According to a report, the average length of stay for a hospital's flu-stricken patients is 4.1 days, with a maximum stay of 18 days, and a recovery rate of 95%. An auditor selected a random group of

The system of linear equations that has an unique solution has this feature:

Different slopes.

Then we must replace into the equations the variables x = 2 and y = -1, and verify if the equations are satisfied.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The number of solutions for a system of two linear functions is defined as follows:

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

The problem requires finding the area under the curve \(y = f(x) = x^4\) over the interval \([2,4]\) and including a diagram of the region.

To calculate the area under the curve \(y = x^4\) over the interval \([2,4]\), we need to integrate the function with respect to \(x\) over that interval. The definite integral will give us the desired area.

The diagram of the region is a plot of the function \(y = x^4\) over the interval \([2,4]\), bounded by the x-axis and the curve. The region is a closed shape between x = 2 and x = 4.

To calculate the area, we integrate the function \(y = x^4\) over the interval \([2,4]\):

\[A = \int_{2}^{4} x^4 \, dx.\]

By evaluating this definite integral, we can determine the area under the curve. The result will give us the numerical value of the area.

To know more about area under the curve here: brainly.com/question/15122151

#SPJ11

Answer:

30 percent

Step-by-step explanation:

In a percentage, you first need a fraction. A fraction has 1) a part, and 2) the whole.

\(\frac{part}{whole}\)

At her birthday party, she had 7 chocolate cupcakes, 9 vanilla cupcakes, and

14 strawberry cupcakes. In total, when you add 7 + 9 + 14, you get 30

cupcakes in total.

So, the whole is 30.

The question asks for vanilla cupcakes, so the part is 9 vanilla cupcakes.

Now, you have your fraction. \(\frac{9}{30}\)

Next, to convert to a percent, you first need to divide.

9 ÷ 30 = 0.3.

To covert to a percent, you can multiply 0.3 × 100 = 30.

So the percentage of the cupcakes at Maria's birthday party that were vanilla cupcakes is 30.

To test whether the statement "Out of sight, out of mind" is true or not, an experiment should be conducted where participants are asked to recall objects they've seen before, some being visible and some being hidden.

To conduct an experiment on the statement "Out of sight, out of mind," researchers can conduct a recall experiment. The experiment can involve 2 groups of participants who are shown a list of items for a few seconds.Group 1 will view a list of items, with each item visible to the participants for a few seconds. Group 2 will be shown the same list of items, with some items visible to the participants for a few seconds and others hidden from view. Both groups will then be asked to recall the items they saw on the list. This way, researchers can analyze whether the statement "Out of sight, out of mind" is true or not.This experiment will enable researchers to compare the number of items remembered by both groups of participants. If the statement is true, the group that viewed the entire list of items will remember more objects than the group that was shown only some of the items. On the other hand, if the statement is false, both groups should recall the same number of objects.

Therefore, by conducting a recall experiment, it will be possible to test whether the statement "Out of sight, out of mind" is true or not.

To know more about recall experiment visit:

brainly.com/question/28388980

#SPJ11

The maximum profit is 6 and it is obtained when we mix 0.6 kg of type A, 0 kg of type B, and 0.4 kg of type C.

The optimal mix for the maximum profit can be found as follows:

The company mixes three types of toffees, A, B, and C. Let the weights of type A, B, and C be a, b, and c kg, respectively. Let us assume that we are making 1kg of toffee pack. Therefore, the weight of type C should be 1 - (a + b) kg. Also, the mixture must contain at least 300 gms of type A i.e a >= 0.3 kg

Also, the weight of the first two types (A and B) must be at least equal to the weight of type C, i.e a + b >= c. This condition can also be written as a + b - c >= 0

Let us now calculate the total cost of making 1kg of toffee pack.

Cost = 20a + 10b + 5c

If the pack is sold at Rs. 17, then the profit per 1kg of toffee pack is by

Profit = Selling Price - Cost = 17 - (20a + 10b + 5c)

Now we have the following linear programming problem:

Maximize P = 17 - (20a + 10b + 5c)

Subject to constraints: a + b + c = 1 (since we are making 1kg of toffee pack)

a >= 0.3a + b - c >= 0a, b, c >= 0

We can use the simplex method to solve this linear programming problem. However, to save time, we can solve it graphically. The feasible region is as follows:

We can see that the corner points of the feasible region are: (0.3, 0, 0.7), (0.6, 0, 0.4), (0, 0.5, 0.5), and (0, 1, 0).

Let us calculate the profit at each of these corner points. For example, at the point (0.3, 0, 0.7), we have a = 0.3, b = 0, and c = 0.7. Therefore, the profit is

P = 17 - (20(0.3) + 10(0) + 5(0.7)) = 3.5

Similarly, we can calculate the profit at the other corner points as well. The corner point (0.3, 0, 0.7) gives a profit of 3.5

Corner point (0.6, 0, 0.4) result in a profit of 6

Corner point (0, 0.5, 0.5) results in a profit of 5

Corner point (0, 1, 0) gives a profit of 3

You can learn more about optimal mix at: brainly.com/question/30629565

#SPJ11

Answer:

250 ml

Step-by-step explanation:

300ml + 250ml =550ml

550ml - 200ml=350ml

350ml - 150ml + 100ml=300ml

300ml - 50ml=250ml

Answer:

(24x^3y^2-6xy)/3x

8x^2y^2-2y

Step-by-step explanation:

Answer:

Angle 4 = 135, angle 5 = 45

Step-by-step explanation:

Consecutive interior angles are supplementary, therefore angle 5 + angle 8 = 180 degrees. Since the complement of 5 is the supplement of 4, we can write the system of equations.

180 - x = 90 - y or -x + y - 90 - 180 or -x + y = -90 or x - y = 90

x + y = 180

x - y = 90

Where angle 4 is x and angle 5 is y.

y = 180 - x

x - (180 - x) = 90

x - 180 + x =90

x + x = 270

2x = 270

x = 135

By plugging that in to an equation we can solve for y.

y = 45

Answer:

answer is 26.07 L.

Step-by-step explanation:

P= 0.884 atm

V= ?

n= 0.857 moles (where 28 g/mole is the molar mass of N₂, that is, the amount of mass that the substance contains in one mole.)

R=0.082

T= 328 K

do 0.884 atm × V= 0.857 moles× 0.082 ×328 K

Answer:

2 will give you the larger value of 17

Step-by-step explanation:

When the slope of the line is 3 the equation of the line using point slope formula is

D. у - 8 = 3 (x - 6)

Point slope formula is giving by (y - y₁) = m (x - x₁)

where

m = slope

x₂ and x₁ = points in x coordinates

y₂ and y₁ = points in y coordinates

For slope of 3, equation passing through point (5, 8)

(y - y₁) = m (x - x₁)

y - 8 = 3 (x - 6)

y - 8 = 3x - 18

y = 3x - 18 + 8

y = 3x - 10

Learn more about linear function at:

https://brainly.com/question/30125370

#SPJ1

The capacity of the tank is 240 cm³.

Capacity means the volume of a solid shape.

To calculate the capacity of the tank, we use the formula below.

Note: When the water from the 8 small containers is poured into the tank that was initially half full, becomes 1.4 full that means the water from the 8 small containers fills the tank 0.9

Formula:

Where:

Solve for V

Hence, the capacity of the tank is 240 cm³.

Learn more about capacity here: https://brainly.com/question/3945391

#SPJ1

Answer:

Option 4

Step-by-step explanation:

This is a standard formula.

The equation of the line through \((x_1, y_1)\) with slope \(m\) is \(y-y_1=m(x-x_1)\).

Step-by-step explanation:

Triangle a) is half of an equilateral triangle therefore the height divides the base into two equal parts, same thing for triangle b), triangle c) instead is half square, therefore congruent catheti.

a)

n = 6 : 2

n = 3

m = √(6²+3²)

m = √45

b)

x = 10 x 2 = 20

y = √(20²-10²)

y = √300

c)

a = √(5²+5²)

a = √50

\(\\ \rm\bullet\rightarrowtail c^2=a^2+b^2\)

\(\\ \rm\bullet\rightarrowtail c^2=3^2+4^2\)

\(\\ \rm\bullet\rightarrowtail c^2=9+16\)

\(\\ \rm\bullet\rightarrowtail c^2=25\)

\(\\ \rm\bullet\rightarrowtail c=5\)

Answer: 244 degrees

Step-by-step explanation:

The term that refers to the fact that the distance between two or more points is equal is "equidistant".

In geometry, the concept of equidistance is important when dealing with circles, which are sets of points that are equidistant from a single point called the center. This property is what allows circles to be defined in terms of their radius, which is the distance between the center and any point on the circle.

Equidistance is also important in other areas of mathematics and science. For example, in physics, equidistant points can be used to define a plane or surface that is perpendicular to a given line or axis. This is useful in many applications, such as designing electronic circuit boards or constructing buildings.

The concept of equidistance is not limited to mathematics and science, however. It can also be applied in everyday life. For instance, if you are planning a road trip and want to visit several destinations that are equidistant from your starting point, you can use this information to help plan your route and estimate your travel time.

for such more question on equidistant

https://brainly.com/question/15683939

#SPJ11

Answer:

total earnings at 6th hour: 111

hourly wage (slope): 18.5

Step-by-step explanation:

A linear function has a linear relationship, which essentially states as x increases by one, the y-value increases by some constant amount yielding a straight line.

The slope, or how much the y-value changes as x changes by 1 is generally written as: \(m=\frac{y_2-y_1}{x_2-x_1}\)

We can choose any two points and this should yield the slope of the function, but it's a lot easier to choose y-values that are only separated by an x-value of one.

Let's say: \((x_1, y_1)=(4,\ 74)\text{ and }(x_2,y_2)=(5,\ 92.50)\)

If we plug the values into the slope formula we just get: \(\frac{92.50-74}{5-4}=\frac{92.50-74}{1}=92.50-74\)

And this makes sense, since by definition of a slope, it's just the change in y over change in x. This is equivalent to how much the y-value changes as x increases by one, so if we select two values with a difference of one in their x-values, the slope just turns out to be the difference between the two numbers.

Simplifying our expression we get: \(92.50-74=18.5\)

This slope in this context represents how earnings increases as the hour increases, or in other words the hourly wage.

To calculate the earnings of the 6th hour we can just use the definition of a slope. From the x-value 5 to the x-value 6, the y-value should simply increase 18.5

So adding 18.5 to the y-value at x=5 we get: \(92.5+18.5=111\)

The value of angle a is 54⁰.

The value of angle b is 30⁰.

The value of angle c is 96⁰.

The value of angle a, b, c is calculated by applying intersecting chord theorem which states that the angle at tangent is half of the arc angle of the two intersecting chords.

m∠a = ¹/₂ x (108⁰) (interior angles of intersecting secants)

m∠a = 54⁰

The value of angle b is calculated as;

m∠b = ¹/₂ x (60⁰) (interior angles of intersecting secants)

m∠b = 30⁰

The value of angle c is calculated as;

adjacent angle to c = ¹/₂ x (108⁰ + 60⁰) (interior angles of intersecting secants)

adjacent angle to c = 84⁰

angle c = 180 - 84⁰ (sum of angles on a straight line)

angle c = 96⁰

Learn more about chord angles here: brainly.com/question/23732231

#SPJ1

In the triangle ABC, i) ABC = 52.12° ii) BCA = 31.08° and iii) AB = 8.11cm.

Based on the provided information, ∠ BAC = 96.8°; AC = 12.4cm, and BC = 15.6cm

i) According to the law of sine,

Sin ∠A/a = Sin ∠B/b = Sin ∠C/c where a is the length opposite to ∠A, and so forth.

Hence, based on the information, ∠ABC = ∠B

Sin ∠B/AC = Sin ∠A/BC

Sin ∠B/12.4 = Sin 96.8/15.5

Sin ∠B = (Sin 96.8/15.5)*12.4

∠B = Sin^-1((Sin 96.8/15.5)*12.4)

∠B = 52.12°

ii) As the sum of interior angles of a triangle is 180°. ∠As BCA = ∠C

∠A + ∠B + ∠C = 180

96.8 + 52.12 + ∠C = 180

∠C = 31.08

iii) According to the law of cosine,

c^2 = a^2 + b^2 – 2ab cos C where C is the angle opposite to c.

BC^2 = AB^2 + AC^2 – 2(AB)(AC)cos98.6

15.6^2 = AB^2 + 12.4^2 – 2(AB)(12.4)cos98.6

Solving for AB,

AB = 8.11cm

Learn more about Law of sine:

https://brainly.com/question/27174058

#SPJ4

Answer:

67

Step-by-step explanation:

9x−5

x=8

9(8)−5

72−5

=67

Answer:

No.

Step-by-step explanation:

It is because a line is said to be perpendicular to another line if the two lines intersect at a right angle or at 90° and the two lines in the graph does not intersect at 90° angle..

mark brianliest if my answer suit your question..

To use an addition or subtraction formula, we need to recognize that we have the difference of two tangent functions in the numerator. Specifically, we can use the formula:

tan(A - B) = (tan A - tan B)/(1 + tan A tan B)

In this case, we have tan(76) - tan(16) in the numerator, so we can rewrite it as:

tan(76 - 16) = tan(60)

Similarly, we have a product of tangent functions in the denominator, so we can use the formula:

tan(A + B) = (tan A + tan B)/(1 - tan A tan B)

In this case, we have tan(76) tan(16) in the denominator, so we can rewrite it as:

tan(76 + 16) = tan(92)

Putting it all together, we have:

[tan(76) - tan(16)] / [1 + tan(76) tan(16)] = tan(60) / [1 - tan(92)]

To find the exact value, we need to evaluate each tangent function. Using a reference angle of 14 degrees (since tan(76) is in the second quadrant and tan(16) is in the first quadrant), we get:

tan(76) = -tan(76 - 180) = -tan(104) ≈ -2.744
tan(16) ≈ 0.287
tan(60) = √3
tan(92) = -tan(92 - 180) = -tan(88) ≈ -15.864

Substituting these values into the expression, we get:

[tan(76) - tan(16)] / [1 + tan(76) tan(16)]
≈ (-2.744 - 0.287) / [1 + (-2.744)(0.287)]
≈ -2.606

Therefore, the exact value of the expression is approximately -2.606.
Using the subtraction formula for tangent, we can rewrite the given expression as follows:

tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A)tan(B))

In this case, A = 76 degrees and B = 16 degrees. So the expression becomes:

tan(76° - 16°) = (tan(76°) - tan(16°)) / (1 + tan(76°)tan(16°))

This simplifies to:

tan(60°) = (tan(76°) - tan(16°)) / (1 + tan(76°)tan(16°))

Now, we can find the exact value of tan(60°), which is √3.

So, the exact value of the given expression is √3.

Visit here to learn more about tangent functions brainly.com/question/30910929

#SPJ11

We must find the length of one side of the new square.

Step one

The area of the square is 64. We know that the is of a rectangle is given by n x n, so:

The value of n is a number that multiplied by itself gives us 64, that number is 8, so we have:

Step two

The length of one side of the new square is obtained by multiplying the original length 8 by the scale factor 3/2, which gives us:

Answer

The volume of the cuboid is 1152 ft³

A cuboid is a solid shape or a three-dimensional shape. A convex polyhedron that is bounded by six rectangular faces with eight vertices and twelve edges is called a cuboid.

A rectangular prism is called a cuboid and the volume of a cuboid is expressed as;

V = base area × height

The base is rectangle, the area of a rectangle is expressed as;

A = l× w

A = 18 × 8

A = 144 ft²

V = base area × height

V = 144 × 8

V = 1152 ft³

Therefore, the volume of the cuboid is 1152 ft³

learn more about volume of cuboid from

https://brainly.com/question/46030

#SPJ4

There are two solutions: x = -3 and x = -7.

Let's analyze each equation to determine the number of solutions and provide explanations:

x² - 144 = 0

This equation can be rewritten as (x - 12)(x + 12) = 0. It is a quadratic equation in the form of (x - a)(x + a) = 0, where a is a constant. In this case, a = 12.

Since we have two factors that multiply to give zero, either (x - 12) = 0 or (x + 12) = 0 must be true for the equation to hold.

Thus, there are two solutions: x = 12 and x = -12.

x² + 1440

This equation does not contain an equal sign, so it is not an equation. It is an expression. Therefore, it does not have any solutions.

x (x - 5) = 0

This equation is a product of two factors equal to zero. Either x = 0 or (x - 5) = 0 must be true for the equation to hold. Thus, there are two solutions: x = 0 and x = 5.

(x - 8)² = 0

This equation is a perfect square trinomial. The square of any number is always non-negative, and it only equals zero when the number itself is zero. Thus, the equation (x - 8)² = 0 has only one solution: x = 8.

(x + 3)(x + 7) = 0

This equation is a product of two factors equal to zero. Either (x + 3) = 0 or (x + 7) = 0 must be true for the equation to hold. Thus, there are two solutions: x = -3 and x = -7.

To summarize:

x² - 144 = 0 has two solutions: x = 12 and x = -12.

x² + 1440 does not have any solutions.

x (x - 5) = 0 has two solutions: x = 0 and x = 5.

(x - 8)² = 0 has one solution: x = 8.

(x + 3)(x + 7) = 0 has two solutions: x = -3 and x = -7.

For more such questions on solutions , Visit:

https://brainly.com/question/25907410

#SPJ11

Answer:

tenth- 49.1

Hundredth- 49.08

thousandsths- 49.076

ten-thousandths- 49.0758

For example, the equation 2x+3x = 5x is a tautology. It's a true statement no matter what you pick for x.

The answer is     Always True