1. The table shows the relationship between y, the cost to rent a bicycle, and x, the amount of time the bicycle is rented in hours. Ab Bicycle Rental Costs Time, x (hours) Total Cost, y (dollars) 1 $10 2 $20 3 $30 Part 1: A student drew the following graph to represent this situation. Explain the error in the graph​

Answer:

Area is 40

perimeter is 26

Step-by-step explanation:

area = l×w

\(8 \times 5 = 40\)

Perimeter = 2L +2W

\(2 \times 8 + 2 \times 5 \\ 16 + 10 \\ 26\)

Russ James' commission for selling $100,000 worth of chemicals last month is $5,000.

What is the percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.

Russ James is paid a commission rate of 5% on all sales. If he sold $100,000 worth of chemicals last month, his commission can be calculated by multiplying the sales amount by the commission rate:

Commission = Sales Amount * Commission Rate

Commission = $100,000 * 0.05

Commission = $5,000

Therefore, Russ James' commission for selling $100,000 worth of chemicals last month is $5,000.

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Answer:

Step-by-step explanation:

large necklace; $5.70

$4.60 x 6= $27.60

$33.30 total

See attachment for the graph of the function g(x)=log4(x-1)+2

The equation of the logarithmic function is given as

g(x)=log4(x-1)+2

The parent function of the above logarithmic function is

f(x) = log4(x)

This means that the parent function is translated right by 1 unit and translated up by 2 units

Next, we plot the graph of the function g(x)=log4(x-1)+2

See attachment for the graph of the function g(x)=log4(x-1)+2

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In this context, the dependent variable is t (amount of tax due) and the independent variable is c (cost of the order).In this scenario, the variables are t (the amount of tax due) and c (the cost of the order).

To determine which variable is independent and which is dependent, we need to understand their relationship.In this case, the amount of tax due, t, is calculated based on the cost of the customer's order, c. The tax amount is dependent on the cost of the order because it is directly influenced by the value of c. As the cost of the order changes, the amount of tax due will also change accordingly.

On the other hand, the cost of the order, c, is independent. It is not influenced or determined by the amount of tax due. The customer can choose the cost of their order, and the tax will be calculated based on that chosen amount.

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Answer:

x = 11.25

Step-by-step explanation:

-6 = 0.8x - 15

Add 15 to both sides;

-6 + 15 = 0.8x - 15 + 15

9 = 0.8x

Divide both sides by 0.8;

x = 11.25

Answer:

Divide both sides by 0.8;

x = 11.25

Step-by-step explanation:

2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

To prove that the expression 2n^3 + 3n + 10 is in the set Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3), we need to show that the expression can be written in the form a(n^3) for some constant "a".

Let's start by factoring out the common factor of n^3 from each term:

2n^3 + 3n + 10 = n^3(2 + 3/n^2 + 10/n^3)

Now, let's rewrite the expression as a single term multiplied by n^3:

2n^3 + 3n + 10 = (2 + 3/n^2 + 10/n^3)n^3

Simplifying the expression inside the parentheses:

= (2n^3 + 3n^2 + 10n^3)/n^3

= (12n^3 + 3n^2)/n^3

= 12 + 3/n

ow, we can see that the expression can be written in the form a(n^3), where a = 12 and n^3 = 3/n.

Therefore, we have shown that 2n^3 + 3n + 10 can be written as a polynomial of the form Q(n^3), where Q(n^3) represents the set of polynomials of the form a(n^3).

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It could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

The most accurate interpretation of the given confidence interval is as follows:

We are 95% confident that the true difference in mean wait time between Facility A and Facility B falls within the range of 0.32 minutes to 1.47 minutes.

This means that if we were to repeat the study multiple times and calculate a new confidence interval each time, we would expect that approximately 95% of those intervals would contain the true difference in mean wait time between the two facilities.

Furthermore, based on the observed data and the calculated confidence interval, we can conclude that the difference in mean wait time between Facility A and Facility B is likely to be positive, with Facility B having a higher mean wait time than Facility A. However, we cannot say with certainty that the true difference is exactly within this specific range; it could be slightly lower or higher, but we can be confident that it falls somewhere between 0.32 minutes and 1.47 minutes.

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For the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to

7 : 3.

As given in the question,

Probability of any particular event occurring is equal to 7 /10

Probability of any particular event not occurring is = 1- (7/10)

                                                                                    = (10 -7) /10

                                                                                    = 3/10

Probability of the odds favoring the events which are not occurring

= (7 /10) / (3/10)

= ( 7 × 10) / (3 × 10)

= 7 /3

Odds favoring the events which are not occurring in the form a: b

= 7 : 3

Therefore, for the probability of any particular event occurring is 7 /10 then odds of favoring the event which is not occurring in the form of a: b is equal to 7 : 3.

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The argument "All cats are mammals. I am a mammal. Therefore, I am a cat" is fallacious and can be shown as such using set theory and a Venn diagram.

Let's represent the sets using a Venn diagram:

   -------------

   |    Mammals   |

   -------------

       /       \

      /         \

     /           \

----          ----

| Cats |        | You |

----          ----

In the Venn diagram, the circle labeled "Mammals" represents the set of all mammals, and the circle labeled "Cats" represents the set of all cats. The region where the circles overlap represents the set of mammals that are also cats.

According to the argument, "All cats are mammals," which means that the set of cats is entirely contained within the set of mammals. This relationship is correctly represented in the Venn diagram.

The argument also states, "I am a mammal," which means that you are part of the set of mammals. In the Venn diagram, your position would be within the circle labeled "Mammals" but outside the circle labeled "Cats."

The fallacy occurs when the argument concludes, "Therefore, I am a cat." This conclusion is not valid because being a mammal does not automatically make you a cat. The Venn diagram clearly shows that there is a region within the set of mammals that is not within the set of cats.

To summarize, the fallacy in the argument arises from incorrectly inferring that being a mammal automatically implies being a cat. The Venn diagram visually demonstrates that being a mammal is a broader category that encompasses various animals, including cats, but being a mammal alone does not make one a cat.

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Yes, an 11, 60, 61 triangle has a right angle. This is because the Pythagorean theorem applies to right triangles, stating that the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse).

In this case, we can apply the theorem and see that 11^2 + 60^2 = 3721 + 3600 = 7321. Taking the square root of 7321 gives us approximately 85.4, which is the length of the hypotenuse.

Now, if we compare the square of the hypotenuse (85.4^2 = 7291.16) to the sum of the squares of the legs (11^2 + 60^2 = 3721 + 3600 = 7321), we can see that they are not equal. Therefore, the 11, 60, 61 triangle is not a right triangle.

However, if we compare the square of the hypotenuse (61^2 = 3721) to the sum of the squares of the legs (11^2 + 60^2 = 3721), we can see that they are equal. Therefore, the 11, 60, 61 triangle is a right triangle.

In conclusion, the 11, 60, 61 triangle has a right angle because it satisfies the Pythagorean theorem, which applies only to right triangles.

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The derivative of f(x) = √3x +1 at x = 8 is equal to [24 + √3]/√(192 + 48√3).The function is f(x) = √3x +1.

We need to find the derivative of the given function using the definition of the derivative.

Using the definition of the derivative:

f'(a) = lim x→a f(x)-f(a)/x-a

We need to find the derivative of the given function at x = 8, then the point of interest is a = 8.

Therefore, f'(8) = lim x→8 f(x)-f(8)/x-8

For the function f(x) = √3x + 1,f(8)

= √(3 × 8) + 1

=√24 + 1

 f(x) = √3x + 1 =

(√3 × √3x)/(√3) + 1

= ( √3 √3x + 1 √3)/ √3x + 1 √3

Now, we substitute the values of a and f(a) = f(8) and simplify,

f'(8) = lim x→8 f(x)-f(8)/x-8

= lim x→8 [(√3 √3x + 1 √3)/ √3x + 1 √3 - (√24 + 1)]/(x - 8)

= lim x→8 [(3x + √3)/(√3(x + √3)(√3x + √3))]

= lim x→8 [(3x + √3)/√3(x² + √3x + √3x + 3)]

= lim x→8 [(3x + √3)/√3(x² + 2√3x + 3)]

= [(3(8) + √3)/√3(8² + 2√3(8) + 3)]

= [24 + √3]/√(192 + 48√3)

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The congruence theorem that can be used to prove that the triangles are congruent is F. Not enough information is given to prove that the triangles are congruent

If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent.

According to the Angle-Side-Angle Theorem (ASA), if two angles and their included side are congruent to two angles and their included side, then these two triangles are congruent.

The hypotenuse is always the opposite side of the right angle. The legs of the triangle are the other two sides of a right triangle. Because a right triangle has two legs and a hypotenuse, it is also known as a hypotenuse-leg (or HL) triangle.

In this situation, enough information aren't given about the triangles. Therefore, the correct option is F.

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Answer:

1

Step-by-step explanation:

Is the correct way to do it

Answer:

y+75°=180°[co interior angle]

or,y=180-75

•°•y=105

again,

y=z(alternate angle)

•°•z=105°

now

z+x+68°=180(sum of angle of triangle is 180)

or,105+68+x=180

or,x+173=180

or,x=180-173

•°•x=7

Answer:

85 questions

Step-by-step explanation:

Math test: .9 x 50 = 45 correct

History test: .8 x 50 = 40 correct

45 + 40 = 85 questions

Hope that helps!

Answer:

16

Step-by-step explanation:

Answer: X=-3.

Anne was correct at fist, but likely didn’t solve the rest of the equation. The correct answer is X=-3, from 5(2x - 3)= 20x + 15, simplified by the distributive property going to 10x - 15 = 20x + 15. You then subtract +15 from the right side, or left side if you want to have a more positive answer, though it depends. That leaves you with 10x - 30 = 20x.  You subtract 10x from itself and from 20x. Then you have -30 = 10x. You divide 10x by -30, and you get -3. Therefore, X = -3.

Step-by-step explanation:

Answer:

144cm2

Step-by-step explanation:

Area of the circle is the area covered by that circle. The area of the circle whose circumference is 7π m is 12.25π m².

The area of the circle is the area covered by that circle. It is given by the formula,

\(\text{Area of the circle}=\pi r^2\)

where r is the radius of the circle.

As it is given that the circumference of a circle is 7π m. Therefore, the radius of the circle can be written as,

\(\text{Circumference of the circle} = 2\pi r\)

\(7 \pi = 2 \pi r\\\\r = 3.5\rm\ m\)

Now, we know the formula of the area of a circle, therefore, the area of the circle can be written as,

\(\text{Area of the circle}=\pi r^2\)

                           \(= \pi \times (3.5)^2\\\\= 12.25\pi\rm \ m\)

Hence, the area of the circle whose circumference is 7π m is 12.25π m².

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Answer:

28 meters cubed

Step-by-step explanation:

V = 1/3 BH

V = 1/3 (4)(21)

V = 28

Hope this helped :))

have a great day :D <3

Value of ∫90f(x)dx is 2/3. By property 1 of integration ∫f(x)dx  = ∫f(t)dt Because f(x) is a continuous function ,so we can apply property 1.

A function f(x) is said to be a continuous function in calculus at a point x = a if the curve of the function does NOT break at the point x = a. The mathematical definition of the continuity of a function is as follows. A function f(x) is continuous at a point x = a if

f(a) exists;

limₓ → ₐ f(x) exists;

[i.e., limₓ → ₐ₋ f(x) = limₓ → ₐ₊ f(x)] and

Both of the above values are equal. i.e., limₓ → ₐ f(x) = f(a).

Is this definition really giving the meaning that the function shouldn't have a break at x = a? Let's see. "limₓ → ₐ f(x) exists" means, the function should approach the same value both from the left side and right side of the value x = a and "limₓ → ₐ f(x) = f(a)" means the limit of the function at x = a is same as f(a). These two conditions together will make the function to be continuous at that point.

A function is said to be continuous over an interval if it is continuous at each and every point on the interval. i.e., over that interval, the graph of the function shouldn't break or jump.

∫90f(x)dx = 4

Therefore,   ∫f(x)dx = 4/90  

Let,    X² = t

By differentiate both side ,

We get,

2xdx = dt

so, 30/2 ∫f(t)dt

from property 1 : ∫f(x)dx = ∫f(t)dt    

15∫f(t)dt = (4/90) × 15 = 2/3

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Answer:

1) pencils

2)60

Step-by-step explanation:

So pencils are 70 which is the first sentence.

4*15 is 4x15 or 4x3x5 which is 60

Hope this helpz plz hit the crown :D

A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

What is a confidence interval?

A confidence interval (CI) is a range of values that, with a particular level of certainty, is likely to encompass a population value. A population mean that sits between an upper and lower interval is frequently stated as a percentage.

Here,

From the standard normal table, the z-critical value at 98% confidence interval is 2.33 so,

98%C.I. = µ ± z * σ /   n = 98.90 ± 2.33 * 42.30 / sqrt of 16  = 98.90 ± 24.64 = 74.26 to 125.54

The mean wake time of 102.80 minutes before the treatment due to the mean wake time of 102.80 minutes included in the 98% confidence interval which is between 74.26 and 125.54. Zopiclone does not appear effective.

Hence, A 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments is 74.26 to 125.54.

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Answer:

Quadrant IV

Step-by-step explanation:

The eigenvalues is λ = -3 and eigenvectors for the coefficient matrix [0, 0, -3/5, 1].

An eigenvalue of a matrix is a scalar value that, when multiplied by the matrix, produces a multiple of the original matrix. An eigenvector is a non-zero vector that, when multiplied by the matrix, results in a multiple of itself.

First, let's define what an eigenvalue and eigenvector are in the context of matrices.

Now, let's apply these definitions to the given matrix. We want to find values λ such that:

[−3 −2 5 3][x₁] [λx₁]

[x₂] = [λx₂]

[x₃] [λx₃]

[x₄] [λx₄]

To do this, we need to solve the equation:

det([-3-λ -2 5 3]

[0 -2-λ 0 0]

[0 0 5-λ 0]

[0 0 0 3-λ]) = 0

where det denotes the determinant of the matrix. Solving this equation will give us the eigenvalues of the matrix.

After some calculations, we find that the eigenvalues of the matrix are λ = -3, -2, 5, and 3.

Next, we need to find the eigenvectors corresponding to each of these eigenvalues. We do this by solving the equation:

([-3-λ -2 5 3][x₁] [0]

[x₂] = [0]

[x₃] [0]

[x₄] [0])

for each eigenvalue. This will give us a system of linear equations that we can solve to find the eigenvector.

Let's consider the eigenvalue λ = -3. Solving the equation above, we get:

[0 -2 5 3][x₁] [0]

[x₂] = [0]

[x₃] [0]

[x₄] [0]

This gives us the system of equations:

-2x2 + 5x3 + 3x4 = 0

x2 = 0

x3 = 0

x4 = 0

From the second equation, we know that x₂ = 0. Substituting this into the first equation, we get -2x₂ + 5x₃ + 3x₄ = 0, which simplifies to 5x₃ + 3x₄ = 0.

We can choose any value for x₄, but for simplicity, let's choose x₄ = 1. Then, we have 5x₃ = -3, which gives us x₃ = -3/5. Therefore, the eigenvector corresponding to λ = -3 is [0, 0, -3/5, 1].

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Complete Question:

Consider the linear system

Y′ =[−3 −2 5 3]Y.

Find the eigenvalues and eigenvectors for the coefficient matrix.

Line passing through AB is perpendicular. A pair of angles that are linear have an angle sum of 180 degrees. The lines are therefore shown to be perpendicular to one another because the angles are 90 degrees in size.

Two lines intersect to generate perpendicular lines, and the angle formed between the two lines must be 90 degrees (right angle).

Given,

Create another line perpendicular to AB passing through C on AB..

Line passing through AB is perpendicular.

Two lines are perpendicular if they cross at a point where a pair of linear congruent angles results. In a plane, a transversal is perpendicular to the other line if it is parallel to one of the two parallel lines.

A pair of angles that are linear have an angle sum of 180 degrees. The lines are therefore shown to be perpendicular to one another because the angles are 90 degrees in size. The linear pair perpendicular theorem is demonstrated by this.

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Answer:

Your answer would be 37°

Step-by-step explanation:

Since BC and DE are parallel, certain angles will be the same, such as the missing interior angle of the triangle and ∠DAF, which will also have the same measure as x.

We know that the sum of all of the interior angles of a triangle must equal 180°. So, we add 41 and 102 to get 143. This means that the missing interior angle must be 37°, since 37+143=180.

As mentioned above, because BC and DE are parallel, the missing interior angle has the same measure as ∠DAF, which is a vertical angle to x, and therefore also has the same measure. So, the measure of x is 37°.

Hope this helps you!

from the given information in the question we have found that all the three sets form a partition from the universal sets

What is a set?

A set is a mathematical model for a collection of items; it comprises elements or members, which may be any mathematical object: numbers, symbols, points in space, lines, other geometrical structures, variables, or even other sets.

As it is given that there are 3 sets where the first set A1 has 10 or more elements, A2 has 20 or more elements, and A3 has 15 or more elements.

1. If A1 ⊆ A2 and A2 ⊆ A3 then the union of these three will contain the same number of elements as that of A3.

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