Mrs. Ruiz bought 5 bags of balloons for a party. Each bag contained 70 balloons. Andy said Mrs. Ruiz bought a total of 75 balloons. Andy is incorrect. What error did Andy make when make calculations the total number of balloons?

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

Learn more about distributed here:

https://brainly.com/question/29664127

#SPJ11

Answer:

10.4

Step-by-step explanation:

cosine rule=\(a^{2}=b^{2} +c^{2} -2bc*cosa\)

                \((2\sqrt{3}) ^{2}=(x+2)^{2} +x^{2} -2(x+2)x*cos60\\12=x^{2} +4x+4+x^{2} -2x^{2} -4x*\frac{1}{2}\\2x-8=0\\x=4\\Area=\frac{1}{2}absinc\\ = \frac{1}{2}*6*4*sin60\\\\ =6\sqrt{3}\\=10.4(3 sig.fig)\)

Answer: 60

Step-by-step explanation:

Line=180 degrees

180-120=60

In "gas-mileage" experiment : (a) "gasoline-brand" is "categorical-variable" and weight is "quantitative-variable".

In this experiment, the brand of gasoline is a categorical variable because it represents different distinct categories or labels, namely Amoco, Marathon, and Speedway. Gasoline brands cannot be measured on a numerical scale, but rather they represent different brands.

The weight of the car is a quantitative variable because it can be measured on a numerical scale. The weight is given in pounds and represents a continuous range of values, such as 3,000, 3,500, or 4,000 pounds. It can be measured and compared using mathematical operations, such as addition or subtraction.

Therefore, the correct option is (a).

Learn more about Categorical Variable here

https://brainly.com/question/24244518

#SPJ4

The given question is incomplete, the complete question is

You are planning an experiment to determine the effect of the brand of gasoline and the weight of a car on gas mileage measured in miles per gallon. You will use a single test car, adding weights so that its total weight is 3,000, 3,500, or 4,000 pounds. The car will drive on a test track at each weight using each of Amoco, Marathon, and Speedway gasoline.

In the gas mileage experiment,

(a) gasoline brand is a categorical variable and weight is a quantitative variable.

(b) gasoline brand and weight are both categorical variables.

(c) gasoline brand and weight are both quantitative variables.

(d) gasoline brand is a quantitative variable and weight is a categorical variable.

Answer:15$

Step-by-step explanation:

The distance between 85th and 95th percentile is 0.345.

What is a normal distribution?

It is also known as Gaussian distribution. . It shows the data near the more. This appears as bell curve in graphical form. It is a bell shaped frequency distribution curve of a continuous random variable.

A normally distributed random variable x with mean μ=24 and standard deviation=σ=5

X≈N(μ,σ²)

X≈N(24,25)

Let, 85th percentile=x₁ and 95th percentile=x₂

p(X ≤ x₁)=0.85 and p(X ≤ x₂)=0.95

p((X-μ/σ)≤ ((x₁-24)/5)=0.85 and p((X-μ/σ)≤ ((x₂-24)/5)=0.95

p(z≤ (x₁-24)/5)=0.85 and p(z≤ (x₂-24)/5)=0.95

\(\bar\)\(\bar{\phi}\)((x₁-24)/5)=0.85 and \(\bar\)\(\bar{\phi}\)((x₂-24)/5)=0.95

(x₁-24)/5)= \(\bar\)\(\bar{\phi}\)⁻¹(0.85) and (x₂-24)/5)= \(\bar\)\(\bar{\phi}\)⁻¹(0.95)

x₁=24+5×1.036 and x₂=24+5×1.645

x₁=29.18 and x₂=32.225

The distance between 85th and 95th percentile

Δx=|x₁-x₂|=|29.18-32.225|

Δx=0.345

To know more about normal distribution, visit:

https://brainly.com/question/15103234

#SPJ4

Answer:

b

Step-by-step explanation:

Answer:

Im not really sure but i think is D

Step-by-step explanation:

Plz let me know if its wrong

i hope it helped <3

Given a line with the equation -3x+8y=-10, its slope can be calculated using the slope intercept form of the line that is 3/8.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x). A line's slope is how steeply it slopes from LEFT to RIGHT. The slope of a line is determined by dividing its rise, or vertical change, by its run, or horizontal change. No matter which two locations on the line you choose, the slope of a line is always constant (it never varies). The slope of a line in mathematics indicates how steep a line is. It is also referred to as the gradient. The "change in y" over the "change in x" of a line is referred to as the slope.

Here,

-3x+8y=-10

y=mx+c

where m=slope of line

8y=3x-10

y=3x/8-10/8

slope=3/8

The slope of given line whose equation is -3x+8y=-10 is 3/8 using slope intercept form of line.

To know more about slope,

https://brainly.com/question/28771374

#SPJ4

Answer:

girl I have the same question

Answer: 60

Step-by-step explanation:

See

Hence

m<COB=60°

The dimensions of the vector spaces are:

(a) 3

(b) 6

(c) 1

(d) 4

(e) 7

(f) 2

To find the dimensions of the given vector spaces, we need to determine the number of linearly independent vectors that form a basis for each space.

(a) The vector space of all diagonal 3x3 matrices:

A diagonal matrix has non-zero entries only along the main diagonal, and the remaining entries are zero. In a 3x3 matrix, there are three positions on the main diagonal. Each of these positions can have a different non-zero entry, giving us three linearly independent vectors. Therefore, the dimension of this vector space is 3.

(b) The vector space R^6:

The vector space R^6 consists of all 6-dimensional real-valued vectors. Each vector in this space has six components. Therefore, the dimension of this vector space is 6.

(c) The vector space of all upper triangular 2x2 matrices:

An upper triangular matrix has zero entries below the main diagonal. In a 2x2 matrix, there is one position below the main diagonal. Therefore, there is only one linearly independent vector that can be formed. The dimension of this vector space is 1.

(d) The vector space P₁[x] of polynomials with degree less than 4:

The vector space P₁[x] consists of all polynomials with degrees less than 4. A polynomial of degree less than 4 can have coefficients for x^0, x^1, x^2, and x^3. Therefore, there are four linearly independent vectors. The dimension of this vector space is 4.

(e) The vector space R^7:

The vector space R^7 consists of all 7-dimensional real-valued vectors. Each vector in this space has seven components. Therefore, the dimension of this vector space is 7.

(f) The vector space of 3x3 matrices with trace 0:

The trace of a matrix is the sum of its diagonal elements. For a 3x3 matrix with trace 0, there is one constraint: the sum of the diagonal elements must be zero. We can choose two diagonal elements freely, but the third element is determined by the sum of the other two. Therefore, we have two degrees of freedom, and the dimension of this vector space is 2.

In summary, the dimensions of the vector spaces are:

(a) 3

(b) 6

(c) 1

(d) 4

(e) 7

(f) 2

Learn more about Vector Spaces here

brainly.com/question/30531953

#SPJ11

The dimensions of various vector spaces: 3 for diagonal 3x3 matrices, 6 for R6, 3 for upper triangular 2x2 matrices, 4 for polynomials with degree less than 4, 7 for R7, and 8 for 3x3 matrices with trace 0.

(a) The vector space of all diagonal 3 x 3 matrices has a fixed dimension of 3, because every diagonal matrix has only 3 diagonal elements.

(b) The vector space R6 has a dimension of 6, because it consists of all 6-dimensional vectors.

(c) The vector space of all upper triangular 2 x 2 matrices has a dimension of 3, because there are 3 independent entries in the upper triangle.

(d) The vector space P₁[x] of polynomials with degree less than 4 has a dimension of 4, because it can be represented by the coefficients of a polynomial of degree 3.

(e) The vector space R7 has a dimension of 7, because it consists of all 7-dimensional vectors.

(f) The vector space of 3 x 3 matrices with trace 0 has a dimension of 8, because there are 8 independent entries in a 3 x 3 matrix with trace 0.

https://brainly.com/question/35413023

#SPJ2

Answer:

See below

Step-by-step explanation:

The LHS and RHS are exactly the same, so the equality is true.

The associate property of addition says that

\(\boxed{a+(b+c)=(a+b)+c}\)

In order to make the addition of fractions, the denominators should be same. So we can write three fractions as one.

\(\dfrac{1}{2} +\left(\dfrac{2}{3}+\dfrac{3}{4} \right )\)

\(\dfrac{1}{2} +\dfrac{2}{3}+\dfrac{3}{4}\)

\(\dfrac{1\cdot 6 }{2\cdot 6} +\dfrac{2 \cdot 4}{3 \cdot 4}+\dfrac{3 \cdot 3 }{4 \cdot 3}\)

\(\dfrac{ 6 }{12} +\dfrac{8}{12}+\dfrac{9 }{12}\)

\(\dfrac{ 23 }{12}\)

Answer:

You gotta give me (us) more to work with homie.

Step-by-step explanation:

If I have more of a picture with it I could possibly help but all there is a barely readable and legible nonsense equation. Sorry :(

Answer:

A i think

Step-by-step explanation:

Answer:

you have it correct sir

Step-by-step explanation:

If e is an algebraic extension of a field f and r is a ring with \(f\subseteq r\subseteq e$,\) then r must be a field.

we have \(a^{-1} = -\frac{1}{c_0}(a^{n-1} + c_{n-1}a^{n-2} + \cdots + c_1)$,\) and all of the terms on the right-hand side of this equation belong to $r$.

Therefore, \($a^{-1}\in r$\), and we have shown that r is a field.

Since e is an algebraic extension of f, every element \($x\in e$\) satisfies some non-zero polynomial with coefficients in \($f$\), say \($f(x)=0$\)  for some non-zero polynomial\($f(t) \in f[t]$.\)

Now, suppose \($r$\) is a subring of  \($e$\) containing f.

To show that r is a field, it suffices to show that every non-zero element of r has a multiplicative inverse in r.

Let \($a\in r$\) be a non-zero element.

Since \($a\in e$\) , there exists a non-zero polynomial \($f(t)\in f[t]$\)  such that \(f(a)=0$.\)

Let n be the degree of f(t), so that \(f(t) = t^n + c_{n-1}t^{n-1} + \cdots + c_1 t + c_0$ for some $c_i\in f$, $0\leq i\leq n-1$.\)

Then, we have \(a^{-1} = -\frac{1}{c_0}(a^{n-1} + c_{n-1}a^{n-2} + \cdots + c_1)$,\) and all of the terms on the right-hand side of this equation belong to r.  

Therefore, \($a^{-1}\in r$\), and we have shown that r is a field.

For similar question on algebraic extension.

https://brainly.com/question/30323989

#SPJ11

The equation is: G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

The formula for the equation of a line in slope intercept form is:

y = mx + c

where:

m is slope

c is y-intercept

From the graph, we see that:

y-intercept = 15 gallons

Now, the slope is gotten from the formula:

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 5)/(4 - 8)

Slope = -⁵/₄

Thus, equation is:

G = -⁵/₄t + 15

The slope of the function represents that ⁵/₄ gallons of gas is consumed to drive the car for one hour.

Read more about Linear equation graph at: https://brainly.com/question/28732353

#SPJ1

The probability of the interval -1.62 < z < 2.01 in a standard normal distribution is approximately 0.9262 or 92.62%.

In a standard normal distribution, the mean is 0 and the standard deviation is 1. The z-score represents the number of standard deviations a data point is from the mean. To find the probability of a specific interval, we calculate the area under the curve between the corresponding z-values.

Given the interval -1.62 < z < 2.01, we need to find the area under the standard normal curve between these two z-values. This can be done using a standard normal distribution table or by using a statistical software or calculator.

By looking up the z-values in the table or using software, we find the corresponding probabilities: P(z < -1.62) = 0.0526 and P(z < 2.01) = 0.9788.

To find the probability of the interval -1.62 < z < 2.01, we subtract the probability of the lower bound from the probability of the upper bound: P(-1.62 < z < 2.01) = P(z < 2.01) - P(z < -1.62 = 0.9788 - 0.0526 = 0.9262.

Learn more about normal distribution here:

https://brainly.com/question/15103234

#SPJ11

Answer:

x(x-2)

Step-by-step explanation:

Answer:

The answer is 1 5/6

Step-by-step explanation:

the girl will be scoring a total of 30 goals.

What is number line?

A number line is an image of numbers plotted on a straight line, either horizontally or vertically. We can compare numbers and execute simple arithmetic operations on them easily by writing the numbers down on a number line. The starting point of a number line is often regarded as zero (0). These numbers to the left of zero are all negative while the numbers just on right of zero are all positive. As a result, we can argue that on a number line, the value of numbers grows as we approach the right. The numbers on the right are therefore larger than the ones on the left, according to this statement.

Given, the goal scored

3 times 2

4 times 1

and 5 times 4.

So the total goal scored will be 3*2=6

4*1=4

and 5*4=20

Score = 6+4+20=30

Hence the girl will be scoring a total of 30 goals.

Learn more about the number line, by the following link

https://brainly.com/question/23379455

#SPJ1

Answer:

$54

Step-by-step explanation:

Answer:

B.)$54

Step-by-step explanation:

20%->0.20

45(0.20)=9

45+9=54

Continuous on. f(x)=x21x+2 is an illustration of a rational function (the fraction of two polynomials).

A rational function is any function that can be formally stated as an algebraic fraction in which both the numerator and the denominator are polynomials. The coefficients of the polynomials may appear in any field K and need not be rational values. A function that measures two polynomials in comparison. As a ratio, it is "rational" because one is divided by the other. Write the number in decimal form before determining whether it is rational or irrational if you are required to do so. The number is rational if it comes to an end. You should search for a recurring pattern of digits if it goes on forever. The number is irrational if there is no pattern that repeats itself.

Determine the continuous of the function.

Continuous on.

Learn more about rational function here

https://brainly.com/question/1851758

#SPJ4

The function f(x) = (x^2 - 1)/(x + 2) is a rational function that is continuous for all values of x except x = -2. This is because division by zero is undefined, and the denominator of the function becomes zero at x = -2.

The given function f(x) = (x^2 - 1)/(x + 2) is a rational function, which is a fraction of two polynomials. To check the continuity of the function, we need to find any values of x that make the denominator equal to zero since division by zero is undefined. In this case, the denominator becomes zero at x = -2, so the function is discontinuous at x = -2. Therefore, f(x) is continuous for all values of x except x = -2. This means that the function is defined and has a well-defined output value for every input value, except when x is equal to -2.

Learn more about polynomials here: brainly.com/question/11536910

#SPJ4

Answer:

9.63

Step-by-step explanation:

Since the ratio of the length of the horizontal leg to the length of the vertical length is 12:1, then the horizontal leg must be 12 × 0.8 m = 9.6 m.

We have a right triangle with legs of lengths 0.8 m and 9.6 m.

We can find the length of the hypotenuse by using the Pythagoras theorem.

a² + b² = c²

(0.8 m)² + (9.6 m)² = c²

c² = 92.8 m²

c = 9.63 m

Answer: 9.63

The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

To learn more about set ,

https://brainly.com/question/30368748

#SPJ4

Answer:

Step-by-step explanation:

\(4x^2-16x-9.\\Writ -16x - as -a -difference\\ 4x^2 +2x-18x -9 \\Factor -out- common- terms\\2x(2x+1)-9(2x+1)\\ Factor -out (2x+1)\\(2x+1)(2x-9)\)

I Hope It Helps :)

Answer:

\( \boxed{\sf (2x - 9)(2x + 1)} \)

Step-by-step explanation:

\( \sf Factor \: the \: following: \\ \sf \implies 4 {x}^{2} - 16x - 9 \\ \\ \sf Factor \: the \: quadratic \: 4 {x}^{2} - 16 x - 9. \\ \sf The \: coefficient \: of \: {x}^{2} \: is \: 4 \: and \: the \: constant \\ \sf term \: is \: - 9. \: The \: product \: of \: 4 \: and \: - 9 \: is \\ \sf - 36. \: The \: factors \: of \: - 36 \: which \: sum \: to \\ \sf - 16 \: are \: 2 \: and \: - 18. \\ \sf So, \\ \sf \implies 4 {x}^{2} - (18 - 2)x - 9 \\ \\ \sf \implies 4 {x}^{2} - 18x + 2x - 9 \\ \\ \sf \implies 2x(2x - 9) + 1(2x - 9) \\ \\ \sf Factor \: 2x - 9 \: from \: 2x(2x - 9) + 1(2x - 9) : \\ \sf \implies (2x - 9)(2x + 1)\)