2x + 9y = -7
6x - 3y = 9

The probability of a work is 0.90 and the probability of b functions is also 0.90. the probability the system works under these conditions is  0.81 (0.90 x 0.90 = 0.81).

This is because the system works if both components a and b are functioning, so we need to calculate the probability of both of them working, which is the probability of component a working (0.90) multiplied by the probability of component b working (0.90).

To get this answer, we can use the concept of joint probability which is the probability of two or more independent events happening at the same time. We can calculate the joint probability by multiplying the probabilities of each of the individual events.

In this case, the probability of the system working is the product of the probability of component a working (0.90) and the probability of component b working (0.90). This gives us a joint probability of 0.81, which is the probability the system works under these conditions.

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Answer:

0.1

Step-by-step explanation:

Just take 24/24 which is 1 and move the decimal one place to the left because there is an extra 0 on the denominator

Answer:

\(\large\boxed{\textsf{Acute Angle.}}\)

Step-by-step explanation:

\(\textsf{We are asked what type of angle is an 11}^{\circ} \textsf{angle.}\)

\(\textsf{There are a few types of angles. Let's review them.}\)

\(\large\underline{\textsf{Types of Angles:}}\)

\(\textsf{Acute Angles are angles less than 90}^{\circ}.\)

\(\textsf{Right Angles are angles equal to 90}^{\circ}.\)

\(\textsf{Obtuse Angles are angles less than 180}^{\circ}, \ \textsf{but greater than 90}^{\circ}.\)

\(\textsf{Straight Angles are angles equal to 180}^{\circ}.\)

\(\textsf{Reflex Angles are angles greater than 180}^{\circ}, \ \textsf{but less than 360}^{\circ}.\)

\(\textsf{Because our angle is less than 90}^{\circ}, \ \textsf{this angle is Acute.}\)

The ratio of the number of cakes at first of 5 : 2 and the new ratio after Ann sold 28 cakes which is 3 : 4, indicates that Ann had 40 cakes while Rose had 16 cakes

A ratio between two quantities,  indicates the number of times one quantity is contained in the other quantity.

Let X represent the initial number of cakes Ann had, and let Y represent the initial number of cakes Rose had, we get;

\(\dfrac{X}{Y} =\dfrac{5}{2}\)...(1)

\(\dfrac{X-28}{Y} =\dfrac{3}{4}\)...(2)

The expression in equation (1) indicates;

2 × X = 5 × Y

X = 5 × Y ÷ 2 = 2.5·Y

Therefore;

\(\dfrac{X-28}{Y} =\dfrac{3}{4}\)

We get;

\(\dfrac{2.5\cdot Y-28}{Y} =\dfrac{3}{4}\)

4 × (2.5·Y - 28) = 3 × Y

10·Y - 4 × 28 = 3·Y

10·Y - 3·Y = 4 × 28 = 112

7·Y = 112

Y = 112/7 = 16

Y = 16

X = 2.5·Y

Therefore; X= 2.5 × 16 = 40

X = 40

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The dimensions of the rectangle with the greatest possible area are 2\(\sqrt{(2)}\) by 4.

Let's denote the dimensions of the rectangle as length (L) and width (W). Since the base of the rectangle is on the x-axis, the width of the rectangle is equal to the x-coordinate of the upper corners of the rectangle.

Let's assume that the x-coordinate of the upper corners of the rectangle is x. Then, the width of the rectangle is W = 2x, and the length of the rectangle is L = 6 -\(x^2\).

The area of the rectangle is A = LW = \(2x(6 - x^2) = 12x - 2x^3.\)

To find the maximum area, we need to take the derivative of A with respect to x and set it equal to zero:

\(dA/dx = 12 - 6x^2 = 0\)

Solving for x, we get:

x = ±sqrt(2)

Since we are interested in the dimensions of the rectangle on the parabola, we take the positive value of x.

Therefore, the width of the rectangle is:

W = 2x = 2sqrt(2)

And the length of the rectangle is:

L = 6 - \(x^2\)= 6 - 2 = 4

So the dimensions of the rectangle with the greatest possible area are 2sqrt(2) by 4.

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Answer:

an = -6(1)n-1.

Step-by-step explanation:

since a = 1

Answer:

14 is the answer if you mean 3 by that e

Answer:

(3, 9 )

Step-by-step explanation:

y = 3x → (1)

y = 2x + 3 → (2)

Substitute y = 3x into (2)

3x = 2x + 3 ( subtract 2x from both sides )

x = 3

Substitute x = 3 into (1)

y = 3 × 3 = 9

solution is (3, 9 )

As he travelled the final 3 hours of his journey at a constant speed of 80 km/h, the value of d is 240 km.

From the graph, Tomas traveled the final 3 hours of his journey at a constant speed of 80 km/h. We mut find the distance he traveled during this time period.

Since speed is defined as distance divided by time, we will use: Distance = speed × time.

Given data: Tomas traveled for 3 hours at a constant speed of 80 km/h,

Distance = Speed × Time

Distance = 80 km/h × 3 h

Distance = 240 km.

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Answer:

Facts.

Step-by-step explanation:

The idealized regression line is y = β₀ + β₁x + ε, and the least-squares regression line is Y = b₀ + b₁x. Four assumptions for regression inference are linearity, independence, homoscedasticity, and normality. The standard error of the regression slope is affected by the spread, sample size, and relationship strength. The formula for the standard error of the slope is SEb₁ = √[ Σ(\(y_i - Y_i\))² / (n-2) ] / √[ Σ(\(x_i\) - X)² ]. If there is no association between two variables, the slope of the regression line should be zero.

There are two equations commonly used in regression analysis: the idealized regression line and the least-squares regression line.

The equation for the idealized regression line is

y = β₀ + β₁x + ε

where

y is the dependent variable

x is the independent variable

β₀ is the intercept

β₁ is the slope

ε is the error term

The equation for the least-squares regression line is

Y = b₀ + b₁x

where

Y is the predicted value of y

x is the independent variable

b₀ is the intercept

b₁ is the slope

There are four assumptions and conditions that must be met in order to perform inference for regression

The relationship between the independent variable and dependent variables is called Linearity . To check linearity, plot the dependent variable against the independent variable and look for a straight-line pattern.

Independence, The observations are independent of each other. To check independence, ensure that there is no relationship between the residuals (the difference between the observed value and the predicted value) and any other variables.

The constant variance of errors across independent variable of all level is called homoscedasticity. To check homoscedasticity, plot the residuals against the predicted values and look for a consistent spread of points around zero.

Normality, The errors are normally distributed. To check normality, plot a histogram of the residuals and look for a roughly bell-shaped distribution.

The formula for the standard error for the slope is

SEb₁ = √[ Σ(\(y_i\)- \(Y_i\))² / (n-2) ] / √[ Σ(\(x_i\) - X)² ]

where

\(y_i\), observed value of variable which is dependent for the ith observation

\(Y_i\) is the predicted value of the dependent variable for the ith observation

\(x_i\), the observed value of variable which is independent for the ith observation

X is the mean of the independent variable

n is the sample size

The formula for the sampling distribution for regression slopes is

b₁ ~ N(β₁, σ² / Σ(\(x_i\) - X)²)

where

b₁, least-squares regression line's slope

β₁ is the true population slope

σ² is the variance of the errors

If there is no association between two variables, the slope of the regression line should be zero. it depicts that the variable which is independent has no effect on the variable which is dependent.

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Answer:

B

Step-by-step explanation:

A'C'

Answer:

the numbers are 20, 21 and 22

Step-by-step explanation:

x+(x+1) + (x+2) = 63

3x +3 = 63

3x = 60

x = 20

doing this for ponits

Answer:

the numbers are 20, 21 and 22

Step-by-step explanation:

x+(x+1) + (x+2) = 63

3x +3 = 63

3x = 60

x = 20

Therefore , the solution of the given problem of equation comes out to be y = (-1/6)x + 3.

A recovery model built on linearity is based on the equation y=mx+b. The inclination is B, and the y-intercept is m. The aforementioned statement is often referred to as "Bivariate linear formulas have two components," even though y and y are distinct parts. There are no simple answers when it arrives at using linear functions. and. The formula is Y=mx+b, where m represents slopes and b represents the y-intercept.

Here,

specified that the specified line has a slope of 6, the perpendicular line's slope is:

=> m = -1/6

We can now determine the equation of the vertical line using the point-slope form of the equation of a line:

=> y - y1 = m(x - x1)

where m is the slope we just discovered and (x1, y1) is the provided point on the line (-6, 4):

=> y - 4 = (-1/6)(x - (-6))

Simplifying:

=> y - 4 = (-1/6)(x + 6)

=> y - 4 = (-1/6)x - 1

=> y = (-1/6)x + 3

The line that passes through (-6, 4) and is orthogonal to y = 6x - 1 has the equation:

=> y = (-1/6)x + 3.

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The total of the two terms that represent the length of the garden's walkway:  26x + 28

A walkway around a rectangular garden.

Simplifying each equation.

Area of the garden : 4(4.5 x + 1.5) = 18x + 6

Combined area:  5.5(8 x + 4) = 44x + 22

Thus,

Area of walkway = Combined area - Area of the garden

                                = 44x + 22 - 18x + 6

                                = 26x + 28

Thus, the total of the two terms that represent the length of the garden's walkway:  26x + 28

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If f: rn → rm is a linear map, then its derivative is simply the map itself. This is because a linear map is a function that preserves vector addition and scalar multiplication.

In other words, if we take two vectors in the domain and add them together, and then apply the linear map, it is the same as applying the linear map to each vector separately and then adding the results. Similarly, if we multiply a vector in the domain by a scalar and then apply the linear map, it is the same as multiplying the result of applying the linear map to the original vector by the same scalar.
Formally, we can express this idea using the concept of a Jacobian matrix. The Jacobian matrix of a function describes the rate at which the function changes near a particular point. For a linear map, the Jacobian matrix is simply the matrix that represents the map. This means that the derivative of f is the matrix A such that f(x) = Ax for all x in rn.
To see why this makes sense, consider the simplest case of a linear map from R1 to R1, given by f(x) = ax, where a is a constant. The derivative of this function is f'(x) = a, which is just the constant coefficient of the linear map. More generally, the derivative of a linear map f: rn → rm is the matrix A such that f(x) = Ax for all x in rn.

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Answer:

She would have $1080 dollars in 48 months.

Step-by-step explanation:

So she earned 8% interest in 48 months.

So you find 8% of 1000 and that would be 80 and add 80 to 1000 because she gained 80 dollars in interest over 48 months so in 48 months she has $1080 dollars.

The statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

A group of numbers built up in a rectangular array with rows and columns. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the fields of engineering, physics, economics, and statistics.

The statement is false. An eigenvector is a non-zero vector that, when multiplied by a matrix, produces a scalar multiple of itself. In other words, if v is an eigenvector of a matrix A, then Av = λv, where λ is the corresponding eigenvalue.

The statement suggests that if a is an nn matrix (presumably an n x n matrix), and a scalar α exists such that αv is an eigenvector of a, then v must also be an eigenvector of a. However, this is not necessarily true.

Let's consider a counterexample to demonstrate this. Suppose we have the 2x2 identity matrix I:

I = [[1, 0],

    [0, 1]]

In this case, any non-zero vector v will satisfy the condition αv = v for α = 1. However, not all non-zero vectors v are eigenvectors of I. In fact, the only eigenvectors of I are [1, 0] and [0, 1] with corresponding eigenvalues of 1.

Therefore, the statement is false. The existence of a scalar α such that αv is an eigenvector of a does not imply that v itself is an eigenvector of a.

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Answer:

You can do this! Everyone believes you can do it!

Step-by-step explanation:

The expression for the power delivered to a resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

According to the given information, the power delivered to a resistance R when an alternating current of frequency f and peak current I_0 passes through it is represented by the equation P = I^2_0 R sin^2 2 pi ft.

To express this equation in terms of csc^2 2 pi ft, we can use the trigonometric identity csc^2 x = 1/sin^2 x. Substituting this identity into the equation, we get P = I^2_0 R (1/sin^2 2 pi ft).

Since csc^2 x is the reciprocal of sin^2 x, we can rewrite the equation as P = I^2_0 R (csc^2 2 pi ft). This expression represents the power delivered to the resistance in terms of csc^2 2 pi ft.

Therefore, the correct expression for the power delivered to the resistance in terms of csc^2 2 pi ft is P = I^2_0 R (csc^2 2 pi ft).

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Answer:

the solution is (21/2, 19/2)

Step-by-step explanation:

The first equation, x = y + 1, has already been solved for x.  We can eliminate x in the second equatin by substituting y + 1 for x:

y = -(1/3)(y + 1) + 6

Let's eliminate fractions by multiplying all three terms by 3:

3y = y + 1 + 18

Combining like terms results in:

2y = 19, so that y = 19/2.

Substituting this 19/2 for y in the first equation, we get:

19/2 + 2/2 = x, or

x = 21/2

Thus the solution is (21/2, 19/2)

(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes

a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.

z = (x - μ) / σ

where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes

Substituting the given values, we get

z = (65 - 70) / 20

z = -0.25

Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.

b) The standard deviation (standard error) of the sample mean can be calculated using the formula:

SE = σ/√n

where,σ = 20 minutes, n = 49

Substituting the given values, we get

SE = 20/√49

SE = 2.857 minutes

Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.

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Answer:

Friday

Step-by-step explanation:

Thursday 7/2 ÷ 4 = 7/8 inches an hour (.875)

Friday 8 ÷ 9 = 8/9 inches an hour (.888)

Friday it was snowing faster

Answer:

Friday

if Thursday snowed 3½ inch 4 hours

then for Friday

9 ÷ 8 = 1.125 inches for one hour

1.125 × 4 = 4.5 inches for 4 hours

1.25 inches more than Thursday. So, the answer is Friday ^^

Answer:

have a great day:)))))

Step-by-step explanation:

The probability of picking a red ball is 2/3.

As given in the student question,

The probability that a randomly selected person would be a protestant and at the same time be a democrat or a republican is not given in the problem statement.

Hence, it cannot be determined without further information.

Probability is the branch of mathematics that deals with the study of uncertainty.

It provides a framework for analyzing random events that occur in the real world.

Probability helps us to estimate the likelihood of a particular event occurring. It helps us to make informed decisions when faced with uncertain outcomes.

It plays a critical role in many fields such as science, engineering, economics, and finance.

Probability formula:

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes.

The formula for probability is given by:

P (A) = Number of favorable outcomes/ Total number of outcomes

where P (A) represents the probability of event A.

Example:

Suppose we have a bag containing 10 red balls and 5 blue balls.

The total number of outcomes = 10 + 5 = 15

The number of favorable outcomes = 10P (Red ball) = 10/15 = 2/3

Therefore, the probability of picking a red ball is 2/3.

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Answer:

86 sq units

Step-by-step explanation:

it is the because:

18*4=72

3.5*4/2=7

7+7+72=86 sq units

Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).

To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.

Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.

Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.

Consider the derivative of the function f(x) = x^3 - 15x + c:

f'(x) = 3x^2 - 15

Setting f'(c) = 0, we have:

3c^2 - 15 = 0

c^2 - 5 = 0

c^2 = 5

Taking the square root of both sides, we get:

c = ±√5

Now, let's consider the function values at the endpoints of the interval (-2, 2):

f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c

f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c

If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.

If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.

In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.

However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.

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Answer:

it will be (3)

Step-by-step explanation:

since DB is a median

then DB= half AC , AB=BC

then AB=BD

then the two triangles are isosceles

The required m∠BDC is 32° .

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side. Every triangle has exactly three medians, one from each vertex, and they all intersect each other at the triangle's centroid.

According to the given question ;

DB is a median;

By the symmetry ;

Then DB = half AC ,

        = AB = BC

Then= AB = BD

In a triangle, a line that connects one corner (or vertices ) to the middle point of the opposite side is called a median. A property of isosceles triangles, which is simple to prove using triangle congruence, is that in an isosceles triangle the median to the base is perpendicular to the base.

Then the two triangles are isosceles.

Means m∠DAB = m∠BDC = 32°

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Answer:

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

Let's assume the volume of syrup is x, then we set up equation: