedom = n-1=8-1=7

The critical values can be found using the t-distribution table at (0.05,7) = ±1.895

Calculation of Paired differences for each sample d = (Population 1 – Population 2)

Pair Population 1 Population 2 d (Population 1 – Population 2)1 10 12 -22 8 7 13 13 0 4 13 -9 5 17 15 27 6 12 9 37 12 12 08 11 7 4

Sum of differences d=12

Now,Calculate the mean difference:d¯ = ∑d/n=12/8 =1.5t =d¯/sd/√n

where, sd² = ∑d²/n - d¯² = 156/8- (1.5)² = 19.17

sd = √19.17 = 4.375

t = 1.5/4.375/√8 = 0.876

At the 10% level of significance, the critical value is ±1.895.

Since the calculated t-value (0.876) is less than the critical value (1.895), we do not reject the null hypothesis that is µ1= µ2.

Therefore, the correct option is:t=0.875, critical value=+/-0.895, do not reject the null hypothesis. This is option 3

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Answer:

Step-by-step explanation:

6x-y=-5

-6x+y=5

Adding the 2 equations we have:

0 + 0 = 0

0 = 0

This means there are infinite solutions

- the equations are identical.

System B

x+3y=13

-x+3y=5

Adding:

6y = 18

y = 3.

x = 13 - 3(3) = 4.

The system has a unique solution

(x. y) = (4, 3).

Answer: 33.3%

Step-by-step explanation: I did this on saavas. also for part b the answer is 32.5.

Answer:

unit rate is 120

Step-by-step explanation:

240 / 2 = 120

480 / 4 = 120

etc

Answer:

-1.6.

Step-by-step explanation:

So we have the equation:

\(4(3-5p)=-5(3p-4)\)

Distribute both sides:

\(12-20p=-15p+20\)

Add 15p to both sides. The right side will cancel:

\(12-5p=20\)

Subtract 12 from both sides:

\(-5p=8\)

Divide both sides by -5:

\(p=-\frac{8}{5}\)

Or -1.6.

And we're done!

Step-by-step explanation:

x is the number

so, the equation is

x - 8 = 31

x = 39

Answer:

n is the number

Step-by-step explanation:

n-8=31

n = 39

hoped that helped:P

Answer:

Step-by-step explanation:

1.89/14= .135

estimating to the nearest cent would be .14

The expression is factored completely into x(-x(x − b)(x − 4b)). To factor completely the expression 14bx^2 − 7x^3 − 4b^2x,

we need to look for common factors among the terms and apply various factoring techniques.

Step 1: Find the common factor.

In this expression, the common factor among the terms is x. We can factor out x:

x(14bx^2 − 7x^3 − 4b^2)

Step 2: Factor the remaining terms.

Now we focus on factoring the expression inside the parentheses: 14bx^2 − 7x^3 − 4b^2. We can factor out the greatest common factor (GCF) among the coefficients, which is 7:

x(7bx^2 − x^3 − 4b^2)

Step 3: Rearrange the terms.

To factor the remaining terms, we can rearrange them in descending order of the powers of x:

x(-x^3 + 7bx^2 − 4b^2)

Step 4: Factor out a common binomial factor.

Now we can factor out the common binomial factor from the terms inside the parentheses. To do this, we look for common factors among the terms. In this case, there is a common factor of (-x) among all the terms:

x(-x(x^2 − 7bx + 4b^2))

Step 5: Factor the quadratic expression.

To further factor the quadratic expression x^2 − 7bx + 4b^2, we can look for two binomials that multiply together to give us the quadratic expression. The factors will have the form (px − q)(rx − s). We need to find values of p, q, r, and s that satisfy the equation:

px * rx + (-q * rx) + (px * -s) + (-q * -s) = x^2 − 7bx + 4b^2

By trial and error, we can find the factors of the quadratic expression as:

(x − b)(x − 4b)

Putting it all together, the completely factored form of 14bx^2 − 7x^3 − 4b^2x is:

x(-x(x − b)(x − 4b))

So, the expression is factored completely into x(-x(x − b)(x − 4b)).

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Answer:

\(\textsf{P}=\left(-\dfrac{44}{7},-\dfrac{5}{7}\right)\)

Step-by-step explanation:

Given:

Therefore, point P on the segment AB should be 3/7 of the way from point A.

\(x_P=\dfrac{3}{7}(x_B-x_A)+x_A=\dfrac{3}{7}(0-(-11))-11=\dfrac{-44}{7}\)

\(y_P=\dfrac{3}{7}(y_B-y_A)+y_A=\dfrac{3}{7}(-3-1)+1=-\dfrac{5}{7}\)

\(\implies \textsf{P}=\left(-\dfrac{44}{7},-\dfrac{5}{7}\right)\)

or P = (-6.3, -0.7) to 1 decimal place

(Please see attached image, where the segment AB has been divided into 7 equal parts.)

Answer: C: 0.4

Step-by-step explanation:

1/5 is 0.2 and double that is 0.4 since there are 2 half hours in an hour :)

The denominator in the formula for P(IC∣D) represents the product of several probabilities: P(C), P(C,IC), P(D), and P(IC). This denominator is derived from the application of Bayes' theorem in Bayesian analysis.

It is used to calculate the posterior probability of the hypothesis IC (Hypothesis of Interest given Data) given the observed data D.

The formula for P(IC∣D) is given by:

P(IC∣D) = [P(C∣IC) P(IC)] / [P(C) P(C,IC) + P(~C) P(~C,IC)]

In this formula, the numerator represents the prior probability P(IC) multiplied by the conditional probability P(C∣IC). The denominator represents the joint probabilities of C and IC occurring together, as well as the joint probabilities of ~C (not C) and IC occurring together, weighted by the respective probabilities of C and ~C.

By dividing the numerator by the denominator, we obtain the posterior probability of IC given the observed data D, which allows for inference and decision-making based on Bayesian analysis.

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A trigonometric function and you need to solve for x, you would need to manipulate the equation algebraically to isolate x on one side.

To find the equation that you should solve to find the value of x, we need more information about the problem.

The options provided in your question are not clear or complete.

I can provide you with general information about trigonometric equations and how to solve them.

Trigonometric equations involve trigonometric functions such as sine (sin), cosine (cos), and tangent (tan), and you typically need to find the values of the variables that satisfy the equation.

In the options you provided, A, B, C, and D seem to refer to trigonometric functions, but there are no equations present.

Equations typically involve an equal sign (=), which is missing in your options.

Then you can use various techniques, such as applying trigonometric identities or using a calculator, to find the values of x that satisfy the equation.

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Answer:

15x - 6

Step-by-step explanation:

To solve this, Given the expression 12 x + 3 ( x − 2 )

To simplify, expand

12 x + 3 * x −3 * 2

Knowing that

- * + = -

then the expression becomes

= 12 x + 3x - 6

= 15x - 6

The expression given is equivalent to 15x - 6

The dimensions (in m) maximize its volume  is  mathematically given as

\(x=\frac{4\sqrt{3}}{3}\) m   for Lenght and Width

\(h=\frac{2\sqrt{3}}{3}\) m  for height

Generally, the equation for is  mathematically given as

The equation for the area is given as

\(A=x^2+4xh\\\\A=16=4xh\\\\ A=16-x^2\)

\(h=\frac{16-x^2}{4x^2}\)

Volume of box

\(V=x^2 *h\\\\V=x^2*(\frac{16-x^2}{4x^2})\\\\V=4x-x^3\)

Therefore, by differentiating V and making x the subject of the formula we have

\(V'=4-\frac{3x^2}{4}\)

Therefore, with V' =0

\(x^2=16/3\)

\(x^2=\sqrt{16/3}\\\\x=\frac{4}{\sqrt{3}}\\\\\)

\(x=\frac{4\sqrt{3}}{3}\)

Now we will sub the value of x to the h equation

\(\begin{aligned}&h=\frac{16-(\frac{4}{\sqrt{3}})^2}{4 (\frac{4}{\sqrt{3}})} \\\\&h=\frac{16-\frac{16}{3}}{\frac{16}{\sqrt{2}}} \\\\&h=\frac{2 \sqrt{3}}{3} \mathrm{~m}\end{aligned}\)

Now we differntite the derivate of V (V')

\(V''=\frac{-3x}{2}\\V''=\frac{3(\frac{4\sqrt{3}}{3})}{2} \\V''=-2\sqrt{3} < 0 \\\\\) at maximium

In conclusion, the dimensions (in m) maximize its volume.

\(x=\frac{4\sqrt{3}}{3}\)    for Lenght and Width

\(h=\frac{2\sqrt{3}}{3}\)   for height

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Answer:

F type connector

Step-by-step explanation:

Use an F-type connector for broadband cable connections that use coaxial cable.

The F connector is a coaxial RF connector commonly used for "over the air" terrestrial television, cable television and universally for satellite television and cable modems,

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Answer:

-7

Step-by-step explanation:

3=-3x-18

3x=-18-3

3x=-21

x=-7

To show that the equation x^2 + y^2 = 16 is an implicit solution of the equation y' = -x/y. Therefore, two explicit solutions on the interval ]-4, 4[ are y = √(16 - x^2) and y = -√(16 - x^2).

We need to take the derivative of both sides of the implicit equation and verify that it satisfies the given differential equation.

Differentiating x^2 + y^2 = 16 with respect to x, we get:

2x + 2yy' = 0

Now let's substitute y' = -x/y into this equation:

2x + 2y(-x/y) = 0

2x - 2x = 0

As we can see, the derivative of the implicit equation satisfies the differential equation. Therefore, x^2 + y^2 = 16 is an implicit solution of y' = -x/y.

To find explicit solutions on the interval ]-4, 4[, we can solve the implicit equation for y in terms of x.

Starting with x^2 + y^2 = 16, we can isolate y:

y^2 = 16 - x^2

y = ±√(16 - x^2)

Now we can find two explicit solutions for y by taking the positive and negative square roots:

1. y = √(16 - x^2)

2. y = -√(16 - x^2)

Both of these equations represent explicit solutions for y in terms of x on the interval ]-4, 4[.

For example, when x = 3, the corresponding values of y are:

1. y = √(16 - 3^2) = √7

2. y = -√(16 - 3^2) = -√7

Therefore, two explicit solutions on the interval ]-4, 4[ are y = √(16 - x^2) and y = -√(16 - x^2).

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Answer:

x= -3

Step-by-step explanation:

Distribute 4(2-4x) which leaves you with 8-16x-3x=65

combine the like terms which leaves you with 8-19x=65

subtract 8 from both sides 8-19x-8=65-8 which leaves you with -19x=57

lastly divide -19 from both sides which leaves you with x= -3

===================================================

Explanation:

A truncated cone is where we start with a regular 3D cone and chop off the top. The portion up top is a smaller cone, which we'll ignore. The bottom part is the truncated cone portion.

In the real world, a lampshade is one example of a truncated cone.

----------------

Let x be the radius of the sphere.

We'll be focusing on a vertical cross section of the truncated cone. Refer to figure 1 in the diagram below.

We have the following points

We'll connect a few of those points forming the dashed lines in figure 1.

To start off, draw a segment from D to G. This forms rectangle BGDE with sides of EB = 2x and BG = 2. The side BC is 18 units, so that must mean GC = BC - BG = 18 - 2 = 16.

Since EB = 2x, this means DG is also 2x.

------------------

Now focus on triangles ABC and AFC. They are congruent right triangles. We can prove this using the HL (hypotenuse leg) theorem. Recall that the radius of a circle is perpendicular to the tangent line, which is why angle AFC is 90 degrees. Angle ABC is a similar story.

Because they are congruent right triangles, this indicates side BC is the same length as side FC. Therefore, FC = 18

Through similar logic, triangles ADE and ADF are congruent as well which leads to ED = FD = 2.

Combine sides FD and FC to get the length of DC

DC = FD+FC = 2+18 = 20

This is the hypotenuse of the right triangle GCD

------------------

After all that, we have the right triangle GCD with the legs of 2x and 16. The hypotenuse is 20. Refer to figure 2 shown below.

As you can probably guess, we'll use the pythagorean theorem to find the value of x.

a^2 + b^2 = c^2

(DG)^2 + (GC)^2 = (CD)^2

(2x)^2 + (16)^2 = (20)^2

4x^2 + 256 = 400

4x^2 = 400-256

4x^2 = 144

x^2 = 144/4

x^2 = 36

x = sqrt(36)

x = 6 is the radius of the sphere.

Answer:

C

Step-by-step explanation:

Answer:

c) 14/5 = 2.8 each  (better value)

Step-by-step explanation:

a) 9/3 = 3 each

b) 28/7 = 4 each

c) 14/5 = 2.8 each  (better value)

This random assignment of participants and comparison of outcomes helps to establish a cause-and-effect relationship between the medication and the reduction in symptoms.

The experimental units in this study are the adult volunteers who suffer from allergies.

These volunteers were randomly assigned to two groups: the treatment group, which received the new experimental medication, and the control group, which received an existing medication.

The researchers then measured the percentage of participants in each group who reported a significant reduction in their allergy symptoms without experiencing drowsiness. The results showed that 44% of those in the treatment group and 28% of those in the control group experienced this improvement.

By comparing the outcomes between the two groups, the researchers can determine if the new medication effectively reduces allergy symptoms without causing drowsiness compared to the existing medication.

This random assignment of participants and comparison of outcomes helps to establish a cause-and-effect relationship between the medication and the reduction in symptoms.

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Factor:

A factor is a number that divides another number, leaving no remainder. In other words, if multiplying two whole numbers gives us a product, then the numbers we are multiplying are factors of the product because they are divisible by the product. There are two methods of finding factors: multiplication and division.

Multiple:

multiple in math are the numbers you get when you multiply a certain number by an integer. For example, multiples of 5 are: 10, 15, 20, 25, 30…etc. Multiples of 7 are: 14, 21, 28, 35, 42, 49…etc.

How to find hcf of two or more numbers :

Steps 1:

Find all the factors of each given number.

Step 2:

Find common factors of the given number.

Step 3:

The greatest of all the factors obtained in Step 2, is the required highest common factor (H.C.F).

I'm only writing the answers below as I already told how to find it.

Highest common factor:

1. The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 20 are: 1, 2, 4, 5, 10, 20

Then the greatest common factor is 2.

2. The factors of 15 are: 1, 3, 5, 15

The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 15 are: 1, 3, 5, 15The factors of 20 are: 1, 2, 4, 5, 10, 20Then the greatest common factor is 5.

3. 8

4. 12

5. 10

6. 14

How to find lcm. of numbers :

Step 1: Find the prime factors of the given numbers by repeated division method.

Step 2: Write the numbers in their exponent form. Find the product of only those prime factors that have the highest power.

Step 3: The product of these factors with the highest powers is the LCM of the given numbers.

I'm only writing the answers below as I already told how to find it.

Lowest common multiple :

1. 42

2. 12

3. 40

4. 20

5. 80

6. 42

hope it helps you..