The graph of the function f(x) = (x – 4)(x + 1) is shown below.

On a coordinate plane, a parabola opens up. It goes through (negative 1, 0), has a vertex at (1.75, negative 6.2), and goes through (4, 0).

Which statement about the function is true?

The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and where x > 4.
The function is decreasing for all real values of x where
–1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.

According to the T distribution, the correct option is (d) All the above

T distribution:

In statistics, t-distribution is used in all forms of t-tests. Where the T-tests are all classified as inferential statistical tests and will follow all of the same steps required to complete the process of null hypothesis significance testing. And it defines the exact shape of the t-distribution is governed by the degrees of freedom. And the t-distribution is associated with a degrees of freedom equal to the sample size minus a value of 1.

Given,

Here we need to find the correct option according to the T distribution.

As per the given options, the correct answer is best represented by option D. All of the above are correct.

Because, the t-distribution, along with the normal distribution, both assume data is normally distributed in the population.

When the sample size increases towards 30, the t-distribution will resemble the normal distribution, provided the data in the population is normally distributed.

If it is correct to state that the tails of the t-distribution are thicker compared to the normal distribution.

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The probability that exactly one of the next three vehicles fail is 0.737 .

Given :

64% of all vehicles examined at a certain emissions inspection station pass the inspection. assuming that successive vehicles pass or fail independently of one another .

probability that exactly one of the next three vehicles fail is :

P = 1 -  probability that all of the next three vehicles passes .

= 1 - 64 % * 64 % * 64 %

= 1 - 64/100 - 64/100 - 64/100

= 1 - 0.64 * 0.64 * 0.64

= 1 - 0.4096 * 0.64

= 1 - 0.262

= 0.737

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A statement that associates s with a set that contains the following elements: 23, 42, -11, 89 is s = set ( [ 23 , 42 , -11 , 89 ] )

Given :

a statement that associates s with a set that contains the following elements: 23, 42, -11, 89.

Statement :

A statement is an instruction that the Python interpreter can execute.

We have seen two kinds of statements: print and assignment.

When you type a statement on the command line, Python executes it and displays the result, if there is one. The result of a print statement is a value.

we can write :

s = set ( [ 23 , 42 , -11 , 89 ] )

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a) 270° counter clockwise rotation of figure 1

b) The image of point (-3,-4) is (3,4).

c) The new image of point (7,8) is (8,-7) after 90° degree clockwise rotation.

d) The new image of point (7,8) is (-8,7) after 90° degree anticlockwise rotation

e) The fig. abcd will moves to second quardent after 90° counter clockwise rotation.

f) The rotation angle of figure is 270° , in the counterclockwise direction about origin.

A rotation is an isometric transformation that turns every point of a figure through a specified angle and direction about a fixed point.

To describe a rotation, you need three things:

Direction (clockwise or counterclcokwise.

90 Degree Rotation:

When rotating a point 90 degrees counterclockwise about the origin of a point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

180 Degree Rotation :

When we rotating a point 180 degrees counterclockwise about the origin a point A(x,y) it becomes A'(-x,-y). So all we do is make both x and y negative.

We have given that,

a) The given figure is rotated aoround 90° clockwise or 270° counter clockwise.

b) A point (-3,-4) is rotated around the origin 180 degrees , then the new point or position after the rotation is (3,4).

c) Rotate the point (7 , 8) around the origin 90 degrees , the new point or image of (7,8) is ( 8,-7).

d) If a point (7,8) is rotate around the origin 90 degrees counterclockwise then new point is (-8,7).

e) If you were to rotate abcd 90 degrees counterclockwise then the image of figures abcd will enter in quadrent 2nd with all coordinate changes.

f) when a figure is rotated in counterclockwise rotation about the origin the angle of rotation is 270 degrees.

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Answer:

14/2

Step-by-step explanation:

We can write 7 as 7/1

Multiply the top and bottom by 2/2

7/1 * 2/2 = 14/2

We could multiply by any number over itself

7/1 * 3/3 = 21/3

This is an equivalent fraction

Answer:

See below

Step-by-step explanation:

Examples ( choose one)

14/2

7/1

21/3

98/14

The solutions are,

(a) 1.1825

(b) 0.0985

(c) Reject the null hypothesis since the test's p-value (0.001) is less than 0.05. One might draw the conclusion that there is evidence of a difference in the mean ratios for the 4 neighborhoods based on the sample data.

Given data,

A realtor wants to compare the mean sales-to-appraisal ratios of residential properties sold in four neighborhoods (A, B, C, and D). Four properties are randomly selected from each neighborhood ;

(a) The within-group sum of squares for this analysis will be

4.3644 - 3.1819 = 1.1825

Hence, within the group sum of squares for this analysis is 1.1825.

(b) There are four groups so df for within groups is 12 so the within-group mean squares for this analysis will be,

[tex]\frac{1.1825}{12}=0.0985[/tex]

(c) Since the p-value of the test (0.001) is less than 0.05, reject the null hypothesis. That is based on sample evidence one can conclude that there is evidence of a difference in the mean ratios for the 4 neighborhoods.

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Answer:

I hope the best for you

Step-by-step explanation:

have a good day :)!!

The equation that can be used to model the total time y for number of chimes is y = 2x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

From the information, it takes Ernest's grandfather clock 2 seconds to chime.

Therefore, the equation that can be used to model the total time y for number of chimes x will be:

y = 2 × x

y = 2x.

The equation is y = 2x.

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The number of hours that plan A last is 1 hour and the number of hours that plan B last is 1 1/2 hours.

The first step is to form a system of equations using the information in the question:

3a + 8b = 15  equation 1

5a + 2b = 8 equation 2

Where:

The elimination method would be used to determine the required values

In order to determine the value of a, multiply equation 2 by 4

20a + 8b = 32 equation 3

Subtract equation 1 from equation 3 :

17a = 17

Divide both sides of the equation by 17

a = 17/17

a = 1 hour

Substitute for a in equation 1 :

3(1) + 8b = 15

3 + 8b = 15

8b = 15 - 3

8b = 12

b = 12 / 8

b = 1 4/8 = 1 1/2 hours

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The probability of getting a tails and a number less than 3 is equal to 1/6.

As given in the question,

Probability of getting heads or tail is:

P (H) = P(T) = 1/2

The probability of getting any number on the die is:

P (1) = P (2) = P(3) = P (4) = P (5) = P (6) = 1/6

The probability of getting a tail on the coin and a number less than 3 on the die is:

P(tails and a number less than 3) = P(tails) x P( a number less than 3)

= 1/2 x [P(1) +P(2)]

= 1/2 x [1/6 +1/6]

= 1/6.

Therefore ,the required probability of getting tails and a number less than 3 is  equal to 1/6.

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The time is taken by the substance to decay, if A radioactive substance decays according to [tex]A = A_o \times e^{-0.0037t}[/tex] Where A₀ is the initial amount and t is the time in years. If A0=740 grams is  185.18 years.

Atoms in radioactive materials naturally decay. They are capable of emitting gamma radiation, beta radiation, and alpha radiation. They cannot be turned off, so controlling them is more challenging than controlling X-ray sources.

Given:

The initial amount, A₀ = 740 g,

The final amount, A = 373 g,

Calculate the time by using the formula given below,

[tex]A = A_o \times e^{-0.0037t}[/tex]

373 = 740 [tex]\times e^{-0.0037t}[/tex]

[tex]e^{-0.0037t}[/tex] = 373 / 740

[tex]e^{-0.0037t}[/tex] = 0.504

Taking log on both sides,

㏑ 0.504 - ㏑ 0.0037 = t

t = 185.18

Therefore, the time taken by the substance to decay if A radioactive substance decays according to A=A0e−0.0037t, where A0 is the initial amount and t is the time in years. If A0=740 grams is 185.18 years.

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Answer:is c or 3:5

Step-by-step explanation:

The statement which is true about triangle inequalities is that the sum of the lengths of the 2 sides of a triangle is equal than the third side of the triangle.

In Euclidean geometry, triangle inequalities are a theorem which states that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In shorts, the theorem states that the shortest distance between two points is a straight line.

If the length of a side is equal to the sum of the other two sides, then the vertices have to be colinear, meaning that the three sides form a line segment rather than a triangle. This is called the triangle inequality.

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True, Regardless of the testing point used we arrive at the same answer for the direction of a phase plane.

We were able to sketch the solution, y(t), in the y-t plane for the single differential equation case and observe actual solutions. Due to the fact that our answers are actually vectors, this would be fairly challenging in this situation.

Here, we're going to plot the points that we represent as the system's solutions as points in the x1x2 plane. Our equilibrium solution will line up with the x1x2 plane's origin, which is also known as the phase plane.

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Answer:

1.85

Step-by-step explanation:

185/100 equals 1.85

if I'm reading the problem correctly this is what we have:

0.54 = 1.85 + 0.54

for the left side to equal the right side you must add 1.85 or 185/100

The probabilities of each marble is given as follows:

Hence the order of the likelihoods, from least to greatest, is given as follows:

Orange, Blue, Red, Yellow, Green.

In the context of a problem, a probability is calculated as the division of the number of desired outcomes divided by the number of total outcomes.

There are 30 marbles in this problem, hence the probability of each marble is calculated as the division of the amounts of each marble by 30.

As all the fractions have a denominator of 30, they are ordered from the lowest numerator, as follows:

Orange, Blue, Red, Yellow, Green. (from the numerator of 4 to the numerator of 8).

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a) The median waiting time until the next telephone order is of: 2.91 minutes.

b) The upper quartile of waiting time before the next telephone order is of: 5.82 minutes.

c) The upper 10% of waiting time until the next telephone order is of: 9.67 minutes.

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The mean for this problem is of:

m = 4.2.

Hence the decay parameter is of:

[tex]\mu = \frac{1}{4.2} = 0.2381[/tex]

The mass function is then given as follows:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

Hence:

[tex]P(X \leq x) = 1 - e^{-0.2381x}[/tex]

The median time is the value of x for which P(X < x) = 0.5, hence:

[tex]0.5 = 1 - e^{-0.2381x}[/tex]

[tex]e^{-0.2381x} = 0.5[/tex]

[tex]\ln{e^{-0.2381x}} = \ln{0.5}[/tex]

-0.2381x = ln(0.5)

x = -ln(0.5)/0.2381

x = 2.91 minutes.

The upper quartile is the value of x for which P(X < x) = 0.75, hence:

[tex]0.75 = 1 - e^{-0.2381x}[/tex]

[tex]e^{-0.2381x} = 0.25[/tex]

[tex]\ln{e^{-0.2381x}} = \ln{0.25}[/tex]

-0.2381x = ln(0.25)

x = -ln(0.25)/0.2381

x = 5.82 minutes.

The upper 10% is the value of x for which P(X < x) = 0.9, hence:

[tex]0.9 = 1 - e^{-0.2381x}[/tex]

[tex]e^{-0.2381x} = 0.1[/tex]

[tex]\ln{e^{-0.2381x}} = \ln{0.1}[/tex]

-0.2381x = ln(0.1)

x = -ln(0.1)/0.2381

x = 9.67 minutes.

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Answer:

B

hope you like it

The average daily inventory is 253 cases

In this question, we have been given we have been given the number of cases of zippers on inventory t days after the shipment arrives is

N(t) = 630 − 30√18t

We need to find the average daily inventory.

We use the definite integral to compute for the average value over that interval from a to b.

(∫[a_b] f(x) dx )/ (b - a)

Here, a = 1 and b = 18

so, the average daily inventory would be,

∫[18_1] N(t)dt / (18 - 1)

= ∫[18_1] (630 − 30√18t) dt / 17

= 4314.85 / 17

= 253.81

= 253

Therefore,  the average daily inventory = 253 cases

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The complete question is:

the dog days clothing company receives 630 cases of imported zippers every 18 days. the number of cases of zippers on inventory t days after the shipment arrives is  N(t) = 630 − 30√18t. Find the average daily inventory.

The given series diverges.

Given:

aₙ = n²/√n³+7n

using series divergence test

If limₙ→∞ aₙ ≠0, then ∑  aₙ diverges .

limₙ→∞ (n²/√n³+7n) = limₙ→∞ (n²/√n³(1+7/n²)

= limₙ→∞ (n²/n³/²√1+7/n²)

= limₙ→∞ (√n/√1+7/n²)

= (∞/√1+0)

= ∞

Therefore the series diverges.

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Answer:

35:1 because that is the most likely answer

Check the picture below.

The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).

Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.

Assuming a semiannual compounding rate of 8%,

As per the given information, the required solution would be as:

Amount to be paid into the fund each semi-annual period will be

= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))

= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))

= $1535.21

Thus, the required amount to be paid into the fund each period is $1535.21.

Hence, the correct answer would be an option (B).

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A vertex is a point where two or more curves, lines, or edges meet.

In geometry, vertex generally refers to an intersection point or a corner where lines, curves or edges meet. As a consequence of this definition, the point where two lines meet to form an angle called an included angle are considered vertices. Hence, the corners of triangle, polygons and polyhedral are vertices. For example, the lines of square or rectangle intersect at four corners which are called its vertices (which is the plural of vertex). Similarly, the vertex of curve(s) is where they intersect with each other or with its line of symmetry.

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Answer:

3

Step-by-step explanation:

Figure A is a dilation of Figure B by a factor of 3

That means that Figure A is 3 times larger than Figure B.

From Figure B to Figure A, the scale factor is 3.

True statement for Protecting classified data is classified material must be appropriately marked.

Classified information being transmitted from one commission office to another shall be protected with a classified document cover sheet and hand delivered by an appropriately cleared person to another appropriately cleared person.

Classified information is material that a government body deems to be sensitive information that must be protected. Access is restricted by law or regulation to particular groups of people with the necessary security clearance and need to know, and mishandling of the material can incur criminal penalties.

Data classification is broadly defined as the process of organizing data by relevant categories so that it may be used and protected more efficiently. Data classification involves tagging data to make it easily searchable and trackable.  

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Answer:

[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4  

Step-by-step explanation:

cos(a + b) = cos (a) cos(b) – sin (a) sin (b)

cos(75) =

cos(45 + 30) =  ==> break it down into more solvable angles

cos (45) cos(30) – sin (45) sin (30) =

[tex]\sqrt{2}[/tex]/2 * [tex]\sqrt{3}[/tex]/2 – [tex]\sqrt{2}[/tex]/2 * 1/2 =  ==> simplify

([tex]\sqrt{2}[/tex]*[tex]\sqrt{3}[/tex])/(2*2) – ([tex]\sqrt{2}[/tex]*1)/(2*2) =[[tex]\sqrt{6}[/tex]/4 – [tex]\sqrt{2}[/tex]/4]

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The relationship shows a ratio.

What is a relationship?

A relation in mathematics describes the connection between two sets of values for ordered pairs. The set of items in the first set are referred to as domain, and they are connected to the set of elements in the second set, referred to as range.

How can one tell whether a relationship is a function?

A function is described as having one and only one output for each input value. In this case, the output values are referred to as the range and the input values as the domain.

In the rate the unit of two variables are different. In the ratio the unit of the variable is the same.

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An equation for the nth term of the arithmetic sequence is 2 + 0.5n.

What is an arithmetic sequence?

An arithmetic sequence is a set of integers where each term (except the first) is created by adding a fixed amount to the term before it.

Given, initial distance = 2 miles

Let n be each day on which he jogs one-half (1/2 = 0.5) mile.

Then, according to the question,

nth term = 2 + 0.5n

Hence, an equation for the nth term of the arithmetic sequence is 2 + 0.5n.

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The additional jump in inches that John must make to beat the record is

5 1/4 inches

The problem is solved by converting the given dimensions in ft to  inches

conversion to inches is solved using

12 inches = 1 ft

The record jump is

= 23 feet 1 3/4 in

= 23 * 12 + 1 3/4 in

= 276 + 1 3/4

= 277.75 in

John's best long jump

= 22 ft 8 1/2 in

= 22 * 12 + 8 1/2 in

= 264 + 8 1/2

= 272.5 in

John's additional jump

= record jump - John's best long jump

= 277.75 - 272.5

= 5.25 in

= 5 1/4 in

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