Consider the system of linear equations y=ax+4 and y=bx-2, where a and b are real numbers. Determine whether each statement is always, sometimes, or never true.

Answer:

Yes, He'll make it

Step-by-step explanation:

If Doug travels at 55 MPH for 5 hours, he will have driven 275 miles. Since the deadline and his current speed allow him to drive farther than his set location at 273 miles, then Doug should be able to make it within the time given.

The amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2

The meaning of unit price is a price quoted in terms of so much per agreed or standard unit of product or service

Given that, a woman bought 1.8 kg of chicken and 1.6 kg of meat. The chicken cost $5.40 and the meat cost $6.40,

We need to find, if she had bought 2.4 kg of chicken and 2 kg of meat, how much would she have had to pay,

To find the same, we will first find the unit price of each,

Unit price = total price / total quantity

Since, 1.8 kg of chicken costs $5.40,

Therefore, 1 kg will cost = 5.40 / 1.8 = $3

Similarly,

If 1.6 kg of meat costs $6.40,

Therefore, 1 kg will cost = 6.40 / 1.6 = $4

Now, to find the cost of 2.4 kg of chicken and 2 kg of meat, we will multiply the unit prices to the required quantities,

Therefore,

2.4 kg of chicken will cost = 2.4 x 3 = $7.2

2 kg of meat will cost = 2 x 4 = $8

In total, she had to pay = 8+7.2 = $15.2

Hence, the amount the women would pay for 2.4 kg of chicken and 2 kg of meat in total is $15.2

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Number of  gallon containers of paint required are 2.

Find the area that its outer surfaces possess. Sum of all those surfaces' area is the surface area of the considered object.

Given;

A gallon of paint can cover 250 square feet

The paint should be bought to paint 3 coats on each wall of a rectangular room with dimensions 16 feet by 8 feet and walls that are 10-feet tall.

Now,

The surface area for 3 coats on the wall;

=2(16*10)+2(8*10)

=320+160

=480

1gallon covers 250sq ft

For 480sq ft

=480/250

=1.92

Therefore, to paint he room of given area approximately 2 cans will be required.

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An equation represent the given scenario is 725=y-12.5x.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Given that, the Buckingham fountain holds 725 gallons of water.

Due to the harsh winter, it was discovered that it was cracked and leaking rate of 12.5 gallons per hour.

Let y represent the amount of water in gallons after x hours of leaking.

Now, equation is 725=y-12.5x

Therefore, an equation is 725=y-12.5x.

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If intersection of A & B null set and P(A) = 0.4, P(A ∪ B) = 0.9 then P(B) = 0.5

In mathematics, a set is a collection of distinct objects, called elements, which can be anything from numbers, to letters, to functions, or even other sets. The objects in a set are unordered, meaning their position or arrangement doesn't matter. Sets are often denoted using curly braces {} and the elements within the set are separated by commas.

For example, the set of positive even numbers less than 10 can be written as {2, 4, 6, 8}.

Given that,

A ∩ B = ∅,

P(A) = 0.4,

P(A ∪ B) = 0.9,

P(B) = ?

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

0.9 = 0.4 + P(B) - 0

P(B) = 0.9 - 0.4

       = 0.5

Hence, the probability of event B is 0.5

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The estimate the sum of 9/10 and 5/6 is 1 1/15

From the question, we have the following parameters that can be used in our computation:

The sum of 9/10 and 5/6

Mathematically, this can be represented as

9/10 + 5/6

Take the LCM of teh numbers

So, we have

(54 + 50)/60

Evaluate the like terms

104/60

Simplify the fraction

1 1/15

Hence, the estimate is 1 1/15

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a) The proportion of observations, P(z < -0.67) = 0.2514.

b) The proportion of observations, P(z > -0.67) = 0.7486.

c) The proportion of observations, P(z < 1.46) = 0.9279.

d) The proportion of observations, P(-0.67< z < 1.46) = 0.6765.

A z-table, or standard normal table, helps to reveals what percentage of values fall below a certain z-score in a normal distribution. We have a standard normal table present above .

a) P( z < -0.67 )

Split -0.67 such as (-0.6 + 0.07 ) and look -0.6 in first column and 0.07 in first row then look cross value. So, P( z < -0.67 )

= 0.2514

b) P( z > - 0.67 ) = 1 - P( z < -0.67 )

From part (a ) , P( z < -0.67 ) = 0.2514

So, P( z > - 0.67 ) = 1 - 0.2514 = 0.7486

=> P( z > - 0.67 ) = 0.7486

c ) P( z < 1.46 ) = 1 - P( z < -1.46 )

Using Table, P( z < -1.46 ) is,

=> P( z < -1.46 ) = 0.0721

So, P( z < 1.46 ) = 1 - 0.0721 = 0.9279

=> P( z < 1.46 ) = 0.9279

d) P(-0.67 < z < 1.46 ) = P( z < 1.46) - P( z < -0.67 ) from part( a) , P( z < -0.67 ) = 0.2514

and from par (c) , P( z < 1.46 ) = 0.9279

So, P(-0.67 < z < 1.46 ) = 0.9279 - 0.2514

= 0.6765

=> P(-0.67 < z < 1.46 ) = 0.6765

Hence, all the required proportion are determined.

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Complete question:

Use The above table A to find the proportion of observations from a standard Normal distribution that satisfies each of the following statements. Give your answers to four decimal places.

a) z < -0.67=

b) z > -0.67=

c) z < 1.46=

d) -0.67 < z < 1.46=

Answer: The domain of the function f refers to the set of all input values (x) for which the function is defined. Based on the information provided, it is not possible to determine the full domain of the function f. The only information provided are the outputs (f(1)=10, f(2)=-7, f(3)=4) for specific input values (1, 2, 3).

Step-by-step explanation:

The solution of the initial value problem is y = -3x/(3㏑x - 1)

An initial value problem is a differential equation in which the initial value of the function is given.

Now we have the initial value problem

y' = (xy + y²)/x² , y(1) = 3.

We notice that it is a homogeneous differential equation.

A homogeneous differential equation is a differential equation in which the powers of x and y are the same.

So, we proceed to solve the equation as folows.

Let y = vx.

So,

y/x = v and

dy/dx = xdv/dx + v

We now substitute these into the differential equation, we have that

y' = (xy + y²)/x²

dy/dx = (xy/x² + y²/x²

xdv/dx + v = y/x + (y/x)²

xdv/dx + v = v + v²

xdv/dx = v²

So using the method of separation of variables, we have

dv/v² = dx/x

Thus Integrating both sides, we have

∫dv/v² = ∫dx/x

-v⁻¹ = ㏑x + C

-1/v = ㏑x + C

We now substitute v = y/x into the equation, we have

- 1/y/x = ㏑x + C

-x/y = ㏑x + C

So, making y subject of the formula, we have

y = -x/(㏑x + C)

Since y(1) = 3, we have

3 = -1/(㏑1 + C)

3 = -1/(0 + C)

3 = -1/C

C = -1/3

So, y = -x/(㏑x + (-1/3))

y = -x/(㏑x - 1/3)

y = -x/(3㏑x - 1)/3

y = -3x/(3㏑x - 1)

So, the solution is y = -3x/(3㏑x - 1)

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A company make 92 stereos in a month.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

A company makes car stereos the manufacturing cost for each stereo is $45.

And, The company fixed cost of $4150 per month.

Now, Let number of cars manufacturing by a company in a month is,

⇒ $4150 ÷ $45

⇒ 92

Thus, Number of cars manufacturing by a company in a month is, 92.

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The fractions and the equivalent equations is solved

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

a)

Let the value of fraction A = 3

Now , the value of 3/1 = 3

The value of 6/2 = 3

The value of 12/4 = 3

Therefore , the equivalent fractions are 3/1 , 6/2 and 12/4

b)

Let the value of fraction A = 4

Now , the value of 4/1 = 4

The value of 8/2 = 4

The value of 16/4 = 4

Therefore , the equivalent fractions are 4/1 , 8/2 and 16/4

c)

Let the value of fraction A = 1

The value of 3/3 = 1

The value of 12/12 = 1

Therefore , the equivalent fractions are 3/3 and 12/12

d)

Let the value of fraction A = 4

The value of 40/10 = 4

The value of 8/2 = 4

Therefore , the equivalent fractions are 40/10 and 8/2

e)

Let the value of fraction A = 3

The value of 12/4 = 3

The value of 18/6 = 3

Therefore , the equivalent fractions are 12/4 and 18/6

Hence , the fractions are solved

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The numerical value of cosh(7) is 25.78543.

The  hyperbolic cosine function, cosh(x), is the inverse of the hyperbolic sine function, sinh(x). It is defined as the sum of the series cosh(x) = 1 + x²/2! + x⁴/4! + x⁶/6! + …, where x is any real number and n! is the factorial of n.

To find the numerical value of cosh(7), we need to evaluate the series at x = 7. To do this, we start by calculating the first two terms of the series, 1 and 7²/2!. The first term is 1, and the second term is 7²/2! = 49/2 = 24.5. Then we add them together to get the result cosh(7) = 25.5.

To get a more accurate result, we can add more terms to the series. For instance, by adding the third term, 7⁴/4!, we get cosh(7) = 25.5 + 585/24 = 25.70833. We can continue this process to get an even more accurate result.

After adding the sixth term, 7⁶/6!, we get cosh(7) = 25.70833 + 90090/720 = 25.78542.

Finally, we round the result to five decimal places to get cosh(7) = 25.78542 ≈ 25.78543.

The numerical value of cosh(7) is 25.78543.

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Answer:

Step-by-step explanation:

it would take 30minutes

The most general antiderivative of the function f(x) = sqrt(6) is given by F(x) = (3/2)sqrt(6x) + C, where C is an arbitrary constant. To check the answer by differentiation, you can take the derivative of F(x) with respect to x:

F'(x) = (3/2)sqrt(6)x^(-1/2) = sqrt(6),

which is equal to f(x).

The gamma function is an extension of the factorial function to complex numbers. It is defined for all complex numbers except the non-positive integers.

The gamma function satisfies the following properties:

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Answer:

It depends on the question as x and y are variables. so they can be any number

Step-by-step explanation:

It can be inferred that as one variable increases, so does the other. Additionally, a change in one variable is likely to be accompanied by a corresponding change in the other.

A significant positive correlation between two variables means that as one variable increases, the other also increases. This implies that when one variable changes, the other is likely to follow suit. For example, if Variable X increases, Variable Y is likely to increase as well. This can be interpreted as a direct relationship between the two variables. Additionally, a significant positive correlation indicates that the two variables have a strong relationship, meaning that as one variable increases or decreases, the other is likely to follow suit. This can be used to help make predictions and draw conclusions about the relationship between the two variables.

The complete question: A significant positive correlation is found between variables x and y. Which one of the following may be safely inferred? a. As x increases, y increases. b. As x increases, y decreases. c. y causes x. d. x causes y.

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The slope, x intercept and y intercepts of the graph of the equations given are found as below.

Slope of a line is the ratio of the change in y coordinates to the change in the x coordinates of two points given.

13. x intercept is the point on a line where the line touches the X axis.

y coordinate will be zero at that point.

x + 6y = 7

y = 0, then x = 7

x intercept = 7

14. 4x + y = 3

y = 0, then 4x = 3 or x = 3/4

x intercept = 3/4

15. y intercept is the point where the line touches the Y axis.

x coordinate will be 0 there.

y - 3x = 4

x = 0, then y = 4

y intercept = 4

16. 2y + x = 8

x = 0, then 2y = 8 or y = 4

y intercept = 4

17. Points given are (2,4) and (1,3).

Slope = (3 - 4) / (1 - 2) = -1 / -1 = 1

18. Points given are (2,7) and (5,6)

Slope = (6 - 7) / (5 - 2) = -1/3

Hence the required values are found.

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The solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0

A quadratic equation is a second-order polynomial equation in a single variable x , ax²+bx+c=0. with a ≠ 0 .

The quadratic formula to find solution of an equation is

x=-b±√b²-4ac/2a

The given equation is x²-2x+2=0

a=1, b=-2, c=2

x=2±√4-4(1)(2)/2(1)

x=2±√-4/2

x=2±2i/2

x=1+i, 1-i

Hence, the solutions are 1+i and 1-i of the quadratic equation x²-2x+2=0

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Answer:

23

Step-by-step explanation:

You have 6 numbers

So starting at 2^0, we write out 6 of those to get a benchmark. Well also solve them for now. To the left, we put your numbers, which are 111010

1: 2^0 = 1

1: 2^1 = 2

1: 2^2 = 4

0: 2^3 = 8

1: 2^4 = 16

0: 2^5 = 32

^ Everywhere there's a one, we use the number, everywhere there's a 0, we throw that out. Theres a 1 next to the first, second, third, and fifth numbers. Taking those numbers, we add them

1 + 2 + 4 + 16

Which equals 23, your decimal equivalent

A logical inference on the composition of the marbles in the bag is that there are approximately 3 green, 2 blue, 4 red, and 3 yellow marbles.

Probability is a number that expresses the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given, A bag containing 12 colored marbles. Dan drew a single marble from the bag 25 times, replacing the marble each time.

He recorded drawing a red marble 9 times.

Thus, the number of red marvels = 12 * 9 /25

the number of red marvels = 4.32 or 4

He recorded drawing a yellow marble 6 times,

Thus, the number of yellow marbles = 12 *6/25

the number of yellow marbles = 2.88 or 3 approx

He recorded drawing a blue marble 4 times,

Thus, the number of blue marbles = 12 *4/25

the number of blue marbles =  1.92 or 2 approx

He recorded drawing and a green marble 6 times.

Thus, the number of green marbles = 12 *6/25

the number of green marbles = 2.88 or 3 approx,

Therefore, A reasonable conclusion about the makeup of the marbles in the bag is that there are approx 3 green marbles, 2 blue marbles, 4 red marbles, and 3 yellow marbles.

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Answer:

A

Step-by-step explanation:

Answer:

I'm sorry, but without additional information such as the magnitude, direction, and orientation of the two forces, it is impossible to determine the magnitude of the resultant.

The value of variables x and y are, x = 67  and y = 40.

An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

Given that;

Figure is shown in image.

Now, By definition of vertically opposite angle,

⇒ (y + 23)° = 63°

Solve for y;

⇒ y + 23 = 63

Subtract 23 both side,

⇒ y + 23 - 23 = 63 - 23

⇒ y = 40

And, By definition of supplementary angles, we get;

⇒ (2x - 17)° + 63° = 180°

Solve for x;

⇒ 2x - 17 + 63 = 180

⇒ 2x + 46 = 180

⇒ 2x + 46 - 46 = 180 - 46

⇒ 2x = 134

⇒ x = 134/2

⇒ x = 67

Thus, The value of variables x and y are, x = 67  and y = 40.

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Answer:

2

Step-by-step explanation:

well I so yeah and this plus that

The greatest common factor of 50,12,and 8 is,

⇒ 2

We have to given that,

All the numbers are,

⇒ 50, 12 and 8

Now, We know that,

The highest number that divides exactly into two more numbers, is called  Greatest common factors.

Here, Numbers are,

50 = 2 x 5 x 5

12 = 2 x 2 x 3

8 = 2 x 2 x 2

Hence, The greatest common factor of 50,12,and 8 is,

⇒ 2

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Answer:

The number can be expressed in multiple forms

Fraction form [tex]x=\frac{2962}{67}[/tex]  or decimal form  [tex]x=44.21[/tex]

Step-by-step explanation:

Lets break the problem down

"times" is multiplication *

The difference between 2 numbers is subtraction  [tex](x-y)[/tex]

A number plus a number is addition [tex]x+y[/tex]

[tex]68(x-45)=x+-98[/tex]

Lets solve for [tex]x[/tex].

Lets start on the left side.

Distribute 68 to the terms inside the parenthesis.

[tex]68x-3060=x+-98[/tex]

A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign.

[tex]68x-3060=x-98[/tex]

Subtract [tex]x[/tex] from both sides of the equation.

[tex]68x-3060-x=-98[/tex]

Subtract [tex]x[/tex] from [tex]68x[/tex].

[tex]67x-3060=-98[/tex]

Add 3060 to both sides of the equation.

[tex]67x=2962[/tex]

Divide both sides of the equation by 67.

[tex]x=\frac{2962}{67}[/tex] or as a decimal [tex]x=44.21[/tex]

The percent of infections for Hospital 6 is given as follows:

44.81%.

The percentage is obtained applying the proportions in the context of this problem.

A proportion is applied because a percentage is calculated with the division of the number of desired outcomes by the number of total outcomes, a result which is then multiplied by 100%.

Out of 540 patients in Hospital 6, 67 were infected in hospital and 175 after release, hence the percentage is obtained as follows:

P = (67 + 175)/540 = 44.81%.

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There could be 150 sequences of rolls

Let's find the sets of 5 integers less than or equal to 6 that could multiply to 300 (where order doesn't matter for right now):

1, 2, 5, 5, 6

1, 3, 4, 5, 5

2, 2, 3, 5, 5

Now let's find the number of unique ways we could reorder these sets

There are

5!/2!=60 ways to order {1, 2, 5, 5, 6}

There are

5!/2! =60 ways to order {1, 3, 4, 5, 5}

There are

5!/2!2! =30 ways to order {2, 2, 3, 5, 5}

There could have, therefore, been 60 + 60 + 30 = 150 different sequences of rolls

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The matrix is undefined.

A matrix, which is used to represent a mathematical object or an attribute of one, is a rectangular array or table containing numbers, symbols, or expressions that are organized in rows and columns.

Matrix addition or subtraction can only be performed if the matrices have the same dimensions, i.e. the same number of rows and columns. In this case, two matrices are given, but their dimensions are not specified, so it is impossible to determine if they are the same or not. Therefore, the result is undefined.

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