a hospital director believes that 75% of the lab reports contain errors. a sample of 140 reports found 98 errors. is there sufficient evidence at the 0.10 level to refute the hospital director's claim? state the null and alternative hypotheses for the above scenario.

The quotient from the synthetic division (9a^4-31a^3-21a^2+6a-13)/(a-4) is 9a⁴ - 22a³ - a² + 5a - 8/a -4

Synthetic division can be defined as a mathematical method of dividing a polynomial by a  binomial x - c

Such that, c is a constant.

The steps to take in synthetic division;

Given the polynomial;

(9a^4-31a^3-21a^2+6a-13)/(a-4)

[tex]\sqrt[a -4]{9a^4 -31a^3 +6a -13}[/tex]

c of divisor x-c

                4         coefficients of dividend

                           9     -31     -21      6     -13

                          _____9__-22__-1___ 5_______

                          9       -22     -1      5       -8

The quotient is the;

9a⁴ - 22a³ - a² + 5a - 8/a-4

Hence, the expression is  9a⁴ - 22a³ - a² + 5a - 8/a-4

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Answer:

x = -1

Step-by-step explanation:
y-0.8x=0.5

5y-2.5-4x

Get y by itself.
y = 1.3

Put 1.3 into the second equation

5(1.3) - 2.5 - 4x
6.5-2.5 - 4x
4 - 4x = 0
Get x by itself
-4x = 4
x = -1

I hope this was able to help you :D

Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.

What is axis ?

An axis is a line about which a body rotates or a system oscillates. In mathematics and physics, an axis is often represented as a straight line that serves as a reference point for the measurement of coordinates.

The correct answers are :

(a) The distance from the point (3, 9, -7) to the xy-plane is the distance from the point to the z-axis, which is 7, since the xy-plane is at z = 0

(b) The distance from the point (3, 9, -7) to the yz-plane is the distance from the point to the x-axis, which is 3, since the yz-plane is at x = 0

(c) The distance from the point (3, 9, -7) to the xz-plane is the distance from the point to the y-axis, which is 9, since the xz-plane is at y = 0

(d) The distance from the point (3, 9, -7) to the x-axis is the distance from the point to the x-axis, which is 0, since the point is already on the x-axis

(e) The distance from the point (3, 9, -7) to the y-axis is the distance from the point to the y-axis, which is 0, since the point is already on the y-axis

(f) The distance from the point (3, 9, -7) to the z-axis is the distance from the point to the z-axis, which is 0, since the point is already on the z-axis

Distance from point (3,9,-7) to xy-plane is 7, yz-plane is 3, xz-plane is 9, x-axis, y-axis and z-axis is 0.

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On solving the expression, the standard form is obtained as 8x³ + 26x² - 32x + 6.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The given expression is - (−4x + 3)(−2x² − 8x + 2)

To solve this expression first expand the equation using arithmetic operation of multiplication.

(−4x + 3)(−2x² − 8x + 2)

-4x(−2x² − 8x + 2) + 3(−2x² − 8x + 2)

8x³ + 32x² - 8x - 6x² - 24x + 6

Collect the like terms together -

8x³ + 32x² - 6x² - 8x - 24x + 6

Perform the arithmetic operation of addition and subtraction -

8x³ + 26x² - 32x + 6

Therefore, the standard form is 8x³ + 26x² - 32x + 6.

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Terra is correct. In order for a relationship to be a function, each input value must result in only one input.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is often represented as y = f. (x).

We know that for a function each input value must result in a unique output value. Terra claims this statement, and hence she is correct.

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Answer:

y=f(x)-6 is a vertical translation down by 6 units so draw the same graph but 6 units down with the point at which it crosses the y-axis as (0,-4)

Total number sixth graders were surveyed is 600.

"percent" is Latin for "out of 100," so 5 % is literally 5 out of 100

Now--if it were 5 kids with birds, you would know that there were 100 total kids. But it's 30 kids, which is way more than 5; so your total number of kids is going to be way more than 100.

So what you need to do here is figure that "30 sixth graders own birds

i.e. 30 is 5% of some number."

How many times bigger than 5 is 30? (6 times, because 5 x 6 = 30, or you can think of it as 30 divided by 6 = 5)

So if you had to do 5 TIMES 6 to get to 30, you have to do 100 TIMES 6 to get the total number sixth graders were surveyed.

What's 100 x 6?

= 600.

So your total number sixth graders were surveyed is 600.

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A  Linear Function best explains the relationship between the return and time.

What is the scatter plot?

A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.

It is given that this scatter plot was created using daily stock market returns.

To determine which type of function fits the data of the graph best see the points of the graphs.

The scatter plot is not forming a parabola or curved graph so it can be a quadratic function.

The scattered in such a form that only a straight line can be the best fit for the scatter plot.

Therefore, a linear function is the best representation.

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The character Hannah is sent back in time to the Holocaust in Jane Yolen's book "The Devil's Arithmetic," where the Nazis tattoo a number on her arm.

The guy who tattooed Hannah's arm begs her not to forget the number because it serves as a powerful reminder of the significance of remembering and never forgetting the past and acts as a permanent reminder of the crimes done during the Holocaust. Hannah must remember the number since it is also a way of tracking and identifying people within the concentration camp.

Hannah is questioned about her name by the prisoner who is in charge of tattooing the ladies. That person is Chaya Abramowicz, she responds. She is wearing his daughter's outfit, he informs her. She had the same name, Chaya. He advises her to live for all the Chayas in the world and to never forget her prisoner number.

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The possible equation of the sequence is f(x) = -2x + 5

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

Sequence type = arithmetic

Also, we have the following features

slope = negative

y-intercept = positive

A linear equation (or an arithmetic sequence) can be represented as

y = mx + c

Where

slope = m

y-intercept = c

Using the given features, we can use the following assumed values

m = -2

c = 5

So, the sequence is

f(x) = -2x + 5

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Answer:

see below

Step-by-step explanation:

7. (4-4). K =0

d+12-8/4+5 = d+12-2+5 =d+15

Answer:

¿Qué quieres comer?

Step-by-step explanation:

The correct statement relative to the polynomial function is given as follows:

A. p(1)= 4

B. p(x)= (x^2 + 5x + 2) +4/x-1

The polynomial function for this problem is given as follows:

p(x) = x^3+4x^2-3x+2

Dividing the polynomial function by x - 1, the quotient and the remainder are given as follows:

Meaning that:

Hence the correct options are given by option A and option B.

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The selling price for the article if it is equal to marked price will be $117

using profit and loss formulas.

What is profit and loss formula?

Profit and Loss formula is used in mathematics to determine the price of a commodity in the market and understand how profitable a business is. Every product has a cost price and a selling price. Based on the values of these prices, we can calculate the profit gained or the loss incurred for a particular product. The important terms covered under this are cost price, fixed, variable and semi-variable cost, selling price, marked price, list price, margin, etc.

For example, for a shopkeeper, if the value of the selling price is more than the cost price of a commodity, then it is a profit and if the cost price is more than the selling price, it becomes a loss.

Now,

Given Cost price=$65

Marked up price = 180%*$65

As

Marked up price = selling price

Therefore

     selling price= 180%*$65

                 selling price =$117

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The value of x is 14.28 units, this is determined using the trigonometric functions.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the sides and angles of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions.

Consider the smaller triangle:

Sin (30) = Opposite side ÷ Hypotenuse

0.5 = Opposite side ÷ 10

Opposite side = 5

Consider the bigger triangle:

Sin (22) = Opposite side ÷ Hypotenuse

0.37 = 5 ÷ x

x = 5 / 0.35

x = 14.28

Hence, the value of x is 14.28 units, this is determined using the trigonometric identities.

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a. The length of the arc is 6.28cm

b. The area of the sector is 25.12cm²

The arc of a circle is defined as the part or segment of the circumference of a circle. A sector is the space bounded by the arc and the radii of the circle. The smaller area is known as the minor sector and the bigger area is known as the major sector.

The length of an arc = tetha /360 ×2πr

= 45/360 × 2×3.14× 8

= 2×3.142 = 6.28cm

The area of a sector = tetha / 360 × πr²

= 45/360 × 3.14 × 8× 8

= 3.14× 8

= 25.12 cm²

Therefore, the length of the arc is 6.28cm and the area of the sector is 25.12cm²

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The surface area of the rectangular prism is  182m²

It is important to note that the surface area of a rectangular prism is expressed as;

Surface area = 2(wl + hw + hl)

Where;

Now, from the diagram show, we have the values as;

Length = 3

Height = 7

Width = 7

Substitute the values into the formula

Surface area = 2(7×3 + 7×3 + 7 ×7)

multiply the values

Surface area = 2(21 + 21 + 49)

expand the bracket

Surface = 182m²

Thus, the value is 182m²

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Answer:

$16.8

Step-by-step explanation:

u got to trust me

Answer: $16.8

im sure its this it has to be

You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.

Linear regression is a statistical method that is used to study the relationship between two continuous variables, often referred to as the independent variable (x) and the dependent variable (y). The goal of linear regression is to find the best-fitting line that describes the relationship between these two variables. The best-fitting line is known as the regression line, and it is represented by the equation y = mx + b, where m is the slope of the line, and b is the y-intercept.

To find the linear regression equation, we need to use the least squares method to find the line of best fit that describes the relationship between the homework grade (x) and the test grade (y). The equation of the line is in the form of y = mx + b, where m is the slope and b is the y-intercept.

To find the slope (m) and y-intercept (b) we can use the following formulas:

m = (n(Σxy) - (Σx)(Σy)) / (n(Σx²) - (Σx)²)

b = (Σy - m(Σx)) / n

where n is the number of data points, Σx and Σy are the sum of x and y values, Σxy is the sum of the product of x and y values, and Σx² is the sum of the squares of x values.

Given the data points, we can use this information to calculate the slope and y-intercept, and write the linear regression equation.

Given the linear regression equation of the form y = mx + b

You can substitute a homework grade of 37 into the equation in place of x, to find the projected test grade.

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The value of distance after calculating are  AB = 4 ft and BC = 16 ft.

What is ratio?

A ratio is a comparison between two numbers or quantities. It is typically expressed as a fraction, with the first number being divided by the second number. Ratios are often used to compare values or to express a portion of a whole.

It is given in the question, that Ladd is rearranging his living room furniture. He wants his couch to sit along the 20-ft wall.

To find the length of AB and BC we need to relate them using the equations.

AB + BC = 20 ft (from the diagram) ----------- (Equation 1)

∵ AB : BC = 1 : 4

⇒ 4AB = BC

Substituting,  BC = 4AB into equation 1.

AB + 4AB = 20 ft

5AB = 20 ft

AB = 4 ft

Plugging AB = 4 ft into equation 1.

4 + BC = 20

BC = 20 ft - 4 ft

BC = 16 ft

Thus, the value of sides AB = 4 ft and BC = 16 ft , and here AB and BC are in ratio 1:4.

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The value of x in the figure shown above is equal to 4.

In Mathematics, parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

By critically observing the image of this geometric figure, we can reasonably infer and logically deduce that it is a type of quadrilateral with both pairs of opposite sides being parallel to each other and the opposite angles (vertical angles) are equal and congruent:

Side length A = Side length B

4 + 6 = 6 + x

10 = 6 + x

By collecting like terms, we have the following:

x = 10 - 6

x = 4 units.

In conclusion, the value of x is equal to 4 units.

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Answer:

So, the question is asking how many pounds are there in 48 shipments if ever 12 shipments are 3 pounds, so what you want to do is so how many times 12 will go into 48 and then multiply that by 3!

48/12 = 4

4 * 3 = 12

The total 48 shipments weigh 12 pounds!

Step-by-step explanation:

Hope it helps! =D

Answer:

The weight of one pack of sardines is 3 pounds / 12 packs = 0.25 pounds/pack

So the weight of 48 packs of sardines is 0.25 pounds/pack * 48 packs = 12 pounds.

A graph of the line that passes through the two points (-3/2, -3/2) and (3/2, 3/2) is shown in the image attached below.

In Mathematics and Geometry, the slope of any straight line can be calculated by using this mathematical equation (expression);

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

From the information provided above, we have the following data points located on the line:

Points on the x-coordinate = (-3/2, 3/2).

Points on the y-coordinate = (-3/2, 3/2).

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3/2 + 3/2)/(3/2 + 3/2)

Slope (m) = 3/3 = 1

At point (-3/2, -3/2), an equation of this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

Where:

y - (-3/2) = 1(x - (-3/2))

y + 1.5 = x + 1.5

y = x

Next, we would use an online graphing calculator to plot the linear equation as shown in the graph attached below.

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They will be equal at the same altitude at x= 48 seconds

Assume the question is when the planes will be at the same altitude.

A is 2184+30.25x, where x is the number of seconds.

The aircraft B is 75.75x

They will be equal at the same altitude if

75.75x=2184+30.25x

Collecting like terms and making x the subject of the relation

75.75x -30.25x = 2184

45.5x = 2184

Making x the subject

x = 2184/45.5

x=48 seconds

The two airplanes  will be at the same altitude at 48 seconds

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Answer: 1.2 miles

You can find the answer by using the pythagorean theorem.

a^2 + b^2 = c^2.

(5000)^2 + (4000)^2 = c^2

25 million +16 million = c^2

41 million = c^2

Take the square root of both sides in order to get the value of C.

C = about 6,403 feet.

1 mile = 5280 feet

6403/5280 = 1.2

Buddy would walk about 1.2 miles

Answer:

8

Step-by-step explanation:

42/7 =

6..

Since +6 more to 42 = 48 =

42+6=

48.

Just add 1 more month =

7+1=

8

Need more explanation I am happy to help :)

A graph which shows the relationship given in the table is: B. graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 56 through the point 1 comma 54.

In this scenario, the number of days would be plotted on the x-axis (x-coordinate) of the scatter plot while the total amount of sunglasses would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

From the scatter plot (see attachment) which models the relationship between the number of days and total amount of sunglasses, a linear equation for the line of best fit is given by:

y = -2x + 56

In conclusion, we can reasonably infer and logically deduce that the y-intercept is equal to (0, 56).

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Answer:

YOUR WELCOME THE ANSWER IS

Step-by-step explanation:

B (-:{

The volume of the prism in this problem is given as follows:

C. 9/16 cubic feet.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, as follows:

Volume = length x width x height.

For this problem, two of the dimensions are formed by three cubes, hence their measures are:

3 x 1/4 = 3/4 foot.

The remaining dimensions is composed by four cubes, hence the measures are:

4 x 1/4 = 1 foot.

Hence the volume is given as follows:

V = 1 x 3/4 x 3/4

V = 9/16 cubic feet.

The problem is given by the image presented at the end of the answer.

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Answer:

The answer in intercept form will be

[tex] - 1 \div 3 = 5 \div 3x + c \\ [/tex]