a market researcher asked a group of men and women to choose their favorite color design from a sample of advertisements. the results are shown in the following table. red with black green with black yellow with black red with blue green with blue yellow with blue men 21 15 8 12 35 9 women 15 3 11 31 24 16 which of the following statements is not supported by the table? responses more men than women chose the color design red with black. more men than women chose the color design red with black. more women than men chose the color design yellow with black. more women than men chose the color design yellow with black. for men, the number who chose a design with black was greater than the number who chose a design with blue. for men, the number who chose a design with black was greater than the number who chose a design with blue. the color design chosen by the most people was green with blue. the color design chosen by the most people was green with blue. the total number of men surveyed by the market researcher was equal to the total number of women surveyed by the market researcher.

The unit rate of Printer B = 25 pages per minute, which is greater than the unit rate of Printer A that is 15 pages per minute.

The unit rate of a graph can b determined by using any point, (x, y), on the graph and solve by finding, m, which is the ratio of y to x, if x and y represents the variables of the relationship that is graphed.

Thus, unit rate (m) = y/x.

The printing rate for Printer A is represented by the graph. To find the unit rate for Printer A, use a point on the graph, (2, 30) to find the unit rate, m.

Printer A's Unit rate (m) = y/x = 30/2

Printer A's unit rate (m) = 15 pages per minute.

The printing rate for Printer B is given as 25 pages per minute. 25 pages per minute is a greater unit rate compared to 15 pages per minute.

Therefore, we can conclude that Printer B has a greater printing rate than Printer A, because the unit rate of 25 pages per minute is greater than 15 pages per minute.

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To find the roots of a third-degree polynomial, also known as a cubic polynomial, we can use a method called factoring or apply the cubic formula.

The first step is to check if there are any common factors that can be factored out. Next, we can use the rational root theorem to determine potential rational roots. By applying synthetic division or long division, we can divide the polynomial by the potential roots to see if they are indeed roots.

If a rational root is found, we can then use synthetic division to factor out the corresponding quadratic equation. Finally, we can solve the quadratic equation using methods like factoring, completing the square, or using the quadratic formula to find the remaining roots.

It's important to note that not all cubic polynomials can be easily factored or solved algebraically. In such cases, numerical methods or approximation techniques may be used to find the roots.

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To find the roots of a third degree polynomial, you can follow these steps: 1) Check for rational roots using the Rational Root Theorem. 2) Use synthetic division to divide the polynomial by a linear factor. 3) Factor the resulting quadratic equation. 4) Solve for the roots by setting each factor equal to zero.

To find the roots of a third degree polynomial, we can follow these steps:

Remember, the Fundamental Theorem of Algebra states that every polynomial equation of degree n has exactly n complex roots, counting multiplicities.

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To determine the sum of money Jeff should invest on January 21, 2020, in order to reach $80000 on August 8, 2020, at an annual interest rate of 5%, we need to calculate the present value of the future amount using the time value of money concepts.

We can use the formula for the present value of a future amount to calculate the initial investment required. The formula is:

Present Value = Future Value / (1 + interest rate)^time

In this case, the future value is $80000, the interest rate is 5% per year, and the time period is from January 21, 2020, to August 8, 2020. The time period is approximately 6.5 months or 0.542 years.

Plugging these values into the formula, we have:

Present Value = $80000 / (1 + 0.05)^0.542

Evaluating the expression, we find that the present value is approximately $75609. Therefore, Jeff should invest approximately $75609 on January 21, 2020, to amount to $80000 on August 8, 2020, at a 5% annual interest rate.

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(a) The curve defined by the parametric equations x = t^2, y = -1/4t (t > 0) represents a parabolic trajectory, the point of intersection between the curve and the hyperbola is (4∛2, -1/(4∛2)).

To find the points on the curve where the tangent line is parallel to the line y = x, we need to determine when the slope of the tangent line is equal to 1.

The slope of the tangent line is given by dy/dx. Using the chain rule, we can calculate dy/dt and dx/dt as follows:

dy/dt = d/dt(-1/4t) = -1/4

dx/dt = d/dt(\(t^2\)) = 2t

To find when the slope is equal to 1, we equate dy/dt and dx/dt:

-1/4 = 2t

t = -1/8

However, since t > 0 in this case, there are no points on the curve where the tangent line is parallel to y = x.

(b) To determine the points on the curve where it intersects the hyperbola xy = 1, we can substitute the parametric equations into the equation of the hyperbola:

\((t^2)(-1/4t) = 1 \\-1/4t^3 = 1\\t^3 = -4\\\)

Taking the cube root of both sides, we find that t = -∛4. Substituting this value back into the parametric equations, we get:

x = (-∛4)^2 = 4∛2

y = -1/(4∛2)

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9514 1404 393

Answer:

  see attached

Step-by-step explanation:

The graph has a line with a slope of 1/2 beginning at the origin and extending as far as you like into the first quadrant.

Answer: do you still need help

Step-by-step explanation:

Answer:

28 blocks are filled in so I don't know how this a decimal... maybe it's .28

Step-by-step explanation:

The volume of the solid obtained by rotating the region bounded by y = x and y = 2x² about the line y = 2 is π/24 units cube.

option D.

The volume of the solid obtained by rotating the region bounded by y = x and y = 2x² about the line y = 2 is calculated as follows;

y = 2x²

x² = y/2

x = √(y/2) ----- (1)

x = y -------- (2)

Solve (1) and (2) to obtain the limit of the integration.

y =  √(y/2)

y² = y/2

y = 1/2 or 0

The volume obtained by the rotation is calculated as follows;

V = 2π∫(R² - r²)

V = 2π ∫[(√(y/2)² - (y)² ] dy

V = 2π ∫ [ y/2  - y² ] dy

V = 2π [ y²/4 - y³/3 ]

Substitute the limit of the integration as follows;

y = 1/2 to 0

V = 2π [ 1/16  -  1/24 ]

V = 2π [1/48]

V = π/24 units cube

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Answer:

$1.25 for one slice  is the uint rate  is the measure B

Step-by-step explanation:

Answer:

my answer isn't on the list, but doing the math the median increased from 39 to 40, but the mean decreased from 49.16 to 45.57

The exact value of q in the form a + √b. IS -6 + √44 / 2 = -3 + √22.

An equation is a mathematical statement that asserts the equality of two expressions. It contains variables and operators (such as +, -, x, ÷) and the goal is often to find the value of the variables that make the equation true. For example, 2x + 3 = 7 is an equation where x is the variable and the goal is to find the value of x that makes the equation true.

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The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.

Especially, he has been credited with proving the following five theorems:  a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same;  the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.

In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.

In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a  theorem and is maximum extensively used in the domain of science.

2-1and interval = [4]

since function text is continuous in a given interval. And also

+(4) = 42+4 = 4-1

20 = 6667

$(5/4) = ($145/2

stone-1

= 5.833

simple, f(4) > $(5/2), hence Intermediate

Theorem & applies to the indicated proved.

Now,

= 6 C-1

C-5c +6 = 0

C=2 or c=3

1=3 or

C= 2, 3

<= 2

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The Quick Meals Diner served 131 child plates and 157 adult plates.

Let's use a system of two equations to represent the given information:

c + a = 288     (1)   // The number of child and adult plates served add up to 288

2.5c + 8.2a = 1614.9   (2)   // The total amount collected is the sum of the prices of all plates served

where c represents the number of child plates served and a represents the number of adult plates served.

We can use equation (1) to solve for c in terms of a:

c = 288 - a

Substituting this expression for c into equation (2), we get:

2.5(288 - a) + 8.2a = 1614.9

720 - 2.5a + 8.2a = 1614.9

5.7a = 894.9

a = 157

So, 157 adult plates were served. Substituting this value into equation (1), we get:

So, 157 adult plates were served. Substituting this value into equation (1), we get:

So, 131 child plates were served.

Therefore, The result is 131 child plates and 157 adult plates.

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The inverse function of f(x) = 7x and verifying that it satisfies the properties of inverse function.

The inverse function of f(x), we need to solve for x in terms of f(x). Starting with f(x) = 7x,

we can divide both sides by 7 to get x = f(x)/7.

So the inverse function of f(x) is:

f^(-1)(x) = x/7

This inverse function satisfies the properties of inverse functions.

The first property is that f(f^(-1)(x)) = x for all x in the domain of f^(-1).

Plugging in f^(-1)(x) = x/7 into f(x), we get:

f(f^(-1)(x)) = f(x/7) = 7(x/7) = x

So f(f^(-1)(x)) does indeed equal x.

The second property is that f^(-1)(f(x)) = x for all x in the domain of f.

Plugging in f(x) = 7x into f^(-1)(x), we get:

f^(-1)(f(x)) = f^(-1)(7x) = (7x)/7 = x

So f^(-1)(f(x)) also equals x.

We have successfully found the inverse function of f(x) and verified that it satisfies the properties of inverse functions.

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In match play, when the players agree to consider the hole tied after it has begun, the ruling is known as "halving the hole."

In match play, if the players agree to consider the hole tied after it has begun, the hole is deemed halved, and the players move on to the next hole without any penalty strokes. This is called "conceding the hole" and is a common practice in match play.

This means that both players receive half a point for the hole, and the match proceeds to the next hole.

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It step 3 I got The same question on khan academy

Answer:

The mean is 2.875 so its between 2 and 3

Step-by-step explanation:

Answer:

Step-by-step explanation:

So you want to isolate the y, so add 4x to both sides of the problem. So now we have y < -7 + 4x. Now since adding can go both ways (in its own equation) you can turn around the 7 and 4. So we have y < 4x -7

After answering the provided question, we can conclude that x + y + z + 60 = 200 (total number of people surveyed) (total number of people expression surveyed) (10/3)

In mathematics, an expression is a collection of symbols, digits, and companies that portray a statistical correlation or formula. An expression can be a single number, a mutable, or a combination of both of them. Addition, subtraction, proliferation, division, and exponentiation are examples of mathematical operators.  Expressions are used extensively in mathematics, including arithmetic, calculus, and geometry. They are used in mathematical formula representation, equation solution, and mathematical relationship simplification.

Let x represent the number of people infected solely by the delta variant.

Let y represent the number of people infected solely by the omicron variant.

Let z represent the total number of people infected by both variants.

Based on the information provided, we can construct the following equation system:

x/y = 5/3 (ratio of delta to omicron) (ratio of delta to omicron)

z = (1/2)*y (half of those infected by omicron are also infected by delta) (half of those infected by omicron are also infected by delta)

x + y + z + 60 = 200 (total number of people surveyed) (total number of people surveyed)

(10/3)

\(z + 2z + z + 60 = 200\s(16/3)\\z = 140\sz = 65/6\\x = (10/3)\\z = (10/3)\\11 = 110/3 ≈ 36.67\sy = 2z = 211 = 22\)

We also know that neither variant infected 60 people. This information can be represented in a Venn diagram as follows:

 _____________

  /                      / \

 /    D              / O \

/_________/____\

    N      B     (total = 200)

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The sample space for the chance experiment of which direction the next two cars will turn is {LL, LR, RL, RR}, where the first letter represents the direction of the first car and the second letter represents the direction of the second car.

A person observes which direction a car turns at a T-intersection and records an L for a left-hand turn and an R for a right-hand turn. He records his observations for the next two cars that enter the intersection. What is the sample space for the chance experiment of which direction the next two cars will turn,Let E be the event that the first car turns right. List the outcomes of E,Compute P(E),Let F be the event that at least one of the cars turns left. List the outcomes of F,Compute P(F).

The sample space for the chance experiment of which direction the next two cars will turn is {LL, LR, RL, RR}, where the first letter represents the direction of the first car and the second letter represents the direction of the second car.

The outcomes of event E, where the first car turns right, are {RL, RR}.

P(E) is the probability of the event E, which is the probability that the first car turns right. Since there are two outcomes in E and four possible outcomes in the sample space, P(E) = 2/4 = 1/2.

The outcomes of event F, where at least one of the cars turns left, are {LL, LR, RL}.

P(F) is the probability of the event F, which is the probability that at least one of the cars turns left. Since there are three outcomes in F and four possible outcomes in the sample space, P(F) = 3/4.

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The 98% confidence interval for the true proportion is (0.506, 0.614).

Given that a local news outlet reported that 56% of 600 randomly sampled Kansas residents planned to set off fireworks on July 4th and we need to compute the 98% confidence interval for the true proportion.

The formula to find the confidence interval is given by;

\(CI = \hat{p} \pm z_{\alpha/2} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\)

Where,

\(\hat{p}\) = Sample proportion\(n\)

= Sample size\(z_{\alpha/2}\)

= Critical value for the confidence level\(\alpha\)

= Level of significance

Let's put the given values in the above formula:

\(\hat{p} = 56\%

= 0.56\)\(n

= 600\)\(\alpha

= 0.02\) (As the level of significance is 1 - 0.98)\(z_{\alpha/2}\)

= 2.33 (From standard normal distribution table)N

ow, we will compute the confidence interval by putting the above values in the formula;

\(\begin{aligned}CI

= \hat{p} \pm z_{\alpha/2} \times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\

= 0.56 \pm 2.33 \times \sqrt{\frac{0.56(1-0.56)}{600}} \\

= 0.56 \pm 0.054 \\

= (0.506, 0.614) \end{aligned}\)

Therefore, the 98% confidence interval for the true proportion is (0.506, 0.614).

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a)The value of c can be found by using the fact that the sum of all probabilities in a probability mass function (PMF) must equal 1. Therefore, we have:

ΣP(x) = cM + c(M + 1) + c(M + 2) + ... = 1

This is an infinite geometric series with the first term a = cM and common ratio r = 1, so we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r) = cM / (1 - 1) = cM / 0

Since we cannot divide by zero, the only way to satisfy this equation is for cM = 0, which means c = 0.

b) P(X = 0) can be found by simply plugging x = 0 into the probability mass function P(x) = cM:

P(X = 0) = c(0) = 0

c) P(X > 2) can be found by summing the probabilities of all possible values greater than 2:

P(X > 2) = P(X = 3) + P(X = 4) + P(X = 5) + ...

Using the PMF P(x) = cM, we have:

P(X > 2) = c(3) + c(4) + c(5) + ... = 0 (since c = 0)

So, the answers to your question are: c = 0, P(X = 0) = 0, and P(X > 2) = 0.

First, let me clarify that a probability mass function is a function that maps each possible value of a random variable to the probability of that value occurring. In this case, we have a discrete random variable X that can take on the values 0, 1, 2, and so on.

Now, let's tackle the questions one by one:

a) To find the value of c, we need to use the fact that the probabilities for all possible values of X must add up to 1. In other words, we need to find the sum of P(X = x) over all possible values of x, and set it equal to 1:

P(X=0) + P(X=1) + P(X=2) + ... = 1

Using the formula given, we can write this as:

CM + CM + C(M+1) + C(M+2) + ... = 1

Simplifying the sum using the formula for the sum of an arithmetic series, we get:

CM(1 + 1 + 2 + 3 + ...) = 1

Note that the sum 1 + 1 + 2 + 3 + ... is equal to the sum of the first M natural numbers, which is M(M+1)/2. Substituting this, we get:

CM(M(M+1)/2) = 1

Solving for c, we get:

c = 2/(M(M+1))

b) To find P(X=0), we simply plug in x=0 into the formula given:

P(X=0) = CM = c(0) = 0

c) To find P(X > 2), we need to sum up the probabilities for all values of X that are greater than 2:

P(X > 2) = P(X=3) + P(X=4) + ...

Using the formula given, we can write this as:

P(X > 2) = C(M+3) + C(M+4) + ...

Simplifying the sum using the formula for the sum of an arithmetic series, we get:

P(X > 2) = C(3+4+...) = C(1+2+3+...) = CM(M+1)/2

Substituting the value of c we found in part a), we get:
P(X > 2) = 1/2

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Step-by-step explanation:

It seems here that they are asking us to solve for x

to do this we first need to factor

Since we can't factor this using the normal method we can instead do this

x^2 -4x-17=0

add 4 to both sides as it is a perfect square

x^2 - 4x + 4  = 17 +4

(x-2)^2 = sqrt 21

x-2 = ±  4.58

x -2 = 4.58    x-2 = -4.58

x= 6.58          x=-2.58

Or just say x=2+√21 or x=2−√21

Answer:

3/11

Step-by-step explanation:

because 334443

Answer:

91. The probability that Caroline will be ready before Andrew is 0.25 (Option B). Since the service times are exponentially distributed with a mean 15 minutes, the remaining service time for Andrew when Caroline arrives is also exponentially distributed with the mean 15 minutes. The service time for Caroline is also exponentially distributed with mean 15 minutes. The probability that Caroline’s service time is less than Andrew’s remaining service time is given by the formula P(X < Y) = 1 / (1 + λY / λX), where λX and λY are the rates of the exponential distributions for X and Y respectively. Since both service times have the same rate (λ = 1/15), the formula simplifies to P(X < Y) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Andrew is 0.25.

92. The probability that Caroline will be ready before Bob is 0.35 (Option A). Since Bob arrived 10 minutes after Andrew, his remaining service time when Caroline arrives is exponentially distributed with mean 15 minutes. Using the same formula as above, we get P(X < Y) = 1 / (1 + λY / λX) = 1 / (1 + 1) = 0.5. Therefore, the probability that Caroline will be ready before Bob is 0.35.

Answer:

12%

Step-by-step explanation:

Multiply 0.12 by 100 to get the percentage.

\(0.12*100=12\)

Answer:

the answer is just 7/9